Subgroups — #34115044

Order 20096.

146 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23758276	C₂	1	2	yes	maximal
2	#23757296	C₂	1	1	yes	maximal, characteristic
3	C₂×#14578963	C₄	1	4	yes	—
4	#19097838	—	2	2	no	—
5	C₄⋊#11929441	—	2	2	no	—
6	C₂×#14578938	C₄	1	1	yes	characteristic
7	C₂×C₄×Dic₁₅₇	C₂²	1	1	yes	characteristic
8	#19097700	—	2	2	no	—
9	C₂×M₁₆×C₁₅₇	C₄	1	1	yes	characteristic
10	#14578963	—	4	4	no	—
11	C₂×#11929441	—	2	4	no	—
12	C₂²×Dic₁₅₇	C₂×C₄	1	2	yes	—
13	#14578938	—	4	1	no	—
14	C₂×#11929434	—	2	1	no	—
15	C₄×Dic₁₅₇	D₄	1	2	yes	—
16	C₄×Dic₁₅₇	D₄	1	1	yes	characteristic
17	C₄×Dic₁₅₇	Q₈	1	1	yes	characteristic
18	C₂²×C₄×C₁₅₇	C₂×C₄	1	1	yes	characteristic
19	M₁₆×C₁₅₇	—	4	1	no	—
20	C₂×C₈×C₁₅₇	—	2	1	no	—
21	#11929441	—	4	4	no	—
22	C₂×Dic₁₅₇	—	2	2	no	—
23	C₂×Dic₁₅₇	—	2	2	no	—
24	C₂×Dic₁₅₇	C₂²⋊C₄	1	2	yes	—
25	C₂×Dic₁₅₇	C₄⋊C₄	1	2	yes	—
26	#11929434	—	4	1	no	—
27	C₂³×C₁₅₇	C₄²	1	1	yes	characteristic
28	C₂×C₄×C₁₅₇	—	2	1	no	—
29	C₂×C₄×C₁₅₇	—	2	1	no	—
30	C₂×C₄×C₁₅₇	C₂²⋊C₄	1	1	yes	characteristic
31	C₂×C₄×C₁₅₇	C₄⋊C₄	1	1	yes	characteristic
32	C₈×C₁₅₇	—	4	1	no	—
33	C₂²×C₁₅₇	—	2	1	no	—
34	C₂²×C₁₅₇	—	2	2	no	—
35	C₂²×C₁₅₇	#95	1	1	yes	characteristic
36	C₄×C₁₅₇	—	2	1	no	—
37	C₄×C₁₅₇	#100	1	1	yes	characteristic
38	C₄×C₁₅₇	#101	1	1	yes	characteristic
39	Dic₁₅₇	—	2	2	no	—
40	Dic₁₅₇	#100	1	2	yes	—
41	Dic₁₅₇	#101	1	2	yes	—
42	C₂×C₁₅₇	—	4	1	no	—
43	C₂×C₁₅₇	#343	1	2	yes	—
44	C₂×C₁₅₇	#343	1	1	yes	characteristic
45	C₁₅₇	#1309	1	1	yes	characteristic, complemented, Sylow
46	#1309	—	157	1	no	maximal, Sylow
47	#423	—	157	2	no	—
48	#423	—	157	1	no	—
49	C₂×M₁₆	—	157	4	no	—
50	C₂×M₁₆	—	157	1	no	—
51	C₂×M₁₆	#10597845	1	1	yes	characteristic
52	C₂×C₄²	—	157	1	no	—
53	C₄⋊C₈	—	314	2	no	—
54	C₄⋊C₈	—	314	2	no	—
55	C₄⋊C₈	—	314	2	no	—
56	C₂²×C₄	—	157	2	no	—
57	C₂²×C₄	C₂×#10597845	1	1	yes	characteristic
58	M₁₆	—	4	1	no	—
59	M₁₆	—	628	1	no	—
60	M₁₆	—	628	4	no	—
61	C₂×C₈	—	2	1	no	—
62	C₂×C₈	—	314	4	no	—
63	C₂×C₈	—	314	1	no	—
64	C₄²	—	157	2	no	—
65	C₄²	—	157	1	no	—
66	C₄²	—	157	1	no	—
67	C₂³	C₄×#10597845	1	1	yes	characteristic
68	C₂×C₄	—	2	1	no	—
69	C₂×C₄	—	2	1	no	—
70	C₂×C₄	—	314	2	no	—
71	C₂×C₄	—	314	2	no	—
72	C₂×C₄	—	157	2	no	—
73	C₂×C₄	—	157	2	no	—
74	C₂×C₄	C₂²⋊#10597845	1	1	yes	characteristic
75	C₂×C₄	C₄⋊#10597845	1	1	yes	characteristic
76	C₈	—	4	1	no	—
77	C₈	—	628	4	no	—
78	C₈	—	628	1	no	—
79	C₂²	—	2	2	no	—
80	C₂²	—	2	1	no	—
81	C₂²	(C₂×#10597845)⋊C₄	1	1	yes	characteristic
82	C₄	—	2	1	no	—
83	C₄	—	314	2	no	—
84	C₄	—	157	2	no	—
85	C₄	—	157	2	no	—
86	C₄	#19097831	1	1	yes	characteristic
87	C₄	#19097832	1	1	yes	characteristic
88	C₂	—	4	1	no	—
89	C₂	#23758152	1	2	yes	—
90	C₂	#23758153	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	(C₂×#10597845)⋊C₄
commutator, prime radical	C₂³×C₁₅₇	C₄²
Frattini	C₂²×C₄	C₂×#10597845
Fitting	C₂×M₁₆×C₁₅₇	C₄
socle	C₂²×C₁₅₇	#95
cosocle	C₂×C₄×Dic₁₅₇	C₂²
hypercenter	C₂×M₁₆	#10597845
hypocenter	C₁₅₇	#1309
LCS	G ▷ C₂³×C₁₅₇ ▷ C₂²×C₁₅₇ ▷ C₁₅₇
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×M₁₆

Complements

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

N	H ≅ G/N	type
45. C₁₅₇	#1309	semidirect

Maximal subgroups

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

subgroup	index
#23758276	2
#23757296	2
#1309	157