Finite Group Databasebeta

← #17979157

Subgroups — #17979157

Order 4352.

3960 conjugacy classes of subgroups.

The subgroup lattice has 1788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763876C211yesmaximal, characteristic, complemented
2C22×D4×#595C211yesmaximal, characteristic, complemented
3#14545314C211yesmaximal, characteristic, complemented
4#14545312C212yesmaximal, complemented
5#14545311C211yesmaximal, characteristic, complemented
6#14545309C211yesmaximal, characteristic, complemented
7#14545306C212yesmaximal, complemented
8#14545306C212yesmaximal, complemented
9#14545300C211yesmaximal, characteristic, complemented
10#14545297C211yesmaximal, characteristic, complemented
11D4×C22⋊#595C212yesmaximal, complemented
12D4×C22⋊#595C211yesmaximal, characteristic, complemented
13D4×C22⋊#595C211yesmaximal, characteristic, complemented
14#14545276C211yesmaximal, characteristic, complemented
15#14545273C212yesmaximal, complemented
16#14545272C211yesmaximal, characteristic, complemented
17#14545269C212yesmaximal, complemented
18#121×#595C211yesmaximal, characteristic, complemented
19#120×#595C212yesmaximal, complemented
20#14545238C211yesmaximal, characteristic, complemented
21C2×#11763757C212yesmaximal, complemented
22#14545223C211yesmaximal, characteristic, complemented
23D42×D17C211yesmaximal, characteristic
24C24×#595C2212yescomplemented
25#11763876—28no—
26C2×D4×#595—28no—
27C2×D4×#595C2211yescharacteristic
28C2×D4×#595C2211yescharacteristic
29C2×D4×#595C2211yescharacteristic
30C2×D4×#595C2211yescharacteristic
31C2×D4×#595C2212yescomplemented
32C2×D4×#595C2211yescharacteristic, complemented
33C2×D4×#595C2212yescomplemented
34C2×D4×#595C2211yescharacteristic, complemented
35C2×D4×#595C2212yescomplemented
36C2×D4×#595C2211yescharacteristic, complemented
37C2×D4×#595C2212yescomplemented
38C2×D4×#595C2211yescharacteristic, complemented
39C2×D4×#595C2212yescomplemented
40C2×D4×#595C2212yescomplemented
41C2×D4×#595C2212yescomplemented
42C2×#10587677C2211yescharacteristic, complemented
43C2×#10587677C2211yescharacteristic, complemented
44C22×C4⋊#595C2211yescharacteristic, complemented
45C22×C22⋊#595C2212yescomplemented
46C22×C22⋊#595C2212yescomplemented
47C22×C22⋊#595C2212yescomplemented
48C22×C22⋊#595C2212yescomplemented
49C22×C22⋊#595C2212yescomplemented
50C22×C4×#595C2211yescharacteristic, complemented
51#11763761C2211yescharacteristic, complemented
52#11763761C2212yescomplemented
53#11763761C2212yescomplemented
54#11763761C2212yescomplemented
55#11763761C2211yescharacteristic, complemented
56#11763761C2211yescharacteristic, complemented
57#11763761C2211yescharacteristic, complemented
58#11763760C2211yescharacteristic, complemented
59#11763760C2211yescharacteristic, complemented
60#11763759C2211yescharacteristic, complemented
61#11763759C2211yescharacteristic, complemented
62#11763759C2212yescomplemented
63#11763759C2212yescomplemented
64#11763759C2212yescomplemented
65#11763759C2212yescomplemented
66#11763759C2212yescomplemented
67#11763758C2211yescharacteristic, complemented
68#11763758C2211yescharacteristic, complemented
69#11763758C2212yescomplemented
70#11763757C2211yescharacteristic
71#11763757C2212yes—
72#11763757C2211yescharacteristic
73#11763757C2212yescomplemented
74#11763757C2212yescomplemented
75#11763757C2212yescomplemented
76#11763757C2212yescomplemented
77#11763757C2212yescomplemented
78#11763757C2212yescomplemented
79#11763757C2212yescomplemented
80#11763757C2212yescomplemented
81#11763757C2212yescomplemented
82#11763757C2212yescomplemented
83#11763757C2212yescomplemented
84#11763757C2212yescomplemented
85#11763757C2212yescomplemented
86#11763757C2212yescomplemented
87#11763756C2211yescharacteristic, complemented
88#11763756C2211yescharacteristic, complemented
89#11763756C2212yescomplemented
90#11763756C2212yescomplemented
91#11763756C2212yescomplemented
92#11763756C2212yescomplemented
93#11763753C2211yescharacteristic, complemented
94#11763751C2211yescharacteristic, complemented
95#11763751C2211yescharacteristic, complemented
96#11763751C2212yescomplemented
97#11763750C2212yescomplemented
98#11763750C2212yescomplemented
99C4⋊C4×#595C2211yescharacteristic, complemented
100C4⋊C4×#595C2211yescharacteristic, complemented
101C4×C4⋊#595C2211yescharacteristic, complemented
102C4×C4⋊#595C2211yescharacteristic, complemented
103C22⋊C4×#595C2212yescomplemented
104C22⋊C4×#595C2212yescomplemented
105C22⋊C4×#595C2212yescomplemented
106C22⋊C4×#595C2212yescomplemented
107C22⋊C4×#595C2212yescomplemented
108C4×C22⋊#595C2212yescomplemented
109C4×C22⋊#595C2211yescharacteristic, complemented
110C4×C22⋊#595C2211yescharacteristic, complemented
111#11763745C2211yescharacteristic, complemented
112C2×(C2×#595)⋊C4C2212yescomplemented
113C2×(C2×#595)⋊C4C2212yescomplemented
114C22×D4×D17C2211yescharacteristic
115C22×D4×D17C2211yescharacteristic
116C22×D4×D17C2212yes—
117D4×D68C411yescharacteristic, complemented
118D4×D68C411yescharacteristic, complemented
119#11763444C411yescharacteristic, complemented
120#11763443C411yescharacteristic, complemented
121#11763443C411yescharacteristic, complemented
122#11763443C412yescomplemented
123D4×C22⋊D17C411yescharacteristic, complemented
124D4×C22⋊D17C411yescharacteristic, complemented
125D4×C22⋊D17C412yescomplemented
126#11763441C412yescomplemented
127#11763441C412yescomplemented
128#127×D17C2211yescharacteristic
129#121×D17C2211yescharacteristic
130#121×D17C2211yescharacteristic
131#121×D17C2212yes—
132#120×D17C2212yes—
133#120×D17C2212yes—
134C4×D4×D17C2211yescharacteristic
135C4×D4×D17C2211yescharacteristic
136D42×C17C411yescharacteristic, complemented
137C24×D17C2312yes—
138C24×D17C2312yes—
139C23×#595—28no—
140C23×#595—44no—
141C23×#595—44no—
142C23×#595C2311yescharacteristic
143C23×#595C2312yes—
144C23×#595C2312yes—
145C23×#595C2312yes—
146C23×#595C2311yescharacteristic
147C23×#595C2312yes—
148C23×#595C2312yes—
149C23×#595C2312yes—
150C23×#595C2312yes—
151C23×#595C2312yes—
152C23×#595C2312yes—
153C22×D4×C17C2×C411yescharacteristic, complemented
154C22×D4×C17C2×C411yescharacteristic, complemented
155C22×D4×C17C2×C412yescomplemented
156C22×C22⋊D17C2×C412yescomplemented
157C22×C22⋊D17C2×C412yescomplemented
