Finite Group Databasebeta

← #11870505

Subgroups — #11870505

Order 1152.

990 conjugacy classes of subgroups.

The subgroup lattice has 791 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×#624C211yesmaximal, characteristic
2#10594397C211yesmaximal, characteristic, complemented
3#10592475C211yesmaximal, characteristic
4C3×#4761C211yesmaximal, characteristic, complemented
5C3×#4758C211yesmaximal, characteristic, complemented
6#10591489C211yesmaximal, characteristic, complemented
7#10591467C211yesmaximal, characteristic
8#10591401C211yesmaximal, characteristic, complemented
9#10590760C211yesmaximal, characteristic, complemented
10#10590758C211yesmaximal, characteristic, complemented
11#10590686C211yesmaximal, characteristic, complemented
12#10590643C211yesmaximal, characteristic, complemented
13#10590466C211yesmaximal, characteristic, complemented
14#10590458C211yesmaximal, characteristic, complemented
15#10590443C211yesmaximal, characteristic, complemented
16#81044—31nomaximal
17#79651—31nomaximal
18C2×D4×C3⋊D3C2211yescharacteristic
19C22×#624—21no—
20C2×#3754C2211yescharacteristic
21C2×#3744C2211yescharacteristic
22#64106C2211yescharacteristic
23C3×D4×Dic3C2211yescharacteristic
24C3×D4×Dic3C2211yescharacteristic
25C2×C3×#214C2211yescharacteristic
26C3×#888C2211yescharacteristic, complemented
27C3×#887C2211yescharacteristic, complemented
28#63974—21no—
29#63952—21no—
30#63952—21no—
31#63900C2211yescharacteristic
32#63894C2211yescharacteristic
33#63894C2211yescharacteristic
34#63888—21no—
35C4×#624C2211yescharacteristic
36#63871C2211yescharacteristic
37#63866C2211yescharacteristic, complemented
38#63845—21no—
39#63844C2211yescharacteristic, complemented
40Dic3×Dic6—21no—
41#63836—21no—
42C2×#3717C2211yescharacteristic
43C32×#102C2211yescharacteristic
44#63647C2211yescharacteristic
45#63636C2211yescharacteristic
46C3×#832C2211yescharacteristic
47C3×#817C2211yescharacteristic, complemented
48C3×#816C2211yescharacteristic, complemented
49C3×Dic3⋊C8C2211yescharacteristic, complemented
50C3×C8×Dic3C2211yescharacteristic, complemented
51C3×#808C2211yescharacteristic, complemented
52C3×#808C2211yescharacteristic, complemented
53#63574C2211yescharacteristic, complemented
54Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
55#63567C2211yescharacteristic, complemented
56#63567C2211yescharacteristic, complemented
57#63565C2211yescharacteristic, complemented
58#63564C2211yescharacteristic
59#63557C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic, complemented
61#5728—31no—
62#5578—31no—
63C4×D3×D4—31no—
64C4×D3×D4—31no—
65C3×#476—31no—
66C3×C4×SD16—31no—
67#5169—31no—
68#5162—31no—
69#5084—31no—
70C4×#215—31no—
71#5019—31no—
72C4×#214—31no—
73#4870—31no—
74#4862—31no—
75#4862—31no—
76#4862—31no—
77#4852—31no—
78#4852—31no—
79#4841—31no—
80#4833—31no—
81#4818—31no—
82#4805—31no—
83#4776—31no—
