Subgroups — #19151981

Order 5696.

130 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₃₅₆	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#13083562	C₂	1	2	yes	maximal, complemented
3	#15667999	C₂	1	2	yes	maximal, complemented
4	C₈×Dic₈₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₈×C₈₉	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₁₇₈	C₂²	1	2	yes	—
7	Dic₃₅₆	—	2	2	no	—
8	#13083562	—	2	4	no	—
9	C₂×#10623494	C₂²	1	1	yes	characteristic
10	C₂²⋊Dic₈₉	—	2	4	no	—
11	C₄×Dic₈₉	C₂²	1	1	yes	characteristic
12	C₂×D₄×C₈₉	C₂²	1	2	yes	—
13	D₈×C₈₉	—	2	2	no	—
14	C₂×C₈×C₈₉	C₂²	1	1	yes	characteristic
15	C₂³×C₈₉	—	2	2	no	—
16	D₄×C₈₉	—	2	2	no	—
17	D₄×C₈₉	—	2	2	no	—
18	C₂×C₄×C₈₉	C₂³	1	1	yes	characteristic
19	C₂×Dic₈₉	—	2	2	no	—
20	C₂×Dic₈₉	D₄	1	2	yes	—
21	Dic₁₇₈	—	2	2	no	—
22	Dic₁₇₈	—	2	2	no	—
23	C₈×C₈₉	D₄	1	2	yes	—
24	#10623494	D₄	1	2	yes	—
25	C₂²×C₈₉	—	4	2	no	—
26	C₂²×C₈₉	—	4	4	no	—
27	C₂²×C₈₉	C₂×D₄	1	1	yes	characteristic
28	C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
29	C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
30	Dic₈₉	—	2	2	no	—
31	Dic₈₉	—	4	2	no	—
32	C₂×C₈₉	—	8	2	no	—
33	C₂×C₈₉	#127	1	1	yes	characteristic
34	C₂×C₈₉	#135	1	2	yes	—
35	C₈₉	#495	1	1	yes	characteristic, complemented, Sylow
36	#495	—	89	1	no	maximal, Sylow
37	C₂×Q₁₆	—	89	1	no	—
38	C₂×SD₁₆	—	89	2	no	—
39	C₂×D₈	D₈₉	1	1	yes	characteristic
40	#124	—	89	2	no	—
41	C₄×C₈	—	89	1	no	—
42	C₂×Q₈	—	89	2	no	—
43	C₂×D₄	C₂×D₈₉	1	2	yes	—
44	Q₁₆	—	178	2	no	—
45	SD₁₆	—	178	4	no	—
46	D₈	—	2	2	no	—
47	C₂×C₈	—	89	1	no	—
48	C₂×C₈	C₂×D₈₉	1	1	yes	characteristic
49	C₂²⋊C₄	—	178	4	no	—
50	C₄²	—	89	1	no	—
51	C₂³	—	2	2	no	—
52	Q₈	—	178	2	no	—
53	Q₈	—	178	2	no	—
54	D₄	—	2	2	no	—
55	D₄	—	2	2	no	—
56	C₂×C₄	—	89	2	no	—
57	C₂×C₄	—	178	2	no	—
58	C₂×C₄	C₂²×D₈₉	1	1	yes	characteristic
59	C₈	—	89	2	no	—
60	C₈	C₂²⋊D₈₉	1	2	yes	—
61	C₂²	—	4	2	no	—
62	C₂²	—	4	4	no	—
63	C₂²	D₄×D₈₉	1	1	yes	characteristic
64	C₄	—	356	2	no	—
65	C₄	—	178	2	no	—
66	C₄	D₄×D₈₉	1	1	yes	characteristic
67	C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
68	C₂	—	8	2	no	—
69	C₂	#15668008	1	1	yes	characteristic
70	C₂	#15668031	1	2	yes	—

	subgroup	G/H
center	C₂²	D₄×D₈₉
commutator	C₂×C₄×C₈₉	C₂³
Frattini	C₂×C₄	C₂²×D₈₉
Fitting	C₂×D₈×C₈₉	C₂
socle	C₂²×C₈₉	C₂×D₄
hypercenter	C₂×D₈	D₈₉
hypocenter	C₈₉	#495
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×D₈

Complements

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

N	H ≅ G/N	type
1. C₂×Dic₃₅₆	C₂	semidirect
2. C₂×#13083562	C₂	semidirect
3. #15667999	C₂	semidirect
4. C₈×Dic₈₉	C₂	semidirect
35. C₈₉	#495	semidirect