Subgroups — C₂×#23752080 #34071500

Order 19328.

624 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23752080	C₂	1	8	yes	maximal, direct product factor
2	C₂×C₁₅₁⋊#95	C₂	1	6	yes	maximal
3	C₂²×C₄²×C₁₅₁	C₂	1	1	yes	maximal, characteristic
4	C₂³×Dic₁₅₁	C₂²	1	4	yes	—
5	C₁₅₁⋊#95	C₂²	1	24	yes	—
6	C₂³×C₄×C₁₅₁	C₂²	1	3	yes	—
7	C₂×C₄²×C₁₅₁	C₄	1	8	yes	complemented
8	C₂×C₄²×C₁₅₁	C₂²	1	4	yes	—
9	C₂²×Dic₁₅₁	—	2	24	no	—
10	C₂²×Dic₁₅₁	C₂³	1	8	yes	—
11	C₂⁴×C₁₅₁	C₂³	1	1	yes	characteristic
12	C₂²×C₄×C₁₅₁	—	2	12	no	—
13	C₂²×C₄×C₁₅₁	C₂×C₄	1	12	yes	—
14	C₂²×C₄×C₁₅₁	C₂³	1	6	yes	—
15	C₄²×C₁₅₁	C₂×C₄	1	16	yes	complemented
16	C₂×Dic₁₅₁	—	2	24	no	—
17	C₂×Dic₁₅₁	—	4	16	no	—
18	C₂³×C₁₅₁	C₂²×C₄	1	2	yes	—
19	C₂³×C₁₅₁	#41	1	12	yes	—
20	C₂³×C₁₅₁	C₂⁴	1	1	yes	characteristic
21	C₂×C₄×C₁₅₁	—	2	24	no	—
22	C₂×C₄×C₁₅₁	—	2	12	no	—
23	C₂×C₄×C₁₅₁	C₂²×C₄	1	12	yes	—
24	C₂²×C₁₅₁	#117	1	12	yes	—
25	C₂²×C₁₅₁	#126	1	16	yes	—
26	C₂²×C₁₅₁	C₂³×C₄	1	1	yes	characteristic
27	C₂²×C₁₅₁	C₂×#41	1	6	yes	—
28	C₄×C₁₅₁	—	2	12	no	—
29	Dic₁₅₁	—	4	8	no	—
30	C₂×C₁₅₁	#383	1	8	yes	complemented
31	C₂×C₁₅₁	C₂×#117	1	3	yes	—
32	C₂×C₁₅₁	C₂×#126	1	4	yes	—
33	C₁₅₁	C₂×#383	1	1	yes	characteristic, complemented, Sylow
34	C₂×#383	—	151	1	no	maximal, Sylow
35	C₂²×C₄²	D₁₅₁	1	1	yes	characteristic
36	#383	—	151	8	no	—
37	C₂×#95	—	151	6	no	—
38	C₂³×C₄	—	151	4	no	—
39	C₂³×C₄	C₂×D₁₅₁	1	3	yes	—
40	C₂×C₄²	Dic₁₅₁	1	8	yes	complemented
41	C₂×C₄²	C₂×D₁₅₁	1	4	yes	—
42	#95	—	151	24	no	—
43	C₂⁴	C₂²×D₁₅₁	1	1	yes	characteristic
44	C₂²×C₄	—	2	12	no	—
45	C₂²×C₄	—	302	24	no	—
46	C₂²×C₄	—	151	8	no	—
47	C₂²×C₄	C₂×Dic₁₅₁	1	12	yes	—
48	C₂²×C₄	C₂²×D₁₅₁	1	6	yes	—
49	C₄²	C₂×Dic₁₅₁	1	16	yes	complemented
50	C₂³	C₂²×Dic₁₅₁	1	2	yes	—
51	C₂³	#14559004	1	12	yes	—
52	C₂³	C₂³×D₁₅₁	1	1	yes	characteristic
53	C₂×C₄	—	2	24	no	—
54	C₂×C₄	—	2	12	no	—
55	C₂×C₄	—	302	24	no	—
56	C₂×C₄	—	604	16	no	—
57	C₂×C₄	C₂²×Dic₁₅₁	1	12	yes	—
58	C₂²	#18012698	1	12	yes	—
59	C₂²	#18012733	1	16	yes	—
60	C₂²	C₂³×Dic₁₅₁	1	1	yes	characteristic
61	C₂²	C₂×#14559004	1	6	yes	—
62	C₄	—	2	12	no	—
63	C₄	—	604	8	no	—
64	C₂	#23752080	1	8	yes	direct product factor
65	C₂	C₂×#18012698	1	3	yes	—
66	C₂	C₂×#18012733	1	4	yes	—

	subgroup	G/H
center	C₂⁴	C₂²×D₁₅₁
commutator	C₂²×C₁₅₁	C₂³×C₄
Frattini	C₂³	C₂³×D₁₅₁
Fitting	C₂²×C₄²×C₁₅₁	C₂
socle, prime radical	C₂⁴×C₁₅₁	C₂³
cosocle	C₂³×C₁₅₁	C₂⁴
hypercenter	C₂²×C₄²	D₁₅₁
hypocenter	C₁₅₁	C₂×#383
LCS	G ▷ C₂²×C₁₅₁ ▷ C₁₅₁
UCS	C₁ ◁ C₂⁴ ◁ C₂²×C₄²

Complements

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

N	H ≅ G/N	type
1. #23752080	C₂	direct (N × H)
7. C₂×C₄²×C₁₅₁	C₄	semidirect
15. C₄²×C₁₅₁	C₂×C₄	semidirect
30. C₂×C₁₅₁	#383	semidirect
33. C₁₅₁	C₂×#383	semidirect
40. C₂×C₄²	Dic₁₅₁	semidirect
49. C₄²	C₂×Dic₁₅₁	semidirect
64. C₂	#23752080	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#23752080	2
C₂×C₁₅₁⋊#95	2
C₂²×C₄²×C₁₅₁	2
C₂×#383	151

Subgroups — C2×#23752080 #34071500

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#23752080 #34071500