Group #22625850 — subgroups

Subgroups — #22625850

Order 9344.

172 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 172 conjugacy classes of subgroups — too many to draw. Only its 62 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	D₇₃⋊#108	C₂	1	1	yes	maximal, characteristic
2	#17989597	C₂	1	1	yes	maximal, characteristic
3	#17989469	C₂	1	2	yes	maximal
4	#17989454	C₂	1	2	yes	maximal
5	#17988541	C₂	1	1	yes	maximal, characteristic
6	D₇₃⋊M₁₆	C₂²	1	2	yes	—
7	#14556670	C₂²	1	2	yes	—
8	#14556662	—	2	1	no	—
9	#14556661	—	2	1	no	—
10	#14556660	—	2	1	no	—
11	#14556659	—	2	1	no	—
12	C₂×#11924011	C₂²	1	1	yes	characteristic
13	C₂×C₈×D₇₃	C₂²	1	1	yes	characteristic
14	#14556548	C₂²	1	1	yes	characteristic
15	#14556502	C₄	1	1	yes	characteristic, complemented
16	#14556501	C₄	1	1	yes	characteristic, complemented
17	C₈×Dic₇₃	C₄	1	1	yes	characteristic, complemented
18	C₄×C₈×C₇₃	C₄	1	1	yes	characteristic, complemented
19	#11924038	—	2	2	no	—
20	#11924037	—	2	2	no	—
21	#11924036	—	2	2	no	—
22	C₄⋊#64408	—	2	2	no	—
23	C₂²⋊#64408	—	2	2	no	—
24	C₄×#64408	—	2	2	no	—
25	C₂×C₄×D₇₃	C₂³	1	1	yes	characteristic
26	#11924011	—	2	1	no	—
27	#11924011	—	2	1	no	—
28	C₂×#10596831	C₂×C₄	1	1	yes	characteristic
29	C₂×#10596831	C₂×C₄	1	1	yes	characteristic
30	C₈×D₇₃	D₄	1	1	yes	characteristic
31	C₈×D₇₃	D₄	1	1	yes	characteristic
32	C₈×D₇₃	Q₈	1	1	yes	characteristic
33	C₈×D₇₃	Q₈	1	1	yes	characteristic
34	#11924007	—	2	1	no	—
35	#11924005	—	2	1	no	—
36	C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
37	C₂×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
38	C₂×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
39	C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
40	C₂²×D₇₃	#41	1	1	yes	characteristic
41	C₂×#64408	—	4	2	no	—
42	C₂×C₄×C₇₃	—	2	1	no	—
43	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
44	C₂×Dic₇₃	—	2	1	no	—
45	C₂×Dic₇₃	#41	1	1	yes	characteristic
46	C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
47	C₄×D₇₃	C₂×Q₈	1	1	yes	characteristic
48	C₄×D₇₃	#41	1	1	yes	characteristic
49	C₄×D₇₃	#41	1	1	yes	characteristic
50	#10596833	—	4	2	no	—
51	C₈×C₇₃	—	2	1	no	—
52	C₈×C₇₃	C₄⋊C₄	1	1	yes	characteristic
53	C₈×C₇₃	C₄⋊C₄	1	1	yes	characteristic
54	#10596831	—	2	1	no	—
55	#10596831	C₄⋊C₄	1	1	yes	characteristic
56	#10596831	C₄⋊C₄	1	1	yes	characteristic
