Subgroups — #23749397

Order 9536.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14558720	C₂	1	1	yes	maximal, characteristic
2	#18011870	C₂	1	1	yes	maximal, characteristic
3	C₂×M₁₆×C₁₄₉	C₂	1	1	yes	maximal, characteristic
4	#14558720	—	2	1	no	—
5	#14558720	—	2	1	no	—
6	C₂×#11924746	C₄	1	2	yes	complemented
7	C₄⋊Dic₁₄₉	—	2	1	no	—
8	C₂²⋊Dic₁₄₉	C₄	1	2	yes	—
9	C₄×Dic₁₄₉	—	2	1	no	—
10	C₂²×C₄×C₁₄₉	C₂²	1	1	yes	characteristic
11	M₁₆×C₁₄₉	—	2	1	no	—
12	M₁₆×C₁₄₉	C₄	1	2	yes	complemented
13	C₂×C₈×C₁₄₉	—	2	1	no	—
14	C₂×Dic₁₄₉	—	2	2	no	—
15	#11924746	—	2	2	no	—
16	C₂³×C₁₄₉	C₂×C₄	1	1	yes	characteristic
17	C₂×C₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
18	C₂×C₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
19	C₂×C₄×C₁₄₉	D₄	1	1	yes	characteristic
20	C₂×C₄×C₁₄₉	D₄	1	1	yes	characteristic
21	C₂×C₄×C₁₄₉	D₄	1	1	yes	characteristic
22	C₂×C₄×C₁₄₉	Q₈	1	1	yes	characteristic
23	C₈×C₁₄₉	—	2	2	no	—
24	C₂²×C₁₄₉	—	4	1	no	—
25	C₂²×C₁₄₉	C₄²	1	1	yes	characteristic
26	C₂²×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
27	C₂²×C₁₄₉	C₄⋊C₄	1	1	yes	characteristic
28	C₄×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
29	C₄×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
30	C₄×C₁₄₉	C₄⋊C₄	1	1	yes	characteristic
31	C₄×C₁₄₉	C₄⋊C₄	1	1	yes	characteristic
32	Dic₁₄₉	—	4	2	no	—
33	C₂×C₁₄₉	—	2	1	no	—
34	C₂×C₁₄₉	—	2	1	no	—
35	C₂×C₁₄₉	—	2	1	no	—
36	C₂×C₁₄₉	#95	1	1	yes	characteristic
37	C₁₄₉	#344	1	1	yes	characteristic, complemented, Sylow
38	#344	—	149	1	no	maximal, Sylow
39	C₂×M₁₆	—	149	1	no	—
40	C₂×M₁₆	D₁₄₉	1	1	yes	characteristic
41	#117	—	149	1	no	—
42	C₂²×C₄	C₂×D₁₄₉	1	1	yes	characteristic
43	M₁₆	—	2	1	no	—
44	M₁₆	—	298	1	no	—
45	M₁₆	—	298	1	no	—
46	M₁₆	Dic₁₄₉	1	2	yes	complemented
47	C₂×C₈	—	2	1	no	—
48	C₂×C₈	—	149	2	no	—
49	C₄⋊C₄	—	298	1	no	—
50	C₂²⋊C₄	—	149	2	no	—
51	C₄²	—	298	1	no	—
52	C₂³	C₄×D₁₄₉	1	1	yes	characteristic
53	C₂×C₄	—	298	2	no	—
54	C₂×C₄	C₄×D₁₄₉	1	1	yes	characteristic
55	C₂×C₄	C₂×Dic₁₄₉	1	1	yes	characteristic
56	C₂×C₄	C₂²⋊D₁₄₉	1	1	yes	characteristic
57	C₂×C₄	C₂²⋊D₁₄₉	1	1	yes	characteristic
58	C₂×C₄	D₅₉₆	1	1	yes	characteristic
59	C₂×C₄	Dic₂₉₈	1	1	yes	characteristic
60	C₈	—	2	2	no	—
61	C₈	—	298	2	no	—
62	C₂²	—	4	1	no	—
63	C₂²	C₄×Dic₁₄₉	1	1	yes	characteristic
64	C₂²	#14558713	1	1	yes	characteristic
65	C₂²	#14558715	1	1	yes	characteristic
66	C₄	—	596	2	no	—
67	C₄	#14558713	1	1	yes	characteristic
68	C₄	C₂²⋊Dic₁₄₉	1	1	yes	characteristic
69	C₄	#14558715	1	1	yes	characteristic
70	C₄	C₄⋊Dic₁₄₉	1	1	yes	characteristic
71	C₂	—	2	1	no	—
72	C₂	—	2	1	no	—
73	C₂	—	2	1	no	—
74	C₂	#18011818	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#14558713
commutator	C₂²×C₁₄₉	C₄²
Frattini	C₂²×C₄	C₂×D₁₄₉
Fitting	C₂×M₁₆×C₁₄₉	C₂
socle	C₂×C₁₄₉	#95
prime radical	C₂³×C₁₄₉	C₂×C₄
cosocle	C₂²×C₄×C₁₄₉	C₂²
hypercenter	C₂×M₁₆	D₁₄₉
hypocenter	C₁₄₉	#344
LCS	G ▷ C₂²×C₁₄₉ ▷ C₂×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂×M₁₆

Complements

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

N	H ≅ G/N	type
6. C₂×#11924746	C₄	semidirect
12. M₁₆×C₁₄₉	C₄	semidirect
37. C₁₄₉	#344	semidirect
46. M₁₆	Dic₁₄₉	semidirect