Finite Group Databasebeta

← #11887528

Subgroups — #11887528

Order 1152.

902 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594906C211yesmaximal, characteristic
2Dic6×#67C211yesmaximal, characteristic, complemented
3#10592813C211yesmaximal, characteristic, complemented
4C3×C8×#67C211yesmaximal, characteristic, complemented
5C2×C3×#816C211yesmaximal, characteristic, complemented
6#10591174C211yesmaximal, characteristic, complemented
7#10591124C211yesmaximal, characteristic, complemented
8#10590951C211yesmaximal, characteristic, complemented
9#10590890C211yesmaximal, characteristic, complemented
10#10590847C211yesmaximal, characteristic, complemented
11#10590803C211yesmaximal, characteristic, complemented
12#10590792C211yesmaximal, characteristic, complemented
13#10590760C211yesmaximal, characteristic, complemented
14#10590675C211yesmaximal, characteristic, complemented
15D3×#816C211yesmaximal, characteristic, complemented
16#79447—31nomaximal
17#78805—31nomaximal
18C22×C3×Dic6C2211yescharacteristic
19C2×#3804—21no—
20C2×D3×Dic6C2211yescharacteristic
21C22×C32×C8C2211yescharacteristic
22#64139C2211yescharacteristic
23#64133C2211yescharacteristic
24C2×#3744C2211yescharacteristic
25C3×C4×#67C2211yescharacteristic
26C2×C3×C4⋊Dic3C2211yescharacteristic
27C2×C3×D3×C8C2211yescharacteristic
28Dic3×#67—21no—
29#63966—21no—
30#63964—21no—
31#63918C2211yescharacteristic
32#63909C2211yescharacteristic
33#63895—21no—
34#63894C2211yescharacteristic
35#63890—21no—
36D3×C4⋊Dic3C2211yescharacteristic
37#63887—21no—
38#63866C2211yescharacteristic
39#63856C2211yescharacteristic
40Dic3×Dic6C2211yescharacteristic
41#63839—21no—
42C2×#3717C2211yescharacteristic
43C2×#3717C2211yescharacteristic
44#63648C2211yescharacteristic
45#63644C2211yescharacteristic
46#63643C2211yescharacteristic
47C3×#830C2211yescharacteristic
48C3×(C2×D3)⋊C8C2211yescharacteristic
49C3×#816C2211yescharacteristic
50C3×#816C2211yescharacteristic
51C3×#816C2211yescharacteristic
52C3×#816C2211yescharacteristic
53C3×Dic3⋊C8C2211yescharacteristic
54C3×C8×Dic3C2211yescharacteristic
55#63573C2211yescharacteristic
56#63573C2211yescharacteristic
57#63567C2211yescharacteristic
58#63567C2211yescharacteristic
59#63566C2211yescharacteristic
60#63566C2211yescharacteristic
61Q8×#67—31no—
62#5555—31no—
63D4×Dic6—31no—
64#5507—31no—
65C3×C8×D4—31no—
66C2×C3×#103—31no—
67#5227—31no—
68#5114—31no—
69#5114—31no—
70#5114—31no—
71#5114—61no—
72C8×#67D311yescharacteristic, complemented
73C2×#816—31no—
74C2×#816D311yescharacteristic, complemented
75#4971—31no—
76#4851—31no—
77#4841—31no—
78#4818—31no—
79#4807—31no—
80#4806—31no—
81#4805—31no—
82D3×#103—31no—
83#4792—31no—
84#4791—31no—
85#4788—31no—
86#4738—31no—
87#4738—31no—
88#4721—31no—
89#4721—31no—
90C4×#204—31no—
91#4681—31no—
92C22×C32×C4C2311yescharacteristic
