Finite Group Databasebeta

← #11870519

Subgroups — #11870519

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
1C4×D3×D12C211yesmaximal, characteristic
2#10593873C211yesmaximal, characteristic, complemented
3C4×#3744C211yesmaximal, characteristic, complemented
4C3×C4×#204C211yesmaximal, characteristic, complemented
5C3×#4685C211yesmaximal, characteristic, complemented
6#10590946C211yesmaximal, characteristic
7#10590942C211yesmaximal, characteristic
8#10590760C211yesmaximal, characteristic, complemented
9#10590759C211yesmaximal, characteristic, complemented
10#10590757C211yesmaximal, characteristic, complemented
11#10590752C211yesmaximal, characteristic, complemented
12#10590675C211yesmaximal, characteristic, complemented
13#10590674C211yesmaximal, characteristic, complemented
14C4×#3717C211yesmaximal, characteristic, complemented
15C4×#3716C211yesmaximal, characteristic, complemented
16#79651—31nomaximal
17#79298—31nomaximal
18C2×D3×D12C2211yescharacteristic
19C2×C4×D32—21no—
20C2×#3744C2211yescharacteristic
21C4×C4⋊(C3⋊D3)C2211yescharacteristic
22C4×#634C2211yescharacteristic, complemented
23C2×C3×#204C2211yescharacteristic
24C3×C4×D12C2211yescharacteristic
25C3×C42×D3C2211yescharacteristic
26C3×C4×Dic6C2211yescharacteristic, complemented
27D3×(C2×D3)⋊C4—21no—
28#63918C2211yescharacteristic, complemented
29C4×#627—21no—
30C4×#626—21no—
31#63894C2211yescharacteristic
32Dic3×D12C2211yescharacteristic
33D3×C4⋊Dic3C2211yescharacteristic
34#63880—21no—
35#63867—21no—
36#63866C2211yescharacteristic, complemented
37#63857C2211yescharacteristic
38#63856C2211yescharacteristic
39#63855—21no—
40#63851—21no—
41C2×#3717C2211yescharacteristic
42C2×#3716C2211yescharacteristic
43C32×C4×C8C2211yescharacteristic, complemented
44#63648C2211yescharacteristic
45#63644C2211yescharacteristic, complemented
46#63643C2211yescharacteristic, complemented
47C3×#821C2211yescharacteristic
48C3×(C2×D3)⋊C8C2211yescharacteristic
49C3×(C2×D3)⋊C8C2211yescharacteristic
50C3×#817C2211yescharacteristic, complemented
51C3×#816C2211yescharacteristic, complemented
52C3×Dic3⋊C8C2211yescharacteristic, complemented
53C3×Dic3⋊C8C2211yescharacteristic, complemented
54C3×C4×C3⋊C8C2211yescharacteristic, complemented
55#63573C2211yescharacteristic, complemented
56#63573C2211yescharacteristic, complemented
57#63567C2211yescharacteristic, complemented
58#63566C2211yescharacteristic, complemented
59#63564C2211yescharacteristic
60#63563C2211yescharacteristic
61#5578—31no—
62C4×D3×D4—31no—
63C2×C4×D12—31no—
64#5470—31no—
65C3×C4×SD16—31no—
66C3×#431—31no—
67#5169—31no—
68#5162—31no—
69C4×#215—31no—
70C4×#214—31no—
71#4870—31no—
72#4862—31no—
73#4842—31no—
74#4842—31no—
75#4841—31no—
76#4841—31no—
77#4818—31no—
78#4805—31no—
79#4776—31no—
80#4761—31no—
81#4731—31no—
82#4731—31no—
83#4721—31no—
84#4721—31no—
85C4×#204—31no—
86C4×#204—31no—
87C4×#204—31no—
88C4×#204—31no—
