Finite Group Databasebeta

← #11888610

Subgroups — #11888610

Order 1152.

869 conjugacy classes of subgroups.

The subgroup lattice has 805 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595248C211yesmaximal, characteristic, complemented
2#10594578C211yesmaximal, characteristic, complemented
3#10592480C211yesmaximal, characteristic, complemented
4C3×#4772C211yesmaximal, characteristic, complemented
5C3×#4763C211yesmaximal, characteristic, complemented
6#10591452C211yesmaximal, characteristic, complemented
7#10591418C211yesmaximal, characteristic, complemented
8#10591404C211yesmaximal, characteristic, complemented
9#10590830C211yesmaximal, characteristic, complemented
10#10590760C211yesmaximal, characteristic, complemented
11#10590727C211yesmaximal, characteristic, complemented
12#10590686C211yesmaximal, characteristic, complemented
13#10590562C211yesmaximal, characteristic, complemented
14#10590522C211yesmaximal, characteristic, complemented
15#10590429C211yesmaximal, characteristic, complemented
16#81188—31nomaximal
17#78853—31nomaximal
18C2×#3830C2211yescharacteristic
19C2×C3×#237C2211yescharacteristic
20C2×#3753C2211yescharacteristic
21C2×#3744C2211yescharacteristic
22#64104C2211yescharacteristic
23C3×D4×Dic3C2211yescharacteristic
24C2×C3×D3×C8C2211yescharacteristic
25C3×#892C2211yescharacteristic
26C3×#890C2211yescharacteristic
27#63978—21no—
28#63966—21no—
29C2×Dic3⋊Dic3—21no—
30#63962—21no—
31#63910—21no—
32#63909C2211yescharacteristic
33C4×#626C2211yescharacteristic
34#63900C2211yescharacteristic
35#63894—21no—
36#63894C2211yescharacteristic
37#63871C2211yescharacteristic
38#63868—21no—
39#63866C2211yescharacteristic
40#63857C2211yescharacteristic
41#63854—21no—
42C2×#3717C2211yescharacteristic
43C2×#3712C2211yescharacteristic
44C32×#102C2211yescharacteristic
45#63647C2211yescharacteristic
46#63637C2211yescharacteristic
47C3×#832C2211yescharacteristic
48C3×#832C2211yescharacteristic
49C3×#817C2211yescharacteristic
50C3×#816C2211yescharacteristic
51C3×Dic3⋊C8C2211yescharacteristic
52C3×#810C2211yescharacteristic
53C3×#807C2211yescharacteristic
54#63574C2211yescharacteristic
55#63567C2211yescharacteristic
56#63567C2211yescharacteristic
57#63565C2211yescharacteristic
58#63564C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60#63554C2211yescharacteristic
61#5824—31no—
62#5695—31no—
63#5555—31no—
64#5530—31no—
65C3×#478—31no—
66C3×#416—31no—
67#5238—31no—
68#5114—31no—
69#5111—31no—
70#5069—31no—
71#5014—31no—
72#4996—31no—
73#4888—31no—
74#4886—31no—
75#4864—31no—
76#4862—31no—
77#4841—31no—
78#4836—31no—
79#4818—31no—
80#4812—31no—
81#4805—31no—
82#4797—31no—
83#4785—31no—
84#4781—31no—
85#4781—31no—
86#4781—31no—
87#4781—61no—
88#4772D311yescharacteristic, complemented
89#4771—31no—
90#4771—31no—
91#4763D311yescharacteristic, complemented