84#4776—31no—
85#4776—31no—
86#4776—61no—
87#4761D311yescharacteristic, complemented
88#4758—31no—
89#4758D311yescharacteristic, complemented
90C4×#204—31no—
91#4685—31no—
92C23×C3⋊D3—21no—
93C2×C32×D4C2311yescharacteristic
94C2×#638—21no—
95D4×C3⋊D3—22no—
96D4×C3⋊D3—22no—
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×C4×C3⋊D3C2311yescharacteristic
99C2×#634C2311yescharacteristic
100C22×C3×Dic3—21no—
101C22×C3×Dic3—21no—
102C2×C3×Dic6—21no—
103C2×C3×Dic6C2311yescharacteristic
104C2×#624—21no—
105C2×#624—21no—
106C2×#624—21no—
107C2×#624—44no—
108C2×#624D411yescharacteristic
109C2×#624D411yescharacteristic
110C2×C32×C8C2311yescharacteristic
111C32×C4⋊C4C2311yescharacteristic
112#3754—22no—
113#3752—21no—
114C4⋊(C3⋊Dic3)—21no—
115C2×C3⋊(C3⋊C8)C2311yescharacteristic
116#3744—22no—
117C3×#217—21no—
118C3×#217—21no—
119C3×#214—22no—
120C3×C4⋊Dic3C2311yescharacteristic
121C3×C4⋊Dic3C2311yescharacteristic
122C3×C4⋊Dic3C2311yescharacteristic
123C3×Dic3⋊C4—21no—
124C3×Dic3⋊C4—21no—
125C3×C4×Dic3—21no—
126C3×C4×Dic3C2311yescharacteristic
127C3×C4×Dic3C2311yescharacteristic
128C2×C3×C3⋊C8C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130#3724—21no—
131#3724—21no—
132Dic3⋊Dic3—21no—
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3—21no—
135#3722—21no—
136#3722—21no—
137#3722—21no—
138Dic32—21no—
139Dic32D411yescharacteristic
140Dic32D411yescharacteristic
141#3717—22no—
142#3101—91noSylow
143C2×D3×D4—31no—
144C2×D3×D4—31no—
145C2×D3×D4—61no—
146C22×C4×D3—61no—
147C22×C4×D3—61no—
148C2×C3×SD16—31no—
149C3×C4⋊Q8—31no—
150C3×C4×Q8—31no—
151C3×C4×D4—31no—
152C3×C4×D4—31no—
153#946—31no—
154#946—61no—
155Q8×Dic3—61no—
156#944—31no—
157C2×#215—31no—
158D4×Dic3C2×D311yescharacteristic
159D4×Dic3C2×D311yescharacteristic
160C2×#214—31no—
161C2×#214—31no—
162C2×#214—61no—
163C2×#214C2×D311yescharacteristic
164C4×#67—61no—
165C4×#67—61no—
166C2×#204—31no—
167C2×#204—31no—
168C2×#204—31no—
169C2×#204—61no—
170#897—31no—
171#897—31no—
172#897—31no—
173#897—61no—
174#896—61no—
175#893—31no—
176#893—31no—
177#892—61no—
178D3×C4⋊C4—31no—
179D3×C4⋊C4—31no—
180#890—61no—
181#889—61no—
182#888C2×D311yescharacteristic, complemented
183#887—31no—
184#887C2×D311yescharacteristic, complemented
185#67⋊C4—61no—
186#67⋊C4—61no—
187D3×C22⋊C4—61no—
188D3×C22⋊C4—61no—
189C4×D12—31no—
190C4×D12—31no—
191#872—61no—
192C42×D3—31no—
193C42×D3—31no—
194#869—31no—
195C4×Dic6—31no—
196C4×Dic6—61no—
197C3×#106—31no—
198C3×#106—31no—
199C3×#106—31no—
200C3×C4⋊C8—31no—
201C3×#103—31no—
202C3×#102—21no—
203C3×#102—31no—
204C3×#102C2×D311yescharacteristic
205C3×#102C2×D311yescharacteristic
206C3×C4×C8—31no—
207#835—31no—
208#832C2×D311yescharacteristic
209#821—31no—
210(C2×D3)⋊C8—31no—
211(C2×D3)⋊C8—31no—
212(C2×D3)⋊C8—31no—
213(C2×D3)⋊C8—31no—
214(C2×D3)⋊C8—61no—
215#817C2×D311yescharacteristic, complemented
216#816—31no—
