Subgroups — #26018451

Order 11392.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15667918	C₂	1	1	yes	maximal, characteristic
2	#19151424	C₂	1	1	yes	maximal, characteristic
3	#366×C₈₉	C₂	1	1	yes	maximal, characteristic
4	#15667946	—	2	1	no	—
5	#15667918	C₄	1	2	yes	complemented
6	C₂×C₁₆×C₈₉	C₂²	1	1	yes	characteristic
7	#107×C₈₉	—	2	1	no	—
8	C₄⋊Dic₈₉	—	4	1	no	—
9	C₂×C₈×C₈₉	D₄	1	1	yes	characteristic
10	C₄⋊C₄×C₈₉	—	4	1	no	—
11	C₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic
12	C₁₆×C₈₉	Q₈	1	1	yes	characteristic
13	C₂×C₄×C₈₉	—	8	1	no	—
14	C₂×C₄×C₈₉	D₈	1	1	yes	characteristic
15	C₂×Dic₈₉	—	8	1	no	—
16	C₈×C₈₉	C₄⋊C₄	1	1	yes	characteristic
17	C₈×C₈₉	Q₁₆	1	1	yes	characteristic
18	C₂²×C₈₉	D₁₆	1	1	yes	characteristic
19	C₄×C₈₉	—	16	1	no	—
20	C₄×C₈₉	#107	1	1	yes	characteristic
21	C₄×C₈₉	Q₃₂	1	1	yes	characteristic
22	Dic₈₉	—	16	1	no	—
23	C₂×C₈₉	#366	1	1	yes	characteristic
24	C₂×C₈₉	D₃₂	1	1	yes	characteristic
25	C₂×C₈₉	Q₆₄	1	1	yes	characteristic
26	#1423	—	89	1	no	maximal, Sylow
27	C₈₉	#1423	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₃₂	—	89	1	no	—
29	#366	—	89	1	no	—
30	#366	D₈₉	1	1	yes	characteristic
31	C₂×C₁₆	C₂×D₈₉	1	1	yes	characteristic
32	#107	—	2	1	no	—
33	#107	—	178	1	no	—
34	C₃₂	—	89	2	no	—
35	C₂×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
36	C₄⋊C₄	—	4	1	no	—
37	C₄⋊C₄	—	356	1	no	—
38	C₁₆	Dic₁₇₈	1	1	yes	characteristic
39	C₁₆	C₄×D₈₉	1	1	yes	characteristic
40	C₂×C₄	—	8	1	no	—
41	C₂×C₄	—	712	1	no	—
42	C₂×C₄	#13083559	1	1	yes	characteristic
43	C₈	#13083553	1	1	yes	characteristic
44	C₈	#13083564	1	1	yes	characteristic
45	C₂²	#15667953	1	1	yes	characteristic
46	C₄	—	16	1	no	—
47	C₄	—	1424	1	no	—
48	C₄	#15667945	1	1	yes	characteristic
49	C₄	#15667958	1	1	yes	characteristic
50	C₂	#19151423	1	1	yes	characteristic
51	C₂	#19151433	1	1	yes	characteristic
52	C₂	#19151438	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#15667953
commutator	C₁₆×C₈₉	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₈₉
Fitting	#366×C₈₉	C₂
socle, prime radical	C₂²×C₈₉	D₁₆
cosocle	C₂×C₁₆×C₈₉	C₂²
hypercenter	#366	D₈₉
hypocenter	C₈₉	#1423
LCS	G ▷ C₁₆×C₈₉ ▷ C₈×C₈₉ ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ #366

Complements

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

N	H ≅ G/N	type
5. #15667918	C₄	semidirect
27. C₈₉	#1423	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15667918	2
#19151424	2
#366×C₈₉	2
#1423	89