Subgroups — C₂×#23757671 #34110635

Order 20096.

424 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19097771	C₂	1	2	yes	maximal
2	#23757671	C₂	1	8	yes	maximal, direct product factor
3	C₂×#19097703	C₂	1	4	yes	maximal
4	C₂×C₄×C₈×C₁₅₇	C₂	1	1	yes	maximal, characteristic
5	C₂²×Dic₃₁₄	—	2	2	no	—
6	#19097771	—	2	4	no	—
7	#19097771	C₂²	1	8	yes	—
8	C₂×C₄⋊Dic₁₅₇	—	2	2	no	—
9	C₂×C₄⋊Dic₁₅₇	C₂²	1	4	yes	—
10	#19097703	C₂²	1	16	yes	—
11	C₂²×C₈×C₁₅₇	C₂²	1	2	yes	—
12	C₂×C₄²×C₁₅₇	C₂²	1	1	yes	characteristic
13	C₄×C₈×C₁₅₇	C₂²	1	4	yes	—
14	C₂×Dic₃₁₄	—	2	8	no	—
15	C₂×Dic₃₁₄	—	4	8	no	—
16	C₂²×Dic₁₅₇	—	2	4	no	—
17	C₄⋊Dic₁₅₇	—	2	8	no	—
18	C₄⋊Dic₁₅₇	—	2	4	no	—
19	C₄⋊Dic₁₅₇	C₂³	1	8	yes	—
20	C₂²×C₄×C₁₅₇	D₄	1	2	yes	—
21	C₂²×C₄×C₁₅₇	C₂³	1	1	yes	characteristic
22	C₂×C₈×C₁₅₇	Q₈	1	8	yes	complemented
23	C₂×C₈×C₁₅₇	C₂³	1	4	yes	—
24	C₄²×C₁₅₇	D₄	1	2	yes	—
25	C₄²×C₁₅₇	C₂³	1	2	yes	—
26	Dic₃₁₄	—	4	16	no	—
27	C₂×Dic₁₅₇	—	2	8	no	—
28	C₂×Dic₁₅₇	—	4	8	no	—
29	C₂³×C₁₅₇	C₂×D₄	1	1	yes	characteristic
30	C₂×C₄×C₁₅₇	SD₁₆	1	8	yes	—
31	C₂×C₄×C₁₅₇	C₂×D₄	1	1	yes	characteristic
32	C₂×C₄×C₁₅₇	C₂×D₄	1	4	yes	—
33	C₂×C₄×C₁₅₇	C₂×Q₈	1	4	yes	—
34	C₂×C₄×C₁₅₇	C₂⁴	1	1	yes	characteristic
35	C₈×C₁₅₇	C₂×Q₈	1	8	yes	complemented
36	C₂²×C₁₅₇	C₄⋊Q₈	1	2	yes	—
37	C₂²×C₁₅₇	C₂×SD₁₆	1	4	yes	—
38	C₂²×C₁₅₇	C₂²×D₄	1	1	yes	characteristic
39	C₄×C₁₅₇	C₄⋊Q₈	1	2	yes	—
40	C₄×C₁₅₇	C₂×SD₁₆	1	8	yes	—
41	C₄×C₁₅₇	C₂²×Q₈	1	2	yes	—
42	Dic₁₅₇	—	4	8	no	—
43	C₂×C₁₅₇	#498	1	4	yes	complemented
44	C₂×C₁₅₇	C₂×C₄⋊Q₈	1	1	yes	characteristic
45	C₂×C₁₅₇	C₂²×SD₁₆	1	2	yes	—
46	C₁₅₇	C₂×#498	1	1	yes	characteristic, complemented, Sylow
47	C₂×#498	—	157	1	no	maximal, Sylow
48	C₂×C₄⋊Q₈	—	157	2	no	—
49	#498	—	157	8	no	—
50	C₂×#106	—	157	4	no	—
51	C₂×C₄×C₈	D₁₅₇	1	1	yes	characteristic
52	C₂²×Q₈	—	314	2	no	—
53	C₂²×C₈	C₂×D₁₅₇	1	2	yes	—
54	C₄⋊Q₈	—	314	4	no	—
55	C₄⋊Q₈	—	157	8	no	—
56	C₂×C₄⋊C₄	—	314	2	no	—