92C2×C32×D4C2311yescharacteristic
93C2×#638—21no—
94C22×C3⋊Dic3—21no—
95#3830—22no—
96#3830—41no—
97C2×C4⋊(C3⋊D3)—21no—
98C2×C4⋊(C3⋊D3)C2311yescharacteristic
99C2×C4×C3⋊D3C2311yescharacteristic
100C2×#634C2311yescharacteristic
101C2×C3×#67—21no—
102C22×C3×Dic3—21no—
103C22×C3×Dic3—21no—
104C3×#237—22no—
105C3×#237—41no—
106C2×C3×C4×D3C2311yescharacteristic
107C2×C3×Dic6C2311yescharacteristic
108C2×#626—21no—
109C2×#626D411yescharacteristic
110C2×#624—21no—
111C2×#624—21no—
112C2×C32×C8C2311yescharacteristic
113C32×C4⋊C4C2311yescharacteristic
114#3753—22no—
115#3752—21no—
116C2×C3⋊(C3⋊C8)C2311yescharacteristic
117#3744—41no—
118C3×#217—21no—
119C3×(C2×D3)⋊C4—21no—
120C3×C4⋊Dic3—21no—
121C3×C4⋊Dic3C2311yescharacteristic
122C3×C4⋊Dic3C2311yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×Dic3⋊C4—21no—
125C3×C4×Dic3—21no—
126C3×C4×Dic3C2311yescharacteristic
127C2×C3×C3⋊C8C2311yescharacteristic
128C2×C3×C3⋊C8C2311yescharacteristic
129C3×D3×C8—41no—
130#3724—21no—
131Dic3⋊Dic3—21no—
132Dic3⋊Dic3—21no—
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3—21no—
135Dic3⋊Dic3D411yescharacteristic
136#3722—21no—
137#3722—21no—
138#3722—21no—
139#3722D411yescharacteristic
140(C2×D3)⋊Dic3—21no—
141(C2×D3)⋊Dic3D411yescharacteristic
142#3717—41no—
143#3712—41no—
144#3307—91noSylow
145C2×C3×#41—31no—
146C2×#237—31no—
147C2×#237—31no—
148C2×#237—61no—
149C2×#237C2×D311yescharacteristic
150C22×C3×C8—31no—
151C3×#125—31no—
152C3×C4×D4—31no—
153C3×#117—31no—
154#946—31no—
155#944—31no—
156C2×#215—31no—
157#939—61no—
158#935—61no—
159D4×Dic3C2×D311yescharacteristic
160C2×#213—31no—
161C2×#213—31no—
162C2×#213—61no—
163#930—31no—
164#930—61no—
165#929—61no—
166C4×#67—31no—
167C2×C4⋊Dic3—61no—
168#924—31no—
169C2×Dic3⋊C4—61no—
170C2×#204—31no—
171C2×#204—31no—
172C2×#204—31no—
173C2×#204—61no—
174C2×ΓL(1,𝔽25)—31no—
175C2×ΓL(1,𝔽25)—31no—
176C2×D3×C8C2×D311yescharacteristic
177#898—61no—
178#897—31no—
179#897—31no—
180#895—31no—
181#895—31no—
182#895—31no—
183#895—61no—
184#895—61no—
185#894—61no—
186#893—31no—
187#893—61no—
188#892C2×D311yescharacteristic
189D3×C4⋊C4—31no—
190D3×C4⋊C4—31no—
191#890C2×D311yescharacteristic
192#886—61no—
193#886—61no—
194#884—61no—
195#883—61no—
196#876—61no—
197C4×D12—31no—
198C4×D12—31no—
199C4×D12—61no—
200#869—31no—
201C3×#107—31no—
202C3×#106—31no—
203C3×C4⋊C8—31no—
204C3×#103—31no—
205C3×#103—31no—
206C3×#102—21no—
207C3×#102—31no—
208C3×#102—31no—
209C3×#102C2×D311yescharacteristic
210C3×#102C2×D311yescharacteristic
211#835—31no—
212#832C2×D311yescharacteristic
213#832C2×D311yescharacteristic
214#830—31no—
215#821—31no—
216(C2×D3)⋊C8—31no—
217(C2×D3)⋊C8—31no—
218(C2×D3)⋊C8—31no—
219(C2×D3)⋊C8—61no—
220#817C2×D311yescharacteristic
221#816—31no—
222#816—31no—
223#816C2×D311yescharacteristic
224#815—31no—
