Subgroups — #34115180

Order 20096.

148 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×C₄×#11929434	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	C₄	1	1	yes	characteristic
7	C₂²×#11929434	C₂²	1	1	yes	characteristic
8	C₄×#11929434	—	2	2	no	—
9	C₂×C₄²×C₁₅₇	C₄	1	1	yes	characteristic
10	#14578957	—	2	4	no	—
11	C₂×#11929434	—	2	1	no	—
12	C₂×#11929434	—	2	1	no	—
13	C₂×#11929434	C₈	1	2	yes	—
14	C₂×#11929434	C₂×C₄	1	2	yes	—
15	C₂×#11929434	D₄	1	2	yes	—
16	C₂×#11929434	D₄	1	1	yes	characteristic
17	C₂×#11929434	Q₈	1	1	yes	characteristic
18	C₂²×C₄×C₁₅₇	—	2	1	no	—
19	C₂²×C₄×C₁₅₇	C₂×C₄	1	1	yes	characteristic
20	C₄²×C₁₅₇	—	2	1	no	—
21	C₄²×C₁₅₇	C₈	1	2	yes	—
22	#11929434	—	2	2	no	—
23	#11929434	C₂²⋊C₄	1	2	yes	—
24	#11929434	C₄⋊C₄	1	2	yes	—
25	C₂³×C₁₅₇	M₁₆	1	1	yes	characteristic
26	C₂×C₄×C₁₅₇	—	2	4	no	—
27	C₂×C₄×C₁₅₇	—	2	2	no	—
28	C₂×C₄×C₁₅₇	C₄²	1	1	yes	characteristic
29	C₂×C₄×C₁₅₇	C₂²⋊C₄	1	1	yes	characteristic
30	C₂×C₄×C₁₅₇	C₄⋊C₄	1	1	yes	characteristic
31	C₂×C₄×C₁₅₇	C₂×C₈	1	1	yes	characteristic
32	C₂×C₄×C₁₅₇	C₂×C₈	1	1	yes	characteristic
33	C₂×C₄×C₁₅₇	M₁₆	1	1	yes	characteristic
34	C₂²×C₁₅₇	—	2	2	no	—
35	C₂²×C₁₅₇	#97	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	—	2	4	no	—
39	C₄×C₁₅₇	#95	1	1	yes	characteristic
40	C₄×C₁₅₇	C₄×C₈	1	1	yes	characteristic
41	C₄×C₁₅₇	C₂²⋊C₈	1	1	yes	characteristic
42	C₄×C₁₅₇	C₄⋊C₈	1	1	yes	characteristic
43	C₂×C₁₅₇	—	2	1	no	—
44	C₂×C₁₅₇	—	2	1	no	—
45	C₂×C₁₅₇	#336	1	1	yes	characteristic
46	C₂×C₁₅₇	#364	1	2	yes	—
47	C₁₅₇	#1376	1	1	yes	characteristic, complemented, Sylow
48	#1376	—	157	1	no	maximal, Sylow
49	C₂×M₃₂	—	157	2	no	—
50	C₂×C₄×C₈	—	157	1	no	—
51	C₂²×C₈	—	157	1	no	—
52	C₂²×C₈	—	157	1	no	—
53	C₂×C₄²	#10597845	1	1	yes	characteristic
54	M₃₂	—	314	2	no	—
55	M₃₂	—	157	4	no	—
56	C₂×C₁₆	—	314	2	no	—
57	C₄×C₈	—	314	2	no	—
58	C₂²×C₄	—	2	1	no	—
59	C₂²×C₄	C₂×#10597845	1	1	yes	characteristic
60	C₂×C₈	—	314	1	no	—
61	C₂×C₈	—	314	1	no	—
62	C₂×C₈	—	157	2	no	—
63	C₂×C₈	—	157	2	no	—
64	C₂×C₈	—	157	2	no	—
65	C₂×C₈	—	157	1	no	—
66	C₂×C₈	—	157	1	no	—
67	C₄²	—	2	1	no	—
68	C₄²	#11929441	1	2	yes	—
69	C₁₆	—	314	4	no	—
70	C₂³	#14578963	1	1	yes	characteristic
71	C₂×C₄	—	2	4	no	—
72	C₂×C₄	—	2	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	D₁₅₇⋊C₈	1	1	yes	characteristic
78	C₂×C₄	#14578964	1	1	yes	characteristic
79	C₈	—	314	2	no	—
80	C₈	—	157	2	no	—
81	C₈	—	157	2	no	—
82	C₂²	—	2	2	no	—
83	C₂²	#19097826	1	1	yes	characteristic
84	C₂²	C₂²⋊#11929441	1	1	yes	characteristic
85	C₂²	#19097838	1	1	yes	characteristic
86	C₄	—	2	4	no	—
87	C₄	(C₂×#10597845)⋊C₄	1	1	yes	characteristic
88	C₄	C₄×#11929441	1	1	yes	characteristic
89	C₄	#19097828	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	#23758196	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₄⋊#10597845
commutator	C₄×C₁₅₇	C₄×C₈
Frattini	C₂²×C₄	C₂×#10597845
Fitting	C₂×C₄²×C₁₅₇	C₄
socle	C₂²×C₁₅₇	C₄⋊C₈
prime radical	C₂³×C₁₅₇	M₁₆
cosocle	C₂²×#11929434	C₂²
hypercenter	C₂×C₄²	#10597845
hypocenter	C₁₅₇	#1376
LCS	G ▷ C₄×C₁₅₇ ▷ C₂×C₁₅₇ ▷ C₁₅₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
4. #19097845	C₄	semidirect
47. C₁₅₇	#1376	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×C₄×#11929434	2
#1376	157