Finite Group Databasebeta

← #11887450

Subgroups — #11887450

Order 1152.

907 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595229C211yesmaximal, characteristic, complemented
2#10594562C211yesmaximal, characteristic, complemented
3#10592474C211yesmaximal, characteristic, complemented
4C3×D3×#102C211yesmaximal, characteristic, complemented
5C3×#4768C211yesmaximal, characteristic, complemented
6#10591448C211yesmaximal, characteristic, complemented
7#10591432C211yesmaximal, characteristic, complemented
8#10591425C211yesmaximal, characteristic, complemented
9#10590956C211yesmaximal, characteristic, complemented
10#10590847C211yesmaximal, characteristic, complemented
11#10590745C211yesmaximal, characteristic, complemented
12C8×#626C211yesmaximal, characteristic, complemented
13#10590617C211yesmaximal, characteristic, complemented
14#10590517C211yesmaximal, characteristic, complemented
15#10590467C211yesmaximal, characteristic, complemented
16#81653—31nomaximal
17#78760—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19C2×#3796C2211yescharacteristic
20#64147C2211yescharacteristic
21C2×#3753C2211yescharacteristic
22C2×C8×C3⋊D3C2211yescharacteristic, complemented
23#64104C2211yescharacteristic, complemented
24C3×#936C2211yescharacteristic
25C2×C3×D3×C8C2211yescharacteristic
26C3×D3×C4⋊C4C2211yescharacteristic
27C3×#890C2211yescharacteristic, complemented
28#63977—21no—
29#63971—21no—
30#63969—21no—
31D3×#217—21no—
32#63909—21no—
33#63909C2211yescharacteristic
34#63904—21no—
35C4×#626C2211yescharacteristic
36#63897—21no—
37#63894C2211yescharacteristic, complemented
38Dic3×D12C2211yescharacteristic
39#63856C2211yescharacteristic
40#63849C2211yescharacteristic, complemented
41#63848—21no—
42C2×#3717C2211yescharacteristic, complemented
43C2×#3714C2211yescharacteristic
44C32×#102C2211yescharacteristic
45#63648C2211yescharacteristic, complemented
46#63634C2211yescharacteristic, complemented
47C3×#832C2211yescharacteristic
48C3×#832C2211yescharacteristic
49C3×#821C2211yescharacteristic
50C3×#816C2211yescharacteristic, complemented
51C3×C8×Dic3C2211yescharacteristic, complemented
52C3×#810C2211yescharacteristic, complemented
53C3×#809C2211yescharacteristic
54#63575C2211yescharacteristic, complemented
55#63573C2211yescharacteristic, complemented
56Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
57#63565C2211yescharacteristic, complemented
58#63562C2211yescharacteristic
59#63557C2211yescharacteristic, complemented
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
61#5806—31no—
62#5695—31no—
