Subgroups — #19152002

Order 5696.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15668011	C₂	1	2	yes	maximal
2	#15667946	C₂	1	1	yes	maximal, characteristic
3	#15667945	C₂	1	2	yes	maximal
4	C₈×Dic₈₉	C₂	1	1	yes	maximal, characteristic
5	#107×C₈₉	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₁₇₈	—	2	2	no	—
7	C₂×#10623494	C₂²	1	1	yes	characteristic
8	C₄⋊Dic₈₉	C₂²	1	2	yes	—
9	#13083553	—	2	2	no	—
10	C₄×Dic₈₉	C₂²	1	1	yes	characteristic
11	C₂×C₈×C₈₉	C₂²	1	1	yes	characteristic
12	C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
13	C₂×C₄×C₈₉	—	2	2	no	—
14	C₂×C₄×C₈₉	C₂³	1	1	yes	characteristic
15	C₂×Dic₈₉	—	2	2	no	—
16	C₂×Dic₈₉	D₄	1	1	yes	characteristic
17	C₂×Dic₈₉	D₄	1	1	yes	characteristic
18	Dic₁₇₈	—	4	4	no	—
19	C₈×C₈₉	Q₈	1	2	yes	complemented
20	#10623494	Q₈	1	2	yes	complemented
21	C₂²×C₈₉	C₂×D₄	1	1	yes	characteristic
22	C₄×C₈₉	—	4	2	no	—
23	C₄×C₈₉	C₂×Q₈	1	1	yes	characteristic
24	C₄×C₈₉	C₂×Q₈	1	1	yes	characteristic
25	Dic₈₉	—	4	2	no	—
26	Dic₈₉	D₈	1	2	yes	—
27	Dic₈₉	Q₁₆	1	2	yes	—
28	C₂×C₈₉	C₄⋊Q₈	1	1	yes	characteristic
29	C₂×C₈₉	C₂×D₈	1	1	yes	characteristic
30	C₂×C₈₉	C₂×Q₁₆	1	1	yes	characteristic
31	C₈₉	#500	1	1	yes	characteristic, complemented, Sylow
32	#500	—	89	1	no	maximal, Sylow
33	C₄⋊Q₈	—	89	2	no	—
34	#107	—	89	1	no	—
35	#107	—	89	2	no	—
36	#107	D₈₉	1	1	yes	characteristic
37	C₄×C₈	—	89	1	no	—
38	C₂×Q₈	—	178	2	no	—
39	C₂×C₈	—	89	1	no	—
40	C₂×C₈	C₂×D₈₉	1	1	yes	characteristic
41	C₄⋊C₄	—	89	2	no	—
42	C₄⋊C₄	—	178	2	no	—
43	C₄⋊C₄	C₂×D₈₉	1	2	yes	—
44	C₄²	—	89	1	no	—
45	Q₈	—	356	4	no	—
46	C₂×C₄	—	2	2	no	—
47	C₂×C₄	—	89	1	no	—
48	C₂×C₄	—	89	1	no	—
49	C₂×C₄	—	178	2	no	—
50	C₂×C₄	C₂²×D₈₉	1	1	yes	characteristic
51	C₈	—	89	2	no	—
52	C₈	Dic₁₇₈	1	2	yes	complemented
53	C₂²	D₄×D₈₉	1	1	yes	characteristic
54	C₄	—	4	2	no	—
55	C₄	—	89	2	no	—
56	C₄	—	89	2	no	—
57	C₄	—	356	2	no	—
58	C₄	Q₈×D₈₉	1	1	yes	characteristic
59	C₄	C₂×Dic₁₇₈	1	1	yes	characteristic
60	C₂	#15668011	1	1	yes	characteristic
61	C₂	D₈×D₈₉	1	1	yes	characteristic
62	C₂	Q₁₆×D₈₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₈₉
commutator	C₂×C₄×C₈₉	C₂³
Frattini	C₂×C₄	C₂²×D₈₉
Fitting	#107×C₈₉	C₂
socle	C₂²×C₈₉	C₂×D₄
hypercenter	#107	D₈₉
hypocenter	C₈₉	#500
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #107

Complements

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

N	H ≅ G/N	type
19. C₈×C₈₉	Q₈	semidirect
20. #10623494	Q₈	semidirect
31. C₈₉	#500	semidirect
52. C₈	Dic₁₇₈	semidirect