Finite Group Databasebeta

← #11859104

Subgroups — #11859104

Order 1152.

863 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594954C211yesmaximal, characteristic
2#10592426C211yesmaximal, characteristic
3C3×#4720C211yesmaximal, characteristic, complemented
4C3×#4719C211yesmaximal, characteristic, complemented
5#10591153C211yesmaximal, characteristic
6#10591056C211yesmaximal, characteristic, complemented
7#10591053C211yesmaximal, characteristic, complemented
8#10590910C211yesmaximal, characteristic, complemented
9#10590703C211yesmaximal, characteristic, complemented
10#10590666C211yesmaximal, characteristic, complemented
11#10590665C211yesmaximal, characteristic, complemented
12#10590658C211yesmaximal, characteristic, complemented
13#10590647C211yesmaximal, characteristic, complemented
14#10590647C211yesmaximal, characteristic, complemented
15#10590643C211yesmaximal, characteristic, complemented
16#79375—31nomaximal
17#79334—31nomaximal
18C2×#3828C2211yescharacteristic
19C2×#3743C2211yescharacteristic
20C2×C8×C3⋊D3C2211yescharacteristic
21C3×#926C2211yescharacteristic
22C2×C3×C4×Dic3C2211yescharacteristic
23#63952C411yescharacteristic
24#63952C411yescharacteristic
25#63952C411yescharacteristic
26#63952C411yescharacteristic
27#63894C411yescharacteristic
28#63894C411yescharacteristic
29C4×#624C2211yescharacteristic
30C4×#624C2211yescharacteristic
31#63874C2211yescharacteristic
32#63874C2211yescharacteristic
33#63844C411yescharacteristic
34#63844C411yescharacteristic
35C2×#3712C2211yescharacteristic
36C2×#3710C2211yescharacteristic
37C32×C22⋊C8C2211yescharacteristic
38#63657C2211yescharacteristic
39#63647C2211yescharacteristic
40#63647C2211yescharacteristic
41C3×#830C2211yescharacteristic
42C3×#830C2211yescharacteristic
43C3×#815C2211yescharacteristic
44C3×#815C2211yescharacteristic
45C3×#815C2211yescharacteristic
46C3×Dic3⋊C8C2211yescharacteristic
47C3×Dic3⋊C8C2211yescharacteristic
48C3×Dic3⋊C8C2211yescharacteristic
49C3×Dic3⋊C8C2211yescharacteristic
50C3×C8×Dic3C2211yescharacteristic
51Dic3⋊(C3⋊C8)C2211yescharacteristic
52Dic3⋊(C3⋊C8)C2211yescharacteristic
53Dic3⋊(C3⋊C8)C2211yescharacteristic
54Dic3⋊(C3⋊C8)C2211yescharacteristic
55#63557C2211yescharacteristic
56#63557C2211yescharacteristic
57#63554C2211yescharacteristic
58Dic3×C3⋊C8C2211yescharacteristic
59Dic3×C3⋊C8C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61#5522—31no—
62C4×#235—31no—
63C3×#433—31no—
64C3×#432—31no—
65#5000—31no—
66#4925—31no—
67#4840—31no—
68#4840—31no—
69#4837—31no—
