Group #22618115 — subgroups

Subgroups — #22618115

Order 9344.

372 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 115 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	C₇₃⋊#401	C₂	1	1	yes	maximal, characteristic, complemented
2	#17988524	C₂	1	1	yes	maximal, characteristic
3	#17988521	C₂	1	3	yes	maximal, complemented
4	#17988519	C₂	1	3	yes	maximal, complemented
5	#17988516	C₂	1	3	yes	maximal
6	#17988461	C₂	1	3	yes	maximal
7	#401×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₄×D₇₃	C₂²	1	1	yes	characteristic
9	C₂×C₄⋊Dic₇₃	C₂²	1	3	yes	—
10	C₂×C₄⋊Dic₇₃	C₂²	1	3	yes	—
11	C₂×#11924007	C₂²	1	3	yes	—
12	C₂×#11924007	C₂²	1	3	yes	—
13	C₂×#11924005	C₂²	1	3	yes	—
14	C₂×#11924005	C₂²	1	3	yes	—
15	#14556498	C₂²	1	3	yes	—
16	#14556498	C₂²	1	3	yes	—
17	#14556498	C₂²	1	3	yes	—
18	#95×C₇₃	C₂²	1	3	yes	—
19	#95×C₇₃	C₂²	1	3	yes	—
20	#95×C₇₃	C₂²	1	1	yes	characteristic
21	C₂³×D₇₃	C₂³	1	1	yes	characteristic
22	C₂²×Dic₇₃	C₂³	1	3	yes	—
23	C₂²×Dic₇₃	C₂³	1	1	yes	characteristic
24	C₂²×Dic₇₃	C₂³	1	3	yes	—
25	C₂×C₄×D₇₃	—	4	3	no	—
26	C₄⋊Dic₇₃	—	4	3	no	—
27	C₄⋊Dic₇₃	—	4	3	no	—
28	#11924007	—	4	3	no	—
29	#11924007	—	4	3	no	—
30	#11924005	—	2	6	no	—
31	#11924005	—	4	3	no	—
32	C₂²×C₄×C₇₃	C₂³	1	3	yes	—
33	C₂²×C₄×C₇₃	C₂³	1	3	yes	—
34	C₂²×C₄×C₇₃	C₂³	1	1	yes	characteristic
35	C₂³×C₇₃	C₂⁴	1	1	yes	characteristic
36	C₂²×D₇₃	—	2	3	no	—
37	C₂²×D₇₃	—	2	3	no	—
38	C₂²×D₇₃	#41	1	2	yes	—
39	C₂×C₄×C₇₃	—	2	3	no	—
40	C₂×C₄×C₇₃	—	2	3	no	—
41	C₂×C₄×C₇₃	—	2	3	no	—
42	C₂×C₄×C₇₃	—	2	3	no	—
43	C₂×C₄×C₇₃	—	2	3	no	—
44	C₂×C₄×C₇₃	—	2	6	no	—
45	C₂×Dic₇₃	—	2	3	no	—
46	C₂×Dic₇₃	—	2	3	no	—
47	C₂×Dic₇₃	—	2	3	no	—
48	C₂×Dic₇₃	—	2	3	no	—
49	C₂×Dic₇₃	—	2	3	no	—
50	C₂×Dic₇₃	—	2	3	no	—
51	C₂×Dic₇₃	—	2	3	no	—
52	C₄×D₇₃	—	4	4	no	—
53	C₂²×C₇₃	C₂×#41	1	1	yes	characteristic
54	C₂²×C₇₃	H(5,𝔽₂)	1	3	yes	—
55	C₂²×C₇₃	2₋¹⁺⁴	1	3	yes	—
56	C₂×D₇₃	—	2	6	no	—
57	C₂×D₇₃	—	4	1	no	—
58	C₂×D₇₃	—	4	3	no	—
59	C₄×C₇₃	—	4	3	no	—
60	C₄×C₇₃	—	4	1	no	—
61	C₄×C₇₃	—	4	3	no	—
