Finite Group Databasebeta

← #11887183

Subgroups — #11887183

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#10596110C211yesmaximal, characteristic, complemented
2#10596083C211yesmaximal, characteristic
3C32×#465C211yesmaximal, characteristic, complemented
4#10592868C211yesmaximal, characteristic, complemented
5#10592865C211yesmaximal, characteristic, complemented
6#10592812C211yesmaximal, characteristic, complemented
7C8×#638C211yesmaximal, characteristic, complemented
8#10592746C211yesmaximal, characteristic, complemented
9#10592734C211yesmaximal, characteristic, complemented
10#10592570C211yesmaximal, characteristic, complemented
11#10592561C211yesmaximal, characteristic, complemented
12#10592512C211yesmaximal, characteristic, complemented
13#10592487C211yesmaximal, characteristic, complemented
14C3⋊D3×#102C211yesmaximal, characteristic, complemented
15#10592467C211yesmaximal, characteristic, complemented
16#80671—34nomaximal
17C2×D4×C3⋊D3C2211yescharacteristic
18C2×#3828C2211yescharacteristic
19C2×C32×SD16C2211yescharacteristic
20C22×C32×C8C2211yescharacteristic, complemented
21C32×C22⋊Q8C2211yescharacteristic, complemented
22C32×#121C2211yescharacteristic
23#64155C2211yescharacteristic
24Q8×C3⋊Dic3C2211yescharacteristic, complemented
25C2×#3756C2211yescharacteristic, complemented
26C2×#3755C2211yescharacteristic
27#64147—21no—
28#64146—21no—
29#64145C2211yescharacteristic
30C4×#638C2211yescharacteristic
31#64135C2211yescharacteristic, complemented
32C2×C8×C3⋊D3C2211yescharacteristic
33#64106C2211yescharacteristic
34#64102C2211yescharacteristic
35#64101—21no—
36C4⋊C4×C3⋊D3C2211yescharacteristic
37#64099C2211yescharacteristic, complemented
38#64098—21no—
39#64092—21no—
40#64092—21no—
41C22⋊C4×C3⋊D3—21no—
42#64088—21no—
43C32×#106C2211yescharacteristic, complemented
44C32×#103C2211yescharacteristic, complemented
45C32×#102C2211yescharacteristic
46#63659C2211yescharacteristic
47#63659C2211yescharacteristic
48#63657C2211yescharacteristic, complemented
49#63648C2211yescharacteristic
50#63648C2211yescharacteristic
51#63647C2211yescharacteristic
52#63643C2211yescharacteristic, complemented
53#63643C2211yescharacteristic, complemented
54#63641C2211yescharacteristic, complemented
55C8×C3⋊Dic3C2211yescharacteristic, complemented
56#63637C2211yescharacteristic, complemented
57#63636C2211yescharacteristic
58#63635C2211yescharacteristic, complemented
59#63634C2211yescharacteristic, complemented
60#5639—34no—
61#5612—34no—
62C3×#465D314yescomplemented
63#5169—34no—
64#5166—34no—
65#5113—34no—
66C8×#67—34no—
67#5047—34no—
68#5035—34no—
69#4871—34no—
70#4862—34no—
71#4813—34no—
72#4788—34no—
73D3×#102—34no—
74#4768—34no—
75C23×C3⋊D3—21no—
76C2×C32×Q8C2311yescharacteristic
77C2×C32×D4—21no—
78C2×C32×D4C2311yescharacteristic
79C22×C32×C4C2311yescharacteristic
80C2×#638—21no—
81C2×#638—21no—
82C2×#638D411yescharacteristic
