Group #20242112 — subgroups

Subgroups — #20242112

Order 6016.

228 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 67 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	C₄⋊Q₈×D₄₇	C₂	1	1	yes	maximal, characteristic
2	#15689179	C₂	1	2	yes	maximal
3	#15688872	C₂	1	1	yes	maximal, characteristic, complemented
4	#15688871	C₂	1	2	yes	maximal, complemented
5	C₄₇×#333	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×Q₈×D₄₇	C₄	1	2	yes	—
7	#13094024	C₂²	1	1	yes	characteristic
8	#13094023	—	2	2	no	—
9	#13094022	C₄	1	2	yes	—
10	C₄⋊C₄×D₄₇	—	2	2	no	—
11	C₄²×D₄₇	C₂²	1	1	yes	characteristic
12	C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
13	(C₂×D₄₇)⋊C₈	—	2	2	no	—
14	#13093934	—	2	2	no	—
15	C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
16	C₄⋊C₈×C₄₇	C₂²	1	2	yes	—
17	C₂×Q₈×C₄₇	C₂×C₄	1	2	yes	—
18	Q₈×D₄₇	—	4	4	no	—
19	C₂×C₄×D₄₇	—	2	2	no	—
20	C₂×C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
21	C₂×C₄×D₄₇	D₄	1	2	yes	—
22	C₂×Dic₉₄	—	2	2	no	—
23	C₂×Dic₉₄	C₂×C₄	1	2	yes	—
24	C₂×C₈×C₄₇	—	2	2	no	—
25	C₄⋊C₄×C₄₇	—	2	2	no	—
26	C₄²×C₄₇	C₂³	1	1	yes	characteristic
27	C₄⋊Dic₄₇	—	2	2	no	—
28	Dic₄₇⋊C₄	—	2	4	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	Q₈×C₄₇	—	4	2	no	—
34	C₂×C₄×C₄₇	—	2	2	no	—
35	C₂×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
36	C₂×C₄×C₄₇	C₂×D₄	1	2	yes	—
37	C₂×Dic₄₇	—	2	2	no	—
38	C₂×Dic₄₇	C₂²⋊C₄	1	2	yes	—
39	C₂×Dic₄₇	C₂²⋊C₄	1	1	yes	characteristic
40	C₄×D₄₇	—	2	2	no	—
41	C₄×D₄₇	—	2	2	no	—
42	C₄×D₄₇	—	2	2	no	—
43	C₄×D₄₇	—	4	4	no	—
44	Dic₉₄	—	4	4	no	—
45	Dic₉₄	—	4	2	no	—
46	C₈×C₄₇	—	4	2	no	—
47	C₄₇⋊C₈	—	4	2	no	—
48	C₂²×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
49	C₂×D₄₇	—	2	2	no	—
50	C₂×D₄₇	#100	1	2	yes	—
51	C₄×C₄₇	—	2	1	no	—
52	C₄×C₄₇	—	4	2	no	—
53	C₄×C₄₇	#137	1	2	yes	—
54	C₄×C₄₇	#137	1	2	yes	—
55	Dic₄₇	—	2	1	no	—
56	Dic₄₇	—	2	2	no	—
57	Dic₄₇	—	4	2	no	—
58	#1558	—	47	1	no	maximal, Sylow
59	C₂×C₄₇	C₂×#100	1	1	yes	characteristic
60	C₂×C₄₇	#419	1	2	yes	—
61	D₄₇	—	2	2	no	—
62	C₂×C₄⋊Q₈	—	47	1	no	—
63	#432	—	47	2	no	—
64	#333	—	47	1	no	—
65	#333	—	47	2	no	—
66	#333	D₄₇	1	1	yes	characteristic, complemented
67	C₄₇	#1558	1	1	yes	characteristic, complemented, Sylow
68	C₂²×Q₈	—	47	2	no	—
69	C₄⋊Q₈	—	47	2	no	—
70	C₄⋊Q₈	—	47	1	no	—
71	C₄⋊Q₈	—	94	2	no	—
72	C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
73	C₂×C₄⋊C₄	—	94	2	no	—
74	C₂×C₄²	—	47	1	no	—
75	C₄⋊C₈	—	47	2	no	—
76	C₄⋊C₈	C₂×D₄₇	1	2	yes	—
77	C₂²⋊C₈	—	94	2	no	—
78	#97	—	94	2	no	—
79	C₂×Q₈	—	47	2	no	—
80	C₂×Q₈	—	94	2	no	—
81	C₂×Q₈	—	188	4	no	—
82	C₂×Q₈	C₄×D₄₇	1	2	yes	—
83	C₂²×C₄	—	47	1	no	—
84	C₂²×C₄	—	47	2	no	—
85	C₂²×C₄	—	94	2	no	—
86	C₂×C₈	—	2	2	no	—
87	C₂×C₈	—	94	2	no	—
88	C₄⋊C₄	—	2	2	no	—
89	C₄⋊C₄	—	94	4	no	—
90	C₄⋊C₄	—	94	2	no	—
91	C₄²	—	47	1	no	—
92	C₄²	—	47	2	no	—
93	C₄²	C₂²×D₄₇	1	1	yes	characteristic
94	C₂³	—	47	1	no	—
95	Q₈	—	4	2	no	—
96	Q₈	—	188	2	no	—
97	Q₈	—	188	4	no	—
98	C₂×C₄	—	2	2	no	—
99	C₂×C₄	—	47	2	no	—
100	C₂×C₄	—	47	1	no	—
101	C₂×C₄	—	94	2	no	—
102	C₂×C₄	—	94	2	no	—
103	C₂×C₄	—	94	2	no	—
104	C₂×C₄	—	94	2	no	—
105	C₂×C₄	—	188	4	no	—
106	C₂×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
107	C₂×C₄	D₄×D₄₇	1	2	yes	—
108	C₈	—	4	2	no	—
109	C₈	—	188	2	no	—
110	C₂²	—	47	2	no	—
111	C₂²	—	94	2	no	—
112	C₂²	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
113	C₄	—	2	1	no	—
114	C₄	—	4	2	no	—
115	C₄	—	94	1	no	—
116	C₄	—	94	2	no	—
117	C₄	—	188	2	no	—
118	C₄	#13094053	1	2	yes	—
119	C₄	#13094056	1	2	yes	—
120	C₂	—	94	2	no	—
121	C₂	#100×D₄₇	1	1	yes	characteristic
122	C₂	#15689130	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₄⋊Q₈×D₄₇

