Group #32923753 — subgroups

Subgroups — C₇₃×#14349 #32923753

Order 18688.

1638 conjugacy classes of subgroups; only the 462 normal subgroups are shown.

normal subgroups only

This group has 1638 conjugacy classes of subgroups — too many to draw. Only its 462 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×#95×C₇₃	C₂	1	1	yes	maximal, characteristic
2	C₇₃×#1443	C₂	1	8	yes	maximal, complemented
3	C₇₃×C₂²⋊#95	C₂	1	6	yes	maximal
4	C₂⁴×C₄×C₇₃	C₂²	1	3	yes	—
5	C₂²×C₂²⋊C₄×C₇₃	C₂²	1	4	yes	—
6	C₂×#95×C₇₃	C₄	1	8	yes	complemented
7	C₂×#95×C₇₃	C₂²	1	24	yes	—
8	C₂×#95×C₇₃	C₂²	1	4	yes	—
9	C₂⁵×C₇₃	C₂³	1	1	yes	characteristic
10	C₂³×C₄×C₇₃	—	2	12	no	—
11	C₂³×C₄×C₇₃	—	4	12	no	—
12	C₂³×C₄×C₇₃	C₂×C₄	1	12	yes	—
13	C₂³×C₄×C₇₃	C₂³	1	8	yes	—
14	C₂³×C₄×C₇₃	C₂³	1	6	yes	—
15	C₂×C₂²⋊C₄×C₇₃	—	2	24	no	—
16	#95×C₇₃	—	4	24	no	—
17	#95×C₇₃	C₂×C₄	1	16	yes	—
18	C₂⁴×C₇₃	—	2	6	no	—
19	C₂⁴×C₇₃	—	2	2	no	—
20	C₂⁴×C₇₃	C₂²×C₄	1	2	yes	—
21	C₂⁴×C₇₃	#41	1	12	yes	—
22	C₂⁴×C₇₃	C₂⁴	1	1	yes	characteristic
23	C₂²×C₄×C₇₃	—	2	24	no	—
24	C₂²×C₄×C₇₃	—	2	12	no	—
25	C₂²×C₄×C₇₃	—	2	24	no	—
26	C₂²×C₄×C₇₃	—	2	24	no	—
27	C₂²×C₄×C₇₃	—	2	24	no	—
28	C₂²×C₄×C₇₃	—	2	8	no	—
29	C₂²×C₄×C₇₃	—	4	24	no	—
30	C₂²×C₄×C₇₃	—	4	48	no	—
31	C₂²×C₄×C₇₃	C₂²×C₄	1	12	yes	—
32	C₂²⋊C₄×C₇₃	—	4	16	no	—
33	C₂³×C₇₃	—	2	6	no	—
34	C₂³×C₇₃	—	2	2	no	—
35	C₂³×C₇₃	—	2	24	no	—
36	C₂³×C₇₃	—	2	24	no	—
37	C₂³×C₇₃	#117	1	12	yes	—
38	C₂³×C₇₃	#126	1	16	yes	—
39	C₂³×C₇₃	C₂³×C₄	1	1	yes	characteristic
40	C₂³×C₇₃	C₂×#41	1	6	yes	—
41	C₂³×C₇₃	H(5,𝔽₂)	1	6	yes	—
42	C₂³×C₇₃	2₋¹⁺⁴	1	2	yes	—
43	C₂×C₄×C₇₃	—	2	12	no	—
44	C₂×C₄×C₇₃	—	2	24	no	—
45	C₂×C₄×C₇₃	—	4	48	no	—
46	C₂×C₄×C₇₃	—	4	24	no	—
47	C₂×C₄×C₇₃	—	4	8	no	—
48	C₂×C₄×C₇₃	—	4	24	no	—
49	C₂×C₄×C₇₃	—	4	24	no	—
50	C₂²×C₇₃	—	2	12	no	—
51	C₂²×C₇₃	—	2	12	no	—
52	C₂²×C₇₃	—	2	32	no	—
53	C₂²×C₇₃	#383	1	8	yes	—
54	C₂²×C₇₃	C₂×#117	1	3	yes	—
55	C₂²×C₇₃	#518	1	3	yes	—
56	C₂²×C₇₃	#519	1	1	yes	characteristic
57	C₂²×C₇₃	C₂×#126	1	4	yes	—
58	C₂²×C₇₃	#538	1	12	yes	—
59	C₂²×C₇₃	#539	1	12	yes	—
60	C₄×C₇₃	—	4	12	no	—
61	C₄×C₇₃	—	8	8	no	—
