Subgroups — #19151795

Order 5696.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13083562	C₂	1	2	yes	maximal, complemented
2	C₄×Dic₁₇₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄⋊#10623494	C₂	1	1	yes	maximal, characteristic, complemented
4	#15667933	C₂	1	2	yes	maximal, complemented
5	#127×C₈₉	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₁₇₈	C₂²	1	1	yes	characteristic
7	#13083562	—	2	4	no	—
8	C₂×#10623494	C₂²	1	2	yes	—
9	C₄⋊Dic₈₉	C₂²	1	1	yes	characteristic
10	#13083553	—	2	1	no	—
11	C₄×Dic₈₉	—	2	1	no	—
12	C₂×D₄×C₈₉	—	2	1	no	—
13	C₂×D₄×C₈₉	—	2	1	no	—
14	C₂×D₄×C₈₉	C₂²	1	2	yes	—
15	C₄²×C₈₉	C₂²	1	1	yes	characteristic
16	C₂³×C₈₉	—	2	2	no	—
17	D₄×C₈₉	—	2	2	no	—
18	D₄×C₈₉	—	2	2	no	—
19	D₄×C₈₉	—	4	2	no	—
20	D₄×C₈₉	—	4	2	no	—
21	C₂×C₄×C₈₉	D₄	1	1	yes	characteristic
22	C₂×C₄×C₈₉	D₄	1	1	yes	characteristic
23	C₂×C₄×C₈₉	C₂³	1	1	yes	characteristic
24	C₂×Dic₈₉	—	2	1	no	—
25	C₂×Dic₈₉	—	2	1	no	—
26	Dic₁₇₈	—	2	1	no	—
27	Dic₁₇₈	D₄	1	2	yes	complemented
28	#10623494	—	2	2	no	—
29	C₂²×C₈₉	—	4	2	no	—
30	C₂²×C₈₉	—	4	2	no	—
31	C₂²×C₈₉	—	4	2	no	—
32	C₂²×C₈₉	C₂×D₄	1	1	yes	characteristic
33	C₄×C₈₉	—	2	1	no	—
34	C₄×C₈₉	SD₁₆	1	2	yes	complemented
35	C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
36	C₄×C₈₉	#41	1	1	yes	characteristic
37	Dic₈₉	—	2	2	no	—
38	Dic₈₉	—	4	1	no	—
39	C₂×C₈₉	—	8	2	no	—
40	C₂×C₈₉	#121	1	1	yes	characteristic
41	C₂×C₈₉	C₂×SD₁₆	1	1	yes	characteristic
42	C₂×C₈₉	AGL(1,ℤ/8)	1	1	yes	characteristic
43	C₈₉	#460	1	1	yes	characteristic, complemented, Sylow
44	#460	—	89	1	no	maximal, Sylow
45	C₂×SD₁₆	—	89	2	no	—
46	#127	D₈₉	1	1	yes	characteristic
47	C₄×Q₈	—	89	1	no	—
48	C₄⋊C₈	—	89	1	no	—
49	#102	—	89	2	no	—
50	C₂×Q₈	—	89	1	no	—
51	C₂×D₄	—	2	1	no	—
52	C₂×D₄	—	2	1	no	—
53	C₂×D₄	C₂×D₈₉	1	2	yes	—
54	SD₁₆	—	178	4	no	—
55	C₂×C₈	—	89	2	no	—
56	C₄⋊C₄	—	89	1	no	—
57	C₄⋊C₄	—	178	1	no	—
58	C₄²	—	178	1	no	—
59	C₄²	C₂×D₈₉	1	1	yes	characteristic
60	C₂³	—	2	2	no	—
61	Q₈	—	89	2	no	—
62	Q₈	—	178	1	no	—
63	D₄	—	2	2	no	—
64	D₄	—	2	2	no	—
65	D₄	—	4	2	no	—
66	D₄	—	4	2	no	—
67	C₂×C₄	—	178	1	no	—
68	C₂×C₄	—	178	1	no	—
69	C₂×C₄	C₂²⋊D₈₉	1	1	yes	characteristic
70	C₂×C₄	C₂²⋊D₈₉	1	1	yes	characteristic
71	C₂×C₄	C₂²×D₈₉	1	1	yes	characteristic
72	C₈	—	178	2	no	—
73	C₂²	—	4	2	no	—
74	C₂²	—	4	2	no	—
75	C₂²	—	4	2	no	—
76	C₂²	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
77	C₄	—	2	1	no	—
78	C₄	—	356	1	no	—
79	C₄	—	178	2	no	—
80	C₄	#13083562	1	2	yes	complemented
81	C₄	D₄×D₈₉	1	1	yes	characteristic
82	C₄	#13083573	1	1	yes	characteristic
83	C₂	—	8	2	no	—
84	C₂	#15667983	1	1	yes	characteristic
85	C₂	C₂×#13083562	1	1	yes	characteristic
86	C₂	#15668038	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₈₉
commutator	C₂×C₄×C₈₉	C₂³
Frattini	C₂×C₄	C₂²×D₈₉
Fitting	#127×C₈₉	C₂
socle	C₂²×C₈₉	C₂×D₄
hypercenter	#127	D₈₉
hypocenter	C₈₉	#460
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #127

Complements

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

N	H ≅ G/N	type
1. C₂×#13083562	C₂	semidirect
2. C₄×Dic₁₇₈	C₂	semidirect
3. C₄⋊#10623494	C₂	semidirect
4. #15667933	C₂	semidirect
27. Dic₁₇₈	D₄	semidirect
34. C₄×C₈₉	SD₁₆	semidirect
43. C₈₉	#460	semidirect
80. C₄	#13083562	semidirect