Finite Group Databasebeta

← #11888688

Subgroups — #11888688

Order 1152.

840 conjugacy classes of subgroups.

The subgroup lattice has 789 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595358C211yesmaximal, characteristic, complemented
2#10594489C211yesmaximal, characteristic, complemented
3#10592504C211yesmaximal, characteristic, complemented
4C3×#4810C211yesmaximal, characteristic, complemented
5C3×#4797C211yesmaximal, characteristic, complemented
6#10591590C211yesmaximal, characteristic, complemented
7#10591564C211yesmaximal, characteristic, complemented
8#10591556C211yesmaximal, characteristic, complemented
9#10590963C211yesmaximal, characteristic, complemented
10#10590771C211yesmaximal, characteristic, complemented
11#10590728C211yesmaximal, characteristic, complemented
12#10590711C211yesmaximal, characteristic, complemented
13#10590612C211yesmaximal, characteristic, complemented
14#10590514C211yesmaximal, characteristic, complemented
15#10590469C211yesmaximal, characteristic, complemented
16#81748—31nomaximal
17#80107—31nomaximal
18C2×C3×#239C2211yescharacteristic
19C2×#3796C2211yescharacteristic
20#64155C2211yescharacteristic
21C4⋊C4×C3⋊D3C2211yescharacteristic
22C3×#944C2211yescharacteristic
23C2×C3×#215C2211yescharacteristic
24C2×C3×D24C2211yescharacteristic
25C3×#895C2211yescharacteristic
26C3×#890C2211yescharacteristic
27#63916—21no—
28#63916C2211yescharacteristic
29C4×#626C2211yescharacteristic
30Dic3×D12C2211yescharacteristic
31Dic3×D12C2211yescharacteristic
32#63886—21no—
33#63884—21no—
34#63884—21no—
35#63881—21no—
36D3×Dic3⋊C4—21no—
37#63858—21no—
38#63856C2211yescharacteristic
39#63850—21no—
40#63841C2211yescharacteristic
41C2×#3715C2211yescharacteristic
42C2×#3712C2211yescharacteristic
43C2×D3×C3⋊C8C2211yescharacteristic
44C32×#103C2211yescharacteristic
45#63662C2211yescharacteristic
46#63647C2211yescharacteristic
47#63644C2211yescharacteristic
48#63635C2211yescharacteristic
49C3×#835C2211yescharacteristic
50C3×(C2×D3)⋊C8C2211yescharacteristic
51C3×#816C2211yescharacteristic
52C3×#815C2211yescharacteristic
53C3×#810C2211yescharacteristic
54C3×#809C2211yescharacteristic
55#63575C2211yescharacteristic
56Dic3⋊(C3⋊C8)C2211yescharacteristic
57#63566C2211yescharacteristic
58#63563C2211yescharacteristic
59#63563C2211yescharacteristic
60#63562C2211yescharacteristic
61#5824—31no—
62#5726—31no—
63#5695—31no—
64#5614—31no—
65C3×#491—31no—
66C3×#449—31no—
67#5233—31no—
68#5174—31no—
69#5162—31no—
70#5158—31no—
71#5152—31no—
72#5083—31no—
73#5066—31no—
74#5041—31no—
75#4815—31no—
76#4812—31no—
77#4810—31no—
78#4810D311yescharacteristic, complemented
79#4807—31no—
80#4805—31no—
81#4805—31no—
82#4805—61no—
83#4804—31no—
84#4803—31no—
85#4797D311yescharacteristic, complemented