158C22×C22⋊D17C2×C412yescomplemented
159C22×C22⋊D17C2×C412yescomplemented
160C2×D4×D17—24no—
161C2×D4×D17—24no—
162C2×D4×D17—24no—
163C2×D4×D17—24no—
164C2×D4×D17—44no—
165C2×D4×D17—44no—
166C2×D4×D17C2×C412yescomplemented
167C2×D4×D17C2×C411yescharacteristic, complemented
168C2×D4×D17C2×C411yescharacteristic, complemented
169C2×D4×D17C2×C411yescharacteristic, complemented
170C2×D4×D17C2×C412yescomplemented
171C2×D4×D17C2×C412yescomplemented
172C2×D4×D17C2×C412yescomplemented
173C2×D4×D17C2×C411yescharacteristic, complemented
174C2×D4×D17C2×C412yescomplemented
175C2×D4×D17C2×C412yescomplemented
176C2×D4×D17C2311yescharacteristic
177C2×D4×D17C2312yes—
178C2×D4×D17C2312yes—
179C2×D4×D17C2311yescharacteristic
180C2×D4×D17C2311yescharacteristic
181C2×D4×D17C2312yes—
182C2×D4×D17C2311yescharacteristic
183C2×D4×D17C2312yes—
184C2×D4×D17C2312yes—
185C2×D4×D17C2312yes—
186C22×D68C2×C411yescharacteristic, complemented
187C22×D68C2×C411yescharacteristic, complemented
188C22×D68C2×C412yescomplemented
189C22×C4×D17C2311yescharacteristic
190C22×C4×D17C2311yescharacteristic
191C22×C4×D17C2312yes—
192C2×C22⋊#595—28no—
193C2×C22⋊#595—28no—
194C2×C22⋊#595—28no—
195C2×C22⋊#595—44no—
196C2×C22⋊#595—44no—
197C2×C22⋊#595C2312yes—
198C2×C22⋊#595C2311yescharacteristic
199C2×C22⋊#595C2311yescharacteristic
200C2×C22⋊#595C2311yescharacteristic
201C2×C22⋊#595C2312yes—
202C2×C22⋊#595C2312yes—
203C2×C22⋊#595C2312yes—
204C2×C22⋊#595C2312yes—
205C2×C22⋊#595C2311yescharacteristic
206C2×C22⋊#595C2312yes—
207C2×C22⋊#595C2311yescharacteristic
208C2×C22⋊#595C2312yes—
209C2×C22⋊#595C2312yes—
210C2×C22⋊#595C2312yes—
211C2×C22⋊#595C2312yes—
212C2×C22⋊#595C2311yescharacteristic
213C2×C22⋊#595C2312yes—
214C2×C22⋊#595C2312yes—
215C2×C22⋊#595C2312yes—
216C2×C22⋊#595C2312yes—
217C2×C22⋊#595C2312yes—
218C2×C22⋊#595C2312yes—
219C2×C22⋊#595C2312yes—
220C2×C22⋊#595C2312yes—
221C2×C22⋊#595C2312yes—
222D4×#595—28no—
223D4×#595—28no—
224D4×#595—24no—
225D4×#595—24no—
226D4×#595—24no—
227D4×#595—28no—
228D4×#595—28no—
229D4×#595—24no—
230D4×#595—24no—
231D4×#595—24no—
232D4×#595—24no—
233D4×#595—44no—
234D4×#595—44no—
235D4×#595—44no—
236D4×#595D418yescomplemented
237#10587677—24no—
238#10587677—24no—
239C2×C4⋊#595—24no—
240C2×C4⋊#595C2311yescharacteristic
241C2×C4⋊#595C2311yescharacteristic
242C2×C4⋊#595C2311yescharacteristic
243C2×C4⋊#595C2311yescharacteristic
244C2×C4⋊#595C2311yescharacteristic
245C2×C4⋊#595C2312yes—
246C2×C4⋊#595C2311yescharacteristic
247C2×C4⋊#595C2311yescharacteristic
248C2×C4⋊#595C2312yes—
249C2×C4⋊#595C2312yes—
250C2×C4⋊#595C2311yescharacteristic
251C2×C4×#595—24no—
252C2×C4×#595C2311yescharacteristic
253C2×C4×#595C2311yescharacteristic
254C2×C4×#595C2311yescharacteristic
255C2×C4×#595C2311yescharacteristic
256C2×C4×#595C2312yes—
257C2×C4×#595C2311yescharacteristic
258C2×C4×#595C2312yes—
259C2×C4×#595C2312yes—
260C2×C4×#595C2312yes—
261C2×C4×#595C2311yescharacteristic
262C17×#127C2×C411yescharacteristic, complemented
263C17×#121C2×C411yescharacteristic, complemented
264C17×#121C2×C411yescharacteristic, complemented
265C17×#121C2×C412yescomplemented
266C17×#120C2×C412yescomplemented
267C17×#120C2×C412yescomplemented
268C4×D4×C17C2×C411yescharacteristic, complemented
269C4×D4×C17C2×C411yescharacteristic, complemented
270#10587639C2×C412yescomplemented
271#10587639C2×C412yescomplemented
272#10587626C2×C411yescharacteristic, complemented
273#10587626C2×C412yescomplemented
274#10587626C2×C412yescomplemented
275#10587626C2×C411yescharacteristic, complemented
276#10587625C2×C412yescomplemented
277#10587625C2×C412yescomplemented
278#10587625C2×C412yescomplemented
279#10587625C2×C412yescomplemented
280#10587624C2×C411yescharacteristic, complemented
281#10587624C2×C412yescomplemented
282#10587624C2×C411yescharacteristic, complemented
283#10587623C2×C412yescomplemented
284#10587623C2×C412yescomplemented
285#10587623C2×C412yescomplemented
286#10587623C2×C412yescomplemented
287#10587623C2×C412yescomplemented
288#10587623C2×C412yescomplemented
289D4×Dic17C2×C411yescharacteristic, complemented
290D4×Dic17C2×C411yescharacteristic, complemented
291#10587616C2×C411yescharacteristic, complemented
292#10587616C2×C411yescharacteristic, complemented
293#10587616C2×C412yescomplemented
294C4×C22⋊D17C2×C411yescharacteristic, complemented
295C4×C22⋊D17C2×C411yescharacteristic, complemented
296C4×C22⋊D17C2×C412yescomplemented
297#10587581C2×C411yescharacteristic, complemented
298#10587581C2×C411yescharacteristic, complemented
299#10587581C2×C412yescomplemented
300#10587579C2×C411yescharacteristic, complemented
301#10587579C2×C411yescharacteristic, complemented
302C4⋊C4×D17C2311yescharacteristic
303C4⋊C4×D17C2311yescharacteristic
304#10587570C2×C412yescomplemented
305#10587570C2×C412yescomplemented
306#10587570C2×C412yescomplemented
307#10587570C2×C412yescomplemented
308#10587568C2×C412yescomplemented
309#10587568C2×C412yescomplemented
310#10587568C2×C412yescomplemented
311#10587568C2×C412yescomplemented
312#10587568C2×C412yescomplemented
313#10587568C2×C412yescomplemented
314#10587567C2×C411yescharacteristic, complemented
315#10587567C2×C411yescharacteristic, complemented
316#10587567C2×C412yescomplemented
317C22⋊C4×D17C2311yescharacteristic
318C22⋊C4×D17C2312yes—
319C22⋊C4×D17C2312yes—
320C22⋊C4×D17C2312yes—
321C22⋊C4×D17C2311yescharacteristic
322#10587560C2×C411yescharacteristic, complemented
323C4×D68C2×C411yescharacteristic, complemented
324C4×D68C2×C411yescharacteristic, complemented
325C42×D17C2311yescharacteristic
326(C2×#595)⋊C4C2311yescharacteristic
327(C2×#595)⋊C4C2311yescharacteristic
328(C2×#595)⋊C4C2312yes—
329(C2×#595)⋊C4C2312yes—
330(C2×#595)⋊C4C2312yes—
331(C2×#595)⋊C4C2312yes—
332(C2×#595)⋊C4C2312yes—
333(C2×#595)⋊C4C2312yes—
334(C2×#595)⋊C4C2311yescharacteristic
335(C2×#595)⋊C4C2311yescharacteristic
336(C2×#595)⋊C4C2311yescharacteristic
337(C2×#595)⋊C4C2311yescharacteristic
338(C2×#595)⋊C4C2311yescharacteristic
339(C2×#595)⋊C4C2311yescharacteristic
340(C2×#595)⋊C4C2311yescharacteristic
341(C2×#595)⋊C4C2312yes—
342(C2×#595)⋊C4C2312yes—
343(C2×#595)⋊C4C2312yes—
344(C2×#595)⋊C4C2311yescharacteristic
345C24×C17C22×C412yes—
346C24×C17C22×C412yescomplemented
347C23×D17—24no—
348C23×D17—24no—
