Finite Group Databasebeta

← #34030819

Subgroups — #34030819

Order 18688.

3296 conjugacy classes of subgroups.

The subgroup lattice has 1632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989654C211yesmaximal, characteristic, complemented
2C2×#41×#64408C211yesmaximal, characteristic, complemented
3#22626462C211yesmaximal, characteristic, complemented
4#22626458C211yesmaximal, characteristic, complemented
5#22626457C211yesmaximal, characteristic, complemented
6#22626456C212yesmaximal, complemented
7#22626454C212yesmaximal, complemented
8#22626453C212yesmaximal, complemented
9#22626449C211yesmaximal, characteristic, complemented
10D4×C4⋊#64408C211yesmaximal, characteristic, complemented
11#22626437C212yesmaximal, complemented
12#22626434C211yesmaximal, characteristic, complemented
13D4×C22⋊#64408C211yesmaximal, characteristic, complemented
14#22626421C211yesmaximal, characteristic, complemented
15#22626420C212yesmaximal, complemented
16#22626418C211yesmaximal, characteristic, complemented
17#22626416C212yesmaximal, complemented
18#123×#64408C212yesmaximal, complemented
19#121×#64408C211yesmaximal, characteristic, complemented
20#22626385C211yesmaximal, characteristic, complemented
21C2×#17989537C212yesmaximal, complemented
22#22626370C211yesmaximal, characteristic, complemented
23#546×D73C211yesmaximal, characteristic
24#17989654—28no—
25#41×#64408—28no—
26C2×Q8×#64408C2211yescharacteristic, complemented
27C2×Q8×#64408C2211yescharacteristic, complemented
28C2×D4×#64408C2211yescharacteristic
29C2×D4×#64408C2211yescharacteristic
30C2×D4×#64408C2211yescharacteristic
31C2×D4×#64408C2212yes—
32C2×D4×#64408C2211yescharacteristic
33C2×D4×#64408C2212yes—
34C2×D4×#64408C2211yescharacteristic
35C2×D4×#64408C2211yescharacteristic
36C2×D4×#64408C2212yescomplemented
37C2×D4×#64408C2212yescomplemented
38C2×D4×#64408C2212yescomplemented
39C2×#14556670C2211yescharacteristic
40C2×#14556670C2211yescharacteristic
41C2×#14556670C2212yescomplemented
42C2×#14556670C2211yescharacteristic, complemented
43C22×C4⋊#64408C2212yescomplemented
44C22×C22⋊#64408C2212yes—
45C22×C22⋊#64408C2212yes—
46C22×C22⋊#64408C2212yes—
47C22×C4×#64408C2212yescomplemented
48C22×C4×#64408C2211yescharacteristic, complemented
49(C2×#64408)⋊Q8C2211yescharacteristic, complemented
50(C2×#64408)⋊Q8C2211yescharacteristic, complemented
51#17989539C2211yescharacteristic
52#17989539C2212yes—
53#17989539C2211yescharacteristic
54#17989539C2212yescomplemented
55#17989538C2211yescharacteristic, complemented
56#17989538C2211yescharacteristic, complemented
57#17989538C2212yescomplemented
58#17989537C2211yescharacteristic
59#17989537C2212yes—
60#17989537C2212yes—
61#17989537C2212yes—
62#17989537C2211yescharacteristic
63#17989537C2212yes—
64#17989537C2212yes—
65#17989537C2212yescomplemented
66#17989537C2212yescomplemented
67#17989537C2212yescomplemented
68#17989537C2212yescomplemented
69#17989537C2212yescomplemented
70#17989537C2212yescomplemented
71#17989537C2212yescomplemented
72#17989536C2211yescharacteristic, complemented
73#17989536C2211yescharacteristic, complemented
74#17989536C2212yescomplemented
75#17989536C2212yescomplemented
76#17989535C2211yescharacteristic
77#17989535C2211yescharacteristic
78#17989535C2212yes—
79#17989535C2212yes—
80#17989535C2212yescomplemented
81#17989535C2212yescomplemented
82#17989535C2212yescomplemented
83#17989535C2212yescomplemented
84#17989534C2211yescharacteristic, complemented
85#17989534C2211yescharacteristic, complemented
86#17989534C2212yescomplemented
87#17989534C2212yescomplemented
88#17989534C2212yescomplemented
89#17989534C2212yescomplemented
90#17989534C2212yescomplemented
91#17989533C2211yescharacteristic, complemented
92#17989530C2212yescomplemented
93#17989529C2211yescharacteristic
94#17989529C2211yescharacteristic, complemented
95#17989529C2212yescomplemented
96#17989528C2212yes—
97C4⋊C4×#64408C2211yescharacteristic, complemented
98C4⋊C4×#64408C2211yescharacteristic, complemented
99C4⋊C4×#64408C2212yescomplemented
100C4⋊C4×#64408C2212yescomplemented
101C4×C4⋊#64408C2211yescharacteristic, complemented
102C4×C4⋊#64408C2211yescharacteristic, complemented
103C22⋊C4×#64408C2212yescomplemented
104C22⋊C4×#64408C2212yescomplemented
105C22⋊C4×#64408C2212yescomplemented
106C22⋊C4×#64408C2212yescomplemented
107C22⋊C4×#64408C2212yescomplemented
108C4×C22⋊#64408C2211yescharacteristic
109C4×C22⋊#64408C2212yescomplemented
110C4×C22⋊#64408C2211yescharacteristic, complemented
111#17989523C2211yescharacteristic, complemented
112C2×(C2×#64408)⋊C4C2212yescomplemented
113C2×(C2×#64408)⋊C4C2212yescomplemented
114C2×#41×D73C2211yescharacteristic
115C22×D4×D73C2211yescharacteristic
116#17989234C411yescharacteristic, complemented
117#17989233C411yescharacteristic, complemented
118#17989232C411yescharacteristic, complemented
119#17989231C411yescharacteristic, complemented
120#17989230C411yescharacteristic, complemented
121#17989229C412yescomplemented
122#17989228C411yescharacteristic, complemented
123#17989227C412yescomplemented
124#17989226C412yescomplemented
125#17989225C411yescharacteristic, complemented
126#17989224C412yescomplemented
127#124×D73C2211yescharacteristic
128#123×D73C2212yes—
129C22⋊Q8×D73C2211yescharacteristic
130#121×D73C2211yescharacteristic
131#121×D73C2212yes—
132#120×D73C2212yes—
133C4×D4×D73C2211yescharacteristic
134C4×D4×D73C2211yescharacteristic
135C2×C22⋊C4×D73C2212yes—
136#546×C73C411yescharacteristic, complemented
137C23×#64408C2312yes—
138C23×#64408C2311yescharacteristic