63#5676—31no—
64#5514—31no—
65C3×#488—31no—
66C2×C3×#102—31no—
67#5217—31no—
68#5114—31no—
69C8×#67—31no—
70#5066—31no—
71#5057—31no—
72#4970—31no—
73#4811—31no—
74#4810—31no—
75#4807—31no—
76#4804—31no—
77#4787—31no—
78#4784—31no—
79#4781—31no—
80#4779—31no—
81#4775—31no—
82#4775—31no—
83#4775—61no—
84#4773—31no—
85#4772—31no—
86D3×#102D311yescharacteristic, complemented
87#4768D311yescharacteristic, complemented
88#4763—31no—
89#4756—31no—
90C4×D24—31no—
91C8×D12—31no—
92C23×C3×D3—21no—
93C2×C32×D4C2311yescharacteristic
94C2×#638—21no—
95C2×C4⋊(C3⋊D3)—21no—
96C2×C4⋊(C3⋊D3)C2311yescharacteristic
97C2×C4×C3⋊D3C2311yescharacteristic
98C2×C3×#67—21no—
99C3×D3×D4—22no—
100C3×D3×D4—41no—
101C2×C3×D12C2311yescharacteristic
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3C2311yescharacteristic
104C2×C3×Dic6C2311yescharacteristic
105C2×#626—21no—
106C2×#626—21no—
107C2×#626D411yescharacteristic
108C2×#624—21no—
109C2×D3×Dic3—21no—
110C2×D3×Dic3—21no—
111#3796—22no—
112#3796—41no—
113C2×C32×C8C2311yescharacteristic
114C32×C4⋊C4C2311yescharacteristic
115#3757—21no—
116#3753—41no—
117#3752—21no—
118C4⋊(C3⋊Dic3)C2311yescharacteristic
119C2×C3⋊(C3⋊C8)C2311yescharacteristic
120C8×C3⋊D3—41no—
121C3×#217—21no—
122C3×#217—21no—
123C3×C4⋊Dic3—21no—
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×Dic3⋊C4—21no—
127C3×Dic3⋊C4—21no—
128C3×C4×Dic3C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131C3×D3×C8—41no—
132#3724—21no—
133Dic3⋊Dic3D411yescharacteristic
134#3722—21no—
135#3722—21no—
136#3722—21no—
137#3722D411yescharacteristic
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3D411yescharacteristic
141Dic32—21no—
142#3717—41no—
143#3714—22no—
144#3297—91noSylow
145C22×C3×D4—31no—
146C2×#239—31no—
147C2×#237—31no—
148C2×D3×D4C2×D311yescharacteristic
149C22×C3×C8—31no—
150C3×#125—31no—
151C3×#124—31no—
152C2×C3×C4⋊C4—31no—
153#953—61no—
154C2×#217—61no—
155#946—31no—
156C2×#215—31no—
157#939—61no—
158#938—31no—
159#938—31no—
160#938—61no—
161#936C2×D311yescharacteristic
162#935—61no—
163D4×Dic3—31no—
164C2×#213—31no—
165C2×#213—31no—
166C2×#213—31no—
167C2×#213—61no—
168#930—31no—
169#930—61no—
170C4×#67—31no—
171C4×#67—61no—
172#924—31no—
173C2×D24—31no—
174C2×#204—31no—
175C2×D3×C8—31no—
176C2×D3×C8—31no—
177C2×D3×C8—61no—
178C2×D3×C8C2×D311yescharacteristic
179#898—61no—
180#898—61no—
181#895—31no—
182#895—31no—
183#895—31no—
184#895—61no—
185#895—61no—
186#894—61no—
187#894—61no—
188#893—31no—
189#893—61no—
190#892—31no—
191#892—31no—
192D3×C4⋊C4C2×D311yescharacteristic
