Group #20242301 — subgroups

Subgroups — #20242301

Order 6016.

176 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 63 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×D₃₇₆	C₂	1	1	yes	maximal, characteristic
2	#15689200	C₂	1	2	yes	maximal, complemented
3	#15688850	C₂	1	2	yes	maximal, complemented
4	#15688844	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₇×#334	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₃₇₆	C₄	1	1	yes	characteristic
7	C₂×#10625324	—	2	2	no	—
8	C₄×D₁₈₈	C₂²	1	2	yes	—
9	#13093958	C₄	1	1	yes	characteristic
10	#13093946	C₄	1	2	yes	—
11	(C₂×D₄₇)⋊C₈	—	2	2	no	—
12	C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
13	C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
14	C₄⋊C₈×C₄₇	C₂²	1	2	yes	—
15	C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
16	C₂×D₁₈₈	C₂×C₄	1	2	yes	—
17	C₂×C₄×D₄₇	—	2	2	no	—
18	C₂×C₈×C₄₇	—	2	2	no	—
19	C₂×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
20	C₂×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
21	C₄²×C₄₇	C₂³	1	1	yes	characteristic
22	(C₂×D₄₇)⋊C₄	—	2	2	no	—
23	C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
24	C₂×C₄₇⋊C₈	—	2	1	no	—
25	C₂×C₄₇⋊C₈	D₄	1	2	yes	—
26	D₃₇₆	—	2	2	no	—
27	#10625324	—	4	4	no	—
28	C₂²×D₄₇	—	2	2	no	—
29	C₂×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
30	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
31	C₂×C₄×C₄₇	#41	1	1	yes	characteristic
32	C₂×Dic₄₇	—	2	2	no	—
33	D₁₈₈	—	2	2	no	—
34	D₁₈₈	—	2	2	no	—
35	C₄×D₄₇	—	4	2	no	—
36	C₄×D₄₇	—	4	2	no	—
37	C₈×C₄₇	—	2	1	no	—
38	C₈×C₄₇	—	4	2	no	—
39	C₈×C₄₇	M₁₆	1	2	yes	complemented
40	C₄₇⋊C₈	—	2	2	no	—
41	C₄₇⋊C₈	—	4	1	no	—
42	C₂²×C₄₇	C₄×D₄	1	1	yes	characteristic
43	C₂×D₄₇	—	4	2	no	—
44	C₂×D₄₇	—	4	2	no	—
45	C₂×D₄₇	—	4	2	no	—
46	C₄×C₄₇	—	2	1	no	—
47	C₄×C₄₇	C₂×M₁₆	1	1	yes	characteristic
48	C₄×C₄₇	#131	1	1	yes	characteristic
49	C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
50	Dic₄₇	—	4	2	no	—
51	#1594	—	47	1	no	maximal, Sylow
52	C₂×C₄₇	#436	1	1	yes	characteristic
53	C₂×C₄₇	#442	1	1	yes	characteristic
54	C₂×C₄₇	#444	1	1	yes	characteristic
55	D₄₇	—	8	2	no	—
56	C₄×D₈	—	47	1	no	—
57	#436	—	47	2	no	—
58	#334	D₄₇	1	1	yes	characteristic, complemented
59	D₄⋊C₈	—	47	2	no	—
60	#322	—	47	1	no	—
61	C₄₇	#1594	1	1	yes	characteristic, complemented, Sylow
62	C₂×D₈	—	47	1	no	—
63	C₂×M₁₆	—	94	2	no	—
64	C₄×D₄	—	47	2	no	—
65	#107	—	47	1	no	—
66	C₄⋊C₈	C₂×D₄₇	1	2	yes	—
67	#102	—	47	2	no	—
68	C₂²⋊C₈	—	94	2	no	—
69	C₄×C₈	—	47	1	no	—
70	C₄×C₈	—	47	1	no	—
71	C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
72	C₂×D₄	—	47	2	no	—
73	C₂²×C₄	—	94	2	no	—
74	D₈	—	94	2	no	—
75	M₁₆	—	188	4	no	—
76	C₂×C₈	—	2	2	no	—
77	C₂×C₈	—	47	2	no	—
78	C₂×C₈	—	94	1	no	—
79	C₂×C₈	C₄×D₄₇	1	1	yes	characteristic
80	C₂×C₈	C₄×D₄₇	1	1	yes	characteristic
81	C₄⋊C₄	—	47	2	no	—
82	C₂²⋊C₄	—	94	2	no	—
83	C₄²	C₂²×D₄₇	1	1	yes	characteristic
84	C₂³	—	94	2	no	—
85	D₄	—	94	2	no	—
86	D₄	—	94	2	no	—
87	C₂×C₄	—	94	2	no	—
88	C₂×C₄	—	188	2	no	—
89	C₂×C₄	—	188	2	no	—
90	C₂×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
91	C₂×C₄	D₄×D₄₇	1	1	yes	characteristic
92	C₂×C₄	#10625354	1	1	yes	characteristic
93	C₈	—	2	1	no	—
94	C₈	—	4	2	no	—
95	C₈	—	94	2	no	—
96	C₈	—	188	1	no	—
97	C₈	#10625324	1	2	yes	complemented
98	C₂²	—	188	2	no	—
99	C₂²	—	188	2	no	—
100	C₂²	—	188	2	no	—
101	C₂²	#13093986	1	1	yes	characteristic
102	C₄	—	2	1	no	—
103	C₄	—	188	2	no	—
104	C₄	C₂×#10625324	1	1	yes	characteristic
105	C₄	#13094032	1	1	yes	characteristic
106	C₄	#13094051	1	2	yes	—
107	C₂	—	376	2	no	—
108	C₂	#15689200	1	1	yes	characteristic
109	C₂	#15689234	1	1	yes	characteristic
110	C₂	#15689244	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₄×D₃₇₆

