Finite Group Databasebeta

← #11887319

Subgroups — #11887319

Order 1152.

869 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#10594629C211yesmaximal, characteristic
2#10594457C211yesmaximal, characteristic, complemented
3#10592584C211yesmaximal, characteristic, complemented
4C3×#4891C211yesmaximal, characteristic, complemented
5C3×#4887C211yesmaximal, characteristic, complemented
6#10590965C211yesmaximal, characteristic, complemented
7D3×#821C211yesmaximal, characteristic, complemented
8#10590801C211yesmaximal, characteristic, complemented
9#10590720C211yesmaximal, characteristic, complemented
10#10590611C211yesmaximal, characteristic, complemented
11#10590596C211yesmaximal, characteristic, complemented
12#10590537C211yesmaximal, characteristic, complemented
13#10590523C211yesmaximal, characteristic, complemented
14#10590475C211yesmaximal, characteristic, complemented
15#10590439C211yesmaximal, characteristic, complemented
16#81186—31nomaximal
17#80775—31nomaximal
18C2×D3×D12C2211yescharacteristic
19C2×#3796C2211yescharacteristic
20#64104C2211yescharacteristic
21#64101C2211yescharacteristic, complemented
22C2×C3×Dic12C2211yescharacteristic, complemented
23C2×C3×D3×C8C2211yescharacteristic
24C3×#897C2211yescharacteristic
25C3×#897C2211yescharacteristic
26C3×#893C2211yescharacteristic
27C3×#890C2211yescharacteristic, complemented
28#63923—21no—
29D3×(C2×D3)⋊C4—21no—
30#63909—21no—
31C4×#626C2211yescharacteristic
32#63890—21no—
33#63890—21no—
34D3×C4⋊Dic3C2211yescharacteristic
35#63878—21no—
36#63872—21no—
37#63871C2211yescharacteristic, complemented
38#63864C2211yescharacteristic
39#63848—21no—
40Dic3×Dic6C2211yescharacteristic, complemented
41C2×#3717C2211yescharacteristic
42C2×#3715C2211yescharacteristic
43C2×#3710C2211yescharacteristic, complemented
44C32×#107C2211yescharacteristic, complemented
45#63648C2211yescharacteristic
46#63647C2211yescharacteristic, complemented
47#63636C2211yescharacteristic
48#63635C2211yescharacteristic, complemented
49C3×#821C2211yescharacteristic
50C3×Dic3⋊C8C2211yescharacteristic, complemented
51C3×#810C2211yescharacteristic, complemented
52C3×#810C2211yescharacteristic, complemented
53C3×#809C2211yescharacteristic
54C3×#808C2211yescharacteristic, complemented
55#63566C2211yescharacteristic, complemented
56#63565C2211yescharacteristic, complemented
57#63564C2211yescharacteristic
58#63563C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic, complemented
61#5694—31no—
62#5642—31no—
63#5630—31no—
64#5554—31no—
65C3×#478—31no—
66C3×#467—31no—
67#5187—31no—
68#5185—31no—
69C2×#821—31no—
70C8×#67—31no—
71#5068—31no—
72#5046—31no—
73#5043—31no—
74C4×#214—31no—
75#4891D311yescharacteristic, complemented
76#4887D311yescharacteristic, complemented
77#4885—31no—
78#4885—31no—
79#4885—61no—
80#4864—31no—
81#4862—31no—
82#4845—31no—
83#4834—31no—
84#4807—31no—
85#4804—31no—
86#4800—31no—
87#4788—31no—
88#4783—31no—
89#4776—31no—
