Finite Group Databasebeta

← #11887559

Subgroups — #11887559

Order 1152.

889 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595400C211yesmaximal, characteristic, complemented
2#10594370C211yesmaximal, characteristic
3#10592491C211yesmaximal, characteristic, complemented
4C3×#4807C211yesmaximal, characteristic, complemented
5C3×D3×#103C211yesmaximal, characteristic, complemented
6#10591583C211yesmaximal, characteristic, complemented
7#10591569C211yesmaximal, characteristic, complemented
8#10591549C211yesmaximal, characteristic, complemented
9#10590825C211yesmaximal, characteristic, complemented
10#10590742C211yesmaximal, characteristic, complemented
11C8×#625C211yesmaximal, characteristic, complemented
12D3×#816C211yesmaximal, characteristic, complemented
13#10590603C211yesmaximal, characteristic, complemented
14#10590497C211yesmaximal, characteristic, complemented
15#10590426C211yesmaximal, characteristic, complemented
16#80689—31nomaximal
17#78805—31nomaximal
18C2×C3×D3×Q8C2211yescharacteristic
19C2×#3795—21no—
20C2×D3×Dic6C2211yescharacteristic
21#64153C2211yescharacteristic
22#64097C2211yescharacteristic
23C3×#946C2211yescharacteristic
24C2×C3×#215C2211yescharacteristic
25C2×C3×D3×C8C2211yescharacteristic
26C2×C3×D3×C8C2211yescharacteristic
27C3×#895C2211yescharacteristic
28C3×D3×C4⋊C4C2211yescharacteristic
29#63908C2211yescharacteristic
30#63905—21no—
31C4×#625C2211yescharacteristic
32#63898C2211yescharacteristic
33#63896—21no—
34D3×C4⋊Dic3C2211yescharacteristic
35#63887—21no—
36#63884—21no—
37#63879—21no—
38#63857C2211yescharacteristic
39#63851—21no—
40#63843C2211yescharacteristic
41#63839—21no—
42C2×#3716C2211yescharacteristic
43C2×#3715C2211yescharacteristic
44C32×#103C2211yescharacteristic
45#63662C2211yescharacteristic
46#63643C2211yescharacteristic
47C8×C3⋊Dic3C2211yescharacteristic
48#63637C2211yescharacteristic
49C3×#835C2211yescharacteristic
50C3×#821C2211yescharacteristic
51C3×#816C2211yescharacteristic
52C3×#810C2211yescharacteristic
53C3×#808C2211yescharacteristic
54#63574C2211yescharacteristic
55#63573C2211yescharacteristic
56#63572C2211yescharacteristic
57#63567C2211yescharacteristic
58#63566C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
61Q8×#67—31no—
62#5632—31no—
63#5611—31no—
64#5507—31no—
65C3×#465—31no—
66C2×C3×#103—31no—
67#5227—31no—
68#5170—31no—
69#5162—31no—
70#5114—31no—
71C8×#67—31no—
72C8×#67—31no—
73C2×#816—31no—
74#5043—31no—
75#5040—31no—
76#4971—31no—
77#4862—31no—
78#4854—31no—
79#4818—31no—
80#4807D311yescharacteristic, complemented
81#4806—31no—
82#4805—31no—
83D3×#103—31no—
84D3×#103D311yescharacteristic, complemented
85#4792—31no—
86#4792—31no—
87#4792—61no—
88#4791—31no—
89#4788—31no—
90#4778—31no—