349C23×D17—24no—
350C23×D17—24no—
351C23×D17—24no—
352C23×D17—24no—
353C23×D17—42no—
354C23×D17—42no—
355C23×D17—42no—
356C23×D17—42no—
357C23×D17—42no—
358C23×D17—42no—
359C23×D17C22×C412yes—
360C23×D17C22×C412yes—
361C23×D17C22×C412yes—
362C23×D17C22×C412yescomplemented
363C23×D17C22×C412yescomplemented
364C23×D17C22×C412yescomplemented
365C23×D17C2411yescharacteristic
366C23×D17C2412yes—
367C23×D17C2412yes—
368C23×D17C2412yes—
369C23×D17C2411yescharacteristic
370C22×#595—22no—
371C22×#595—22no—
372C22×#595—22no—
373C22×#595—24no—
374C22×#595—22no—
375C22×#595—24no—
376C22×#595—24no—
377C22×#595—24no—
378C22×#595—22no—
379C22×#595—24no—
380C22×#595—24no—
381C22×#595—24no—
382C22×#595—24no—
383C22×#595—24no—
384C22×#595—24no—
385C22×#595—24no—
386C22×#595—42no—
387C22×#595—42no—
388C22×#595—42no—
389C22×#595—42no—
390C22×#595—42no—
391C22×#595—42no—
392C22×#595—42no—
393C22×#595—41no—
394C22×#595—42no—
395C22×#595—42no—
396C22×#595—42no—
397C22×#595—42no—
398C22×#595—42no—
399C22×#595—42no—
400C22×#595—42no—
401C22×#595—42no—
402C22×#595—432no—
403C22×#595C2×D418yescomplemented
404C22×#595C2411yescharacteristic
405C22×#595C2411yescharacteristic
406C22×#595C2412yes—
407C22×#595C2411yescharacteristic
408C22×#595C2412yes—
409C22×#595C2411yescharacteristic
410C22×#595C2411yescharacteristic
411C22×#595C2412yes—
412C22×#595C2411yescharacteristic
413C22×#595C2412yes—
414C22×#595C2411yescharacteristic
415C22×#595C2411yescharacteristic
416C2×D4×C17—24no—
417C2×D4×C17—24no—
418C2×D4×C17—44no—
419C2×D4×C17C22×C411yescharacteristic
420C2×D4×C17C22×C411yescharacteristic
421C2×D4×C17C22×C412yes—
422C2×D4×C17C22×C412yes—
423C2×D4×C17C22×C411yescharacteristic
424C2×D4×C17C22×C411yescharacteristic, complemented
425C2×D4×C17C22×C412yescomplemented
426C2×D4×C17C22×C412yescomplemented
427C2×D4×C17C22×C412yescomplemented
428C2×D4×C17C22×C412yescomplemented
429C22×C4×C17C22×C411yescharacteristic
430C22×C4×C17C22×C411yescharacteristic, complemented
431C22×C4×C17C22×C412yescomplemented
432C2×C22⋊D17—28no—
433C2×C22⋊D17—28no—
434C2×C22⋊D17—44no—
435C2×C22⋊D17—44no—
436C2×C22⋊D17C22×C411yescharacteristic
437C2×C22⋊D17C22×C411yescharacteristic
438C2×C22⋊D17C22×C412yes—
439C2×C22⋊D17C22×C412yes—
440C2×C22⋊D17C22×C412yes—
441C2×C22⋊D17C22×C412yes—
442C2×C22⋊D17C22×C412yes—
443C2×C22⋊D17C22×C412yes—
444C2×C22⋊D17C22×C412yescomplemented
445C2×C22⋊D17C22×C412yescomplemented
446C2×C22⋊D17C22×C412yescomplemented
447C2×C22⋊D17C22×C412yescomplemented
448C2×C22⋊D17C22×C412yescomplemented
449C2×C22⋊D17C22×C412yescomplemented
450C2×C22⋊D17C22×C412yescomplemented
451C2×C22⋊D17C22×C412yescomplemented
452C2×C22⋊D17C22×C412yescomplemented
453C22×Dic17C22×C411yescharacteristic
454C22×Dic17C22×C411yescharacteristic, complemented
455C22×Dic17C22×C412yescomplemented
456D4×D17—24no—
457D4×D17—24no—
458D4×D17—24no—
459D4×D17—24no—
460D4×D17—24no—
461D4×D17—24no—
462D4×D17—22no—
463D4×D17—22no—
464D4×D17—24no—
465D4×D17—24no—
466D4×D17—28no—
467D4×D17—28no—
468D4×D17—24no—
469D4×D17—24no—
470D4×D17—22no—
471D4×D17—22no—
472D4×D17—22no—
473D4×D17—22no—
474D4×D17—42no—
475D4×D17—42no—
476D4×D17—42no—
477D4×D17—42no—
478D4×D17—42no—
479D4×D17—42no—
480D4×D17—44no—
481D4×D17—44no—
482D4×D17—44no—
483D4×D17—44no—
484D4×D17C2×D414yes—
485D4×D17#4114yes—
486C2×D68—24no—
487C2×D68—24no—
488C2×D68—44no—
489C2×D68C22×C411yescharacteristic
490C2×D68C22×C411yescharacteristic
491C2×D68C22×C412yes—
492C2×D68C22×C412yes—
493C2×D68C22×C411yescharacteristic
494C2×D68C22×C411yescharacteristic, complemented
495C2×D68C22×C412yescomplemented
496C2×D68C22×C412yescomplemented
497C2×D68C22×C412yescomplemented
498C2×D68C22×C412yescomplemented
499C2×C4×D17—22no—
500C2×C4×D17—22no—
501C2×C4×D17—22no—
502C2×C4×D17—22no—
503C2×C4×D17—42no—
504C2×C4×D17—42no—
505C2×C4×D17C22×C411yescharacteristic
506C2×C4×D17C22×C411yescharacteristic
507C2×C4×D17C22×C411yescharacteristic, complemented
508C2×C4×D17C22×C411yescharacteristic, complemented
509C2×C4×D17C22×C412yescomplemented
510C2×C4×D17C22×C412yescomplemented
511C2×C4×D17C2411yescharacteristic
512C2×C4×D17C2411yescharacteristic
513C2×C4×D17C2412yes—
514C2×C4×D17C2411yescharacteristic
515C2×C4×D17C2411yescharacteristic
516C2×C4×D17C2411yescharacteristic
517C22⋊#595—24no—
518C22⋊#595—24no—
519C22⋊#595—24no—
520C22⋊#595—22no—
521C22⋊#595—24no—
522C22⋊#595—22no—
523C22⋊#595—22no—
524C22⋊#595—22no—
525C22⋊#595—24no—
526C22⋊#595—24no—
527C22⋊#595—24no—
528C22⋊#595—24no—
529C22⋊#595—24no—
530C22⋊#595—24no—
531C22⋊#595—22no—
532C22⋊#595—42no—
533C22⋊#595—42no—
534C22⋊#595—42no—
535C22⋊#595—42no—
536C22⋊#595—42no—
537C22⋊#595—42no—
538C22⋊#595—42no—
539C22⋊#595—41no—
540C22⋊#595—42no—
541C22⋊#595C2×D418yescomplemented
542C4⋊#595—24no—
543C4⋊#595—22no—
544C4⋊#595—22no—
545C4⋊#595—22no—
546C4⋊#595—22no—
547C4⋊#595—22no—
548C4⋊#595—22no—
549C4⋊#595—41no—
550C4⋊#595—42no—
551C4⋊#595—42no—
552C4⋊#595C2×D414yescomplemented
553C4×#595—22no—
554C4×#595—22no—
555C4×#595—24no—
556C4×#595—22no—
557C4×#595—22no—
558C4×#595—22no—
559C4×#595—42no—
560C4×#595—42no—
561C4×#595—42no—
562C4×#595C2×D414yescomplemented
563C4⋊C4×C17C22×C411yescharacteristic, complemented
564C4⋊C4×C17C22×C411yescharacteristic, complemented
565C22⋊C4×C17C22×C411yescharacteristic
566C22⋊C4×C17C22×C411yescharacteristic, complemented
567C22⋊C4×C17C22×C412yescomplemented
568C22⋊C4×C17C22×C412yescomplemented
569C22⋊C4×C17C22×C412yescomplemented
570C42×C17C22×C411yescharacteristic, complemented
571C22⋊Dic17C22×C411yescharacteristic
572C22⋊Dic17C22×C411yescharacteristic, complemented
573C22⋊Dic17C22×C412yescomplemented
574C22⋊Dic17C22×C412yescomplemented
575C22⋊Dic17C22×C412yescomplemented
576#63227C22×C411yescharacteristic
577#63227C22×C411yescharacteristic
578#63227C22×C411yescharacteristic, complemented
579#63227C22×C412yescomplemented
580#63227C22×C411yescharacteristic, complemented
581#63227C22×C412yescomplemented
582#63227C22×C412yescomplemented
583#63227C22×C412yescomplemented
584#63227C22×C412yescomplemented
585#63227C22×C412yescomplemented
586C4⋊Dic17C22×C411yescharacteristic, complemented
587C4⋊Dic17C22×C411yescharacteristic, complemented
588#63225C22×C411yescharacteristic, complemented
589#63225C22×C411yescharacteristic, complemented
