Subgroups — #34098228

Order 20096.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19097705	C₂	1	2	yes	maximal
2	C₂²×C₁₆×C₁₅₇	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄⋊Dic₁₅₇	—	2	2	no	—
4	#19097705	—	2	2	no	—
5	#19097705	C₄	1	4	yes	complemented
6	C₂²×C₈×C₁₅₇	C₂²	1	1	yes	characteristic
7	C₂×C₁₆×C₁₅₇	—	2	2	no	—
8	C₂×C₁₆×C₁₅₇	C₄	1	2	yes	complemented
9	C₂²×Dic₁₅₇	—	4	2	no	—
10	C₄⋊Dic₁₅₇	—	2	4	no	—
11	C₄⋊Dic₁₅₇	—	4	2	no	—
12	C₂²×C₄×C₁₅₇	D₄	1	1	yes	characteristic
13	C₂×C₈×C₁₅₇	C₂×C₄	1	2	yes	—
14	C₂×C₈×C₁₅₇	C₂×C₄	1	1	yes	characteristic
15	C₂×C₈×C₁₅₇	D₄	1	2	yes	—
16	C₂×C₈×C₁₅₇	Q₈	1	1	yes	characteristic
17	C₁₆×C₁₅₇	—	2	2	no	—
18	C₂×Dic₁₅₇	—	4	4	no	—
19	C₂×Dic₁₅₇	—	8	2	no	—
20	C₂×Dic₁₅₇	—	8	2	no	—
21	C₂³×C₁₅₇	D₈	1	1	yes	characteristic
22	C₂×C₄×C₁₅₇	C₂²⋊C₄	1	2	yes	—
23	C₂×C₄×C₁₅₇	C₄⋊C₄	1	1	yes	characteristic
24	C₂×C₄×C₁₅₇	SD₁₆	1	2	yes	—
25	C₂×C₄×C₁₅₇	Q₁₆	1	1	yes	characteristic
26	C₈×C₁₅₇	C₄²	1	1	yes	characteristic
27	C₈×C₁₅₇	C₂²⋊C₄	1	1	yes	characteristic
28	C₈×C₁₅₇	C₄⋊C₄	1	2	yes	—
29	C₂²×C₁₅₇	#102	1	2	yes	—
30	C₂²×C₁₅₇	#107	1	1	yes	characteristic
31	C₂²×C₁₅₇	D₁₆	1	1	yes	characteristic
32	C₂²×C₁₅₇	SD₃₂	1	2	yes	—
33	C₂²×C₁₅₇	Q₃₂	1	1	yes	characteristic
34	C₄×C₁₅₇	#95	1	1	yes	characteristic
35	C₄×C₁₅₇	#103	1	2	yes	—
36	C₄×C₁₅₇	#106	1	1	yes	characteristic
37	Dic₁₅₇	—	8	4	no	—
38	C₂×C₁₅₇	#340	1	1	yes	characteristic
39	C₂×C₁₅₇	#357	1	2	yes	—
40	C₂×C₁₅₇	#358	1	2	yes	—
41	C₂×C₁₅₇	#366	1	1	yes	characteristic
42	C₂×C₁₅₇	#367	1	1	yes	characteristic
43	C₁₅₇	#1380	1	1	yes	characteristic, complemented, Sylow
44	#1380	—	157	1	no	maximal, Sylow
45	C₂²×C₁₆	D₁₅₇	1	1	yes	characteristic
46	C₂×#107	—	157	2	no	—
47	C₂²×C₈	C₂×D₁₅₇	1	1	yes	characteristic
48	C₂×C₄⋊C₄	—	314	2	no	—
49	C₂×C₁₆	—	2	2	no	—
50	C₂×C₁₆	Dic₁₅₇	1	2	yes	complemented
51	#107	—	314	2	no	—
52	#107	—	157	4	no	—
53	C₂²×C₄	—	628	2	no	—
54	C₂²×C₄	D₆₂₈	1	1	yes	characteristic
55	C₂×C₈	C₄×D₁₅₇	1	2	yes	—
56	C₂×C₈	C₂×Dic₁₅₇	1	1	yes	characteristic
57	C₂×C₈	C₂²⋊D₁₅₇	1	2	yes	—
58	C₂×C₈	Dic₃₁₄	1	1	yes	characteristic
59	C₄⋊C₄	—	314	4	no	—
60	C₄⋊C₄	—	628	2	no	—
61	C₁₆	—	2	2	no	—
62	C₂³	D₁₂₅₆	1	1	yes	characteristic
63	C₂×C₄	—	628	4	no	—
64	C₂×C₄	—	1256	2	no	—
65	C₂×C₄	—	1256	2	no	—
66	C₂×C₄	#14578931	1	2	yes	—
67	C₂×C₄	C₄⋊Dic₁₅₇	1	1	yes	characteristic
68	C₂×C₄	#14578943	1	2	yes	—
69	C₂×C₄	Dic₆₂₈	1	1	yes	characteristic
70	C₈	C₄×Dic₁₅₇	1	1	yes	characteristic
71	C₈	C₂²⋊Dic₁₅₇	1	1	yes	characteristic
72	C₈	#14578933	1	2	yes	—
73	C₂²	#19097693	1	2	yes	—
74	C₂²	#19097705	1	1	yes	characteristic
75	C₂²	D₂₅₁₂	1	1	yes	characteristic
76	C₂²	#19097716	1	2	yes	—
77	C₂²	Dic₁₂₅₆	1	1	yes	characteristic
78	C₄	—	1256	4	no	—
79	C₄	#19097678	1	1	yes	characteristic
80	C₄	#19097696	1	2	yes	—
81	C₄	#19097703	1	1	yes	characteristic
82	C₂	#23757036	1	1	yes	characteristic
83	C₂	#23757075	1	2	yes	—
84	C₂	#23757078	1	2	yes	—
85	C₂	#23757099	1	1	yes	characteristic
86	C₂	#23757101	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	D₁₂₅₆
commutator	C₈×C₁₅₇	C₄²
Frattini	C₂²×C₈	C₂×D₁₅₇
Fitting	C₂²×C₁₆×C₁₅₇	C₂
socle, prime radical	C₂³×C₁₅₇	D₈
cosocle	C₂²×C₈×C₁₅₇	C₂²
hypercenter	C₂²×C₁₆	D₁₅₇
hypocenter	C₁₅₇	#1380
LCS	G ▷ C₈×C₁₅₇ ▷ C₄×C₁₅₇ ▷ C₂×C₁₅₇ ▷ C₁₅₇
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×C₁₆

Complements

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

N	H ≅ G/N	type
5. #19097705	C₄	semidirect
8. C₂×C₁₆×C₁₅₇	C₄	semidirect
43. C₁₅₇	#1380	semidirect
50. C₂×C₁₆	Dic₁₅₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19097705	2
C₂²×C₁₆×C₁₅₇	2
#1380	157