Subgroups — #19151865

Order 5696.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15668038	C₂	1	2	yes	maximal, complemented
2	#15668018	C₂	1	1	yes	maximal, characteristic, complemented
3	#15667948	C₂	1	1	yes	maximal, characteristic, complemented
4	#15667929	C₂	1	2	yes	maximal, complemented
5	C₂×D₈×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#13083574	C₂²	1	1	yes	characteristic
7	#13083562	—	2	2	no	—
8	#13083559	—	2	2	no	—
9	#13083558	C₂²	1	1	yes	characteristic
10	#13083558	C₂²	1	2	yes	—
11	#13083557	—	2	1	no	—
12	C₈×D₈₉	—	2	1	no	—
13	C₂×D₄×C₈₉	C₂²	1	2	yes	—
14	D₈×C₈₉	—	2	1	no	—
15	D₈×C₈₉	—	2	1	no	—
16	C₂×C₈×C₈₉	C₂²	1	1	yes	characteristic
17	C₂³×C₈₉	—	2	2	no	—
18	D₄×C₈₉	—	2	2	no	—
19	D₄×C₈₉	—	2	2	no	—
20	C₂×C₄×C₈₉	C₂³	1	1	yes	characteristic
21	C₂²⋊D₈₉	—	2	1	no	—
22	D₃₅₆	D₄	1	1	yes	characteristic
23	C₄×D₈₉	—	2	1	no	—
24	Dic₁₇₈	D₄	1	1	yes	characteristic
25	C₈×C₈₉	D₄	1	1	yes	characteristic
26	C₈×C₈₉	D₄	1	1	yes	characteristic
27	#10623494	—	2	1	no	—
28	#10623494	—	2	2	no	—
29	C₂²×C₈₉	—	4	2	no	—
30	C₂²×C₈₉	—	8	2	no	—
31	C₂²×C₈₉	#41	1	1	yes	characteristic
32	C₂×D₈₉	—	2	1	no	—
33	C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
34	C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
35	Dic₈₉	—	2	1	no	—
36	C₂×C₈₉	—	2	1	no	—
37	C₂×C₈₉	—	8	2	no	—
38	C₂×C₈₉	#121	1	1	yes	characteristic
39	D₈₉	—	4	1	no	—
40	C₈₉	#472	1	1	yes	characteristic, complemented, Sylow
41	#472	—	89	1	no	maximal, Sylow
42	AGL(1,ℤ/8)	—	89	2	no	—
43	C₂×D₈	D₈₉	1	1	yes	characteristic, complemented
44	#131	—	89	1	no	—
45	#108	—	89	1	no	—
46	#100	—	89	2	no	—
47	#41	—	89	1	no	—
48	C₂×D₄	C₂×D₈₉	1	2	yes	—
49	SD₁₆	—	178	2	no	—
50	D₈	—	2	1	no	—
51	D₈	—	2	1	no	—
52	D₈	—	178	2	no	—
53	M₁₆	—	89	1	no	—
54	M₁₆	—	89	2	no	—
55	M₁₆	—	178	1	no	—
56	C₂×C₈	—	178	1	no	—
57	C₂×C₈	C₂×D₈₉	1	1	yes	characteristic
58	C₂³	—	2	2	no	—
59	Q₈	—	89	1	no	—
60	D₄	—	2	2	no	—
61	D₄	—	2	2	no	—
62	D₄	—	89	1	no	—
63	D₄	—	178	1	no	—
64	C₂×C₄	—	178	1	no	—
65	C₂×C₄	C₂²×D₈₉	1	1	yes	characteristic
66	C₈	—	178	2	no	—
67	C₈	—	178	1	no	—
68	C₈	C₂²⋊D₈₉	1	1	yes	characteristic
69	C₈	C₂²⋊D₈₉	1	1	yes	characteristic
70	C₂²	—	4	2	no	—
71	C₂²	—	8	2	no	—
72	C₂²	—	178	1	no	—
73	C₂²	#13083573	1	1	yes	characteristic
74	C₄	—	178	1	no	—
75	C₄	D₄×D₈₉	1	1	yes	characteristic
76	C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
77	C₂	—	2	1	no	—
78	C₂	—	8	2	no	—
79	C₂	—	356	1	no	—
80	C₂	#15667983	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#15667983
commutator	C₂×C₄×C₈₉	C₂³
Frattini	C₂×C₄	C₂²×D₈₉
Fitting	C₂×D₈×C₈₉	C₂
socle	C₂×C₈₉	#121
hypercenter	C₂×D₈	D₈₉
hypocenter	C₈₉	#472
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×D₈

Complements

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

N	H ≅ G/N	type
1. #15668038	C₂	semidirect
2. #15668018	C₂	semidirect
3. #15667948	C₂	semidirect
4. #15667929	C₂	semidirect
5. C₂×D₈×C₈₉	C₂	semidirect
40. C₈₉	#472	semidirect
43. C₂×D₈	D₈₉	semidirect