Finite Group Databasebeta

← #11888696

Subgroups — #11888696

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#10594489C211yesmaximal, characteristic, complemented
2#10594381C211yesmaximal, characteristic, complemented
3#10592561C211yesmaximal, characteristic, complemented
4C3×#4871C211yesmaximal, characteristic, complemented
5C3×#4864C211yesmaximal, characteristic, complemented
6#10590964C211yesmaximal, characteristic, complemented
7#10590954C211yesmaximal, characteristic, complemented
8#10590752C211yesmaximal, characteristic, complemented
9#10590727C211yesmaximal, characteristic, complemented
10#10590613C211yesmaximal, characteristic, complemented
11#10590612C211yesmaximal, characteristic, complemented
12#10590562C211yesmaximal, characteristic, complemented
13#10590506C211yesmaximal, characteristic, complemented
14#10590455C211yesmaximal, characteristic, complemented
15#10590448C211yesmaximal, characteristic, complemented
16#81188—31nomaximal
17#80684—31nomaximal
18C2×#3796C2211yescharacteristic
19C2×#3795C2211yescharacteristic
20#64106C2211yescharacteristic
21C4⋊C4×C3⋊D3C2211yescharacteristic
22C2×C3×#204C2211yescharacteristic
23C2×C3×D3×C8C2211yescharacteristic
24C3×#897C2211yescharacteristic
25C3×#895C2211yescharacteristic
26C3×#893C2211yescharacteristic
27C3×#890C2211yescharacteristic
28#63916—21no—
29#63916C2211yescharacteristic
30#63906—21no—
31C4×#626C2211yescharacteristic
32Dic3×D12C2211yescharacteristic
33#63891—21no—
34#63890—21no—
35D3×C4⋊Dic3—21no—
36#63884—21no—
37#63881—21no—
38#63866C2211yescharacteristic
39#63858—21no—
40#63841C2211yescharacteristic
41C2×#3716C2211yescharacteristic
42C2×#3713C2211yescharacteristic
43C2×#3712C2211yescharacteristic
44C32×#106C2211yescharacteristic
45#63647C2211yescharacteristic
46#63643C2211yescharacteristic
47#63637C2211yescharacteristic
48#63635C2211yescharacteristic
49C3×#821C2211yescharacteristic
50C3×Dic3⋊C8C2211yescharacteristic
51C3×#810C2211yescharacteristic
52C3×#809C2211yescharacteristic
53C3×#809C2211yescharacteristic
54C3×#807C2211yescharacteristic
55#63567C2211yescharacteristic
56#63566C2211yescharacteristic
57#63565C2211yescharacteristic
58#63563C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60#63554C2211yescharacteristic
61#5695—31no—
62#5631—31no—
63#5614—31no—
64#5555—31no—
65C3×#478—31no—
66C3×#465—31no—
67#5172—31no—
68#5162—31no—
69#5113—31no—
70#5111—31no—
71#5069—31no—
72#5045—31no—
73#5037—31no—
74#5014—31no—
75#4888—31no—
76#4886—31no—
77#4871D311yescharacteristic, complemented
78#4864D311yescharacteristic, complemented
79#4862—31no—
80#4862—31no—
81#4862—61no—
82#4841—31no—
83#4836—31no—
84#4803—31no—
85#4797—31no—
86#4785—31no—
87#4781—31no—
88#4781—31no—
89#4780—31no—
90#4772—31no—
