Finite Group Databasebeta

← #11887225

Subgroups — #11887225

Order 1152.

883 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595070C211yesmaximal, characteristic
2#10594970C211yesmaximal, characteristic, complemented
3#10592424C211yesmaximal, characteristic, complemented
4C3×#4737C211yesmaximal, characteristic, complemented
5C3×#4733C211yesmaximal, characteristic, complemented
6#10591179C211yesmaximal, characteristic, complemented
7#10591083C211yesmaximal, characteristic, complemented
8#10590943C211yesmaximal, characteristic, complemented
9#10590940C211yesmaximal, characteristic, complemented
10#10590868C211yesmaximal, characteristic, complemented
11#10590857C211yesmaximal, characteristic, complemented
12#10590797C211yesmaximal, characteristic, complemented
13#10590780C211yesmaximal, characteristic, complemented
14#10590775C211yesmaximal, characteristic, complemented
15#10590686C211yesmaximal, characteristic, complemented
16#81381—31nomaximal
17#80246—31nomaximal
18C2×C3×#235C2211yescharacteristic
19C2×#3802C2211yescharacteristic
20C4×#638C2211yescharacteristic
21C22×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
22C2×C8×C3⋊D3C2211yescharacteristic
23C3×#930C2211yescharacteristic
24C3×#926C2211yescharacteristic, complemented
25C3×#924C2211yescharacteristic, complemented
26C2×C3×Dic12C2211yescharacteristic, complemented
27C2×C3×#204C2211yescharacteristic
28#63983—21no—
29#63975—21no—
30#63970—21no—
31#63956—21no—
32D3×(C2×D3)⋊C4—21no—
33#63905—21no—
34#63900C2211yescharacteristic
35#63898C2211yescharacteristic
36#63872C2211yescharacteristic, complemented
37#63871C2211yescharacteristic
38#63871C2211yescharacteristic
39#63867—21no—
40#63863C2211yescharacteristic
41#63843C2211yescharacteristic, complemented
42#63836—21no—
43C2×#3715C2211yescharacteristic
44C32×C22⋊C8C2211yescharacteristic, complemented
45#63647C2211yescharacteristic
46#63641C2211yescharacteristic, complemented
47C8×C3⋊Dic3C2211yescharacteristic, complemented
48C3×#821C2211yescharacteristic
49C3×#821C2211yescharacteristic
50C3×#821C2211yescharacteristic
51C3×#818C2211yescharacteristic, complemented
52C3×#817C2211yescharacteristic, complemented
53C3×#816C2211yescharacteristic, complemented
54#63574C2211yescharacteristic, complemented
55#63565C2211yescharacteristic, complemented
56#63565C2211yescharacteristic, complemented
57#63565C2211yescharacteristic, complemented
58#63562C2211yescharacteristic
59#63562C2211yescharacteristic
60#63562C2211yescharacteristic
61#5829—31no—
62#5639—31no—
