Group #20248630 — subgroups

Subgroups — #20248630

Order 6016.

380 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 165 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	#15689062	C₂	1	4	yes	maximal
2	#15689022	C₂	1	4	yes	maximal
3	#15688988	C₂	1	4	yes	maximal
4	C₄×C₄⋊Dic₄₇	C₂	1	2	yes	maximal
5	C₄₇×#384	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄⋊Dic₄₇	C₂²	1	2	yes	—
7	C₂×C₄⋊Dic₄₇	C₂²	1	2	yes	—
8	C₂×C₄⋊Dic₄₇	C₂²	1	4	yes	—
9	C₂×C₄×Dic₄₇	C₂²	1	4	yes	—
10	C₄₇⋊#95	C₂²	1	4	yes	—
11	C₄₇⋊#95	C₂²	1	4	yes	—
12	C₄₇⋊#95	C₂²	1	8	yes	—
13	C₂×C₄⋊C₄×C₄₇	C₂²	1	4	yes	—
14	C₂×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
15	C₂×C₄²×C₄₇	C₂²	1	1	yes	characteristic
16	C₂²×C₄×C₄₇	C₂³	1	4	yes	—
17	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
18	C₂²×C₄×C₄₇	C₂³	1	2	yes	—
19	C₂²×Dic₄₇	C₂³	1	4	yes	—
20	C₂²×Dic₄₇	C₂³	1	4	yes	—
21	C₄⋊C₄×C₄₇	—	2	8	no	—
22	C₄⋊C₄×C₄₇	—	4	2	no	—
23	C₄²×C₄₇	Q₈	1	4	yes	—
24	C₄⋊Dic₄₇	—	2	4	no	—
25	C₄⋊Dic₄₇	—	2	4	no	—
26	C₄⋊Dic₄₇	—	4	4	no	—
27	C₄×Dic₄₇	—	2	8	no	—
28	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
29	C₂×C₄×C₄₇	—	2	1	no	—
30	C₂×C₄×C₄₇	—	2	1	no	—
31	C₂×C₄×C₄₇	—	2	8	no	—
32	C₂×C₄×C₄₇	—	2	4	no	—
33	C₂×C₄×C₄₇	C₂×Q₈	1	2	yes	—
34	C₂×C₄×C₄₇	C₂×Q₈	1	4	yes	—
35	C₂×C₄×C₄₇	#41	1	4	yes	—
36	C₂×C₄×C₄₇	#41	1	4	yes	—
37	C₂×Dic₄₇	—	2	4	no	—
38	C₂×Dic₄₇	—	2	4	no	—
39	C₂×Dic₄₇	—	2	4	no	—
40	C₂×Dic₄₇	—	2	4	no	—
41	C₂×Dic₄₇	—	2	4	no	—
42	C₂×Dic₄₇	—	2	4	no	—
43	C₂²×C₄₇	C₂²×Q₈	1	1	yes	characteristic
44	C₂²×C₄₇	C₂×#41	1	2	yes	—
45	C₂²×C₄₇	C₂×#41	1	2	yes	—
46	C₂²×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
47	C₂²×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
48	C₄×C₄₇	—	2	2	no	—
49	C₄×C₄₇	—	4	4	no	—
50	C₄×C₄₇	#125	1	8	yes	—
51	Dic₄₇	—	4	4	no	—
52	Dic₄₇	—	4	4	no	—
53	#2571	—	47	1	no	maximal, Sylow
54	C₂×C₄₇	C₂×#125	1	2	yes	—
55	C₂×C₄₇	#544	1	1	yes	characteristic
56	C₂×C₄₇	#555	1	1	yes	characteristic
57	C₂×C₄₇	#556	1	2	yes	—
58	C₂×C₄₇	#559	1	1	yes	characteristic
59	#400	—	47	4	no	—
60	#389	—	47	4	no	—
61	#384	D₄₇	1	1	yes	characteristic
62	#382	—	47	4	no	—
63	C₄×C₄⋊C₄	—	47	2	no	—
64	C₄₇	#2571	1	1	yes	characteristic, complemented, Sylow
65	C₂×C₄⋊C₄	—	47	2	no	—
66	C₂×C₄⋊C₄	—	47	2	no	—
67	C₂×C₄⋊C₄	—	47	4	no	—
68	C₂×C₄⋊C₄	C₂×D₄₇	1	4	yes	—
69	C₂×C₄⋊C₄	C₂×D₄₇	1	2	yes	—
70	C₂×C₄²	—	47	4	no	—
71	C₂×C₄²	C₂×D₄₇	1	1	yes	characteristic
72	#95	—	47	4	no	—
73	#95	—	47	4	no	—
74	#95	—	47	8	no	—
75	C₂²×C₄	—	47	4	no	—
76	C₂²×C₄	—	47	4	no	—
77	C₂²×C₄	C₂²×D₄₇	1	4	yes	—
78	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
79	C₂²×C₄	C₂²×D₄₇	1	2	yes	—
80	C₄⋊C₄	—	2	8	no	—
81	C₄⋊C₄	—	4	2	no	—
82	C₄⋊C₄	—	94	4	no	—
83	C₄⋊C₄	—	94	4	no	—
84	C₄⋊C₄	—	188	4	no	—
85	C₄²	—	94	8	no	—
86	C₄²	Dic₉₄	1	4	yes	—
87	C₂³	C₂³×D₄₇	1	1	yes	characteristic
88	C₂×C₄	—	2	1	no	—
89	C₂×C₄	—	2	1	no	—
90	C₂×C₄	—	2	8	no	—
91	C₂×C₄	—	2	4	no	—
92	C₂×C₄	—	94	4	no	—
93	C₂×C₄	—	94	4	no	—
94	C₂×C₄	—	94	4	no	—
95	C₂×C₄	—	94	4	no	—
96	C₂×C₄	—	94	4	no	—
97	C₂×C₄	—	94	4	no	—
98	C₂×C₄	C₂×Dic₉₄	1	2	yes	—
99	C₂×C₄	C₂×Dic₉₄	1	4	yes	—
100	C₂×C₄	#10625352	1	4	yes	—
101	C₂×C₄	#10625354	1	4	yes	—
102	C₂²	C₂²×Dic₉₄	1	1	yes	characteristic
103	C₂²	C₂×#10625352	1	2	yes	—
104	C₂²	C₂×#10625354	1	2	yes	—
105	C₂²	#13094069	1	1	yes	characteristic
106	C₂²	#13094072	1	1	yes	characteristic
107	C₄	—	2	2	no	—
108	C₄	—	4	4	no	—
109	C₄	—	188	4	no	—
110	C₄	—	188	4	no	—
111	C₄	#13094015	1	8	yes	—
112	C₂	C₂×#13094015	1	2	yes	—
113	C₂	#15689754	1	1	yes	characteristic
114	C₂	#15689839	1	1	yes	characteristic
115	C₂	#15689847	1	2	yes	—
116	C₂	#15689859	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#15689062

