Subgroups — #26018551

Order 11392.

178 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19151649	C₂	1	3	yes	maximal
2	#19151320	C₂	1	3	yes	maximal, complemented
3	C₈²×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄²×D₈₉	C₂²	1	1	yes	characteristic
5	#15667941	C₄	1	6	yes	—
6	#15667924	C₄	1	6	yes	—
7	C₄×#10623494	C₂²	1	3	yes	—
8	C₄×C₈×C₈₉	C₂²	1	3	yes	—
9	C₂×C₄×D₈₉	C₂×C₄	1	3	yes	—
10	C₂×#10623494	C₂×C₄	1	6	yes	—
11	C₄×Dic₈₉	C₂×C₄	1	3	yes	—
12	C₂×C₈×C₈₉	C₂×C₄	1	6	yes	—
13	C₄²×C₈₉	C₂³	1	1	yes	characteristic
14	C₂²×D₈₉	C₄²	1	1	yes	characteristic
15	C₂×C₄×C₈₉	C₂²×C₄	1	3	yes	—
16	C₂×Dic₈₉	C₄²	1	3	yes	—
17	C₄×D₈₉	—	2	6	no	—
18	C₈×C₈₉	—	2	6	no	—
19	#10623494	—	2	6	no	—
20	C₂²×C₈₉	C₂×C₄²	1	1	yes	characteristic
21	C₂×D₈₉	—	2	3	no	—
22	C₄×C₈₉	#131	1	6	yes	—
23	Dic₈₉	—	2	3	no	—
24	C₂×C₈₉	#405	1	3	yes	—
25	D₈₉	—	4	1	no	—
26	#1454	—	89	1	no	maximal, Sylow
27	C₈₉	#1454	1	1	yes	characteristic, complemented, Sylow
28	#431	—	89	3	no	—
29	#322	—	89	3	no	—
30	C₈²	D₈₉	1	1	yes	characteristic, complemented
31	C₂×C₄²	—	89	1	no	—
32	C₄⋊C₈	—	89	6	no	—
33	C₂²⋊C₈	—	89	6	no	—
34	C₄×C₈	—	89	3	no	—
35	C₄×C₈	C₂×D₈₉	1	3	yes	—
36	C₂²×C₄	—	89	3	no	—
37	C₂×C₈	—	89	6	no	—
38	C₂×C₈	C₄×D₈₉	1	6	yes	—
39	C₄²	—	89	3	no	—
40	C₄²	C₂²×D₈₉	1	1	yes	characteristic
41	C₂³	—	89	1	no	—
42	C₂×C₄	—	89	3	no	—
43	C₂×C₄	—	178	6	no	—
44	C₂×C₄	C₂×C₄×D₈₉	1	3	yes	—
45	C₈	—	2	6	no	—
46	C₈	—	178	6	no	—
47	C₂²	—	178	3	no	—
48	C₂²	C₄²×D₈₉	1	1	yes	characteristic
49	C₄	—	178	3	no	—
50	C₄	#15668018	1	6	yes	—
51	C₂	—	356	1	no	—
52	C₂	#19151552	1	3	yes	—

	subgroup	G/H
center, Frattini	C₄²	C₂²×D₈₉
commutator, socle	C₂²×C₈₉	C₂×C₄²
Fitting	C₈²×C₈₉	C₂
prime radical	C₂²×D₈₉	C₄²
cosocle	C₄²×C₈₉	C₂³
hypercenter	C₈²	D₈₉
hypocenter	C₈₉	#1454
LCS	G ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₄² ◁ C₈²

Complements

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

N	H ≅ G/N	type
2. #19151320	C₂	semidirect
3. C₈²×C₈₉	C₂	semidirect
27. C₈₉	#1454	semidirect
30. C₈²	D₈₉	semidirect

Maximal subgroups

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

subgroup	index
#19151649	2
#19151320	2
C₈²×C₈₉	2
#1454	89