Finite Group Databasebeta

← #10779130

Subgroups — #10779130

Order 768.

608 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#83354C211yesmaximal, characteristic
2#83339C211yesmaximal, characteristic, complemented
3#79348C211yesmaximal, characteristic
4#79276C211yesmaximal, characteristic
5C3×#1554C211yesmaximal, characteristic, complemented
6#70794C211yesmaximal, characteristic, complemented
7#70781C211yesmaximal, characteristic, complemented
8#68509C211yesmaximal, characteristic, complemented
9#68508C211yesmaximal, characteristic, complemented
10#68497C211yesmaximal, characteristic, complemented
11#68496C211yesmaximal, characteristic, complemented
12#68467C211yesmaximal, characteristic, complemented
13#68466C211yesmaximal, characteristic, complemented
14#68443C211yesmaximal, characteristic, complemented
15#68442C211yesmaximal, characteristic, complemented
16#19273—31nomaximal, Sylow
17C3×#533C2211yescharacteristic
18C4×#235C2211yescharacteristic
19#5470C2211yescharacteristic
20C3×#432C2211yescharacteristic
21C3×#431C2211yescharacteristic
22#5091C2211yescharacteristic
23#5090C2211yescharacteristic
24#5084C2211yescharacteristic
25#5083C2211yescharacteristic
26#5080C2211yescharacteristic
27#5080C2211yescharacteristic
28#5078C2211yescharacteristic
29#5078C2211yescharacteristic
30#5065—21no—
31#5065—21no—
32#5047—21no—
33#5045—21no—
34#5030—21no—
35#5026—21no—
36#4998—21no—
37#4998—21no—
38#4926C2211yescharacteristic
39C2×C4×C3⋊C8C2211yescharacteristic
40#4850C2211yescharacteristic
41#4849C2211yescharacteristic
42#4842C2211yescharacteristic
43#4841C2211yescharacteristic
44#4834C2211yescharacteristic
45#4834C2211yescharacteristic
46#4830C2211yescharacteristic
47#4830C2211yescharacteristic
48#4733—21no—
49#67⋊C8—21no—
50#67⋊C8—21no—
51#4723—21no—
52#4716—21no—
53#4710—21no—
54#4685—21no—
55C4×D3×C8—21no—
56C3×#333C2211yescharacteristic
57C3×#333C2211yescharacteristic
58C3×#332C2211yescharacteristic
59C3×#332C2211yescharacteristic
60#4486C2211yescharacteristic
61#4486C2211yescharacteristic
62#4481C2211yescharacteristic
63#4481C2211yescharacteristic
64#4480C2211yescharacteristic
65#4480C2211yescharacteristic
66#4479C2211yescharacteristic
67#4479C2211yescharacteristic
68#3160—31no—
69#3116—31no—
70#3116—31no—
71C8×#41—31no—
72#1676—31no—
73#1675—31no—
74#1674—31no—
75#1673—31no—
76#1672—31no—
77#1672—31no—
78#1671—31no—
79#1671—31no—
80#1568—31no—
81#1554—31no—
82#1554D311yescharacteristic, complemented
83C2×#235D411yescharacteristic
84C3×C4⋊Q8C2311yescharacteristic
85C3×C4⋊Q8C2311yescharacteristic
86C3×#125—21no—
87C3×C22⋊Q8—21no—
88C3×C22⋊Q8—21no—
89C3×C4×Q8—21no—
90C3×C4×Q8—21no—
91C3×#117—21no—
92C2×C3×C42C2311yescharacteristic
93C2×#216—21no—
94C2×#215—21no—
95C4×#67—21no—
96C4×#67—21no—
97#926—21no—
98#926D411yescharacteristic
99#924—21no—
100#924—21no—
101C22×C3⋊C8D411yescharacteristic
102C22×C3⋊C8D411yescharacteristic
103C2×Dic12—21no—
104C2×#204—21no—
105C2×D3×C8—21no—
106C2×D3×C8—21no—
107C4×D12D411yescharacteristic
108C4×D12C2311yescharacteristic
109#872—21no—