83D4×C3⋊D3—22no—
84D4×C3⋊D3—41no—
85#3828—22no—
86#3828—41no—
87C2×C4⋊(C3⋊D3)C2311yescharacteristic
88C2×C4×C3⋊D3—21no—
89C2×C4×C3⋊D3—21no—
90C2×C4×C3⋊D3—21no—
91C2×C4×C3⋊D3C2311yescharacteristic
92C2×#634C2311yescharacteristic
93C32×SD16—41no—
94C2×C32×C8—41no—
95C2×C32×C8C2311yescharacteristic
96C2×C32×C8C2311yescharacteristic
97C32×C4⋊C4—21no—
98C32×C4⋊C4C2311yescharacteristic
99C32×C4⋊C4C2311yescharacteristic
100C32×C22⋊C4—21no—
101C32×C22⋊C4—21no—
102#3757—21no—
103#3757—21no—
104#3757—21no—
105#3757D411yescharacteristic
106#3756—41no—
107#3755—22no—
108#3752—21no—
109#3752—21no—
110#3752—21no—
111#3752D411yescharacteristic
112C4⋊(C3⋊Dic3)—21no—
113C4⋊(C3⋊Dic3)—21no—
114C4⋊(C3⋊Dic3)—21no—
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117#3750—21no—
118#3750—21no—
119#3750—21no—
120#3750D411yescharacteristic
121C4×C3⋊Dic3—21no—
122C4×C3⋊Dic3—21no—
123C4×C3⋊Dic3C2311yescharacteristic
124C2×C3⋊(C3⋊C8)C2311yescharacteristic
125C2×C3⋊(C3⋊C8)C2311yescharacteristic
126C8×C3⋊D3—41no—
127#3296—91noSylow
128C2×D3×D4—34no—
129C2×#235—34no—
130C2×C3×SD16C2×D314yes—
131C22×C3×C8C2×D314yescomplemented
132C3×C22⋊Q8C2×D314yescomplemented
133C3×#121C2×D314yes—
134#946—34no—
135Q8×Dic3—34no—
136C2×#216—34no—
137C2×#215—34no—
138#938—64no—
139#937—64no—
140#936—34no—
141C4×#67—34no—
142#926—34no—
143C2×D3×C8—34no—
144#897—34no—
145#893—34no—
146#892—64no—
147D3×C4⋊C4—34no—
148#890—34no—
149#889—64no—
150#883—64no—
151#883—64no—
152D3×C22⋊C4—64no—
153#879—64no—
154C3×#106C2×D314yescomplemented
155C3×#103C2×D314yescomplemented
156C3×#102C2×D314yes—
157#832—34no—
158#832—34no—
159#830—34no—
160#821—34no—
161#821—34no—
162(C2×D3)⋊C8—34no—
163#816—34no—
164#816—34no—
165Dic3⋊C8—34no—
166C8×Dic3—34no—
167#810—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—21no—
182C32×D4—81no—
183C2×C32×C4—21no—
184C2×C32×C4—21no—
185C2×C32×C4—21no—
186C2×C32×C4—21no—
187C2×C32×C4—21no—
188C2×C32×C4C2×D411yescharacteristic
189C2×C32×C4C2411yescharacteristic
190#638—22no—
191#638—42no—
192#638—42no—
193C2×C3⋊Dic3—21no—
194C2×C3⋊Dic3—21no—
195C2×C3⋊Dic3—21no—
196C2×C3⋊Dic3C2×D411yescharacteristic
197C2×C3⋊Dic3C2×D411yescharacteristic
198C2×C3⋊Dic3C2×D411yescharacteristic
199C4⋊(C3⋊D3)—21no—
200C4⋊(C3⋊D3)#4112yes—
201C4×C3⋊D3—21no—
202C4×C3⋊D3—21no—
203C4×C3⋊D3—42no—
204C4×C3⋊D3—42no—
205C4×C3⋊D3—81no—
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#465C3⋊D311yescharacteristic, complemented
220#464—91no—
221#452—91no—
222#450—91no—
223C4×SD16—91no—
224C8×D4—91no—
225#416—91no—
226C2×#102—91no—
227C23×D3—64no—
228C2×C3×Q8C22×D314yes—
229C2×C3×D4—24no—
230C2×C3×D4C22×D314yes—
231C22×C3×C4C22×D314yes—
232C2×#67—34no—
233C2×#67—64no—
234C2×#67—64no—
235D3×D4—68no—
236D3×D4—124no—
237#235—68no—
238#235—124no—
239C2×D12—34no—
240C2×C4×D3—34no—
241C2×C4×D3—64no—
242C2×C4×D3—64no—
243C2×C4×D3—64no—
244C2×Dic6—34no—
245C3×SD16—44no—
