Subgroups — #26021769

Order 11392.

222 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19151647	C₂	1	3	yes	maximal, complemented
2	#19151561	C₂	1	3	yes	maximal
3	#338×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₄×D₈₉	C₂²	1	1	yes	characteristic
5	C₂×#13083558	C₂²	1	3	yes	—
6	#15667948	—	2	6	no	—
7	#15667924	—	2	6	no	—
8	C₂×M₁₆×C₈₉	C₂²	1	3	yes	—
9	C₂³×D₈₉	Q₈	1	1	yes	characteristic
10	C₂²×Dic₈₉	Q₈	1	1	yes	characteristic
11	C₂×C₄×D₈₉	—	2	3	no	—
12	C₂×C₄×D₈₉	—	2	3	no	—
13	#13083558	—	2	6	no	—
14	C₂×#10623494	—	2	3	no	—
15	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
16	M₁₆×C₈₉	—	2	6	no	—
17	C₂×C₈×C₈₉	D₄	1	6	yes	—
18	C₂³×C₈₉	C₂×Q₈	1	1	yes	characteristic
19	C₂²×D₈₉	—	2	3	no	—
20	C₂²×D₈₉	—	4	2	no	—
21	C₂×C₄×C₈₉	C₂×D₄	1	3	yes	—
22	C₂×C₄×C₈₉	#41	1	3	yes	—
23	C₂×Dic₈₉	—	2	3	no	—
24	C₄×D₈₉	—	4	3	no	—
25	C₄×D₈₉	—	4	1	no	—
26	C₈×C₈₉	—	2	6	no	—
27	#10623494	—	4	3	no	—
28	C₂²×C₈₉	—	4	1	no	—
29	C₂²×C₈₉	C₂²⋊Q₈	1	3	yes	—
30	C₂×D₈₉	—	2	6	no	—
31	C₂×D₈₉	—	4	3	no	—
32	C₂×D₈₉	—	4	1	no	—
33	C₄×C₈₉	#123	1	3	yes	—
34	C₄×C₈₉	#127	1	1	yes	characteristic
35	Dic₈₉	—	4	1	no	—
36	C₂×C₈₉	—	2	3	no	—
37	C₂×C₈₉	#399	1	1	yes	characteristic
38	D₈₉	—	4	2	no	—
39	#2091	—	89	1	no	maximal, Sylow
40	C₈₉	#2091	1	1	yes	characteristic, complemented, Sylow
41	#430	—	89	3	no	—
42	#407	—	89	3	no	—
43	#338	D₈₉	1	1	yes	characteristic, complemented
44	C₂³×C₄	—	89	1	no	—
45	C₂×M₁₆	—	89	3	no	—
46	C₂×M₁₆	C₂×D₈₉	1	3	yes	—
47	#108	—	178	6	no	—
48	C₂²⋊C₈	—	178	6	no	—
49	C₂⁴	—	89	1	no	—
50	C₂²×C₄	—	89	1	no	—
51	C₂²×C₄	—	178	3	no	—
52	C₂²×C₄	—	178	3	no	—
53	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
54	M₁₆	—	2	6	no	—
55	M₁₆	—	178	6	no	—
56	C₂×C₈	—	178	3	no	—
57	C₂×C₈	D₃₅₆	1	6	yes	—
58	C₂³	—	356	2	no	—
59	C₂³	—	178	3	no	—
60	C₂³	Q₈×D₈₉	1	1	yes	characteristic
61	C₂×C₄	—	356	3	no	—
62	C₂×C₄	—	356	1	no	—
63	C₂×C₄	—	178	3	no	—
64	C₂×C₄	C₂×D₃₅₆	1	3	yes	—
65	C₂×C₄	#13083573	1	3	yes	—
66	C₈	—	2	6	no	—
67	C₈	—	356	3	no	—
68	C₂²	—	4	1	no	—
69	C₂²	—	356	3	no	—
70	C₂²	—	356	1	no	—
71	C₂²	—	178	6	no	—
72	C₂²	#15667992	1	3	yes	—
73	C₄	—	356	1	no	—
74	C₄	#15667996	1	3	yes	—
75	C₄	#15668009	1	1	yes	characteristic
76	C₂	—	2	3	no	—
77	C₂	—	356	2	no	—
78	C₂	#19151535	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#15668009
commutator, cosocle	C₂²×C₄×C₈₉	C₂³
Frattini	C₂²×C₄	C₂²×D₈₉
Fitting	#338×C₈₉	C₂
socle	C₂×C₈₉	#399
prime radical	C₂³×D₈₉	Q₈
hypercenter	#338	D₈₉
hypocenter	C₈₉	#2091
LCS	G ▷ C₂²×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #338

Complements

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

N	H ≅ G/N	type
1. #19151647	C₂	semidirect
3. #338×C₈₉	C₂	semidirect
40. C₈₉	#2091	semidirect
43. #338	D₈₉	semidirect

Maximal subgroups

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

subgroup	index
#19151647	2
#19151561	2
#338×C₈₉	2
#2091	89