217#816—31no—
218#816C2×D311yescharacteristic, complemented
219Dic3⋊C8—31no—
220Dic3⋊C8C2×D311yescharacteristic, complemented
221C8×Dic3—31no—
222C8×Dic3C2×D311yescharacteristic, complemented
223#810—31no—
224#810—31no—
225#810—31no—
226#809—31no—
227#809—31no—
228#809—31no—
229#809—61no—
230#808—31no—
231#808—31no—
232#808C2×D311yescharacteristic, complemented
233#808C2×D311yescharacteristic, complemented
234C4⋊(C3⋊C8)—31no—
235C4×C3⋊C8—31no—
236C23×C32—21no—
237C22×C3⋊D3—24no—
238C22×C3⋊D3—21no—
239C22×C3⋊D3—42no—
240C22×C3⋊D3—42no—
241C22×C3⋊D3C2×D411yescharacteristic
242C32×D4—21no—
243C32×D4#4112yes—
244C2×C32×C4—21no—
245C2×C32×C4C2411yescharacteristic
246#638—24no—
247C2×C3⋊Dic3—21no—
248C2×C3⋊Dic3C2×D411yescharacteristic
249C4⋊(C3⋊D3)—21no—
250C4⋊(C3⋊D3)#4112yes—
251C4×C3⋊D3—21no—
252C4×C3⋊D3—21no—
253#634—21no—
254#634—21no—
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
264C2×C3×Dic3C2×D411yescharacteristic
265C3×Dic6—21no—
266C3×Dic6—21no—
267C3×Dic6—42no—
268#624—41no—
269#624—42no—
270#624—42no—
271#624—42no—
272#624SD1614yescomplemented
273C32×C8—21no—
274C3⋊(C3⋊C8)—21no—
275C3×C3⋊C8—21no—
276C3×C3⋊C8—21no—
277#533—91no—
278C2×C4×D4—91no—
279#483—91no—
280#483—91no—
281#476—31no—
282#476—91no—
283#461—91no—
284#461—91no—
285#450—91no—
286#450—91no—
287C4×SD16—31no—
288C4×SD16—91no—
289C4×SD16—91no—
290C4×SD16—91no—
291#431—91no—
292C23×D3—61no—
293C23×D3—61no—
294C23×D3—121no—
295C2×C3×Q8—31no—
296C2×C3×Q8—61no—
297C2×C3×D4—21no—
298C2×C3×D4C22×D311yescharacteristic
299C2×C3×D4C22×D311yescharacteristic
300C22×C3×C4—61no—
301C22×C3×C4—61no—
302C2×#67—61no—
303C2×#67—61no—
304C2×#67—121no—
305C22×Dic3—21no—
306C22×Dic3—21no—
307D3×D4—62no—
308D3×D4—62no—
309D3×D4—62no—
310D3×D4—62no—
311D3×D4—122no—
312D3×D4—122no—
313C2×D12—31no—
314C2×D12—31no—
315C2×D12—61no—
316C2×C4×D3—31no—
317C2×C4×D3—31no—
318C2×C4×D3—31no—
319C2×C4×D3—31no—
320C2×C4×D3—31no—
321C2×C4×D3—31no—
322C2×C4×D3—61no—
323C2×C4×D3—61no—
324C2×C4×D3—61no—
325C2×C4×D3—61no—
326C2×C4×D3—61no—
327C2×C4×D3—61no—
328C2×C4×D3—61no—
329C2×C4×D3—124no—
330C2×C4×D3—124no—
331C2×Dic6—21no—
332C2×Dic6—31no—
333C2×Dic6—31no—
334C2×Dic6—61no—
335C2×Dic6C22×D311yescharacteristic
336C3×SD16—62no—
337C2×C3×C8—21no—
338C2×C3×C8—31no—
339C2×C3×C8—31no—
340C2×C3×C8C22×D311yescharacteristic
341C2×C3×C8C22×D311yescharacteristic
342C3×C4⋊C4—21no—
343C3×C4⋊C4—31no—
344C3×C4⋊C4—31no—
345C3×C4⋊C4—31no—
346C3×C4⋊C4—61no—
347C3×C4⋊C4—61no—
348C3×C4⋊C4C22×D311yescharacteristic
349C3×C4⋊C4C22×D311yescharacteristic
350C3×C22⋊C4—61no—
351C3×C22⋊C4—61no—
352C3×C42—31no—
353C3×C42—31no—
354C3×C42—61no—
355#217—21no—
356#217—21no—
357#215—62no—
358#214—22no—
359#214—62no—
360#214—62no—
361#214—122no—
362(C2×D3)⋊C4—61no—
363(C2×D3)⋊C4—61no—
364(C2×D3)⋊C4—61no—
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—61no—
372C4⋊Dic3—61no—
