Subgroups — #26019853

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	#19151971	C₂	1	1	yes	maximal, characteristic
3	#19151949	C₂	1	2	yes	maximal, complemented
4	#19151945	C₂	1	2	yes	maximal
5	C₈²×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#13083563	—	2	2	no	—
7	#15668012	C₂²	1	2	yes	—
8	#15668012	C₂²	1	1	yes	characteristic
9	#15668009	C₂²	1	1	yes	characteristic
10	#15667944	—	2	2	no	—
11	#15667937	—	2	4	no	—
12	#15667934	—	2	4	no	—
13	C₄×C₈×C₈₉	C₂²	1	2	yes	—
14	C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
15	C₂×Dic₁₇₈	—	2	1	no	—
16	C₂×Dic₁₇₈	—	2	2	no	—
17	C₂×D₃₅₆	—	2	1	no	—
18	C₂×D₃₅₆	—	2	2	no	—
19	#13083563	—	4	4	no	—
20	C₄⋊Dic₈₉	—	2	2	no	—
21	C₄⋊Dic₈₉	—	2	2	no	—
22	C₄⋊Dic₈₉	—	2	2	no	—
23	C₂×C₈×C₈₉	D₄	1	4	yes	—
24	C₂×C₈×C₈₉	D₄	1	2	yes	—
25	C₄²×C₈₉	C₂³	1	1	yes	characteristic
26	C₂²×D₈₉	—	4	1	no	—
27	C₂×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
28	C₂×C₄×C₈₉	C₂×D₄	1	2	yes	—
29	C₂×Dic₈₉	—	4	1	no	—
30	C₂×Dic₈₉	—	4	2	no	—
31	D₃₅₆	—	4	2	no	—
32	D₃₅₆	—	4	4	no	—
33	Dic₁₇₈	—	4	2	no	—
34	Dic₁₇₈	—	4	4	no	—
35	C₈×C₈₉	—	2	4	no	—
36	C₈×C₈₉	SD₁₆	1	4	yes	—
37	C₂²×C₈₉	#127	1	1	yes	characteristic
38	C₂×D₈₉	—	8	1	no	—
39	C₂×D₈₉	—	8	2	no	—
40	C₄×C₈₉	C₂×SD₁₆	1	2	yes	—
41	C₄×C₈₉	#135	1	4	yes	—
42	Dic₈₉	—	8	1	no	—
43	Dic₈₉	—	8	2	no	—
44	C₂×C₈₉	#492	1	1	yes	characteristic
45	C₂×C₈₉	#495	1	2	yes	—
46	D₈₉	—	16	1	no	—
47	#1708	—	89	1	no	maximal, Sylow
48	C₈₉	#1708	1	1	yes	characteristic, complemented, Sylow
49	#498	—	89	1	no	—
50	#492	—	89	1	no	—
51	#487	—	89	2	no	—
52	#486	—	89	2	no	—
53	C₈²	D₈₉	1	1	yes	characteristic, complemented
54	C₂×SD₁₆	—	178	2	no	—
55	C₄⋊Q₈	—	89	2	no	—
56	C₄⋊Q₈	—	89	1	no	—
57	#127	—	89	1	no	—
58	#106	—	178	2	no	—
59	#103	—	178	4	no	—
60	#102	—	178	4	no	—
61	C₄×C₈	C₂×D₈₉	1	2	yes	—
62	C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
63	C₂×Q₈	—	178	2	no	—
64	C₂×Q₈	—	178	1	no	—
65	C₂×D₄	—	178	2	no	—
66	C₂×D₄	—	178	1	no	—
67	SD₁₆	—	356	4	no	—
68	C₂×C₈	D₃₅₆	1	4	yes	—
69	C₂×C₈	D₃₅₆	1	2	yes	—
70	C₄⋊C₄	—	178	2	no	—
71	C₄⋊C₄	—	178	2	no	—
72	C₄⋊C₄	—	178	2	no	—
73	C₄²	C₂²×D₈₉	1	1	yes	characteristic
74	C₂³	—	356	1	no	—
75	Q₈	—	356	2	no	—
76	Q₈	—	356	4	no	—
77	D₄	—	356	2	no	—
78	D₄	—	356	4	no	—
79	C₂×C₄	—	356	1	no	—
80	C₂×C₄	—	356	2	no	—
81	C₂×C₄	C₂×D₃₅₆	1	1	yes	characteristic
82	C₂×C₄	C₂×D₃₅₆	1	2	yes	—
83	C₈	—	2	4	no	—
84	C₈	#13083563	1	4	yes	—
85	C₂²	—	712	1	no	—
86	C₂²	—	712	2	no	—
87	C₂²	#15668009	1	1	yes	characteristic
88	C₄	—	712	1	no	—
89	C₄	—	712	2	no	—
90	C₄	C₂×#13083563	1	2	yes	—
91	C₄	#15668034	1	4	yes	—
92	C₂	—	1424	1	no	—
93	C₂	#19151971	1	1	yes	characteristic
94	C₂	#19151982	1	2	yes	—

	subgroup	G/H
center	C₂²	#15668009
commutator, cosocle	C₄²×C₈₉	C₂³
Frattini	C₄²	C₂²×D₈₉
Fitting	C₈²×C₈₉	C₂
socle	C₂²×C₈₉	#127
prime radical	#15668009	C₂²
hypercenter	C₈²	D₈₉
hypocenter	C₈₉	#1708
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
1. #19151996	C₂	semidirect
3. #19151949	C₂	semidirect
5. C₈²×C₈₉	C₂	semidirect
48. C₈₉	#1708	semidirect
53. C₈²	D₈₉	semidirect

Maximal subgroups

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

subgroup	index
#19151996	2
#19151971	2
#19151949	2
#19151945	2
C₈²×C₈₉	2
#1708	89