Finite Group Databasebeta

← #31021675

Subgroups — #31021675

Order 17152.

2224 conjugacy classes of subgroups.

The subgroup lattice has 1512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22563375C211yesmaximal, characteristic, complemented
2#22563366C211yesmaximal, characteristic, complemented
3#22563357C211yesmaximal, characteristic, complemented
4#22563309C211yesmaximal, characteristic, complemented
5#22563294C211yesmaximal, characteristic, complemented
6#22563284C211yesmaximal, characteristic, complemented
7#22563284C211yesmaximal, characteristic, complemented
8#22563261C211yesmaximal, characteristic, complemented
9#22563261C211yesmaximal, characteristic, complemented
10#22563251C211yesmaximal, characteristic, complemented
11#22563240C211yesmaximal, characteristic, complemented
12#22563240C211yesmaximal, characteristic, complemented
13#22563205C211yesmaximal, characteristic, complemented
14#22563205C211yesmaximal, characteristic, complemented
15#22563205C211yesmaximal, characteristic, complemented
16#22563024C211yesmaximal, characteristic, complemented
17#22563024C211yesmaximal, characteristic, complemented
18#22563015C211yesmaximal, characteristic, complemented
19#22563003C211yesmaximal, characteristic, complemented
20#22563003C211yesmaximal, characteristic, complemented
21#22563003C211yesmaximal, characteristic, complemented
22#22562944C211yesmaximal, characteristic, complemented
23#22562944C211yesmaximal, characteristic, complemented
24#22562914C211yesmaximal, characteristic, complemented
25#22562904C211yesmaximal, characteristic, complemented
26#22562904C211yesmaximal, characteristic, complemented
27#22562893C211yesmaximal, characteristic, complemented
28C22⋊Q8×Dic67C211yesmaximal, characteristic, complemented
29#123×Dic67C211yesmaximal, characteristic, complemented
30#121×Dic67C211yesmaximal, characteristic, complemented
31C2×#562×C67C211yesmaximal, characteristic
32C2×Q8×Dic67C2211yescharacteristic
33C2×Q8×Dic67C2211yescharacteristic
34C2×D4×Dic67C2211yescharacteristic
35C2×D4×Dic67C2211yescharacteristic
36C2×D4×Dic67C2211yescharacteristic
37C2×D4×Dic67C2211yescharacteristic
38C2×D4×Dic67C2211yescharacteristic
39C2×D4×Dic67C2211yescharacteristic
40C2×#14524002C2211yescharacteristic
41C2×#14524002C2211yescharacteristic
42C2×#14524002C2211yescharacteristic
43C22×C4×Dic67C2211yescharacteristic
44#16863303C2211yescharacteristic
45#16863303C2211yescharacteristic
46#16863303C2211yescharacteristic
47#16863303C2211yescharacteristic
48#16863303C2211yescharacteristic
49#16863303C2211yescharacteristic
50#16863299C2211yescharacteristic
51#16863299C2211yescharacteristic
52#16863299C2211yescharacteristic
53#16863299C2211yescharacteristic
54#16863299C2211yescharacteristic
55#16863299C2211yescharacteristic
56#16863295C2211yescharacteristic
57#16863295C2211yescharacteristic
58#16863295C2211yescharacteristic
59#16863295C2211yescharacteristic
60#16863295C2211yescharacteristic
61#16863295C2211yescharacteristic
62#16863295C2211yescharacteristic
63#16863295C2211yescharacteristic
64#16863295C2211yescharacteristic
65#16863295C2211yescharacteristic
66#16863289C2211yescharacteristic
67#16863289C2211yescharacteristic
68#16863289C2211yescharacteristic
69#16863289C2211yescharacteristic
70#16863289C2211yescharacteristic
71#16863289C2211yescharacteristic
72#16863289C2211yescharacteristic
73#16863289C2211yescharacteristic
74#16863289C2211yescharacteristic
75#16863289C2211yescharacteristic
76#16863289C2211yescharacteristic
77#16863289C2211yescharacteristic
78#16863289C2211yescharacteristic
79#16863289C2211yescharacteristic
80#16863289C2211yescharacteristic
81#16863289C2211yescharacteristic
82#16863289C2211yescharacteristic
83#16863289C2211yescharacteristic
84#16863289C2211yescharacteristic
85#16863289C2211yescharacteristic
86#16863289C2211yescharacteristic
87#16863289C2211yescharacteristic
88#16863289C2211yescharacteristic
89#16863289C2211yescharacteristic
90#16863282C2211yescharacteristic
91#16863282C2211yescharacteristic
92#16863282C2211yescharacteristic
93#16863282C2211yescharacteristic
94#16863282C2211yescharacteristic
95#16863282C2211yescharacteristic
96#16863282C2211yescharacteristic
97#16863282C2211yescharacteristic
98#16863282C2211yescharacteristic
99#16863282C2211yescharacteristic
100#16863282C2211yescharacteristic
101#16863282C2211yescharacteristic
102#16863282C2211yescharacteristic
103#16863282C2211yescharacteristic
104#16863282C2211yescharacteristic
105#16863282C2211yescharacteristic
106#16863282C2211yescharacteristic
107#16863282C2211yescharacteristic
108#16863282C2211yescharacteristic
109#16863282C2211yescharacteristic
110#16863276C2211yescharacteristic
111#16863276C2211yescharacteristic
112#16863276C2211yescharacteristic
113#16863276C2211yescharacteristic
114#16863276C2211yescharacteristic
115#16863276C2211yescharacteristic
116#16863276C2211yescharacteristic
117#16863276C2211yescharacteristic