373C4⋊Dic3—61no—
374C4⋊Dic3—61no—
375C4⋊Dic3—61no—
376C4⋊Dic3—121no—
377C4⋊Dic3C22×D311yescharacteristic
378C4⋊Dic3C22×D311yescharacteristic
379C4⋊Dic3C22×D311yescharacteristic
380Dic3⋊C4—21no—
381Dic3⋊C4—21no—
382Dic3⋊C4—61no—
383Dic3⋊C4—61no—
384Dic3⋊C4—61no—
385Dic3⋊C4—61no—
386Dic3⋊C4—61no—
387Dic3⋊C4—61no—
388Dic3⋊C4—61no—
389C4×Dic3—21no—
390C4×Dic3—31no—
391C4×Dic3—31no—
392C4×Dic3—31no—
393C4×Dic3—31no—
394C4×Dic3—61no—
395C4×Dic3—61no—
396C4×Dic3C22×D311yescharacteristic
397C4×Dic3C22×D311yescharacteristic
398C2×C3⋊C8—31no—
399C2×C3⋊C8—31no—
400C2×C3⋊C8—61no—
401C2×C3⋊C8C22×D311yescharacteristic
402C2×C3⋊C8C22×D311yescharacteristic
403#204—62no—
404#204—62no—
405#204—62no—
406#204—122no—
407C22×C32—22no—
408C22×C32—41no—
409C22×C32—41no—
410C22×C32C22×D411yescharacteristic
411C2×C3⋊D3—21no—
412C2×C3⋊D3—21no—
413C2×C3⋊D3—22no—
414C2×C3⋊D3—48no—
415C2×C3⋊D3—41no—
416C2×C3⋊D3—41no—
417C2×C3⋊D3C2×SD1612yes—
418C32×C4—41no—
419C32×C4C2×#4111yescharacteristic
420C32×C4C2×#4111yescharacteristic
421C3⋊Dic3—21no—
422C3⋊Dic3—41no—
423C3×Dic3—21no—
424C3×Dic3—21no—
425C3×Dic3—41no—
426C3×Dic3—41no—
427C3×Dic3—41no—
428C3×Dic3—41no—
429C3×Dic3C2×SD1612yes—
430C3×Dic3C2×SD1612yes—
431C22×D4—91no—
432C23×C4—181no—
433C2×SD16—31no—
434C2×SD16—91no—
435C2×SD16—91no—
436C2×SD16—91no—
437C4⋊Q8—31no—
438C4⋊Q8—91no—
439#125—181no—
440C22⋊Q8—91no—
441C22⋊Q8—91no—
442C22⋊Q8—181no—
443C4×Q8—31no—
444C4×Q8—91no—
445C4×Q8—181no—
446C4×D4—31no—
447C4×D4—31no—
448C4×D4—91no—
449C4×D4—91no—
450C4×D4—181no—
451C4×D4—181no—
452#117—181no—
453C2×C4⋊C4—91no—
454C2×C22⋊C4—181no—
455C2×C42—91no—
456#106—31no—
457#106—31no—
458#106—31no—
459#106—91no—
460C4⋊C8—31no—
461C4⋊C8—91no—
462#103—31no—
463#103—91no—
464#103—91no—
465#103—91no—
466#102—31no—
467#102—91no—
468#102—91no—
469#102D3211yescharacteristic
470C22⋊C8—91no—
471C22⋊C8—91no—
472C4×C8—31no—
473C4×C8—91no—
474C23×C3—21no—
475C23×C3—21no—
476C23×C3—41no—
477C22×D3—31no—
478C22×D3—31no—
479C22×D3—61no—
480C22×D3—64no—
481C22×D3—64no—
482C22×D3—61no—
483C22×D3—61no—
484C22×D3—121no—
485C22×D3—124no—
486C22×D3—122no—
487C22×D3—122no—
488C22×D3—122no—
489C22×D3—122no—
490C22×D3—242no—
491C22×D3—242no—
492C3×Q8—61no—
493C3×Q8—61no—
494C3×Q8—122no—
495C3×D4—21no—
496C3×D4—21no—
497C3×D4—22no—
498C3×D4—41no—
499C3×D4#23512yes—
500C3×D4#23912yes—
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—31no—
508C2×C3×C4—41no—
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—64no—
518#67—64no—
519#67—124no—
520C2×Dic3—21no—
521C2×Dic3—21no—
522C2×Dic3—21no—
523C2×Dic3—21no—
524C2×Dic3—31no—
525C2×Dic3—31no—
526C2×Dic3—42no—
527C2×Dic3—42no—
528C2×Dic3—61no—
529C2×Dic3—61no—
530C2×Dic3—61no—
531C2×Dic3—121no—
532C2×Dic3D3×D411yescharacteristic
533C2×Dic3D3×D411yescharacteristic
534C2×Dic3D3×D411yescharacteristic
535C2×Dic3D3×D411yescharacteristic
536D12—32no—
537D12—32no—