70#4837—31no—
71#4835—31no—
72#4833—31no—
73D3×C4⋊C8—31no—
74D3×C4⋊C8—31no—
75#4727—31no—
76#4727—31no—
77#4727—31no—
78#4727—31no—
79#4727—61no—
80#4720—31no—
81#4720D311yescharacteristic, complemented
82#4719D311yescharacteristic, complemented
83#4718—31no—
84#4709—31no—
85#4709—31no—
86#4708—31no—
87#4708—31no—
88#4708—31no—
89#4705—31no—
90#4689—31no—
91#4685—31no—
92C22×C32×C4C2311yescharacteristic
93C2×#638C2×C411yescharacteristic
94C2×#638C2×C411yescharacteristic
95#3828—22no—
96#3828—22no—
97C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
98C2×C4×C3⋊D3C2311yescharacteristic
99C2×C4×C3⋊D3C2311yescharacteristic
100C2×#634C2×C411yescharacteristic
101C22×C3×Dic3C2×C411yescharacteristic
102C22×C3×Dic3C2×C411yescharacteristic
103C2×#624C2×C411yescharacteristic
104C2×#624C2×C411yescharacteristic
105C2×#624C2×C411yescharacteristic
106C2×#624C2×C411yescharacteristic
107C2×C32×C8C2311yescharacteristic
108C2×C32×C8C2311yescharacteristic
109C2×C3⋊(C3⋊C8)C2311yescharacteristic
110C2×C3⋊(C3⋊C8)C2311yescharacteristic
111#3743—22no—
112C8×C3⋊D3—22no—
113C3×#217C2×C411yescharacteristic
114C3×#217C2×C411yescharacteristic
115C3×C4⋊Dic3C2×C411yescharacteristic
116C3×C4⋊Dic3C2×C411yescharacteristic
117C3×C4×Dic3C2×C411yescharacteristic
118C3×C4×Dic3C2×C411yescharacteristic
119C3×C4×Dic3C2311yescharacteristic
120C3×C4×Dic3C2311yescharacteristic
121C3×C4×Dic3C2311yescharacteristic
122C3×C4×Dic3C2311yescharacteristic
123C2×C3×C3⋊C8C2311yescharacteristic
124C2×C3×C3⋊C8C2311yescharacteristic
125C2×C3×C3⋊C8C2311yescharacteristic
126C2×C3×C3⋊C8C2311yescharacteristic
127#3724C2×C411yescharacteristic
128#3724C2×C411yescharacteristic
129#3724C2×C411yescharacteristic
130#3724C2×C411yescharacteristic
131#3722C2×C411yescharacteristic
132#3722C2×C411yescharacteristic
133#3722C2×C411yescharacteristic
134#3722C2×C411yescharacteristic
135Dic32C2×C411yescharacteristic
136Dic32C2×C411yescharacteristic
137Dic32C2×C411yescharacteristic
138Dic32C2×C411yescharacteristic
139#3712—22no—
140#3710—22no—
141#2925—91noSylow
142C2×#235—31no—
143C2×#235—31no—
144C2×#235—61no—
145C3×#117—31no—
146C2×C3×C42—31no—
147C4×#67—31no—
148C4×#67—31no—
149C4×#67—31no—
150C4×#67—31no—
151#926C2×D311yescharacteristic
152C2×C4×Dic3C2×D311yescharacteristic
153C2×ΓL(1,𝔽25)—31no—
154C2×ΓL(1,𝔽25)—31no—
155C2×ΓL(1,𝔽25)—31no—
156C2×ΓL(1,𝔽25)—31no—
157C2×ΓL(1,𝔽25)—61no—
158C2×D3×C8—31no—
159C2×D3×C8—31no—
160C2×D3×C8—31no—
161C2×D3×C8—31no—
162C2×D3×C8—61no—
163#893—31no—
164#893—31no—
165#887—31no—
166#887—31no—