118#16863276C2211yescharacteristic
119#16863276C2211yescharacteristic
120#16863276C2211yescharacteristic
121#16863276C2211yescharacteristic
122#16863271C2211yescharacteristic
123#16863271C2211yescharacteristic
124#16863271C2211yescharacteristic
125#16863271C2211yescharacteristic
126#16863271C2211yescharacteristic
127#16863271C2211yescharacteristic
128#16863271C2211yescharacteristic
129#16863271C2211yescharacteristic
130#16863271C2211yescharacteristic
131#16863271C2211yescharacteristic
132#16863271C2211yescharacteristic
133#16863271C2211yescharacteristic
134#16863264C2211yescharacteristic
135#16863259C2211yescharacteristic
136#16863256C2211yescharacteristic
137#16863256C2211yescharacteristic
138#16863256C2211yescharacteristic
139#16863256C2211yescharacteristic
140#16863256C2211yescharacteristic
141C4⋊C4×Dic67C2211yescharacteristic
142C4⋊C4×Dic67C2211yescharacteristic
143C4⋊C4×Dic67C2211yescharacteristic
144C4⋊C4×Dic67C2211yescharacteristic
145C4⋊C4×Dic67C2211yescharacteristic
146C4⋊C4×Dic67C2211yescharacteristic
147C4⋊C4×Dic67C2211yescharacteristic
148C4⋊C4×Dic67C2211yescharacteristic
149C4⋊C4×Dic67C2211yescharacteristic
150C4⋊C4×Dic67C2211yescharacteristic
151C4×C4⋊Dic67C2211yescharacteristic
152C4×C4⋊Dic67C2211yescharacteristic
153C4×C4⋊Dic67C2211yescharacteristic
154C22⋊C4×Dic67C2211yescharacteristic
155C22⋊C4×Dic67C2211yescharacteristic
156C22⋊C4×Dic67C2211yescharacteristic
157C22⋊C4×Dic67C2211yescharacteristic
158C22⋊C4×Dic67C2211yescharacteristic
159C22⋊C4×Dic67C2211yescharacteristic
160C22⋊C4×Dic67C2211yescharacteristic
161C22⋊C4×Dic67C2211yescharacteristic
162C22⋊C4×Dic67C2211yescharacteristic
163C22⋊C4×Dic67C2211yescharacteristic
164C22⋊C4×Dic67C2211yescharacteristic
165C22⋊C4×Dic67C2211yescharacteristic
166C4×C22⋊Dic67C2211yescharacteristic
167C4×C22⋊Dic67C2211yescharacteristic
168C4×C22⋊Dic67C2211yescharacteristic
169C2×C67⋊#95C2211yescharacteristic
170C2×C67⋊#95C2211yescharacteristic
171C2×C67⋊#95C2211yescharacteristic
172#562×C67C4116yescomplemented
173C2×#125×C67C2211yescharacteristic
174C2×#124×C67C2211yescharacteristic
175C2×#124×C67C2211yescharacteristic
176C2×#123×C67C2211yescharacteristic
177C2×#123×C67C2211yescharacteristic
178C2×#123×C67C2211yescharacteristic
179C2×#123×C67C2211yescharacteristic
180C2×C22⋊Q8×C67C2211yescharacteristic
181C2×C22⋊Q8×C67C2211yescharacteristic
182C2×C22⋊Q8×C67C2211yescharacteristic
183C2×C22⋊Q8×C67C2211yescharacteristic
184C2×#121×C67C2211yescharacteristic
185C2×#121×C67C2211yescharacteristic
186C2×#121×C67C2211yescharacteristic
187C2×#121×C67C2211yescharacteristic
188C23×Dic67C2311yescharacteristic
189C23×Dic67C2311yescharacteristic
190C23×Dic67C2311yescharacteristic
191C23×Dic67C2311yescharacteristic
192C23×Dic67C2311yescharacteristic
193C23×Dic67C2311yescharacteristic
194C23×Dic67C2311yescharacteristic
195C23×Dic67C2311yescharacteristic
196Q8×Dic67—42no—
197Q8×Dic67—42no—
198D4×Dic67—42no—
199D4×Dic67—42no—
200D4×Dic67—42no—
201D4×Dic67—42no—
202D4×Dic67—42no—
203D4×Dic67—42no—
204#14524002—42no—
205#14524002—42no—
206#14524002—42no—
207C2×C4⋊Dic67C2311yescharacteristic
208C2×C4⋊Dic67C2311yescharacteristic
209C2×C4⋊Dic67C2311yescharacteristic
210C2×C4⋊Dic67C2311yescharacteristic
211C2×C4⋊Dic67C2311yescharacteristic
212C2×C4⋊Dic67C2311yescharacteristic
213C2×C4⋊Dic67C2311yescharacteristic
214C2×C4⋊Dic67C2311yescharacteristic
215C2×C4⋊Dic67C2311yescharacteristic
216C2×C4⋊Dic67C2311yescharacteristic
217C2×C4⋊Dic67C2311yescharacteristic
218C2×C4⋊Dic67C2311yescharacteristic
219C2×C4⋊Dic67C2311yescharacteristic
220C2×C4⋊Dic67C2311yescharacteristic
221C2×C4⋊Dic67C2311yescharacteristic
222C2×C4⋊Dic67C2311yescharacteristic
223C2×C4⋊Dic67C2311yescharacteristic
224C2×C4⋊Dic67C2311yescharacteristic
225C2×C4⋊Dic67C2311yescharacteristic
226C2×C4⋊Dic67C2311yescharacteristic
227C2×C4⋊Dic67C2311yescharacteristic
228C2×C4⋊Dic67C2311yescharacteristic
229C2×C22⋊Dic67C2311yescharacteristic
230C2×C22⋊Dic67C2311yescharacteristic
231C2×C22⋊Dic67C2311yescharacteristic
232C2×C22⋊Dic67C2311yescharacteristic
233C2×C22⋊Dic67C2311yescharacteristic
234C2×C22⋊Dic67C2311yescharacteristic
235C2×C22⋊Dic67C2311yescharacteristic
236C2×C22⋊Dic67C2311yescharacteristic
237C2×C22⋊Dic67C2311yescharacteristic
238C2×C22⋊Dic67C2311yescharacteristic
239C2×C22⋊Dic67C2311yescharacteristic
240C2×C22⋊Dic67C2311yescharacteristic
241C2×C22⋊Dic67C2311yescharacteristic
242C2×C22⋊Dic67C2311yescharacteristic
243C2×C22⋊Dic67C2311yescharacteristic
244C2×C22⋊Dic67C2311yescharacteristic
245C2×C22⋊Dic67C2311yescharacteristic
246C2×C22⋊Dic67C2311yescharacteristic
247C2×C22⋊Dic67C2311yescharacteristic
248C2×C22⋊Dic67C2311yescharacteristic
249C2×C22⋊Dic67C2311yescharacteristic
250C2×C22⋊Dic67C2311yescharacteristic
251C2×C22⋊Dic67C2311yescharacteristic
252C2×C22⋊Dic67C2311yescharacteristic
253C2×C4×Dic67—42no—
254C2×C4×Dic67C2311yescharacteristic
255C2×C4×Dic67C2311yescharacteristic
256C2×C4×Dic67C2311yescharacteristic
