Group #20245195 — subgroups

Subgroups — #20245195

Order 6016.

138 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 138 conjugacy classes of subgroups — too many to draw. Only its 85 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⋊(C₄₇⋊C₁₆)	C₂	1	2	yes	maximal, complemented
2	C₂²⋊(C₄₇⋊C₁₆)	C₂	1	2	yes	maximal
3	#15688899	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×C₄₇⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₇×#405	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄₇⋊C₁₆	C₂²	1	2	yes	—
7	C₂×C₄₇⋊C₁₆	C₂²	1	2	yes	—
8	C₂×M₁₆×C₄₇	C₄	1	1	yes	characteristic
9	C₂²×C₈×C₄₇	C₂²	1	1	yes	characteristic
10	#117×C₄₇	C₄	1	1	yes	characteristic
11	#97×C₄₇	C₄	1	1	yes	characteristic
12	#97×C₄₇	C₄	1	1	yes	characteristic
13	C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
14	C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
15	C₂²×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
16	M₁₆×C₄₇	—	2	2	no	—
17	C₂×C₈×C₄₇	—	2	2	no	—
18	C₂×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
19	C₂×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
20	C₂×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
21	C₂×C₈×C₄₇	C₂³	1	1	yes	characteristic
22	C₄⋊C₄×C₄₇	C₈	1	2	yes	—
23	C₂²⋊C₄×C₄₇	C₈	1	2	yes	—
24	C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
25	C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
26	C₄₇⋊C₁₆	—	2	2	no	—
27	C₄₇⋊C₁₆	—	2	2	no	—
28	C₂³×C₄₇	C₂×C₈	1	1	yes	characteristic
29	C₂×C₄×C₄₇	—	2	1	no	—
30	C₂×C₄×C₄₇	—	2	1	no	—
31	C₂×C₄×C₄₇	C₂×C₈	1	2	yes	—
32	C₂×C₄×C₄₇	C₂×C₈	1	2	yes	—
33	C₂×C₄×C₄₇	C₂×C₈	1	1	yes	characteristic
34	C₂×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
35	C₈×C₄₇	—	2	1	no	—
36	C₈×C₄₇	—	2	1	no	—
37	C₈×C₄₇	M₁₆	1	2	yes	—
38	C₈×C₄₇	#41	1	2	yes	—
39	C₂²×C₄₇	—	2	1	no	—
40	C₂²×C₄₇	—	2	2	no	—
41	C₂²×C₄₇	C₂²×C₈	1	1	yes	characteristic
42	C₄×C₄₇	—	2	1	no	—
