Subgroups — #19151852

Order 5696.

130 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₇₁₂	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#13083557	C₂	1	1	yes	maximal, characteristic, complemented
3	#15667987	C₂	1	2	yes	maximal, complemented
4	#15667932	C₂	1	2	yes	maximal, complemented
5	#106×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₃₅₆	—	2	2	no	—
7	C₂×D₃₅₆	C₂²	1	2	yes	—
8	C₂×C₄×D₈₉	C₂²	1	1	yes	characteristic
9	D₇₁₂	—	2	2	no	—
10	#13083557	—	2	2	no	—
11	C₂×#10623494	C₂²	1	1	yes	characteristic
12	#13083551	—	2	2	no	—
13	C₂×C₈×C₈₉	C₂²	1	1	yes	characteristic
14	C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
15	C₂²×D₈₉	—	2	2	no	—
16	C₂²×D₈₉	D₄	1	1	yes	characteristic
17	C₂×C₄×C₈₉	—	2	2	no	—
18	C₂×C₄×C₈₉	C₂³	1	1	yes	characteristic
19	C₂×Dic₈₉	D₄	1	1	yes	characteristic
20	D₃₅₆	—	2	2	no	—
21	D₃₅₆	—	2	2	no	—
22	D₃₅₆	—	4	4	no	—
23	C₄×D₈₉	—	2	1	no	—
24	C₄×D₈₉	—	2	1	no	—
25	C₈×C₈₉	D₄	1	2	yes	complemented
26	#10623494	—	2	1	no	—
27	C₂²×C₈₉	C₂×D₄	1	1	yes	characteristic
28	C₂×D₈₉	—	2	1	no	—
29	C₂×D₈₉	—	2	2	no	—
30	C₂×D₈₉	—	4	2	no	—
31	C₂×D₈₉	—	4	2	no	—
32	C₂×D₈₉	—	4	2	no	—
33	C₄×C₈₉	—	4	2	no	—
34	C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
35	C₄×C₈₉	#41	1	1	yes	characteristic
36	Dic₈₉	—	2	1	no	—
37	C₂×C₈₉	#121	1	1	yes	characteristic
38	C₂×C₈₉	AGL(1,ℤ/8)	1	2	yes	—
39	D₈₉	—	4	1	no	—
40	D₈₉	—	8	2	no	—
41	C₈₉	#469	1	1	yes	characteristic, complemented, Sylow
42	#469	—	89	1	no	maximal, Sylow
43	C₂×D₈	—	89	1	no	—
44	C₂×M₁₆	—	89	1	no	—
45	#121	—	89	2	no	—
46	#106	D₈₉	1	1	yes	characteristic, complemented
47	#102	—	89	2	no	—
48	C₂×D₄	—	89	2	no	—
49	C₂×D₄	—	178	2	no	—
50	C₂²×C₄	—	89	1	no	—
51	D₈	—	178	2	no	—
52	M₁₆	—	178	2	no	—
53	C₂×C₈	—	89	1	no	—
54	C₂×C₈	C₂×D₈₉	1	1	yes	characteristic
55	C₄⋊C₄	C₂×D₈₉	1	2	yes	—
56	C₂²⋊C₄	—	178	2	no	—
57	C₂³	—	89	1	no	—
58	C₂³	—	178	2	no	—
59	D₄	—	356	4	no	—
60	D₄	—	178	2	no	—
61	D₄	—	178	2	no	—
62	C₂×C₄	—	2	2	no	—
63	C₂×C₄	—	89	1	no	—
64	C₂×C₄	—	178	1	no	—
65	C₂×C₄	—	178	1	no	—
66	C₂×C₄	C₂²×D₈₉	1	1	yes	characteristic
67	C₈	—	178	1	no	—
68	C₈	D₃₅₆	1	2	yes	complemented
69	C₂²	—	356	2	no	—
70	C₂²	—	356	2	no	—
71	C₂²	—	356	2	no	—
72	C₂²	—	178	1	no	—
73	C₂²	—	178	2	no	—
74	C₂²	D₄×D₈₉	1	1	yes	characteristic
75	C₄	—	4	2	no	—
76	C₄	—	178	1	no	—
77	C₄	C₂×D₃₅₆	1	1	yes	characteristic
78	C₄	#13083575	1	1	yes	characteristic
79	C₂	—	356	1	no	—
80	C₂	—	712	2	no	—
81	C₂	#15667987	1	1	yes	characteristic
82	C₂	#15668039	1	2	yes	—

	subgroup	G/H
center	C₂²	D₄×D₈₉
commutator	C₂×C₄×C₈₉	C₂³
Frattini	C₂×C₄	C₂²×D₈₉
Fitting	#106×C₈₉	C₂
socle	C₂²×C₈₉	C₂×D₄
hypercenter	#106	D₈₉
hypocenter	C₈₉	#469
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #106

Complements

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

N	H ≅ G/N	type
1. C₂×D₇₁₂	C₂	semidirect
2. C₂×#13083557	C₂	semidirect
3. #15667987	C₂	semidirect
4. #15667932	C₂	semidirect
5. #106×C₈₉	C₂	semidirect
25. C₈×C₈₉	D₄	semidirect
41. C₈₉	#469	semidirect
46. #106	D₈₉	semidirect
68. C₈	D₃₅₆	semidirect