Subgroups — #19151985

Order 5696.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13083562	C₂	1	2	yes	maximal, complemented
2	C₂×#13083559	C₂	1	2	yes	maximal, complemented
3	#15668000	C₂	1	1	yes	maximal, characteristic, complemented
4	#15667923	C₂	1	1	yes	maximal, characteristic, complemented
5	#127×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×Dic₁₇₈	C₂²	1	1	yes	characteristic
7	C₂×D₃₅₆	C₂²	1	1	yes	characteristic
8	#13083562	—	2	4	no	—
9	#13083559	—	2	4	no	—
10	C₂×#10623494	C₂²	1	2	yes	—
11	#13083551	—	2	2	no	—
12	C₂×D₄×C₈₉	—	2	2	no	—
13	C₂×D₄×C₈₉	C₂²	1	2	yes	—
14	C₄²×C₈₉	C₂²	1	1	yes	characteristic
15	C₂³×C₈₉	—	2	2	no	—
16	C₂²×D₈₉	—	2	1	no	—
17	D₄×C₈₉	—	2	2	no	—
18	D₄×C₈₉	—	2	2	no	—
19	D₄×C₈₉	—	4	4	no	—
20	C₂×C₄×C₈₉	D₄	1	2	yes	—
21	C₂×C₄×C₈₉	C₂³	1	1	yes	characteristic
22	C₂×Dic₈₉	—	2	1	no	—
23	D₃₅₆	—	2	2	no	—
24	Dic₁₇₈	—	2	2	no	—
25	#10623494	D₄	1	4	yes	complemented
26	C₂²×C₈₉	—	4	2	no	—
27	C₂²×C₈₉	—	4	4	no	—
28	C₂²×C₈₉	C₂×D₄	1	1	yes	characteristic
29	C₂×D₈₉	—	4	1	no	—
30	C₂×D₈₉	—	4	2	no	—
31	C₄×C₈₉	—	2	2	no	—
32	C₄×C₈₉	C₂×D₄	1	2	yes	—
33	Dic₈₉	—	4	1	no	—
34	C₂×C₈₉	—	8	2	no	—
35	C₂×C₈₉	#127	1	1	yes	characteristic
36	C₂×C₈₉	AGL(1,ℤ/8)	1	2	yes	—
37	D₈₉	—	8	1	no	—
38	C₈₉	#496	1	1	yes	characteristic, complemented, Sylow
39	#496	—	89	1	no	maximal, Sylow
40	C₂×SD₁₆	—	89	2	no	—
41	C₂×D₈	—	89	2	no	—
42	#127	D₈₉	1	1	yes	characteristic, complemented
43	#124	—	89	1	no	—
44	#97	—	89	1	no	—
45	C₂×Q₈	—	89	1	no	—
46	C₂×D₄	—	2	2	no	—
47	C₂×D₄	—	89	1	no	—
48	C₂×D₄	C₂×D₈₉	1	2	yes	—
49	SD₁₆	—	178	4	no	—
50	D₈	—	178	4	no	—
51	C₂×C₈	—	89	2	no	—
52	C₂²⋊C₄	—	178	2	no	—
53	C₄²	C₂×D₈₉	1	1	yes	characteristic
54	C₂³	—	2	2	no	—
55	C₂³	—	178	1	no	—
56	Q₈	—	178	2	no	—
57	D₄	—	2	2	no	—
58	D₄	—	2	2	no	—
59	D₄	—	4	4	no	—
60	D₄	—	178	2	no	—
61	C₂×C₄	—	178	1	no	—
62	C₂×C₄	C₂²⋊D₈₉	1	2	yes	—
63	C₂×C₄	C₂²×D₈₉	1	1	yes	characteristic
64	C₈	—	89	4	no	—
65	C₂²	—	4	2	no	—
66	C₂²	—	4	4	no	—
67	C₂²	—	356	1	no	—
68	C₂²	—	356	2	no	—
69	C₂²	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
70	C₄	—	2	2	no	—
71	C₄	—	356	1	no	—
72	C₄	D₄×D₈₉	1	2	yes	—
73	C₂	—	8	2	no	—
74	C₂	—	712	1	no	—
75	C₂	#15668008	1	1	yes	characteristic
76	C₂	#15668038	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₈₉
commutator	C₂×C₄×C₈₉	C₂³
Frattini	C₂×C₄	C₂²×D₈₉
Fitting	#127×C₈₉	C₂
socle	C₂²×C₈₉	C₂×D₄
hypercenter	#127	D₈₉
hypocenter	C₈₉	#496
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #127

Complements

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

N	H ≅ G/N	type
1. C₂×#13083562	C₂	semidirect
2. C₂×#13083559	C₂	semidirect
3. #15668000	C₂	semidirect
4. #15667923	C₂	semidirect
5. #127×C₈₉	C₂	semidirect
25. #10623494	D₄	semidirect
38. C₈₉	#496	semidirect
42. #127	D₈₉	semidirect