43	C₄×C₄₇	—	2	2	no	—
44	C₄×C₄₇	—	2	2	no	—
45	C₄×C₄₇	#117	1	1	yes	characteristic
46	C₄×C₄₇	C₂×M₁₆	1	1	yes	characteristic
47	#2164	—	47	1	no	maximal, Sylow
48	C₂×C₄₇	—	4	1	no	—
49	C₂×C₄₇	#431	1	1	yes	characteristic
50	C₂×C₄₇	#504	1	2	yes	—
51	#405	D₄₇	1	1	yes	characteristic
52	C₄⋊C₁₆	—	47	2	no	—
53	C₂²⋊C₁₆	—	47	2	no	—
54	#346	—	47	1	no	—
55	C₄×C₁₆	—	47	1	no	—
56	C₄₇	#2164	1	1	yes	characteristic, complemented, Sylow
57	C₂×M₁₆	Dic₄₇	1	1	yes	characteristic
58	C₂²×C₈	C₂×D₄₇	1	1	yes	characteristic
59	#117	Dic₄₇	1	1	yes	characteristic
60	C₂×C₁₆	—	47	2	no	—
61	C₂×C₁₆	—	47	2	no	—
62	#97	Dic₄₇	1	1	yes	characteristic
63	#97	Dic₄₇	1	1	yes	characteristic
64	C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
65	C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
66	C₂²×C₄	C₂×Dic₄₇	1	1	yes	characteristic
67	M₁₆	—	2	2	no	—
68	C₂×C₈	—	2	2	no	—
69	C₂×C₈	C₂×Dic₄₇	1	1	yes	characteristic
70	C₂×C₈	C₂×Dic₄₇	1	1	yes	characteristic
71	C₂×C₈	C₂×Dic₄₇	1	1	yes	characteristic
72	C₂×C₈	C₂²×D₄₇	1	1	yes	characteristic
73	C₄⋊C₄	C₄₇⋊C₈	1	2	yes	—
74	C₂²⋊C₄	C₄₇⋊C₈	1	2	yes	—
75	C₄²	C₂×Dic₄₇	1	1	yes	characteristic
76	C₄²	C₂×Dic₄₇	1	1	yes	characteristic
77	C₁₆	—	94	2	no	—
78	C₁₆	—	94	2	no	—
79	C₂³	C₂×C₄₇⋊C₈	1	1	yes	characteristic
80	C₂×C₄	—	2	1	no	—
81	C₂×C₄	—	2	1	no	—
82	C₂×C₄	C₂×C₄₇⋊C₈	1	2	yes	—
83	C₂×C₄	C₂×C₄₇⋊C₈	1	2	yes	—
84	C₂×C₄	C₂×C₄₇⋊C₈	1	1	yes	characteristic
85	C₂×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
86	C₈	—	2	1	no	—
87	C₈	—	2	1	no	—
88	C₈	#10625329	1	2	yes	—
89	C₈	#10625350	1	2	yes	—
90	C₂²	—	2	2	no	—
91	C₂²	—	2	1	no	—
92	C₂²	C₂²×C₄₇⋊C₈	1	1	yes	characteristic
93	C₄	—	2	2	no	—
94	C₄	—	2	2	no	—
95	C₄	—	2	1	no	—
96	C₄	#13093983	1	1	yes	characteristic
97	C₄	C₂×#10625329	1	1	yes	characteristic
98	C₂	—	4	1	no	—
99	C₂	#15689176	1	1	yes	characteristic
100	C₂	#15689540	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₄⋊(C₄₇⋊C₁₆)