63#5612—31no—
64#5529—31no—
65C3×#482—31no—
66C3×#452—31no—
67#5233—31no—
68#5188—31no—
69#5185—31no—
70#5169—31no—
71Dic3×SD16—31no—
72#5048—31no—
73#5041—31no—
74#5002—31no—
75#4891—31no—
76#4887—31no—
77#4862—31no—
78#4852—31no—
79#4805—31no—
80#4800—31no—
81#4776—31no—
82D3×#102—31no—
83D3×#102—31no—
84#4768—31no—
85#4767—31no—
86#4766—31no—
87#4737D311yescharacteristic, complemented
88#4733D311yescharacteristic, complemented
89#67⋊C8—31no—
90#67⋊C8—31no—
91#67⋊C8—61no—
92C22×D32—21no—
93C22×C32×C4C2311yescharacteristic
94C2×#638D411yescharacteristic
95C2×C4×C3⋊D3C2311yescharacteristic
96C2×C3×#67—21no—
97C2×C3×#67—21no—
98C3×#235—22no—
99C3×#235—41no—
100C2×C3×D12C2311yescharacteristic
101C2×C3×D12C2311yescharacteristic
102C2×C3×C4×D3—21no—
103C2×C3×Dic6C2311yescharacteristic
104C2×C3×Dic6C2311yescharacteristic
105C2×#625—21no—
106C2×#624—21no—
107C2×D3×Dic3—21no—
108#3802—22no—
109#3802—41no—
110C2×C32×C8C2311yescharacteristic
111C2×C32×C8C2311yescharacteristic
112#3757D411yescharacteristic
113#3752D411yescharacteristic
114#3750D411yescharacteristic
115C4×C3⋊Dic3C2311yescharacteristic
116C2×C3⋊(C3⋊C8)—41no—
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119C8×C3⋊D3—41no—
120C3×#217—21no—
121C3×#217—21no—
122C3×(C2×D3)⋊C4—21no—
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×Dic3⋊C4—21no—
128C3×C4×Dic3—21no—
129C3×Dic12—41no—
130C3×#204—22no—
131#3724—21no—
132Dic3⋊Dic3—21no—
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3—21no—
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3—21no—
137#3722—21no—
138#3722—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141(C2×D3)⋊Dic3—21no—
142Dic32—21no—
143#3715—41no—
144#3296—91noSylow
145C2×C3×#41—31no—
146C2×D3×D4—31no—
147C2×D3×D4—31no—
148C2×#235C2×D311yescharacteristic
149C2×C3×Q16—31no—
150C2×C3×SD16—31no—
151C3×C22⋊Q8—31no—
152C3×#121—31no—
153C3×#117—31no—
154#947—31no—
155#946—31no—
156#946—31no—
157Q8×Dic3—31no—
158C2×#215—31no—
159#939—61no—
160#938—61no—
161#937—61no—
162#937—61no—
163#936—31no—
164D4×Dic3—31no—
165C2×#214—31no—
166#930C2×D311yescharacteristic
167#929—61no—
168C4×#67—31no—
169C4×#67—31no—
170C4×#67—61no—
171C2×(C2×D3)⋊C4—61no—
172#926C2×D311yescharacteristic, complemented
173#924C2×D311yescharacteristic, complemented
174C22×C3⋊C8—31no—
175C22×C3⋊C8—31no—
176C22×C3⋊C8—61no—
177C2×Dic12C2×D311yescharacteristic, complemented
178C2×#204C2×D311yescharacteristic
179C2×D3×C8—31no—
180C2×D3×C8—31no—
181C2×D3×C8—61no—
182#897—31no—
183#897—31no—
184#893—31no—
185#892—61no—
