Finite Group Databasebeta

← #11870528

Subgroups — #11870528

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
1#10595368C211yesmaximal, characteristic, complemented
2D3×#893C211yesmaximal, characteristic
3#10592487C211yesmaximal, characteristic, complemented
4C3×#4818C211yesmaximal, characteristic, complemented
5C3×#4805C211yesmaximal, characteristic, complemented
6#10591651C211yesmaximal, characteristic
7#10591571C211yesmaximal, characteristic, complemented
8#10591565C211yesmaximal, characteristic, complemented
9#10590942C211yesmaximal, characteristic
10#10590775C211yesmaximal, characteristic, complemented
11#10590759C211yesmaximal, characteristic, complemented
12#10590656C211yesmaximal, characteristic, complemented
13#10590558C211yesmaximal, characteristic, complemented
14#10590516C211yesmaximal, characteristic, complemented
15#10590483C211yesmaximal, characteristic, complemented
16#81412—31nomaximal
17#80408—31nomaximal
18C2×D3×D12C2211yescharacteristic
19C2×C4×D32—21no—
20Q8×C3⋊Dic3C2211yescharacteristic, complemented
21C2×#3755C2211yescharacteristic
22#64102C2211yescharacteristic
23C3×#946C2211yescharacteristic
24C3×#944C2211yescharacteristic, complemented
25C2×C3×#215C2211yescharacteristic
26C2×C3×#204C2211yescharacteristic
27C3×#893C2211yescharacteristic
28C3×D3×C4⋊C4C2211yescharacteristic
29D3×(C2×D3)⋊C4—21no—
30#63918C2211yescharacteristic, complemented
31#63904—21no—
32#63898C2211yescharacteristic
33#63894C2211yescharacteristic
34#63893—21no—
35#63881—21no—
36#63878—21no—
37C4×D3×Dic3C2211yescharacteristic
38#63856C2211yescharacteristic
39#63845—21no—
40#63843C2211yescharacteristic, complemented
41#63838—21no—
42C2×#3717C2211yescharacteristic
43C32×#103C2211yescharacteristic, complemented
44#63648C2211yescharacteristic
45C8×C3⋊Dic3C2211yescharacteristic, complemented
46#63635C2211yescharacteristic, complemented
47C3×#835C2211yescharacteristic, complemented
48C3×(C2×D3)⋊C8C2211yescharacteristic
49C3×#817C2211yescharacteristic, complemented
50C3×Dic3⋊C8C2211yescharacteristic, complemented
51C3×#810C2211yescharacteristic, complemented
52C3×#808C2211yescharacteristic, complemented
53#63573C2211yescharacteristic, complemented
54Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
55#63565C2211yescharacteristic, complemented
56#63564C2211yescharacteristic
57#63563C2211yescharacteristic
58#63562C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60#63553C2211yescharacteristic, complemented
61#5728—31no—
62#5622—31no—
63C4×D3×D4—31no—
64C2×#893—31no—
65C3×#483—31no—
66C3×#461—31no—
67#5169—31no—
68#5169—31no—
69Dic3×SD16—31no—
70Dic3×SD16—31no—
71#5083—31no—
72#5046—31no—
73#5008—31no—
74#4971—31no—
75#4870—31no—
76#4870—31no—
77#4852—31no—
78#4852—31no—
79#4842—31no—
80#4833—31no—
81#4818—31no—
82#4818D311yescharacteristic, complemented
83#4805—31no—
84#4805D311yescharacteristic, complemented
85#4788—31no—
86#4788—31no—
87#4788—31no—
88#4788—31no—
89#4788—61no—
90#4731—31no—
91#4718—31no—
92C22×D32—21no—
93C2×C32×Q8C2311yescharacteristic
94C2×C4⋊(C3⋊D3)C2311yescharacteristic
95C2×C4×C3⋊D3—21no—
96C2×C3×D12C2311yescharacteristic
97C2×C3×C4×D3—21no—
98C2×C3×C4×D3—21no—
99C2×C3×C4×D3C2311yescharacteristic
100C2×C3×Dic6C2311yescharacteristic
101C2×#627—21no—
102C2×#626—21no—
103C2×#624—21no—
104C2×D3×Dic3—21no—
105C2×D3×Dic3D411yescharacteristic
106C2×D3×Dic3D411yescharacteristic
107D3×D12—22no—
108D3×D12—22no—
109C4×D32—44no—
110C2×C32×C8C2311yescharacteristic
111C32×C4⋊C4C2311yescharacteristic
112#3755—22no—
113#3752—21no—
114C4⋊(C3⋊Dic3)—21no—
