Finite Group Databasebeta

← #11888697

Subgroups — #11888697

Order 1152.

854 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594559C211yesmaximal, characteristic, complemented
2#10594530C211yesmaximal, characteristic, complemented
3#10592568C211yesmaximal, characteristic, complemented
4C3×#4868C211yesmaximal, characteristic, complemented
5C3×#4862C211yesmaximal, characteristic, complemented
6#10590967C211yesmaximal, characteristic, complemented
7#10590967C211yesmaximal, characteristic, complemented
8#10590904C211yesmaximal, characteristic, complemented
9#10590725C211yesmaximal, characteristic, complemented
10#10590610C211yesmaximal, characteristic, complemented
11#10590609C211yesmaximal, characteristic, complemented
12#10590585C211yesmaximal, characteristic, complemented
13#10590577C211yesmaximal, characteristic, complemented
14#10590565C211yesmaximal, characteristic, complemented
15#10590435C211yesmaximal, characteristic, complemented
16#81546—31nomaximal
17#81432—31nomaximal
18C2×#3799C2211yescharacteristic
19C2×#3799C2211yescharacteristic
20C2×#3745C2211yescharacteristic
21#64102C2211yescharacteristic
22#64102C2211yescharacteristic
23C3×#897C2211yescharacteristic
24C3×#897C2211yescharacteristic
25C3×#892C2211yescharacteristic
26C3×D3×C4⋊C4C2211yescharacteristic
27#63912—21no—
28#63909C2211yescharacteristic
29#63909C2211yescharacteristic
30#63906—21no—
31C4×#626—21no—
32C4×#625C2211yescharacteristic
33#63900—21no—
34#63873C2211yescharacteristic
35#63872C2211yescharacteristic
36#63868—21no—
37#63854—21no—
38#63854—21no—
39#63853—21no—
40C2×#3717C2211yescharacteristic
41C2×#3717C2211yescharacteristic
42C2×#3711C2211yescharacteristic
43C2×D3×C3⋊C8C2211yescharacteristic
44C32×#106C2211yescharacteristic
45#63642C2211yescharacteristic
46#63636C2211yescharacteristic
47#63636C2211yescharacteristic
48C3×(C2×D3)⋊C8C2211yescharacteristic
49C3×(C2×D3)⋊C8C2211yescharacteristic
50C3×#816C2211yescharacteristic
51C3×#816C2211yescharacteristic
52C3×#810C2211yescharacteristic
53C3×#810C2211yescharacteristic
54C3×#808C2211yescharacteristic
55C3×#807C2211yescharacteristic
56#63572C2211yescharacteristic
57#63565C2211yescharacteristic
58#63565C2211yescharacteristic
59#63564C2211yescharacteristic
60#63564C2211yescharacteristic
61#5631—31no—
62#5631—31no—
63#5530—31no—
64#5514—31no—
65C3×#485—31no—
66C3×#483—31no—
67#5049—31no—
68#5048—31no—
69#5002—31no—
70#4966—31no—
71#4891—31no—
72#4886—31no—
73#4871—31no—
74#4869—31no—
75#4869—31no—
76#4869—61no—
77#4868D311yescharacteristic, complemented
78#4864—31no—
79#4862D311yescharacteristic, complemented
80#4818—31no—
81#4818—31no—
