Finite Group Databasebeta

← #11882241

Subgroups — #11882241

Order 1152.

846 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5622C211yesmaximal, characteristic, complemented
2#10594910C211yesmaximal, characteristic
3#10592747C211yesmaximal, characteristic, complemented
4C3×#5048C211yesmaximal, characteristic, complemented
5#10591617C211yesmaximal, characteristic, complemented
6#10591565C211yesmaximal, characteristic, complemented
7#10591564C211yesmaximal, characteristic, complemented
8#10591544C211yesmaximal, characteristic, complemented
9#10591179C211yesmaximal, characteristic, complemented
10#10591177C211yesmaximal, characteristic, complemented
11C2×Dic3⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
12#10590556C211yesmaximal, characteristic, complemented
13#10590549C211yesmaximal, characteristic, complemented
14#10590466C211yesmaximal, characteristic, complemented
15#10590465C211yesmaximal, characteristic, complemented
16#83363—31nomaximal
17#80640—31nomaximal
18C2×#3804—21no—
19C32×C22⋊Q8C2211yescharacteristic
20C2×#3755C2211yescharacteristic
21#64139C2211yescharacteristic
22C22×C3⋊(C3⋊C8)C2211yescharacteristic
23C3×Q8×Dic3C2211yescharacteristic
24C3×#944C2211yescharacteristic
25C2×C3×#215C2211yescharacteristic
26C3×#930C2211yescharacteristic
27C3×#924C2211yescharacteristic
28C2×C3×C4×Dic3C2211yescharacteristic
29C22×C3×C3⋊C8C2211yescharacteristic
30C3×#889—21no—
31C3×#888C2211yescharacteristic
32C3×#887—21no—
33C3×#887C2211yescharacteristic
34C3×#878—21no—
35C3×#877—21no—
36#63978—21no—
37#63918C2211yescharacteristic
38#63911C2211yescharacteristic
39#63894C2211yescharacteristic
40Dic3×D12C2211yescharacteristic
41#63880—21no—
42#63852—21no—
43C2×#3717C2211yescharacteristic
44C2×#3715C2211yescharacteristic
45#63662C2211yescharacteristic
46#63636C2211yescharacteristic
47#63635C2211yescharacteristic
48C3×#835C2211yescharacteristic
49C3×#809C2211yescharacteristic
50C3×#808C2211yescharacteristic
51#63574C2211yescharacteristic
52#63573C2211yescharacteristic
53Dic3⋊(C3⋊C8)C2211yescharacteristic
54Dic3⋊(C3⋊C8)C2211yescharacteristic
55Dic3⋊(C3⋊C8)C2211yescharacteristic
56Dic3⋊(C3⋊C8)C2211yescharacteristic
57#63566C2211yescharacteristic
58#63565C2211yescharacteristic
59#63564C2211yescharacteristic
60#63562C2211yescharacteristic
61C3×#533—31no—
62#5622D311yescharacteristic, complemented
63#5596—31no—
64#5477—31no—
65C3×#465—31no—
66#5163—31no—
67#5162—31no—
68#5114—31no—
69C2×Dic3⋊C8—31no—
70#5084—31no—
71#5084—31no—
72#5083—31no—
73#5083—31no—
74#5048—31no—
75#5048—31no—
76#5048—31no—
77#5048—31no—
78#5048—61no—
79#5048D311yescharacteristic, complemented
80#5041—31no—
81#5027—31no—
82#5027—31no—
83#5020—31no—
84#5020—31no—
85C2×C4⋊(C3⋊C8)—31no—
86#4870—31no—
87#4854—31no—
88#4818—31no—
