Finite Group Databasebeta

← #11887555

Subgroups — #11887555

Order 1152.

892 conjugacy classes of subgroups.

The subgroup lattice has 785 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595403C211yesmaximal, characteristic, complemented
2#10594515C211yesmaximal, characteristic
3#10592504C211yesmaximal, characteristic, complemented
4C3×#4818C211yesmaximal, characteristic, complemented
5C3×D3×#103C211yesmaximal, characteristic, complemented
6#10591623C211yesmaximal, characteristic, complemented
7#10591591C211yesmaximal, characteristic, complemented
8#10591583C211yesmaximal, characteristic, complemented
9#10590829C211yesmaximal, characteristic, complemented
10#10590824C211yesmaximal, characteristic, complemented
11#10590803C211yesmaximal, characteristic, complemented
12#10590720C211yesmaximal, characteristic, complemented
13#10590601C211yesmaximal, characteristic, complemented
14#10590516C211yesmaximal, characteristic, complemented
15#10590475C211yesmaximal, characteristic, complemented
16#80450—31nomaximal
17#78805—31nomaximal
18C2×C3×D3×Q8C2211yescharacteristic
19C2×#3798—21no—
20C2×#3797C2211yescharacteristic
21#64155C2211yescharacteristic
22C4⋊C4×C3⋊D3C2211yescharacteristic
23C3×#944C2211yescharacteristic
24C2×C3×#215C2211yescharacteristic
25C2×C3×#204C2211yescharacteristic
26C2×C3×D3×C8C2211yescharacteristic
27C3×#893C2211yescharacteristic
28C3×D3×C4⋊C4C2211yescharacteristic
29#63918C2211yescharacteristic
30#63916C2211yescharacteristic
31#63908C2211yescharacteristic
32#63905—21no—
33#63904—21no—
34C4×#626C2211yescharacteristic
35#63888—21no—
36#63856C2211yescharacteristic
37#63853—21no—
38#63851—21no—
39#63851—21no—
40Dic3×Dic6C2211yescharacteristic
41#63839—21no—
42C2×#3715C2211yescharacteristic
43C2×#3710C2211yescharacteristic
44C32×#103C2211yescharacteristic
45#63662C2211yescharacteristic
46#63647C2211yescharacteristic
47#63644C2211yescharacteristic
48#63635C2211yescharacteristic
49C3×#835C2211yescharacteristic
50C3×#816C2211yescharacteristic
51C3×Dic3⋊C8C2211yescharacteristic
52C3×#810C2211yescharacteristic
53C3×#810C2211yescharacteristic
54#63573C2211yescharacteristic
55#63566C2211yescharacteristic
56#63566C2211yescharacteristic
57#63565C2211yescharacteristic
58#63563C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61Q8×#67—31no—
62#5727—31no—
63#5551—31no—
64#5507—31no—
65C3×#461—31no—
66C2×C3×#103—31no—
67#5227—31no—
68#5171—31no—
69#5171—31no—
70#5170—31no—
71#5170—31no—
72#5114—31no—
73C8×#67—31no—
74#5079—31no—
75C4×#214—31no—
76#4971—31no—
77#4851—31no—
78#4834—31no—
79#4818D311yescharacteristic, complemented
80#4807—31no—
