Finite Group Databasebeta

← #11882324

Subgroups — #11882324

Order 1152.

865 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594965C211yesmaximal, characteristic, complemented
2#10594929C211yesmaximal, characteristic, complemented
3C2×#63641C211yesmaximal, characteristic, complemented
4C3×#5115C211yesmaximal, characteristic, complemented
5C3×#5114C211yesmaximal, characteristic, complemented
6#10591179C211yesmaximal, characteristic, complemented
7#10591166C211yesmaximal, characteristic, complemented
8#10590876C211yesmaximal, characteristic, complemented
9#10590817C211yesmaximal, characteristic, complemented
10#10590782C211yesmaximal, characteristic, complemented
11#10590780C211yesmaximal, characteristic, complemented
12#10590776C211yesmaximal, characteristic, complemented
13#10590751C211yesmaximal, characteristic, complemented
14#10590750C211yesmaximal, characteristic, complemented
15#10590749C211yesmaximal, characteristic, complemented
16#80703—31nomaximal
17#80641—31nomaximal
18C2×#3805—21no—
19C22×C32×C8C2211yescharacteristic
20C2×C4×C3⋊Dic3C2211yescharacteristic
21C22×C3⋊(C3⋊C8)C2211yescharacteristic
22C3×#930C2211yescharacteristic
23C3×#930C2211yescharacteristic
24C3×#930C2211yescharacteristic
25C3×#924C2211yescharacteristic
26C2×C3×D24C2211yescharacteristic
27C2×C3×#204C2211yescharacteristic
28#63980—21no—
29#67⋊Dic3—21no—
30#63962—21no—
31#63919C2211yescharacteristic
32#63915—21no—
33#63914C2211yescharacteristic
34#63902—21no—
35#63898C2211yescharacteristic
36#63898C2211yescharacteristic
37#63898C2211yescharacteristic
38#63878—21no—
39#63872C2211yescharacteristic
40#63863C2211yescharacteristic
41#63862—21no—
42#63843C2211yescharacteristic
43C2×#3715C2211yescharacteristic
44C2×#3713C2211yescharacteristic
45#63641C2211yescharacteristic
46#63641C2211yescharacteristic
47#63641C2211yescharacteristic
48#63641C2211yescharacteristic
49C3×#821C2211yescharacteristic
50C3×#821C2211yescharacteristic
51C3×#821C2211yescharacteristic
52C3×#818C2211yescharacteristic
53C3×#817C2211yescharacteristic
54C3×#816C2211yescharacteristic
55#63576C2211yescharacteristic
56#63574C2211yescharacteristic
57#63565C2211yescharacteristic
58#63562C2211yescharacteristic
59#63562C2211yescharacteristic
60#63562C2211yescharacteristic
61#5624—31no—
62#5600—31no—
63#5596—31no—
64#5596—31no—
65C3×#466—31no—
66C3×#465—31no—
67#5165—31no—
68#5163—31no—
69#5153—31no—
70#5150—31no—
71#5115D311yescharacteristic, complemented
72#5114D311yescharacteristic, complemented
73C2×Dic3⋊C8—31no—
74C2×Dic3⋊C8—31no—
75C2×Dic3⋊C8—61no—
76#5048—31no—
77#5041—31no—
78#5038—31no—
79#5038—31no—
80#4891—31no—
81#4875—31no—
82#4871—31no—
83#4870—31no—
84#4819—31no—
85#4793—31no—
86#4787—31no—
87#4786—31no—