57	C₂²×C₇₃	#117	1	1	yes	characteristic
58	C₂×D₇₃	—	4	1	no	—
59	C₂×D₇₃	#124	1	1	yes	characteristic
60	C₂×D₇₃	#125	1	1	yes	characteristic
61	#64408	—	8	2	no	—
62	C₄×C₇₃	—	4	1	no	—
63	C₄×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
64	C₄×C₇₃	#117	1	1	yes	characteristic
65	Dic₇₃	—	4	1	no	—
66	Dic₇₃	#124	1	1	yes	characteristic
67	Dic₇₃	#125	1	1	yes	characteristic
68	C₂×C₇₃	—	2	1	no	—
69	C₂×C₇₃	#382	1	1	yes	characteristic
70	D₇₃	—	2	1	no	—
71	D₇₃	—	2	1	no	—
72	#1833	—	73	1	no	maximal, Sylow
73	C₇₃	#1833	1	1	yes	characteristic, complemented, Sylow
74	C₂×#108	—	73	1	no	—
75	#427	—	73	1	no	—
76	#405	—	73	1	no	—
77	#344	—	73	2	no	—
78	H(3,ℤ/4)	—	73	2	no	—
79	C₂×M₁₆	—	73	1	no	—
80	C₂×M₁₆	—	73	2	no	—
81	C₂²×C₈	—	73	1	no	—
82	#117	—	73	1	no	—
83	#117	—	73	2	no	—
84	#108	—	146	1	no	—
85	#108	—	146	1	no	—
86	#107	—	146	1	no	—
87	#106	—	146	1	no	—
88	#97	—	73	1	no	—
89	#97	—	73	1	no	—
90	C₄×C₈	—	73	1	no	—
91	C₄×C₈	#64408	1	1	yes	characteristic, complemented
92	C₂²×C₄	—	73	1	no	—
93	M₁₆	—	146	1	no	—
94	M₁₆	—	146	1	no	—
95	M₁₆	—	146	2	no	—
96	M₁₆	—	146	2	no	—
97	C₂×C₈	—	73	1	no	—
98	C₂×C₈	—	73	1	no	—
99	C₂×C₈	—	73	1	no	—
100	C₂×C₈	—	73	1	no	—
101	C₂×C₈	—	73	1	no	—
102	C₂×C₈	—	73	1	no	—
103	C₂×C₈	—	146	2	no	—
104	C₂×C₈	C₂×#64408	1	1	yes	characteristic
105	C₂×C₈	C₂×#64408	1	1	yes	characteristic
106	C₄⋊C₄	—	146	1	no	—
107	C₄⋊C₄	—	146	2	no	—
108	C₂²⋊C₄	—	146	1	no	—
109	C₂²⋊C₄	—	146	2	no	—
110	C₄²	—	73	1	no	—
111	C₄²	—	146	2	no	—
112	C₄²	C₂×#64408	1	1	yes	characteristic
113	C₂³	—	73	1	no	—
114	C₂×C₄	—	2	1	no	—
115	C₂×C₄	—	292	2	no	—
116	C₂×C₄	—	73	1	no	—
117	C₂×C₄	—	73	1	no	—
118	C₂×C₄	—	73	1	no	—
119	C₂×C₄	—	73	1	no	—
120	C₂×C₄	—	73	1	no	—
121	C₂×C₄	—	146	1	no	—
122	C₂×C₄	C₂²×#64408	1	1	yes	characteristic
123	C₈	—	2	1	no	—
124	C₈	—	292	2	no	—
125	C₈	—	73	1	no	—
126	C₈	—	73	1	no	—
127	C₈	—	146	1	no	—
128	C₈	C₄⋊#64408	1	1	yes	characteristic
129	C₈	C₄⋊#64408	1	1	yes	characteristic
130	C₂²	—	292	1	no	—
131	C₂²	—	73	1	no	—
132	C₂²	—	73	1	no	—
133	C₂²	#14556670	1	1	yes	characteristic
134	C₄	—	4	1	no	—
135	C₄	—	292	1	no	—
136	C₄	—	584	2	no	—
137	C₄	—	73	1	no	—
138	C₄	—	73	1	no	—
139	C₄	C₂×C₄⋊#64408	1	1	yes	characteristic
140	C₄	#14556670	1	1	yes	characteristic
141	C₂	—	2	1	no	—
142	C₂	—	146	1	no	—
143	C₂	—	146	1	no	—
144	C₂	#17989531	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

