Subgroups — #23749862

Order 9536.

134 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, complemented
2	C₂×C₈×D₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#18011886	C₂	1	2	yes	maximal, complemented
4	#18011831	C₂	1	2	yes	maximal, complemented
5	#107×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₅₉₆	—	2	2	no	—
7	C₂×D₅₉₆	C₂²	1	2	yes	—
8	C₂×C₄×D₁₄₉	C₂²	1	1	yes	characteristic
9	D₁₁₉₂	—	2	2	no	—
10	C₂×#11924746	C₂²	1	1	yes	characteristic
11	C₈×D₁₄₉	—	2	2	no	—
12	#14558713	—	2	2	no	—
13	C₂×C₈×C₁₄₉	C₂²	1	1	yes	characteristic
14	C₄⋊C₄×C₁₄₉	C₂²	1	2	yes	—
15	C₂²×D₁₄₉	—	2	2	no	—
16	C₂²×D₁₄₉	D₄	1	1	yes	characteristic
17	D₅₉₆	—	2	2	no	—
18	D₅₉₆	—	2	2	no	—
19	D₅₉₆	—	4	4	no	—
20	C₂×Dic₁₄₉	D₄	1	1	yes	characteristic
21	C₄×D₁₄₉	—	2	1	no	—
22	C₄×D₁₄₉	—	2	1	no	—
23	#11924746	—	2	1	no	—
24	C₂×C₄×C₁₄₉	—	2	2	no	—
25	C₂×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
26	C₈×C₁₄₉	D₄	1	2	yes	complemented
27	C₂²×C₁₄₉	C₂×D₄	1	1	yes	characteristic
28	C₂×D₁₄₉	—	2	1	no	—
29	C₂×D₁₄₉	—	2	1	no	—
30	C₂×D₁₄₉	—	4	2	no	—
31	C₂×D₁₄₉	—	4	2	no	—
32	C₂×D₁₄₉	—	4	2	no	—
33	C₂×D₁₄₉	D₈	1	2	yes	complemented
34	C₄×C₁₄₉	—	4	2	no	—
35	C₄×C₁₄₉	C₂×D₄	1	1	yes	characteristic
36	C₄×C₁₄₉	#41	1	1	yes	characteristic
37	Dic₁₄₉	—	2	1	no	—
38	C₂×C₁₄₉	#121	1	1	yes	characteristic
39	C₂×C₁₄₉	C₂×D₈	1	1	yes	characteristic
40	C₂×C₁₄₉	#135	1	1	yes	characteristic
41	D₁₄₉	—	2	2	no	—
42	D₁₄₉	—	8	2	no	—
43	C₁₄₉	#466	1	1	yes	characteristic, complemented, Sylow
44	#466	—	149	1	no	maximal, Sylow
45	C₂×D₈	—	149	1	no	—
46	C₂²×C₈	—	149	1	no	—
47	#121	—	149	2	no	—
48	#107	D₁₄₉	1	1	yes	characteristic, complemented
49	#102	—	149	2	no	—
50	C₂×D₄	—	298	2	no	—
51	C₂×D₄	—	149	2	no	—
52	C₂²×C₄	—	149	1	no	—
53	D₈	—	298	2	no	—
54	C₂×C₈	—	298	2	no	—
55	C₂×C₈	—	149	1	no	—
56	C₂×C₈	C₂×D₁₄₉	1	1	yes	characteristic
57	C₄⋊C₄	C₂×D₁₄₉	1	2	yes	—
58	C₂²⋊C₄	—	298	2	no	—
59	C₂³	—	298	2	no	—
60	C₂³	—	149	1	no	—
61	D₄	—	298	2	no	—
62	D₄	—	298	2	no	—
63	D₄	—	596	4	no	—
64	C₂×C₄	—	2	2	no	—
65	C₂×C₄	—	298	1	no	—
66	C₂×C₄	—	298	1	no	—
67	C₂×C₄	—	149	1	no	—
68	C₂×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
69	C₈	—	298	1	no	—
70	C₈	D₅₉₆	1	2	yes	complemented
71	C₂²	—	298	1	no	—
72	C₂²	—	298	1	no	—
73	C₂²	—	596	2	no	—
74	C₂²	—	596	2	no	—
75	C₂²	—	596	2	no	—
76	C₂²	—	149	2	no	—
77	C₂²	D₄×D₁₄₉	1	1	yes	characteristic
78	C₄	—	4	2	no	—
79	C₄	—	298	1	no	—
80	C₄	C₂×D₅₉₆	1	1	yes	characteristic
81	C₄	#14558737	1	1	yes	characteristic
82	C₂	—	298	2	no	—
83	C₂	—	1192	2	no	—
84	C₂	#18011886	1	1	yes	characteristic
85	C₂	D₈×D₁₄₉	1	1	yes	characteristic
86	C₂	#18011934	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₁₄₉
commutator, cosocle	C₂×C₄×C₁₄₉	C₂³
Frattini	C₂×C₄	C₂²×D₁₄₉
Fitting	#107×C₁₄₉	C₂
socle	C₂²×C₁₄₉	C₂×D₄
hypercenter	#107	D₁₄₉
hypocenter	C₁₄₉	#466
LCS	G ▷ C₂×C₄×C₁₄₉ ▷ C₂×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #107

Complements

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

N	H ≅ G/N	type
1. C₂×D₁₁₉₂	C₂	semidirect
2. C₂×C₈×D₁₄₉	C₂	semidirect
3. #18011886	C₂	semidirect
4. #18011831	C₂	semidirect
5. #107×C₁₄₉	C₂	semidirect
26. C₈×C₁₄₉	D₄	semidirect
33. C₂×D₁₄₉	D₈	semidirect
43. C₁₄₉	#466	semidirect
48. #107	D₁₄₉	semidirect
70. C₈	D₅₉₆	semidirect