Finite Group Databasebeta

← #11869697

Subgroups — #11869697

Order 1152.

897 conjugacy classes of subgroups.

The subgroup lattice has 779 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595022C211yesmaximal, characteristic
2D3×#926C211yesmaximal, characteristic, complemented
3#10592805C211yesmaximal, characteristic, complemented
4C3×#5113C211yesmaximal, characteristic, complemented
5C2×C3×(C2×D3)⋊C8C211yesmaximal, characteristic, complemented
6#10591122C211yesmaximal, characteristic, complemented
7#10591084C211yesmaximal, characteristic, complemented
8#10590837C211yesmaximal, characteristic, complemented
9#10590834C211yesmaximal, characteristic, complemented
10#10590711C211yesmaximal, characteristic, complemented
11#10590710C211yesmaximal, characteristic, complemented
12#10590682C211yesmaximal, characteristic, complemented
13#10590680C211yesmaximal, characteristic, complemented
14#10590676C211yesmaximal, characteristic, complemented
15#10590675C211yesmaximal, characteristic, complemented
16#78842—31nomaximal
17#78591—31nomaximal
18C2×C3×#235C2211yescharacteristic
19C22×C3×C4×D3C2211yescharacteristic
20C22×C32×C8C2211yescharacteristic
21#64135C2211yescharacteristic
22#64135C2211yescharacteristic
23C3×#926C2211yescharacteristic
24C22×C3×C3⋊C8C2211yescharacteristic
25#63976—21no—
26D3×#217—21no—
27#63961—21no—
28#63955—21no—
29#63908C2211yescharacteristic
30#63908C2211yescharacteristic
31C4×#625—21no—
32C4×#625—21no—
33D3×C4⋊Dic3C2211yescharacteristic
34D3×C4⋊Dic3C2211yescharacteristic
35C4×D3×Dic3—21no—
36#63856C2211yescharacteristic
37#63856C2211yescharacteristic
38#63855—21no—
39#63841C2211yescharacteristic
40#63841C2211yescharacteristic
41#63645C2211yescharacteristic, complemented
42#63645C2211yescharacteristic, complemented
43#63644C2211yescharacteristic, complemented
44#63644C2211yescharacteristic, complemented
45C3×#821C2211yescharacteristic, complemented
46C3×#821C2211yescharacteristic, complemented
47C3×(C2×D3)⋊C8C2211yescharacteristic
48C3×(C2×D3)⋊C8C2211yescharacteristic
49C3×(C2×D3)⋊C8C2211yescharacteristic
50C3×(C2×D3)⋊C8C2211yescharacteristic
51C3×#816C2211yescharacteristic, complemented
52C3×#816C2211yescharacteristic, complemented
53#63575C2211yescharacteristic, complemented
54#63575C2211yescharacteristic, complemented
55#63573C2211yescharacteristic, complemented
56#63573C2211yescharacteristic, complemented
57#63566C2211yescharacteristic, complemented
58#63566C2211yescharacteristic, complemented
59#63563C2211yescharacteristic, complemented
60#63563C2211yescharacteristic, complemented
61#5828—31no—
62#5791—31no—
63C2×#926—31no—
64D3×#117—31no—
65C3×#416—31no—
66C2×C3×C22⋊C8—31no—
67#5233—31no—
68#5113—31no—
69#5113D311yescharacteristic, complemented
70C2×(C2×D3)⋊C8D311yescharacteristic, complemented
71#5106—31no—
72#5106—31no—
73#5106—31no—
74#5106—61no—
75#4998—31no—
76#4815—31no—
77#4814—31no—
78#4811—31no—
79#4805—31no—