C₂

yes

maximal, characteristic

#15689179

C₂

yes

maximal

#15688872

C₂

yes

maximal, characteristic, complemented

#15688871

C₂

yes

maximal, complemented

C₄₇×#333

C₂

yes

maximal, characteristic, complemented

C₂×Q₈×D₄₇

C₄

yes

—

#13094024

C₂²

yes

characteristic

#13094023

—

#13094022

C₄

yes

—

C₄⋊C₄×D₄₇

—

C₄²×D₄₇

C₂²

yes

characteristic

C₄⋊(C₄₇⋊C₈)

C₂²

yes

—

(C₂×D₄₇)⋊C₈

—

#13093934

—

C₄⋊Q₈×C₄₇

C₂²

yes

characteristic

C₄⋊C₈×C₄₇

C₂²

yes

—

C₂×Q₈×C₄₇

C₂×C₄

yes

—

Q₈×D₄₇

—

C₂×C₄×D₄₇

—

C₂×C₄×D₄₇

C₂×C₄

yes

characteristic

C₂×C₄×D₄₇

D₄

yes

—

C₂×Dic₉₄

—

C₂×Dic₉₄

C₂×C₄

yes

—

C₂×C₈×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄²×C₄₇

C₂³

yes

characteristic

C₄⋊Dic₄₇

—

Dic₄₇⋊C₄

—

C₄×Dic₄₇

C₂×C₄

yes

characteristic

C₄×Dic₄₇

D₄

yes

—

C₂×C₄₇⋊C₈

—

C₂²×D₄₇

C₂²⋊C₄

yes

characteristic

Q₈×C₄₇

—

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

—

C₄×D₄₇

—

C₄×D₄₇

—

Dic₉₄

—

Dic₉₄

—

C₈×C₄₇

—

C₄₇⋊C₈

—

C₂²×C₄₇

C₂×C₂²⋊C₄

yes

characteristic

C₂×D₄₇

—

C₂×D₄₇

#100

yes

—

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

#137

yes

—

C₄×C₄₇

#137

yes

—

Dic₄₇

—

Dic₄₇

—

Dic₄₇

—

—

C₂×C₄₇

yes

C₂×C₄₇

yes

—

D₄₇

—

C₂×C₄⋊Q₈

—

—

—

—

D₄₇

yes

characteristic, complemented

C₄₇

#1558

yes

characteristic, complemented, Sylow

C₂²×Q₈

—

C₄⋊Q₈

—

C₄⋊Q₈

—

C₄⋊Q₈

—

C₄⋊Q₈

C₂×D₄₇

yes

characteristic

C₂×C₄⋊C₄

—

C₂×C₄²

—

C₄⋊C₈

—

C₄⋊C₈

C₂×D₄₇

yes

—

C₂²⋊C₈

—

#97

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

188

—

C₂×Q₈

C₄×D₄₇

yes

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₄²

—

C₄²

C₂²×D₄₇

yes

characteristic

C₂³

—

Q₈

—

Q₈

—

188

—

Q₈

—

188

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

188

—

106

C₂×C₄

C₂×C₄×D₄₇

yes

characteristic

107

C₂×C₄

D₄×D₄₇

yes

—

108

C₈

—

109

C₈

—

188

—

110

C₂²

—

111

C₂²

—

112

C₂²

C₂²⋊C₄×D₄₇

yes

characteristic

113

C₄

—

114

C₄

—

115

C₄

—

116

C₄

—

117

C₄

—

188

—

118

C₄

#13094053

yes

—

119

C₄

#13094056

yes

—

120

C₂

—

121

C₂

#100×D₄₇

yes

characteristic

122

C₂

#15689130

yes

—

	subgroup	G/H
center	C₂²	C₂²⋊C₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂²×C₄
Frattini	C₄²	C₂²×D₄₇
Fitting	C₄₇×#333	C₂
socle	C₂²×C₄₇	C₂×C₂²⋊C₄
hypercenter	#333	D₄₇
hypocenter	C₄₇	#1558
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #333

subgroup

G/H

center

C₂²

C₂²⋊C₄×D₄₇

commutator

C₂×C₄×C₄₇

C₂²×C₄

Frattini

C₄²

C₂²×D₄₇

Fitting

C₄₇×#333

C₂

socle

C₂²×C₄₇

C₂×C₂²⋊C₄

D₄₇

C₄₇

G ▷ C₂×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #333

N	H ≅ G/N	type
3. #15688872	C₂	semidirect
4. #15688871	C₂	semidirect
5. C₄₇×#333	C₂	semidirect
66. #333	D₄₇	semidirect
67. C₄₇	#1558	semidirect

H ≅ G/N

type

3. #15688872

C₂

semidirect

4. #15688871

C₂

semidirect

5. C₄₇×#333

C₂

semidirect

66. #333

D₄₇

semidirect

67. C₄₇

#1558

semidirect

Subgroups — #20242112

Conjugacy classes of subgroups

Complements