139C23×#64408C2311yescharacteristic
140C23×#64408C2312yes—
141C23×#64408C2312yes—
142C23×#64408C2312yes—
143C23×#64408C2312yes—
144C23×#64408C2312yes—
145Q8×#64408—24no—
146Q8×#64408—24no—
147D4×#64408—28no—
148D4×#64408—28no—
149D4×#64408—24no—
150D4×#64408—28no—
151D4×#64408—28no—
152D4×#64408—24no—
153D4×#64408—24no—
154D4×#64408—24no—
155D4×#64408—24no—
156D4×#64408—44no—
157D4×#64408D418yescomplemented
158#14556670—24no—
159#14556670—24no—
160#14556670—28no—
161#14556670—24no—
162C2×C4⋊#64408—44no—
163C2×C4⋊#64408C2311yescharacteristic
164C2×C4⋊#64408C2312yes—
165C2×C4⋊#64408C2311yescharacteristic
166C2×C4⋊#64408C2311yescharacteristic
167C2×C4⋊#64408C2311yescharacteristic
168C2×C4⋊#64408C2311yescharacteristic
169C2×C4⋊#64408C2312yes—
170C2×C4⋊#64408C2312yes—
171C2×C4⋊#64408C2311yescharacteristic
172C2×C4⋊#64408C2312yes—
173C2×C4⋊#64408C2312yes—
174C2×C4⋊#64408C2311yescharacteristic
175C2×C4⋊#64408C2312yes—
176C2×C4⋊#64408C2311yescharacteristic
177C2×C22⋊#64408—28no—
178C2×C22⋊#64408—28no—
179C2×C22⋊#64408—44no—
180C2×C22⋊#64408C2311yescharacteristic
181C2×C22⋊#64408C2311yescharacteristic
182C2×C22⋊#64408C2312yes—
183C2×C22⋊#64408C2311yescharacteristic
184C2×C22⋊#64408C2312yes—
185C2×C22⋊#64408C2312yes—
186C2×C22⋊#64408C2312yes—
187C2×C22⋊#64408C2312yes—
188C2×C22⋊#64408C2312yes—
189C2×C22⋊#64408C2312yes—
190C2×C22⋊#64408C2312yes—
191C2×C22⋊#64408C2312yes—
192C2×C22⋊#64408C2312yes—
193C2×C22⋊#64408C2312yes—
194C2×C22⋊#64408C2311yescharacteristic
195C2×C22⋊#64408C2311yescharacteristic
196C2×C22⋊#64408C2311yescharacteristic
197C2×C22⋊#64408C2312yes—
198C2×C22⋊#64408C2312yes—
199C2×C22⋊#64408C2312yes—
200C2×C4×#64408—28no—
201C2×C4×#64408—24no—
202C2×C4×#64408C2311yescharacteristic
203C2×C4×#64408C2311yescharacteristic
204C2×C4×#64408C2312yes—
205C2×C4×#64408C2311yescharacteristic
206C2×C4×#64408C2312yes—
207C2×C4×#64408C2312yes—
208C2×C4×#64408C2311yescharacteristic
209C2×C4×#64408C2312yes—
210C2×C4×#64408C2311yescharacteristic
211C2×C4×#64408C2312yes—
212C2×C4×#64408C2312yes—
213C2×C4×#64408C2312yes—
214C2×C4×#64408C2311yescharacteristic
215(C2×#64408)⋊C4C2311yescharacteristic
216(C2×#64408)⋊C4C2311yescharacteristic
217(C2×#64408)⋊C4C2312yes—
218(C2×#64408)⋊C4C2312yes—
219(C2×#64408)⋊C4C2312yes—
220(C2×#64408)⋊C4C2312yes—
221(C2×#64408)⋊C4C2312yes—
222(C2×#64408)⋊C4C2312yes—
223(C2×#64408)⋊C4C2311yescharacteristic
224(C2×#64408)⋊C4C2311yescharacteristic
225(C2×#64408)⋊C4C2311yescharacteristic
226(C2×#64408)⋊C4C2311yescharacteristic
227(C2×#64408)⋊C4C2311yescharacteristic
228(C2×#64408)⋊C4C2311yescharacteristic
229(C2×#64408)⋊C4C2311yescharacteristic
230(C2×#64408)⋊C4C2312yes—
231(C2×#64408)⋊C4C2312yes—
232(C2×#64408)⋊C4C2312yes—
233(C2×#64408)⋊C4C2311yescharacteristic
234(C2×#64408)⋊C4C2312yes—
235(C2×#64408)⋊C4C2312yes—
236C24×D73C2312yes—
237C2×#11924029C2×C411yescharacteristic, complemented
238C2×#11924028C2×C412yescomplemented
239C2×#11924028C2×C411yescharacteristic, complemented
240C2×#11924027C2×C412yescomplemented
241C2×#11924027C2×C411yescharacteristic, complemented
242#41×D73—24no—
243#41×D73—24no—
244C2×Q8×D73C2311yescharacteristic
245C22×D292C2×C411yescharacteristic, complemented
246C22×C22⋊D73C2×C412yescomplemented
247C2×D4×D73—24no—
248C2×D4×D73—24no—
249C2×D4×D73C2×C411yescharacteristic, complemented
250C2×D4×D73C2×C412yescomplemented
251C2×D4×D73C2×C411yescharacteristic, complemented
252C2×D4×D73C2312yes—
253C2×D4×D73C2311yescharacteristic
254C2×D4×D73C2312yes—
255C2×D4×D73C2312yes—
256C2×D4×D73C2311yescharacteristic
257C2×D4×D73C2311yescharacteristic
258C22×C4×D73C2312yes—
259C22×C4×D73C2311yescharacteristic
260C22×C4×D73C2311yescharacteristic
261C22×C4×D73C2312yes—
262#14556580C2×C411yescharacteristic, complemented
263#14556579C2×C411yescharacteristic, complemented
264#14556578C2×C411yescharacteristic, complemented
265#14556577C2×C412yescomplemented
266#14556577C2×C412yescomplemented
267#14556576C2×C412yescomplemented
268#14556576C2×C412yescomplemented
269#14556575C2×C412yescomplemented
270#14556574C2×C412yescomplemented
271#14556573C2×C412yescomplemented
272#14556573C2×C412yescomplemented
273#14556572C2×C412yescomplemented
274#14556571C2×C411yescharacteristic, complemented
275#14556570C2×C411yescharacteristic, complemented
276#14556569C2×C412yescomplemented
277#14556568C2×C412yescomplemented
278#14556567C2×C411yescharacteristic, complemented
279#14556566C2×C412yescomplemented
280#14556566C2×C411yescharacteristic, complemented
281#14556565C2×C411yescharacteristic, complemented
282#14556565C2×C412yescomplemented
283#14556564C2×C412yescomplemented
284#14556564C2×C412yescomplemented
285#14556564C2×C412yescomplemented
286#14556563C2×C412yescomplemented
287#14556563C2×C412yescomplemented
288#14556563C2×C412yescomplemented
289#14556562C2×C412yescomplemented
290#14556562C2×C411yescharacteristic, complemented
291#14556561C2×C412yescomplemented
292#14556561C2×C412yescomplemented
293#14556561C2×C412yescomplemented
294#14556560C2×C412yescomplemented
295#14556559C2×C412yescomplemented
296#14556559C2×C412yescomplemented
297#14556559C2×C412yescomplemented
298C4×D292C2×C411yescharacteristic, complemented
299C4×D292C2×C411yescharacteristic, complemented
300D4×Dic73C2×C411yescharacteristic, complemented
301D4×Dic73C2×C411yescharacteristic, complemented
302#14556553C2×C411yescharacteristic, complemented
303#14556553C2×C411yescharacteristic, complemented
304C4×C22⋊D73C2×C411yescharacteristic, complemented
305C4×C22⋊D73C2×C412yescomplemented