80#4784—31no—
81#4779—31no—
82#4777—31no—
83#4774—31no—
84#4737—31no—
85#4737—31no—
86#4736—31no—
87#4735—31no—
88#4723—31no—
89#4723—31no—
90#4722—31no—
91#4721—31no—
92C23×C3×D3D411yescharacteristic
93C22×C32×C4C2311yescharacteristic
94C2×C3×#67—21no—
95C22×C3×Dic3D411yescharacteristic
96C3×#235—22no—
97C3×#235—22no—
98C2×C3×D12C2311yescharacteristic
99C2×C3×C4×D3—22no—
100C2×C3×C4×D3—22no—
101C2×C3×C4×D3—21no—
102C2×C3×C4×D3D411yescharacteristic
103C2×C3×C4×D3D411yescharacteristic
104C2×C3×C4×D3C2311yescharacteristic
105C2×C3×C4×D3C2311yescharacteristic
106C2×C3×Dic6C2311yescharacteristic
107C2×#625—21no—
108C2×#625—21no—
109C2×D3×Dic3—21no—
110C2×D3×Dic3—21no—
111C2×C32×C8—22no—
112C2×C32×C8C2311yescharacteristic
113C2×C32×C8C2311yescharacteristic
114#3757—21no—
115#3757—21no—
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117C4⋊(C3⋊Dic3)C2311yescharacteristic
118C4⋊(C3⋊Dic3)C2311yescharacteristic
119C4⋊(C3⋊Dic3)C2311yescharacteristic
120C4×C3⋊Dic3—21no—
121C4×C3⋊Dic3—21no—
122C3×#217—21no—
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4×Dic3—21no—
126C2×C3×C3⋊C8—22no—
127C2×C3×C3⋊C8C2311yescharacteristic
128C2×C3×C3⋊C8C2311yescharacteristic
129#3724—21no—
130#3724—21no—
131Dic3⋊Dic3—21no—
132Dic3⋊Dic3—21no—
133(C2×D3)⋊Dic3—21no—
134(C2×D3)⋊Dic3—21no—
135(C2×D3)⋊Dic3—21no—
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139Dic32—21no—
140Dic32—21no—
141#3091—91noSylow
142C2×C3×#41—31no—
143C23×C3×C4—31no—
144C2×#235C2×D311yescharacteristic
145C22×C4×D3C2×D311yescharacteristic
146C22×C3×C8—21no—
147C22×C3×C8—31no—
148C22×C3×C8C2×D311yescharacteristic
149C22×C3×C8C2×D311yescharacteristic
150C3×#117—31no—
151#953—61no—
152C2×#217—61no—
153#946—31no—
154#946—31no—
155#938—31no—
156#938—31no—
157#937—61no—
158#935—61no—
159#930—31no—
160#930—31no—
161#929—61no—
162C4×#67—61no—
163C4×#67—61no—
164C4×#67—61no—
165C4×#67—61no—
166#926—31no—
167#926—31no—
168#926—31no—
169#926—31no—
170#926—31no—
171#926—31no—
172#926—61no—
173#926—61no—
174#926—61no—
175#926—61no—
176#926C2×D311yescharacteristic
177C2×C4⋊Dic3—31no—
178C2×C4⋊Dic3—31no—
179#924—31no—
180#924—31no—
181C2×C4×Dic3—61no—
182C22×C3⋊C8C2×D311yescharacteristic
183#892—31no—
184#892—31no—
185D3×C4⋊C4—31no—
186D3×C4⋊C4—31no—
187D3×C22⋊C4—61no—
188#877—61no—
189#872—61no—
190C42×D3—61no—
191C3×#103—31no—
192C3×#103—31no—
193C3×#102—31no—
194C3×#102—31no—
195C3×C22⋊C8—31no—
196C3×C22⋊C8—31no—
197C3×C22⋊C8—31no—
198C3×C22⋊C8—31no—
199#835—31no—
200#835—31no—
201#832—31no—
202#832—31no—
203#821—31no—
204#821—31no—
205#821C2×D311yescharacteristic, complemented
206#821C2×D311yescharacteristic, complemented
207(C2×D3)⋊C8C2×D311yescharacteristic
208(C2×D3)⋊C8C2×D311yescharacteristic
209(C2×D3)⋊C8C2×D311yescharacteristic
210(C2×D3)⋊C8C2×D311yescharacteristic
211#818—31no—
212#818—31no—
213#818—31no—
214#818—31no—
215#818—31no—
216#818—31no—
217#818—61no—
218#818—61no—
219#817—31no—
220#817—31no—
