Subgroups — #19151990

Order 5696.

124 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13083564	C₂	1	2	yes	maximal, complemented
2	C₂×#13083561	C₂	1	2	yes	maximal
3	#15668000	C₂	1	1	yes	maximal, characteristic
4	#15667923	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄⋊Q₈×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	#13083564	—	2	4	no	—
9	#13083561	—	2	4	no	—
10	C₂×#10623494	C₂²	1	2	yes	—
11	#13083551	—	2	2	no	—
12	C₂×Q₈×C₈₉	C₂²	1	2	yes	—
13	C₄⋊C₄×C₈₉	—	2	2	no	—
14	C₄²×C₈₉	C₂²	1	1	yes	characteristic
15	C₂²×D₈₉	—	2	1	no	—
16	Q₈×C₈₉	—	2	2	no	—
17	Q₈×C₈₉	—	2	2	no	—
18	C₂×C₄×C₈₉	—	2	2	no	—
19	C₂×C₄×C₈₉	D₄	1	2	yes	—
20	C₂×C₄×C₈₉	C₂³	1	1	yes	characteristic
21	C₂×Dic₈₉	—	2	1	no	—
22	D₃₅₆	—	2	2	no	—
23	Dic₁₇₈	—	2	2	no	—
24	#10623494	D₄	1	4	yes	—
25	C₂²×C₈₉	C₂×D₄	1	1	yes	characteristic
26	C₂×D₈₉	—	4	1	no	—
27	C₂×D₈₉	—	4	2	no	—
28	C₄×C₈₉	—	2	2	no	—
29	C₄×C₈₉	—	4	2	no	—
30	C₄×C₈₉	C₂×D₄	1	2	yes	—
31	Dic₈₉	—	4	1	no	—
32	C₂×C₈₉	#127	1	1	yes	characteristic
33	C₂×C₈₉	#137	1	2	yes	—
34	D₈₉	—	8	1	no	—
35	C₈₉	#497	1	1	yes	characteristic, complemented, Sylow
36	#497	—	89	1	no	maximal, Sylow
37	C₂×Q₁₆	—	89	2	no	—
38	C₂×SD₁₆	—	89	2	no	—
39	C₄⋊Q₈	D₈₉	1	1	yes	characteristic, complemented
40	#124	—	89	1	no	—
41	#97	—	89	1	no	—
42	C₂×Q₈	—	89	1	no	—
43	C₂×Q₈	C₂×D₈₉	1	2	yes	—
44	C₂×D₄	—	89	1	no	—
45	Q₁₆	—	178	4	no	—
46	SD₁₆	—	178	4	no	—
47	C₂×C₈	—	89	2	no	—
48	C₄⋊C₄	—	2	2	no	—
49	C₂²⋊C₄	—	178	2	no	—
50	C₄²	C₂×D₈₉	1	1	yes	characteristic
51	C₂³	—	178	1	no	—
52	Q₈	—	2	2	no	—
53	Q₈	—	2	2	no	—
54	Q₈	—	178	2	no	—
55	D₄	—	178	2	no	—
56	C₂×C₄	—	2	2	no	—
57	C₂×C₄	—	178	1	no	—
58	C₂×C₄	C₂²⋊D₈₉	1	2	yes	—
59	C₂×C₄	C₂²×D₈₉	1	1	yes	characteristic
60	C₈	—	89	4	no	—
61	C₂²	—	356	1	no	—
62	C₂²	—	356	2	no	—
63	C₂²	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
64	C₄	—	2	2	no	—
65	C₄	—	4	2	no	—
66	C₄	—	356	1	no	—
67	C₄	D₄×D₈₉	1	2	yes	—
68	C₂	—	712	1	no	—
69	C₂	#15668008	1	1	yes	characteristic
70	C₂	#15668043	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₈₉
commutator	C₂×C₄×C₈₉	C₂³
Frattini	C₂×C₄	C₂²×D₈₉
Fitting	C₄⋊Q₈×C₈₉	C₂
socle	C₂²×C₈₉	C₂×D₄
hypercenter	C₄⋊Q₈	D₈₉
hypocenter	C₈₉	#497
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄⋊Q₈

Complements

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

N	H ≅ G/N	type
1. C₂×#13083564	C₂	semidirect
4. #15667923	C₂	semidirect
5. C₄⋊Q₈×C₈₉	C₂	semidirect
35. C₈₉	#497	semidirect
39. C₄⋊Q₈	D₈₉	semidirect