91#4758—31no—
92C2×C32×Q8C2311yescharacteristic
93C2×#634—21no—
94C2×#634C2311yescharacteristic
95C3×D3×Q8—22no—
96C3×D3×Q8—41no—
97C2×C3×D12—21no—
98C2×C3×D12C2311yescharacteristic
99C2×C3×C4×D3—21no—
100C2×C3×C4×D3—21no—
101C2×C3×C4×D3C2311yescharacteristic
102C2×C3×C4×D3C2311yescharacteristic
103C2×C3×Dic6—21no—
104C2×C3×Dic6C2311yescharacteristic
105C2×#627—21no—
106C2×#625—21no—
107C2×#625D411yescharacteristic
108C2×D3×Dic3—21no—
109C2×D3×Dic3—21no—
110C2×D3×Dic3—21no—
111#3795—44no—
112D3×Dic6—22no—
113D3×Dic6—41no—
114C2×C32×C8C2311yescharacteristic
115C32×C4⋊C4C2311yescharacteristic
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117#3750—21no—
118#3750—21no—
119#3750—21no—
120C4×C3⋊Dic3C2311yescharacteristic
121C2×C3⋊(C3⋊C8)C2311yescharacteristic
122C3×#215—41no—
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4—21no—
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×Dic3⋊C4—21no—
128C3×Dic3⋊C4—21no—
129C2×C3×C3⋊C8C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131C3×D3×C8—41no—
132C3×D3×C8—41no—
133#3724D411yescharacteristic
134Dic3⋊Dic3—21no—
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3D411yescharacteristic
141(C2×D3)⋊Dic3D411yescharacteristic
142Dic32—21no—
143#3716—41no—
144#3715—22no—
145#3298—91noSylow
146C22×C3×Q8—31no—
147C2×D3×Q8—31no—
148C2×D3×Q8C2×D311yescharacteristic
149C2×#237—61no—
150C2×#235—61no—
151C22×Dic6—31no—
152C2×C3×SD16—31no—
153C22×C3×C8—31no—
154C22×C3×C8—31no—
155C3×C22⋊Q8—31no—
156C3×#121—31no—
157C2×C3×C4⋊C4—31no—
158#946—61no—
159#946C2×D311yescharacteristic
160Q8×Dic3—31no—
161#944—31no—
162#944—31no—
163#944—61no—
164#944—61no—
165C2×#215—31no—
166C2×#215C2×D311yescharacteristic
167#938—31no—
168#935—61no—
169D4×Dic3—31no—
170C2×#214—31no—
171C2×#214—31no—
172#930—31no—
173#929—61no—
174C4×#67—31no—
175C4×#67—31no—
176C4×#67—61no—
177C2×C4⋊Dic3—31no—
178#924—31no—
179#924—61no—
180C2×#204—31no—
181C2×D3×C8C2×D311yescharacteristic
182C2×D3×C8C2×D311yescharacteristic
183#897—31no—
184#896—61no—
185#896—61no—
186#895C2×D311yescharacteristic
187#894—61no—
188#893—31no—
189D3×C4⋊C4—31no—
190D3×C4⋊C4C2×D311yescharacteristic
191#888—31no—
192#888—31no—
193#888—61no—
194#888—61no—
195#887—31no—
196#883—61no—
197#67⋊C4—61no—
198#878—61no—
199#878—61no—
200C3×#106—31no—
201C3×#103—21no—
202C3×#103—31no—
203C3×#103—31no—
204C3×#103—31no—
205C3×#103C2×D311yescharacteristic
206C3×#103C2×D311yescharacteristic
207C3×#102—31no—
208#835—31no—
209#835—31no—
210#835—31no—
211#835—61no—
212#835C2×D311yescharacteristic
213#830—31no—
214#830—31no—
215#821C2×D311yescharacteristic
216(C2×D3)⋊C8—31no—
217(C2×D3)⋊C8—31no—
218#817—31no—
219#816—31no—
220#816—31no—
221#816—31no—
222#816—31no—
223#816—61no—