221#817—31no—
222#817—31no—
223#817—31no—
224#817—31no—
225#817—61no—
226#817—61no—
227#816—31no—
228#816—31no—
229#816C2×D311yescharacteristic, complemented
230#816C2×D311yescharacteristic, complemented
231#808—31no—
232#808—31no—
233#807—31no—
234#807—31no—
235C23×C32C2×D411yescharacteristic
236C22×C3×D3—22no—
237C22×C3×D3—22no—
238C22×C3×D3—21no—
239C22×C3×D3—41no—
240C22×C3×D3C2×D411yescharacteristic
241C22×C3×D3C2×D411yescharacteristic
242C2×C32×C4C2×D411yescharacteristic
243C2×C32×C4#4112yes—
244C2×C32×C4#4112yes—
245C2×C32×C4C2411yescharacteristic
246C2×C3⋊Dic3—21no—
247C2×C3⋊Dic3—21no—
248C2×C3⋊Dic3—21no—
249C2×C3⋊Dic3—21no—
250C3×#67—42no—
251C2×C3×Dic3—22no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3C2×D411yescharacteristic
256C2×C3×Dic3C2×D411yescharacteristic
257C3×D12—21no—
258C3×D12—21no—
259C3×C4×D3—22no—
260C3×C4×D3—22no—
261C3×C4×D3—21no—
262C3×C4×D3—21no—
263C3×C4×D3—21no—
264C3×C4×D3—21no—
265C3×C4×D3—42no—
266C3×Dic6—21no—
267C3×Dic6—21no—
268#625—42no—
269#625—42no—
270D3×Dic3—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—91no—
279#485—91no—
280#484—91no—
281#483—91no—
282#482—91no—
283#482—91no—
284#481—91no—
285#480—91no—
286#427—91no—
287#427—91no—
288#416—31no—
289#416—91no—
290C2×C22⋊C8—31no—
291C24×C3—31no—
292C23×D3D1211yescharacteristic
293C3×#41—62no—
294C3×#41—62no—
295C2×C3×Q8—31no—
296C2×C3×D4—31no—
297C2×C3×D4—61no—
298C22×C3×C4—21no—
299C22×C3×C4—31no—
300C22×C3×C4—31no—
301C22×C3×C4—31no—
302C22×C3×C4—31no—
303C22×C3×C4—31no—
304C22×C3×C4—62no—
305C22×C3×C4—62no—
306C22×C3×C4—61no—
307C22×C3×C4C22×D311yescharacteristic
308C22×C3×C4C22×D311yescharacteristic
309C2×#67—21no—
310C2×#67—61no—
311C2×#67—61no—
312C2×#67—61no—
313C2×#67—61no—
314C22×Dic3—61no—
315C22×Dic3—61no—
316C22×Dic3D1211yescharacteristic
317#235—22no—
318#235—22no—
319C2×D12C22×D311yescharacteristic
320C2×C4×D3—22no—
321C2×C4×D3—22no—
322C2×C4×D3—21no—
323C2×C4×D3—61no—
324C2×C4×D3—61no—
325C2×C4×D3D1211yescharacteristic
326C2×C4×D3D1211yescharacteristic
327C2×C4×D3C22×D311yescharacteristic
328C2×C4×D3C22×D311yescharacteristic
329C2×Dic6C22×D311yescharacteristic
330C2×C3×C8—24no—
331C2×C3×C8—22no—
332C2×C3×C8—22no—
333C2×C3×C8—21no—
334C2×C3×C8—21no—
335C2×C3×C8—31no—
336C2×C3×C8—31no—
337C2×C3×C8—62no—
338C2×C3×C8C22×D311yescharacteristic
339C2×C3×C8C22×D311yescharacteristic
340C2×C3×C8C22×D311yescharacteristic
341C2×C3×C8C22×D311yescharacteristic
342C3×C4⋊C4—31no—
343C3×C4⋊C4—31no—
344C3×C22⋊C4—61no—
345C3×C42—61no—
346#217—21no—
347#217—61no—
348#217—61no—
349#217—61no—
350#217—61no—
351#217—61no—
352#217—61no—
353#217—61no—
354#217—61no—
355#217—61no—
356#217—61no—
357#217—121no—
358#217—121no—
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—
365C4⋊Dic3—31no—
366C4⋊Dic3—31no—
367C4⋊Dic3—31no—
368C4⋊Dic3—31no—
369C4⋊Dic3—31no—
370C4⋊Dic3—31no—
371C4⋊Dic3—31no—
372C4⋊Dic3—31no—
373C4⋊Dic3—61no—
374C4⋊Dic3—61no—
375C4⋊Dic3—61no—
