Group #22607880 — subgroups

Subgroups — #22607880

Order 9344.

158 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 158 conjugacy classes of subgroups — too many to draw. Only its 37 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	#17988459	C₂	1	1	yes	maximal, characteristic
2	#17988311	C₂	1	1	yes	maximal, characteristic
3	#323×C₇₃	C₂	1	1	yes	maximal, characteristic
4	C₂³×Dic₇₃	C₄	1	1	yes	characteristic
5	C₂×#11924007	—	2	1	no	—
6	C₂×C₂²⋊Dic₇₃	C₄	1	1	yes	characteristic
7	C₂²⋊#10596831	—	2	1	no	—
8	#14556498	—	2	1	no	—
9	C₂×C₂²⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
10	C₂²⋊C₈×C₇₃	—	2	1	no	—
11	C₂²×Dic₇₃	—	2	1	no	—
12	C₂²×Dic₇₃	—	2	1	no	—
13	C₂²×Dic₇₃	—	4	2	no	—
14	C₂²×Dic₇₃	—	4	1	no	—
15	C₂×#10596831	—	4	1	no	—
16	#11924007	—	4	2	no	—
17	C₂²⋊Dic₇₃	—	2	1	no	—
18	C₂²⋊Dic₇₃	C₈	1	2	yes	complemented
19	C₂⁴×C₇₃	C₂×C₄	1	1	yes	characteristic
20	C₂²×C₄×C₇₃	D₄	1	1	yes	characteristic
21	C₂²×C₄×C₇₃	D₄	1	1	yes	characteristic
22	C₂×C₈×C₇₃	—	4	1	no	—
23	C₂²⋊C₄×C₇₃	—	4	1	no	—
24	C₂³×C₇₃	—	2	1	no	—
25	C₂³×C₇₃	—	2	1	no	—
26	C₂³×C₇₃	—	4	1	no	—
27	C₂³×C₇₃	—	4	1	no	—
28	C₂³×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
29	C₂³×C₇₃	C₂×C₈	1	1	yes	characteristic
30	C₂³×C₇₃	M₁₆	1	1	yes	characteristic
31	C₂×C₄×C₇₃	—	2	1	no	—
32	C₂×C₄×C₇₃	—	2	1	no	—
33	C₂×C₄×C₇₃	—	4	1	no	—
34	C₂×C₄×C₇₃	—	4	1	no	—
35	C₂×Dic₇₃	—	2	2	no	—
36	C₂×Dic₇₃	—	2	2	no	—
37	C₂×Dic₇₃	—	4	1	no	—
38	C₂×Dic₇₃	—	4	1	no	—
39	C₂×Dic₇₃	—	4	1	no	—
40	C₂×Dic₇₃	—	4	2	no	—
41	C₂×Dic₇₃	—	4	1	no	—
42	C₂×Dic₇₃	—	4	2	no	—
43	C₈×C₇₃	—	8	1	no	—
44	#10596831	—	8	1	no	—
45	C₂²×C₇₃	—	2	1	no	—
46	C₂²×C₇₃	—	2	1	no	—
47	C₂²×C₇₃	—	2	1	no	—
48	C₂²×C₇₃	—	2	1	no	—
49	C₂²×C₇₃	—	4	1	no	—
50	C₂²×C₇₃	—	4	1	no	—
51	C₂²×C₇₃	—	4	2	no	—
52	C₂²×C₇₃	—	4	1	no	—
53	C₂²×C₇₃	—	4	1	no	—
54	C₂²×C₇₃	C₂²⋊C₈	1	1	yes	characteristic
55	C₂²×C₇₃	#99	1	1	yes	characteristic
56	C₂²×C₇₃	#101	1	1	yes	characteristic
57	C₄×C₇₃	—	4	1	no	—
58	C₄×C₇₃	—	4	1	no	—
59	Dic₇₃	—	4	2	no	—
60	Dic₇₃	—	4	2	no	—
61	C₂×C₇₃	—	2	1	no	—