225Dic3⋊C8C2×D311yescharacteristic
226#810—31no—
227#810—31no—
228#810—31no—
229#810—31no—
230#810—31no—
231#810—61no—
232#810C2×D311yescharacteristic
233#809—31no—
234#808—31no—
235#808—31no—
236#807C2×D311yescharacteristic
237#803—31no—
238C23×C32—21no—
239C22×C3⋊D3—21no—
240C22×C3⋊D3C2×D411yescharacteristic
241C22×C3×D3C2×D411yescharacteristic
242C32×D4—21no—
243C32×D4#4112yes—
244C2×C32×C4—21no—
245C2×C32×C4C2411yescharacteristic
246#638—42no—
247C2×C3⋊Dic3—21no—
248C2×C3⋊Dic3—42no—
249C2×C3⋊Dic3C2×D411yescharacteristic
250C4⋊(C3⋊D3)—21no—
251C4⋊(C3⋊D3)—21no—
252C4⋊(C3⋊D3)—42no—
253C4×C3⋊D3—21no—
254C4×C3⋊D3—21no—
255#634—21no—
256#634—21no—
257C3×#67—42no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—42no—
263C2×C3×Dic3—42no—
264C2×C3×Dic3C2×D411yescharacteristic
265C2×C3×Dic3C2×D411yescharacteristic
266C2×C3×Dic3C2×D411yescharacteristic
267C3×C4×D3—21no—
268C3×C4×D3—21no—
269C3×Dic6—21no—
270C3×Dic6—21no—
271#626—41no—
272#626—81no—
273#624—81no—
274#624—81no—
275C32×C8—21no—
276C3⋊(C3⋊C8)—21no—
277C3×C3⋊C8—21no—
278C3×C3⋊C8—21no—
279#553—91no—
280#547—91no—
281#491—91no—
282#485—91no—
283#483—91no—
284#478—31no—
285#468—91no—
286#465—91no—
287#461—91no—
288#449—91no—
289#449—91no—
290#442—91no—
291#435—91no—
292#417—91no—
293#416—31no—
294C3×#41—62no—
295C3×#41—121no—
296C2×C3×Q8—31no—
297C2×C3×D4—21no—
298C2×C3×D4—61no—
299C2×C3×D4C22×D311yescharacteristic
300C2×C3×D4C22×D311yescharacteristic
301C22×C3×C4—31no—
302C22×C3×C4—61no—
303C22×C3×C4—61no—
304C2×#67—21no—
305C2×#67—31no—
306C2×#67—61no—
307C2×#67—61no—
308C2×#67—61no—
309C2×#67—121no—
310C22×Dic3—21no—
311C22×Dic3—21no—
312C22×Dic3—61no—
313C22×Dic3—61no—
314C22×Dic3—121no—
315#237—22no—
316#237—41no—
317#237—62no—
318#237—62no—
319#237—122no—
320#237—121no—
321#237—121no—
322#237—122no—
323C2×D12—31no—
324C2×D12—31no—
325C2×D12—31no—
326C2×D12—61no—
327C2×D12—61no—
328C2×D12—61no—
329C2×D12—61no—
330C2×D12—121no—
331C2×C4×D3—31no—
332C2×C4×D3—31no—
333C2×C4×D3—61no—
334C2×C4×D3—61no—
335C2×C4×D3—61no—
336C2×C4×D3—61no—
337C2×C4×D3—61no—
338C2×C4×D3C22×D311yescharacteristic
339C2×Dic6—31no—
340C2×Dic6—31no—
341C2×Dic6—61no—
342C2×Dic6C22×D311yescharacteristic
343C2×C3×C8—21no—
344C2×C3×C8—31no—
345C2×C3×C8—31no—
346C2×C3×C8—121no—
347C2×C3×C8C22×D311yescharacteristic
348C2×C3×C8C22×D311yescharacteristic
349C3×C4⋊C4—21no—
350C3×C4⋊C4—31no—
351C3×C4⋊C4—31no—
352C3×C4⋊C4—31no—
353C3×C4⋊C4—61no—
354C3×C4⋊C4—61no—
355C3×C4⋊C4C22×D311yescharacteristic
356C3×C4⋊C4C22×D311yescharacteristic
357C3×C22⋊C4—61no—
358C3×C22⋊C4—61no—
359C3×C42—31no—
360C3×C42—61no—
361#217—21no—
362#217—31no—
363#217—61no—
364#215—121no—
365#213—62no—
366#213—62no—
367#213—122no—
368(C2×D3)⋊C4—21no—
369(C2×D3)⋊C4—31no—
370(C2×D3)⋊C4—31no—
371(C2×D3)⋊C4—31no—
372(C2×D3)⋊C4—61no—
373(C2×D3)⋊C4—61no—
