Group #20242024 — subgroups

Subgroups — #20242024

Order 6016.

194 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 194 conjugacy classes of subgroups — too many to draw. Only its 59 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	#15689679	C₂	1	1	yes	maximal, characteristic
2	#15689178	C₂	1	2	yes	maximal
3	#15688865	C₂	1	1	yes	maximal, characteristic, complemented
4	#15688864	C₂	1	2	yes	maximal, complemented
5	C₄₇×#330	C₂	1	1	yes	maximal, characteristic, complemented
6	#13094023	C₄	1	2	yes	—
7	#13094016	C₂²	1	1	yes	characteristic
8	#13094002	—	2	2	no	—
9	#13093989	—	2	2	no	—
10	#13093982	C₄	1	2	yes	—
11	C₄²×D₄₇	C₂²	1	1	yes	characteristic
12	Dic₄₇⋊C₈	—	2	2	no	—
13	(C₂×D₄₇)⋊C₈	—	2	2	no	—
14	#13093935	C₂²	1	2	yes	—
15	#125×C₄₇	C₂²	1	1	yes	characteristic
16	#97×C₄₇	C₂²	1	2	yes	—
17	C₂×C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
18	C₂×C₄×D₄₇	D₄	1	2	yes	—
19	C₂×Dic₉₄	—	2	2	no	—
20	C₂×C₈×C₄₇	—	2	2	no	—
21	C₄⋊C₄×C₄₇	—	2	2	no	—
22	C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
23	C₄²×C₄₇	C₂³	1	1	yes	characteristic
24	(C₂×D₄₇)⋊C₄	—	2	2	no	—
25	C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
26	Dic₄₇⋊C₄	—	2	2	no	—
27	Dic₄₇⋊C₄	—	2	2	no	—
28	C₄×Dic₄₇	—	2	2	no	—
29	C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
30	C₄×Dic₄₇	D₄	1	2	yes	—
31	C₂×C₄₇⋊C₈	—	2	2	no	—
32	C₂²×D₄₇	C₂²⋊C₄	1	1	yes	characteristic
33	C₂×C₄×C₄₇	—	2	2	no	—
34	C₂×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
35	C₂×C₄×C₄₇	C₂×D₄	1	2	yes	—
36	C₂×Dic₄₇	—	2	2	no	—
37	C₂×Dic₄₇	C₂²⋊C₄	1	2	yes	—
38	C₂×Dic₄₇	C₂²⋊C₄	1	1	yes	characteristic
39	C₄×D₄₇	—	2	2	no	—
40	C₄×D₄₇	—	4	2	no	—
41	Dic₉₄	—	4	4	no	—
42	C₈×C₄₇	—	4	2	no	—
43	C₄₇⋊C₈	—	4	2	no	—
44	C₂²×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
45	C₂×D₄₇	—	2	1	no	—
46	C₂×D₄₇	—	2	2	no	—
47	C₄×C₄₇	—	2	1	no	—
48	C₄×C₄₇	—	2	2	no	—
49	C₄×C₄₇	—	4	2	no	—
50	Dic₄₇	—	2	2	no	—
51	Dic₄₇	—	4	2	no	—
52	Dic₄₇	#101	1	2	yes	—
53	#1537	—	47	1	no	maximal, Sylow
54	C₂×C₄₇	C₂×#101	1	1	yes	characteristic
55	C₂×C₄₇	#421	1	2	yes	—
56	D₄₇	—	4	1	no	—
57	#533	—	47	1	no	—
58	#432	—	47	2	no	—
59	#330	—	47	1	no	—
60	#330	—	47	2	no	—
61	#330	D₄₇	1	1	yes	characteristic, complemented
62	C₄₇	#1537	1	1	yes	characteristic, complemented, Sylow
63	C₄⋊Q₈	—	47	2	no	—
64	#125	—	47	1	no	—
65	#125	C₂×D₄₇	1	1	yes	characteristic
66	C₂²⋊Q₈	—	94	2	no	—
67	C₄×Q₈	—	94	2	no	—
68	#117	—	47	2	no	—
69	C₂×C₄²	—	47	1	no	—
70	C₄⋊C₈	—	94	2	no	—
71	C₂²⋊C₈	—	94	2	no	—
72	#97	—	47	2	no	—
73	#97	C₂×D₄₇	1	2	yes	—
74	C₂×Q₈	—	94	2	no	—
75	C₂²×C₄	—	47	1	no	—
76	C₂²×C₄	—	47	2	no	—
77	C₂×C₈	—	2	2	no	—
78	C₂×C₈	—	94	2	no	—
79	C₄⋊C₄	—	2	2	no	—
80	C₄⋊C₄	—	47	2	no	—
81	C₄⋊C₄	—	94	2	no	—
82	C₄⋊C₄	—	94	2	no	—
83	C₄⋊C₄	C₄×D₄₇	1	2	yes	—
84	C₂²⋊C₄	—	94	2	no	—
85	C₄²	—	47	1	no	—
86	C₄²	—	47	2	no	—
87	C₄²	—	94	2	no	—
88	C₄²	C₂²×D₄₇	1	1	yes	characteristic
89	C₂³	—	47	1	no	—
90	Q₈	—	188	4	no	—
91	C₂×C₄	—	2	2	no	—
92	C₂×C₄	—	47	1	no	—
93	C₂×C₄	—	47	2	no	—
94	C₂×C₄	—	94	2	no	—
95	C₂×C₄	—	94	2	no	—
96	C₂×C₄	—	188	2	no	—
97	C₂×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
98	C₂×C₄	D₄×D₄₇	1	2	yes	—
99	C₈	—	4	2	no	—
100	C₈	—	188	2	no	—
101	C₂²	—	94	1	no	—
102	C₂²	—	94	2	no	—
103	C₂²	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
104	C₄	—	2	1	no	—
105	C₄	—	2	2	no	—
106	C₄	—	4	2	no	—
107	C₄	—	47	2	no	—
108	C₄	—	94	2	no	—
109	C₄	—	188	2	no	—
110	C₂	—	188	1	no	—
111	C₂	#101×D₄₇	1	1	yes	characteristic
112	C₂	#15689138	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#15689679

