Subgroups — #34067278

Order 19328.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23752591	C₂	1	1	yes	maximal, characteristic
2	#23752011	C₂	1	1	yes	maximal, characteristic
3	#356×C₁₅₁	C₂	1	1	yes	maximal, characteristic
4	C₂×#14558994	—	2	1	no	—
5	C₂×#14558994	—	2	1	no	—
6	#18012739	C₄	1	1	yes	characteristic
7	#18012658	—	2	1	no	—
8	C₄×C₁₅₁⋊C₈	C₄	1	1	yes	characteristic
9	C₄⋊Q₈×C₁₅₁	C₂²	1	1	yes	characteristic
10	#101×C₁₅₁	—	2	1	no	—
11	C₂×Dic₃₀₂	—	2	1	no	—
12	#14558994	—	4	2	no	—
13	#14558994	—	4	2	no	—
14	#14558988	—	4	1	no	—
15	C₂×C₁₅₁⋊C₈	—	2	1	no	—
16	C₄⋊Dic₁₅₁	—	4	1	no	—
17	C₂×Q₈×C₁₅₁	D₄	1	1	yes	characteristic
18	C₂×Q₈×C₁₅₁	D₄	1	1	yes	characteristic
19	M₁₆×C₁₅₁	—	4	1	no	—
20	C₄⋊C₄×C₁₅₁	—	4	1	no	—
21	C₄²×C₁₅₁	C₂×C₄	1	1	yes	characteristic
22	Dic₃₀₂	—	4	1	no	—
23	Dic₃₀₂	—	4	1	no	—
24	C₂×Dic₁₅₁	—	4	1	no	—
25	C₁₅₁⋊C₈	—	2	2	no	—
26	C₁₅₁⋊C₈	—	8	1	no	—
27	Q₈×C₁₅₁	—	4	1	no	—
28	Q₈×C₁₅₁	—	4	1	no	—
29	C₂×C₄×C₁₅₁	—	2	1	no	—
30	C₂×C₄×C₁₅₁	—	2	1	no	—
31	C₂×C₄×C₁₅₁	—	2	1	no	—
32	C₂×C₄×C₁₅₁	C₂²⋊C₄	1	1	yes	characteristic
33	C₈×C₁₅₁	—	8	1	no	—
34	C₂²×C₁₅₁	#99	1	1	yes	characteristic
35	C₄×C₁₅₁	—	2	2	no	—
36	C₄×C₁₅₁	—	2	1	no	—
37	C₄×C₁₅₁	—	4	1	no	—
38	C₄×C₁₅₁	—	4	1	no	—
39	Dic₁₅₁	—	8	1	no	—
40	C₂×C₁₅₁	—	2	1	no	—
41	C₂×C₁₅₁	#353	1	1	yes	characteristic
42	C₁₅₁	#1411	1	1	yes	characteristic, complemented, Sylow
43	#1411	—	151	1	no	maximal, Sylow
44	#494	—	151	1	no	—
45	#356	—	151	1	no	—
46	#356	D₁₅₁	1	1	yes	characteristic
47	C₂×Q₁₆	—	302	1	no	—
48	C₂×Q₁₆	—	302	1	no	—
49	C₄⋊Q₈	—	151	1	no	—
50	C₄⋊Q₈	C₂×D₁₅₁	1	1	yes	characteristic
51	#101	—	2	1	no	—
52	#101	—	302	1	no	—
53	C₄×C₈	—	151	1	no	—
54	C₂×Q₈	—	302	1	no	—
55	C₂×Q₈	C₂²⋊D₁₅₁	1	1	yes	characteristic
56	C₂×Q₈	D₆₀₄	1	1	yes	characteristic
57	Q₁₆	—	604	2	no	—
58	Q₁₆	—	604	2	no	—
59	M₁₆	—	4	1	no	—
60	M₁₆	—	604	1	no	—
61	C₂×C₈	—	302	1	no	—
62	C₄⋊C₄	—	4	1	no	—
63	C₄⋊C₄	—	604	1	no	—
64	C₄²	C₄×D₁₅₁	1	1	yes	characteristic
65	Q₈	—	4	1	no	—
66	Q₈	—	4	1	no	—
67	Q₈	—	604	1	no	—
68	Q₈	—	604	1	no	—
69	C₂×C₄	—	2	1	no	—
70	C₂×C₄	—	2	1	no	—
71	C₂×C₄	—	2	1	no	—
72	C₂×C₄	—	604	1	no	—
73	C₂×C₄	(C₂×D₁₅₁)⋊C₄	1	1	yes	characteristic
74	C₈	—	8	1	no	—
75	C₈	—	302	2	no	—
76	C₈	—	1208	1	no	—
77	C₂²	#18012653	1	1	yes	characteristic
78	C₄	—	2	2	no	—
79	C₄	—	2	1	no	—
80	C₄	—	4	1	no	—
81	C₄	—	4	1	no	—
82	C₄	—	1208	1	no	—
83	C₂	—	2	1	no	—
84	C₂	#23752004	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#23752004
commutator	C₄²×C₁₅₁	C₂×C₄
Frattini	C₄⋊Q₈	C₂×D₁₅₁
Fitting	#356×C₁₅₁	C₂
socle	C₂×C₁₅₁	#353
prime radical	C₂²×C₁₅₁	#99
cosocle	C₄⋊Q₈×C₁₅₁	C₂²
hypercenter	#356	D₁₅₁
hypocenter	C₁₅₁	#1411
LCS	G ▷ C₄²×C₁₅₁ ▷ C₂×C₄×C₁₅₁ ▷ C₂²×C₁₅₁ ▷ C₂×C₁₅₁ ▷ C₁₅₁
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ C₄⋊Q₈ ◁ #356

Complements

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

N	H ≅ G/N	type
42. C₁₅₁	#1411	semidirect

Maximal subgroups

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

subgroup	index
#23752591	2
#23752011	2
#356×C₁₅₁	2
#1411	151