110C42×D3—21no—
111#870—21no—
112#869C2311yescharacteristic
113#869C2311yescharacteristic
114C4×Dic6—21no—
115C4×Dic6—21no—
116C4×Dic6D411yescharacteristic
117C4×Dic6C2311yescharacteristic
118C3×C4⋊C8C2311yescharacteristic
119C3×C4⋊C8C2311yescharacteristic
120C3×C4⋊C8C2311yescharacteristic
121C3×C4⋊C8C2311yescharacteristic
122C3×C22⋊C8—21no—
123C3×C22⋊C8—21no—
124C3×#97—21no—
125C3×C4×C8—21no—
126#835—21no—
127#835—21no—
128#830—21no—
129#821—21no—
130(C2×D3)⋊C8—21no—
131(C2×D3)⋊C8—21no—
132#818—21no—
133#817—21no—
134#816—21no—
135#816—21no—
136#816—21no—
137Dic3⋊C8—21no—
138Dic3⋊C8—21no—
139C8×Dic3—21no—
140C8×Dic3—21no—
141#810—21no—
142#809—21no—
143#808—21no—
144#808—21no—
145#808—21no—
146#808—21no—
147#808—21no—
148#807—21no—
149#807—21no—
150#807—21no—
151#807—21no—
152#807—21no—
153C4⋊(C3⋊C8)C2311yescharacteristic
154C4⋊(C3⋊C8)C2311yescharacteristic
155#803—21no—
156C4×C3⋊C8D411yescharacteristic
157C4×C3⋊C8D411yescharacteristic
158C4×C3⋊C8C2311yescharacteristic
159C4×C3⋊C8C2311yescharacteristic
160#533—31no—
161#533C2×D311yescharacteristic
162C4×#41—31no—
163#500—31no—
164#500—31no—
165#499—61no—
166#499—61no—
167#498—31no—
168#498—31no—
169#485—61no—
170#485—61no—
171#477—31no—
172#477—31no—
173#476—31no—
174#476—31no—
175#462—31no—
176#462—31no—
177#461—31no—
178#461—31no—
179#452—61no—
180#452—61no—
181C8×Q8—31no—
182C8×Q8—31no—
183#441—61no—
184#441—61no—
185#440—61no—
186#440—61no—
187C8×D4—31no—
188C8×D4—31no—
189C8×D4—61no—
190C8×D4—61no—
191#432—31no—
192#432C2×D311yescharacteristic
193#431—61no—
194#431C2×D311yescharacteristic
195#427—61no—
196#427—61no—
197C2×C4×C8—31no—
198C2×C4×C8—61no—
199#335—31no—
200#335—31no—
201#334—31no—
202#334—31no—
203#333—31no—
204#333—31no—
205#333C2×D311yescharacteristic
206#333C2×D311yescharacteristic
207#332—31no—
208#332—31no—
209#332C2×D311yescharacteristic
210#332C2×D311yescharacteristic
211C2×C3×Q8—21no—
212C2×C3×Q8—21no—
213C22×C3×C4C2×D411yescharacteristic
214C22×C3×C4C2×D411yescharacteristic
215C22×C3×C4#4111yescharacteristic
216C2×#67—21no—
217#235—22no—
218#235—22no—
219C2×D12C2×D411yescharacteristic
220C2×C4×D3—21no—
221C2×C4×D3—21no—
222C2×C4×D3—21no—
223C2×Dic6—21no—
224C2×Dic6—21no—
225C2×Dic6C2×D411yescharacteristic
226C2×C3×C8—21no—
227C2×C3×C8—21no—
228C2×C3×C8—21no—
229C2×C3×C8—21no—
230C3×C4⋊C4—21no—
231C3×C4⋊C4—21no—
232C3×C4⋊C4—21no—
233C3×C4⋊C4—21no—
234C3×C4⋊C4—41no—
235C3×C4⋊C4—41no—
236C3×C22⋊C4—41no—
237C3×C42—41no—
238C3×C42C2×D411yescharacteristic
239C3×C42C2×D411yescharacteristic
240C3×C42#4111yescharacteristic
241C3×C42C2411yescharacteristic
242#217—21no—
243#217—41no—
244#216—42no—
245#215—42no—
246(C2×D3)⋊C4—21no—
247(C2×D3)⋊C4—21no—
248C4⋊Dic3—21no—
249C4⋊Dic3—21no—
250C4⋊Dic3—21no—
251C4⋊Dic3—21no—
252C4⋊Dic3C2×D411yescharacteristic
253C4⋊Dic3C2×D411yescharacteristic
254Dic3⋊C4—21no—
255Dic3⋊C4—21no—
256Dic3⋊C4—41no—
257Dic3⋊C4—41no—
258C4×Dic3—21no—
259C4×Dic3—21no—
260C4×Dic3—21no—
261C4×Dic3—41no—
262C2×C3⋊C8—22no—
263C2×C3⋊C8—22no—
264C2×C3⋊C8—21no—
265C2×C3⋊C8—21no—
