Finite Group Databasebeta

← #11869701

Subgroups — #11869701

Order 1152.

941 conjugacy classes of subgroups.

The subgroup lattice has 801 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594969C211yesmaximal, characteristic, complemented
2#10594922C211yesmaximal, characteristic
3C3⋊D3×C22⋊C8C211yesmaximal, characteristic, complemented
4C3×#4737C211yesmaximal, characteristic, complemented
5C3×#4723C211yesmaximal, characteristic, complemented
6#10591102C211yesmaximal, characteristic, complemented
7#10591090C211yesmaximal, characteristic, complemented
8#10590956C211yesmaximal, characteristic, complemented
9#10590956C211yesmaximal, characteristic, complemented
10#10590714C211yesmaximal, characteristic, complemented
11#10590712C211yesmaximal, characteristic, complemented
12#10590689C211yesmaximal, characteristic, complemented
13#10590686C211yesmaximal, characteristic, complemented
14#10590650C211yesmaximal, characteristic, complemented
15#10590649C211yesmaximal, characteristic, complemented
16#81515—31nomaximal
17#81371—31nomaximal
18C22×C4×C3⋊D3C2211yescharacteristic
19C2×#3796C2211yescharacteristic
20C2×C8×C3⋊D3C2211yescharacteristic
21C2×C8×C3⋊D3C2211yescharacteristic
22C3×#930C2211yescharacteristic
23C3×#926C2211yescharacteristic
24C3×#926C2211yescharacteristic
25C3×#924C2211yescharacteristic
26#63981—21no—
27#63974—21no—
28#67⋊Dic3—21no—
29#63957—21no—
30#63916C2211yescharacteristic
31#63900C2211yescharacteristic
32#63900C2211yescharacteristic
33C4×#624—21no—
34#63881—21no—
35#63874—21no—
36#63871C2211yescharacteristic
37#63853—21no—
38#63849C2211yescharacteristic
39#63849C2211yescharacteristic
40#63849C2211yescharacteristic
41C32×C22⋊C8C2211yescharacteristic
42#63657C2211yescharacteristic
43#63647C2211yescharacteristic
44#63647C2211yescharacteristic
45C3×#821C2211yescharacteristic, complemented
46C3×#821C2211yescharacteristic, complemented
47C3×#818C2211yescharacteristic, complemented
48C3×#818C2211yescharacteristic, complemented
49C3×#817C2211yescharacteristic, complemented
50C3×#817C2211yescharacteristic, complemented
51C3×#816C2211yescharacteristic, complemented
52C3×#816C2211yescharacteristic, complemented
53#63576C2211yescharacteristic, complemented
54#63576C2211yescharacteristic, complemented
55#63574C2211yescharacteristic, complemented
56#63574C2211yescharacteristic, complemented
57#63565C2211yescharacteristic, complemented
58#63565C2211yescharacteristic, complemented
59#63562C2211yescharacteristic, complemented
60#63562C2211yescharacteristic, complemented
61#5627—31no—
62#5606—31no—
63D3×#117—31no—
64D3×#117—31no—
65C3×#485—31no—
66C3×#482—31no—
67#5045—31no—
68#5035—31no—
69#5003—31no—
70#4996—31no—
71#4884—31no—
72#4882—31no—
73#4880—31no—
74#4880—31no—
75#4863—31no—
76#4862—31no—
77#4860—31no—
78#4860—31no—
79#4811—31no—
80#4805—31no—
81#4804—31no—
82#4804—31no—
83#4777—31no—
84#4774—31no—
85#4772—31no—
86#4772—31no—