590#63225C22×C412yescomplemented
591C4×Dic17C22×C411yescharacteristic, complemented
592C4×Dic17C22×C411yescharacteristic, complemented
593C4×Dic17C22×C411yescharacteristic, complemented
594#34290—171nomaximal, Sylow
595C23×C17—24no—
596C23×C17—24no—
597C23×C17—24no—
598C23×C17—42no—
599C23×C17—42no—
600C23×C17—42no—
601C23×C17C23×C411yescharacteristic
602C23×C17C23×C412yes—
603C23×C17C23×C412yes—
604C23×C17C23×C412yes—
605C23×C17C23×C411yescharacteristic
606C22×D17—21no—
607C22×D17—21no—
608C22×D17—22no—
609C22×D17—22no—
610C22×D17—21no—
611C22×D17—22no—
612C22×D17—21no—
613C22×D17—22no—
614C22×D17—24no—
615C22×D17—24no—
616C22×D17—24no—
617C22×D17—24no—
618C22×D17—24no—
619C22×D17—24no—
620C22×D17—24no—
621C22×D17—21no—
622C22×D17—22no—
623C22×D17—22no—
624C22×D17—21no—
625C22×D17—22no—
626C22×D17—22no—
627C22×D17—21no—
628C22×D17—22no—
629C22×D17—22no—
630C22×D17—22no—
631C22×D17—22no—
632C22×D17—22no—
633C22×D17—21no—
634C22×D17—21no—
635C22×D17—22no—
636C22×D17—22no—
637C22×D17—21no—
638C22×D17—22no—
639C22×D17—24no—
640C22×D17—24no—
641C22×D17—42no—
642C22×D17—42no—
643C22×D17—42no—
644C22×D17—48no—
645C22×D17—48no—
646C22×D17—48no—
647C22×D17—48no—
648C22×D17—42no—
649C22×D17—42no—
650C22×D17—42no—
651C22×D17—42no—
652C22×D17—42no—
653C22×D17—42no—
654C22×D17—84no—
655C22×D17—84no—
656C22×D17—84no—
657C22×D17—84no—
658C22×D17C23×C411yescharacteristic
659C22×D17C23×C412yes—
660C22×D17C23×C412yes—
661C22×D17C23×C412yes—
662C22×D17C23×C411yescharacteristic
663C22×D17C22×D414yes—
664C22×D17C2×#4114yes—
665C22×D17H(5,𝔽2)12yes—
666C22×D17H(5,𝔽2)12yes—
667C22×D17C2511yescharacteristic
668C2×#595—28no—
669C2×#595—21no—
670C2×#595—21no—
671C2×#595—22no—
672C2×#595—22no—
673C2×#595—21no—
674C2×#595—21no—
675C2×#595—21no—
676C2×#595—21no—
677C2×#595—21no—
678C2×#595—21no—
679C2×#595—22no—
680C2×#595—21no—
681C2×#595—22no—
682C2×#595—21no—
683C2×#595—21no—
684C2×#595—22no—
685C2×#595—21no—
686C2×#595—22no—
687C2×#595—22no—
688C2×#595—21no—
689C2×#595—21no—
690C2×#595—21no—
691C2×#595—22no—
692C2×#595—22no—
693C2×#595—21no—
694C2×#595—21no—
695C2×#595—21no—
696C2×#595—22no—
697C2×#595—21no—
698C2×#595—21no—
699C2×#595—21no—
700C2×#595—22no—
701C2×#595—48no—
702C2×#595—48no—
703C2×#595—44no—
704C2×#595—48no—
705C2×#595—48no—
706C2×#595—48no—
707C2×#595—84no—
708C2×#595—84no—
709C2×#595—84no—
710C2×#595—84no—
711C2×#595C22×D412yes—
712C2×#595C22×D412yes—
713C2×#595C22×D414yes—
714C2×#595H(5,𝔽2)12yes—
715D4×C17—24no—
716D4×C17—24no—
717D4×C17—22no—
718D4×C17—24no—
719D4×C17—22no—
720D4×C17—22no—
721D4×C17—42no—
722D4×C17—42no—
723D4×C17—42no—
724D4×C17C4×D414yescomplemented
725C2×C4×C17—22no—
726C2×C4×C17—22no—
727C2×C4×C17—42no—
728C2×C4×C17C23×C411yescharacteristic
729C2×C4×C17C23×C411yescharacteristic
730C2×C4×C17C23×C411yescharacteristic
731C2×C4×C17C23×C411yescharacteristic
732C2×C4×C17C23×C412yes—
733C2×C4×C17C23×C411yescharacteristic
734C22⋊D17—24no—
735C22⋊D17—24no—
736C22⋊D17—22no—
737C22⋊D17—24no—
738C22⋊D17—24no—
739C22⋊D17—24no—
740C22⋊D17—22no—
741C22⋊D17—24no—
742C22⋊D17—24no—
743C22⋊D17—24no—
744C22⋊D17—42no—
745C22⋊D17—42no—
746C22⋊D17—42no—
747C22⋊D17—42no—
748C22⋊D17—42no—
749C22⋊D17—42no—
750C22⋊D17C4×D418yescomplemented
751C2×Dic17—22no—
752C2×Dic17—22no—
753C2×Dic17—42no—
754C2×Dic17C23×C411yescharacteristic
755C2×Dic17C23×C411yescharacteristic
756C2×Dic17C23×C411yescharacteristic
757C2×Dic17C23×C412yes—
758C2×Dic17C23×C411yescharacteristic
759C2×Dic17C23×C411yescharacteristic
760D68—24no—
761D68—24no—
762D68—22no—
763D68—24no—
764D68—22no—
765D68—22no—
766D68—42no—
767D68—42no—
768D68—42no—
769D68C4×D414yescomplemented
770C4×D17—21no—
771C4×D17—21no—
772C4×D17—21no—
773C4×D17—21no—
774C4×D17—21no—
775C4×D17—22no—
776C4×D17—22no—
777C4×D17—21no—
778C4×D17—21no—
779C4×D17—21no—
780C4×D17—22no—
781C4×D17—22no—
782C4×D17—22no—
783C4×D17—22no—
784C4×D17—42no—
785C4×D17—42no—
786C4×D17C22×D412yes—
787C4×D17C2×#4112yes—
788C2×D42—171no—
789C2×#518—171no—
790C22×C4×D4—171no—
791#2366—171no—
792#2364—172no—
793#2363—171no—
794#2361—171no—
795#2358—172no—
796#2358—172no—
797#2352—171no—
798#2349—171no—
799D4×C22⋊C4—172no—
800D4×C22⋊C4—171no—
801D4×C22⋊C4—171no—
802#2328—171no—
803#2325—172no—
804#2324—171no—
805#2321—172no—
806C4×#121—171no—
807C4×#120—172no—
808#2290—171no—
809C2×#386—172no—
810#2275—171no—
811C22×C17—21no—
812C22×C17—22no—
813C22×C17—21no—
814C22×C17—22no—
815C22×C17—21no—
816C22×C17—22no—
817C22×C17—22no—
818C22×C17—21no—
819C22×C17—22no—
820C22×C17—22no—
821C22×C17—22no—
822C22×C17—22no—
823C22×C17—21no—
824C22×C17—48no—
825C22×C17—84no—
826C22×C17C2×C4×D414yes—
827C22×C17#51812yescomplemented
828C22×C17C24×C411yescharacteristic
829C2×D17—21no—
830C2×D17—22no—
831C2×D17—21no—
832C2×D17—22no—
833C2×D17—22no—
834C2×D17—24no—
835C2×D17—22no—
836C2×D17—24no—
837C2×D17—22no—
838C2×D17—24no—
839C2×D17—24no—
840C2×D17—22no—
841C2×D17—21no—
842C2×D17—22no—
843C2×D17—22no—
844C2×D17—21no—
845C2×D17—22no—
846C2×D17—22no—
847C2×D17—22no—
848C2×D17—22no—
849C2×D17—21no—
850C2×D17—48no—
851C2×D17—48no—
852C2×D17—48no—
853C2×D17—42no—
854C2×D17—42no—
855C2×D17—41no—
856C2×D17—42no—
857C2×D17—42no—
858C2×D17—41no—
859C2×D17—42no—
860C2×D17—42no—
861C2×D17—41no—
862C2×D17—42no—
863C2×D17—42no—
864C2×D17—41no—
865C2×D17—84no—
866C2×D17—84no—
867C2×D17—84no—
868C2×D17C2×C4×D414yes—
869C2×D17#51812yescomplemented
870C2×D17C23×D411yescharacteristic
871C2×D17C22×#4111yescharacteristic
872C2×D17C2×H(5,𝔽2)11yescharacteristic
873C2×D17C2×H(5,𝔽2)11yescharacteristic
874C2×D17C2×H(5,𝔽2)11yescharacteristic
875C2×D17#58511yescharacteristic
876#595—22no—
877#595—22no—
878#595—24no—
879#595—22no—
880#595—42no—
881#595—41no—
882#595—41no—
883#595—42no—
884#595—41no—
885#595—41no—
886#595—42no—
887#595—41no—
888C4×C17—21no—
889C4×C17—21no—
890C4×C17—21no—
891C4×C17—22no—
892C4×C17—21no—
893C4×C17C2×C4×D412yes—
894Dic17—21no—
895Dic17—21no—
896Dic17—21no—
897Dic17—22no—
898Dic17—21no—
899Dic17C2×C4×D412yes—
900C23×D4—171no—
901C23×D4—171no—
902C23×D4—172no—
903C24×C4—172no—
904D42—171no—
905D42—172no—
906D42—171no—
907D42—171no—
908D42—171no—
909D42—172no—
910D42—171no—
911D42—172no—
912D42—172no—
913D42—171no—
914D42—171no—