257C2×C4×Dic67C2311yescharacteristic
258C2×C4×Dic67C2311yescharacteristic
259C2×C4×Dic67C2311yescharacteristic
260C2×C4×Dic67C2311yescharacteristic
261C2×C4×Dic67C2311yescharacteristic
262C2×C4×Dic67C2311yescharacteristic
263C2×C4×Dic67C2311yescharacteristic
264C2×C4×Dic67C2311yescharacteristic
265C2×C4×Dic67C2311yescharacteristic
266C2×C4×Dic67C2311yescharacteristic
267C2×C4×Dic67C2311yescharacteristic
268C2×C4×Dic67C2311yescharacteristic
269C2×C4×Dic67C2311yescharacteristic
270C2×C4×Dic67C2311yescharacteristic
271C2×C4×Dic67C2311yescharacteristic
272C2×C4×Dic67C2311yescharacteristic
273C2×C4×Dic67C2311yescharacteristic
274C2×C4×Dic67C2311yescharacteristic
275C2×C4×Dic67C2311yescharacteristic
276C67⋊#95C2311yescharacteristic
277C67⋊#95C2311yescharacteristic
278C67⋊#95C2311yescharacteristic
279C67⋊#95C2311yescharacteristic
280C67⋊#95C2311yescharacteristic
281C67⋊#95C2311yescharacteristic
282C67⋊#95C2311yescharacteristic
283C67⋊#95C2311yescharacteristic
284C67⋊#95C2311yescharacteristic
285C67⋊#95C2311yescharacteristic
286C67⋊#95C2311yescharacteristic
287C67⋊#95C2311yescharacteristic
288C67⋊#95C2311yescharacteristic
289C67⋊#95C2311yescharacteristic
290C67⋊#95C2311yescharacteristic
291C67⋊#95C2311yescharacteristic
292C67⋊#95C2311yescharacteristic
293C67⋊#95C2311yescharacteristic
294C67⋊#95C2311yescharacteristic
295C67⋊#95C2311yescharacteristic
296C67⋊#95C2311yescharacteristic
297C67⋊#95C2311yescharacteristic
298C67⋊#95C2311yescharacteristic
299C67⋊#95C2311yescharacteristic
300C67⋊#95C2311yescharacteristic
301C67⋊#95C2311yescharacteristic
302C67⋊#95C2311yescharacteristic
303C67⋊#95C2311yescharacteristic
304C67⋊#95C2311yescharacteristic
305C67⋊#95C2311yescharacteristic
306C67⋊#95C2311yescharacteristic
307C67⋊#95C2311yescharacteristic
308C67⋊#95C2311yescharacteristic
309C67⋊#95C2311yescharacteristic
310C67⋊#95C2311yescharacteristic
311C67⋊#95C2311yescharacteristic
312C67⋊#95C2311yescharacteristic
313C67⋊#95C2311yescharacteristic
314C67⋊#95C2311yescharacteristic
315C67⋊#95C2311yescharacteristic
316C67⋊#95C2311yescharacteristic
317C67⋊#95C2311yescharacteristic
318C67⋊#95C2311yescharacteristic
319C67⋊#95C2311yescharacteristic
320C22×Q8×C67C2311yescharacteristic
321C22×Q8×C67C2311yescharacteristic
322C22×D4×C67C2311yescharacteristic
323C22×D4×C67C2311yescharacteristic
324C22×D4×C67C2311yescharacteristic
325C22×D4×C67C2311yescharacteristic
326C22×D4×C67C2311yescharacteristic
327C22×D4×C67C2311yescharacteristic
328C23×C4×C67C2311yescharacteristic
329C23×C4×C67C2311yescharacteristic
330C23×C4×C67C2311yescharacteristic
331C23×C4×C67C2311yescharacteristic
332#125×C67C2×C418yescomplemented
333#124×C67C2×C418yescomplemented
334#124×C67C2×C418yescomplemented
335#123×C67C2×C418yescomplemented
336#123×C67C2×C418yescomplemented
337#123×C67C2×C418yescomplemented
338#123×C67C2×C418yescomplemented
339C22⋊Q8×C67C2×C418yescomplemented
340C22⋊Q8×C67C2×C418yescomplemented
341C22⋊Q8×C67C2×C418yescomplemented
342C22⋊Q8×C67C2×C418yescomplemented
343#121×C67C2×C418yescomplemented
344#121×C67C2×C418yescomplemented
345#121×C67C2×C418yescomplemented
346#121×C67C2×C418yescomplemented
347C2×C4⋊C4×C67C2311yescharacteristic
348C2×C4⋊C4×C67C2311yescharacteristic
349C2×C4⋊C4×C67C2311yescharacteristic
350C2×C4⋊C4×C67C2311yescharacteristic
351C2×C4⋊C4×C67C2311yescharacteristic
352C2×C4⋊C4×C67C2311yescharacteristic
353C2×C4⋊C4×C67C2311yescharacteristic
354C2×C4⋊C4×C67C2311yescharacteristic
355C2×C4⋊C4×C67C2311yescharacteristic
356C2×C4⋊C4×C67C2311yescharacteristic
357C2×C22⋊C4×C67C2311yescharacteristic
358C2×C22⋊C4×C67C2311yescharacteristic
359C2×C22⋊C4×C67C2311yescharacteristic
360C2×C22⋊C4×C67C2311yescharacteristic
361C2×C22⋊C4×C67C2311yescharacteristic
362C2×C22⋊C4×C67C2311yescharacteristic
363C2×C22⋊C4×C67C2311yescharacteristic
364C2×C22⋊C4×C67C2311yescharacteristic
365C2×C22⋊C4×C67C2311yescharacteristic
366C2×C22⋊C4×C67C2311yescharacteristic
367C2×C22⋊C4×C67C2311yescharacteristic
368C2×C22⋊C4×C67C2311yescharacteristic
369C2×C42×C67C2311yescharacteristic
370C22×Dic67—22no—
371C22×Dic67—22no—
372C22×Dic67—22no—
373C22×Dic67—22no—
374C22×Dic67—22no—
375C22×Dic67—22no—
376C22×Dic67—41no—
377C22×Dic67—41no—
378C22×Dic67—41no—
379C22×Dic67—41no—
380C22×Dic67—41no—
381C22×Dic67—41no—
382C22×Dic67—41no—
383C22×Dic67—41no—
384C22×Dic67—41no—
385C22×Dic67—41no—
386C22×Dic67—41no—
387C22×Dic67—41no—
388C22×Dic67—41no—
389C22×Dic67—41no—
390C22×Dic67—41no—
391C22×Dic67—41no—
392C22×Dic67—41no—
393C22×Dic67—41no—
394C22×Dic67C2411yescharacteristic
395C22×Dic67C2411yescharacteristic
396C22×Dic67C2411yescharacteristic
397C22×Dic67C2411yescharacteristic
398C22×Dic67C2411yescharacteristic
399C22×Dic67C2411yescharacteristic
400C22×Dic67C2411yescharacteristic
401C22×Dic67C2411yescharacteristic
402C22×Dic67C2411yescharacteristic
403C22×Dic67C2411yescharacteristic
404C22×Dic67C2411yescharacteristic
405C22×Dic67C2411yescharacteristic
406C22×Dic67C2411yescharacteristic
407C22×Dic67C2411yescharacteristic