81#4806—31no—
82#4805—31no—
83#4805—31no—
84#4805—31no—
85#4805—61no—
86D3×#103—31no—
87D3×#103—31no—
88D3×#103D311yescharacteristic, complemented
89#4792—31no—
90#4791—31no—
91#4788—31no—
92C2×C32×Q8C2311yescharacteristic
93C2×C4×C3⋊D3—21no—
94C2×C4×C3⋊D3C2311yescharacteristic
95C3×D3×Q8—22no—
96C3×D3×Q8—41no—
97C2×C3×D12C2311yescharacteristic
98C2×C3×C4×D3—21no—
99C2×C3×C4×D3—21no—
100C2×C3×C4×D3—21no—
101C2×C3×C4×D3C2311yescharacteristic
102C2×C3×Dic6—21no—
103C2×C3×Dic6C2311yescharacteristic
104C2×C3×Dic6C2311yescharacteristic
105C2×#627—21no—
106C2×#627—21no—
107C2×#626—21no—
108C2×#626D411yescharacteristic
109C2×#625—21no—
110C2×#624—21no—
111#3798—44no—
112#3797—22no—
113#3797—41no—
114C2×C32×C8C2311yescharacteristic
115C32×C4⋊C4C2311yescharacteristic
116#3752—21no—
117C4⋊(C3⋊Dic3)C2311yescharacteristic
118C4⋊(C3⋊Dic3)C2311yescharacteristic
119#3750—21no—
120#3750—21no—
121C2×C3⋊(C3⋊C8)C2311yescharacteristic
122C3×#215—41no—
123C3×(C2×D3)⋊C4—21no—
124C3×C4⋊Dic3C2311yescharacteristic
125C3×Dic3⋊C4—21no—
126C3×Dic3⋊C4—21no—
127C3×Dic3⋊C4—21no—
128C3×C4×Dic3C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131C3×#204—41no—
132C3×D3×C8—41no—
133#3724—21no—
134Dic3⋊Dic3—21no—
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3D411yescharacteristic
137#3722D411yescharacteristic
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141(C2×D3)⋊Dic3D411yescharacteristic
142Dic32—21no—
143#3715—22no—
144#3710—41no—
145#3298—91noSylow
146C22×C3×Q8—31no—
147C2×D3×Q8—31no—
148C2×D3×Q8—31no—
149C2×D3×Q8C2×D311yescharacteristic
150C2×#235—61no—
151C2×#235—61no—
152C2×C3×SD16—31no—
153C2×C3×SD16—31no—
154C22×C3×C8—31no—
155C3×C4⋊Q8—31no—
156C3×C4×D4—31no—
157C2×C3×C4⋊C4—31no—
158#946—31no—
159#946—31no—
160#946—31no—
161#946—61no—
162#946—61no—
163Q8×Dic3—31no—
164#944—61no—
165#944C2×D311yescharacteristic
166C2×#215—31no—
167C2×#215C2×D311yescharacteristic
168#938—31no—
169#938—31no—
170C2×#214—31no—
171#930—31no—
172#929—61no—
173C4×#67—31no—
174C4×#67—61no—
175#924—31no—
176#924—61no—
177#924—61no—
178C2×#204C2×D311yescharacteristic
179C2×D3×C8—31no—
180C2×D3×C8—31no—
181C2×D3×C8C2×D311yescharacteristic
182#896—61no—
183#896—61no—
184#896—61no—
185#895—31no—
186#894—61no—
187#893—61no—
188#893C2×D311yescharacteristic
189D3×C4⋊C4—31no—
190D3×C4⋊C4—31no—
191D3×C4⋊C4—61no—
192D3×C4⋊C4C2×D311yescharacteristic
193#888—31no—
194#888—61no—
195#883—61no—
196#883—61no—
197C4×D12—31no—
198#869—31no—
199C4×Dic6—31no—
200C3×C4⋊C8—31no—
201C3×#103—21no—
202C3×#103—31no—
203C3×#103—31no—
204C3×#103—31no—
205C3×#103—31no—
206C3×#103C2×D311yescharacteristic
