Group #20242908 — subgroups

Subgroups — #20242908

Order 6016.

154 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 154 conjugacy classes of subgroups — too many to draw. Only its 55 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	#15689410	C₂	1	2	yes	maximal
2	#15689202	C₂	1	1	yes	maximal, characteristic
3	#15688874	C₂	1	1	yes	maximal, characteristic, complemented
4	#15688872	C₂	1	2	yes	maximal, complemented
5	C₄₇×#500	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#10625324	—	2	1	no	—
7	C₄×D₁₈₈	C₂²	1	1	yes	characteristic
8	#13093955	—	2	2	no	—
9	C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
10	C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
11	#13093944	—	2	2	no	—
12	(C₂×D₄₇)⋊C₈	—	2	1	no	—
13	C₄⋊Q₈×C₄₇	C₂²	1	2	yes	—
14	#107×C₄₇	—	2	1	no	—
15	#107×C₄₇	—	2	1	no	—
16	C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
17	C₂×Q₈×C₄₇	—	2	2	no	—
18	C₂×D₁₈₈	D₄	1	1	yes	characteristic
19	C₂×C₄×D₄₇	—	2	1	no	—
20	C₂×C₈×C₄₇	D₄	1	1	yes	characteristic
21	C₂×C₈×C₄₇	D₄	1	1	yes	characteristic
22	C₄⋊C₄×C₄₇	—	2	2	no	—
23	C₄⋊C₄×C₄₇	—	2	2	no	—
24	C₄²×C₄₇	C₂³	1	1	yes	characteristic
25	(C₂×D₄₇)⋊C₄	—	2	1	no	—
26	C₄⋊Dic₄₇	D₄	1	1	yes	characteristic
27	C₂×C₄₇⋊C₈	—	2	1	no	—
28	C₂×C₄₇⋊C₈	—	2	2	no	—
29	#10625324	—	4	2	no	—
30	C₂²×D₄₇	—	2	1	no	—
31	Q₈×C₄₇	—	8	2	no	—
32	C₂×C₄×C₄₇	—	4	2	no	—
33	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
34	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
35	C₂×C₄×C₄₇	#41	1	1	yes	characteristic
36	C₂×Dic₄₇	—	2	1	no	—
37	D₁₈₈	—	2	2	no	—
38	C₄×D₄₇	—	4	1	no	—
39	C₄×D₄₇	—	4	1	no	—
40	C₈×C₄₇	—	2	1	no	—
41	C₈×C₄₇	SD₁₆	1	2	yes	—
42	C₄₇⋊C₈	—	4	1	no	—
43	C₄₇⋊C₈	—	4	2	no	—
44	C₂²×C₄₇	#121	1	1	yes	characteristic
45	C₂×D₄₇	—	4	1	no	—
46	C₂×D₄₇	—	4	1	no	—
47	C₂×D₄₇	—	4	1	no	—
48	C₄×C₄₇	—	2	1	no	—
49	C₄×C₄₇	—	8	2	no	—
50	C₄×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
51	C₄×C₄₇	#137	1	1	yes	characteristic
52	C₄×C₄₇	#137	1	2	yes	—
53	Dic₄₇	—	4	1	no	—
54	#1695	—	47	1	no	maximal, Sylow
55	C₂×C₄₇	#461	1	1	yes	characteristic
56	C₂×C₄₇	#470	1	1	yes	characteristic
57	C₂×C₄₇	#472	1	1	yes	characteristic
58	D₄₇	—	8	1	no	—
59	#500	D₄₇	1	1	yes	characteristic, complemented
60	#476	—	47	2	no	—
61	#436	—	47	1	no	—
62	#334	—	47	1	no	—
63	#333	—	47	2	no	—
64	C₄₇	#1695	1	1	yes	characteristic, complemented, Sylow
65	C₂×M₁₆	—	94	1	no	—
66	C₄⋊Q₈	C₂×D₄₇	1	2	yes	—
67	C₄×D₄	—	47	1	no	—
68	#107	—	2	1	no	—
69	#107	—	2	1	no	—
70	#106	—	94	2	no	—
71	C₄⋊C₈	—	47	1	no	—
72	C₄⋊C₈	—	47	2	no	—
73	#102	—	94	2	no	—
74	C₂²⋊C₈	—	94	1	no	—
75	C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
76	C₂×Q₈	—	2	2	no	—
77	C₂×D₄	—	47	1	no	—
78	C₂²×C₄	—	94	1	no	—
79	M₁₆	—	188	2	no	—
80	C₂×C₈	—	94	2	no	—
81	C₂×C₈	—	94	1	no	—
82	C₂×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
83	C₂×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
84	C₄⋊C₄	—	2	2	no	—
85	C₄⋊C₄	—	2	2	no	—
86	C₄⋊C₄	—	47	1	no	—
87	C₂²⋊C₄	—	94	1	no	—
88	C₄²	C₂²×D₄₇	1	1	yes	characteristic
89	C₂³	—	94	1	no	—
90	Q₈	—	8	2	no	—
91	D₄	—	94	2	no	—
92	C₂×C₄	—	4	2	no	—
93	C₂×C₄	—	94	1	no	—
94	C₂×C₄	—	188	1	no	—
95	C₂×C₄	—	188	1	no	—
96	C₂×C₄	D₄×D₄₇	1	1	yes	characteristic
97	C₂×C₄	#10625352	1	1	yes	characteristic
98	C₂×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
99	C₈	—	2	1	no	—
100	C₈	—	188	1	no	—
101	C₈	—	188	2	no	—
102	C₈	#10625336	1	2	yes	—
103	C₂²	—	188	1	no	—
104	C₂²	—	188	1	no	—
105	C₂²	—	188	1	no	—
106	C₂²	#13093995	1	1	yes	characteristic
107	C₄	—	2	1	no	—
108	C₄	—	8	2	no	—
109	C₄	—	188	1	no	—
110	C₄	C₂×#10625336	1	1	yes	characteristic
111	C₄	#13094055	1	1	yes	characteristic
112	C₄	#13094056	1	2	yes	—
113	C₂	—	376	1	no	—
114	C₂	#15689325	1	1	yes	characteristic
115	C₂	#15689378	1	1	yes	characteristic
116	C₂	#15689390	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#15689410

