Subgroups — C₂×#15667956 #19152022

Order 5696.

90 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	#15667956	C₂	1	4	yes	maximal, direct product factor
3	C₂×#13083549	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₈×C₈₉	C₂	1	1	yes	maximal, characteristic
5	C₂×Dic₁₇₈	—	2	1	no	—
6	Dic₃₅₆	—	2	1	no	—
7	Dic₃₅₆	C₂²	1	2	yes	complemented
8	#13083549	C₂²	1	2	yes	complemented
9	C₂×D₄×C₈₉	—	2	1	no	—
10	D₈×C₈₉	—	2	1	no	—
11	D₈×C₈₉	C₂²	1	2	yes	—
12	C₂×C₈×C₈₉	C₂²	1	1	yes	characteristic
13	C₂³×C₈₉	—	4	1	no	—
14	D₄×C₈₉	—	2	2	no	—
15	D₄×C₈₉	—	4	1	no	—
16	C₂×C₄×C₈₉	D₄	1	1	yes	characteristic
17	C₂×Dic₈₉	—	4	1	no	—
18	Dic₁₇₈	—	2	2	no	—
19	Dic₁₇₈	—	4	1	no	—
20	C₈×C₈₉	D₄	1	1	yes	characteristic
21	C₈×C₈₉	C₂³	1	1	yes	characteristic
22	C₂²×C₈₉	—	4	2	no	—
23	C₂²×C₈₉	—	8	2	no	—
24	C₂²×C₈₉	D₈	1	1	yes	characteristic
25	C₄×C₈₉	D₈	1	1	yes	characteristic
26	C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
27	Dic₈₉	—	4	2	no	—
28	C₂×C₈₉	—	8	2	no	—
29	C₂×C₈₉	SD₃₂	1	2	yes	complemented
30	C₂×C₈₉	C₂×D₈	1	1	yes	characteristic
31	C₈₉	C₂×SD₃₂	1	1	yes	characteristic, complemented, Sylow
32	C₂×SD₃₂	—	89	1	no	maximal, Sylow
33	C₂×Q₁₆	—	89	1	no	—
34	C₂×D₈	D₈₉	1	1	yes	characteristic
35	SD₃₂	—	89	4	no	—
36	C₂×C₁₆	—	89	1	no	—
37	C₂×Q₈	—	178	1	no	—
38	C₂×D₄	—	2	1	no	—
39	Q₁₆	—	89	2	no	—
40	Q₁₆	—	178	1	no	—
41	D₈	—	2	1	no	—
42	D₈	C₂×D₈₉	1	2	yes	—
43	C₂×C₈	C₂×D₈₉	1	1	yes	characteristic
44	C₁₆	—	89	2	no	—
45	C₂³	—	4	1	no	—
46	Q₈	—	356	1	no	—
47	Q₈	—	178	2	no	—
48	D₄	—	2	2	no	—
49	D₄	—	4	1	no	—
50	C₂×C₄	—	356	1	no	—
51	C₂×C₄	C₂²⋊D₈₉	1	1	yes	characteristic
52	C₈	C₂²⋊D₈₉	1	1	yes	characteristic
53	C₈	C₂²×D₈₉	1	1	yes	characteristic
54	C₂²	—	4	2	no	—
55	C₂²	—	8	2	no	—
56	C₂²	#13083559	1	1	yes	characteristic
57	C₄	—	356	2	no	—
58	C₄	#13083559	1	1	yes	characteristic
59	C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
60	C₂	—	8	2	no	—
61	C₂	#15667956	1	2	yes	direct product factor
62	C₂	C₂×#13083559	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#13083559
commutator	C₈×C₈₉	C₂³
Frattini	C₈	C₂²×D₈₉
Fitting	C₂×D₈×C₈₉	C₂
socle	C₂²×C₈₉	D₈
hypercenter	C₂×D₈	D₈₉
hypocenter	C₈₉	C₂×SD₃₂
LCS	G ▷ C₈×C₈₉ ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×D₈

Complements

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

N	H ≅ G/N	type
1. C₂×Dic₃₅₆	C₂	semidirect
2. #15667956	C₂	direct (N × H)
3. C₂×#13083549	C₂	semidirect
7. Dic₃₅₆	C₂²	semidirect
8. #13083549	C₂²	semidirect
29. C₂×C₈₉	SD₃₂	semidirect
31. C₈₉	C₂×SD₃₂	semidirect
61. C₂	#15667956	direct (N × H)

Subgroups — C2×#15667956 #19152022

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#15667956 #19152022