Finite Group Databasebeta

← #11889273

Subgroups — #11889273

Order 1152.

860 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#10595228C211yesmaximal, characteristic
2#10594581C211yesmaximal, characteristic, complemented
3#10592466C211yesmaximal, characteristic, complemented
4C3×#4779C211yesmaximal, characteristic, complemented
5C3×#4770C211yesmaximal, characteristic, complemented
6#10591496C211yesmaximal, characteristic, complemented
7#10591460C211yesmaximal, characteristic, complemented
8#10591459C211yesmaximal, characteristic, complemented
9#10590969C211yesmaximal, characteristic, complemented
10#10590853C211yesmaximal, characteristic, complemented
11#10590776C211yesmaximal, characteristic, complemented
12#10590724C211yesmaximal, characteristic, complemented
13#10590608C211yesmaximal, characteristic, complemented
14#10590461C211yesmaximal, characteristic, complemented
15#10590429C211yesmaximal, characteristic, complemented
16#81401—31nomaximal
17#78935—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19C2×#3795C2211yescharacteristic
20#64145C2211yescharacteristic
21C2×#3754C2211yescharacteristic
22C2×#3746C2211yescharacteristic, complemented
23#64096C2211yescharacteristic, complemented
24C3×#938C2211yescharacteristic
25C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
26C3×#892C2211yescharacteristic
27C3×#892C2211yescharacteristic, complemented
28#63976—21no—
29#63970—21no—
30#63969—21no—
31D3×#217—21no—
32#63919C2211yescharacteristic, complemented
33C4×#627—21no—
34#63915—21no—
35C4×#625C2211yescharacteristic
36#63898C2211yescharacteristic
37#63859—21no—
38#63859—21no—
39#63857C2211yescharacteristic
40#63857C2211yescharacteristic
41#63857C2211yescharacteristic, complemented
42C2×#3716C2211yescharacteristic
43C2×D3×C3⋊C8C2211yescharacteristic, complemented
44C32×#102C2211yescharacteristic
45#63641C2211yescharacteristic, complemented
46#63637C2211yescharacteristic, complemented
47C3×#832C2211yescharacteristic
48C3×#832C2211yescharacteristic
49C3×#821C2211yescharacteristic
50C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
51C3×#817C2211yescharacteristic, complemented
52C3×#809C2211yescharacteristic
53C3×#807C2211yescharacteristic, complemented
54#63574C2211yescharacteristic, complemented
55#63567C2211yescharacteristic, complemented
56#63567C2211yescharacteristic, complemented
57#63567C2211yescharacteristic, complemented
58#63562C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60#63555C2211yescharacteristic, complemented
61#5806—31no—
62#5612—31no—
63#5533—31no—
64#5533—31no—
65C3×#482—31no—
66C3×#418—31no—
67#5218—31no—
68#5137—31no—
69#5127—31no—
70#5041—31no—
71#5002—31no—
72#4996—31no—
73#4889—31no—
74#4888—31no—
75#4870—31no—
76#4867—31no—
77#4783—31no—
78#4779D311yescharacteristic, complemented
79#4778—31no—
80#4776—31no—
