Group #34021322 — subgroups

Subgroups — D₇₃⋊#1843 #34021322

Order 18688.

1230 conjugacy classes of subgroups; only the 416 normal subgroups are shown.

normal subgroups only

This group has 1230 conjugacy classes of subgroups — too many to draw. Only its 416 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	C₂×#17989588	C₂	1	6	yes	maximal
2	#22625865	C₂	1	8	yes	maximal, complemented
3	#376×D₇₃	C₂	1	1	yes	maximal, characteristic
4	C₂²×#11924036	C₂²	1	4	yes	—
5	C₂×#14556658	C₂²	1	12	yes	—
6	#17989588	—	2	24	no	—
7	C₂×C₄⋊#10596833	C₂²	1	12	yes	—
8	C₂×C₄²×D₇₃	C₂²	1	3	yes	—
9	#17988433	C₄	1	3	yes	—
10	#17988432	C₂²	1	4	yes	—
11	#95×D₇₃	C₄	1	4	yes	—
12	#376×C₇₃	C₄	1	1	yes	characteristic
13	C₂×#11924036	—	2	24	no	—
14	C₂²×#10596833	C₂³	1	8	yes	—
15	#14556658	—	2	24	no	—
16	C₄⋊#10596833	—	2	24	no	—
17	C₂²×C₄×D₇₃	C₂×C₄	1	6	yes	—
18	C₂²×C₄×D₇₃	C₂³	1	1	yes	characteristic
19	C₂×C₄×Dic₇₃	C₂×C₄	1	3	yes	—
20	C₂×C₄×Dic₇₃	C₂³	1	6	yes	—
21	C₄²×D₇₃	D₄	1	12	yes	—
22	C₄²×D₇₃	Q₈	1	12	yes	—
23	#14556498	C₂×C₄	1	12	yes	—
24	C₂×C₄²×C₇₃	C₂×C₄	1	3	yes	—
25	#95×C₇₃	C₂×C₄	1	4	yes	—
26	#11924036	—	4	16	no	—
27	C₂×#10596833	—	2	24	no	—
28	C₂³×D₇₃	C₂²×C₄	1	1	yes	characteristic
29	C₂²×Dic₇₃	C₂²×C₄	1	6	yes	—
30	C₂²×Dic₇₃	C₂⁴	1	1	yes	characteristic
31	C₂×C₄×D₇₃	—	2	24	no	—
32	C₂×C₄×D₇₃	C₄⋊C₄	1	24	yes	—
33	C₂×C₄×D₇₃	C₂×D₄	1	6	yes	—
34	C₂×C₄×D₇₃	C₂×Q₈	1	6	yes	—
35	C₄×Dic₇₃	C₄⋊C₄	1	12	yes	—
36	C₄×Dic₇₃	C₂×D₄	1	12	yes	—
37	C₄×Dic₇₃	C₂×Q₈	1	12	yes	—
38	C₂²×C₄×C₇₃	C₂²×C₄	1	6	yes	—
39	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
40	C₄²×C₇₃	C₄⋊C₄	1	12	yes	—
41	C₂³×C₇₃	C₂³×C₄	1	1	yes	characteristic
42	C₂²×D₇₃	C₂×C₄⋊C₄	1	6	yes	—
43	C₂²×D₇₃	#131	1	8	yes	—
44	C₂×C₄×C₇₃	—	2	12	no	—
45	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	12	yes	—
46	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	6	yes	—
47	C₂×Dic₇₃	—	2	12	no	—
48	C₂×Dic₇₃	C₂×C₄⋊C₄	1	12	yes	—
49	C₂×Dic₇₃	C₂²×D₄	1	3	yes	—
50	C₂×Dic₇₃	C₂²×Q₈	1	3	yes	—
51	C₄×D₇₃	—	2	48	no	—
52	C₄×D₇₃	#127	1	4	yes	—
53	C₄×D₇₃	C₄⋊Q₈	1	12	yes	—
54	#10596833	—	4	8	no	—
55	C₂²×C₇₃	C₂²×C₄⋊C₄	1	3	yes	—
56	C₂²×C₇₃	C₂×#131	1	4	yes	—
57	C₂×D₇₃	#384	1	4	yes	—
58	C₂×D₇₃	#424	1	24	yes	—
59	C₄×C₇₃	—	2	12	no	—
60	C₄×C₇₃	#384	1	4	yes	—
61	Dic₇₃	—	2	12	no	—
62	Dic₇₃	C₂×#127	1	1	yes	characteristic
63	Dic₇₃	C₂×C₄⋊Q₈	1	3	yes	—
64	C₂×#1843	—	73	1	no	maximal, Sylow
65	C₂×C₇₃	C₂×#384	1	1	yes	characteristic
66	C₂×C₇₃	C₂×#424	1	6	yes	—
67	D₇₃	#1843	1	8	yes	complemented
68	C₂²×C₄⋊C₈	—	73	6	no	—
69	C₂×#376	—	73	1	no	—
70	#1843	—	73	8	no	—
71	C₇₃	C₂×#1843	1	1	yes	characteristic, complemented, Sylow
72	C₂³×C₈	—	73	4	no	—
73	C₂²×C₄²	—	73	3	no	—
74	C₂×C₄⋊C₈	—	73	12	no	—
75	C₂×C₄⋊C₈	—	73	12	no	—
76	C₂×C₄⋊C₈	—	146	24	no	—
77	#376	—	73	3	no	—
78	#376	—	73	4	no	—
79	#376	#64408	1	1	yes	characteristic
80	C₂×#95	—	73	4	no	—
81	C₂³×C₄	—	73	1	no	—
82	C₂³×C₄	—	73	6	no	—
83	C₂²×C₈	—	73	8	no	—
84	C₂²×C₈	—	146	24	no	—
85	C₂×C₄²	—	73	6	no	—
86	C₂×C₄²	—	73	3	no	—
87	C₂×C₄²	—	73	12	no	—
88	C₂×C₄²	—	73	12	no	—
89	C₂×C₄²	C₂×#64408	1	3	yes	—
90	C₄⋊C₈	—	146	24	no	—
91	C₄⋊C₈	—	146	24	no	—
92	#95	—	73	12	no	—
93	#95	C₂×#64408	1	4	yes	—
94	C₂⁴	—	73	1	no	—
95	C₂²×C₄	—	73	1	no	—
96	C₂²×C₄	—	73	6	no	—
97	C₂²×C₄	—	73	6	no	—
98	C₂²×C₄	—	73	6	no	—
99	C₂²×C₄	—	73	24	no	—
100	C₂²×C₄	—	146	24	no	—
101	C₂²×C₄	C₂²×#64408	1	6	yes	—
102	C₂²×C₄	C₂²×#64408	1	1	yes	characteristic
103	C₂×C₈	—	292	16	no	—
104	C₂×C₈	—	146	24	no	—
105	C₄²	—	73	12	no	—
106	C₄²	—	73	12	no	—
107	C₄²	—	73	12	no	—
108	C₄²	C₄⋊#64408	1	12	yes	—
109	C₂³	—	73	6	no	—
110	C₂³	—	73	8	no	—
111	C₂³	C₂³×#64408	1	1	yes	characteristic
112	C₂×C₄	—	2	12	no	—
113	C₂×C₄	—	73	3	no	—
114	C₂×C₄	—	73	3	no	—
115	C₂×C₄	—	73	4	no	—
116	C₂×C₄	—	73	12	no	—
117	C₂×C₄	—	73	12	no	—
118	C₂×C₄	—	146	48	no	—
119	C₂×C₄	—	146	12	no	—
120	C₂×C₄	C₂×C₄⋊#64408	1	12	yes	—
121	C₂×C₄	C₂×C₄⋊#64408	1	6	yes	—
122	C₈	—	292	8	no	—
123	C₂²	—	73	24	no	—
124	C₂²	—	73	4	no	—
125	C₂²	C₂²×C₄⋊#64408	1	3	yes	—
126	C₂²	D₇₃⋊#131	1	4	yes	—
127	C₄	—	2	12	no	—
128	C₄	—	73	1	no	—
129	C₄	—	73	3	no	—
130	C₄	—	146	12	no	—
131	C₄	#17989533	1	4	yes	—
132	C₂	—	73	8	no	—
133	C₂	C₂×#17989533	1	1	yes	characteristic
134	C₂	D₇₃⋊#424	1	6	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#17989588