224#816C2×D311yescharacteristic
225Dic3⋊C8—31no—
226Dic3⋊C8—31no—
227C8×Dic3—31no—
228C8×Dic3—31no—
229C8×Dic3—61no—
230#810—31no—
231#810—31no—
232#810—31no—
233#810—61no—
234#810C2×D311yescharacteristic
235#808—31no—
236#808—31no—
237#808—31no—
238#808C2×D311yescharacteristic
239C22×C3×D3—21no—
240C22×C3×D3C2×D411yescharacteristic
241C22×C3×D3C2×D411yescharacteristic
242C32×Q8—21no—
243C32×Q8—21no—
244C2×C32×C4—21no—
245C2×C32×C4—21no—
246C2×C32×C4C2411yescharacteristic
247C2×C3⋊Dic3—21no—
248C2×C3⋊Dic3—21no—
249C2×C3⋊Dic3C2×D411yescharacteristic
250C2×C3⋊Dic3C2×D411yescharacteristic
251#634—21no—
252#634—21no—
253#634—42no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3C2×D411yescharacteristic
258C2×C3×Dic3C2×D411yescharacteristic
259C3×D12—21no—
260C3×D12—21no—
261C3×D12—42no—
262C3×C4×D3—21no—
263C3×C4×D3—21no—
264C3×C4×D3—21no—
265C3×C4×D3—21no—
266C3×C4×D3—42no—
267C3×C4×D3—42no—
268C3×Dic6—21no—
269C3×Dic6—42no—
270C3×Dic6#4112yescomplemented
271#627—42no—
272#625—42no—
273#625SD1614yescomplemented
274D3×Dic3—42no—
275D3×Dic3—42no—
276D3×Dic3—42no—
277C32×C8—21no—
278C3⋊(C3⋊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—31no—
288#465—91no—
289#461—91no—
290#448—91no—
291#448—91no—
292C4×SD16—91no—
293C8×D4—91no—
294C2×#103—31no—
295C2×#103—91no—
296C2×C3×Q8—21no—
297C2×C3×Q8—31no—
298C2×C3×Q8—61no—
299C2×C3×Q8—62no—
300C2×C3×Q8—121no—
301C2×C3×Q8C22×D311yescharacteristic
302C2×C3×Q8C22×D311yescharacteristic
303C2×C3×D4—31no—
304C2×C3×D4—61no—
305C22×C3×C4—31no—
306C22×C3×C4—31no—
307C22×C3×C4—61no—
308C22×C3×C4—61no—
309C2×#67—31no—
310C2×#67—31no—
311C2×#67—61no—
312C2×#67—61no—
313C22×Dic3—61no—
314C22×Dic3—61no—
315C22×Dic3—61no—
316D3×Q8—22no—
317D3×Q8—41no—
318D3×Q8—62no—
319D3×Q8—121no—
320#237—124no—
321#235—124no—
322C2×D12—21no—
323C2×D12C22×D311yescharacteristic
324C2×C4×D3—21no—
325C2×C4×D3—21no—
326C2×C4×D3—61no—
327C2×C4×D3—61no—
328C2×C4×D3—61no—
329C2×C4×D3C22×D311yescharacteristic
330C2×C4×D3C22×D311yescharacteristic
331C2×Dic6—21no—
332C2×Dic6—31no—
333C2×Dic6—31no—
334C2×Dic6—61no—
335C2×Dic6—62no—
336C2×Dic6—61no—
337C2×Dic6—61no—
338C2×Dic6—61no—
339C2×Dic6—61no—
340C2×Dic6—121no—
341C2×Dic6—121no—
342C2×Dic6C22×D311yescharacteristic
343C3×SD16—121no—
344C2×C3×C8—21no—
345C2×C3×C8—31no—
346C2×C3×C8—31no—
347C2×C3×C8—121no—
348C2×C3×C8—121no—
349C2×C3×C8C22×D311yescharacteristic
350C2×C3×C8C22×D311yescharacteristic
351C3×C4⋊C4—21no—
352C3×C4⋊C4—31no—
353C3×C4⋊C4—31no—
354C3×C4⋊C4—61no—
355C3×C4⋊C4—61no—
356C3×C4⋊C4C22×D311yescharacteristic
357C3×C4⋊C4C22×D311yescharacteristic
358C3×C22⋊C4—61no—
359C3×C22⋊C4—61no—
360#217—31no—
361#217—31no—
362#217—61no—
363#217—61no—
364#217—61no—
365#215—41no—
366#215—62no—