374(C2×D3)⋊C4—61no—
375(C2×D3)⋊C4—61no—
376(C2×D3)⋊C4—61no—
377(C2×D3)⋊C4—61no—
378(C2×D3)⋊C4—61no—
379(C2×D3)⋊C4—61no—
380(C2×D3)⋊C4—61no—
381(C2×D3)⋊C4—121no—
382C4⋊Dic3—21no—
383C4⋊Dic3—31no—
384C4⋊Dic3—61no—
385C4⋊Dic3—61no—
386C4⋊Dic3—61no—
387C4⋊Dic3—61no—
388C4⋊Dic3C22×D311yescharacteristic
389C4⋊Dic3C22×D311yescharacteristic
390C4⋊Dic3C22×D311yescharacteristic
391Dic3⋊C4—21no—
392Dic3⋊C4—31no—
393Dic3⋊C4—61no—
394Dic3⋊C4—61no—
395Dic3⋊C4—61no—
396Dic3⋊C4—61no—
397Dic3⋊C4—61no—
398Dic3⋊C4—61no—
399C4×Dic3—21no—
400C4×Dic3C22×D311yescharacteristic
401C2×C3⋊C8—31no—
402C2×C3⋊C8—31no—
403C2×C3⋊C8—61no—
404C2×C3⋊C8C22×D311yescharacteristic
405C2×C3⋊C8C22×D311yescharacteristic
406#204—121no—
407#204—121no—
408#204—122no—
409#204—121no—
410ΓL(1,𝔽25)—121no—
411ΓL(1,𝔽25)—121no—
412D3×C8—41no—
413C22×C32—22no—
414C22×C32—41no—
415C22×C32—41no—
416C22×C32C22×D411yescharacteristic
417C2×C3⋊D3—21no—
418C2×C3⋊D3—21no—
419C2×C3⋊D3—21no—
420C2×C3⋊D3—41no—
421C2×C3⋊D3—41no—
422C2×C3⋊D3—41no—
423C2×C3×D3—21no—
424C2×C3×D3—21no—
425C2×C3×D3—21no—
426C32×C4—41no—
427C32×C4C2×#4111yescharacteristic
428C32×C4H(5,𝔽2)11yescharacteristic
429C3⋊Dic3—21no—
430C3⋊Dic3—41no—
431C3×Dic3—21no—
432C3×Dic3—21no—
433C3×Dic3—21no—
434C3×Dic3—41no—
435C3×Dic3—41no—
436C3×Dic3—41no—
437C3×Dic3—41no—
438C2×#41—31no—
439C2×#41—91no—
440C2×SD16—91no—
441C2×SD16—91no—
442C2×D8—91no—
443C2×M16—91no—
444C22×C8—31no—
445C4⋊Q8—91no—
446#126—181no—
447#125—31no—
448#123—181no—
449#123—181no—
450#123—181no—
451C22⋊Q8—91no—
452C22⋊Q8—91no—
453#121—91no—
454#121—91no—
455#121—181no—
456#121—181no—
457C4×D4—31no—
458C4×D4—91no—
459C4×D4—91no—
460C4×D4—181no—
461#117—31no—
462C2×C4⋊C4—91no—
463C2×C4⋊C4—181no—
464#107—31no—
465#106—31no—
466#106—91no—
467C4⋊C8—31no—
468#103—31no—
469#103—31no—
470#103—91no—
471#103—91no—
472#103—91no—
473#103—91no—
474#102—31no—
475#102—31no—
476#102—91no—
477#102D3211yescharacteristic
478C22⋊C8—91no—
479C22⋊C8—91no—
480#97—91no—
481C23×C3—21no—
482C23×C3—21no—
483C23×C3—31no—
484C23×C3—41no—
485C22×D3—31no—
486C22×D3—31no—
487C22×D3—61no—
488C22×D3—61no—
489C22×D3—61no—
490C22×D3—121no—
491C22×D3D3×D411yescharacteristic
492C3×Q8—61no—
493C3×Q8—61no—
494C3×D4—21no—
495C3×D4—21no—
496C3×D4—22no—
497C3×D4—41no—
498C3×D4—122no—
499C3×D4#23512yes—
500C3×D4#23912yes—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—31no—
505C2×C3×C4—31no—
506C2×C3×C4—31no—
507C2×C3×C4—41no—
508C2×C3×C4—61no—
509C2×C3×C4—61no—
510C2×C3×C4—61no—
511C2×C3×C4—61no—
512C2×C3×C4—61no—
513C2×C3×C4—61no—
514C2×C3×C4—122no—
515C2×C3×C4—122no—
516C2×C3×C4C23×D311yescharacteristic
517C2×C3×C4C23×D311yescharacteristic
518#67—42no—
519#67—121no—
520#67—122no—
521#67—122no—
522#67—124no—
523#67—241no—
524C2×Dic3—21no—
525C2×Dic3—21no—
526C2×Dic3—21no—
527C2×Dic3—21no—
528C2×Dic3—31no—