306C4×C22⋊D73C2×C411yescharacteristic, complemented
307#14556551C2×C412yescomplemented
308#14556551C2×C411yescharacteristic, complemented
309#14556551C2×C411yescharacteristic, complemented
310C4⋊C4×D73C2311yescharacteristic
311C4⋊C4×D73C2311yescharacteristic
312C4⋊C4×D73C2312yes—
313C2×C22⋊Dic73C2×C412yescomplemented
314C2×#11924005C2×C412yescomplemented
315C2×#11924005C2×C412yescomplemented
316C22⋊C4×D73C2×C412yescomplemented
317C22⋊C4×D73C2×C412yescomplemented
318C22⋊C4×D73C2×C412yescomplemented
319C22⋊C4×D73C2×C412yescomplemented
320C22⋊C4×D73C2312yes—
321C22⋊C4×D73C2312yes—
322C22⋊C4×D73C2312yes—
323C22⋊C4×D73C2312yes—
324C22⋊C4×D73C2311yescharacteristic
325C22⋊C4×D73C2311yescharacteristic
326C22⋊C4×D73C2312yes—
327C42×D73C2311yescharacteristic
328C2×#41×C73C2×C411yescharacteristic, complemented
329C22×D4×C73C2×C411yescharacteristic, complemented
330#124×C73C2×C411yescharacteristic, complemented
331#123×C73C2×C412yescomplemented
332C22⋊Q8×C73C2×C411yescharacteristic, complemented
333#121×C73C2×C412yescomplemented
334#121×C73C2×C411yescharacteristic, complemented
335#120×C73C2×C412yescomplemented
336C4×D4×C73C2×C411yescharacteristic, complemented
337C4×D4×C73C2×C411yescharacteristic, complemented
338C2×C22⋊C4×C73C2×C412yescomplemented
339C22×#64408—24no—
340C22×#64408—24no—
341C22×#64408—24no—
342C22×#64408—22no—
343C22×#64408—22no—
344C22×#64408—24no—
345C22×#64408—22no—
346C22×#64408—24no—
347C22×#64408—24no—
348C22×#64408—42no—
349C22×#64408—42no—
350C22×#64408—41no—
351C22×#64408—41no—
352C22×#64408—42no—
353C22×#64408—41no—
354C22×#64408—42no—
355C22×#64408—42no—
356C22×#64408—42no—
357C22×#64408—42no—
358C22×#64408—42no—
359C22×#64408—42no—
360C22×#64408—42no—
361C22×#64408—42no—
362C22×#64408C2×D418yes—
363C22×#64408C2411yescharacteristic
364C22×#64408C2411yescharacteristic
365C22×#64408C2412yes—
366C22×#64408C2411yescharacteristic
367C22×#64408C2412yes—
368C22×#64408C2411yescharacteristic
369C22×#64408C2412yes—
370C22×#64408C2411yescharacteristic
371C22×#64408C2411yescharacteristic
372C22×#64408C2411yescharacteristic
373C22×#64408C2412yes—
374C22×#64408C2411yescharacteristic
375C4⋊#64408—24no—
376C4⋊#64408—24no—
377C4⋊#64408—22no—
378C4⋊#64408—22no—
379C4⋊#64408—22no—
380C4⋊#64408—24no—
381C4⋊#64408—22no—
382C4⋊#64408—22no—
383C4⋊#64408—22no—
384C4⋊#64408—42no—
385C4⋊#64408—42no—
386C4⋊#64408—41no—
387C4⋊#64408—42no—
388C4⋊#64408C2×D414yes—
389C22⋊#64408—24no—
390C22⋊#64408—24no—
391C22⋊#64408—24no—
392C22⋊#64408—22no—
393C22⋊#64408—24no—
394C22⋊#64408—22no—
395C22⋊#64408—24no—
396C22⋊#64408—24no—
397C22⋊#64408—24no—
398C22⋊#64408—22no—
399C22⋊#64408—24no—
400C22⋊#64408—42no—
401C22⋊#64408—42no—
402C22⋊#64408—41no—
403C22⋊#64408—42no—
404C22⋊#64408—42no—
405C22⋊#64408—41no—
406C22⋊#64408—41no—
407C22⋊#64408—42no—
408C22⋊#64408C2×D418yes—
409C4×#64408—24no—
410C4×#64408—24no—
411C4×#64408—22no—
412C4×#64408—24no—
413C4×#64408—22no—
414C4×#64408—24no—
415C4×#64408—22no—
416C4×#64408—22no—
417C4×#64408—22no—
418C4×#64408—42no—
419C4×#64408—42no—
420C4×#64408—42no—
421C4×#64408C2×D414yes—
422C23×D73—24no—
423C23×D73—24no—
424C23×D73—42no—
425C23×D73—42no—
426C23×D73—42no—
427C23×D73—42no—
428C23×D73C22×C412yes—
429C23×D73C22×C412yes—
430C23×D73C22×C412yes—
431C23×D73C2412yes—
432C23×D73C2411yescharacteristic
433C23×D73C2411yescharacteristic
434C23×D73C2412yes—
435#11924029—24no—
436#11924028—28no—
437#11924028—24no—
438#11924027—24no—
439#11924027—28no—
440C2×Dic146C22×C412yes—
441C2×Dic146C22×C411yescharacteristic
442Q8×D73—22no—
443Q8×D73—22no—
444C2×D292—24no—
445C2×D292C22×C412yes—
446C2×D292C22×C412yes—
447C2×D292C22×C411yescharacteristic
448C2×D292C22×C411yescharacteristic
449C2×D292C22×C412yes—
450C2×D292C22×C411yescharacteristic
451C2×C22⋊D73—28no—
452C2×C22⋊D73C22×C412yes—
453C2×C22⋊D73C22×C412yes—
454C2×C22⋊D73C22×C412yes—
455C2×C22⋊D73C22×C412yes—
456C2×C22⋊D73C22×C412yes—
457C2×C22⋊D73C22×C411yescharacteristic
458C2×C22⋊D73C22×C411yescharacteristic
459C2×C22⋊D73C22×C412yes—
460C2×C22⋊D73C22×C412yes—
461C2×C22⋊D73C22×C412yes—
462D4×D73—24no—
463D4×D73—24no—
464D4×D73—24no—
465D4×D73—24no—
466D4×D73—24no—
467D4×D73—28no—
468D4×D73—24no—
469D4×D73—22no—
470D4×D73—22no—
471D4×D73—42no—
472D4×D73—41no—
473D4×D73—41no—
474D4×D73—42no—
475D4×D73C2×D414yes—
476D4×D73#4114yes—
477C22×Dic73C22×C412yes—
478C22×Dic73C22×C411yescharacteristic
479C22×Dic73C22×C411yescharacteristic
480C22×Dic73C22×C412yes—
481C2×C4×D73—24no—
482C2×C4×D73—24no—
483C2×C4×D73—22no—
484C2×C4×D73—22no—
485C2×C4×D73—22no—
486C2×C4×D73—22no—
487C2×C4×D73—42no—
488C2×C4×D73—42no—
489C2×C4×D73C22×C412yes—
490C2×C4×D73C22×C412yes—
491C2×C4×D73C22×C411yescharacteristic
492C2×C4×D73C22×C411yescharacteristic
493C2×C4×D73C22×C411yescharacteristic
494C2×C4×D73C22×C411yescharacteristic
495C2×C4×D73C22×C412yes—
496C2×C4×D73C22×C412yes—
497C2×C4×D73C2411yescharacteristic
498C2×C4×D73C2411yescharacteristic
499C2×C4×D73C2412yes—
500C2×C4×D73C2411yescharacteristic
501C2×C4×D73C2412yes—
502C2×C4×D73C2411yescharacteristic
503C2×C4×D73C2411yescharacteristic
504C4⋊Dic73C22×C411yescharacteristic
505C4⋊Dic73C22×C411yescharacteristic
506C4⋊Dic73C22×C412yes—
507#11924007C22×C412yes—
508#11924007C22×C411yescharacteristic
509#11924007C22×C411yescharacteristic
510#11924007C22×C412yes—
511#11924007C22×C412yes—
512C22⋊Dic73C22×C411yescharacteristic
513C22⋊Dic73C22×C412yes—
514C22⋊Dic73C22×C412yes—
515C22⋊Dic73C22×C412yes—
516C22⋊Dic73C22×C412yes—
517C22⋊Dic73C22×C411yescharacteristic
518C22⋊Dic73C22×C412yes—
519#11924005C22×C411yescharacteristic
