Group #20253897 — subgroups

Subgroups — #20253897

Order 6016.

356 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 356 conjugacy classes of subgroups — too many to draw. Only its 145 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	#15689678	C₂	1	2	yes	maximal
2	#15689526	C₂	1	2	yes	maximal, complemented
3	#15689523	C₂	1	4	yes	maximal, complemented
4	#15689521	C₂	1	1	yes	maximal, characteristic, complemented
5	#15689158	C₂	1	4	yes	maximal
6	C₄×C₈×D₄₇	C₂	1	1	yes	maximal, characteristic
7	C₄₇×#498	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₈×D₄₇	C₂²	1	2	yes	—
9	#13094024	C₂²	1	2	yes	—
10	#13094015	C₂²	1	4	yes	—
11	#13094004	—	2	2	no	—
12	#13094000	—	2	2	no	—
13	Q₈×Dic₄₇	—	2	2	no	—
14	#13093989	—	2	2	no	—
15	#13093982	C₂²	1	4	yes	—
16	C₄²×D₄₇	C₂²	1	1	yes	characteristic
17	#13093957	C₂²	1	8	yes	—
18	#13093956	C₂²	1	4	yes	—
19	C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
20	C₈×Dic₄₇	C₂²	1	2	yes	—
21	C₄⋊Q₈×C₄₇	C₂²	1	2	yes	—
22	#106×C₄₇	C₂²	1	4	yes	—
23	C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
24	C₂×Q₈×C₄₇	—	2	2	no	—
25	C₂×C₄×D₄₇	D₄	1	2	yes	—
26	C₂×C₄×D₄₇	C₂³	1	1	yes	characteristic
27	C₂×Dic₉₄	—	2	2	no	—
28	C₂×C₈×C₄₇	C₂³	1	2	yes	—
29	C₄⋊C₄×C₄₇	—	2	2	no	—
30	C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
31	C₄²×C₄₇	C₂³	1	1	yes	characteristic
32	(C₂×D₄₇)⋊C₄	—	2	4	no	—
33	C₄⋊Dic₄₇	—	2	2	no	—
34	C₄⋊Dic₄₇	—	2	4	no	—
35	C₄⋊Dic₄₇	C₂³	1	4	yes	—
36	Dic₄₇⋊C₄	—	2	4	no	—
37	C₄×Dic₄₇	—	2	4	no	—
38	C₄×Dic₄₇	D₄	1	2	yes	—
39	C₄×Dic₄₇	C₂³	1	1	yes	characteristic
40	C₂×C₄₇⋊C₈	C₂³	1	2	yes	—
41	C₈×D₄₇	Q₈	1	8	yes	complemented
42	C₂²×D₄₇	C₂×D₄	1	1	yes	characteristic
43	Q₈×C₄₇	—	4	4	no	—
44	C₂×C₄×C₄₇	—	2	4	no	—
45	C₂×C₄×C₄₇	C₂×D₄	1	2	yes	—
46	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
47	C₂×Dic₄₇	—	2	4	no	—
48	C₂×Dic₄₇	C₂×D₄	1	2	yes	—
49	C₂×Dic₄₇	C₂×D₄	1	1	yes	characteristic
50	C₄×D₄₇	—	2	4	no	—
51	C₄×D₄₇	C₂×Q₈	1	4	yes	—
52	Dic₉₄	—	4	4	no	—
53	C₈×C₄₇	C₂×Q₈	1	4	yes	—
54	C₄₇⋊C₈	C₂×Q₈	1	4	yes	—
55	C₂²×C₄₇	C₂²×D₄	1	1	yes	characteristic