89C4×#204—61no—
90C4×#204D311yescharacteristic, complemented
91#4685D311yescharacteristic, complemented
92C22×D32—21no—
93C2×C4⋊(C3⋊D3)C2311yescharacteristic
94C2×C4×C3⋊D3—21no—
95C2×#634C2311yescharacteristic
96C2×C3×D12C2311yescharacteristic
97C2×C3×C4×D3—21no—
98C2×C3×C4×D3D411yescharacteristic
99C2×C3×C4×D3D411yescharacteristic
100C2×C3×C4×D3C2311yescharacteristic
101C2×C3×Dic6C2311yescharacteristic
102C2×#627—21no—
103C2×#626—21no—
104C2×#624—21no—
105C2×D3×Dic3—21no—
106C2×D3×Dic3—21no—
107D3×D12—22no—
108D3×D12—22no—
109C4×D32—44no—
110C2×C32×C8C2311yescharacteristic
111C2×C32×C8C2311yescharacteristic
112C32×C42C2311yescharacteristic
113#3752—21no—
114C4⋊(C3⋊Dic3)C2311yescharacteristic
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116#3750—21no—
117C4×C3⋊Dic3—21no—
118#3744—22no—
119C3×(C2×D3)⋊C4—21no—
120C3×C4⋊Dic3C2311yescharacteristic
121C3×C4⋊Dic3C2311yescharacteristic
122C3×Dic3⋊C4—21no—
123C3×C4×Dic3—21no—
124C3×C4×Dic3D411yescharacteristic
125C3×C4×Dic3D411yescharacteristic
126C3×C4×Dic3C2311yescharacteristic
127C2×C3×C3⋊C8C2311yescharacteristic
128C2×C3×C3⋊C8C2311yescharacteristic
129C3×#204—22no—
130#3724—21no—
131Dic3⋊Dic3—21no—
132Dic3⋊Dic3—21no—
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3—21no—
135Dic3⋊Dic3—21no—
136#3722—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140#3717—22no—
141#3716—22no—
142#3101—91noSylow
143C2×D3×D4—31no—
144C22×D12—31no—
145C22×C4×D3—61no—
146C22×C4×D3—61no—
147C2×C3×SD16—31no—
148C3×C4×Q8—31no—
149C3×C4×D4—31no—
150C2×C3×C42—31no—
151#946—31no—
152#944—31no—
153C2×#215—31no—
154D4×Dic3—31no—
155C2×#214—31no—
156C4×#67—61no—
157C2×(C2×D3)⋊C4—61no—
158#926—61no—
159C2×C4⋊Dic3—31no—
160#924—31no—
161#924—31no—
162#924—61no—
163C2×#204—31no—
164C2×#204—31no—
165C2×#204—31no—
166C2×#204—31no—
167C2×#204—61no—
168C2×#204C2×D311yescharacteristic
169#897—31no—
170#896—61no—
171#893—31no—
172D3×C4⋊C4—31no—
173#889—61no—
174#888—31no—
175#67⋊C4—61no—
176D3×C22⋊C4—61no—
177C4×D12—31no—
178C4×D12—31no—
179C4×D12—31no—
180C4×D12—31no—
181C4×D12—61no—
182C4×D12—61no—
183C4×D12—61no—
184C4×D12C2×D311yescharacteristic
185#872—61no—
186C42×D3C2×D311yescharacteristic
187#870—61no—
188#869—31no—
189#869—31no—
190C4×Dic6—31no—
191C4×Dic6—31no—
192C4×Dic6—61no—
193C4×Dic6—61no—
194C4×Dic6—61no—
195C4×Dic6C2×D311yescharacteristic, complemented
196C3×#106—31no—
197C3×C4⋊C8—31no—
198C3×C4⋊C8—31no—
199C3×#103—31no—
200C3×#102—31no—
201C3×C22⋊C8—31no—
202C3×C22⋊C8—31no—
203C3×C4×C8—21no—
204C3×C4×C8—31no—
205C3×C4×C8C2×D311yescharacteristic, complemented
206C3×C4×C8C2×D311yescharacteristic, complemented
207#835—31no—
208#832—31no—
209#821—31no—
210#821—31no—
211#821—31no—
212#821—31no—
213#821—61no—
214#821C2×D311yescharacteristic
215(C2×D3)⋊C8C2×D311yescharacteristic
216(C2×D3)⋊C8C2×D311yescharacteristic
217#817—31no—
218#817—31no—
219#817—31no—
220#817—31no—
221#817—61no—