367#214—62no—
368#214—121no—
369(C2×D3)⋊C4—21no—
370(C2×D3)⋊C4—21no—
371(C2×D3)⋊C4—31no—
372(C2×D3)⋊C4—31no—
373(C2×D3)⋊C4—61no—
374(C2×D3)⋊C4—61no—
375(C2×D3)⋊C4—61no—
376C4⋊Dic3—31no—
377C4⋊Dic3—31no—
378C4⋊Dic3—61no—
379C4⋊Dic3—61no—
380C4⋊Dic3—61no—
381C4⋊Dic3—61no—
382C4⋊Dic3C22×D311yescharacteristic
383C4⋊Dic3C22×D311yescharacteristic
384Dic3⋊C4—21no—
385Dic3⋊C4—21no—
386Dic3⋊C4—31no—
387Dic3⋊C4—31no—
388Dic3⋊C4—61no—
389Dic3⋊C4—61no—
390Dic3⋊C4—61no—
391Dic3⋊C4—61no—
392Dic3⋊C4—61no—
393Dic3⋊C4—61no—
394Dic3⋊C4—61no—
395Dic3⋊C4—61no—
396Dic3⋊C4—61no—
397Dic3⋊C4—121no—
398Dic3⋊C4—121no—
399Dic3⋊C4—121no—
400C4×Dic3—31no—
401C4×Dic3—31no—
402C4×Dic3—61no—
403C4×Dic3—61no—
404C4×Dic3—61no—
405C2×C3⋊C8—31no—
406C2×C3⋊C8—31no—
407C2×C3⋊C8—61no—
408C2×C3⋊C8C22×D311yescharacteristic
409C2×C3⋊C8C22×D311yescharacteristic
410#204—121no—
411D3×C8—41no—
412D3×C8—41no—
413C22×C32C22×D411yescharacteristic
414C2×C3×D3—21no—
415C2×C3×D3—21no—
416C2×C3×D3—21no—
417C2×C3×D3—21no—
418C2×C3×D3—41no—
419C2×C3×D3—41no—
420C2×C3×D3—41no—
421C2×C3×D3C2×SD1612yes—
422C2×C3×D3C2×SD1612yes—
423C32×C4—41no—
424C32×C4—41no—
425C32×C4C2×#4111yescharacteristic
426C32×C4H(5,𝔽2)11yescharacteristic
427C3⋊Dic3—21no—
428C3⋊Dic3—41no—
429C3⋊Dic3—41no—
430C3⋊Dic3C2×SD1612yes—
431C3×Dic3—22no—
432C3×Dic3—21no—
433C3×Dic3—21no—
434C3×Dic3—41no—
435C3×Dic3—41no—
436C2×#41—181no—
437C22×Q8—31no—
438C22×Q8—91no—
439C2×SD16—31no—
440C2×SD16—91no—
441C2×SD16—91no—
442C22×C8—31no—
443C22×C8—31no—
444C4⋊Q8—91no—
445C4⋊Q8—91no—
446C4⋊Q8—181no—
447#123—181no—
448#123—181no—
449C22⋊Q8—31no—
450C22⋊Q8—91no—
451C22⋊Q8—181no—
452C22⋊Q8—181no—
453C22⋊Q8—181no—
454#121—31no—
455#121—91no—
456C4×Q8—91no—
457C4×D4—91no—
458C4×D4—91no—
459C4×D4—181no—
460C2×C4⋊C4—31no—
461C2×C4⋊C4—91no—
462#106—31no—
463#106—91no—
464#106—91no—
465C4⋊C8—91no—
466#103—31no—
467#103—31no—
468#103—31no—
469#103—91no—
470#103—91no—
471#103—91no—
472#103—91no—
473#103—91no—
474#103D3211yescharacteristic
475#102—31no—
476C22⋊C8—91no—
477C22⋊C8—91no—
478C4×C8—91no—
479C23×C3—31no—
480C23×C3—31no—
481C23×C3—61no—
482C22×D3—21no—
483C22×D3D3×D411yescharacteristic
484C22×D3D3×D411yescharacteristic
485C3×Q8—21no—
486C3×Q8—21no—
487C3×Q8—21no—
488C3×Q8—21no—
489C3×Q8—32no—
490C3×Q8—41no—
491C3×Q8—41no—
492C3×Q8—61no—
493C3×Q8—122no—
494C3×D4—61no—
495C3×D4—61no—
496C3×D4—122no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
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—61no—
513C2×C3×C4—122no—
514C2×C3×C4—122no—
515C2×C3×C4C23×D311yescharacteristic
516C2×C3×C4C23×D311yescharacteristic
517#67—34no—
518#67—34no—
519#67—122no—
520#67—122no—
521C2×Dic3—21no—
522C2×Dic3—21no—
523C2×Dic3—21no—
524C2×Dic3—31no—
525C2×Dic3—31no—
