Subgroups — C₂²×#14578944 #23758049

Order 10048.

258 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Dic₃₁₄	C₂	1	1	yes	maximal, characteristic
2	C₂×#14578944	C₂	1	12	yes	maximal, direct product factor
3	C₂²×#11929434	C₂	1	1	yes	maximal, characteristic
4	C₂²×Q₈×C₁₅₇	C₂	1	1	yes	maximal, characteristic
5	C₂×Dic₃₁₄	—	2	3	no	—
6	C₂×Dic₃₁₄	C₂²	1	6	yes	—
7	C₂²×Dic₁₅₇	—	2	1	no	—
8	#14578944	C₂²	1	16	yes	direct product factor
9	C₂×#11929434	C₂²	1	6	yes	—
10	C₂×Q₈×C₁₅₇	—	2	3	no	—
11	C₂×Q₈×C₁₅₇	C₂²	1	6	yes	—
12	C₂²×C₄×C₁₅₇	—	2	1	no	—
13	C₂²×C₄×C₁₅₇	C₂²	1	1	yes	characteristic
14	Dic₃₁₄	—	2	6	no	—
15	Dic₃₁₄	C₂³	1	4	yes	—
16	C₂×Dic₁₅₇	—	2	6	no	—
17	#11929434	C₂³	1	4	yes	—
18	C₂³×C₁₅₇	D₄	1	1	yes	characteristic
19	Q₈×C₁₅₇	—	2	6	no	—
20	Q₈×C₁₅₇	C₂³	1	4	yes	—
21	C₂×C₄×C₁₅₇	—	2	6	no	—
22	C₂×C₄×C₁₅₇	D₄	1	3	yes	—
23	C₂×C₄×C₁₅₇	C₂³	1	3	yes	—
24	C₂²×C₁₅₇	Q₁₆	1	4	yes	complemented
25	C₂²×C₁₅₇	C₂×D₄	1	3	yes	—
26	C₄×C₁₅₇	—	2	4	no	—
27	C₄×C₁₅₇	C₂×D₄	1	3	yes	—
28	C₄×C₁₅₇	C₂⁴	1	1	yes	characteristic
29	Dic₁₅₇	—	2	4	no	—
30	C₂×C₁₅₇	C₂×Q₁₆	1	6	yes	complemented
31	C₂×C₁₅₇	C₂²×D₄	1	1	yes	characteristic
32	C₁₅₇	C₂²×Q₁₆	1	1	yes	characteristic, complemented, Sylow
33	C₂²×Q₁₆	—	157	1	no	maximal, Sylow
34	C₂²×Q₈	—	157	1	no	—
35	C₂²×Q₈	D₁₅₇	1	1	yes	characteristic
36	C₂×Q₁₆	—	157	12	no	—
37	C₂²×C₈	—	157	1	no	—
38	C₂×Q₈	—	2	3	no	—
39	C₂×Q₈	—	314	3	no	—
40	C₂×Q₈	—	157	6	no	—
41	C₂×Q₈	C₂×D₁₅₇	1	6	yes	—
42	C₂²×C₄	—	2	1	no	—
43	C₂²×C₄	—	314	1	no	—
44	C₂²×C₄	C₂×D₁₅₇	1	1	yes	characteristic
45	Q₁₆	—	157	16	no	—
46	C₂×C₈	—	157	6	no	—
47	C₂³	C₂²⋊D₁₅₇	1	1	yes	characteristic
48	Q₈	—	2	6	no	—
49	Q₈	—	314	6	no	—
50	Q₈	—	157	4	no	—
51	Q₈	C₂²×D₁₅₇	1	4	yes	—
52	C₂×C₄	—	2	6	no	—
53	C₂×C₄	—	314	6	no	—
54	C₂×C₄	C₂²⋊D₁₅₇	1	3	yes	—
55	C₂×C₄	C₂²×D₁₅₇	1	3	yes	—
56	C₈	—	157	4	no	—
57	C₂²	#14578944	1	4	yes	direct product factor
58	C₂²	C₂×C₂²⋊D₁₅₇	1	3	yes	—
59	C₄	—	2	4	no	—
60	C₄	—	314	4	no	—
61	C₄	C₂×C₂²⋊D₁₅₇	1	3	yes	—
62	C₄	C₂³×D₁₅₇	1	1	yes	characteristic
63	C₂	C₂×#14578944	1	6	yes	direct product factor
64	C₂	C₂²×C₂²⋊D₁₅₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²⋊D₁₅₇
commutator, cosocle	C₄×C₁₅₇	C₂⁴
Frattini	C₄	C₂³×D₁₅₇
Fitting	C₂²×Q₈×C₁₅₇	C₂
socle, prime radical	C₂³×C₁₅₇	D₄
hypercenter	C₂²×Q₈	D₁₅₇
hypocenter	C₁₅₇	C₂²×Q₁₆
LCS	G ▷ C₄×C₁₅₇ ▷ C₂×C₁₅₇ ▷ C₁₅₇
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×Q₈

Complements

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

N	H ≅ G/N	type
2. C₂×#14578944	C₂	direct (N × H)
8. #14578944	C₂²	direct (N × H)
24. C₂²×C₁₅₇	Q₁₆	semidirect
30. C₂×C₁₅₇	C₂×Q₁₆	semidirect
32. C₁₅₇	C₂²×Q₁₆	semidirect
57. C₂²	#14578944	direct (N × H)
63. C₂	C₂×#14578944	direct (N × H)

Subgroups — C22×#14578944 #23758049

Conjugacy classes of subgroups

Complements

Subgroups — C₂²×#14578944 #23758049