Finite Group Databasebeta

← #11882323

Subgroups — #11882323

Order 1152.

863 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594955C211yesmaximal, characteristic, complemented
2#10594910C211yesmaximal, characteristic, complemented
3#10592814C211yesmaximal, characteristic, complemented
4C3×#5114C211yesmaximal, characteristic, complemented
5C2×C3×Dic3⋊C8C211yesmaximal, characteristic, complemented
6#10591177C211yesmaximal, characteristic, complemented
7#10591164C211yesmaximal, characteristic, complemented
8#10590804C211yesmaximal, characteristic, complemented
9#10590799C211yesmaximal, characteristic, complemented
10#10590770C211yesmaximal, characteristic, complemented
11#10590769C211yesmaximal, characteristic, complemented
12#10590767C211yesmaximal, characteristic, complemented
13#10590765C211yesmaximal, characteristic, complemented
14#10590759C211yesmaximal, characteristic, complemented
15#10590754C211yesmaximal, characteristic, complemented
16#80641—31nomaximal
17#79028—31nomaximal
18C2×#3804—21no—
19C22×C32×C8C2211yescharacteristic
20#64139C2211yescharacteristic
21#64139C2211yescharacteristic
22C2×#3745C2211yescharacteristic
23C3×#930C2211yescharacteristic
24C3×#924C2211yescharacteristic
25C2×C3×C4×Dic3C2211yescharacteristic
26C22×C3×C3⋊C8C2211yescharacteristic
27C2×C3×#204C2211yescharacteristic
28#63978—21no—
29#63966—21no—
30#63952—21no—
31#63918C2211yescharacteristic
32#63911C2211yescharacteristic
33#63894C2211yescharacteristic
34#63894C2211yescharacteristic
35Dic3×D12C2211yescharacteristic
36#63880—21no—
37#63869C2211yescharacteristic
38#63868—21no—
39#63864C2211yescharacteristic
40#63852—21no—
41Dic3×Dic6C2211yescharacteristic
42#63836—21no—
43C2×#3717C2211yescharacteristic
44C2×#3714C2211yescharacteristic
45#63648C2211yescharacteristic
46#63648C2211yescharacteristic
47#63645C2211yescharacteristic
48C3×#821C2211yescharacteristic
49C3×#817C2211yescharacteristic
50C3×#816C2211yescharacteristic
51C3×Dic3⋊C8C2211yescharacteristic
52C3×Dic3⋊C8C2211yescharacteristic
53C3×Dic3⋊C8C2211yescharacteristic
54C3×Dic3⋊C8C2211yescharacteristic
55#63575C2211yescharacteristic
56#63573C2211yescharacteristic
57#63566C2211yescharacteristic
58#63564C2211yescharacteristic
59#63564C2211yescharacteristic
60#63563C2211yescharacteristic
61#5624—31no—
62#5596—31no—
63#5479—31no—
64#5477—31no—
65C3×#465—31no—
66C2×C3×C4⋊C8—31no—
67#5165—31no—
68#5163—31no—
69#5115—31no—
70#5115—31no—
71#5115—31no—
72#5115—61no—
73#5114—31no—
74#5114D311yescharacteristic, complemented
75C2×Dic3⋊C8D311yescharacteristic, complemented
76#5048—31no—
77#5038—31no—
78#4871—31no—
79#4870—31no—
80#4850—31no—
81#4848—31no—
