Subgroups — #26018228

Order 11392.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19151419	C₂	1	1	yes	maximal, characteristic, complemented
2	#19151319	C₂	1	1	yes	maximal, characteristic, complemented
3	#443×C₈₉	C₂	1	1	yes	maximal, characteristic
4	#15667952	—	2	1	no	—
5	C₄×#10623494	—	2	1	no	—
6	#135×C₈₉	C₄	1	1	yes	characteristic
7	#131×C₈₉	—	2	1	no	—
8	#108×C₈₉	C₄	1	1	yes	characteristic
9	#104×C₈₉	—	2	1	no	—
10	C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
11	C₂×#10623494	—	2	2	no	—
12	#13083549	—	4	1	no	—
13	#41×C₈₉	—	2	1	no	—
14	Q₁₆×C₈₉	C₈	1	1	yes	characteristic, complemented
15	SD₁₆×C₈₉	—	2	1	no	—
16	D₈×C₈₉	C₈	1	1	yes	characteristic, complemented
17	M₁₆×C₈₉	—	2	1	no	—
18	M₁₆×C₈₉	—	4	1	no	—
19	C₂×C₈×C₈₉	—	4	1	no	—
20	C₂×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
21	C₂×C₈×C₈₉	D₄	1	1	yes	characteristic
22	C₄²×C₈₉	D₄	1	1	yes	characteristic
23	Q₈×C₈₉	—	2	1	no	—
24	D₄×C₈₉	—	2	1	no	—
25	D₄×C₈₉	—	4	1	no	—
26	C₂×C₄×C₈₉	—	2	1	no	—
27	C₂×C₄×C₈₉	—	4	1	no	—
28	C₂×C₄×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
29	C₈×C₈₉	—	4	1	no	—
30	C₈×C₈₉	C₂×C₈	1	1	yes	characteristic
31	C₈×C₈₉	M₁₆	1	1	yes	characteristic
32	C₈×C₈₉	D₈	1	1	yes	characteristic
33	C₈×C₈₉	SD₁₆	1	1	yes	characteristic
34	#10623494	—	4	2	no	—
35	C₂²×C₈₉	—	4	1	no	—
36	C₂²×C₈₉	#104	1	1	yes	characteristic
37	C₄×C₈₉	—	2	2	no	—
38	C₄×C₈₉	—	4	1	no	—
39	C₄×C₈₉	C₂²⋊C₈	1	1	yes	characteristic
40	C₄×C₈₉	#102	1	1	yes	characteristic
41	C₂×C₈₉	—	2	1	no	—
42	C₂×C₈₉	—	8	1	no	—
43	C₂×C₈₉	D₄⋊C₈	1	1	yes	characteristic
44	#1336	—	89	1	no	maximal, Sylow
45	C₈₉	#1336	1	1	yes	characteristic, complemented, Sylow
46	#443	D₈₉	1	1	yes	characteristic
47	#364	—	89	1	no	—
48	#322	—	89	1	no	—
49	#135	Dic₈₉	1	1	yes	characteristic
50	#131	—	2	1	no	—
51	M₃₂	—	178	1	no	—
52	#108	Dic₈₉	1	1	yes	characteristic
53	#104	—	2	1	no	—
54	C₄×C₈	—	178	1	no	—
55	C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
56	#41	—	2	1	no	—
57	Q₁₆	#10623494	1	1	yes	characteristic, complemented
58	SD₁₆	—	2	1	no	—
59	D₈	#10623494	1	1	yes	characteristic, complemented
60	M₁₆	—	2	1	no	—
61	M₁₆	—	4	1	no	—
62	C₂×C₈	—	4	1	no	—
63	C₂×C₈	—	178	2	no	—
64	C₂×C₈	C₂×Dic₈₉	1	1	yes	characteristic
65	C₂×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
66	C₄²	C₂²⋊D₈₉	1	1	yes	characteristic
67	C₁₆	—	356	1	no	—
68	Q₈	—	2	1	no	—
69	D₄	—	2	1	no	—
70	D₄	—	4	1	no	—
71	C₂×C₄	—	2	1	no	—
72	C₂×C₄	—	4	1	no	—
73	C₂×C₄	C₂²⋊Dic₈₉	1	1	yes	characteristic
74	C₈	—	4	1	no	—
75	C₈	—	356	2	no	—
76	C₈	C₂×#10623494	1	1	yes	characteristic
77	C₈	#13083558	1	1	yes	characteristic
78	C₈	#13083559	1	1	yes	characteristic
79	C₈	#13083562	1	1	yes	characteristic
80	C₂²	—	4	1	no	—
81	C₂²	#15667939	1	1	yes	characteristic
82	C₄	—	2	2	no	—
83	C₄	—	4	1	no	—
84	C₄	C₂²⋊#10623494	1	1	yes	characteristic
85	C₄	#15667933	1	1	yes	characteristic
86	C₂	—	2	1	no	—
87	C₂	—	8	1	no	—
88	C₂	D₄⋊#10623494	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#15667933
commutator	C₈×C₈₉	C₂×C₈
Frattini	C₄×C₈	C₂×D₈₉
Fitting	#443×C₈₉	C₂
socle	C₂×C₈₉	D₄⋊C₈
prime radical	#135×C₈₉	C₄
cosocle	C₄×C₈×C₈₉	C₂²
hypercenter	#443	D₈₉
hypocenter	C₈₉	#1336
LCS	G ▷ C₈×C₈₉ ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₄ ◁ C₂×C₈ ◁ C₄×C₈ ◁ #443

Complements

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

N	H ≅ G/N	type
1. #19151419	C₂	semidirect
2. #19151319	C₂	semidirect
14. Q₁₆×C₈₉	C₈	semidirect
16. D₈×C₈₉	C₈	semidirect
45. C₈₉	#1336	semidirect
57. Q₁₆	#10623494	semidirect
59. D₈	#10623494	semidirect

Maximal subgroups

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

subgroup	index
#19151419	2
#19151319	2
#443×C₈₉	2
#1336	89