Finite Group Databasebeta

← #11889272

Subgroups — #11889272

Order 1152.

857 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595229C211yesmaximal, characteristic
2#10594565C211yesmaximal, characteristic, complemented
3#10592478C211yesmaximal, characteristic, complemented
4C3×#4770C211yesmaximal, characteristic, complemented
5C3×#4767C211yesmaximal, characteristic, complemented
6#10591488C211yesmaximal, characteristic, complemented
7#10591465C211yesmaximal, characteristic, complemented
8#10591458C211yesmaximal, characteristic, complemented
9#10590965C211yesmaximal, characteristic, complemented
10#10590854C211yesmaximal, characteristic, complemented
11#10590757C211yesmaximal, characteristic, complemented
12#10590738C211yesmaximal, characteristic, complemented
13#10590611C211yesmaximal, characteristic, complemented
14#10590521C211yesmaximal, characteristic, complemented
15#10590454C211yesmaximal, characteristic, complemented
16#80617—31nomaximal
17#78935—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19C2×#3796C2211yescharacteristic
20#64147C2211yescharacteristic
21#64101C2211yescharacteristic, complemented
22C3×#936C2211yescharacteristic
23C2×C3×#214C2211yescharacteristic
24C2×C3×Dic12C2211yescharacteristic, complemented
25C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
26C3×#892C2211yescharacteristic
27C3×#887C2211yescharacteristic, complemented
28#63977—21no—
29#63971—21no—
30#63969—21no—
31D3×#217—21no—
32#63918C2211yescharacteristic, complemented
33C4×#627—21no—
34C4×#626C2211yescharacteristic
35Dic3×D12C2211yescharacteristic
36#63871C2211yescharacteristic, complemented
37#63868—21no—
38#63862—21no—
39#63856C2211yescharacteristic
40#63856C2211yescharacteristic
41#63852—21no—
42C2×#3715C2211yescharacteristic
43C2×#3710C2211yescharacteristic, complemented
44C32×#102C2211yescharacteristic
45#63659C2211yescharacteristic
46#63647C2211yescharacteristic, complemented
47#63644C2211yescharacteristic, complemented
48#63634C2211yescharacteristic, complemented
49C3×#832C2211yescharacteristic
50C3×#821C2211yescharacteristic
51C3×Dic3⋊C8C2211yescharacteristic, complemented
52C3×#810C2211yescharacteristic, complemented
53C3×#809C2211yescharacteristic
54#63573C2211yescharacteristic, complemented
55#63566C2211yescharacteristic, complemented
56#63566C2211yescharacteristic, complemented
57#63565C2211yescharacteristic, complemented
58#63563C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60#63554C2211yescharacteristic, complemented
61#5806—31no—
62#5676—31no—
63#5584—31no—
64#5533—31no—
65C3×#464—31no—
66C3×#418—31no—
67#5218—31no—
68#5189—31no—
69#5187—31no—
70#5171—31no—
71#5169—31no—
72#5137—31no—
73#5127—31no—
74#5055—31no—
75#5026—31no—
76#4996—31no—
77#4842—31no—
78#4836—31no—
79#4815—31no—
80#4804—31no—
81#4783—31no—
82#4779—31no—
83#4779—31no—
84#4779—61no—
85#4778—31no—
