Group #22627125 — subgroups

Subgroups — #22627125

Order 9344.

168 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 168 conjugacy classes of subgroups — too many to draw. Only its 69 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	#17989706	C₂	1	2	yes	maximal
2	#17989692	C₂	1	2	yes	maximal, complemented
3	#17989691	C₂	1	2	yes	maximal, complemented
4	C₂×C₈×#64408	C₂	1	1	yes	maximal, characteristic
5	#14556688	C₂²	1	4	yes	—
6	#14556687	—	2	2	no	—
7	#14556686	—	2	2	no	—
8	C₂×#11924036	C₂²	1	1	yes	characteristic
9	C₂×C₄×#64408	C₄	1	1	yes	characteristic
10	C₈×#64408	C₄	1	1	yes	characteristic
11	C₈×#64408	C₄	1	1	yes	characteristic
12	C₈×#64408	C₂²	1	1	yes	characteristic
13	C₈×#64408	C₂²	1	1	yes	characteristic
14	C₂×C₈×D₇₃	C₄	1	1	yes	characteristic
15	#11924040	—	2	4	no	—
16	C₂²×#64408	—	2	1	no	—
17	#11924036	C₂×C₄	1	1	yes	characteristic
18	#11924036	D₄	1	1	yes	characteristic
19	#11924036	Q₈	1	1	yes	characteristic
20	#11924036	C₂³	1	1	yes	characteristic
21	C₂×#10596833	D₄	1	1	yes	characteristic
22	C₂×#10596833	Q₈	1	1	yes	characteristic
23	C₄×#64408	—	2	1	no	—
24	C₄×#64408	C₂×C₄	1	1	yes	characteristic
25	C₄×#64408	C₂×C₄	1	1	yes	characteristic
26	C₂×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
27	C₂×#10596831	C₈	1	1	yes	characteristic
28	C₈×D₇₃	C₈	1	1	yes	characteristic
29	C₈×D₇₃	C₈	1	1	yes	characteristic
30	C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
31	C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
32	C₂×C₈×C₇₃	C₈	1	1	yes	characteristic
33	C₂²×D₇₃	M₁₆	1	1	yes	characteristic
34	C₂×#64408	—	2	4	no	—
35	C₂×#64408	—	2	1	no	—
36	C₂×#64408	—	2	1	no	—
37	C₂×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
38	C₂×Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
39	C₄×D₇₃	C₄⋊C₄	1	1	yes	characteristic
40	C₄×D₇₃	C₂×C₈	1	1	yes	characteristic
41	C₄×D₇₃	M₁₆	1	1	yes	characteristic
42	C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
43	#10596833	C₄⋊C₄	1	1	yes	characteristic
44	#10596833	C₄⋊C₄	1	1	yes	characteristic
45	#10596833	C₂×D₄	1	1	yes	characteristic
46	#10596833	C₂×Q₈	1	1	yes	characteristic
47	C₈×C₇₃	C₂×C₈	1	1	yes	characteristic
48	C₈×C₇₃	C₂×C₈	1	1	yes	characteristic
49	#10596831	C₂×C₈	1	1	yes	characteristic