82#4847—31no—
83#4847—31no—
84#4844—31no—
85#4844—31no—
86#4843—31no—
87#4842—31no—
88#4819—31no—
89#4793—31no—
90#4786—31no—
91#4766—31no—
92C22×C32×C4C2311yescharacteristic
93C2×#638—21no—
94C2×#638—21no—
95C2×C4⋊(C3⋊D3)C2311yescharacteristic
96C2×C4⋊(C3⋊D3)C2311yescharacteristic
97C2×C3×#67—21no—
98C22×C3×Dic3D411yescharacteristic
99C22×C3×Dic3D411yescharacteristic
100C2×C3×D12C2311yescharacteristic
101C2×C3×Dic6C2311yescharacteristic
102C2×#627—21no—
103C2×#626—21no—
104C2×#626—21no—
105C2×#624—21no—
106C2×#624—21no—
107#3804—44no—
108C2×D3×Dic3—21no—
109C2×C32×C8—41no—
110C2×C32×C8C2311yescharacteristic
111C2×C32×C8C2311yescharacteristic
112#3752—21no—
113#3752—21no—
114C4⋊(C3⋊Dic3)C2311yescharacteristic
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116#3745—41no—
117C3×#217—21no—
118C3×(C2×D3)⋊C4—21no—
119C3×C4⋊Dic3C2311yescharacteristic
120C3×C4⋊Dic3C2311yescharacteristic
121C3×Dic3⋊C4—21no—
122C3×C4×Dic3D411yescharacteristic
123C3×C4×Dic3D411yescharacteristic
124C3×C4×Dic3C2311yescharacteristic
125C3×C4×Dic3C2311yescharacteristic
126C2×C3×C3⋊C8—41no—
127C2×C3×C3⋊C8C2311yescharacteristic
128C2×C3×C3⋊C8C2311yescharacteristic
129C3×#204—41no—
130#3724—21no—
131Dic3⋊Dic3—21no—
132Dic3⋊Dic3—21no—
133Dic3⋊Dic3—21no—
134#3722—21no—
135#3722—21no—
136#3722—21no—
137#3722—21no—
138(C2×D3)⋊Dic3—21no—
139Dic32—21no—
140#3717—41no—
141#3714—41no—
142#3247—91noSylow
143C2×#237—61no—
144C2×#235—61no—
145C2×C3×SD16—31no—
146C22×C3×C8—21no—
147C22×C3×C8—31no—
148C22×C3×C8C2×D311yescharacteristic
149C22×C3×C8C2×D311yescharacteristic
150C3×C22⋊Q8—31no—
151C3×#121—31no—
152C2×C3×C42—31no—
153#947—31no—
154Q8×Dic3—31no—
155C2×#215—31no—
156#940—31no—
157#939—61no—
158D4×Dic3—31no—
159C2×#213—31no—
160#930—31no—
161#930—31no—
162#930—31no—
163#930—31no—
164#930—61no—
165#930—61no—
166#930—61no—
167#930C2×D311yescharacteristic
168#929—61no—
169C4×#67—61no—
170#924C2×D311yescharacteristic
171C2×C4×Dic3C2×D311yescharacteristic
172C22×C3⋊C8C2×D311yescharacteristic
173C2×D24—31no—
174C2×D24—31no—
175C2×D24—31no—
176C2×D24—61no—
177C2×#204—31no—
178C2×#204C2×D311yescharacteristic
179#898—61no—
180#893—31no—
181#893—31no—
182#892—61no—
183#890—31no—
184#888—31no—
185#886—61no—
186#885—61no—
187#67⋊C4—61no—
188#67⋊C4—61no—
189#876—61no—
190#875—31no—
191#875—61no—
192#874—31no—
193C4×D12—31no—
194C4×D12—31no—
195C4×D12—31no—
196C4×D12—61no—
197#872—61no—
198#870—31no—
199#869—31no—
200C4×Dic6—31no—
201C3×#106—31no—
202C3×C4⋊C8—31no—
203C3×C4⋊C8—31no—
204C3×C4⋊C8—31no—
205C3×C4⋊C8—31no—
206C3×#103—31no—
207C3×#102—31no—
208#835—31no—
209#832—31no—
210#821—31no—
211#821—31no—
212#821—31no—
213#821—31no—