89#4791—31no—
90#4762—31no—
91#4761—31no—
92C2×C32×Q8C2311yescharacteristic
93C22×C32×C4C2311yescharacteristic
94C2×#638—21no—
95C2×C4⋊(C3⋊D3)C2311yescharacteristic
96C2×C3×#67—21no—
97C22×C3×Dic3D411yescharacteristic
98C22×C3×Dic3D411yescharacteristic
99C2×C3×D12C2311yescharacteristic
100C2×C3×Dic6—21no—
101C2×C3×Dic6C2311yescharacteristic
102C2×#627—21no—
103C2×#626—21no—
104C2×#626—21no—
105C2×#624—21no—
106#3804—44no—
107C2×D3×Dic3—21no—
108C32×C4⋊C4—21no—
109C32×C4⋊C4C2311yescharacteristic
110C32×C22⋊C4—21no—
111#3755—41no—
112#3752—21no—
113C4⋊(C3⋊Dic3)C2311yescharacteristic
114C2×C3⋊(C3⋊C8)—41no—
115C2×C3⋊(C3⋊C8)C2311yescharacteristic
116C2×C3⋊(C3⋊C8)C2311yescharacteristic
117C3×#217—21no—
118C3×#215—41no—
119C3×(C2×D3)⋊C4—21no—
120C3×C4⋊Dic3—21no—
121C3×C4⋊Dic3C2311yescharacteristic
122C3×C4⋊Dic3C2311yescharacteristic
123C3×Dic3⋊C4—21no—
124C3×Dic3⋊C4—21no—
125C3×Dic3⋊C4—21no—
126C3×Dic3⋊C4—21no—
127C3×Dic3⋊C4—21no—
128C3×C4×Dic3—21no—
129C3×C4×Dic3—21no—
130C3×C4×Dic3D411yescharacteristic
131C3×C4×Dic3D411yescharacteristic
132C3×C4×Dic3C2311yescharacteristic
133C3×C4×Dic3C2311yescharacteristic
134C2×C3×C3⋊C8—41no—
135C2×C3×C3⋊C8C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137Dic3⋊Dic3—21no—
138#3722—21no—
139(C2×D3)⋊Dic3—21no—
140#3717—41no—
141#3715—41no—
142#3246—91noSylow
143C2×#237—61no—
144C2×#235—61no—
145C2×C3×SD16—31no—
146C22×C3×C8—31no—
147C3×C4⋊Q8—31no—
148C3×C4⋊Q8—31no—
149C3×#125—61no—
150C3×C22⋊Q8—21no—
151C3×C22⋊Q8—31no—
152C3×C22⋊Q8—61no—
153C3×C22⋊Q8C2×D311yescharacteristic
154C3×C22⋊Q8C2×D311yescharacteristic
155C3×#121—31no—
156C3×C4×Q8—31no—
157C3×C4×Q8—31no—
158C3×C4×Q8—61no—
159C3×#117—61no—
160C2×C3×C42—31no—
161Q8×Dic3C2×D311yescharacteristic
162#944C2×D311yescharacteristic
163C2×#215—31no—
164C2×#215—31no—
165C2×#215—31no—
166C2×#215—31no—
167C2×#215—61no—
168C2×#215C2×D311yescharacteristic
169#940—31no—
170#939—61no—
171D4×Dic3—31no—
172C2×#214—31no—
173#930—31no—
174#930—31no—
175#930—61no—
176#930—61no—
177#930C2×D311yescharacteristic
178#924C2×D311yescharacteristic
179C2×C4×Dic3C2×D311yescharacteristic
180C22×C3⋊C8—31no—
181C22×C3⋊C8—31no—
182C22×C3⋊C8—61no—
183C22×C3⋊C8C2×D311yescharacteristic
184C2×#204—31no—
185#893—31no—
186#889—21no—
187#888—31no—
188#888C2×D311yescharacteristic
189#887—21no—
190#887C2×D311yescharacteristic
191#885—61no—
192#67⋊C4—61no—
193#878—21no—
194#877—21no—
195#875—61no—
196#874—31no—
197C4×D12—31no—
198C4×D12—31no—
199C4×D12—61no—
200#869—31no—
201C3×#106—31no—
202C3×#103—31no—
203C3×#102—31no—
204#835—31no—
205#835—31no—
206#835—31no—
207#835—31no—
208#835—61no—
209#835C2×D311yescharacteristic
210#832—31no—
211#821—31no—
212#817—31no—
213#816—31no—
214Dic3⋊C8—31no—
215Dic3⋊C8—31no—
216Dic3⋊C8—31no—
217Dic3⋊C8—31no—