207C3×#103C2×D311yescharacteristic
208#835—31no—
209#835—31no—
210#835—31no—
211#835—31no—
212#835—31no—
213#835—61no—
214#835C2×D311yescharacteristic
215#832—31no—
216#830—31no—
217#821—31no—
218(C2×D3)⋊C8—31no—
219(C2×D3)⋊C8—31no—
220(C2×D3)⋊C8—31no—
221(C2×D3)⋊C8—61no—
222#817—31no—
223#817—31no—
224#817—31no—
225#817—61no—
226#816—31no—
227#816—31no—
228#816C2×D311yescharacteristic
229Dic3⋊C8C2×D311yescharacteristic
230C8×Dic3—31no—
231#810—31no—
232#810C2×D311yescharacteristic
233#810C2×D311yescharacteristic
234#808—31no—
235#808—31no—
236#808—31no—
237#808—61no—
238C4×C3⋊C8—31no—
239C22×C3⋊D3C2×D411yescharacteristic
240C22×C3×D3—21no—
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
250C4×C3⋊D3—21no—
251C4×C3⋊D3—21no—
252C4×C3⋊D3—42no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3C2×D411yescharacteristic
257C2×C3×Dic3C2×D411yescharacteristic
258C2×C3×Dic3C2×D411yescharacteristic
259C3×D12—21no—
260C3×D12—21no—
261C3×C4×D3—21no—
262C3×C4×D3—21no—
263C3×C4×D3—42no—
264C3×C4×D3—42no—
265C3×C4×D3—42no—
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#626SD1614yescomplemented
275#625—42no—
276#624—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—91no—
288#465—91no—
289#461—31no—
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—31no—
299C2×C3×Q8—61no—
300C2×C3×Q8—62no—
301C2×C3×Q8—121no—
302C2×C3×Q8C22×D311yescharacteristic
303C2×C3×Q8C22×D311yescharacteristic
304C2×C3×D4—31no—
305C22×C3×C4—31no—
306C22×C3×C4—61no—
307C22×C3×C4—61no—
308C22×C3×C4—61no—
309C2×#67—31no—
310C2×#67—61no—
311C2×#67—61no—
312C2×#67—61no—
313D3×Q8—22no—
314D3×Q8—41no—
315D3×Q8—62no—
316D3×Q8—62no—
317D3×Q8—121no—
318D3×Q8—121no—
319#235—124no—
320#235—124no—
321C2×D12—31no—
322C2×D12—61no—
323C2×D12C22×D311yescharacteristic
324C2×C4×D3—21no—
325C2×C4×D3—21no—
326C2×C4×D3—21no—
327C2×C4×D3—31no—
328C2×C4×D3—31no—
329C2×C4×D3—61no—
330C2×C4×D3—61no—
331C2×C4×D3—61no—
332C2×C4×D3—61no—
333C2×C4×D3—61no—
334C2×C4×D3—121no—
335C2×C4×D3C22×D311yescharacteristic
336C2×Dic6—21no—
337C2×Dic6—61no—
338C2×Dic6—61no—
339C2×Dic6—61no—
340C2×Dic6—61no—
341C2×Dic6C22×D311yescharacteristic
342C2×Dic6C22×D311yescharacteristic
343C3×SD16—121no—
344C3×SD16—121no—
345C2×C3×C8—21no—
346C2×C3×C8—31no—
347C2×C3×C8—31no—
348C2×C3×C8—121no—
349C2×C3×C8C22×D311yescharacteristic
350C2×C3×C8C22×D311yescharacteristic
351C3×C4⋊C4—21no—
352C3×C4⋊C4—31no—
353C3×C4⋊C4—61no—
354C3×C4⋊C4—61no—
355C3×C4⋊C4—61no—
356C3×C4⋊C4C22×D311yescharacteristic
357C3×C4⋊C4C22×D311yescharacteristic
358C3×C22⋊C4—61no—
359C3×C42—31no—
360#217—31no—
361#217—61no—
362#217—61no—
363#217—61no—