91#4771—31no—
92C2×C4×C3⋊D3—21no—
93C2×C4×C3⋊D3C2311yescharacteristic
94C2×#634C2311yescharacteristic
95C2×C3×D12—21no—
96C2×C3×D12C2311yescharacteristic
97C2×C3×D12C2311yescharacteristic
98C2×C3×C4×D3—21no—
99C2×C3×C4×D3C2311yescharacteristic
100C2×C3×Dic6C2311yescharacteristic
101C2×#626—21no—
102C2×#626—21no—
103C2×#626D411yescharacteristic
104C2×#625—21no—
105C2×D3×Dic3—21no—
106C2×D3×Dic3—21no—
107C2×D3×Dic3—21no—
108#3796—22no—
109#3796—41no—
110#3795—22no—
111#3795—41no—
112C2×C32×C8C2311yescharacteristic
113C32×C4⋊C4C2311yescharacteristic
114C32×C4⋊C4C2311yescharacteristic
115#3752—21no—
116C4⋊(C3⋊Dic3)—21no—
117C4⋊(C3⋊Dic3)C2311yescharacteristic
118#3750—21no—
119C2×C3⋊(C3⋊C8)C2311yescharacteristic
120C3×(C2×D3)⋊C4—21no—
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4—21no—
123C3×C4⋊Dic3—21no—
124C3×C4⋊Dic3—21no—
125C3×C4⋊Dic3C2311yescharacteristic
126C3×Dic3⋊C4—21no—
127C3×C4×Dic3C2311yescharacteristic
128C2×C3×C3⋊C8C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130C3×#204—41no—
131C3×D3×C8—41no—
132Dic3⋊Dic3—21no—
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3D411yescharacteristic
135#3722D411yescharacteristic
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3D411yescharacteristic
140Dic32—21no—
141#3716—41no—
142#3713—22no—
143#3712—41no—
144#3307—91noSylow
145C2×#239—31no—
146C2×#237—31no—
147C2×#237—31no—
148C2×#235—31no—
149C2×C3×SD16—31no—
150C22×C3×C8—31no—
151C3×#125—31no—
152C3×C22⋊Q8—31no—
153C3×#121—31no—
154C3×C4×D4—31no—
155#944—31no—
156#938—31no—
157#938—61no—
158#935—61no—
159D4×Dic3—31no—
160C2×#214—31no—
161C2×#213—31no—
162C2×#213—31no—
163#930—61no—
164C4×#67—31no—
165#926—31no—
166C2×C4⋊Dic3—61no—
167C2×#204—31no—
168C2×#204C2×D311yescharacteristic
169C2×ΓL(1,𝔽25)—31no—
170C2×ΓL(1,𝔽25)—31no—
171C2×D3×C8C2×D311yescharacteristic
172#898—61no—
173#897—31no—
174#897—31no—
175#897—61no—
176#897C2×D311yescharacteristic
177#895—31no—
178#895—61no—
179#895C2×D311yescharacteristic
180#894—61no—
181#894—61no—
182#893—61no—
183#893C2×D311yescharacteristic
184#892—31no—
185D3×C4⋊C4—31no—
186D3×C4⋊C4—31no—
187D3×C4⋊C4—61no—
188D3×C4⋊C4—61no—
189#890C2×D311yescharacteristic
190#886—61no—
191#886—61no—
192#884—61no—
193#883—61no—
194#67⋊C4—61no—
195#879—61no—
196C4×D12—31no—
197C4×D12—31no—
198#869—31no—
199C3×#107—31no—
200C3×#106—21no—
201C3×#106C2×D311yescharacteristic
202C3×#106C2×D311yescharacteristic
203C3×C4⋊C8—31no—
204C3×#103—31no—
205C3×#102—31no—
206C3×#102—31no—
207C3×#102—31no—
208#835—31no—
209#835—31no—
210#832—31no—
211#830—31no—
212#821—31no—
213#821C2×D311yescharacteristic
214(C2×D3)⋊C8—31no—
215(C2×D3)⋊C8—31no—
216(C2×D3)⋊C8—31no—
217(C2×D3)⋊C8—61no—
218#816—31no—
219#816—31no—
220#816—31no—
221#816—31no—