C₂

yes

maximal, characteristic

#15689178

C₂

yes

maximal

#15688865

C₂

yes

maximal, characteristic, complemented

#15688864

C₂

yes

maximal, complemented

C₄₇×#330

C₂

yes

maximal, characteristic, complemented

#13094023

C₄

yes

—

#13094016

C₂²

yes

—

—

C₄

yes

—

C₄²×D₄₇

C₂²

yes

characteristic

Dic₄₇⋊C₈

—

(C₂×D₄₇)⋊C₈

—

#13093935

C₂²

yes

—

#125×C₄₇

C₂²

yes

characteristic

#97×C₄₇

C₂²

yes

—

C₂×C₄×D₄₇

C₂×C₄

yes

characteristic

C₂×C₄×D₄₇

D₄

yes

—

C₂×Dic₉₄

—

C₂×C₈×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

C₂×C₄

yes

—

C₄²×C₄₇

C₂³

yes

characteristic

(C₂×D₄₇)⋊C₄

—

C₄⋊Dic₄₇

C₂×C₄

yes

—

Dic₄₇⋊C₄

—

Dic₄₇⋊C₄

—

C₄×Dic₄₇

—

C₄×Dic₄₇

C₂×C₄

yes

characteristic

C₄×Dic₄₇

D₄

yes

—

C₂×C₄₇⋊C₈

—

C₂²×D₄₇

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₇

C₂×D₄

yes

—

C₂×Dic₄₇

—

C₂×Dic₄₇

C₂²⋊C₄

yes

—

C₂×Dic₄₇

C₂²⋊C₄

yes

characteristic

C₄×D₄₇

—

C₄×D₄₇

—

Dic₉₄

—

C₈×C₄₇

—

C₄₇⋊C₈

—

C₂²×C₄₇

C₂×C₂²⋊C₄

yes

characteristic

C₂×D₄₇

—

C₂×D₄₇

—

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

—

Dic₄₇

—

Dic₄₇

—

Dic₄₇

#101

yes

—

—

C₂×C₄₇

yes

C₂×C₄₇

yes

—

D₄₇

—

—

—

—

—

D₄₇

yes

characteristic, complemented

C₄₇

#1537

yes

characteristic, complemented, Sylow

C₄⋊Q₈

—

#125

—

#125

C₂×D₄₇

yes

characteristic

C₂²⋊Q₈

—

C₄×Q₈

—

#117

—

C₂×C₄²

—

C₄⋊C₈

—

C₂²⋊C₈

—

#97

—

#97

C₂×D₄₇

yes

—

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

C₄×D₄₇

yes

—

C₂²⋊C₄

—

C₄²

—

C₄²

—

C₄²

—

C₄²

C₂²×D₄₇

yes

characteristic

C₂³

—

Q₈

—

188

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

188

—

C₂×C₄

C₂×C₄×D₄₇

yes

characteristic

C₂×C₄

D₄×D₄₇

yes

—

C₈

—

100

C₈

—

188

—

101

C₂²

—

102

C₂²

—

103

C₂²

C₂²⋊C₄×D₄₇

yes

characteristic

104

C₄

—

105

C₄

—

106

C₄

—

107

C₄

—

108

C₄

—

109

C₄

—

188

—

110

C₂

—

188

—

111

C₂

#101×D₄₇

yes

characteristic

112

C₂

#15689138

yes

—

	subgroup	G/H
center	C₂²	C₂²⋊C₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂²×C₄
Frattini	C₄²	C₂²×D₄₇
Fitting	C₄₇×#330	C₂
socle	C₂²×C₄₇	C₂×C₂²⋊C₄
hypercenter	#330	D₄₇
hypocenter	C₄₇	#1537
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #330

subgroup

G/H

center

C₂²

C₂²⋊C₄×D₄₇

commutator

C₂×C₄×C₄₇

C₂²×C₄

Frattini

C₄²

C₂²×D₄₇

Fitting

C₄₇×#330

C₂

socle

C₂²×C₄₇

C₂×C₂²⋊C₄

D₄₇

C₄₇

G ▷ C₂×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #330

N	H ≅ G/N	type
3. #15688865	C₂	semidirect
4. #15688864	C₂	semidirect
5. C₄₇×#330	C₂	semidirect
61. #330	D₄₇	semidirect
62. C₄₇	#1537	semidirect

H ≅ G/N

type

3. #15688865

C₂

semidirect

4. #15688864

C₂

semidirect

5. C₄₇×#330

C₂

semidirect

61. #330

D₄₇

semidirect

62. C₄₇

#1537

semidirect

Subgroups — #20242024

Conjugacy classes of subgroups

Complements