364#215—41no—
365#215—62no—
366#214—62no—
367(C2×D3)⋊C4—21no—
368(C2×D3)⋊C4—31no—
369(C2×D3)⋊C4—31no—
370(C2×D3)⋊C4—31no—
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—121no—
377C4⋊Dic3—31no—
378C4⋊Dic3—31no—
379C4⋊Dic3—31no—
380C4⋊Dic3—31no—
381C4⋊Dic3—31no—
382C4⋊Dic3—61no—
383C4⋊Dic3—61no—
384C4⋊Dic3—61no—
385C4⋊Dic3—61no—
386C4⋊Dic3C22×D311yescharacteristic
387Dic3⋊C4—21no—
388Dic3⋊C4—21no—
389Dic3⋊C4—21no—
390Dic3⋊C4—31no—
391Dic3⋊C4—61no—
392Dic3⋊C4—61no—
393Dic3⋊C4—61no—
394Dic3⋊C4—61no—
395Dic3⋊C4—61no—
396Dic3⋊C4—61no—
397Dic3⋊C4—61no—
398Dic3⋊C4—61no—
399Dic3⋊C4—121no—
400Dic3⋊C4—121no—
401C4×Dic3—61no—
402C4×Dic3—61no—
403C4×Dic3C22×D311yescharacteristic
404C2×C3⋊C8—31no—
405C2×C3⋊C8—31no—
406C2×C3⋊C8—61no—
407C2×C3⋊C8C22×D311yescharacteristic
408C2×C3⋊C8C22×D311yescharacteristic
409#204—41no—
410D3×C8—41no—
411D3×C8—121no—
412D3×C8—121no—
413C22×C32C22×D411yescharacteristic
414C2×C3⋊D3—21no—
415C2×C3⋊D3—21no—
416C2×C3⋊D3C2×SD1612yes—
417C2×C3×D3—21no—
418C2×C3×D3—21no—
419C2×C3×D3—41no—
420C2×C3×D3—41no—
421C2×C3×D3—41no—
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×Dic3—22no—
431C3×Dic3—21no—
432C3×Dic3—21no—
433C3×Dic3—41no—
434C3×Dic3—41no—
435C3×Dic3C2×SD1612yes—
436C2×#41—181no—
437C22×Q8—31no—
438C22×Q8—91no—
439C2×SD16—31no—
440C2×SD16—31no—
441C2×SD16—91no—
442C22×C8—31no—
443C22×C8—91no—
444C4⋊Q8—31no—
445C4⋊Q8—91no—
446C4⋊Q8—181no—
447#123—181no—
448#123—181no—
449C22⋊Q8—91no—
450C22⋊Q8—91no—
451C22⋊Q8—181no—
452C22⋊Q8—181no—
453C22⋊Q8—181no—
454#121—91no—
455#121—91no—
456C4×Q8—91no—
457C4×D4—31no—
458C4×D4—91no—
459C4×D4—181no—
460C2×C4⋊C4—31no—
461C2×C4⋊C4—91no—
462#106—91no—
463#106—91no—
464#106—91no—
465C4⋊C8—31no—
466#103—31no—
467#103—31no—
468#103—31no—
469#103—31no—
470#103—91no—
471#103—91no—
472#103—91no—
473#103—91no—
474#103D3211yescharacteristic
475#102—91no—
476C22⋊C8—91no—
477C22⋊C8—91no—
478C4×C8—91no—
479C23×C3—31no—
480C23×C3—61no—
481C22×D3—21no—
482C22×D3—31no—
483C22×D3—31no—
484C22×D3—61no—
485C22×D3D3×D411yescharacteristic
486C3×Q8—21no—
487C3×Q8—21no—
488C3×Q8—21no—
489C3×Q8—21no—
490C3×Q8—32no—
491C3×Q8—41no—
492C3×Q8—41no—
493C3×Q8—61no—
494C3×Q8—61no—
495C3×Q8—61no—
496C3×Q8—122no—
497C3×D4—61no—
498C3×D4—61no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—31no—
505C2×C3×C4—31no—
506C2×C3×C4—31no—
507C2×C3×C4—41no—
508C2×C3×C4—41no—
509C2×C3×C4—61no—
510C2×C3×C4—61no—
511C2×C3×C4—61no—
512C2×C3×C4—61no—
513C2×C3×C4—61no—
514C2×C3×C4—122no—
515C2×C3×C4—122no—
516C2×C3×C4—122no—
517C2×C3×C4C23×D311yescharacteristic
518C2×C3×C4C23×D311yescharacteristic
519#67—34no—
520#67—122no—
