Group #20242472 — subgroups

Subgroups — #20242472

Order 6016.

240 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 53 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	#15689839	C₂	1	1	yes	maximal, characteristic, complemented
2	#15689497	C₂	1	1	yes	maximal, characteristic, complemented
3	#15689319	C₂	1	2	yes	maximal, complemented
4	#15688850	C₂	1	2	yes	maximal, complemented
5	C₄₇×#333	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#10625336	—	2	2	no	—
7	C₂×D₃₇₆	—	2	2	no	—
8	#13094021	C₂²	1	1	yes	characteristic
9	#13094013	—	2	2	no	—
10	#13093999	—	2	2	no	—
11	C₄×D₁₈₈	C₂²	1	2	yes	—
12	#13093982	—	2	2	no	—
13	#13093946	—	2	2	no	—
14	C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
15	C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
16	C₄⋊C₈×C₄₇	C₂²	1	2	yes	—
17	C₂×Q₈×C₄₇	D₄	1	2	yes	—
18	C₂×D₁₈₈	—	2	2	no	—
19	C₂×D₁₈₈	—	2	1	no	—
20	C₂×D₁₈₈	—	2	2	no	—
21	C₂×D₁₈₈	D₄	1	2	yes	—
22	C₂×C₄×D₄₇	—	2	2	no	—
23	C₂×C₈×C₄₇	—	2	2	no	—
24	C₄⋊C₄×C₄₇	—	2	2	no	—
25	C₄²×C₄₇	C₂³	1	1	yes	characteristic
26	#10625336	—	4	4	no	—
27	(C₂×D₄₇)⋊C₄	—	2	4	no	—
28	(C₂×D₄₇)⋊C₄	—	2	2	no	—
29	C₄⋊Dic₄₇	D₄	1	2	yes	—
30	C₄×Dic₄₇	—	2	2	no	—
31	C₂×C₄₇⋊C₈	—	2	1	no	—
32	D₃₇₆	—	4	4	no	—
33	C₂²×D₄₇	—	2	2	no	—
34	C₂²×D₄₇	—	4	1	no	—
35	Q₈×C₄₇	—	4	2	no	—
36	C₂×C₄×C₄₇	—	2	2	no	—
37	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
38	C₂×C₄×C₄₇	C₂×D₄	1	2	yes	—
39	C₂×Dic₄₇	—	2	2	no	—
40	D₁₈₈	—	2	2	no	—
41	D₁₈₈	—	2	2	no	—
42	D₁₈₈	—	4	2	no	—
43	D₁₈₈	—	4	2	no	—
44	D₁₈₈	—	4	2	no	—
45	D₁₈₈	—	8	2	no	—
46	C₄×D₄₇	—	4	2	no	—
47	C₄×D₄₇	—	4	2	no	—
48	C₈×C₄₇	—	4	2	no	—
49	C₄₇⋊C₈	—	2	2	no	—
50	C₂²×C₄₇	#120	1	1	yes	characteristic
51	C₂×D₄₇	—	4	2	no	—
52	C₂×D₄₇	—	4	2	no	—
53	C₂×D₄₇	—	4	2	no	—
54	C₂×D₄₇	—	8	2	no	—
55	C₂×D₄₇	—	8	1	no	—
56	C₄×C₄₇	—	2	1	no	—
57	C₄×C₄₇	—	4	2	no	—
58	C₄×C₄₇	#135	1	2	yes	—