186D3×C4⋊C4—31no—
187D3×C4⋊C4—31no—
188#890—31no—
189#890—31no—
190#889—61no—
191#887—31no—
192#883—61no—
193#883—61no—
194#883—61no—
195D3×C22⋊C4—61no—
196#879—61no—
197#879—61no—
198#872—61no—
199#870—61no—
200C3×#107—31no—
201C3×#106—31no—
202C3×#103—31no—
203C3×#102—31no—
204C3×#102—31no—
205C3×#102—31no—
206C3×C22⋊C8—21no—
207C3×C22⋊C8C2×D311yescharacteristic, complemented
208C3×C22⋊C8C2×D311yescharacteristic, complemented
209#835—31no—
210#835—31no—
211#835—31no—
212#832—31no—
213#832—31no—
214#832—31no—
215#821C2×D311yescharacteristic
216#821C2×D311yescharacteristic
217#821C2×D311yescharacteristic
218(C2×D3)⋊C8—31no—
219(C2×D3)⋊C8—31no—
220(C2×D3)⋊C8—61no—
221#818C2×D311yescharacteristic, complemented
222#817C2×D311yescharacteristic, complemented
223#816C2×D311yescharacteristic, complemented
224Dic3⋊C8—31no—
225Dic3⋊C8—31no—
226Dic3⋊C8—61no—
227C8×Dic3—31no—
228C8×Dic3—31no—
229C8×Dic3—61no—
230#810—31no—
231#810—31no—
232#810—31no—
233#809—31no—
234#809—31no—
235#809—31no—
236#808—31no—
237#808—31no—
238C23×C32C2×D411yescharacteristic
239C22×C3⋊D3C2×D411yescharacteristic
240C22×C3×D3—21no—
241C22×C3×D3—21no—
242C2×D32—42no—
243C2×D32—42no—
244C2×D32—81no—
245C2×C32×C4—21no—
246C2×C32×C4—21no—
247C2×C32×C4C2×D411yescharacteristic
248C2×C32×C4C2411yescharacteristic
249#638—22no—
250C2×C3⋊Dic3C2×D411yescharacteristic
251C2×C3⋊Dic3C2×D411yescharacteristic
252C2×C3⋊Dic3C2×D411yescharacteristic
253C4×C3⋊D3—21no—
254C4×C3⋊D3—21no—
255C3×#67—42no—
256C3×#67—81no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C3×D12—21no—
264C3×D12—21no—
265C3×D12—21no—
266C3×D12#4112yes—
267C3×C4×D3—42no—
268C3×Dic6—21no—
269C3×Dic6—21no—
270C3×Dic6—21no—
271C3×Dic6—21no—
272#625—42no—
273#624—42no—
274D3×Dic3—81no—
275C32×C8—21no—
276C32×C8—21no—
277C3⋊(C3⋊C8)—21no—
278C3⋊(C3⋊C8)—21no—
279#552—91no—
280#546—91no—
281#488—91no—
282#483—91no—
283#482—31no—
284#478—91no—
285#467—91no—
286#465—91no—
287#464—91no—
288#452—31no—
289#450—91no—
290C4×SD16—91no—
291C8×D4—91no—
292#416—91no—
293C2×#102—91no—
294C23×D3—61no—
295C23×D3—61no—
296C3×#41—62no—
297C3×#41—121no—
298C2×C3×Q8—31no—
299C2×C3×Q8—31no—
300C2×C3×D4—31no—
301C2×C3×D4—31no—
302C2×C3×D4—61no—
303C2×C3×D4—61no—
304C22×C3×C4—21no—
305C22×C3×C4—61no—
306C22×C3×C4C22×D311yescharacteristic
307C22×C3×C4C22×D311yescharacteristic
308C2×#67—21no—
309C2×#67—21no—
310C2×#67—31no—
311C2×#67—31no—
312C2×#67—61no—
313C2×#67—61no—
314C2×#67—61no—
315C22×Dic3—61no—
316D3×D4—62no—
317D3×D4—62no—
318D3×D4—121no—
319D3×D4—121no—
