Subgroups — #23749404

Order 9536.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×D₁₄₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#14558711	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₆×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄×D₁₄₉	C₄	1	1	yes	characteristic
5	C₂×#11924746	C₄	1	1	yes	characteristic
6	C₈×D₁₄₉	—	2	1	no	—
7	C₈×D₁₄₉	—	2	1	no	—
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	—	2	1	no	—
22	C₂×D₁₄₉	C₁₆	1	2	yes	complemented
23	C₄×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
24	C₄×C₁₄₉	M₁₆	1	1	yes	characteristic
25	Dic₁₄₉	—	2	1	no	—
26	C₂×C₁₄₉	C₂²⋊C₈	1	1	yes	characteristic
27	C₂×C₁₄₉	C₂×C₁₆	1	1	yes	characteristic
28	C₂×C₁₄₉	M₃₂	1	1	yes	characteristic
29	D₁₄₉	—	2	2	no	—
30	C₁₄₉	C₂²⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
31	C₂²⋊C₁₆	—	149	1	no	maximal, Sylow
32	C₂²×C₈	—	149	1	no	—
33	C₂×C₁₆	—	149	1	no	—
34	C₂×C₁₆	D₁₄₉	1	1	yes	characteristic, complemented
35	C₂²×C₄	—	149	1	no	—
36	C₂×C₈	—	298	1	no	—
37	C₂×C₈	—	298	1	no	—
38	C₂×C₈	—	149	1	no	—
39	C₂×C₈	C₂×D₁₄₉	1	1	yes	characteristic
40	C₁₆	—	2	1	no	—
41	C₁₆	—	298	1	no	—
42	C₂³	—	149	1	no	—
43	C₂×C₄	—	298	1	no	—
44	C₂×C₄	—	298	1	no	—
45	C₂×C₄	—	149	1	no	—
46	C₂×C₄	C₄×D₁₄₉	1	1	yes	characteristic
47	C₈	—	298	1	no	—
48	C₈	C₂²⋊D₁₄₉	1	1	yes	characteristic
49	C₈	D₅₉₆	1	1	yes	characteristic
50	C₂²	—	298	1	no	—
51	C₂²	—	298	1	no	—
52	C₂²	—	149	2	no	—
53	C₂²	C₈×D₁₄₉	1	1	yes	characteristic
54	C₄	—	298	1	no	—
55	C₄	#14558713	1	1	yes	characteristic
56	C₄	#14558719	1	1	yes	characteristic
57	C₂	—	298	2	no	—
58	C₂	#18011823	1	1	yes	characteristic
59	C₂	C₁₆×D₁₄₉	1	1	yes	characteristic
60	C₂	#18011850	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂×D₁₄₉
commutator	C₂×C₁₄₉	C₂×C₁₆
Fitting	C₂×C₁₆×C₁₄₉	C₂
socle	C₂²×C₁₄₉	C₂×C₈
prime radical	C₂²×D₁₄₉	C₈
cosocle	C₂×C₈×C₁₄₉	C₂²
hypercenter	C₂×C₁₆	D₁₄₉
hypocenter	C₁₄₉	C₂²⋊C₁₆
LCS	G ▷ C₂×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
2. C₂×#14558711	C₂	semidirect
3. C₂×C₁₆×C₁₄₉	C₂	semidirect
22. C₂×D₁₄₉	C₁₆	semidirect
30. C₁₄₉	C₂²⋊C₁₆	semidirect
34. C₂×C₁₆	D₁₄₉	semidirect