Group #22609971 — subgroups

Subgroups — #22609971

Order 9344.

272 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 93 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	C₂²×#11924012	C₂	1	1	yes	maximal, characteristic
2	C₂×#14556526	C₂	1	2	yes	maximal, complemented
3	#17988551	C₂	1	1	yes	maximal, characteristic
4	#17988351	C₂	1	2	yes	maximal, complemented
5	#407×C₇₃	C₂	1	1	yes	maximal, characteristic
6	C₂×#11924012	—	2	4	no	—
7	C₂×#11924012	C₄	1	4	yes	—
8	C₂×#11924012	C₂²	1	2	yes	—
9	C₂²×#10596831	C₂²	1	1	yes	characteristic
10	C₂²×#10596831	C₂²	1	1	yes	characteristic
11	#14556526	—	2	4	no	—
12	C₂²⋊#10596831	—	2	2	no	—
13	C₂³×C₄×C₇₃	C₂²	1	1	yes	characteristic
14	C₂×M₁₆×C₇₃	C₂²	1	2	yes	—
15	C₂²⋊C₈×C₇₃	—	2	2	no	—
16	#11924012	—	2	8	no	—
17	#11924012	—	2	2	no	—
18	#11924012	—	2	2	no	—
19	C₂×#10596831	—	2	2	no	—
20	C₂×#10596831	—	2	2	no	—
21	C₂×#10596831	C₂×C₄	1	2	yes	—
22	C₂×#10596831	C₂×C₄	1	2	yes	—
23	C₂×#10596831	D₄	1	4	yes	—
24	C₂⁴×C₇₃	Q₈	1	1	yes	characteristic
25	C₂²×C₄×C₇₃	—	2	2	no	—
26	C₂²×C₄×C₇₃	—	2	2	no	—
27	C₂²×C₄×C₇₃	C₂×C₄	1	2	yes	—
28	C₂²×C₄×C₇₃	D₄	1	2	yes	—
29	C₂²×C₄×C₇₃	Q₈	1	1	yes	characteristic
30	C₂²×C₄×C₇₃	C₂³	1	1	yes	characteristic
31	M₁₆×C₇₃	—	2	2	no	—
32	M₁₆×C₇₃	—	2	2	no	—
33	C₂×C₈×C₇₃	—	2	2	no	—
34	C₂³×C₇₃	—	2	2	no	—
35	C₂³×C₇₃	—	4	2	no	—
36	C₂³×C₇₃	C₄⋊C₄	1	2	yes	—
37	C₂³×C₇₃	C₂×Q₈	1	1	yes	characteristic
38	C₂×C₄×C₇₃	—	2	2	no	—
39	C₂×C₄×C₇₃	—	2	2	no	—
40	C₂×C₄×C₇₃	—	2	2	no	—
41	C₂×C₄×C₇₃	—	2	4	no	—
42	C₂×C₄×C₇₃	C₄⋊C₄	1	2	yes	—
43	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
44	C₂×C₄×C₇₃	C₂×D₄	1	2	yes	—
45	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
46	C₂×C₄×C₇₃	#41	1	2	yes	—
47	C₈×C₇₃	—	4	2	no	—
48	#10596831	—	2	2	no	—
49	#10596831	—	4	2	no	—
50	#10596831	C₂²⋊C₄	1	4	yes	—
51	C₂²×C₇₃	—	2	2	no	—
52	C₂²×C₇₃	—	2	2	no	—
53	C₂²×C₇₃	—	2	4	no	—
54	C₂²×C₇₃	—	4	4	no	—
55	C₂²×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
56	C₂²×C₇₃	C₂²⋊Q₈	1	2	yes	—
57	C₄×C₇₃	—	2	2	no	—
58	C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
