Finite Group Databasebeta

← #11870506

Subgroups — #11870506

Order 1152.

957 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×D4×Dic3C211yesmaximal, characteristic
2#10594387C211yesmaximal, characteristic, complemented
3#10592457C211yesmaximal, characteristic, complemented
4C3×#4776C211yesmaximal, characteristic
5C3×#4761C211yesmaximal, characteristic, complemented
6#10591489C211yesmaximal, characteristic, complemented
7#10591459C211yesmaximal, characteristic
8#10591445C211yesmaximal, characteristic, complemented
9#10590775C211yesmaximal, characteristic, complemented
10#10590752C211yesmaximal, characteristic, complemented
11#10590674C211yesmaximal, characteristic, complemented
12#10590656C211yesmaximal, characteristic, complemented
13#10590465C211yesmaximal, characteristic, complemented
14#10590460C211yesmaximal, characteristic, complemented
15#10590439C211yesmaximal, characteristic, complemented
16#81044—31nomaximal
17#80132—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19C22×D3×Dic3—21no—
20D4×C3⋊Dic3C2211yescharacteristic
21C2×#3754C2211yescharacteristic
22#64096C2211yescharacteristic, complemented
23C3×D4×Dic3C2211yescharacteristic
24C2×C3×#214C2211yescharacteristic
25C2×C3×#204C2211yescharacteristic
26C3×#897C2211yescharacteristic
27C3×#888C2211yescharacteristic, complemented
28#67⋊Dic3—21no—
29Dic3×#67—21no—
30D3×#217—21no—
31#63898C2211yescharacteristic
32Dic3×D12C2211yescharacteristic
33D3×C4⋊Dic3C2211yescharacteristic
34#63887—21no—
35#63878—21no—
36C4×D3×Dic3C2211yescharacteristic
37#63866C2211yescharacteristic, complemented
38#63857C2211yescharacteristic
39#63846—21no—
40#63843—21no—
41#63843C2211yescharacteristic, complemented
42C2×#3716C2211yescharacteristic
43C32×#102C2211yescharacteristic
44#63643C2211yescharacteristic, complemented
45C8×C3⋊Dic3C2211yescharacteristic, complemented
46#63635C2211yescharacteristic, complemented
47C3×#832C2211yescharacteristic
48C3×(C2×D3)⋊C8C2211yescharacteristic
49C3×#817C2211yescharacteristic, complemented
50C3×Dic3⋊C8C2211yescharacteristic, complemented
51C3×#809C2211yescharacteristic
52C3×#808C2211yescharacteristic, complemented
53#63573C2211yescharacteristic, complemented
54Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
55#63567C2211yescharacteristic, complemented
56#63566C2211yescharacteristic, complemented
57#63565C2211yescharacteristic, complemented
58#63562C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60#63553C2211yescharacteristic, complemented
61C2×D4×Dic3—31no—
62#5728—31no—
63#5622—31no—
64C4×D3×D4—31no—
65C3×#476—31no—
66C3×#450—31no—
67#5218—31no—
68#5162—31no—
69#5162—31no—
70Dic3×SD16—31no—
71Dic3×SD16—31no—
72#5084—31no—
73#5043—31no—
74#5019—31no—
75#4862—31no—
76#4862—31no—
77#4852—31no—
78#4852—31no—
79#4841—31no—
80#4833—31no—
81#4776—31no—
