Group #45719183 — subgroups

Subgroups — C₁₃₁×#33299 #45719183

Order 33536.

662 conjugacy classes of subgroups; only the 286 normal subgroups are shown.

normal subgroups only

This group has 662 conjugacy classes of subgroups — too many to draw. Only its 286 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2859×C₁₃₁	C₂	1	2	yes	maximal
2	#1992×C₁₃₁	C₂	1	8	yes	maximal
3	#1835×C₁₃₁	C₂	1	4	yes	maximal
4	C₄×#97×C₁₃₁	C₂	1	1	yes	maximal, characteristic
5	C₂×#125×C₁₃₁	C₂²	1	4	yes	—
6	C₂×#97×C₁₃₁	C₂²	1	4	yes	—
7	C₂×C₄×C₈×C₁₃₁	C₂²	1	2	yes	—
8	#389×C₁₃₁	—	2	8	no	—
9	#384×C₁₃₁	C₂²	1	4	yes	—
10	#382×C₁₃₁	C₂²	1	4	yes	—
11	C₄³×C₁₃₁	C₂²	1	1	yes	characteristic
12	#340×C₁₃₁	C₂²	1	16	yes	—
13	C₂²×C₈×C₁₃₁	C₂³	1	4	yes	—
14	#125×C₁₃₁	—	2	16	no	—
15	C₂×C₄⋊C₄×C₁₃₁	—	2	8	no	—
16	C₂×C₄⋊C₄×C₁₃₁	—	2	8	no	—
17	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	8	yes	—
18	C₂×C₄²×C₁₃₁	D₄	1	4	yes	—
19	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
20	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
21	#97×C₁₃₁	—	2	8	no	—
22	C₄×C₈×C₁₃₁	Q₈	1	8	yes	—
23	#95×C₁₃₁	—	2	8	no	—
24	C₂²×C₄×C₁₃₁	—	2	8	no	—
25	C₂²×C₄×C₁₃₁	C₂×D₄	1	4	yes	—
26	C₂²×C₄×C₁₃₁	C₂×D₄	1	2	yes	—
27	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
28	C₂×C₈×C₁₃₁	—	2	8	no	—
29	C₂×C₈×C₁₃₁	C₂×Q₈	1	8	yes	—
30	C₄⋊C₄×C₁₃₁	—	2	16	no	—
31	C₄⋊C₄×C₁₃₁	—	4	16	no	—
32	C₄⋊C₄×C₁₃₁	—	4	16	no	—
33	C₄²×C₁₃₁	—	4	4	no	—
34	C₄²×C₁₃₁	C₂×Q₈	1	4	yes	—
35	C₄²×C₁₃₁	#41	1	8	yes	—
36	C₂³×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
37	C₂×C₄×C₁₃₁	—	2	8	no	—
38	C₂×C₄×C₁₃₁	—	2	4	no	—
39	C₂×C₄×C₁₃₁	—	4	8	no	—
40	C₂×C₄×C₁₃₁	—	4	16	no	—
41	C₂×C₄×C₁₃₁	#124	1	8	yes	—
42	C₂×C₄×C₁₃₁	C₄⋊Q₈	1	4	yes	—
43	C₂×C₄×C₁₃₁	C₂²×Q₈	1	2	yes	—
44	C₂×C₄×C₁₃₁	C₂×#41	1	4	yes	—
45	C₈×C₁₃₁	—	2	8	no	—
46	C₂²×C₁₃₁	C₂×#124	1	2	yes	—
47	C₂²×C₁₃₁	C₂×C₄⋊Q₈	1	1	yes	characteristic
48	C₂²×C₁₃₁	#575	1	4	yes	—
49	C₄×C₁₃₁	—	2	8	no	—
50	C₄×C₁₃₁	—	2	4	no	—
51	C₄×C₁₃₁	—	8	8	no	—