193#890C2×D311yescharacteristic, complemented
194#884—61no—
195#883—61no—
196#882—61no—
197D3×C22⋊C4—61no—
198C4×D12—31no—
199C4×D12—31no—
200C4×D12—31no—
201C3×#103—31no—
202C3×#103—31no—
203C3×#102—21no—
204C3×#102—31no—
205C3×#102—31no—
206C3×#102—31no—
207C3×#102—31no—
208C3×#102C2×D311yescharacteristic
209C3×#102C2×D311yescharacteristic
210C3×C4×C8—31no—
211#835—31no—
212#832—31no—
213#832C2×D311yescharacteristic
214#832C2×D311yescharacteristic
215#830—31no—
216#821—31no—
217#821—31no—
218#821—61no—
219#821C2×D311yescharacteristic
220(C2×D3)⋊C8—31no—
221(C2×D3)⋊C8—31no—
222(C2×D3)⋊C8—31no—
223#818—31no—
224#817—31no—
225#816C2×D311yescharacteristic, complemented
226Dic3⋊C8—31no—
227C8×Dic3C2×D311yescharacteristic, complemented
228#810—31no—
229#810C2×D311yescharacteristic, complemented
230#809—31no—
231#809C2×D311yescharacteristic
232#808—31no—
233#807—31no—
234#807—31no—
235#807—31no—
236#807—61no—
237C4⋊(C3⋊C8)—31no—
238C23×C32—21no—
239C22×C3⋊D3—21no—
240C22×C3⋊D3C2×D411yescharacteristic
241C22×C3×D3—21no—
242C22×C3×D3—42no—
243C22×C3×D3—42no—
244C22×C3×D3—81no—
245C22×C3×D3C2×D411yescharacteristic
246C32×D4—21no—
247C32×D4—21no—
248C2×C32×C4—21no—
249C2×C32×C4C2411yescharacteristic
250#638—81no—
251C2×C3⋊Dic3—21no—
252C2×C3⋊Dic3C2×D411yescharacteristic
253C4⋊(C3⋊D3)—21no—
254C4⋊(C3⋊D3)—21no—
255C4⋊(C3⋊D3)—81no—
256C4×C3⋊D3—21no—
257C4×C3⋊D3—21no—
258C3×#67—42no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3C2×D411yescharacteristic
263C2×C3×Dic3C2×D411yescharacteristic
264C2×C3×Dic3C2×D411yescharacteristic
265C3×D12—21no—
266C3×D12#4112yes—
267C3×C4×D3—21no—
268C3×C4×D3—21no—
269C3×C4×D3—81no—
270C3×Dic6—21no—
271C3×Dic6—21no—
272#626—22no—
273#626—42no—
274#626—42no—
275#624—81no—
276D3×Dic3—42no—
277D3×Dic3—81no—
278C32×C8—21no—
279C3⋊(C3⋊C8)—21no—
280C3×C3⋊C8—21no—
281C3×C3⋊C8—21no—
282#553—91no—
283#546—91no—
284#488—31no—
285#484—91no—
286#482—91no—
287#478—91no—
288#466—91no—
289#465—91no—
290#463—91no—
291#449—91no—
292#447—91no—
293C4×D8—91no—
294C8×D4—91no—
295#416—91no—
296C2×#102—31no—
297C24×C3—61no—
298C23×D3—21no—
299C2×C3×Q8—31no—
300C2×C3×D4—21no—
301C2×C3×D4—31no—
302C2×C3×D4—61no—
303C2×C3×D4—62no—
304C2×C3×D4—121no—
305C2×C3×D4C22×D311yescharacteristic
306C2×C3×D4C22×D311yescharacteristic
307C22×C3×C4—31no—
308C22×C3×C4—61no—
309C2×#67—21no—
310C2×#67—31no—
311C2×#67—61no—
312C2×#67—61no—
313C2×#67—61no—
314C2×#67—61no—
315C2×#67—121no—
316C22×Dic3—61no—
317C22×Dic3—61no—
318#239—62no—
319#239—121no—
320#237—62no—
321#237—121no—
322D3×D4—22no—
323D3×D4—41no—
324C2×D12—31no—
325C2×D12—31no—