529C2×Dic3—31no—
530C2×Dic3—42no—
531C2×Dic3—42no—
532C2×Dic3—61no—
533C2×Dic3—61no—
534C2×Dic3—61no—
535C2×Dic3—121no—
536C2×Dic3—122no—
537C2×Dic3—122no—
538C2×Dic3—124no—
539C2×Dic3D3×D411yescharacteristic
540C2×Dic3D3×D411yescharacteristic
541C2×Dic3D3×D411yescharacteristic
542D12—61no—
543D12—61no—
544D12—61no—
545D12—61no—
546D12—121no—
547D12—121no—
548D12—122no—
549D12—122no—
550D12—121no—
551D12—242no—
552D12—241no—
553C4×D3—21no—
554C4×D3—21no—
555C4×D3—61no—
556C4×D3—61no—
557C4×D3—61no—
558C4×D3—61no—
559C4×D3—121no—
560C4×D3—121no—
561C4×D3—241no—
562C4×D3—241no—
563C4×D3—241no—
564C4×D3—241no—
565Dic6—21no—
566Dic6—21no—
567Dic6—62no—
568Dic6—61no—
569Dic6—61no—
570Dic6—61no—
571Dic6—61no—
572Dic6—121no—
573C3×C8—21no—
574C3×C8—21no—
575C3×C8—41no—
576C3×C8—61no—
577C3×C8—61no—
578C3⋊C8—21no—
579C3⋊C8—21no—
580C3⋊C8—61no—
581C3⋊C8—61no—
582C3⋊C8—121no—
583C2×C32—42no—
584C2×C32#54611yescharacteristic
585C2×C32#57511yescharacteristic
586C2×C32#57711yescharacteristic
587C3⋊D3—41no—
588C3⋊D3—81no—
589C3×D3—41no—
590#41—62no—
591#41—121no—
592#41—182no—
593#41—361no—
594C2×Q8—31no—
595C2×Q8—91no—
596C2×D4—61no—
597C2×D4—91no—
598C2×D4—91no—
599C2×D4—181no—
600C2×D4—181no—
601C2×D4—181no—
602C2×D4C2×D3211yescharacteristic
603C22×C4—31no—
604C22×C4—61no—
605C22×C4—61no—
606C22×C4—91no—
607C22×C4—181no—
608C22×C4—181no—
609C22×C4—181no—
610SD16—361no—
611SD16—361no—
612D8—182no—
613M16—361no—
614C2×C8—31no—
615C2×C8—31no—
616C2×C8—91no—
617C2×C8—121no—
618C2×C8C2×D3211yescharacteristic
619C4⋊C4—31no—
620C4⋊C4—31no—
621C4⋊C4—31no—
622C4⋊C4—61no—
623C4⋊C4—61no—
624C4⋊C4—91no—
625C4⋊C4—181no—
626C4⋊C4—181no—
627C4⋊C4—181no—
628C4⋊C4—181no—
629C4⋊C4—181no—
630C4⋊C4C2×D3211yescharacteristic
631C22⋊C4—61no—
632C22⋊C4—61no—
633C22⋊C4—91no—
634C22⋊C4—91no—
635C22⋊C4—181no—
636C22⋊C4—181no—
637C22⋊C4—181no—
638C22⋊C4—181no—
639C22⋊C4—181no—
640C42—31no—
641C42—61no—
642C22×C3—22no—
643C22×C3—22no—
644C22×C3—21no—
645C22×C3—42no—
646C22×C3—41no—
647C22×C3—41no—
648C22×C3—41no—
649C22×C3—41no—
650C22×C3—61no—
651C22×C3—61no—
652C22×C3—61no—
653C22×C3—81no—
654C22×C3—81no—
655C22×C3C2×D3×D411yescharacteristic
656C22×C3C2×D3×D411yescharacteristic
657C2×D3—21no—
658C2×D3—21no—
659C2×D3—21no—
660C2×D3—61no—
661C2×D3—61no—
662C2×D3—61no—
663C2×D3—61no—
664C2×D3—61no—
665C2×D3—61no—
666C2×D3—121no—
667C2×D3—121no—
668C2×D3—121no—
669C2×D3—121no—
670C2×D3—121no—
671C2×D3—121no—
672C2×D3—121no—
673C2×D3—121no—
674C2×D3—121no—
675C2×D3—241no—
676C2×D3—241no—
677C2×D3—241no—
678C3×C4—21no—
679C3×C4—21no—
680C3×C4—41no—
681C3×C4—41no—
682C3×C4—61no—
683C3×C4—61no—
684C3×C4—61no—
685C3×C4—81no—
686C3×C4—121no—
687C3×C4—121no—
688C3×C4—121no—
689C3×C4—121no—
690C3×C4C2×#23511yescharacteristic
691C3×C4#100411yescharacteristic
692C3×C4C2×#23911yescharacteristic