C₂

yes

maximal

#15689022

C₂

yes

maximal

#15688988

C₂

yes

maximal

C₄×C₄⋊Dic₄₇

C₂

yes

maximal

C₄₇×#384

C₂

yes

maximal, characteristic

C₂×C₄⋊Dic₄₇

C₂²

yes

—

C₂×C₄⋊Dic₄₇

C₂²

yes

—

C₂×C₄⋊Dic₄₇

C₂²

yes

—

C₂×C₄×Dic₄₇

C₂²

yes

—

C₄₇⋊#95

C₂²

yes

—

C₄₇⋊#95

C₂²

yes

—

C₄₇⋊#95

C₂²

yes

—

C₂×C₄⋊C₄×C₄₇

C₂²

yes

—

C₂×C₄⋊C₄×C₄₇

C₂²

yes

—

C₂×C₄²×C₄₇

C₂²

yes

characteristic

C₂²×C₄×C₄₇

C₂³

yes

—

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₂²×C₄×C₄₇

C₂³

yes

—

C₂²×Dic₄₇

C₂³

yes

—

C₂²×Dic₄₇

C₂³

yes

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄²×C₄₇

Q₈

yes

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

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×Q₈

yes

—

C₂×C₄×C₄₇

C₂×Q₈

yes

—

C₂×C₄×C₄₇

#41

yes

—

C₂×C₄×C₄₇

#41

yes

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂²×C₄₇

C₂²×Q₈

yes

characteristic

C₂²×C₄₇

C₂×#41

yes

—

C₂²×C₄₇

C₂×#41

yes

—

C₂²×C₄₇

H(5,𝔽₂)

yes

characteristic

C₂²×C₄₇

2₋¹⁺⁴

yes

characteristic

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

#125

yes

—

Dic₄₇

—

Dic₄₇

—

#2571

—

maximal, Sylow

C₂×C₄₇

C₂×#125

yes

—

C₂×C₄₇

yes

C₂×C₄₇

yes

C₂×C₄₇

yes

—

C₂×C₄₇

yes

—

—

D₄₇

yes

characteristic

#382

—

C₄×C₄⋊C₄

—

C₄₇

#2571

yes

characteristic, complemented, Sylow

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₄₇

yes

—

C₂×C₄⋊C₄

C₂×D₄₇

yes

—

C₂×C₄²

—

C₂×C₄²

C₂×D₄₇

yes

—

—

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₄₇

yes

—

C₂²×C₄

C₂²×D₄₇

yes

characteristic

C₂²×C₄

C₂²×D₄₇

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

188

—

C₄²

—

C₄²

Dic₉₄

yes

—

C₂³

C₂³×D₄₇

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×Dic₉₄

yes

—

C₂×C₄

C₂×Dic₉₄

yes

—

100

C₂×C₄

#10625352

yes

—

101

C₂×C₄

#10625354

yes

—

102

C₂²

C₂²×Dic₉₄

yes

characteristic

103

C₂²

C₂×#10625352

yes

—

104

C₂²

C₂×#10625354

yes

—

105

C₂²

#13094069

yes

characteristic

106

C₂²

#13094072

yes

characteristic

107

C₄

—

108

C₄

—

109

C₄

—

188

—

110

C₄

—

188

—

111

C₄

#13094015

yes

—

112

C₂

C₂×#13094015

yes

—

113

C₂

#15689754

yes

characteristic

114

C₂

#15689839

yes

characteristic

115

C₂

#15689847

yes

—

116

C₂

#15689859

yes

characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₄₇
commutator, socle	C₂³×C₄₇	C₂⁴
Fitting	C₄₇×#384	C₂
hypercenter	#384	D₄₇
hypocenter	C₄₇	#2571
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ #384

subgroup

G/H

center, Frattini

C₂³

C₂³×D₄₇

commutator, socle

C₂³×C₄₇

C₂⁴

Fitting

C₄₇×#384

C₂

D₄₇

C₄₇

G ▷ C₂³×C₄₇ ▷ C₄₇

C₁ ◁ C₂³ ◁ #384

N	H ≅ G/N	type
64. C₄₇	#2571	semidirect

H ≅ G/N

type

64. C₄₇

#2571

semidirect

Subgroups — #20248630

Conjugacy classes of subgroups

Complements