62	#14349	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
63	C₂×C₇₃	—	2	8	no	—
64	C₂×C₇₃	C₂×#383	1	1	yes	characteristic
65	C₂×C₇₃	#2312	1	3	yes	—
66	C₂×C₇₃	#2313	1	3	yes	—
67	C₂×C₇₃	#2643	1	8	yes	—
68	C₂²×#95	C₂×C₇₃	1	1	yes	characteristic
69	#1443	C₂×C₇₃	1	8	yes	complemented
70	C₂²⋊#95	C₂×C₇₃	1	6	yes	—
71	C₇₃	#14349	1	1	yes	characteristic, direct product factor, Sylow
72	C₂⁴×C₄	C₂²×C₇₃	1	3	yes	—
73	C₂²×C₂²⋊C₄	C₂²×C₇₃	1	4	yes	—
74	C₂×#95	C₄×C₇₃	1	8	yes	complemented
75	C₂×#95	C₂²×C₇₃	1	24	yes	—
76	C₂×#95	C₂²×C₇₃	1	4	yes	—
77	C₂⁵	C₂³×C₇₃	1	1	yes	characteristic
78	C₂³×C₄	—	2	12	no	—
79	C₂³×C₄	—	4	12	no	—
80	C₂³×C₄	C₂×C₄×C₇₃	1	12	yes	—
81	C₂³×C₄	C₂³×C₇₃	1	8	yes	—
82	C₂³×C₄	C₂³×C₇₃	1	6	yes	—
83	C₂×C₂²⋊C₄	—	2	24	no	—
84	#95	—	4	24	no	—
85	#95	C₂×C₄×C₇₃	1	16	yes	—
86	C₂⁴	—	2	6	no	—
87	C₂⁴	—	2	2	no	—
88	C₂⁴	C₂²×C₄×C₇₃	1	2	yes	—
89	C₂⁴	#41×C₇₃	1	12	yes	—
90	C₂⁴	C₂⁴×C₇₃	1	1	yes	characteristic
91	C₂²×C₄	—	2	24	no	—
92	C₂²×C₄	—	2	12	no	—
93	C₂²×C₄	—	2	24	no	—
94	C₂²×C₄	—	2	24	no	—
95	C₂²×C₄	—	2	24	no	—
96	C₂²×C₄	—	2	8	no	—
97	C₂²×C₄	—	4	24	no	—
98	C₂²×C₄	—	4	48	no	—
99	C₂²×C₄	C₂²×C₄×C₇₃	1	12	yes	—
100	C₂²⋊C₄	—	4	16	no	—
101	C₂³	—	2	6	no	—
102	C₂³	—	2	2	no	—
103	C₂³	—	2	24	no	—
104	C₂³	—	2	24	no	—
105	C₂³	#117×C₇₃	1	12	yes	—
106	C₂³	#126×C₇₃	1	16	yes	—
107	C₂³	C₂³×C₄×C₇₃	1	1	yes	characteristic
108	C₂³	C₂×#41×C₇₃	1	6	yes	—
109	C₂³	H(5,𝔽₂)×C₇₃	1	6	yes	—
110	C₂³	2₋¹⁺⁴×C₇₃	1	2	yes	—
111	C₂×C₄	—	2	12	no	—
112	C₂×C₄	—	2	24	no	—
113	C₂×C₄	—	4	48	no	—
114	C₂×C₄	—	4	24	no	—
115	C₂×C₄	—	4	8	no	—
116	C₂×C₄	—	4	24	no	—
117	C₂×C₄	—	4	24	no	—
118	C₂²	—	2	12	no	—
119	C₂²	—	2	12	no	—
120	C₂²	—	2	32	no	—
121	C₂²	#383×C₇₃	1	8	yes	—
122	C₂²	C₂×#117×C₇₃	1	3	yes	—
123	C₂²	#518×C₇₃	1	3	yes	—
124	C₂²	#519×C₇₃	1	1	yes	characteristic
125	C₂²	C₂×#126×C₇₃	1	4	yes	—
126	C₂²	#538×C₇₃	1	12	yes	—
127	C₂²	#539×C₇₃	1	12	yes	—
128	C₄	—	4	12	no	—
129	C₄	—	8	8	no	—
130	C₂	—	2	8	no	—
131	C₂	C₂×#383×C₇₃	1	1	yes	characteristic
132	C₂	C₇₃×#2312	1	3	yes	—
133	C₂	C₇₃×#2313	1	3	yes	—
134	C₂	C₇₃×#2643	1	8	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×#95×C₇₃