87#4737D311yescharacteristic, complemented
88D3×C22⋊C8—31no—
89D3×C22⋊C8—31no—
90D3×C22⋊C8—61no—
91#4723D311yescharacteristic, complemented
92C23×C3⋊D3D411yescharacteristic
93C22×C32×C4C2311yescharacteristic
94C22×C3⋊Dic3D411yescharacteristic
95C2×C4×C3⋊D3—22no—
96C2×C4×C3⋊D3—22no—
97C2×C4×C3⋊D3D411yescharacteristic
98C2×C4×C3⋊D3D411yescharacteristic
99C2×C4×C3⋊D3C2311yescharacteristic
100C2×C4×C3⋊D3C2311yescharacteristic
101C2×C3×#67—21no—
102C2×C3×D12C2311yescharacteristic
103C2×C3×Dic6C2311yescharacteristic
104C2×#626—21no—
105C2×#626—21no—
106C2×#624—21no—
107C2×#624—21no—
108C2×D3×Dic3—21no—
109#3796—22no—
110#3796—22no—
111C2×C32×C8C2311yescharacteristic
112C2×C32×C8C2311yescharacteristic
113C2×C3⋊(C3⋊C8)C2311yescharacteristic
114C2×C3⋊(C3⋊C8)C2311yescharacteristic
115C8×C3⋊D3—22no—
116C8×C3⋊D3—22no—
117C3×#217—21no—
118C3×#217—21no—
119C3×#217—21no—
120C3×(C2×D3)⋊C4—21no—
121C3×C4⋊Dic3C2311yescharacteristic
122C3×C4⋊Dic3C2311yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×Dic3⋊C4—21no—
128C3×C4×Dic3—21no—
129C3×C4×Dic3—21no—
130#3724—21no—
131#3724—21no—
132Dic3⋊Dic3—21no—
133#3722—21no—
134#3722—21no—
135#3722—21no—
136#3722—21no—
137(C2×D3)⋊Dic3—21no—
138Dic32—21no—
139Dic32—21no—
140Dic32—21no—
141#3091—91noSylow
142C2×#239—31no—
143C2×#237—31no—
144C22×C4×D3—31no—
145C22×C4×D3—31no—
146C22×C4×D3—61no—
147C3×C22⋊Q8—31no—
148C3×#121—31no—
149C3×#117—31no—
150C3×#117—31no—
151#946—31no—
152#938—31no—
153#937—61no—
154D4×Dic3—61no—
155#930C2×D311yescharacteristic
156#926C2×D311yescharacteristic
157#926C2×D311yescharacteristic
158#924C2×D311yescharacteristic
159C2×D3×C8—31no—
160C2×D3×C8—31no—
161C2×D3×C8—31no—
162C2×D3×C8—31no—
163C2×D3×C8—61no—
164C2×D3×C8—61no—
165#897—31no—
166#895—31no—
167#894—61no—
168#893—61no—
169#892—31no—
170#892—31no—
171#892—31no—
172#892—31no—
173#892—31no—
174#892—31no—
175D3×C4⋊C4—31no—
176D3×C4⋊C4—31no—
177D3×C4⋊C4—31no—
178D3×C4⋊C4—31no—
179#883—61no—
180#882—61no—
181#67⋊C4—61no—
182#67⋊C4—61no—
183D3×C22⋊C4—61no—
184D3×C22⋊C4—61no—
185#877—61no—
186#877—61no—
187#872—61no—
188#872—61no—
189C42×D3—61no—
190C42×D3—61no—
191C3×#107—31no—
192C3×#107—31no—
193C3×#106—31no—
194C3×#106—31no—
195C3×#103—31no—
196C3×#103—31no—
197C3×#102—31no—
198C3×#102—31no—
199C3×C22⋊C8—21no—
200C3×C22⋊C8C2×D311yescharacteristic
201C3×C22⋊C8C2×D311yescharacteristic
202#835—31no—
203#835—31no—
204#832—31no—
205#832—31no—
206#830—31no—
207#830—31no—
208#830—61no—
209#821C2×D311yescharacteristic, complemented
210#821C2×D311yescharacteristic, complemented
211(C2×D3)⋊C8—31no—
212(C2×D3)⋊C8—31no—
213(C2×D3)⋊C8—31no—
214(C2×D3)⋊C8—31no—
215(C2×D3)⋊C8—61no—
216(C2×D3)⋊C8—61no—
217#818C2×D311yescharacteristic, complemented
218#818C2×D311yescharacteristic, complemented
219#817C2×D311yescharacteristic, complemented
220#817C2×D311yescharacteristic, complemented
221#816C2×D311yescharacteristic, complemented
