Subgroups — #19151953

Order 5696.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15668004	C₂	1	1	yes	maximal, characteristic, complemented
2	#15668000	C₂	1	1	yes	maximal, characteristic
3	#15667937	C₂	1	2	yes	maximal, complemented
4	#15667934	C₂	1	2	yes	maximal
5	C₄×C₈×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	C₄⋊Dic₈₉	C₂²	1	2	yes	—
9	#13083553	—	2	2	no	—
10	#13083551	—	2	2	no	—
11	C₂×C₈×C₈₉	C₂²	1	2	yes	—
12	C₄²×C₈₉	C₂²	1	1	yes	characteristic
13	C₂²×D₈₉	—	2	1	no	—
14	C₂×C₄×C₈₉	D₄	1	2	yes	—
15	C₂×C₄×C₈₉	C₂³	1	1	yes	characteristic
16	C₂×Dic₈₉	—	2	1	no	—
17	C₂×Dic₈₉	—	2	2	no	—
18	D₃₅₆	—	2	2	no	—
19	Dic₁₇₈	—	2	2	no	—
20	C₈×C₈₉	—	2	2	no	—
21	C₂²×C₈₉	C₂×D₄	1	1	yes	characteristic
22	C₂×D₈₉	—	4	1	no	—
23	C₂×D₈₉	—	4	2	no	—
24	C₄×C₈₉	—	2	2	no	—
25	C₄×C₈₉	#41	1	2	yes	—
26	Dic₈₉	—	4	1	no	—
27	Dic₈₉	—	4	2	no	—
28	C₂×C₈₉	#124	1	1	yes	characteristic
29	C₂×C₈₉	#135	1	2	yes	—
30	D₈₉	—	8	1	no	—
31	C₈₉	#488	1	1	yes	characteristic, complemented, Sylow
32	#488	—	89	1	no	maximal, Sylow
33	#125	—	89	1	no	—
34	#124	—	89	1	no	—
35	#103	—	89	2	no	—
36	#102	—	89	2	no	—
37	C₄×C₈	D₈₉	1	1	yes	characteristic, complemented
38	C₂×Q₈	—	89	1	no	—
39	C₂×D₄	—	89	1	no	—
40	C₂×C₈	C₂×D₈₉	1	2	yes	—
41	C₄⋊C₄	—	89	2	no	—
42	C₄⋊C₄	—	178	2	no	—
43	C₂²⋊C₄	—	178	2	no	—
44	C₄²	C₂×D₈₉	1	1	yes	characteristic
45	C₂³	—	178	1	no	—
46	Q₈	—	178	2	no	—
47	D₄	—	178	2	no	—
48	C₂×C₄	—	178	1	no	—
49	C₂×C₄	—	178	2	no	—
50	C₂×C₄	D₃₅₆	1	2	yes	—
51	C₂×C₄	C₂²×D₈₉	1	1	yes	characteristic
52	C₈	—	2	2	no	—
53	C₂²	—	356	1	no	—
54	C₂²	—	356	2	no	—
55	C₂²	C₂×D₃₅₆	1	1	yes	characteristic
56	C₄	—	2	2	no	—
57	C₄	—	356	1	no	—
58	C₄	—	356	2	no	—
59	C₄	#13083574	1	2	yes	—
60	C₂	—	712	1	no	—
61	C₂	#15668000	1	1	yes	characteristic
62	C₂	#15668034	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×D₃₅₆
commutator	C₂×C₄×C₈₉	C₂³
Frattini	C₂×C₄	C₂²×D₈₉
Fitting	C₄×C₈×C₈₉	C₂
socle	C₂²×C₈₉	C₂×D₄
hypercenter	C₄×C₈	D₈₉
hypocenter	C₈₉	#488
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
1. #15668004	C₂	semidirect
3. #15667937	C₂	semidirect
5. C₄×C₈×C₈₉	C₂	semidirect
31. C₈₉	#488	semidirect
37. C₄×C₈	D₈₉	semidirect