56	C₂×D₄₇	—	2	2	no	—
57	C₂×D₄₇	C₄⋊Q₈	1	2	yes	—
58	C₄×C₄₇	—	4	4	no	—
59	C₄×C₄₇	#135	1	4	yes	—
60	C₄×C₄₇	C₂²×Q₈	1	2	yes	—
61	Dic₄₇	—	2	2	no	—
62	Dic₄₇	—	4	4	no	—
63	Dic₄₇	C₄⋊Q₈	1	2	yes	—
64	#3160	—	47	1	no	maximal, Sylow
65	C₂×C₄₇	C₂×C₄⋊Q₈	1	1	yes	characteristic
66	C₂×C₄₇	C₂×#135	1	2	yes	—
67	D₄₇	—	2	2	no	—
68	#533	—	47	2	no	—
69	#500	—	47	2	no	—
70	#499	—	47	4	no	—
71	#498	—	47	1	no	—
72	#498	D₄₇	1	1	yes	characteristic, complemented
73	#427	—	47	4	no	—
74	C₂×C₄×C₈	—	47	1	no	—
75	C₄₇	#3160	1	1	yes	characteristic, complemented, Sylow
76	C₂²×C₈	—	47	2	no	—
77	C₄⋊Q₈	—	47	2	no	—
78	C₄⋊Q₈	C₂×D₄₇	1	2	yes	—
79	#125	—	47	4	no	—
80	C₂²⋊Q₈	—	94	2	no	—
81	C₂²⋊Q₈	—	94	2	no	—
82	C₄×Q₈	—	94	2	no	—
83	C₄×Q₈	—	94	2	no	—
84	#117	—	47	4	no	—
85	C₂×C₄²	—	47	1	no	—
86	#107	—	47	8	no	—
87	#106	—	47	4	no	—
88	#106	C₂×D₄₇	1	4	yes	—
89	C₄×C₈	—	47	2	no	—
90	C₄×C₈	—	47	1	no	—
91	C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
92	C₂×Q₈	—	2	2	no	—
93	C₂×Q₈	—	94	2	no	—
94	C₂²×C₄	—	47	1	no	—
95	C₂²×C₄	—	47	2	no	—
96	C₂×C₈	—	47	2	no	—
97	C₂×C₈	—	47	8	no	—
98	C₂×C₈	C₂²×D₄₇	1	2	yes	—
99	C₄⋊C₄	—	2	2	no	—
100	C₄⋊C₄	—	47	4	no	—
101	C₄⋊C₄	—	94	4	no	—
102	C₄⋊C₄	—	94	4	no	—
103	C₄⋊C₄	—	94	2	no	—
104	C₄⋊C₄	C₂²×D₄₇	1	4	yes	—
105	C₂²⋊C₄	—	94	4	no	—
106	C₄²	—	47	2	no	—
107	C₄²	—	47	1	no	—
108	C₄²	—	94	4	no	—
109	C₄²	C₂²×D₄₇	1	1	yes	characteristic
110	C₂³	—	47	1	no	—
111	Q₈	—	4	4	no	—
112	Q₈	—	188	4	no	—
113	C₂×C₄	—	2	4	no	—
114	C₂×C₄	—	47	1	no	—
115	C₂×C₄	—	47	4	no	—
116	C₂×C₄	—	47	2	no	—
117	C₂×C₄	—	94	4	no	—
118	C₂×C₄	—	94	4	no	—
119	C₂×C₄	D₄×D₄₇	1	2	yes	—
120	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
121	C₈	—	47	4	no	—
122	C₈	Q₈×D₄₇	1	4	yes	—
123	C₂²	—	47	2	no	—
124	C₂²	—	94	2	no	—
125	C₂²	C₂×D₄×D₄₇	1	1	yes	characteristic
126	C₄	—	4	4	no	—
127	C₄	—	47	2	no	—
128	C₄	—	94	2	no	—
129	C₄	—	188	4	no	—
130	C₄	#13094045	1	4	yes	—
131	C₄	C₂×Q₈×D₄₇	1	2	yes	—
132	C₂	—	94	2	no	—
133	C₂	C₄⋊Q₈×D₄₇	1	1	yes	characteristic
134	C₂	C₂×#13094045	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#15689678

