Finite Group Databasebeta

← #11887201

Subgroups — #11887201

Order 1152.

1224 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596300C211yesmaximal, characteristic
2#10596000C211yesmaximal, characteristic, complemented
3C32×#416C211yesmaximal, characteristic, complemented
4#10592938C211yesmaximal, characteristic, complemented
5#10592813C211yesmaximal, characteristic, complemented
6C8×#638C211yesmaximal, characteristic, complemented
7#10592702C211yesmaximal, characteristic, complemented
8#10592512C211yesmaximal, characteristic, complemented
9#10592504C211yesmaximal, characteristic, complemented
10#10592499C211yesmaximal, characteristic, complemented
11#10592497C211yesmaximal, characteristic, complemented
12#10592475C211yesmaximal, characteristic, complemented
13C3⋊D3×#102C211yesmaximal, characteristic, complemented
14#10592462C211yesmaximal, characteristic, complemented
15#10592457C211yesmaximal, characteristic, complemented
16#78845—34nomaximal
17C2×C32×#41C2211yescharacteristic
18C2×D4×C3⋊D3C2211yescharacteristic
19C22×C32×C8C2211yescharacteristic, complemented
20C32×#117C2211yescharacteristic, complemented
21#64156C2211yescharacteristic
22#64155C2211yescharacteristic
23C2×#3756C2211yescharacteristic, complemented
24#64148—21no—
25#64146—21no—
26D4×C3⋊Dic3C2211yescharacteristic
27C2×#3754C2211yescharacteristic
28#64139C2211yescharacteristic
29#64138—21no—
30C4×#638C2211yescharacteristic
31C2×#3752—21no—
32#64133C2211yescharacteristic, complemented
33C2×#3744C2211yescharacteristic
34C2×C8×C3⋊D3C2211yescharacteristic
35#64106C2211yescharacteristic
36C4⋊C4×C3⋊D3C2211yescharacteristic
37#64099C2211yescharacteristic, complemented
38#64096C2211yescharacteristic, complemented
39#64092—21no—
40#64088—21no—
41#64081—21no—
42#64079—21no—
43C32×#103C2211yescharacteristic, complemented
44C32×#103C2211yescharacteristic, complemented
45C32×#102C2211yescharacteristic
46C32×#102C2211yescharacteristic
47#63662C2211yescharacteristic, complemented
48#63659C2211yescharacteristic
49#63657C2211yescharacteristic, complemented
50#63648C2211yescharacteristic
51#63647C2211yescharacteristic
52#63644C2211yescharacteristic, complemented
53#63643C2211yescharacteristic, complemented
54#63641C2211yescharacteristic, complemented
55C8×C3⋊Dic3C2211yescharacteristic, complemented
56#63636C2211yescharacteristic
57#63636C2211yescharacteristic
58#63635C2211yescharacteristic, complemented
59#63634C2211yescharacteristic, complemented
60#5829—34no—
61#5529—34no—
62C3×#416D314yescomplemented
63#5239—34no—
64#5114—34no—
65C8×#67—34no—
66#5003—34no—
67#4813—34no—
68#4805—34no—
69#4800—34no—
70#4798—34no—
71#4776—34no—