93C2×#638—21no—
94C2×C4⋊(C3⋊D3)C2311yescharacteristic
95C2×#634C2311yescharacteristic
96C2×C3×#67D411yescharacteristic
97C22×C3×Dic3—21no—
98C22×C3×Dic3—21no—
99C2×C3×C4×D3C2311yescharacteristic
100C2×C3×Dic6—22no—
101C2×C3×Dic6—21no—
102C2×C3×Dic6—41no—
103C2×C3×Dic6C2311yescharacteristic
104C2×C3×Dic6C2311yescharacteristic
105C2×#627—21no—
106C2×#627—21no—
107C2×#626—21no—
108C2×#624—21no—
109#3804—44no—
110C2×D3×Dic3—21no—
111C2×D3×Dic3—21no—
112D3×Dic6—22no—
113D3×Dic6—41no—
114C2×C32×C8—41no—
115C2×C32×C8C2311yescharacteristic
116C2×C32×C8C2311yescharacteristic
117#3757—21no—
118#3752—21no—
119C4⋊(C3⋊Dic3)C2311yescharacteristic
120C4⋊(C3⋊Dic3)C2311yescharacteristic
121#3750—21no—
122#3744—41no—
123C3×#217D411yescharacteristic
124C3×(C2×D3)⋊C4D411yescharacteristic
125C3×C4⋊Dic3—21no—
126C3×C4⋊Dic3C2311yescharacteristic
127C3×C4⋊Dic3C2311yescharacteristic
128C3×Dic3⋊C4D411yescharacteristic
129C3×C4×Dic3C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131C2×C3×C3⋊C8C2311yescharacteristic
132C3×D3×C8—41no—
133#3724—21no—
134Dic3⋊Dic3—21no—
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3—21no—
137Dic3⋊Dic3—21no—
138Dic3⋊Dic3—21no—
139#3722—21no—
140#3722—21no—
141(C2×D3)⋊Dic3—21no—
142Dic32—21no—
143#3717—22no—
144#3717—41no—
145#3298—91noSylow
146C22×C3×Q8—31no—
147C2×D3×Q8—31no—
148C2×#237—61no—
149C2×#235—61no—
150C22×Dic6—31no—
151C22×Dic6C2×D311yescharacteristic
152C22×C3×C8—21no—
153C22×C3×C8—31no—
154C22×C3×C8C2×D311yescharacteristic
155C22×C3×C8C2×D311yescharacteristic
156C3×C4×D4—31no—
157C2×C3×C4⋊C4—31no—
158#946—31no—
159#946—61no—
160Q8×Dic3—31no—
161#944—31no—
162#944—61no—
163C2×#215—31no—
164C2×#215—31no—
165D4×Dic3—61no—
166#930—31no—
167#930—31no—
168#930—31no—
169#930—61no—
170#929—61no—
171C4×#67—61no—
172C4×#67C2×D311yescharacteristic
173C2×C4⋊Dic3—31no—
174C2×C4⋊Dic3C2×D311yescharacteristic
175#924—31no—
176#924—31no—
177#924—31no—
178#924—61no—
179#924—61no—
180C2×#204—31no—
181C2×#204—31no—
182C2×#204—31no—
183C2×#204—31no—
184C2×#204—61no—
185C2×D3×C8C2×D311yescharacteristic
186#897—61no—
187#896—61no—
188#895—31no—
189#894—61no—
190#893—31no—
191D3×C4⋊C4—31no—
192#888—31no—
193#888—61no—
194#886—61no—
195#886—61no—
196#878—61no—
197#878—61no—
198C4×D12—31no—
199#869—31no—
200#869—31no—
201C4×Dic6—31no—
202C3×C4⋊C8—31no—
203C3×#103—31no—
204C3×#103—31no—
205C3×#103—31no—
206C3×#103—31no—
207C3×C22⋊C8—31no—
208C3×C22⋊C8—31no—
209C3×C4×C8—31no—
210#835—31no—
211#835—31no—
212#830C2×D311yescharacteristic
213#821—31no—
214#821—31no—
215#821—61no—
216(C2×D3)⋊C8C2×D311yescharacteristic
217#817—31no—
218#817—31no—
219#817—31no—
220#817—31no—
221#817—61no—
222#816—31no—
223#816—31no—
224#816—31no—
225#816—31no—
226#816—31no—
227#816—31no—
228#816—61no—
229#816C2×D311yescharacteristic
230#816C2×D311yescharacteristic
