Subgroups — #19151908

Order 5696.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15668003	C₂	1	1	yes	maximal, characteristic
2	#15667977	C₂	1	1	yes	maximal, characteristic
3	#15667945	C₂	1	1	yes	maximal, characteristic
4	#15667941	C₂	1	1	yes	maximal, characteristic
5	#15667937	C₂	1	1	yes	maximal, characteristic
6	#15667935	C₂	1	1	yes	maximal, characteristic
7	#106×C₈₉	C₂	1	1	yes	maximal, characteristic
8	C₂×Dic₁₇₈	C₂²	1	1	yes	characteristic
9	C₂×#10623494	C₂²	1	1	yes	characteristic
10	C₄⋊Dic₈₉	—	2	1	no	—
11	C₄⋊Dic₈₉	C₂²	1	1	yes	characteristic
12	#13083553	—	2	1	no	—
13	#13083553	—	2	1	no	—
14	C₄×Dic₈₉	—	2	1	no	—
15	C₄×Dic₈₉	C₂²	1	1	yes	characteristic
16	C₂×C₈×C₈₉	C₂²	1	1	yes	characteristic
17	C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
18	C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
19	C₂×C₄×C₈₉	—	2	1	no	—
20	C₂×C₄×C₈₉	—	2	1	no	—
21	C₂×C₄×C₈₉	C₂³	1	1	yes	characteristic
22	C₂×Dic₈₉	—	2	1	no	—
23	C₂×Dic₈₉	—	2	1	no	—
24	C₂×Dic₈₉	D₄	1	1	yes	characteristic
25	C₂×Dic₈₉	D₄	1	1	yes	characteristic
26	Dic₁₇₈	—	2	1	no	—
27	Dic₁₇₈	Q₈	1	2	yes	—
28	C₈×C₈₉	—	2	1	no	—
29	#10623494	—	2	1	no	—
30	C₂²×C₈₉	C₂×D₄	1	1	yes	characteristic
31	C₄×C₈₉	—	4	1	no	—
32	C₄×C₈₉	—	4	1	no	—
33	C₄×C₈₉	C₂×Q₈	1	1	yes	characteristic
34	C₄×C₈₉	#41	1	1	yes	characteristic
35	Dic₈₉	—	2	2	no	—
36	Dic₈₉	—	2	1	no	—
37	Dic₈₉	—	2	1	no	—
38	Dic₈₉	—	4	1	no	—
39	C₂×C₈₉	C₂²⋊Q₈	1	1	yes	characteristic
40	C₂×C₈₉	#135	1	1	yes	characteristic
41	C₂×C₈₉	#137	1	1	yes	characteristic
42	C₈₉	#479	1	1	yes	characteristic, complemented, Sylow
43	#479	—	89	1	no	maximal, Sylow
44	#125	—	89	1	no	—
45	C₄×Q₈	—	89	1	no	—
46	#107	—	89	1	no	—
47	#106	D₈₉	1	1	yes	characteristic
48	C₄⋊C₈	—	89	1	no	—
49	#103	—	89	1	no	—
50	#103	—	89	1	no	—
51	C₂×Q₈	—	89	1	no	—
52	C₂×C₈	—	89	1	no	—
53	C₂×C₈	C₂×D₈₉	1	1	yes	characteristic
54	C₄⋊C₄	—	89	1	no	—
55	C₄⋊C₄	—	178	1	no	—
56	C₄⋊C₄	—	178	1	no	—
57	C₄⋊C₄	—	178	1	no	—
58	C₄⋊C₄	C₂×D₈₉	1	1	yes	characteristic
59	C₄⋊C₄	C₂×D₈₉	1	1	yes	characteristic
60	C₄²	—	89	1	no	—
61	C₄²	—	178	1	no	—
62	Q₈	—	89	2	no	—
63	Q₈	—	178	1	no	—
64	C₂×C₄	—	2	1	no	—
65	C₂×C₄	—	2	1	no	—
66	C₂×C₄	—	89	1	no	—
67	C₂×C₄	—	89	1	no	—
68	C₂×C₄	—	178	1	no	—
69	C₂×C₄	—	178	1	no	—
70	C₂×C₄	C₂²×D₈₉	1	1	yes	characteristic
71	C₈	—	2	1	no	—
72	C₈	—	178	1	no	—
73	C₂²	D₄×D₈₉	1	1	yes	characteristic
74	C₄	—	4	1	no	—
75	C₄	—	4	1	no	—
76	C₄	—	356	1	no	—
77	C₄	—	178	2	no	—
78	C₄	—	178	1	no	—
79	C₄	—	178	1	no	—
80	C₄	Q₈×D₈₉	1	1	yes	characteristic
81	C₄	#13083574	1	1	yes	characteristic
82	C₂	#15667990	1	1	yes	characteristic
83	C₂	#15668033	1	1	yes	characteristic
84	C₂	#15668041	1	1	yes	characteristic

	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	#479
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
42. C₈₉	#479	semidirect