520#11924005C22×C411yescharacteristic
521#11924005C22×C412yes—
522#11924005C22×C412yes—
523#11924005C22×C412yes—
524#11924005C22×C412yes—
525#11924005C22×C412yes—
526#11924005C22×C412yes—
527#11924005C22×C412yes—
528#11924005C22×C411yescharacteristic
529#11924005C22×C412yes—
530#11924005C22×C411yescharacteristic
531#11924005C22×C412yes—
532#11924005C22×C412yes—
533C4×Dic73C22×C411yescharacteristic
534C4×Dic73C22×C411yescharacteristic
535C4×Dic73C22×C411yescharacteristic
536C24×C73C22×C412yes—
537#41×C73—24no—
538C2×Q8×C73C22×C411yescharacteristic
539C2×D4×C73—24no—
540C2×D4×C73C22×C412yes—
541C2×D4×C73C22×C412yes—
542C2×D4×C73C22×C411yescharacteristic
543C2×D4×C73C22×C411yescharacteristic
544C2×D4×C73C22×C412yes—
545C2×D4×C73C22×C411yescharacteristic
546C22×C4×C73C22×C412yes—
547C22×C4×C73C22×C411yescharacteristic
548C22×C4×C73C22×C411yescharacteristic
549C22×C4×C73C22×C412yes—
550C4⋊C4×C73C22×C411yescharacteristic
551C4⋊C4×C73C22×C411yescharacteristic
552C4⋊C4×C73C22×C412yes—
553C22⋊C4×C73C22×C411yescharacteristic
554C22⋊C4×C73C22×C412yes—
555C22⋊C4×C73C22×C412yes—
556C22⋊C4×C73C22×C412yes—
557C22⋊C4×C73C22×C412yes—
558C22⋊C4×C73C22×C411yescharacteristic
559C22⋊C4×C73C22×C412yes—
560C42×C73C22×C411yescharacteristic
561C23×C73—24no—
562C23×C73—42no—
563C23×C73—42no—
564C23×C73C23×C411yescharacteristic
565C23×C73C23×C412yes—
566C23×C73C23×C411yescharacteristic
567C23×C73C23×C412yes—
568C22×D73—22no—
569C22×D73—22no—
570C22×D73—22no—
571C22×D73—22no—
572C22×D73—24no—
573C22×D73—21no—
574C22×D73—21no—
575C22×D73—22no—
576C22×D73—21no—
577C22×D73—21no—
578C22×D73—22no—
579C22×D73—21no—
580C22×D73—22no—
581C22×D73—21no—
582C22×D73—21no—
583C22×D73—21no—
584C22×D73—21no—
585C22×D73—22no—
586C22×D73—21no—
587C22×D73—21no—
588C22×D73—21no—
589C22×D73—22no—
590C22×D73—22no—
591C22×D73—24no—
592C22×D73—24no—
593C22×D73—42no—
594C22×D73—42no—
595C22×D73—42no—
596C22×D73—42no—
597C22×D73—42no—
598C22×D73—42no—
599C22×D73—84no—
600C22×D73—84no—
601C22×D73—84no—
602C22×D73—84no—
603C22×D73C23×C411yescharacteristic
604C22×D73C23×C412yes—
605C22×D73C23×C411yescharacteristic
606C22×D73C23×C412yes—
607C22×D73C22×D414yes—
608C22×D73C2×#4114yes—
609C22×D73C2511yescharacteristic
610C2×#64408—21no—
611C2×#64408—21no—
612C2×#64408—22no—
613C2×#64408—22no—
614C2×#64408—21no—
615C2×#64408—21no—
616C2×#64408—21no—
617C2×#64408—21no—
618C2×#64408—21no—
619C2×#64408—22no—
620C2×#64408—21no—
621C2×#64408—22no—
622C2×#64408—21no—
623C2×#64408—21no—
624C2×#64408—21no—
625C2×#64408—22no—
626C2×#64408—22no—
627C2×#64408—21no—
628C2×#64408—22no—
629C2×#64408—22no—
630C2×#64408—21no—
631C2×#64408—21no—
632C2×#64408—22no—
633C2×#64408—21no—
634C2×#64408—21no—
635C2×#64408—21no—
636C2×#64408—22no—
637C2×#64408—21no—
638C2×#64408—21no—
639C2×#64408—21no—
640C2×#64408—21no—
641C2×#64408—22no—
642C2×#64408—48no—
643C2×#64408—44no—
644C2×#64408—48no—
645C2×#64408—44no—
646C2×#64408—84no—
647C2×#64408—84no—
648C2×#64408—84no—
649C2×#64408—84no—
650C2×#64408C22×D412yes—
651C2×#64408C22×D414yes—
652C2×#64408C22×D412yes—
653C2×#64408H(5,𝔽2)12yes—
654Q8×C73—22no—
655D4×C73—24no—
656D4×C73—24no—
657D4×C73—22no—
658D4×C73—41no—
659D4×C73—42no—
660D4×C73C4×D414yescomplemented
661C2×C4×C73—24no—
662C2×C4×C73—22no—
663C2×C4×C73—22no—
664C2×C4×C73—42no—
665C2×C4×C73C23×C411yescharacteristic
666C2×C4×C73C23×C411yescharacteristic
667C2×C4×C73C23×C412yes—
668C2×C4×C73C23×C411yescharacteristic
669C2×C4×C73C23×C412yes—
670C2×C4×C73C23×C411yescharacteristic
671C2×C4×C73C23×C411yescharacteristic
672C22⋊D73—24no—
673C22⋊D73—24no—
674C22⋊D73—24no—
675C22⋊D73—24no—
676C22⋊D73—24no—
677C22⋊D73—41no—
678C22⋊D73—41no—
679C22⋊D73—42no—
680C22⋊D73—42no—
681C22⋊D73C4×D418yescomplemented
682C2×Dic73—24no—
683C2×Dic73—22no—
684C2×Dic73—22no—
685C2×Dic73—42no—
686C2×Dic73C23×C411yescharacteristic
687C2×Dic73C23×C411yescharacteristic
688C2×Dic73C23×C412yes—
689C2×Dic73C23×C411yescharacteristic
690C2×Dic73C23×C412yes—
691C2×Dic73C23×C411yescharacteristic
692C2×Dic73C23×C411yescharacteristic
693D292—24no—
694D292—24no—
695D292—22no—
696D292—41no—
697D292—42no—
698D292C4×D414yescomplemented
699C4×D73—24no—
700C4×D73—24no—
701C4×D73—21no—
702C4×D73—21no—
703C4×D73—22no—
704C4×D73—21no—
705C4×D73—21no—
706C4×D73—22no—
707C4×D73—21no—
708C4×D73—22no—
709C4×D73—21no—
710C4×D73—22no—
711C4×D73—21no—
712C4×D73—21no—
713C4×D73—22no—
714C4×D73—22no—
715C4×D73—22no—
716C4×D73—22no—
717C4×D73—42no—
718C4×D73—42no—
719C4×D73C22×D412yes—
720C4×D73C2×#4112yes—
721Dic146—22no—
722Dic146—24no—
723C22×C73—22no—
724C22×C73—22no—
725C22×C73—21no—
726C22×C73—21no—
727C22×C73—22no—
728C22×C73—21no—
729C22×C73—21no—
730C22×C73—22no—
731C22×C73—21no—
732C22×C73—22no—
733C22×C73—21no—
734C22×C73—84no—
735C22×C73C2×C4×D414yes—
736C22×C73C24×C411yescharacteristic
737C2×D73—22no—
738C2×D73—22no—
739C2×D73—24no—
740C2×D73—24no—
741C2×D73—24no—
742C2×D73—24no—
743C2×D73—21no—
744C2×D73—21no—
745C2×D73—22no—
746C2×D73—21no—
747C2×D73—21no—
748C2×D73—22no—
749C2×D73—21no—
750C2×D73—22no—
751C2×D73—21no—
752C2×D73—41no—
753C2×D73—42no—
754C2×D73—41no—
755C2×D73—41no—
756C2×D73—42no—
757C2×D73—41no—
758C2×D73—41no—
759C2×D73—42no—
760C2×D73—41no—
761C2×D73—41no—
762C2×D73—42no—
763C2×D73—41no—
764C2×D73—84no—
765C2×D73—84no—
766C2×D73—84no—
767C2×D73C2×C4×D414yes—
768C2×D73C23×D411yescharacteristic
769C2×D73C22×#4111yescharacteristic
770C2×D73C2×H(5,𝔽2)11yescharacteristic
771C2×D73#58511yescharacteristic
772C2×D73#58511yescharacteristic