214#821—31no—
215#821—31no—
216#821—31no—
217#821—61no—
218#821—61no—
219#821C2×D311yescharacteristic
220#818—31no—
221#818—31no—
222#818—31no—
223#818—61no—
224#817—31no—
225#817C2×D311yescharacteristic
226#816—31no—
227#816C2×D311yescharacteristic
228Dic3⋊C8C2×D311yescharacteristic
229Dic3⋊C8C2×D311yescharacteristic
230Dic3⋊C8C2×D311yescharacteristic
231Dic3⋊C8C2×D311yescharacteristic
232#809—31no—
233#809—31no—
234#808—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
244#638—42no—
245#638—42no—
246C2×C3⋊Dic3—21no—
247C2×C3⋊Dic3—21no—
248C4⋊(C3⋊D3)—21no—
249C4⋊(C3⋊D3)—21no—
250C4⋊(C3⋊D3)—21no—
251C4⋊(C3⋊D3)—21no—
252C3×#67—42no—
253C2×C3×Dic3—22no—
254C2×C3×Dic3—22no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3C2×D411yescharacteristic
259C2×C3×Dic3C2×D411yescharacteristic
260C2×C3×Dic3C2×D411yescharacteristic
261C2×C3×Dic3C2×D411yescharacteristic
262C3×D12—21no—
263C3×D12—21no—
264C3×Dic6—21no—
265C3×Dic6—21no—
266#627—42no—
267#626—42no—
268#626—42no—
269#624—42no—
270#624—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—91no—
283#466—91no—
284#465—31no—
285#465—91no—
286#463—91no—
287#463—91no—
288#460—91no—
289#459—91no—
290C2×C4⋊C8—31no—
291C2×C3×Q8—31no—
292C2×C3×D4—31no—
293C2×C3×D4—61no—
294C22×C3×C4—21no—
295C22×C3×C4—31no—
296C22×C3×C4—31no—
297C22×C3×C4C22×D311yescharacteristic
298C22×C3×C4C22×D311yescharacteristic
299C2×#67—21no—
300C2×#67—61no—
301C2×#67—61no—
302C2×#67—61no—
303C2×#67—61no—
304C2×#67—61no—
305C2×#67—61no—
306C2×#67—121no—
307C2×#67—121no—
308C22×Dic3—61no—
309C22×Dic3D1211yescharacteristic
310C22×Dic3D1211yescharacteristic
311#237—124no—
312#235—124no—
313C2×D12—31no—
314C2×D12—31no—
315C2×D12—31no—
316C2×D12—31no—
317C2×D12—61no—
318C2×D12—61no—
319C2×D12—61no—
320C2×D12—61no—
321C2×D12C22×D311yescharacteristic
322C2×C4×D3—61no—
323C2×C4×D3—61no—
324C2×C4×D3—61no—
325C2×C4×D3—61no—
326C2×C4×D3—61no—
327C2×Dic6—61no—
328C2×Dic6—61no—
329C2×Dic6C22×D311yescharacteristic
330C3×SD16—121no—
331C2×C3×C8—21no—
332C2×C3×C8—21no—
333C2×C3×C8—31no—
334C2×C3×C8—31no—
335C2×C3×C8—41no—
336C2×C3×C8—41no—
337C2×C3×C8—42no—
338C2×C3×C8—121no—
339C2×C3×C8C22×D311yescharacteristic
340C2×C3×C8C22×D311yescharacteristic
341C2×C3×C8C22×D311yescharacteristic
342C2×C3×C8C22×D311yescharacteristic
343C3×C4⋊C4—31no—
344C3×C4⋊C4—31no—
345C3×C4⋊C4—61no—
346C3×C22⋊C4—61no—
347C3×C22⋊C4—61no—
348C3×C42—31no—
349C3×C42—31no—
350C3×C42—31no—
351C3×C42—31no—
352#217—21no—
353#217—61no—
354#215—121no—
355#213—121no—
356(C2×D3)⋊C4—21no—
357(C2×D3)⋊C4—61no—
358(C2×D3)⋊C4—61no—
359(C2×D3)⋊C4—61no—
360(C2×D3)⋊C4—61no—
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—