320#235—22no—
321#235—41no—
322C2×D12C22×D311yescharacteristic
323C2×D12C22×D311yescharacteristic
324C2×C4×D3—21no—
325C2×C4×D3—31no—
326C2×C4×D3—31no—
327C2×C4×D3—61no—
328C2×C4×D3—61no—
329C2×C4×D3—61no—
330C2×C4×D3—61no—
331C2×Dic6C22×D311yescharacteristic
332C2×Dic6C22×D311yescharacteristic
333C3×Q16—121no—
334C3×SD16—62no—
335C2×C3×C8—21no—
336C2×C3×C8—21no—
337C2×C3×C8C22×D311yescharacteristic
338C2×C3×C8C22×D311yescharacteristic
339C2×C3×C8C22×D311yescharacteristic
340C2×C3×C8C22×D311yescharacteristic
341C3×C4⋊C4—31no—
342C3×C4⋊C4—31no—
343C3×C4⋊C4—31no—
344C3×C4⋊C4—31no—
345C3×C4⋊C4—61no—
346C3×C22⋊C4—61no—
347C3×C22⋊C4—61no—
348C3×C22⋊C4—61no—
349C3×C42—61no—
350#217—21no—
351#217—21no—
352#217—31no—
353#217—31no—
354#217—61no—
355#217—61no—
356#217—61no—
357#217—61no—
358#215—121no—
359#214—121no—
360(C2×D3)⋊C4—21no—
361(C2×D3)⋊C4—31no—
362(C2×D3)⋊C4—31no—
363(C2×D3)⋊C4—61no—
364(C2×D3)⋊C4—61no—
365(C2×D3)⋊C4—61no—
366(C2×D3)⋊C4—61no—
367(C2×D3)⋊C4—61no—
368(C2×D3)⋊C4—61no—
369(C2×D3)⋊C4—61no—
370(C2×D3)⋊C4—61no—
371C4⋊Dic3—61no—
372C4⋊Dic3—61no—
373C4⋊Dic3—61no—
374C4⋊Dic3—61no—
375C4⋊Dic3—61no—
376C4⋊Dic3C22×D311yescharacteristic
377C4⋊Dic3C22×D311yescharacteristic
378C4⋊Dic3C22×D311yescharacteristic
379C4⋊Dic3C22×D311yescharacteristic
380Dic3⋊C4—21no—
381Dic3⋊C4—31no—
382Dic3⋊C4—31no—
383Dic3⋊C4—61no—
384Dic3⋊C4—61no—
385Dic3⋊C4—61no—
386Dic3⋊C4—61no—
387Dic3⋊C4—61no—
388Dic3⋊C4—61no—
389Dic3⋊C4—61no—
390Dic3⋊C4—61no—
391C4×Dic3—21no—
392C4×Dic3—31no—
393C4×Dic3—31no—
394C4×Dic3—61no—
395C4×Dic3—61no—
396C4×Dic3—61no—
397C2×C3⋊C8—31no—
398C2×C3⋊C8—31no—
399C2×C3⋊C8—31no—
400C2×C3⋊C8—31no—
401C2×C3⋊C8—61no—
402C2×C3⋊C8—61no—
403C2×C3⋊C8—121no—
404C2×C3⋊C8—121no—
405C2×C3⋊C8—122no—
406Dic12—41no—
407#204—22no—
408D3×C8—121no—
409D3×C8—121no—
410D3×C8—122no—
411C22×C32—21no—
412C22×C32—21no—
413C22×C32—21no—
414C22×C32C22×D411yescharacteristic
415C2×C3⋊D3—21no—
416C2×C3⋊D3—21no—
417C2×C3⋊D3#13512yes—
418C2×C3×D3—22no—
419C2×C3×D3—41no—
420C2×C3×D3—41no—
421C2×C3×D3—41no—
422C2×C3×D3—41no—
423C2×C3×D3—41no—
424D32—84no—
425C32×C4—21no—
426C32×C4C2×#4111yescharacteristic
427C32×C4H(5,𝔽2)11yescharacteristic
428C3⋊Dic3—21no—
429C3⋊Dic3—21no—
430C3⋊Dic3—21no—
431C3×Dic3—41no—
432C3×Dic3—41no—
433C3×Dic3—41no—
434C3×Dic3—41no—
435C3×Dic3—41no—
436C3×Dic3—41no—
437C2×#41—31no—
438C22×D4—91no—
439C2×Q16—31no—
440C2×SD16—31no—
441C2×SD16—91no—
442C22×C8—91no—
443C22×C8—91no—
444#126—181no—
445#125—91no—
446#125—181no—
447#124—91no—
448#123—181no—
449#123—181no—