86#4771—31no—
87#4766—31no—
88#4730—31no—
89#4723—31no—
90#4711—31no—
91#4706—31no—
92C2×C32×Q8C2311yescharacteristic
93C2×C4×C3⋊D3—21no—
94C2×C4×C3⋊D3C2311yescharacteristic
95C3×#239—22no—
96C3×#239—41no—
97C2×C3×D12—21no—
98C2×C3×D12—21no—
99C2×C3×D12C2311yescharacteristic
100C2×C3×D12C2311yescharacteristic
101C2×C3×C4×D3—21no—
102C2×C3×C4×D3C2311yescharacteristic
103C2×C3×Dic6C2311yescharacteristic
104C2×#626—21no—
105C2×#626—21no—
106C2×#626D411yescharacteristic
107C2×D3×Dic3—21no—
108C2×D3×Dic3—21no—
109C2×D3×Dic3—21no—
110#3796—22no—
111#3796—41no—
112C2×C32×C8C2311yescharacteristic
113C32×C4⋊C4C2311yescharacteristic
114#3752—21no—
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117#3750—21no—
118#3750—21no—
119C2×C3⋊(C3⋊C8)C2311yescharacteristic
120C3×#215—41no—
121C3×(C2×D3)⋊C4—21no—
122C3×C4⋊Dic3—21no—
123C3×C4⋊Dic3C2311yescharacteristic
124C3×Dic3⋊C4—21no—
125C3×Dic3⋊C4—21no—
126C3×Dic3⋊C4—21no—
127C3×C4×Dic3C2311yescharacteristic
128C2×C3×C3⋊C8C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130C3×D24—22no—
131#3724—21no—
132Dic3⋊Dic3D411yescharacteristic
133#3722D411yescharacteristic
134(C2×D3)⋊Dic3—21no—
135(C2×D3)⋊Dic3—21no—
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3D411yescharacteristic
140Dic32—21no—
141#3715—41no—
142#3712—41no—
143D3×C3⋊C8—41no—
144#3307—91noSylow
145C2×C3×#41—31no—
146C2×#239—31no—
147C2×#239C2×D311yescharacteristic
148C2×#237—31no—
149C2×C3×SD16—31no—
150C2×C3×D8—31no—
151C3×C4⋊Q8—31no—
152C3×#125—31no—
153C3×#121—31no—
154#946—31no—
155#946—31no—
156#946—31no—
157#946—61no—
158#944C2×D311yescharacteristic
159C2×#215—31no—
160C2×#215C2×D311yescharacteristic
161#939—61no—
162#938—31no—
163#938—61no—
164#935—61no—
165#935—61no—
166D4×Dic3—31no—
167D4×Dic3—31no—
168C2×#214—31no—
169#929—61no—
170C4×#67—31no—
171#926—31no—
172#924—31no—
173C2×Dic3⋊C4—61no—
174C22×C3⋊C8—31no—
175C2×D24C2×D311yescharacteristic
176C2×ΓL(1,𝔽25)—31no—
177C2×ΓL(1,𝔽25)—31no—
178C2×D3×C8—31no—
179#898—61no—
180#895—31no—
181#895—61no—
182#895—61no—
183#895C2×D311yescharacteristic
184#894—61no—
185#894—61no—
186#894—61no—
187#893—61no—
188#892—31no—
189D3×C4⋊C4—31no—
190D3×C4⋊C4—31no—
191D3×C4⋊C4—61no—
192D3×C4⋊C4—61no—
193#890C2×D311yescharacteristic
194#67⋊C4—61no—
195#879—61no—
196C4×D12—31no—
197C4×D12—31no—
198C4×D12—31no—
199C3×#103—21no—
200C3×#103—31no—
201C3×#103—31no—
202C3×#103—31no—
203C3×#103C2×D311yescharacteristic
204C3×#103C2×D311yescharacteristic
205C3×#102—31no—
206C3×C22⋊C8—31no—
207C3×#97—31no—
208#835—31no—
209#835—31no—
210#835—31no—
211#835—61no—
212#835C2×D311yescharacteristic
213#832—31no—
214#832—31no—
215#832—31no—
216#821—31no—
217#821—31no—
218(C2×D3)⋊C8—31no—
219(C2×D3)⋊C8—31no—
220(C2×D3)⋊C8—61no—
221(C2×D3)⋊C8C2×D311yescharacteristic
222#818—31no—
