Subgroups — #34067103

Order 19328.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23752470	C₂	1	1	yes	maximal, characteristic
2	#23751994	C₂	1	1	yes	maximal, characteristic
3	#338×C₁₅₁	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₆₀₄	C₄	1	1	yes	characteristic
5	#18012718	—	2	1	no	—
6	#18012679	—	2	1	no	—
7	#18012671	C₄	1	1	yes	characteristic
8	#18012664	—	2	1	no	—
9	C₂×M₁₆×C₁₅₁	—	2	1	no	—
10	C₂×M₁₆×C₁₅₁	C₂²	1	1	yes	characteristic
11	C₂×Dic₃₀₂	—	2	1	no	—
12	Dic₆₀₄	—	4	1	no	—
13	C₄⋊Dic₁₅₁	—	2	1	no	—
14	Dic₁₅₁⋊C₄	—	4	1	no	—
15	C₂²⋊Dic₁₅₁	—	4	1	no	—
16	C₁₅₁⋊C₁₆	—	4	1	no	—
17	C₂²×C₄×C₁₅₁	D₄	1	1	yes	characteristic
18	M₁₆×C₁₅₁	—	4	1	no	—
19	M₁₆×C₁₅₁	—	4	1	no	—
20	M₁₆×C₁₅₁	—	4	1	no	—
21	C₂×C₈×C₁₅₁	—	2	2	no	—
22	C₂×C₈×C₁₅₁	C₂×C₄	1	1	yes	characteristic
23	C₂×C₈×C₁₅₁	D₄	1	1	yes	characteristic
24	Dic₃₀₂	—	4	1	no	—
25	Dic₃₀₂	—	4	1	no	—
26	C₂×Dic₁₅₁	—	4	1	no	—
27	C₂×Dic₁₅₁	—	4	1	no	—
28	C₂³×C₁₅₁	SD₁₆	1	1	yes	characteristic
29	C₂×C₄×C₁₅₁	—	2	1	no	—
30	C₂×C₄×C₁₅₁	—	2	1	no	—
31	C₂×C₄×C₁₅₁	C₂²⋊C₄	1	1	yes	characteristic
32	C₂×C₄×C₁₅₁	D₈	1	1	yes	characteristic
33	C₈×C₁₅₁	—	2	1	no	—
34	C₈×C₁₅₁	—	2	1	no	—
35	C₈×C₁₅₁	—	4	2	no	—
36	C₂²×C₁₅₁	—	2	1	no	—
37	C₂²×C₁₅₁	—	4	1	no	—
38	C₂²×C₁₅₁	#102	1	1	yes	characteristic
39	C₄×C₁₅₁	—	2	1	no	—
40	C₄×C₁₅₁	#99	1	1	yes	characteristic
41	C₄×C₁₅₁	#104	1	1	yes	characteristic
42	Dic₁₅₁	—	8	1	no	—
43	Dic₁₅₁	—	8	1	no	—
44	C₂×C₁₅₁	—	2	1	no	—
45	C₂×C₁₅₁	—	4	1	no	—
46	C₂×C₁₅₁	#327	1	1	yes	characteristic
47	C₁₅₁	#1342	1	1	yes	characteristic, complemented, Sylow
48	#1342	—	151	1	no	maximal, Sylow
49	#470	—	151	1	no	—
50	#349	—	151	1	no	—
51	#338	D₁₅₁	1	1	yes	characteristic
52	C₂×Q₁₆	—	151	1	no	—
53	C₂×M₁₆	—	2	1	no	—
54	C₂×M₁₆	C₂×D₁₅₁	1	1	yes	characteristic
55	C₂²⋊Q₈	—	302	1	no	—
56	M₃₂	—	302	1	no	—
57	#106	—	151	1	no	—
58	#103	—	302	1	no	—
59	C₂×Q₈	—	302	1	no	—
60	C₂²×C₄	C₂²⋊D₁₅₁	1	1	yes	characteristic
61	Q₁₆	—	604	1	no	—
62	M₁₆	—	4	1	no	—
63	M₁₆	—	4	1	no	—
64	M₁₆	—	4	1	no	—
65	C₂×C₈	—	2	2	no	—
66	C₂×C₈	C₄×D₁₅₁	1	1	yes	characteristic
67	C₂×C₈	D₆₀₄	1	1	yes	characteristic
68	C₄⋊C₄	—	302	1	no	—
69	C₄⋊C₄	—	604	1	no	—
70	C₂²⋊C₄	—	604	1	no	—
71	C₁₆	—	604	1	no	—
72	C₂³	#14558991	1	1	yes	characteristic
73	Q₈	—	604	1	no	—
74	Q₈	—	604	1	no	—
75	C₂×C₄	—	2	1	no	—
76	C₂×C₄	—	2	1	no	—
77	C₂×C₄	—	604	1	no	—
78	C₂×C₄	—	604	1	no	—
79	C₂×C₄	(C₂×D₁₅₁)⋊C₄	1	1	yes	characteristic
80	C₂×C₄	#14558989	1	1	yes	characteristic
81	C₈	—	2	1	no	—
82	C₈	—	2	1	no	—
83	C₈	—	4	2	no	—
84	C₂²	—	2	1	no	—
85	C₂²	—	4	1	no	—
86	C₂²	#18012659	1	1	yes	characteristic
87	C₄	—	2	1	no	—
88	C₄	—	1208	1	no	—
89	C₄	—	1208	1	no	—
90	C₄	#18012653	1	1	yes	characteristic
91	C₄	#18012667	1	1	yes	characteristic
92	C₂	—	2	1	no	—
93	C₂	—	4	1	no	—
94	C₂	#23751945	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#23751945
commutator	C₂×C₈×C₁₅₁	C₂×C₄
Frattini	C₂×M₁₆	C₂×D₁₅₁
Fitting	#338×C₁₅₁	C₂
socle	C₂×C₁₅₁	#327
prime radical	C₂³×C₁₅₁	SD₁₆
cosocle	C₂×M₁₆×C₁₅₁	C₂²
hypercenter	#338	D₁₅₁
hypocenter	C₁₅₁	#1342
LCS	G ▷ C₂×C₈×C₁₅₁ ▷ C₂×C₄×C₁₅₁ ▷ C₂×C₁₅₁ ▷ C₁₅₁
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×M₁₆ ◁ #338

Complements

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

N	H ≅ G/N	type
47. C₁₅₁	#1342	semidirect

Maximal subgroups

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

subgroup	index
#23752470	2
#23751994	2
#338×C₁₅₁	2
#1342	151