86#4772—31no—
87#4770D311yescharacteristic, complemented
88#4767D311yescharacteristic, complemented
89#4765—31no—
90#4761—31no—
91#4757—31no—
92C23×C3×D3—21no—
93C2×C32×D4C2311yescharacteristic
94C2×#638—21no—
95C2×C4×C3⋊D3C2311yescharacteristic
96C2×C3×#67—21no—
97C3×D3×D4—22no—
98C3×D3×D4—41no—
99C2×C3×D12C2311yescharacteristic
100C2×C3×C4×D3C2311yescharacteristic
101C2×C3×Dic6C2311yescharacteristic
102C2×C3×Dic6C2311yescharacteristic
103C2×#627—21no—
104C2×#626—21no—
105C2×#626D411yescharacteristic
106C2×D3×Dic3—21no—
107C2×D3×Dic3—21no—
108#3796—22no—
109#3796—41no—
110C2×C32×C8C2311yescharacteristic
111C32×C4⋊C4C2311yescharacteristic
112#3757—21no—
113#3752—21no—
114C4⋊(C3⋊Dic3)C2311yescharacteristic
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116C4×C3⋊Dic3—21no—
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118C3×#217—21no—
119C3×#217—21no—
120C3×#214—41no—
121C3×(C2×D3)⋊C4—21no—
122C3×C4⋊Dic3C2311yescharacteristic
123C3×Dic3⋊C4—21no—
124C3×C4×Dic3—21no—
125C3×C4×Dic3—21no—
126C3×C4×Dic3C2311yescharacteristic
127C2×C3×C3⋊C8C2311yescharacteristic
128C2×C3×C3⋊C8C2311yescharacteristic
129C3×Dic12—41no—
130C3×ΓL(1,𝔽25)—41no—
131#3724—21no—
132#3724—21no—
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3—21no—
135Dic3⋊Dic3D411yescharacteristic
136#3722—21no—
137#3722D411yescharacteristic
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141(C2×D3)⋊Dic3D411yescharacteristic
142#3715—22no—
143#3710—41no—
144#3311—91noSylow
145C22×C3×D4—31no—
146C2×#239—31no—
147C2×#237—31no—
148C2×D3×D4C2×D311yescharacteristic
149C2×C3×Q16—31no—
150C2×C3×SD16—31no—
151C2×C3×M16—31no—
152C3×#124—31no—
153C3×C4×Q8—31no—
154C3×#117—31no—
155#953—61no—
156C2×#217—61no—
157#946—31no—
158#946—31no—
159#946—31no—
160C2×#215—31no—
161#939—61no—
162#938—31no—
163#938—31no—
164#938—61no—
165#936C2×D311yescharacteristic
166#935—61no—
167D4×Dic3—31no—
168C2×#214—31no—
169C2×#214C2×D311yescharacteristic
170C4×#67—31no—
171#924—31no—
172#924—31no—
173C2×Dic12C2×D311yescharacteristic, complemented
174C2×ΓL(1,𝔽25)C2×D311yescharacteristic
175C2×D3×C8—31no—
176C2×D3×C8—31no—
177#898—61no—
178#898—61no—
179#897—31no—
180#892—31no—
181#892—31no—
182#892—61no—
183#892C2×D311yescharacteristic
184#888—31no—
185#887C2×D311yescharacteristic, complemented
186#885—61no—
187#884—61no—
188#883—61no—
189#882—61no—
190D3×C22⋊C4—61no—
191#879—61no—
192#876—61no—
193#875—61no—
194C4×D12—31no—
195C4×D12—31no—
196#869—31no—
197C4×Dic6—61no—
198C4×Dic6—61no—
199C3×C4⋊C8—31no—
200C3×#103—31no—
201C3×#102—21no—
202C3×#102—31no—
203C3×#102—31no—
204C3×#102—31no—
205C3×#102C2×D311yescharacteristic
206C3×#102C2×D311yescharacteristic
207#835—31no—
208#835—31no—
209#835—31no—
210#832—31no—
211#832—31no—
212#832—31no—
213#832—61no—
214#832C2×D311yescharacteristic
215#830—31no—
216#821—31no—
217#821C2×D311yescharacteristic