223#817—31no—
224#817—31no—
225#817—61no—
226#816—31no—
227#816C2×D311yescharacteristic
228#815C2×D311yescharacteristic
229Dic3⋊C8—31no—
230#810C2×D311yescharacteristic
231#809—31no—
232#809C2×D311yescharacteristic
233#808—31no—
234#808—31no—
235#808—61no—
236#807—31no—
237C4⋊(C3⋊C8)—31no—
238C22×C3⋊D3C2×D411yescharacteristic
239C22×C3×D3—21no—
240C22×C3×D3—21no—
241C22×C3×D3C2×D411yescharacteristic
242C32×Q8—21no—
243C32×Q8—21no—
244C2×C32×C4—21no—
245C2×C32×C4—21no—
246C2×C32×C4C2411yescharacteristic
247C2×C3⋊Dic3—21no—
248C2×C3⋊Dic3—21no—
249C2×C3⋊Dic3C2×D411yescharacteristic
250C4×C3⋊D3—21no—
251C4×C3⋊D3—21no—
252C4×C3⋊D3—81no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3C2×D411yescharacteristic
256C2×C3×Dic3C2×D411yescharacteristic
257C2×C3×Dic3C2×D411yescharacteristic
258C3×D12—21no—
259C3×D12—21no—
260C3×D12—21no—
261C3×D12—42no—
262C3×D12—81no—
263C3×D12#4112yes—
264C3×C4×D3—21no—
265C3×C4×D3—21no—
266C3×C4×D3—42no—
267C3×Dic6—21no—
268C3×Dic6—21no—
269#626—41no—
270#626—42no—
271#626—42no—
272D3×Dic3—42no—
273D3×Dic3—42no—
274D3×Dic3—81no—
275C32×C8—21no—
276C3⋊(C3⋊C8)—21no—
277C3×C3⋊C8—21no—
278C3×C3⋊C8—21no—
279#553—91no—
280#547—91no—
281#491—31no—
282#485—91no—
283#483—91no—
284#478—91no—
285#468—91no—
286#465—91no—
287#461—91no—
288#449—31no—
289#449—91no—
290#442—91no—
291#435—91no—
292#417—91no—
293#416—91no—
294C3×#41—62no—
295C3×#41—121no—
296C2×C3×Q8—21no—
297C2×C3×Q8—31no—
298C2×C3×Q8C22×D311yescharacteristic
299C2×C3×Q8C22×D311yescharacteristic
300C2×C3×D4—31no—
301C2×C3×D4—31no—
302C2×C3×D4—61no—
303C2×C3×D4—61no—
304C22×C3×C4—31no—
305C22×C3×C4—61no—
306C2×#67—31no—
307C2×#67—61no—
308C2×#67—61no—
309C22×Dic3—61no—
310C22×Dic3—61no—
311C22×Dic3—61no—
312#239—22no—
313#239—41no—
314#239—62no—
315#239—121no—
316#237—62no—
317#237—121no—
318C2×D12—21no—
319C2×D12—21no—
320C2×D12—31no—
321C2×D12—61no—
322C2×D12—61no—
323C2×D12C22×D311yescharacteristic
324C2×D12C22×D311yescharacteristic
325C2×C4×D3—21no—
326C2×C4×D3—31no—
327C2×C4×D3—31no—
328C2×C4×D3—61no—
329C2×C4×D3—61no—
330C2×C4×D3—61no—
331C2×C4×D3—61no—
332C2×C4×D3—61no—
333C2×C4×D3—61no—
334C2×C4×D3—121no—
335C2×C4×D3C22×D311yescharacteristic
336C2×Dic6C22×D311yescharacteristic
337C3×SD16—121no—
338C3×D8—62no—
339C2×C3×C8—21no—
340C2×C3×C8—31no—
341C2×C3×C8—31no—
342C2×C3×C8C22×D311yescharacteristic
343C2×C3×C8C22×D311yescharacteristic
344C3×C4⋊C4—21no—
345C3×C4⋊C4—31no—
346C3×C4⋊C4—61no—
347C3×C4⋊C4—61no—
348C3×C4⋊C4—61no—
349C3×C4⋊C4—61no—
350C3×C4⋊C4C22×D311yescharacteristic
351C3×C4⋊C4C22×D311yescharacteristic
352C3×C22⋊C4—61no—
353C3×C42—31no—
354#217—31no—
355#217—61no—
356#217—61no—
357#217—61no—
358#217—61no—
359#217—61no—
360#215—41no—
361#215—121no—
362#214—121no—
363(C2×D3)⋊C4—21no—
364(C2×D3)⋊C4—31no—