167#67⋊C4—31no—
168#67⋊C4—31no—
169#67⋊C4—31no—
170#67⋊C4—31no—
171C4×D12—31no—
172C4×D12—31no—
173#872—31no—
174#872—31no—
175#872—31no—
176#872—31no—
177C42×D3—31no—
178C42×D3—31no—
179C42×D3—31no—
180C42×D3—31no—
181C4×Dic6—31no—
182C4×Dic6—31no—
183C3×C4⋊C8—31no—
184C3×C4⋊C8—31no—
185C3×C4⋊C8—31no—
186C3×C4⋊C8—31no—
187C3×C22⋊C8—21no—
188C3×C22⋊C8—31no—
189C3×C22⋊C8—31no—
190C3×C22⋊C8C2×D311yescharacteristic
191C3×C22⋊C8C2×D311yescharacteristic
192C3×#97—31no—
193C3×#97—31no—
194C3×#97—31no—
195C3×C4×C8—31no—
196#830—31no—
197#830—31no—
198#830—61no—
199#830C2×D311yescharacteristic
200#830C2×D311yescharacteristic
201(C2×D3)⋊C8—31no—
202(C2×D3)⋊C8—31no—
203(C2×D3)⋊C8—31no—
204(C2×D3)⋊C8—31no—
205(C2×D3)⋊C8—31no—
206(C2×D3)⋊C8—31no—
207(C2×D3)⋊C8—31no—
208(C2×D3)⋊C8—31no—
209(C2×D3)⋊C8—61no—
210(C2×D3)⋊C8—61no—
211#815—31no—
212#815C2×D311yescharacteristic
213#815C2×D311yescharacteristic
214#815C2×D311yescharacteristic
215Dic3⋊C8—31no—
216Dic3⋊C8—31no—
217Dic3⋊C8—31no—
218Dic3⋊C8—31no—
219Dic3⋊C8C2×D311yescharacteristic
220Dic3⋊C8C2×D311yescharacteristic
221Dic3⋊C8C2×D311yescharacteristic
222Dic3⋊C8C2×D311yescharacteristic
223C8×Dic3—31no—
224C8×Dic3—31no—
225C8×Dic3—31no—
226C8×Dic3C2×D311yescharacteristic
227C4⋊(C3⋊C8)—31no—
228C4⋊(C3⋊C8)—31no—
229C4⋊(C3⋊C8)—31no—
230C4⋊(C3⋊C8)—31no—
231#803—31no—
232C4×C3⋊C8—31no—
233C4×C3⋊C8—31no—
234C4×C3⋊C8—31no—
235C23×C32C22×C411yescharacteristic
236C22×C3⋊D3C22×C411yescharacteristic
237C22×C3⋊D3C22×C411yescharacteristic
238C2×C32×C4—21no—
239C2×C32×C4—21no—
240C2×C32×C4C22×C411yescharacteristic
241C2×C32×C4C2411yescharacteristic
242#638—22no—
243#638—22no—
244C2×C3⋊Dic3C22×C411yescharacteristic
245C2×C3⋊Dic3C22×C411yescharacteristic
246C4⋊(C3⋊D3)—22no—
247C4×C3⋊D3—21no—
248C4×C3⋊D3—21no—
249C4×C3⋊D3#4112yes—
250C4×C3⋊D3#4112yes—
251#634—22no—
252C2×C3×Dic3—22no—
253C2×C3×Dic3—41no—
254C2×C3×Dic3C22×C411yescharacteristic
255C2×C3×Dic3C22×C411yescharacteristic
256C2×C3×Dic3C22×C411yescharacteristic
257C2×C3×Dic3C22×C411yescharacteristic
258C2×C3×Dic3C22×C411yescharacteristic
259C2×C3×Dic3C22×C411yescharacteristic
260C2×C3×Dic3C22×C411yescharacteristic
261C2×C3×Dic3C22×C411yescharacteristic
262#624—22no—
263#624—22no—
264#624—41no—
265#624—41no—
266C32×C8—21no—
267C32×C8—21no—
268C3⋊(C3⋊C8)—21no—
269C3⋊(C3⋊C8)—21no—
270C3×C3⋊C8—21no—
271C3×C3⋊C8—21no—
272C3×C3⋊C8—21no—
273C3×C3⋊C8—21no—
274C4×#41—91no—
275#433—31no—
276#433—91no—
277#433—91no—
278#433—91no—
279#432—31no—
280#432—91no—
281#431—91no—
282#431—91no—
