Subgroups — #1292×C₂₅₁ #44545879

Order 32128.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#423×C₂₅₁	C₂	1	2	yes	maximal
2	C₂×C₄⋊C₈×C₂₅₁	C₂	1	1	yes	maximal, characteristic
3	C₂×M₁₆×C₂₅₁	—	2	2	no	—
4	C₂²×C₈×C₂₅₁	C₄	1	2	yes	—
5	C₂×C₄²×C₂₅₁	C₂²	1	1	yes	characteristic
6	C₄⋊C₈×C₂₅₁	—	2	2	no	—
7	C₄⋊C₈×C₂₅₁	—	2	2	no	—
8	C₄⋊C₈×C₂₅₁	C₄	1	4	yes	—
9	C₂²×C₄×C₂₅₁	C₂×C₄	1	1	yes	characteristic
10	C₂²×C₄×C₂₅₁	D₄	1	1	yes	characteristic
11	C₂²×C₄×C₂₅₁	Q₈	1	1	yes	characteristic
12	M₁₆×C₂₅₁	—	4	2	no	—
13	M₁₆×C₂₅₁	—	4	2	no	—
14	C₂×C₈×C₂₅₁	—	2	2	no	—
15	C₂×C₈×C₂₅₁	—	2	4	no	—
16	C₂×C₈×C₂₅₁	—	4	2	no	—
17	C₄²×C₂₅₁	C₂×C₄	1	2	yes	—
18	C₄²×C₂₅₁	D₄	1	2	yes	—
19	C₂³×C₂₅₁	C₄⋊C₄	1	1	yes	characteristic
20	C₂×C₄×C₂₅₁	—	2	1	no	—
21	C₂×C₄×C₂₅₁	—	2	1	no	—
22	C₂×C₄×C₂₅₁	—	4	1	no	—
23	C₂×C₄×C₂₅₁	C₄²	1	1	yes	characteristic
24	C₂×C₄×C₂₅₁	C₂²⋊C₄	1	1	yes	characteristic
25	C₂×C₄×C₂₅₁	C₂²⋊C₄	1	2	yes	—
26	C₂×C₄×C₂₅₁	C₄⋊C₄	1	2	yes	—
27	C₂×C₄×C₂₅₁	D₈	1	1	yes	characteristic
28	C₂×C₄×C₂₅₁	SD₁₆	1	2	yes	—
29	C₂×C₄×C₂₅₁	Q₁₆	1	1	yes	characteristic
30	C₈×C₂₅₁	—	4	2	no	—
31	C₈×C₂₅₁	—	4	4	no	—
32	C₂²×C₂₅₁	—	2	1	no	—
33	C₂²×C₂₅₁	—	2	1	no	—
34	C₂²×C₂₅₁	#95	1	1	yes	characteristic
35	C₂²×C₂₅₁	#106	1	1	yes	characteristic
36	C₂²×C₂₅₁	#107	1	1	yes	characteristic
37	C₄×C₂₅₁	—	2	2	no	—
38	C₄×C₂₅₁	—	2	1	no	—
39	C₄×C₂₅₁	#100	1	1	yes	characteristic
40	C₄×C₂₅₁	#101	1	1	yes	characteristic
41	C₄×C₂₅₁	#102	1	2	yes	—
42	C₄×C₂₅₁	#103	1	2	yes	—
43	C₂×C₂₅₁	—	2	1	no	—
44	C₂×C₂₅₁	—	2	1	no	—
45	C₂×C₂₅₁	#338	1	1	yes	characteristic
46	C₂×C₂₅₁	#340	1	1	yes	characteristic
47	C₂×C₂₅₁	#343	1	1	yes	characteristic
48	C₂₅₁	#1292	1	1	yes	characteristic, direct product factor, Sylow
49	#1292	C₂₅₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
50	#423	C₂×C₂₅₁	1	2	yes	—
51	C₂×C₄⋊C₈	C₂×C₂₅₁	1	1	yes	characteristic
52	C₂×M₁₆	—	2	2	no	—
53	C₂²×C₈	C₄×C₂₅₁	1	2	yes	—
54	C₂×C₄²	C₂²×C₂₅₁	1	1	yes	characteristic
55	C₄⋊C₈	—	2	2	no	—
56	C₄⋊C₈	—	2	2	no	—
57	C₄⋊C₈	C₄×C₂₅₁	1	4	yes	—
58	C₂²×C₄	C₂×C₄×C₂₅₁	1	1	yes	characteristic
59	C₂²×C₄	D₄×C₂₅₁	1	1	yes	characteristic
60	C₂²×C₄	Q₈×C₂₅₁	1	1	yes	characteristic
61	M₁₆	—	4	2	no	—
62	M₁₆	—	4	2	no	—
63	C₂×C₈	—	2	2	no	—
64	C₂×C₈	—	2	4	no	—
65	C₂×C₈	—	4	2	no	—
66	C₄²	C₂×C₄×C₂₅₁	1	2	yes	—
67	C₄²	D₄×C₂₅₁	1	2	yes	—
68	C₂³	C₄⋊C₄×C₂₅₁	1	1	yes	characteristic
69	C₂×C₄	—	2	1	no	—
70	C₂×C₄	—	2	1	no	—
71	C₂×C₄	—	4	1	no	—
72	C₂×C₄	C₄²×C₂₅₁	1	1	yes	characteristic
73	C₂×C₄	C₂²⋊C₄×C₂₅₁	1	1	yes	characteristic
74	C₂×C₄	C₂²⋊C₄×C₂₅₁	1	2	yes	—
75	C₂×C₄	C₄⋊C₄×C₂₅₁	1	2	yes	—
76	C₂×C₄	D₈×C₂₅₁	1	1	yes	characteristic
77	C₂×C₄	SD₁₆×C₂₅₁	1	2	yes	—
78	C₂×C₄	Q₁₆×C₂₅₁	1	1	yes	characteristic
79	C₈	—	4	2	no	—
80	C₈	—	4	4	no	—
81	C₂²	—	2	1	no	—
82	C₂²	—	2	1	no	—
83	C₂²	#95×C₂₅₁	1	1	yes	characteristic
84	C₂²	#106×C₂₅₁	1	1	yes	characteristic
85	C₂²	#107×C₂₅₁	1	1	yes	characteristic
86	C₄	—	2	2	no	—
87	C₄	—	2	1	no	—
88	C₄	#100×C₂₅₁	1	1	yes	characteristic
89	C₄	#101×C₂₅₁	1	1	yes	characteristic
90	C₄	#102×C₂₅₁	1	2	yes	—
91	C₄	#103×C₂₅₁	1	2	yes	—
92	C₂	—	2	1	no	—
93	C₂	—	2	1	no	—
94	C₂	#338×C₂₅₁	1	1	yes	characteristic
95	C₂	#340×C₂₅₁	1	1	yes	characteristic
96	C₂	#343×C₂₅₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₅₁	#95
commutator	C₂×C₄	C₄²×C₂₅₁
Frattini, cosocle	C₂×C₄²	C₂²×C₂₅₁
prime radical	C₂³×C₂₅₁	C₄⋊C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₅₁ ◁ C₂×C₄²×C₂₅₁ ◁ G

Complements

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

N	H ≅ G/N	type
48. C₂₅₁	#1292	direct (N × H)
49. #1292	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
#423×C₂₅₁	2
C₂×C₄⋊C₈×C₂₅₁	2
#1292	251

Subgroups — #1292×C251 #44545879

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #1292×C₂₅₁ #44545879