218(C2×D3)⋊C8—31no—
219(C2×D3)⋊C8—31no—
220(C2×D3)⋊C8—31no—
221(C2×D3)⋊C8—61no—
222#817—31no—
223#817—31no—
224#817—31no—
225#817—61no—
226#816—31no—
227#816—31no—
228#815—31no—
229Dic3⋊C8C2×D311yescharacteristic, complemented
230#810—31no—
231#810C2×D311yescharacteristic, complemented
232#809C2×D311yescharacteristic
233#808—31no—
234#807—31no—
235#807—31no—
236#807—61no—
237#803—31no—
238C23×C32—21no—
239C22×C3⋊D3C2×D411yescharacteristic
240C22×C3×D3—21no—
241C22×C3×D3—42no—
242C22×C3×D3—42no—
243C22×C3×D3—81no—
244C22×C3×D3C2×D411yescharacteristic
245C32×D4—21no—
246C32×D4—21no—
247C2×C32×C4—21no—
248C2×C32×C4C2411yescharacteristic
249#638—81no—
250C2×C3⋊Dic3—21no—
251C2×C3⋊Dic3—21no—
252C2×C3⋊Dic3C2×D411yescharacteristic
253C4×C3⋊D3—21no—
254C4×C3⋊D3—21no—
255C3×#67—42no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3C2×D411yescharacteristic
260C2×C3×Dic3C2×D411yescharacteristic
261C2×C3×Dic3C2×D411yescharacteristic
262C3×D12—21no—
263C3×D12#4112yes—
264C3×C4×D3—21no—
265C3×C4×D3—21no—
266C3×Dic6—21no—
267C3×Dic6—21no—
268C3×Dic6—21no—
269C3×Dic6—21no—
270#627—42no—
271#626—41no—
272#626—42no—
273D3×Dic3—42no—
274D3×Dic3—81no—
275C32×C8—21no—
276C3⋊(C3⋊C8)—21no—
277C3×C3⋊C8—21no—
278C3×C3⋊C8—21no—
279#556—91no—
280#546—91no—
281#489—91no—
282#485—91no—
283#482—91no—
284#476—91no—
285#470—91no—
286#465—91no—
287#464—31no—
288#452—91no—
289#450—91no—
290#440—91no—
291#435—91no—
292#418—31no—
293#416—91no—
294C24×C3—61no—
295C23×D3—21no—
296C2×C3×Q8—31no—
297C2×C3×Q8—31no—
298C2×C3×D4—21no—
299C2×C3×D4—31no—
300C2×C3×D4—61no—
301C2×C3×D4—62no—
302C2×C3×D4—121no—
303C2×C3×D4C22×D311yescharacteristic
304C2×C3×D4C22×D311yescharacteristic
305C22×C3×C4—31no—
306C2×#67—21no—
307C2×#67—31no—
308C2×#67—61no—
309C2×#67—61no—
310C2×#67—61no—
311C2×#67—121no—
312C22×Dic3—61no—
313C22×Dic3—61no—
314#239—62no—
315#239—121no—
316#237—62no—
317#237—121no—
318D3×D4—22no—
319D3×D4—41no—
320C2×D12—31no—
321C2×D12—61no—
322C2×D12C22×D311yescharacteristic
323C2×C4×D3—31no—
324C2×C4×D3—31no—
325C2×C4×D3—61no—
326C2×C4×D3—61no—
327C2×C4×D3—61no—
328C2×C4×D3C22×D311yescharacteristic
329C2×Dic6—61no—
330C2×Dic6—61no—
331C2×Dic6C22×D311yescharacteristic
332C2×Dic6C22×D311yescharacteristic
333C3×Q16—121no—
334C3×SD16—121no—
335C3×M16—121no—
336C2×C3×C8—21no—
337C2×C3×C8—31no—
338C2×C3×C8—31no—
339C2×C3×C8C22×D311yescharacteristic
340C2×C3×C8C22×D311yescharacteristic
341C3×C4⋊C4—21no—
342C3×C4⋊C4—31no—
343C3×C4⋊C4—61no—
344C3×C4⋊C4C22×D311yescharacteristic
345C3×C4⋊C4C22×D311yescharacteristic
346C3×C22⋊C4—61no—
347C3×C22⋊C4—61no—
348C3×C22⋊C4—61no—
349C3×C42—31no—
350C3×C42—61no—
351C3×C42—61no—
352#217—21no—
353#217—21no—
354#217—31no—
355#217—61no—
356#217—61no—
357#217—61no—
358#217—61no—
359#217—61no—
360#217—121no—
361#215—62no—
362#214—41no—
363#214—62no—
364(C2×D3)⋊C4—21no—
365(C2×D3)⋊C4—31no—
366(C2×D3)⋊C4—31no—
