Subgroups — #26018354

Order 11392.

132 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19151636	C₂	1	2	yes	maximal
2	C₂×M₃₂×C₈₉	C₂	1	1	yes	maximal, characteristic
3	#15667971	—	2	2	no	—
4	#15667946	—	2	2	no	—
5	#15667944	C₄	1	4	yes	complemented
6	C₂²×C₈×C₈₉	C₂²	1	1	yes	characteristic
7	M₃₂×C₈₉	—	2	2	no	—
8	C₂×C₁₆×C₈₉	C₄	1	2	yes	complemented
9	C₄⋊Dic₈₉	—	2	4	no	—
10	C₂²⋊Dic₈₉	—	4	2	no	—
11	C₄×Dic₈₉	—	4	2	no	—
12	C₂²×C₄×C₈₉	D₄	1	1	yes	characteristic
13	C₂×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
14	C₂×C₈×C₈₉	C₂×C₄	1	2	yes	—
15	C₂×C₈×C₈₉	D₄	1	2	yes	—
16	C₂×C₈×C₈₉	Q₈	1	1	yes	characteristic
17	C₁₆×C₈₉	—	2	2	no	—
18	C₂³×C₈₉	D₈	1	1	yes	characteristic
19	C₂×C₄×C₈₉	C₂²⋊C₄	1	2	yes	—
20	C₂×C₄×C₈₉	C₄⋊C₄	1	1	yes	characteristic
21	C₂×C₄×C₈₉	SD₁₆	1	2	yes	—
22	C₂×C₄×C₈₉	Q₁₆	1	1	yes	characteristic
23	C₂×Dic₈₉	—	4	4	no	—
24	C₈×C₈₉	C₄²	1	1	yes	characteristic
25	C₈×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
26	C₈×C₈₉	C₄⋊C₄	1	2	yes	—
27	C₂²×C₈₉	—	4	1	no	—
28	C₂²×C₈₉	#102	1	2	yes	—
29	C₂²×C₈₉	#107	1	1	yes	characteristic
30	C₄×C₈₉	#95	1	1	yes	characteristic
31	C₄×C₈₉	#103	1	2	yes	—
32	C₄×C₈₉	#106	1	1	yes	characteristic
33	Dic₈₉	—	8	4	no	—
34	C₂×C₈₉	—	2	2	no	—
35	C₂×C₈₉	—	2	1	no	—
36	C₂×C₈₉	#340	1	1	yes	characteristic
37	#1384	—	89	1	no	maximal, Sylow
38	C₈₉	#1384	1	1	yes	characteristic, complemented, Sylow
39	C₂×M₃₂	D₈₉	1	1	yes	characteristic
40	#427	—	89	2	no	—
41	C₂²×C₈	C₂×D₈₉	1	1	yes	characteristic
42	#117	—	178	2	no	—
43	M₃₂	—	2	2	no	—
44	C₂×C₁₆	Dic₈₉	1	2	yes	complemented
45	#107	—	178	2	no	—
46	#106	—	89	4	no	—
47	C₂²×C₄	D₃₅₆	1	1	yes	characteristic
48	C₂×C₈	Dic₁₇₈	1	1	yes	characteristic
49	C₂×C₈	C₄×D₈₉	1	2	yes	—
50	C₂×C₈	C₂×Dic₈₉	1	1	yes	characteristic
51	C₂×C₈	C₂²⋊D₈₉	1	2	yes	—
52	C₄⋊C₄	—	178	4	no	—
53	C₂²⋊C₄	—	356	2	no	—
54	C₄²	—	356	2	no	—
55	C₁₆	—	2	2	no	—
56	C₂³	D₇₁₂	1	1	yes	characteristic
57	C₂×C₄	—	356	4	no	—
58	C₂×C₄	#13083551	1	2	yes	—
59	C₂×C₄	C₄⋊Dic₈₉	1	1	yes	characteristic
60	C₂×C₄	#13083563	1	2	yes	—
61	C₂×C₄	Dic₃₅₆	1	1	yes	characteristic
62	C₈	C₄×Dic₈₉	1	1	yes	characteristic
63	C₈	C₂²⋊Dic₈₉	1	1	yes	characteristic
64	C₈	#13083553	1	2	yes	—
65	C₂²	—	4	1	no	—
66	C₂²	#15667934	1	2	yes	—
67	C₂²	#15667946	1	1	yes	characteristic
68	C₄	—	712	4	no	—
69	C₄	#15667919	1	1	yes	characteristic
70	C₄	#15667937	1	2	yes	—
71	C₄	#15667944	1	1	yes	characteristic
72	C₂	—	2	2	no	—
73	C₂	—	2	1	no	—
74	C₂	#19151361	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#15667944
commutator	C₈×C₈₉	C₄²
Frattini	C₂²×C₈	C₂×D₈₉
Fitting	C₂×M₃₂×C₈₉	C₂
socle	C₂×C₈₉	#340
prime radical	C₂³×C₈₉	D₈
cosocle	C₂²×C₈×C₈₉	C₂²
hypercenter	C₂×M₃₂	D₈₉
hypocenter	C₈₉	#1384
LCS	G ▷ C₈×C₈₉ ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×M₃₂

Complements

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

N	H ≅ G/N	type
5. #15667944	C₄	semidirect
8. C₂×C₁₆×C₈₉	C₄	semidirect
38. C₈₉	#1384	semidirect
44. C₂×C₁₆	Dic₈₉	semidirect

Maximal subgroups

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

subgroup	index
#19151636	2
C₂×M₃₂×C₈₉	2
#1384	89