81#4772—31no—
82#4770D311yescharacteristic, complemented
83#4767—31no—
84#4767—31no—
85#4767—61no—
86#4765—31no—
87#4765—31no—
88#4761—31no—
89#4757—31no—
90#4733—31no—
91#4730—31no—
92C23×C3×D3—21no—
93C2×C32×D4C2311yescharacteristic
94C2×#634C2311yescharacteristic
95C2×#634C2311yescharacteristic
96C2×C3×#67—21no—
97C2×C3×#67—21no—
98C3×D3×D4—22no—
99C3×D3×D4—41no—
100C2×C3×D12C2311yescharacteristic
101C2×C3×C4×D3C2311yescharacteristic
102C2×C3×C4×D3C2311yescharacteristic
103C2×#627—21no—
104C2×#625—21no—
105C2×#625D411yescharacteristic
106C2×D3×Dic3—21no—
107C2×D3×Dic3—21no—
108#3795—22no—
109#3795—41no—
110C2×C32×C8C2311yescharacteristic
111C32×C4⋊C4C2311yescharacteristic
112#3757—21no—
113#3757—21no—
114#3754—41no—
115#3750—21no—
116C4×C3⋊Dic3—21no—
117C4×C3⋊Dic3C2311yescharacteristic
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119#3746—41no—
120C3×#217—21no—
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4—21no—
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4×Dic3—21no—
127C3×C4×Dic3—21no—
128C2×C3×C3⋊C8C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130C3×ΓL(1,𝔽25)—41no—
131#3724—21no—
132#3724D411yescharacteristic
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3—21no—
135Dic3⋊Dic3—21no—
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3D411yescharacteristic
141(C2×D3)⋊Dic3D411yescharacteristic
142#3716—22no—
143D3×C3⋊C8—41no—
144#3311—91noSylow
145C22×C3×D4—31no—
146C2×#237—31no—
147C2×D3×D4C2×D311yescharacteristic
148C2×#235—31no—
149C2×C3×M16—31no—
150C3×#121—31no—
151C3×#117—31no—
152C3×#117—31no—
153#953—61no—
154C2×#217—61no—
155#939—61no—
156#938—61no—
157#938C2×D311yescharacteristic
158#937—61no—
159#936—31no—
160#936—31no—
161#936—61no—
162#935—61no—
163D4×Dic3—31no—
164C2×#214—31no—
165C2×#214—31no—
166C2×#214—31no—
167C2×#214—61no—
168C4×#67—31no—
169C4×#67—31no—
170#924—31no—
171#924—31no—
172#924—31no—
173C22×C3⋊C8—31no—
174C2×Dic12—31no—
175C2×Dic12—31no—
176C2×Dic12—61no—
177C2×#204—31no—
178C2×ΓL(1,𝔽25)C2×D311yescharacteristic
179C2×D3×C8—31no—
180#897—31no—
181#897—31no—
182#897—31no—
183#893—31no—
184#892C2×D311yescharacteristic
185#892C2×D311yescharacteristic, complemented
186#888—31no—
187#888—31no—
188#887—31no—
189#887—31no—
190#887—61no—
191#885—61no—
192#885—61no—
193#883—61no—
194D3×C22⋊C4—61no—
195#879—61no—
196#879—61no—
197#876—61no—
198#876—61no—
199C4×Dic6—61no—
200C4×Dic6—61no—
201C3×#107—31no—
202C3×#106—31no—
203C3×#102—21no—
204C3×#102—31no—
205C3×#102—31no—
206C3×#102—31no—
207C3×#102—31no—
208C3×#102C2×D311yescharacteristic
209C3×#102C2×D311yescharacteristic
210C3×C22⋊C8—31no—
211#832—31no—
212#832C2×D311yescharacteristic
213#832C2×D311yescharacteristic
214#830—31no—
215#821C2×D311yescharacteristic
216(C2×D3)⋊C8—31no—
217(C2×D3)⋊C8C2×D311yescharacteristic, complemented