408C22×Dic67C2411yescharacteristic
409C22×Dic67C2411yescharacteristic
410C4⋊Dic67—22no—
411C4⋊Dic67—22no—
412C4⋊Dic67—22no—
413C4⋊Dic67—22no—
414C4⋊Dic67—22no—
415C4⋊Dic67—22no—
416C4⋊Dic67—41no—
417C4⋊Dic67—41no—
418C4⋊Dic67—41no—
419C4⋊Dic67—41no—
420C4⋊Dic67—41no—
421C4⋊Dic67—41no—
422C4⋊Dic67—41no—
423C4⋊Dic67—41no—
424C4⋊Dic67—41no—
425C4⋊Dic67—41no—
426C4⋊Dic67—41no—
427C4⋊Dic67—41no—
428C4⋊Dic67—41no—
429C4⋊Dic67—41no—
430C4⋊Dic67—41no—
431C4⋊Dic67—41no—
432C22⋊Dic67—22no—
433C22⋊Dic67—22no—
434C22⋊Dic67—22no—
435C22⋊Dic67—22no—
436C22⋊Dic67—22no—
437C22⋊Dic67—22no—
438C22⋊Dic67—41no—
439C22⋊Dic67—41no—
440C22⋊Dic67—41no—
441C22⋊Dic67—41no—
442C22⋊Dic67—41no—
443C22⋊Dic67—41no—
444C22⋊Dic67—41no—
445C22⋊Dic67—41no—
446C22⋊Dic67—41no—
447C22⋊Dic67—41no—
448C22⋊Dic67—41no—
449C22⋊Dic67—41no—
450C22⋊Dic67—41no—
451C22⋊Dic67—41no—
452C22⋊Dic67—41no—
453C22⋊Dic67—41no—
454C22⋊Dic67—41no—
455C22⋊Dic67—41no—
456C4×Dic67—22no—
457C4×Dic67—22no—
458C4×Dic67—22no—
459C4×Dic67—22no—
460C4×Dic67—22no—
461C4×Dic67—41no—
462C4×Dic67—41no—
463C4×Dic67—41no—
464C4×Dic67—41no—
465C4×Dic67—41no—
466C4×Dic67—41no—
467C4×Dic67—41no—
468C4×Dic67—41no—
469C4×Dic67—41no—
470C4×Dic67—41no—
471C4×Dic67—41no—
472C4×Dic67—41no—
473C4×Dic67—41no—
474C4×Dic67—41no—
475C4×Dic67—41no—
476C4×Dic67—41no—
477C4×Dic67—41no—
478C24×C67C2411yescharacteristic
479C24×C67C2411yescharacteristic
480C24×C67C2411yescharacteristic
481C24×C67C2411yescharacteristic
482C2×Q8×C67—41no—
483C2×Q8×C67—41no—
484C2×Q8×C67—41no—
485C2×Q8×C67—41no—
486C2×Q8×C67C22×C414yes—
487C2×Q8×C67C22×C414yes—
488C2×D4×C67—41no—
489C2×D4×C67—41no—
490C2×D4×C67—41no—
491C2×D4×C67—41no—
492C2×D4×C67—41no—
493C2×D4×C67—41no—
494C2×D4×C67—41no—
495C2×D4×C67—41no—
496C2×D4×C67—41no—
497C2×D4×C67—41no—
498C2×D4×C67—41no—
499C2×D4×C67—41no—
500C2×D4×C67C22×C414yes—
501C2×D4×C67C22×C414yes—
502C2×D4×C67C22×C414yes—
503C2×D4×C67C22×C414yes—
504C2×D4×C67C22×C414yes—
505C2×D4×C67C22×C414yes—
506C22×C4×C67—41no—
507C22×C4×C67—41no—
508C22×C4×C67—41no—
509C22×C4×C67—41no—
510C22×C4×C67—41no—
511C22×C4×C67—41no—
512C22×C4×C67—41no—
513C22×C4×C67—41no—
514C22×C4×C67C22×C414yes—
515C22×C4×C67C22×C414yes—
516C22×C4×C67C22×C414yes—
517C22×C4×C67C22×C414yes—
518C22×C4×C67C2411yescharacteristic
519C22×C4×C67C2411yescharacteristic
520C22×C4×C67C2411yescharacteristic
521C22×C4×C67C2411yescharacteristic
522C22×C4×C67C2411yescharacteristic
523C22×C4×C67C2411yescharacteristic
524C22×C4×C67C2411yescharacteristic
525C22×C4×C67C2411yescharacteristic
526C22×C4×C67C2411yescharacteristic
527C22×C4×C67C2411yescharacteristic
528C22×C4×C67C2411yescharacteristic
529C4⋊C4×C67C22×C414yes—
530C4⋊C4×C67C22×C414yes—
531C4⋊C4×C67C22×C414yes—
532C4⋊C4×C67C22×C414yes—
533C4⋊C4×C67C22×C414yes—
534C4⋊C4×C67C22×C414yes—
535C4⋊C4×C67C22×C414yes—
536C4⋊C4×C67C22×C414yes—
537C4⋊C4×C67C22×C414yes—
538C4⋊C4×C67C22×C414yes—
539C22⋊C4×C67C22×C414yes—
540C22⋊C4×C67C22×C414yes—
541C22⋊C4×C67C22×C414yes—
542C22⋊C4×C67C22×C414yes—
543C22⋊C4×C67C22×C414yes—
544C22⋊C4×C67C22×C414yes—
545C22⋊C4×C67C22×C414yes—
546C22⋊C4×C67C22×C414yes—
547C22⋊C4×C67C22×C414yes—
548C22⋊C4×C67C22×C414yes—
549C22⋊C4×C67C22×C414yes—
550C22⋊C4×C67C22×C414yes—
551C42×C67C22×C414yes—
552C23×C67—21no—
553C23×C67—21no—
554C23×C67—21no—
555C23×C67—21no—
556C23×C67—21no—
557C23×C67—21no—
558C23×C67—21no—
559C23×C67—21no—
560C23×C67—21no—
561C23×C67—21no—
562C23×C67—21no—
563C23×C67—21no—
564C23×C67—21no—
565C23×C67—21no—
566C23×C67—21no—
567C23×C67—21no—
568C23×C67—21no—
569C23×C67—21no—
570C23×C67—21no—
571C23×C67—21no—
572C23×C67—21no—
573C23×C67—21no—
574C23×C67—21no—
575C23×C67—21no—
576C23×C67C23×C412yes—
577C23×C67C23×C412yes—
578C23×C67C23×C412yes—
579C23×C67C23×C412yes—
580C23×C67C2511yescharacteristic
581Q8×C67—44no—
582Q8×C67—44no—
583D4×C67—44no—
584D4×C67—44no—
585D4×C67—44no—
586D4×C67—44no—
587D4×C67—44no—
588D4×C67—44no—
589C2×C4×C67—21no—
590C2×C4×C67—21no—
591C2×C4×C67—21no—
592C2×C4×C67—21no—
593C2×C4×C67—21no—
594C2×C4×C67—21no—
595C2×C4×C67—21no—
596C2×C4×C67—21no—
597C2×C4×C67—21no—
598C2×C4×C67—21no—
599C2×C4×C67—21no—
600C2×C4×C67—21no—
601C2×C4×C67—21no—
602C2×C4×C67—21no—
603C2×C4×C67—21no—
604C2×C4×C67—21no—
605C2×C4×C67—21no—
606C2×C4×C67—21no—
607C2×C4×C67—21no—
608C2×C4×C67—21no—
609C2×C4×C67—21no—
610C2×C4×C67—21no—
611C2×C4×C67—44no—
612C2×C4×C67—44no—
613C2×C4×C67—44no—
614C2×C4×C67—44no—
615C2×C4×C67C23×C412yes—
616C2×C4×C67C23×C412yes—
617C2×C4×C67C23×C412yes—
618C2×C4×C67C23×C412yes—
619C2×C4×C67C23×C412yes—
620C2×C4×C67C23×C412yes—
621C2×C4×C67C23×C412yes—
622C2×C4×C67C23×C412yes—
623C2×C4×C67C23×C412yes—
624C2×C4×C67C23×C412yes—
625C2×C4×C67C23×C412yes—
626C2×Dic67—21no—
627C2×Dic67—21no—
628C2×Dic67—21no—
629C2×Dic67—21no—
630C2×Dic67—21no—
631C2×Dic67—21no—
632C2×Dic67—21no—
633C2×Dic67—21no—
634C2×Dic67—21no—
635C2×Dic67—21no—
636C2×Dic67—21no—
637C2×Dic67—21no—
638C2×Dic67—21no—
639C2×Dic67—21no—
