Group #20251768 — subgroups

Subgroups — #20251768

Order 6016.

408 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 149 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	#15689027	C₂	1	3	yes	maximal
2	#15689020	C₂	1	3	yes	maximal
3	#15689010	C₂	1	3	yes	maximal
4	#15689006	C₂	1	3	yes	maximal
5	#15688991	C₂	1	1	yes	maximal, characteristic
6	C₄²×Dic₄₇	C₂	1	1	yes	maximal, characteristic
7	C₄₇×#383	C₂	1	1	yes	maximal, characteristic
8	C₂²×Dic₉₄	C₂²	1	1	yes	characteristic
9	C₂×C₄⋊Dic₄₇	C₂²	1	3	yes	—
10	C₂×Dic₄₇⋊C₄	C₂²	1	3	yes	—
11	C₂×Dic₄₇⋊C₄	C₂²	1	3	yes	—
12	C₂×C₄×Dic₄₇	C₂²	1	3	yes	—
13	C₂×C₄×Dic₄₇	C₂²	1	3	yes	—
14	C₄₇⋊#95	C₂²	1	3	yes	—
15	C₄₇⋊#95	C₂²	1	3	yes	—
16	C₄₇⋊#95	C₂²	1	3	yes	—
17	C₄₇⋊#95	C₂²	1	3	yes	—
18	C₂×C₄²×C₄₇	C₂²	1	1	yes	characteristic
19	#95×C₄₇	C₂²	1	3	yes	—
20	#95×C₄₇	C₂²	1	3	yes	—
21	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
22	C₂²×C₄×C₄₇	C₂³	1	3	yes	—
23	C₂²×C₄×C₄₇	C₂³	1	3	yes	—
24	C₂²×Dic₄₇	C₂³	1	1	yes	characteristic
25	C₂²×Dic₄₇	C₂³	1	3	yes	—
26	C₂²×Dic₄₇	C₂³	1	3	yes	—
27	C₂²×Dic₄₇	C₂³	1	1	yes	characteristic
28	C₂×Dic₉₄	—	2	6	no	—
29	C₄²×C₄₇	Q₈	1	4	yes	complemented
30	C₄⋊Dic₄₇	—	2	6	no	—
31	Dic₄₇⋊C₄	—	2	6	no	—
32	Dic₄₇⋊C₄	—	2	6	no	—
33	C₄×Dic₄₇	—	2	6	no	—
34	C₄×Dic₄₇	—	2	6	no	—
35	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
36	C₂×C₄×C₄₇	—	2	3	no	—
37	C₂×C₄×C₄₇	—	2	3	no	—
38	C₂×C₄×C₄₇	—	2	3	no	—
39	C₂×C₄×C₄₇	—	2	3	no	—
40	C₂×C₄×C₄₇	—	2	3	no	—
41	C₂×C₄×C₄₇	—	2	3	no	—
42	C₂×C₄×C₄₇	C₂×Q₈	1	6	yes	—
43	C₂×Dic₄₇	—	2	3	no	—
44	C₂×Dic₄₇	—	2	3	no	—
45	C₂×Dic₄₇	—	2	3	no	—
46	C₂×Dic₄₇	—	2	3	no	—
47	C₂×Dic₄₇	—	2	3	no	—
48	C₂×Dic₄₇	—	2	3	no	—
49	C₂×Dic₄₇	#41	1	6	yes	—
50	C₂×Dic₄₇	#41	1	6	yes	—
51	Dic₉₄	—	4	4	no	—
52	C₂²×C₄₇	C₂²×Q₈	1	1	yes	characteristic
53	C₂²×C₄₇	C₂×#41	1	3	yes	—
54	C₂²×C₄₇	C₂×#41	1	3	yes	—
55	C₄×C₄₇	—	2	6	no	—
56	C₄×C₄₇	—	4	1	no	—
57	C₄×C₄₇	—	4	3	no	—