C₂

yes

maximal, characteristic

C₇₃×#1443

C₂

yes

maximal, complemented

C₇₃×C₂²⋊#95

C₂

yes

maximal

C₂⁴×C₄×C₇₃

C₂²

yes

—

C₂²×C₂²⋊C₄×C₇₃

C₂²

yes

—

C₂×#95×C₇₃

C₄

yes

complemented

C₂×#95×C₇₃

C₂²

yes

—

C₂×#95×C₇₃

C₂²

yes

—

C₂⁵×C₇₃

C₂³

yes

characteristic

C₂³×C₄×C₇₃

—

C₂³×C₄×C₇₃

—

C₂³×C₄×C₇₃

C₂×C₄

yes

—

C₂³×C₄×C₇₃

C₂³

yes

—

C₂³×C₄×C₇₃

C₂³

yes

—

C₂×C₂²⋊C₄×C₇₃

—

#95×C₇₃

—

#95×C₇₃

C₂×C₄

yes

—

C₂⁴×C₇₃

—

C₂⁴×C₇₃

—

C₂⁴×C₇₃

C₂²×C₄

yes

—

C₂⁴×C₇₃

#41

yes

—

C₂⁴×C₇₃

C₂⁴

yes

characteristic

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

C₂²×C₄

yes

—

C₂²⋊C₄×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

#117

yes

—

C₂³×C₇₃

#126

yes

—

C₂³×C₇₃

C₂³×C₄

yes

characteristic

C₂³×C₇₃

C₂×#41

yes

—

C₂³×C₇₃

H(5,𝔽₂)