326C2×D12—31no—
327C2×D12—61no—
328C2×D12—61no—
329C2×D12—61no—
330C2×D12—61no—
331C2×D12—61no—
332C2×D12—121no—
333C2×D12C22×D311yescharacteristic
334C2×C4×D3—21no—
335C2×C4×D3—31no—
336C2×C4×D3—31no—
337C2×C4×D3—61no—
338C2×C4×D3—61no—
339C2×C4×D3—61no—
340C2×C4×D3—61no—
341C2×C4×D3—61no—
342C2×C4×D3C22×D311yescharacteristic
343C2×Dic6C22×D311yescharacteristic
344C2×C3×C8—21no—
345C2×C3×C8—31no—
346C2×C3×C8—31no—
347C2×C3×C8—121no—
348C2×C3×C8C22×D311yescharacteristic
349C2×C3×C8C22×D311yescharacteristic
350C3×C4⋊C4—21no—
351C3×C4⋊C4—31no—
352C3×C4⋊C4—31no—
353C3×C4⋊C4—61no—
354C3×C4⋊C4—61no—
355C3×C4⋊C4—61no—
356C3×C4⋊C4C22×D311yescharacteristic
357C3×C4⋊C4C22×D311yescharacteristic
358C3×C22⋊C4—61no—
359C3×C22⋊C4—61no—
360C3×C42—31no—
361#217—21no—
362#217—21no—
363#217—31no—
364#217—61no—
365#217—61no—
366#217—61no—
367#217—61no—
368#217—121no—
369#215—121no—
370#213—62no—
371#213—121no—
372#213—121no—
373#213—122no—
374(C2×D3)⋊C4—31no—
375(C2×D3)⋊C4—31no—
376(C2×D3)⋊C4—31no—
377(C2×D3)⋊C4—61no—
378(C2×D3)⋊C4—61no—
379(C2×D3)⋊C4—61no—
380(C2×D3)⋊C4—61no—
381(C2×D3)⋊C4—61no—
382(C2×D3)⋊C4—61no—
383(C2×D3)⋊C4—61no—
384(C2×D3)⋊C4—61no—
385(C2×D3)⋊C4—61no—
386(C2×D3)⋊C4—61no—
387(C2×D3)⋊C4—121no—
388C4⋊Dic3—21no—
389C4⋊Dic3—31no—
390C4⋊Dic3—31no—
391C4⋊Dic3—31no—
392C4⋊Dic3—61no—
393C4⋊Dic3C22×D311yescharacteristic
394C4⋊Dic3C22×D311yescharacteristic
395Dic3⋊C4—21no—
396Dic3⋊C4—21no—
397Dic3⋊C4—31no—
398Dic3⋊C4—61no—
399Dic3⋊C4—61no—
400C4×Dic3—61no—
401C4×Dic3—61no—
402C4×Dic3C22×D311yescharacteristic
403C2×C3⋊C8—31no—
404C2×C3⋊C8—31no—
405C2×C3⋊C8—61no—
406C2×C3⋊C8C22×D311yescharacteristic
407C2×C3⋊C8C22×D311yescharacteristic
408D24—62no—
409#204—121no—
410D3×C8—41no—
411D3×C8—121no—
412D3×C8—121no—
413D3×C8—122no—
414C22×C32—41no—
415C22×C32—41no—
416C22×C32—41no—
417C22×C32C22×D411yescharacteristic
418C2×C3⋊D3—21no—
419C2×C3⋊D3—21no—
420C2×C3⋊D3—21no—
421C2×C3⋊D3—41no—
422C2×C3⋊D3—41no—
423C2×C3⋊D3—41no—
424C2×C3×D3—21no—
425C2×C3×D3—21no—
426C2×C3×D3—22no—
427C2×C3×D3—41no—
428C2×C3×D3—41no—
429C2×C3×D3—84no—
430C2×C3×D3#13512yes—
431C32×C4—41no—
432C32×C4C2×#4111yescharacteristic
433C32×C4H(5,𝔽2)11yescharacteristic
434C3⋊Dic3—21no—
435C3⋊Dic3—41no—
436C3×Dic3—21no—
437C3×Dic3—21no—
438C3×Dic3—21no—
439C3×Dic3—41no—
440C3×Dic3—41no—
441C3×Dic3—41no—
442C2×#41—91no—
443C22×D4—31no—
444C2×SD16—91no—
445C2×D8—91no—
446C2×D8—91no—
447C22×C8—31no—
448C22×C8—91no—
449#126—181no—
450#125—31no—
451#124—31no—
452#123—181no—
453#123—181no—
454C22⋊Q8—91no—
455#121—91no—
456#121—91no—
457#121—91no—