218#810—31no—
219#809—31no—
220#809—31no—
221#809—31no—
222#809—31no—
223#809—61no—
224#809C2×D311yescharacteristic
225#808—31no—
226#808—31no—
227#808—31no—
228#808—31no—
229#808—31no—
230#808—61no—
231#808C2×D311yescharacteristic
232C4⋊(C3⋊C8)—31no—
233C4⋊(C3⋊C8)—31no—
234C4⋊(C3⋊C8)—31no—
235C4⋊(C3⋊C8)—31no—
236C23×C32C2×D411yescharacteristic
237C22×C3⋊D3—21no—
238C22×C3×D3—21no—
239C32×Q8—21no—
240C32×Q8—21no—
241C2×C32×C4—21no—
242C2×C32×C4—21no—
243C2×C32×C4—21no—
244C2×C32×C4—21no—
245C2×C32×C4C2×D411yescharacteristic
246C2×C32×C4C2411yescharacteristic
247#638—42no—
248C2×C3⋊Dic3—21no—
249C4⋊(C3⋊D3)—21no—
250C4⋊(C3⋊D3)—21no—
251C3×#67—42no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—41no—
256C2×C3×Dic3SD1614yescomplemented
257C2×C3×Dic3C2×D411yescharacteristic
258C2×C3×Dic3C2×D411yescharacteristic
259C2×C3×Dic3C2×D411yescharacteristic
260C2×C3×Dic3C2×D411yescharacteristic
261C3×D12—21no—
262C3×D12—21no—
263C3×Dic6—21no—
264C3×Dic6—21no—
265C3×Dic6—42no—
266#627—42no—
267#626—42no—
268#626—42no—
269#624—42no—
270D3×Dic3—42no—
271C3⋊(C3⋊C8)—21no—
272C3⋊(C3⋊C8)—21no—
273C3×C3⋊C8—21no—
274C3×C3⋊C8—21no—
275#533—31no—
276#532—91no—
277#476—91no—
278#476—91no—
279#475—91no—
280#475—91no—
281#465—31no—
282#465—91no—
283#465—91no—
284#465—91no—
285#461—91no—
286#461—91no—
287#460—91no—
288#460—91no—
289C2×C4⋊C8—91no—
290C2×C3×Q8—21no—
291C2×C3×Q8—31no—
292C2×C3×Q8—61no—
293C2×C3×Q8C22×D311yescharacteristic
294C2×C3×Q8C22×D311yescharacteristic
295C2×C3×D4—31no—
296C2×C3×D4—61no—
297C22×C3×C4—21no—
298C22×C3×C4—31no—
299C22×C3×C4—31no—
300C22×C3×C4C22×D311yescharacteristic
301C22×C3×C4C22×D311yescharacteristic
302C2×#67—21no—
303C2×#67—61no—
304C2×#67—61no—
305C2×#67—61no—
306C2×#67—61no—
307C2×#67—121no—
308C22×Dic3—61no—
309C22×Dic3#6711yescharacteristic
310C22×Dic3#6711yescharacteristic
311#237—124no—
312#235—124no—
313C2×D12—31no—
314C2×D12—31no—
315C2×D12—61no—
316C2×D12—61no—
317C2×D12—61no—
318C2×D12C22×D311yescharacteristic
319C2×C4×D3—61no—
320C2×C4×D3—61no—
321C2×C4×D3—61no—
322C2×Dic6—21no—
323C2×Dic6—61no—
324C2×Dic6—61no—
325C2×Dic6C22×D311yescharacteristic
326C3×SD16—121no—
327C2×C3×C8—31no—
328C2×C3×C8—31no—
329C2×C3×C8—121no—
330C3×C4⋊C4—21no—
331C3×C4⋊C4—21no—
332C3×C4⋊C4—21no—
333C3×C4⋊C4—31no—
334C3×C4⋊C4—31no—
335C3×C4⋊C4—41no—
336C3×C4⋊C4—61no—
337C3×C4⋊C4—61no—
338C3×C4⋊C4—61no—
339C3×C4⋊C4—61no—
340C3×C4⋊C4—61no—
341C3×C4⋊C4—61no—
342C3×C4⋊C4C22×D311yescharacteristic
343C3×C4⋊C4C22×D311yescharacteristic
344C3×C22⋊C4—21no—
345C3×C22⋊C4—21no—
346C3×C22⋊C4—41no—
347C3×C22⋊C4—61no—
348C3×C22⋊C4—61no—
349C3×C42—31no—
350C3×C42—31no—
351C3×C42—31no—
352C3×C42—31no—
353C3×C42—61no—
354C3×C42—61no—
355#217—21no—
356#217—61no—
357#215—41no—
358#215—121no—
359#215—121no—