82#4776D311yescharacteristic
83#4761—31no—
84#4761D311yescharacteristic, complemented
85#4758—31no—
86#4758—31no—
87#4758—31no—
88#4758—31no—
89#4758—61no—
90#4721—31no—
91#4718—31no—
92C23×C3×D3—21no—
93C2×C32×D4C2311yescharacteristic
94C22×C3⋊Dic3—21no—
95C2×#634C2311yescharacteristic
96C2×C3×#67—21no—
97C22×C3×Dic3—21no—
98C3×D3×D4—22no—
99C3×D3×D4—22no—
100C2×C3×D12C2311yescharacteristic
101C2×C3×C4×D3C2311yescharacteristic
102C2×C3×Dic6—21no—
103C2×C3×Dic6C2311yescharacteristic
104C2×D3×Dic3—21no—
105C2×D3×Dic3—21no—
106C2×D3×Dic3—21no—
107C2×D3×Dic3—44no—
108C2×D3×Dic3D411yescharacteristic
109C2×D3×Dic3D411yescharacteristic
110C2×C32×C8C2311yescharacteristic
111C32×C4⋊C4C2311yescharacteristic
112#3757—21no—
113#3754—22no—
114C4⋊(C3⋊Dic3)C2311yescharacteristic
115#3750—21no—
116C4×C3⋊Dic3—21no—
117C4×C3⋊Dic3C2311yescharacteristic
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119C3×#217—21no—
120C3×#214—22no—
121C3×(C2×D3)⋊C4—21no—
122C3×C4⋊Dic3—21no—
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×Dic3⋊C4—21no—
126C3×C4×Dic3C2311yescharacteristic
127C2×C3×C3⋊C8C2311yescharacteristic
128C2×C3×C3⋊C8C2311yescharacteristic
129C3×#204—22no—
130Dic3⋊Dic3—21no—
131Dic3⋊Dic3—21no—
132Dic3⋊Dic3—21no—
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3—21no—
135(C2×D3)⋊Dic3—21no—
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138Dic32—21no—
139Dic32D411yescharacteristic
140Dic32D411yescharacteristic
141#3716—22no—
142#3101—91noSylow
143C22×C3×D4—31no—
144C23×Dic3—61no—
145C2×D3×D4C2×D311yescharacteristic
146C22×C4×D3—61no—
147C2×C3×SD16—31no—
148C2×C3×SD16—31no—
149C3×C4⋊Q8—31no—
150C3×C22⋊Q8—31no—
151C3×C4×D4—31no—
152C2×#217—61no—
153#946—61no—
154Q8×Dic3—31no—
155Q8×Dic3—61no—
156#944—31no—
157D4×Dic3—31no—
158D4×Dic3—31no—
159D4×Dic3—31no—
160D4×Dic3—31no—
161D4×Dic3—61no—
162D4×Dic3—61no—
163D4×Dic3—61no—
164D4×Dic3C2×D311yescharacteristic
165C2×#214—31no—
166C2×#214—31no—
167C2×#214—31no—
168C2×#214—61no—
169C2×#214C2×D311yescharacteristic
170C4×#67—61no—
171C2×C4⋊Dic3—31no—
172#924—31no—
173C2×C4×Dic3—31no—
174C2×#204—31no—
175C2×#204C2×D311yescharacteristic
176#897—31no—
177#897C2×D311yescharacteristic
178#893—31no—
179#892—61no—
180D3×C4⋊C4—31no—
181#890—61no—
182#889—61no—
183#888C2×D311yescharacteristic, complemented
184#887—31no—
185#887—31no—
186#887—31no—
187#887—61no—
188#887—61no—
189#67⋊C4—61no—
190D3×C22⋊C4—61no—
191#878—61no—
192#877—61no—
193C4×D12—31no—
194C42×D3—31no—
195#869—31no—
196C3×#106—31no—
197C3×#106—31no—
198C3×C4⋊C8—31no—
199C3×#102—21no—
200C3×#102—31no—
201C3×#102—31no—
202C3×#102C2×D311yescharacteristic
203C3×#102C2×D311yescharacteristic
204C3×C22⋊C8—31no—
205#835—31no—
206#835—31no—
207#832—31no—
208#832C2×D311yescharacteristic
209#830—31no—
210(C2×D3)⋊C8—31no—
211(C2×D3)⋊C8C2×D311yescharacteristic