283#423—91no—
284C2×C4⋊C8—91no—
285#408—91no—
286#408—91no—
287#405—91no—
288#405—91no—
289C22×C3×C4—21no—
290C22×C3×C4—31no—
291C22×C3×C4—31no—
292C22×C3×C4C22×D311yescharacteristic
293C22×C3×C4C22×D311yescharacteristic
294C2×#67—31no—
295C2×#67—31no—
296C2×#67—31no—
297C2×#67—31no—
298C2×#67—61no—
299C2×#67—61no—
300C22×Dic3C4×D311yescharacteristic
301C22×Dic3C4×D311yescharacteristic
302#235—62no—
303#235—62no—
304#235—62no—
305#235—62no—
306#235—122no—
307#235—122no—
308C2×D12—31no—
309C2×D12—31no—
310C2×D12—61no—
311C2×C4×D3—31no—
312C2×C4×D3—31no—
313C2×C4×D3—31no—
314C2×C4×D3—31no—
315C2×C4×D3—31no—
316C2×C4×D3—31no—
317C2×C4×D3—31no—
318C2×C4×D3—31no—
319C2×C4×D3—31no—
320C2×C4×D3—31no—
321C2×C4×D3—31no—
322C2×C4×D3—31no—
323C2×C4×D3—61no—
324C2×C4×D3—61no—
325C2×Dic6—31no—
326C2×Dic6—31no—
327C2×Dic6—61no—
328C2×C3×C8—21no—
329C2×C3×C8—21no—
330C2×C3×C8—31no—
331C2×C3×C8—31no—
332C2×C3×C8—31no—
333C2×C3×C8—31no—
334C2×C3×C8C22×D311yescharacteristic
335C2×C3×C8C22×D311yescharacteristic
336C2×C3×C8C22×D311yescharacteristic
337C2×C3×C8C22×D311yescharacteristic
338C3×C4⋊C4—31no—
339C3×C4⋊C4—31no—
340C3×C22⋊C4—31no—
341C3×C22⋊C4—31no—
342C3×C42—31no—
343C3×C42—31no—
344C3×C42—31no—
345C3×C42—31no—
346C3×C42—31no—
347C3×C42—31no—
348#217C4×D311yescharacteristic
349#217C4×D311yescharacteristic
350(C2×D3)⋊C4—31no—
351(C2×D3)⋊C4—31no—
352(C2×D3)⋊C4—31no—
353(C2×D3)⋊C4—31no—
354(C2×D3)⋊C4—31no—
355(C2×D3)⋊C4—31no—
356(C2×D3)⋊C4—31no—
357(C2×D3)⋊C4—31no—
358C4⋊Dic3C4×D311yescharacteristic
359C4⋊Dic3C4×D311yescharacteristic
360Dic3⋊C4—31no—
361Dic3⋊C4—31no—
362Dic3⋊C4—31no—
363Dic3⋊C4—31no—
364Dic3⋊C4—31no—
365Dic3⋊C4—31no—
366Dic3⋊C4—31no—
367Dic3⋊C4—31no—
368C4×Dic3—31no—
369C4×Dic3—31no—
370C4×Dic3—31no—
371C4×Dic3—31no—
372C4×Dic3—31no—
373C4×Dic3—31no—
374C4×Dic3—31no—
375C4×Dic3—31no—
376C4×Dic3C4×D311yescharacteristic
377C4×Dic3C4×D311yescharacteristic
378C4×Dic3C22×D311yescharacteristic
379C4×Dic3C22×D311yescharacteristic
380C4×Dic3C22×D311yescharacteristic
381C4×Dic3C22×D311yescharacteristic
382C2×C3⋊C8—31no—
383C2×C3⋊C8—31no—
384C2×C3⋊C8—31no—
385C2×C3⋊C8—31no—
386C2×C3⋊C8—61no—
387C2×C3⋊C8—61no—
388C2×C3⋊C8C22×D311yescharacteristic
389C2×C3⋊C8C22×D311yescharacteristic
390C2×C3⋊C8C22×D311yescharacteristic
391C2×C3⋊C8C22×D311yescharacteristic
392ΓL(1,𝔽25)—62no—
393ΓL(1,𝔽25)—62no—
394ΓL(1,𝔽25)—62no—
395ΓL(1,𝔽25)—62no—
396ΓL(1,𝔽25)—122no—
397D3×C8—62no—
398D3×C8—62no—
399D3×C8—62no—
400D3×C8—62no—
401D3×C8—122no—
402C22×C32—21no—
403C22×C32—21no—