521#67—122no—
522#67—122no—
523C2×Dic3—21no—
524C2×Dic3—21no—
525C2×Dic3—21no—
526C2×Dic3—31no—
527C2×Dic3—31no—
528C2×Dic3—61no—
529C2×Dic3—61no—
530C2×Dic3—61no—
531C2×Dic3—61no—
532C2×Dic3—61no—
533C2×Dic3—121no—
534C2×Dic3—121no—
535C2×Dic3D3×D411yescharacteristic
536C2×Dic3D3×D411yescharacteristic
537C2×Dic3D3×D411yescharacteristic
538D12—21no—
539D12—21no—
540D12—34no—
541D12—122no—
542C4×D3—21no—
543C4×D3—21no—
544C4×D3—42no—
545C4×D3—42no—
546C4×D3—42no—
547C4×D3—61no—
548C4×D3—61no—
549C4×D3—61no—
550C4×D3—61no—
551C4×D3—121no—
552C4×D3—121no—
553C4×D3—122no—
554C4×D3—122no—
555C4×D3—122no—
556C4×D3—122no—
557C4×D3—242no—
558Dic6—21no—
559Dic6—21no—
560Dic6—21no—
561Dic6—42no—
562Dic6—122no—
563Dic6—122no—
564Dic6—122no—
565Dic6—122no—
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—31no—
586C2×Q8—61no—
587C2×Q8—62no—
588C2×Q8—121no—
589C2×Q8—181no—
590C2×Q8—181no—
591C2×Q8—182no—
592C2×Q8—361no—
593C2×Q8C2×D3211yescharacteristic
594C2×D4—31no—
595C2×D4—91no—
596C2×D4—181no—
597C2×D4—181no—
598C22×C4—31no—
599C22×C4—61no—
600C22×C4—61no—
601C22×C4—61no—
602C22×C4—91no—
603C22×C4—181no—
604C22×C4—181no—
605SD16—121no—
606SD16—121no—
607SD16—182no—
608C2×C8—31no—
609C2×C8—31no—
610C2×C8—91no—
611C2×C8—121no—
612C2×C8—361no—
613C2×C8C2×D3211yescharacteristic
614C4⋊C4—31no—
615C4⋊C4—61no—
616C4⋊C4—61no—
617C4⋊C4—61no—
618C4⋊C4—91no—
619C4⋊C4—91no—
620C4⋊C4—91no—
621C4⋊C4—181no—
622C4⋊C4—181no—
623C4⋊C4—181no—
624C4⋊C4—181no—
625C4⋊C4—181no—
626C4⋊C4C2×D3211yescharacteristic
627C22⋊C4—61no—
628C22⋊C4—91no—
629C22⋊C4—91no—
630C22⋊C4—181no—
631C22⋊C4—181no—
632C22⋊C4—181no—
633C22⋊C4—181no—
634C42—31no—
635C42—181no—
636C22×C3—21no—
637C22×C3—32no—
638C22×C3—61no—
639C22×C3—61no—
640C22×C3—121no—
641C22×C3—121no—
642C22×C3—121no—
643C22×C3C2×D3×D411yescharacteristic
644C22×C3C2×D3×D411yescharacteristic
645C2×D3—21no—
646C2×D3—21no—
647C2×D3—32no—
648C2×D3—32no—
649C2×D3—41no—
650C2×D3—41no—
651C2×D3—41no—
652C2×D3—62no—
653C2×D3—61no—
654C2×D3—61no—
655C2×D3—61no—
656C2×D3—61no—
657C2×D3—121no—
658C2×D3—121no—
659C2×D3D3×SD1612yes—
660C3×C4—21no—
661C3×C4—21no—
662C3×C4—32no—
663C3×C4—41no—
664C3×C4—41no—
665C3×C4—41no—
666C3×C4—41no—
667C3×C4—61no—
668C3×C4—62no—
669C3×C4—61no—
670C3×C4—81no—
671C3×C4—81no—
672C3×C4—121no—
673C3×C4—121no—
674C3×C4C2×#23511yescharacteristic
675C3×C4#100411yescharacteristic
676C3×C4#100411yescharacteristic
677C3×C4D3×#4111yescharacteristic
678Dic3—22no—
679Dic3—21no—
680Dic3—21no—
681Dic3—41no—
682Dic3—41no—
683Dic3—61no—
684Dic3—61no—
685Dic3—121no—
686Dic3—121no—
687Dic3—121no—
688Dic3—121no—
689Dic3—121no—