366(C2×D3)⋊C4—61no—
367(C2×D3)⋊C4—61no—
368(C2×D3)⋊C4—61no—
369(C2×D3)⋊C4—61no—
370(C2×D3)⋊C4—121no—
371(C2×D3)⋊C4—121no—
372C4⋊Dic3—31no—
373C4⋊Dic3—31no—
374C4⋊Dic3—31no—
375C4⋊Dic3—31no—
376C4⋊Dic3—61no—
377C4⋊Dic3—61no—
378C4⋊Dic3—61no—
379C4⋊Dic3—61no—
380C4⋊Dic3—61no—
381C4⋊Dic3C22×D311yescharacteristic
382C4⋊Dic3C22×D311yescharacteristic
383Dic3⋊C4—21no—
384Dic3⋊C4—61no—
385Dic3⋊C4—61no—
386Dic3⋊C4—61no—
387Dic3⋊C4—61no—
388Dic3⋊C4—61no—
389C4×Dic3—61no—
390C4×Dic3—61no—
391C4×Dic3D1211yescharacteristic
392C4×Dic3D1211yescharacteristic
393C4×Dic3C22×D311yescharacteristic
394C4×Dic3C22×D311yescharacteristic
395C2×C3⋊C8—41no—
396C2×C3⋊C8C22×D311yescharacteristic
397C2×C3⋊C8C22×D311yescharacteristic
398D24—121no—
399D24—121no—
400D24—122no—
401D24—121no—
402#204—41no—
403#204—121no—
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—41no—
421C3⋊Dic3—41no—
422C3×Dic3—21no—
423C3×Dic3—21no—
424C3×Dic3—21no—
425C3×Dic3—41no—
426C3×Dic3—41no—
427C3×Dic3—41no—
428C3×Dic3#13512yes—
429C2×#41—181no—
430C2×SD16—31no—
431C2×SD16—91no—
432C2×D8—91no—
433C2×D8—91no—
434C22×C8—31no—
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—91no—
446#121—91no—
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—31no—
456#107—91no—
457#107—91no—
458#106—31no—
459#106—91no—
460C4⋊C8—31no—
461C4⋊C8—31no—
462C4⋊C8—31no—
463C4⋊C8—31no—
464#103—31no—
465#103—91no—
466#102—31no—
467#102—91no—
468#102—91no—
469#102—91no—
470#102—91no—
471#102—91no—
472C23×C3—21no—
473C23×C3—61no—
474C23×C3C2×D1211yescharacteristic
475C23×C3D3×D411yescharacteristic
476C22×D3—21no—
477C22×D3—61no—
478C22×D3—61no—
479C22×D3—61no—
480C22×D3—61no—
481C22×D3—121no—
482C22×D3—121no—
483C3×Q8—61no—
484C3×Q8—61no—
485C3×D4—61no—
486C3×D4—61no—
487C3×D4—122no—
488C2×C3×C4—21no—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—21no—
493C2×C3×C4—21no—
494C2×C3×C4—31no—
495C2×C3×C4—31no—
496C2×C3×C4—31no—
497C2×C3×C4—31no—
498C2×C3×C4—41no—
499C2×C3×C4—41no—
500C2×C3×C4—62no—
501C2×C3×C4—62no—
502C2×C3×C4—61no—
503C2×C3×C4—61no—
504C2×C3×C4—61no—
505C2×C3×C4C2×D1211yescharacteristic
506C2×C3×C4D3×D411yescharacteristic
507C2×C3×C4C23×D311yescharacteristic
508C2×C3×C4C23×D311yescharacteristic
509#67—42no—
510#67—122no—
511#67—122no—
512#67—122no—
513#67—122no—
514#67—122no—
515#67—122no—
516#67—242no—
517#67—242no—
518C2×Dic3—22no—
519C2×Dic3—22no—
520C2×Dic3—21no—
521C2×Dic3—21no—
522C2×Dic3—21no—
523C2×Dic3—61no—
524C2×Dic3—61no—
525C2×Dic3—61no—
526C2×Dic3—61no—
527C2×Dic3—121no—
528C2×Dic3—121no—
529C2×Dic3—122no—
530C2×Dic3C2×D1211yescharacteristic
531C2×Dic3C2×D1211yescharacteristic
532C2×Dic3C2×D1211yescharacteristic
