Subgroups — #23749406

Order 9536.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14558719	C₂	1	1	yes	maximal, characteristic
2	#18011851	C₂	1	1	yes	maximal, characteristic, complemented
3	M₃₂×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄×D₁₄₉	C₄	1	1	yes	characteristic
5	#14558719	—	2	1	no	—
6	#14558719	—	2	1	no	—
7	C₂×#11924746	C₄	1	1	yes	characteristic
8	#14558711	—	2	1	no	—
9	C₂×C₈×C₁₄₉	C₂²	1	1	yes	characteristic
10	C₁₆×C₁₄₉	—	2	1	no	—
11	C₂²×D₁₄₉	C₈	1	1	yes	characteristic
12	C₂×Dic₁₄₉	C₈	1	1	yes	characteristic
13	C₄×D₁₄₉	—	2	1	no	—
14	C₄×D₁₄₉	—	2	1	no	—
15	#11924746	—	2	1	no	—
16	C₂×C₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
17	C₈×C₁₄₉	D₄	1	1	yes	characteristic
18	C₈×C₁₄₉	D₄	1	1	yes	characteristic
19	C₂²×C₁₄₉	C₂×C₈	1	1	yes	characteristic
20	C₂×D₁₄₉	—	2	1	no	—
21	C₂×D₁₄₉	—	4	1	no	—
22	C₄×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
23	C₄×C₁₄₉	M₁₆	1	1	yes	characteristic
24	Dic₁₄₉	—	2	1	no	—
25	C₂×C₁₄₉	—	2	1	no	—
26	C₂×C₁₄₉	C₂²⋊C₈	1	1	yes	characteristic
27	D₁₄₉	—	4	1	no	—
28	C₁₄₉	#349	1	1	yes	characteristic, complemented, Sylow
29	#349	—	149	1	no	maximal, Sylow
30	C₂×M₁₆	—	149	1	no	—
31	M₃₂	—	149	1	no	—
32	M₃₂	D₁₄₉	1	1	yes	characteristic, complemented
33	C₂²×C₄	—	149	1	no	—
34	M₁₆	—	298	1	no	—
35	M₁₆	—	298	1	no	—
36	C₂×C₈	—	149	1	no	—
37	C₂×C₈	C₂×D₁₄₉	1	1	yes	characteristic
38	C₁₆	—	2	1	no	—
39	C₁₆	—	298	1	no	—
40	C₂³	—	149	1	no	—
41	C₂×C₄	—	298	1	no	—
42	C₂×C₄	—	298	1	no	—
43	C₂×C₄	—	149	1	no	—
44	C₂×C₄	C₄×D₁₄₉	1	1	yes	characteristic
45	C₈	—	298	1	no	—
46	C₈	C₂²⋊D₁₄₉	1	1	yes	characteristic
47	C₈	D₅₉₆	1	1	yes	characteristic
48	C₂²	—	298	1	no	—
49	C₂²	—	596	1	no	—
50	C₂²	C₈×D₁₄₉	1	1	yes	characteristic
51	C₄	—	298	1	no	—
52	C₄	#14558713	1	1	yes	characteristic
53	C₄	#14558719	1	1	yes	characteristic
54	C₂	—	2	1	no	—
55	C₂	—	596	1	no	—
56	C₂	#18011823	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#14558713
commutator	C₂²×C₁₄₉	C₂×C₈
Frattini	C₂×C₈	C₂×D₁₄₉
Fitting	M₃₂×C₁₄₉	C₂
socle	C₂×C₁₄₉	C₂²⋊C₈
prime radical	C₂²×D₁₄₉	C₈
cosocle	C₂×C₈×C₁₄₉	C₂²
hypercenter	M₃₂	D₁₄₉
hypocenter	C₁₄₉	#349
LCS	G ▷ C₂²×C₁₄₉ ▷ C₂×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₄ ◁ C₂×C₈ ◁ M₃₂

Complements

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

N	H ≅ G/N	type
2. #18011851	C₂	semidirect
3. M₃₂×C₁₄₉	C₂	semidirect
28. C₁₄₉	#349	semidirect
32. M₃₂	D₁₄₉	semidirect