690Dic3—241no—
691Dic3—241no—
692Dic3D3×SD1612yes—
693C32#329811yescharacteristic, complemented, Sylow
694C23—31no—
695C23—61no—
696C23—91no—
697Q8—21no—
698Q8—21no—
699Q8—32no—
700Q8—61no—
701Q8—61no—
702Q8—61no—
703Q8—122no—
704Q8—362no—
705Q8—362no—
706D4—61no—
707D4—61no—
708D4—94no—
709D4—362no—
710D4—362no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—31no—
714C2×C4—31no—
715C2×C4—31no—
716C2×C4—61no—
717C2×C4—61no—
718C2×C4—61no—
719C2×C4—61no—
720C2×C4—61no—
721C2×C4—91no—
722C2×C4—122no—
723C2×C4—122no—
724C2×C4—122no—
725C2×C4—181no—
726C2×C4—181no—
727C2×C4—181no—
728C2×C4—181no—
729C2×C4—362no—
730C2×C4—362no—
731C2×C4C22×D3211yescharacteristic
732C8—21no—
733C8—61no—
734C8—61no—
735C8—181no—
736C2×C3—21no—
737C2×C3—21no—
738C2×C3—21no—
739C2×C3—62no—
740C2×C3—241no—
741C2×C3#549011yescharacteristic
742C2×C3#561211yescharacteristic
743C2×C3C2×D3×SD1611yescharacteristic
744C2×C3C2×D3×SD1611yescharacteristic
745C2×C3#576611yescharacteristic
746C2×C3#577911yescharacteristic
747D3—22no—
748D3—62no—
749D3—62no—
750D3—81no—
751D3—122no—
752C22—32no—
753C22—61no—
754C22—61no—
755C22—92no—
756C22—121no—
757C22—121no—
758C22—121no—
759C22—181no—
760C22—181no—
761C22D32×D411yescharacteristic
762C4—32no—
763C4—41no—
764C4—41no—
765C4—61no—
766C4—61no—
767C4—62no—
768C4—121no—
769C4—121no—
770C4—181no—
771C4—361no—
772C4—361no—
773C4D3×#23511yescharacteristic
774C4#6431311yescharacteristic
775C3—21no—
776C3#7880511yescharacteristic, complemented
777C3#8045011yescharacteristic, complemented
778C2—62no—
779C2—182no—
780C2—241no—
781C2#1059427811yescharacteristic
782C2D32×SD1611yescharacteristic
783C2#1059476611yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
prime radical#10594515C2
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. #10595403C2semidirect
3. #10592504C2semidirect
4. C3×#4818C2semidirect
5. C3×D3×#103C2semidirect
6. #10591623C2semidirect
7. #10591591C2semidirect
8. #10591583C2semidirect
9. #10590829C2semidirect
10. #10590824C2semidirect
11. #10590803C2semidirect
12. #10590720C2semidirect
13. #10590601C2semidirect
14. #10590516C2semidirect
15. #10590475C2semidirect
79. #4818D3semidirect
88. D3×#103D3semidirect
270. C3×Dic6#41semidirect
274. #626SD16semidirect
566. Dic6#235semidirect
693. C32#3298semidirect
776. C3#78805semidirect
777. C3#80450semidirect

Maximal subgroups

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

subgroupindex
#105954032
#105945152
#105925042
C3×#48182
C3×D3×#1032
#105916232
#105915912
#105915832
#105908292
#105908242
#105908032
#105907202
#105906012
#105905162
#105904752
#804503
#788053