Subgroups — C₂²×#19097682 #34108540

Order 20096.

680 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×#11929434	C₂	1	2	yes	maximal
2	C₂×#19097682	C₂	1	12	yes	maximal, direct product factor
3	C₂²×C₄²×C₁₅₇	C₂	1	1	yes	maximal, characteristic
4	C₂²×#11929434	C₄	1	16	yes	complemented
5	C₂²×#11929434	C₂²	1	12	yes	—
6	#19097682	C₂²	1	16	yes	direct product factor
7	C₂³×C₄×C₁₅₇	C₄	1	2	yes	—
8	C₂³×C₄×C₁₅₇	C₂²	1	1	yes	characteristic
9	C₂×C₄²×C₁₅₇	C₄	1	6	yes	—
10	C₂×C₄²×C₁₅₇	C₂²	1	6	yes	—
11	C₂×#11929434	C₂×C₄	1	48	yes	complemented
12	C₂×#11929434	C₂³	1	8	yes	—
13	C₂⁴×C₁₅₇	C₂×C₄	1	1	yes	characteristic
14	C₂²×C₄×C₁₅₇	—	2	8	no	—
15	C₂²×C₄×C₁₅₇	C₂×C₄	1	8	yes	—
16	C₂²×C₄×C₁₅₇	C₂×C₄	1	12	yes	—
17	C₂²×C₄×C₁₅₇	C₂×C₄	1	3	yes	—
18	C₂²×C₄×C₁₅₇	C₂³	1	3	yes	—
19	C₄²×C₁₅₇	C₂×C₄	1	12	yes	—
20	C₄²×C₁₅₇	C₂³	1	4	yes	—
21	#11929434	C₂²×C₄	1	16	yes	complemented
22	C₂³×C₁₅₇	C₄²	1	4	yes	—
23	C₂³×C₁₅₇	M₁₆	1	8	yes	—
24	C₂³×C₁₅₇	C₂²×C₄	1	3	yes	—
25	C₂×C₄×C₁₅₇	—	2	24	no	—
26	C₂×C₄×C₁₅₇	C₄²	1	12	yes	—
27	C₂×C₄×C₁₅₇	C₂²×C₄	1	12	yes	—
28	C₂×C₄×C₁₅₇	C₂²×C₄	1	8	yes	—
29	C₂×C₄×C₁₅₇	C₂²×C₄	1	3	yes	—
30	C₂×C₄×C₁₅₇	C₂⁴	1	1	yes	characteristic
31	C₂²×C₁₅₇	#97	1	16	yes	complemented
32	C₂²×C₁₅₇	C₂×C₄²	1	6	yes	—
33	C₂²×C₁₅₇	C₂×M₁₆	1	12	yes	—
34	C₂²×C₁₅₇	C₂³×C₄	1	1	yes	characteristic
35	C₄×C₁₅₇	—	2	8	no	—
36	C₄×C₁₅₇	C₂×C₄²	1	6	yes	—
37	C₄×C₁₅₇	C₂³×C₄	1	2	yes	—
38	C₂×C₁₅₇	C₂×#97	1	12	yes	complemented
39	C₂×C₁₅₇	C₂²×C₄²	1	1	yes	characteristic
40	C₂×C₁₅₇	C₂²×M₁₆	1	2	yes	—
41	C₁₅₇	C₂²×#97	1	1	yes	characteristic, complemented, Sylow
42	C₂²×#97	—	157	1	no	maximal, Sylow
43	C₂³×C₈	—	157	2	no	—
44	C₂²×C₄²	D₁₅₇	1	1	yes	characteristic
45	C₂×#97	—	157	12	no	—
46	C₂³×C₄	Dic₁₅₇	1	2	yes	—
47	C₂³×C₄	C₂×D₁₅₇	1	1	yes	characteristic
48	C₂²×C₈	—	157	16	no	—
49	C₂²×C₈	—	157	12	no	—
50	C₂×C₄²	Dic₁₅₇	1	6	yes	—
51	C₂×C₄²	C₂×D₁₅₇	1	6	yes	—
52	#97	—	157	16	no	—
53	C₂⁴	C₂×Dic₁₅₇	1	1	yes	characteristic
54	C₂²×C₄	—	2	8	no	—
55	C₂²×C₄	C₄×D₁₅₇	1	8	yes	—
56	C₂²×C₄	C₂×Dic₁₅₇	1	12	yes	—
57	C₂²×C₄	C₂×Dic₁₅₇	1	3	yes	—
58	C₂²×C₄	C₂²×D₁₅₇	1	3	yes	—
59	C₂×C₈	—	157	48	no	—
60	C₂×C₈	—	157	8	no	—
61	C₄²	C₂×Dic₁₅₇	1	12	yes	—
62	C₄²	C₂²×D₁₅₇	1	4	yes	—
63	C₂³	C₄×Dic₁₅₇	1	4	yes	—
64	C₂³	#14578938	1	8	yes	—
65	C₂³	C₂²×Dic₁₅₇	1	3	yes	—
66	C₂×C₄	—	2	24	no	—
67	C₂×C₄	C₄×Dic₁₅₇	1	12	yes	—
68	C₂×C₄	C₂×C₄×D₁₅₇	1	12	yes	—
69	C₂×C₄	C₂²×Dic₁₅₇	1	8	yes	—
70	C₂×C₄	C₂²×Dic₁₅₇	1	3	yes	—
71	C₂×C₄	C₂³×D₁₅₇	1	1	yes	characteristic
72	C₈	—	157	16	no	—
73	C₂²	#19097682	1	16	yes	direct product factor
74	C₂²	C₂×C₄×Dic₁₅₇	1	6	yes	—
75	C₂²	C₂×#14578938	1	12	yes	—
76	C₂²	C₂³×Dic₁₅₇	1	1	yes	characteristic
77	C₄	—	2	8	no	—
78	C₄	C₂×C₄×Dic₁₅₇	1	6	yes	—
79	C₄	C₂²×C₄×D₁₅₇	1	2	yes	—
80	C₂	C₂×#19097682	1	12	yes	direct product factor
81	C₂	C₂²×C₄×Dic₁₅₇	1	1	yes	characteristic
82	C₂	C₂²×#14578938	1	2	yes	—

