Subgroups — #23750541

Order 9536.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#18011986	C₂	1	1	yes	maximal, characteristic, complemented
2	#18011979	C₂	1	1	yes	maximal, characteristic, complemented
3	#18011930	C₂	1	1	yes	maximal, characteristic
4	C₄⋊#10597010	—	2	1	no	—
5	#14558739	—	2	1	no	—
6	#14558735	—	2	1	no	—
7	Dic₅₉₆	C₄	1	1	yes	characteristic, complemented
8	#14558724	—	2	1	no	—
9	C₈×D₁₄₉	C₂²	1	1	yes	characteristic
10	D₈×C₁₄₉	C₄	1	1	yes	characteristic, complemented
11	C₂×#10597010	—	4	1	no	—
12	Dic₂₉₈	—	2	1	no	—
13	C₂²⋊D₁₄₉	—	4	1	no	—
14	C₂×Dic₁₄₉	—	4	1	no	—
15	C₄×D₁₄₉	D₄	1	1	yes	characteristic
16	#11924746	D₄	1	1	yes	characteristic
17	D₄×C₁₄₉	—	2	1	no	—
18	C₈×C₁₄₉	C₂×C₄	1	1	yes	characteristic
19	C₂²×C₁₄₉	—	4	1	no	—
20	C₂×D₁₄₉	D₈	1	1	yes	characteristic
21	#10597010	—	8	1	no	—
22	C₄×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
23	Dic₁₄₉	—	4	1	no	—
24	Dic₁₄₉	SD₁₆	1	1	yes	characteristic
25	C₂×C₁₄₉	—	8	1	no	—
26	C₂×C₁₄₉	#102	1	1	yes	characteristic
27	D₁₄₉	—	2	1	no	—
28	C₁₄₉	#360	1	1	yes	characteristic, complemented, Sylow
29	#360	—	149	1	no	maximal, Sylow
30	#135	—	149	1	no	—
31	M₃₂	—	149	1	no	—
32	#106	—	149	1	no	—
33	#41	—	298	1	no	—
34	Q₁₆	—	149	1	no	—
35	SD₁₆	—	298	1	no	—
36	D₈	#10597010	1	1	yes	characteristic, complemented
37	C₂×C₈	—	149	1	no	—
38	C₄⋊C₄	—	298	1	no	—
39	C₁₆	—	298	1	no	—
40	Q₈	—	298	1	no	—
41	D₄	—	2	1	no	—
42	D₄	—	596	1	no	—
43	C₂×C₄	—	596	1	no	—
44	C₂×C₄	—	596	1	no	—
45	C₂×C₄	—	149	1	no	—
46	C₈	—	149	1	no	—
47	C₈	C₂×#10597010	1	1	yes	characteristic
48	C₂²	—	4	1	no	—
49	C₂²	—	149	1	no	—
50	C₄	—	596	1	no	—
51	C₄	—	149	1	no	—
52	C₄	—	1192	1	no	—
53	C₄	C₂²⋊#10597010	1	1	yes	characteristic
54	C₂	—	8	1	no	—
55	C₂	—	298	1	no	—
56	C₂	#18011973	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#18011973
commutator	C₈×C₁₄₉	C₂×C₄
Frattini	C₈	C₂×#10597010
Fitting	D₈×C₁₄₉	C₄
socle	C₂×C₁₄₉	#102
prime radical	#18011930	C₂
cosocle	C₈×D₁₄₉	C₂²
hypercenter	D₈	#10597010
hypocenter	C₁₄₉	#360
LCS	G ▷ C₈×C₁₄₉ ▷ C₄×C₁₄₉ ▷ C₂×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ D₈

Complements

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

N	H ≅ G/N	type
1. #18011986	C₂	semidirect
2. #18011979	C₂	semidirect
7. Dic₅₉₆	C₄	semidirect
10. D₈×C₁₄₉	C₄	semidirect
28. C₁₄₉	#360	semidirect
36. D₈	#10597010	semidirect