Subgroups — #23750543

Order 9536.

62 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	#18011981	C₂	1	1	yes	maximal, characteristic, complemented
3	D₈×D₁₄₉	C₂	1	1	yes	maximal, characteristic
4	#14558746	—	2	1	no	—
5	#14558739	—	2	1	no	—
6	D₄×D₁₄₉	—	2	1	no	—
7	D₁₁₉₂	C₄	1	1	yes	characteristic
8	#14558721	—	2	1	no	—
9	C₈×D₁₄₉	C₂²	1	1	yes	characteristic
10	D₈×C₁₄₉	C₄	1	1	yes	characteristic
11	#11924753	—	4	1	no	—
12	C₂²×D₁₄₉	—	4	1	no	—
13	D₅₉₆	—	2	1	no	—
14	C₂²⋊D₁₄₉	—	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	—	4	1	no	—
21	C₂×D₁₄₉	—	8	2	no	—
22	C₂×D₁₄₉	SD₁₆	1	1	yes	characteristic
23	C₄×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
24	Dic₁₄₉	D₈	1	1	yes	characteristic
25	C₂×C₁₄₉	—	8	1	no	—
26	C₂×C₁₄₉	#102	1	1	yes	characteristic
27	D₁₄₉	—	2	1	no	—
28	D₁₄₉	—	8	1	no	—
29	C₁₄₉	#361	1	1	yes	characteristic, complemented, Sylow
30	#361	—	149	1	no	maximal, Sylow
31	C₂×D₈	—	149	1	no	—
32	M₃₂	—	149	1	no	—
33	#108	—	149	1	no	—
34	C₂×D₄	—	298	1	no	—
35	D₈	—	298	1	no	—
36	D₈	—	149	1	no	—
37	D₈	#10597010	1	1	yes	characteristic
38	M₁₆	—	298	1	no	—
39	C₂×C₈	—	149	1	no	—
40	C₁₆	—	298	1	no	—
41	C₂³	—	596	1	no	—
42	D₄	—	2	1	no	—
43	D₄	—	298	1	no	—
44	D₄	—	596	1	no	—
45	C₂×C₄	—	149	1	no	—
46	C₈	—	596	1	no	—
47	C₈	—	149	1	no	—
48	C₈	C₂×#10597010	1	1	yes	characteristic
49	C₂²	—	4	1	no	—
50	C₂²	—	596	1	no	—
51	C₂²	—	149	1	no	—
52	C₂²	—	1192	2	no	—
53	C₄	—	149	1	no	—
54	C₄	C₂²⋊#10597010	1	1	yes	characteristic
55	C₂	—	8	1	no	—
56	C₂	—	298	1	no	—
57	C₂	—	1192	1	no	—
58	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	D₈×D₁₄₉	C₂
cosocle	C₈×D₁₄₉	C₂²
hypercenter	D₈	#10597010
hypocenter	C₁₄₉	#361
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. #18011981	C₂	semidirect
29. C₁₄₉	#361	semidirect