212#817—31no—
213#817C2×D311yescharacteristic, complemented
214#816—31no—
215#816—31no—
216#816—31no—
217#816—31no—
218#816—61no—
219Dic3⋊C8—31no—
220Dic3⋊C8C2×D311yescharacteristic, complemented
221C8×Dic3—31no—
222C8×Dic3—31no—
223C8×Dic3—31no—
224C8×Dic3—31no—
225C8×Dic3—61no—
226#810—31no—
227#810—31no—
228#809—31no—
229#809C2×D311yescharacteristic
230#808—31no—
231#808—31no—
232#808—31no—
233#808—61no—
234#808C2×D311yescharacteristic, complemented
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
246C2×C3⋊Dic3—21no—
247C2×C3⋊Dic3—21no—
248C2×C3⋊Dic3—42no—
249C2×C3⋊Dic3C2×D411yescharacteristic
250C2×C3⋊Dic3C2×D411yescharacteristic
251#634—21no—
252#634—21no—
253C3×#67—24no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—42no—
258C2×C3×Dic3C2×D411yescharacteristic
259C2×C3×Dic3C2×D411yescharacteristic
260C2×C3×Dic3C2×D411yescharacteristic
261C3×D12—21no—
262C3×D12#4112yes—
263C3×C4×D3—21no—
264C3×C4×D3—21no—
265C3×Dic6—21no—
266C3×Dic6—21no—
267C3×Dic6—42no—
268D3×Dic3—41no—
269D3×Dic3—42no—
270D3×Dic3—42no—
271D3×Dic3—42no—
272D3×Dic3SD1614yescomplemented
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—31no—
286#450—91no—
287C4×SD16—91no—
288C4×SD16—91no—
289C4×SD16—91no—
290C4×SD16—91no—
291#431—91no—
292C24×C3—61no—
293C23×D3—21no—
294C2×C3×Q8—31no—
295C2×C3×Q8—61no—
296C2×C3×D4—21no—
297C2×C3×D4—31no—
298C2×C3×D4—61no—
299C2×C3×D4—62no—
300C2×C3×D4—62no—
301C2×C3×D4C22×D311yescharacteristic
302C2×C3×D4C22×D311yescharacteristic
303C22×C3×C4—31no—
304C22×C3×C4—61no—
305C2×#67—21no—
306C22×Dic3—21no—
307C22×Dic3—31no—
308C22×Dic3—31no—
309C22×Dic3—61no—
310C22×Dic3—61no—
311C22×Dic3—61no—
312C22×Dic3—61no—
313C22×Dic3—61no—
314C22×Dic3—121no—
315C22×Dic3—124no—
316D3×D4—22no—
317D3×D4—22no—
318C2×D12C22×D311yescharacteristic
319C2×C4×D3—31no—
320C2×C4×D3—31no—
321C2×C4×D3—61no—
322C2×C4×D3—61no—
323C2×C4×D3—61no—
324C2×C4×D3—124no—
325C2×C4×D3C22×D311yescharacteristic
326C2×Dic6—21no—
327C2×Dic6—31no—
328C2×Dic6—31no—
329C2×Dic6—61no—
330C2×Dic6C22×D311yescharacteristic
331C3×SD16—62no—
332C3×SD16—62no—
333C2×C3×C8—21no—
334C2×C3×C8—31no—
335C2×C3×C8—31no—
336C2×C3×C8C22×D311yescharacteristic
337C2×C3×C8C22×D311yescharacteristic
338C3×C4⋊C4—21no—
339C3×C4⋊C4—31no—
340C3×C4⋊C4—31no—
341C3×C4⋊C4—61no—
342C3×C4⋊C4—61no—
343C3×C4⋊C4C22×D311yescharacteristic
344C3×C4⋊C4C22×D311yescharacteristic
345C3×C22⋊C4—61no—
346C3×C22⋊C4—61no—
347C3×C42—31no—
348#217—21no—
349#217—61no—
350#217—61no—
351#217—61no—
352#217—61no—
353#217—61no—
354#217—121no—
355#214—22no—
356#214—62no—
357#214—64no—
358#214—62no—
359#214—62no—
360(C2×D3)⋊C4—21no—
361(C2×D3)⋊C4—61no—
362(C2×D3)⋊C4—61no—
363(C2×D3)⋊C4—61no—
364C4⋊Dic3—21no—
365C4⋊Dic3—31no—
366C4⋊Dic3—31no—
367C4⋊Dic3—61no—
368C4⋊Dic3—61no—
369C4⋊Dic3—61no—
370C4⋊Dic3—61no—
371C4⋊Dic3—61no—
372C4⋊Dic3—61no—