72D3×#102—34no—
73#4763—34no—
74#4758—34no—
75C23×C3⋊D3—21no—
76C32×#41—22no—
77C32×#41—41no—
78C2×C32×Q8C2311yescharacteristic
79C2×C32×D4—21no—
80C2×C32×D4C2311yescharacteristic
81C22×C32×C4—21no—
82C22×C32×C4C2311yescharacteristic
83C2×#638—21no—
84C2×#638—21no—
85C2×#638D411yescharacteristic
86C22×C3⋊Dic3—21no—
87D4×C3⋊D3—22no—
88D4×C3⋊D3—41no—
89C2×C4⋊(C3⋊D3)C2311yescharacteristic
90C2×C4×C3⋊D3—21no—
91C2×C4×C3⋊D3C2311yescharacteristic
92C2×#634C2311yescharacteristic
93C2×C32×C8—41no—
94C2×C32×C8C2311yescharacteristic
95C2×C32×C8C2311yescharacteristic
96C32×C4⋊C4C2311yescharacteristic
97C32×C4⋊C4C2311yescharacteristic
98C32×C22⋊C4—21no—
99C32×C42—21no—
100#3757—21no—
101#3757—21no—
102#3757D411yescharacteristic
103#3756—41no—
104#3754—22no—
105#3752—21no—
106#3752—21no—
107#3752—21no—
108#3752—21no—
109#3752—21no—
110#3752D411yescharacteristic
111C4⋊(C3⋊Dic3)—21no—
112C4⋊(C3⋊Dic3)—21no—
113C4⋊(C3⋊Dic3)C2311yescharacteristic
114C4⋊(C3⋊Dic3)C2311yescharacteristic
115#3750—21no—
116#3750—21no—
117#3750—21no—
118#3750—21no—
119#3750—21no—
120#3750D411yescharacteristic
121C4×C3⋊Dic3—21no—
122C4×C3⋊Dic3C2311yescharacteristic
123C2×C3⋊(C3⋊C8)C2311yescharacteristic
124C2×C3⋊(C3⋊C8)C2311yescharacteristic
125#3744—41no—
126C8×C3⋊D3—41no—
127#3296—91noSylow
128C2×C3×#41C2×D314yes—
129C2×D3×D4—34no—
130C22×C3×C8C2×D314yescomplemented
131C3×#117C2×D314yescomplemented
132#947—34no—
133#946—34no—
134C2×#216—34no—
135#939—64no—
136#937—64no—
137D4×Dic3—34no—
138C2×#214—34no—
139#930—34no—
140#929—64no—
141C4×#67—34no—
142C2×(C2×D3)⋊C4—64no—
143#924—34no—
144C2×#204—34no—
145C2×D3×C8—34no—
146#897—34no—
147D3×C4⋊C4—34no—
148#890—34no—
149#887—34no—
150#883—64no—
151#879—64no—
152#872—64no—
153#870—64no—
154C3×#103C2×D314yescomplemented
155C3×#103C2×D314yescomplemented
156C3×#102C2×D314yes—
157C3×#102C2×D314yes—
158#835—34no—
159#832—34no—
160#830—34no—
161#821—34no—
162(C2×D3)⋊C8—34no—
163#817—34no—
164#816—34no—
165Dic3⋊C8—34no—
166C8×Dic3—34no—
167#809—34no—
168#809—34no—
169#808—34no—
170#807—34no—
171C23×C32—21no—
172C23×C32C2×D411yescharacteristic
173C22×C3⋊D3—21no—
174C22×C3⋊D3—42no—
175C22×C3⋊D3—42no—
176C22×C3⋊D3—81no—
177C22×C3⋊D3C2×D411yescharacteristic
178C32×Q8—21no—
179C32×Q8—21no—
180C32×D4—21no—
181C32×D4—42no—
182C32×D4#4112yes—
183C2×C32×C4—21no—
184C2×C32×C4—21no—
185C2×C32×C4—21no—
186C2×C32×C4—21no—
187C2×C32×C4—21no—
188C2×C32×C4—42no—
189C2×C32×C4C2×D411yescharacteristic
190C2×C32×C4C2411yescharacteristic
191#638—22no—
192#638—42no—
193#638—81no—
194C2×C3⋊Dic3—21no—
195C2×C3⋊Dic3—21no—
196C2×C3⋊Dic3—21no—
197C2×C3⋊Dic3—81no—
198C2×C3⋊Dic3C2×D411yescharacteristic