C₂

yes

maximal

#15689202

C₂

yes

maximal, characteristic

#15688874

C₂

yes

maximal, characteristic, complemented

#15688872

C₂

yes

maximal, complemented

C₄₇×#500

C₂

yes

maximal, characteristic, complemented

C₂×#10625324

—

C₄×D₁₈₈

C₂²

yes

characteristic

#13093955

—

C₄⋊(C₄₇⋊C₈)

C₂²

yes

characteristic

C₄⋊(C₄₇⋊C₈)

C₂²

yes

—

#13093944

—

(C₂×D₄₇)⋊C₈

—

C₄⋊Q₈×C₄₇

C₂²

yes

—

#107×C₄₇

—

#107×C₄₇

—

C₄×C₈×C₄₇

C₂²

yes

characteristic

C₂×Q₈×C₄₇

—

C₂×D₁₈₈

D₄

yes

characteristic

C₂×C₄×D₄₇

—

C₂×C₈×C₄₇

D₄

yes

characteristic

C₂×C₈×C₄₇

D₄

yes

characteristic

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄²×C₄₇

C₂³

yes

characteristic

(C₂×D₄₇)⋊C₄

—

C₄⋊Dic₄₇

D₄

yes

characteristic

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

#10625324

—

C₂²×D₄₇

—

Q₈×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

#41

yes

characteristic

C₂×Dic₄₇

—

D₁₈₈

—

C₄×D₄₇

—

C₄×D₄₇

—

C₈×C₄₇

—

C₈×C₄₇

SD₁₆

yes

—

C₄₇⋊C₈

—

C₄₇⋊C₈

—

C₂²×C₄₇

#121

yes

characteristic

C₂×D₄₇

—

C₂×D₄₇

—

C₂×D₄₇

—

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

C₂×SD₁₆

yes

C₄×C₄₇

yes

C₄×C₄₇

yes

—

Dic₄₇

—

—

C₂×C₄₇

yes

C₂×C₄₇

yes

C₂×C₄₇

yes

D₄₇

—

#500

D₄₇

yes

characteristic, complemented

—

—

—

—

C₄₇

#1695

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₄⋊Q₈

C₂×D₄₇

yes

—

C₄×D₄

—

#107

—

#107

—

#106

—

C₄⋊C₈

—

C₄⋊C₈

—

#102

—

C₂²⋊C₈

—

C₄×C₈

C₂×D₄₇

yes

characteristic

C₂×Q₈

—

C₂×D₄

—

C₂²×C₄

—

M₁₆

—

188

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂²⋊D₄₇

yes

characteristic

C₂×C₈

C₂²⋊D₄₇

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

C₂²×D₄₇

yes

characteristic

C₂³

—

Q₈

—

D₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

188

—

C₂×C₄

—

188

—

C₂×C₄

D₄×D₄₇

yes

characteristic

C₂×C₄

#10625352

yes

characteristic

C₂×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

C₈

—

100

C₈

—

188

—

101

C₈

—

188

—

102

C₈

#10625336

yes

—

103

C₂²

—

188

—

104

C₂²

—

188

—

105

C₂²

—

188

—

106

C₂²

#13093995

yes

characteristic

107

C₄

—

108

C₄

—

109

C₄

—

188

—

110

C₄

C₂×#10625336

yes

characteristic

111

C₄

#13094055

yes

characteristic

112

C₄

#13094056

yes

—

113

C₂

—

376

—

114

C₂

#15689325

yes

characteristic

115

C₂

#15689378

yes

characteristic

116

C₂

#15689390

yes

characteristic

	subgroup	G/H
center	C₂²	#13093995
commutator	C₄²×C₄₇	C₂³
Frattini	C₄²	C₂²×D₄₇
Fitting	C₄₇×#500	C₂
socle	C₂²×C₄₇	#121
hypercenter	#500	D₄₇
hypocenter	C₄₇	#1695
LCS	G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #500

subgroup

G/H

center

C₂²

#13093995

commutator

C₄²×C₄₇

C₂³

Frattini

C₄²

C₂²×D₄₇

Fitting

C₄₇×#500

C₂

C₂²×C₄₇

D₄₇

C₄₇

G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #500

N	H ≅ G/N	type
3. #15688874	C₂	semidirect
4. #15688872	C₂	semidirect
5. C₄₇×#500	C₂	semidirect
59. #500	D₄₇	semidirect
64. C₄₇	#1695	semidirect

H ≅ G/N

type

3. #15688874

C₂

semidirect

4. #15688872

C₂

semidirect

5. C₄₇×#500

C₂

semidirect

59. #500

D₄₇

semidirect

64. C₄₇

#1695

semidirect

Subgroups — #20242908

Conjugacy classes of subgroups

Complements