367(C2×D3)⋊C4—31no—
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—61no—
375(C2×D3)⋊C4—121no—
376C4⋊Dic3—31no—
377C4⋊Dic3—31no—
378C4⋊Dic3—31no—
379C4⋊Dic3—31no—
380C4⋊Dic3—31no—
381C4⋊Dic3—61no—
382C4⋊Dic3—61no—
383C4⋊Dic3—61no—
384C4⋊Dic3—61no—
385C4⋊Dic3C22×D311yescharacteristic
386Dic3⋊C4—21no—
387Dic3⋊C4—31no—
388Dic3⋊C4—61no—
389Dic3⋊C4—61no—
390Dic3⋊C4—61no—
391Dic3⋊C4—61no—
392Dic3⋊C4—61no—
393Dic3⋊C4—61no—
394C4×Dic3—21no—
395C4×Dic3—21no—
396C4×Dic3—61no—
397C4×Dic3—61no—
398C4×Dic3—121no—
399C4×Dic3C22×D311yescharacteristic
400C2×C3⋊C8—31no—
401C2×C3⋊C8—31no—
402C2×C3⋊C8—61no—
403C2×C3⋊C8C22×D311yescharacteristic
404C2×C3⋊C8C22×D311yescharacteristic
405Dic12—41no—
406ΓL(1,𝔽25)—41no—
407D3×C8—121no—
408D3×C8—121no—
409C22×C32—41no—
410C22×C32—41no—
411C22×C32—41no—
412C22×C32C22×D411yescharacteristic
413C2×C3⋊D3—21no—
414C2×C3⋊D3—21no—
415C2×C3⋊D3—21no—
416C2×C3×D3—22no—
417C2×C3×D3—21no—
418C2×C3×D3—21no—
419C2×C3×D3—21no—
420C2×C3×D3—41no—
421C2×C3×D3—41no—
422C2×C3×D3—84no—
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—
434C3×Dic3—41no—
435C2×#41—91no—
436C22×D4—31no—
437C2×Q16—31no—
438C2×SD16—31no—
439C2×SD16—91no—
440C2×M16—31no—
441C22×C8—91no—
442C4⋊Q8—91no—
443#126—181no—
444#126—181no—
445#124—31no—
446#124—181no—
447#123—181no—
448C22⋊Q8—91no—
449C22⋊Q8—91no—
450C22⋊Q8—91no—
451#121—91no—
452#121—181no—
453#120—181no—
454C4×Q8—31no—
455C4×Q8—181no—
456C4×D4—91no—
457C4×D4—91no—
458#117—31no—
459#117—91no—
460C2×C22⋊C4—181no—
461#107—91no—
462#106—91no—
463#106—91no—
464C4⋊C8—31no—
465#103—31no—
466#103—91no—
467#103—91no—
468#103—91no—
469#102—31no—
470#102—31no—
471#102—31no—
472#102—91no—
473#102—91no—
474#102D3211yescharacteristic
475C22⋊C8—91no—
476C22⋊C8—91no—
477#97—91no—
478C23×C3—21no—
479C23×C3—21no—
480C23×C3—31no—
481C23×C3—41no—
482C23×C3—61no—
483C23×C3—122no—
484C23×C3—122no—
485C23×C3—241no—
486C22×D3—21no—
487C22×D3—31no—
488C22×D3—31no—
489C22×D3—42no—
490C22×D3—42no—
491C22×D3—61no—
492C22×D3—81no—
493C22×D3D3×D411yescharacteristic
494C3×Q8—61no—
495C3×Q8—61no—
496C3×Q8—61no—
497C3×Q8—61no—
498C3×D4—21no—
499C3×D4—21no—
500C3×D4—21no—
501C3×D4—21no—
502C3×D4—32no—
503C3×D4—41no—
504C3×D4—41no—
505C3×D4—61no—
506C3×D4—122no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—31no—
511C2×C3×C4—31no—
512C2×C3×C4—31no—
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×C4C23×D311yescharacteristic
520C2×C3×C4C23×D311yescharacteristic
521#67—42no—
522#67—121no—
523#67—122no—
524#67—241no—
525#67—241no—
526#67—242no—
527C2×Dic3—21no—
528C2×Dic3—21no—
529C2×Dic3—21no—
530C2×Dic3—31no—
531C2×Dic3—31no—
532C2×Dic3—61no—
533C2×Dic3—61no—
534C2×Dic3—61no—
535C2×Dic3—61no—
536C2×Dic3—61no—
537C2×Dic3—121no—
538C2×Dic3—121no—
539C2×Dic3—122no—
540C2×Dic3—241no—
541C2×Dic3D3×D411yescharacteristic
542C2×Dic3D3×D411yescharacteristic