450C22⋊Q8—31no—
451C22⋊Q8—91no—
452C22⋊Q8—91no—
453#121—31no—
454#121—181no—
455#120—181no—
456C4×Q8—91no—
457C4×D4—91no—
458C4×D4—91no—
459#117—31no—
460#117—181no—
461C2×C4⋊C4—91no—
462C2×C22⋊C4—181no—
463#107—31no—
464#106—31no—
465#106—91no—
466C4⋊C8—91no—
467#103—31no—
468#103—91no—
469#103—91no—
470#103—91no—
471#102—31no—
472#102—31no—
473#102—31no—
474#102—91no—
475#102—91no—
476#102—91no—
477C22⋊C8—91no—
478C22⋊C8D3211yescharacteristic, complemented
479C4×C8—91no—
480C23×C3—21no—
481C23×C3—61no—
482C23×C3—61no—
483C23×C3D3×D411yescharacteristic
484C23×C3D3×D411yescharacteristic
485C22×D3—21no—
486C22×D3—21no—
487C22×D3—31no—
488C22×D3—31no—
489C22×D3—61no—
490C22×D3—122no—
491C22×D3—122no—
492C22×D3—122no—
493C22×D3—122no—
494C22×D3—241no—
495C22×D3—241no—
496C3×Q8—61no—
497C3×Q8—61no—
498C3×Q8—61no—
499C3×Q8—61no—
500C3×D4—32no—
501C3×D4—61no—
502C3×D4—61no—
503C3×D4—61no—
504C3×D4—122no—
505C3×D4—241no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—41no—
513C2×C3×C4—41no—
514C2×C3×C4—61no—
515C2×C3×C4—61no—
516C2×C3×C4—61no—
517C2×C3×C4—61no—
518C2×C3×C4—61no—
519C2×C3×C4—61no—
520C2×C3×C4—122no—
521C2×C3×C4D3×D411yescharacteristic
522C2×C3×C4D3×D411yescharacteristic
523C2×C3×C4C23×D311yescharacteristic
524C2×C3×C4C23×D311yescharacteristic
525#67—42no—
526#67—62no—
527#67—62no—
528#67—64no—
529#67—81no—
530#67—122no—
531#67—122no—
532C2×Dic3—21no—
533C2×Dic3—21no—
534C2×Dic3—21no—
535C2×Dic3—21no—
536C2×Dic3—21no—
537C2×Dic3—21no—
538C2×Dic3—31no—
539C2×Dic3—31no—
540C2×Dic3—31no—
541C2×Dic3—31no—
542C2×Dic3—31no—
543C2×Dic3—31no—
544C2×Dic3—61no—
545C2×Dic3—61no—
546C2×Dic3—61no—
547C2×Dic3—241no—
548D12—21no—
549D12—21no—
550D12—21no—
551D12#23712yes—
552C4×D3—42no—
553C4×D3—61no—
554C4×D3—61no—
555C4×D3—61no—
556C4×D3—61no—
557C4×D3—121no—
558C4×D3—121no—
559C4×D3—122no—
560C4×D3—122no—
561C4×D3—241no—
562Dic6—21no—
563Dic6—21no—
564Dic6—21no—
565Dic6—21no—
566C3×C8—21no—
567C3×C8—21no—
568C3×C8—21no—
569C3×C8—21no—
570C3×C8—41no—
571C3×C8—41no—
572C3⋊C8—62no—
573C3⋊C8—61no—
574C3⋊C8—61no—
575C3⋊C8—61no—
576C3⋊C8—61no—
577C3⋊C8—121no—
578C2×C32—41no—
579C2×C32#54611yescharacteristic
580C2×C32C2×#13511yescharacteristic
581C2×C32#57711yescharacteristic
582C3⋊D3—22no—
583C3×D3—42no—
584C3×D3—81no—
585C24—181no—
586#41—62no—
587#41—121no—
588C2×Q8—31no—
589C2×Q8—31no—
590C2×D4—31no—
591C2×D4—31no—
592C2×D4—61no—
593C2×D4—61no—
594C2×D4—91no—
595C2×D4—181no—
596C2×D4—182no—
597C2×D4—361no—
598C22×C4—61no—
599C22×C4—91no—
600C22×C4—181no—
601C22×C4—181no—