yes

—

C₂³×C₇₃

2₋¹⁺⁴

yes

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

#383

yes

—

C₂²×C₇₃

C₂×#117

yes

—

C₂²×C₇₃

#518

yes

—

C₂²×C₇₃

#519

yes

characteristic

C₂²×C₇₃

C₂×#126

yes

—

C₂²×C₇₃

#538

yes

—

C₂²×C₇₃

#539

yes

—

C₄×C₇₃

—

C₄×C₇₃

—

#14349

C₇₃

yes

maximal, characteristic, direct product factor, Sylow

C₂×C₇₃

—

C₂×C₇₃

C₂×#383

yes

characteristic

C₂×C₇₃

#2312

yes

—

C₂×C₇₃

#2313

yes

—

C₂×C₇₃

#2643

yes

—

C₂²×#95

C₂×C₇₃

yes

characteristic

#1443

C₂×C₇₃

yes

complemented

C₂²⋊#95

C₂×C₇₃

yes

—

C₇₃

#14349

yes

characteristic, direct product factor, Sylow

C₂⁴×C₄

C₂²×C₇₃

yes

—

C₂²×C₂²⋊C₄

C₂²×C₇₃

yes

—

C₂×#95

C₄×C₇₃

yes

complemented

C₂×#95

C₂²×C₇₃

yes

—

C₂×#95

C₂²×C₇₃

yes

—

C₂⁵

C₂³×C₇₃

yes

characteristic

C₂³×C₄

—

C₂³×C₄

—

C₂³×C₄

C₂×C₄×C₇₃

yes

—

C₂³×C₄

C₂³×C₇₃

yes

—

C₂³×C₄

C₂³×C₇₃

yes

—

C₂×C₂²⋊C₄

—

#95

—

#95

C₂×C₄×C₇₃

yes

—

C₂⁴

—

C₂⁴

—

C₂⁴

C₂²×C₄×C₇₃

yes

—

C₂⁴

#41×C₇₃

yes

—

C₂⁴

C₂⁴×C₇₃

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×C₄×C₇₃

yes

—

100

C₂²⋊C₄

—

101

C₂³

—

102

C₂³

—

103

C₂³

—

104

C₂³

—

105

C₂³

#117×C₇₃

yes

—

106

C₂³

#126×C₇₃

yes

—

107

C₂³

C₂³×C₄×C₇₃

yes

characteristic

108

C₂³

C₂×#41×C₇₃

yes

—

109

C₂³

H(5,𝔽₂)×C₇₃

yes

—

110

C₂³

2₋¹⁺⁴×C₇₃

yes

—

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂²

—

119

C₂²

—

120

C₂²

—

121

C₂²

#383×C₇₃

yes

—

122

C₂²

C₂×#117×C₇₃

yes

—

123

C₂²

#518×C₇₃

yes

—

124

C₂²

#519×C₇₃

yes

characteristic

125

C₂²

C₂×#126×C₇₃

yes

—

126

C₂²

#538×C₇₃

yes

—

127

C₂²

#539×C₇₃

yes

—

128

C₄

—

129

C₄

—

130

C₂

—

131

C₂

C₂×#383×C₇₃

yes

characteristic

132

C₂

C₇₃×#2312

yes

—

133

C₂

C₇₃×#2313

yes

—

134

C₂

C₇₃×#2643

yes

—

	subgroup	G/H
center, socle	C₂⁴×C₇₃	C₂⁴
commutator	C₂³	C₂³×C₄×C₇₃
Frattini, cosocle	C₂⁴	C₂⁴×C₇₃
prime radical	C₂⁵×C₇₃	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₇₃ ◁ G

subgroup

G/H

center, socle

C₂⁴×C₇₃

C₂⁴

commutator

C₂³

C₂³×C₄×C₇₃

Frattini, cosocle

C₂⁴

C₂⁴×C₇₃

prime radical

C₂⁵×C₇₃

C₂³

LCS

G ▷ C₂³ ▷ C₁

UCS

C₁ ◁ C₂⁴×C₇₃ ◁ G

N	H ≅ G/N	type
2. C₇₃×#1443	C₂	semidirect
6. C₂×#95×C₇₃	C₄	semidirect
62. #14349	C₇₃	direct (N × H)
69. #1443	C₂×C₇₃	semidirect
71. C₇₃	#14349	direct (N × H)
74. C₂×#95	C₄×C₇₃	semidirect

H ≅ G/N

type

2. C₇₃×#1443

C₂

semidirect

6. C₂×#95×C₇₃

C₄

semidirect

62. #14349

C₇₃

direct (N × H)

69. #1443

C₂×C₇₃

semidirect

71. C₇₃

#14349

direct (N × H)

74. C₂×#95

C₄×C₇₃

semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×#95×C₇₃	2
C₇₃×#1443	2
C₇₃×C₂²⋊#95	2
#14349	73

subgroup

index

C₂²×#95×C₇₃

C₇₃×#1443

C₇₃×C₂²⋊#95

#14349

Subgroups — C₇₃×#14349 #32923753

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C73×#14349 #32923753

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#14349 #32923753