Subgroups — #34067296

Order 19328.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23752644	C₂	1	1	yes	maximal, characteristic
2	#23752046	C₂	1	1	yes	maximal, characteristic, complemented
3	#367×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
4	#18012761	—	2	1	no	—
5	Dic₁₂₀₈	C₄	1	1	yes	characteristic, complemented
6	#18012684	—	2	1	no	—
7	D₂₄₁₆	C₄	1	1	yes	characteristic, complemented
8	C₁₅₁⋊C₃₂	—	2	1	no	—
9	C₂×C₁₆×C₁₅₁	C₂²	1	1	yes	characteristic
10	#107×C₁₅₁	—	2	1	no	—
11	#14559004	—	4	1	no	—
12	Dic₆₀₄	—	2	1	no	—
13	#14558993	—	4	1	no	—
14	D₁₂₀₈	—	2	1	no	—
15	C₂×C₈×C₁₅₁	D₄	1	1	yes	characteristic
16	C₄⋊C₄×C₁₅₁	—	4	1	no	—
17	C₁₆×C₁₅₁	C₂×C₄	1	1	yes	characteristic
18	C₁₆×C₁₅₁	D₄	1	1	yes	characteristic
19	Dic₃₀₂	—	4	1	no	—
20	D₆₀₄	—	4	1	no	—
21	C₂²⋊D₁₅₁	—	8	1	no	—
22	C₄×D₁₅₁	—	8	1	no	—
23	C₂×C₄×C₁₅₁	—	8	1	no	—
24	C₂×C₄×C₁₅₁	D₈	1	1	yes	characteristic
25	C₈×C₁₅₁	C₂²⋊C₄	1	1	yes	characteristic
26	C₈×C₁₅₁	SD₁₆	1	1	yes	characteristic
27	C₂²×C₁₅₁	D₁₆	1	1	yes	characteristic
28	C₂×D₁₅₁	—	8	1	no	—
29	C₄×C₁₅₁	—	16	1	no	—
30	C₄×C₁₅₁	#102	1	1	yes	characteristic
31	C₄×C₁₅₁	SD₃₂	1	1	yes	characteristic
32	Dic₁₅₁	—	8	1	no	—
33	C₂×C₁₅₁	—	2	1	no	—
34	C₂×C₁₅₁	#357	1	1	yes	characteristic
35	D₁₅₁	—	16	1	no	—
36	C₁₅₁	#1418	1	1	yes	characteristic, complemented, Sylow
37	#1418	—	151	1	no	maximal, Sylow
38	#508	—	151	1	no	—
39	M₆₄	—	151	1	no	—
40	#367	D₁₅₁	1	1	yes	characteristic, complemented
41	#135	—	302	1	no	—
42	Q₃₂	—	151	1	no	—
43	SD₃₂	—	302	1	no	—
44	D₁₆	—	151	1	no	—
45	C₂×C₁₆	C₂×D₁₅₁	1	1	yes	characteristic
46	#107	—	2	1	no	—
47	C₃₂	—	302	1	no	—
48	#41	—	604	1	no	—
49	Q₁₆	—	302	1	no	—
50	SD₁₆	—	604	1	no	—
51	D₈	—	302	1	no	—
52	C₂×C₈	C₂²⋊D₁₅₁	1	1	yes	characteristic
53	C₄⋊C₄	—	4	1	no	—
54	C₁₆	C₄×D₁₅₁	1	1	yes	characteristic
55	C₁₆	D₆₀₄	1	1	yes	characteristic
56	Q₈	—	604	1	no	—
57	D₄	—	604	1	no	—
58	D₄	—	1208	1	no	—
59	C₂×C₄	—	8	1	no	—
60	C₂×C₄	—	1208	1	no	—
61	C₂×C₄	#14558989	1	1	yes	characteristic
62	C₈	(C₂×D₁₅₁)⋊C₄	1	1	yes	characteristic
63	C₈	#14558991	1	1	yes	characteristic
64	C₂²	—	1208	1	no	—
65	C₂²	#18012680	1	1	yes	characteristic
66	C₄	—	16	1	no	—
67	C₄	—	1208	1	no	—
68	C₄	#18012659	1	1	yes	characteristic
69	C₄	#18012682	1	1	yes	characteristic
70	C₂	—	2	1	no	—
71	C₂	—	2416	1	no	—
72	C₂	#23752012	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#23752012
commutator	C₁₆×C₁₅₁	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₁₅₁
Fitting	#367×C₁₅₁	C₂
socle	C₂×C₁₅₁	#357
prime radical	#23752644	C₂
cosocle	C₂×C₁₆×C₁₅₁	C₂²
hypercenter	#367	D₁₅₁
hypocenter	C₁₅₁	#1418
LCS	G ▷ C₁₆×C₁₅₁ ▷ C₈×C₁₅₁ ▷ C₄×C₁₅₁ ▷ C₂×C₁₅₁ ▷ C₁₅₁
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ #367

Complements

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

N	H ≅ G/N	type
2. #23752046	C₂	semidirect
3. #367×C₁₅₁	C₂	semidirect
5. Dic₁₂₀₈	C₄	semidirect
7. D₂₄₁₆	C₄	semidirect
36. C₁₅₁	#1418	semidirect
40. #367	D₁₅₁	semidirect

Maximal subgroups

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

subgroup	index
#23752644	2
#23752046	2
#367×C₁₅₁	2
#1418	151