360#215—121no—
361#215—121no—
362#215—122no—
363#214—121no—
364(C2×D3)⋊C4—21no—
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—121no—
371C4⋊Dic3—21no—
372C4⋊Dic3—31no—
373C4⋊Dic3—31no—
374C4⋊Dic3—61no—
375C4⋊Dic3—61no—
376C4⋊Dic3C22×D311yescharacteristic
377C4⋊Dic3C22×D311yescharacteristic
378Dic3⋊C4—21no—
379Dic3⋊C4—21no—
380Dic3⋊C4—21no—
381Dic3⋊C4—21no—
382Dic3⋊C4—21no—
383Dic3⋊C4—61no—
384C4×Dic3—21no—
385C4×Dic3—21no—
386C4×Dic3#6711yescharacteristic
387C4×Dic3#6711yescharacteristic
388C4×Dic3C22×D311yescharacteristic
389C4×Dic3C22×D311yescharacteristic
390C2×C3⋊C8—31no—
391C2×C3⋊C8—31no—
392C2×C3⋊C8—31no—
393C2×C3⋊C8—31no—
394C2×C3⋊C8—41no—
395C2×C3⋊C8—61no—
396C2×C3⋊C8—61no—
397C2×C3⋊C8—121no—
398C2×C3⋊C8—121no—
399C2×C3⋊C8—122no—
400C2×C3⋊C8C22×D311yescharacteristic
401C2×C3⋊C8C22×D311yescharacteristic
402#204—121no—
403C22×C32—21no—
404C22×C32—21no—
405C22×C32C2×SD1612yes—
406C22×C32C22×D411yescharacteristic
407C2×C3⋊D3—41no—
408C2×C3⋊D3—41no—
409C2×C3⋊D3—41no—
410C2×C3×D3—41no—
411C2×C3×D3—41no—
412C2×C3×D3—41no—
413C32×C4—21no—
414C32×C4—41no—
415C32×C4—41no—
416C32×C4H(5,𝔽2)11yescharacteristic
417C32×C42−1+411yescharacteristic
418C3⋊Dic3—41no—
419C3×Dic3—21no—
420C3×Dic3—21no—
421C3×Dic3—41no—
422C3×Dic3—41no—
423C3×Dic3—41no—
424C3×Dic3C2×SD1612yes—
425C3×Dic3C2×SD1612yes—
426C2×#41—181no—
427C2×SD16—31no—
428C2×SD16—91no—
429C2×SD16—91no—
430C2×SD16—91no—
431C22×C8—31no—
432C22×C8—91no—
433C4⋊Q8—31no—
434C4⋊Q8—31no—
435C4⋊Q8—91no—
436#127—91no—
437#125—61no—
438#124—181no—
439C22⋊Q8—31no—
440C22⋊Q8—61no—
441C22⋊Q8D3211yescharacteristic
442#121—31no—
443#121—91no—
444#121—181no—
445C4×Q8—31no—
446C4×Q8—31no—
447C4×Q8—61no—
448C4×D4—91no—
449C4×D4—91no—
450C4×D4—181no—
451#117—61no—
452C2×C42—31no—
453#106—31no—
454#106—91no—
455#106—91no—
456#106—91no—
457C4⋊C8—91no—
458C4⋊C8—91no—
459C4⋊C8—91no—
460C4⋊C8—91no—
461#103—31no—
462#103—91no—
463#103—91no—
464#103—91no—
465#102—31no—
466#102—91no—
467#102—91no—
468#102—91no—
469C23×C3—21no—
470C23×C3—61no—
471C23×C3D3×D411yescharacteristic
472C23×C3C2×#6711yescharacteristic
473C22×D3—21no—
474C22×D3—61no—
475C22×D3—61no—
476C22×D3—121no—
477C3×Q8—21no—
478C3×Q8—21no—
479C3×Q8—21no—
480C3×Q8—21no—
481C3×Q8—41no—
482C3×Q8—41no—
483C3×Q8—61no—
484C3×Q8—61no—
485C3×Q8—122no—
486C3×D4—61no—
487C3×D4—61no—
488C3×D4—122no—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—21no—
493C2×C3×C4—21no—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—34no—
500C2×C3×C4—31no—
501C2×C3×C4—31no—
502C2×C3×C4—31no—
503C2×C3×C4—31no—
504C2×C3×C4—41no—
505C2×C3×C4—41no—
506C2×C3×C4—41no—
507C2×C3×C4—41no—
508C2×C3×C4—61no—
509C2×C3×C4—61no—
510C2×C3×C4—61no—
511C2×C3×C4—121no—
512C2×C3×C4D3×D411yescharacteristic
513C2×C3×C4C2×#6711yescharacteristic
