Group #26106714 — subgroups

Subgroups — #26106714

Order 12032.

478 conjugacy classes of subgroups; only the 203 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 203 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	C₄×#13093934	C₂	1	3	yes	maximal
2	C₄₇⋊#1273	C₂	1	3	yes	maximal
3	C₄₇×#1273	C₂	1	1	yes	maximal, characteristic
4	C₂×#13093934	C₄	1	6	yes	—
5	C₂×#13093934	C₄	1	6	yes	—
6	C₂×C₄×C₄₇⋊C₈	C₂²	1	3	yes	—
7	C₄²×Dic₄₇	C₂²	1	1	yes	characteristic
8	C₂×C₄×C₈×C₄₇	C₂²	1	3	yes	—
9	C₂²×C₄₇⋊C₈	C₂×C₄	1	6	yes	—
10	C₂×C₄×Dic₄₇	C₂×C₄	1	3	yes	—
11	C₂×C₄×Dic₄₇	C₂×C₄	1	3	yes	—
12	#13093934	—	2	12	no	—
13	#13093934	—	2	12	no	—
14	C₄×C₄₇⋊C₈	—	2	3	no	—
15	C₄×C₄₇⋊C₈	—	2	3	no	—
16	C₂²×C₈×C₄₇	C₂×C₄	1	6	yes	—
17	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
18	C₄×C₈×C₄₇	—	2	6	no	—
19	C₂²×C₄×C₄₇	C₂²×C₄	1	3	yes	—
20	C₂²×Dic₄₇	C₄²	1	1	yes	characteristic
21	C₂²×Dic₄₇	C₄²	1	3	yes	—
22	C₂×C₈×C₄₇	—	2	6	no	—
23	C₂×C₈×C₄₇	—	2	6	no	—
24	C₂×C₈×C₄₇	M₁₆	1	12	yes	—
25	C₄²×C₄₇	#41	1	3	yes	—
26	C₄²×C₄₇	#41	1	1	yes	characteristic
27	C₄×Dic₄₇	—	2	6	no	—
28	C₄×Dic₄₇	—	2	6	no	—
29	C₂×C₄₇⋊C₈	—	2	6	no	—
30	C₂×C₄₇⋊C₈	—	2	6	no	—
31	C₂×C₄₇⋊C₈	M₁₆	1	12	yes	—
32	C₂³×C₄₇	C₂×C₄²	1	1	yes	characteristic
33	C₂×C₄×C₄₇	#117	1	3	yes	—
34	C₂×C₄×C₄₇	#117	1	3	yes	—
35	C₂×C₄×C₄₇	C₂×M₁₆	1	6	yes	—
36	C₂×C₄×C₄₇	C₂×M₁₆	1	6	yes	—
37	C₂×Dic₄₇	—	2	3	no	—
38	C₂×Dic₄₇	—	2	3	no	—
39	C₂×Dic₄₇	—	2	6	no	—
40	C₈×C₄₇	—	2	12	no	—
41	C₄₇⋊C₈	—	2	12	no	—
42	#8136	—	47	1	no	maximal, Sylow
43	C₂²×C₄₇	#376	1	1	yes	characteristic
44	C₂²×C₄₇	C₄×M₁₆	1	3	yes	—
45	C₂²×C₄₇	C₄×M₁₆	1	3	yes	—
46	C₄×C₄₇	#432	1	6	yes	—
47	C₄×C₄₇	#432	1	6	yes	—
48	Dic₄₇	—	4	1	no	—
49	Dic₄₇	—	4	3	no	—
50	C₄×#97	—	47	3	no	—
51	#1273	—	47	3	no	—
52	#1273	D₄₇	1	1	yes	characteristic
53	C₂×C₄₇	#1455	1	1	yes	characteristic
54	C₂×C₄₇	#1455	1	3	yes	—
55	C₂×C₄₇	#1745	1	3	yes	—
56	C₂×#97	—	47	6	no	—
57	C₂×#97	—	47	6	no	—
58	C₂×C₄×C₈	—	47	3	no	—
59	C₂×C₄×C₈	C₂×D₄₇	1	3	yes	—
60	C₄³	—	47	1	no	—
61	C₄₇	#8136	1	1	yes	characteristic, complemented, Sylow
62	C₂²×C₈	—	47	6	no	—
63	C₂²×C₈	C₄×D₄₇	1	6	yes	—
64	C₂×C₄²	—	47	3	no	—
65	C₂×C₄²	—	47	3	no	—
66	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
67	#97	—	94	12	no	—
68	#97	—	94	12	no	—
69	C₄×C₈	—	2	6	no	—
70	C₄×C₈	—	94	3	no	—
71	C₄×C₈	—	94	3	no	—
72	C₂²×C₄	—	47	1	no	—
73	C₂²×C₄	—	47	3	no	—
74	C₂²×C₄	C₂×C₄×D₄₇	1	3	yes	—
75	C₂×C₈	—	2	6	no	—
76	C₂×C₈	—	2	6	no	—
77	C₂×C₈	—	47	12	no	—
78	C₂×C₈	—	94	6	no	—
79	C₂×C₈	—	94	6	no	—
80	C₂×C₈	#10625324	1	12	yes	—
81	C₄²	—	94	6	no	—
82	C₄²	—	94	6	no	—
83	C₄²	#10625352	1	3	yes	—
84	C₄²	#10625354	1	1	yes	characteristic
85	C₂³	C₄²×D₄₇	1	1	yes	characteristic
86	C₂×C₄	—	94	3	no	—
87	C₂×C₄	—	94	3	no	—
88	C₂×C₄	—	94	6	no	—
89	C₂×C₄	#13093980	1	3	yes	—
90	C₂×C₄	#13093982	1	3	yes	—
91	C₂×C₄	M₁₆×D₄₇	1	6	yes	—
92	C₂×C₄	C₂×#10625324	1	6	yes	—
93	C₈	—	2	12	no	—
94	C₈	—	94	12	no	—
95	C₂²	#15688968	1	1	yes	characteristic
96	C₂²	C₄×#10625324	1	3	yes	—
97	C₂²	#15689075	1	3	yes	—
98	C₄	—	188	1	no	—
99	C₄	—	188	3	no	—
100	C₄	#15689177	1	6	yes	—
101	C₄	#15689179	1	6	yes	—
102	C₂	#20241690	1	1	yes	characteristic
103	C₂	#20241692	1	3	yes	—
104	C₂	#20243135	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₄×#13093934