640C2×Dic67—21no—
641C2×Dic67—21no—
642C2×Dic67—21no—
643C2×Dic67—21no—
644C2×Dic67—21no—
645C2×Dic67—21no—
646C2×Dic67—21no—
647C2×Dic67—21no—
648C2×Dic67—21no—
649C2×Dic67—21no—
650C2×Dic67—21no—
651C2×Dic67—21no—
652C2×Dic67—21no—
653C2×Dic67—21no—
654C2×Dic67—21no—
655C2×Dic67—21no—
656C2×Dic67—21no—
657C2×Dic67—21no—
658C2×Dic67—21no—
659C2×Dic67—21no—
660C2×Dic67—21no—
661C2×Dic67—21no—
662C2×Dic67—21no—
663C2×Dic67—21no—
664C2×Dic67—21no—
665C2×Dic67—21no—
666C2×Dic67—21no—
667C2×Dic67—21no—
668C2×Dic67—21no—
669C2×Dic67—21no—
670C2×Dic67—21no—
671C2×Dic67—44no—
672C2×Dic67—44no—
673C2×Dic67—82no—
674C2×Dic67—82no—
675C2×Dic67—82no—
676C2×Dic67—82no—
677C2×Dic67—82no—
678C2×Dic67—82no—
679C2×Dic67H(5,𝔽2)12yes—
680C2×Dic67H(5,𝔽2)12yes—
681C2×Dic672−1+412yes—
682C22×C67—22no—
683C22×C67—22no—
684C22×C67—22no—
685C22×C67—22no—
686C22×C67—22no—
687C22×C67—22no—
688C22×C67—22no—
689C22×C67—22no—
690C22×C67—22no—
691C22×C67—22no—
692C22×C67—22no—
693C22×C67—22no—
694C22×C67—41no—
695C22×C67—41no—
696C22×C67—41no—
697C22×C67—41no—
698C22×C67—41no—
699C22×C67—41no—
700C22×C67—41no—
701C22×C67—41no—
702C22×C67—41no—
703C22×C67—41no—
704C22×C67—41no—
705C22×C67—41no—
706C22×C67—41no—
707C22×C67—41no—
708C22×C67—41no—
709C22×C67—41no—
710C22×C67C24×C411yescharacteristic
711C22×C67C2×H(5,𝔽2)11yescharacteristic
712C22×C67C2×H(5,𝔽2)11yescharacteristic
713C22×C67C2×2−1+411yescharacteristic
714C22×C67#58511yescharacteristic
715C22×C67#58511yescharacteristic
716C22×C67#58511yescharacteristic
717C4×C67—22no—
718C4×C67—22no—
719C4×C67—22no—
720C4×C67—22no—
721C4×C67—22no—
722C4×C67—22no—
723C4×C67—22no—
724C4×C67—22no—
725C4×C67—22no—
726C4×C67—22no—
727C4×C67—22no—
728Dic67—22no—
729Dic67—22no—
730Dic67—22no—
731Dic67—41no—
732Dic67—41no—
733Dic67—41no—
734Dic67—41no—
735Dic67—41no—
736Dic67—41no—
737Dic67—41no—
738Dic67—41no—
739Dic67—41no—
740Dic67—41no—
741Dic67—41no—
742Dic67—41no—
743Dic67—41no—
744#34513—671nomaximal, Sylow
745C2×C67—42no—
746C2×C67—42no—
747C2×C67—42no—
748C2×C67—42no—
749C2×C67C4×H(5,𝔽2)11yescharacteristic
750C2×C67C4×H(5,𝔽2)11yescharacteristic
751C2×C67C4×2−1+411yescharacteristic
752C2×C67#353311yescharacteristic
753C2×C67#353611yescharacteristic
754C2×C67#356211yescharacteristic
755C2×C67#356511yescharacteristic
756C2×#562D6711yescharacteristic
757#2378—671no—
758#2377—671no—
759#2376—671no—
760#2370—671no—
761#2368—671no—
762#2367—671no—
763#2367—671no—
764#2364—671no—
765#2364—671no—
766#2363—671no—
767#2362—671no—
768#2362—671no—
769#2359—671no—
770#2359—671no—
771#2359—671no—
772#2337—671no—
773#2337—671no—
774#2336—671no—
775#2335—671no—
776#2335—671no—
777#2335—671no—
778#2329—671no—
779#2329—671no—
780#2325—671no—
781#2324—671no—
782#2324—671no—
783#2323—671no—
784C4×C22⋊Q8—671no—
785C4×#123—671no—
786C4×#121—671no—
787C67#3451311yescharacteristic, complemented, Sylow
788#562Dic67116yescomplemented
789C2×#125C2×D6711yescharacteristic
790C2×#124C2×D6711yescharacteristic
791C2×#124C2×D6711yescharacteristic
792C2×#123C2×D6711yescharacteristic
793C2×#123C2×D6711yescharacteristic
794C2×#123C2×D6711yescharacteristic
795C2×#123C2×D6711yescharacteristic
796C2×C22⋊Q8C2×D6711yescharacteristic
797C2×C22⋊Q8C2×D6711yescharacteristic
798C2×C22⋊Q8C2×D6711yescharacteristic
799C2×C22⋊Q8C2×D6711yescharacteristic
800C2×#121C2×D6711yescharacteristic
801C2×#121C2×D6711yescharacteristic
802C2×#121C2×D6711yescharacteristic
803C2×#121C2×D6711yescharacteristic
804C2×C4×Q8—671no—
805C2×C4×Q8—671no—
806C2×C4×D4—671no—
807C2×C4×D4—671no—
808C2×C4×D4—671no—
809C2×C4×D4—671no—
810C2×C4×D4—671no—
811C2×C4×D4—671no—
812C2×#117—671no—
813C2×#117—671no—
814C2×#117—671no—
815C22×C42—671no—
816#391—671no—
817#391—671no—
818#391—671no—
819#391—671no—
820#391—671no—
821#391—671no—
822#390—671no—
823#390—671no—
824#390—671no—
825#390—671no—
826#390—671no—
827#390—671no—
828#389—671no—
829#389—671no—
830#389—671no—
831#389—671no—
832#389—671no—
833#389—671no—
834#389—671no—
835#389—671no—
836#389—671no—
837#389—671no—
838#388—671no—
839#388—671no—
840#388—671no—
841#388—671no—
842#388—671no—
843#388—671no—
844#388—671no—
845#388—671no—
846#388—671no—
847#388—671no—
848#388—671no—
849#388—671no—
850#388—671no—
851#388—671no—
852#388—671no—
853#388—671no—
854#388—671no—
855#388—671no—
856#388—671no—
857#388—671no—
858#388—671no—
859#388—671no—
860#388—671no—
861#388—671no—
862#387—671no—
863#387—671no—
864#387—671no—
865#387—671no—
866#387—671no—
867#387—671no—
868#387—671no—
869#387—671no—
870#387—671no—
871#387—671no—
872#387—671no—
873#387—671no—
874#387—671no—
875#387—671no—
876#387—671no—
877#387—671no—
878#387—671no—
879#387—671no—
880#387—671no—
881#387—671no—
882#386—671no—
883#386—671no—
884#386—671no—
885#386—671no—
886#386—671no—
887#386—671no—
888#386—671no—
889#386—671no—
890#386—671no—
891#386—671no—
892#386—671no—
893#386—671no—
894#385—671no—
895#385—671no—
896#385—671no—
897#385—671no—
898#385—671no—
899#385—671no—