90#4772—31no—
91D3×#102—31no—
92C22×D32—21no—
93C2×C4⋊(C3⋊D3)—21no—
94C2×C4⋊(C3⋊D3)C2311yescharacteristic
95C2×C4×C3⋊D3C2311yescharacteristic
96C2×C3×D12C2311yescharacteristic
97C2×C3×C4×D3—21no—
98C2×C3×C4×D3C2311yescharacteristic
99C2×C3×Dic6C2311yescharacteristic
100C2×C3×Dic6C2311yescharacteristic
101C2×#626—21no—
102C2×#626—21no—
103C2×#626D411yescharacteristic
104C2×D3×Dic3—21no—
105C2×D3×Dic3—21no—
106D3×D12—22no—
107D3×D12—41no—
108#3796—22no—
109#3796—41no—
110C2×C32×C8C2311yescharacteristic
111C32×C4⋊C4C2311yescharacteristic
112C32×C4⋊C4C2311yescharacteristic
113#3752—21no—
114#3752—21no—
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116C4×C3⋊Dic3—21no—
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118C3×(C2×D3)⋊C4—21no—
119C3×(C2×D3)⋊C4—21no—
120C3×(C2×D3)⋊C4—21no—
121C3×C4⋊Dic3—21no—
122C3×C4⋊Dic3—21no—
123C3×C4⋊Dic3—21no—
124C3×C4⋊Dic3C2311yescharacteristic
125C3×Dic3⋊C4—21no—
126C3×C4×Dic3C2311yescharacteristic
127C2×C3×C3⋊C8C2311yescharacteristic
128C2×C3×C3⋊C8C2311yescharacteristic
129C3×Dic12—41no—
130C3×D3×C8—41no—
131Dic3⋊Dic3—21no—
132Dic3⋊Dic3—21no—
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3D411yescharacteristic
135#3722—21no—
136#3722—21no—
137#3722—21no—
138#3722D411yescharacteristic
139(C2×D3)⋊Dic3D411yescharacteristic
140Dic32—21no—
141#3717—41no—
142#3715—22no—
143#3710—41no—
144#3296—91noSylow
145C2×#239—31no—
146C2×#237—31no—
147C2×D3×D4—31no—
148C22×D12—31no—
149C2×C3×Q16—31no—
150C22×C3×C8—31no—
151C3×#125—31no—
152C3×C22⋊Q8—31no—
153C3×C22⋊Q8—31no—
154C3×C4×D4—31no—
155#947—31no—
156#946—31no—
157Q8×Dic3—31no—
158C2×#215—31no—
159C2×#215—31no—
160C2×#214—31no—
161#930—61no—
162C4×#67—31no—
163C2×(C2×D3)⋊C4—61no—
164C2×C4⋊Dic3—31no—
165C2×Dic12C2×D311yescharacteristic, complemented
166C2×#204—31no—
167C2×D3×C8—31no—
168C2×D3×C8—31no—
169C2×D3×C8C2×D311yescharacteristic
170#898—61no—
171#898—61no—
172#897—31no—
173#897C2×D311yescharacteristic
174#897C2×D311yescharacteristic
175#895—31no—
176#895—31no—
177#895—61no—
178#895—61no—
179#894—61no—
180#894—61no—
181#893C2×D311yescharacteristic
182#892—31no—
183#892—31no—
184#892—61no—
185#892—61no—
186D3×C4⋊C4—31no—
187#890—61no—
188#890—61no—
189#890C2×D311yescharacteristic, complemented
190#886—61no—
191#886—61no—
192#882—61no—
193#882—61no—
194D3×C22⋊C4—61no—
195#877—61no—
196#875—31no—
197C4×D12—31no—
198C4×Dic6—31no—
199C3×#107—21no—
200C3×#107C2×D311yescharacteristic, complemented
201C3×#107C2×D311yescharacteristic, complemented
202C3×#106—31no—
203C3×C4⋊C8—31no—
204C3×#103—31no—
205C3×#103—31no—
206C3×#102—31no—
207C3×#102—31no—
208#835—31no—
209#835—31no—
210#832—31no—
211#830—31no—
212#821—31no—
213#821—31no—
214#821—31no—
215#821—31no—
216#821—61no—
217#821C2×D311yescharacteristic
218(C2×D3)⋊C8—31no—
219(C2×D3)⋊C8—31no—
220(C2×D3)⋊C8—31no—
221(C2×D3)⋊C8—61no—
222#816—31no—
223Dic3⋊C8C2×D311yescharacteristic, complemented
224C8×Dic3—31no—
225#810—31no—