373C4⋊Dic3C22×D311yescharacteristic
374C4⋊Dic3C22×D311yescharacteristic
375Dic3⋊C4—21no—
376Dic3⋊C4—61no—
377Dic3⋊C4—61no—
378Dic3⋊C4—61no—
379Dic3⋊C4—61no—
380Dic3⋊C4—61no—
381Dic3⋊C4—61no—
382Dic3⋊C4—61no—
383Dic3⋊C4—121no—
384C4×Dic3—31no—
385C4×Dic3—31no—
386C4×Dic3—31no—
387C4×Dic3—31no—
388C4×Dic3—31no—
389C4×Dic3—31no—
390C4×Dic3—61no—
391C4×Dic3—61no—
392C4×Dic3—61no—
393C4×Dic3—61no—
394C4×Dic3—61no—
395C4×Dic3—121no—
396C4×Dic3C22×D311yescharacteristic
397C2×C3⋊C8—31no—
398C2×C3⋊C8—31no—
399C2×C3⋊C8—61no—
400C2×C3⋊C8C22×D311yescharacteristic
401C2×C3⋊C8C22×D311yescharacteristic
402#204—22no—
403#204—62no—
404C22×C32—22no—
405C22×C32—41no—
406C22×C32—41no—
407C22×C32C22×D411yescharacteristic
408C2×C3×D3—21no—
409C2×C3×D3—21no—
410C2×C3×D3—22no—
411C2×C3×D3—48no—
412C2×C3×D3—41no—
413C2×C3×D3—41no—
414C2×C3×D3C2×SD1612yes—
415C32×C4—41no—
416C32×C4C2×#4111yescharacteristic
417C32×C4C2×#4111yescharacteristic
418C3⋊Dic3—21no—
419C3⋊Dic3—41no—
420C3⋊Dic3—41no—
421C3⋊Dic3C2×SD1612yes—
422C3×Dic3—21no—
423C3×Dic3—21no—
424C3×Dic3—41no—
425C3×Dic3—41no—
426C3×Dic3—41no—
427C3×Dic3C2×SD1612yes—
428C22×D4—31no—
429C23×C4—181no—
430C2×SD16—31no—
431C2×SD16—31no—
432C2×SD16—91no—
433C2×SD16—91no—
434C4⋊Q8—31no—
435C4⋊Q8—91no—
436#125—181no—
437C22⋊Q8—31no—
438C22⋊Q8—91no—
439C22⋊Q8—181no—
440C4×Q8—91no—
441C4×Q8—91no—
442C4×Q8—181no—
443C4×D4—31no—
444C4×D4—91no—
445C4×D4—91no—
446C4×D4—91no—
447C4×D4—181no—
448C4×D4—181no—
449#117—181no—
450C2×C4⋊C4—91no—
451C2×C22⋊C4—181no—
452C2×C42—91no—
453#106—31no—
454#106—31no—
455#106—91no—
456#106—91no—
457C4⋊C8—31no—
458C4⋊C8—91no—
459#103—91no—
460#103—91no—
461#103—91no—
462#103—91no—
463#102—31no—
464#102—31no—
465#102—91no—
466#102D3211yescharacteristic
467C22⋊C8—31no—
468C22⋊C8—91no—
469C4×C8—91no—
470C4×C8—91no—
471C23×C3—21no—
472C23×C3—21no—
473C23×C3—31no—
474C23×C3—41no—
475C23×C3—64no—
476C23×C3—61no—
477C23×C3—122no—
478C23×C3—122no—
479C22×D3—24no—
480C22×D3—21no—
481C22×D3—42no—
482C22×D3—42no—
483C22×D3D3×D411yescharacteristic
484C3×Q8—61no—
485C3×Q8—61no—
486C3×Q8—122no—
487C3×D4—21no—
488C3×D4—21no—
489C3×D4—22no—
490C3×D4—32no—
491C3×D4—41no—
492C3×D4—64no—
493C3×D4—61no—
494C3×D4#23712yes—
495C3×D4#23912yes—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—31no—
500C2×C3×C4—31no—
501C2×C3×C4—31no—
502C2×C3×C4—41no—
503C2×C3×C4—61no—
504C2×C3×C4—61no—
505C2×C3×C4—61no—
506C2×C3×C4—61no—
507C2×C3×C4—61no—
508C2×C3×C4—122no—
509C2×C3×C4C23×D311yescharacteristic
510C2×C3×C4C23×D311yescharacteristic
511#67—24no—
512C2×Dic3—21no—
513C2×Dic3—21no—
514C2×Dic3—21no—
515C2×Dic3—31no—
516C2×Dic3—31no—
517C2×Dic3—34no—
518C2×Dic3—31no—
519C2×Dic3—31no—
520C2×Dic3—42no—
521C2×Dic3—61no—
522C2×Dic3—61no—
523C2×Dic3—61no—
524C2×Dic3—61no—
525C2×Dic3—61no—
526C2×Dic3—61no—
527C2×Dic3—121no—
