Group #20241325 — subgroups

Subgroups — #20241325

Order 6016.

112 conjugacy classes of subgroups; only the 33 normal subgroups are shown.

normal subgroups only

This group has 112 conjugacy classes of subgroups — too many to draw. Only its 33 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	#15689091	C₂	1	1	yes	maximal, characteristic
2	#15688905	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₇×#349	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#10625350	C₄	1	1	yes	characteristic
5	C₂²×C₄₇⋊C₈	C₄	1	1	yes	characteristic
6	#13093964	—	2	1	no	—
7	(C₂×D₄₇)⋊C₈	—	2	1	no	—
8	(C₂×D₄₇)⋊C₈	—	2	1	no	—
9	C₂×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
10	M₃₂×C₄₇	—	2	1	no	—
11	C₂²×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
12	C₂×C₂²⋊D₄₇	—	2	1	no	—
13	#10625350	—	4	1	no	—
14	#10625350	—	4	1	no	—
15	C₂×D₁₈₈	C₈	1	1	yes	characteristic
16	C₂×C₄×D₄₇	—	2	1	no	—
17	C₂×Dic₉₄	C₈	1	1	yes	characteristic
18	M₁₆×C₄₇	—	4	1	no	—
19	C₂×C₈×C₄₇	D₄	1	1	yes	characteristic
20	C₂×C₈×C₄₇	D₄	1	1	yes	characteristic
21	C₂×C₄₇⋊C₈	—	2	1	no	—
22	C₂×C₄₇⋊C₈	—	4	1	no	—
23	C₁₆×C₄₇	—	4	1	no	—
24	C₄₇⋊C₁₆	—	4	1	no	—
25	C₂³×C₄₇	M₁₆	1	1	yes	characteristic
26	C₂²×D₄₇	—	2	1	no	—
27	C₂×C₄×C₄₇	—	2	1	no	—
28	C₂×C₄×C₄₇	—	2	1	no	—
29	C₂×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
30	C₂×C₄×C₄₇	C₂×C₈	1	1	yes	characteristic
31	C₂²⋊D₄₇	—	4	2	no	—
32	C₂×Dic₄₇	—	2	1	no	—
33	D₁₈₈	—	4	1	no	—
34	C₄×D₄₇	—	4	1	no	—
35	C₄×D₄₇	—	4	1	no	—
36	Dic₉₄	—	4	1	no	—
37	C₈×C₄₇	—	2	1	no	—
38	C₈×C₄₇	—	2	1	no	—
39	C₄₇⋊C₈	—	4	1	no	—
40	C₂²×C₄₇	—	2	1	no	—
41	C₂²×C₄₇	—	4	1	no	—
42	C₂²×C₄₇	C₂²⋊C₈	1	1	yes	characteristic
43	C₂×D₄₇	—	4	2	no	—
44	C₂×D₄₇	—	4	1	no	—
45	C₄×C₄₇	—	2	1	no	—
46	C₄×C₄₇	#99	1	1	yes	characteristic
47	C₄×C₄₇	#100	1	1	yes	characteristic
48	Dic₄₇	—	4	1	no	—
49	#1321	—	47	1	no	maximal, Sylow
50	C₂×C₄₇	—	2	1	no	—
51	C₂×C₄₇	—	4	1	no	—
52	C₂×C₄₇	#323	1	1	yes	characteristic
53	D₄₇	—	8	1	no	—
54	#408	—	47	1	no	—
55	#349	—	47	1	no	—
56	#349	D₄₇	1	1	yes	characteristic, complemented
57	C₄₇	#1321	1	1	yes	characteristic, complemented, Sylow
58	C₂×#41	—	47	1	no	—
59	C₂×M₁₆	C₂×D₄₇	1	1	yes	characteristic
60	C₂²×C₈	—	47	1	no	—
61	M₃₂	—	2	1	no	—
62	M₃₂	—	94	1	no	—
63	C₂²⋊C₈	—	94	1	no	—
64	C₂²⋊C₈	—	94	1	no	—
65	#41	—	188	1	no	—
66	#41	—	188	1	no	—
67	C₂×Q₈	—	47	1	no	—
68	C₂×D₄	—	47	1	no	—
69	C₂×D₄	—	94	1	no	—
70	C₂²×C₄	—	94	1	no	—
71	C₂²×C₄	C₄×D₄₇	1	1	yes	characteristic
72	M₁₆	—	4	1	no	—
73	C₂×C₈	—	94	1	no	—
74	C₂×C₈	—	188	1	no	—
75	C₂×C₈	D₁₈₈	1	1	yes	characteristic
76	C₂×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
77	C₁₆	—	4	1	no	—
78	C₁₆	—	188	1	no	—
79	C₂³	—	94	1	no	—
80	C₂³	#10625324	1	1	yes	characteristic
81	Q₈	—	188	1	no	—
82	D₄	—	188	1	no	—
83	D₄	—	188	2	no	—
84	C₂×C₄	—	2	1	no	—
85	C₂×C₄	—	2	1	no	—
86	C₂×C₄	—	94	1	no	—
87	C₂×C₄	—	188	1	no	—
88	C₂×C₄	—	188	1	no	—
89	C₂×C₄	C₈×D₄₇	1	1	yes	characteristic
90	C₂×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
91	C₈	—	2	1	no	—
92	C₈	—	2	1	no	—
93	C₈	—	188	1	no	—
94	C₂²	—	2	1	no	—
95	C₂²	—	4	1	no	—
96	C₂²	—	188	2	no	—
97	C₂²	—	188	1	no	—
98	C₂²	(C₂×D₄₇)⋊C₈	1	1	yes	characteristic
99	C₄	—	2	1	no	—
100	C₄	—	188	1	no	—
101	C₄	#13093938	1	1	yes	characteristic
102	C₄	#13093940	1	1	yes	characteristic
103	C₂	—	2	1	no	—
104	C₂	—	4	1	no	—
105	C₂	—	376	1	no	—
106	C₂	#15688846	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#15689091

