Group #22615906 — subgroups

Subgroups — #22615906

Order 9344.

360 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 149 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	#17988529	C₂	1	4	yes	maximal
2	#17988521	C₂	1	4	yes	maximal
3	#17988485	C₂	1	2	yes	maximal
4	#17988485	C₂	1	2	yes	maximal
5	#17988457	C₂	1	1	yes	maximal, characteristic
6	#17988453	C₂	1	1	yes	maximal, characteristic
7	#376×C₇₃	C₂	1	1	yes	maximal, characteristic
8	C₂×C₄⋊Dic₇₃	C₂²	1	2	yes	—
9	C₂×C₄⋊Dic₇₃	C₂²	1	2	yes	—
10	C₂×C₄⋊Dic₇₃	C₂²	1	4	yes	—
11	C₂×#11924007	C₂²	1	4	yes	—
12	C₂×#11924007	C₂²	1	4	yes	—
13	#14556498	C₂²	1	4	yes	—
14	#14556498	C₂²	1	4	yes	—
15	#14556498	C₂²	1	4	yes	—
16	C₂×C₄²×C₇₃	C₂²	1	1	yes	characteristic
17	C₂×C₄²×C₇₃	C₂²	1	1	yes	characteristic
18	C₂×C₄²×C₇₃	C₂²	1	1	yes	characteristic
19	#95×C₇₃	C₂²	1	2	yes	—
20	#95×C₇₃	C₂²	1	2	yes	—
21	C₂²×Dic₇₃	C₂³	1	4	yes	—
22	C₂²×Dic₇₃	C₂³	1	4	yes	—
23	C₄⋊Dic₇₃	—	2	4	no	—
24	C₄⋊Dic₇₃	—	2	4	no	—
25	C₄⋊Dic₇₃	—	4	4	no	—
26	#11924007	—	4	4	no	—
27	#11924007	—	4	4	no	—
28	C₂²×C₄×C₇₃	C₂³	1	1	yes	characteristic
29	C₂²×C₄×C₇₃	C₂³	1	2	yes	—
30	C₂²×C₄×C₇₃	C₂³	1	1	yes	characteristic
31	C₂²×C₄×C₇₃	C₂³	1	2	yes	—
32	C₂²×C₄×C₇₃	C₂³	1	1	yes	characteristic
33	C₄²×C₇₃	—	2	2	no	—
34	C₄²×C₇₃	—	2	2	no	—
35	C₄²×C₇₃	Q₈	1	4	yes	—
36	C₂³×C₇₃	C₂⁴	1	1	yes	characteristic
37	C₂×C₄×C₇₃	—	2	2	no	—
38	C₂×C₄×C₇₃	—	2	2	no	—
39	C₂×C₄×C₇₃	—	2	1	no	—
40	C₂×C₄×C₇₃	—	2	1	no	—
41	C₂×C₄×C₇₃	—	2	2	no	—
42	C₂×C₄×C₇₃	—	2	2	no	—
43	C₂×C₄×C₇₃	—	2	2	no	—
44	C₂×C₄×C₇₃	—	2	2	no	—
45	C₂×C₄×C₇₃	—	2	2	no	—
46	C₂×C₄×C₇₃	C₂×Q₈	1	4	yes	—
47	C₂×C₄×C₇₃	C₂×Q₈	1	2	yes	—
48	C₂×C₄×C₇₃	#41	1	2	yes	—
49	C₂×C₄×C₇₃	#41	1	2	yes	—
50	C₂×Dic₇₃	—	2	4	no	—
51	C₂×Dic₇₃	—	2	4	no	—
52	C₂×Dic₇₃	—	2	4	no	—
53	C₂×Dic₇₃	—	2	4	no	—
54	C₂×Dic₇₃	—	2	4	no	—
55	C₂×Dic₇₃	—	2	4	no	—
56	C₂²×C₇₃	C₂²×Q₈	1	1	yes	characteristic
57	C₂²×C₇₃	C₂×#41	1	1	yes	characteristic
58	C₂²×C₇₃	C₂×#41	1	1	yes	characteristic
59	C₂²×C₇₃	H(5,𝔽₂)	1	2	yes	—
60	C₂²×C₇₃	2₋¹⁺⁴	1	2	yes	—
61	C₄×C₇₃	—	2	4	no	—
62	C₄×C₇₃	—	4	1	no	—
63	C₄×C₇₃	—	4	1	no	—
64	C₄×C₇₃	—	4	2	no	—
65	C₄×C₇₃	#125	1	4	yes	—
66	Dic₇₃	—	4	4	no	—
67	Dic₇₃	—	4	4	no	—
68	C₂×C₇₃	C₂×#125	1	1	yes	characteristic