222#816—61no—
223#815—31no—
224Dic3⋊C8C2×D311yescharacteristic
225#810—31no—
226#810—31no—
227#810—31no—
228#810—31no—
229#810—61no—
230#810C2×D311yescharacteristic
231#809C2×D311yescharacteristic
232#809C2×D311yescharacteristic
233#808—31no—
234#808—31no—
235#808—61no—
236#807C2×D311yescharacteristic
237#803—31no—
238C22×C3⋊D3C2×D411yescharacteristic
239C22×C3×D3—21no—
240C22×C3×D3—21no—
241C22×C3×D3C2×D411yescharacteristic
242C2×C32×C4—21no—
243C2×C32×C4—21no—
244C2×C32×C4C2411yescharacteristic
245C2×C3⋊Dic3—21no—
246C2×C3⋊Dic3—21no—
247C2×C3⋊Dic3C2×D411yescharacteristic
248C4×C3⋊D3—21no—
249C4×C3⋊D3—21no—
250C4×C3⋊D3—81no—
251#634—21no—
252#634—21no—
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—81no—
262C3×D12#4112yes—
263C3×C4×D3—21no—
264C3×C4×D3—21no—
265C3×C4×D3—42no—
266C3×Dic6—21no—
267C3×Dic6—21no—
268#626—41no—
269#626—42no—
270#626—42no—
271#625—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—91no—
282#485—91no—
283#483—91no—
284#478—31no—
285#468—91no—
286#465—31no—
287#461—91no—
288#449—91no—
289#449—91no—
290#442—91no—
291#435—91no—
292#417—91no—
293#416—91no—
294C2×C3×Q8—31no—
295C2×C3×D4—31no—
296C2×C3×D4—31no—
297C2×C3×D4—61no—
298C22×C3×C4—31no—
299C22×C3×C4—61no—
300C2×#67—31no—
301C2×#67—61no—
302C2×#67—61no—
303C2×#67—61no—
304C2×#67—61no—
305C22×Dic3—61no—
306C22×Dic3—61no—
307C22×Dic3—61no—
308#239—62no—
309#239—121no—
310#237—62no—
311#237—62no—
312#237—121no—
313#237—121no—
314#235—62no—
315#235—121no—
316C2×D12—21no—
317C2×D12—31no—
318C2×D12—61no—
319C2×D12—61no—
320C2×D12C22×D311yescharacteristic
321C2×D12C22×D311yescharacteristic
322C2×C4×D3—21no—
323C2×C4×D3—31no—
324C2×C4×D3—31no—
325C2×C4×D3—61no—
326C2×C4×D3—61no—
327C2×C4×D3—61no—
328C2×C4×D3—61no—
329C2×C4×D3—61no—
330C2×C4×D3—61no—
331C2×C4×D3—121no—
332C2×C4×D3C22×D311yescharacteristic
333C2×Dic6—31no—
334C2×Dic6—31no—
335C2×Dic6—61no—
336C2×Dic6C22×D311yescharacteristic
337C3×SD16—121no—
338C2×C3×C8—21no—
339C2×C3×C8—31no—
340C2×C3×C8—31no—
341C2×C3×C8—121no—
342C2×C3×C8C22×D311yescharacteristic
343C2×C3×C8C22×D311yescharacteristic
344C3×C4⋊C4—21no—
345C3×C4⋊C4—21no—
346C3×C4⋊C4—31no—
347C3×C4⋊C4—61no—
348C3×C4⋊C4—61no—
349C3×C4⋊C4—61no—
350C3×C4⋊C4C22×D311yescharacteristic
351C3×C4⋊C4C22×D311yescharacteristic
352C3×C4⋊C4C22×D311yescharacteristic
353C3×C4⋊C4C22×D311yescharacteristic
354C3×C22⋊C4—61no—
355C3×C22⋊C4—61no—
356C3×C22⋊C4—61no—
357C3×C42—31no—
358#217—31no—
359#217—61no—
360#217—61no—
361#217—61no—
362#214—121no—
363#213—62no—
364#213—62no—
365(C2×D3)⋊C4—21no—
366(C2×D3)⋊C4—21no—
367(C2×D3)⋊C4—21no—
368(C2×D3)⋊C4—31no—
369(C2×D3)⋊C4—31no—
370(C2×D3)⋊C4—31no—
371(C2×D3)⋊C4—61no—
372(C2×D3)⋊C4—61no—
373(C2×D3)⋊C4—61no—
374(C2×D3)⋊C4—61no—
375(C2×D3)⋊C4—61no—