266C2×C3⋊C8C2×D411yescharacteristic
267C2×C3⋊C8C2×D411yescharacteristic
268C2×C3⋊C8C2×D411yescharacteristic
269C2×C3⋊C8C2×D411yescharacteristic
270Dic12—42no—
271#204—42no—
272D3×C8—42no—
273D3×C8—42no—
274C2×#41—31no—
275C2×Q16—61no—
276C2×Q16—61no—
277C2×SD16—61no—
278C2×SD16—61no—
279C22×C8—31no—
280C22×C8—31no—
281C22×C8—61no—
282C22×C8—61no—
283C4⋊Q8—31no—
284C4⋊Q8—31no—
285C4⋊Q8C22×D311yescharacteristic
286C4⋊Q8C22×D311yescharacteristic
287#125—21no—
288#125—61no—
289C22⋊Q8—21no—
290C22⋊Q8—21no—
291C22⋊Q8—61no—
292C22⋊Q8—61no—
293C4×Q8—21no—
294C4×Q8—21no—
295C4×Q8—31no—
296C4×Q8—31no—
297C4×Q8—61no—
298C4×Q8—61no—
299C4×D4—31no—
300C4×D4—31no—
301C4×D4—61no—
302C4×D4—61no—
303#117—21no—
304#117—31no—
305#117—61no—
306#117—61no—
307C2×C42—61no—
308C2×C42C22×D311yescharacteristic
309#107—61no—
310#107—61no—
311#107—61no—
312#107—61no—
313#107—61no—
314#107—61no—
315#106—61no—
316#106—61no—
317#106—61no—
318#106—61no—
319#106—61no—
320#106—61no—
321C4⋊C8—31no—
322C4⋊C8—31no—
323C4⋊C8—61no—
324C4⋊C8—61no—
325C4⋊C8C22×D311yescharacteristic
326C4⋊C8C22×D311yescharacteristic
327C4⋊C8C22×D311yescharacteristic
328C4⋊C8C22×D311yescharacteristic
329#103—61no—
330#103—61no—
331#103—61no—
332#103—61no—
333#103—61no—
334#103—61no—
335#102—61no—
336#102—61no—
337C22⋊C8—21no—
338C22⋊C8—21no—
339C22⋊C8—61no—
340C22⋊C8—61no—
341C22⋊C8—61no—
342#97—21no—
343#97—61no—
344C4×C8—21no—
345C4×C8—31no—
346C4×C8—31no—
347C4×C8—31no—
348C4×C8—31no—
349C4×C8—61no—
350C4×C8—61no—
351C23×C3#12111yescharacteristic
352C22×D3—21no—
353C3×Q8—41no—
354C3×Q8—41no—
355C3×Q8—81no—
356C2×C3×C4—21no—
357C2×C3×C4—21no—
358C2×C3×C4—21no—
359C2×C3×C4—21no—
360C2×C3×C4—41no—
361C2×C3×C4—41no—
362C2×C3×C4—41no—
363C2×C3×C4#12111yescharacteristic
364C2×C3×C4#12111yescharacteristic
365C2×C3×C4#12111yescharacteristic
366C2×C3×C4C22×D411yescharacteristic
367C2×C3×C4C22×D411yescharacteristic
368C2×C3×C4C2×#4111yescharacteristic
369#67—24no—
370C2×Dic3—21no—
371C2×Dic3—21no—
372C2×Dic3—21no—
373C2×Dic3—41no—
374C2×Dic3—41no—
375D12—21no—
376D12#13512yes—
377C4×D3—24no—
378C4×D3—42no—
379C4×D3—41no—
380C4×D3—41no—
381Dic6—21no—
382Dic6—41no—
383Dic6—41no—
384Dic6—81no—
385Dic6#13512yes—
386C3×C8—41no—
387C3×C8—41no—
388C3×C8—41no—
389C3×C8—41no—
390C3⋊C8—21no—
391C3⋊C8—21no—
392C3⋊C8—41no—
393C3⋊C8—41no—
394C3⋊C8#13712yes—
395C3⋊C8#13712yes—
396#41—62no—
397#41—62no—
398C2×Q8—21no—
399C2×Q8—21no—
400C2×Q8—31no—
401C2×Q8—61no—
402C2×Q8—61no—
403C2×D4—31no—
404C2×D4—61no—
405C22×C4—61no—
406C22×C4—61no—
407C22×C4—61no—
408C22×C4#23511yescharacteristic
409C22×C4D3×D411yescharacteristic
410C22×C4D3×D411yescharacteristic
411Q16—122no—
412Q16—122no—
413SD16—122no—
414SD16—122no—
415C2×C8—21no—
416C2×C8—21no—
417C2×C8—21no—
418C2×C8—21no—
419C2×C8—31no—
420C2×C8—31no—
421C2×C8—31no—
422C2×C8—31no—
423C2×C8—62no—
424C2×C8—62no—
425C2×C8—61no—
426C2×C8—61no—
427C2×C8—122no—
428C2×C8—122no—
429C4⋊C4—21no—
430C4⋊C4—21no—
431C4⋊C4—21no—
432C4⋊C4—21no—
433C4⋊C4—31no—
434C4⋊C4—31no—
435C4⋊C4—41no—
436C4⋊C4—41no—
437C4⋊C4—61no—