231#816C2×D311yescharacteristic
232#816C2×D311yescharacteristic
233Dic3⋊C8C2×D311yescharacteristic
234C8×Dic3C2×D311yescharacteristic
235#810—31no—
236#810—31no—
237#808—31no—
238#808—31no—
239C23×C32C2×D411yescharacteristic
240C22×C3⋊D3—21no—
241C22×C3×D3C2×D411yescharacteristic
242C2×C32×C4—21no—
243C2×C32×C4—21no—
244C2×C32×C4C2×D411yescharacteristic
245C2×C32×C4C2411yescharacteristic
246#638—42no—
247C2×C3⋊Dic3—21no—
248C2×C3⋊Dic3—21no—
249C2×C3⋊Dic3—21no—
250C4⋊(C3⋊D3)—21no—
251C4⋊(C3⋊D3)—21no—
252#634—21no—
253#634—21no—
254C3×#67SD1614yescomplemented
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—42no—
260C2×C3×Dic3—42no—
261C2×C3×Dic3C2×D411yescharacteristic
262C2×C3×Dic3C2×D411yescharacteristic
263C2×C3×Dic3C2×D411yescharacteristic
264C3×C4×D3—21no—
265C3×C4×D3—21no—
266C3×Dic6—21no—
267C3×Dic6—21no—
268C3×Dic6—21no—
269C3×Dic6—42no—
270C3×Dic6#4112yescomplemented
271#627—42no—
272#627—42no—
273#626—42no—
274#624—42no—
275D3×Dic3—42no—
276D3×Dic3—42no—
277C32×C8—21no—
278C32×C8—21no—
279C3×C3⋊C8—21no—
280C3×C3⋊C8—21no—
281D4×Q8—91no—
282#547—91no—
283#487—91no—
284#483—91no—
285#483—91no—
286#475—91no—
287#465—91no—
288#465—91no—
289#461—91no—
290#448—91no—
291#448—91no—
292C4×SD16—91no—
293C8×D4—31no—
294C2×#103—31no—
295C2×#103—91no—
296C2×C3×Q8—31no—
297C2×C3×Q8—31no—
298C2×C3×Q8—62no—
299C2×C3×Q8—61no—
300C2×C3×Q8—121no—
301C2×C3×D4—31no—
302C22×C3×C4—21no—
303C22×C3×C4—31no—
304C22×C3×C4—61no—
305C22×C3×C4—61no—
306C22×C3×C4C22×D311yescharacteristic
307C22×C3×C4C22×D311yescharacteristic
308C2×#67—61no—
309C2×#67—61no—
310C2×#67—61no—
311C2×#67—121no—
312C2×#67D1211yescharacteristic
313C22×Dic3—21no—
314C22×Dic3—21no—
315C22×Dic3—61no—
316C22×Dic3—61no—
317D3×Q8—62no—
318D3×Q8—121no—
319#237—124no—
320#235—124no—
321C2×D12—31no—
322C2×D12—31no—
323C2×D12—61no—
324C2×D12—61no—
325C2×C4×D3—61no—
326C2×C4×D3—61no—
327C2×C4×D3—61no—
328C2×C4×D3—61no—
329C2×C4×D3C22×D311yescharacteristic
330C2×Dic6—22no—
331C2×Dic6—21no—
332C2×Dic6—31no—
333C2×Dic6—31no—
334C2×Dic6—41no—
335C2×Dic6—61no—
336C2×Dic6—62no—
337C2×Dic6—61no—
338C2×Dic6—61no—
339C2×Dic6—61no—
340C2×Dic6—61no—
341C2×Dic6—121no—
342C2×Dic6C22×D311yescharacteristic
343C2×Dic6C22×D311yescharacteristic
344C2×C3×C8—21no—
345C2×C3×C8—21no—
346C2×C3×C8—31no—
347C2×C3×C8—31no—
348C2×C3×C8—41no—
349C2×C3×C8—41no—
350C2×C3×C8—42no—
351C2×C3×C8—121no—
352C2×C3×C8C22×D311yescharacteristic
353C2×C3×C8C22×D311yescharacteristic
354C2×C3×C8C22×D311yescharacteristic
355C2×C3×C8C22×D311yescharacteristic
356C3×C4⋊C4—31no—
357C3×C4⋊C4—31no—
358C3×C4⋊C4—31no—
359C3×C4⋊C4—61no—
360C3×C22⋊C4—31no—
361C3×C22⋊C4—31no—
362C3×C42—31no—
363#217—61no—
364#217—61no—
365#217—61no—
366#217—121no—
367#217D1211yescharacteristic
368#215—62no—
369#215—121no—
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—61no—