62	C₂×C₇₃	—	2	1	no	—
63	C₂×C₇₃	—	4	1	no	—
64	C₂×C₇₃	—	4	1	no	—
65	C₂×C₇₃	#324	1	1	yes	characteristic
66	C₂×C₇₃	AΣL(1,𝔽₁₆)	1	1	yes	characteristic
67	C₂×C₇₃	#352	1	1	yes	characteristic
68	#1326	—	73	1	no	maximal, Sylow
69	C₇₃	#1326	1	1	yes	characteristic, complemented, Sylow
70	#385	—	73	1	no	—
71	#323	—	73	1	no	—
72	#323	D₇₃	1	1	yes	characteristic
73	C₂³×C₄	—	73	1	no	—
74	C₂×C₄⋊C₄	—	146	1	no	—
75	C₂×C₂²⋊C₄	—	73	1	no	—
76	C₂×C₂²⋊C₄	C₂×D₇₃	1	1	yes	characteristic
77	C₂²⋊C₈	—	2	1	no	—
78	C₂²⋊C₈	—	146	1	no	—
79	#95	—	146	1	no	—
80	C₂⁴	C₄×D₇₃	1	1	yes	characteristic
81	C₂²×C₄	—	292	1	no	—
82	C₂²×C₄	—	292	2	no	—
83	C₂²×C₄	—	146	1	no	—
84	C₂²×C₄	—	146	1	no	—
85	C₂²×C₄	D₂₉₂	1	1	yes	characteristic
86	C₂²×C₄	C₂²⋊D₇₃	1	1	yes	characteristic
87	C₂×C₈	—	4	1	no	—
88	C₂×C₈	—	292	1	no	—
89	C₄⋊C₄	—	292	2	no	—
90	C₂²⋊C₄	—	4	1	no	—
91	C₂²⋊C₄	—	73	2	no	—
92	C₂²⋊C₄	—	146	1	no	—
93	C₂³	—	2	1	no	—
94	C₂³	—	2	1	no	—
95	C₂³	—	4	1	no	—
96	C₂³	—	4	1	no	—
97	C₂³	#11924005	1	1	yes	characteristic
98	C₂³	C₈×D₇₃	1	1	yes	characteristic
99	C₂³	#11924011	1	1	yes	characteristic
100	C₂×C₄	—	2	1	no	—
101	C₂×C₄	—	2	1	no	—
102	C₂×C₄	—	4	1	no	—
103	C₂×C₄	—	4	1	no	—
104	C₂×C₄	—	292	1	no	—
105	C₂×C₄	—	292	1	no	—
106	C₂×C₄	—	292	1	no	—
107	C₂×C₄	—	292	2	no	—
108	C₂×C₄	—	292	1	no	—
109	C₂×C₄	—	292	2	no	—
110	C₂×C₄	—	146	2	no	—
111	C₂×C₄	—	146	2	no	—
112	C₈	—	8	1	no	—
113	C₈	—	584	1	no	—
114	C₂²	—	2	1	no	—
115	C₂²	—	2	1	no	—
116	C₂²	—	2	1	no	—
117	C₂²	—	2	1	no	—
118	C₂²	—	4	1	no	—
119	C₂²	—	4	1	no	—
120	C₂²	—	4	2	no	—
121	C₂²	—	4	1	no	—
122	C₂²	—	4	1	no	—
123	C₂²	#14556503	1	1	yes	characteristic
124	C₂²	#14556505	1	1	yes	characteristic
125	C₂²	#14556509	1	1	yes	characteristic
126	C₄	—	4	1	no	—
127	C₄	—	4	1	no	—
128	C₄	—	292	2	no	—
129	C₄	—	292	2	no	—
130	C₂	—	2	1	no	—
131	C₂	—	2	1	no	—
132	C₂	—	4	1	no	—
133	C₂	—	4	1	no	—
134	C₂	#17988312	1	1	yes	characteristic
135	C₂	#17988375	1	1	yes	characteristic
136	C₂	#17988376	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17988459