438C4⋊C4—61no—
439C4⋊C4—61no—
440C4⋊C4—61no—
441C4⋊C4—61no—
442C4⋊C4—61no—
443C4⋊C4—121no—
444C4⋊C4—121no—
445C22⋊C4—41no—
446C22⋊C4—61no—
447C22⋊C4—61no—
448C22⋊C4—61no—
449C22⋊C4—121no—
450C42—41no—
451C42—61no—
452C42—61no—
453C42—61no—
454C42—121no—
455C42#23511yescharacteristic
456C42D3×D411yescharacteristic
457C42D3×D411yescharacteristic
458C42C23×D311yescharacteristic
459C22×C3—21no—
460C22×C3—21no—
461C22×C3—21no—
462C22×C3C2×#12111yescharacteristic
463C2×D3—22no—
464C2×D3—41no—
465C2×D3—41no—
466C3×C4—21no—
467C3×C4—21no—
468C3×C4—21no—
469C3×C4—21no—
470C3×C4—81no—
471C3×C4—81no—
472C3×C4C2×#13511yescharacteristic
473C3×C4C2×#13511yescharacteristic
474C3×C4C2×#13711yescharacteristic
475C3×C4C2×#13711yescharacteristic
476Dic3—22no—
477Dic3—41no—
478Dic3—41no—
479Dic3—81no—
480Dic3—81no—
481C23—61no—
482C23#88411yescharacteristic
483Q8—32no—
484Q8—41no—
485Q8—41no—
486Q8—61no—
487Q8—81no—
488Q8—121no—
489Q8—121no—
490Q8—241no—
491D4—32no—
492D4—64no—
493D4—61no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—64no—
502C2×C4—61no—
503C2×C4—61no—
504C2×C4—61no—
505C2×C4—122no—
506C2×C4—121no—
507C2×C4—121no—
508C2×C4—121no—
509C2×C4—121no—
510C2×C4#88411yescharacteristic
511C2×C4#88411yescharacteristic
512C2×C4#88411yescharacteristic
513C2×C4C2×#23511yescharacteristic
514C2×C4C2×D3×D411yescharacteristic
515C2×C4C2×D3×D411yescharacteristic
516C8—32no—
517C8—32no—
518C8—41no—
519C8—41no—
520C8—41no—
521C8—41no—
522C8—61no—
523C8—61no—
524C8—121no—
525C8—121no—
526C2×C3—41no—
527C2×C3#303911yescharacteristic
528C2×C3#305011yescharacteristic
529C2×C3#306711yescharacteristic
530D3—42no—
531C22—21no—
532C22—21no—
533C22—21no—
534C22—62no—
535C22—121no—
536C22—121no—
537C22C2×#88411yescharacteristic
538C4—21no—
539C4—21no—
540C4—21no—
541C4—21no—
542C4—62no—
543C4—81no—
544C4—81no—
545C4—121no—
546C4—121no—
547C4—241no—
548C4—241no—
549C4D3×#13511yescharacteristic
550C4D3×#13511yescharacteristic
551C4D3×#13711yescharacteristic
552C4D3×#13711yescharacteristic
553C3#1927311yescharacteristic, complemented, Sylow
554C2—41no—
555C2—122no—
556C2#7871911yescharacteristic
557C2#7883811yescharacteristic
558C2#7897411yescharacteristic
subgroupG/H
centerC22C2×#884
commutator, cosocleC3×C42C24
FrattiniC42C23×D3
FittingC3×#1554C2
socleC22×C3C2×#121
prime radicalC2×#235D4
hypercenter#1554D3
hypocenterC3#19273
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1554

Complements

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

NH ≅ G/Ntype
2. #83339C2semidirect
5. C3×#1554C2semidirect
6. #70794C2semidirect
7. #70781C2semidirect
8. #68509C2semidirect
9. #68508C2semidirect
10. #68497C2semidirect
11. #68496C2semidirect
12. #68467C2semidirect
13. #68466C2semidirect
14. #68443C2semidirect
15. #68442C2semidirect
82. #1554D3semidirect
553. C3#19273semidirect

Maximal subgroups

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

subgroupindex
#833542
#833392
#793482
#792762
C3×#15542
#707942
#707812
#685092
#685082
#684972
#684962
#684672
#684662
#684432
#684422
#192733