222#816C2×D311yescharacteristic, complemented
223#810—31no—
224#810—31no—
225#809—31no—
226#809—31no—
227#808—31no—
228#808—31no—
229#808—31no—
230#808—31no—
231#807—31no—
232#807—31no—
233#807—31no—
234#807—31no—
235C23×C32C2×D411yescharacteristic
236C22×C3⋊D3—22no—
237C22×C3⋊D3—22no—
238C22×C3⋊D3—41no—
239C22×C3⋊D3C2×D411yescharacteristic
240C22×C3⋊D3C2×D411yescharacteristic
241C22×C3×D3—21no—
242C2×C32×C4—21no—
243C2×C32×C4—21no—
244C2×C32×C4C2×D411yescharacteristic
245C2×C32×C4C2411yescharacteristic
246C2×C3⋊Dic3—22no—
247C2×C3⋊Dic3C2×D411yescharacteristic
248C2×C3⋊Dic3C2×D411yescharacteristic
249C4×C3⋊D3—22no—
250C4×C3⋊D3—21no—
251C4×C3⋊D3—21no—
252C4×C3⋊D3—22no—
253C4×C3⋊D3#4112yes—
254C4×C3⋊D3#4112yes—
255C3×#67—42no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C3×D12—21no—
264C3×D12—21no—
265C3×Dic6—21no—
266C3×Dic6—21no—
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#525—91no—
277C2×#117—91no—
278#485—31no—
279#485—91no—
280#484—91no—
281#483—91no—
282#482—31no—
283#482—91no—
284#481—91no—
285#480—91no—
286#427—91no—
287#427—91no—
288#416—91no—
289#416—91no—
290C2×C22⋊C8—91no—
291C23×D3—31no—
292C23×D3—31no—
293C23×D3—61no—
294C2×C3×Q8—31no—
295C2×C3×D4—31no—
296C2×C3×D4—61no—
297C22×C3×C4—21no—
298C22×C3×C4C22×D311yescharacteristic
299C22×C3×C4C22×D311yescharacteristic
300C2×#67—21no—
301C2×#67—61no—
302C2×#67—61no—
303C22×Dic3—31no—
304C22×Dic3—31no—
305C22×Dic3—61no—
306C22×Dic3—61no—
307#239—62no—
308#239—62no—
309#237—62no—
310#237—62no—
311C2×D12—61no—
312C2×D12—61no—
313C2×D12C22×D311yescharacteristic
314C2×C4×D3—31no—
315C2×C4×D3—31no—
316C2×C4×D3—31no—
317C2×C4×D3—31no—
318C2×C4×D3—31no—
319C2×C4×D3—31no—
320C2×C4×D3—31no—
321C2×C4×D3—31no—
322C2×C4×D3—61no—
323C2×C4×D3—61no—
324C2×C4×D3—61no—
325C2×C4×D3—61no—
326C2×C4×D3—62no—
327C2×C4×D3—62no—
328C2×C4×D3—62no—
329C2×C4×D3—62no—
330C2×C4×D3—61no—
331C2×C4×D3—61no—
332C2×C4×D3—61no—
333C2×C4×D3—61no—
334C2×C4×D3—61no—
335C2×C4×D3—122no—
336C2×C4×D3—122no—
337C2×Dic6C22×D311yescharacteristic
338C2×C3×C8—21no—
339C2×C3×C8—21no—
340C2×C3×C8C22×D311yescharacteristic
341C2×C3×C8C22×D311yescharacteristic
342C2×C3×C8C22×D311yescharacteristic
343C2×C3×C8C22×D311yescharacteristic
344C3×C4⋊C4—31no—
345C3×C4⋊C4—31no—
346C3×C4⋊C4—31no—
347C3×C4⋊C4—31no—
348C3×C4⋊C4—31no—
349C3×C4⋊C4—31no—
350C3×C4⋊C4—61no—
351C3×C22⋊C4—61no—
352C3×C22⋊C4—61no—
353C3×C22⋊C4—61no—
354C3×C22⋊C4—61no—
355C3×C42—61no—
356C3×C42—61no—
357#217—21no—
358#217—21no—
359#217—21no—
360#217—61no—
361(C2×D3)⋊C4—21no—
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—61no—
371C4⋊Dic3—61no—
372C4⋊Dic3C22×D311yescharacteristic
373C4⋊Dic3C22×D311yescharacteristic
374C4⋊Dic3C22×D311yescharacteristic
375C4⋊Dic3C22×D311yescharacteristic
376C4⋊Dic3C22×D311yescharacteristic
377C4⋊Dic3C22×D311yescharacteristic
378Dic3⋊C4—21no—
379Dic3⋊C4—61no—
380Dic3⋊C4—61no—
381Dic3⋊C4—61no—
382Dic3⋊C4—61no—
383Dic3⋊C4—61no—