82#4810—31no—
83#4810—31no—
84#4804—31no—
85#4803—31no—
86#4797—31no—
87#4797—31no—
88#4734—31no—
89#4734—31no—
90#4730—31no—
91#4728—31no—
92C2×C4⋊(C3⋊D3)C2311yescharacteristic
93C2×C4⋊(C3⋊D3)C2311yescharacteristic
94C2×C4×C3⋊D3—21no—
95C2×C4×C3⋊D3—21no—
96C2×C3×C4×D3—21no—
97C2×C3×C4×D3C2311yescharacteristic
98C2×C3×C4×D3C2311yescharacteristic
99C2×C3×Dic6C2311yescharacteristic
100C2×C3×Dic6C2311yescharacteristic
101C2×#626—21no—
102C2×#626—21no—
103C2×#626—21no—
104C2×#626—21no—
105C2×#625D411yescharacteristic
106C2×#624—21no—
107C2×#624—21no—
108#3799—22no—
109#3799—22no—
110#3799—41no—
111#3799—41no—
112C2×C32×C8C2311yescharacteristic
113C32×C4⋊C4C2311yescharacteristic
114C32×C4⋊C4C2311yescharacteristic
115#3752—21no—
116#3752—21no—
117C4×C3⋊Dic3C2311yescharacteristic
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119#3745—22no—
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×C4⋊Dic3C2311yescharacteristic
127C3×Dic3⋊C4—21no—
128C3×C4×Dic3—21no—
129C2×C3×C3⋊C8C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131#3724—21no—
132#3724—21no—
133#3724D411yescharacteristic
134Dic3⋊Dic3—21no—
135Dic3⋊Dic3—21no—
136#3722—21no—
137#3722—21no—
138(C2×D3)⋊Dic3D411yescharacteristic
139(C2×D3)⋊Dic3D411yescharacteristic
140#3717—41no—
141#3717—41no—
142#3711—41no—
143D3×C3⋊C8—41no—
144#3307—91noSylow
145C2×#239—31no—
146C2×#239—31no—
147C2×#235—31no—
148C2×#235—31no—
149C3×C22⋊Q8—31no—
150C3×C22⋊Q8—31no—
151C3×#117—31no—
152C2×C3×C4⋊C4—31no—
153#944—31no—
154#944—31no—
155C2×#215—31no—
156C2×#215—31no—
157#930—31no—
158#930—31no—
159#930—61no—
160C4×#67—31no—
161C4×#67—31no—
162C4×#67—61no—
163C2×#208—31no—
164C22×C3⋊C8—31no—
165C2×D24—31no—
166C2×D24—31no—
167C2×D24—61no—
168C2×#204—31no—
169C2×#204—31no—
170C2×ΓL(1,𝔽25)—31no—
171C2×D3×C8—31no—
172#898—61no—
173#897C2×D311yescharacteristic
174#897C2×D311yescharacteristic
175#895—31no—
176#895—31no—
177#894—61no—
178#894—61no—
179#894—61no—
180#893—31no—
181#893—31no—
182#893—31no—
183#893—31no—
184#893—61no—
185#893—61no—
186#892C2×D311yescharacteristic
187D3×C4⋊C4—61no—
188D3×C4⋊C4—61no—
189D3×C4⋊C4C2×D311yescharacteristic
190#890—31no—
191#890—31no—
192#884—61no—
193#884—61no—
194#884—61no—
195#883—61no—
196#883—61no—
197#883—61no—
198#876—61no—
199C4×D12—61no—
200C3×#107—31no—
201C3×#106—21no—
202C3×#106—31no—
203C3×#106C2×D311yescharacteristic
204C3×#106C2×D311yescharacteristic
205C3×#103—31no—
206C3×#103—31no—
207C3×#103—31no—
208C3×#103—31no—
209C3×C22⋊C8—31no—
210C3×C22⋊C8—31no—
211#835—31no—
212#835—31no—
213#821—31no—
214#821—31no—
215(C2×D3)⋊C8C2×D311yescharacteristic
216(C2×D3)⋊C8C2×D311yescharacteristic