376(C2×D3)⋊C4—121no—
377C4⋊Dic3—21no—
378C4⋊Dic3—21no—
379C4⋊Dic3—31no—
380C4⋊Dic3—31no—
381C4⋊Dic3—31no—
382C4⋊Dic3—61no—
383C4⋊Dic3—61no—
384C4⋊Dic3—61no—
385C4⋊Dic3—61no—
386C4⋊Dic3—61no—
387C4⋊Dic3—121no—
388C4⋊Dic3C22×D311yescharacteristic
389Dic3⋊C4—21no—
390Dic3⋊C4—31no—
391Dic3⋊C4—61no—
392Dic3⋊C4—61no—
393Dic3⋊C4—61no—
394Dic3⋊C4—61no—
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⋊C8C22×D311yescharacteristic
403C2×C3⋊C8C22×D311yescharacteristic
404#204—41no—
405#204—121no—
406ΓL(1,𝔽25)—121no—
407ΓL(1,𝔽25)—121no—
408D3×C8—41no—
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—91no—
435C2×#41—91no—
436C2×SD16—31no—
437C2×SD16—91no—
438C2×D8—91no—
439C2×M16—91no—
440C22×C8—31no—
441C4⋊Q8—91no—
442#126—181no—
443#125—31no—
444#123—181no—
445#123—181no—
446#123—181no—
447C22⋊Q8—31no—
448C22⋊Q8—91no—
449#121—31no—
450#121—91no—
451#121—181no—
452#121—181no—
453C4×D4—31no—
454C4×D4—91no—
455C4×D4—91no—
456C4×D4—181no—
457#117—91no—
458C2×C4⋊C4—91no—
459C2×C4⋊C4—181no—
460#107—31no—
461#106—91no—
462#106D3211yescharacteristic
463C4⋊C8—31no—
464#103—31no—
465#103—91no—
466#103—91no—
467#103—91no—
468#103—91no—
469#103—91no—
470#102—31no—
471#102—31no—
472#102—31no—
473#102—91no—
474C22⋊C8—91no—
475C22⋊C8—91no—
476#97—91no—
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—61no—
487C3×Q8—61no—
488C3×D4—32no—
489C3×D4—61no—
490C3×D4—61no—
491C3×D4—61no—
492C3×D4—241no—
493C2×C3×C4—21no—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—31no—
499C2×C3×C4—31no—
500C2×C3×C4—31no—
501C2×C3×C4—41no—
502C2×C3×C4—41no—
503C2×C3×C4—61no—
504C2×C3×C4—61no—
505C2×C3×C4—61no—
506C2×C3×C4—61no—
507C2×C3×C4—122no—
508C2×C3×C4C23×D311yescharacteristic
509C2×C3×C4C23×D311yescharacteristic
510#67—121no—
511#67—122no—
512#67—122no—
513#67—122no—
514#67—122no—
515C2×Dic3—21no—
516C2×Dic3—21no—
517C2×Dic3—31no—
518C2×Dic3—31no—
519C2×Dic3—61no—
520C2×Dic3—61no—
521C2×Dic3—61no—
522C2×Dic3—61no—
523C2×Dic3—61no—
524C2×Dic3—121no—
525C2×Dic3—121no—
526C2×Dic3—122no—
527C2×Dic3—122no—
528C2×Dic3—241no—
529C2×Dic3D3×D411yescharacteristic
530C2×Dic3D3×D411yescharacteristic
531C2×Dic3D3×D411yescharacteristic
532D12—21no—
533D12—21no—
534D12—21no—
535D12—81no—
536D12—121no—
537D12—122no—
538D12—122no—
539D12#23912yes—
540C4×D3—21no—
541C4×D3—21no—
542C4×D3—42no—
543C4×D3—61no—
544C4×D3—61no—
545C4×D3—61no—
546C4×D3—61no—
547C4×D3—121no—
548C4×D3—121no—
549C4×D3—122no—
550C4×D3—122no—
551C4×D3—241no—
552C4×D3—241no—
553C4×D3—241no—
554C4×D3—242no—
555Dic6—21no—
556Dic6—21no—
557Dic6—61no—
558Dic6—61no—
559Dic6—61no—
560Dic6—61no—
561Dic6—121no—
562Dic6—121no—
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—182no—
581#41—182no—
582#41—361no—
583#41—361no—
584C2×Q8—31no—
585C2×Q8—91no—