384C4×Dic3—21no—
385C4×Dic3—21no—
386C4×Dic3—61no—
387C4×Dic3—61no—
388C4×Dic3—61no—
389C4×Dic3—61no—
390C4×Dic3—61no—
391C4×Dic3—61no—
392C2×C3⋊C8—31no—
393C2×C3⋊C8—31no—
394C2×C3⋊C8—31no—
395C2×C3⋊C8—31no—
396C2×C3⋊C8—61no—
397C2×C3⋊C8—61no—
398D3×C8—62no—
399D3×C8—62no—
400D3×C8—62no—
401D3×C8—62no—
402D3×C8—122no—
403D3×C8—122no—
404C22×C32—21no—
405C22×C32—21no—
406C22×C32—21no—
407C22×C32C22×D411yescharacteristic
408C2×C3⋊D3—21no—
409C2×C3⋊D3—21no—
410C2×C3⋊D3—21no—
411C2×C3⋊D3—21no—
412C2×C3⋊D3—44no—
413C2×C3⋊D3#12312yes—
414C2×C3⋊D3#13512yes—
415C2×C3×D3—41no—
416C2×C3×D3—41no—
417C2×C3×D3—41no—
418C32×C4—21no—
419C32×C4C2×#4111yescharacteristic
420C32×C4C2×#4111yescharacteristic
421C3⋊Dic3—21no—
422C3⋊Dic3#12312yes—
423C3×Dic3—41no—
424C3×Dic3—41no—
425C3×Dic3—41no—
426C3×Dic3—41no—
427C3×Dic3—41no—
428C3×Dic3—41no—
429C3×Dic3—41no—
430C2×#41—91no—
431C23×C4—91no—
432C22×C8—91no—
433C22×C8—91no—
434#123—181no—
435C22⋊Q8—31no—
436C22⋊Q8—91no—
437#121—31no—
438#121—91no—
439#120—181no—
440C4×D4—181no—
441C4×D4—181no—
442#117—31no—
443#117—31no—
444#117—91no—
445#117—91no—
446#117—91no—
447#117—181no—
448#117—181no—
449C2×C4⋊C4—91no—
450C2×C4⋊C4—91no—
451C2×C22⋊C4—181no—
452C2×C42—181no—
453#107—31no—
454#107—31no—
455#107—91no—
456#107—91no—
457#106—31no—
458#106—31no—
459#106—91no—
460#106—91no—
461#103—31no—
462#103—31no—
463#103—91no—
464#103—91no—
465#102—31no—
466#102—31no—
467#102—91no—
468#102—91no—
469C22⋊C8—91no—
470C22⋊C8—91no—
471C22⋊C8—91no—
472C22⋊C8D3211yescharacteristic
473C23×C3—21no—
474C23×C3—61no—
475C23×C3D3×D411yescharacteristic
476C23×C3D3×D411yescharacteristic
477C22×D3—21no—
478C22×D3—31no—
479C22×D3—31no—
480C22×D3—31no—
481C22×D3—31no—
482C22×D3—61no—
483C22×D3—61no—
484C22×D3—62no—
485C22×D3—62no—
486C22×D3—62no—
487C22×D3—62no—
488C22×D3—64no—
489C22×D3—122no—
490C22×D3—121no—
491C22×D3—121no—
492C22×D3—122no—
493C3×Q8—61no—
494C3×Q8—61no—
495C3×D4—61no—
496C3×D4—61no—
497C3×D4—122no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—41no—
505C2×C3×C4—41no—
506C2×C3×C4—61no—
507C2×C3×C4—61no—
508C2×C3×C4—61no—
509C2×C3×C4—61no—
510C2×C3×C4—61no—
511C2×C3×C4—61no—
512C2×C3×C4—61no—
513C2×C3×C4D3×D411yescharacteristic
514C2×C3×C4D3×D411yescharacteristic
515C2×C3×C4C23×D311yescharacteristic
516C2×C3×C4C23×D311yescharacteristic
517#67—42no—
518#67—122no—
519#67—122no—
520C2×Dic3—21no—
521C2×Dic3—21no—
522C2×Dic3—21no—
523C2×Dic3—21no—
524C2×Dic3—21no—
525C2×Dic3—21no—
526C2×Dic3—21no—
527C2×Dic3—31no—
528C2×Dic3—31no—
529C2×Dic3—31no—
530C2×Dic3—31no—
531C2×Dic3—61no—
532C2×Dic3—61no—
533C2×Dic3—62no—
534C2×Dic3—62no—
535C2×Dic3—122no—
536C2×Dic3—122no—
537D12—21no—
538D12—21no—
539D12—122no—
540D12—122no—
541C4×D3—32no—
542C4×D3—32no—
543C4×D3—32no—
544C4×D3—32no—
545C4×D3—62no—
546C4×D3—62no—
547C4×D3—62no—
548C4×D3—62no—
549C4×D3—62no—
550C4×D3—62no—
551C4×D3—61no—
552C4×D3—61no—
553C4×D3—61no—