458#121—181no—
459#121—181no—
460#120—181no—
461C4×D4—91no—
462C4×D4—91no—
463C4×D4—91no—
464C4×D4—181no—
465#117—91no—
466C2×C4⋊C4—31no—
467C2×C22⋊C4—181no—
468#107—91no—
469#107—91no—
470#106—91no—
471C4⋊C8—91no—
472#103—31no—
473#103—31no—
474#103—91no—
475#102—31no—
476#102—31no—
477#102—31no—
478#102—31no—
479#102—91no—
480#102—91no—
481#102D3211yescharacteristic
482C22⋊C8—91no—
483C22⋊C8—91no—
484C4×C8—31no—
485C23×C3—21no—
486C23×C3—21no—
487C23×C3—31no—
488C23×C3—41no—
489C23×C3—61no—
490C23×C3—122no—
491C23×C3—122no—
492C23×C3—241no—
493C22×D3—21no—
494C22×D3—31no—
495C22×D3—31no—
496C22×D3—42no—
497C22×D3—42no—
498C22×D3—61no—
499C22×D3—61no—
500C22×D3—61no—
501C22×D3—81no—
502C22×D3—121no—
503C22×D3D3×D411yescharacteristic
504C3×Q8—61no—
505C3×Q8—61no—
506C3×D4—21no—
507C3×D4—21no—
508C3×D4—21no—
509C3×D4—21no—
510C3×D4—32no—
511C3×D4—41no—
512C3×D4—41no—
513C3×D4—61no—
514C3×D4—122no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—31no—
519C2×C3×C4—31no—
520C2×C3×C4—31no—
521C2×C3×C4—41no—
522C2×C3×C4—61no—
523C2×C3×C4—61no—
524C2×C3×C4—61no—
525C2×C3×C4—61no—
526C2×C3×C4—61no—
527C2×C3×C4—241no—
528C2×C3×C4C23×D311yescharacteristic
529C2×C3×C4C23×D311yescharacteristic
530#67—42no—
531#67—62no—
532#67—122no—
533#67—122no—
534#67—241no—
535#67—241no—
536#67—242no—
537C2×Dic3—21no—
538C2×Dic3—21no—
539C2×Dic3—21no—
540C2×Dic3—31no—
541C2×Dic3—31no—
542C2×Dic3—61no—
543C2×Dic3—61no—
544C2×Dic3—61no—
545C2×Dic3—121no—
546C2×Dic3—122no—
547C2×Dic3—241no—
548C2×Dic3D3×D411yescharacteristic
549C2×Dic3D3×D411yescharacteristic
550C2×Dic3D3×D411yescharacteristic
551D12—21no—
552D12—62no—
553D12—61no—
554D12—61no—
555D12—61no—
556D12—61no—
557D12—121no—
558D12—121no—
559D12—122no—
560D12—122no—
561D12—241no—
562D12—241no—
563D12—242no—
564D12#23512yes—
565C4×D3—21no—
566C4×D3—21no—
567C4×D3—61no—
568C4×D3—61no—
569C4×D3—61no—
570C4×D3—61no—
571C4×D3—81no—
572C4×D3—121no—
573C4×D3—121no—
574C4×D3—122no—
575C4×D3—241no—
576C4×D3—241no—
577C4×D3—241no—
578Dic6—21no—
579Dic6—21no—
580C3×C8—21no—
581C3×C8—21no—
582C3×C8—41no—
583C3×C8—61no—
584C3×C8—61no—
585C3⋊C8—21no—
586C3⋊C8—21no—
587C3⋊C8—62no—
588C3⋊C8—61no—
589C3⋊C8—61no—
590C2×C32—81no—
591C2×C32#54611yescharacteristic
592C2×C32C2×#13511yescharacteristic
593C2×C32#57611yescharacteristic
594C3⋊D3—41no—
595C3⋊D3—81no—
596C3×D3—22no—
597C3×D3—42no—
598C24—61no—
599#41—182no—
600#41—361no—
601C2×Q8—31no—
602C2×D4—31no—
603C2×D4—61no—
604C2×D4—62no—
605C2×D4—91no—
606C2×D4—91no—
607C2×D4—121no—
608C2×D4—181no—
609C2×D4—181no—
610C2×D4—181no—