773C2×D73#58511yescharacteristic
774#64408—22no—
775#64408—24no—
776#64408—22no—
777#64408—22no—
778#64408—41no—
779#64408—41no—
780#64408—42no—
781#64408—42no—
782#64408—41no—
783#64408—42no—
784#64408—41no—
785#64408—41no—
786C4×C73—22no—
787C4×C73—21no—
788C4×C73—21no—
789C4×C73—21no—
790C4×C73—21no—
791C4×C73—22no—
792C4×C73C2×C4×D412yes—
793Dic73—22no—
794Dic73—21no—
795Dic73—21no—
796Dic73—21no—
797Dic73—21no—
798Dic73—22no—
799Dic73C2×C4×D412yes—
800#34292—731nomaximal, Sylow
801C2×C73—24no—
802C2×C73—41no—
803C2×C73—42no—
804C2×C73—41no—
805C2×C73C22×C4×D411yescharacteristic
806C2×C73#342811yescharacteristic
807C2×C73C4×H(5,𝔽2)11yescharacteristic
808D73—24no—
809D73—41no—
810D73—42no—
811D73—41no—
812D73#348511yescharacteristic
813D73#348811yescharacteristic
814D73#351411yescharacteristic
815D73#352111yescharacteristic
816C2×#546—731no—
817C2×#518—731no—
818C2×C4×#41—731no—
819#2367—731no—
820#2363—731no—
821#2362—731no—
822#2361—732no—
823#2359—732no—
824#2358—732no—
825#2354—731no—
826D4×C4⋊C4—731no—
827#2342—732no—
828#2339—731no—
829D4×C22⋊C4—731no—
830#2326—731no—
831#2325—732no—
832#2323—731no—
833#2321—732no—
834C4×#123—732no—
835C4×#121—731no—
836#2290—731no—
837C2×#388—732no—
838#2275—731no—
839C73#3429211yescharacteristic, complemented, Sylow
840C22×#41—731no—
841C23×D4—731no—
842#546—731no—
843#546—731no—
844#546—731no—
845#546—732no—
846#546—731no—
847#546—732no—
848#546—731no—
849#546—732no—
850#546—731no—
851#546—731no—
852#546—732no—
853#546#6440811yescharacteristic, complemented
854C2×#124—731no—
855C2×#123—732no—
856C2×C22⋊Q8—731no—
857C2×#121—732no—
858C2×#121—731no—
859C2×#120—732no—
860#518—1468no—
861C4×#41—1468no—
862C2×C4×Q8—731no—
863C2×C4×Q8—731no—
864C2×C4×D4—732no—
865C2×C4×D4—731no—
866C2×C4×D4—731no—
867C2×C4×D4—731no—
868C2×C4×D4—732no—
869C2×C4×D4—732no—
870C2×C4×D4—731no—
871C2×C4×D4—731no—
872C2×C4×D4—731no—
873C2×C4×D4—731no—
874C2×C4×D4—732no—
875C2×C4×D4—731no—
876C2×C4×D4—732no—
877C2×#117—731no—
878C2×#117—731no—
879C2×#117—732no—
880C2×#117—731no—
881C22×C4⋊C4—732no—
882C22×C22⋊C4—732no—
883C22×C22⋊C4—732no—
884C22×C22⋊C4—732no—
885C22×C22⋊C4—732no—
886C22×C42—732no—
887C22×C42—731no—
888#391—731no—
889#391—731no—
890#390—732no—
891#390—732no—
892#390—731no—
893#390—731no—
894#389—731no—
895#389—732no—
896#389—731no—
897#388—732no—
898#388—732no—
899#388—732no—
900#388—732no—
901#388—732no—
902#388—732no—
903#388—732no—
904#388—731no—
905#388—732no—
906#388—732no—
907#388—732no—
908#388—732no—
909#388—731no—
910#388—732no—
911#387—732no—
912#387—732no—
913#387—731no—
914#387—731no—
915#386—731no—
916#386—732no—
917#386—732no—
918#386—732no—
919#386—732no—
920#386—732no—
921#386—732no—
922#386—731no—
923#385—732no—
924#385—731no—
925#385—732no—
926#385—732no—
927#385—732no—
928#385—732no—
929#385—731no—
930#384—731no—
931#381—732no—
932#380—731no—
933#380—732no—
934#380—731no—
935#379—732no—
936C4×C4⋊C4—731no—
937C4×C4⋊C4—731no—
938C4×C4⋊C4—732no—
939C4×C4⋊C4—731no—
940C4×C4⋊C4—732no—
941C4×C4⋊C4—731no—
942C4×C22⋊C4—732no—
943C4×C22⋊C4—731no—
944C4×C22⋊C4—731no—
945C4×C22⋊C4—732no—
946C4×C22⋊C4—732no—
947C4×C22⋊C4—732no—
948C4×C22⋊C4—732no—
949C4×C22⋊C4—732no—
950#376—731no—
951C2×#95—732no—
952C2×#95—732no—
953C25—732no—
954C2×#41—731no—
955C2×#41—731no—
956C2×#41—732no—
957C2×#41—731no—
958C2×#41—732no—
959C2×#41—1464no—
960C2×#41—1464no—
961C2×#41C2×#6440811yescharacteristic, complemented
962C22×Q8—731no—
963C22×D4—731no—
964C22×D4—732no—
965C22×D4—731no—
966C22×D4—732no—
967C22×D4—732no—
968C22×D4—732no—
969C22×D4—731no—
970C22×D4—732no—
971C22×D4—731no—
972C22×D4—731no—
973C22×D4—731no—
974C22×D4—1464no—
975C22×D4—1464no—
976C22×D4C2×#6440811yescharacteristic, complemented
977C23×C4—732no—
978C23×C4—732no—
979C23×C4—732no—
980C23×C4—732no—
981C23×C4—732no—
982C23×C4—732no—
983C23×C4—731no—
984C23×C4—732no—
985C23×C4—731no—
986C23×C4—732no—
987C23×C4—731no—
988C23×C4—731no—
989#124—731no—
990#124—731no—
991#124—732no—
992#124—732no—
993#124—731no—
994#124C2×#6440811yescharacteristic, complemented
995#123—732no—
996#123—732no—
997#123—732no—
998#123—732no—
999#123—732no—
1000#123—732no—
1001#123—732no—
1002#123C2×#6440812yescomplemented
1003C22⋊Q8—731no—
1004C22⋊Q8—731no—
1005C22⋊Q8—732no—
1006C22⋊Q8—731no—
1007C22⋊Q8—732no—
1008C22⋊Q8C2×#6440811yescharacteristic, complemented
1009#121—731no—
1010#121—732no—
1011#121—732no—
1012#121—732no—
1013#121—732no—
1014#121—731no—
1015#121—732no—
1016#121—731no—
1017#121—732no—
1018#121—732no—
1019#121—732no—
1020#121—732no—
1021#121C2×#6440811yescharacteristic, complemented
1022#121C2×#6440812yescomplemented
1023#120—732no—
1024#120—732no—
1025#120—732no—
1026#120—732no—
1027#120—732no—
1028#120—732no—
1029#120—732no—
1030#120C2×#6440812yescomplemented
1031C4×Q8—1464no—
1032C4×Q8—1464no—
1033C4×D4—2924no—
1034C4×D4—738no—
1035C4×D4—731no—
1036C4×D4—731no—
1037C4×D4—731no—
1038C4×D4—732no—
1039C4×D4—731no—
1040C4×D4—731no—
1041C4×D4—731no—
1042C4×D4—731no—
1043C4×D4—732no—
1044C4×D4—731no—
1045C4×D4—731no—
1046C4×D4—731no—
1047C4×D4—1464no—
1048C4×D4—1468no—
1049C4×D4—1468no—
1050C4×D4—1464no—
1051C4×D4—1468no—
1052C4×D4—1468no—
1053C4×D4—1464no—
1054C4×D4—1464no—
1055C4×D4—1464no—
1056C4×D4C2×#6440811yescharacteristic, complemented
1057C4×D4C2×#6440811yescharacteristic, complemented
1058#117—1464no—
1059#117—1468no—
1060#117—1464no—
1061#117—1464no—
1062C2×C4⋊C4—2924no—
1063C2×C4⋊C4—732no—
1064C2×C4⋊C4—732no—
1065C2×C4⋊C4—731no—
1066C2×C4⋊C4—732no—
1067C2×C4⋊C4—731no—
1068C2×C4⋊C4—731no—
