Subgroups — #26019851

Order 11392.

190 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19151996	C₂	1	1	yes	maximal, characteristic, complemented
2	#19151950	C₂	1	2	yes	maximal, complemented
3	#19151944	C₂	1	2	yes	maximal
4	C₈×#10623494	C₂	1	1	yes	maximal, characteristic, complemented
5	#492×C₈₉	C₂	1	1	yes	maximal, characteristic
6	#15668012	C₂²	1	2	yes	—
7	#15667944	—	2	2	no	—
8	#15667935	—	2	4	no	—
9	#15667933	—	2	4	no	—
10	C₄×#10623494	C₂²	1	2	yes	—
11	C₂×SD₁₆×C₈₉	—	2	2	no	—
12	C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
13	#127×C₈₉	C₂²	1	1	yes	characteristic
14	C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
15	C₂×Dic₁₇₈	—	2	2	no	—
16	C₂×#10623494	D₄	1	4	yes	—
17	C₄⋊Dic₈₉	—	2	2	no	—
18	C₄⋊Dic₈₉	—	2	2	no	—
19	C₂×Q₈×C₈₉	—	2	1	no	—
20	C₂×D₄×C₈₉	—	2	1	no	—
21	C₂×D₄×C₈₉	—	2	2	no	—
22	SD₁₆×C₈₉	—	4	4	no	—
23	C₂×C₈×C₈₉	D₄	1	2	yes	—
24	C₄⋊C₄×C₈₉	—	2	2	no	—
25	C₄²×C₈₉	C₂³	1	1	yes	characteristic
26	C₂³×C₈₉	—	4	1	no	—
27	Q₈×C₈₉	—	4	2	no	—
28	D₄×C₈₉	—	4	2	no	—
29	D₄×C₈₉	—	4	4	no	—
30	C₂×C₄×C₈₉	—	4	1	no	—
31	C₂×C₄×C₈₉	C₂×D₄	1	2	yes	—
32	C₂×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
33	C₂×Dic₈₉	—	4	2	no	—
34	Dic₁₇₈	—	4	4	no	—
35	C₈×C₈₉	SD₁₆	1	4	yes	—
36	#10623494	—	2	4	no	—
37	C₂²×C₈₉	—	8	1	no	—
38	C₂²×C₈₉	—	8	2	no	—
39	C₂²×C₈₉	#127	1	1	yes	characteristic
40	C₄×C₈₉	—	8	1	no	—
41	C₄×C₈₉	C₂×SD₁₆	1	2	yes	—
42	C₄×C₈₉	#135	1	4	yes	—
43	Dic₈₉	—	8	2	no	—
44	C₂×C₈₉	—	16	1	no	—
45	C₂×C₈₉	#492	1	1	yes	characteristic
46	C₂×C₈₉	#495	1	2	yes	—
47	#1708	—	89	1	no	maximal, Sylow
48	C₈₉	#1708	1	1	yes	characteristic, complemented, Sylow
49	#498	—	89	1	no	—
50	#492	D₈₉	1	1	yes	characteristic
51	#487	—	89	2	no	—
52	#486	—	89	2	no	—
53	C₈²	—	89	1	no	—
54	C₂×SD₁₆	—	2	2	no	—
55	C₄⋊Q₈	—	89	2	no	—
56	C₄⋊Q₈	C₂×D₈₉	1	1	yes	characteristic
57	#127	C₂×D₈₉	1	1	yes	characteristic
58	#106	—	178	2	no	—
59	#103	—	178	4	no	—
60	#102	—	178	4	no	—
61	C₄×C₈	—	89	2	no	—
62	C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
63	C₂×Q₈	—	2	1	no	—
64	C₂×Q₈	—	178	2	no	—
65	C₂×D₄	—	2	2	no	—
66	C₂×D₄	—	2	1	no	—
67	SD₁₆	—	4	4	no	—
68	C₂×C₈	—	89	4	no	—
69	C₂×C₈	C₂²⋊D₈₉	1	2	yes	—
70	C₄⋊C₄	—	2	2	no	—
71	C₄⋊C₄	—	178	2	no	—
72	C₄⋊C₄	—	178	2	no	—
73	C₄²	C₂²×D₈₉	1	1	yes	characteristic
74	C₂³	—	4	1	no	—
75	Q₈	—	4	2	no	—
76	Q₈	—	356	4	no	—
77	D₄	—	4	2	no	—
78	D₄	—	4	4	no	—
79	C₂×C₄	—	4	1	no	—
80	C₂×C₄	—	356	2	no	—
81	C₂×C₄	D₄×D₈₉	1	2	yes	—
82	C₂×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
83	C₈	—	178	4	no	—
84	C₈	#13083562	1	4	yes	—
85	C₂²	—	8	1	no	—
86	C₂²	—	8	2	no	—
87	C₂²	#15668008	1	1	yes	characteristic
88	C₄	—	8	1	no	—
89	C₄	—	712	2	no	—
90	C₄	C₂×#13083562	1	2	yes	—
91	C₄	#15668033	1	4	yes	—
92	C₂	—	16	1	no	—
93	C₂	#19151970	1	1	yes	characteristic
94	C₂	#19151979	1	2	yes	—

	subgroup	G/H
center	C₂²	#15668008
commutator, cosocle	C₄²×C₈₉	C₂³
Frattini	C₄²	C₂²×D₈₉
Fitting	#492×C₈₉	C₂
socle	C₂²×C₈₉	#127
prime radical	#127×C₈₉	C₂²
hypercenter	#492	D₈₉
hypocenter	C₈₉	#1708
LCS	G ▷ C₄²×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #492

Complements

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

N	H ≅ G/N	type
1. #19151996	C₂	semidirect
2. #19151950	C₂	semidirect
4. C₈×#10623494	C₂	semidirect
48. C₈₉	#1708	semidirect

Maximal subgroups

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

subgroup	index
#19151996	2
#19151950	2
#19151944	2
C₈×#10623494	2
#492×C₈₉	2
#1708	89