D₇₃⋊#108

C₂

yes

maximal, characteristic

#17989597

C₂

yes

maximal, characteristic

#17989469

C₂

yes

maximal

#17989454

C₂

yes

maximal

#17988541

C₂

yes

maximal, characteristic

D₇₃⋊M₁₆

C₂²

yes

—

#14556670

C₂²

yes

—

—

—

—

—

C₂²

yes

characteristic

C₂×C₈×D₇₃

C₂²

yes

characteristic

#14556548

C₂²

yes

characteristic

#14556502

C₄

yes

characteristic, complemented

#14556501

C₄

yes

characteristic, complemented

C₈×Dic₇₃

C₄

yes

characteristic, complemented

C₄×C₈×C₇₃

C₄

yes

characteristic, complemented

—

—

—

—

—

—

C₂×C₄×D₇₃

C₂³

yes

—

—

C₂×C₄

yes

characteristic

C₂×#10596831

C₂×C₄

yes

characteristic

C₈×D₇₃

D₄

yes

characteristic

C₈×D₇₃

D₄

yes

characteristic

C₈×D₇₃

Q₈

yes

characteristic

C₈×D₇₃

Q₈

yes

characteristic

#11924007

—

#11924005

—

C₄×Dic₇₃

C₂×C₄

yes

characteristic

C₂×C₈×C₇₃

C₂×C₄

yes

characteristic

C₂×C₈×C₇₃

C₂×C₄

yes

characteristic

C₄²×C₇₃

C₂×C₄

yes

C₂²×D₇₃

yes

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂²×C₄

yes

characteristic

C₂×Dic₇₃

—

C₂×Dic₇₃

#41

yes

characteristic

C₄×D₇₃

C₂×D₄

yes

characteristic

C₄×D₇₃

C₂×Q₈

yes

C₄×D₇₃

yes

C₄×D₇₃

yes

—

C₈×C₇₃

—

C₈×C₇₃

C₄⋊C₄

yes

characteristic

C₈×C₇₃

C₄⋊C₄

yes

characteristic

#10596831

—

#10596831

C₄⋊C₄

yes

characteristic

#10596831

C₄⋊C₄

yes

characteristic

C₂²×C₇₃

#117

yes

characteristic

C₂×D₇₃

—

C₂×D₇₃

yes

C₂×D₇₃

yes

—

C₄×C₇₃

—

C₄×C₇₃

C₂×C₄⋊C₄

yes

characteristic

C₄×C₇₃

#117

yes

characteristic

Dic₇₃

—

Dic₇₃

yes

Dic₇₃

yes

C₂×C₇₃

—

C₂×C₇₃

#382

yes

characteristic

D₇₃

—

D₇₃

—

#1833

—

maximal, Sylow

C₇₃

#1833

yes

characteristic, complemented, Sylow

—

—

—

—

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂²×C₈

—

#117

—

#117

—

#108

—

146

—

#108

—

146

—

#107

—

146

—

#106

—

146

—

#97

—

#97

—

C₄×C₈

—

C₄×C₈

#64408

yes

characteristic, complemented

C₂²×C₄

—

M₁₆

—

146

—

M₁₆

—

146

—

M₁₆

—

146

—

M₁₆

—

146

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

100

C₂×C₈

—

101

C₂×C₈

—

102

C₂×C₈

—

103

C₂×C₈

—

146

—

104

C₂×C₈

C₂×#64408

yes

characteristic

105

C₂×C₈

C₂×#64408

yes

characteristic

106

C₄⋊C₄

—

146

—

107

C₄⋊C₄

—

146

—

108

C₂²⋊C₄

—

146

—

109

C₂²⋊C₄

—

146

—

110

C₄²

—

111

C₄²

—

146

—

112

C₄²

C₂×#64408

yes

characteristic

113

C₂³

—

114

C₂×C₄

—

115

C₂×C₄

—

292

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

—

146

—

122

C₂×C₄

C₂²×#64408

yes

characteristic

123

C₈

—

124

C₈

—

292

—

125

C₈

—

126

C₈

—

127

C₈

—

146

—

128

C₈

C₄⋊#64408

yes

characteristic

129

C₈

C₄⋊#64408

yes

characteristic

130

C₂²

—

292

—

131

C₂²

—

132

C₂²

—

133

C₂²

#14556670

yes

characteristic

134

C₄

—

135

C₄

—

292

—

136

C₄

—

584

—

137

C₄

—

138

C₄

—

139

C₄

C₂×C₄⋊#64408

yes

characteristic

140

C₄

#14556670

yes

characteristic

141

C₂

—

142

C₂

—

146

—

143

C₂

—

146

—

144

C₂

#17989531

yes

characteristic

	subgroup	G/H
center	C₄	#14556670
commutator	C₂×C₄×C₇₃	C₂²×C₄
Frattini	C₂×C₄	C₂²×#64408
Fitting	C₄×C₈×C₇₃	C₄
socle	C₂×C₇₃	#382
hypercenter	C₄×C₈	#64408
hypocenter	C₇₃	#1833
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₄ ◁ C₄² ◁ C₄×C₈

subgroup

G/H

center

C₄

#14556670

commutator

C₂×C₄×C₇₃

C₂²×C₄

Frattini

C₂×C₄

C₂²×#64408

Fitting

C₄×C₈×C₇₃

C₄

C₂×C₇₃

C₄×C₈

C₇₃

G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₄ ◁ C₄² ◁ C₄×C₈

N	H ≅ G/N	type
15. #14556502	C₄	semidirect
16. #14556501	C₄	semidirect
17. C₈×Dic₇₃	C₄	semidirect
18. C₄×C₈×C₇₃	C₄	semidirect
73. C₇₃	#1833	semidirect
91. C₄×C₈	#64408	semidirect

H ≅ G/N

type

15. #14556502

C₄

semidirect

16. #14556501

C₄

semidirect

17. C₈×Dic₇₃

C₄

semidirect

18. C₄×C₈×C₇₃

C₄

semidirect

73. C₇₃

#1833

semidirect

91. C₄×C₈

#64408

semidirect

Subgroups — #22625850

Conjugacy classes of subgroups

Complements