915D42#59511yescharacteristic, complemented
916C2×#127—171no—
917C2×#121—171no—
918C2×#121—172no—
919C2×#121—171no—
920C2×#120—172no—
921C2×#120—172no—
922#518—348no—
923C2×C4×D4—171no—
924C2×C4×D4—171no—
925C2×C4×D4—171no—
926C2×C4×D4—172no—
927C2×C4×D4—171no—
928C2×C4×D4—172no—
929C2×C4×D4—171no—
930C2×C4×D4—171no—
931C2×C4×D4—171no—
932C2×C4×D4—171no—
933C2×C4×D4—172no—
934C2×C4×D4—172no—
935C2×C4×D4—171no—
936C2×C4×D4—171no—
937C2×C4×D4—172no—
938C2×C4×D4—172no—
939C2×C4×D4—172no—
940C2×C4×D4—348no—
941C2×#117—171no—
942C2×#117—171no—
943C22×C4⋊C4—171no—
944C22×C22⋊C4—172no—
945C22×C22⋊C4—172no—
946C22×C22⋊C4—172no—
947C22×C22⋊C4—172no—
948C22×C22⋊C4—172no—
949C22×C42—171no—
950#390—172no—
951#390—172no—
952#390—172no—
953#390—171no—
954#390—171no—
955#390—171no—
956#390—171no—
957#389—171no—
958#389—171no—
959#388—171no—
960#388—172no—
961#388—172no—
962#388—172no—
963#388—172no—
964#388—172no—
965#388—171no—
966#387—171no—
967#387—172no—
968#387—171no—
969#386—172no—
970#386—172no—
971#386—172no—
972#386—172no—
973#386—172no—
974#386—172no—
975#386—172no—
976#386—172no—
977#386—172no—
978#386—171no—
979#386—172no—
980#386—172no—
981#386—171no—
982#386—172no—
983#386—172no—
984#386—172no—
985#386—172no—
986#385—172no—
987#385—172no—
988#385—172no—
989#385—172no—
990#385—171no—
991#385—171no—
992#382—171no—
993#380—171no—
994#380—172no—
995#380—171no—
996#379—172no—
997#379—172no—
998C4×C4⋊C4—171no—
999C4×C4⋊C4—171no—
1000C4×C4⋊C4—171no—
1001C4×C4⋊C4—171no—
1002C4×C22⋊C4—172no—
1003C4×C22⋊C4—171no—
1004C4×C22⋊C4—171no—
1005C4×C22⋊C4—172no—
1006C4×C22⋊C4—172no—
1007C4×C22⋊C4—172no—
1008C4×C22⋊C4—172no—
1009C4×C22⋊C4—172no—
1010#376—171no—
1011C2×#95—172no—
1012C2×#95—172no—
1013C2×C17—22no—
1014C2×C17—24no—
1015C2×C17—42no—
1016C2×C17—41no—
1017C2×C17—42no—
1018C2×C17C22×C4×D411yescharacteristic
1019C2×C17C2×#51811yescharacteristic
1020C2×C17C4×H(5,𝔽2)11yescharacteristic
1021D17—22no—
1022D17—24no—
1023D17—42no—
1024D17—42no—
1025D17—41no—
1026D17#348411yescharacteristic
1027D17#348811yescharacteristic
1028D17#351311yescharacteristic
1029D17#351911yescharacteristic
1030C25—172no—
1031C25—172no—
1032C22×D4—171no—
1033C22×D4—172no—
1034C22×D4—172no—
1035C22×D4—172no—
1036C22×D4—172no—
1037C22×D4—172no—
1038C22×D4—172no—
1039C22×D4—171no—
1040C22×D4—171no—
1041C22×D4—172no—
1042C22×D4—171no—
1043C22×D4—171no—
1044C22×D4—171no—
1045C22×D4—172no—
1046C22×D4—171no—
1047C22×D4—172no—
1048C22×D4—171no—
1049C22×D4—172no—
1050C22×D4—172no—
1051C22×D4—172no—
1052C22×D4—172no—
1053C22×D4—172no—
1054C22×D4—172no—
1055C22×D4—172no—
1056C22×D4—171no—
1057C22×D4—171no—
1058C22×D4—172no—
1059C22×D4—344no—
1060C22×D4—344no—
1061C22×D4—344no—
1062C22×D4—344no—
1063C22×D4—684no—
1064C22×D4—684no—
1065C22×D4C2×#59511yescharacteristic, complemented
1066C22×D4C2×#59511yescharacteristic, complemented
1067C22×D4C2×#59512yescomplemented
1068C23×C4—172no—
1069C23×C4—171no—
1070C23×C4—171no—
1071C23×C4—172no—
1072C23×C4—171no—
1073C23×C4—171no—
1074C23×C4—172no—
1075C23×C4—172no—
1076C23×C4—172no—
1077C23×C4—172no—
1078C23×C4—172no—
1079C23×C4—172no—
1080C23×C4—172no—
1081C23×C4—172no—
1082C23×C4—348no—
1083C23×C4—684no—
1084C23×C4—684no—
1085#127—171no—
1086#127—172no—
1087#127—172no—
1088#127—171no—
1089#127—171no—
1090#127C2×#59511yescharacteristic, complemented
1091#121—171no—
1092#121—172no—
1093#121—172no—
1094#121—171no—
1095#121—172no—
1096#121—172no—
1097#121—172no—
1098#121—171no—
1099#121—171no—
1100#121—172no—
1101#121—171no—
1102#121—171no—
1103#121—172no—
1104#121—172no—
1105#121—172no—
1106#121—172no—
1107#121—172no—
1108#121C2×#59511yescharacteristic, complemented
1109#121C2×#59511yescharacteristic, complemented
1110#121C2×#59512yescomplemented
1111#120—172no—
1112#120—172no—
1113#120—172no—
1114#120—172no—
1115#120—172no—
1116#120—172no—
1117#120—172no—
1118#120—172no—
1119#120—172no—
1120#120—172no—
1121#120—172no—
1122#120—172no—
1123#120—172no—
1124#120—172no—
1125#120C2×#59512yescomplemented
1126#120C2×#59512yescomplemented
1127C4×D4—178no—
1128C4×D4—171no—
1129C4×D4—171no—
1130C4×D4—171no—
1131C4×D4—171no—
1132C4×D4—172no—
1133C4×D4—171no—
1134C4×D4—171no—
1135C4×D4—171no—
1136C4×D4—171no—
1137C4×D4—172no—
1138C4×D4—171no—
1139C4×D4—171no—
1140C4×D4—344no—
1141C4×D4—344no—
1142C4×D4—348no—
1143C4×D4—348no—
1144C4×D4—344no—
1145C4×D4—344no—
1146C4×D4—348no—
1147C4×D4—348no—
1148C4×D4—344no—
1149C4×D4—344no—
1150C4×D4—344no—
1151C4×D4—684no—
1152C4×D4—684no—
1153C4×D4—684no—
1154C4×D4C2×#59511yescharacteristic, complemented
1155C4×D4C2×#59511yescharacteristic, complemented
1156#117—344no—
1157#117—344no—
1158C2×C4⋊C4—171no—
1159C2×C4⋊C4—171no—
1160C2×C4⋊C4—171no—
1161C2×C4⋊C4—171no—
1162C2×C4⋊C4—172no—
1163C2×C4⋊C4—171no—
1164C2×C4⋊C4—171no—
1165C2×C4⋊C4—171no—
1166C2×C4⋊C4—171no—
1167C2×C4⋊C4—171no—
1168C2×C4⋊C4—172no—
1169C2×C4⋊C4—172no—
1170C2×C4⋊C4—171no—
1171C2×C4⋊C4—344no—
1172C2×C22⋊C4—172no—
1173C2×C22⋊C4—171no—
1174C2×C22⋊C4—172no—
1175C2×C22⋊C4—171no—
1176C2×C22⋊C4—172no—
1177C2×C22⋊C4—172no—
1178C2×C22⋊C4—171no—
1179C2×C22⋊C4—172no—
1180C2×C22⋊C4—171no—
1181C2×C22⋊C4—171no—
1182C2×C22⋊C4—171no—
1183C2×C22⋊C4—172no—
1184C2×C22⋊C4—172no—
1185C2×C22⋊C4—172no—
1186C2×C22⋊C4—172no—
1187C2×C22⋊C4—172no—
1188C2×C22⋊C4—172no—
1189C2×C22⋊C4—172no—
1190C2×C22⋊C4—172no—
1191C2×C22⋊C4—171no—
1192C2×C22⋊C4—172no—
1193C2×C22⋊C4—172no—
1194C2×C22⋊C4—172no—
1195C2×C22⋊C4—172no—
1196C2×C22⋊C4—172no—
1197C2×C22⋊C4—172no—
1198C2×C22⋊C4—172no—
1199C2×C22⋊C4—172no—
1200C2×C22⋊C4—171no—
1201C2×C22⋊C4—172no—
1202C2×C22⋊C4—348no—
1203C2×C22⋊C4—348no—
1204C2×C22⋊C4—348no—
1205C2×C22⋊C4—684no—
1206C2×C22⋊C4—684no—
1207C2×C42—171no—
1208C2×C42—171no—
1209C2×C42—172no—
1210C2×C42—171no—
1211C2×C42—171no—
1212C2×C42—171no—
1213C2×C42—171no—
1214C2×C42—171no—
1215C2×C42—172no—
1216C2×C42—172no—
1217C2×C42—172no—
1218C2×C42—344no—
1219#95—171no—
1220#95—171no—
1221#95—172no—
1222#95—172no—
1223#95—172no—
1224#95—172no—
1225#95—172no—
1226#95—172no—
1227#95—171no—
1228#95—171no—
1229#95—171no—
1230#95—171no—
1231#95—172no—
1232#95—172no—
1233#95—172no—
1234#95—171no—
1235#95—171no—
1236#95—171no—
1237#95—171no—
1238C17#3429011yescharacteristic, complemented, Sylow
1239C24—172no—