365(C2×D3)⋊C4—31no—
366(C2×D3)⋊C4—31no—
367(C2×D3)⋊C4—61no—
368(C2×D3)⋊C4—61no—
369(C2×D3)⋊C4—61no—
370(C2×D3)⋊C4—61no—
371(C2×D3)⋊C4—61no—
372(C2×D3)⋊C4—61no—
373(C2×D3)⋊C4—61no—
374(C2×D3)⋊C4—121no—
375C4⋊Dic3—21no—
376C4⋊Dic3—31no—
377C4⋊Dic3—31no—
378C4⋊Dic3—31no—
379C4⋊Dic3—31no—
380C4⋊Dic3—31no—
381C4⋊Dic3—61no—
382C4⋊Dic3—61no—
383C4⋊Dic3C22×D311yescharacteristic
384Dic3⋊C4—21no—
385Dic3⋊C4—21no—
386Dic3⋊C4—21no—
387Dic3⋊C4—31no—
388Dic3⋊C4—61no—
389Dic3⋊C4—61no—
390Dic3⋊C4—61no—
391Dic3⋊C4—61no—
392Dic3⋊C4—61no—
393Dic3⋊C4—61no—
394Dic3⋊C4—121no—
395Dic3⋊C4—121no—
396C4×Dic3—61no—
397C4×Dic3—61no—
398C4×Dic3C22×D311yescharacteristic
399C2×C3⋊C8—31no—
400C2×C3⋊C8—31no—
401C2×C3⋊C8—61no—
402C2×C3⋊C8—121no—
403C2×C3⋊C8C22×D311yescharacteristic
404C2×C3⋊C8C22×D311yescharacteristic
405D24—22no—
406ΓL(1,𝔽25)—121no—
407ΓL(1,𝔽25)—121no—
408D3×C8—121no—
409C22×C32C22×D411yescharacteristic
410C2×C3⋊D3—21no—
411C2×C3⋊D3—21no—
412C2×C3⋊D3—21no—
413C2×C3×D3—22no—
414C2×C3×D3—21no—
415C2×C3×D3—21no—
416C2×C3×D3—21no—
417C2×C3×D3—41no—
418C2×C3×D3—41no—
419C2×C3×D3—41no—
420C2×C3×D3—41no—
421C2×C3×D3—41no—
422C32×C4—41no—
423C32×C4—41no—
424C32×C4C2×#4111yescharacteristic
425C32×C4H(5,𝔽2)11yescharacteristic
426C3⋊Dic3—21no—
427C3⋊Dic3—41no—
428C3⋊Dic3—41no—
429C3×Dic3—21no—
430C3×Dic3—21no—
431C3×Dic3—21no—
432C3×Dic3—41no—
433C3×Dic3—41no—
434C2×#41—31no—
435C2×#41—91no—
436C2×SD16—31no—
437C2×SD16—91no—
438C2×D8—31no—
439C2×M16—91no—
440C22×C8—91no—
441C4⋊Q8—31no—
442#126—181no—
443#125—31no—
444#123—181no—
445#123—181no—
446#123—181no—
447C22⋊Q8—91no—
448C22⋊Q8—91no—
449#121—31no—
450#121—91no—
451#121—181no—
452#121—181no—
453C4×D4—91no—
454C4×D4—91no—
455C4×D4—91no—
456C4×D4—181no—
457#117—91no—
458C2×C4⋊C4—91no—
459C2×C4⋊C4—181no—
460#107—91no—
461#106—91no—
462#106—91no—
463C4⋊C8—91no—
464#103—31no—
465#103—31no—
466#103—31no—
467#103—91no—
468#103—91no—
469#103D3211yescharacteristic
470#102—31no—
471#102—91no—
472#102—91no—
473#102—91no—
474C22⋊C8—31no—
475C22⋊C8—91no—
476#97—31no—
477C23×C3—31no—
478C23×C3—61no—
479C23×C3—61no—
480C22×D3—21no—
481C22×D3—21no—
482C22×D3—31no—
483C22×D3—31no—
484C22×D3—61no—
485C22×D3D3×D411yescharacteristic
486C3×Q8—21no—
487C3×Q8—21no—
488C3×Q8—21no—
489C3×Q8—21no—
490C3×Q8—41no—
491C3×Q8—41no—
492C3×Q8—61no—
493C3×Q8—61no—
494C3×D4—32no—
495C3×D4—61no—
496C3×D4—61no—
497C3×D4—61no—
498C3×D4—122no—
499C3×D4—241no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—31no—
506C2×C3×C4—31no—
507C2×C3×C4—31no—
508C2×C3×C4—41no—
509C2×C3×C4—41no—
510C2×C3×C4—61no—
511C2×C3×C4—61no—
512C2×C3×C4—61no—
513C2×C3×C4—61no—
514C2×C3×C4—122no—
515C2×C3×C4C23×D311yescharacteristic
516C2×C3×C4C23×D311yescharacteristic
517#67—121no—
518#67—122no—
519#67—122no—
520C2×Dic3—21no—
