Subgroups — #23750524

Order 9536.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#18011985	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#14558739	C₂	1	1	yes	maximal, characteristic, complemented
3	#18011919	C₂	1	1	yes	maximal, characteristic
4	#14558739	—	2	1	no	—
5	#14558739	—	2	1	no	—
6	#14558736	C₄	1	1	yes	characteristic
7	#14558719	—	2	1	no	—
8	C₂×#11924746	C₂²	1	1	yes	characteristic
9	C₈×D₁₄₉	—	2	1	no	—
10	M₁₆×C₁₄₉	C₄	1	1	yes	characteristic
11	Dic₂₉₈	C₈	1	1	yes	characteristic
12	D₅₉₆	C₈	1	1	yes	characteristic
13	C₂²⋊D₁₄₉	—	2	1	no	—
14	C₄×D₁₄₉	—	2	1	no	—
15	#11924746	D₄	1	1	yes	characteristic
16	#11924746	D₄	1	1	yes	characteristic
17	C₂×C₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
18	C₈×C₁₄₉	—	2	1	no	—
19	C₂²×C₁₄₉	M₁₆	1	1	yes	characteristic
20	C₂×D₁₄₉	—	2	1	no	—
21	C₄×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
22	C₄×C₁₄₉	C₂×C₈	1	1	yes	characteristic
23	Dic₁₄₉	—	2	1	no	—
24	C₂×C₁₄₉	—	2	1	no	—
25	C₂×C₁₄₉	C₂²⋊C₈	1	1	yes	characteristic
26	D₁₄₉	—	4	1	no	—
27	C₁₄₉	#350	1	1	yes	characteristic, complemented, Sylow
28	#350	—	149	1	no	maximal, Sylow
29	#131	—	149	1	no	—
30	M₃₂	—	149	1	no	—
31	C₂×C₁₆	—	149	1	no	—
32	#41	—	149	1	no	—
33	M₁₆	—	298	1	no	—
34	M₁₆	#10597010	1	1	yes	characteristic
35	C₂×C₈	—	298	1	no	—
36	C₂×C₈	—	149	1	no	—
37	C₁₆	—	298	1	no	—
38	C₁₆	—	298	1	no	—
39	Q₈	—	149	1	no	—
40	D₄	—	298	1	no	—
41	D₄	—	149	1	no	—
42	C₂×C₄	—	298	1	no	—
43	C₂×C₄	C₂×#10597010	1	1	yes	characteristic
44	C₈	—	2	1	no	—
45	C₈	—	149	1	no	—
46	C₈	—	149	1	no	—
47	C₂²	—	298	1	no	—
48	C₂²	#14558746	1	1	yes	characteristic
49	C₄	—	298	1	no	—
50	C₄	C₂²⋊#10597010	1	1	yes	characteristic
51	C₄	D₁₄₉⋊C₈	1	1	yes	characteristic
52	C₂	—	2	1	no	—
53	C₂	—	596	1	no	—
54	C₂	#18011968	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂²⋊#10597010
commutator	C₄×C₁₄₉	C₂×C₈
Frattini	C₂×C₄	C₂×#10597010
Fitting	M₁₆×C₁₄₉	C₄
socle	C₂×C₁₄₉	C₂²⋊C₈
prime radical	#14558736	C₄
cosocle	C₂×#11924746	C₂²
hypercenter	M₁₆	#10597010
hypocenter	C₁₄₉	#350
LCS	G ▷ C₄×C₁₄₉ ▷ C₂×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ M₁₆

Complements

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

N	H ≅ G/N	type
1. #18011985	C₂	semidirect
2. C₂×#14558739	C₂	semidirect
27. C₁₄₉	#350	semidirect