1240C24—171no—
1241C24—171no—
1242C24—172no—
1243C24—172no—
1244C24—172no—
1245C24—172no—
1246C24—172no—
1247C24—172no—
1248C24—172no—
1249C24—172no—
1250C24—344no—
1251C24—344no—
1252C24—344no—
1253C24—344no—
1254C24—344no—
1255C24—344no—
1256C24—682no—
1257C24—682no—
1258C24—682no—
1259C24—682no—
1260C24—682no—
1261C24—682no—
1262C24C22×#59512yes—
1263C24C22×#59512yescomplemented
1264C2×D4—24no—
1265C2×D4—24no—
1266C2×D4—44no—
1267C2×D4—172no—
1268C2×D4—174no—
1269C2×D4—174no—
1270C2×D4—171no—
1271C2×D4—171no—
1272C2×D4—172no—
1273C2×D4—172no—
1274C2×D4—172no—
1275C2×D4—172no—
1276C2×D4—172no—
1277C2×D4—172no—
1278C2×D4—172no—
1279C2×D4—172no—
1280C2×D4—172no—
1281C2×D4—172no—
1282C2×D4—172no—
1283C2×D4—172no—
1284C2×D4—172no—
1285C2×D4—172no—
1286C2×D4—171no—
1287C2×D4—171no—
1288C2×D4—172no—
1289C2×D4—172no—
1290C2×D4—171no—
1291C2×D4—172no—
1292C2×D4—171no—
1293C2×D4—172no—
1294C2×D4—172no—
1295C2×D4—172no—
1296C2×D4—344no—
1297C2×D4—344no—
1298C2×D4—342no—
1299C2×D4—342no—
1300C2×D4—342no—
1301C2×D4—342no—
1302C2×D4—348no—
1303C2×D4—348no—
1304C2×D4—344no—
1305C2×D4—344no—
1306C2×D4—344no—
1307C2×D4—344no—
1308C2×D4—344no—
1309C2×D4—344no—
1310C2×D4—344no—
1311C2×D4—344no—
1312C2×D4—342no—
1313C2×D4—342no—
1314C2×D4—348no—
1315C2×D4—348no—
1316C2×D4—344no—
1317C2×D4—344no—
1318C2×D4—684no—
1319C2×D4—682no—
1320C2×D4—682no—
1321C2×D4—682no—
1322C2×D4—682no—
1323C2×D4—682no—
1324C2×D4—682no—
1325C2×D4—684no—
1326C2×D4—684no—
1327C2×D4—684no—
1328C2×D4—684no—
1329C2×D4—684no—
1330C2×D4—684no—
1331C2×D4C22×#59511yescharacteristic
1332C2×D4C22×#59512yes—
1333C2×D4C22×#59512yes—
1334C2×D4C22×#59511yescharacteristic
1335C2×D4C22×#59511yescharacteristic
1336C2×D4C22×#59512yescomplemented
1337C2×D4C22×#59511yescharacteristic, complemented
1338C2×D4C22×#59512yescomplemented
1339C2×D4C22×#59512yescomplemented
1340C2×D4C22×#59512yescomplemented
1341C22×C4—171no—
1342C22×C4—171no—
1343C22×C4—171no—
1344C22×C4—171no—
1345C22×C4—172no—
1346C22×C4—171no—
1347C22×C4—171no—
1348C22×C4—178no—
1349C22×C4—172no—
1350C22×C4—171no—
1351C22×C4—171no—
1352C22×C4—171no—
1353C22×C4—171no—
1354C22×C4—171no—
1355C22×C4—171no—
1356C22×C4—171no—
1357C22×C4—171no—
1358C22×C4—172no—
1359C22×C4—172no—
1360C22×C4—172no—
1361C22×C4—171no—
1362C22×C4—171no—
1363C22×C4—172no—
1364C22×C4—171no—
1365C22×C4—172no—
1366C22×C4—172no—
1367C22×C4—171no—
1368C22×C4—171no—
1369C22×C4—342no—
1370C22×C4—342no—
1371C22×C4—342no—
1372C22×C4—342no—
1373C22×C4—342no—
1374C22×C4—342no—
1375C22×C4—342no—
1376C22×C4—344no—
1377C22×C4—344no—
1378C22×C4—344no—
1379C22×C4—344no—
1380C22×C4—344no—
1381C22×C4—344no—
1382C22×C4—344no—
1383C22×C4—342no—
1384C22×C4—344no—
1385C22×C4—342no—
1386C22×C4—344no—
1387C22×C4—344no—
1388C22×C4—344no—
1389C22×C4—682no—
1390C22×C4—682no—
1391C22×C4—681no—
1392C22×C4—682no—
1393C22×C4—682no—
1394C22×C4—682no—
1395C22×C4—682no—
1396C22×C4—682no—
1397C22×C4—682no—
1398C22×C4—682no—
1399C22×C4—682no—
1400C22×C4—682no—
1401C22×C4—682no—
1402C22×C4—682no—
1403C22×C4—682no—
1404C22×C4—682no—
1405C22×C4—682no—
1406C22×C4—682no—
1407C22×C4—6832no—
1408C22×C4C22×#59511yescharacteristic
1409C22×C4C22×#59511yescharacteristic, complemented
1410C22×C4C22×#59512yescomplemented
1411C4⋊C4—174no—
1412C4⋊C4—172no—
1413C4⋊C4—171no—
1414C4⋊C4—171no—
1415C4⋊C4—171no—
1416C4⋊C4—171no—
1417C4⋊C4—342no—
1418C4⋊C4—344no—
1419C4⋊C4—342no—
1420C4⋊C4—342no—
1421C4⋊C4—342no—
1422C4⋊C4—342no—
1423C4⋊C4—342no—
1424C4⋊C4—681no—
1425C4⋊C4—682no—
1426C4⋊C4—682no—
1427C4⋊C4C22×#59511yescharacteristic, complemented
1428C4⋊C4C22×#59511yescharacteristic, complemented
1429C22⋊C4—178no—
1430C22⋊C4—171no—
1431C22⋊C4—171no—
1432C22⋊C4—172no—
1433C22⋊C4—172no—
1434C22⋊C4—172no—
1435C22⋊C4—171no—
1436C22⋊C4—171no—
1437C22⋊C4—171no—
1438C22⋊C4—172no—
1439C22⋊C4—172no—
1440C22⋊C4—171no—
1441C22⋊C4—172no—
1442C22⋊C4—172no—
1443C22⋊C4—172no—
1444C22⋊C4—172no—
1445C22⋊C4—342no—
1446C22⋊C4—342no—
1447C22⋊C4—344no—
1448C22⋊C4—344no—
1449C22⋊C4—344no—
1450C22⋊C4—344no—
1451C22⋊C4—344no—
1452C22⋊C4—342no—
1453C22⋊C4—344no—
1454C22⋊C4—344no—
1455C22⋊C4—344no—
1456C22⋊C4—342no—
1457C22⋊C4—344no—
1458C22⋊C4—344no—
1459C22⋊C4—342no—
1460C22⋊C4—681no—
1461C22⋊C4—682no—
1462C22⋊C4—682no—
1463C22⋊C4—682no—
1464C22⋊C4—682no—
1465C22⋊C4—682no—
1466C22⋊C4—682no—
1467C22⋊C4—682no—
1468C22⋊C4—682no—
1469C22⋊C4C22×#59511yescharacteristic
1470C22⋊C4C22×#59511yescharacteristic, complemented
1471C22⋊C4C22×#59512yescomplemented
1472C22⋊C4C22×#59512yescomplemented
1473C22⋊C4C22×#59512yescomplemented
1474C42—174no—
1475C42—171no—
1476C42—171no—
1477C42—171no—
1478C42—342no—
1479C42—342no—
1480C42—342no—
1481C42—342no—
1482C42—344no—
1483C42—342no—
1484C42—682no—
1485C42—682no—
1486C42—682no—
1487C42C22×#59511yescharacteristic, complemented
1488C23—24no—
1489C23—24no—
1490C23—24no—
1491C23—42no—
1492C23—42no—
1493C23—42no—
1494C23—171no—
1495C23—174no—
1496C23—174no—
1497C23—172no—
1498C23—172no—
1499C23—172no—
1500C23—171no—
1501C23—171no—
1502C23—172no—
1503C23—172no—
1504C23—341no—
1505C23—341no—
1506C23—342no—
1507C23—341no—
1508C23—342no—
1509C23—342no—
1510C23—341no—
1511C23—342no—
1512C23—341no—
1513C23—342no—
1514C23—342no—
1515C23—341no—
1516C23—342no—
1517C23—342no—
1518C23—342no—
1519C23—342no—
1520C23—342no—
1521C23—342no—
1522C23—341no—
1523C23—341no—
1524C23—342no—
1525C23—342no—
1526C23—344no—
1527C23—342no—
1528C23—342no—
1529C23—344no—
1530C23—341no—
1531C23—341no—
1532C23—344no—
1533C23—344no—
1534C23—344no—
1535C23—344no—
1536C23—344no—
1537C23—344no—
1538C23—344no—
1539C23—682no—
1540C23—682no—
1541C23—682no—
1542C23—682no—
1543C23—682no—
1544C23—682no—
1545C23—682no—
1546C23—682no—
1547C23—682no—
1548C23—688no—
1549C23—688no—
1550C23—688no—
1551C23—688no—
1552C23—1364no—
1553C23—1364no—
1554C23—1364no—
1555C23—1364no—
1556C23C23×#59511yescharacteristic
1557C23C23×#59512yes—
1558C23C23×#59512yes—
1559C23C23×#59512yes—
1560C23C23×#59511yescharacteristic
1561D4—24no—
1562D4—24no—
1563D4—22no—
1564D4—24no—
1565D4—22no—
1566D4—22no—
1567D4—42no—
1568D4—42no—
1569D4—42no—
1570D4—178no—
1571D4—174no—
1572D4—344no—
1573D4—344no—
1574D4—342no—
1575D4—344no—
1576D4—344no—
1577D4—344no—
1578D4—344no—
1579D4—344no—