218#817C2×D311yescharacteristic, complemented
219#816—31no—
220#816—31no—
221#816—31no—
222#815—31no—
223#815—31no—
224Dic3⋊C8—31no—
225Dic3⋊C8—31no—
226Dic3⋊C8—61no—
227#810—31no—
228#810—31no—
229#810—31no—
230#810—31no—
231#810—31no—
232#810—61no—
233#809—31no—
234#809C2×D311yescharacteristic
235#808—31no—
236#808—31no—
237#807C2×D311yescharacteristic, complemented
238C23×C32—21no—
239C22×C3×D3—21no—
240C22×C3×D3—42no—
241C22×C3×D3—42no—
242C22×C3×D3—81no—
243C22×C3×D3C2×D411yescharacteristic
244C22×C3×D3C2×D411yescharacteristic
245C32×D4—21no—
246C32×D4—21no—
247C2×C32×C4—21no—
248C2×C32×C4C2411yescharacteristic
249C2×C3⋊Dic3—21no—
250C2×C3⋊Dic3—21no—
251C2×C3⋊Dic3C2×D411yescharacteristic
252C2×C3⋊Dic3C2×D411yescharacteristic
253#634—21no—
254#634—21no—
255#634—21no—
256#634—21no—
257C3×#67—42no—
258C3×#67—81no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3C2×D411yescharacteristic
263C2×C3×Dic3C2×D411yescharacteristic
264C3×D12—21no—
265C3×D12#4112yes—
266C3×C4×D3—21no—
267C3×C4×D3—21no—
268C3×C4×D3—21no—
269C3×C4×D3—21no—
270#627—42no—
271#625—41no—
272#625—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—31no—
284#476—91no—
285#470—91no—
286#465—91no—
287#464—91no—
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×D4—21no—
297C2×C3×D4—31no—
298C2×C3×D4—61no—
299C2×C3×D4—62no—
300C2×C3×D4—61no—
301C2×C3×D4—121no—
302C2×C3×D4C22×D311yescharacteristic
303C2×C3×D4C22×D311yescharacteristic
304C22×C3×C4—31no—
305C22×C3×C4—31no—
306C2×#67—21no—
307C2×#67—21no—
308C2×#67—31no—
309C2×#67—31no—
310C2×#67—61no—
311C2×#67—61no—
312C22×Dic3—61no—
313C22×Dic3—61no—
314#237—62no—
315#237—121no—
316D3×D4—22no—
317D3×D4—41no—
318#235—62no—
319#235—121no—
320C2×D12C22×D311yescharacteristic
321C2×C4×D3—61no—
322C2×C4×D3—61no—
323C2×C4×D3C22×D311yescharacteristic
324C2×C4×D3C22×D311yescharacteristic
325C2×Dic6—31no—
326C2×Dic6—31no—
327C2×Dic6—31no—
328C2×Dic6—31no—
329C2×Dic6—61no—
330C2×Dic6—61no—
331C2×Dic6—61no—
332C2×Dic6—61no—
333C3×M16—121no—
334C2×C3×C8—21no—
335C2×C3×C8—31no—
336C2×C3×C8—31no—
337C2×C3×C8C22×D311yescharacteristic
338C2×C3×C8C22×D311yescharacteristic
339C3×C4⋊C4—21no—
340C3×C4⋊C4—31no—
341C3×C4⋊C4—31no—
342C3×C4⋊C4—31no—
343C3×C4⋊C4C22×D311yescharacteristic
344C3×C4⋊C4C22×D311yescharacteristic
345C3×C22⋊C4—61no—
346C3×C22⋊C4—61no—
347C3×C22⋊C4—61no—
348C3×C42—61no—
349C3×C42—61no—
350#217—21no—
351#217—31no—
352#217—31no—
353#217—61no—
354#217—61no—
355#217—61no—
356#217—61no—
357#217—61no—
358#217—61no—
359#217—61no—
360#217—61no—
361#217—121no—
362#217—121no—
363#214—62no—
364#214—121no—
365#214—121no—
366#214—122no—
367(C2×D3)⋊C4—21no—
368(C2×D3)⋊C4—21no—
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—
375C4⋊Dic3—61no—
376C4⋊Dic3—61no—
377C4⋊Dic3—61no—
378C4⋊Dic3C22×D311yescharacteristic
379C4⋊Dic3C22×D311yescharacteristic