1069C2×C4⋊C4—731no—
1070C2×C4⋊C4—732no—
1071C2×C4⋊C4—731no—
1072C2×C4⋊C4—732no—
1073C2×C4⋊C4—731no—
1074C2×C4⋊C4—731no—
1075C2×C4⋊C4—731no—
1076C2×C4⋊C4—731no—
1077C2×C4⋊C4—732no—
1078C2×C4⋊C4—732no—
1079C2×C4⋊C4—731no—
1080C2×C22⋊C4—2924no—
1081C2×C22⋊C4—732no—
1082C2×C22⋊C4—732no—
1083C2×C22⋊C4—732no—
1084C2×C22⋊C4—731no—
1085C2×C22⋊C4—732no—
1086C2×C22⋊C4—732no—
1087C2×C22⋊C4—731no—
1088C2×C22⋊C4—731no—
1089C2×C22⋊C4—732no—
1090C2×C22⋊C4—732no—
1091C2×C22⋊C4—732no—
1092C2×C22⋊C4—732no—
1093C2×C22⋊C4—731no—
1094C2×C22⋊C4—732no—
1095C2×C22⋊C4—732no—
1096C2×C22⋊C4—732no—
1097C2×C22⋊C4—732no—
1098C2×C22⋊C4—732no—
1099C2×C22⋊C4—732no—
1100C2×C22⋊C4—732no—
1101C2×C22⋊C4—732no—
1102C2×C22⋊C4—731no—
1103C2×C22⋊C4—732no—
1104C2×C22⋊C4—731no—
1105C2×C22⋊C4—731no—
1106C2×C22⋊C4—732no—
1107C2×C22⋊C4—731no—
1108C2×C22⋊C4—732no—
1109C2×C22⋊C4—732no—
1110C2×C22⋊C4—732no—
1111C2×C22⋊C4—732no—
1112C2×C22⋊C4—732no—
1113C2×C22⋊C4—732no—
1114C2×C22⋊C4—732no—
1115C2×C22⋊C4—1468no—
1116C2×C22⋊C4—1468no—
1117C2×C22⋊C4C2×#6440812yescomplemented
1118C2×C42—732no—
1119C2×C42—732no—
1120C2×C42—732no—
1121C2×C42—731no—
1122C2×C42—731no—
1123C2×C42—731no—
1124C2×C42—732no—
1125C2×C42—731no—
1126C2×C42—732no—
1127C2×C42—732no—
1128C2×C42—731no—
1129C2×C42—732no—
1130C2×C42—731no—
1131C2×C42—731no—
1132C2×C42—1464no—
1133C2×C42—1468no—
1134#95—731no—
1135#95—731no—
1136#95—732no—
1137#95—732no—
1138#95—732no—
1139#95—732no—
1140#95—732no—
1141#95—732no—
1142#95—731no—
1143#95—731no—
1144#95—731no—
1145#95—731no—
1146#95—731no—
1147#95—731no—
1148#95—732no—
1149#95—732no—
1150#95—732no—
1151#95—731no—
1152#95—732no—
1153#95—732no—
1154#95—731no—
1155C24—2922no—
1156C24—2922no—
1157C24—2922no—
1158C24—2922no—
1159C24—732no—
1160C24—732no—
1161C24—732no—
1162C24—732no—
1163C24—731no—
1164C24—732no—
1165C24—731no—
1166C24—1464no—
1167C24—1464no—
1168C24C22×#6440812yes—
1169#41—24no—
1170#41—1468no—
1171#41—1464no—
1172#41—1468no—
1173#41—1464no—
1174#41—1464no—
1175C2×Q8—732no—
1176C2×Q8—731no—
1177C2×Q8—1462no—
1178C2×Q8—1462no—
1179C2×Q8C22×#6440811yescharacteristic
1180C2×D4—24no—
1181C2×D4—2922no—
1182C2×D4—2921no—
1183C2×D4—2922no—
1184C2×D4—2921no—
1185C2×D4—731no—
1186C2×D4—731no—
1187C2×D4—732no—
1188C2×D4—732no—
1189C2×D4—732no—
1190C2×D4—734no—
1191C2×D4—734no—
1192C2×D4—732no—
1193C2×D4—732no—
1194C2×D4—732no—
1195C2×D4—732no—
1196C2×D4—732no—
1197C2×D4—731no—
1198C2×D4—732no—
1199C2×D4—731no—
1200C2×D4—732no—
1201C2×D4—732no—
1202C2×D4—731no—
1203C2×D4—1464no—
1204C2×D4—1462no—
1205C2×D4—1462no—
1206C2×D4—1468no—
1207C2×D4—1464no—
1208C2×D4—1464no—
1209C2×D4—1464no—
1210C2×D4—1464no—
1211C2×D4—1464no—
1212C2×D4—1468no—
1213C2×D4—1464no—
1214C2×D4C22×#6440812yes—
1215C2×D4C22×#6440812yes—
1216C2×D4C22×#6440811yescharacteristic
1217C2×D4C22×#6440811yescharacteristic
1218C2×D4C22×#6440812yes—
1219C2×D4C22×#6440811yescharacteristic
1220C22×C4—2922no—
1221C22×C4—2922no—
1222C22×C4—2921no—
1223C22×C4—2921no—
1224C22×C4—2922no—
1225C22×C4—2921no—
1226C22×C4—2922no—
1227C22×C4—2922no—
1228C22×C4—2922no—
1229C22×C4—2922no—
1230C22×C4—2922no—
1231C22×C4—2922no—
1232C22×C4—2922no—
1233C22×C4—2922no—
1234C22×C4—2922no—
1235C22×C4—2922no—
1236C22×C4—738no—
1237C22×C4—732no—
1238C22×C4—732no—
1239C22×C4—732no—
1240C22×C4—731no—
1241C22×C4—731no—
1242C22×C4—732no—
1243C22×C4—731no—
1244C22×C4—731no—
1245C22×C4—732no—
1246C22×C4—731no—
1247C22×C4—731no—
1248C22×C4—732no—
1249C22×C4—732no—
1250C22×C4—731no—
1251C22×C4—731no—
1252C22×C4—731no—
1253C22×C4—731no—
1254C22×C4—731no—
1255C22×C4—731no—
1256C22×C4—732no—
1257C22×C4—732no—
1258C22×C4—731no—
1259C22×C4—731no—
1260C22×C4—731no—
1261C22×C4—731no—
1262C22×C4—732no—
1263C22×C4—731no—
1264C22×C4—731no—
1265C22×C4—732no—
1266C22×C4—731no—
1267C22×C4—732no—
1268C22×C4—1462no—
1269C22×C4—1462no—
1270C22×C4—1462no—
1271C22×C4—1462no—
1272C22×C4—1464no—
1273C22×C4—1464no—
1274C22×C4—1462no—
1275C22×C4—1462no—
1276C22×C4—1464no—
1277C22×C4—1462no—
1278C22×C4—1464no—
1279C22×C4—1464no—
1280C22×C4—1464no—
1281C22×C4—1464no—
1282C22×C4—1464no—
1283C22×C4C22×#6440812yes—
1284C22×C4C22×#6440811yescharacteristic
1285C22×C4C22×#6440811yescharacteristic
1286C22×C4C22×#6440812yes—
1287C4⋊C4—2922no—
1288C4⋊C4—2922no—
1289C4⋊C4—2922no—
1290C4⋊C4—2921no—
1291C4⋊C4—734no—
1292C4⋊C4—732no—
1293C4⋊C4—731no—
1294C4⋊C4—731no—
1295C4⋊C4—732no—
1296C4⋊C4—732no—
1297C4⋊C4—731no—
1298C4⋊C4—731no—
1299C4⋊C4—732no—
1300C4⋊C4—1462no—
1301C4⋊C4—1464no—
1302C4⋊C4—1462no—
1303C4⋊C4—1462no—
1304C4⋊C4—1462no—
1305C4⋊C4—1462no—
1306C4⋊C4—1464no—
1307C4⋊C4—1464no—
1308C4⋊C4—1462no—
1309C4⋊C4C22×#6440811yescharacteristic
1310C4⋊C4C22×#6440811yescharacteristic
1311C4⋊C4C22×#6440812yes—
1312C22⋊C4—2922no—
1313C22⋊C4—2922no—
1314C22⋊C4—2921no—
1315C22⋊C4—2922no—
1316C22⋊C4—2922no—
1317C22⋊C4—2921no—
1318C22⋊C4—2921no—
1319C22⋊C4—2922no—
1320C22⋊C4—738no—
1321C22⋊C4—731no—
1322C22⋊C4—732no—
1323C22⋊C4—732no—
1324C22⋊C4—732no—
1325C22⋊C4—732no—
1326C22⋊C4—731no—
1327C22⋊C4—732no—
1328C22⋊C4—731no—
1329C22⋊C4—731no—
1330C22⋊C4—732no—
1331C22⋊C4—732no—
1332C22⋊C4—732no—
1333C22⋊C4—732no—
1334C22⋊C4—732no—
1335C22⋊C4—732no—
1336C22⋊C4—732no—
1337C22⋊C4—732no—
1338C22⋊C4—731no—
1339C22⋊C4—731no—
1340C22⋊C4—732no—
1341C22⋊C4—732no—
1342C22⋊C4—1462no—
1343C22⋊C4—1464no—
1344C22⋊C4—1462no—
1345C22⋊C4—1462no—
1346C22⋊C4—1464no—
1347C22⋊C4—1464no—
1348C22⋊C4—1464no—
1349C22⋊C4—1464no—
1350C22⋊C4—1464no—
1351C22⋊C4—1464no—
1352C22⋊C4—1464no—
1353C22⋊C4C22×#6440811yescharacteristic
1354C22⋊C4C22×#6440812yes—