222#817C2×D311yescharacteristic, complemented
223#816—31no—
224#816—31no—
225#816—31no—
226#816—31no—
227#816—61no—
228#816C2×D311yescharacteristic, complemented
229Dic3⋊C8C2×D311yescharacteristic, complemented
230Dic3⋊C8C2×D311yescharacteristic, complemented
231#810—31no—
232#809—31no—
233#808—31no—
234#808—31no—
235C4×C3⋊C8C2×D311yescharacteristic, complemented
236C22×C3⋊D3—21no—
237C22×C3×D3—21no—
238C22×C3×D3C2×D411yescharacteristic
239C2×D32—24no—
240C2×D32—42no—
241C2×D32—42no—
242C2×C32×C4C2×D411yescharacteristic
243C2×C32×C4C2×D411yescharacteristic
244C2×C32×C4C2411yescharacteristic
245C2×C3⋊Dic3—21no—
246C2×C3⋊Dic3—21no—
247C2×C3⋊Dic3—21no—
248C4⋊(C3⋊D3)—21no—
249C4⋊(C3⋊D3)#4112yes—
250C4×C3⋊D3—42no—
251#634—21no—
252#634—21no—
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#4112yes—
261C3×C4×D3—21no—
262C3×C4×D3—21no—
263C3×C4×D3—41no—
264C3×C4×D3—42no—
265C3×C4×D3SD1614yescomplemented
266C3×Dic6—21no—
267C3×Dic6—21no—
268#627—42no—
269#626—24no—
270#624—42no—
271D3×Dic3—42no—
272D3×Dic3—42no—
273C32×C8—21no—
274C32×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—91no—
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—31no—
292C23×D3—61no—
293C23×D3—61no—
294C2×C3×Q8—31no—
295C2×C3×D4—31no—
296C22×C3×C4—31no—
297C22×C3×C4—31no—
298C22×C3×C4—31no—
299C22×C3×C4—61no—
300C2×#67—61no—
301C22×Dic3—61no—
302C22×Dic3—61no—
303D3×D4—62no—
304D3×D4—62no—
305C2×D12—31no—
306C2×D12—31no—
307C2×D12—61no—
308C2×D12—62no—
309C2×D12—61no—
310C2×D12—62no—
311C2×D12C22×D311yescharacteristic
312C2×C4×D3—21no—
313C2×C4×D3—61no—
314C2×C4×D3—61no—
315C2×C4×D3—61no—
316C2×C4×D3—61no—
317C2×C4×D3—61no—
318C2×C4×D3—61no—
319C2×C4×D3—121no—
320C2×C4×D3—124no—
321C2×C4×D3—124no—
322C2×C4×D3D1211yescharacteristic
323C2×C4×D3D1211yescharacteristic
324C2×C4×D3C22×D311yescharacteristic
325C2×Dic6—31no—
326C2×Dic6—31no—
327C2×Dic6—61no—
328C2×Dic6—61no—
329C2×Dic6—61no—
330C2×Dic6C22×D311yescharacteristic
331C3×SD16—62no—
332C2×C3×C8—21no—
333C2×C3×C8—21no—
334C2×C3×C8—31no—
335C2×C3×C8—31no—
336C2×C3×C8C22×D311yescharacteristic
337C2×C3×C8C22×D311yescharacteristic
338C2×C3×C8C22×D311yescharacteristic
339C2×C3×C8C22×D311yescharacteristic
340C3×C4⋊C4—31no—
341C3×C4⋊C4—31no—
342C3×C4⋊C4—61no—
343C3×C22⋊C4—61no—
344C3×C42—21no—
345C3×C42—31no—
346C3×C42—31no—
347C3×C42—31no—
348C3×C42—61no—
349C3×C42C22×D311yescharacteristic
350C3×C42C22×D311yescharacteristic
351#217—61no—
352#217—61no—
353#217—61no—
354#215—62no—
355#214—62no—
356(C2×D3)⋊C4—21no—
357(C2×D3)⋊C4—61no—
358(C2×D3)⋊C4—61no—
359(C2×D3)⋊C4—61no—
360(C2×D3)⋊C4—61no—
361(C2×D3)⋊C4—61no—
362(C2×D3)⋊C4—61no—
363(C2×D3)⋊C4—61no—
364(C2×D3)⋊C4—121no—
365C4⋊Dic3—31no—
366C4⋊Dic3—31no—
367C4⋊Dic3—31no—
368C4⋊Dic3—31no—
369C4⋊Dic3—61no—
370C4⋊Dic3—61no—
371C4⋊Dic3—61no—
372C4⋊Dic3—61no—
373C4⋊Dic3—61no—
374C4⋊Dic3—61no—
375C4⋊Dic3—61no—
376C4⋊Dic3C22×D311yescharacteristic