404C22×C32—21no—
405C22×C32C23×C411yescharacteristic
406C2×C3⋊D3—21no—
407C2×C3⋊D3—21no—
408C2×C3⋊D3—21no—
409C2×C3⋊D3—21no—
410C2×C3⋊D3—21no—
411C2×C3⋊D3#11712yes—
412C32×C4—21no—
413C32×C4C2×#4111yescharacteristic
414C32×C4C2×#4111yescharacteristic
415C3⋊Dic3—21no—
416C3⋊Dic3#11712yes—
417C3×Dic3—21no—
418C3×Dic3—21no—
419C3×Dic3—21no—
420C3×Dic3—21no—
421C3×Dic3—21no—
422C3×Dic3—21no—
423C3×Dic3—21no—
424C3×Dic3#13112yes—
425C2×#41—91no—
426C2×M16—91no—
427C2×M16—91no—
428C22×C8—91no—
429C22×C8—91no—
430C4×Q8—91no—
431C4×Q8—91no—
432C4×D4—91no—
433C4×D4—91no—
434C4×D4—91no—
435C4×D4—91no—
436C4×D4—91no—
437C4×D4—91no—
438#117—31no—
439#117—91no—
440#117—91no—
441C2×C42—31no—
442C2×C42—91no—
443C2×C42—91no—
444C4⋊C8—31no—
445C4⋊C8—31no—
446C4⋊C8—31no—
447C4⋊C8—31no—
448C4⋊C8—91no—
449C4⋊C8—91no—
450C4⋊C8—91no—
451C4⋊C8—91no—
452C22⋊C8—31no—
453C22⋊C8—31no—
454C22⋊C8—91no—
455C22⋊C8—91no—
456C22⋊C8—91no—
457C22⋊C8—91no—
458C22⋊C8—91no—
459C22⋊C8D3211yescharacteristic
460#97—31no—
461#97—31no—
462#97—31no—
463#97—91no—
464C4×C8—31no—
465C4×C8—91no—
466C4×C8—91no—
467C4×C8—91no—
468C23×C3—21no—
469C23×C3C2×C4×D311yescharacteristic
470C23×C3C2×C4×D311yescharacteristic
471C22×D3—31no—
472C22×D3—31no—
473C22×D3—31no—
474C22×D3—31no—
475C22×D3—61no—
476C22×D3—61no—
477C2×C3×C4—21no—
478C2×C3×C4—21no—
479C2×C3×C4—21no—
480C2×C3×C4—21no—
481C2×C3×C4—21no—
482C2×C3×C4—21no—
483C2×C3×C4—31no—
484C2×C3×C4—31no—
485C2×C3×C4—31no—
486C2×C3×C4—31no—
487C2×C3×C4—31no—
488C2×C3×C4—31no—
489C2×C3×C4—31no—
490C2×C3×C4—31no—
491C2×C3×C4—41no—
492C2×C3×C4—41no—
493C2×C3×C4—62no—
494C2×C3×C4—121no—
495C2×C3×C4C2×C4×D311yescharacteristic
496C2×C3×C4C2×C4×D311yescharacteristic
497C2×C3×C4C23×D311yescharacteristic
498C2×C3×C4C23×D311yescharacteristic
499#67—62no—
500#67—62no—
501#67—62no—
502#67—62no—
503#67—122no—
504#67—122no—
505C2×Dic3—22no—
506C2×Dic3—31no—
507C2×Dic3—31no—
508C2×Dic3—31no—
509C2×Dic3—31no—
510C2×Dic3—41no—
511C2×Dic3—61no—
512C2×Dic3—61no—
513C2×Dic3C2×C4×D311yescharacteristic
514C2×Dic3C2×C4×D311yescharacteristic
515C2×Dic3C2×C4×D311yescharacteristic
516C2×Dic3C2×C4×D311yescharacteristic
517C2×Dic3C2×C4×D311yescharacteristic
518C2×Dic3C2×C4×D311yescharacteristic
519C2×Dic3C2×C4×D311yescharacteristic
520C2×Dic3C2×C4×D311yescharacteristic
521D12—62no—
522D12—62no—
523D12—122no—
524C4×D3—32no—
525C4×D3—32no—
526C4×D3—32no—
527C4×D3—32no—
528C4×D3—62no—
529C4×D3—62no—
530C4×D3—62no—
531C4×D3—62no—
532C4×D3—61no—
533C4×D3—61no—
534C4×D3—61no—
535C4×D3—61no—