88#4766—31no—
89#4763—31no—
90#4762—31no—
91#4761—31no—
92C22×C32×C4C2311yescharacteristic
93C22×C3⋊Dic3D411yescharacteristic
94C22×C3⋊Dic3D411yescharacteristic
95C2×C3×#67—21no—
96C2×C3×#67—21no—
97C2×C3×#67—21no—
98C2×C3×D12C2311yescharacteristic
99C2×C3×D12C2311yescharacteristic
100C2×C3×D12C2311yescharacteristic
101C2×C3×Dic6C2311yescharacteristic
102C2×#627—21no—
103C2×#625—21no—
104C2×#625—21no—
105#3805—44no—
106C2×D3×Dic3—21no—
107C2×D3×Dic3—21no—
108C2×D3×Dic3—21no—
109C2×C32×C8—41no—
110C2×C32×C8C2311yescharacteristic
111C2×C32×C8C2311yescharacteristic
112C4×C3⋊Dic3D411yescharacteristic
113C4×C3⋊Dic3D411yescharacteristic
114C4×C3⋊Dic3C2311yescharacteristic
115C4×C3⋊Dic3C2311yescharacteristic
116C2×C3⋊(C3⋊C8)—41no—
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119C3×#217—21no—
120C3×(C2×D3)⋊C4—21no—
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4—21no—
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×Dic3⋊C4—21no—
128C3×D24—41no—
129C3×#204—41no—
130#3724—21no—
131Dic3⋊Dic3—21no—
132Dic3⋊Dic3—21no—
133Dic3⋊Dic3—21no—
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—
139Dic32—21no—
140#3715—41no—
141#3713—41no—
142#3247—91noSylow
143C2×#237—61no—
144C2×#237—61no—
145C2×C3×SD16—31no—
146C2×C3×D8—31no—
147C22×C3×C8—21no—
148C22×C3×C8C2×D311yescharacteristic
149C22×C3×C8C2×D311yescharacteristic
150C3×C22⋊Q8—31no—
151C3×#121—31no—
152C3×#121—31no—
153C3×#121—31no—
154#947—31no—
155Q8×Dic3—31no—
156C2×#215—31no—
157#940—31no—
158#940—31no—
159#939—61no—
160#939—61no—
161#936—31no—
162#935—61no—
163D4×Dic3—31no—
164D4×Dic3—31no—
165D4×Dic3—31no—
166D4×Dic3—61no—
167C2×#214—31no—
168C2×#213—31no—
169C2×#213—31no—
170#930C2×D311yescharacteristic
171#930C2×D311yescharacteristic
172#930C2×D311yescharacteristic
173#924C2×D311yescharacteristic
174C2×C4×Dic3—31no—
175C2×C4×Dic3—31no—
176C2×C4×Dic3—61no—
177C22×C3⋊C8—31no—
178C22×C3⋊C8—31no—
179C22×C3⋊C8—61no—
180C2×D24C2×D311yescharacteristic
181C2×#204C2×D311yescharacteristic
182#898—61no—
183#893—31no—
184#893—31no—
185#893—31no—
186#892—61no—
187#890—31no—
188#890—31no—
189#888—31no—
190#888—31no—
191#887—31no—
192#886—61no—
193#885—61no—
194#885—61no—
195#67⋊C4—61no—
196#67⋊C4—61no—
197#67⋊C4—61no—
198#879—61no—
199#877—61no—
200C3×#107—31no—
201C3×#106—31no—
202C3×#103—31no—
203C3×#102—31no—
204C3×#102—31no—
205C3×#102—31no—
206#835—31no—
207#832—31no—
208#832—31no—
209#832—31no—
210#821C2×D311yescharacteristic
211#821C2×D311yescharacteristic
212#821C2×D311yescharacteristic
213#818C2×D311yescharacteristic
214#817C2×D311yescharacteristic
215#816C2×D311yescharacteristic
216Dic3⋊C8—31no—
217Dic3⋊C8—31no—
218Dic3⋊C8—31no—
219Dic3⋊C8—31no—
220Dic3⋊C8—31no—
221Dic3⋊C8—31no—
222Dic3⋊C8—31no—
