Subgroups — #19152041

Order 5696.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15668034	C₂	1	1	yes	maximal, characteristic
2	C₂×Dic₃₅₆	C₂	1	1	yes	maximal, characteristic, complemented
3	Dic₇₁₂	C₂	1	2	yes	maximal, complemented
4	#15667957	C₂	1	2	yes	maximal, complemented
5	M₃₂×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#13083574	—	2	1	no	—
7	C₂×Dic₁₇₈	—	2	1	no	—
8	Dic₃₅₆	—	2	1	no	—
9	Dic₃₅₆	C₂²	1	2	yes	—
10	Dic₃₅₆	C₂²	1	1	yes	characteristic
11	#13083563	—	2	1	no	—
12	D₇₁₂	C₂²	1	1	yes	characteristic
13	C₂×C₈×C₈₉	C₂²	1	1	yes	characteristic
14	C₁₆×C₈₉	C₂²	1	2	yes	—
15	C₂×C₄×C₈₉	D₄	1	1	yes	characteristic
16	C₂²⋊D₈₉	—	4	1	no	—
17	C₂×Dic₈₉	—	4	1	no	—
18	D₃₅₆	—	2	1	no	—
19	C₄×D₈₉	—	4	1	no	—
20	Dic₁₇₈	—	2	1	no	—
21	Dic₁₇₈	—	2	2	no	—
22	Dic₁₇₈	—	4	1	no	—
23	C₈×C₈₉	D₄	1	1	yes	characteristic
24	C₈×C₈₉	C₂³	1	1	yes	characteristic
25	C₂²×C₈₉	D₈	1	1	yes	characteristic
26	C₂×D₈₉	—	4	1	no	—
27	C₄×C₈₉	D₈	1	1	yes	characteristic
28	C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
29	Dic₈₉	—	4	2	no	—
30	Dic₈₉	—	4	1	no	—
31	C₂×C₈₉	—	2	1	no	—
32	C₂×C₈₉	C₂×D₈	1	1	yes	characteristic
33	D₈₉	—	8	1	no	—
34	C₈₉	#510	1	1	yes	characteristic, complemented, Sylow
35	#510	—	89	1	no	maximal, Sylow
36	#135	—	89	1	no	—
37	C₂×Q₁₆	—	89	1	no	—
38	Q₃₂	—	89	2	no	—
39	SD₃₂	—	89	2	no	—
40	M₃₂	D₈₉	1	1	yes	characteristic, complemented
41	#41	—	178	1	no	—
42	C₂×Q₈	—	178	1	no	—
43	Q₁₆	—	89	2	no	—
44	Q₁₆	—	89	1	no	—
45	Q₁₆	—	178	1	no	—
46	SD₁₆	—	178	1	no	—
47	D₈	—	89	1	no	—
48	C₂×C₈	C₂×D₈₉	1	1	yes	characteristic
49	C₁₆	C₂×D₈₉	1	2	yes	—
50	Q₈	—	356	1	no	—
51	Q₈	—	178	1	no	—
52	Q₈	—	178	2	no	—
53	D₄	—	356	1	no	—
54	D₄	—	178	1	no	—
55	C₂×C₄	—	356	1	no	—
56	C₂×C₄	—	356	1	no	—
57	C₂×C₄	D₃₅₆	1	1	yes	characteristic
58	C₈	D₃₅₆	1	1	yes	characteristic
59	C₈	C₂²×D₈₉	1	1	yes	characteristic
60	C₂²	—	356	1	no	—
61	C₂²	D₇₁₂	1	1	yes	characteristic
62	C₄	—	356	1	no	—
63	C₄	—	356	2	no	—
64	C₄	D₇₁₂	1	1	yes	characteristic
65	C₄	C₂×D₃₅₆	1	1	yes	characteristic
66	C₂	—	2	1	no	—
67	C₂	—	712	1	no	—
68	C₂	C₂×D₇₁₂	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×D₇₁₂
commutator	C₈×C₈₉	C₂³
Frattini	C₈	C₂²×D₈₉
Fitting	M₃₂×C₈₉	C₂
socle	C₂×C₈₉	C₂×D₈
hypercenter	M₃₂	D₈₉
hypocenter	C₈₉	#510
LCS	G ▷ C₈×C₈₉ ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ M₃₂

Complements

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

N	H ≅ G/N	type
2. C₂×Dic₃₅₆	C₂	semidirect
3. Dic₇₁₂	C₂	semidirect
4. #15667957	C₂	semidirect
5. M₃₂×C₈₉	C₂	semidirect
34. C₈₉	#510	semidirect
40. M₃₂	D₈₉	semidirect