217#816C2×D311yescharacteristic
218#816C2×D311yescharacteristic
219#815—31no—
220#815—31no—
221#815—61no—
222Dic3⋊C8—31no—
223Dic3⋊C8—31no—
224#810—31no—
225#810—31no—
226#810C2×D311yescharacteristic
227#810C2×D311yescharacteristic
228#809—31no—
229#809—31no—
230#809—31no—
231#809—31no—
232#809—31no—
233#809—31no—
234#809—61no—
235#809—61no—
236#808C2×D311yescharacteristic
237#807C2×D311yescharacteristic
238C22×C3⋊D3—21no—
239C22×C3⋊D3—21no—
240C22×C3×D3C2×D411yescharacteristic
241C22×C3×D3C2×D411yescharacteristic
242C2×C32×C4—21no—
243C2×C32×C4—21no—
244C2×C32×C4C2411yescharacteristic
245C2×C3⋊Dic3C2×D411yescharacteristic
246C2×C3⋊Dic3C2×D411yescharacteristic
247C4⋊(C3⋊D3)—21no—
248C4⋊(C3⋊D3)—21no—
249C4⋊(C3⋊D3)—21no—
250C4⋊(C3⋊D3)#4112yes—
251C4×C3⋊D3—42no—
252C4×C3⋊D3—81no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3C2×D411yescharacteristic
258C2×C3×Dic3C2×D411yescharacteristic
259C3×C4×D3—21no—
260C3×C4×D3—21no—
261C3×C4×D3—21no—
262C3×C4×D3—21no—
263C3×C4×D3—81no—
264C3×Dic6—21no—
265C3×Dic6—21no—
266C3×Dic6—21no—
267C3×Dic6—21no—
268#626—42no—
269#626—42no—
270#626—42no—
271#626—81no—
272#625—41no—
273#624—42no—
274#624—42no—
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—31no—
283#483—31no—
284#478—91no—
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—91no—
294C2×C3×Q8—31no—
295C2×C3×Q8—31no—
296C22×C3×C4—31no—
297C22×C3×C4—31no—
298C22×C3×C4—61no—
299C2×#67—31no—
300C2×#67—31no—
301C2×#67—61no—
302C2×#67—61no—
303C2×#67—61no—
304C2×#67—61no—
305#239—62no—
306#239—62no—
307#239—121no—
308#239—121no—
309#235—62no—
310#235—62no—
311#235—121no—
312#235—121no—
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×D12—61no—
322C2×D12—61no—
323C2×C4×D3—21no—
324C2×C4×D3—61no—
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—61no—
332C2×C4×D3—121no—
333C2×C4×D3—121no—
334C2×C4×D3C22×D311yescharacteristic
335C2×C4×D3C22×D311yescharacteristic
336C2×Dic6C22×D311yescharacteristic
337C2×Dic6C22×D311yescharacteristic
338C2×C3×C8—21no—
339C2×C3×C8—31no—
340C2×C3×C8—31no—
341C2×C3×C8C22×D311yescharacteristic
342C2×C3×C8C22×D311yescharacteristic
343C3×C4⋊C4—21no—
344C3×C4⋊C4—21no—
345C3×C4⋊C4—31no—
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—61no—
358#217—31no—
359#217—31no—
360#215—121no—
361#215—121no—
362(C2×D3)⋊C4—21no—
363(C2×D3)⋊C4—21no—
364(C2×D3)⋊C4—21no—
365(C2×D3)⋊C4—31no—
366(C2×D3)⋊C4—31no—
367(C2×D3)⋊C4—61no—
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—
376(C2×D3)⋊C4—121no—
377C4⋊Dic3—21no—
378C4⋊Dic3—21no—
379C4⋊Dic3—61no—
380C4⋊Dic3—61no—
381C4⋊Dic3C22×D311yescharacteristic
382C4⋊Dic3C22×D311yescharacteristic