602C22×C4C2×D3211yescharacteristic
603Q16—121no—
604SD16—62no—
605SD16—361no—
606C2×C8—91no—
607C2×C8—91no—
608C2×C8—361no—
609C2×C8—361no—
610C2×C8C2×D3211yescharacteristic
611C2×C8C2×D3211yescharacteristic
612C4⋊C4—31no—
613C4⋊C4—31no—
614C4⋊C4—31no—
615C4⋊C4—31no—
616C4⋊C4—61no—
617C4⋊C4—91no—
618C4⋊C4—181no—
619C4⋊C4—181no—
620C4⋊C4—181no—
621C4⋊C4—181no—
622C4⋊C4—181no—
623C4⋊C4—181no—
624C22⋊C4—61no—
625C22⋊C4—61no—
626C22⋊C4—61no—
627C22⋊C4—91no—
628C22⋊C4—91no—
629C22⋊C4—181no—
630C22⋊C4—181no—
631C22⋊C4—181no—
632C22⋊C4—181no—
633C22⋊C4—181no—
634C42—61no—
635C42—91no—
636C42—181no—
637C22×C3—22no—
638C22×C3—21no—
639C22×C3—21no—
640C22×C3—21no—
641C22×C3—21no—
642C22×C3—21no—
643C22×C3—21no—
644C22×C3—21no—
645C22×C3—41no—
646C22×C3—41no—
647C22×C3—62no—
648C22×C3—121no—
649C22×C3—121no—
650C22×C3—121no—
651C22×C3—121no—
652C22×C3—121no—
653C22×C3C2×D3×D411yescharacteristic
654C22×C3C2×D3×D411yescharacteristic
655C2×D3—22no—
656C2×D3—32no—
657C2×D3—32no—
658C2×D3—41no—
659C2×D3—41no—
660C2×D3—41no—
661C2×D3—41no—
662C2×D3—41no—
663C2×D3—62no—
664C2×D3—61no—
665C2×D3—61no—
666C2×D3—61no—
667C2×D3—61no—
668C2×D3—121no—
669C2×D3—121no—
670C2×D3—244no—
671C2×D3—244no—
672C3×C4—21no—
673C3×C4—21no—
674C3×C4—21no—
675C3×C4—21no—
676C3×C4—41no—
677C3×C4—121no—
678C3×C4—121no—
679C3×C4—121no—
680C3×C4—121no—
681C3×C4—121no—
682C3×C4—121no—
683C3×C4C2×#23711yescharacteristic
684C3×C4#100411yescharacteristic
685C3×C4D3×#4111yescharacteristic
686C3×C4#100911yescharacteristic
687Dic3—41no—
688Dic3—41no—
689Dic3—41no—
690Dic3—41no—
691Dic3—41no—
692Dic3—41no—
693Dic3—62no—
694Dic3—61no—
695Dic3—61no—
696Dic3—61no—
697Dic3—61no—
698Dic3—61no—
699Dic3—61no—
700Dic3—121no—
701Dic3—121no—
702C32#329611yescharacteristic, complemented, Sylow
703C23—61no—
704C23—61no—
705C23—91no—
706C23—362no—
707C23—362no—
708C23—721no—
709C23#380211yescharacteristic
710Q8—61no—
711Q8—61no—
712Q8—61no—
713Q8—61no—
714D4—32no—
715D4—61no—
716D4—61no—
717D4—61no—
718D4—122no—
719D4—182no—
720D4—241no—
721D4—362no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—61no—
725C2×C4—61no—
726C2×C4—61no—
727C2×C4—61no—
728C2×C4—61no—
729C2×C4—61no—
730C2×C4—91no—
731C2×C4—91no—
732C2×C4—91no—
733C2×C4—122no—
734C2×C4—181no—
735C2×C4—181no—
736C2×C4—362no—
737C2×C4—721no—
738C2×C4#380211yescharacteristic
739C2×C4C22×D3211yescharacteristic
740C8—21no—
741C8—21no—
742C8—181no—
743C8—181no—
744C2×C3—21no—
745C2×C3—21no—
746C2×C3—21no—
747C2×C3—42no—
748C2×C3—41no—
749C2×C3—41no—
750C2×C3—122no—
