Group #20242467 — subgroups

Subgroups — #20242467

Order 6016.

228 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 57 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	#15689853	C₂	1	1	yes	maximal, characteristic, complemented
2	#15689497	C₂	1	1	yes	maximal, characteristic
3	#15689324	C₂	1	2	yes	maximal
4	#15688853	C₂	1	2	yes	maximal, complemented
5	C₄₇×#333	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#10625325	—	2	2	no	—
7	C₂×#10625336	—	2	2	no	—
8	#13094023	—	2	2	no	—
9	#13094022	—	2	2	no	—
10	#13094021	C₂²	1	1	yes	characteristic
11	C₄×Dic₉₄	C₂²	1	2	yes	—
12	#13093989	—	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×Dic₉₄	—	2	2	no	—
21	C₂×Dic₉₄	D₄	1	2	yes	—
22	C₂×C₈×C₄₇	—	2	2	no	—
23	C₄⋊C₄×C₄₇	—	2	2	no	—
24	C₄²×C₄₇	C₂³	1	1	yes	characteristic
25	#10625336	—	4	4	no	—
26	C₄⋊Dic₄₇	D₄	1	2	yes	—
27	Dic₄₇⋊C₄	—	2	4	no	—
28	Dic₄₇⋊C₄	—	2	2	no	—
29	C₄×Dic₄₇	—	2	2	no	—
30	C₄×Dic₄₇	—	2	2	no	—
31	C₂×C₄₇⋊C₈	—	2	1	no	—
32	#10625325	—	4	4	no	—
33	C₂²×D₄₇	—	4	1	no	—
34	Q₈×C₄₇	—	4	2	no	—
35	C₂×C₄×C₄₇	—	2	2	no	—
36	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
37	C₂×C₄×C₄₇	C₂×D₄	1	2	yes	—
38	C₂×Dic₄₇	—	2	2	no	—
39	C₂×Dic₄₇	—	2	2	no	—
40	D₁₈₈	—	4	2	no	—
41	D₁₈₈	—	4	2	no	—
42	D₁₈₈	—	4	2	no	—
43	Dic₉₄	—	2	2	no	—
44	Dic₉₄	—	8	2	no	—
45	Dic₉₄	SD₁₆	1	4	yes	complemented
46	C₈×C₄₇	—	4	2	no	—
47	C₄₇⋊C₈	—	2	2	no	—
48	C₂²×C₄₇	#120	1	1	yes	characteristic
49	C₂×D₄₇	—	8	2	no	—
50	C₂×D₄₇	—	8	1	no	—
51	C₄×C₄₇	—	2	1	no	—
52	C₄×C₄₇	—	4	2	no	—
53	C₄×C₄₇	C₂×SD₁₆	1	2	yes	—
54	C₄×C₄₇	#137	1	2	yes	—
55	Dic₄₇	—	2	4	no	—
56	Dic₄₇	—	4	2	no	—
57	#1623	—	47	1	no	maximal, Sylow
58	C₂×C₄₇	#448	1	2	yes	—
59	C₂×C₄₇	#453	1	1	yes	characteristic
60	D₄₇	—	16	1	no	—
61	Q₈²	—	47	1	no	—
62	#492	—	47	1	no	—
63	#460	—	47	2	no	—
64	#333	D₄₇	1	1	yes	characteristic, complemented
65	Q₈⋊C₈	—	47	2	no	—
66	C₄₇	#1623	1	1	yes	characteristic, complemented, Sylow
67	C₂×SD₁₆	—	94	2	no	—
68	C₂×SD₁₆	—	94	2	no	—
69	C₄⋊Q₈	—	94	2	no	—
70	C₄⋊Q₈	—	94	2	no	—
71	C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
72	#127	—	47	1	no	—
73	C₄×Q₈	—	47	2	no	—
74	C₄×Q₈	—	94	2	no	—
75	C₄⋊C₈	C₂×D₄₇	1	2	yes	—
76	#102	—	94	2	no	—
77	C₄×C₈	—	47	1	no	—
78	C₂×Q₈	—	47	2	no	—
79	C₂×Q₈	—	94	2	no	—
80	C₂×Q₈	D₁₈₈	1	2	yes	—
81	C₂×D₄	—	94	1	no	—
82	C₂×D₄	—	94	2	no	—
83	SD₁₆	—	188	4	no	—
84	SD₁₆	—	188	4	no	—
85	C₂×C₈	—	2	2	no	—
86	C₂×C₈	—	94	1	no	—
87	C₄⋊C₄	—	2	2	no	—
88	C₄⋊C₄	—	47	2	no	—
89	C₄⋊C₄	—	94	4	no	—
90	C₄⋊C₄	—	94	2	no	—
91	C₄²	—	94	2	no	—
92	C₄²	—	94	2	no	—
93	C₄²	C₂²×D₄₇	1	1	yes	characteristic
94	C₂³	—	188	1	no	—
95	Q₈	—	4	2	no	—
96	Q₈	—	47	4	no	—
97	Q₈	—	94	2	no	—
98	Q₈	—	376	2	no	—
99	D₄	—	188	2	no	—
100	D₄	—	188	2	no	—
101	D₄	—	188	2	no	—
102	C₂×C₄	—	2	2	no	—
103	C₂×C₄	—	94	2	no	—
104	C₂×C₄	—	94	2	no	—
105	C₂×C₄	C₂×D₁₈₈	1	1	yes	characteristic
106	C₂×C₄	D₄×D₄₇	1	2	yes	—
107	C₈	—	4	2	no	—
108	C₈	—	94	2	no	—
109	C₂²	—	376	2	no	—
110	C₂²	—	376	1	no	—
111	C₂²	#13093994	1	1	yes	characteristic
112	C₄	—	2	1	no	—
113	C₄	—	4	2	no	—
114	C₄	—	94	4	no	—
115	C₄	—	188	2	no	—
116	C₄	SD₁₆×D₄₇	1	2	yes	—
117	C₄	#13094056	1	2	yes	—
118	C₂	—	752	1	no	—
119	C₂	#15689263	1	2	yes	—
120	C₂	#15689293	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#15689853