514C2×C3×C4C23×D311yescharacteristic
515C2×C3×C4C23×D311yescharacteristic
516#67—42no—
517#67—122no—
518#67—122no—
519#67—122no—
520#67—122no—
521#67—242no—
522C2×Dic3—21no—
523C2×Dic3—21no—
524C2×Dic3—21no—
525C2×Dic3—41no—
526C2×Dic3—61no—
527C2×Dic3—61no—
528C2×Dic3—121no—
529C2×Dic3—122no—
530C2×Dic3#21514yescomplemented
531C2×Dic3C2×#6711yescharacteristic
532C2×Dic3C2×#6711yescharacteristic
533C2×Dic3C2×#6711yescharacteristic
534C2×Dic3C2×#6711yescharacteristic
535D12—21no—
536D12—21no—
537D12—61no—
538D12—61no—
539D12—61no—
540D12—61no—
541D12—121no—
542D12—121no—
543D12—122no—
544D12—122no—
545C4×D3—122no—
546C4×D3—122no—
547C4×D3—122no—
548Dic6—21no—
549Dic6—21no—
550Dic6—42no—
551Dic6—122no—
552Dic6—122no—
553C3×C8—61no—
554C3×C8—61no—
555C3⋊C8—21no—
556C3⋊C8—21no—
557C3⋊C8—62no—
558C3⋊C8—61no—
559C3⋊C8—61no—
560C3⋊C8—61no—
561C3⋊C8—61no—
562C3⋊C8—121no—
563C2×C32—22no—
564C2×C32#53711yescharacteristic
565C2×C32C22×SD1611yescharacteristic
566C2×C32#57511yescharacteristic
567C3⋊D3—81no—
568C3×D3—81no—
569#41—364no—
570C2×Q8—31no—
571C2×Q8—61no—
572C2×Q8—181no—
573C2×Q8C2×D3211yescharacteristic
574C2×D4—31no—
575C2×D4—61no—
576C2×D4—91no—
577C2×D4—181no—
578C2×D4—181no—
579C2×D4—181no—
580C22×C4—31no—
581C22×C4—31no—
582C22×C4—181no—
583C22×C4—181no—
584C22×C4C2×D3211yescharacteristic
585SD16—121no—
586SD16—361no—
587SD16—361no—
588SD16—361no—
589C2×C8—31no—
590C2×C8—31no—
591C2×C8—91no—
592C2×C8—91no—
593C2×C8—121no—
594C2×C8—361no—
595C4⋊C4—21no—
596C4⋊C4—31no—
597C4⋊C4—31no—
598C4⋊C4—61no—
599C4⋊C4—61no—
600C4⋊C4—61no—
601C4⋊C4—61no—
602C4⋊C4—61no—
603C4⋊C4—61no—
604C4⋊C4—91no—
605C4⋊C4—181no—
606C4⋊C4C2×D3211yescharacteristic
607C22⋊C4—21no—
608C22⋊C4—61no—
609C22⋊C4—61no—
610C22⋊C4—181no—
611C22⋊C4—181no—
612C22⋊C4—181no—
613C42—31no—
614C42—31no—
615C42—31no—
616C42—31no—
617C42—61no—
618C42—61no—
619C22×C3—21no—
620C22×C3—21no—
621C22×C3—21no—
622C22×C3—21no—
623C22×C3—21no—
624C22×C3—22no—
625C22×C3—41no—
626C22×C3—41no—
627C22×C3—121no—
628C22×C3—121no—
629C22×C3—121no—
630C22×C3D3×SD1612yes—
631C22×C3C2×#21512yes—
632C22×C3C2×D3×D411yescharacteristic
633C22×C3C22×#6711yescharacteristic
634C2×D3—41no—
635C2×D3—41no—
636C2×D3—41no—
637C2×D3—121no—
638C2×D3—121no—
639C2×D3—121no—
640C2×D3—121no—
641C2×D3—121no—
642C2×D3—121no—
643C2×D3—241no—
644C2×D3—241no—
645C2×D3—241no—
646C3×C4—21no—
647C3×C4—21no—
648C3×C4—21no—
649C3×C4—21no—
650C3×C4—32no—
651C3×C4—32no—
652C3×C4—41no—
653C3×C4—41no—
654C3×C4—41no—
655C3×C4—41no—
656C3×C4—41no—
657C3×C4—61no—
658C3×C4—61no—
659C3×C4—81no—
660C3×C4—81no—
661C3×C4—121no—
662C3×C4—121no—
663C3×C4—121no—
664C3×C4#100411yescharacteristic
665C3×C4#100911yescharacteristic
666C3×C4#101011yescharacteristic
667C3×C4#101011yescharacteristic