380C4⋊Dic3C22×D311yescharacteristic
381Dic3⋊C4—31no—
382Dic3⋊C4—31no—
383Dic3⋊C4—61no—
384Dic3⋊C4—61no—
385Dic3⋊C4—61no—
386Dic3⋊C4—61no—
387Dic3⋊C4—61no—
388Dic3⋊C4—61no—
389Dic3⋊C4—61no—
390Dic3⋊C4—121no—
391C4×Dic3—21no—
392C4×Dic3—21no—
393C4×Dic3—31no—
394C4×Dic3—31no—
395C4×Dic3—61no—
396C4×Dic3—61no—
397C4×Dic3—61no—
398C4×Dic3—121no—
399C2×C3⋊C8—31no—
400C2×C3⋊C8—31no—
401C2×C3⋊C8—61no—
402C2×C3⋊C8—121no—
403C2×C3⋊C8C22×D311yescharacteristic
404C2×C3⋊C8C22×D311yescharacteristic
405Dic12—121no—
406Dic12—121no—
407Dic12—122no—
408#204—62no—
409ΓL(1,𝔽25)—41no—
410D3×C8—121no—
411C22×C32—41no—
412C22×C32—41no—
413C22×C32—41no—
414C22×C32C22×D411yescharacteristic
415C2×C3×D3—22no—
416C2×C3×D3—21no—
417C2×C3×D3—21no—
418C2×C3×D3—21no—
419C2×C3×D3—21no—
420C2×C3×D3—21no—
421C2×C3×D3—21no—
422C2×C3×D3—41no—
423C2×C3×D3—41no—
424C2×C3×D3—84no—
425C32×C4—41no—
426C32×C4C2×#4111yescharacteristic
427C32×C4H(5,𝔽2)11yescharacteristic
428C3⋊Dic3—21no—
429C3⋊Dic3—21no—
430C3⋊Dic3—41no—
431C3⋊Dic3—41no—
432C3×Dic3—21no—
433C3×Dic3—21no—
434C3×Dic3—41no—
435C3×Dic3—41no—
436C3×Dic3—41no—
437C2×#41—91no—
438C22×D4—31no—
439C2×Q16—91no—
440C2×SD16—91no—
441C2×SD16—91no—
442C2×M16—31no—
443C22×C8—91no—
444C4⋊Q8—91no—
445#126—181no—
446#126—181no—
447#124—91no—
448#124—181no—
449#123—181no—
450C22⋊Q8—91no—
451C22⋊Q8—91no—
452C22⋊Q8—91no—
453#121—31no—
454#121—181no—
455#120—181no—
456C4×Q8—91no—
457C4×Q8—181no—
458C4×D4—91no—
459C4×D4—91no—
460#117—31no—
461#117—31no—
462C2×C22⋊C4—181no—
463#107—31no—
464#106—31no—
465#106—91no—
466C4⋊C8—91no—
467#103—91no—
468#103—91no—
469#103—91no—
470#103—91no—
471#102—31no—
472#102—31no—
473#102—31no—
474#102—31no—
475#102—91no—
476#102D3211yescharacteristic
477C22⋊C8—31no—
478C22⋊C8—91no—
479#97—91no—
480C23×C3—21no—
481C23×C3—21no—
482C23×C3—31no—
483C23×C3—31no—
484C23×C3—41no—
485C23×C3—61no—
486C23×C3—122no—
487C23×C3—122no—
488C23×C3—241no—
489C22×D3—21no—
490C22×D3—42no—
491C22×D3—42no—
492C22×D3—81no—
493C22×D3D3×D411yescharacteristic
494C22×D3D3×D411yescharacteristic
495C3×D4—21no—
496C3×D4—21no—
497C3×D4—21no—
498C3×D4—21no—
499C3×D4—32no—
500C3×D4—41no—
501C3×D4—41no—
502C3×D4—61no—
503C3×D4—122no—
504C3×D4—241no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—31no—
509C2×C3×C4—31no—
510C2×C3×C4—41no—
511C2×C3×C4—61no—
512C2×C3×C4—61no—
513C2×C3×C4—61no—
514C2×C3×C4—61no—
515C2×C3×C4—61no—
516C2×C3×C4—61no—
517C2×C3×C4—61no—
518C2×C3×C4C23×D311yescharacteristic
519C2×C3×C4C23×D311yescharacteristic
520#67—42no—
521#67—81no—
522#67—121no—
523#67—121no—
524#67—122no—
525#67—122no—
526C2×Dic3—21no—
527C2×Dic3—21no—
528C2×Dic3—21no—
529C2×Dic3—31no—
530C2×Dic3—31no—
531C2×Dic3—31no—
532C2×Dic3—31no—
533C2×Dic3—61no—
534C2×Dic3—61no—
535C2×Dic3—61no—
536C2×Dic3—61no—
537C2×Dic3—61no—
538C2×Dic3—61no—