611C2×D4—181no—
612C2×D4C2×D3211yescharacteristic
613C22×C4—31no—
614C22×C4—61no—
615C22×C4—91no—
616C22×C4—181no—
617C22×C4—181no—
618C22×C4—181no—
619SD16—361no—
620D8—182no—
621D8—361no—
622C2×C8—31no—
623C2×C8—31no—
624C2×C8—91no—
625C2×C8—121no—
626C2×C8—361no—
627C2×C8C2×D3211yescharacteristic
628C4⋊C4—31no—
629C4⋊C4—31no—
630C4⋊C4—61no—
631C4⋊C4—61no—
632C4⋊C4—61no—
633C4⋊C4—91no—
634C4⋊C4—91no—
635C4⋊C4—181no—
636C4⋊C4C2×D3211yescharacteristic
637C22⋊C4—61no—
638C22⋊C4—61no—
639C22⋊C4—91no—
640C22⋊C4—91no—
641C22⋊C4—181no—
642C22⋊C4—181no—
643C22⋊C4—181no—
644C22⋊C4—181no—
645C22⋊C4—181no—
646C22⋊C4—181no—
647C22⋊C4—181no—
648C42—31no—
649C42—181no—
650C22×C3—21no—
651C22×C3—32no—
652C22×C3—41no—
653C22×C3—41no—
654C22×C3—41no—
655C22×C3—41no—
656C22×C3—41no—
657C22×C3—41no—
658C22×C3—61no—
659C22×C3—61no—
660C22×C3—62no—
661C22×C3—81no—
662C22×C3—81no—
663C22×C3—81no—
664C22×C3—121no—
665C22×C3—121no—
666C22×C3—244no—
667C22×C3C2×D3×D411yescharacteristic
668C22×C3C2×D3×D411yescharacteristic
669C2×D3—21no—
670C2×D3—21no—
671C2×D3—22no—
672C2×D3—41no—
673C2×D3—41no—
674C2×D3—62no—
675C2×D3—61no—
676C2×D3—61no—
677C2×D3—61no—
678C2×D3—61no—
679C2×D3—61no—
680C2×D3—61no—
681C2×D3—84no—
682C2×D3—121no—
683C2×D3—121no—
684C2×D3—121no—
685C2×D3—121no—
686C2×D3—121no—
687C2×D3—121no—
688C2×D3—121no—
689C2×D3—121no—
690C2×D3—241no—
691C2×D3—241no—
692C2×D3—241no—
693C2×D3#91612yes—
694C3×C4—21no—
695C3×C4—21no—
696C3×C4—41no—
697C3×C4—41no—
698C3×C4—61no—
699C3×C4—61no—
700C3×C4—61no—
701C3×C4—81no—
702C3×C4—121no—
703C3×C4—121no—
704C3×C4—121no—
705C3×C4C2×#23511yescharacteristic
706C3×C4#100411yescharacteristic
707C3×C4D3×#4111yescharacteristic
708C3×C4#100911yescharacteristic
709Dic3—21no—
710Dic3—21no—
711Dic3—21no—
712Dic3—41no—
713Dic3—41no—
714Dic3—41no—
715Dic3—61no—
716Dic3—61no—
717Dic3—121no—
718Dic3—121no—
719Dic3—121no—
720Dic3—241no—
721C32#329711yescharacteristic, complemented, Sylow
722C23—21no—
723C23—31no—
724C23—61no—
725C23—91no—
726C23—122no—
727C23—122no—
728C23—181no—
729C23—241no—
730Q8—61no—
731Q8—61no—
732D4—21no—
733D4—21no—
734D4—32no—
735D4—61no—
736D4—122no—
737D4—182no—
738D4—181no—
739D4—181no—
740D4—362no—
741D4—362no—
742D4—721no—
743D4—721no—
744C2×C4—21no—
745C2×C4—31no—
746C2×C4—31no—
747C2×C4—31no—
748C2×C4—61no—
749C2×C4—61no—
750C2×C4—61no—
751C2×C4—61no—
752C2×C4—61no—
753C2×C4—91no—
754C2×C4—181no—
755C2×C4—181no—
756C2×C4—181no—
757C2×C4—241no—
758C2×C4—362no—
759C2×C4—721no—
760C2×C4—721no—
761C2×C4C22×D3211yescharacteristic
762C8—21no—
763C8—61no—