58	Dic₄₇	—	2	6	no	—
59	Dic₄₇	—	4	1	no	—
60	Dic₄₇	—	4	3	no	—
61	Dic₄₇	#126	1	4	yes	—
62	#2863	—	47	1	no	maximal, Sylow
63	C₂×C₄₇	C₂×#126	1	1	yes	characteristic
64	C₂×C₄₇	#529	1	3	yes	—
65	C₂×C₄₇	#533	1	3	yes	—
66	#391	—	47	3	no	—
67	#389	—	47	3	no	—
68	#387	—	47	3	no	—
69	#387	—	47	3	no	—
70	#383	—	47	1	no	—
71	#383	D₄₇	1	1	yes	characteristic
72	C₄³	—	47	1	no	—
73	C₄₇	#2863	1	1	yes	characteristic, complemented, Sylow
74	C₂²×Q₈	—	47	1	no	—
75	C₂×C₄⋊C₄	—	47	3	no	—
76	C₂×C₄⋊C₄	—	47	3	no	—
77	C₂×C₄⋊C₄	—	47	3	no	—
78	C₂×C₄²	—	47	3	no	—
79	C₂×C₄²	—	47	3	no	—
80	C₂×C₄²	C₂×D₄₇	1	1	yes	characteristic
81	#95	—	47	3	no	—
82	#95	—	47	3	no	—
83	#95	—	47	3	no	—
84	#95	—	47	3	no	—
85	#95	C₂×D₄₇	1	3	yes	—
86	#95	C₂×D₄₇	1	3	yes	—
87	C₂×Q₈	—	94	6	no	—
88	C₂²×C₄	—	47	1	no	—
89	C₂²×C₄	—	47	3	no	—
90	C₂²×C₄	—	47	1	no	—
91	C₂²×C₄	—	47	3	no	—
92	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
93	C₂²×C₄	C₂²×D₄₇	1	3	yes	—
94	C₂²×C₄	C₂²×D₄₇	1	3	yes	—
95	C₄⋊C₄	—	94	6	no	—
96	C₄⋊C₄	—	94	6	no	—
97	C₄⋊C₄	—	94	6	no	—
98	C₄²	—	94	6	no	—
99	C₄²	—	94	6	no	—
100	C₄²	Dic₉₄	1	4	yes	complemented
101	C₂³	C₂³×D₄₇	1	1	yes	characteristic
102	Q₈	—	188	4	no	—
103	C₂×C₄	—	2	3	no	—
104	C₂×C₄	—	2	3	no	—
105	C₂×C₄	—	2	3	no	—
106	C₂×C₄	—	2	3	no	—
107	C₂×C₄	—	2	3	no	—
108	C₂×C₄	—	2	3	no	—
109	C₂×C₄	—	47	6	no	—
110	C₂×C₄	—	47	6	no	—
111	C₂×C₄	—	94	3	no	—
112	C₂×C₄	—	94	3	no	—
113	C₂×C₄	—	94	3	no	—
114	C₂×C₄	—	94	3	no	—
115	C₂×C₄	—	94	3	no	—
116	C₂×C₄	—	94	3	no	—
117	C₂×C₄	C₂×Dic₉₄	1	6	yes	—
118	C₂²	C₂²×Dic₉₄	1	1	yes	characteristic
119	C₂²	#41×D₄₇	1	3	yes	—
120	C₂²	#41×D₄₇	1	3	yes	—
121	C₄	—	2	6	no	—
122	C₄	—	4	1	no	—
123	C₄	—	4	3	no	—
124	C₄	—	47	4	no	—
125	C₄	—	94	6	no	—
126	C₄	—	188	1	no	—
127	C₄	—	188	3	no	—
128	C₂	#126×D₄₇	1	1	yes	characteristic
129	C₂	#15689656	1	3	yes	—
130	C₂	#15689676	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#15689027