377C4⋊Dic3C22×D311yescharacteristic
378Dic3⋊C4—21no—
379Dic3⋊C4—61no—
380Dic3⋊C4—61no—
381Dic3⋊C4—61no—
382Dic3⋊C4—61no—
383Dic3⋊C4—61no—
384Dic3⋊C4—61no—
385Dic3⋊C4—61no—
386Dic3⋊C4—61no—
387Dic3⋊C4—61no—
388Dic3⋊C4—121no—
389C4×Dic3—21no—
390C4×Dic3—61no—
391C4×Dic3—61no—
392C4×Dic3—121no—
393C4×Dic3D1211yescharacteristic
394C4×Dic3D1211yescharacteristic
395C4×Dic3C22×D311yescharacteristic
396C2×C3⋊C8C22×D311yescharacteristic
397C2×C3⋊C8C22×D311yescharacteristic
398#204—22no—
399#204—62no—
400#204—62no—
401#204—64no—
402#204—62no—
403#204—62no—
404C22×C32C22×D411yescharacteristic
405C2×C3⋊D3—22no—
406C2×C3⋊D3—41no—
407C2×C3⋊D3—41no—
408C2×C3×D3—21no—
409C2×C3×D3—21no—
410C2×C3×D3—22no—
411C2×C3×D3—41no—
412C2×C3×D3—41no—
413C2×C3×D3C2×SD1612yes—
414D32—48no—
415C32×C4—21no—
416C32×C4C2×SD1612yes—
417C32×C4C2×#4111yescharacteristic
418C32×C4C2×#4111yescharacteristic
419C3⋊Dic3—41no—
420C3⋊Dic3—41no—
421C3⋊Dic3—41no—
422C3×Dic3—21no—
423C3×Dic3—21no—
424C3×Dic3—41no—
425C3×Dic3—41no—
426C3×Dic3—41no—
427C3×Dic3C2×SD1612yes—
428C22×D4—91no—
429C23×C4—181no—
430C2×SD16—31no—
431C2×SD16—91no—
432C2×SD16—91no—
433C2×SD16—91no—
434C4⋊Q8—91no—
435C4⋊Q8—91no—
436#125—181no—
437C22⋊Q8—91no—
438C22⋊Q8—91no—
439C22⋊Q8—181no—
440C4×Q8—31no—
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—31no—
453#106—31no—
454#106—91no—
455#106—91no—
456#106—91no—
457C4⋊C8—31no—
458C4⋊C8—31no—
459#103—31no—
460#103—91no—
461#103—91no—
462#103—91no—
463#102—31no—
464#102—91no—
465#102—91no—
466#102—91no—
467C22⋊C8—31no—
468C22⋊C8—31no—
469C4×C8—31no—
470C4×C8D3211yescharacteristic, complemented
471C23×C3—31no—
472C23×C3—61no—
473C22×D3—21no—
474C22×D3—64no—
475C22×D3—64no—
476C22×D3—61no—
477C22×D3—61no—
478C22×D3—121no—
479C22×D3—122no—
480C22×D3—122no—
481C22×D3—122no—
482C22×D3—122no—
483C22×D3C2×D1211yescharacteristic
484C3×Q8—61no—
485C3×Q8—61no—
486C3×D4—32no—
487C3×D4—61no—
488C2×C3×C4—21no—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—31no—
492C2×C3×C4—34no—
493C2×C3×C4—31no—
494C2×C3×C4—31no—
495C2×C3×C4—61no—
496C2×C3×C4—61no—
497C2×C3×C4—61no—
498C2×C3×C4—61no—
499C2×C3×C4—61no—
500C2×C3×C4—121no—
501C2×C3×C4—122no—
502C2×C3×C4C2×D1211yescharacteristic
503C2×C3×C4C2×D1211yescharacteristic
504C2×C3×C4D3×D411yescharacteristic
505C2×C3×C4D3×D411yescharacteristic
506C2×C3×C4C23×D311yescharacteristic
507C2×C3×C4C23×D311yescharacteristic
508#67—64no—
509C2×Dic3—21no—
510C2×Dic3—21no—
511C2×Dic3—21no—
512C2×Dic3—61no—
513C2×Dic3—61no—
514C2×Dic3—61no—
515C2×Dic3—61no—
516C2×Dic3—61no—
517C2×Dic3—61no—
518C2×Dic3—121no—
519C2×Dic3—121no—
520C2×Dic3—121no—
521C2×Dic3—122no—
522C2×Dic3—122no—
523C2×Dic3C2×D1211yescharacteristic
524C2×Dic3C2×D1211yescharacteristic
525C2×Dic3C2×D1211yescharacteristic
526D12—21no—
527D12—32no—
528D12—32no—
529D12—62no—
530D12—64no—
531D12—61no—
532D12—61no—
533D12—121no—
534D12#23512yes—
535C4×D3—21no—
536C4×D3—21no—