1355C22⋊C4C22×#6440812yes—
1356C22⋊C4C22×#6440812yes—
1357C22⋊C4C22×#6440812yes—
1358C22⋊C4C22×#6440811yescharacteristic
1359C22⋊C4C22×#6440812yes—
1360C42—2922no—
1361C42—2922no—
1362C42—2922no—
1363C42—734no—
1364C42—731no—
1365C42—731no—
1366C42—731no—
1367C42—1462no—
1368C42—1462no—
1369C42—1464no—
1370C42—1462no—
1371C42—1464no—
1372C42—1464no—
1373C42—1462no—
1374C42—1464no—
1375C42—1462no—
1376C42C22×#6440811yescharacteristic
1377C23—24no—
1378C23—42no—
1379C23—42no—
1380C23—2922no—
1381C23—2922no—
1382C23—2922no—
1383C23—2922no—
1384C23—2922no—
1385C23—2922no—
1386C23—5844no—
1387C23—5844no—
1388C23—5844no—
1389C23—5844no—
1390C23—731no—
1391C23—734no—
1392C23—734no—
1393C23—732no—
1394C23—731no—
1395C23—732no—
1396C23—731no—
1397C23—1461no—
1398C23—1461no—
1399C23—1462no—
1400C23—1461no—
1401C23—1461no—
1402C23—1462no—
1403C23—1462no—
1404C23—1461no—
1405C23—1461no—
1406C23—1461no—
1407C23—1462no—
1408C23—1461no—
1409C23—1462no—
1410C23—1461no—
1411C23—1461no—
1412C23—1461no—
1413C23—1461no—
1414C23—1462no—
1415C23—1464no—
1416C23—1464no—
1417C23—1462no—
1418C23—1462no—
1419C23—1462no—
1420C23—1462no—
1421C23—1464no—
1422C23C23×#6440811yescharacteristic
1423C23C23×#6440812yes—
1424C23C23×#6440811yescharacteristic
1425C23C23×#6440812yes—
1426Q8—22no—
1427Q8—1464no—
1428Q8—1462no—
1429D4—24no—
1430D4—24no—
1431D4—22no—
1432D4—41no—
1433D4—42no—
1434D4—2921no—
1435D4—2922no—
1436D4—2921no—
1437D4—2921no—
1438D4—2922no—
1439D4—2922no—
1440D4—738no—
1441D4—734no—
1442D4—1464no—
1443D4—1464no—
1444D4—1464no—
1445D4—1464no—
1446D4—1464no—
1447D4—1464no—
1448D4—1464no—
1449D4—1462no—
1450D4D4×#6440814yescomplemented
1451C2×C4—24no—
1452C2×C4—22no—
1453C2×C4—22no—
1454C2×C4—42no—
1455C2×C4—2922no—
1456C2×C4—2922no—
1457C2×C4—2924no—
1458C2×C4—2928no—
1459C2×C4—2922no—
1460C2×C4—2924no—
1461C2×C4—2928no—
1462C2×C4—5844no—
1463C2×C4—5844no—
1464C2×C4—5844no—
1465C2×C4—5844no—
1466C2×C4—731no—
1467C2×C4—732no—
1468C2×C4—732no—
1469C2×C4—732no—
1470C2×C4—732no—
1471C2×C4—734no—
1472C2×C4—732no—
1473C2×C4—731no—
1474C2×C4—731no—
1475C2×C4—732no—
1476C2×C4—731no—
1477C2×C4—732no—
1478C2×C4—731no—
1479C2×C4—1462no—
1480C2×C4—1462no—
1481C2×C4—1461no—
1482C2×C4—1462no—
1483C2×C4—1462no—
1484C2×C4—1461no—
1485C2×C4—1461no—
1486C2×C4—1462no—
1487C2×C4—1461no—
1488C2×C4—1461no—
1489C2×C4—1461no—
1490C2×C4—1461no—
1491C2×C4—1461no—
1492C2×C4—1462no—
1493C2×C4—1464no—
1494C2×C4—1464no—
1495C2×C4—1461no—
1496C2×C4—1462no—
1497C2×C4—1462no—
1498C2×C4—1462no—
1499C2×C4—1461no—
1500C2×C4—1461no—
1501C2×C4—1462no—
1502C2×C4—1461no—
1503C2×C4—1461no—
1504C2×C4—1461no—
1505C2×C4—1461no—
1506C2×C4—1461no—
1507C2×C4—1462no—
1508C2×C4—1461no—
1509C2×C4—1462no—
1510C2×C4—1462no—
1511C2×C4—1461no—
1512C2×C4—1461no—
1513C2×C4—1461no—
1514C2×C4—1461no—
1515C2×C4—1462no—
1516C2×C4—1461no—
1517C2×C4—1462no—
1518C2×C4—1461no—
1519C2×C4—1462no—
1520C2×C4—1462no—
1521C2×C4—1461no—
1522C2×C4—1462no—
1523C2×C4—1462no—
1524C2×C4—1461no—
1525C2×C4—1461no—
1526C2×C4—1461no—
1527C2×C4—1461no—
1528C2×C4—1461no—
1529C2×C4—1464no—
1530C2×C4—1462no—
1531C2×C4—1462no—
1532C2×C4C23×#6440811yescharacteristic
1533C2×C4C23×#6440811yescharacteristic
1534C2×C4C23×#6440812yes—
1535C2×C4C23×#6440811yescharacteristic
1536C2×C4C23×#6440812yes—
1537C2×C4C23×#6440811yescharacteristic
1538C2×C4C23×#6440811yescharacteristic
1539C22—22no—
1540C22—22no—
1541C22—21no—
1542C22—21no—
1543C22—22no—
1544C22—21no—
1545C22—21no—
1546C22—22no—
1547C22—21no—
1548C22—22no—
1549C22—21no—
1550C22—84no—
1551C22—2921no—
1552C22—2921no—
1553C22—2922no—
1554C22—2922no—
1555C22—2921no—
1556C22—2921no—
1557C22—2921no—
1558C22—2921no—
1559C22—2922no—
1560C22—2922no—
1561C22—2921no—
1562C22—2921no—
1563C22—5844no—
1564C22—5844no—
1565C22—5844no—
1566C22—731no—
1567C22—731no—
1568C22—731no—
1569C22—731no—
1570C22—731no—
1571C22—731no—
1572C22—734no—
1573C22—1464no—
1574C22—1464no—
1575C22—1464no—
1576C22—1464no—
1577C22—1461no—
1578C22—1461no—
1579C22—1462no—
1580C22—1461no—
1581C22—1461no—
1582C22—1462no—
1583C22—1461no—
1584C22—1462no—
1585C22—1461no—
1586C22—1462no—
1587C22—1462no—
1588C22C2×D4×#6440814yes—
1589C22C24×#6440811yescharacteristic
1590C4—21no—
1591C4—21no—
1592C4—22no—
1593C4—21no—
1594C4—21no—
1595C4—22no—
1596C4—2922no—
1597C4—2921no—
1598C4—2921no—
1599C4—2922no—
1600C4—2921no—
1601C4—2921no—
1602C4—2922no—
1603C4—2921no—
1604C4—732no—
1605C4—1462no—
1606C4—1462no—
1607C4—1462no—
1608C4—1464no—
1609C4—1461no—
1610C4—1461no—
1611C4—1462no—
1612C4—1461no—
1613C4—1461no—
1614C4—1462no—
1615C4C2×D4×#6440812yes—
1616C2—24no—
1617C2—41no—
1618C2—42no—
1619C2—41no—
1620C2—2921no—
1621C2—2922no—
1622C2—2921no—
1623C2—731no—
1624C2—731no—
1625C2—731no—
1626C2—731no—
1627C2—1464no—
1628C2C22×D4×#6440811yescharacteristic
1629C2#2262691111yescharacteristic
1630C2H(5,𝔽2)×#6440811yescharacteristic
subgroupG/H
center, FrattiniC22C24×#64408
commutator, socleC22×C73C24×C4
Fitting#546×C73C4
prime radical#546×D73C2
cosocleC22×D73C25
hypercenter#546#64408
hypocenterC73#34292
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ #546

Complements

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

NH ≅ G/Ntype
1. C2×#17989654C2semidirect
2. C2×#41×#64408C2semidirect
3. #22626462C2semidirect
4. #22626458C2semidirect
5. #22626457C2semidirect
6. #22626456C2semidirect
7. #22626454C2semidirect
8. #22626453C2semidirect
9. #22626449C2semidirect
10. D4×C4⋊#64408C2semidirect
11. #22626437C2semidirect
12. #22626434C2semidirect
13. D4×C22⋊#64408C2semidirect