536C4×D3—62no—
537C4×D3—62no—
538C4×D3—121no—
539C4×D3—121no—
540C4×D3—121no—
541C4×D3—121no—
542C4×D3—121no—
543C4×D3—121no—
544Dic6—62no—
545Dic6—62no—
546Dic6—122no—
547C3×C8—21no—
548C3×C8—21no—
549C3×C8—21no—
550C3×C8—21no—
551C3×C8—41no—
552C3×C8—41no—
553C3×C8—61no—
554C3×C8—61no—
555C3×C8—61no—
556C3×C8—61no—
557C3⋊C8—21no—
558C3⋊C8—21no—
559C3⋊C8—21no—
560C3⋊C8—21no—
561C3⋊C8—61no—
562C3⋊C8—61no—
563C3⋊C8—61no—
564C3⋊C8—61no—
565C3⋊C8—121no—
566C3⋊C8—121no—
567C2×C32—41no—
568C2×C32C2×#11711yescharacteristic
569C2×C32C2×#13111yescharacteristic
570C2×C32#56811yescharacteristic
571C3⋊D3—22no—
572C3⋊D3—41no—
573#41—182no—
574#41—182no—
575C2×Q8—91no—
576C2×D4—91no—
577C2×D4—91no—
578C2×D4—91no—
579C22×C4—31no—
580C22×C4—31no—
581C22×C4—91no—
582C22×C4—91no—
583C22×C4—91no—
584C22×C4—91no—
585C22×C4—91no—
586C22×C4—91no—
587C22×C4C2×D3211yescharacteristic
588M16—182no—
589M16—182no—
590C2×C8—31no—
591C2×C8—31no—
592C2×C8—31no—
593C2×C8—31no—
594C2×C8—91no—
595C2×C8—91no—
596C2×C8—182no—
597C2×C8—182no—
598C2×C8C2×D3211yescharacteristic
599C2×C8C2×D3211yescharacteristic
600C4⋊C4—31no—
601C4⋊C4—31no—
602C4⋊C4—91no—
603C4⋊C4—91no—
604C4⋊C4—91no—
605C4⋊C4—91no—
606C22⋊C4—31no—
607C22⋊C4—31no—
608C22⋊C4—91no—
609C22⋊C4—91no—
610C22⋊C4—91no—
611C22⋊C4—91no—
612C42—31no—
613C42—31no—
614C42—31no—
615C42—31no—
616C42—31no—
617C42—31no—
618C42—91no—
619C42—91no—
620C42—91no—
621C42—91no—
622C22×C3—21no—
623C22×C3—21no—
624C22×C3—21no—
625C22×C3—21no—
626C22×C3—21no—
627C22×C3—21no—
628C22×C3—21no—
629C22×C3—41no—
630C22×C3—41no—
631C22×C3—41no—
632C22×C3C22×C4×D311yescharacteristic
633C22×C3C22×C4×D311yescharacteristic
634C2×D3—32no—
635C2×D3—32no—
636C2×D3—62no—
637C2×D3—61no—
638C2×D3—61no—
639C2×D3—61no—
640C2×D3—61no—
641C2×D3—61no—
642C2×D3—61no—
643C2×D3—61no—
644C2×D3—61no—
645C2×D3—61no—
646C2×D3—61no—
647C2×D3—121no—
648C2×D3—121no—
649C2×D3—121no—
650C2×D3—121no—
651C2×D3—121no—
652C3×C4—21no—
653C3×C4—21no—
654C3×C4—21no—
655C3×C4—21no—
656C3×C4—32no—
657C3×C4—41no—
658C3×C4—61no—
659C3×C4—61no—
660C3×C4—61no—
661C3×C4—61no—
662C3×C4—61no—
663C3×C4—61no—
664C3×C4—61no—
665C3×C4D3×#4111yescharacteristic
666C3×C4D3×#4111yescharacteristic
667C3×C4D3×#4111yescharacteristic
668C3×C4D3×#4111yescharacteristic
669Dic3—21no—
670Dic3—21no—
671Dic3—21no—
672Dic3—21no—
673Dic3—21no—
674Dic3—21no—
675Dic3—21no—
676Dic3—32no—
677Dic3—32no—
678Dic3—62no—
679Dic3—61no—
680Dic3—61no—
681Dic3—121no—
682Dic3#90712yes—
683C32#292511yescharacteristic, complemented, Sylow