62	Dic₇₃	—	4	3	no	—
63	Dic₇₃	—	4	1	no	—
64	Dic₇₃	—	4	3	no	—
65	C₂×C₇₃	#539	1	3	yes	—
66	C₂×C₇₃	#560	1	1	yes	characteristic
67	C₂×C₇₃	#563	1	3	yes	—
68	D₇₃	—	4	2	no	—
69	#2834	—	73	1	no	maximal, Sylow
70	C₇₃	#2834	1	1	yes	characteristic, complemented, Sylow
71	#401	—	73	1	no	—
72	#401	D₇₃	1	1	yes	characteristic, complemented
73	#399	—	73	1	no	—
74	#398	—	73	3	no	—
75	#398	—	73	3	no	—
76	#397	—	73	3	no	—
77	#385	—	73	3	no	—
78	C₂³×C₄	—	73	1	no	—
79	C₂×C₄⋊C₄	—	73	3	no	—
80	C₂×C₄⋊C₄	—	73	3	no	—
81	C₂×C₄⋊C₄	—	73	3	no	—
82	C₂×C₄⋊C₄	—	73	3	no	—
83	C₂×C₂²⋊C₄	—	73	3	no	—
84	C₂×C₂²⋊C₄	—	73	3	no	—
85	#95	—	73	3	no	—
86	#95	—	73	3	no	—
87	#95	—	73	3	no	—
88	#95	C₂×D₇₃	1	3	yes	—
89	#95	C₂×D₇₃	1	3	yes	—
90	#95	C₂×D₇₃	1	1	yes	characteristic
91	C₂⁴	—	73	1	no	—
92	C₂²×C₄	—	292	3	no	—
93	C₂²×C₄	—	73	3	no	—
94	C₂²×C₄	—	73	1	no	—
95	C₂²×C₄	—	73	3	no	—
96	C₂²×C₄	C₂²×D₇₃	1	3	yes	—
97	C₂²×C₄	C₂²×D₇₃	1	3	yes	—
98	C₂²×C₄	C₂²×D₇₃	1	1	yes	characteristic
99	C₄⋊C₄	—	292	3	no	—
100	C₄⋊C₄	—	292	3	no	—
101	C₄⋊C₄	—	292	3	no	—
102	C₄⋊C₄	—	292	3	no	—
103	C₂²⋊C₄	—	292	3	no	—
104	C₂²⋊C₄	—	146	6	no	—
105	C₂³	—	73	2	no	—
106	C₂³	—	146	3	no	—
107	C₂³	—	146	3	no	—
108	C₂³	C₂³×D₇₃	1	1	yes	characteristic
109	C₂×C₄	—	2	3	no	—
110	C₂×C₄	—	2	3	no	—
111	C₂×C₄	—	2	3	no	—
112	C₂×C₄	—	2	3	no	—
113	C₂×C₄	—	2	3	no	—
114	C₂×C₄	—	2	6	no	—
115	C₂×C₄	—	292	4	no	—
116	C₂×C₄	—	146	3	no	—
117	C₂×C₄	—	146	3	no	—
118	C₂×C₄	—	146	3	no	—
119	C₂×C₄	—	146	3	no	—
120	C₂×C₄	—	146	3	no	—
121	C₂×C₄	—	146	3	no	—
122	C₂×C₄	—	146	3	no	—
123	C₂²	—	292	1	no	—
124	C₂²	—	292	3	no	—
125	C₂²	—	146	6	no	—
126	C₂²	#41×D₇₃	1	1	yes	characteristic
127	C₂²	#14556637	1	3	yes	—
128	C₂²	#14556638	1	3	yes	—
129	C₄	—	4	3	no	—
130	C₄	—	4	1	no	—
131	C₄	—	4	3	no	—
132	C₄	—	292	3	no	—
133	C₄	—	292	1	no	—
134	C₄	—	292	3	no	—
135	C₂	—	292	2	no	—
136	C₂	#17989178	1	3	yes	—
137	C₂	#17989328	1	1	yes	characteristic
138	C₂	#17989339	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₇₃⋊#401

