Subgroups — #34115184

Order 20096.

140 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19097845	C₂	1	2	yes	maximal
2	C₂×#19097681	C₂	1	1	yes	maximal, characteristic
3	#19097845	—	2	2	no	—
4	#19097845	C₄	1	4	yes	complemented
5	C₂×#14578957	—	2	2	no	—
6	C₂²×#11929434	C₂²	1	1	yes	characteristic
7	C₂×C₄×Dic₁₅₇	C₄	1	1	yes	characteristic
8	#19097681	—	2	2	no	—
9	C₂²×C₈×C₁₅₇	C₄	1	1	yes	characteristic
10	#14578957	—	2	4	no	—
11	C₂²×Dic₁₅₇	C₈	1	2	yes	—
12	C₂×#11929434	C₂×C₄	1	2	yes	—
13	C₂×#11929434	D₄	1	2	yes	—
14	C₂×#11929434	D₄	1	1	yes	characteristic
15	C₂×#11929434	Q₈	1	1	yes	characteristic
16	C₄×Dic₁₅₇	—	2	1	no	—
17	C₄×Dic₁₅₇	—	2	1	no	—
18	C₂²×C₄×C₁₅₇	C₂×C₄	1	1	yes	characteristic
19	C₂×C₈×C₁₅₇	—	2	1	no	—
20	C₂×C₈×C₁₅₇	—	2	1	no	—
21	C₂×C₈×C₁₅₇	C₈	1	2	yes	—
22	C₂×Dic₁₅₇	—	2	2	no	—
23	C₂×Dic₁₅₇	—	4	2	no	—
24	#11929434	C₂²⋊C₄	1	2	yes	—
25	#11929434	C₄⋊C₄	1	2	yes	—
26	C₂³×C₁₅₇	C₂×C₈	1	1	yes	characteristic
27	C₂×C₄×C₁₅₇	C₄²	1	1	yes	characteristic
28	C₂×C₄×C₁₅₇	C₂²⋊C₄	1	1	yes	characteristic
29	C₂×C₄×C₁₅₇	C₄⋊C₄	1	1	yes	characteristic
30	C₂×C₄×C₁₅₇	C₂×C₈	1	1	yes	characteristic
31	C₂×C₄×C₁₅₇	M₁₆	1	1	yes	characteristic
32	C₂×C₄×C₁₅₇	M₁₆	1	1	yes	characteristic
33	C₈×C₁₅₇	—	2	2	no	—
34	C₂²×C₁₅₇	—	2	2	no	—
35	C₂²×C₁₅₇	C₄×C₈	1	1	yes	characteristic
36	C₂²×C₁₅₇	C₂²⋊C₈	1	1	yes	characteristic
37	C₂²×C₁₅₇	C₄⋊C₈	1	1	yes	characteristic
38	C₄×C₁₅₇	#95	1	1	yes	characteristic
39	C₄×C₁₅₇	#97	1	1	yes	characteristic
40	C₄×C₁₅₇	C₂²⋊C₈	1	1	yes	characteristic
41	C₄×C₁₅₇	C₄⋊C₈	1	1	yes	characteristic
42	Dic₁₅₇	—	4	2	no	—
43	C₂×C₁₅₇	—	2	1	no	—
44	C₂×C₁₅₇	—	2	1	no	—
45	C₂×C₁₅₇	#336	1	1	yes	characteristic
46	C₂×C₁₅₇	#349	1	2	yes	—
47	C₁₅₇	#1377	1	1	yes	characteristic, complemented, Sylow
48	#1377	—	157	1	no	maximal, Sylow
49	C₂×M₃₂	—	157	2	no	—
50	C₂×#97	—	157	1	no	—
51	C₂²×C₈	—	157	1	no	—
52	C₂²×C₈	#10597845	1	1	yes	characteristic
53	C₂×C₄²	—	157	1	no	—
54	M₃₂	—	314	2	no	—
55	M₃₂	—	157	4	no	—
56	C₂×C₁₆	—	314	2	no	—
57	#97	—	314	2	no	—
58	C₂²×C₄	—	157	2	no	—
59	C₂²×C₄	C₂×#10597845	1	1	yes	characteristic
60	C₂×C₈	—	2	1	no	—
61	C₂×C₈	—	2	1	no	—
62	C₂×C₈	—	157	2	no	—
63	C₂×C₈	—	157	2	no	—
64	C₂×C₈	—	157	1	no	—
65	C₂×C₈	—	157	1	no	—
66	C₂×C₈	#11929441	1	2	yes	—
67	C₄²	—	314	1	no	—
68	C₄²	—	314	1	no	—
69	C₁₆	—	314	4	no	—
70	C₂³	D₁₅₇⋊C₈	1	1	yes	characteristic
71	C₂×C₄	—	314	2	no	—
72	C₂×C₄	—	628	2	no	—
73	C₂×C₄	C₄×#10597845	1	1	yes	characteristic
74	C₂×C₄	C₂²⋊#10597845	1	1	yes	characteristic
75	C₂×C₄	C₄⋊#10597845	1	1	yes	characteristic
76	C₂×C₄	C₂×#11929441	1	1	yes	characteristic
77	C₂×C₄	#14578963	1	1	yes	characteristic
78	C₂×C₄	#14578964	1	1	yes	characteristic
79	C₈	—	2	2	no	—
80	C₈	—	157	2	no	—
81	C₈	—	157	2	no	—
82	C₂²	—	2	2	no	—
83	C₂²	C₄×#11929441	1	1	yes	characteristic
84	C₂²	#19097828	1	1	yes	characteristic
85	C₂²	#19097838	1	1	yes	characteristic
86	C₄	—	628	2	no	—
87	C₄	(C₂×#10597845)⋊C₄	1	1	yes	characteristic
88	C₄	#19097826	1	1	yes	characteristic
89	C₄	C₂²⋊#11929441	1	1	yes	characteristic
90	C₄	C₄⋊#11929441	1	1	yes	characteristic
91	C₂	—	2	1	no	—
92	C₂	—	2	1	no	—
93	C₂	#23758139	1	1	yes	characteristic
94	C₂	#23758170	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂²⋊#10597845
commutator	C₂²×C₁₅₇	C₄×C₈
Frattini	C₂²×C₄	C₂×#10597845
Fitting	C₂²×C₈×C₁₅₇	C₄
socle	C₂²×C₁₅₇	C₂²⋊C₈
prime radical	C₂³×C₁₅₇	C₂×C₈
cosocle	C₂²×#11929434	C₂²
hypercenter	C₂²×C₈	#10597845
hypocenter	C₁₅₇	#1377
LCS	G ▷ C₂²×C₁₅₇ ▷ C₂×C₁₅₇ ▷ C₁₅₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
4. #19097845	C₄	semidirect
47. C₁₅₇	#1377	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19097845	2
C₂×#19097681	2
#1377	157