Subgroups — #23750522

Order 9536.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#18011985	C₂	1	2	yes	maximal, complemented
2	C₂×#14558719	C₂	1	1	yes	maximal, characteristic
3	#14558739	—	2	2	no	—
4	C₂×C₄×D₁₄₉	C₄	1	1	yes	characteristic
5	#14558719	—	2	2	no	—
6	C₂×#11924746	C₂²	1	1	yes	characteristic
7	C₂×C₈×C₁₄₉	C₄	1	1	yes	characteristic
8	C₂²×D₁₄₉	C₈	1	1	yes	characteristic
9	C₂×Dic₁₄₉	C₈	1	1	yes	characteristic
10	C₄×D₁₄₉	—	2	1	no	—
11	C₄×D₁₄₉	—	2	1	no	—
12	#11924746	D₄	1	2	yes	—
13	C₂×C₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
14	C₈×C₁₄₉	—	2	1	no	—
15	C₂²×C₁₄₉	C₂×C₈	1	1	yes	characteristic
16	C₂×D₁₄₉	—	2	1	no	—
17	C₂×D₁₄₉	—	4	1	no	—
18	C₄×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
19	C₄×C₁₄₉	M₁₆	1	1	yes	characteristic
20	Dic₁₄₉	—	2	1	no	—
21	C₂×C₁₄₉	—	2	1	no	—
22	C₂×C₁₄₉	C₂²⋊C₈	1	1	yes	characteristic
23	D₁₄₉	—	4	1	no	—
24	C₁₄₉	#349	1	1	yes	characteristic, complemented, Sylow
25	#349	—	149	1	no	maximal, Sylow
26	C₂×M₁₆	—	149	1	no	—
27	M₃₂	—	149	2	no	—
28	C₂²×C₄	—	149	1	no	—
29	M₁₆	—	298	2	no	—
30	C₂×C₈	—	149	1	no	—
31	C₂×C₈	#10597010	1	1	yes	characteristic
32	C₁₆	—	298	2	no	—
33	C₂³	—	149	1	no	—
34	C₂×C₄	—	298	1	no	—
35	C₂×C₄	—	298	1	no	—
36	C₂×C₄	—	149	1	no	—
37	C₂×C₄	C₂×#10597010	1	1	yes	characteristic
38	C₈	—	2	1	no	—
39	C₈	—	149	2	no	—
40	C₂²	—	298	1	no	—
41	C₂²	—	596	1	no	—
42	C₂²	D₁₄₉⋊C₈	1	1	yes	characteristic
43	C₄	—	298	1	no	—
44	C₄	C₂²⋊#10597010	1	1	yes	characteristic
45	C₄	#14558746	1	1	yes	characteristic
46	C₂	—	2	1	no	—
47	C₂	—	596	1	no	—
48	C₂	#18011968	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂²⋊#10597010
commutator	C₂²×C₁₄₉	C₂×C₈
Frattini	C₂×C₄	C₂×#10597010
Fitting	C₂×C₈×C₁₄₉	C₄
socle	C₂×C₁₄₉	C₂²⋊C₈
prime radical	C₂²×D₁₄₉	C₈
cosocle	C₂×#11924746	C₂²
hypercenter	C₂×C₈	#10597010
hypocenter	C₁₄₉	#349
LCS	G ▷ C₂²×C₁₄₉ ▷ C₂×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
1. #18011985	C₂	semidirect
24. C₁₄₉	#349	semidirect