538D12—62no—
539D12—61no—
540D12—61no—
541D12—121no—
542C4×D3—34no—
543C4×D3—34no—
544C4×D3—61no—
545C4×D3—61no—
546C4×D3—61no—
547C4×D3—61no—
548C4×D3—121no—
549C4×D3—121no—
550C4×D3—121no—
551C4×D3—121no—
552C4×D3—122no—
553C4×D3—122no—
554C4×D3—122no—
555C4×D3—122no—
556C4×D3—122no—
557C4×D3—122no—
558Dic6—21no—
559Dic6—21no—
560Dic6—42no—
561Dic6—61no—
562Dic6—61no—
563Dic6—61no—
564Dic6—61no—
565Dic6—121no—
566Dic6—121no—
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—42no—
578C2×C32#52511yescharacteristic
579C2×C32C22×SD1611yescharacteristic
580C2×C32#57511yescharacteristic
581C3⋊D3—22no—
582C3⋊D3—42no—
583C24—181no—
584C2×Q8—31no—
585C2×Q8—61no—
586C2×Q8—91no—
587C2×D4—91no—
588C2×D4—181no—
589C2×D4—182no—
590C2×D4—182no—
591C2×D4C2×D3211yescharacteristic
592C22×C4—61no—
593C22×C4—61no—
594C22×C4—91no—
595C22×C4—91no—
596C22×C4—91no—
597C22×C4—181no—
598C22×C4—181no—
599C22×C4—181no—
600C22×C4—364no—
601SD16—62no—
602SD16—182no—
603SD16—182no—
604SD16—182no—
605C2×C8—31no—
606C2×C8—31no—
607C2×C8—91no—
608C2×C8C2×D3211yescharacteristic
609C4⋊C4—31no—
610C4⋊C4—31no—
611C4⋊C4—31no—
612C4⋊C4—61no—
613C4⋊C4—61no—
614C4⋊C4—181no—
615C4⋊C4—181no—
616C4⋊C4—181no—
617C4⋊C4—181no—
618C4⋊C4—181no—
619C4⋊C4—181no—
620C4⋊C4C2×D3211yescharacteristic
621C22⋊C4—61no—
622C22⋊C4—61no—
623C22⋊C4—181no—
624C22⋊C4—181no—
625C22⋊C4—181no—
626C22⋊C4—181no—
627C42—31no—
628C42—31no—
629C42—61no—
630C42—91no—
631C42—91no—
632C42—181no—
633C22×C3—22no—
634C22×C3—22no—
635C22×C3—21no—
636C22×C3—42no—
637C22×C3—41no—
638C22×C3—41no—
639C22×C3—41no—
640C22×C3—41no—
641C22×C3—81no—
642C22×C3—81no—
643C22×C3C2×D3×D411yescharacteristic
644C22×C3C2×D3×D411yescharacteristic
645C2×D3—32no—
646C2×D3—32no—
647C2×D3—62no—
648C2×D3—61no—
649C2×D3—61no—
650C2×D3—61no—
651C2×D3—61no—
652C2×D3—62no—
653C2×D3—62no—
654C2×D3—121no—
655C2×D3—121no—
656C2×D3—122no—
657C2×D3—128no—
658C2×D3—128no—
659C2×D3—121no—
660C2×D3—121no—
661C2×D3—121no—
662C2×D3—121no—
663C2×D3—248no—
664C2×D3—241no—
665C2×D3—241no—
666C3×C4—21no—
667C3×C4—21no—
668C3×C4—32no—
669C3×C4—32no—
670C3×C4—41no—
671C3×C4—41no—
672C3×C4—61no—
673C3×C4—61no—
674C3×C4—81no—
675C3×C4—121no—
676C3×C4—121no—
677C3×C4—121no—
678C3×C4—121no—
679C3×C4C2×#23511yescharacteristic
680C3×C4C2×#23911yescharacteristic
681C3×C4D3×#4111yescharacteristic
682C3×C4D3×#4111yescharacteristic
683Dic3—21no—
684Dic3—21no—
685Dic3—41no—
686Dic3—41no—
687Dic3—41no—
688Dic3—41no—
689Dic3—61no—
690Dic3—61no—
691Dic3—121no—
692Dic3—121no—
693Dic3—121no—
694Dic3—241no—
695Dic3D3×SD1612yes—
696Dic3D3×SD1612yes—
697C32#310111yescharacteristic, complemented, Sylow
698C23—21no—
699C23—91no—
700C23—184no—
701C23—181no—
702C23—362no—
703C23—362no—
704Q8—61no—
705Q8—61no—
706Q8—122no—
707Q8—181no—
708Q8—181no—
709D4—21no—
710D4—92no—
711D4—184no—
712D4—181no—
713D4#379912yes—
714C2×C4—21no—