376C4⋊Dic3—61no—
377C4⋊Dic3—61no—
378C4⋊Dic3—61no—
379C4⋊Dic3C22×D311yescharacteristic
380C4⋊Dic3C22×D311yescharacteristic
381Dic3⋊C4—61no—
382Dic3⋊C4—61no—
383Dic3⋊C4—61no—
384Dic3⋊C4—61no—
385Dic3⋊C4—61no—
386Dic3⋊C4—61no—
387C4×Dic3—21no—
388C4×Dic3—61no—
389C4×Dic3—61no—
390C4×Dic3—61no—
391C4×Dic3—61no—
392C4×Dic3—61no—
393C4×Dic3—61no—
394C4×Dic3—61no—
395C4×Dic3—61no—
396C4×Dic3—121no—
397C4×Dic3—121no—
398C2×C3⋊C8—22no—
399C2×C3⋊C8C22×D311yescharacteristic
400C2×C3⋊C8C22×D311yescharacteristic
401C22×C32—21no—
402C22×C32—21no—
403C22×C32#12312yes—
404C22×C32C22×D411yescharacteristic
405C2×C3×D3—21no—
406C2×C3×D3—21no—
407C2×C3×D3—21no—
408C2×C3×D3—21no—
409C2×C3×D3—21no—
410C2×C3×D3—44no—
411C2×C3×D3—41no—
412C2×C3×D3—41no—
413C2×C3×D3—41no—
414C2×C3×D3#13512yes—
415C32×C4#12312yes—
416C32×C4C2×#4111yescharacteristic
417C32×C4C2×#4111yescharacteristic
418C3⋊Dic3—41no—
419C3⋊Dic3—41no—
420C3⋊Dic3—41no—
421C3⋊Dic3—41no—
422C3×Dic3—21no—
423C3×Dic3—21no—
424C3×Dic3—41no—
425C3×Dic3—41no—
426C3×Dic3—41no—
427C2×#41—31no—
428C23×C4—31no—
429C22×C8—31no—
430C22×C8D3211yescharacteristic
431#123—181no—
432C22⋊Q8—91no—
433C22⋊Q8—91no—
434#121—91no—
435#121—91no—
436#120—181no—
437C4×D4—181no—
438C4×D4—181no—
439#117—31no—
440#117—91no—
441#117—91no—
442#117—91no—
443#117—91no—
444#117—181no—
445#117—181no—
446C2×C4⋊C4—91no—
447C2×C4⋊C4—91no—
448C2×C22⋊C4—181no—
449C2×C42—181no—
450#107—91no—
451#107—91no—
452#107—91no—
453#107—91no—
454#106—91no—
455#106—91no—
456#106—91no—
457#106—91no—
458#103—31no—
459#103—31no—
460#103—91no—
461#103—91no—
462#102—31no—
463#102—31no—
464#102—91no—
465#102—91no—
466C22⋊C8—31no—
467C22⋊C8—31no—
468C22⋊C8—31no—
469C22⋊C8—31no—
470C23×C3—21no—
471C23×C3—31no—
472C23×C3—31no—
473C23×C3—62no—
474C23×C3—62no—
475C23×C3—61no—
476C23×C3—121no—
477C23×C3C2×D1211yescharacteristic
478C23×C3D3×D411yescharacteristic
479C22×D3—22no—
480C22×D3—22no—
481C22×D3—21no—
482C22×D3—41no—
483C22×D3C2×D1211yescharacteristic
484C22×D3C2×D1211yescharacteristic
485C3×Q8—61no—
486C3×Q8—61no—
487C3×D4—61no—
488C3×D4—61no—
489C3×D4—122no—
490C2×C3×C4—21no—
491C2×C3×C4—22no—
492C2×C3×C4—21no—
493C2×C3×C4—22no—
494C2×C3×C4—31no—
495C2×C3×C4—31no—
496C2×C3×C4—62no—
497C2×C3×C4—62no—
498C2×C3×C4—62no—
499C2×C3×C4—61no—
500C2×C3×C4—61no—
501C2×C3×C4—61no—
502C2×C3×C4—61no—
503C2×C3×C4—61no—
504C2×C3×C4—61no—
505C2×C3×C4—61no—
506C2×C3×C4—122no—
507C2×C3×C4C2×D1211yescharacteristic
508C2×C3×C4#23512yes—
509C2×C3×C4D3×D411yescharacteristic
510C2×C3×C4#23712yes—
511C2×C3×C4#23712yes—
512C2×C3×C4#23712yes—
513C2×C3×C4C23×D311yescharacteristic
514C2×C3×C4C23×D311yescharacteristic
515#67—42no—
516#67—122no—
517#67—122no—
518#67—122no—
519#67—122no—
520C2×Dic3—22no—
521C2×Dic3—21no—
522C2×Dic3—21no—
523C2×Dic3—21no—
524C2×Dic3—61no—
525C2×Dic3—61no—
526C2×Dic3—61no—
527C2×Dic3—61no—
528C2×Dic3—61no—
529C2×Dic3—61no—
530C2×Dic3—61no—
531C2×Dic3—61no—