69	C₂×C₇₃	#540	1	1	yes	characteristic
70	C₂×C₇₃	#541	1	1	yes	characteristic
71	C₂×C₇₃	#542	1	2	yes	—
72	C₂×C₇₃	#544	1	2	yes	—
73	#2647	—	73	1	no	maximal, Sylow
74	C₇₃	#2647	1	1	yes	characteristic, complemented, Sylow
75	#400	—	73	4	no	—
76	#398	—	73	4	no	—
77	#389	—	73	2	no	—
78	#389	—	73	2	no	—
79	#384	—	73	1	no	—
80	#382	—	73	1	no	—
81	#376	D₇₃	1	1	yes	characteristic
82	C₂×C₄⋊C₄	—	73	4	no	—
83	C₂×C₄⋊C₄	—	73	4	no	—
84	C₂×C₄⋊C₄	—	73	4	no	—
85	C₂×C₄⋊C₄	—	73	2	no	—
86	C₂×C₄⋊C₄	—	73	2	no	—
87	C₂×C₄²	C₂×D₇₃	1	1	yes	characteristic
88	C₂×C₄²	C₂×D₇₃	1	1	yes	characteristic
89	C₂×C₄²	C₂×D₇₃	1	1	yes	characteristic
90	#95	—	73	4	no	—
91	#95	—	73	4	no	—
92	#95	—	73	4	no	—
93	#95	C₂×D₇₃	1	2	yes	—
94	#95	C₂×D₇₃	1	2	yes	—
95	C₂²×C₄	—	73	4	no	—
96	C₂²×C₄	—	73	4	no	—
97	C₂²×C₄	C₂²×D₇₃	1	1	yes	characteristic
98	C₂²×C₄	C₂²×D₇₃	1	2	yes	—
99	C₂²×C₄	C₂²×D₇₃	1	1	yes	characteristic
100	C₂²×C₄	C₂²×D₇₃	1	2	yes	—
101	C₂²×C₄	C₂²×D₇₃	1	1	yes	characteristic
102	C₄⋊C₄	—	292	4	no	—
103	C₄⋊C₄	—	292	4	no	—
104	C₄⋊C₄	—	292	4	no	—
105	C₄⋊C₄	—	146	4	no	—
106	C₄⋊C₄	—	146	4	no	—
107	C₄²	—	2	2	no	—
108	C₄²	—	2	2	no	—
109	C₄²	Dic₁₄₆	1	4	yes	—
110	C₂³	C₂³×D₇₃	1	1	yes	characteristic
111	C₂×C₄	—	2	2	no	—
112	C₂×C₄	—	2	2	no	—
113	C₂×C₄	—	2	1	no	—
114	C₂×C₄	—	2	1	no	—
115	C₂×C₄	—	2	2	no	—
116	C₂×C₄	—	2	2	no	—
117	C₂×C₄	—	2	2	no	—
118	C₂×C₄	—	2	2	no	—
119	C₂×C₄	—	2	2	no	—
120	C₂×C₄	—	146	4	no	—
121	C₂×C₄	—	146	4	no	—
122	C₂×C₄	—	146	4	no	—
123	C₂×C₄	—	146	4	no	—
124	C₂×C₄	—	146	4	no	—
125	C₂×C₄	—	146	4	no	—
126	C₂×C₄	C₂×Dic₁₄₆	1	4	yes	—
127	C₂×C₄	C₂×Dic₁₄₆	1	2	yes	—
128	C₂×C₄	#11924028	1	2	yes	—
129	C₂×C₄	#11924028	1	2	yes	—
130	C₂²	C₂²×Dic₁₄₆	1	1	yes	characteristic
131	C₂²	C₂×#11924028	1	1	yes	characteristic
132	C₂²	C₂×#11924028	1	1	yes	characteristic
133	C₂²	#14556637	1	2	yes	—
134	C₂²	#14556638	1	2	yes	—
135	C₄	—	2	4	no	—
136	C₄	—	4	1	no	—
137	C₄	—	4	1	no	—
138	C₄	—	4	2	no	—
139	C₄	—	292	4	no	—
140	C₄	—	292	4	no	—
141	C₄	#14556583	1	4	yes	—
142	C₂	C₂×#14556583	1	1	yes	characteristic
143	C₂	#17989192	1	1	yes	characteristic
144	C₂	#17989199	1	1	yes	characteristic
145	C₂	#17989208	1	2	yes	—
146	C₂	#17989215	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#17988529