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116C4×C3⋊Dic3—21no—
117C4×C3⋊Dic3C2311yescharacteristic
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119C3×#215—22no—
120C3×(C2×D3)⋊C4—21no—
121C3×(C2×D3)⋊C4—21no—
122C3×C4⋊Dic3C2311yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×Dic3⋊C4—21no—
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—22no—
132#3724—21no—
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3—21no—
135#3722—21no—
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138Dic32—21no—
139Dic32D411yescharacteristic
140Dic32D411yescharacteristic
141#3717—22no—
142#3101—91noSylow
143C2×D3×D4—31no—
144C22×D12—31no—
145C22×C4×D3—61no—
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×C3×C4⋊C4—31no—
153#946—31no—
154#946C2×D311yescharacteristic
155Q8×Dic3—31no—
156Q8×Dic3—31no—
157Q8×Dic3—31no—
158Q8×Dic3—61no—
159#944C2×D311yescharacteristic, complemented
160C2×#215—31no—
161C2×#215—31no—
162C2×#215—31no—
163C2×#215—61no—
164C2×#215C2×D311yescharacteristic
165D4×Dic3—31no—
166C4×#67—61no—
167C2×(C2×D3)⋊C4—61no—
168#924—31no—
169C2×C4×Dic3—31no—
170C2×#204—31no—
171C2×#204C2×D311yescharacteristic
172#897—61no—
173#893—31no—
174#893—31no—
175#893—31no—
176#893—31no—
177#893—61no—
178#893—61no—
179#893—61no—
180#893C2×D311yescharacteristic
181#892—61no—
182D3×C4⋊C4C2×D311yescharacteristic
183#890—61no—
184#889—61no—
185#888—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×#103—21no—
200C3×#103—31no—
201C3×#103—31no—
202C3×#103C2×D311yescharacteristic, complemented
203C3×#103C2×D311yescharacteristic, complemented
204C3×C22⋊C8—31no—
205#835—31no—
206#835C2×D311yescharacteristic, complemented
207#832—31no—
208#832—31no—
209#830—31no—
210#821—31no—
211#821—31no—
212#821—31no—
213#821—31no—
214#821—61no—
215(C2×D3)⋊C8—31no—
216(C2×D3)⋊C8C2×D311yescharacteristic
217#817—31no—
218#817C2×D311yescharacteristic, complemented
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#810C2×D311yescharacteristic, complemented
228#809—31no—
229#809—31no—
230#808—31no—
231#808—31no—
232#808—31no—
233#808—61no—
234#808C2×D311yescharacteristic, complemented
235C4⋊(C3⋊C8)—31no—
236C22×C3⋊D3—21no—
237C22×C3×D3—21no—
238C22×C3×D3C2×D411yescharacteristic
239C2×D32—24no—
240C2×D32—42no—
241C2×D32—42no—
242C32×Q8—21no—
243C32×Q8—21no—
244C2×C32×C4—21no—
245C2×C32×C4—21no—
246C2×C32×C4C2411yescharacteristic
247C2×C3⋊Dic3—21no—
248C2×C3⋊Dic3C2×D411yescharacteristic
249C2×C3⋊Dic3C2×D411yescharacteristic
250C4⋊(C3⋊D3)—21no—
251C4⋊(C3⋊D3)#4112yes—
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#4112yes—
261C3×C4×D3—21no—
262C3×C4×D3—21no—
263C3×C4×D3—42no—
264C3×C4×D3—42no—
265C3×Dic6—21no—
266C3×Dic6—21no—
267#627—42no—
268#626—24no—
269#624—42no—
270D3×Dic3—41no—
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—31no—
280#483—91no—
281#476—91no—
282#476—91no—
283#461—31no—
284#461—91no—
285#450—91no—
286#450—91no—
287C4×SD16—91no—
288C4×SD16—91no—
289C4×SD16—91no—
290C4×SD16—91no—
291#431—91no—
292C23×D3—61no—
293C23×D3—61no—
294C2×C3×Q8—21no—
295C2×C3×Q8—31no—
296C2×C3×Q8C22×D311yescharacteristic
297C2×C3×Q8C22×D311yescharacteristic
298C2×C3×D4—31no—
299C22×C3×C4—31no—
300C22×C3×C4—61no—
301C22×C3×C4—61no—
302C2×#67—61no—
303C22×Dic3—31no—
304C22×Dic3—31no—
305C22×Dic3—61no—
306D3×D4—62no—
307D3×D4—62no—
308C2×D12—31no—
309C2×D12—31no—
310C2×D12—61no—
311C2×D12—62no—
312C2×D12—61no—
313C2×D12—62no—
314C2×D12C22×D311yescharacteristic
315C2×C4×D3—21no—
316C2×C4×D3—21no—
317C2×C4×D3—31no—
318C2×C4×D3—31no—
319C2×C4×D3—61no—
320C2×C4×D3—61no—