900#385—671no—
901#385—671no—
902#385—671no—
903#385—671no—
904#385—671no—
905#385—671no—
906#383—671no—
907#381—671no—
908#380—671no—
909#380—671no—
910#380—671no—
911#380—671no—
912#380—671no—
913C4×C4⋊C4—671no—
914C4×C4⋊C4—671no—
915C4×C4⋊C4—671no—
916C4×C4⋊C4—671no—
917C4×C4⋊C4—671no—
918C4×C4⋊C4—671no—
919C4×C4⋊C4—671no—
920C4×C4⋊C4—671no—
921C4×C4⋊C4—671no—
922C4×C4⋊C4—671no—
923C4×C4⋊C4—671no—
924C4×C4⋊C4—671no—
925C4×C4⋊C4—671no—
926C4×C22⋊C4—671no—
927C4×C22⋊C4—671no—
928C4×C22⋊C4—671no—
929C4×C22⋊C4—671no—
930C4×C22⋊C4—671no—
931C4×C22⋊C4—671no—
932C4×C22⋊C4—671no—
933C4×C22⋊C4—671no—
934C4×C22⋊C4—671no—
935C4×C22⋊C4—671no—
936C4×C22⋊C4—671no—
937C4×C22⋊C4—671no—
938C4×C22⋊C4—671no—
939C4×C22⋊C4—671no—
940C4×C22⋊C4—671no—
941C2×#95—671no—
942C2×#95—671no—
943C2×#95—671no—
944C22×Q8C22×D6711yescharacteristic
945C22×Q8C22×D6711yescharacteristic
946C22×D4C22×D6711yescharacteristic
947C22×D4C22×D6711yescharacteristic
948C22×D4C22×D6711yescharacteristic
949C22×D4C22×D6711yescharacteristic
950C22×D4C22×D6711yescharacteristic
951C22×D4C22×D6711yescharacteristic
952C23×C4—671no—
953C23×C4—671no—
954C23×C4—671no—
955C23×C4—671no—
956C23×C4—671no—
957C23×C4—671no—
958C23×C4—671no—
959C23×C4—671no—
960C23×C4C22×D6711yescharacteristic
961C23×C4C22×D6711yescharacteristic
962C23×C4C22×D6711yescharacteristic
963C23×C4C22×D6711yescharacteristic
964#125C2×Dic6718yescomplemented
965#124C2×Dic6718yescomplemented
966#124C2×Dic6718yescomplemented
967#123C2×Dic6718yescomplemented
968#123C2×Dic6718yescomplemented
969#123C2×Dic6718yescomplemented
970#123C2×Dic6718yescomplemented
971C22⋊Q8C2×Dic6718yescomplemented
972C22⋊Q8C2×Dic6718yescomplemented
973C22⋊Q8C2×Dic6718yescomplemented
974C22⋊Q8C2×Dic6718yescomplemented
975#121C2×Dic6718yescomplemented
976#121C2×Dic6718yescomplemented
977#121C2×Dic6718yescomplemented
978#121C2×Dic6718yescomplemented
979C4×Q8—2682no—
980C4×Q8—2682no—
981C4×D4—2682no—
982C4×D4—2682no—
983C4×D4—2682no—
984C4×D4—2682no—
985C4×D4—2682no—
986C4×D4—2682no—
987#117—2682no—
988#117—2682no—
989#117—2682no—
990C2×C4⋊C4—671no—
991C2×C4⋊C4—671no—
992C2×C4⋊C4—671no—
993C2×C4⋊C4—671no—
994C2×C4⋊C4—671no—
995C2×C4⋊C4—671no—
996C2×C4⋊C4—671no—
997C2×C4⋊C4—671no—
998C2×C4⋊C4—671no—
999C2×C4⋊C4—671no—
1000C2×C4⋊C4—671no—
1001C2×C4⋊C4—671no—
1002C2×C4⋊C4—671no—
1003C2×C4⋊C4—671no—
1004C2×C4⋊C4—671no—
1005C2×C4⋊C4—671no—
1006C2×C4⋊C4—671no—
1007C2×C4⋊C4—671no—
1008C2×C4⋊C4—671no—
1009C2×C4⋊C4—671no—
1010C2×C4⋊C4—671no—
1011C2×C4⋊C4—671no—
1012C2×C4⋊C4C22×D6711yescharacteristic
1013C2×C4⋊C4C22×D6711yescharacteristic
1014C2×C4⋊C4C22×D6711yescharacteristic
1015C2×C4⋊C4C22×D6711yescharacteristic
1016C2×C4⋊C4C22×D6711yescharacteristic
1017C2×C4⋊C4C22×D6711yescharacteristic
1018C2×C4⋊C4C22×D6711yescharacteristic
1019C2×C4⋊C4C22×D6711yescharacteristic
1020C2×C4⋊C4C22×D6711yescharacteristic
1021C2×C4⋊C4C22×D6711yescharacteristic
1022C2×C22⋊C4—671no—
1023C2×C22⋊C4—671no—
1024C2×C22⋊C4—671no—
1025C2×C22⋊C4—671no—
1026C2×C22⋊C4—671no—
1027C2×C22⋊C4—671no—
1028C2×C22⋊C4—671no—
1029C2×C22⋊C4—671no—
1030C2×C22⋊C4—671no—
1031C2×C22⋊C4—671no—
1032C2×C22⋊C4—671no—
1033C2×C22⋊C4—671no—
1034C2×C22⋊C4—671no—
1035C2×C22⋊C4—671no—
1036C2×C22⋊C4—671no—
1037C2×C22⋊C4—671no—
1038C2×C22⋊C4—671no—
1039C2×C22⋊C4—671no—
1040C2×C22⋊C4—671no—
1041C2×C22⋊C4—671no—
1042C2×C22⋊C4—671no—
1043C2×C22⋊C4—671no—
1044C2×C22⋊C4—671no—
1045C2×C22⋊C4—671no—
1046C2×C22⋊C4C22×D6711yescharacteristic
1047C2×C22⋊C4C22×D6711yescharacteristic
1048C2×C22⋊C4C22×D6711yescharacteristic
1049C2×C22⋊C4C22×D6711yescharacteristic
1050C2×C22⋊C4C22×D6711yescharacteristic
1051C2×C22⋊C4C22×D6711yescharacteristic
1052C2×C22⋊C4C22×D6711yescharacteristic
1053C2×C22⋊C4C22×D6711yescharacteristic
1054C2×C22⋊C4C22×D6711yescharacteristic
1055C2×C22⋊C4C22×D6711yescharacteristic
1056C2×C22⋊C4C22×D6711yescharacteristic
1057C2×C22⋊C4C22×D6711yescharacteristic
1058C2×C42—2682no—
1059C2×C42—671no—
1060C2×C42—671no—
1061C2×C42—671no—
1062C2×C42—671no—
1063C2×C42—671no—
1064C2×C42—671no—
1065C2×C42—671no—
1066C2×C42—671no—
1067C2×C42—671no—
1068C2×C42—671no—
1069C2×C42—671no—
1070C2×C42—671no—
1071C2×C42—671no—
1072C2×C42—671no—
1073C2×C42—671no—
1074C2×C42—671no—
1075C2×C42—671no—
1076C2×C42—671no—
1077C2×C42—671no—
1078C2×C42—671no—
1079C2×C42—671no—
1080C2×C42—671no—
1081C2×C42C22×D6711yescharacteristic
1082#95—671no—
1083#95—671no—
1084#95—671no—
1085#95—671no—
1086#95—671no—
1087#95—671no—
1088#95—671no—
1089#95—671no—
1090#95—671no—
1091#95—671no—
1092#95—671no—
1093#95—671no—
1094#95—671no—
1095#95—671no—
1096#95—671no—
1097#95—671no—
1098#95—671no—
1099#95—671no—
1100#95—671no—
1101#95—671no—
1102#95—671no—
1103#95—671no—
1104#95—671no—
1105#95—671no—
1106#95—671no—
1107#95—671no—
1108#95—671no—
1109#95—671no—
1110#95—671no—
1111#95—671no—
1112#95—671no—
1113#95—671no—
1114#95—671no—
1115#95—671no—
1116#95—671no—
1117#95—671no—
1118#95—671no—
1119#95—671no—
1120#95—671no—
1121#95—671no—
