Subgroups — #26019870

Order 11392.

192 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19152003	C₂	1	4	yes	maximal
2	#19151978	C₂	1	2	yes	maximal
3	C₈²×C₈₉	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₃₅₆	—	2	4	no	—
5	#15668012	C₂²	1	4	yes	—
6	#15667946	—	2	8	no	—
7	C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
8	C₄×C₈×C₈₉	C₂²	1	2	yes	—
9	C₂×Dic₁₇₈	—	2	4	no	—
10	Dic₃₅₆	—	4	8	no	—
11	C₄⋊Dic₈₉	—	2	8	no	—
12	C₂×C₈×C₈₉	D₄	1	2	yes	—
13	C₂×C₈×C₈₉	D₄	1	4	yes	—
14	C₄²×C₈₉	C₂³	1	1	yes	characteristic
15	C₂×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
16	C₂×C₄×C₈₉	C₂×D₄	1	2	yes	—
17	C₂×Dic₈₉	—	4	4	no	—
18	Dic₁₇₈	—	4	8	no	—
19	C₈×C₈₉	D₈	1	4	yes	—
20	C₈×C₈₉	Q₁₆	1	8	yes	complemented
21	C₂²×C₈₉	#127	1	1	yes	characteristic
22	C₄×C₈₉	C₂×D₈	1	2	yes	—
23	C₄×C₈₉	C₂×Q₁₆	1	4	yes	—
24	Dic₈₉	—	8	4	no	—
25	C₂×C₈₉	#493	1	1	yes	characteristic
26	C₂×C₈₉	#494	1	2	yes	—
27	#1713	—	89	1	no	maximal, Sylow
28	C₈₉	#1713	1	1	yes	characteristic, complemented, Sylow
29	#500	—	89	4	no	—
30	#494	—	89	2	no	—
31	C₈²	D₈₉	1	1	yes	characteristic
32	C₂×Q₁₆	—	178	4	no	—
33	C₄⋊Q₈	—	89	4	no	—
34	#107	—	178	8	no	—
35	C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
36	C₄×C₈	C₂×D₈₉	1	2	yes	—
37	C₂×Q₈	—	178	4	no	—
38	Q₁₆	—	356	8	no	—
39	C₂×C₈	D₃₅₆	1	2	yes	—
40	C₂×C₈	D₃₅₆	1	4	yes	—
41	C₄⋊C₄	—	178	8	no	—
42	C₄²	C₂²×D₈₉	1	1	yes	characteristic
43	Q₈	—	356	8	no	—
44	C₂×C₄	—	356	4	no	—
45	C₂×C₄	C₂×D₃₅₆	1	1	yes	characteristic
46	C₂×C₄	C₂×D₃₅₆	1	2	yes	—
47	C₈	D₇₁₂	1	4	yes	—
48	C₈	Dic₃₅₆	1	8	yes	complemented
49	C₂²	#15668009	1	1	yes	characteristic
50	C₄	—	712	4	no	—
51	C₄	C₂×D₇₁₂	1	2	yes	—
52	C₄	C₂×Dic₃₅₆	1	4	yes	—
53	C₂	#19151975	1	1	yes	characteristic
54	C₂	#19151978	1	2	yes	—

	subgroup	G/H
center	C₂²	#15668009
commutator, cosocle	C₄²×C₈₉	C₂³
Frattini	C₄²	C₂²×D₈₉
Fitting	C₈²×C₈₉	C₂
socle, prime radical	C₂²×C₈₉	#127
hypercenter	C₈²	D₈₉
hypocenter	C₈₉	#1713
LCS	G ▷ C₄²×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₈²

Complements

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

N	H ≅ G/N	type
20. C₈×C₈₉	Q₁₆	semidirect
28. C₈₉	#1713	semidirect
48. C₈	Dic₃₅₆	semidirect

Maximal subgroups

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

subgroup	index
#19152003	2
#19151978	2
C₈²×C₈₉	2
#1713	89