543C2×Dic3D3×D411yescharacteristic
544D12—21no—
545D12—121no—
546D12—122no—
547D12#23512yes—
548C4×D3—21no—
549C4×D3—21no—
550C4×D3—61no—
551C4×D3—61no—
552C4×D3—61no—
553C4×D3—61no—
554C4×D3—121no—
555C4×D3—121no—
556C4×D3—122no—
557C4×D3—241no—
558Dic6—21no—
559Dic6—21no—
560Dic6—21no—
561Dic6—21no—
562Dic6—122no—
563Dic6—122no—
564C3×C8—21no—
565C3×C8—21no—
566C3×C8—41no—
567C3×C8—61no—
568C3×C8—61no—
569C3⋊C8—21no—
570C3⋊C8—21no—
571C3⋊C8—61no—
572C3⋊C8—61no—
573C3⋊C8—121no—
574C2×C32—81no—
575C2×C32#54611yescharacteristic
576C2×C32#57511yescharacteristic
577C2×C32#57711yescharacteristic
578C3⋊D3—41no—
579C3×D3—41no—
580C3×D3—42no—
581C24—61no—
582#41—182no—
583#41—361no—
584C2×Q8—31no—
585C2×Q8—31no—
586C2×Q8—181no—
587C2×D4—31no—
588C2×D4—61no—
589C2×D4—62no—
590C2×D4—91no—
591C2×D4—121no—
592C2×D4—181no—
593C2×D4—181no—
594C2×D4C2×D3211yescharacteristic
595C22×C4—31no—
596C22×C4—91no—
597C22×C4—181no—
598C22×C4—181no—
599Q16—121no—
600SD16—121no—
601SD16—182no—
602M16—121no—
603C2×C8—31no—
604C2×C8—31no—
605C2×C8—91no—
606C2×C8—361no—
607C2×C8C2×D3211yescharacteristic
608C4⋊C4—31no—
609C4⋊C4—61no—
610C4⋊C4—91no—
611C4⋊C4—91no—
612C4⋊C4—91no—
613C4⋊C4—181no—
614C4⋊C4—181no—
615C4⋊C4—181no—
616C4⋊C4—181no—
617C4⋊C4C2×D3211yescharacteristic
618C22⋊C4—61no—
619C22⋊C4—61no—
620C22⋊C4—61no—
621C22⋊C4—91no—
622C22⋊C4—91no—
623C22⋊C4—181no—
624C22⋊C4—181no—
625C22⋊C4—181no—
626C22⋊C4—181no—
627C22⋊C4—181no—
628C22⋊C4—181no—
629C42—31no—
630C42—61no—
631C42—61no—
632C42—181no—
633C22×C3—21no—
634C22×C3—41no—
635C22×C3—41no—
636C22×C3—41no—
637C22×C3—41no—
638C22×C3—41no—
639C22×C3—41no—
640C22×C3—61no—
641C22×C3—61no—
642C22×C3—62no—
643C22×C3—61no—
644C22×C3—81no—
645C22×C3—81no—
646C22×C3—81no—
647C22×C3—121no—
648C22×C3—121no—
649C22×C3—244no—
650C22×C3C2×D3×D411yescharacteristic
651C22×C3C2×D3×D411yescharacteristic
652C2×D3—21no—
653C2×D3—22no—
654C2×D3—21no—
655C2×D3—21no—
656C2×D3—41no—
657C2×D3—41no—
658C2×D3—61no—
659C2×D3—61no—
660C2×D3—61no—
661C2×D3—61no—
662C2×D3—61no—
663C2×D3—61no—
664C2×D3—84no—
665C2×D3—121no—
666C2×D3—121no—
667C2×D3—121no—
668C3×C4—21no—
669C3×C4—21no—
670C3×C4—41no—
671C3×C4—41no—
672C3×C4—61no—
673C3×C4—61no—
674C3×C4—61no—
675C3×C4—81no—
676C3×C4—121no—
677C3×C4—121no—
678C3×C4—121no—
679C3×C4C2×#23511yescharacteristic
680C3×C4#100411yescharacteristic
681C3×C4#100411yescharacteristic
682C3×C4D3×#4111yescharacteristic
683Dic3—21no—
684Dic3—21no—
685Dic3—21no—
686Dic3—41no—
687Dic3—41no—
688Dic3—41no—
689Dic3—61no—
690Dic3—61no—
691Dic3—121no—
692Dic3—121no—
693Dic3—121no—
694Dic3—121no—
695Dic3—121no—
696Dic3—241no—
697Dic3—241no—
698C32#331111yescharacteristic, complemented, Sylow
699C23—21no—
700C23—31no—
701C23—61no—
702C23—91no—
703C23—122no—
704C23—122no—
705C23—241no—
706Q8—61no—
707Q8—61no—
708Q8—61no—
709Q8—61no—
710Q8—362no—
711D4—21no—
712D4—21no—