C₂

yes

maximal, characteristic

#15689200

C₂

yes

maximal, complemented

#15688850

C₂

yes

maximal, complemented

#15688844

C₂

yes

maximal, characteristic, complemented

C₄₇×#334

C₂

yes

maximal, characteristic, complemented

C₂×D₃₇₆

C₄

yes

characteristic

C₂×#10625324

—

C₄×D₁₈₈

C₂²

yes

—

#13093958

C₄

yes

characteristic

#13093946

C₄

yes

—

(C₂×D₄₇)⋊C₈

—

C₄×C₄₇⋊C₈

C₂²

yes

characteristic

C₄×C₄₇⋊C₈

C₂²

yes

characteristic

C₄⋊C₈×C₄₇

C₂²

yes

—

C₄×C₈×C₄₇

C₂²

yes

characteristic

C₂×D₁₈₈

C₂×C₄

yes

—

C₂×C₄×D₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

C₂×C₄

yes

characteristic

C₂×C₈×C₄₇

C₂×C₄

yes

characteristic

C₄²×C₄₇

C₂³

yes

characteristic

(C₂×D₄₇)⋊C₄

—

C₄⋊Dic₄₇

C₂×C₄

yes

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

D₄

yes

—

D₃₇₆

—

#10625324

—

C₂²×D₄₇

—

C₂×C₄×C₄₇

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

#41

yes

characteristic

C₂×Dic₄₇

—

D₁₈₈

—

D₁₈₈

—

C₄×D₄₇

—

C₄×D₄₇

—

C₈×C₄₇

—

C₈×C₄₇

—

C₈×C₄₇

M₁₆

yes

complemented

C₄₇⋊C₈

—

C₄₇⋊C₈

—

C₂²×C₄₇

C₄×D₄

yes

characteristic

C₂×D₄₇

—

C₂×D₄₇

—

C₂×D₄₇

—

C₄×C₄₇

—

C₄×C₄₇

C₂×M₁₆

yes

C₄×C₄₇

yes

C₄×C₄₇

yes

—

Dic₄₇

—

—

C₂×C₄₇

yes

C₂×C₄₇

yes

C₂×C₄₇

yes

D₄₇

—

C₄×D₈

—

#436

—

#334

D₄₇

yes

characteristic, complemented

D₄⋊C₈

—

#322

—

C₄₇

#1594

yes

characteristic, complemented, Sylow

C₂×D₈

—

C₂×M₁₆

—

C₄×D₄

—

#107

—

C₄⋊C₈

C₂×D₄₇

yes

—

#102

—

C₂²⋊C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

C₂×D₄₇

yes

characteristic

C₂×D₄

—

C₂²×C₄

—

D₈

—

M₁₆

—

188

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄×D₄₇

yes

characteristic

C₂×C₈

C₄×D₄₇

yes

characteristic

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

C₂²×D₄₇

yes

characteristic

C₂³

—

D₄

—

D₄

—

C₂×C₄

—

C₂×C₄

—

188

—

C₂×C₄

—

188

—

C₂×C₄

C₂×C₄×D₄₇

yes

characteristic

C₂×C₄

D₄×D₄₇

yes

characteristic

C₂×C₄

#10625354

yes

characteristic

C₈

—

C₈

—

C₈

—

C₈

—

188

—

C₈

#10625324

yes

complemented

C₂²

—

188

—

C₂²

—

188

—

100

C₂²

—

188

—

101

C₂²

#13093986

yes

characteristic

102

C₄

—

103

C₄

—

188

—

104

C₄

C₂×#10625324

yes

characteristic

105

C₄

#13094032

yes

characteristic

106

C₄

#13094051

yes

—

107

C₂

—

376

—

108

C₂

#15689200

yes

characteristic

109

C₂

#15689234

yes

characteristic

110

C₂

#15689244

yes

characteristic

	subgroup	G/H
center	C₂×C₄	D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂²×C₄
Frattini	C₄²	C₂²×D₄₇
Fitting	C₄₇×#334	C₂
socle	C₂²×C₄₇	C₄×D₄
hypercenter	#334	D₄₇
hypocenter	C₄₇	#1594
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ #334

subgroup

G/H

center

C₂×C₄

D₄×D₄₇

commutator

C₂×C₄×C₄₇

C₂²×C₄

Frattini

C₄²

C₂²×D₄₇

Fitting

C₄₇×#334

C₂

socle

C₂²×C₄₇

C₄×D₄

D₄₇

C₄₇

G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂×C₄ ◁ C₄² ◁ #334

N	H ≅ G/N	type
2. #15689200	C₂	semidirect
3. #15688850	C₂	semidirect
4. #15688844	C₂	semidirect
5. C₄₇×#334	C₂	semidirect
39. C₈×C₄₇	M₁₆	semidirect
58. #334	D₄₇	semidirect
61. C₄₇	#1594	semidirect
97. C₈	#10625324	semidirect

H ≅ G/N

type

2. #15689200

C₂

semidirect

3. #15688850

C₂

semidirect

4. #15688844

C₂

semidirect

5. C₄₇×#334

C₂

semidirect

39. C₈×C₄₇

M₁₆

semidirect

58. #334

D₄₇

semidirect

61. C₄₇

#1594

semidirect

97. C₈

#10625324

semidirect

Subgroups — #20242301

Conjugacy classes of subgroups

Complements