Group #22610844 — subgroups

Subgroups — #22610844

Order 9344.

276 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 276 conjugacy classes of subgroups — too many to draw. Only its 89 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×Dic₂₉₂	C₂	1	1	yes	maximal, characteristic
2	#17988597	C₂	1	2	yes	maximal
3	C₂×#14556509	C₂	1	2	yes	maximal
4	#17988542	C₂	1	1	yes	maximal, characteristic
5	C₂×#108×C₇₃	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₁₄₆	C₂²	1	2	yes	—
7	C₂×Dic₂₉₂	—	2	1	no	—
8	C₂×Dic₂₉₂	—	2	1	no	—
9	C₂×Dic₂₉₂	—	2	2	no	—
10	C₂×Dic₂₉₂	C₄	1	4	yes	complemented
11	C₂×#11924012	C₂²	1	1	yes	characteristic
12	#14556550	C₂²	1	1	yes	characteristic
13	#14556516	—	2	4	no	—
14	#14556509	—	2	4	no	—
15	#14556501	—	2	1	no	—
16	C₈×Dic₇₃	—	2	1	no	—
17	C₂×M₁₆×C₇₃	C₂²	1	2	yes	—
18	C₂²×C₈×C₇₃	C₂²	1	1	yes	characteristic
19	#108×C₇₃	—	2	2	no	—
20	C₂×Dic₁₄₆	—	2	2	no	—
21	C₂×Dic₁₄₆	—	2	2	no	—
22	C₂×Dic₁₄₆	—	2	2	no	—
23	C₂×Dic₁₄₆	—	2	2	no	—
24	C₂×Dic₁₄₆	—	2	2	no	—
25	C₂×Dic₁₄₆	C₂×C₄	1	4	yes	—
26	C₂²×Dic₇₃	—	2	2	no	—
27	Dic₂₉₂	—	2	4	no	—
28	Dic₂₉₂	—	2	4	no	—
29	#11924012	—	2	1	no	—
30	#11924012	D₄	1	2	yes	—
31	C₂×#10596831	—	2	1	no	—
32	C₄⋊Dic₇₃	D₄	1	2	yes	—
33	C₂²⋊Dic₇₃	—	2	1	no	—
34	C₄×Dic₇₃	—	2	1	no	—
35	C₂²×C₄×C₇₃	C₂³	1	1	yes	characteristic
36	M₁₆×C₇₃	—	2	2	no	—
37	M₁₆×C₇₃	—	2	2	no	—
38	C₂×C₈×C₇₃	—	2	2	no	—
39	C₂×C₈×C₇₃	C₂×C₄	1	2	yes	—
40	C₂×C₈×C₇₃	D₄	1	1	yes	characteristic
41	C₂×C₈×C₇₃	D₄	1	1	yes	characteristic
42	C₂×C₈×C₇₃	D₄	1	2	yes	—
43	C₂³×C₇₃	#41	1	1	yes	characteristic
44	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
45	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
46	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
47	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
48	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
49	C₂×C₄×C₇₃	#41	1	1	yes	characteristic
50	C₂×Dic₇₃	—	2	4	no	—
51	C₂×Dic₇₃	—	2	2	no	—
52	C₂×Dic₇₃	—	4	2	no	—
53	C₂×Dic₇₃	—	4	2	no	—
54	Dic₁₄₆	—	2	4	no	—
55	Dic₁₄₆	—	2	4	no	—
56	Dic₁₄₆	—	4	2	no	—
57	Dic₁₄₆	—	4	2	no	—
58	C₈×C₇₃	—	4	2	no	—
59	C₈×C₇₃	C₂²⋊C₄	1	2	yes	—
60	C₈×C₇₃	C₂²⋊C₄	1	2	yes	—
61	#10596831	—	2	2	no	—
62	C₂²×C₇₃	—	2	2	no	—
63	C₂²×C₇₃	C₄×D₄	1	1	yes	characteristic
64	C₂²×C₇₃	#121	1	1	yes	characteristic
65	C₂²×C₇₃	#124	1	1	yes	characteristic
66	C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
67	C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
68	C₄×C₇₃	#121	1	1	yes	characteristic