199C2×C3⋊Dic3C2×D411yescharacteristic
200C2×C3⋊Dic3C2×D411yescharacteristic
201C4⋊(C3⋊D3)—21no—
202C4⋊(C3⋊D3)—21no—
203C4×C3⋊D3—21no—
204C4×C3⋊D3—21no—
205C4×C3⋊D3—42no—
206#634—21no—
207#634—21no—
208C32×C8—21no—
209C32×C8—21no—
210C3⋊(C3⋊C8)—21no—
211C3⋊(C3⋊C8)—21no—
212#552—91no—
213#546—91no—
214#488—91no—
215#483—91no—
216#482—91no—
217#478—91no—
218#467—91no—
219#465—91no—
220#464—91no—
221#452—91no—
222#450—91no—
223C4×SD16—91no—
224C8×D4—91no—
225#416C3⋊D311yescharacteristic, complemented
226C2×#102—91no—
227C23×D3—64no—
228C3×#41—28no—
229C3×#41—44no—
230C2×C3×Q8C22×D314yes—
231C2×C3×D4—24no—
232C2×C3×D4C22×D314yes—
233C22×C3×C4—24no—
234C22×C3×C4C22×D314yes—
235C2×#67—34no—
236C2×#67—64no—
237C2×#67—64no—
238C22×Dic3—64no—
239D3×D4—68no—
240D3×D4—124no—
241C2×D12—34no—
242C2×C4×D3—34no—
243C2×C4×D3—64no—
244C2×Dic6—34no—
245C2×C3×C8—44no—
246C2×C3×C8C22×D314yes—
247C2×C3×C8C22×D314yes—
248C3×C4⋊C4C22×D314yes—
249C3×C4⋊C4C22×D314yes—
250C3×C22⋊C4—24no—
251C3×C42—24no—
252#217—34no—
253#217—64no—
254#217—64no—
255#216—124no—
256#214—68no—
257(C2×D3)⋊C4—34no—
258(C2×D3)⋊C4—64no—
259(C2×D3)⋊C4—64no—
260(C2×D3)⋊C4—64no—
261(C2×D3)⋊C4—64no—
262(C2×D3)⋊C4—64no—
263C4⋊Dic3—34no—
264C4⋊Dic3—34no—
265C4⋊Dic3—64no—
266C4⋊Dic3—64no—
267Dic3⋊C4—34no—
268Dic3⋊C4—64no—
269Dic3⋊C4—64no—
270Dic3⋊C4—64no—
271Dic3⋊C4—64no—
272Dic3⋊C4—64no—
273C4×Dic3—34no—
274C4×Dic3—64no—
275C2×C3⋊C8—34no—
276C2×C3⋊C8—34no—
277#204—124no—
278D3×C8—124no—
279C22×C32—22no—
280C22×C32—21no—
281C22×C32—21no—
282C22×C32—21no—
283C22×C32—41no—
284C22×C32—41no—
285C22×C32C22×D411yescharacteristic
286C2×C3⋊D3—21no—
287C2×C3⋊D3—21no—
288C2×C3⋊D3—41no—
289C2×C3⋊D3—41no—
290C2×C3⋊D3—41no—
291C2×C3⋊D3—84no—
292C2×C3⋊D3#13512yes—
293C32×C4—21no—
294C32×C4—41no—
295C32×C4—41no—
296C32×C4—41no—
297C32×C4C2×#4111yescharacteristic
298C32×C4H(5,𝔽2)11yescharacteristic
299C3⋊Dic3—21no—
300C3⋊Dic3—21no—
301C3⋊Dic3—21no—
302C3⋊Dic3—41no—
303C3⋊Dic3—41no—
304C3⋊Dic3—41no—
305C2×#41C2×C3⋊D311yescharacteristic
306C22×D4—91no—
307C2×Q16—91no—
308C2×SD16—91no—
309C2×SD16—91no—
310C22×C8—91no—
311C22×C8C2×C3⋊D311yescharacteristic, complemented
312#126—181no—
313#125—91no—
314#125—181no—
315#124—91no—
316#123—181no—
317#123—181no—
318C22⋊Q8—91no—
319C22⋊Q8—91no—
320C22⋊Q8—91no—
321#121—91no—
322#121—181no—
323#120—181no—
324C4×Q8—91no—
325C4×D4—91no—
326C4×D4—91no—
327#117—181no—
328#117C2×C3⋊D311yescharacteristic, complemented
329C2×C4⋊C4—91no—
330C2×C22⋊C4—181no—
331#107—91no—
332#106—91no—
333#106—91no—
334C4⋊C8—91no—
335#103—91no—
336#103—91no—
337#103C2×C3⋊D311yescharacteristic, complemented
338#103C2×C3⋊D311yescharacteristic, complemented
339#102—91no—