528C2×Dic3—121no—
529C2×Dic3—121no—
530C2×Dic3—122no—
531C2×Dic3—122no—
532C2×Dic3—122no—
533C2×Dic3—122no—
534C2×Dic3—122no—
535C2×Dic3—242no—
536C2×Dic3D3×D411yescharacteristic
537C2×Dic3D3×D411yescharacteristic
538C2×Dic3D3×D411yescharacteristic
539D12—21no—
540D12#23712yes—
541C4×D3—21no—
542C4×D3—21no—
543C4×D3—34no—
544C4×D3—122no—
545C4×D3—121no—
546C4×D3—122no—
547C4×D3—122no—
548Dic6—21no—
549Dic6—21no—
550Dic6—42no—
551Dic6—62no—
552Dic6—61no—
553Dic6—61no—
554Dic6—61no—
555Dic6—61no—
556Dic6—121no—
557C3×C8—21no—
558C3×C8—21no—
559C3×C8—41no—
560C3×C8—61no—
561C3×C8—61no—
562C3⋊C8—21no—
563C3⋊C8—21no—
564C3⋊C8—62no—
565C3⋊C8—61no—
566C3⋊C8—61no—
567C2×C32—42no—
568C2×C32#52511yescharacteristic
569C2×C32C22×SD1611yescharacteristic
570C2×C32#57511yescharacteristic
571C3×D3—22no—
572C3×D3—42no—
573C24—61no—
574C2×Q8—31no—
575C2×Q8—61no—
576C2×Q8—91no—
577C2×D4—31no—
578C2×D4—61no—
579C2×D4—62no—
580C2×D4—62no—
581C2×D4C2×D3211yescharacteristic
582C22×C4—31no—
583C22×C4—61no—
584C22×C4—91no—
585C22×C4—91no—
586C22×C4—181no—
587C22×C4—181no—
588C22×C4—181no—
589C22×C4—181no—
590C22×C4—364no—
591SD16—62no—
592SD16—62no—
593SD16—182no—
594SD16—182no—
595C2×C8—31no—
596C2×C8—31no—
597C2×C8—91no—
598C2×C8C2×D3211yescharacteristic
599C4⋊C4—31no—
600C4⋊C4—31no—
601C4⋊C4—61no—
602C4⋊C4—61no—
603C4⋊C4—91no—
604C4⋊C4—181no—
605C4⋊C4—181no—
606C4⋊C4—181no—
607C4⋊C4—181no—
608C4⋊C4—181no—
609C4⋊C4—181no—
610C4⋊C4C2×D3211yescharacteristic
611C22⋊C4—61no—
612C22⋊C4—61no—
613C22⋊C4—181no—
614C22⋊C4—181no—
615C22⋊C4—181no—
616C22⋊C4—181no—
617C42—31no—
618C42—91no—
619C42—91no—
620C42—91no—
621C42—181no—
622C42—181no—
623C22×C3—22no—
624C22×C3—22no—
625C22×C3—21no—
626C22×C3—32no—
627C22×C3—42no—
628C22×C3—41no—
629C22×C3—41no—
630C22×C3—41no—
631C22×C3—41no—
632C22×C3—61no—
633C22×C3—61no—
634C22×C3—62no—
635C22×C3—81no—
636C22×C3—81no—
637C22×C3—128no—
638C22×C3—121no—
639C22×C3—121no—
640C22×C3C2×D3×D411yescharacteristic
641C22×C3C2×D3×D411yescharacteristic
642C2×D3—21no—
643C2×D3—21no—
644C2×D3—22no—
645C2×D3—48no—
646C2×D3—41no—
647C2×D3—41no—
648C2×D3D3×SD1612yes—
649C3×C4—21no—
650C3×C4—21no—
651C3×C4—32no—
652C3×C4—41no—
653C3×C4—41no—
654C3×C4—61no—
655C3×C4—61no—
656C3×C4—81no—
657C3×C4—121no—
658C3×C4—121no—
659C3×C4—121no—
660C3×C4C2×#23711yescharacteristic
661C3×C4C2×#23711yescharacteristic
662C3×C4C2×#23911yescharacteristic
663C3×C4D3×#4111yescharacteristic
664Dic3—21no—
665Dic3—21no—
666Dic3—32no—
667Dic3—32no—
668Dic3—41no—
669Dic3—41no—
670Dic3—41no—
671Dic3—62no—
672Dic3—61no—
673Dic3—61no—
674Dic3—121no—
675Dic3—122no—
676Dic3—121no—
677Dic3—121no—
678Dic3—121no—
679Dic3—121no—
680Dic3—241no—
681Dic3D3×SD1612yes—
682C32#310111yescharacteristic, complemented, Sylow
683C23—21no—
684C23—31no—
685C23—64no—
686C23—61no—
687C23—122no—
688C23—122no—