751C2×C3—241no—
752C2×C3#559111yescharacteristic
753C2×C3#565411yescharacteristic
754C2×C3D3×#13511yescharacteristic
755C2×C3D3×#13511yescharacteristic
756C2×C3#577511yescharacteristic
757C2×C3#577811yescharacteristic
758D3—42no—
759D3—62no—
760D3—62no—
761D3—81no—
762D3—122no—
763C22—21no—
764C22—21no—
765C22—21no—
766C22—62no—
767C22—92no—
768C22—121no—
769C22—121no—
770C22—121no—
771C22—121no—
772C22—121no—
773C22—181no—
774C22—181no—
775C22—724no—
776C22C2×#380211yescharacteristic
777C4—21no—
778C4—121no—
779C4—121no—
780C4—121no—
781C4—121no—
782C4—121no—
783C4—121no—
784C4—181no—
785C4—181no—
786C4—181no—
787C4D3×#23711yescharacteristic
788C4#6431411yescharacteristic
789C3—21no—
790C3#8024611yescharacteristic, complemented
791C3#8138111yescharacteristic, complemented
792C2—41no—
793C2—122no—
794C2—182no—
795C2—241no—
796C2#1059429411yescharacteristic
797C2#1059468411yescharacteristic
798C2#1059471911yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊C8C22
socleC22×C32C22×D4
prime radical#10595070C2
hypercenterC22⋊C8D32
hypocenterC32#3296
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
2. #10594970C2semidirect
3. #10592424C2semidirect
4. C3×#4737C2semidirect
5. C3×#4733C2semidirect
6. #10591179C2semidirect
7. #10591083C2semidirect
8. #10590943C2semidirect
9. #10590940C2semidirect
10. #10590868C2semidirect
11. #10590857C2semidirect
12. #10590797C2semidirect
13. #10590780C2semidirect
14. #10590775C2semidirect
15. #10590686C2semidirect
21. C22×C3⋊(C3⋊C8)C22semidirect
24. C3×#926C22semidirect
25. C3×#924C22semidirect
26. C2×C3×Dic12C22semidirect
36. #63872C22semidirect
41. #63843C22semidirect
44. C32×C22⋊C8C22semidirect
46. #63641C22semidirect
47. C8×C3⋊Dic3C22semidirect
51. C3×#818C22semidirect
52. C3×#817C22semidirect
53. C3×#816C22semidirect
54. #63574C22semidirect
55. #63565C22semidirect
56. #63565C22semidirect
57. #63565C22semidirect
87. #4737D3semidirect
88. #4733D3semidirect
172. #926C2×D3semidirect
173. #924C2×D3semidirect
177. C2×Dic12C2×D3semidirect
207. C3×C22⋊C8C2×D3semidirect
208. C3×C22⋊C8C2×D3semidirect
221. #818C2×D3semidirect
222. #817C2×D3semidirect
223. #816C2×D3semidirect
478. C22⋊C8D32semidirect
702. C32#3296semidirect
790. C3#80246semidirect
791. C3#81381semidirect

Maximal subgroups

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

subgroupindex
#105950702
#105949702
#105924242
C3×#47372
C3×#47332
#105911792
#105910832
#105909432
#105909402
#105908682
#105908572
#105907972
#105907802
#105907752
#105906862
#813813
#802463