C₂

yes

maximal, characteristic, complemented

#17988524

C₂

yes

maximal, characteristic

#17988521

C₂

yes

maximal, complemented

#17988519

C₂

yes

maximal, complemented

#17988516

C₂

yes

maximal

#17988461

C₂

yes

maximal

#401×C₇₃

C₂

yes

maximal, characteristic, complemented

C₂²×C₄×D₇₃

C₂²

yes

characteristic

C₂×C₄⋊Dic₇₃

C₂²

yes

—

C₂×C₄⋊Dic₇₃

C₂²

yes

—

C₂×#11924007

C₂²

yes

—

C₂×#11924007

C₂²

yes

—

C₂×#11924005

C₂²

yes

—

C₂×#11924005

C₂²

yes

—

#14556498

C₂²

yes

—

#14556498

C₂²

yes

—

#14556498

C₂²

yes

—

#95×C₇₃

C₂²

yes

—

#95×C₇₃

C₂²

yes

—

#95×C₇₃

C₂²

yes

characteristic

C₂³×D₇₃

C₂³

yes

characteristic

C₂²×Dic₇₃

C₂³

yes

—

C₂²×Dic₇₃

C₂³

yes

characteristic

C₂²×Dic₇₃

C₂³

yes

—

C₂×C₄×D₇₃

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

—

—

—

—

C₂²×C₄×C₇₃

C₂³

yes

—

C₂²×C₄×C₇₃

C₂³

yes

—

C₂²×C₄×C₇₃

C₂³

yes

characteristic

C₂³×C₇₃

C₂⁴

yes

characteristic

C₂²×D₇₃

—

C₂²×D₇₃

—

C₂²×D₇₃

#41

yes

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₄×D₇₃

—

C₂²×C₇₃

C₂×#41

yes

characteristic

C₂²×C₇₃

H(5,𝔽₂)

yes

—

C₂²×C₇₃

2₋¹⁺⁴

yes

—

C₂×D₇₃

—

C₂×D₇₃

—

C₂×D₇₃

—

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

—

Dic₇₃

—

Dic₇₃

—

Dic₇₃

—

C₂×C₇₃

#539

yes

—

C₂×C₇₃

#560

yes

characteristic

C₂×C₇₃

#563

yes

—

D₇₃

—

#2834

—

maximal, Sylow

C₇₃

#2834

yes

characteristic, complemented, Sylow

#401

—

#401

D₇₃

yes

characteristic, complemented

—

—

—

—

—

C₂³×C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

—

—

—

C₂×D₇₃

yes

—

#95

C₂×D₇₃

yes

—

#95

C₂×D₇₃

yes

characteristic

C₂⁴

—

C₂²×C₄

—

292

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₇₃

yes

—

C₂²×C₄

C₂²×D₇₃

yes

—

C₂²×C₄

C₂²×D₇₃

yes

characteristic

C₄⋊C₄

—

292

—

100

C₄⋊C₄

—

292

—

101

C₄⋊C₄

—

292

—

102

C₄⋊C₄

—

292

—

103

C₂²⋊C₄

—

292

—

104

C₂²⋊C₄

—

146

—

105

C₂³

—

106

C₂³

—

146

—

107

C₂³

—

146

—

108

C₂³

C₂³×D₇₃

yes

characteristic

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

292

—

116

C₂×C₄

—

146

—

117

C₂×C₄

—

146

—

118

C₂×C₄

—

146

—

119

C₂×C₄

—

146

—

120

C₂×C₄

—

146

—

121

C₂×C₄

—

146

—

122

C₂×C₄

—

146

—

123

C₂²

—

292

—

124

C₂²

—

292

—

125

C₂²

—

146

—

126

C₂²

#41×D₇₃

yes

characteristic

127

C₂²

#14556637

yes

—

128

C₂²

#14556638

yes

—

129

C₄

—

130

C₄

—

131

C₄

—

132

C₄

—

292

—

133

C₄

—

292

—

134

C₄

—

292

—

135

C₂

—

292

—

136

C₂

#17989178

yes

—

137

C₂

#17989328

yes

characteristic

138

C₂

#17989339

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₇₃
commutator, socle	C₂³×C₇₃	C₂⁴
Fitting	#401×C₇₃	C₂
hypercenter	#401	D₇₃
hypocenter	C₇₃	#2834
LCS	G ▷ C₂³×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂³ ◁ #401

subgroup

G/H

center, Frattini

C₂³

C₂³×D₇₃

commutator, socle

C₂³×C₇₃

C₂⁴

Fitting

#401×C₇₃

C₂

D₇₃

C₇₃

G ▷ C₂³×C₇₃ ▷ C₇₃

C₁ ◁ C₂³ ◁ #401

N	H ≅ G/N	type
1. C₇₃⋊#401	C₂	semidirect
3. #17988521	C₂	semidirect
4. #17988519	C₂	semidirect
7. #401×C₇₃	C₂	semidirect
70. C₇₃	#2834	semidirect
72. #401	D₇₃	semidirect

H ≅ G/N

type

1. C₇₃⋊#401

C₂

semidirect

3. #17988521

C₂

semidirect

4. #17988519

C₂

semidirect

7. #401×C₇₃

C₂

semidirect

70. C₇₃

#2834

semidirect

72. #401

D₇₃

semidirect

Subgroups — #22618115

Conjugacy classes of subgroups

Complements