340#102—91no—
341#102—91no—
342#102—91no—
343#102C2×C3⋊D311yescharacteristic
344#102C2×C3⋊D311yescharacteristic
345C22⋊C8—91no—
346C22⋊C8—91no—
347C4×C8—91no—
348C23×C3—24no—
349C23×C3D3×D414yes—
350C22×D3—34no—
351C22×D3—64no—
352C22×D3—128no—
353C22×D3—128no—
354C22×D3—244no—
355C3×Q8—24no—
356C3×Q8—24no—
357C3×D4—24no—
358C3×D4—48no—
359C3×D4#23518yes—
360C2×C3×C4—24no—
361C2×C3×C4—24no—
362C2×C3×C4—24no—
363C2×C3×C4—24no—
364C2×C3×C4—24no—
365C2×C3×C4—48no—
366C2×C3×C4D3×D414yes—
367C2×C3×C4C23×D314yes—
368#67—68no—
369#67—128no—
370#67—244no—
371C2×Dic3—34no—
372C2×Dic3—34no—
373C2×Dic3—34no—
374C2×Dic3—64no—
375C2×Dic3—64no—
376C2×Dic3—64no—
377C2×Dic3—244no—
378D12—64no—
379D12—64no—
380C4×D3—64no—
381C4×D3—64no—
382C4×D3—128no—
383Dic6—64no—
384Dic6—64no—
385C3×C8—24no—
386C3×C8—24no—
387C3⋊C8—64no—
388C3⋊C8—64no—
389C2×C32—42no—
390C2×C32—41no—
391C2×C32#54611yescharacteristic
392C2×C32C2×#13511yescharacteristic
393C2×C32#57711yescharacteristic
394C3⋊D3—22no—
395C3⋊D3—81no—
396C24—181no—
397#41—22no—
398#41—41no—
399C2×Q8—91no—
400C2×Q8C22×C3⋊D311yescharacteristic
401C2×D4—21no—
402C2×D4—91no—
403C2×D4—91no—
404C2×D4—181no—
405C2×D4—182no—
406C2×D4—181no—
407C2×D4—361no—
408C2×D4C22×C3⋊D311yescharacteristic
409C22×C4—21no—
410C22×C4—91no—
411C22×C4—181no—
412C22×C4—181no—
413C22×C4C22×C3⋊D311yescharacteristic
414Q16—361no—
415SD16—182no—
416SD16—361no—
417C2×C8—41no—
418C2×C8—91no—
419C2×C8—91no—
420C2×C8—361no—
421C2×C8C22×C3⋊D311yescharacteristic
422C2×C8C22×C3⋊D311yescharacteristic
423C4⋊C4—91no—
424C4⋊C4—91no—
425C4⋊C4—91no—
426C4⋊C4—181no—
427C4⋊C4—181no—
428C4⋊C4—181no—
429C4⋊C4—181no—
430C4⋊C4—181no—
431C4⋊C4—181no—
432C4⋊C4—181no—
433C4⋊C4C22×C3⋊D311yescharacteristic
434C4⋊C4C22×C3⋊D311yescharacteristic
435C22⋊C4—21no—
436C22⋊C4—91no—
437C22⋊C4—91no—
438C22⋊C4—181no—
439C22⋊C4—181no—
440C22⋊C4—181no—
441C22⋊C4—181no—
442C22⋊C4—181no—
443C22⋊C4—181no—
444C22⋊C4—181no—
445C42—21no—
446C42—91no—
447C42—181no—
448C22×C3—28no—
449C22×C3—24no—
450C22×C3—24no—
451C22×C3—24no—
452C22×C3—44no—
453C22×C3—44no—
454C22×C3C2×D3×D414yes—
455C2×D3—38no—
456C2×D3—64no—
457C2×D3—64no—
458C2×D3—124no—
459C2×D3—124no—
460C2×D3—124no—
461C2×D3—2416no—
462C3×C4—24no—
463C3×C4—44no—
464C3×C4—44no—
465C3×C4—44no—
466C3×C4C2×#23514yes—
467C3×C4#100414yes—
468Dic3—64no—
469Dic3—64no—
470Dic3—64no—
471Dic3—124no—
472Dic3—124no—
473Dic3—124no—
474C32#329611yescharacteristic, complemented, Sylow
475C23—21no—
476C23—91no—
477C23—181no—
478C23—362no—
479C23—362no—
480C23—721no—
481C23D4×C3⋊D311yescharacteristic
482Q8—21no—
483Q8—21no—
484Q8—181no—
485Q8—181no—
486D4—21no—
487D4—42no—
488D4—182no—