52	C₄×C₁₃₁	#533	1	4	yes	—
53	C₂×C₁₃₁	#2862	1	1	yes	characteristic
54	C₂×C₁₃₁	#3142	1	4	yes	—
55	C₂×C₁₃₁	#3162	1	2	yes	—
56	#33299	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
57	C₁₃₁	#33299	1	1	yes	characteristic, direct product factor, Sylow
58	#2859	C₂×C₁₃₁	1	2	yes	—
59	#1992	C₂×C₁₃₁	1	8	yes	—
60	#1835	C₂×C₁₃₁	1	4	yes	—
61	C₄×#97	C₂×C₁₃₁	1	1	yes	characteristic
62	C₂×#125	C₂²×C₁₃₁	1	4	yes	—
63	C₂×#97	C₂²×C₁₃₁	1	4	yes	—
64	C₂×C₄×C₈	C₂²×C₁₃₁	1	2	yes	—
65	#389	—	2	8	no	—
66	#384	C₂²×C₁₃₁	1	4	yes	—
67	#382	C₂²×C₁₃₁	1	4	yes	—
68	C₄³	C₂²×C₁₃₁	1	1	yes	characteristic
69	#340	C₂²×C₁₃₁	1	16	yes	—
70	C₂²×C₈	C₂³×C₁₃₁	1	4	yes	—
71	#125	—	2	16	no	—
72	C₂×C₄⋊C₄	—	2	8	no	—
73	C₂×C₄⋊C₄	—	2	8	no	—
74	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	8	yes	—
75	C₂×C₄²	D₄×C₁₃₁	1	4	yes	—
76	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
77	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
78	#97	—	2	8	no	—
79	C₄×C₈	Q₈×C₁₃₁	1	8	yes	—
80	#95	—	2	8	no	—
81	C₂²×C₄	—	2	8	no	—
82	C₂²×C₄	C₂×D₄×C₁₃₁	1	4	yes	—
83	C₂²×C₄	C₂×D₄×C₁₃₁	1	2	yes	—
84	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
85	C₂×C₈	—	2	8	no	—
86	C₂×C₈	C₂×Q₈×C₁₃₁	1	8	yes	—
87	C₄⋊C₄	—	2	16	no	—
88	C₄⋊C₄	—	4	16	no	—
89	C₄⋊C₄	—	4	16	no	—
90	C₄²	—	4	4	no	—
91	C₄²	C₂×Q₈×C₁₃₁	1	4	yes	—
92	C₄²	#41×C₁₃₁	1	8	yes	—
93	C₂³	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
94	C₂×C₄	—	2	8	no	—
95	C₂×C₄	—	2	4	no	—
96	C₂×C₄	—	4	8	no	—
97	C₂×C₄	—	4	16	no	—
98	C₂×C₄	#124×C₁₃₁	1	8	yes	—
99	C₂×C₄	C₄⋊Q₈×C₁₃₁	1	4	yes	—
100	C₂×C₄	C₂²×Q₈×C₁₃₁	1	2	yes	—
101	C₂×C₄	C₂×#41×C₁₃₁	1	4	yes	—
102	C₈	—	2	8	no	—
103	C₂²	C₂×#124×C₁₃₁	1	2	yes	—
104	C₂²	C₂×C₄⋊Q₈×C₁₃₁	1	1	yes	characteristic
105	C₂²	#575×C₁₃₁	1	4	yes	—
106	C₄	—	2	8	no	—
107	C₄	—	2	4	no	—
108	C₄	—	8	8	no	—
109	C₄	#533×C₁₃₁	1	4	yes	—
110	C₂	#2862×C₁₃₁	1	1	yes	characteristic
111	C₂	#3142×C₁₃₁	1	4	yes	—
112	C₂	#3162×C₁₃₁	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#2859×C₁₃₁