223Dic3⋊C8—31no—
224Dic3⋊C8—61no—
225Dic3⋊C8—61no—
226Dic3⋊C8—61no—
227Dic3⋊C8—61no—
228#810—31no—
229#809—31no—
230#809—31no—
231#809—31no—
232#808—31no—
233#808—31no—
234#807—31no—
235#807—31no—
236C23×C32C2×D411yescharacteristic
237C22×C3×D3—21no—
238C22×C3×D3—21no—
239C22×C3×D3—21no—
240C2×C32×C4—21no—
241C2×C32×C4—21no—
242C2×C32×C4C2×D411yescharacteristic
243C2×C32×C4C2411yescharacteristic
244C2×C3⋊Dic3—22no—
245C2×C3⋊Dic3—22no—
246C2×C3⋊Dic3C2×D411yescharacteristic
247C2×C3⋊Dic3C2×D411yescharacteristic
248C2×C3⋊Dic3C2×D411yescharacteristic
249C2×C3⋊Dic3C2×D411yescharacteristic
250C3×#67—42no—
251C3×#67—42no—
252C3×#67—42no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C3×D12—21no—
259C3×D12—21no—
260C3×D12—21no—
261C3×D12—21no—
262C3×D12—21no—
263C3×D12—21no—
264C3×Dic6—21no—
265C3×Dic6—21no—
266#627—42no—
267#625—42no—
268#625—42no—
269D3×Dic3—42no—
270D3×Dic3—42no—
271D3×Dic3—42no—
272C32×C8—21no—
273C32×C8—21no—
274C3⋊(C3⋊C8)—21no—
275C3⋊(C3⋊C8)—21no—
276#532—91no—
277#529—91no—
278#478—91no—
279#478—91no—
280#477—91no—
281#476—91no—
282#466—31no—
283#466—91no—
284#465—31no—
285#465—91no—
286#463—91no—
287#463—91no—
288#460—91no—
289#459—91no—
290C2×C4⋊C8—91no—
291C2×C3×Q8—31no—
292C2×C3×D4—31no—
293C2×C3×D4—31no—
294C2×C3×D4—31no—
295C2×C3×D4—61no—
296C2×C3×D4—61no—
297C2×C3×D4—61no—
298C22×C3×C4—21no—
299C22×C3×C4C22×D311yescharacteristic
300C22×C3×C4C22×D311yescharacteristic
301C2×#67—21no—
302C2×#67—21no—
303C2×#67—21no—
304C2×#67—61no—
305C2×#67—61no—
306C2×#67—61no—
307C2×#67—61no—
308C22×Dic3—31no—
309C22×Dic3—31no—
310C22×Dic3—31no—
311C22×Dic3—31no—
312C22×Dic3—61no—
313C22×Dic3—61no—
314C22×Dic3—61no—
315C22×Dic3—61no—
316C22×Dic3—61no—
317#237—124no—
318#237—124no—
319C2×D12C22×D311yescharacteristic
320C2×D12C22×D311yescharacteristic
321C2×D12C22×D311yescharacteristic
322C2×C4×D3—61no—
323C2×C4×D3—61no—
324C2×C4×D3—61no—
325C2×Dic6—61no—
326C2×Dic6—61no—
327C2×Dic6C22×D311yescharacteristic
328C3×SD16—121no—
329C3×D8—121no—
330C2×C3×C8—21no—
331C2×C3×C8—21no—
332C2×C3×C8—41no—
333C2×C3×C8—41no—
334C2×C3×C8—42no—
335C2×C3×C8C22×D311yescharacteristic
336C2×C3×C8C22×D311yescharacteristic
337C2×C3×C8C22×D311yescharacteristic
338C2×C3×C8C22×D311yescharacteristic
339C3×C4⋊C4—31no—
340C3×C4⋊C4—31no—
341C3×C4⋊C4—31no—
342C3×C4⋊C4—31no—
343C3×C4⋊C4—61no—
344C3×C22⋊C4—61no—
345C3×C22⋊C4—61no—
346C3×C22⋊C4—61no—
347C3×C22⋊C4—61no—
348#217—21no—
349#217—61no—
350#217—61no—
351#217—61no—
352#217—61no—
353#217—61no—
354#215—121no—
355#214—121no—
356#213—121no—
357#213—121no—
358(C2×D3)⋊C4—21no—
359(C2×D3)⋊C4—21no—
360(C2×D3)⋊C4—21no—
361(C2×D3)⋊C4—61no—
362(C2×D3)⋊C4—61no—
363(C2×D3)⋊C4—61no—
364(C2×D3)⋊C4—61no—
365(C2×D3)⋊C4—61no—
366C4⋊Dic3—61no—