539C2×Dic3—121no—
540C2×Dic3—121no—
541C2×Dic3—122no—
542C2×Dic3—241no—
543C2×Dic3D3×D411yescharacteristic
544C2×Dic3D3×D411yescharacteristic
545D12—21no—
546D12#23512yes—
547C4×D3—21no—
548C4×D3—21no—
549C4×D3—21no—
550C4×D3—21no—
551C4×D3—122no—
552C4×D3—241no—
553Dic6—62no—
554Dic6—61no—
555Dic6—61no—
556Dic6—61no—
557Dic6—61no—
558Dic6—61no—
559Dic6—61no—
560Dic6—61no—
561Dic6—61no—
562Dic6—121no—
563Dic6—121no—
564Dic6—121no—
565Dic6—122no—
566Dic6—122no—
567C3×C8—21no—
568C3×C8—21no—
569C3×C8—41no—
570C3×C8—61no—
571C3×C8—61no—
572C3⋊C8—21no—
573C3⋊C8—21no—
574C3⋊C8—61no—
575C3⋊C8—61no—
576C3⋊C8—121no—
577C2×C32—81no—
578C2×C32#54611yescharacteristic
579C2×C32#57511yescharacteristic
580C2×C32#57711yescharacteristic
581C3×D3—41no—
582C3×D3—41no—
583C3×D3—42no—
584C24—61no—
585#41—182no—
586#41—361no—
587C2×Q8—91no—
588C2×Q8—91no—
589C2×Q8—181no—
590C2×D4—31no—
591C2×D4—61no—
592C2×D4—62no—
593C2×D4—61no—
594C2×D4—91no—
595C2×D4—121no—
596C2×D4—181no—
597C2×D4C2×D3211yescharacteristic
598C22×C4—31no—
599C22×C4—31no—
600C22×C4—181no—
601C22×C4—181no—
602Q16—361no—
603SD16—182no—
604SD16—361no—
605M16—121no—
606C2×C8—31no—
607C2×C8—31no—
608C2×C8—91no—
609C2×C8—361no—
610C2×C8C2×D3211yescharacteristic
611C4⋊C4—31no—
612C4⋊C4—31no—
613C4⋊C4—31no—
614C4⋊C4—91no—
615C4⋊C4—181no—
616C4⋊C4—181no—
617C4⋊C4—181no—
618C4⋊C4—181no—
619C4⋊C4—181no—
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—
630C22⋊C4—181no—
631C22⋊C4—181no—
632C42—61no—
633C42—61no—
634C42—91no—
635C42—181no—
636C22×C3—21no—
637C22×C3—41no—
638C22×C3—41no—
639C22×C3—41no—
640C22×C3—41no—
641C22×C3—41no—
642C22×C3—41no—
643C22×C3—62no—
644C22×C3—61no—
645C22×C3—61no—
646C22×C3—61no—
647C22×C3—61no—
648C22×C3—61no—
649C22×C3—61no—
650C22×C3—81no—
651C22×C3—81no—
652C22×C3—81no—
653C22×C3—121no—
654C22×C3—121no—
655C22×C3—244no—
656C22×C3C2×D3×D411yescharacteristic
657C22×C3C2×D3×D411yescharacteristic
658C2×D3—21no—
659C2×D3—21no—
660C2×D3—22no—
661C2×D3—21no—
662C2×D3—21no—
663C2×D3—21no—
664C2×D3—21no—
665C2×D3—41no—
666C2×D3—41no—
667C2×D3—84no—
668C3×C4—21no—
669C3×C4—21no—
670C3×C4—41no—
671C3×C4—41no—
672C3×C4—61no—
673C3×C4—61no—
674C3×C4—81no—
675C3×C4—121no—
676C3×C4—121no—
677C3×C4—121no—
678C3×C4C2×#23511yescharacteristic
679C3×C4#100411yescharacteristic
680C3×C4D3×#4111yescharacteristic
681C3×C4#100911yescharacteristic
682Dic3—21no—
683Dic3—21no—
684Dic3—41no—
685Dic3—41no—
686Dic3—41no—
687Dic3—61no—
688Dic3—61no—
689Dic3—61no—
690Dic3—61no—
691Dic3—121no—
692Dic3—121no—
693Dic3—122no—
694Dic3—121no—
695Dic3—121no—
696Dic3—121no—
697Dic3—121no—
698Dic3—241no—
699C32#331111yescharacteristic, complemented, Sylow
700C23—21no—
701C23—31no—
702C23—31no—
703C23—61no—
704C23—122no—
705C23—122no—
706C23—241no—
707Q8—181no—
708Q8—181no—
709Q8—181no—
710Q8—181no—
711Q8—362no—
712D4—21no—