	subgroup	G/H
center	C₂³×C₄	C₂×D₁₅₇
commutator	C₂×C₁₅₇	C₂²×C₄²
Frattini	C₂×C₄	C₂³×D₁₅₇
Fitting	C₂²×C₄²×C₁₅₇	C₂
socle, prime radical	C₂⁴×C₁₅₇	C₂×C₄
cosocle	C₂×C₄×C₁₅₇	C₂⁴
hypercenter	C₂²×C₄²	D₁₅₇
hypocenter	C₁₅₇	C₂²×#97
LCS	G ▷ C₂×C₁₅₇ ▷ C₁₅₇
UCS	C₁ ◁ C₂³×C₄ ◁ C₂²×C₄²

Complements

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

N	H ≅ G/N	type
2. C₂×#19097682	C₂	direct (N × H)
4. C₂²×#11929434	C₄	semidirect
6. #19097682	C₂²	direct (N × H)
11. C₂×#11929434	C₂×C₄	semidirect
21. #11929434	C₂²×C₄	semidirect
31. C₂²×C₁₅₇	#97	semidirect
38. C₂×C₁₅₇	C₂×#97	semidirect
41. C₁₅₇	C₂²×#97	semidirect
73. C₂²	#19097682	direct (N × H)
80. C₂	C₂×#19097682	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×#11929434	2
C₂×#19097682	2
C₂²×C₄²×C₁₅₇	2
C₂²×#97	157

Subgroups — C22×#19097682 #34108540

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#19097682 #34108540