226#810C2×D311yescharacteristic, complemented
227#810C2×D311yescharacteristic, complemented
228#809—31no—
229#809—31no—
230#809—31no—
231#809—61no—
232#809C2×D311yescharacteristic
233#808—31no—
234#808—31no—
235#808—61no—
236#808C2×D311yescharacteristic, complemented
237C4×C3⋊C8—31no—
238C22×C3⋊D3—21no—
239C22×C3⋊D3C2×D411yescharacteristic
240C22×C3×D3—21no—
241C22×C3×D3C2×D411yescharacteristic
242C2×D32—42no—
243C2×D32—42no—
244C2×D32—81no—
245C2×C32×C4—21no—
246C2×C32×C4—21no—
247C2×C32×C4C2411yescharacteristic
248C2×C3⋊Dic3—21no—
249C2×C3⋊Dic3C2×D411yescharacteristic
250C4⋊(C3⋊D3)—21no—
251C4⋊(C3⋊D3)—21no—
252C4⋊(C3⋊D3)—81no—
253C4×C3⋊D3—21no—
254C4×C3⋊D3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3C2×D411yescharacteristic
259C2×C3×Dic3C2×D411yescharacteristic
260C2×C3×Dic3C2×D411yescharacteristic
261C3×D12—21no—
262C3×D12#4112yes—
263C3×C4×D3—21no—
264C3×C4×D3—21no—
265C3×C4×D3—81no—
266C3×Dic6—21no—
267C3×Dic6—21no—
268C3×Dic6—21no—
269C3×Dic6—21no—
270#626—22no—
271#626—42no—
272#626—42no—
273D3×Dic3—42no—
274D3×Dic3—42no—
275C32×C8—21no—
276C3⋊(C3⋊C8)—21no—
277C3×C3⋊C8—21no—
278C3×C3⋊C8—21no—
279#552—91no—
280#546—91no—
281#488—91no—
282#483—91no—
283#482—91no—
284#478—31no—
285#467—31no—
286#465—91no—
287#464—91no—
288#452—91no—
289#450—91no—
290C4×SD16—91no—
291C8×D4—91no—
292#416—91no—
293C2×#102—91no—
294C23×D3—61no—
295C23×D3—61no—
296C2×C3×Q8—31no—
297C2×C3×Q8—31no—
298C2×C3×D4—31no—
299C22×C3×C4—31no—
300C22×C3×C4—61no—
301C2×#67—31no—
302C2×#67—61no—
303C2×#67—61no—
304C22×Dic3—61no—
305C22×Dic3—61no—
306#239—62no—
307#239—121no—
308#237—62no—
309#237—121no—
310D3×D4—62no—
311D3×D4—121no—
312C2×D12—31no—
313C2×D12—31no—
314C2×D12—31no—
315C2×D12—61no—
316C2×D12—62no—
317C2×D12—61no—
318C2×D12—61no—
319C2×D12—61no—
320C2×D12—61no—
321C2×D12—121no—
322C2×D12—121no—
323C2×D12C22×D311yescharacteristic
324C2×C4×D3—21no—
325C2×C4×D3—31no—
326C2×C4×D3—31no—
327C2×C4×D3—61no—
328C2×C4×D3—61no—
329C2×C4×D3—61no—
330C2×C4×D3C22×D311yescharacteristic
331C2×Dic6C22×D311yescharacteristic
332C2×Dic6C22×D311yescharacteristic
333C3×Q16—121no—
334C2×C3×C8—21no—
335C2×C3×C8—31no—
336C2×C3×C8—31no—
337C2×C3×C8—121no—
338C2×C3×C8C22×D311yescharacteristic
339C2×C3×C8C22×D311yescharacteristic
340C3×C4⋊C4—21no—
341C3×C4⋊C4—21no—
342C3×C4⋊C4—31no—
343C3×C4⋊C4—61no—
344C3×C4⋊C4—61no—
345C3×C4⋊C4—61no—
346C3×C4⋊C4—61no—
347C3×C4⋊C4C22×D311yescharacteristic
348C3×C4⋊C4C22×D311yescharacteristic
349C3×C4⋊C4C22×D311yescharacteristic
350C3×C4⋊C4C22×D311yescharacteristic
351C3×C22⋊C4—61no—
352C3×C22⋊C4—61no—
353C3×C22⋊C4—61no—
354C3×C42—31no—
355#217—31no—
356#215—62no—
357#215—121no—
358#214—62no—
359(C2×D3)⋊C4—21no—
360(C2×D3)⋊C4—21no—
361(C2×D3)⋊C4—21no—
362(C2×D3)⋊C4—31no—
363(C2×D3)⋊C4—31no—
364(C2×D3)⋊C4—31no—
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—
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—21no—
380C4⋊Dic3—31no—
381C4⋊Dic3—31no—
382C4⋊Dic3—31no—