554C4×D3—61no—
555C4×D3—122no—
556C4×D3—121no—
557C4×D3—121no—
558C4×D3—122no—
559C4×D3—122no—
560C4×D3—122no—
561C4×D3—122no—
562C4×D3—122no—
563C4×D3—122no—
564Dic6—21no—
565Dic6—21no—
566C3×C8—21no—
567C3×C8—21no—
568C3×C8—21no—
569C3×C8—21no—
570C3×C8—41no—
571C3×C8—41no—
572C3⋊C8—61no—
573C3⋊C8—61no—
574C3⋊C8—61no—
575C3⋊C8—61no—
576C3⋊C8—121no—
577C3⋊C8—121no—
578C2×C32—41no—
579C2×C32C2×#12311yescharacteristic
580C2×C32C2×#13511yescharacteristic
581C2×C32#57511yescharacteristic
582C3⋊D3—22no—
583C3⋊D3—22no—
584C3×D3—81no—
585C24—91no—
586#41—182no—
587#41—182no—
588C2×Q8—31no—
589C2×D4—31no—
590C2×D4—61no—
591C2×D4—181no—
592C2×D4—181no—
593C22×C4—91no—
594C22×C4—91no—
595C22×C4—91no—
596C22×C4—91no—
597C22×C4—91no—
598C22×C4—182no—
599C22×C4—182no—
600C22×C4—181no—
601C22×C4—181no—
602C22×C4—181no—
603C22×C4C2×D3211yescharacteristic
604C2×C8—91no—
605C2×C8—91no—
606C2×C8—182no—
607C2×C8—182no—
608C2×C8C2×D3211yescharacteristic
609C2×C8C2×D3211yescharacteristic
610C4⋊C4—31no—
611C4⋊C4—31no—
612C4⋊C4—31no—
613C4⋊C4—31no—
614C4⋊C4—31no—
615C4⋊C4—31no—
616C4⋊C4—61no—
617C4⋊C4—181no—
618C4⋊C4—181no—
619C4⋊C4—181no—
620C22⋊C4—61no—
621C22⋊C4—61no—
622C22⋊C4—61no—
623C22⋊C4—61no—
624C22⋊C4—181no—
625C22⋊C4—181no—
626C22⋊C4—181no—
627C22⋊C4—181no—
628C22⋊C4—181no—
629C42—61no—
630C42—61no—
631C42—181no—
632C42—181no—
633C42—181no—
634C22×C3—22no—
635C22×C3—21no—
636C22×C3—21no—
637C22×C3—21no—
638C22×C3—21no—
639C22×C3—21no—
640C22×C3—21no—
641C22×C3—21no—
642C22×C3—41no—
643C22×C3—41no—
644C22×C3—121no—
645C22×C3—121no—
646C22×C3—121no—
647C22×C3C2×D3×D411yescharacteristic
648C22×C3C2×D3×D411yescharacteristic
649C2×D3—32no—
650C2×D3—32no—
651C2×D3—32no—
652C2×D3—32no—
653C2×D3—41no—
654C2×D3—41no—
655C2×D3—41no—
656C2×D3—62no—
657C2×D3—62no—
658C2×D3—62no—
659C2×D3—62no—
660C2×D3—61no—
661C2×D3—61no—
662C2×D3—61no—
663C2×D3—61no—
664C2×D3—61no—
665C2×D3—61no—
666C2×D3—61no—
667C2×D3—61no—
668C2×D3—121no—
669C2×D3—121no—
670C2×D3—124no—
671C2×D3—124no—
672C2×D3—128no—
673C3×C4—21no—
674C3×C4—21no—
675C3×C4—21no—
676C3×C4—21no—
677C3×C4—41no—
678C3×C4—121no—
679C3×C4—121no—
680C3×C4—121no—
681C3×C4—121no—
682C3×C4—121no—
683C3×C4—121no—
684C3×C4—121no—
685C3×C4D3×#4111yescharacteristic
686C3×C4D3×#4111yescharacteristic
687C3×C4D3×#4111yescharacteristic
688C3×C4D3×#4111yescharacteristic
689Dic3—32no—
690Dic3—32no—
691Dic3—41no—
692Dic3—41no—
693Dic3—41no—
694Dic3—41no—
695Dic3—41no—
696Dic3—41no—
697Dic3—41no—
698Dic3—62no—
699Dic3—61no—
700Dic3—61no—
701Dic3—121no—
702C32#309111yescharacteristic, complemented, Sylow
703C23—61no—
704C23—91no—
705C23—91no—
706C23—182no—
707C23—182no—
708C23—361no—
709C23#380211yescharacteristic
710Q8—61no—
711Q8—61no—
712D4—61no—
713D4—61no—
714D4—122no—
715D4—362no—
716D4—362no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—61no—
720C2×C4—61no—
721C2×C4—61no—
722C2×C4—61no—
723C2×C4—61no—