C₂

yes

maximal

#15689526

C₂

yes

maximal, complemented

#15689523

C₂

yes

maximal, complemented

#15689521

C₂

yes

maximal, characteristic, complemented

#15689158

C₂

yes

maximal

C₄×C₈×D₄₇

C₂

yes

maximal, characteristic

C₄₇×#498

C₂

yes

maximal, characteristic, complemented

C₂×C₈×D₄₇

C₂²

yes

—

#13094024

C₂²

yes

—

#13094015

C₂²

yes

—

#13094004

—

#13094000

—

Q₈×Dic₄₇

—

#13093989

—

#13093982

C₂²

yes

—

C₄²×D₄₇

C₂²

yes

characteristic

#13093957

C₂²

yes

—

#13093956

C₂²

yes

—

C₄×C₄₇⋊C₈

C₂²

yes

characteristic

C₈×Dic₄₇

C₂²

yes

—

C₄⋊Q₈×C₄₇

C₂²

yes

—

#106×C₄₇

C₂²

yes

—

C₄×C₈×C₄₇

C₂²

yes

characteristic

C₂×Q₈×C₄₇

—

C₂×C₄×D₄₇

D₄

yes

—

C₂×C₄×D₄₇

C₂³

yes

characteristic

C₂×Dic₉₄

—

C₂×C₈×C₄₇

C₂³

yes

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

C₂³

yes

—

C₄²×C₄₇

C₂³

yes

characteristic

(C₂×D₄₇)⋊C₄

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

C₂³

yes

—

Dic₄₇⋊C₄

—

C₄×Dic₄₇

—

C₄×Dic₄₇

D₄

yes

—

C₄×Dic₄₇

C₂³

yes

characteristic

C₂×C₄₇⋊C₈

C₂³

yes

—

C₈×D₄₇

Q₈

yes

complemented

C₂²×D₄₇

C₂×D₄

yes

characteristic

Q₈×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂×D₄

yes

—

C₂×C₄×C₄₇

C₂⁴

yes

characteristic

C₂×Dic₄₇

—

C₂×Dic₄₇

C₂×D₄

yes

—

C₂×Dic₄₇

C₂×D₄

yes

characteristic

C₄×D₄₇

—

C₄×D₄₇

C₂×Q₈

yes

—

Dic₉₄

—

C₈×C₄₇

C₂×Q₈

yes

—

C₄₇⋊C₈

C₂×Q₈

yes

—

C₂²×C₄₇

C₂²×D₄

yes

characteristic

C₂×D₄₇

—

C₂×D₄₇

C₄⋊Q₈

yes

—

C₄×C₄₇

—

C₄×C₄₇

#135

yes

—

C₄×C₄₇

C₂²×Q₈

yes

—

Dic₄₇

—

Dic₄₇

—

Dic₄₇

C₄⋊Q₈

yes

—

#3160

—

maximal, Sylow

C₂×C₄₇

C₂×C₄⋊Q₈

yes

characteristic

C₂×C₄₇

C₂×#135

yes

—

D₄₇

—

—

—

—

—

D₄₇

yes

characteristic, complemented

#427

—

C₂×C₄×C₈

—

C₄₇

#3160

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₄⋊Q₈

—

C₄⋊Q₈

C₂×D₄₇

yes

—

#125

—

C₂²⋊Q₈

—

C₂²⋊Q₈

—

C₄×Q₈

—

C₄×Q₈

—

#117

—

C₂×C₄²

—

#107

—

#106

—

#106

C₂×D₄₇

yes

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

C₂×D₄₇

yes

characteristic

C₂×Q₈

—

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂²×D₄₇

yes

—

C₄⋊C₄

—

100

C₄⋊C₄

—

101

C₄⋊C₄

—

102

C₄⋊C₄

—

103

C₄⋊C₄

—

104

C₄⋊C₄

C₂²×D₄₇

yes

—

105

C₂²⋊C₄

—

106

C₄²

—

107

C₄²

—

108

C₄²

—

109

C₄²

C₂²×D₄₇

yes

characteristic

110

C₂³

—

111

Q₈

—

112

Q₈

—

188

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

D₄×D₄₇

yes

—

120

C₂×C₄

C₂³×D₄₇

yes

characteristic

121

C₈

—

122

C₈

Q₈×D₄₇

yes

—

123

C₂²

—

124

C₂²

—

125

C₂²

C₂×D₄×D₄₇

yes

characteristic

126

C₄

—

127

C₄

—

128

C₄

—

129

C₄

—

188

—

130

C₄

#13094045

yes

—

131

C₄

C₂×Q₈×D₄₇

yes

—

132

C₂

—

133

C₂

C₄⋊Q₈×D₄₇

yes

characteristic

134

C₂

C₂×#13094045

yes

—

	subgroup	G/H
center	C₂²	C₂×D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂⁴
Frattini	C₂×C₄	C₂³×D₄₇
Fitting	C₄₇×#498	C₂
socle	C₂²×C₄₇	C₂²×D₄
hypercenter	#498	D₄₇
hypocenter	C₄₇	#3160
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #498

subgroup

G/H

center

C₂²

C₂×D₄×D₄₇

commutator

C₂×C₄×C₄₇

C₂⁴

Frattini

C₂×C₄

C₂³×D₄₇

Fitting

C₄₇×#498

C₂

socle

C₂²×C₄₇

C₂²×D₄

D₄₇

C₄₇

G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #498

N	H ≅ G/N	type
2. #15689526	C₂	semidirect
3. #15689523	C₂	semidirect
4. #15689521	C₂	semidirect
7. C₄₇×#498	C₂	semidirect
41. C₈×D₄₇	Q₈	semidirect
72. #498	D₄₇	semidirect
75. C₄₇	#3160	semidirect

H ≅ G/N

type

2. #15689526

C₂

semidirect

3. #15689523

C₂

semidirect

4. #15689521

C₂

semidirect

7. C₄₇×#498

C₂

semidirect

41. C₈×D₄₇

Q₈

semidirect

72. #498

D₄₇

semidirect

75. C₄₇

#3160

semidirect

Subgroups — #20253897

Conjugacy classes of subgroups

Complements