489D4—181no—
490D4—181no—
491D4—362no—
492D4—721no—
493D4#382812yes—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—42no—
500C2×C4—91no—
501C2×C4—91no—
502C2×C4—91no—
503C2×C4—181no—
504C2×C4—181no—
505C2×C4—181no—
506C2×C4—181no—
507C2×C4—181no—
508C2×C4—362no—
509C2×C4—721no—
510C2×C4D4×C3⋊D311yescharacteristic
511C2×C4C23×C3⋊D311yescharacteristic
512C8—21no—
513C8—21no—
514C8—181no—
515C8—181no—
516C2×C3—48no—
517C2×C3—44no—
518C2×C3#549014yes—
519C2×C3D3×#13514yes—
520C2×C3#577014yes—
521D3—68no—
522D3—244no—
523C22—21no—
524C22—22no—
525C22—21no—
526C22—21no—
527C22—41no—
528C22—41no—
529C22—92no—
530C22—181no—
531C22—181no—
532C22—361no—
533C22—361no—
534C22—361no—
535C22—724no—
536C22C2×D4×C3⋊D311yescharacteristic
537C4—21no—
538C4—41no—
539C4—41no—
540C4—41no—
541C4—181no—
542C4—181no—
543C4—181no—
544C4—361no—
545C4—361no—
546C4—361no—
547C4C2×#382811yescharacteristic
548C4#6436111yescharacteristic
549C3#7884514yescomplemented
550C2—41no—
551C2—42no—
552C2—182no—
553C2—721no—
554C2#1059596111yescharacteristic
555C2C3⋊D3×#13511yescharacteristic
556C2#1059624111yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#416C2
socleC22×C32C22×D4
prime radical#10596300C2
hypercenter#416C3⋊D3
hypocenterC32#3296
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
2. #10596000C2semidirect
3. C32×#416C2semidirect
4. #10592938C2semidirect
5. #10592813C2semidirect
6. C8×#638C2semidirect
7. #10592702C2semidirect
8. #10592512C2semidirect
9. #10592504C2semidirect
10. #10592499C2semidirect
11. #10592497C2semidirect
12. #10592475C2semidirect
13. C3⋊D3×#102C2semidirect
14. #10592462C2semidirect
15. #10592457C2semidirect
19. C22×C32×C8C22semidirect
20. C32×#117C22semidirect
23. C2×#3756C22semidirect
32. #64133C22semidirect
37. #64099C22semidirect
38. #64096C22semidirect
43. C32×#103C22semidirect
44. C32×#103C22semidirect
47. #63662C22semidirect
49. #63657C22semidirect
52. #63644C22semidirect
53. #63643C22semidirect
54. #63641C22semidirect
55. C8×C3⋊Dic3C22semidirect
58. #63635C22semidirect
59. #63634C22semidirect
62. C3×#416D3semidirect
130. C22×C3×C8C2×D3semidirect
131. C3×#117C2×D3semidirect
154. C3×#103C2×D3semidirect
155. C3×#103C2×D3semidirect
225. #416C3⋊D3semidirect
311. C22×C8C2×C3⋊D3semidirect
328. #117C2×C3⋊D3semidirect
337. #103C2×C3⋊D3semidirect
338. #103C2×C3⋊D3semidirect
474. C32#3296semidirect
549. C3#78845semidirect

Maximal subgroups

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

subgroupindex
#105963002
#105960002
C32×#4162
#105929382
#105928132
C8×#6382
#105927022
#105925122
#105925042
#105924992
#105924972
#105924752
C3⋊D3×#1022
#105924622
#105924572
#788453