376(C2×D3)⋊C4—61no—
377(C2×D3)⋊C4—121no—
378(C2×D3)⋊C4D1211yescharacteristic
379C4⋊Dic3—21no—
380C4⋊Dic3—31no—
381C4⋊Dic3—31no—
382C4⋊Dic3—31no—
383C4⋊Dic3—31no—
384C4⋊Dic3—61no—
385C4⋊Dic3—61no—
386C4⋊Dic3—61no—
387C4⋊Dic3—61no—
388C4⋊Dic3—61no—
389C4⋊Dic3—61no—
390C4⋊Dic3—61no—
391C4⋊Dic3C22×D311yescharacteristic
392C4⋊Dic3C22×D311yescharacteristic
393Dic3⋊C4—61no—
394Dic3⋊C4—61no—
395Dic3⋊C4—61no—
396Dic3⋊C4—61no—
397Dic3⋊C4—61no—
398Dic3⋊C4—61no—
399Dic3⋊C4—61no—
400Dic3⋊C4—61no—
401Dic3⋊C4—61no—
402Dic3⋊C4—121no—
403Dic3⋊C4D1211yescharacteristic
404C4×Dic3—61no—
405C4×Dic3—61no—
406C4×Dic3C22×D311yescharacteristic
407C2×C3⋊C8C22×D311yescharacteristic
408C2×C3⋊C8C22×D311yescharacteristic
409#204—62no—
410#204—121no—
411#204—121no—
412#204—122no—
413#204—121no—
414D3×C8—41no—
415C22×C32—21no—
416C22×C32—21no—
417C22×C32C2×SD1612yes—
418C22×C32C22×D411yescharacteristic
419C2×C3⋊D3—41no—
420C2×C3⋊D3—41no—
421C2×C3⋊D3—41no—
422C2×C3×D3—21no—
423C2×C3×D3—21no—
424C2×C3×D3C2×SD1612yes—
425C32×C4—21no—
426C32×C4C2×#4111yescharacteristic
427C32×C4H(5,𝔽2)11yescharacteristic
428C3⋊Dic3—41no—
429C3⋊Dic3—41no—
430C3⋊Dic3—41no—
431C3×Dic3—22no—
432C3×Dic3—21no—
433C3×Dic3—21no—
434C3×Dic3—41no—
435C3×Dic3—41no—
436C3×Dic3—41no—
437C3×Dic3C2×SD1612yes—
438C2×#41—181no—
439C22×Q8—31no—
440C22×Q8—91no—
441C2×SD16—91no—
442C2×SD16—91no—
443C2×SD16—91no—
444C22×C8—31no—
445C22×C8D3211yescharacteristic
446C4⋊Q8—91no—
447C4⋊Q8—91no—
448C4⋊Q8—181no—
449#123—181no—
450#123—181no—
451C22⋊Q8—91no—
452C22⋊Q8—91no—
453C22⋊Q8—181no—
454C22⋊Q8—181no—
455C22⋊Q8—181no—
456#121—91no—
457#121—91no—
458C4×Q8—91no—
459C4×D4—31no—
460C4×D4—91no—
461C4×D4—181no—
462C2×C4⋊C4—31no—
463C2×C4⋊C4—91no—
464#106—91no—
465#106—91no—
466#106—91no—
467C4⋊C8—31no—
468#103—31no—
469#103—31no—
470#103—31no—
471#103—31no—
472#103—91no—
473#103—91no—
474#103—91no—
475#103—91no—
476#103—91no—
477#102—91no—
478C22⋊C8—31no—
479C22⋊C8—31no—
480C4×C8—31no—
481C23×C3—21no—
482C23×C3—31no—
483C23×C3C2×D1211yescharacteristic
484C23×C3D3×D411yescharacteristic
485C22×D3—61no—
486C22×D3—61no—
487C22×D3—121no—
488C22×D3C2×D1211yescharacteristic
489C3×Q8—32no—
490C3×Q8—61no—
491C3×Q8—61no—
492C3×Q8—61no—
493C3×Q8—122no—
494C3×D4—34no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—31no—
502C2×C3×C4—31no—
503C2×C3×C4—31no—
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—122no—
513C2×C3×C4—122no—
514C2×C3×C4C2×D1211yescharacteristic
515C2×C3×C4D3×D411yescharacteristic
516C2×C3×C4C23×D311yescharacteristic
517C2×C3×C4C23×D311yescharacteristic
518#67—122no—
519#67—122no—
520#67—122no—
521#67—242no—
522#67#20414yescomplemented
523C2×Dic3—21no—
524C2×Dic3—21no—
525C2×Dic3—21no—
526C2×Dic3—21no—
527C2×Dic3—42no—
528C2×Dic3—42no—
529C2×Dic3—61no—
530C2×Dic3—61no—
531C2×Dic3—61no—
