Subgroups — #479×C₂₅₇ #30656348

Order 16448.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#125×C₂₅₇	C₂	1	1	yes	maximal, characteristic
2	C₄×Q₈×C₂₅₇	C₂	1	1	yes	maximal, characteristic
3	#107×C₂₅₇	C₂	1	1	yes	maximal, characteristic
4	#106×C₂₅₇	C₂	1	1	yes	maximal, characteristic
5	C₄⋊C₈×C₂₅₇	C₂	1	1	yes	maximal, characteristic
6	#103×C₂₅₇	C₂	1	1	yes	maximal, characteristic
7	#103×C₂₅₇	C₂	1	1	yes	maximal, characteristic
8	C₂×Q₈×C₂₅₇	C₂²	1	1	yes	characteristic
9	C₂×C₈×C₂₅₇	C₂²	1	1	yes	characteristic
10	C₂×C₈×C₂₅₇	C₂²	1	1	yes	characteristic
11	C₄⋊C₄×C₂₅₇	—	2	1	no	—
12	C₄⋊C₄×C₂₅₇	—	2	1	no	—
13	C₄⋊C₄×C₂₅₇	—	2	1	no	—
14	C₄⋊C₄×C₂₅₇	C₂²	1	1	yes	characteristic
15	C₄⋊C₄×C₂₅₇	C₂²	1	1	yes	characteristic
16	C₄⋊C₄×C₂₅₇	C₂²	1	1	yes	characteristic
17	C₄²×C₂₅₇	—	2	1	no	—
18	C₄²×C₂₅₇	C₂²	1	1	yes	characteristic
19	Q₈×C₂₅₇	—	2	1	no	—
20	Q₈×C₂₅₇	Q₈	1	2	yes	—
21	C₂×C₄×C₂₅₇	—	2	1	no	—
22	C₂×C₄×C₂₅₇	—	2	1	no	—
23	C₂×C₄×C₂₅₇	—	2	1	no	—
24	C₂×C₄×C₂₅₇	—	2	1	no	—
25	C₂×C₄×C₂₅₇	D₄	1	1	yes	characteristic
26	C₂×C₄×C₂₅₇	D₄	1	1	yes	characteristic
27	C₂×C₄×C₂₅₇	C₂³	1	1	yes	characteristic
28	C₈×C₂₅₇	—	2	1	no	—
29	C₈×C₂₅₇	—	2	1	no	—
30	C₂²×C₂₅₇	C₂×D₄	1	1	yes	characteristic
31	C₄×C₂₅₇	—	2	2	no	—
32	C₄×C₂₅₇	—	2	1	no	—
33	C₄×C₂₅₇	—	2	1	no	—
34	C₄×C₂₅₇	—	4	1	no	—
35	C₄×C₂₅₇	—	4	1	no	—
36	C₄×C₂₅₇	—	4	1	no	—
37	C₄×C₂₅₇	C₂×Q₈	1	1	yes	characteristic
38	C₄×C₂₅₇	#41	1	1	yes	characteristic
39	C₂×C₂₅₇	C₂²⋊Q₈	1	1	yes	characteristic
40	C₂×C₂₅₇	#135	1	1	yes	characteristic
41	C₂×C₂₅₇	#137	1	1	yes	characteristic
42	C₂₅₇	#479	1	1	yes	characteristic, direct product factor, Sylow
43	#479	C₂₅₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
44	#125	C₂×C₂₅₇	1	1	yes	characteristic
45	C₄×Q₈	C₂×C₂₅₇	1	1	yes	characteristic
46	#107	C₂×C₂₅₇	1	1	yes	characteristic
47	#106	C₂×C₂₅₇	1	1	yes	characteristic
48	C₄⋊C₈	C₂×C₂₅₇	1	1	yes	characteristic
49	#103	C₂×C₂₅₇	1	1	yes	characteristic
50	#103	C₂×C₂₅₇	1	1	yes	characteristic
51	C₂×Q₈	C₂²×C₂₅₇	1	1	yes	characteristic
52	C₂×C₈	C₂²×C₂₅₇	1	1	yes	characteristic
53	C₂×C₈	C₂²×C₂₅₇	1	1	yes	characteristic
54	C₄⋊C₄	—	2	1	no	—
55	C₄⋊C₄	—	2	1	no	—
56	C₄⋊C₄	—	2	1	no	—
57	C₄⋊C₄	C₂²×C₂₅₇	1	1	yes	characteristic
58	C₄⋊C₄	C₂²×C₂₅₇	1	1	yes	characteristic
59	C₄⋊C₄	C₂²×C₂₅₇	1	1	yes	characteristic
60	C₄²	—	2	1	no	—
61	C₄²	C₂²×C₂₅₇	1	1	yes	characteristic
62	Q₈	—	2	1	no	—
63	Q₈	Q₈×C₂₅₇	1	2	yes	—
64	C₂×C₄	—	2	1	no	—
65	C₂×C₄	—	2	1	no	—
66	C₂×C₄	—	2	1	no	—
67	C₂×C₄	—	2	1	no	—
68	C₂×C₄	D₄×C₂₅₇	1	1	yes	characteristic
69	C₂×C₄	D₄×C₂₅₇	1	1	yes	characteristic
70	C₂×C₄	C₂³×C₂₅₇	1	1	yes	characteristic
71	C₈	—	2	1	no	—
72	C₈	—	2	1	no	—
73	C₂²	C₂×D₄×C₂₅₇	1	1	yes	characteristic
74	C₄	—	2	2	no	—
75	C₄	—	2	1	no	—
76	C₄	—	2	1	no	—
77	C₄	—	4	1	no	—
78	C₄	—	4	1	no	—
79	C₄	—	4	1	no	—
80	C₄	C₂×Q₈×C₂₅₇	1	1	yes	characteristic
81	C₄	#41×C₂₅₇	1	1	yes	characteristic
82	C₂	C₂²⋊Q₈×C₂₅₇	1	1	yes	characteristic
83	C₂	#135×C₂₅₇	1	1	yes	characteristic
84	C₂	#137×C₂₅₇	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂²×C₂₅₇	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂³×C₂₅₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₅₇ ◁ C₄²×C₂₅₇ ◁ G

Complements

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

N	H ≅ G/N	type
42. C₂₅₇	#479	direct (N × H)
43. #479	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
#125×C₂₅₇	2
C₄×Q₈×C₂₅₇	2
#107×C₂₅₇	2
#106×C₂₅₇	2
C₄⋊C₈×C₂₅₇	2
#103×C₂₅₇	2
#479	257

Subgroups — #479×C257 #30656348

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #479×C₂₅₇ #30656348