246C2×C3×C8—44no—
247C2×C3×C8C22×D314yes—
248C2×C3×C8C22×D314yes—
249C3×C4⋊C4—24no—
250C3×C4⋊C4C22×D314yes—
251C3×C4⋊C4C22×D314yes—
252C3×C22⋊C4—24no—
253C3×C22⋊C4—24no—
254#217—34no—
255#217—64no—
256#217—64no—
257#217—64no—
258#216—124no—
259#215—68no—
260(C2×D3)⋊C4—34no—
261(C2×D3)⋊C4—64no—
262(C2×D3)⋊C4—64no—
263(C2×D3)⋊C4—64no—
264C4⋊Dic3—34no—
265C4⋊Dic3—34no—
266C4⋊Dic3—64no—
267C4⋊Dic3—64no—
268C4⋊Dic3—64no—
269Dic3⋊C4—34no—
270Dic3⋊C4—64no—
271Dic3⋊C4—64no—
272Dic3⋊C4—64no—
273C4×Dic3—34no—
274C4×Dic3—64no—
275C4×Dic3—64no—
276C2×C3⋊C8—34no—
277C2×C3⋊C8—34no—
278D3×C8—124no—
279C22×C32—21no—
280C22×C32—21no—
281C22×C32—21no—
282C22×C32—41no—
283C22×C32—41no—
284C22×C32—41no—
285C22×C32C22×D411yescharacteristic
286C2×C3⋊D3—21no—
287C2×C3⋊D3—21no—
288C2×C3⋊D3—22no—
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×#41—91no—
306C22×D4—91no—
307C2×Q16—91no—
308C2×SD16—91no—
309C2×SD16C2×C3⋊D311yescharacteristic
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⋊Q8C2×C3⋊D311yescharacteristic, complemented
321#121—181no—
322#121C2×C3⋊D311yescharacteristic
323#120—181no—
324C4×Q8—91no—
325C4×D4—91no—
326C4×D4—91no—
327#117—91no—
328#117—181no—
329C2×C4⋊C4—91no—
330C2×C22⋊C4—181no—
331#107—91no—
332#106—91no—
333#106C2×C3⋊D311yescharacteristic, complemented
334C4⋊C8—91no—
335#103—91no—
336#103—91no—
337#103—91no—
338#103C2×C3⋊D311yescharacteristic, complemented
339#102—91no—
340#102—91no—
341#102—91no—
342#102—91no—
343#102—91no—
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—24no—
359C3×D4—84no—
360C2×C3×C4—24no—
361C2×C3×C4—24no—
362C2×C3×C4—24no—
363C2×C3×C4—24no—
364C2×C3×C4—24no—
365C2×C3×C4D3×D414yes—
366C2×C3×C4C23×D314yes—
367#67—68no—
368#67—128no—
369#67—128no—
370C2×Dic3—34no—
371C2×Dic3—34no—
372C2×Dic3—34no—
373C2×Dic3—64no—
374C2×Dic3—64no—
375C2×Dic3—64no—
376D12—38no—
377D12—64no—
378C4×D3—64no—
379C4×D3—64no—
380C4×D3—128no—
381C4×D3—128no—
382C4×D3—244no—
383Dic6—64no—
384Dic6—64no—
385C3×C8—24no—
386C3×C8—24no—
387C3⋊C8—64no—
388C3⋊C8—64no—
389C2×C32—41no—
390C2×C32—81no—
391C2×C32#54611yescharacteristic
392C2×C32C2×#13511yescharacteristic
393C2×C32#57711yescharacteristic
394C3⋊D3—22no—
395C3⋊D3—42no—
396C24—181no—
397#41—182no—
398#41—361no—
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—91no—
410C22×C4—181no—
411C22×C4—181no—
412C22×C4—181no—
413C22×C4C22×C3⋊D311yescharacteristic
414Q16—361no—
415SD16—41no—
416SD16—182no—
417C2×C8—41no—
418C2×C8—91no—
419C2×C8—91no—
420C2×C8—361no—
421C2×C8C22×C3⋊D311yescharacteristic
422C2×C8C22×C3⋊D311yescharacteristic
423C4⋊C4—21no—
424C4⋊C4—91no—
425C4⋊C4—91no—
426C4⋊C4—91no—
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—21no—
437C22⋊C4—91no—
438C22⋊C4—91no—
439C22⋊C4—181no—
440C22⋊C4—181no—
441C22⋊C4—181no—
442C22⋊C4—181no—
443C22⋊C4—181no—
444C22⋊C4—181no—
445C42—91no—
446C42—181no—
447C42—181no—
448C22×C3—24no—
