Subgroups — #26020390

Order 11392.

188 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19151622	C₂	1	2	yes	maximal
2	#19151363	C₂	1	4	yes	maximal
3	C₂×C₄×C₈×C₈₉	C₂	1	1	yes	maximal, characteristic
4	C₂×#13083558	C₂²	1	4	yes	—
5	C₄⋊#10623494	—	2	4	no	—
6	C₂²×C₈×C₈₉	C₂²	1	2	yes	—
7	C₂×C₄²×C₈₉	C₂²	1	1	yes	characteristic
8	C₄×C₈×C₈₉	C₄	1	2	yes	—
9	C₄×C₈×C₈₉	C₄	1	2	yes	—
10	#13083558	—	2	8	no	—
11	C₂×#10623494	—	2	4	no	—
12	C₂²×C₄×C₈₉	Q₈	1	2	yes	—
13	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
14	C₂×C₈×C₈₉	—	2	4	no	—
15	C₂×C₈×C₈₉	C₂×C₄	1	4	yes	—
16	C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
17	C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
18	C₄²×C₈₉	D₄	1	2	yes	—
19	C₂³×C₈₉	C₂×Q₈	1	1	yes	characteristic
20	C₂×C₄×C₈₉	—	2	4	no	—
21	C₂×C₄×C₈₉	C₄⋊C₄	1	2	yes	—
22	C₂×C₄×C₈₉	C₄⋊C₄	1	2	yes	—
23	C₂×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
24	C₂×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
25	C₂×C₄×C₈₉	#41	1	4	yes	—
26	C₈×C₈₉	—	2	4	no	—
27	#10623494	—	4	4	no	—
28	C₂²×C₈₉	—	2	2	no	—
29	C₂²×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
30	C₂²×C₈₉	#125	1	2	yes	—
31	C₄×C₈₉	—	2	2	no	—
32	C₄×C₈₉	#108	1	4	yes	—
33	C₄×C₈₉	#117	1	2	yes	—
34	C₄×C₈₉	#124	1	2	yes	—
35	C₂×C₈₉	—	2	2	no	—
36	C₂×C₈₉	#382	1	1	yes	characteristic
37	C₂×C₈₉	C₂×#108	1	2	yes	—
38	#1837	—	89	1	no	maximal, Sylow
39	C₈₉	#1837	1	1	yes	characteristic, complemented, Sylow
40	#423	—	89	2	no	—
41	C₂×C₄×C₈	D₈₉	1	1	yes	characteristic
42	#341	—	89	4	no	—
43	C₂×M₁₆	—	89	4	no	—
44	C₂²×C₈	C₂×D₈₉	1	2	yes	—
45	C₂×C₄²	C₂×D₈₉	1	1	yes	characteristic
46	C₄⋊C₈	—	178	4	no	—
47	C₄×C₈	Dic₈₉	1	2	yes	—
48	C₄×C₈	Dic₈₉	1	2	yes	—
49	C₂²×C₄	Dic₁₇₈	1	2	yes	—
50	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
51	M₁₆	—	178	8	no	—
52	C₂×C₈	—	2	4	no	—
53	C₂×C₈	—	178	4	no	—
54	C₂×C₈	C₂×Dic₈₉	1	4	yes	—
55	C₄²	D₃₅₆	1	2	yes	—
56	C₄²	C₂×Dic₈₉	1	1	yes	characteristic
57	C₄²	C₂×Dic₈₉	1	1	yes	characteristic
58	C₂³	C₂×Dic₁₇₈	1	1	yes	characteristic
59	C₂×C₄	—	2	4	no	—
60	C₂×C₄	C₄⋊Dic₈₉	1	2	yes	—
61	C₂×C₄	C₄⋊Dic₈₉	1	2	yes	—
62	C₂×C₄	C₂²×Dic₈₉	1	1	yes	characteristic
63	C₂×C₄	C₂×D₃₅₆	1	1	yes	characteristic
64	C₂×C₄	#13083574	1	4	yes	—
65	C₈	—	2	4	no	—
66	C₈	—	356	4	no	—
67	C₂²	—	2	2	no	—
68	C₂²	C₂×C₄⋊Dic₈₉	1	1	yes	characteristic
69	C₂²	#15668004	1	2	yes	—
70	C₄	—	2	2	no	—
71	C₄	#15667948	1	4	yes	—
72	C₄	#15667971	1	2	yes	—
73	C₄	#15668000	1	2	yes	—
74	C₂	—	2	2	no	—
75	C₂	#19151464	1	1	yes	characteristic
76	C₂	C₂×#15667948	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×D₃₅₆
commutator	C₂×C₄×C₈₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₈₉
Fitting	C₂×C₄×C₈×C₈₉	C₂
socle	C₂²×C₈₉	C₂×C₄⋊C₄
prime radical	C₂³×C₈₉	C₂×Q₈
cosocle	C₂²×C₄×C₈₉	C₂³
hypercenter	C₂×C₄×C₈	D₈₉
hypocenter	C₈₉	#1837
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
39. C₈₉	#1837	semidirect

Maximal subgroups

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

subgroup	index
#19151622	2
#19151363	2
C₂×C₄×C₈×C₈₉	2
#1837	89