668Dic3—21no—
669Dic3—21no—
670Dic3—41no—
671Dic3—41no—
672Dic3—41no—
673Dic3—121no—
674Dic3—121no—
675Dic3—241no—
676Dic3C2×#21512yes—
677Dic3C2×#21512yes—
678C32#324611yescharacteristic, complemented, Sylow
679C23—61no—
680C23—181no—
681C23D3×#6711yescharacteristic
682Q8—21no—
683Q8—21no—
684Q8—61no—
685Q8—61no—
686Q8—122no—
687Q8—362no—
688D4—61no—
689D4—61no—
690D4—122no—
691D4—181no—
692D4—181no—
693D4—362no—
694D4—362no—
695D4—362no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—31no—
701C2×C4—31no—
702C2×C4—34no—
703C2×C4—31no—
704C2×C4—31no—
705C2×C4—61no—
706C2×C4—61no—
707C2×C4—61no—
708C2×C4—121no—
709C2×C4—181no—
710C2×C4—362no—
711C2×C4—362no—
712C2×C4D3×#6711yescharacteristic
713C2×C4C22×D3211yescharacteristic
714C8—61no—
715C8—61no—
716C8—181no—
717C8—181no—
718C2×C3—22no—
719C2×C3—22no—
720C2×C3—21no—
721C2×C3—21no—
722C2×C3—21no—
723C2×C3—42no—
724C2×C3—241no—
725C2×C3#559711yescharacteristic
726C2×C3C2×D3×SD1611yescharacteristic
727C2×C3#576811yescharacteristic
728C2×C3C22×#21511yescharacteristic
729C2×C3#582211yescharacteristic
730C2×C3#583311yescharacteristic
731D3—81no—
732D3—241no—
733D3—241no—
734D3—481no—
735C22—21no—
736C22—21no—
737C22—121no—
738C22—121no—
739C22—121no—
740C22—361no—
741C22—361no—
742C22—361no—
743C22D3×#21512yes—
744C22C2×D3×#6711yescharacteristic
745C4—21no—
746C4—32no—
747C4—32no—
748C4—41no—
749C4—41no—
750C4—61no—
751C4—61no—
752C4—121no—
753C4—121no—
754C4—121no—
755C4—361no—
756C4#6430911yescharacteristic
757C4#6431411yescharacteristic
758C3—21no—
759C3#8064011yescharacteristic, complemented
760C3#8336311yescharacteristic, complemented
761C2—22no—
762C2—241no—
763C2—721no—
764C2#1059515611yescharacteristic
765C2C2×D3×#21511yescharacteristic
766C2#1059545311yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊Q8C22
socleC22×C32C22×D4
prime radical#10594910C2
hypercenterC22⋊Q8D32
hypocenterC32#3246
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C3×#5622C2semidirect
3. #10592747C2semidirect
4. C3×#5048C2semidirect
5. #10591617C2semidirect
6. #10591565C2semidirect
7. #10591564C2semidirect
8. #10591544C2semidirect
9. #10591179C2semidirect
10. #10591177C2semidirect
11. C2×Dic3⋊(C3⋊C8)C2semidirect
12. #10590556C2semidirect
13. #10590549C2semidirect
14. #10590466C2semidirect
15. #10590465C2semidirect
62. #5622D3semidirect
79. #5048D3semidirect
256. C2×C3×Dic3SD16semidirect
530. C2×Dic3#215semidirect
678. C32#3246semidirect
759. C3#80640semidirect
760. C3#83363semidirect

Maximal subgroups

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

subgroupindex
C3×#56222
#105949102
#105927472
C3×#50482
#105916172
#105915652
#105915642
#105915442
#105911792
#105911772
C2×Dic3⋊(C3⋊C8)2
#105905562
#105905492
#105904662
#105904652
#833633
#806403