Subgroups — #23750653

Order 9536.

134 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₁₄₉⋊C₈	C₂	1	2	yes	maximal, complemented
2	C₄⋊#11924753	C₂	1	1	yes	maximal, characteristic, complemented
3	#18011968	C₂	1	2	yes	maximal, complemented
4	C₄×#11924753	C₂	1	1	yes	maximal, characteristic, complemented
5	#18011873	C₂	1	1	yes	maximal, characteristic
6	D₁₄₉⋊C₈	—	2	4	no	—
7	C₂×#11924753	C₂²	1	1	yes	characteristic
8	C₂×#11924753	C₂²	1	2	yes	—
9	C₂×#11924753	C₂²	1	1	yes	characteristic
10	C₂×D₅₉₆	C₄	1	1	yes	characteristic
11	C₂×C₄×D₁₄₉	C₂²	1	2	yes	—
12	#14558713	C₄	1	2	yes	—
13	C₄×Dic₁₄₉	C₂²	1	1	yes	characteristic
14	C₄⋊C₄×C₁₄₉	C₄	1	1	yes	characteristic
15	#11924753	—	2	2	no	—
16	#11924753	—	2	1	no	—
17	#11924753	D₄	1	2	yes	complemented
18	C₂²×D₁₄₉	C₂×C₄	1	2	yes	—
19	D₅₉₆	C₈	1	4	yes	complemented
20	C₂×Dic₁₄₉	C₂×C₄	1	1	yes	characteristic
21	C₂×Dic₁₄₉	C₂³	1	1	yes	characteristic
22	C₄×D₁₄₉	—	2	2	no	—
23	C₄×D₁₄₉	—	2	2	no	—
24	C₂×C₄×C₁₄₉	C₂×C₄	1	2	yes	—
25	C₂×C₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
26	C₂²×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
27	C₂×D₁₄₉	—	2	2	no	—
28	C₂×D₁₄₉	—	2	2	no	—
29	C₂×D₁₄₉	C₂×C₈	1	4	yes	complemented
30	C₄×C₁₄₉	—	2	2	no	—
31	C₄×C₁₄₉	C₂×C₈	1	2	yes	complemented
32	Dic₁₄₉	—	2	1	no	—
33	Dic₁₄₉	C₂×D₄	1	1	yes	characteristic
34	Dic₁₄₉	#41	1	1	yes	characteristic
35	C₂×C₁₄₉	C₄×D₄	1	1	yes	characteristic
36	C₂×C₁₄₉	C₂²×C₈	1	1	yes	characteristic
37	C₂×C₁₄₉	#131	1	1	yes	characteristic
38	D₁₄₉	—	2	4	no	—
39	C₁₄₉	C₈×D₄	1	1	yes	characteristic, complemented, Sylow
40	C₈×D₄	—	149	1	no	maximal, Sylow
41	C₂²×C₈	—	149	2	no	—
42	C₄×D₄	—	149	1	no	—
43	C₄⋊C₈	—	149	1	no	—
44	C₂²⋊C₈	—	149	2	no	—
45	C₄×C₈	—	149	1	no	—
46	C₂×D₄	—	149	1	no	—
47	C₂²×C₄	—	149	2	no	—
48	C₂×C₈	—	298	4	no	—
49	C₂×C₈	—	149	1	no	—
50	C₂×C₈	—	149	2	no	—
51	C₂×C₈	—	149	1	no	—
52	C₄⋊C₄	#10597010	1	1	yes	characteristic
53	C₂²⋊C₄	—	149	2	no	—
54	C₄²	—	149	1	no	—
55	C₂³	—	149	2	no	—
56	D₄	—	149	4	no	—
57	C₂×C₄	—	298	2	no	—
58	C₂×C₄	—	298	2	no	—
59	C₂×C₄	—	149	1	no	—
60	C₂×C₄	—	149	1	no	—
61	C₂×C₄	C₂×#10597010	1	2	yes	—
62	C₂×C₄	C₂×#10597010	1	1	yes	characteristic
63	C₈	—	298	2	no	—
64	C₈	—	298	1	no	—
65	C₈	—	149	2	no	—
66	C₂²	—	298	2	no	—
67	C₂²	—	298	2	no	—
68	C₂²	—	149	4	no	—
69	C₂²	C₂²×#10597010	1	1	yes	characteristic
70	C₄	—	2	2	no	—
71	C₄	—	298	1	no	—
72	C₄	—	149	1	no	—
73	C₄	—	149	1	no	—
74	C₄	D₁₄₉⋊C₈	1	2	yes	complemented
75	C₂	—	298	4	no	—
76	C₂	D₄×#10597010	1	1	yes	characteristic
77	C₂	C₂×D₁₄₉⋊C₈	1	1	yes	characteristic
78	C₂	#18011999	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂²×#10597010
commutator	C₂×C₁₄₉	C₂²×C₈
Fitting	C₄⋊C₄×C₁₄₉	C₄
socle	C₂²×C₁₄₉	C₂²×C₄
prime radical	C₂×D₅₉₆	C₄
cosocle	C₂×Dic₁₄₉	C₂³
hypercenter	C₄⋊C₄	#10597010
hypocenter	C₁₄₉	C₈×D₄
LCS	G ▷ C₂×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₂² ◁ C₄⋊C₄

Complements

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

N	H ≅ G/N	type
1. C₂×D₁₄₉⋊C₈	C₂	semidirect
2. C₄⋊#11924753	C₂	semidirect
3. #18011968	C₂	semidirect
4. C₄×#11924753	C₂	semidirect
17. #11924753	D₄	semidirect
19. D₅₉₆	C₈	semidirect
29. C₂×D₁₄₉	C₂×C₈	semidirect
31. C₄×C₁₄₉	C₂×C₈	semidirect
39. C₁₄₉	C₈×D₄	semidirect
74. C₄	D₁₄₉⋊C₈	semidirect