724C2×C4—61no—
725C2×C4—61no—
726C2×C4—91no—
727C2×C4—92no—
728C2×C4—92no—
729C2×C4—91no—
730C2×C4—182no—
731C2×C4—182no—
732C2×C4—182no—
733C2×C4—181no—
734C2×C4—181no—
735C2×C4—362no—
736C2×C4—362no—
737C2×C4—362no—
738C2×C4#380211yescharacteristic
739C2×C4C22×D3211yescharacteristic
740C8—21no—
741C8—21no—
742C8—181no—
743C8—181no—
744C2×C3—21no—
745C2×C3—21no—
746C2×C3—21no—
747C2×C3—42no—
748C2×C3—41no—
749C2×C3—41no—
750C2×C3—241no—
751C2×C3D3×#12311yescharacteristic
752C2×C3D3×#12311yescharacteristic
753C2×C3D3×#13511yescharacteristic
754C2×C3D3×#13511yescharacteristic
755C2×C3#577311yescharacteristic
756C2×C3#577711yescharacteristic
757D3—64no—
758D3—62no—
759D3—62no—
760D3—62no—
761D3—62no—
762D3—81no—
763D3—122no—
764C22—21no—
765C22—21no—
766C22—21no—
767C22—92no—
768C22—92no—
769C22—121no—
770C22—121no—
771C22—121no—
772C22—181no—
773C22—181no—
774C22—181no—
775C22—181no—
776C22—364no—
777C22C2×#380211yescharacteristic
778C4—21no—
779C4—92no—
780C4—121no—
781C4—121no—
782C4—121no—
783C4—121no—
784C4—121no—
785C4—121no—
786C4—121no—
787C4—181no—
788C4#6431211yescharacteristic
789C4#6431211yescharacteristic
790C3—21no—
791C3#8137111yescharacteristic, complemented
792C3#8151511yescharacteristic, complemented
793C2—41no—
794C2—182no—
795C2—182no—
796C2—241no—
797C2#1059429511yescharacteristic
798C2#1059468411yescharacteristic
799C2#1059471811yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊C8C22
socleC22×C32C22×D4
prime radical#10594922C2
hypercenterC22⋊C8D32
hypocenterC32#3091
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. #10594969C2semidirect
3. C3⋊D3×C22⋊C8C2semidirect
4. C3×#4737C2semidirect
5. C3×#4723C2semidirect
6. #10591102C2semidirect
7. #10591090C2semidirect
8. #10590956C2semidirect
9. #10590956C2semidirect
10. #10590714C2semidirect
11. #10590712C2semidirect
12. #10590689C2semidirect
13. #10590686C2semidirect
14. #10590650C2semidirect
15. #10590649C2semidirect
45. C3×#821C22semidirect
46. C3×#821C22semidirect
47. C3×#818C22semidirect
48. C3×#818C22semidirect
49. C3×#817C22semidirect
50. C3×#817C22semidirect
51. C3×#816C22semidirect
52. C3×#816C22semidirect
53. #63576C22semidirect
54. #63576C22semidirect
55. #63574C22semidirect
56. #63574C22semidirect
57. #63565C22semidirect
58. #63565C22semidirect
59. #63562C22semidirect
60. #63562C22semidirect
87. #4737D3semidirect
91. #4723D3semidirect
209. #821C2×D3semidirect
210. #821C2×D3semidirect
217. #818C2×D3semidirect
218. #818C2×D3semidirect
219. #817C2×D3semidirect
220. #817C2×D3semidirect
221. #816C2×D3semidirect
222. #816C2×D3semidirect
702. C32#3091semidirect
791. C3#81371semidirect
792. C3#81515semidirect

Maximal subgroups

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

subgroupindex
#105949692
#105949222
C3⋊D3×C22⋊C82
C3×#47372
C3×#47232
#105911022
#105910902
#105909562
#105907142
#105907122
#105906892
#105906862
#105906502
#105906492
#815153
#813713