532C2×Dic3—121no—
533C2×Dic3—121no—
534C2×Dic3—121no—
535C2×Dic3—121no—
536C2×Dic3—122no—
537C2×Dic3—122no—
538C2×Dic3C2×D1211yescharacteristic
539C2×Dic3C2×D1211yescharacteristic
540D12—21no—
541D12—21no—
542C4×D3—22no—
543C4×D3—22no—
544C4×D3—21no—
545C4×D3—21no—
546C4×D3—21no—
547C4×D3—21no—
548C4×D3—42no—
549C4×D3—122no—
550C4×D3—122no—
551Dic6—21no—
552Dic6—21no—
553C3×C8—22no—
554C3×C8—22no—
555C3×C8—21no—
556C3×C8—21no—
557C3×C8—21no—
558C3×C8—21no—
559C3×C8—61no—
560C3×C8—61no—
561C3⋊C8—21no—
562C3⋊C8—21no—
563C2×C32—22no—
564C2×C32C2×#12311yescharacteristic
565C2×C32C2×#13511yescharacteristic
566C2×C32#57511yescharacteristic
567C3×D3—22no—
568C3×D3—41no—
569C3×D3—81no—
570C24—31no—
571#41—62no—
572#41—62no—
573C2×Q8—31no—
574C2×D4—31no—
575C2×D4—61no—
576C2×D4—181no—
577C2×D4—181no—
578C22×C4—31no—
579C22×C4—31no—
580C22×C4—31no—
581C22×C4—31no—
582C22×C4—31no—
583C22×C4—62no—
584C22×C4—62no—
585C22×C4—61no—
586C22×C4—181no—
587C22×C4—181no—
588C22×C4C2×D3211yescharacteristic
589C2×C8—22no—
590C2×C8—31no—
591C2×C8—31no—
592C2×C8—62no—
593C2×C8C2×D3211yescharacteristic
594C2×C8C2×D3211yescharacteristic
595C4⋊C4—31no—
596C4⋊C4—31no—
597C4⋊C4—91no—
598C4⋊C4—91no—
599C4⋊C4—91no—
600C4⋊C4—91no—
601C4⋊C4—181no—
602C4⋊C4—181no—
603C4⋊C4—181no—
604C4⋊C4—181no—
605C22⋊C4—61no—
606C22⋊C4—181no—
607C22⋊C4—181no—
608C22⋊C4—181no—
609C22⋊C4—181no—
610C22⋊C4—181no—
611C22⋊C4—181no—
612C22⋊C4—181no—
613C22⋊C4—181no—
614C42—61no—
615C42—181no—
616C42—181no—
617C42—181no—
618C42—181no—
619C22×C3—21no—
620C22×C3—21no—
621C22×C3—21no—
622C22×C3—21no—
623C22×C3—21no—
624C22×C3—22no—
625C22×C3—32no—
626C22×C3—41no—
627C22×C3—41no—
628C22×C3—61no—
629C22×C3—61no—
630C22×C3—61no—
631C22×C3—61no—
632C22×C3—61no—
633C22×C3—124no—
634C22×C3—121no—
635C22×C3—121no—
636C22×C3—121no—
637C22×C3#88312yes—
638C22×C3#88612yes—
639C22×C3C22×D1211yescharacteristic
640C22×C3C2×D3×D411yescharacteristic
641C2×D3—21no—
642C2×D3—21no—
643C2×D3—21no—
644C2×D3—21no—
645C2×D3—21no—
646C2×D3—44no—
647C2×D3—41no—
648C2×D3—41no—
649C2×D3—41no—
650C2×D3#90412yes—
651C3×C4—21no—
652C3×C4—21no—
653C3×C4—22no—
654C3×C4—61no—
655C3×C4—61no—
656C3×C4—121no—
657C3×C4—121no—
658C3×C4—121no—
659C3×C4#88312yes—
660C3×C4#88612yes—
661C3×C4C2×#23511yescharacteristic
662C3×C4C2×#23711yescharacteristic
663C3×C4C2×#23711yescharacteristic
664C3×C4C2×#23711yescharacteristic
665Dic3—21no—
666Dic3—21no—
667Dic3—41no—
668Dic3—41no—
669Dic3—41no—
670Dic3—121no—
671Dic3—121no—
672Dic3—121no—
673Dic3—121no—
674Dic3—121no—
675Dic3—121no—
676Dic3—121no—
677Dic3—121no—
678Dic3—241no—
679Dic3—241no—
680Dic3—241no—
681Dic3—241no—
682C32#309111yescharacteristic, complemented, Sylow
683C23—31no—
684C23—31no—
685C23—62no—
686C23—62no—
687C23—61no—
688C23—121no—
689C23D3×D1211yescharacteristic
690Q8—61no—
691Q8—61no—
692D4—61no—
693D4—61no—
694D4—122no—
695D4—362no—
696D4—362no—
697C2×C4—31no—
698C2×C4—31no—
699C2×C4—62no—