533C2×Dic3C2×D1211yescharacteristic
534D12—21no—
535D12—21no—
536D12—61no—
537D12—61no—
538D12—61no—
539D12—61no—
540D12—61no—
541D12—61no—
542D12—61no—
543D12—61no—
544D12—121no—
545D12—121no—
546D12—121no—
547D12—121no—
548D12—122no—
549D12—122no—
550C4×D3—122no—
551C4×D3—122no—
552C4×D3—122no—
553C4×D3—122no—
554C4×D3—122no—
555Dic6—21no—
556Dic6—21no—
557Dic6—122no—
558Dic6—122no—
559C3×C8—22no—
560C3×C8—21no—
561C3×C8—21no—
562C3×C8—21no—
563C3×C8—21no—
564C3×C8—41no—
565C3×C8—61no—
566C3×C8—61no—
567C3⋊C8—21no—
568C3⋊C8—21no—
569C2×C32—22no—
570C2×C32#53711yescharacteristic
571C2×C32C2×#13511yescharacteristic
572C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
573C3⋊D3—81no—
574C3⋊D3—81no—
575C3×D3—81no—
576#41—364no—
577C2×Q8—31no—
578C2×Q8—181no—
579C2×D4—31no—
580C2×D4—61no—
581C2×D4—91no—
582C2×D4—91no—
583C2×D4—181no—
584C2×D4—181no—
585C2×D4—181no—
586C2×D4—181no—
587C22×C4—31no—
588C22×C4—31no—
589C22×C4—181no—
590C22×C4—181no—
591C22×C4—181no—
592C22×C4C2×D3211yescharacteristic
593SD16—121no—
594SD16—361no—
595D8—361no—
596D8—361no—
597C2×C8—31no—
598C2×C8—31no—
599C2×C8—41no—
600C2×C8—121no—
601C2×C8C2×D3211yescharacteristic
602C2×C8C2×D3211yescharacteristic
603C4⋊C4—31no—
604C4⋊C4—31no—
605C4⋊C4—61no—
606C4⋊C4—91no—
607C4⋊C4—91no—
608C4⋊C4—181no—
609C4⋊C4—181no—
610C4⋊C4—181no—
611C4⋊C4—181no—
612C22⋊C4—61no—
613C22⋊C4—61no—
614C22⋊C4—181no—
615C22⋊C4—181no—
616C22⋊C4—181no—
617C22⋊C4—181no—
618C22⋊C4—181no—
619C22⋊C4—181no—
620C22⋊C4—181no—
621C42—31no—
622C42—31no—
623C42—31no—
624C42—31no—
625C42—181no—
626C22×C3—21no—
627C22×C3—21no—
628C22×C3—21no—
629C22×C3—21no—
630C22×C3—21no—
631C22×C3—22no—
632C22×C3—41no—
633C22×C3—41no—
634C22×C3—121no—
635C22×C3—121no—
636C22×C3—121no—
637C22×C3#90812yes—
638C22×C3#91412yes—
639C22×C3C22×D1211yescharacteristic
640C22×C3C2×D3×D411yescharacteristic
641C2×D3—41no—
642C2×D3—41no—
643C2×D3—41no—
644C2×D3—121no—
645C2×D3—121no—
646C2×D3—121no—
647C2×D3—121no—
648C2×D3—121no—
649C2×D3—121no—
650C2×D3—121no—
651C2×D3—121no—
652C2×D3—121no—
653C2×D3—121no—
654C2×D3—121no—
655C2×D3—121no—
656C2×D3—241no—
657C2×D3—241no—
658C2×D3—241no—
659C2×D3—241no—
660C2×D3—241no—
661C2×D3—241no—
662C3×C4—21no—
663C3×C4—21no—
664C3×C4—21no—
665C3×C4—21no—
666C3×C4—32no—
667C3×C4—41no—
668C3×C4—61no—
669C3×C4—61no—
670C3×C4—61no—
671C3×C4—121no—
672C3×C4—121no—
673C3×C4—121no—
674C3×C4#100411yescharacteristic
675C3×C4#100411yescharacteristic
676C3×C4#100711yescharacteristic
677C3×C4#101011yescharacteristic
678Dic3—21no—
679Dic3—21no—
680Dic3—21no—
681Dic3—41no—
682Dic3—41no—
683Dic3—41no—
684Dic3—121no—
685Dic3—121no—
686Dic3—121no—
687Dic3—121no—