C₂

yes

maximal

C₄₇⋊#1273

C₂

yes

maximal

C₄₇×#1273

C₂

yes

maximal, characteristic

C₂×#13093934

C₄

yes

—

C₂×#13093934

C₄

yes

—

C₂×C₄×C₄₇⋊C₈

C₂²

yes

—

C₄²×Dic₄₇

C₂²

yes

characteristic

C₂×C₄×C₈×C₄₇

C₂²

yes

—

C₂²×C₄₇⋊C₈

C₂×C₄

yes

—

C₂×C₄×Dic₄₇

C₂×C₄

yes

—

C₂×C₄×Dic₄₇

C₂×C₄

yes

—

#13093934

—

#13093934

—

C₄×C₄₇⋊C₈

—

C₄×C₄₇⋊C₈

—

C₂²×C₈×C₄₇

C₂×C₄

yes

—

C₂×C₄²×C₄₇

C₂³

yes

characteristic

C₄×C₈×C₄₇

—

C₂²×C₄×C₄₇

C₂²×C₄

yes

—

C₂²×Dic₄₇

C₄²

yes

characteristic

C₂²×Dic₄₇

C₄²

yes

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

M₁₆

yes

—

C₄²×C₄₇

#41

yes

—

C₄²×C₄₇

#41

yes

characteristic

C₄×Dic₄₇

—

C₄×Dic₄₇

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

M₁₆

yes

—

C₂³×C₄₇

C₂×C₄²

yes

characteristic

C₂×C₄×C₄₇

#117

yes

—

C₂×C₄×C₄₇

#117

yes

—

C₂×C₄×C₄₇

C₂×M₁₆

yes

—

C₂×C₄×C₄₇

C₂×M₁₆

yes

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₈×C₄₇

—

C₄₇⋊C₈

—

—

C₂²×C₄₇

yes

C₂²×C₄₇

C₄×M₁₆

yes

—

C₂²×C₄₇

C₄×M₁₆

yes

—

C₄×C₄₇

#432

yes

—

C₄×C₄₇

#432

yes

—

Dic₄₇

—

Dic₄₇

—

C₄×#97

—

#1273

—

#1273

D₄₇

yes

C₂×C₄₇

yes

C₂×C₄₇

yes

—

C₂×C₄₇

#1745

yes

—

C₂×#97

—

C₂×#97

—

C₂×C₄×C₈

—

C₂×C₄×C₈

C₂×D₄₇

yes

—

C₄³

—

C₄₇

#8136

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂²×C₈

C₄×D₄₇

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂²×D₄₇

yes

characteristic

#97

—

#97

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×C₄×D₄₇

yes

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

#10625324

yes

—

C₄²

—

C₄²

—

C₄²

#10625352

yes

—

C₄²

#10625354

yes

characteristic

C₂³

C₄²×D₄₇

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

#13093980

yes

—

C₂×C₄

#13093982

yes

—

C₂×C₄

M₁₆×D₄₇

yes

—

C₂×C₄

C₂×#10625324

yes

—

C₈

—

C₈

—

C₂²

#15688968

yes

characteristic

C₂²

C₄×#10625324

yes

—

C₂²

#15689075

yes

—

C₄

—

188

—

C₄

—

188

—

100

C₄

#15689177

yes

—

101

C₄

#15689179

yes

—

102

C₂

#20241690

yes

characteristic

103

C₂

#20241692

yes

—

104

C₂

#20243135

yes

—

	subgroup	G/H
center, Frattini	C₂×C₄²	C₂²×D₄₇
commutator, socle, prime radical	C₂³×C₄₇	C₂×C₄²
Fitting	C₄₇×#1273	C₂
cosocle	C₂×C₄²×C₄₇	C₂³
hypercenter	#1273	D₄₇
hypocenter	C₄₇	#8136
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄² ◁ #1273

subgroup

G/H

center, Frattini

C₂×C₄²

C₂²×D₄₇

commutator, socle, prime radical

C₂³×C₄₇

C₂×C₄²

Fitting

C₄₇×#1273

C₂

cosocle

C₂×C₄²×C₄₇

C₂³

D₄₇

C₄₇

G ▷ C₂³×C₄₇ ▷ C₄₇

C₁ ◁ C₂×C₄² ◁ #1273

N	H ≅ G/N	type
61. C₄₇	#8136	semidirect

H ≅ G/N

type

61. C₄₇

#8136

semidirect

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

subgroup	index
C₄×#13093934	2
C₄₇⋊#1273	2
C₄₇×#1273	2
#8136	47

subgroup

index

C₄×#13093934

C₄₇⋊#1273

C₄₇×#1273

#8136

Subgroups — #26106714

Conjugacy classes of subgroups

Complements

Maximal subgroups