383C4⋊Dic3—61no—
384C4⋊Dic3—61no—
385C4⋊Dic3—61no—
386C4⋊Dic3—61no—
387C4⋊Dic3C22×D311yescharacteristic
388Dic3⋊C4—21no—
389Dic3⋊C4—31no—
390Dic3⋊C4—61no—
391Dic3⋊C4—61no—
392Dic3⋊C4—61no—
393C4×Dic3—61no—
394C4×Dic3—61no—
395C4×Dic3—61no—
396C4×Dic3—61no—
397C4×Dic3—121no—
398C4×Dic3C22×D311yescharacteristic
399C2×C3⋊C8—31no—
400C2×C3⋊C8—31no—
401C2×C3⋊C8—61no—
402C2×C3⋊C8C22×D311yescharacteristic
403C2×C3⋊C8C22×D311yescharacteristic
404Dic12—41no—
405#204—121no—
406D3×C8—41no—
407D3×C8—121no—
408D3×C8—121no—
409C22×C32C22×D411yescharacteristic
410C2×C3⋊D3—21no—
411C2×C3⋊D3—21no—
412C2×C3⋊D3—21no—
413C2×C3⋊D3—41no—
414C2×C3⋊D3—41no—
415C2×C3⋊D3—41no—
416C2×C3×D3—21no—
417C2×C3×D3—21no—
418C2×C3×D3—22no—
419C2×C3×D3—41no—
420C2×C3×D3—41no—
421C2×C3×D3#13512yes—
422D32—84no—
423C32×C4—41no—
424C32×C4—41no—
425C32×C4C2×#4111yescharacteristic
426C32×C4H(5,𝔽2)11yescharacteristic
427C3⋊Dic3—21no—
428C3⋊Dic3—41no—
429C3×Dic3—21no—
430C3×Dic3—21no—
431C3×Dic3—21no—
432C3×Dic3—41no—
433C3×Dic3—41no—
434C3×Dic3—41no—
435C2×#41—91no—
436C22×D4—91no—
437C2×Q16—31no—
438C2×SD16—91no—
439C2×SD16—91no—
440C22×C8—31no—
441C22×C8—91no—
442#126—181no—
443#125—31no—
444#125—181no—
445#124—91no—
446#123—181no—
447#123—181no—
448C22⋊Q8—31no—
449C22⋊Q8—31no—
450C22⋊Q8—91no—
451#121—91no—
452#121—181no—
453#120—181no—
454C4×Q8—91no—
455C4×D4—31no—
456C4×D4—91no—
457#117—91no—
458#117—181no—
459C2×C4⋊C4—91no—
460C2×C22⋊C4—181no—
461#107D3211yescharacteristic, complemented
462#106—31no—
463#106—91no—
464C4⋊C8—31no—
465#103—31no—
466#103—31no—
467#103—91no—
468#103—91no—
469#102—31no—
470#102—31no—
471#102—91no—
472#102—91no—
473#102—91no—
474#102—91no—
475C22⋊C8—91no—
476C22⋊C8—91no—
477C4×C8—91no—
478C23×C3—31no—
479C23×C3—61no—
480C22×D3—21no—
481C22×D3—31no—
482C22×D3—31no—
483C22×D3—61no—
484C22×D3—61no—
485C22×D3—61no—
486C22×D3—121no—
487C22×D3—122no—
488C22×D3—122no—
489C22×D3—122no—
490C22×D3—122no—
491C22×D3—241no—
492C22×D3—241no—
493C22×D3D3×D411yescharacteristic
494C3×Q8—61no—
495C3×Q8—61no—
496C3×Q8—61no—
497C3×Q8—61no—
498C3×D4—32no—
499C3×D4—61no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—31no—
506C2×C3×C4—31no—
507C2×C3×C4—31no—
508C2×C3×C4—41no—
509C2×C3×C4—41no—
510C2×C3×C4—61no—
511C2×C3×C4—61no—
512C2×C3×C4—61no—
513C2×C3×C4—61no—
514C2×C3×C4—61no—
515C2×C3×C4—241no—
516C2×C3×C4C23×D311yescharacteristic
517C2×C3×C4C23×D311yescharacteristic
518#67—62no—
519#67—122no—
520#67—122no—
521C2×Dic3—21no—
522C2×Dic3—21no—
523C2×Dic3—21no—
524C2×Dic3—31no—
525C2×Dic3—31no—
526C2×Dic3—61no—
527C2×Dic3—61no—
528C2×Dic3—61no—
529C2×Dic3—121no—
530C2×Dic3—122no—
531C2×Dic3—122no—
532C2×Dic3D3×D411yescharacteristic
533C2×Dic3D3×D411yescharacteristic
534C2×Dic3D3×D411yescharacteristic
535D12—21no—
536D12—62no—
537D12—61no—
538D12—61no—
539D12—61no—
540D12—61no—
541D12—121no—
542D12—121no—
543D12—122no—
544D12—122no—
545D12—241no—
546D12—241no—
547D12—242no—
548D12#23912yes—
549C4×D3—21no—