532C2×Dic3—61no—
533C2×Dic3—61no—
534C2×Dic3—61no—
535C2×Dic3—121no—
536C2×Dic3—121no—
537C2×Dic3—121no—
538C2×Dic3—122no—
539C2×Dic3—122no—
540C2×Dic3C2×D1211yescharacteristic
541C2×Dic3C2×D1211yescharacteristic
542C2×Dic3C2×D1211yescharacteristic
543D12—61no—
544D12—61no—
545D12—61no—
546D12—61no—
547D12—121no—
548D12—121no—
549D12—122no—
550C4×D3—21no—
551C4×D3—21no—
552C4×D3—122no—
553C4×D3—122no—
554C4×D3—122no—
555C4×D3—122no—
556Dic6—21no—
557Dic6—21no—
558Dic6—21no—
559Dic6—42no—
560Dic6—61no—
561Dic6—61no—
562Dic6—61no—
563Dic6—61no—
564Dic6—121no—
565Dic6—121no—
566Dic6—122no—
567Dic6—122no—
568Dic6—122no—
569Dic6—122no—
570Dic6#23512yescomplemented
571C3×C8—22no—
572C3×C8—21no—
573C3×C8—21no—
574C3×C8—21no—
575C3×C8—21no—
576C3×C8—41no—
577C3×C8—61no—
578C3×C8—61no—
579C3⋊C8—21no—
580C3⋊C8—21no—
581C2×C32—22no—
582C2×C32#54611yescharacteristic
583C2×C32C22×SD1611yescharacteristic
584C2×C32#57811yescharacteristic
585C3⋊D3—81no—
586C3×D3—22no—
587#41—364no—
588C2×Q8—31no—
589C2×Q8—31no—
590C2×Q8—62no—
591C2×Q8—61no—
592C2×Q8—91no—
593C2×Q8—121no—
594C2×Q8—181no—
595C2×Q8—181no—
596C2×Q8—182no—
597C2×Q8—361no—
598C2×D4—31no—
599C2×D4—91no—
600C2×D4—181no—
601C2×D4—181no—
602C22×C4—31no—
603C22×C4—61no—
604C22×C4—61no—
605C22×C4—181no—
606C22×C4—181no—
607C22×C4—181no—
608C22×C4C2×D3211yescharacteristic
609SD16—182no—
610SD16—361no—
611SD16—361no—
612C2×C8—31no—
613C2×C8—31no—
614C2×C8—41no—
615C2×C8—121no—
616C2×C8C2×D3211yescharacteristic
617C2×C8C2×D3211yescharacteristic
618C4⋊C4—31no—
619C4⋊C4—31no—
620C4⋊C4—31no—
621C4⋊C4—61no—
622C4⋊C4—91no—
623C4⋊C4—91no—
624C4⋊C4—181no—
625C4⋊C4—181no—
626C4⋊C4—181no—
627C4⋊C4—181no—
628C4⋊C4—181no—
629C4⋊C4—181no—
630C4⋊C4—181no—
631C22⋊C4—31no—
632C22⋊C4—31no—
633C22⋊C4—181no—
634C22⋊C4—181no—
635C22⋊C4—181no—
636C22⋊C4—181no—
637C22⋊C4—181no—
638C42—31no—
639C42—181no—
640C22×C3—21no—
641C22×C3—21no—
642C22×C3—21no—
643C22×C3—21no—
644C22×C3—21no—
645C22×C3—22no—
646C22×C3—32no—
647C22×C3—41no—
648C22×C3—41no—
649C22×C3—61no—
650C22×C3—61no—
651C22×C3C2×#20412yes—
652C22×C3D3×SD1612yes—
653C22×C3C22×D1211yescharacteristic
654C22×C3C2×D3×D411yescharacteristic
655C2×D3—21no—
656C2×D3—21no—
657C2×D3—121no—
658C2×D3—121no—
659C2×D3—121no—
660C2×D3—121no—
661C2×D3—121no—
662C2×D3—121no—
663C2×D3—241no—
664C2×D3—241no—
665C2×D3—241no—
666C2×D3C2×#20412yes—
667C3×C4—21no—
668C3×C4—21no—
669C3×C4—21no—
670C3×C4—21no—
671C3×C4—32no—
672C3×C4—41no—
673C3×C4—61no—
674C3×C4—61no—
675C3×C4—62no—
676C3×C4—121no—
677C3×C4—121no—
678C3×C4—121no—
679C3×C4C2×#23511yescharacteristic
680C3×C4#100411yescharacteristic
681C3×C4#100411yescharacteristic
682C3×C4D3×#4111yescharacteristic
683Dic3—22no—
684Dic3—21no—
685Dic3—21no—
686Dic3—41no—
687Dic3—41no—
688Dic3—41no—
689Dic3—121no—
690Dic3—121no—
691Dic3—121no—
