Subgroups — C₂×#97×C₂₅₇ #30656272

Order 16448.

146 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₈×C₂₅₇	C₂	1	2	yes	maximal
2	C₂×C₄²×C₂₅₇	C₂	1	1	yes	maximal, characteristic
3	#97×C₂₅₇	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₄×C₂₅₇	C₄	1	2	yes	—
5	C₂²×C₄×C₂₅₇	C₂²	1	1	yes	characteristic
6	C₂×C₈×C₂₅₇	C₄	1	8	yes	complemented
7	C₂×C₈×C₂₅₇	C₂²	1	4	yes	—
8	C₄²×C₂₅₇	C₄	1	2	yes	—
9	C₄²×C₂₅₇	C₂²	1	2	yes	—
10	C₂³×C₂₅₇	C₂×C₄	1	1	yes	characteristic
11	C₂×C₄×C₂₅₇	—	2	4	no	—
12	C₂×C₄×C₂₅₇	C₂×C₄	1	4	yes	—
13	C₂×C₄×C₂₅₇	C₂×C₄	1	1	yes	characteristic
14	C₂×C₄×C₂₅₇	C₂×C₄	1	4	yes	—
15	C₂×C₄×C₂₅₇	C₂³	1	1	yes	characteristic
16	C₈×C₂₅₇	C₂×C₄	1	8	yes	complemented
17	C₂²×C₂₅₇	C₄²	1	2	yes	—
18	C₂²×C₂₅₇	M₁₆	1	4	yes	—
19	C₂²×C₂₅₇	C₂²×C₄	1	1	yes	characteristic
20	C₄×C₂₅₇	—	2	4	no	—
21	C₄×C₂₅₇	C₄²	1	2	yes	—
22	C₄×C₂₅₇	C₂²×C₄	1	2	yes	—
23	C₂×C₂₅₇	#97	1	4	yes	direct product factor
24	C₂×C₂₅₇	C₂×C₄²	1	1	yes	characteristic
25	C₂×C₂₅₇	C₂×M₁₆	1	2	yes	—
26	C₂₅₇	C₂×#97	1	1	yes	characteristic, direct product factor, Sylow
27	C₂×#97	C₂₅₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
28	C₂²×C₈	C₂×C₂₅₇	1	2	yes	—
29	C₂×C₄²	C₂×C₂₅₇	1	1	yes	characteristic
30	#97	C₂×C₂₅₇	1	4	yes	direct product factor
31	C₂²×C₄	C₄×C₂₅₇	1	2	yes	—
32	C₂²×C₄	C₂²×C₂₅₇	1	1	yes	characteristic
33	C₂×C₈	C₄×C₂₅₇	1	8	yes	complemented
34	C₂×C₈	C₂²×C₂₅₇	1	4	yes	—
35	C₄²	C₄×C₂₅₇	1	2	yes	—
36	C₄²	C₂²×C₂₅₇	1	2	yes	—
37	C₂³	C₂×C₄×C₂₅₇	1	1	yes	characteristic
38	C₂×C₄	—	2	4	no	—
39	C₂×C₄	C₂×C₄×C₂₅₇	1	4	yes	—
40	C₂×C₄	C₂×C₄×C₂₅₇	1	1	yes	characteristic
41	C₂×C₄	C₂×C₄×C₂₅₇	1	4	yes	—
42	C₂×C₄	C₂³×C₂₅₇	1	1	yes	characteristic
43	C₈	C₂×C₄×C₂₅₇	1	8	yes	complemented
44	C₂²	C₄²×C₂₅₇	1	2	yes	—
45	C₂²	M₁₆×C₂₅₇	1	4	yes	—
46	C₂²	C₂²×C₄×C₂₅₇	1	1	yes	characteristic
47	C₄	—	2	4	no	—
48	C₄	C₄²×C₂₅₇	1	2	yes	—
49	C₄	C₂²×C₄×C₂₅₇	1	2	yes	—
50	C₂	#97×C₂₅₇	1	4	yes	direct product factor
51	C₂	C₂×C₄²×C₂₅₇	1	1	yes	characteristic
52	C₂	C₂×M₁₆×C₂₅₇	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₂₅₇	C₂²
commutator	C₂	C₂×C₄²×C₂₅₇
Frattini, cosocle	C₂×C₄	C₂³×C₂₅₇
socle, prime radical	C₂³×C₂₅₇	C₂×C₄
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₂₅₇ ◁ G

Complements

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

N	H ≅ G/N	type
3. #97×C₂₅₇	C₂	direct (N × H)
6. C₂×C₈×C₂₅₇	C₄	semidirect
16. C₈×C₂₅₇	C₂×C₄	semidirect
23. C₂×C₂₅₇	#97	direct (N × H)
26. C₂₅₇	C₂×#97	direct (N × H)
27. C₂×#97	C₂₅₇	direct (N × H)
30. #97	C₂×C₂₅₇	direct (N × H)
33. C₂×C₈	C₄×C₂₅₇	semidirect
43. C₈	C₂×C₄×C₂₅₇	semidirect
50. C₂	#97×C₂₅₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₈×C₂₅₇	2
C₂×C₄²×C₂₅₇	2
#97×C₂₅₇	2
C₂×#97	257

Subgroups — C2×#97×C257 #30656272

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#97×C₂₅₇ #30656272