59	C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
60	Dic₄₇	—	4	2	no	—
61	#1624	—	47	1	no	maximal, Sylow
62	C₂×C₄₇	#449	1	2	yes	—
63	C₂×C₄₇	#453	1	1	yes	characteristic
64	D₄₇	—	8	2	no	—
65	D₄₇	—	16	1	no	—
66	#555	—	47	1	no	—
67	#492	—	47	1	no	—
68	#459	—	47	2	no	—
69	#333	D₄₇	1	1	yes	characteristic, complemented
70	D₄⋊C₈	—	47	2	no	—
71	C₄₇	#1624	1	1	yes	characteristic, complemented, Sylow
72	C₂×SD₁₆	—	94	2	no	—
73	C₂×D₈	—	94	2	no	—
74	C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
75	#127	—	47	1	no	—
76	#124	—	94	2	no	—
77	#121	—	94	2	no	—
78	C₄×D₄	—	47	2	no	—
79	#117	—	94	2	no	—
80	C₄⋊C₈	C₂×D₄₇	1	2	yes	—
81	#102	—	94	2	no	—
82	C₄×C₈	—	47	1	no	—
83	C₂×Q₈	D₁₈₈	1	2	yes	—
84	C₂×D₄	—	47	2	no	—
85	C₂×D₄	—	94	2	no	—
86	C₂×D₄	—	94	1	no	—
87	C₂×D₄	—	94	2	no	—
88	C₂²×C₄	—	94	2	no	—
89	SD₁₆	—	188	4	no	—
90	D₈	—	188	4	no	—
91	C₂×C₈	—	2	2	no	—
92	C₂×C₈	—	94	1	no	—
93	C₄⋊C₄	—	2	2	no	—
94	C₄⋊C₄	—	47	2	no	—
95	C₂²⋊C₄	—	94	4	no	—
96	C₂²⋊C₄	—	94	2	no	—
97	C₄²	—	94	2	no	—
98	C₄²	C₂²×D₄₇	1	1	yes	characteristic
99	C₂³	—	94	2	no	—
100	C₂³	—	188	1	no	—
101	Q₈	—	4	2	no	—
102	D₄	—	94	2	no	—
103	D₄	—	94	2	no	—
104	D₄	—	376	2	no	—
105	D₄	—	188	2	no	—
106	D₄	—	188	2	no	—
107	D₄	—	188	2	no	—
108	C₂×C₄	—	2	2	no	—
109	C₂×C₄	—	94	2	no	—
110	C₂×C₄	—	188	2	no	—
111	C₂×C₄	—	188	2	no	—
112	C₂×C₄	C₂×D₁₈₈	1	1	yes	characteristic
113	C₂×C₄	D₄×D₄₇	1	2	yes	—
114	C₈	—	4	2	no	—
115	C₈	—	94	2	no	—
116	C₂²	—	376	2	no	—
117	C₂²	—	376	1	no	—
118	C₂²	—	188	2	no	—
119	C₂²	—	188	2	no	—
120	C₂²	—	188	2	no	—
121	C₂²	#13093994	1	1	yes	characteristic
122	C₄	—	2	1	no	—
123	C₄	—	4	2	no	—
124	C₄	—	188	2	no	—
125	C₄	#13094047	1	2	yes	—
126	C₄	#13094051	1	2	yes	—
127	C₂	—	376	2	no	—
128	C₂	—	752	1	no	—
129	C₂	#15689271	1	2	yes	—
130	C₂	#15689293	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#15689839