C₂

yes

maximal, complemented

C₂²⋊(C₄₇⋊C₁₆)

C₂

yes

maximal

#15688899

C₂

yes

maximal, characteristic, complemented

C₄×C₄₇⋊C₁₆

C₂

yes

maximal, characteristic, complemented

C₄₇×#405

C₂

yes

maximal, characteristic

C₂×C₄₇⋊C₁₆

C₂²

yes

—

C₂×C₄₇⋊C₁₆

C₂²

yes

—

C₂×M₁₆×C₄₇

C₄

yes

characteristic

C₂²×C₈×C₄₇

C₂²

yes

characteristic

#117×C₄₇

C₄

yes

characteristic

#97×C₄₇

C₄

yes

characteristic

#97×C₄₇

C₄

yes

characteristic

C₄×C₈×C₄₇

C₂²

yes

characteristic

C₄×C₈×C₄₇

C₂²

yes

characteristic

C₂²×C₄×C₄₇

C₂×C₄

yes

characteristic

M₁₆×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

C₂×C₄

yes

characteristic

C₂×C₈×C₄₇

C₂×C₄

yes

characteristic

C₂×C₈×C₄₇

C₂×C₄

yes

characteristic

C₂×C₈×C₄₇

C₂³

yes

characteristic

C₄⋊C₄×C₄₇

C₈

yes

—

C₂²⋊C₄×C₄₇

C₈

yes

—

C₄²×C₄₇

C₂×C₄

yes

characteristic

C₄²×C₄₇

C₂×C₄

yes

characteristic

C₄₇⋊C₁₆

—

C₄₇⋊C₁₆

—

C₂³×C₄₇

C₂×C₈

yes

characteristic

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂×C₈

yes

—

C₂×C₄×C₄₇

C₂×C₈

yes

—

C₂×C₄×C₄₇

C₂×C₈

yes

characteristic

C₂×C₄×C₄₇

C₂²×C₄

yes

characteristic

C₈×C₄₇

—

C₈×C₄₇

—

C₈×C₄₇

M₁₆

yes

—

C₈×C₄₇

#41

yes

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

C₂²×C₈

yes

characteristic

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

#117

yes

characteristic

C₄×C₄₇

C₂×M₁₆

yes

characteristic

#2164

—

maximal, Sylow

C₂×C₄₇

—

C₂×C₄₇

#431

yes

characteristic

C₂×C₄₇

#504

yes

—

#405

D₄₇

yes

characteristic

C₄⋊C₁₆

—

C₂²⋊C₁₆

—

#346

—

C₄×C₁₆

—

C₄₇

#2164

yes

characteristic, complemented, Sylow

C₂×M₁₆

Dic₄₇

yes

characteristic

C₂²×C₈

C₂×D₄₇

yes

characteristic

#117

Dic₄₇

yes

characteristic

C₂×C₁₆

—

C₂×C₁₆

—

#97

Dic₄₇

yes

characteristic

#97

Dic₄₇

yes

characteristic

C₄×C₈

C₂×D₄₇

yes

characteristic

C₄×C₈

C₂×D₄₇

yes

characteristic

C₂²×C₄

C₂×Dic₄₇

yes

characteristic

M₁₆

—

C₂×C₈

—

C₂×C₈

C₂×Dic₄₇

yes

characteristic

C₂×C₈

C₂×Dic₄₇

yes

characteristic

C₂×C₈

C₂×Dic₄₇

yes

characteristic

C₂×C₈

C₂²×D₄₇

yes

characteristic

C₄⋊C₄

C₄₇⋊C₈

yes

—

C₂²⋊C₄

C₄₇⋊C₈

yes

—

C₄²

C₂×Dic₄₇

yes

characteristic

C₄²

C₂×Dic₄₇

yes

characteristic

C₁₆

—

C₁₆

—

C₂³

C₂×C₄₇⋊C₈

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×C₄₇⋊C₈

yes

—

C₂×C₄

C₂×C₄₇⋊C₈

yes

—

C₂×C₄

C₂×C₄₇⋊C₈

yes

characteristic

C₂×C₄

C₂²×Dic₄₇

yes

characteristic

C₈

—

C₈

—

C₈

#10625329

yes

—

C₈

#10625350

yes

—

C₂²

—

C₂²

—

C₂²

C₂²×C₄₇⋊C₈

yes

characteristic

C₄

—

C₄

—

C₄

—

C₄

yes

C₄

yes

C₂

—

C₂

#15689176

yes

characteristic

100

C₂

#15689540

yes

—

	subgroup	G/H
center, Frattini	C₂×C₈	C₂²×D₄₇
commutator, socle	C₂²×C₄₇	C₂²×C₈
Fitting	C₄₇×#405	C₂
hypercenter	#405	D₄₇
hypocenter	C₄₇	#2164
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₈ ◁ #405

subgroup

G/H

center, Frattini

C₂×C₈

C₂²×D₄₇

commutator, socle

C₂²×C₄₇

C₂²×C₈

Fitting

C₄₇×#405

C₂

D₄₇

C₄₇

G ▷ C₂²×C₄₇ ▷ C₄₇

C₁ ◁ C₂×C₈ ◁ #405

N	H ≅ G/N	type
1. C₄⋊(C₄₇⋊C₁₆)	C₂	semidirect
3. #15688899	C₂	semidirect
4. C₄×C₄₇⋊C₁₆	C₂	semidirect
56. C₄₇	#2164	semidirect

H ≅ G/N

type

1. C₄⋊(C₄₇⋊C₁₆)

C₂

semidirect

3. #15688899

C₂

semidirect

4. C₄×C₄₇⋊C₁₆

C₂

semidirect

56. C₄₇

#2164

semidirect

Subgroups — #20245195

Conjugacy classes of subgroups

Complements