1580D4—342no—
1581D4—344no—
1582D4—344no—
1583D4—344no—
1584D4—342no—
1585D4—344no—
1586D4—342no—
1587D4—342no—
1588D4—682no—
1589D4—682no—
1590D4—682no—
1591D4—682no—
1592D4—682no—
1593D4—682no—
1594D4—682no—
1595D4—682no—
1596D4—682no—
1597D4D4×#59514yescomplemented
1598C2×C4—22no—
1599C2×C4—22no—
1600C2×C4—42no—
1601C2×C4—171no—
1602C2×C4—172no—
1603C2×C4—172no—
1604C2×C4—172no—
1605C2×C4—172no—
1606C2×C4—174no—
1607C2×C4—172no—
1608C2×C4—171no—
1609C2×C4—171no—
1610C2×C4—171no—
1611C2×C4—171no—
1612C2×C4—172no—
1613C2×C4—342no—
1614C2×C4—342no—
1615C2×C4—341no—
1616C2×C4—341no—
1617C2×C4—341no—
1618C2×C4—342no—
1619C2×C4—342no—
1620C2×C4—341no—
1621C2×C4—341no—
1622C2×C4—341no—
1623C2×C4—341no—
1624C2×C4—341no—
1625C2×C4—342no—
1626C2×C4—342no—
1627C2×C4—341no—
1628C2×C4—341no—
1629C2×C4—342no—
1630C2×C4—342no—
1631C2×C4—341no—
1632C2×C4—341no—
1633C2×C4—341no—
1634C2×C4—341no—
1635C2×C4—348no—
1636C2×C4—342no—
1637C2×C4—342no—
1638C2×C4—341no—
1639C2×C4—341no—
1640C2×C4—342no—
1641C2×C4—341no—
1642C2×C4—341no—
1643C2×C4—341no—
1644C2×C4—341no—
1645C2×C4—342no—
1646C2×C4—342no—
1647C2×C4—342no—
1648C2×C4—341no—
1649C2×C4—341no—
1650C2×C4—341no—
1651C2×C4—342no—
1652C2×C4—342no—
1653C2×C4—341no—
1654C2×C4—341no—
1655C2×C4—341no—
1656C2×C4—341no—
1657C2×C4—342no—
1658C2×C4—342no—
1659C2×C4—341no—
1660C2×C4—342no—
1661C2×C4—341no—
1662C2×C4—682no—
1663C2×C4—682no—
1664C2×C4—682no—
1665C2×C4—688no—
1666C2×C4—688no—
1667C2×C4—688no—
1668C2×C4—688no—
1669C2×C4—684no—
1670C2×C4—688no—
1671C2×C4—1364no—
1672C2×C4—1364no—
1673C2×C4—1364no—
1674C2×C4—1364no—
1675C2×C4C23×#59511yescharacteristic
1676C2×C4C23×#59511yescharacteristic
1677C2×C4C23×#59511yescharacteristic
1678C2×C4C23×#59511yescharacteristic
1679C2×C4C23×#59512yes—
1680C2×C4C23×#59511yescharacteristic
1681C22—21no—
1682C22—22no—
1683C22—21no—
1684C22—22no—
1685C22—21no—
1686C22—22no—
1687C22—22no—
1688C22—21no—
1689C22—22no—
1690C22—22no—
1691C22—22no—
1692C22—22no—
1693C22—21no—
1694C22—48no—
1695C22—84no—
1696C22—171no—
1697C22—171no—
1698C22—171no—
1699C22—171no—
1700C22—171no—
1701C22—171no—
1702C22—174no—
1703C22—172no—
1704C22—342no—
1705C22—344no—
1706C22—342no—
1707C22—344no—
1708C22—344no—
1709C22—342no—
1710C22—342no—
1711C22—344no—
1712C22—341no—
1713C22—342no—
1714C22—341no—
1715C22—342no—
1716C22—341no—
1717C22—342no—
1718C22—342no—
1719C22—341no—
1720C22—342no—
1721C22—342no—
1722C22—342no—
1723C22—342no—
1724C22—341no—
1725C22—688no—
1726C22—688no—
1727C22—682no—
1728C22—682no—
1729C22—682no—
1730C22—682no—
1731C22—682no—
1732C22—682no—
1733C22—681no—
1734C22—681no—
1735C22—681no—
1736C22—681no—
1737C22—682no—
1738C22—682no—
1739C22—688no—
1740C22—1364no—
1741C22—1364no—
1742C22—1364no—
1743C22C2×D4×#59514yes—
1744C22#1176387612yescomplemented
1745C22C24×#59511yescharacteristic
1746C4—21no—
1747C4—21no—
1748C4—21no—
1749C4—22no—
1750C4—21no—
1751C4—172no—
1752C4—342no—
1753C4—342no—
1754C4—344no—
1755C4—342no—
1756C4—341no—
1757C4—341no—
1758C4—341no—
1759C4—342no—
1760C4—341no—
1761C4—682no—
1762C4—681no—
1763C4—681no—
1764C4—681no—
1765C4—682no—
1766C4—681no—
1767C4—682no—
1768C4—681no—
1769C4C2×D4×#59512yes—
1770C2—22no—
1771C2—24no—
1772C2—42no—
1773C2—41no—
1774C2—42no—
1775C2—171no—
1776C2—171no—
1777C2—171no—
1778C2—171no—
1779C2—342no—
1780C2—344no—
1781C2—682no—
1782C2—681no—
1783C2—682no—
1784C2C22×D4×#59511yescharacteristic
1785C2C2×#1176387611yescharacteristic
1786C2H(5,𝔽2)×#59511yescharacteristic
subgroupG/H
center, FrattiniC22C24×#595
commutator, socleC22×C17C24×C4
FittingD42×C17C4
prime radicalD42×D17C2
cosocleC22×D17C25
hypercenterD42#595
hypocenterC17#34290
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ D42

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#11763876C2semidirect
2. C22×D4×#595C2semidirect
3. #14545314C2semidirect
4. #14545312C2semidirect
5. #14545311C2semidirect
6. #14545309C2semidirect
7. #14545306C2semidirect
8. #14545306C2semidirect
9. #14545300C2semidirect
10. #14545297C2semidirect
11. D4×C22⋊#595C2semidirect
12. D4×C22⋊#595C2semidirect
13. D4×C22⋊#595C2semidirect
14. #14545276C2semidirect
15. #14545273C2semidirect
16. #14545272C2semidirect
17. #14545269C2semidirect
18. #121×#595C2semidirect
19. #120×#595C2semidirect
20. #14545238C2semidirect
21. C2×#11763757C2semidirect
22. #14545223C2semidirect
24. C24×#595C22semidirect
31. C2×D4×#595C22semidirect
32. C2×D4×#595C22semidirect
33. C2×D4×#595C22semidirect
34. C2×D4×#595C22semidirect
35. C2×D4×#595C22semidirect
36. C2×D4×#595C22semidirect
37. C2×D4×#595C22semidirect
38. C2×D4×#595C22semidirect
39. C2×D4×#595C22semidirect
40. C2×D4×#595C22semidirect
41. C2×D4×#595C22semidirect
42. C2×#10587677C22semidirect
43. C2×#10587677C22semidirect
44. C22×C4⋊#595C22semidirect
45. C22×C22⋊#595C22semidirect
46. C22×C22⋊#595C22semidirect
47. C22×C22⋊#595C22semidirect
48. C22×C22⋊#595C22semidirect
49. C22×C22⋊#595C22semidirect
50. C22×C4×#595C22semidirect
51. #11763761C22semidirect
52. #11763761C22semidirect
53. #11763761C22semidirect
54. #11763761C22semidirect
55. #11763761C22semidirect
56. #11763761C22semidirect
57. #11763761C22semidirect
58. #11763760C22semidirect
59. #11763760C22semidirect
60. #11763759C22semidirect
61. #11763759C22semidirect
62. #11763759C22semidirect
63. #11763759C22semidirect
64. #11763759C22semidirect
65. #11763759C22semidirect
66. #11763759C22semidirect
67. #11763758C22semidirect
68. #11763758C22semidirect
69. #11763758C22semidirect
73. #11763757C22semidirect
74. #11763757C22semidirect
75. #11763757C22semidirect
76. #11763757C22semidirect
77. #11763757C22semidirect
78. #11763757C22semidirect
79. #11763757C22semidirect
80. #11763757C22semidirect
81. #11763757C22semidirect
82. #11763757C22semidirect
83. #11763757C22semidirect
84. #11763757C22semidirect
85. #11763757C22semidirect
86. #11763757C22semidirect
87. #11763756C22semidirect
88. #11763756C22semidirect
89. #11763756C22semidirect
90. #11763756C22semidirect
91. #11763756C22semidirect
92. #11763756C22semidirect
93. #11763753C22semidirect
94. #11763751C22semidirect
95. #11763751C22semidirect
96. #11763751C22semidirect
97. #11763750C22semidirect
98. #11763750C22semidirect
99. C4⋊C4×#595C22semidirect
100. C4⋊C4×#595C22semidirect