521C2×Dic3—21no—
522C2×Dic3—31no—
523C2×Dic3—31no—
524C2×Dic3—61no—
525C2×Dic3—61no—
526C2×Dic3—61no—
527C2×Dic3—61no—
528C2×Dic3—61no—
529C2×Dic3—121no—
530C2×Dic3—121no—
531C2×Dic3—122no—
532C2×Dic3—122no—
533C2×Dic3—241no—
534C2×Dic3D3×D411yescharacteristic
535C2×Dic3D3×D411yescharacteristic
536C2×Dic3D3×D411yescharacteristic
537D12—21no—
538D12—21no—
539D12—21no—
540D12—42no—
541D12—81no—
542D12—121no—
543D12—122no—
544D12—122no—
545D12#23712yes—
546C4×D3—21no—
547C4×D3—21no—
548C4×D3—42no—
549C4×D3—61no—
550C4×D3—61no—
551C4×D3—61no—
552C4×D3—61no—
553C4×D3—121no—
554C4×D3—121no—
555C4×D3—122no—
556C4×D3—122no—
557C4×D3—241no—
558C4×D3—241no—
559C4×D3—241no—
560C4×D3—242no—
561Dic6—21no—
562Dic6—21no—
563C3×C8—21no—
564C3×C8—21no—
565C3×C8—41no—
566C3×C8—61no—
567C3×C8—61no—
568C3⋊C8—21no—
569C3⋊C8—21no—
570C3⋊C8—61no—
571C3⋊C8—61no—
572C3⋊C8—121no—
573C2×C32#54611yescharacteristic
574C2×C32#57511yescharacteristic
575C2×C32#57711yescharacteristic
576C3⋊D3—41no—
577C3×D3—41no—
578C3×D3—42no—
579C3×D3—81no—
580#41—62no—
581#41—121no—
582#41—182no—
583#41—361no—
584C2×Q8—31no—
585C2×Q8C2×D3211yescharacteristic
586C2×D4—31no—
587C2×D4—31no—
588C2×D4—61no—
589C2×D4—61no—
590C2×D4—91no—
591C2×D4—181no—
592C2×D4—181no—
593C22×C4—31no—
594C22×C4—61no—
595C22×C4—91no—
596C22×C4—181no—
597C22×C4—181no—
598C22×C4—181no—
599C22×C4—181no—
600SD16—121no—
601SD16—361no—
602D8—62no—
603M16—361no—
604C2×C8—31no—
605C2×C8—31no—
606C2×C8—91no—
607C2×C8—361no—
608C2×C8C2×D3211yescharacteristic
609C4⋊C4—31no—
610C4⋊C4—61no—
611C4⋊C4—61no—
612C4⋊C4—61no—
613C4⋊C4—61no—
614C4⋊C4—91no—
615C4⋊C4—91no—
616C4⋊C4—91no—
617C4⋊C4—181no—
618C4⋊C4—181no—
619C4⋊C4—181no—
620C4⋊C4C2×D3211yescharacteristic
621C22⋊C4—61no—
622C22⋊C4—91no—
623C22⋊C4—91no—
624C22⋊C4—181no—
625C22⋊C4—181no—
626C22⋊C4—181no—
627C22⋊C4—181no—
628C22⋊C4—181no—
629C22⋊C4—181no—
630C42—31no—
631C42—181no—
632C22×C3—21no—
633C22×C3—62no—
634C22×C3—61no—
635C22×C3—61no—
636C22×C3—61no—
637C22×C3—121no—
638C22×C3—121no—
639C22×C3—121no—
640C22×C3—121no—
641C22×C3—121no—
642C22×C3C2×D3×D411yescharacteristic
643C22×C3C2×D3×D411yescharacteristic
644C2×D3—21no—
645C2×D3—21no—
646C2×D3—21no—
647C2×D3—22no—
648C2×D3—41no—
649C2×D3—41no—
650C2×D3—41no—
651C2×D3—41no—
652C2×D3—41no—
653C2×D3—62no—
654C2×D3—61no—
655C2×D3—61no—
656C2×D3—61no—
657C2×D3—61no—
658C2×D3—61no—
659C2×D3—61no—
660C2×D3—121no—
661C2×D3—121no—
662C3×C4—21no—
663C3×C4—21no—
664C3×C4—41no—
665C3×C4—41no—
666C3×C4—41no—
667C3×C4—41no—
668C3×C4—61no—
669C3×C4—61no—
670C3×C4—61no—
671C3×C4—81no—
672C3×C4—81no—
673C3×C4—121no—
674C3×C4—121no—
675C3×C4C2×#23711yescharacteristic
676C3×C4#100411yescharacteristic
677C3×C4D3×#4111yescharacteristic
678C3×C4#100911yescharacteristic
679Dic3—21no—