C₂

yes

maximal, characteristic

#17988311

C₂

yes

maximal, characteristic

#323×C₇₃

C₂

yes

maximal, characteristic

C₂³×Dic₇₃

C₄

yes

characteristic

C₂×#11924007

—

C₂×C₂²⋊Dic₇₃

C₄

yes

characteristic

C₂²⋊#10596831

—

#14556498

—

C₂×C₂²⋊C₄×C₇₃

C₂²

yes

characteristic

C₂²⋊C₈×C₇₃

—

C₂²×Dic₇₃

—

C₂²×Dic₇₃

—

C₂²×Dic₇₃

—

C₂²×Dic₇₃

—

C₂×#10596831

—

#11924007

—

C₂²⋊Dic₇₃

—

C₂²⋊Dic₇₃

C₈

yes

complemented

C₂⁴×C₇₃

C₂×C₄

yes

characteristic

C₂²×C₄×C₇₃

D₄

yes

characteristic

C₂²×C₄×C₇₃

D₄

yes

characteristic

C₂×C₈×C₇₃

—

C₂²⋊C₄×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

C₂²⋊C₄

yes

characteristic

C₂³×C₇₃

C₂×C₈

yes

characteristic

C₂³×C₇₃

M₁₆

yes

characteristic

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

—

C₂×Dic₇₃

—

C₈×C₇₃

—

#10596831

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

C₂²⋊C₈

yes

C₂²×C₇₃

yes

C₂²×C₇₃

yes

C₄×C₇₃

—

C₄×C₇₃

—

Dic₇₃

—

Dic₇₃

—

C₂×C₇₃

—

C₂×C₇₃

—

C₂×C₇₃

—

C₂×C₇₃

—

C₂×C₇₃

#324

yes

characteristic

C₂×C₇₃

AΣL(1,𝔽₁₆)

yes

C₂×C₇₃

yes

—

C₇₃

yes

characteristic, complemented, Sylow

#385

—

#323

—

#323

D₇₃

yes

characteristic

C₂³×C₄

—

C₂×C₄⋊C₄

—

146

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

C₂×D₇₃

yes

characteristic

C₂²⋊C₈

—

C₂²⋊C₈

—

146

—

#95

—

146

—

C₂⁴

C₄×D₇₃

yes

characteristic

C₂²×C₄

—

292

—

C₂²×C₄

—

292

—

C₂²×C₄

—

146

—

C₂²×C₄

—

146

—

C₂²×C₄

D₂₉₂

yes

characteristic

C₂²×C₄

C₂²⋊D₇₃

yes

characteristic

C₂×C₈

—

C₂×C₈

—

292

—

C₄⋊C₄

—

292

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

146

—

C₂³

—

C₂³

—

C₂³

—

C₂³

—

C₂³

#11924005

yes

characteristic

C₂³

C₈×D₇₃

yes

characteristic

C₂³

#11924011

yes

characteristic

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

292

—

105

C₂×C₄

—

292

—

106

C₂×C₄

—

292

—

107

C₂×C₄

—

292

—

108

C₂×C₄

—

292

—

109

C₂×C₄

—

292

—

110

C₂×C₄

—

146

—

111

C₂×C₄

—

146

—

112

C₈

—

113

C₈

—

584

—

114

C₂²

—

115

C₂²

—

116

C₂²

—

117

C₂²

—

118

C₂²

—

119

C₂²

—

120

C₂²

—

121

C₂²

—

122

C₂²

—

123

C₂²

#14556503

yes

characteristic

124

C₂²

#14556505

yes

characteristic

125

C₂²

#14556509

yes

characteristic

126

C₄

—

127

C₄

—

128

C₄

—

292

—

129

C₄

—

292

—

130

C₂

—

131

C₂

—

132

C₂

—

133

C₂

—

134

C₂

#17988312

yes

characteristic

135

C₂

#17988375

yes

characteristic

136

C₂

#17988376

yes

characteristic

	subgroup	G/H
center	C₂²	#14556505
commutator	C₂³×C₇₃	C₂×C₈
Frattini	C₂×C₂²⋊C₄	C₂×D₇₃
Fitting	#323×C₇₃	C₂
socle	C₂²×C₇₃	#99
hypercenter	#323	D₇₃
hypocenter	C₇₃	#1326
LCS	G ▷ C₂³×C₇₃ ▷ C₂²×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂³ ◁ C₂×C₂²⋊C₄ ◁ #323

subgroup

G/H

center

C₂²

#14556505

commutator

C₂³×C₇₃

C₂×C₈

Frattini

C₂×C₂²⋊C₄

C₂×D₇₃

Fitting

#323×C₇₃

C₂

C₂²×C₇₃

D₇₃

C₇₃

G ▷ C₂³×C₇₃ ▷ C₂²×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₂³ ◁ C₂×C₂²⋊C₄ ◁ #323

N	H ≅ G/N	type
18. C₂²⋊Dic₇₃	C₈	semidirect
69. C₇₃	#1326	semidirect

H ≅ G/N

type

18. C₂²⋊Dic₇₃

C₈

semidirect

69. C₇₃

#1326

semidirect

Subgroups — #22607880

Conjugacy classes of subgroups

Complements