Subgroups — #19151406

Order 5696.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15668034	C₂	1	1	yes	maximal, characteristic
2	#15667948	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₆×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#13083574	—	2	1	no	—
5	Dic₃₅₆	C₄	1	1	yes	characteristic
6	#13083563	—	2	1	no	—
7	D₇₁₂	C₄	1	1	yes	characteristic
8	#13083558	—	2	1	no	—
9	C₂×C₈×C₈₉	C₂²	1	1	yes	characteristic
10	C₁₆×C₈₉	—	2	1	no	—
11	C₂×C₄×C₈₉	D₄	1	1	yes	characteristic
12	C₂²⋊D₈₉	—	4	1	no	—
13	D₃₅₆	—	2	1	no	—
14	C₄×D₈₉	—	4	1	no	—
15	Dic₁₇₈	—	2	1	no	—
16	C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
17	C₈×C₈₉	D₄	1	1	yes	characteristic
18	#10623494	—	4	1	no	—
19	C₂²×C₈₉	SD₁₆	1	1	yes	characteristic
20	C₂×D₈₉	—	4	1	no	—
21	C₄×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
22	C₄×C₈₉	D₈	1	1	yes	characteristic
23	Dic₈₉	—	4	1	no	—
24	C₂×C₈₉	—	2	1	no	—
25	C₂×C₈₉	#102	1	1	yes	characteristic
26	D₈₉	—	8	1	no	—
27	C₈₉	#359	1	1	yes	characteristic, complemented, Sylow
28	#359	—	89	1	no	maximal, Sylow
29	#135	—	89	1	no	—
30	C₂×C₁₆	D₈₉	1	1	yes	characteristic, complemented
31	#108	—	89	1	no	—
32	#41	—	178	1	no	—
33	Q₁₆	—	89	1	no	—
34	SD₁₆	—	178	1	no	—
35	D₈	—	89	1	no	—
36	M₁₆	—	178	1	no	—
37	C₂×C₈	C₂×D₈₉	1	1	yes	characteristic
38	C₁₆	—	2	1	no	—
39	Q₈	—	178	1	no	—
40	D₄	—	356	1	no	—
41	D₄	—	178	1	no	—
42	C₂×C₄	—	356	1	no	—
43	C₂×C₄	D₃₅₆	1	1	yes	characteristic
44	C₈	—	356	1	no	—
45	C₈	C₄×D₈₉	1	1	yes	characteristic
46	C₈	C₂²⋊D₈₉	1	1	yes	characteristic
47	C₂²	—	356	1	no	—
48	C₂²	#13083563	1	1	yes	characteristic
49	C₄	—	356	1	no	—
50	C₄	#13083551	1	1	yes	characteristic
51	C₄	D₇₁₂	1	1	yes	characteristic
52	C₂	—	2	1	no	—
53	C₂	—	712	1	no	—
54	C₂	#15667934	1	1	yes	characteristic

	subgroup	G/H
center	C₄	D₇₁₂
commutator	C₈×C₈₉	C₂×C₄
Frattini	C₂×C₈	C₂×D₈₉
Fitting	C₂×C₁₆×C₈₉	C₂
socle	C₂×C₈₉	#102
hypercenter	C₂×C₁₆	D₈₉
hypocenter	C₈₉	#359
LCS	G ▷ C₈×C₈₉ ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
2. #15667948	C₂	semidirect
3. C₂×C₁₆×C₈₉	C₂	semidirect
27. C₈₉	#359	semidirect
30. C₂×C₁₆	D₈₉	semidirect