383Dic3⋊C4—21no—
384Dic3⋊C4—31no—
385Dic3⋊C4—31no—
386Dic3⋊C4—61no—
387Dic3⋊C4—61no—
388Dic3⋊C4—61no—
389Dic3⋊C4—61no—
390Dic3⋊C4—61no—
391Dic3⋊C4—61no—
392C4×Dic3—21no—
393C4×Dic3—31no—
394C4×Dic3—31no—
395C4×Dic3—61no—
396#208—121no—
397C2×C3⋊C8—31no—
398C2×C3⋊C8—31no—
399C2×C3⋊C8—61no—
400C2×C3⋊C8—121no—
401C2×C3⋊C8C22×D311yescharacteristic
402C2×C3⋊C8C22×D311yescharacteristic
403D24—62no—
404D24—62no—
405D24—64no—
406#204—121no—
407#204—121no—
408ΓL(1,𝔽25)—121no—
409D3×C8—121no—
410C22×C32C22×D411yescharacteristic
411C2×C3⋊D3—22no—
412C2×C3⋊D3—41no—
413C2×C3⋊D3—41no—
414C2×C3⋊D3—41no—
415C2×C3⋊D3—41no—
416C2×C3⋊D3—41no—
417C2×C3×D3—21no—
418C2×C3×D3—21no—
419C2×C3×D3—21no—
420C2×C3×D3—21no—
421C2×C3×D3—21no—
422C2×C3×D3—21no—
423C32×C4—41no—
424C32×C4—41no—
425C32×C4C2×#4111yescharacteristic
426C32×C4H(5,𝔽2)11yescharacteristic
427C3⋊Dic3—21no—
428C3⋊Dic3—21no—
429C3×Dic3—21no—
430C3×Dic3—21no—
431C3×Dic3—41no—
432C3×Dic3—41no—
433C3×Dic3—41no—
434C3×Dic3—41no—
435C2×#41—91no—
436C2×#41—91no—
437C2×SD16—91no—
438C2×SD16—91no—
439C2×D8—91no—
440C2×M16—91no—
441C22×C8—91no—
442C4⋊Q8—91no—
443#126—181no—
444#125—91no—
445#123—181no—
446#123—181no—
447#123—181no—
448C22⋊Q8—31no—
449C22⋊Q8—31no—
450#121—91no—
451#121—91no—
452#121—181no—
453#121—181no—
454C4×D4—91no—
455C4×D4—91no—
456C4×D4—91no—
457C4×D4—181no—
458#117—31no—
459C2×C4⋊C4—31no—
460C2×C4⋊C4—181no—
461#107—31no—
462#106—31no—
463#106D3211yescharacteristic
464C4⋊C8—91no—
465#103—31no—
466#103—31no—
467#103—31no—
468#103—31no—
469#103—91no—
470#103—91no—
471#102—91no—
472#102—91no—
473#102—91no—
474#102—91no—
475C22⋊C8—31no—
476C22⋊C8—31no—
477#97—91no—
478C23×C3—31no—
479C23×C3—31no—
480C22×D3—61no—
481C22×D3—61no—
482C22×D3—61no—
483C22×D3—61no—
484C22×D3—121no—
485C22×D3—121no—
486C22×D3D3×D411yescharacteristic
487C22×D3D3×D411yescharacteristic
488C3×Q8—61no—
489C3×Q8—61no—
490C3×Q8—61no—
491C3×Q8—61no—
492C2×C3×C4—21no—
493C2×C3×C4—21no—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—31no—
498C2×C3×C4—31no—
499C2×C3×C4—41no—
500C2×C3×C4—41no—
501C2×C3×C4—61no—
502C2×C3×C4—61no—
503C2×C3×C4—61no—
504C2×C3×C4—61no—
505C2×C3×C4—61no—
506C2×C3×C4—61no—
507C2×C3×C4—61no—
508C2×C3×C4—61no—
509C2×C3×C4—241no—
510C2×C3×C4C23×D311yescharacteristic
511C2×C3×C4C23×D311yescharacteristic
512#67—122no—
513#67—122no—
514#67—122no—
515#67—121no—
516#67—121no—
517#67—241no—
518C2×Dic3—21no—
519C2×Dic3—21no—
520C2×Dic3—21no—
521C2×Dic3—21no—
522C2×Dic3—31no—
523C2×Dic3—31no—
524C2×Dic3—31no—
525C2×Dic3—31no—
526C2×Dic3—61no—
527C2×Dic3—61no—
528C2×Dic3D3×D411yescharacteristic
529C2×Dic3D3×D411yescharacteristic