50	#10596831	C₂×C₈	1	1	yes	characteristic
51	C₂²×C₇₃	C₄⋊C₈	1	1	yes	characteristic
52	C₂×D₇₃	—	2	2	no	—
53	C₂×D₇₃	C₄⋊C₈	1	1	yes	characteristic
54	C₂×D₇₃	C₂×M₁₆	1	1	yes	characteristic
55	#64408	—	2	2	no	—
56	#64408	—	2	2	no	—
57	C₄×C₇₃	C₄⋊C₈	1	1	yes	characteristic
58	C₄×C₇₃	C₂²×C₈	1	1	yes	characteristic
59	Dic₇₃	C₄⋊C₈	1	1	yes	characteristic
60	Dic₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
61	C₂×C₇₃	—	2	1	no	—
62	C₂×C₇₃	C₂×C₄⋊C₈	1	1	yes	characteristic
63	D₇₃	—	2	1	no	—
64	D₇₃	#364	1	2	yes	complemented
65	C₂×#364	—	73	1	no	maximal, Sylow
66	C₇₃	C₂×#364	1	1	yes	characteristic, complemented, Sylow
67	C₂×M₃₂	—	73	2	no	—
68	C₂×C₄×C₈	—	73	1	no	—
69	#364	—	73	2	no	—
70	#364	—	73	2	no	—
71	C₂²×C₈	—	73	1	no	—
72	C₂²×C₈	—	73	1	no	—
73	C₂×C₄²	—	73	1	no	—
74	M₃₂	—	73	4	no	—
75	M₃₂	—	146	2	no	—
76	C₂×C₁₆	—	146	2	no	—
77	C₄×C₈	—	73	1	no	—
78	C₄×C₈	—	73	1	no	—
79	C₄×C₈	—	73	1	no	—
80	C₄×C₈	—	73	1	no	—
81	C₂²×C₄	—	73	1	no	—
82	C₂²×C₄	—	146	1	no	—
83	C₂×C₈	—	73	1	no	—
84	C₂×C₈	—	73	1	no	—
85	C₂×C₈	—	73	1	no	—
86	C₂×C₈	—	73	1	no	—
87	C₂×C₈	—	73	1	no	—
88	C₂×C₈	—	73	1	no	—
89	C₂×C₈	—	73	1	no	—
90	C₂×C₈	—	73	1	no	—
91	C₂×C₈	—	73	1	no	—
92	C₂×C₈	—	73	1	no	—
93	C₂×C₈	—	73	1	no	—
94	C₂×C₈	#10596842	1	1	yes	characteristic
95	C₄²	—	73	1	no	—
96	C₄²	—	73	1	no	—
97	C₄²	—	146	1	no	—
98	C₁₆	—	146	4	no	—
99	C₂³	—	73	1	no	—
100	C₂×C₄	—	73	1	no	—
101	C₂×C₄	—	73	1	no	—
102	C₂×C₄	—	73	1	no	—
103	C₂×C₄	—	73	1	no	—
104	C₂×C₄	—	73	1	no	—
105	C₂×C₄	—	146	1	no	—
106	C₂×C₄	—	146	1	no	—
107	C₂×C₄	—	146	4	no	—
108	C₂×C₄	C₂×#10596842	1	1	yes	characteristic
109	C₈	—	73	1	no	—
110	C₈	—	73	1	no	—
111	C₈	—	73	1	no	—
112	C₈	—	73	1	no	—
113	C₈	—	73	1	no	—
114	C₈	—	73	1	no	—
115	C₈	C₂×#10596842	1	1	yes	characteristic
116	C₈	C₂×#10596842	1	1	yes	characteristic
117	C₂²	—	73	1	no	—
118	C₂²	—	73	1	no	—
119	C₂²	—	146	2	no	—
120	C₂²	C₄⋊#10596842	1	1	yes	characteristic
121	C₄	—	73	1	no	—
122	C₄	—	73	1	no	—
123	C₄	—	146	2	no	—
124	C₄	—	146	2	no	—
125	C₄	C₄⋊#10596842	1	1	yes	characteristic
126	C₄	C₂²×#10596842	1	1	yes	characteristic
127	C₂	—	2	1	no	—
128	C₂	—	73	2	no	—
129	C₂	—	146	1	no	—
130	C₂	C₂×C₄⋊#10596842	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17989706