1122#95—671no—
1123#95—671no—
1124#95—671no—
1125#95—671no—
1126C24C23×D6711yescharacteristic
1127C24C23×D6711yescharacteristic
1128C24C23×D6711yescharacteristic
1129C24C23×D6711yescharacteristic
1130C2×Q8—41no—
1131C2×Q8—41no—
1132C2×Q8—41no—
1133C2×Q8—41no—
1134C2×Q8C22×Dic6714yes—
1135C2×Q8C22×Dic6714yes—
1136C2×D4—41no—
1137C2×D4—41no—
1138C2×D4—41no—
1139C2×D4—41no—
1140C2×D4—41no—
1141C2×D4—41no—
1142C2×D4—41no—
1143C2×D4—41no—
1144C2×D4—41no—
1145C2×D4—41no—
1146C2×D4—41no—
1147C2×D4—41no—
1148C2×D4C22×Dic6714yes—
1149C2×D4C22×Dic6714yes—
1150C2×D4C22×Dic6714yes—
1151C2×D4C22×Dic6714yes—
1152C2×D4C22×Dic6714yes—
1153C2×D4C22×Dic6714yes—
1154C22×C4—41no—
1155C22×C4—41no—
1156C22×C4—41no—
1157C22×C4—41no—
1158C22×C4—41no—
1159C22×C4—41no—
1160C22×C4—41no—
1161C22×C4—41no—
1162C22×C4—2681no—
1163C22×C4—2681no—
1164C22×C4—2681no—
1165C22×C4—2681no—
1166C22×C4—2681no—
1167C22×C4—2681no—
1168C22×C4—2681no—
1169C22×C4—2681no—
1170C22×C4—2681no—
1171C22×C4—2681no—
1172C22×C4—2681no—
1173C22×C4—2681no—
1174C22×C4—2681no—
1175C22×C4—2681no—
1176C22×C4—2681no—
1177C22×C4—2681no—
1178C22×C4—2681no—
1179C22×C4—2681no—
1180C22×C4—671no—
1181C22×C4—671no—
1182C22×C4—671no—
1183C22×C4—671no—
1184C22×C4—671no—
1185C22×C4—671no—
1186C22×C4—671no—
1187C22×C4—671no—
1188C22×C4—671no—
1189C22×C4—671no—
1190C22×C4—671no—
1191C22×C4—671no—
1192C22×C4—671no—
1193C22×C4—671no—
1194C22×C4—671no—
1195C22×C4—671no—
1196C22×C4—1342no—
1197C22×C4—1342no—
1198C22×C4—1342no—
1199C22×C4—1342no—
1200C22×C4—1342no—
1201C22×C4—1342no—
1202C22×C4C22×Dic6714yes—
1203C22×C4C22×Dic6714yes—
1204C22×C4C22×Dic6714yes—
1205C22×C4C22×Dic6714yes—
1206C22×C4C23×D6711yescharacteristic
1207C22×C4C23×D6711yescharacteristic
1208C22×C4C23×D6711yescharacteristic
1209C22×C4C23×D6711yescharacteristic
1210C22×C4C23×D6711yescharacteristic
1211C22×C4C23×D6711yescharacteristic
1212C22×C4C23×D6711yescharacteristic
1213C22×C4C23×D6711yescharacteristic
1214C22×C4C23×D6711yescharacteristic
1215C22×C4C23×D6711yescharacteristic
1216C22×C4C23×D6711yescharacteristic
1217C4⋊C4—2681no—
1218C4⋊C4—2681no—
1219C4⋊C4—2681no—
1220C4⋊C4—2681no—
1221C4⋊C4—2681no—
1222C4⋊C4—2681no—
1223C4⋊C4—2681no—
1224C4⋊C4—2681no—
1225C4⋊C4—2681no—
1226C4⋊C4—2681no—
1227C4⋊C4—2681no—
1228C4⋊C4—2681no—
1229C4⋊C4—2681no—
1230C4⋊C4—2681no—
1231C4⋊C4—2681no—
1232C4⋊C4—2681no—
1233C4⋊C4—1342no—
1234C4⋊C4—1342no—
1235C4⋊C4—1342no—
1236C4⋊C4—1342no—
1237C4⋊C4—1342no—
1238C4⋊C4—1342no—
1239C4⋊C4C22×Dic6714yes—
1240C4⋊C4C22×Dic6714yes—
1241C4⋊C4C22×Dic6714yes—
1242C4⋊C4C22×Dic6714yes—
1243C4⋊C4C22×Dic6714yes—
1244C4⋊C4C22×Dic6714yes—
1245C4⋊C4C22×Dic6714yes—
1246C4⋊C4C22×Dic6714yes—
1247C4⋊C4C22×Dic6714yes—
1248C4⋊C4C22×Dic6714yes—
1249C22⋊C4—2681no—
1250C22⋊C4—2681no—
1251C22⋊C4—2681no—
1252C22⋊C4—2681no—
1253C22⋊C4—2681no—
1254C22⋊C4—2681no—
1255C22⋊C4—2681no—
1256C22⋊C4—2681no—
1257C22⋊C4—2681no—
1258C22⋊C4—2681no—
1259C22⋊C4—2681no—
1260C22⋊C4—2681no—
1261C22⋊C4—2681no—
1262C22⋊C4—2681no—
1263C22⋊C4—2681no—
1264C22⋊C4—2681no—
1265C22⋊C4—2681no—
1266C22⋊C4—2681no—
1267C22⋊C4—1342no—
1268C22⋊C4—1342no—
1269C22⋊C4—1342no—
1270C22⋊C4—1342no—
1271C22⋊C4—1342no—
1272C22⋊C4—1342no—
1273C22⋊C4C22×Dic6714yes—
1274C22⋊C4C22×Dic6714yes—
1275C22⋊C4C22×Dic6714yes—
1276C22⋊C4C22×Dic6714yes—
1277C22⋊C4C22×Dic6714yes—
1278C22⋊C4C22×Dic6714yes—
1279C22⋊C4C22×Dic6714yes—
1280C22⋊C4C22×Dic6714yes—
1281C22⋊C4C22×Dic6714yes—
1282C22⋊C4C22×Dic6714yes—
1283C22⋊C4C22×Dic6714yes—
1284C22⋊C4C22×Dic6714yes—
1285C42—2681no—
1286C42—2681no—
1287C42—2681no—
1288C42—2681no—
1289C42—2681no—
1290C42—2681no—
1291C42—2681no—
1292C42—2681no—
1293C42—2681no—
1294C42—2681no—
1295C42—2681no—
1296C42—2681no—
1297C42—2681no—
1298C42—2681no—
1299C42—2681no—
1300C42—2681no—
1301C42—2681no—
1302C42—1342no—
1303C42—1342no—
1304C42—1342no—
1305C42—1342no—
1306C42—1342no—
1307C42C22×Dic6714yes—
1308C23—21no—
1309C23—21no—
1310C23—21no—
1311C23—21no—
1312C23—21no—
1313C23—21no—
1314C23—21no—
1315C23—21no—
1316C23—21no—
1317C23—21no—
1318C23—21no—
1319C23—21no—
1320C23—21no—
1321C23—21no—
1322C23—21no—
1323C23—21no—
1324C23—21no—
1325C23—21no—
1326C23—21no—
1327C23—21no—
1328C23—21no—
1329C23—21no—
1330C23—21no—
1331C23—21no—
1332C23C23×Dic6712yes—
1333C23C23×Dic6712yes—
1334C23C23×Dic6712yes—
1335C23C23×Dic6712yes—
1336C23C24×D6711yescharacteristic
1337Q8—44no—
1338Q8—44no—
1339D4—44no—
1340D4—44no—
1341D4—44no—
1342D4—44no—
1343D4—44no—
1344D4—44no—
1345C2×C4—21no—
1346C2×C4—21no—
1347C2×C4—21no—
1348C2×C4—21no—
1349C2×C4—21no—
1350C2×C4—21no—
1351C2×C4—21no—
1352C2×C4—21no—
1353C2×C4—21no—
1354C2×C4—21no—
1355C2×C4—21no—
1356C2×C4—21no—
1357C2×C4—21no—
1358C2×C4—21no—
1359C2×C4—21no—
1360C2×C4—21no—
1361C2×C4—21no—
1362C2×C4—21no—
1363C2×C4—21no—
1364C2×C4—21no—
1365C2×C4—21no—
1366C2×C4—21no—
1367C2×C4—44no—
1368C2×C4—44no—
1369C2×C4—44no—
1370C2×C4—44no—
1371C2×C4—2684no—
1372C2×C4—2684no—
1373C2×C4—5362no—
1374C2×C4—5362no—
1375C2×C4—5362no—