693C3×C4#100911yescharacteristic
694Dic3—21no—
695Dic3—21no—
696Dic3—21no—
697Dic3—41no—
698Dic3—41no—
699Dic3—41no—
700Dic3—41no—
701Dic3—61no—
702Dic3—61no—
703Dic3—121no—
704Dic3—122no—
705Dic3—121no—
706Dic3—121no—
707C32#330711yescharacteristic, complemented, Sylow
708C23—21no—
709C23—31no—
710C23—91no—
711C23—181no—
712Q8—61no—
713Q8—61no—
714Q8—181no—
715Q8—181no—
716D4—21no—
717D4—122no—
718D4—181no—
719D4—181no—
720D4—362no—
721D4—361no—
722D4—362no—
723D4—721no—
724D4#379912yes—
725C2×C4—21no—
726C2×C4—31no—
727C2×C4—31no—
728C2×C4—31no—
729C2×C4—61no—
730C2×C4—61no—
731C2×C4—61no—
732C2×C4—61no—
733C2×C4—61no—
734C2×C4—61no—
735C2×C4—91no—
736C2×C4—122no—
737C2×C4—122no—
738C2×C4—181no—
739C2×C4—181no—
740C2×C4—181no—
741C2×C4—362no—
742C2×C4—721no—
743C2×C4—721no—
744C2×C4C22×D3211yescharacteristic
745C8—21no—
746C8—61no—
747C8—61no—
748C8—181no—
749C2×C3—21no—
750C2×C3—21no—
751C2×C3—21no—
752C2×C3—42no—
753C2×C3—42no—
754C2×C3—82no—
755C2×C3—121no—
756C2×C3#549011yescharacteristic
757C2×C3#563011yescharacteristic
758C2×C3#576811yescharacteristic
759C2×C3#577011yescharacteristic
760C2×C3#577011yescharacteristic
761C2×C3#577311yescharacteristic
762D3—41no—
763D3—121no—
764D3—121no—
765D3—241no—
766D3—241no—
767D3—241no—
768D3—481no—
769C22—22no—
770C22—41no—
771C22—41no—
772C22—61no—
773C22—61no—
774C22—61no—
775C22—181no—
776C22—181no—
777C22—181no—
778C22—361no—
779C22—361no—
780C22—361no—
781C22D32×D411yescharacteristic
782C4—41no—
783C4—61no—
784C4—61no—
785C4—61no—
786C4—121no—
787C4—121no—
788C4—121no—
789C4—121no—
790C4—181no—
791C4—361no—
792C4C2×#379911yescharacteristic
793C4#6431411yescharacteristic
794C3—21no—
795C3#7885311yescharacteristic, complemented
796C3#8118811yescharacteristic, complemented
797C2—42no—
798C2—121no—
799C2—361no—
800C2—721no—
801C2#1059418711yescharacteristic
802C2#1059472911yescharacteristic
803C2#1059475711yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
hypercenter#102D32
hypocenterC32#3307
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
1. #10595248C2semidirect
2. #10594578C2semidirect
3. #10592480C2semidirect
4. C3×#4772C2semidirect
5. C3×#4763C2semidirect
6. #10591452C2semidirect
7. #10591418C2semidirect
8. #10591404C2semidirect
9. #10590830C2semidirect
10. #10590760C2semidirect
11. #10590727C2semidirect
12. #10590686C2semidirect
13. #10590562C2semidirect
14. #10590522C2semidirect
15. #10590429C2semidirect
88. #4772D3semidirect
91. #4763D3semidirect
707. C32#3307semidirect
795. C3#78853semidirect
796. C3#81188semidirect

Maximal subgroups

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

subgroupindex
#105952482
#105945782
#105924802
C3×#47722
C3×#47632
#105914522
#105914182
#105914042
#105908302
#105907602
#105907272
#105906862
#105905622
#105905222
#105904292
#811883
#788533