367C4⋊Dic3—61no—
368C4⋊Dic3—61no—
369C4⋊Dic3C22×D311yescharacteristic
370C4⋊Dic3C22×D311yescharacteristic
371C4⋊Dic3C22×D311yescharacteristic
372C4⋊Dic3C22×D311yescharacteristic
373Dic3⋊C4—21no—
374Dic3⋊C4—61no—
375Dic3⋊C4—61no—
376Dic3⋊C4—61no—
377Dic3⋊C4—61no—
378Dic3⋊C4—61no—
379C4×Dic3—31no—
380C4×Dic3—31no—
381C4×Dic3—31no—
382C4×Dic3—31no—
383C4×Dic3—31no—
384C4×Dic3—31no—
385C4×Dic3—31no—
386C4×Dic3—31no—
387C4×Dic3—61no—
388C4×Dic3—61no—
389C4×Dic3—61no—
390C4×Dic3—61no—
391C4×Dic3—61no—
392C4×Dic3—61no—
393C2×C3⋊C8—31no—
394C2×C3⋊C8—31no—
395C2×C3⋊C8—31no—
396C2×C3⋊C8—31no—
397C2×C3⋊C8—61no—
398C2×C3⋊C8—61no—
399C2×C3⋊C8—121no—
400C2×C3⋊C8—121no—
401C2×C3⋊C8—122no—
402D24—41no—
403#204—41no—
404C22×C32—21no—
405C22×C32—21no—
406C22×C32AGL(1,ℤ/8)12yes—
407C22×C32C22×D411yescharacteristic
408C2×C3×D3—41no—
409C2×C3×D3—41no—
410C2×C3×D3—41no—
411C2×C3×D3—41no—
412C2×C3×D3—41no—
413C2×C3×D3—41no—
414C2×C3×D3—41no—
415C2×C3×D3—41no—
416C2×C3×D3—41no—
417C32×C4—21no—
418C32×C4H(5,𝔽2)11yescharacteristic
419C32×C42−1+411yescharacteristic
420C3⋊Dic3—21no—
421C3⋊Dic3—21no—
422C3⋊Dic3—21no—
423C3⋊Dic3#13512yes—
424C3×Dic3—41no—
425C3×Dic3—41no—
426C3×Dic3—41no—
427C3×Dic3—41no—
428C3×Dic3—41no—
429C2×#41—181no—
430C2×SD16—31no—
431C2×SD16—91no—
432C2×D8—31no—
433C2×D8—91no—
434C22×C8—91no—
435C22×C8D3211yescharacteristic
436C4⋊Q8—91no—
437#127—91no—
438#126—181no—
439#125—91no—
440#124—91no—
441#124—181no—
442#123—181no—
443C22⋊Q8—31no—
444#121—31no—
445#121—31no—
446#121—31no—
447#121—181no—
448C4×Q8—91no—
449C4×D4—91no—
450C4×D4—91no—
451C4×D4—91no—
452C4×D4—181no—
453C4×D4—181no—
454#117—181no—
455C2×C42—91no—
456#107—31no—
457#107—91no—
458#106—31no—
459#106—91no—
460C4⋊C8—91no—
461C4⋊C8—91no—
462C4⋊C8—91no—
463C4⋊C8—91no—
464#103—31no—
465#103—91no—
466#102—31no—
467#102—31no—
468#102—31no—
469#102—91no—
470#102—91no—
471#102—91no—
472C23×C3—21no—
473C23×C3—61no—
474C23×C3—61no—
475C23×C3—61no—
476C23×C3D3×D411yescharacteristic
477C23×C3D3×D411yescharacteristic
478C22×D3—21no—
479C22×D3—21no—
480C22×D3—21no—
481C3×Q8—61no—
482C3×Q8—61no—
483C3×D4—61no—
484C3×D4—61no—
485C3×D4—61no—
486C3×D4—61no—
487C3×D4—61no—
488C3×D4—61no—
489C3×D4—122no—
490C3×D4—122no—
491C3×D4—122no—
492C2×C3×C4—22no—
493C2×C3×C4—22no—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—61no—
501C2×C3×C4—61no—
502C2×C3×C4—61no—
503C2×C3×C4—61no—
504C2×C3×C4—61no—
505C2×C3×C4D3×D411yescharacteristic
506C2×C3×C4D3×D411yescharacteristic
507C2×C3×C4C23×D311yescharacteristic
508C2×C3×C4C23×D311yescharacteristic
509#67—42no—
510#67—42no—
511#67—42no—
512#67—122no—
513#67—122no—
514#67—122no—
515#67—122no—
516C2×Dic3—21no—
517C2×Dic3—21no—
518C2×Dic3—21no—
519C2×Dic3—21no—
520C2×Dic3—21no—