586C2×D4—31no—
587C2×D4—31no—
588C2×D4—61no—
589C2×D4—91no—
590C2×D4—181no—
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—182no—
603M16—361no—
604C2×C8—31no—
605C2×C8—31no—
606C2×C8—91no—
607C2×C8—121no—
608C2×C8C2×D3211yescharacteristic
609C4⋊C4—31no—
610C4⋊C4—61no—
611C4⋊C4—61no—
612C4⋊C4—61no—
613C4⋊C4—91no—
614C4⋊C4—91no—
615C4⋊C4—181no—
616C4⋊C4—181no—
617C4⋊C4—181no—
618C4⋊C4—181no—
619C4⋊C4C2×D3211yescharacteristic
620C4⋊C4C2×D3211yescharacteristic
621C22⋊C4—61no—
622C22⋊C4—61no—
623C22⋊C4—61no—
624C22⋊C4—91no—
625C22⋊C4—91no—
626C22⋊C4—181no—
627C22⋊C4—181no—
628C22⋊C4—181no—
629C22⋊C4—181no—
630C42—31no—
631C42—181no—
632C22×C3—21no—
633C22×C3—61no—
634C22×C3—61no—
635C22×C3—62no—
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×C4#100411yescharacteristic
676C3×C4C2×#23911yescharacteristic
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—61no—
699Q8—61no—
700Q8—181no—
701Q8—181no—
702D4—32no—
703D4—61no—
704D4—61no—
705D4—61no—
706D4—241no—
707D4—361no—
708D4—362no—
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#561011yescharacteristic
742C2×C3#563011yescharacteristic
743C2×C3#576211yescharacteristic
744C2×C3#576811yescharacteristic
745C2×C3#577011yescharacteristic
746C2×C3#577311yescharacteristic
747D3—42no—
748D3—41no—
749D3—81no—
750D3—122no—
751D3—121no—
752D3—121no—
753C22—61no—
754C22—62no—
755C22—61no—
756C22—61no—
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×#23911yescharacteristic
778C3—21no—
779C3#8068411yescharacteristic, complemented
780C3#8118811yescharacteristic, complemented
781C2—121no—
782C2—122no—
783C2—241no—
784C2—361no—
785C2#1059462211yescharacteristic
786C2#1059474511yescharacteristic
787C2#1059475311yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#106C22
socleC22×C32C22×D4
hypercenter#106D32
hypocenterC32#3307
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #106

Complements

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

NH ≅ G/Ntype
1. #10594489C2semidirect
2. #10594381C2semidirect
3. #10592561C2semidirect
4. C3×#4871C2semidirect
5. C3×#4864C2semidirect
6. #10590964C2semidirect
7. #10590954C2semidirect
8. #10590752C2semidirect
9. #10590727C2semidirect
10. #10590613C2semidirect
11. #10590612C2semidirect
12. #10590562C2semidirect
13. #10590506C2semidirect
14. #10590455C2semidirect
15. #10590448C2semidirect
77. #4871D3semidirect
78. #4864D3semidirect
693. C32#3307semidirect
779. C3#80684semidirect
780. C3#81188semidirect

Maximal subgroups

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

subgroupindex
#105944892
#105943812
#105925612
C3×#48712
C3×#48642
#105909642
#105909542
#105907522
#105907272
#105906132
#105906122
#105905622
#105905062
#105904552
#105904482
#811883
#806843