321C2×C4×D3—61no—
322C2×C4×D3—61no—
323C2×C4×D3—61no—
324C2×C4×D3—121no—
325C2×C4×D3—124no—
326C2×C4×D3—124no—
327C2×C4×D3C22×D311yescharacteristic
328C2×Dic6—61no—
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⋊C4—61no—
344C3×C4⋊C4—61no—
345C3×C4⋊C4C22×D311yescharacteristic
346C3×C4⋊C4C22×D311yescharacteristic
347C3×C22⋊C4—61no—
348C3×C22⋊C4—61no—
349C3×C42—31no—
350#217—61no—
351#217—61no—
352#215—22no—
353#215—62no—
354#215—62no—
355#215—62no—
356#215—64no—
357(C2×D3)⋊C4—21no—
358(C2×D3)⋊C4—21no—
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—61no—
365(C2×D3)⋊C4—121no—
366C4⋊Dic3—31no—
367C4⋊Dic3—31no—
368C4⋊Dic3—61no—
369C4⋊Dic3—61no—
370C4⋊Dic3—61no—
371C4⋊Dic3—61no—
372C4⋊Dic3—61no—
373C4⋊Dic3—121no—
374C4⋊Dic3C22×D311yescharacteristic
375C4⋊Dic3C22×D311yescharacteristic
376Dic3⋊C4—21no—
377Dic3⋊C4—21no—
378Dic3⋊C4—21no—
379Dic3⋊C4—21no—
380Dic3⋊C4—61no—
381Dic3⋊C4—61no—
382Dic3⋊C4—61no—
383Dic3⋊C4—61no—
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×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—41no—
416C32×C4—41no—
417C32×C4C2×#4111yescharacteristic
418C32×C4C2×#4111yescharacteristic
419C3⋊Dic3—21no—
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—91no—
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—31no—
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—31no—
460#103—31no—
461#103—91no—
462#103D3211yescharacteristic, complemented
463#102—91no—
464#102—91no—
465#102—91no—
466#102—91no—
467C22⋊C8—31no—
468C22⋊C8—91no—
469C4×C8—91no—
470C4×C8—91no—
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×D3D3×D411yescharacteristic
484C3×Q8—22no—
485C3×Q8—21no—
486C3×Q8—21no—
487C3×Q8—21no—
488C3×Q8—21no—
489C3×Q8—41no—
490C3×Q8—61no—
491C3×Q8—61no—
492C3×D4—32no—
493C3×D4—61no—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
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—41no—
504C2×C3×C4—61no—
505C2×C3×C4—61no—
506C2×C3×C4—61no—
507C2×C3×C4—61no—
508C2×C3×C4—61no—
509C2×C3×C4—122no—
510C2×C3×C4—122no—
511C2×C3×C4C23×D311yescharacteristic
512C2×C3×C4C23×D311yescharacteristic
513#67—64no—
514C2×Dic3—21no—
515C2×Dic3—21no—
516C2×Dic3—21no—
517C2×Dic3—31no—
518C2×Dic3—31no—
519C2×Dic3—34no—
520C2×Dic3—31no—
521C2×Dic3—31no—
522C2×Dic3—61no—
523C2×Dic3—61no—
524C2×Dic3—61no—
525C2×Dic3—61no—
526C2×Dic3—121no—
527C2×Dic3—121no—
528C2×Dic3—122no—
529C2×Dic3D3×D411yescharacteristic
530C2×Dic3D3×D411yescharacteristic
531C2×Dic3D3×D411yescharacteristic
532D12—21no—
533D12—32no—
534D12—32no—
535D12—62no—
536D12—64no—
537D12—61no—
538D12—61no—
539D12—121no—
540D12#23712yes—
541C4×D3—21no—
542C4×D3—21no—
543C4×D3—34no—
544C4×D3—42no—
545C4×D3—42no—
546C4×D3—122no—
547C4×D3—122no—
548C4×D3—122no—
549C4×D3—122no—
550C4×D3—121no—
551C4×D3—122no—
552C4×D3—242no—
553Dic6—21no—
554Dic6—21no—
555Dic6—122no—
556Dic6—122no—
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#52511yescharacteristic
568C2×C32C22×SD1611yescharacteristic
569C2×C32#57511yescharacteristic
570C3⋊D3—42no—
571C3×D3—22no—
572C3×D3—42no—
573C24—181no—
574C2×Q8—31no—
575C2×Q8—181no—
576C2×Q8C2×D3211yescharacteristic
577C2×D4—31no—
578C2×D4—91no—
579C2×D4—181no—
580C2×D4—182no—
581C2×D4—182no—
582C22×C4—31no—
583C22×C4—61no—
584C22×C4—61no—
585C22×C4—91no—
586C22×C4—91no—
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—61no—
604C4⋊C4—61no—
605C4⋊C4—91no—
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—21no—
624C22×C3—32no—
625C22×C3—61no—
626C22×C3—61no—
627C22×C3—62no—
628C22×C3—121no—
629C22×C3—121no—
630C22×C3C2×D3×D411yescharacteristic
