Subgroups — #23750508

Order 9536.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14558746	C₂	1	1	yes	maximal, characteristic
2	#18011990	C₂	1	1	yes	maximal, characteristic
3	M₁₆×D₁₄₉	C₂	1	1	yes	maximal, characteristic
4	#14558746	—	2	1	no	—
5	#14558746	—	2	1	no	—
6	C₂×#11924753	C₄	1	2	yes	complemented
7	C₄⋊#10597010	—	2	1	no	—
8	C₂²⋊#10597010	C₄	1	2	yes	—
9	C₄×#10597010	—	2	1	no	—
10	C₂×C₄×D₁₄₉	C₂²	1	1	yes	characteristic
11	#14558720	C₄	1	1	yes	characteristic, complemented
12	#14558719	—	2	1	no	—
13	C₈×D₁₄₉	—	2	1	no	—
14	M₁₆×C₁₄₉	C₄	1	1	yes	characteristic, complemented
15	C₂×#10597010	—	2	2	no	—
16	#11924753	—	2	2	no	—
17	C₂²×D₁₄₉	C₂×C₄	1	1	yes	characteristic
18	C₂×Dic₁₄₉	C₂×C₄	1	1	yes	characteristic
19	C₄×D₁₄₉	D₄	1	1	yes	characteristic
20	C₄×D₁₄₉	D₄	1	1	yes	characteristic
21	C₄×D₁₄₉	D₄	1	1	yes	characteristic
22	C₄×D₁₄₉	Q₈	1	1	yes	characteristic
23	#11924746	—	2	1	no	—
24	C₂×C₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
25	C₈×C₁₄₉	—	2	1	no	—
26	C₂²×C₁₄₉	C₄²	1	1	yes	characteristic
27	C₂×D₁₄₉	—	4	1	no	—
28	C₂×D₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
29	C₂×D₁₄₉	C₄⋊C₄	1	1	yes	characteristic
30	#10597010	—	4	2	no	—
31	C₄×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
32	C₄×C₁₄₉	C₄⋊C₄	1	1	yes	characteristic
33	Dic₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
34	Dic₁₄₉	C₄⋊C₄	1	1	yes	characteristic
35	C₂×C₁₄₉	—	2	1	no	—
36	C₂×C₁₄₉	#95	1	1	yes	characteristic
37	D₁₄₉	—	2	1	no	—
38	D₁₄₉	—	2	1	no	—
39	C₁₄₉	#344	1	1	yes	characteristic, complemented, Sylow
40	#344	—	149	1	no	maximal, Sylow
41	C₂×M₁₆	—	149	1	no	—
42	C₂×M₁₆	—	149	1	no	—
43	#117	—	149	1	no	—
44	C₂²×C₄	—	149	1	no	—
45	M₁₆	—	298	1	no	—
46	M₁₆	—	298	1	no	—
47	M₁₆	—	298	1	no	—
48	M₁₆	—	149	1	no	—
49	M₁₆	#10597010	1	1	yes	characteristic, complemented
50	C₂×C₈	—	298	1	no	—
51	C₂×C₈	—	149	2	no	—
52	C₄⋊C₄	—	298	1	no	—
53	C₂²⋊C₄	—	149	2	no	—
54	C₄²	—	298	1	no	—
55	C₂³	—	149	1	no	—
56	C₂×C₄	—	298	2	no	—
57	C₂×C₄	—	149	1	no	—
58	C₂×C₄	—	149	1	no	—
59	C₂×C₄	—	149	1	no	—
60	C₂×C₄	—	149	1	no	—
61	C₂×C₄	—	149	1	no	—
62	C₂×C₄	C₂×#10597010	1	1	yes	characteristic
63	C₈	—	2	1	no	—
64	C₈	—	298	2	no	—
65	C₈	—	298	1	no	—
66	C₂²	—	596	1	no	—
67	C₂²	—	149	1	no	—
68	C₂²	—	149	1	no	—
69	C₂²	C₄×#10597010	1	1	yes	characteristic
70	C₄	—	596	2	no	—
71	C₄	—	149	1	no	—
72	C₄	—	149	1	no	—
73	C₄	C₂²⋊#10597010	1	1	yes	characteristic
74	C₄	C₄⋊#10597010	1	1	yes	characteristic
75	C₂	—	2	1	no	—
76	C₂	—	298	1	no	—
77	C₂	—	298	1	no	—
78	C₂	(C₂×#10597010)⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂	(C₂×#10597010)⋊C₄
commutator	C₂²×C₁₄₉	C₄²
Frattini	C₂×C₄	C₂×#10597010
Fitting	M₁₆×C₁₄₉	C₄
socle	C₂×C₁₄₉	#95
prime radical	C₂²×D₁₄₉	C₂×C₄
cosocle	C₂×C₄×D₁₄₉	C₂²
hypercenter	M₁₆	#10597010
hypocenter	C₁₄₉	#344
LCS	G ▷ C₂²×C₁₄₉ ▷ C₂×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ M₁₆

Complements

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

N	H ≅ G/N	type
6. C₂×#11924753	C₄	semidirect
11. #14558720	C₄	semidirect
14. M₁₆×C₁₄₉	C₄	semidirect
39. C₁₄₉	#344	semidirect
49. M₁₆	#10597010	semidirect