Subgroups — #1381×C₂₅₁ #44545968

Order 32128.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₆×C₂₅₁	C₂	1	1	yes	maximal, characteristic
2	C₂×#108×C₂₅₁	C₂	1	2	yes	maximal
3	C₂×M₁₆×C₂₅₁	—	2	2	no	—
4	C₂²×C₈×C₂₅₁	C₂²	1	1	yes	characteristic
5	C₂×C₁₆×C₂₅₁	—	2	2	no	—
6	C₂×C₁₆×C₂₅₁	C₄	1	2	yes	—
7	#108×C₂₅₁	—	2	2	no	—
8	#108×C₂₅₁	C₄	1	4	yes	—
9	C₂²×C₄×C₂₅₁	D₄	1	1	yes	characteristic
10	M₁₆×C₂₅₁	—	2	4	no	—
11	M₁₆×C₂₅₁	—	4	2	no	—
12	C₂×C₈×C₂₅₁	—	4	2	no	—
13	C₂×C₈×C₂₅₁	C₂×C₄	1	1	yes	characteristic
14	C₂×C₈×C₂₅₁	C₂×C₄	1	2	yes	—
15	C₂×C₈×C₂₅₁	D₄	1	2	yes	—
16	C₂×C₈×C₂₅₁	Q₈	1	1	yes	characteristic
17	C₁₆×C₂₅₁	—	2	2	no	—
18	C₂³×C₂₅₁	Q₁₆	1	1	yes	characteristic
19	C₂×C₄×C₂₅₁	C₂²⋊C₄	1	2	yes	—
20	C₂×C₄×C₂₅₁	C₄⋊C₄	1	1	yes	characteristic
21	C₂×C₄×C₂₅₁	D₈	1	1	yes	characteristic
22	C₂×C₄×C₂₅₁	SD₁₆	1	2	yes	—
23	C₈×C₂₅₁	—	4	4	no	—
24	C₈×C₂₅₁	C₄²	1	1	yes	characteristic
25	C₈×C₂₅₁	C₂²⋊C₄	1	1	yes	characteristic
26	C₈×C₂₅₁	C₄⋊C₄	1	2	yes	—
27	C₂²×C₂₅₁	—	2	2	no	—
28	C₂²×C₂₅₁	#103	1	2	yes	—
29	C₂²×C₂₅₁	#107	1	1	yes	characteristic
30	C₄×C₂₅₁	#95	1	1	yes	characteristic
31	C₄×C₂₅₁	#102	1	2	yes	—
32	C₄×C₂₅₁	#106	1	1	yes	characteristic
33	C₂×C₂₅₁	—	2	2	no	—
34	C₂×C₂₅₁	#340	1	1	yes	characteristic
35	C₂×C₂₅₁	#368	1	2	yes	—
36	C₂₅₁	#1381	1	1	yes	characteristic, direct product factor, Sylow
37	#1381	C₂₅₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
38	C₂²×C₁₆	C₂×C₂₅₁	1	1	yes	characteristic
39	C₂×#108	C₂×C₂₅₁	1	2	yes	—
40	C₂×M₁₆	—	2	2	no	—
41	C₂²×C₈	C₂²×C₂₅₁	1	1	yes	characteristic
42	C₂×C₁₆	—	2	2	no	—
43	C₂×C₁₆	C₄×C₂₅₁	1	2	yes	—
44	#108	—	2	2	no	—
45	#108	C₄×C₂₅₁	1	4	yes	—
46	C₂²×C₄	D₄×C₂₅₁	1	1	yes	characteristic
47	M₁₆	—	2	4	no	—
48	M₁₆	—	4	2	no	—
49	C₂×C₈	—	4	2	no	—
50	C₂×C₈	C₂×C₄×C₂₅₁	1	1	yes	characteristic
51	C₂×C₈	C₂×C₄×C₂₅₁	1	2	yes	—
52	C₂×C₈	D₄×C₂₅₁	1	2	yes	—
53	C₂×C₈	Q₈×C₂₅₁	1	1	yes	characteristic
54	C₁₆	—	2	2	no	—
55	C₂³	Q₁₆×C₂₅₁	1	1	yes	characteristic
56	C₂×C₄	C₂²⋊C₄×C₂₅₁	1	2	yes	—
57	C₂×C₄	C₄⋊C₄×C₂₅₁	1	1	yes	characteristic
58	C₂×C₄	D₈×C₂₅₁	1	1	yes	characteristic
59	C₂×C₄	SD₁₆×C₂₅₁	1	2	yes	—
60	C₈	—	4	4	no	—
61	C₈	C₄²×C₂₅₁	1	1	yes	characteristic
62	C₈	C₂²⋊C₄×C₂₅₁	1	1	yes	characteristic
63	C₈	C₄⋊C₄×C₂₅₁	1	2	yes	—
64	C₂²	—	2	2	no	—
65	C₂²	#103×C₂₅₁	1	2	yes	—
66	C₂²	#107×C₂₅₁	1	1	yes	characteristic
67	C₄	#95×C₂₅₁	1	1	yes	characteristic
68	C₄	#102×C₂₅₁	1	2	yes	—
69	C₄	#106×C₂₅₁	1	1	yes	characteristic
70	C₂	—	2	2	no	—
71	C₂	#340×C₂₅₁	1	1	yes	characteristic
72	C₂	#368×C₂₅₁	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₂₅₁	D₈
commutator	C₈	C₄²×C₂₅₁
Frattini, cosocle	C₂²×C₈	C₂²×C₂₅₁
socle	C₂²×C₂₅₁	#107
prime radical	C₂³×C₂₅₁	Q₁₆
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₅₁ ◁ C₂²×C₄×C₂₅₁ ◁ C₂²×C₈×C₂₅₁ ◁ G

Complements

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

N	H ≅ G/N	type
36. C₂₅₁	#1381	direct (N × H)
37. #1381	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
C₂²×C₁₆×C₂₅₁	2
C₂×#108×C₂₅₁	2
#1381	251

Subgroups — #1381×C251 #44545968

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #1381×C₂₅₁ #44545968