764C8—61no—
765C8—181no—
766C2×C3—21no—
767C2×C3—21no—
768C2×C3—21no—
769C2×C3—62no—
770C2×C3—81no—
771C2×C3—81no—
772C2×C3—122no—
773C2×C3—161no—
774C2×C3#549011yescharacteristic
775C2×C3#567611yescharacteristic
776C2×C3#575711yescharacteristic
777C2×C3C2×#91611yescharacteristic
778C2×C3D3×#13511yescharacteristic
779C2×C3#576911yescharacteristic
780D3—22no—
781D3—42no—
782D3—122no—
783D3—121no—
784D3—121no—
785D3—241no—
786D3—241no—
787D3—481no—
788C22—32no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—61no—
793C22—61no—
794C22—62no—
795C22—121no—
796C22—121no—
797C22—181no—
798C22—181no—
799C22—181no—
800C22—244no—
801C22—361no—
802C22—361no—
803C22—361no—
804C22D32×D411yescharacteristic
805C4—41no—
806C4—61no—
807C4—61no—
808C4—61no—
809C4—121no—
810C4—121no—
811C4—121no—
812C4—181no—
813C4—361no—
814C4D3×#23511yescharacteristic
815C4#6431411yescharacteristic
816C3—21no—
817C3#7876011yescharacteristic, complemented
818C3#8165311yescharacteristic, complemented
819C2—62no—
820C2—81no—
821C2—122no—
822C2—361no—
823C2—721no—
824C2#1059428011yescharacteristic
825C2#1059473411yescharacteristic
826C2D3×#91611yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
hypercenter#102D32
hypocenterC32#3297
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
1. #10595229C2semidirect
2. #10594562C2semidirect
3. #10592474C2semidirect
4. C3×D3×#102C2semidirect
5. C3×#4768C2semidirect
6. #10591448C2semidirect
7. #10591432C2semidirect
8. #10591425C2semidirect
9. #10590956C2semidirect
10. #10590847C2semidirect
11. #10590745C2semidirect
12. C8×#626C2semidirect
13. #10590617C2semidirect
14. #10590517C2semidirect
15. #10590467C2semidirect
22. C2×C8×C3⋊D3C22semidirect
23. #64104C22semidirect
27. C3×#890C22semidirect
37. #63894C22semidirect
40. #63849C22semidirect
42. C2×#3717C22semidirect
45. #63648C22semidirect
46. #63634C22semidirect
50. C3×#816C22semidirect
51. C3×C8×Dic3C22semidirect
52. C3×#810C22semidirect
54. #63575C22semidirect
55. #63573C22semidirect
56. Dic3⋊(C3⋊C8)C22semidirect
57. #63565C22semidirect
59. #63557C22semidirect
86. D3×#102D3semidirect
87. #4768D3semidirect
193. #890C2×D3semidirect
225. #816C2×D3semidirect
227. C8×Dic3C2×D3semidirect
229. #810C2×D3semidirect
721. C32#3297semidirect
817. C3#78760semidirect
818. C3#81653semidirect

Maximal subgroups

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

subgroupindex
#105952292
#105945622
#105924742
C3×D3×#1022
C3×#47682
#105914482
#105914322
#105914252
#105909562
#105908472
#105907452
C8×#6262
#105906172
#105905172
#105904672
#816533
#787603