526C2×Dic3—31no—
527C2×Dic3—31no—
528C2×Dic3—61no—
529C2×Dic3—61no—
530C2×Dic3—61no—
531C2×Dic3—61no—
532C2×Dic3—61no—
533C2×Dic3—61no—
534C2×Dic3—121no—
535C2×Dic3—121no—
536C2×Dic3—122no—
537C2×Dic3—122no—
538C2×Dic3—122no—
539C2×Dic3D3×D411yescharacteristic
540C2×Dic3D3×D411yescharacteristic
541D12—21no—
542D12—21no—
543D12—42no—
544C4×D3—21no—
545C4×D3—21no—
546C4×D3—21no—
547C4×D3—21no—
548C4×D3—42no—
549C4×D3—42no—
550C4×D3—122no—
551C4×D3—122no—
552C4×D3—122no—
553Dic6—21no—
554Dic6—42no—
555Dic6—61no—
556Dic6—61no—
557Dic6—61no—
558Dic6—61no—
559Dic6—121no—
560Dic6—121no—
561Dic6—122no—
562Dic6—122no—
563Dic6—122no—
564Dic6—122no—
565Dic6—242no—
566Dic6#23512yescomplemented
567C3×C8—21no—
568C3×C8—21no—
569C3×C8—41no—
570C3×C8—61no—
571C3×C8—61no—
572C3⋊C8—21no—
573C3⋊C8—21no—
574C3⋊C8—61no—
575C3⋊C8—61no—
576C3⋊C8—121no—
577C2×C32#54611yescharacteristic
578C2×C32C22×SD1611yescharacteristic
579C2×C32#57811yescharacteristic
580C3×D3—22no—
581C3×D3—22no—
582C3×D3—81no—
583#41—364no—
584C2×Q8—31no—
585C2×Q8—61no—
586C2×Q8—62no—
587C2×Q8—91no—
588C2×Q8—121no—
589C2×Q8—181no—
590C2×Q8—181no—
591C2×Q8—182no—
592C2×Q8—361no—
593C2×Q8C2×D3211yescharacteristic
594C2×D4—31no—
595C2×D4—61no—
596C2×D4—91no—
597C2×D4—181no—
598C22×C4—31no—
599C22×C4—31no—
600C22×C4—61no—
601C22×C4—61no—
602C22×C4—181no—
603C22×C4—181no—
604C22×C4—181no—
605SD16—121no—
606SD16—182no—
607SD16—361no—
608C2×C8—31no—
609C2×C8—31no—
610C2×C8—91no—
611C2×C8—121no—
612C2×C8—121no—
613C2×C8C2×D3211yescharacteristic
614C4⋊C4—31no—
615C4⋊C4—31no—
616C4⋊C4—61no—
617C4⋊C4—61no—
618C4⋊C4—91no—
619C4⋊C4—91no—
620C4⋊C4—181no—
621C4⋊C4—181no—
622C4⋊C4—181no—
623C4⋊C4—181no—
624C4⋊C4—181no—
625C4⋊C4—181no—
626C4⋊C4C2×D3211yescharacteristic
627C22⋊C4—61no—
628C22⋊C4—61no—
629C22⋊C4—91no—
630C22⋊C4—91no—
631C22⋊C4—181no—
632C22⋊C4—181no—
633C22⋊C4—181no—
634C42—91no—
635C42—181no—
636C22×C3—21no—
637C22×C3—32no—
638C22×C3—32no—
639C22×C3—61no—
640C22×C3—61no—
641C22×C3—61no—
642C22×C3—61no—
643C22×C3—121no—
644C22×C3—121no—
645C22×C3—121no—
646C22×C3C2×D3×D411yescharacteristic
647C22×C3C2×D3×D411yescharacteristic
648C2×D3—21no—
649C2×D3—21no—
650C2×D3—21no—
651C2×D3—21no—
652C2×D3—41no—
653C2×D3—41no—
654C2×D3—41no—
655C2×D3D3×SD1612yes—
656C2×D3D3×SD1612yes—
657C3×C4—21no—
658C3×C4—21no—
659C3×C4—41no—
660C3×C4—41no—
661C3×C4—41no—
662C3×C4—41no—
663C3×C4—61no—
664C3×C4—62no—
665C3×C4—61no—
666C3×C4—81no—
667C3×C4—81no—
668C3×C4—121no—
669C3×C4—121no—
670C3×C4C2×#23511yescharacteristic
671C3×C4#100411yescharacteristic
672C3×C4#100411yescharacteristic
673C3×C4D3×#4111yescharacteristic
674Dic3—22no—
675Dic3—21no—
676Dic3—21no—
677Dic3—32no—
678Dic3—32no—
679Dic3—41no—
680Dic3—41no—