101. C4×C4⋊#595C22semidirect
102. C4×C4⋊#595C22semidirect
103. C22⋊C4×#595C22semidirect
104. C22⋊C4×#595C22semidirect
105. C22⋊C4×#595C22semidirect
106. C22⋊C4×#595C22semidirect
107. C22⋊C4×#595C22semidirect
108. C4×C22⋊#595C22semidirect
109. C4×C22⋊#595C22semidirect
110. C4×C22⋊#595C22semidirect
111. #11763745C22semidirect
112. C2×(C2×#595)⋊C4C22semidirect
113. C2×(C2×#595)⋊C4C22semidirect
117. D4×D68C4semidirect
118. D4×D68C4semidirect
119. #11763444C4semidirect
120. #11763443C4semidirect
121. #11763443C4semidirect
122. #11763443C4semidirect
123. D4×C22⋊D17C4semidirect
124. D4×C22⋊D17C4semidirect
125. D4×C22⋊D17C4semidirect
126. #11763441C4semidirect
127. #11763441C4semidirect
136. D42×C17C4semidirect
153. C22×D4×C17C2×C4semidirect
154. C22×D4×C17C2×C4semidirect
155. C22×D4×C17C2×C4semidirect
156. C22×C22⋊D17C2×C4semidirect
157. C22×C22⋊D17C2×C4semidirect
158. C22×C22⋊D17C2×C4semidirect
159. C22×C22⋊D17C2×C4semidirect
166. C2×D4×D17C2×C4semidirect
167. C2×D4×D17C2×C4semidirect
168. C2×D4×D17C2×C4semidirect
169. C2×D4×D17C2×C4semidirect
170. C2×D4×D17C2×C4semidirect
171. C2×D4×D17C2×C4semidirect
172. C2×D4×D17C2×C4semidirect
173. C2×D4×D17C2×C4semidirect
174. C2×D4×D17C2×C4semidirect
175. C2×D4×D17C2×C4semidirect
186. C22×D68C2×C4semidirect
187. C22×D68C2×C4semidirect
188. C22×D68C2×C4semidirect
236. D4×#595D4semidirect
262. C17×#127C2×C4semidirect
263. C17×#121C2×C4semidirect
264. C17×#121C2×C4semidirect
265. C17×#121C2×C4semidirect
266. C17×#120C2×C4semidirect
267. C17×#120C2×C4semidirect
268. C4×D4×C17C2×C4semidirect
269. C4×D4×C17C2×C4semidirect
270. #10587639C2×C4semidirect
271. #10587639C2×C4semidirect
272. #10587626C2×C4semidirect
273. #10587626C2×C4semidirect
274. #10587626C2×C4semidirect
275. #10587626C2×C4semidirect
276. #10587625C2×C4semidirect
277. #10587625C2×C4semidirect
278. #10587625C2×C4semidirect
279. #10587625C2×C4semidirect
280. #10587624C2×C4semidirect
281. #10587624C2×C4semidirect
282. #10587624C2×C4semidirect
283. #10587623C2×C4semidirect
284. #10587623C2×C4semidirect
285. #10587623C2×C4semidirect
286. #10587623C2×C4semidirect
287. #10587623C2×C4semidirect
288. #10587623C2×C4semidirect
289. D4×Dic17C2×C4semidirect
290. D4×Dic17C2×C4semidirect
291. #10587616C2×C4semidirect
292. #10587616C2×C4semidirect
293. #10587616C2×C4semidirect
294. C4×C22⋊D17C2×C4semidirect
295. C4×C22⋊D17C2×C4semidirect
296. C4×C22⋊D17C2×C4semidirect
297. #10587581C2×C4semidirect
298. #10587581C2×C4semidirect
299. #10587581C2×C4semidirect
300. #10587579C2×C4semidirect
301. #10587579C2×C4semidirect
304. #10587570C2×C4semidirect
305. #10587570C2×C4semidirect
306. #10587570C2×C4semidirect
307. #10587570C2×C4semidirect
308. #10587568C2×C4semidirect
309. #10587568C2×C4semidirect
310. #10587568C2×C4semidirect
311. #10587568C2×C4semidirect
312. #10587568C2×C4semidirect
313. #10587568C2×C4semidirect
314. #10587567C2×C4semidirect
315. #10587567C2×C4semidirect
316. #10587567C2×C4semidirect
322. #10587560C2×C4semidirect
323. C4×D68C2×C4semidirect
324. C4×D68C2×C4semidirect
346. C24×C17C22×C4semidirect
362. C23×D17C22×C4semidirect
363. C23×D17C22×C4semidirect
364. C23×D17C22×C4semidirect
403. C22×#595C2×D4semidirect
424. C2×D4×C17C22×C4semidirect
425. C2×D4×C17C22×C4semidirect
426. C2×D4×C17C22×C4semidirect
427. C2×D4×C17C22×C4semidirect
428. C2×D4×C17C22×C4semidirect
430. C22×C4×C17C22×C4semidirect
431. C22×C4×C17C22×C4semidirect
444. C2×C22⋊D17C22×C4semidirect
445. C2×C22⋊D17C22×C4semidirect
446. C2×C22⋊D17C22×C4semidirect
447. C2×C22⋊D17C22×C4semidirect
448. C2×C22⋊D17C22×C4semidirect
449. C2×C22⋊D17C22×C4semidirect
450. C2×C22⋊D17C22×C4semidirect
451. C2×C22⋊D17C22×C4semidirect
452. C2×C22⋊D17C22×C4semidirect
454. C22×Dic17C22×C4semidirect
455. C22×Dic17C22×C4semidirect
494. C2×D68C22×C4semidirect
495. C2×D68C22×C4semidirect
496. C2×D68C22×C4semidirect
497. C2×D68C22×C4semidirect
498. C2×D68C22×C4semidirect
507. C2×C4×D17C22×C4semidirect
508. C2×C4×D17C22×C4semidirect
509. C2×C4×D17C22×C4semidirect
510. C2×C4×D17C22×C4semidirect
541. C22⋊#595C2×D4semidirect
552. C4⋊#595C2×D4semidirect
562. C4×#595C2×D4semidirect
563. C4⋊C4×C17C22×C4semidirect
564. C4⋊C4×C17C22×C4semidirect
566. C22⋊C4×C17C22×C4semidirect
567. C22⋊C4×C17C22×C4semidirect
568. C22⋊C4×C17C22×C4semidirect
569. C22⋊C4×C17C22×C4semidirect
570. C42×C17C22×C4semidirect
572. C22⋊Dic17C22×C4semidirect
573. C22⋊Dic17C22×C4semidirect
574. C22⋊Dic17C22×C4semidirect
575. C22⋊Dic17C22×C4semidirect
578. #63227C22×C4semidirect
579. #63227C22×C4semidirect
580. #63227C22×C4semidirect
581. #63227C22×C4semidirect
582. #63227C22×C4semidirect
583. #63227C22×C4semidirect
584. #63227C22×C4semidirect
585. #63227C22×C4semidirect
586. C4⋊Dic17C22×C4semidirect
587. C4⋊Dic17C22×C4semidirect
588. #63225C22×C4semidirect
589. #63225C22×C4semidirect
590. #63225C22×C4semidirect
591. C4×Dic17C22×C4semidirect
592. C4×Dic17C22×C4semidirect
593. C4×Dic17C22×C4semidirect
724. D4×C17C4×D4semidirect
750. C22⋊D17C4×D4semidirect
769. D68C4×D4semidirect
827. C22×C17#518semidirect
869. C2×D17#518semidirect
915. D42#595semidirect
1065. C22×D4C2×#595semidirect
1066. C22×D4C2×#595semidirect
1067. C22×D4C2×#595semidirect
1090. #127C2×#595semidirect
1108. #121C2×#595semidirect
1109. #121C2×#595semidirect
1110. #121C2×#595semidirect
1125. #120C2×#595semidirect
1126. #120C2×#595semidirect
1154. C4×D4C2×#595semidirect
1155. C4×D4C2×#595semidirect
1238. C17#34290semidirect
1263. C24C22×#595semidirect
1336. C2×D4C22×#595semidirect
1337. C2×D4C22×#595semidirect
1338. C2×D4C22×#595semidirect
1339. C2×D4C22×#595semidirect
1340. C2×D4C22×#595semidirect
1409. C22×C4C22×#595semidirect
1410. C22×C4C22×#595semidirect
1427. C4⋊C4C22×#595semidirect
1428. C4⋊C4C22×#595semidirect
1470. C22⋊C4C22×#595semidirect
1471. C22⋊C4C22×#595semidirect
1472. C22⋊C4C22×#595semidirect
1473. C22⋊C4C22×#595semidirect
1487. C42C22×#595semidirect
1597. D4D4×#595semidirect
1744. C22#11763876semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#117638762
C22×D4×#5952
#145453142
#145453122
#145453112
#145453092
#145453062
#145453002
#145452972
D4×C22⋊#5952
#145452762
#145452732
#145452722
#145452692
#121×#5952
#120×#5952
#145452382
C2×#117637572
#145452232
D42×D172
#3429017