C₂

yes

maximal

#17988521

C₂

yes

maximal

#17988485

C₂

yes

maximal

#17988485

C₂

yes

maximal

#17988457

C₂

yes

maximal, characteristic

#17988453

C₂

yes

maximal, characteristic

#376×C₇₃

C₂

yes

maximal, characteristic

C₂×C₄⋊Dic₇₃

C₂²

yes

—

C₂×C₄⋊Dic₇₃

C₂²

yes

—

C₂×C₄⋊Dic₇₃

C₂²

yes

—

C₂×#11924007

C₂²

yes

—

C₂×#11924007

C₂²

yes

—

#14556498

C₂²

yes

—

#14556498

C₂²

yes

—

#14556498

C₂²

yes

—

C₂×C₄²×C₇₃

C₂²

yes

characteristic

C₂×C₄²×C₇₃

C₂²

yes

characteristic

C₂×C₄²×C₇₃

C₂²

yes

characteristic

#95×C₇₃

C₂²

yes

—

#95×C₇₃

C₂²

yes

—

C₂²×Dic₇₃

C₂³

yes

—

C₂²×Dic₇₃

C₂³

yes

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

#11924007

—

#11924007

—

C₂²×C₄×C₇₃

C₂³

yes

characteristic

C₂²×C₄×C₇₃

C₂³

yes

—

C₂²×C₄×C₇₃

C₂³

yes

characteristic

C₂²×C₄×C₇₃

C₂³

yes

—

C₂²×C₄×C₇₃

C₂³

yes

characteristic

C₄²×C₇₃

—

C₄²×C₇₃

—

C₄²×C₇₃

Q₈

yes

—

C₂³×C₇₃

C₂⁴

yes

characteristic

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂×Q₈

yes

—

C₂×C₄×C₇₃

C₂×Q₈

yes

—

C₂×C₄×C₇₃

#41

yes

—

C₂×C₄×C₇₃

#41

yes

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂²×C₇₃

C₂²×Q₈

yes

characteristic

C₂²×C₇₃

C₂×#41

yes

characteristic

C₂²×C₇₃

C₂×#41

yes

characteristic

C₂²×C₇₃

H(5,𝔽₂)

yes

—

C₂²×C₇₃

2₋¹⁺⁴

yes

—

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

#125

yes

—

Dic₇₃

—

Dic₇₃

—

C₂×C₇₃

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

—

C₂×C₇₃

#544

yes

—

#2647

—

maximal, Sylow

C₇₃

#2647

yes

characteristic, complemented, Sylow

—

—

—

—

—

—

D₇₃

yes

characteristic

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

C₂×D₇₃

yes

characteristic

C₂×C₄²

C₂×D₇₃

yes

characteristic

C₂×C₄²

C₂×D₇₃

yes

—

—

—

C₂×D₇₃

yes

—

#95

C₂×D₇₃

yes

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₇₃

yes

characteristic

C₂²×C₄

C₂²×D₇₃

yes

—

C₂²×C₄

C₂²×D₇₃

yes

characteristic

100

C₂²×C₄

C₂²×D₇₃

yes

—

101

C₂²×C₄

C₂²×D₇₃

yes

characteristic

102

C₄⋊C₄

—

292

—

103

C₄⋊C₄

—

292

—

104

C₄⋊C₄

—

292

—

105

C₄⋊C₄

—

146

—

106

C₄⋊C₄

—

146

—

107

C₄²

—

108

C₄²

—

109

C₄²

Dic₁₄₆

yes

—

110

C₂³

C₂³×D₇₃

yes

characteristic

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

146

—

121

C₂×C₄

—

146

—

122

C₂×C₄

—

146

—

123

C₂×C₄

—

146

—

124

C₂×C₄

—

146

—

125

C₂×C₄

—

146

—

126

C₂×C₄

C₂×Dic₁₄₆

yes

—

127

C₂×C₄

C₂×Dic₁₄₆

yes

—

128

C₂×C₄

#11924028

yes

—

129

C₂×C₄

#11924028

yes

—

130

C₂²

C₂²×Dic₁₄₆

yes

characteristic

131

C₂²

C₂×#11924028

yes

characteristic

132

C₂²

C₂×#11924028

yes

characteristic

133

C₂²

#14556637

yes

—

134

C₂²

#14556638

yes

—

135

C₄

—

136

C₄

—

137

C₄

—

138

C₄

—

139

C₄

—

292

—

140

C₄

—

292

—

141

C₄

#14556583

yes

—

142

C₂

C₂×#14556583

yes

characteristic

143

C₂

#17989192

yes

characteristic

144

C₂

#17989199

yes

characteristic

145

C₂

#17989208

yes

—

146

C₂

#17989215

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₇₃
commutator, socle	C₂³×C₇₃	C₂⁴
Fitting	#376×C₇₃	C₂
hypercenter	#376	D₇₃
hypocenter	C₇₃	#2647
LCS	G ▷ C₂³×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂³ ◁ #376

subgroup

G/H

center, Frattini

C₂³

C₂³×D₇₃

commutator, socle

C₂³×C₇₃

C₂⁴

Fitting

#376×C₇₃

C₂

D₇₃

C₇₃

G ▷ C₂³×C₇₃ ▷ C₇₃

C₁ ◁ C₂³ ◁ #376

N	H ≅ G/N	type
74. C₇₃	#2647	semidirect

H ≅ G/N

type

74. C₇₃

#2647

semidirect

Subgroups — #22615906

Conjugacy classes of subgroups

Complements