537C4×D3—41no—
538C4×D3—42no—
539C4×D3—122no—
540C4×D3—122no—
541C4×D3—122no—
542C4×D3—122no—
543C4×D3—122no—
544C4×D3—122no—
545C4×D3—242no—
546C4×D3#20414yescomplemented
547Dic6—21no—
548Dic6—21no—
549Dic6—62no—
550Dic6—61no—
551Dic6—61no—
552Dic6—61no—
553Dic6—61no—
554Dic6—121no—
555Dic6—122no—
556Dic6—122no—
557C3×C8—22no—
558C3×C8—21no—
559C3×C8—21no—
560C3×C8—21no—
561C3×C8—21no—
562C3×C8—41no—
563C3×C8—61no—
564C3×C8—61no—
565C3⋊C8—21no—
566C3⋊C8—21no—
567C2×C32#52511yescharacteristic
568C2×C32C22×SD1611yescharacteristic
569C2×C32#57511yescharacteristic
570C3⋊D3—42no—
571C3×D3—22no—
572C3×D3—42no—
573C24—181no—
574C2×Q8—31no—
575C2×Q8—91no—
576C2×Q8—181no—
577C2×D4—31no—
578C2×D4—91no—
579C2×D4—181no—
580C2×D4—182no—
581C2×D4—182no—
582C22×C4—31no—
583C22×C4—31no—
584C22×C4—31no—
585C22×C4—61no—
586C22×C4—181no—
587C22×C4—181no—
588C22×C4—181no—
589C22×C4—181no—
590C22×C4—364no—
591SD16—62no—
592SD16—182no—
593SD16—182no—
594SD16—182no—
595C2×C8—31no—
596C2×C8—31no—
597C2×C8C2×D3211yescharacteristic
598C2×C8C2×D3211yescharacteristic
599C4⋊C4—31no—
600C4⋊C4—31no—
601C4⋊C4—61no—
602C4⋊C4—91no—
603C4⋊C4—91no—
604C4⋊C4—181no—
605C4⋊C4—181no—
606C4⋊C4—181no—
607C4⋊C4—181no—
608C4⋊C4—181no—
609C4⋊C4—181no—
610C4⋊C4—181no—
611C22⋊C4—61no—
612C22⋊C4—181no—
613C22⋊C4—181no—
614C22⋊C4—181no—
615C22⋊C4—181no—
616C22⋊C4—181no—
617C42—31no—
618C42—31no—
619C42—31no—
620C42—61no—
621C42—181no—
622C42C2×D3211yescharacteristic
623C22×C3—21no—
624C22×C3—32no—
625C22×C3—61no—
626C22×C3—61no—
627C22×C3—62no—
628C22×C3—121no—
629C22×C3—121no—
630C22×C3C22×D1211yescharacteristic
631C22×C3C2×D3×D411yescharacteristic
632C2×D3—21no—
633C2×D3—21no—
634C2×D3—22no—
635C2×D3—41no—
636C2×D3—41no—
637C2×D3—62no—
638C2×D3—62no—
639C2×D3—122no—
640C2×D3—128no—
641C2×D3—128no—
642C2×D3—121no—
643C2×D3—121no—
644C2×D3—121no—
645C2×D3—121no—
646C2×D3—241no—
647C2×D3—241no—
648C2×D3C2×#20412yes—
649C3×C4—21no—
650C3×C4—21no—
651C3×C4—22no—
652C3×C4—21no—
653C3×C4—21no—
654C3×C4—32no—
655C3×C4—41no—
656C3×C4—61no—
657C3×C4—61no—
658C3×C4—121no—
659C3×C4—121no—
660C3×C4—121no—
661C3×C4C2×#20412yes—
662C3×C4D3×SD1612yes—
663C3×C4C2×#23511yescharacteristic
664C3×C4D3×#4111yescharacteristic
665C3×C4D3×#4111yescharacteristic
666C3×C4D3×#4111yescharacteristic
667Dic3—21no—
668Dic3—21no—
669Dic3—41no—
670Dic3—41no—
671Dic3—41no—
672Dic3—122no—
673Dic3—121no—
674Dic3—121no—
675Dic3—121no—
676Dic3—121no—
677Dic3—121no—
678Dic3—121no—
679Dic3—241no—
680Dic3—241no—
681Dic3C2×#20412yes—
682C32#310111yescharacteristic, complemented, Sylow
683C23—31no—
684C23—61no—
685C23—184no—
686C23—181no—
687C23—362no—
688C23—362no—
689Q8—61no—
690Q8—61no—
691Q8—181no—
692Q8—181no—
693Q8—362no—
694D4—32no—
695D4—61no—
696D4—92no—
697D4—184no—
698D4—181no—
699C2×C4—31no—
700C2×C4—34no—
701C2×C4—31no—
702C2×C4—31no—
703C2×C4—61no—
704C2×C4—61no—
705C2×C4—61no—
706C2×C4—61no—
707C2×C4—61no—