69	C₄×C₇₃	#127	1	1	yes	characteristic
70	Dic₇₃	—	4	4	no	—
71	Dic₇₃	—	4	2	no	—
72	C₂×C₇₃	—	2	1	no	—
73	C₂×C₇₃	—	2	1	no	—
74	C₂×C₇₃	#390	1	1	yes	characteristic
75	C₂×C₇₃	#473	1	2	yes	—
76	#1979	—	73	1	no	maximal, Sylow
77	C₇₃	#1979	1	1	yes	characteristic, complemented, Sylow
78	C₂²×Q₁₆	—	73	1	no	—
79	C₂×#108	D₇₃	1	1	yes	characteristic
80	#419	—	73	2	no	—
81	C₂×#101	—	73	2	no	—
82	#405	—	73	1	no	—
83	C₂²×Q₈	—	73	2	no	—
84	C₂×Q₁₆	—	73	4	no	—
85	C₂×Q₁₆	—	146	1	no	—
86	C₂×Q₁₆	—	146	1	no	—
87	C₂×Q₁₆	—	146	2	no	—
88	C₂×M₁₆	—	73	1	no	—
89	C₂×M₁₆	C₂×D₇₃	1	2	yes	—
90	C₂²×C₈	C₂×D₇₃	1	1	yes	characteristic
91	#117	—	73	1	no	—
92	#108	—	2	2	no	—
93	#103	—	146	4	no	—
94	#101	—	146	4	no	—
95	#97	—	146	1	no	—
96	C₄×C₈	—	146	1	no	—
97	C₂×Q₈	—	73	4	no	—
98	C₂×Q₈	—	146	2	no	—
99	C₂×Q₈	—	146	2	no	—
100	C₂×Q₈	—	146	2	no	—
101	C₂×Q₈	—	146	2	no	—
102	C₂×Q₈	—	146	2	no	—
103	C₂²×C₄	—	146	2	no	—
104	C₂²×C₄	C₂²×D₇₃	1	1	yes	characteristic
105	Q₁₆	—	146	4	no	—
106	Q₁₆	—	146	4	no	—
107	M₁₆	—	2	2	no	—
108	M₁₆	—	2	2	no	—
109	M₁₆	—	73	2	no	—
110	M₁₆	—	146	1	no	—
111	C₂×C₈	—	2	2	no	—
112	C₂×C₈	—	146	1	no	—
113	C₂×C₈	C₄×D₇₃	1	2	yes	—
114	C₂×C₈	D₂₉₂	1	1	yes	characteristic
115	C₂×C₈	D₂₉₂	1	1	yes	characteristic
116	C₂×C₈	C₂²⋊D₇₃	1	2	yes	—
117	C₄⋊C₄	—	73	2	no	—
118	C₂²⋊C₄	—	146	1	no	—
119	C₄²	—	146	1	no	—
120	C₂³	#11924029	1	1	yes	characteristic
121	Q₈	—	292	2	no	—
122	Q₈	—	292	2	no	—
123	Q₈	—	146	4	no	—
124	Q₈	—	146	4	no	—
125	C₂×C₄	—	292	2	no	—
126	C₂×C₄	—	292	2	no	—
127	C₂×C₄	—	146	4	no	—
128	C₂×C₄	—	146	2	no	—
129	C₂×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
130	C₂×C₄	D₄×D₇₃	1	1	yes	characteristic
131	C₂×C₄	D₄×D₇₃	1	1	yes	characteristic
132	C₂×C₄	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
133	C₂×C₄	C₂×D₂₉₂	1	1	yes	characteristic
134	C₂×C₄	#11924029	1	1	yes	characteristic
135	C₈	—	4	2	no	—
136	C₈	—	146	2	no	—
137	C₈	#11924005	1	2	yes	—
138	C₈	#11924005	1	2	yes	—
139	C₂²	—	2	2	no	—
140	C₂²	#14556553	1	1	yes	characteristic
141	C₂²	#14556566	1	1	yes	characteristic
142	C₂²	#14556580	1	1	yes	characteristic
143	C₄	—	292	4	no	—
144	C₄	—	292	2	no	—
145	C₄	C₂×#11924005	1	1	yes	characteristic
146	C₄	#14556553	1	1	yes	characteristic
147	C₄	#14556566	1	1	yes	characteristic
148	C₄	#14556587	1	1	yes	characteristic
149	C₂	—	2	1	no	—
150	C₂	—	2	1	no	—
151	C₂	#17988488	1	1	yes	characteristic
152	C₂	#17988863	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×Dic₂₉₂

