Subgroups — #1362×C₂₅₁ #44545949

Order 32128.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#494×C₂₅₁	C₂	1	1	yes	maximal, characteristic
2	C₄⋊C₁₆×C₂₅₁	C₂	1	1	yes	maximal, characteristic
3	#335×C₂₅₁	C₂	1	1	yes	maximal, characteristic
4	C₂×Q₁₆×C₂₅₁	—	2	1	no	—
5	C₂×Q₁₆×C₂₅₁	C₄	1	2	yes	—
6	C₄⋊Q₈×C₂₅₁	—	2	1	no	—
7	C₂×C₁₆×C₂₅₁	—	2	1	no	—
8	C₄⋊C₈×C₂₅₁	—	2	1	no	—
9	C₄×C₈×C₂₅₁	C₂²	1	1	yes	characteristic
10	C₂×Q₈×C₂₅₁	—	2	2	no	—
11	Q₁₆×C₂₅₁	—	4	2	no	—
12	Q₁₆×C₂₅₁	—	4	1	no	—
13	Q₁₆×C₂₅₁	—	4	1	no	—
14	C₂×C₈×C₂₅₁	—	4	1	no	—
15	C₂×C₈×C₂₅₁	C₂×C₄	1	1	yes	characteristic
16	C₂×C₈×C₂₅₁	D₄	1	1	yes	characteristic
17	C₄⋊C₄×C₂₅₁	—	4	1	no	—
18	C₄⋊C₄×C₂₅₁	—	4	1	no	—
19	C₄²×C₂₅₁	D₄	1	1	yes	characteristic
20	C₁₆×C₂₅₁	—	4	1	no	—
21	Q₈×C₂₅₁	—	4	2	no	—
22	Q₈×C₂₅₁	—	4	2	no	—
23	C₂×C₄×C₂₅₁	—	4	2	no	—
24	C₂×C₄×C₂₅₁	C₂²⋊C₄	1	1	yes	characteristic
25	C₂×C₄×C₂₅₁	D₈	1	1	yes	characteristic
26	C₂×C₄×C₂₅₁	SD₁₆	1	1	yes	characteristic
27	C₈×C₂₅₁	—	2	1	no	—
28	C₈×C₂₅₁	—	8	1	no	—
29	C₈×C₂₅₁	D₈	1	1	yes	characteristic
30	C₈×C₂₅₁	SD₁₆	1	1	yes	characteristic
31	C₂²×C₂₅₁	#102	1	1	yes	characteristic
32	C₄×C₂₅₁	—	2	1	no	—
33	C₄×C₂₅₁	—	8	2	no	—
34	C₄×C₂₅₁	#100	1	1	yes	characteristic
35	C₄×C₂₅₁	#102	1	1	yes	characteristic
36	C₄×C₂₅₁	SD₃₂	1	1	yes	characteristic
37	C₄×C₂₅₁	Q₃₂	1	1	yes	characteristic
38	C₂×C₂₅₁	#331	1	1	yes	characteristic
39	C₂×C₂₅₁	#358	1	1	yes	characteristic
40	C₂×C₂₅₁	#362	1	1	yes	characteristic
41	C₂₅₁	#1362	1	1	yes	characteristic, direct product factor, Sylow
42	#1362	C₂₅₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
43	#494	C₂×C₂₅₁	1	1	yes	characteristic
44	C₄⋊C₁₆	C₂×C₂₅₁	1	1	yes	characteristic
45	#335	C₂×C₂₅₁	1	1	yes	characteristic
46	C₂×Q₁₆	—	2	1	no	—
47	C₂×Q₁₆	C₄×C₂₅₁	1	2	yes	—
48	C₄⋊Q₈	—	2	1	no	—
49	C₂×C₁₆	—	2	1	no	—
50	C₄⋊C₈	—	2	1	no	—
51	C₄×C₈	C₂²×C₂₅₁	1	1	yes	characteristic
52	C₂×Q₈	—	2	2	no	—
53	Q₁₆	—	4	2	no	—
54	Q₁₆	—	4	1	no	—
55	Q₁₆	—	4	1	no	—
56	C₂×C₈	—	4	1	no	—
57	C₂×C₈	C₂×C₄×C₂₅₁	1	1	yes	characteristic
58	C₂×C₈	D₄×C₂₅₁	1	1	yes	characteristic
59	C₄⋊C₄	—	4	1	no	—
60	C₄⋊C₄	—	4	1	no	—
61	C₄²	D₄×C₂₅₁	1	1	yes	characteristic
62	C₁₆	—	4	1	no	—
63	Q₈	—	4	2	no	—
64	Q₈	—	4	2	no	—
65	C₂×C₄	—	4	2	no	—
66	C₂×C₄	C₂²⋊C₄×C₂₅₁	1	1	yes	characteristic
67	C₂×C₄	D₈×C₂₅₁	1	1	yes	characteristic
68	C₂×C₄	SD₁₆×C₂₅₁	1	1	yes	characteristic
69	C₈	—	2	1	no	—
70	C₈	—	8	1	no	—
71	C₈	D₈×C₂₅₁	1	1	yes	characteristic
72	C₈	SD₁₆×C₂₅₁	1	1	yes	characteristic
73	C₂²	#102×C₂₅₁	1	1	yes	characteristic
74	C₄	—	2	1	no	—
75	C₄	—	8	2	no	—
76	C₄	#100×C₂₅₁	1	1	yes	characteristic
77	C₄	#102×C₂₅₁	1	1	yes	characteristic
78	C₄	SD₃₂×C₂₅₁	1	1	yes	characteristic
79	C₄	Q₃₂×C₂₅₁	1	1	yes	characteristic
80	C₂	#331×C₂₅₁	1	1	yes	characteristic
81	C₂	#358×C₂₅₁	1	1	yes	characteristic
82	C₂	#362×C₂₅₁	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂²×C₂₅₁	#102
commutator	C₂×C₈	C₂×C₄×C₂₅₁
Frattini, cosocle	C₄×C₈	C₂²×C₂₅₁
LCS	G ▷ C₂×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₅₁ ◁ C₄²×C₂₅₁ ◁ C₄×C₈×C₂₅₁ ◁ G

Complements

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

N	H ≅ G/N	type
41. C₂₅₁	#1362	direct (N × H)
42. #1362	C₂₅₁	direct (N × H)

Maximal subgroups

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

subgroup	index
#494×C₂₅₁	2
C₄⋊C₁₆×C₂₅₁	2
#335×C₂₅₁	2
#1362	251

Subgroups — #1362×C251 #44545949

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #1362×C₂₅₁ #44545949