59	C₄×C₇₃	#117	1	1	yes	characteristic
60	C₄×C₇₃	#121	1	2	yes	—
61	C₂×C₇₃	—	2	2	no	—
62	C₂×C₇₃	—	4	2	no	—
63	C₂×C₇₃	#380	1	1	yes	characteristic
64	C₂×C₇₃	#430	1	2	yes	—
65	#1811	—	73	1	no	maximal, Sylow
66	C₇₃	#1811	1	1	yes	characteristic, complemented, Sylow
67	C₂²×M₁₆	—	73	1	no	—
68	C₂×#108	—	73	2	no	—
69	#407	—	73	1	no	—
70	#407	D₇₃	1	1	yes	characteristic
71	#341	—	73	2	no	—
72	C₂³×C₄	C₂×D₇₃	1	1	yes	characteristic
73	C₂×M₁₆	—	73	4	no	—
74	C₂×M₁₆	—	73	2	no	—
75	C₂×M₁₆	—	146	4	no	—
76	C₂×M₁₆	C₂×D₇₃	1	2	yes	—
77	C₂²×C₈	—	73	1	no	—
78	C₂²×C₈	—	73	1	no	—
79	#108	—	146	4	no	—
80	C₂²⋊C₈	—	2	2	no	—
81	C₂²⋊C₈	—	146	2	no	—
82	C₂⁴	Dic₁₄₆	1	1	yes	characteristic
83	C₂²×C₄	—	2	2	no	—
84	C₂²×C₄	—	2	2	no	—
85	C₂²×C₄	Dic₁₄₆	1	1	yes	characteristic
86	C₂²×C₄	C₄×D₇₃	1	2	yes	—
87	C₂²×C₄	C₂²⋊D₇₃	1	2	yes	—
88	C₂²×C₄	C₂²×D₇₃	1	1	yes	characteristic
89	M₁₆	—	2	2	no	—
90	M₁₆	—	2	2	no	—
91	M₁₆	—	146	2	no	—
92	M₁₆	—	146	2	no	—
93	M₁₆	—	146	8	no	—
94	C₂×C₈	—	2	2	no	—
95	C₂×C₈	—	73	2	no	—
96	C₂×C₈	—	73	4	no	—
97	C₂×C₈	—	73	2	no	—
98	C₂×C₈	—	146	2	no	—
99	C₂×C₈	—	146	2	no	—
100	C₂³	—	2	2	no	—
101	C₂³	—	4	2	no	—
102	C₂³	#11924007	1	2	yes	—
103	C₂³	C₂×Dic₁₄₆	1	1	yes	characteristic
104	C₂×C₄	—	2	2	no	—
105	C₂×C₄	—	2	2	no	—
106	C₂×C₄	—	2	2	no	—
107	C₂×C₄	—	2	4	no	—
108	C₂×C₄	#11924007	1	2	yes	—
109	C₂×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
110	C₂×C₄	D₄×D₇₃	1	2	yes	—
111	C₂×C₄	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
112	C₂×C₄	#11924027	1	2	yes	—
113	C₈	—	4	2	no	—
114	C₈	—	292	2	no	—
115	C₈	—	73	4	no	—
116	C₈	—	146	2	no	—
117	C₂²	—	2	2	no	—
118	C₂²	—	2	4	no	—
119	C₂²	—	2	2	no	—
120	C₂²	—	4	4	no	—
121	C₂²	C₂×#11924007	1	1	yes	characteristic
122	C₂²	#14556568	1	2	yes	—
123	C₄	—	2	2	no	—
124	C₄	C₂²⋊C₄×D₇₃	1	1	yes	characteristic
125	C₄	#14556547	1	1	yes	characteristic
126	C₄	#14556563	1	2	yes	—
127	C₂	—	2	2	no	—
128	C₂	—	4	2	no	—
129	C₂	#17988445	1	1	yes	characteristic
130	C₂	#17988635	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×#11924012

