Subgroups — #23750537

Order 9536.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₄₉⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	#18011980	C₂	1	1	yes	maximal, characteristic, complemented
3	D₈×D₁₄₉	C₂	1	1	yes	maximal, characteristic
4	C₄⋊#10597010	—	2	1	no	—
5	#14558739	—	2	1	no	—
6	D₄×D₁₄₉	—	2	1	no	—
7	D₁₁₉₂	C₄	1	1	yes	characteristic, complemented
8	#14558721	—	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	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	1	no	—
22	C₂×D₁₄₉	—	8	1	no	—
23	C₂×D₁₄₉	D₈	1	1	yes	characteristic
24	#10597010	—	8	1	no	—
25	C₄×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
26	Dic₁₄₉	SD₁₆	1	1	yes	characteristic
27	C₂×C₁₄₉	—	8	1	no	—
28	C₂×C₁₄₉	#102	1	1	yes	characteristic
29	D₁₄₉	—	8	1	no	—
30	D₁₄₉	D₁₆	1	1	yes	characteristic
31	D₁₄₉	SD₃₂	1	1	yes	characteristic
32	C₁₄₉	#357	1	1	yes	characteristic, complemented, Sylow
33	#357	—	149	1	no	maximal, Sylow
34	C₂×D₈	—	149	1	no	—
35	C₂×C₁₆	—	149	1	no	—
36	#107	—	149	1	no	—
37	C₂×D₄	—	298	1	no	—
38	D₈	—	298	1	no	—
39	D₈	—	149	1	no	—
40	D₈	#10597010	1	1	yes	characteristic, complemented
41	C₂×C₈	—	149	1	no	—
42	C₄⋊C₄	—	298	1	no	—
43	C₁₆	—	298	1	no	—
44	C₂³	—	596	1	no	—
45	D₄	—	2	1	no	—
46	D₄	—	298	1	no	—
47	D₄	—	596	1	no	—
48	C₂×C₄	—	596	1	no	—
49	C₂×C₄	—	149	1	no	—
50	C₈	—	149	1	no	—
51	C₈	C₂×#10597010	1	1	yes	characteristic
52	C₂²	—	4	1	no	—
53	C₂²	—	596	1	no	—
54	C₂²	—	149	1	no	—
55	C₂²	—	1192	1	no	—
56	C₂²	—	1192	1	no	—
57	C₄	—	149	1	no	—
58	C₄	—	1192	1	no	—
59	C₄	C₂²⋊#10597010	1	1	yes	characteristic
60	C₂	—	8	1	no	—
61	C₂	—	149	1	no	—
62	C₂	—	149	1	no	—
63	C₂	—	1192	1	no	—
64	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	#357
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. D₁₄₉⋊C₁₆	C₂	semidirect
2. #18011980	C₂	semidirect
7. D₁₁₉₂	C₄	semidirect
10. D₈×C₁₄₉	C₄	semidirect
32. C₁₄₉	#357	semidirect
40. D₈	#10597010	semidirect