530D12—32no—
531D12—32no—
532D12—62no—
533D12—62no—
534D12—61no—
535D12—61no—
536D12—61no—
537D12—61no—
538D12—61no—
539D12—61no—
540D12—121no—
541D12—121no—
542D12—122no—
543D12—122no—
544D12—122no—
545D12—241no—
546C4×D3—21no—
547C4×D3—21no—
548C4×D3—21no—
549C4×D3—21no—
550C4×D3—81no—
551C4×D3—122no—
552C4×D3—122no—
553C4×D3—122no—
554C4×D3—122no—
555C4×D3—122no—
556C4×D3—122no—
557C4×D3—242no—
558C4×D3—241no—
559C4×D3—241no—
560C4×D3—242no—
561Dic6—21no—
562Dic6—21no—
563Dic6—21no—
564Dic6—21no—
565C3×C8—22no—
566C3×C8—21no—
567C3×C8—21no—
568C3×C8—61no—
569C3×C8—61no—
570C3⋊C8—21no—
571C3⋊C8—21no—
572C3⋊C8—61no—
573C3⋊C8—61no—
574C3⋊C8—121no—
575C2×C32#54611yescharacteristic
576C2×C32#57511yescharacteristic
577C2×C32#57711yescharacteristic
578C3⋊D3—42no—
579C3⋊D3—81no—
580C3×D3—41no—
581C3×D3—41no—
582#41—182no—
583#41—182no—
584#41—361no—
585#41—361no—
586C2×Q8—31no—
587C2×Q8—31no—
588C2×D4—91no—
589C2×D4—91no—
590C2×D4—91no—
591C2×D4—181no—
592C2×D4—181no—
593C2×D4—181no—
594C2×D4—181no—
595C22×C4—31no—
596C22×C4—31no—
597C22×C4—61no—
598C22×C4—181no—
599C22×C4—181no—
600C22×C4—181no—
601C22×C4—181no—
602SD16—361no—
603SD16—361no—
604D8—182no—
605M16—361no—
606C2×C8—31no—
607C2×C8—31no—
608C2×C8—91no—
609C2×C8—361no—
610C2×C8C2×D3211yescharacteristic
611C4⋊C4—31no—
612C4⋊C4—31no—
613C4⋊C4—61no—
614C4⋊C4—61no—
615C4⋊C4—61no—
616C4⋊C4—91no—
617C4⋊C4—181no—
618C4⋊C4—181no—
619C4⋊C4—181no—
620C4⋊C4—181no—
621C4⋊C4C2×D3211yescharacteristic
622C4⋊C4C2×D3211yescharacteristic
623C22⋊C4—61no—
624C22⋊C4—61no—
625C22⋊C4—61no—
626C22⋊C4—91no—
627C22⋊C4—91no—
628C22⋊C4—181no—
629C22⋊C4—181no—
630C22⋊C4—181no—
631C22⋊C4—181no—
632C42—61no—
633C42—91no—
634C22×C3—21no—
635C22×C3—61no—
636C22×C3—61no—
637C22×C3—61no—
638C22×C3—61no—
639C22×C3—61no—
640C22×C3—61no—
641C22×C3C2×D3×D411yescharacteristic
642C22×C3C2×D3×D411yescharacteristic
643C2×D3—21no—
644C2×D3—21no—
645C2×D3—21no—
646C2×D3—21no—
647C2×D3—21no—
648C2×D3—21no—
649C2×D3—62no—
650C2×D3—62no—
651C2×D3—122no—
652C2×D3—121no—
653C2×D3—121no—
654C2×D3—121no—
655C2×D3—121no—
656C2×D3—122no—
657C2×D3—121no—
658C2×D3—121no—
659C2×D3—121no—
660C2×D3—121no—
661C2×D3—121no—
662C2×D3—121no—
663C2×D3—241no—
664C2×D3—241no—
665C2×D3—241no—
666C2×D3—241no—
667C3×C4—21no—
668C3×C4—21no—
669C3×C4—41no—
670C3×C4—41no—
671C3×C4—41no—
672C3×C4—41no—
673C3×C4—61no—
674C3×C4—61no—
675C3×C4—81no—
676C3×C4—81no—
677C3×C4—121no—
678C3×C4—121no—
679C3×C4—121no—
680C3×C4—121no—
681C3×C4D3×#4111yescharacteristic
682C3×C4D3×#4111yescharacteristic
683C3×C4#100911yescharacteristic
684C3×C4#100911yescharacteristic
685Dic3—21no—
686Dic3—21no—