521C2×Dic3—31no—
522C2×Dic3—31no—
523C2×Dic3—31no—
524C2×Dic3—31no—
525C2×Dic3—31no—
526C2×Dic3—31no—
527C2×Dic3—31no—
528C2×Dic3—31no—
529C2×Dic3—61no—
530C2×Dic3—61no—
531C2×Dic3—61no—
532C2×Dic3—61no—
533C2×Dic3—62no—
534C2×Dic3—62no—
535C2×Dic3—64no—
536C2×Dic3—62no—
537C2×Dic3—62no—
538C2×Dic3—122no—
539C2×Dic3—122no—
540C2×Dic3—122no—
541C2×Dic3—122no—
542D12—21no—
543D12—21no—
544D12—21no—
545D12—21no—
546D12—21no—
547D12—21no—
548C4×D3—122no—
549C4×D3—122no—
550C4×D3—122no—
551Dic6—21no—
552Dic6—21no—
553Dic6—122no—
554Dic6—122no—
555C3×C8—21no—
556C3×C8—21no—
557C3×C8—21no—
558C3×C8—21no—
559C3×C8—41no—
560C3×C8—41no—
561C3⋊C8—61no—
562C3⋊C8—61no—
563C3⋊C8—61no—
564C3⋊C8—61no—
565C3⋊C8—121no—
566C3⋊C8—121no—
567C2×C32—22no—
568C2×C32#53711yescharacteristic
569C2×C32C2×#13511yescharacteristic
570C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
571C3×D3—81no—
572C3×D3—81no—
573C3×D3—81no—
574#41—364no—
575C2×Q8—31no—
576C2×Q8—181no—
577C2×D4—31no—
578C2×D4—31no—
579C2×D4—31no—
580C2×D4—61no—
581C2×D4—61no—
582C2×D4—61no—
583C2×D4—181no—
584C2×D4—181no—
585C22×C4—91no—
586C22×C4—91no—
587C22×C4—181no—
588C22×C4—181no—
589C22×C4—181no—
590C22×C4C2×D3211yescharacteristic
591SD16—121no—
592SD16—361no—
593D8—121no—
594D8—361no—
595C2×C8—41no—
596C2×C8—91no—
597C2×C8—91no—
598C2×C8—361no—
599C2×C8C2×D3211yescharacteristic
600C2×C8C2×D3211yescharacteristic
601C4⋊C4—31no—
602C4⋊C4—31no—
603C4⋊C4—31no—
604C4⋊C4—31no—
605C4⋊C4—61no—
606C4⋊C4—181no—
607C4⋊C4—181no—
608C4⋊C4—181no—
609C4⋊C4—181no—
610C22⋊C4—61no—
611C22⋊C4—61no—
612C22⋊C4—61no—
613C22⋊C4—61no—
614C22⋊C4—181no—
615C22⋊C4—181no—
616C22⋊C4—181no—
617C22⋊C4—181no—
618C22⋊C4—181no—
619C42—91no—
620C42—91no—
621C42—91no—
622C42—91no—
623C42—181no—
624C22×C3—22no—
625C22×C3—22no—
626C22×C3—21no—
627C22×C3—21no—
628C22×C3—21no—
629C22×C3—21no—
630C22×C3—21no—
631C22×C3—22no—
632C22×C3—121no—
633C22×C3—121no—
634C22×C3—121no—
635C22×C3—121no—
636C22×C3—121no—
637C22×C3—121no—
638C22×C3—121no—
639C22×C3—121no—
640C22×C3—121no—
641C22×C3#91112yes—
642C22×C3#91412yes—
643C22×C3C2×D3×D411yescharacteristic
644C22×C3C2×D3×D411yescharacteristic
645C2×D3—41no—
646C2×D3—41no—
647C2×D3—41no—
648C2×D3—41no—
649C2×D3—41no—
650C2×D3—41no—
651C2×D3—41no—
652C2×D3—41no—
653C2×D3—41no—
654C3×C4—22no—
655C3×C4—21no—
656C3×C4—21no—
657C3×C4—21no—
658C3×C4—21no—
659C3×C4—121no—
660C3×C4—121no—
661C3×C4—121no—
662C3×C4—121no—
663C3×C4—121no—
664C3×C4#100411yescharacteristic
665C3×C4#100411yescharacteristic
666C3×C4#101011yescharacteristic
667C3×C4#101011yescharacteristic
668Dic3—32no—
669Dic3—32no—
670Dic3—41no—
671Dic3—41no—
672Dic3—41no—
673Dic3—41no—
674Dic3—41no—
675Dic3—62no—
676Dic3—62no—
677Dic3—61no—