C₂

yes

maximal, characteristic

C₂×#14556526

C₂

yes

maximal, complemented

#17988551

C₂

yes

maximal, characteristic

#17988351

C₂

yes

maximal, complemented

#407×C₇₃

C₂

yes

maximal, characteristic

C₂×#11924012

—

C₂×#11924012

C₄

yes

—

C₂×#11924012

C₂²

yes

—

C₂²×#10596831

C₂²

yes

characteristic

C₂²×#10596831

C₂²

yes

characteristic

#14556526

—

C₂²⋊#10596831

—

C₂³×C₄×C₇₃

C₂²

yes

characteristic

C₂×M₁₆×C₇₃

C₂²

yes

—

C₂²⋊C₈×C₇₃

—

—

—

—

—

—

C₂×C₄

yes

—

C₂×#10596831

C₂×C₄

yes

—

C₂×#10596831

D₄

yes

—

C₂⁴×C₇₃

Q₈

yes

characteristic

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

C₂×C₄

yes

—

C₂²×C₄×C₇₃

D₄

yes

—

C₂²×C₄×C₇₃

Q₈

yes

characteristic

C₂²×C₄×C₇₃

C₂³

yes

characteristic

M₁₆×C₇₃

—

M₁₆×C₇₃

—

C₂×C₈×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

C₄⋊C₄

yes

—

C₂³×C₇₃

C₂×Q₈

yes

characteristic

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₄⋊C₄

yes

—

C₂×C₄×C₇₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₇₃

C₂×D₄

yes

—

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×C₄×C₇₃

#41

yes

—

C₈×C₇₃

—

#10596831

—

#10596831

—

#10596831

C₂²⋊C₄

yes

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₇₃

C₂²⋊Q₈

yes

—

C₄×C₇₃

—

C₄×C₇₃

C₂×C₂²⋊C₄

yes

C₄×C₇₃

yes

C₄×C₇₃

yes

—

C₂×C₇₃

—

C₂×C₇₃

—

C₂×C₇₃

#380

yes

characteristic

C₂×C₇₃

#430

yes

—

#1811

—

maximal, Sylow

C₇₃

#1811

yes

characteristic, complemented, Sylow

C₂²×M₁₆

—

C₂×#108

—

#407

—

#407

D₇₃

yes

characteristic

#341

—

C₂³×C₄

C₂×D₇₃

yes

characteristic

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

—

146

—

C₂×M₁₆

C₂×D₇₃

yes

—

C₂²×C₈

—

C₂²×C₈

—

#108

—

146

—

C₂²⋊C₈

—

C₂²⋊C₈

—

146

—

C₂⁴

Dic₁₄₆

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

Dic₁₄₆

yes

characteristic

C₂²×C₄

C₄×D₇₃

yes

—

C₂²×C₄

C₂²⋊D₇₃

yes

—

C₂²×C₄

C₂²×D₇₃

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

146

—

M₁₆

—

146

—

M₁₆

—

146

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

146

—

C₂×C₈

—

146

—

100

C₂³

—

101

C₂³

—

102

C₂³

#11924007

yes

—

103

C₂³

C₂×Dic₁₄₆

yes

characteristic

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

#11924007

yes

—

109

C₂×C₄

C₂×C₄×D₇₃

yes

characteristic

110

C₂×C₄

D₄×D₇₃

yes

—

111

C₂×C₄

C₂×C₂²⋊D₇₃

yes

characteristic

112

C₂×C₄

#11924027

yes

—

113

C₈

—

114

C₈

—

292

—

115

C₈

—

116

C₈

—

146

—

117

C₂²

—

118

C₂²

—

119

C₂²

—

120

C₂²

—

121

C₂²

C₂×#11924007

yes

characteristic

122

C₂²

#14556568

yes

—

123

C₄

—

124

C₄

C₂²⋊C₄×D₇₃

yes

characteristic

125

C₄

#14556547

yes

characteristic

126

C₄

#14556563

yes

—

127

C₂

—

128

C₂

—

129

C₂

#17988445

yes

characteristic

130

C₂

#17988635

yes

—

	subgroup	G/H
center	C₂×C₄	C₂×C₂²⋊D₇₃
commutator	C₂×C₄×C₇₃	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₇₃
Fitting	#407×C₇₃	C₂
socle	C₂²×C₇₃	C₂×C₄⋊C₄
hypercenter	#407	D₇₃
hypocenter	C₇₃	#1811
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ #407

subgroup

G/H

center

C₂×C₄

C₂×C₂²⋊D₇₃

commutator

C₂×C₄×C₇₃

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₇₃

Fitting

#407×C₇₃

C₂

socle

C₂²×C₇₃

C₂×C₄⋊C₄

D₇₃

C₇₃

G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ #407

N	H ≅ G/N	type
2. C₂×#14556526	C₂	semidirect
4. #17988351	C₂	semidirect
66. C₇₃	#1811	semidirect

H ≅ G/N

type

2. C₂×#14556526

C₂

semidirect

4. #17988351

C₂

semidirect

66. C₇₃

#1811

semidirect

Subgroups — #22609971

Conjugacy classes of subgroups

Complements