Subgroups — #23749439

Order 9536.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₁₁₉₂	C₂	1	1	yes	maximal, characteristic
2	#18011847	C₂	1	1	yes	maximal, characteristic, complemented
3	M₃₂×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₅₉₆	—	2	1	no	—
5	D₁₁₉₂	—	2	1	no	—
6	D₁₁₉₂	C₄	1	2	yes	—
7	#14558720	—	2	1	no	—
8	C₂×C₈×C₁₄₉	C₂²	1	1	yes	characteristic
9	C₁₆×C₁₄₉	—	2	1	no	—
10	C₂²×D₁₄₉	—	4	1	no	—
11	D₅₉₆	—	2	2	no	—
12	D₅₉₆	—	4	1	no	—
13	#11924746	—	4	1	no	—
14	C₂×C₄×C₁₄₉	D₄	1	1	yes	characteristic
15	C₈×C₁₄₉	C₂×C₄	1	1	yes	characteristic
16	C₈×C₁₄₉	D₄	1	1	yes	characteristic
17	C₂²×C₁₄₉	SD₁₆	1	1	yes	characteristic
18	C₂×D₁₄₉	—	4	2	no	—
19	C₂×D₁₄₉	—	8	2	no	—
20	C₄×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
21	C₄×C₁₄₉	D₈	1	1	yes	characteristic
22	C₂×C₁₄₉	—	2	1	no	—
23	C₂×C₁₄₉	#102	1	1	yes	characteristic
24	D₁₄₉	—	8	2	no	—
25	C₁₄₉	#361	1	1	yes	characteristic, complemented, Sylow
26	#361	—	149	1	no	maximal, Sylow
27	C₂×D₈	—	149	1	no	—
28	M₃₂	D₁₄₉	1	1	yes	characteristic, complemented
29	#108	—	149	1	no	—
30	C₂×D₄	—	298	1	no	—
31	D₈	—	298	1	no	—
32	D₈	—	149	2	no	—
33	M₁₆	—	298	1	no	—
34	C₂×C₈	C₂×D₁₄₉	1	1	yes	characteristic
35	C₁₆	—	2	1	no	—
36	C₂³	—	596	1	no	—
37	D₄	—	298	2	no	—
38	D₄	—	596	1	no	—
39	C₂×C₄	D₅₉₆	1	1	yes	characteristic
40	C₈	—	596	1	no	—
41	C₈	C₄×D₁₄₉	1	1	yes	characteristic
42	C₈	C₂²⋊D₁₄₉	1	1	yes	characteristic
43	C₂²	—	596	2	no	—
44	C₂²	—	1192	2	no	—
45	C₂²	#14558725	1	1	yes	characteristic
46	C₄	#14558713	1	1	yes	characteristic
47	C₄	D₁₁₉₂	1	1	yes	characteristic
48	C₂	—	2	1	no	—
49	C₂	—	1192	2	no	—
50	C₂	#18011833	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#18011833
commutator	C₈×C₁₄₉	C₂×C₄
Frattini	C₂×C₈	C₂×D₁₄₉
Fitting	M₃₂×C₁₄₉	C₂
socle	C₂×C₁₄₉	#102
prime radical	C₂×D₁₁₉₂	C₂
cosocle	C₂×C₈×C₁₄₉	C₂²
hypercenter	M₃₂	D₁₄₉
hypocenter	C₁₄₉	#361
LCS	G ▷ C₈×C₁₄₉ ▷ C₄×C₁₄₉ ▷ C₂×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ M₃₂

Complements

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

N	H ≅ G/N	type
2. #18011847	C₂	semidirect
3. M₃₂×C₁₄₉	C₂	semidirect
25. C₁₄₉	#361	semidirect
28. M₃₂	D₁₄₉	semidirect