14. #22626421C2semidirect
15. #22626420C2semidirect
16. #22626418C2semidirect
17. #22626416C2semidirect
18. #123×#64408C2semidirect
19. #121×#64408C2semidirect
20. #22626385C2semidirect
21. C2×#17989537C2semidirect
22. #22626370C2semidirect
26. C2×Q8×#64408C22semidirect
27. C2×Q8×#64408C22semidirect
36. C2×D4×#64408C22semidirect
37. C2×D4×#64408C22semidirect
38. C2×D4×#64408C22semidirect
41. C2×#14556670C22semidirect
42. C2×#14556670C22semidirect
43. C22×C4⋊#64408C22semidirect
47. C22×C4×#64408C22semidirect
48. C22×C4×#64408C22semidirect
49. (C2×#64408)⋊Q8C22semidirect
50. (C2×#64408)⋊Q8C22semidirect
54. #17989539C22semidirect
55. #17989538C22semidirect
56. #17989538C22semidirect
57. #17989538C22semidirect
65. #17989537C22semidirect
66. #17989537C22semidirect
67. #17989537C22semidirect
68. #17989537C22semidirect
69. #17989537C22semidirect
70. #17989537C22semidirect
71. #17989537C22semidirect
72. #17989536C22semidirect
73. #17989536C22semidirect
74. #17989536C22semidirect
75. #17989536C22semidirect
80. #17989535C22semidirect
81. #17989535C22semidirect
82. #17989535C22semidirect
83. #17989535C22semidirect
84. #17989534C22semidirect
85. #17989534C22semidirect
86. #17989534C22semidirect
87. #17989534C22semidirect
88. #17989534C22semidirect
89. #17989534C22semidirect
90. #17989534C22semidirect
91. #17989533C22semidirect
92. #17989530C22semidirect
94. #17989529C22semidirect
95. #17989529C22semidirect
97. C4⋊C4×#64408C22semidirect
98. C4⋊C4×#64408C22semidirect
99. C4⋊C4×#64408C22semidirect
100. C4⋊C4×#64408C22semidirect
101. C4×C4⋊#64408C22semidirect
102. C4×C4⋊#64408C22semidirect
103. C22⋊C4×#64408C22semidirect
104. C22⋊C4×#64408C22semidirect
105. C22⋊C4×#64408C22semidirect
106. C22⋊C4×#64408C22semidirect
107. C22⋊C4×#64408C22semidirect
109. C4×C22⋊#64408C22semidirect
110. C4×C22⋊#64408C22semidirect
111. #17989523C22semidirect
112. C2×(C2×#64408)⋊C4C22semidirect
113. C2×(C2×#64408)⋊C4C22semidirect
116. #17989234C4semidirect
117. #17989233C4semidirect
118. #17989232C4semidirect
119. #17989231C4semidirect
120. #17989230C4semidirect
121. #17989229C4semidirect
122. #17989228C4semidirect
123. #17989227C4semidirect
124. #17989226C4semidirect
125. #17989225C4semidirect
126. #17989224C4semidirect
136. #546×C73C4semidirect
157. D4×#64408D4semidirect
237. C2×#11924029C2×C4semidirect
238. C2×#11924028C2×C4semidirect
239. C2×#11924028C2×C4semidirect
240. C2×#11924027C2×C4semidirect
241. C2×#11924027C2×C4semidirect
245. C22×D292C2×C4semidirect
246. C22×C22⋊D73C2×C4semidirect
249. C2×D4×D73C2×C4semidirect
250. C2×D4×D73C2×C4semidirect
251. C2×D4×D73C2×C4semidirect
262. #14556580C2×C4semidirect
263. #14556579C2×C4semidirect
264. #14556578C2×C4semidirect
265. #14556577C2×C4semidirect
266. #14556577C2×C4semidirect
267. #14556576C2×C4semidirect
268. #14556576C2×C4semidirect
269. #14556575C2×C4semidirect
270. #14556574C2×C4semidirect
271. #14556573C2×C4semidirect
272. #14556573C2×C4semidirect
273. #14556572C2×C4semidirect
274. #14556571C2×C4semidirect
275. #14556570C2×C4semidirect
276. #14556569C2×C4semidirect
277. #14556568C2×C4semidirect
278. #14556567C2×C4semidirect
279. #14556566C2×C4semidirect
280. #14556566C2×C4semidirect
281. #14556565C2×C4semidirect
282. #14556565C2×C4semidirect
283. #14556564C2×C4semidirect
284. #14556564C2×C4semidirect
285. #14556564C2×C4semidirect
286. #14556563C2×C4semidirect
287. #14556563C2×C4semidirect
288. #14556563C2×C4semidirect
289. #14556562C2×C4semidirect
290. #14556562C2×C4semidirect
291. #14556561C2×C4semidirect
292. #14556561C2×C4semidirect
293. #14556561C2×C4semidirect
294. #14556560C2×C4semidirect
295. #14556559C2×C4semidirect
296. #14556559C2×C4semidirect
297. #14556559C2×C4semidirect
298. C4×D292C2×C4semidirect
299. C4×D292C2×C4semidirect
300. D4×Dic73C2×C4semidirect
301. D4×Dic73C2×C4semidirect
302. #14556553C2×C4semidirect
303. #14556553C2×C4semidirect
304. C4×C22⋊D73C2×C4semidirect
305. C4×C22⋊D73C2×C4semidirect
306. C4×C22⋊D73C2×C4semidirect
307. #14556551C2×C4semidirect
308. #14556551C2×C4semidirect
309. #14556551C2×C4semidirect
313. C2×C22⋊Dic73C2×C4semidirect
314. C2×#11924005C2×C4semidirect
315. C2×#11924005C2×C4semidirect
316. C22⋊C4×D73C2×C4semidirect
317. C22⋊C4×D73C2×C4semidirect
318. C22⋊C4×D73C2×C4semidirect
319. C22⋊C4×D73C2×C4semidirect
328. C2×#41×C73C2×C4semidirect
329. C22×D4×C73C2×C4semidirect
330. #124×C73C2×C4semidirect
331. #123×C73C2×C4semidirect
332. C22⋊Q8×C73C2×C4semidirect
333. #121×C73C2×C4semidirect
334. #121×C73C2×C4semidirect
335. #120×C73C2×C4semidirect
336. C4×D4×C73C2×C4semidirect
337. C4×D4×C73C2×C4semidirect
338. C2×C22⋊C4×C73C2×C4semidirect
660. D4×C73C4×D4semidirect
681. C22⋊D73C4×D4semidirect
698. D292C4×D4semidirect
839. C73#34292semidirect
853. #546#64408semidirect
961. C2×#41C2×#64408semidirect
976. C22×D4C2×#64408semidirect
994. #124C2×#64408semidirect
1002. #123C2×#64408semidirect
1008. C22⋊Q8C2×#64408semidirect
1021. #121C2×#64408semidirect
1022. #121C2×#64408semidirect
1030. #120C2×#64408semidirect
1056. C4×D4C2×#64408semidirect
1057. C4×D4C2×#64408semidirect
1117. C2×C22⋊C4C2×#64408semidirect
1450. D4D4×#64408semidirect

Maximal subgroups

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

subgroupindex
C2×#179896542
C2×#41×#644082
#226264622
#226264582
#226264572
#226264562
#226264542
#226264532
#226264492
D4×C4⋊#644082
#226264372
#226264342
D4×C22⋊#644082
#226264212
#226264202
#226264182
#226264162
#123×#644082
#121×#644082
#226263852
C2×#179895372
#226263702
#546×D732
#3429273