713D4—21no—
714D4—32no—
715D4—61no—
716D4—122no—
717D4—241no—
718D4—361no—
719D4—362no—
720C2×C4—21no—
721C2×C4—31no—
722C2×C4—31no—
723C2×C4—61no—
724C2×C4—61no—
725C2×C4—61no—
726C2×C4—61no—
727C2×C4—61no—
728C2×C4—61no—
729C2×C4—61no—
730C2×C4—91no—
731C2×C4—91no—
732C2×C4—181no—
733C2×C4—181no—
734C2×C4—362no—
735C2×C4—721no—
736C2×C4C22×D3211yescharacteristic
737C8—21no—
738C8—61no—
739C8—61no—
740C8—181no—
741C2×C3—21no—
742C2×C3—21no—
743C2×C3—21no—
744C2×C3—81no—
745C2×C3—81no—
746C2×C3—121no—
747C2×C3—121no—
748C2×C3—122no—
749C2×C3—161no—
750C2×C3#549011yescharacteristic
751C2×C3#565411yescharacteristic
752C2×C3#576811yescharacteristic
753C2×C3#577311yescharacteristic
754C2×C3#577511yescharacteristic
755C2×C3#577511yescharacteristic
756D3—41no—
757D3—42no—
758D3—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—61no—
763C22—61no—
764C22—61no—
765C22—61no—
766C22—61no—
767C22—61no—
768C22—62no—
769C22—121no—
770C22—121no—
771C22—244no—
772C22D32×D411yescharacteristic
773C4—41no—
774C4—61no—
775C4—61no—
776C4—121no—
777C4—121no—
778C4—121no—
779C4—181no—
780C4—181no—
781C4—361no—
782C4—361no—
783C4D3×#23511yescharacteristic
784C4#6431411yescharacteristic
785C3—21no—
786C3#7893511yescharacteristic, complemented
787C3#8140111yescharacteristic, complemented
788C2—81no—
789C2—121no—
790C2—121no—
791C2—122no—
792C2#1059427211yescharacteristic
793C2#1059473311yescharacteristic
794C2#1059474511yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
prime radical#10595228C2
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. #10594581C2semidirect
3. #10592466C2semidirect
4. C3×#4779C2semidirect
5. C3×#4770C2semidirect
6. #10591496C2semidirect
7. #10591460C2semidirect
8. #10591459C2semidirect
9. #10590969C2semidirect
10. #10590853C2semidirect
11. #10590776C2semidirect
12. #10590724C2semidirect
13. #10590608C2semidirect
14. #10590461C2semidirect
15. #10590429C2semidirect
22. C2×#3746C22semidirect
23. #64096C22semidirect
27. C3×#892C22semidirect
32. #63919C22semidirect
41. #63857C22semidirect
43. C2×D3×C3⋊C8C22semidirect
45. #63641C22semidirect
46. #63637C22semidirect
50. C3×(C2×D3)⋊C8C22semidirect
51. C3×#817C22semidirect
53. C3×#807C22semidirect
54. #63574C22semidirect
55. #63567C22semidirect
56. #63567C22semidirect
57. #63567C22semidirect
60. #63555C22semidirect
78. #4779D3semidirect
82. #4770D3semidirect
185. #892C2×D3semidirect
217. (C2×D3)⋊C8C2×D3semidirect
218. #817C2×D3semidirect
237. #807C2×D3semidirect
699. C32#3311semidirect
786. C3#78935semidirect
787. C3#81401semidirect

Maximal subgroups

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

subgroupindex
#105952282
#105945812
#105924662
C3×#47792
C3×#47702
#105914962
#105914602
#105914592
#105909692
#105908532
#105907762
#105907242
#105906082
#105904612
#105904292
#814013
#789353