C₂

yes

maximal, characteristic

#15688905

C₂

yes

maximal, characteristic, complemented

C₄₇×#349

C₂

yes

maximal, characteristic, complemented

C₂×#10625350

C₄

yes

characteristic

C₂²×C₄₇⋊C₈

C₄

yes

characteristic

#13093964

—

(C₂×D₄₇)⋊C₈

—

(C₂×D₄₇)⋊C₈

—

C₂×M₁₆×C₄₇

C₂²

yes

characteristic

M₃₂×C₄₇

—

C₂²×C₄×C₄₇

C₂×C₄

yes

characteristic

C₂×C₂²⋊D₄₇

—

#10625350

—

#10625350

—

C₂×D₁₈₈

C₈

yes

characteristic

C₂×C₄×D₄₇

—

C₂×Dic₉₄

C₈

yes

characteristic

M₁₆×C₄₇

—

C₂×C₈×C₄₇

D₄

yes

characteristic

C₂×C₈×C₄₇

D₄

yes

characteristic

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₁₆×C₄₇

—

C₄₇⋊C₁₆

—

C₂³×C₄₇

M₁₆

yes

characteristic

C₂²×D₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₇

C₂×C₈

yes

characteristic

C₂²⋊D₄₇

—

C₂×Dic₄₇

—

D₁₈₈

—

C₄×D₄₇

—

C₄×D₄₇

—

Dic₉₄

—

C₈×C₄₇

—

C₈×C₄₇

—

C₄₇⋊C₈

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

C₂²⋊C₈

yes

characteristic

C₂×D₄₇

—

C₂×D₄₇

—

C₄×C₄₇

—

C₄×C₄₇

yes

C₄×C₄₇

yes

Dic₄₇

—

#1321

—

maximal, Sylow

C₂×C₄₇

—

C₂×C₄₇

—

C₂×C₄₇

#323

yes

characteristic

D₄₇

—

#408

—

#349

—

#349

D₄₇

yes

characteristic, complemented

C₄₇

#1321

yes

characteristic, complemented, Sylow

C₂×#41

—

C₂×M₁₆

C₂×D₄₇

yes

characteristic

C₂²×C₈

—

M₃₂

—

M₃₂

—

C₂²⋊C₈

—

C₂²⋊C₈

—

#41

—

188

—

#41

—

188

—

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

—

C₂²×C₄

C₄×D₄₇

yes

characteristic

M₁₆

—

C₂×C₈

—

C₂×C₈

—

188

—

C₂×C₈

D₁₈₈

yes

characteristic

C₂×C₈

C₂²⋊D₄₇

yes

characteristic

C₁₆

—

C₁₆

—

188

—

C₂³

—

C₂³

#10625324

yes

characteristic

Q₈

—

188

—

D₄

—

188

—

D₄

—

188

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

188

—

C₂×C₄

—

188

—

C₂×C₄

C₈×D₄₇

yes

characteristic

C₂×C₄

(C₂×D₄₇)⋊C₄

yes

characteristic

C₈

—

C₈

—

C₈

—

188

—

C₂²

—

C₂²

—

C₂²

—

188

—

C₂²

—

188

—

C₂²

(C₂×D₄₇)⋊C₈

yes

characteristic

C₄

—

100

C₄

—

188

—

101

C₄

#13093938

yes

characteristic

102

C₄

#13093940

yes

characteristic

103

C₂

—

104

C₂

—

105

C₂

—

376

—

106

C₂

#15688846

yes

characteristic

	subgroup	G/H
center	C₄	#13093938
commutator	C₂×C₄×C₄₇	C₂×C₈
Frattini	C₂×M₁₆	C₂×D₄₇
Fitting	C₄₇×#349	C₂
socle	C₂×C₄₇	#323
hypercenter	#349	D₄₇
hypocenter	C₄₇	#1321
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×M₁₆ ◁ #349

subgroup

G/H

center

C₄

#13093938

commutator

C₂×C₄×C₄₇

C₂×C₈

Frattini

C₂×M₁₆

C₂×D₄₇

Fitting

C₄₇×#349

C₂

C₂×C₄₇

D₄₇

C₄₇

G ▷ C₂×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×M₁₆ ◁ #349

N	H ≅ G/N	type
2. #15688905	C₂	semidirect
3. C₄₇×#349	C₂	semidirect
56. #349	D₄₇	semidirect
57. C₄₇	#1321	semidirect

H ≅ G/N

type

2. #15688905

C₂

semidirect

3. C₄₇×#349

C₂

semidirect

56. #349

D₄₇

semidirect

57. C₄₇

#1321

semidirect

Subgroups — #20241325

Conjugacy classes of subgroups

Complements