C₂

yes

maximal

#17989692

C₂

yes

maximal, complemented

#17989691

C₂

yes

maximal, complemented

C₂×C₈×#64408

C₂

yes

maximal, characteristic

#14556688

C₂²

yes

—

#14556687

—

#14556686

—

C₂×#11924036

C₂²

yes

characteristic

C₂×C₄×#64408

C₄

yes

characteristic

C₈×#64408

C₄

yes

characteristic

C₈×#64408

C₄

yes

characteristic

C₈×#64408

C₂²

yes

characteristic

C₈×#64408

C₂²

yes

characteristic

C₂×C₈×D₇₃

C₄

yes

characteristic

#11924040

—

C₂²×#64408

—

#11924036

C₂×C₄

yes

characteristic

#11924036

D₄

yes

characteristic

#11924036

Q₈

yes

characteristic

#11924036

C₂³

yes

characteristic

C₂×#10596833

D₄

yes

characteristic

C₂×#10596833

Q₈

yes

characteristic

C₄×#64408

—

C₄×#64408

C₂×C₄

yes

characteristic

C₄×#64408

C₂×C₄

yes

characteristic

C₂×C₄×D₇₃

C₂×C₄

yes

characteristic

C₂×#10596831

C₈

yes

characteristic

C₈×D₇₃

C₈

yes

characteristic

C₈×D₇₃

C₈

yes

characteristic

C₈×D₇₃

C₂×C₄

yes

characteristic

C₈×D₇₃

C₂×C₄

yes

characteristic

C₂×C₈×C₇₃

C₈

yes

characteristic

C₂²×D₇₃

M₁₆

yes

—

—

—

C₂×C₄×C₇₃

C₂×C₈

yes

characteristic

C₂×Dic₇₃

C₄⋊C₄

yes

characteristic

C₄×D₇₃

C₄⋊C₄

yes

characteristic

C₄×D₇₃

C₂×C₈

yes

characteristic

C₄×D₇₃

M₁₆

yes

characteristic

C₄×D₇₃

C₂²×C₄

yes

characteristic

#10596833

C₄⋊C₄

yes

characteristic

#10596833

C₄⋊C₄

yes

characteristic

#10596833

C₂×D₄

yes

characteristic

#10596833

C₂×Q₈

yes

characteristic

C₈×C₇₃

C₂×C₈

yes

characteristic

C₈×C₇₃

C₂×C₈

yes

characteristic

#10596831

C₂×C₈

yes

characteristic

#10596831

C₂×C₈

yes

characteristic

C₂²×C₇₃

C₄⋊C₈

yes

characteristic

C₂×D₇₃

—

C₂×D₇₃

C₄⋊C₈

yes

characteristic

C₂×D₇₃

C₂×M₁₆

yes

characteristic

#64408

—

#64408

—

C₄×C₇₃

C₄⋊C₈

yes

characteristic

C₄×C₇₃

C₂²×C₈

yes

characteristic

Dic₇₃

C₄⋊C₈

yes

characteristic

Dic₇₃

C₂×C₄⋊C₄

yes

characteristic

C₂×C₇₃

—

C₂×C₇₃

C₂×C₄⋊C₈

yes

characteristic

D₇₃

—

D₇₃

yes

—

C₇₃

yes

characteristic, complemented, Sylow

C₂×M₃₂

—

C₂×C₄×C₈

—

#364

—

#364

—

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

—

M₃₂

—

M₃₂

—

146

—

C₂×C₁₆

—

146

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₂²×C₄

—

C₂²×C₄

—

146

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

#10596842

yes

characteristic

C₄²

—

C₄²

—

C₄²

—

146

—

C₁₆

—

146

—

C₂³

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

146

—

106

C₂×C₄

—

146

—

107

C₂×C₄

—

146

—

108

C₂×C₄

C₂×#10596842

yes

characteristic

109

C₈

—

110

C₈

—

111

C₈

—

112

C₈

—

113

C₈

—

114

C₈

—

115

C₈

C₂×#10596842

yes

characteristic

116

C₈

C₂×#10596842

yes

characteristic

117

C₂²

—

118

C₂²

—

119

C₂²

—

146

—

120

C₂²

C₄⋊#10596842

yes

characteristic

121

C₄

—

122

C₄

—

123

C₄

—

146

—

124

C₄

—

146

—

125

C₄

C₄⋊#10596842

yes

characteristic

126

C₄

C₂²×#10596842

yes

characteristic

127

C₂

—

128

C₂

—

129

C₂

—

146

—

130

C₂

C₂×C₄⋊#10596842

yes

characteristic

	subgroup	G/H
center	C₄	C₄⋊#10596842
commutator	C₄×C₇₃	C₂²×C₈
Frattini	C₄	C₂²×#10596842
Fitting	C₂×C₈×C₇₃	C₈
socle	C₂×C₇₃	C₂×C₄⋊C₈
hypercenter	C₂×C₈	#10596842
hypocenter	C₇₃	C₂×#364
LCS	G ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈

subgroup

G/H

center

C₄

C₄⋊#10596842

commutator

C₄×C₇₃

C₂²×C₈

Frattini

C₄

C₂²×#10596842

Fitting

C₂×C₈×C₇₃

C₈

socle

C₂×C₇₃

C₂×C₄⋊C₈

C₂×C₈

C₇₃

G ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈

N	H ≅ G/N	type
2. #17989692	C₂	semidirect
3. #17989691	C₂	semidirect
64. D₇₃	#364	semidirect
66. C₇₃	C₂×#364	semidirect

H ≅ G/N

type

2. #17989692

C₂

semidirect

3. #17989691

C₂

semidirect

64. D₇₃

#364

semidirect

66. C₇₃

C₂×#364

semidirect

Subgroups — #22627125

Conjugacy classes of subgroups

Complements