C₂

yes

maximal, characteristic, complemented

#15689497

C₂

yes

maximal, characteristic

#15689324

C₂

yes

maximal

#15688853

C₂

yes

maximal, complemented

C₄₇×#333

C₂

yes

maximal, characteristic, complemented

—

—

—

—

C₂²

yes

characteristic

C₄×Dic₉₄

C₂²

yes

—

#13093989

—

#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×Dic₉₄

—

C₂×Dic₉₄

D₄

yes

—

C₂×C₈×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄²×C₄₇

C₂³

yes

characteristic

#10625336

—

C₄⋊Dic₄₇

D₄

yes

—

Dic₄₇⋊C₄

—

Dic₄₇⋊C₄

—

C₄×Dic₄₇

—

C₄×Dic₄₇

—

C₂×C₄₇⋊C₈

—

#10625325

—

C₂²×D₄₇

—

Q₈×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

C₂×D₄

yes

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

D₁₈₈

—

D₁₈₈

—

D₁₈₈

—

Dic₉₄

—

Dic₉₄

—

Dic₉₄

SD₁₆

yes

complemented

C₈×C₄₇

—

C₄₇⋊C₈

—

C₂²×C₄₇

#120

yes

characteristic

C₂×D₄₇

—

C₂×D₄₇

—

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

C₂×SD₁₆

yes

—

C₄×C₄₇

#137

yes

—

Dic₄₇

—

Dic₄₇

—

#1623

—

maximal, Sylow

C₂×C₄₇

#448

yes

—

C₂×C₄₇

#453

yes

characteristic

D₄₇

—

Q₈²

—

#492

—

#460

—

#333

D₄₇

yes

characteristic, complemented

Q₈⋊C₈

—

C₄₇

#1623

yes

characteristic, complemented, Sylow

C₂×SD₁₆

—

C₂×SD₁₆

—

C₄⋊Q₈

—

C₄⋊Q₈

—

C₄⋊Q₈

C₂×D₄₇

yes

characteristic

#127

—

C₄×Q₈

—

C₄×Q₈

—

C₄⋊C₈

C₂×D₄₇

yes

—

#102

—

C₄×C₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

D₁₈₈

yes

—

C₂×D₄

—

C₂×D₄

—

SD₁₆

—

188

—

SD₁₆

—

188

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₄²

—

C₄²

C₂²×D₄₇

yes

characteristic

C₂³

—

188

—

Q₈

—

Q₈

—

Q₈

—

Q₈

—

376

—

D₄

—

188

—

100

D₄

—

188

—

101

D₄

—

188

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

C₂×D₁₈₈

yes

characteristic

106

C₂×C₄

D₄×D₄₇

yes

—

107

C₈

—

108

C₈

—

109

C₂²

—

376

—

110

C₂²

—

376

—

111

C₂²

#13093994

yes

characteristic

112

C₄

—

113

C₄

—

114

C₄

—

115

C₄

—

188

—

116

C₄

SD₁₆×D₄₇

yes

—

117

C₄

#13094056

yes

—

118

C₂

—

752

—

119

C₂

#15689263

yes

—

120

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	#1623
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. #15689853	C₂	semidirect
4. #15688853	C₂	semidirect
5. C₄₇×#333	C₂	semidirect
45. Dic₉₄	SD₁₆	semidirect
64. #333	D₄₇	semidirect
66. C₄₇	#1623	semidirect

H ≅ G/N

type

1. #15689853

C₂

semidirect

4. #15688853

C₂

semidirect

5. C₄₇×#333

C₂

semidirect

45. Dic₉₄

SD₁₆

semidirect

64. #333

D₄₇

semidirect

66. C₄₇

#1623

semidirect

Subgroups — #20242467

Conjugacy classes of subgroups

Complements