550C4×D3—21no—
551C4×D3—61no—
552C4×D3—61no—
553C4×D3—61no—
554C4×D3—61no—
555C4×D3—81no—
556C4×D3—121no—
557C4×D3—121no—
558C4×D3—122no—
559C4×D3—122no—
560Dic6—21no—
561Dic6—21no—
562Dic6—21no—
563Dic6—21no—
564C3×C8—21no—
565C3×C8—21no—
566C3×C8—41no—
567C3×C8—61no—
568C3×C8—61no—
569C3⋊C8—21no—
570C3⋊C8—21no—
571C3⋊C8—61no—
572C3⋊C8—61no—
573C3⋊C8—121no—
574C2×C32#54611yescharacteristic
575C2×C32C2×#13511yescharacteristic
576C2×C32#57711yescharacteristic
577C3⋊D3—41no—
578C3⋊D3—81no—
579C3×D3—22no—
580C3×D3—42no—
581C24—181no—
582#41—182no—
583#41—361no—
584C2×Q8—31no—
585C2×Q8—31no—
586C2×D4—31no—
587C2×D4—91no—
588C2×D4—91no—
589C2×D4—181no—
590C2×D4—181no—
591C2×D4—182no—
592C2×D4—181no—
593C2×D4—361no—
594C22×C4—31no—
595C22×C4—61no—
596C22×C4—91no—
597C22×C4—181no—
598C22×C4—181no—
599Q16—121no—
600SD16—182no—
601SD16—361no—
602C2×C8—31no—
603C2×C8—31no—
604C2×C8—91no—
605C2×C8—121no—
606C2×C8—361no—
607C2×C8C2×D3211yescharacteristic
608C4⋊C4—31no—
609C4⋊C4—61no—
610C4⋊C4—61no—
611C4⋊C4—61no—
612C4⋊C4—61no—
613C4⋊C4—91no—
614C4⋊C4—91no—
615C4⋊C4—181no—
616C4⋊C4—181no—
617C4⋊C4—181no—
618C4⋊C4C2×D3211yescharacteristic
619C4⋊C4C2×D3211yescharacteristic
620C22⋊C4—61no—
621C22⋊C4—61no—
622C22⋊C4—61no—
623C22⋊C4—91no—
624C22⋊C4—91no—
625C22⋊C4—181no—
626C22⋊C4—181no—
627C22⋊C4—181no—
628C22⋊C4—181no—
629C22⋊C4—181no—
630C42—31no—
631C42—181no—
632C42—181no—
633C22×C3—21no—
634C22×C3—32no—
635C22×C3—61no—
636C22×C3—61no—
637C22×C3—62no—
638C22×C3—121no—
639C22×C3—121no—
640C22×C3C2×D3×D411yescharacteristic
641C22×C3C2×D3×D411yescharacteristic
642C2×D3—21no—
643C2×D3—21no—
644C2×D3—22no—
645C2×D3—41no—
646C2×D3—41no—
647C2×D3—61no—
648C2×D3—61no—
649C2×D3—61no—
650C2×D3—61no—
651C2×D3—61no—
652C2×D3—61no—
653C2×D3—121no—
654C2×D3—121no—
655C2×D3—121no—
656C2×D3—121no—
657C2×D3—121no—
658C2×D3—121no—
659C2×D3—121no—
660C2×D3—121no—
661C2×D3—121no—
662C2×D3—241no—
663C2×D3—241no—
664C2×D3—241no—
665C2×D3—244no—
666C2×D3—244no—
667C2×D3#91912yes—
668C3×C4—21no—
669C3×C4—21no—
670C3×C4—41no—
671C3×C4—41no—
672C3×C4—41no—
673C3×C4—41no—
674C3×C4—61no—
675C3×C4—61no—
676C3×C4—61no—
677C3×C4—81no—
678C3×C4—81no—
679C3×C4—121no—
680C3×C4—121no—
681C3×C4—121no—
682C3×C4#100411yescharacteristic
683C3×C4C2×#23911yescharacteristic
684C3×C4D3×#4111yescharacteristic
685C3×C4#100911yescharacteristic
686Dic3—21no—
687Dic3—21no—
688Dic3—21no—
689Dic3—41no—
690Dic3—41no—
691Dic3—41no—
692Dic3—61no—
693Dic3—61no—
694Dic3—121no—
695Dic3—121no—
696Dic3—121no—
697Dic3—241no—
698C32#329611yescharacteristic, complemented, Sylow
699C23—31no—
700C23—61no—
701C23—91no—
702C23—181no—
703C23—362no—
704C23—362no—
705C23—721no—
706Q8—61no—
707Q8—61no—
708Q8—61no—
709Q8—61no—
710D4—32no—
711D4—61no—
712D4—182no—
713D4—181no—
714D4—181no—
715D4—362no—
716D4—362no—
717D4—721no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—31no—
721C2×C4—31no—
722C2×C4—31no—
723C2×C4—61no—
724C2×C4—61no—