689Q8—61no—
690Q8—61no—
691Q8—122no—
692Q8—181no—
693Q8—181no—
694D4—21no—
695D4—32no—
696D4—64no—
697D4—61no—
698D4#379612yes—
699C2×C4—21no—
700C2×C4—31no—
701C2×C4—31no—
702C2×C4—31no—
703C2×C4—61no—
704C2×C4—61no—
705C2×C4—61no—
706C2×C4—61no—
707C2×C4—61no—
708C2×C4—94no—
709C2×C4—91no—
710C2×C4—91no—
711C2×C4—122no—
712C2×C4—181no—
713C2×C4—181no—
714C2×C4—362no—
715C2×C4—361no—
716C2×C4—362no—
717C2×C4—362no—
718C2×C4—362no—
719C2×C4C22×D3211yescharacteristic
720C8—21no—
721C8—61no—
722C8—61no—
723C8—181no—
724C2×C3—21no—
725C2×C3—21no—
726C2×C3—21no—
727C2×C3—42no—
728C2×C3—42no—
729C2×C3—62no—
730C2×C3—82no—
731C2×C3—122no—
732C2×C3#558611yescharacteristic
733C2×C3#562711yescharacteristic
734C2×C3C2×D3×SD1611yescharacteristic
735C2×C3C2×D3×SD1611yescharacteristic
736C2×C3#577311yescharacteristic
737C2×C3#577311yescharacteristic
738D3—22no—
739D3—42no—
740C22—22no—
741C22—32no—
742C22—41no—
743C22—41no—
744C22—61no—
745C22—61no—
746C22—62no—
747C22—128no—
748C22—121no—
749C22—121no—
750C22D32×D411yescharacteristic
751C4—32no—
752C4—41no—
753C4—61no—
754C4—61no—
755C4—92no—
756C4—121no—
757C4—121no—
758C4—121no—
759C4—181no—
760C4—361no—
761C4—361no—
762C4C2×#379611yescharacteristic
763C4D3×#23711yescharacteristic
764C3—21no—
765C3#8013211yescharacteristic, complemented
766C3#8104411yescharacteristic, complemented
767C2—42no—
768C2—62no—
769C2—122no—
770C2#1059405511yescharacteristic
771C2#1059472811yescharacteristic
772C2D32×SD1611yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
prime radicalC2×C3×D3×D4C22
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. #10594387C2semidirect
3. #10592457C2semidirect
5. C3×#4761C2semidirect
6. #10591489C2semidirect
8. #10591445C2semidirect
9. #10590775C2semidirect
10. #10590752C2semidirect
11. #10590674C2semidirect
12. #10590656C2semidirect
13. #10590465C2semidirect
14. #10590460C2semidirect
15. #10590439C2semidirect
22. #64096C22semidirect
27. C3×#888C22semidirect
37. #63866C22semidirect
41. #63843C22semidirect
44. #63643C22semidirect
45. C8×C3⋊Dic3C22semidirect
46. #63635C22semidirect
49. C3×#817C22semidirect
50. C3×Dic3⋊C8C22semidirect
52. C3×#808C22semidirect
53. #63573C22semidirect
54. Dic3⋊(C3⋊C8)C22semidirect
55. #63567C22semidirect
56. #63566C22semidirect
57. #63565C22semidirect
60. #63553C22semidirect
84. #4761D3semidirect
183. #888C2×D3semidirect
213. #817C2×D3semidirect
220. Dic3⋊C8C2×D3semidirect
234. #808C2×D3semidirect
272. D3×Dic3SD16semidirect
682. C32#3101semidirect
765. C3#80132semidirect
766. C3#81044semidirect

Maximal subgroups

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

subgroupindex
D3×D4×Dic32
#105943872
#105924572
C3×#47762
C3×#47612
#105914892
#105914592
#105914452
#105907752
#105907522
#105906742
#105906562
#105904652
#105904602
#105904392
#810443
#801323