708C2×C4—121no—
709C2×C4—122no—
710C2×C4—181no—
711C2×C4—181no—
712C2×C4—181no—
713C2×C4—362no—
714C2×C4—362no—
715C2×C4—362no—
716C2×C4—362no—
717C2×C4D3×D1211yescharacteristic
718C2×C4D3×D1211yescharacteristic
719C2×C4C22×D3211yescharacteristic
720C8—21no—
721C8—21no—
722C8—61no—
723C8—61no—
724C2×C3—21no—
725C2×C3—21no—
726C2×C3—21no—
727C2×C3—62no—
728C2×C3—122no—
729C2×C3#552411yescharacteristic
730C2×C3#554711yescharacteristic
731C2×C3C22×#20411yescharacteristic
732C2×C3#574811yescharacteristic
733C2×C3C2×D3×SD1611yescharacteristic
734C2×C3#576811yescharacteristic
735D3—22no—
736D3—42no—
737D3—122no—
738D3—122no—
739D3—242no—
740C22—32no—
741C22—61no—
742C22—61no—
743C22—62no—
744C22—121no—
745C22—121no—
746C22—182no—
747C22—368no—
748C22—361no—
749C22—361no—
750C22C2×D3×D1211yescharacteristic
751C4—21no—
752C4—32no—
753C4—61no—
754C4—61no—
755C4—121no—
756C4—121no—
757C4—121no—
758C4—361no—
759C4—361no—
760C4—361no—
761C4D3×#20412yes—
762C4D3×#23511yescharacteristic
763C4#6430611yescharacteristic
764C3—21no—
765C3#7929811yescharacteristic, complemented
766C3#7965111yescharacteristic, complemented
767C2—62no—
768C2—122no—
769C2—362no—
770C2#1059399711yescharacteristic
771C2C2×D3×#20411yescharacteristic
772C2#1059467611yescharacteristic
subgroupG/H
centerC2×C4D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×C8C22
socleC22×C32C22×D4
prime radicalC2×D3×D12C22
hypercenterC4×C8D32
hypocenterC32#3101
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
2. #10593873C2semidirect
3. C4×#3744C2semidirect
4. C3×C4×#204C2semidirect
5. C3×#4685C2semidirect
8. #10590760C2semidirect
9. #10590759C2semidirect
10. #10590757C2semidirect
11. #10590752C2semidirect
12. #10590675C2semidirect
13. #10590674C2semidirect
14. C4×#3717C2semidirect
15. C4×#3716C2semidirect
22. C4×#634C22semidirect
26. C3×C4×Dic6C22semidirect
28. #63918C22semidirect
36. #63866C22semidirect
43. C32×C4×C8C22semidirect
45. #63644C22semidirect
46. #63643C22semidirect
50. C3×#817C22semidirect
51. C3×#816C22semidirect
52. C3×Dic3⋊C8C22semidirect
53. C3×Dic3⋊C8C22semidirect
54. C3×C4×C3⋊C8C22semidirect
55. #63573C22semidirect
56. #63573C22semidirect
57. #63567C22semidirect
58. #63566C22semidirect
90. C4×#204D3semidirect
91. #4685D3semidirect
195. C4×Dic6C2×D3semidirect
205. C3×C4×C8C2×D3semidirect
206. C3×C4×C8C2×D3semidirect
222. #817C2×D3semidirect
228. #816C2×D3semidirect
229. Dic3⋊C8C2×D3semidirect
230. Dic3⋊C8C2×D3semidirect
235. C4×C3⋊C8C2×D3semidirect
265. C3×C4×D3SD16semidirect
470. C4×C8D32semidirect
546. C4×D3#204semidirect
682. C32#3101semidirect
765. C3#79298semidirect
766. C3#79651semidirect

Maximal subgroups

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

subgroupindex
C4×D3×D122
#105938732
C4×#37442
C3×C4×#2042
C3×#46852
#105909462
#105909422
#105907602
#105907592
#105907572
#105907522
#105906752
#105906742
C4×#37172
C4×#37162
#796513
#792983