680Dic3—21no—
681Dic3—21no—
682Dic3—41no—
683Dic3—41no—
684Dic3—61no—
685Dic3—61no—
686Dic3—121no—
687Dic3—121no—
688Dic3—121no—
689Dic3—121no—
690Dic3—121no—
691Dic3—241no—
692Dic3—241no—
693C32#330711yescharacteristic, complemented, Sylow
694C23—31no—
695C23—61no—
696C23—61no—
697C23—91no—
698Q8—21no—
699Q8—21no—
700Q8—61no—
701Q8—61no—
702D4—32no—
703D4—61no—
704D4—61no—
705D4—61no—
706D4—122no—
707D4—241no—
708D4—361no—
709D4—362no—
710D4—362no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—31no—
714C2×C4—31no—
715C2×C4—31no—
716C2×C4—61no—
717C2×C4—61no—
718C2×C4—61no—
719C2×C4—61no—
720C2×C4—91no—
721C2×C4—122no—
722C2×C4—181no—
723C2×C4—181no—
724C2×C4—181no—
725C2×C4—181no—
726C2×C4—362no—
727C2×C4—362no—
728C2×C4—721no—
729C2×C4—721no—
730C2×C4C22×D3211yescharacteristic
731C8—21no—
732C8—61no—
733C8—61no—
734C8—181no—
735C2×C3—21no—
736C2×C3—21no—
737C2×C3—21no—
738C2×C3—121no—
739C2×C3—122no—
740C2×C3—241no—
741C2×C3#559111yescharacteristic
742C2×C3#567611yescharacteristic
743C2×C3#576811yescharacteristic
744C2×C3#577511yescharacteristic
745C2×C3#577711yescharacteristic
746C2×C3#577811yescharacteristic
747D3—41no—
748D3—42no—
749D3—81no—
750D3—122no—
751D3—121no—
752D3—121no—
753C22—61no—
754C22—61no—
755C22—61no—
756C22—62no—
757C22—121no—
758C22—121no—
759C22—121no—
760C22—121no—
761C22—121no—
762C22—181no—
763C22—181no—
764C22—181no—
765C22D32×D411yescharacteristic
766C4—41no—
767C4—41no—
768C4—61no—
769C4—61no—
770C4—61no—
771C4—121no—
772C4—121no—
773C4—181no—
774C4—361no—
775C4—361no—
776C4#6430711yescharacteristic
777C4D3×#23711yescharacteristic
778C3—21no—
779C3#8010711yescharacteristic, complemented
780C3#8174811yescharacteristic, complemented
781C2—121no—
782C2—122no—
783C2—241no—
784C2—361no—
785C2#1059428111yescharacteristic
786C2#1059475411yescharacteristic
787C2#1059476311yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
hypercenter#103D32
hypocenterC32#3307
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
1. #10595358C2semidirect
2. #10594489C2semidirect
3. #10592504C2semidirect
4. C3×#4810C2semidirect
5. C3×#4797C2semidirect
6. #10591590C2semidirect
7. #10591564C2semidirect
8. #10591556C2semidirect
9. #10590963C2semidirect
10. #10590771C2semidirect
11. #10590728C2semidirect
12. #10590711C2semidirect
13. #10590612C2semidirect
14. #10590514C2semidirect
15. #10590469C2semidirect
78. #4810D3semidirect
85. #4797D3semidirect
693. C32#3307semidirect
779. C3#80107semidirect
780. C3#81748semidirect

Maximal subgroups

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

subgroupindex
#105953582
#105944892
#105925042
C3×#48102
C3×#47972
#105915902
#105915642
#105915562
#105909632
#105907712
#105907282
#105907112
#105906122
#105905142
#105904692
#817483
#801073