692Dic3—121no—
693Dic3—121no—
694Dic3—121no—
695Dic3—241no—
696Dic3—241no—
697Dic3—241no—
698Dic3C2×#20412yes—
699C32#329811yescharacteristic, complemented, Sylow
700C23—31no—
701C23—181no—
702C23D3×D1211yescharacteristic
703Q8—32no—
704Q8—61no—
705Q8—61no—
706Q8—61no—
707Q8—122no—
708Q8—181no—
709Q8—181no—
710Q8—362no—
711Q8—362no—
712D4—34no—
713D4—181no—
714D4—181no—
715D4—362no—
716D4—362no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—31no—
720C2×C4—31no—
721C2×C4—31no—
722C2×C4—61no—
723C2×C4—61no—
724C2×C4—61no—
725C2×C4—61no—
726C2×C4—61no—
727C2×C4—61no—
728C2×C4—122no—
729C2×C4—122no—
730C2×C4—181no—
731C2×C4—181no—
732C2×C4—181no—
733C2×C4—362no—
734C2×C4—362no—
735C2×C4—362no—
736C2×C4D3×D1211yescharacteristic
737C2×C4C22×D3211yescharacteristic
738C8—21no—
739C8—21no—
740C8—61no—
741C8—61no—
742C2×C3—22no—
743C2×C3—22no—
744C2×C3—21no—
745C2×C3—21no—
746C2×C3—21no—
747C2×C3—42no—
748C2×C3—62no—
749C2×C3#549011yescharacteristic
750C2×C3#555411yescharacteristic
751C2×C3C22×#20411yescharacteristic
752C2×C3#575311yescharacteristic
753C2×C3C2×D3×SD1611yescharacteristic
754C2×C3#576611yescharacteristic
755D3—22no—
756D3—241no—
757D3—241no—
758D3—481no—
759C22—21no—
760C22—21no—
761C22—32no—
762C22—61no—
763C22—61no—
764C22—361no—
765C22—361no—
766C22—361no—
767C22D3×#20412yes—
768C22C2×D3×D1211yescharacteristic
769C4—21no—
770C4—32no—
771C4—61no—
772C4—62no—
773C4—61no—
774C4—121no—
775C4—121no—
776C4—121no—
777C4—361no—
778C4—361no—
779C4—361no—
780C4D3×#23511yescharacteristic
781C4#6433011yescharacteristic
782C3—21no—
783C3#7880511yescharacteristic, complemented
784C3#7944711yescharacteristic, complemented
785C2—22no—
786C2—62no—
787C2—721no—
788C2C2×D3×#20411yescharacteristic
789C2#1059469111yescharacteristic
790C2#1059507311yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC22×C32C22×D4
prime radical#10594906C2
hypercenterC22×C8D32
hypocenterC32#3298
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
2. Dic6×#67C2semidirect
3. #10592813C2semidirect
4. C3×C8×#67C2semidirect
5. C2×C3×#816C2semidirect
6. #10591174C2semidirect
7. #10591124C2semidirect
8. #10590951C2semidirect
9. #10590890C2semidirect
10. #10590847C2semidirect
11. #10590803C2semidirect
12. #10590792C2semidirect
13. #10590760C2semidirect
14. #10590675C2semidirect
15. D3×#816C2semidirect
72. C8×#67D3semidirect
74. C2×#816D3semidirect
254. C3×#67SD16semidirect
270. C3×Dic6#41semidirect
522. #67#204semidirect
570. Dic6#235semidirect
699. C32#3298semidirect
783. C3#78805semidirect
784. C3#79447semidirect

Maximal subgroups

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

subgroupindex
#105949062
Dic6×#672
#105928132
C3×C8×#672
C2×C3×#8162
#105911742
#105911242
#105909512
#105908902
#105908472
#105908032
#105907922
#105907602
#105906752
D3×#8162
#794473
#788053