1376C2×C4—5362no—
1377C2×C4—5362no—
1378C2×C4—5362no—
1379C2×C4—672no—
1380C2×C4—672no—
1381C2×C4—672no—
1382C2×C4—1341no—
1383C2×C4—1341no—
1384C2×C4—1341no—
1385C2×C4—1341no—
1386C2×C4—1341no—
1387C2×C4—1341no—
1388C2×C4—1341no—
1389C2×C4—1341no—
1390C2×C4—1341no—
1391C2×C4—1341no—
1392C2×C4—1341no—
1393C2×C4—1341no—
1394C2×C4—1341no—
1395C2×C4—1341no—
1396C2×C4—1341no—
1397C2×C4—1341no—
1398C2×C4—1341no—
1399C2×C4—1341no—
1400C2×C4—1341no—
1401C2×C4—1341no—
1402C2×C4—1341no—
1403C2×C4—1341no—
1404C2×C4—1341no—
1405C2×C4—1341no—
1406C2×C4—1341no—
1407C2×C4—1341no—
1408C2×C4—1341no—
1409C2×C4—1341no—
1410C2×C4—1341no—
1411C2×C4—1341no—
1412C2×C4—1341no—
1413C2×C4—1341no—
1414C2×C4—1341no—
1415C2×C4—1341no—
1416C2×C4—1341no—
1417C2×C4—1341no—
1418C2×C4—1341no—
1419C2×C4—1341no—
1420C2×C4—1341no—
1421C2×C4—1341no—
1422C2×C4—1341no—
1423C2×C4—1341no—
1424C2×C4—1341no—
1425C2×C4—1341no—
1426C2×C4—1341no—
1427C2×C4C23×Dic6712yes—
1428C2×C4C23×Dic6712yes—
1429C2×C4C23×Dic6712yes—
1430C2×C4C23×Dic6712yes—
1431C2×C4C23×Dic6712yes—
1432C2×C4C23×Dic6712yes—
1433C2×C4C23×Dic6712yes—
1434C2×C4C23×Dic6712yes—
1435C2×C4C23×Dic6712yes—
1436C2×C4C23×Dic6712yes—
1437C2×C4C23×Dic6712yes—
1438C22—22no—
1439C22—22no—
1440C22—22no—
1441C22—22no—
1442C22—22no—
1443C22—22no—
1444C22—22no—
1445C22—22no—
1446C22—22no—
1447C22—22no—
1448C22—22no—
1449C22—22no—
1450C22—41no—
1451C22—41no—
1452C22—41no—
1453C22—41no—
1454C22—41no—
1455C22—41no—
1456C22—41no—
1457C22—41no—
1458C22—41no—
1459C22—41no—
1460C22—41no—
1461C22—41no—
1462C22—41no—
1463C22—41no—
1464C22—41no—
1465C22—41no—
1466C22C24×Dic6711yescharacteristic
1467C22H(5,𝔽2)×D6711yescharacteristic
1468C22H(5,𝔽2)×D6711yescharacteristic
1469C222−1+4×D6711yescharacteristic
1470C22#1686423111yescharacteristic
1471C22#1686423111yescharacteristic
1472C22#1686423311yescharacteristic
1473C4—22no—
1474C4—22no—
1475C4—22no—
1476C4—22no—
1477C4—22no—
1478C4—22no—
1479C4—22no—
1480C4—22no—
1481C4—22no—
1482C4—22no—
1483C4—22no—
1484C4—2681no—
1485C4—2681no—
1486C4—2681no—
1487C4—2681no—
1488C4—2681no—
1489C4—2681no—
1490C4—2681no—
1491C4—2681no—
1492C4—2681no—
1493C4—2681no—
1494C4—2681no—
1495C4—2681no—
1496C4—2681no—
1497C4—1342no—
1498C4—1342no—
1499C4—1342no—
1500C2—42no—
1501C2—42no—
1502C2—42no—
1503C2—42no—
1504C2H(5,𝔽2)×Dic6711yescharacteristic
1505C2H(5,𝔽2)×Dic6711yescharacteristic
1506C22−1+4×Dic6711yescharacteristic
1507C2#2257437111yescharacteristic
1508C2#2257442811yescharacteristic
1509C2#2257479411yescharacteristic
1510C2#2257484311yescharacteristic
subgroupG/H
center, FrattiniC23C24×D67
commutatorC22×C67C24×C4
Fitting, prime radicalC2×#562×C67C2
socle, cosocleC23×C67C25
hypercenterC2×#562D67
hypocenterC67#34513
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×#562

Complements

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

NH ≅ G/Ntype
1. #22563375C2semidirect
2. #22563366C2semidirect
3. #22563357C2semidirect
4. #22563309C2semidirect
5. #22563294C2semidirect
6. #22563284C2semidirect
7. #22563284C2semidirect
8. #22563261C2semidirect
9. #22563261C2semidirect
10. #22563251C2semidirect
11. #22563240C2semidirect
12. #22563240C2semidirect
13. #22563205C2semidirect
14. #22563205C2semidirect
15. #22563205C2semidirect
16. #22563024C2semidirect
17. #22563024C2semidirect
18. #22563015C2semidirect
19. #22563003C2semidirect
20. #22563003C2semidirect
21. #22563003C2semidirect
22. #22562944C2semidirect
23. #22562944C2semidirect
24. #22562914C2semidirect
25. #22562904C2semidirect
26. #22562904C2semidirect
27. #22562893C2semidirect
28. C22⋊Q8×Dic67C2semidirect
29. #123×Dic67C2semidirect
30. #121×Dic67C2semidirect
172. #562×C67C4semidirect
332. #125×C67C2×C4semidirect
333. #124×C67C2×C4semidirect
334. #124×C67C2×C4semidirect
335. #123×C67C2×C4semidirect
336. #123×C67C2×C4semidirect
337. #123×C67C2×C4semidirect
338. #123×C67C2×C4semidirect
339. C22⋊Q8×C67C2×C4semidirect
340. C22⋊Q8×C67C2×C4semidirect
341. C22⋊Q8×C67C2×C4semidirect
342. C22⋊Q8×C67C2×C4semidirect
343. #121×C67C2×C4semidirect
344. #121×C67C2×C4semidirect
345. #121×C67C2×C4semidirect
346. #121×C67C2×C4semidirect
787. C67#34513semidirect
788. #562Dic67semidirect
964. #125C2×Dic67semidirect
965. #124C2×Dic67semidirect
966. #124C2×Dic67semidirect
967. #123C2×Dic67semidirect
968. #123C2×Dic67semidirect
969. #123C2×Dic67semidirect
970. #123C2×Dic67semidirect
971. C22⋊Q8C2×Dic67semidirect
972. C22⋊Q8C2×Dic67semidirect
973. C22⋊Q8C2×Dic67semidirect
974. C22⋊Q8C2×Dic67semidirect
975. #121C2×Dic67semidirect
976. #121C2×Dic67semidirect
977. #121C2×Dic67semidirect
978. #121C2×Dic67semidirect

Maximal subgroups

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

subgroupindex
#225633752
#225633662
#225633572
#225633092
#225632942
#225632842
#225632612
#225632512
#225632402
#225632052
#225630242
#225630152
#225630032
#225629442
#225629142
#225629042
#225628932
C22⋊Q8×Dic672
#123×Dic672
#121×Dic672
C2×#562×C672
#3451367