700C2×C4—61no—
701C2×C4—61no—
702C2×C4—61no—
703C2×C4—61no—
704C2×C4—62no—
705C2×C4—62no—
706C2×C4—61no—
707C2×C4—61no—
708C2×C4—61no—
709C2×C4—122no—
710C2×C4—181no—
711C2×C4—181no—
712C2×C4—181no—
713C2×C4—181no—
714C2×C4—362no—
715C2×C4—362no—
716C2×C4#379512yes—
717C2×C4D3×D1211yescharacteristic
718C2×C4#380512yes—
719C2×C4C22×D3211yescharacteristic
720C8—21no—
721C8—21no—
722C8—61no—
723C8—61no—
724C2×C3—22no—
725C2×C3—22no—
726C2×C3—21no—
727C2×C3—21no—
728C2×C3—21no—
729C2×C3—42no—
730C2×C3—62no—
731C2×C3—121no—
732C2×C3—241no—
733C2×C3C2×#88311yescharacteristic
734C2×C3C2×#88611yescharacteristic
735C2×C3C2×#90411yescharacteristic
736C2×C3#574811yescharacteristic
737C2×C3D3×#13511yescharacteristic
738C2×C3#576811yescharacteristic
739D3—22no—
740D3—41no—
741D3—81no—
742C22—21no—
743C22—21no—
744C22—32no—
745C22—61no—
746C22—61no—
747C22—61no—
748C22—61no—
749C22—61no—
750C22—124no—
751C22—121no—
752C22—121no—
753C22—121no—
754C22#6389112yes—
755C22C2×D3×D1211yescharacteristic
756C4—61no—
757C4—61no—
758C4—121no—
759C4—121no—
760C4—121no—
761C4—361no—
762C4—361no—
763C4—361no—
764C4—361no—
765C4#6389112yes—
766C4C2×#379511yescharacteristic
767C4C2×#380511yescharacteristic
768C3—21no—
769C3#7859111yescharacteristic, complemented
770C3#7884211yescharacteristic, complemented
771C2—22no—
772C2—62no—
773C2—121no—
774C2—241no—
775C2D3×#90411yescharacteristic
776C2#1059467611yescharacteristic
777C2C2×#6389111yescharacteristic
subgroupG/H
centerC2×C4D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC22×C32C22×D4
prime radical#10595022C2
hypercenterC22×C8D32
hypocenterC32#3091
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. D3×#926C2semidirect
3. #10592805C2semidirect
4. C3×#5113C2semidirect
5. C2×C3×(C2×D3)⋊C8C2semidirect
6. #10591122C2semidirect
7. #10591084C2semidirect
8. #10590837C2semidirect
9. #10590834C2semidirect
10. #10590711C2semidirect
11. #10590710C2semidirect
12. #10590682C2semidirect
13. #10590680C2semidirect
14. #10590676C2semidirect
15. #10590675C2semidirect
41. #63645C22semidirect
42. #63645C22semidirect
43. #63644C22semidirect
44. #63644C22semidirect
45. C3×#821C22semidirect
46. C3×#821C22semidirect
51. C3×#816C22semidirect
52. C3×#816C22semidirect
53. #63575C22semidirect
54. #63575C22semidirect
55. #63573C22semidirect
56. #63573C22semidirect
57. #63566C22semidirect
58. #63566C22semidirect
59. #63563C22semidirect
60. #63563C22semidirect
69. #5113D3semidirect
70. C2×(C2×D3)⋊C8D3semidirect
205. #821C2×D3semidirect
206. #821C2×D3semidirect
229. #816C2×D3semidirect
230. #816C2×D3semidirect
682. C32#3091semidirect
769. C3#78591semidirect
770. C3#78842semidirect

Maximal subgroups

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

subgroupindex
#105950222
D3×#9262
#105928052
C3×#51132
C2×C3×(C2×D3)⋊C82
#105911222
#105910842
#105908372
#105908342
#105907112
#105907102
#105906822
#105906802
#105906762
#105906752
#788423
#785913