678Dic3—61no—
679Dic3—61no—
680Dic3—61no—
681Dic3—61no—
682Dic3—61no—
683Dic3—121no—
684Dic3—121no—
685C32#324711yescharacteristic, complemented, Sylow
686C23—61no—
687C23—61no—
688C23—61no—
689C23#380211yescharacteristic
690Q8—61no—
691Q8—61no—
692Q8—362no—
693D4—61no—
694D4—61no—
695D4—61no—
696D4—61no—
697D4—61no—
698D4—61no—
699D4—122no—
700D4—122no—
701D4—122no—
702D4—362no—
703D4—362no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—61no—
707C2×C4—61no—
708C2×C4—61no—
709C2×C4—61no—
710C2×C4—61no—
711C2×C4—91no—
712C2×C4—91no—
713C2×C4—91no—
714C2×C4—91no—
715C2×C4—182no—
716C2×C4—182no—
717C2×C4—362no—
718C2×C4—362no—
719C2×C4—362no—
720C2×C4#380211yescharacteristic
721C2×C4C22×D3211yescharacteristic
722C8—21no—
723C8—21no—
724C8—181no—
725C8—181no—
726C2×C3—24no—
727C2×C3—22no—
728C2×C3—22no—
729C2×C3—21no—
730C2×C3—21no—
731C2×C3—21no—
732C2×C3—241no—
733C2×C3—241no—
734C2×C3—241no—
735C2×C3#559711yescharacteristic
736C2×C3#559711yescharacteristic
737C2×C3C2×#91111yescharacteristic
738C2×C3C2×#91411yescharacteristic
739C2×C3D3×#13511yescharacteristic
740C2×C3D3×#13511yescharacteristic
741D3—81no—
742D3—81no—
743D3—81no—
744C22—21no—
745C22—21no—
746C22—121no—
747C22—121no—
748C22—121no—
749C22—121no—
750C22—121no—
751C22—121no—
752C22—121no—
753C22—121no—
754C22—121no—
755C22#6379812yes—
756C22C2×#380211yescharacteristic
757C4—21no—
758C4—92no—
759C4—121no—
760C4—121no—
761C4—121no—
762C4—121no—
763C4—121no—
764C4—181no—
765C4—181no—
766C4—181no—
767C4#6429811yescharacteristic
768C4#6433011yescharacteristic
769C3—21no—
770C3#8064111yescharacteristic, complemented
771C3#8070311yescharacteristic, complemented
772C2—22no—
773C2—241no—
774C2—241no—
775C2—241no—
776C2C2×#6379811yescharacteristic
777C2#1059468411yescharacteristic
778C2#1059493011yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC22×C32C22×D4
hypercenterC22×C8D32
hypocenterC32#3247
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
1. #10594965C2semidirect
2. #10594929C2semidirect
3. C2×#63641C2semidirect
4. C3×#5115C2semidirect
5. C3×#5114C2semidirect
6. #10591179C2semidirect
7. #10591166C2semidirect
8. #10590876C2semidirect
9. #10590817C2semidirect
10. #10590782C2semidirect
11. #10590780C2semidirect
12. #10590776C2semidirect
13. #10590751C2semidirect
14. #10590750C2semidirect
15. #10590749C2semidirect
71. #5115D3semidirect
72. #5114D3semidirect
685. C32#3247semidirect
770. C3#80641semidirect
771. C3#80703semidirect

Maximal subgroups

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

subgroupindex
#105949652
#105949292
C2×#636412
C3×#51152
C3×#51142
#105911792
#105911662
#105908762
#105908172
#105907822
#105907802
#105907762
#105907512
#105907502
#105907492
#807033
#806413