Subgroups — #34067090

Order 19328.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×Dic₃₀₂	C₂	1	1	yes	maximal, characteristic
2	C₄⋊(C₁₅₁⋊C₁₆)	C₂	1	1	yes	maximal, characteristic
3	C₄×C₁₆×C₁₅₁	C₂	1	1	yes	maximal, characteristic
4	C₄×Dic₃₀₂	C₄	1	1	yes	characteristic
5	C₂×C₁₅₁⋊C₁₆	—	2	1	no	—
6	C₄⋊(C₁₅₁⋊C₈)	C₄	1	1	yes	characteristic
7	Dic₁₅₁⋊C₈	—	2	1	no	—
8	C₈×Dic₁₅₁	—	2	1	no	—
9	C₂×C₁₆×C₁₅₁	—	2	1	no	—
10	C₄×C₈×C₁₅₁	C₂²	1	1	yes	characteristic
11	C₂×Dic₃₀₂	C₈	1	1	yes	characteristic
12	C₂×C₁₅₁⋊C₈	—	2	1	no	—
13	C₄⋊Dic₁₅₁	C₈	1	1	yes	characteristic
14	Dic₁₅₁⋊C₄	—	2	1	no	—
15	C₄×Dic₁₅₁	—	2	1	no	—
16	C₁₅₁⋊C₁₆	—	4	1	no	—
17	C₂×C₈×C₁₅₁	D₄	1	1	yes	characteristic
18	C₂×C₈×C₁₅₁	D₄	1	1	yes	characteristic
19	C₄²×C₁₅₁	C₂×C₄	1	1	yes	characteristic
20	C₁₆×C₁₅₁	—	2	2	no	—
21	Dic₃₀₂	—	2	1	no	—
22	Dic₃₀₂	C₁₆	1	2	yes	complemented
23	C₂×Dic₁₅₁	—	2	1	no	—
24	C₂×Dic₁₅₁	—	2	1	no	—
25	C₁₅₁⋊C₈	—	4	1	no	—
26	C₂×C₄×C₁₅₁	C₂²⋊C₄	1	1	yes	characteristic
27	C₂×C₄×C₁₅₁	C₂×C₈	1	1	yes	characteristic
28	C₂×C₄×C₁₅₁	M₁₆	1	1	yes	characteristic
29	C₈×C₁₅₁	—	2	1	no	—
30	C₈×C₁₅₁	SD₁₆	1	1	yes	characteristic
31	C₈×C₁₅₁	Q₁₆	1	1	yes	characteristic
32	C₂²×C₁₅₁	C₂²⋊C₈	1	1	yes	characteristic
33	C₄×C₁₅₁	—	2	1	no	—
34	C₄×C₁₅₁	#103	1	1	yes	characteristic
35	C₄×C₁₅₁	#104	1	1	yes	characteristic
36	C₄×C₁₅₁	C₂×C₁₆	1	1	yes	characteristic
37	C₄×C₁₅₁	M₃₂	1	1	yes	characteristic
38	Dic₁₅₁	—	2	2	no	—
39	Dic₁₅₁	—	4	1	no	—
40	C₂×C₁₅₁	Q₈⋊C₈	1	1	yes	characteristic
41	C₂×C₁₅₁	C₂²⋊C₁₆	1	1	yes	characteristic
42	C₂×C₁₅₁	#350	1	1	yes	characteristic
43	C₁₅₁	Q₈⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
44	Q₈⋊C₁₆	—	151	1	no	maximal, Sylow
45	C₈×Q₈	—	151	1	no	—
46	C₄⋊C₁₆	—	151	1	no	—
47	C₄×C₁₆	D₁₅₁	1	1	yes	characteristic
48	C₄×Q₈	—	151	1	no	—
49	C₂×C₁₆	—	2	1	no	—
50	C₂×C₁₆	—	302	1	no	—
51	C₄⋊C₈	—	302	1	no	—
52	C₄⋊C₈	—	151	1	no	—
53	C₄×C₈	—	302	1	no	—
54	C₄×C₈	C₂×D₁₅₁	1	1	yes	characteristic
55	C₂×Q₈	—	151	1	no	—
56	C₂×C₈	—	302	1	no	—
57	C₂×C₈	C₂²⋊D₁₅₁	1	1	yes	characteristic
58	C₂×C₈	D₆₀₄	1	1	yes	characteristic
59	C₄⋊C₄	—	302	1	no	—
60	C₄⋊C₄	—	151	1	no	—
61	C₄²	—	302	1	no	—
62	C₄²	C₄×D₁₅₁	1	1	yes	characteristic
63	C₁₆	—	2	2	no	—
64	C₁₆	—	604	1	no	—
65	Q₈	—	302	1	no	—
66	Q₈	—	151	2	no	—
67	C₂×C₄	—	302	1	no	—
68	C₂×C₄	—	302	1	no	—
69	C₂×C₄	(C₂×D₁₅₁)⋊C₄	1	1	yes	characteristic
70	C₂×C₄	C₈×D₁₅₁	1	1	yes	characteristic
71	C₂×C₄	#14558987	1	1	yes	characteristic
72	C₈	—	2	1	no	—
73	C₈	—	604	1	no	—
74	C₈	#14558993	1	1	yes	characteristic
75	C₈	Dic₆₀₄	1	1	yes	characteristic
76	C₂²	(C₂×D₁₅₁)⋊C₈	1	1	yes	characteristic
77	C₄	—	2	1	no	—
78	C₄	—	302	2	no	—
79	C₄	—	604	1	no	—
80	C₄	#18012664	1	1	yes	characteristic
81	C₄	#18012667	1	1	yes	characteristic
82	C₄	C₁₆×D₁₅₁	1	1	yes	characteristic
83	C₄	#18012678	1	1	yes	characteristic
84	C₂	#23751944	1	1	yes	characteristic
85	C₂	(C₂×D₁₅₁)⋊C₁₆	1	1	yes	characteristic
86	C₂	#23751995	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	D₆₀₄
commutator	C₄×C₁₅₁	C₂×C₁₆
Frattini	C₄×C₈	C₂×D₁₅₁
Fitting	C₄×C₁₆×C₁₅₁	C₂
socle, prime radical	C₂²×C₁₅₁	C₂²⋊C₈
cosocle	C₄×C₈×C₁₅₁	C₂²
hypercenter	C₄×C₁₆	D₁₅₁
hypocenter	C₁₅₁	Q₈⋊C₁₆
LCS	G ▷ C₄×C₁₅₁ ▷ C₂×C₁₅₁ ▷ C₁₅₁
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₈ ◁ C₄×C₁₆

Complements

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

N	H ≅ G/N	type
22. Dic₃₀₂	C₁₆	semidirect
43. C₁₅₁	Q₈⋊C₁₆	semidirect

Maximal subgroups

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

subgroup	index
C₈×Dic₃₀₂	2
C₄⋊(C₁₅₁⋊C₁₆)	2
C₄×C₁₆×C₁₅₁	2
Q₈⋊C₁₆	151