684C23—91no—
685C23—91no—
686C23C4×D3211yescharacteristic
687Q8—182no—
688D4—182no—
689D4—182no—
690D4—182no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—31no—
694C2×C4—31no—
695C2×C4—31no—
696C2×C4—31no—
697C2×C4—31no—
698C2×C4—31no—
699C2×C4—31no—
700C2×C4—31no—
701C2×C4—62no—
702C2×C4—91no—
703C2×C4—92no—
704C2×C4—92no—
705C2×C4—91no—
706C2×C4—121no—
707C2×C4—182no—
708C2×C4—182no—
709C2×C4—181no—
710C2×C4—181no—
711C2×C4—361no—
712C2×C4—361no—
713C2×C4C4×D3211yescharacteristic
714C2×C4C22×D3211yescharacteristic
715C8—21no—
716C8—21no—
717C8—61no—
718C8—61no—
719C8—61no—
720C8—61no—
721C8—181no—
722C8—181no—
723C2×C3—21no—
724C2×C3—21no—
725C2×C3—21no—
726C2×C3—41no—
727C2×C3—41no—
728C2×C3—81no—
729C2×C3D3×#11711yescharacteristic
730C2×C3D3×#11711yescharacteristic
731C2×C3C2×#90711yescharacteristic
732C2×C3#574511yescharacteristic
733C2×C3D3×#13111yescharacteristic
734C2×C3#575011yescharacteristic
735D3—62no—
736D3—62no—
737D3—122no—
738D3—121no—
739D3—121no—
740D3—241no—
741C22—21no—
742C22—21no—
743C22—21no—
744C22—92no—
745C22—181no—
746C22—181no—
747C22—181no—
748C22—181no—
749C22—181no—
750C22C2×C4×D3211yescharacteristic
751C4—21no—
752C4—32no—
753C4—61no—
754C4—61no—
755C4—61no—
756C4—61no—
757C4—61no—
758C4—61no—
759C4—61no—
760C4—92no—
761C4—181no—
762C4#6431211yescharacteristic
763C4#6431211yescharacteristic
764C3—21no—
765C3#7933411yescharacteristic, complemented
766C3#7937511yescharacteristic, complemented
767C2—41no—
768C2—182no—
769C2—361no—
770C2#1059405211yescharacteristic
771C2#1059466811yescharacteristic
772C2D3×#90711yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×D32
commutator, socleC22×C32C23×C4
FittingC32×C22⋊C8C22
prime radicalC2×#3828C22
cosocleC2×C32×C4C24
hypercenterC22⋊C8D32
hypocenterC32#2925
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
3. C3×#4720C2semidirect
4. C3×#4719C2semidirect
6. #10591056C2semidirect
7. #10591053C2semidirect
8. #10590910C2semidirect
9. #10590703C2semidirect
10. #10590666C2semidirect
11. #10590665C2semidirect
12. #10590658C2semidirect
13. #10590647C2semidirect
14. #10590647C2semidirect
15. #10590643C2semidirect
81. #4720D3semidirect
82. #4719D3semidirect
683. C32#2925semidirect
765. C3#79334semidirect
766. C3#79375semidirect

Maximal subgroups

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

subgroupindex
#105949542
#105924262
C3×#47202
C3×#47192
#105911532
#105910562
#105910532
#105909102
#105907032
#105906662
#105906652
#105906582
#105906472
#105906432
#793753
#793343