688Dic3—241no—
689Dic3—241no—
690Dic3#90412yes—
691C32#324711yescharacteristic, complemented, Sylow
692C23—61no—
693C23—181no—
694C23—181no—
695C23D3×D1211yescharacteristic
696Q8—61no—
697Q8—61no—
698Q8—362no—
699D4—61no—
700D4—61no—
701D4—122no—
702D4—181no—
703D4—181no—
704D4—181no—
705D4—181no—
706D4—362no—
707D4—362no—
708D4—362no—
709D4—362no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—31no—
713C2×C4—31no—
714C2×C4—31no—
715C2×C4—31no—
716C2×C4—62no—
717C2×C4—62no—
718C2×C4—61no—
719C2×C4—61no—
720C2×C4—61no—
721C2×C4—181no—
722C2×C4—181no—
723C2×C4—362no—
724C2×C4—362no—
725C2×C4—362no—
726C2×C4D3×D1211yescharacteristic
727C2×C4C22×D3211yescharacteristic
728C8—21no—
729C8—21no—
730C8—61no—
731C8—61no—
732C2×C3—22no—
733C2×C3—22no—
734C2×C3—21no—
735C2×C3—21no—
736C2×C3—21no—
737C2×C3—42no—
738C2×C3—241no—
739C2×C3#551011yescharacteristic
740C2×C3#559711yescharacteristic
741C2×C3C2×#90411yescharacteristic
742C2×C3C2×#90811yescharacteristic
743C2×C3C2×#91411yescharacteristic
744C2×C3D3×#13511yescharacteristic
745D3—81no—
746D3—241no—
747D3—241no—
748D3—241no—
749D3—241no—
750D3—481no—
751D3—481no—
752C22—21no—
753C22—21no—
754C22—121no—
755C22—121no—
756C22—121no—
757C22—361no—
758C22—361no—
759C22—361no—
760C22—361no—
761C22—361no—
762C22—361no—
763C22#6379412yes—
764C22C2×D3×D1211yescharacteristic
765C4—21no—
766C4—32no—
767C4—61no—
768C4—61no—
769C4—61no—
770C4—121no—
771C4—121no—
772C4—121no—
773C4—361no—
774C4—361no—
775C4#6429711yescharacteristic
776C4#6433011yescharacteristic
777C3—21no—
778C3#7902811yescharacteristic, complemented
779C3#8064111yescharacteristic, complemented
780C2—22no—
781C2—241no—
782C2—721no—
783C2—721no—
784C2C2×#6379411yescharacteristic
785C2D3×#90411yescharacteristic
786C2#1059491111yescharacteristic
subgroupG/H
centerC22C2×D3×D12
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. #10594955C2semidirect
2. #10594910C2semidirect
3. #10592814C2semidirect
4. C3×#5114C2semidirect
5. C2×C3×Dic3⋊C8C2semidirect
6. #10591177C2semidirect
7. #10591164C2semidirect
8. #10590804C2semidirect
9. #10590799C2semidirect
10. #10590770C2semidirect
11. #10590769C2semidirect
12. #10590767C2semidirect
13. #10590765C2semidirect
14. #10590759C2semidirect
15. #10590754C2semidirect
74. #5114D3semidirect
75. C2×Dic3⋊C8D3semidirect
691. C32#3247semidirect
778. C3#79028semidirect
779. C3#80641semidirect

Maximal subgroups

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

subgroupindex
#105949552
#105949102
#105928142
C3×#51142
C2×C3×Dic3⋊C82
#105911772
#105911642
#105908042
#105907992
#105907702
#105907692
#105907672
#105907652
#105907592
#105907542
#806413
#790283