C₂

yes

maximal, characteristic, complemented

#15689497

C₂

yes

maximal, characteristic, complemented

#15689319

C₂

yes

maximal, complemented

#15688850

C₂

yes

maximal, complemented

C₄₇×#333

C₂

yes

maximal, characteristic, complemented

C₂×#10625336

—

C₂×D₃₇₆

—

#13094021

C₂²

yes

characteristic

#13094013

—

#13093999

—

C₄×D₁₈₈

C₂²

yes

—

#13093982

—

#13093946

—

C₄×C₄₇⋊C₈

C₂²

yes

characteristic

C₄⋊Q₈×C₄₇

C₂²

yes

characteristic

C₄⋊C₈×C₄₇

C₂²

yes

—

C₂×Q₈×C₄₇

D₄

yes

—

C₂×D₁₈₈

—

C₂×D₁₈₈

—

C₂×D₁₈₈

—

C₂×D₁₈₈

D₄

yes

—

C₂×C₄×D₄₇

—

C₂×C₈×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄²×C₄₇

C₂³

yes

characteristic

#10625336

—

(C₂×D₄₇)⋊C₄

—

(C₂×D₄₇)⋊C₄

—

C₄⋊Dic₄₇

D₄

yes

—

C₄×Dic₄₇

—

C₂×C₄₇⋊C₈

—

D₃₇₆

—

C₂²×D₄₇

—

C₂²×D₄₇

—

Q₈×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

C₂×D₄

yes

—

C₂×Dic₄₇

—

D₁₈₈

—

D₁₈₈

—

D₁₈₈

—

D₁₈₈

—

D₁₈₈

—

D₁₈₈

—

C₄×D₄₇

—

C₄×D₄₇

—

C₈×C₄₇

—

C₄₇⋊C₈

—

C₂²×C₄₇

#120

yes

characteristic

C₂×D₄₇

—

C₂×D₄₇

—

C₂×D₄₇

—

C₂×D₄₇

—

C₂×D₄₇

—

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

#135

yes

—

C₄×C₄₇

AGL(1,ℤ/8)

yes

—

Dic₄₇

—

#1624

—

maximal, Sylow

C₂×C₄₇

#449

yes

—

C₂×C₄₇

#453

yes

characteristic

D₄₇

—

D₄₇

—

—

—

—

D₄₇

yes

characteristic, complemented

D₄⋊C₈

—

C₄₇

#1624

yes

characteristic, complemented, Sylow

C₂×SD₁₆

—

C₂×D₈

—

C₄⋊Q₈

C₂×D₄₇

yes

—

—

—

C₄×D₄

—

#117

—

C₄⋊C₈

C₂×D₄₇

yes

—

#102

—

C₄×C₈

—

C₂×Q₈

D₁₈₈

yes

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

—

SD₁₆

—

188

—

D₈

—

188

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₄²

C₂²×D₄₇

yes

characteristic

C₂³

—

100

C₂³

—

188

—

101

Q₈

—

102

D₄

—

103

D₄

—

104

D₄

—

376

—

105

D₄

—

188

—

106

D₄

—

188

—

107

D₄

—

188

—

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

—

188

—

111

C₂×C₄

—

188

—

112

C₂×C₄

C₂×D₁₈₈

yes

characteristic

113

C₂×C₄

D₄×D₄₇

yes

—

114

C₈

—

115

C₈

—

116

C₂²

—

376

—

117

C₂²

—

376

—

118

C₂²

—

188

—

119

C₂²

—

188

—

120

C₂²

—

188

—

121

C₂²

#13093994

yes

characteristic

122

C₄

—

123

C₄

—

124

C₄

—

188

—

125

C₄

#13094047

yes

—

126

C₄

#13094051

yes

—

127

C₂

—

376

—

128

C₂

—

752

—

129

C₂

#15689271

yes

—

130

C₂

#15689293

yes

characteristic

	subgroup	G/H
center	C₂²	#13093994
commutator	C₄²×C₄₇	C₂³
Frattini	C₄²	C₂²×D₄₇
Fitting	C₄₇×#333	C₂
socle	C₂²×C₄₇	#120
hypercenter	#333	D₄₇
hypocenter	C₄₇	#1624
LCS	G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #333

subgroup

G/H

center

C₂²

#13093994

commutator

C₄²×C₄₇

C₂³

Frattini

C₄²

C₂²×D₄₇

Fitting

C₄₇×#333

C₂

C₂²×C₄₇

D₄₇

C₄₇

G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #333

N	H ≅ G/N	type
1. #15689839	C₂	semidirect
2. #15689497	C₂	semidirect
3. #15689319	C₂	semidirect
4. #15688850	C₂	semidirect
5. C₄₇×#333	C₂	semidirect
69. #333	D₄₇	semidirect
71. C₄₇	#1624	semidirect

H ≅ G/N

type

1. #15689839

C₂

semidirect

2. #15689497

C₂

semidirect

3. #15689319

C₂

semidirect

4. #15688850

C₂

semidirect

5. C₄₇×#333

C₂

semidirect

69. #333

D₄₇

semidirect

71. C₄₇

#1624

semidirect

Subgroups — #20242472

Conjugacy classes of subgroups

Complements