713D4—32no—
714D4—61no—
715D4—122no—
716D4—361no—
717D4—362no—
718D4—721no—
719C2×C4—21no—
720C2×C4—31no—
721C2×C4—31no—
722C2×C4—31no—
723C2×C4—61no—
724C2×C4—61no—
725C2×C4—61no—
726C2×C4—61no—
727C2×C4—61no—
728C2×C4—91no—
729C2×C4—181no—
730C2×C4—181no—
731C2×C4—181no—
732C2×C4—181no—
733C2×C4—362no—
734C2×C4—721no—
735C2×C4C22×D3211yescharacteristic
736C8—21no—
737C8—61no—
738C8—61no—
739C8—181no—
740C2×C3—21no—
741C2×C3—21no—
742C2×C3—21no—
743C2×C3—81no—
744C2×C3—81no—
745C2×C3—121no—
746C2×C3—122no—
747C2×C3—161no—
748C2×C3#549011yescharacteristic
749C2×C3#561211yescharacteristic
750C2×C3#577011yescharacteristic
751C2×C3#577311yescharacteristic
752C2×C3#577511yescharacteristic
753C2×C3#577711yescharacteristic
754D3—41no—
755D3—42no—
756D3—121no—
757D3—121no—
758D3—241no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—61no—
763C22—61no—
764C22—61no—
765C22—62no—
766C22—121no—
767C22—121no—
768C22—181no—
769C22—181no—
770C22—181no—
771C22—244no—
772C22D32×D411yescharacteristic
773C4—41no—
774C4—61no—
775C4—61no—
776C4—61no—
777C4—121no—
778C4—121no—
779C4—121no—
780C4—181no—
781C4—361no—
782C4—361no—
783C4D3×#23511yescharacteristic
784C4#6431311yescharacteristic
785C3—21no—
786C3#7893511yescharacteristic, complemented
787C3#8061711yescharacteristic, complemented
788C2—81no—
789C2—121no—
790C2—122no—
791C2—361no—
792C2#1059427811yescharacteristic
793C2#1059473611yescharacteristic
794C2#1059474411yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
prime radical#10595229C2
hypercenter#102D32
hypocenterC32#3311
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
2. #10594565C2semidirect
3. #10592478C2semidirect
4. C3×#4770C2semidirect
5. C3×#4767C2semidirect
6. #10591488C2semidirect
7. #10591465C2semidirect
8. #10591458C2semidirect
9. #10590965C2semidirect
10. #10590854C2semidirect
11. #10590757C2semidirect
12. #10590738C2semidirect
13. #10590611C2semidirect
14. #10590521C2semidirect
15. #10590454C2semidirect
21. #64101C22semidirect
24. C2×C3×Dic12C22semidirect
27. C3×#887C22semidirect
32. #63918C22semidirect
36. #63871C22semidirect
43. C2×#3710C22semidirect
46. #63647C22semidirect
47. #63644C22semidirect
48. #63634C22semidirect
51. C3×Dic3⋊C8C22semidirect
52. C3×#810C22semidirect
54. #63573C22semidirect
55. #63566C22semidirect
56. #63566C22semidirect
57. #63565C22semidirect
60. #63554C22semidirect
87. #4770D3semidirect
88. #4767D3semidirect
173. C2×Dic12C2×D3semidirect
185. #887C2×D3semidirect
229. Dic3⋊C8C2×D3semidirect
231. #810C2×D3semidirect
698. C32#3311semidirect
786. C3#78935semidirect
787. C3#80617semidirect

Maximal subgroups

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

subgroupindex
#105952292
#105945652
#105924782
C3×#47702
C3×#47672
#105914882
#105914652
#105914582
#105909652
#105908542
#105907572
#105907382
#105906112
#105905212
#105904542
#806173
#789353