681Dic3—62no—
682Dic3—62no—
683Dic3—61no—
684Dic3—61no—
685Dic3—121no—
686Dic3—121no—
687Dic3—121no—
688Dic3—121no—
689Dic3—241no—
690Dic3—241no—
691C32#329811yescharacteristic, complemented, Sylow
692C23—31no—
693C23—31no—
694C23—61no—
695Q8—21no—
696Q8—21no—
697Q8—32no—
698Q8—61no—
699Q8—122no—
700Q8—181no—
701Q8—181no—
702Q8—362no—
703Q8—362no—
704D4—61no—
705D4—61no—
706D4—94no—
707D4—122no—
708D4—362no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—31no—
712C2×C4—31no—
713C2×C4—61no—
714C2×C4—61no—
715C2×C4—61no—
716C2×C4—61no—
717C2×C4—61no—
718C2×C4—61no—
719C2×C4—61no—
720C2×C4—91no—
721C2×C4—91no—
722C2×C4—122no—
723C2×C4—122no—
724C2×C4—181no—
725C2×C4—181no—
726C2×C4—362no—
727C2×C4—362no—
728C2×C4—362no—
729C2×C4C22×D3211yescharacteristic
730C8—21no—
731C8—61no—
732C8—61no—
733C8—181no—
734C2×C3—21no—
735C2×C3—21no—
736C2×C3—21no—
737C2×C3—62no—
738C2×C3—62no—
739C2×C3—241no—
740C2×C3#549011yescharacteristic
741C2×C3#561011yescharacteristic
742C2×C3C2×D3×SD1611yescharacteristic
743C2×C3C2×D3×SD1611yescharacteristic
744C2×C3#576611yescharacteristic
745C2×C3#577111yescharacteristic
746D3—22no—
747D3—22no—
748D3—81no—
749C22—32no—
750C22—32no—
751C22—61no—
752C22—61no—
753C22—61no—
754C22—61no—
755C22—121no—
756C22—121no—
757C22—121no—
758C22D32×D411yescharacteristic
759C4—41no—
760C4—41no—
761C4—61no—
762C4—61no—
763C4—62no—
764C4—92no—
765C4—121no—
766C4—121no—
767C4—181no—
768C4—361no—
769C4—361no—
770C4D3×#23511yescharacteristic
771C4#6431311yescharacteristic
772C3—21no—
773C3#7880511yescharacteristic, complemented
774C3#8068911yescharacteristic, complemented
775C2—62no—
776C2—62no—
777C2—241no—
778C2#1059427311yescharacteristic
779C2D32×SD1611yescharacteristic
780C2#1059476811yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
prime radical#10594370C2
hypercenter#103D32
hypocenterC32#3298
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
1. #10595400C2semidirect
3. #10592491C2semidirect
4. C3×#4807C2semidirect
5. C3×D3×#103C2semidirect
6. #10591583C2semidirect
7. #10591569C2semidirect
8. #10591549C2semidirect
9. #10590825C2semidirect
10. #10590742C2semidirect
11. C8×#625C2semidirect
12. D3×#816C2semidirect
13. #10590603C2semidirect
14. #10590497C2semidirect
15. #10590426C2semidirect
80. #4807D3semidirect
84. D3×#103D3semidirect
270. C3×Dic6#41semidirect
273. #625SD16semidirect
566. Dic6#235semidirect
691. C32#3298semidirect
773. C3#78805semidirect
774. C3#80689semidirect

Maximal subgroups

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

subgroupindex
#105954002
#105943702
#105924912
C3×#48072
C3×D3×#1032
#105915832
#105915692
#105915492
#105908252
#105907422
C8×#6252
D3×#8162
#105906032
#105904972
#105904262
#806893
#788053