Subgroups — #19151945

Order 5696.

118 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15668012	C₂	1	1	yes	maximal, characteristic, complemented
2	#15668009	C₂	1	1	yes	maximal, characteristic
3	#15667934	C₂	1	4	yes	maximal, complemented
4	C₄×C₈×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×Dic₁₇₈	—	2	1	no	—
6	C₂×D₃₅₆	—	2	1	no	—
7	C₂×D₃₅₆	—	2	1	no	—
8	C₂×D₃₅₆	C₂²	1	2	yes	—
9	C₄⋊Dic₈₉	—	2	1	no	—
10	C₄⋊Dic₈₉	C₂²	1	2	yes	—
11	C₂×C₈×C₈₉	C₂²	1	2	yes	—
12	C₄²×C₈₉	C₂²	1	1	yes	characteristic
13	C₂²×D₈₉	—	2	2	no	—
14	C₂×C₄×C₈₉	D₄	1	1	yes	characteristic
15	C₂×C₄×C₈₉	D₄	1	1	yes	characteristic
16	C₂×C₄×C₈₉	C₂³	1	1	yes	characteristic
17	C₂×Dic₈₉	—	2	2	no	—
18	D₃₅₆	—	2	4	no	—
19	D₃₅₆	—	4	2	no	—
20	D₃₅₆	—	4	2	no	—
21	Dic₁₇₈	—	4	2	no	—
22	C₈×C₈₉	—	2	2	no	—
23	C₂²×C₈₉	C₂×D₄	1	1	yes	characteristic
24	C₂×D₈₉	—	4	2	no	—
25	C₂×D₈₉	—	4	2	no	—
26	C₂×D₈₉	—	4	2	no	—
27	C₄×C₈₉	D₈	1	2	yes	—
28	C₄×C₈₉	SD₁₆	1	2	yes	—
29	C₄×C₈₉	#41	1	2	yes	—
30	Dic₈₉	—	4	2	no	—
31	C₂×C₈₉	#124	1	1	yes	characteristic
32	C₂×C₈₉	C₂×D₈	1	1	yes	characteristic
33	C₂×C₈₉	C₂×SD₁₆	1	1	yes	characteristic
34	D₈₉	—	8	2	no	—
35	C₈₉	#486	1	1	yes	characteristic, complemented, Sylow
36	#486	—	89	1	no	maximal, Sylow
37	C₄⋊Q₈	—	89	1	no	—
38	#127	—	89	1	no	—
39	#102	—	89	4	no	—
40	C₄×C₈	D₈₉	1	1	yes	characteristic, complemented
41	C₂×Q₈	—	178	1	no	—
42	C₂×D₄	—	89	2	no	—
43	C₂×D₄	—	178	1	no	—
44	C₂×D₄	—	178	1	no	—
45	C₂×C₈	C₂×D₈₉	1	2	yes	—
46	C₄⋊C₄	—	89	2	no	—
47	C₄⋊C₄	—	178	1	no	—
48	C₄²	C₂×D₈₉	1	1	yes	characteristic
49	C₂³	—	178	2	no	—
50	Q₈	—	356	2	no	—
51	D₄	—	356	2	no	—
52	D₄	—	356	2	no	—
53	D₄	—	178	4	no	—
54	C₂×C₄	—	178	2	no	—
55	C₂×C₄	D₃₅₆	1	1	yes	characteristic
56	C₂×C₄	D₃₅₆	1	1	yes	characteristic
57	C₂×C₄	C₂²×D₈₉	1	1	yes	characteristic
58	C₈	—	2	2	no	—
59	C₂²	—	356	2	no	—
60	C₂²	—	356	2	no	—
61	C₂²	—	356	2	no	—
62	C₂²	C₂×D₃₅₆	1	1	yes	characteristic
63	C₄	—	356	2	no	—
64	C₄	D₇₁₂	1	2	yes	—
65	C₄	#13083563	1	2	yes	—
66	C₄	#13083574	1	2	yes	—
67	C₂	—	712	2	no	—
68	C₂	#15668000	1	1	yes	characteristic
69	C₂	C₂×D₇₁₂	1	1	yes	characteristic
70	C₂	C₂×#13083563	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₃₅₆
commutator	C₂×C₄×C₈₉	C₂³
Frattini	C₂×C₄	C₂²×D₈₉
Fitting	C₄×C₈×C₈₉	C₂
socle	C₂²×C₈₉	C₂×D₄
hypercenter	C₄×C₈	D₈₉
hypocenter	C₈₉	#486
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
1. #15668012	C₂	semidirect
3. #15667934	C₂	semidirect
4. C₄×C₈×C₈₉	C₂	semidirect
35. C₈₉	#486	semidirect
40. C₄×C₈	D₈₉	semidirect