C₂

yes

maximal

#1992×C₁₃₁

C₂

yes

maximal

#1835×C₁₃₁

C₂

yes

maximal

C₄×#97×C₁₃₁

C₂

yes

maximal, characteristic

C₂×#125×C₁₃₁

C₂²

yes

—

C₂×#97×C₁₃₁

C₂²

yes

—

C₂×C₄×C₈×C₁₃₁

C₂²

yes

—

#389×C₁₃₁

—

#384×C₁₃₁

C₂²

yes

—

#382×C₁₃₁

C₂²

yes

—

C₄³×C₁₃₁

C₂²

yes

characteristic

#340×C₁₃₁

C₂²

yes

—

C₂²×C₈×C₁₃₁

C₂³

yes

—

#125×C₁₃₁

—

C₂×C₄⋊C₄×C₁₃₁

—

C₂×C₄⋊C₄×C₁₃₁

—

C₂×C₄⋊C₄×C₁₃₁

C₂³

yes

—

C₂×C₄²×C₁₃₁

D₄

yes

—

C₂×C₄²×C₁₃₁

C₂³

yes

characteristic

C₂×C₄²×C₁₃₁

C₂³

yes

—

#97×C₁₃₁

—

C₄×C₈×C₁₃₁

Q₈

yes

—

#95×C₁₃₁

—

C₂²×C₄×C₁₃₁

—

C₂²×C₄×C₁₃₁

C₂×D₄

yes

—

C₂²×C₄×C₁₃₁

C₂×D₄

yes

—

C₂²×C₄×C₁₃₁

C₂⁴

yes

characteristic

C₂×C₈×C₁₃₁

—

C₂×C₈×C₁₃₁

C₂×Q₈

yes

—

C₄⋊C₄×C₁₃₁

—

C₄⋊C₄×C₁₃₁

—

C₄⋊C₄×C₁₃₁

—

C₄²×C₁₃₁

—

C₄²×C₁₃₁

C₂×Q₈

yes

—

C₄²×C₁₃₁

#41

yes

—

C₂³×C₁₃₁

C₂²×D₄

yes

characteristic

C₂×C₄×C₁₃₁

—

C₂×C₄×C₁₃₁

—

C₂×C₄×C₁₃₁

—

C₂×C₄×C₁₃₁

—

C₂×C₄×C₁₃₁

#124

yes

—

C₂×C₄×C₁₃₁

C₄⋊Q₈

yes

—

C₂×C₄×C₁₃₁

C₂²×Q₈

yes

—

C₂×C₄×C₁₃₁

C₂×#41

yes

—

C₈×C₁₃₁

—

C₂²×C₁₃₁

C₂×#124

yes

—

C₂²×C₁₃₁

C₂×C₄⋊Q₈

yes

characteristic

C₂²×C₁₃₁

#575

yes

—

C₄×C₁₃₁

—

C₄×C₁₃₁

—

C₄×C₁₃₁

—

C₄×C₁₃₁

#533

yes

—

C₂×C₁₃₁

#2862

yes

characteristic

C₂×C₁₃₁

#3142

yes

—

C₂×C₁₃₁

#3162

yes

—

#33299

C₁₃₁

yes

maximal, characteristic, direct product factor, Sylow

C₁₃₁

#33299

yes

characteristic, direct product factor, Sylow

#2859

C₂×C₁₃₁

yes

—

#1992

C₂×C₁₃₁

yes

—

#1835

C₂×C₁₃₁

yes

—

C₄×#97

C₂×C₁₃₁

yes

characteristic

C₂×#125

C₂²×C₁₃₁

yes

—

C₂×#97

C₂²×C₁₃₁

yes

—

C₂×C₄×C₈

C₂²×C₁₃₁

yes

—

#389

—

#384

C₂²×C₁₃₁

yes

—

#382

C₂²×C₁₃₁

yes

—

C₄³

C₂²×C₁₃₁

yes

characteristic

#340

C₂²×C₁₃₁

yes

—

C₂²×C₈

C₂³×C₁₃₁

yes

—

#125

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂³×C₁₃₁

yes

—

C₂×C₄²

D₄×C₁₃₁

yes

—

C₂×C₄²

C₂³×C₁₃₁

yes

characteristic

C₂×C₄²

C₂³×C₁₃₁

yes

—

#97

—

C₄×C₈

Q₈×C₁₃₁

yes

—

#95

—

C₂²×C₄

—

C₂²×C₄

C₂×D₄×C₁₃₁

yes

—

C₂²×C₄

C₂×D₄×C₁₃₁

yes

—

C₂²×C₄

C₂⁴×C₁₃₁

yes

characteristic

C₂×C₈

—

C₂×C₈

C₂×Q₈×C₁₃₁

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₄²

C₂×Q₈×C₁₃₁

yes

—

C₄²

#41×C₁₃₁

yes

—

C₂³

C₂²×D₄×C₁₃₁

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

#124×C₁₃₁

yes

—

C₂×C₄

C₄⋊Q₈×C₁₃₁

yes

—

100

C₂×C₄

C₂²×Q₈×C₁₃₁

yes

—

101

C₂×C₄

C₂×#41×C₁₃₁

yes

—

102

C₈

—

103

C₂²

C₂×#124×C₁₃₁

yes

—

104

C₂²

C₂×C₄⋊Q₈×C₁₃₁

yes

characteristic

105

C₂²

#575×C₁₃₁

yes

—

106

C₄

—

107

C₄

—

108

C₄

—

109

C₄

#533×C₁₃₁

yes

—

110

C₂

#2862×C₁₃₁

yes

characteristic

111

C₂

#3142×C₁₃₁

yes

—

112

C₂

#3162×C₁₃₁

yes

—

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₃₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₁
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₁ ◁ C₄³×C₁₃₁ ◁ G

subgroup

G/H

center, socle, prime radical

C₂³×C₁₃₁

C₂²×D₄

commutator, Frattini, cosocle

C₂²×C₄

C₂⁴×C₁₃₁

LCS

G ▷ C₂²×C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂³×C₁₃₁ ◁ C₄³×C₁₃₁ ◁ G

N	H ≅ G/N	type
56. #33299	C₁₃₁	direct (N × H)
57. C₁₃₁	#33299	direct (N × H)

H ≅ G/N

type

56. #33299

C₁₃₁

direct (N × H)

57. C₁₃₁

#33299

direct (N × H)

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

subgroup	index
#2859×C₁₃₁	2
#1992×C₁₃₁	2
#1835×C₁₃₁	2
C₄×#97×C₁₃₁	2
#33299	131

subgroup

index

#2859×C₁₃₁

#1992×C₁₃₁

#1835×C₁₃₁

C₄×#97×C₁₃₁

#33299

131

Subgroups — C₁₃₁×#33299 #45719183

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C131×#33299 #45719183

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#33299 #45719183