C₂

yes

maximal

#15689020

C₂

yes

maximal

#15689010

C₂

yes

maximal

#15689006

C₂

yes

maximal

#15688991

C₂

yes

maximal, characteristic

C₄²×Dic₄₇

C₂

yes

maximal, characteristic

C₄₇×#383

C₂

yes

maximal, characteristic

C₂²×Dic₉₄

C₂²

yes

characteristic

C₂×C₄⋊Dic₄₇

C₂²

yes

—

C₂×Dic₄₇⋊C₄

C₂²

yes

—

C₂×Dic₄₇⋊C₄

C₂²

yes

—

C₂×C₄×Dic₄₇

C₂²

yes

—

C₂×C₄×Dic₄₇

C₂²

yes

—

C₄₇⋊#95

C₂²

yes

—

C₄₇⋊#95

C₂²

yes

—

C₄₇⋊#95

C₂²

yes

—

C₄₇⋊#95

C₂²

yes

—

C₂×C₄²×C₄₇

C₂²

yes

characteristic

#95×C₄₇

C₂²

yes

—

#95×C₄₇

C₂²

yes

—

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₂²×C₄×C₄₇

C₂³

yes

—

C₂²×C₄×C₄₇

C₂³

yes

—

C₂²×Dic₄₇

C₂³

yes

characteristic

C₂²×Dic₄₇

C₂³

yes

—

C₂²×Dic₄₇

C₂³

yes

—

C₂²×Dic₄₇

C₂³

yes

characteristic

C₂×Dic₉₄

—

C₄²×C₄₇

Q₈

yes

complemented

C₄⋊Dic₄₇

—

Dic₄₇⋊C₄

—

Dic₄₇⋊C₄

—

C₄×Dic₄₇

—

C₄×Dic₄₇

—

C₂³×C₄₇

C₂⁴

yes

characteristic

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂×Q₈

yes

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

#41

yes

—

C₂×Dic₄₇

#41

yes

—

Dic₉₄

—

C₂²×C₄₇

C₂²×Q₈

yes

characteristic

C₂²×C₄₇

C₂×#41

yes

—

C₂²×C₄₇

C₂×#41

yes

—

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

—

Dic₄₇

—

Dic₄₇

—

Dic₄₇

—

Dic₄₇

#126

yes

—

—

C₂×C₄₇

yes

C₂×C₄₇

yes

—

C₂×C₄₇

#533

yes

—

—

—

—

—

—

D₄₇

yes

characteristic

C₄³

—

C₄₇

#2863

yes

characteristic, complemented, Sylow

C₂²×Q₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂×D₄₇

yes

—

—

—

—

C₂×D₄₇

yes

—

#95

C₂×D₄₇

yes

—

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₄₇

yes

characteristic

C₂²×C₄

C₂²×D₄₇

yes

—

C₂²×C₄

C₂²×D₄₇

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₄²

—

100

C₄²

Dic₉₄

yes

complemented

101

C₂³

C₂³×D₄₇

yes

characteristic

102

Q₈

—

188

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

C₂×Dic₉₄

yes

—

118

C₂²

C₂²×Dic₉₄

yes

characteristic

119

C₂²

#41×D₄₇

yes

—

120

C₂²

#41×D₄₇

yes

—

121

C₄

—

122

C₄

—

123

C₄

—

124

C₄

—

125

C₄

—

126

C₄

—

188

—

127

C₄

—

188

—

128

C₂

#126×D₄₇

yes

characteristic

129

C₂

#15689656

yes

—

130

C₂

#15689676

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₄₇
commutator, socle	C₂³×C₄₇	C₂⁴
Fitting	C₄₇×#383	C₂
hypercenter	#383	D₄₇
hypocenter	C₄₇	#2863
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ #383

subgroup

G/H

center, Frattini

C₂³

C₂³×D₄₇

commutator, socle

C₂³×C₄₇

C₂⁴

Fitting

C₄₇×#383

C₂

D₄₇

C₄₇

G ▷ C₂³×C₄₇ ▷ C₄₇

C₁ ◁ C₂³ ◁ #383

N	H ≅ G/N	type
29. C₄²×C₄₇	Q₈	semidirect
73. C₄₇	#2863	semidirect
100. C₄²	Dic₉₄	semidirect

H ≅ G/N

type

29. C₄²×C₄₇

Q₈

semidirect

73. C₄₇

#2863

semidirect

100. C₄²

Dic₉₄

semidirect

Subgroups — #20251768

Conjugacy classes of subgroups

Complements