715C2×C4—31no—
716C2×C4—31no—
717C2×C4—31no—
718C2×C4—31no—
719C2×C4—61no—
720C2×C4—61no—
721C2×C4—61no—
722C2×C4—61no—
723C2×C4—94no—
724C2×C4—91no—
725C2×C4—122no—
726C2×C4—122no—
727C2×C4—181no—
728C2×C4—181no—
729C2×C4—181no—
730C2×C4—362no—
731C2×C4—362no—
732C2×C4—361no—
733C2×C4—362no—
734C2×C4C22×D3211yescharacteristic
735C8—21no—
736C8—61no—
737C8—61no—
738C8—181no—
739C2×C3—21no—
740C2×C3—21no—
741C2×C3—21no—
742C2×C3—42no—
743C2×C3—42no—
744C2×C3—82no—
745C2×C3#554711yescharacteristic
746C2×C3#562711yescharacteristic
747C2×C3C2×D3×SD1611yescharacteristic
748C2×C3C2×D3×SD1611yescharacteristic
749C2×C3#576811yescharacteristic
750C2×C3#577311yescharacteristic
751D3—62no—
752D3—62no—
753D3—122no—
754D3—122no—
755D3—122no—
756D3—242no—
757C22—22no—
758C22—41no—
759C22—41no—
760C22—92no—
761C22—181no—
762C22—181no—
763C22—182no—
764C22—368no—
765C22—361no—
766C22—361no—
767C22D32×D411yescharacteristic
768C4—32no—
769C4—32no—
770C4—41no—
771C4—61no—
772C4—61no—
773C4—121no—
774C4—121no—
775C4—121no—
776C4—121no—
777C4—181no—
778C4—361no—
779C4C2×#379911yescharacteristic
780C4#6431211yescharacteristic
781C3—21no—
782C3#7965111yescharacteristic, complemented
783C3#8104411yescharacteristic, complemented
784C2—42no—
785C2—182no—
786C2—362no—
787C2#1059406611yescharacteristic
788C2#1059472911yescharacteristic
789C2D32×SD1611yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
prime radicalC2×D4×C3⋊D3C22
hypercenter#102D32
hypocenterC32#3101
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
2. #10594397C2semidirect
4. C3×#4761C2semidirect
5. C3×#4758C2semidirect
6. #10591489C2semidirect
8. #10591401C2semidirect
9. #10590760C2semidirect
10. #10590758C2semidirect
11. #10590686C2semidirect
12. #10590643C2semidirect
13. #10590466C2semidirect
14. #10590458C2semidirect
15. #10590443C2semidirect
26. C3×#888C22semidirect
27. C3×#887C22semidirect
37. #63866C22semidirect
39. #63844C22semidirect
47. C3×#817C22semidirect
48. C3×#816C22semidirect
49. C3×Dic3⋊C8C22semidirect
50. C3×C8×Dic3C22semidirect
51. C3×#808C22semidirect
52. C3×#808C22semidirect
53. #63574C22semidirect
54. Dic3⋊(C3⋊C8)C22semidirect
55. #63567C22semidirect
56. #63567C22semidirect
57. #63565C22semidirect
60. Dic3×C3⋊C8C22semidirect
87. #4761D3semidirect
89. #4758D3semidirect
182. #888C2×D3semidirect
184. #887C2×D3semidirect
215. #817C2×D3semidirect
218. #816C2×D3semidirect
220. Dic3⋊C8C2×D3semidirect
222. C8×Dic3C2×D3semidirect
232. #808C2×D3semidirect
233. #808C2×D3semidirect
272. #624SD16semidirect
697. C32#3101semidirect
782. C3#79651semidirect
783. C3#81044semidirect

Maximal subgroups

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

subgroupindex
D4×#6242
#105943972
#105924752
C3×#47612
C3×#47582
#105914892
#105914672
#105914012
#105907602
#105907582
#105906862
#105906432
#105904662
#105904582
#105904432
#810443
#796513