449C22×C3—24no—
450C22×C3—24no—
451C22×C3—44no—
452C22×C3—44no—
453C22×C3—44no—
454C22×C3C2×D3×D414yes—
455C2×D3—38no—
456C2×D3—64no—
457C2×D3—64no—
458C2×D3—68no—
459C2×D3—124no—
460C2×D3—124no—
461C2×D3—2416no—
462C3×C4—24no—
463C3×C4—44no—
464C3×C4—44no—
465C3×C4—44no—
466C3×C4#100414yes—
467C3×C4D3×#4114yes—
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—21no—
488D4—81no—
489D4—92no—
490D4—182no—
491D4—181no—
492D4—362no—
493D4—362no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—91no—
500C2×C4—91no—
501C2×C4—91no—
502C2×C4—181no—
503C2×C4—181no—
504C2×C4—181no—
505C2×C4—181no—
506C2×C4—181no—
507C2×C4—362no—
508C2×C4—362no—
509C2×C4—721no—
510C2×C4D4×C3⋊D311yescharacteristic
511C2×C4C23×C3⋊D311yescharacteristic
512C8—21no—
513C8—21no—
514C8—181no—
515C8—181no—
516C2×C3—44no—
517C2×C3—84no—
518C2×C3#561014yes—
519C2×C3#576214yes—
520C2×C3D3×#13514yes—
521D3—68no—
522D3—128no—
523C22—21no—
524C22—21no—
525C22—21no—
526C22—41no—
527C22—41no—
528C22—41no—
529C22—92no—
530C22—181no—
531C22—181no—
532C22—182no—
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—
547C4#6436111yescharacteristic
548C4#41×C3⋊D311yescharacteristic
549C3#8067114yescomplemented
550C2—41no—
551C2—81no—
552C2—182no—
553C2—362no—
554C2#1059608111yescharacteristic
555C2#1059623311yescharacteristic
556C2C3⋊D3×#13511yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#465C2
socleC22×C32C22×D4
prime radical#10596083C2
hypercenter#465C3⋊D3
hypocenterC32#3296
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. #10596110C2semidirect
3. C32×#465C2semidirect
4. #10592868C2semidirect
5. #10592865C2semidirect
6. #10592812C2semidirect
7. C8×#638C2semidirect
8. #10592746C2semidirect
9. #10592734C2semidirect
10. #10592570C2semidirect
11. #10592561C2semidirect
12. #10592512C2semidirect
13. #10592487C2semidirect
14. C3⋊D3×#102C2semidirect
15. #10592467C2semidirect
20. C22×C32×C8C22semidirect
21. C32×C22⋊Q8C22semidirect
24. Q8×C3⋊Dic3C22semidirect
25. C2×#3756C22semidirect
31. #64135C22semidirect
37. #64099C22semidirect
43. C32×#106C22semidirect
44. C32×#103C22semidirect
48. #63657C22semidirect
52. #63643C22semidirect
53. #63643C22semidirect
54. #63641C22semidirect
55. C8×C3⋊Dic3C22semidirect
56. #63637C22semidirect
58. #63635C22semidirect
59. #63634C22semidirect
62. C3×#465D3semidirect
131. C22×C3×C8C2×D3semidirect
132. C3×C22⋊Q8C2×D3semidirect
154. C3×#106C2×D3semidirect
155. C3×#103C2×D3semidirect
219. #465C3⋊D3semidirect
311. C22×C8C2×C3⋊D3semidirect
320. C22⋊Q8C2×C3⋊D3semidirect
333. #106C2×C3⋊D3semidirect
338. #103C2×C3⋊D3semidirect
474. C32#3296semidirect
549. C3#80671semidirect

Maximal subgroups

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

subgroupindex
#105961102
#105960832
C32×#4652
#105928682
#105928652
#105928122
C8×#6382
#105927462
#105927342
#105925702
#105925612
#105925122
#105924872
C3⋊D3×#1022
#105924672
#806713