687Dic3—41no—
688Dic3—41no—
689Dic3—41no—
690Dic3—41no—
691Dic3—61no—
692Dic3—61no—
693Dic3—61no—
694Dic3—61no—
695Dic3—121no—
696Dic3—121no—
697C32#330711yescharacteristic, complemented, Sylow
698C23—31no—
699C23—31no—
700C23—181no—
701C23—181no—
702Q8—61no—
703Q8—61no—
704Q8—61no—
705Q8—61no—
706D4—92no—
707D4—181no—
708D4—181no—
709D4—181no—
710D4—362no—
711D4—362no—
712D4—362no—
713D4—361no—
714D4—721no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—31no—
718C2×C4—31no—
719C2×C4—61no—
720C2×C4—61no—
721C2×C4—61no—
722C2×C4—61no—
723C2×C4—61no—
724C2×C4—61no—
725C2×C4—61no—
726C2×C4—61no—
727C2×C4—91no—
728C2×C4—91no—
729C2×C4—241no—
730C2×C4—362no—
731C2×C4—362no—
732C2×C4—362no—
733C2×C4—721no—
734C2×C4C22×D3211yescharacteristic
735C8—21no—
736C8—61no—
737C8—61no—
738C8—181no—
739C2×C3—21no—
740C2×C3—21no—
741C2×C3—21no—
742C2×C3—121no—
743C2×C3—121no—
744C2×C3#565411yescharacteristic
745C2×C3#565411yescharacteristic
746C2×C3#576211yescharacteristic
747C2×C3#576811yescharacteristic
748C2×C3#577711yescharacteristic
749C2×C3#577811yescharacteristic
750D3—41no—
751D3—41no—
752D3—122no—
753D3—122no—
754D3—242no—
755D3—242no—
756D3—241no—
757D3—241no—
758C22—61no—
759C22—61no—
760C22—61no—
761C22—61no—
762C22—61no—
763C22—61no—
764C22—182no—
765C22—361no—
766C22—361no—
767C22—361no—
768C22—361no—
769C22—361no—
770C22D32×D411yescharacteristic
771C4—41no—
772C4—41no—
773C4—61no—
774C4—61no—
775C4—121no—
776C4—121no—
777C4—121no—
778C4—121no—
779C4—181no—
780C4—181no—
781C4#6430611yescharacteristic
782C4#6432011yescharacteristic
783C3—21no—
784C3#8143211yescharacteristic, complemented
785C3#8154611yescharacteristic, complemented
786C2—121no—
787C2—121no—
788C2—362no—
789C2—721no—
790C2#1059461611yescharacteristic
791C2#1059474611yescharacteristic
792C2#1059475111yescharacteristic
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. #10594559C2semidirect
2. #10594530C2semidirect
3. #10592568C2semidirect
4. C3×#4868C2semidirect
5. C3×#4862C2semidirect
6. #10590967C2semidirect
7. #10590967C2semidirect
8. #10590904C2semidirect
9. #10590725C2semidirect
10. #10590610C2semidirect
11. #10590609C2semidirect
12. #10590585C2semidirect
13. #10590577C2semidirect
14. #10590565C2semidirect
15. #10590435C2semidirect
77. #4868D3semidirect
79. #4862D3semidirect
697. C32#3307semidirect
784. C3#81432semidirect
785. C3#81546semidirect

Maximal subgroups

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

subgroupindex
#105945592
#105945302
#105925682
C3×#48682
C3×#48622
#105909672
#105909042
#105907252
#105906102
#105906092
#105905852
#105905772
#105905652
#105904352
#815463
#814323