C₂

yes

maximal, characteristic

#17988597

C₂

yes

maximal

C₂×#14556509

C₂

yes

maximal

#17988542

C₂

yes

maximal, characteristic

C₂×#108×C₇₃

C₂

yes

maximal, characteristic

C₂²×Dic₁₄₆

C₂²

yes

—

C₂×Dic₂₉₂

—

C₂×Dic₂₉₂

—

C₂×Dic₂₉₂

—

C₂×Dic₂₉₂

C₄

yes

complemented

C₂×#11924012

C₂²

yes

characteristic

#14556550

C₂²

yes

—

—

—

C₈×Dic₇₃

—

C₂×M₁₆×C₇₃

C₂²

yes

—

C₂²×C₈×C₇₃

C₂²

yes

characteristic

#108×C₇₃

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

C₂×C₄

yes

—

C₂²×Dic₇₃

—

Dic₂₉₂

—

Dic₂₉₂

—

#11924012

—

#11924012

D₄

yes

—

C₂×#10596831

—

C₄⋊Dic₇₃

D₄

yes

—

C₂²⋊Dic₇₃

—

C₄×Dic₇₃

—

C₂²×C₄×C₇₃

C₂³

yes

characteristic

M₁₆×C₇₃

—

M₁₆×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

C₂×C₄

yes

—

C₂×C₈×C₇₃

D₄

yes

characteristic

C₂×C₈×C₇₃

D₄

yes

characteristic

C₂×C₈×C₇₃

D₄

yes

—

C₂³×C₇₃

#41

yes

characteristic

C₂×C₄×C₇₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×C₄×C₇₃

#41

yes

characteristic

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

Dic₁₄₆

—

Dic₁₄₆

—

Dic₁₄₆

—

Dic₁₄₆

—

C₈×C₇₃

—

C₈×C₇₃

C₂²⋊C₄

yes

—

C₈×C₇₃

C₂²⋊C₄

yes

—

#10596831

—

C₂²×C₇₃

—

C₂²×C₇₃

C₄×D₄

yes

C₂²×C₇₃

yes

C₂²×C₇₃

yes

C₄×C₇₃

C₂×C₂²⋊C₄

yes

characteristic

C₄×C₇₃

C₄×D₄

yes

C₄×C₇₃

yes

C₄×C₇₃

yes

Dic₇₃

—

Dic₇₃

—

C₂×C₇₃

—

C₂×C₇₃

—

C₂×C₇₃

#390

yes

characteristic

C₂×C₇₃

#473

yes

—

#1979

—

maximal, Sylow

C₇₃

#1979

yes

characteristic, complemented, Sylow

C₂²×Q₁₆

—

C₂×#108

D₇₃

yes

—

—

—

C₂²×Q₈

—

C₂×Q₁₆

—

C₂×Q₁₆

—

146

—

C₂×Q₁₆

—

146

—

C₂×Q₁₆

—

146

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₇₃

yes

—

C₂²×C₈

C₂×D₇₃

yes

—

—

—

146

—

#101

—

146

—

#97

—

146

—

C₄×C₈

—

146

—

C₂×Q₈

—

C₂×Q₈

—

146

—

C₂×Q₈

—

146

—

100

C₂×Q₈

—

146

—

101

C₂×Q₈

—

146

—

102

C₂×Q₈

—

146

—

103

C₂²×C₄

—

146

—

104

C₂²×C₄

C₂²×D₇₃

yes

characteristic

105

Q₁₆

—

146

—

106

Q₁₆

—

146

—

107

M₁₆

—

108

M₁₆

—

109

M₁₆

—

110

M₁₆

—

146

—

111

C₂×C₈

—

112

C₂×C₈

—

146

—

113

C₂×C₈

C₄×D₇₃

yes

—

114

C₂×C₈

D₂₉₂

yes

characteristic

115

C₂×C₈

D₂₉₂

yes

characteristic

116

C₂×C₈

C₂²⋊D₇₃

yes

—

117

C₄⋊C₄

—

118

C₂²⋊C₄

—

146

—

119

C₄²

—

146

—

120

C₂³

#11924029

yes

characteristic

121

Q₈

—

292

—

122

Q₈

—

292

—

123

Q₈

—

146

—

124

Q₈

—

146

—

125

C₂×C₄

—

292

—

126

C₂×C₄

—

292

—

127

C₂×C₄

—

146

—

128

C₂×C₄

—

146

—

129

C₂×C₄

C₂×C₄×D₇₃

yes

characteristic

130

C₂×C₄

D₄×D₇₃

yes

characteristic

131

C₂×C₄

D₄×D₇₃

yes

characteristic

132

C₂×C₄

C₂×C₂²⋊D₇₃

yes

characteristic

133

C₂×C₄

C₂×D₂₉₂

yes

characteristic

134

C₂×C₄

#11924029

yes

characteristic

135

C₈

—

136

C₈

—

146

—

137

C₈

#11924005

yes

—

138

C₈

#11924005

yes

—

139

C₂²

—

140

C₂²

#14556553

yes

characteristic

141

C₂²

#14556566

yes

characteristic

142

C₂²

#14556580

yes

characteristic

143

C₄

—

292

—

144

C₄

—

292

—

145

C₄

C₂×#11924005

yes

characteristic

146

C₄

#14556553

yes

characteristic

147

C₄

#14556566

yes

characteristic

148

C₄

#14556587

yes

characteristic

149

C₂

—

150

C₂

—

151

C₂

#17988488

yes

characteristic

152

C₂

#17988863

yes

—

	subgroup	G/H
center	C₂²	#14556566
commutator	C₂×C₄×C₇₃	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₇₃
Fitting	C₂×#108×C₇₃	C₂
socle	C₂²×C₇₃	#121
hypercenter	C₂×#108	D₇₃
hypocenter	C₇₃	#1979
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#108

subgroup

G/H

center

C₂²

#14556566

commutator

C₂×C₄×C₇₃

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₇₃

Fitting

C₂×#108×C₇₃

C₂

C₂²×C₇₃

D₇₃

C₇₃

G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#108

N	H ≅ G/N	type
10. C₂×Dic₂₉₂	C₄	semidirect
77. C₇₃	#1979	semidirect

H ≅ G/N

type

10. C₂×Dic₂₉₂

C₄

semidirect

77. C₇₃

#1979

semidirect

Subgroups — #22610844

Conjugacy classes of subgroups

Complements