57	C₂×C₄⋊C₄	—	157	4	no	—
58	C₂×C₄²	C₂×D₁₅₇	1	1	yes	characteristic
59	#106	—	157	16	no	—
60	C₄×C₈	C₂×D₁₅₇	1	4	yes	—
61	C₂×Q₈	—	314	8	no	—
62	C₂×Q₈	—	628	8	no	—
63	C₂²×C₄	—	314	4	no	—
64	C₂²×C₄	D₆₂₈	1	2	yes	—
65	C₂²×C₄	C₂²×D₁₅₇	1	1	yes	characteristic
66	C₂×C₈	Dic₃₁₄	1	8	yes	complemented
67	C₂×C₈	C₂²×D₁₅₇	1	4	yes	—
68	C₄⋊C₄	—	314	8	no	—
69	C₄⋊C₄	—	314	4	no	—
70	C₄⋊C₄	—	157	8	no	—
71	C₄²	D₆₂₈	1	2	yes	—
72	C₄²	C₂²×D₁₅₇	1	2	yes	—
73	C₂³	C₂×D₆₂₈	1	1	yes	characteristic
74	Q₈	—	628	16	no	—
75	C₂×C₄	—	314	8	no	—
76	C₂×C₄	—	628	8	no	—
77	C₂×C₄	#14578943	1	8	yes	—
78	C₂×C₄	C₂×D₆₂₈	1	1	yes	characteristic
79	C₂×C₄	C₂×D₆₂₈	1	4	yes	—
80	C₂×C₄	C₂×Dic₃₁₄	1	4	yes	—
81	C₂×C₄	C₂³×D₁₅₇	1	1	yes	characteristic
82	C₈	C₂×Dic₃₁₄	1	8	yes	complemented
83	C₂²	#19097771	1	2	yes	—
84	C₂²	C₂×#14578943	1	4	yes	—
85	C₂²	C₂²×D₆₂₈	1	1	yes	characteristic
86	C₄	—	628	8	no	—
87	C₄	#19097771	1	2	yes	—
88	C₄	C₂×#14578943	1	8	yes	—
89	C₄	C₂²×Dic₃₁₄	1	2	yes	—
90	C₂	#23757671	1	4	yes	direct product factor
91	C₂	C₂×#19097771	1	1	yes	characteristic
92	C₂	C₂²×#14578943	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂×D₆₂₈
commutator, cosocle	C₂×C₄×C₁₅₇	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₅₇
Fitting	C₂×C₄×C₈×C₁₅₇	C₂
socle, prime radical	C₂³×C₁₅₇	C₂×D₄
hypercenter	C₂×C₄×C₈	D₁₅₇
hypocenter	C₁₅₇	C₂×#498
LCS	G ▷ C₂×C₄×C₁₅₇ ▷ C₂×C₁₅₇ ▷ C₁₅₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
2. #23757671	C₂	direct (N × H)
22. C₂×C₈×C₁₅₇	Q₈	semidirect
35. C₈×C₁₅₇	C₂×Q₈	semidirect
43. C₂×C₁₅₇	#498	semidirect
46. C₁₅₇	C₂×#498	semidirect
66. C₂×C₈	Dic₃₁₄	semidirect
82. C₈	C₂×Dic₃₁₄	semidirect
90. C₂	#23757671	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#19097771	2
#23757671	2
C₂×#19097703	2
C₂×C₄×C₈×C₁₅₇	2
C₂×#498	157

Subgroups — C2×#23757671 #34110635

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#23757671 #34110635