725C2×C4—61no—
726C2×C4—61no—
727C2×C4—61no—
728C2×C4—91no—
729C2×C4—181no—
730C2×C4—181no—
731C2×C4—181no—
732C2×C4—241no—
733C2×C4—362no—
734C2×C4—362no—
735C2×C4C22×D3211yescharacteristic
736C8—21no—
737C8—61no—
738C8—61no—
739C8—181no—
740C2×C3—21no—
741C2×C3—21no—
742C2×C3—21no—
743C2×C3—62no—
744C2×C3—122no—
745C2×C3#561011yescharacteristic
746C2×C3#563011yescharacteristic
747C2×C3C2×#91911yescharacteristic
748C2×C3D3×#13511yescharacteristic
749C2×C3#577011yescharacteristic
750C2×C3#577511yescharacteristic
751D3—22no—
752D3—42no—
753D3—121no—
754D3—121no—
755D3—241no—
756D3—241no—
757D3—241no—
758D3—481no—
759C22—32no—
760C22—61no—
761C22—61no—
762C22—62no—
763C22—121no—
764C22—121no—
765C22—181no—
766C22—181no—
767C22—181no—
768C22—361no—
769C22—361no—
770C22—361no—
771C22—724no—
772C22D32×D411yescharacteristic
773C4—41no—
774C4—41no—
775C4—61no—
776C4—61no—
777C4—61no—
778C4—121no—
779C4—121no—
780C4—121no—
781C4—181no—
782C4—361no—
783C4#6430711yescharacteristic
784C4D3×#23911yescharacteristic
785C3—21no—
786C3#8077511yescharacteristic, complemented
787C3#8118611yescharacteristic, complemented
788C2—62no—
789C2—122no—
790C2—361no—
791C2—721no—
792C2#1059462211yescharacteristic
793C2#1059473611yescharacteristic
794C2D3×#91911yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#107C22
socleC22×C32C22×D4
prime radical#10594629C2
hypercenter#107D32
hypocenterC32#3296
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #107

Complements

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

NH ≅ G/Ntype
2. #10594457C2semidirect
3. #10592584C2semidirect
4. C3×#4891C2semidirect
5. C3×#4887C2semidirect
6. #10590965C2semidirect
7. D3×#821C2semidirect
8. #10590801C2semidirect
9. #10590720C2semidirect
10. #10590611C2semidirect
11. #10590596C2semidirect
12. #10590537C2semidirect
13. #10590523C2semidirect
14. #10590475C2semidirect
15. #10590439C2semidirect
21. #64101C22semidirect
22. C2×C3×Dic12C22semidirect
27. C3×#890C22semidirect
37. #63871C22semidirect
40. Dic3×Dic6C22semidirect
43. C2×#3710C22semidirect
44. C32×#107C22semidirect
46. #63647C22semidirect
48. #63635C22semidirect
50. C3×Dic3⋊C8C22semidirect
51. C3×#810C22semidirect
52. C3×#810C22semidirect
54. C3×#808C22semidirect
55. #63566C22semidirect
56. #63565C22semidirect
60. Dic3×C3⋊C8C22semidirect
75. #4891D3semidirect
76. #4887D3semidirect
165. C2×Dic12C2×D3semidirect
189. #890C2×D3semidirect
200. C3×#107C2×D3semidirect
201. C3×#107C2×D3semidirect
223. Dic3⋊C8C2×D3semidirect
226. #810C2×D3semidirect
227. #810C2×D3semidirect
236. #808C2×D3semidirect
461. #107D32semidirect
698. C32#3296semidirect
786. C3#80775semidirect
787. C3#81186semidirect

Maximal subgroups

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

subgroupindex
#105946292
#105944572
#105925842
C3×#48912
C3×#48872
#105909652
D3×#8212
#105908012
#105907202
#105906112
#105905962
#105905372
#105905232
#105904752
#105904392
#811863
#807753