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×D3D3×SD1612yes—
649C3×C4—21no—
650C3×C4—21no—
651C3×C4—32no—
652C3×C4—42no—
653C3×C4—41no—
654C3×C4—41no—
655C3×C4—41no—
656C3×C4—41no—
657C3×C4—61no—
658C3×C4—61no—
659C3×C4—81no—
660C3×C4—121no—
661C3×C4—121no—
662C3×C4—121no—
663C3×C4C2×#23711yescharacteristic
664C3×C4D3×#4111yescharacteristic
665C3×C4D3×#4111yescharacteristic
666C3×C4D3×#4111yescharacteristic
667Dic3—21no—
668Dic3—21no—
669Dic3—32no—
670Dic3—32no—
671Dic3—41no—
672Dic3—41no—
673Dic3—41no—
674Dic3—62no—
675Dic3—61no—
676Dic3—61no—
677Dic3—121no—
678Dic3—121no—
679Dic3—121no—
680Dic3—241no—
681Dic3D3×SD1612yes—
682C32#310111yescharacteristic, complemented, Sylow
683C23—31no—
684C23—61no—
685C23—184no—
686C23—181no—
687C23—362no—
688C23—362no—
689Q8—21no—
690Q8—21no—
691Q8—61no—
692Q8—61no—
693Q8—362no—
694D4—32no—
695D4—61no—
696D4—92no—
697D4—184no—
698D4—181no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—31no—
702C2×C4—31no—
703C2×C4—31no—
704C2×C4—61no—
705C2×C4—61no—
706C2×C4—61no—
707C2×C4—61no—
708C2×C4—61no—
709C2×C4—94no—
710C2×C4—91no—
711C2×C4—91no—
712C2×C4—122no—
713C2×C4—122no—
714C2×C4—181no—
715C2×C4—362no—
716C2×C4—362no—
717C2×C4—361no—
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—62no—
728C2×C3—122no—
729C2×C3#560611yescharacteristic
730C2×C3#565611yescharacteristic
731C2×C3C2×D3×SD1611yescharacteristic
732C2×C3C2×D3×SD1611yescharacteristic
733C2×C3#577711yescharacteristic
734C2×C3#577711yescharacteristic
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—
750C22D32×D411yescharacteristic
751C4—32no—
752C4—41no—
753C4—41no—
754C4—61no—
755C4—61no—
756C4—92no—
757C4—121no—
758C4—121no—
759C4—121no—
760C4—181no—
761C4—361no—
762C4#6430611yescharacteristic
763C4D3×#23711yescharacteristic
764C3—21no—
765C3#8040811yescharacteristic, complemented
766C3#8141211yescharacteristic, complemented
767C2—62no—
768C2—122no—
769C2—362no—
770C2#1059426711yescharacteristic
771C2D32×SD1611yescharacteristic
772C2#1059476211yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
prime radicalC2×D3×D12C22
hypercenter#103D32
hypocenterC32#3101
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. #10595368C2semidirect
3. #10592487C2semidirect
4. C3×#4818C2semidirect
5. C3×#4805C2semidirect
7. #10591571C2semidirect
8. #10591565C2semidirect
10. #10590775C2semidirect
11. #10590759C2semidirect
12. #10590656C2semidirect
13. #10590558C2semidirect
14. #10590516C2semidirect
15. #10590483C2semidirect
20. Q8×C3⋊Dic3C22semidirect
24. C3×#944C22semidirect
30. #63918C22semidirect
40. #63843C22semidirect
43. C32×#103C22semidirect
45. C8×C3⋊Dic3C22semidirect
46. #63635C22semidirect
47. C3×#835C22semidirect
49. C3×#817C22semidirect
50. C3×Dic3⋊C8C22semidirect
51. C3×#810C22semidirect
52. C3×#808C22semidirect
53. #63573C22semidirect
54. Dic3⋊(C3⋊C8)C22semidirect
55. #63565C22semidirect
60. #63553C22semidirect
82. #4818D3semidirect
84. #4805D3semidirect
159. #944C2×D3semidirect
202. C3×#103C2×D3semidirect
203. C3×#103C2×D3semidirect
206. #835C2×D3semidirect
218. #817C2×D3semidirect
220. Dic3⋊C8C2×D3semidirect
227. #810C2×D3semidirect
234. #808C2×D3semidirect
272. D3×Dic3SD16semidirect
462. #103D32semidirect
682. C32#3101semidirect
765. C3#80408semidirect
766. C3#81412semidirect

Maximal subgroups

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

subgroupindex
#105953682
D3×#8932
#105924872
C3×#48182
C3×#48052
#105916512
#105915712
#105915652
#105909422
#105907752
#105907592
#105906562
#105905582
#105905162
#105904832
#814123
#804083