C₂

yes

maximal

#22625865

C₂

yes

maximal, complemented

#376×D₇₃

C₂

yes

maximal, characteristic

C₂²×#11924036

C₂²

yes

—

C₂×#14556658

C₂²

yes

—

#17989588

—

C₂×C₄⋊#10596833

C₂²

yes

—

C₂×C₄²×D₇₃

C₂²

yes

—

#17988433

C₄

yes

—

#17988432

C₂²

yes

—

#95×D₇₃

C₄

yes

—

#376×C₇₃

C₄

yes

characteristic

C₂×#11924036

—

C₂²×#10596833

C₂³

yes

—

#14556658

—

C₄⋊#10596833

—

C₂²×C₄×D₇₃

C₂×C₄

yes

—

C₂²×C₄×D₇₃

C₂³

yes

characteristic

C₂×C₄×Dic₇₃

C₂×C₄

yes

—

C₂×C₄×Dic₇₃

C₂³

yes

—

C₄²×D₇₃

D₄

yes

—

C₄²×D₇₃

Q₈

yes

—

#14556498

C₂×C₄

yes

—

C₂×C₄²×C₇₃

C₂×C₄

yes

—

#95×C₇₃

C₂×C₄

yes

—

#11924036

—

C₂×#10596833

—

C₂³×D₇₃

C₂²×C₄

yes

characteristic

C₂²×Dic₇₃

C₂²×C₄

yes

—

C₂²×Dic₇₃

C₂⁴

yes

characteristic

C₂×C₄×D₇₃

—

C₂×C₄×D₇₃

C₄⋊C₄

yes

—

C₂×C₄×D₇₃

C₂×D₄

yes

—

C₂×C₄×D₇₃

C₂×Q₈

yes

—

C₄×Dic₇₃

C₄⋊C₄

yes

—

C₄×Dic₇₃

C₂×D₄

yes

—

C₄×Dic₇₃

C₂×Q₈

yes

—

C₂²×C₄×C₇₃

C₂²×C₄

yes

—

C₂²×C₄×C₇₃

C₂²×C₄

yes

characteristic

C₄²×C₇₃

C₄⋊C₄

yes

—

C₂³×C₇₃

C₂³×C₄

yes

characteristic

C₂²×D₇₃

C₂×C₄⋊C₄

yes

—

C₂²×D₇₃

#131

yes

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂×C₄⋊C₄

yes

—

C₂×C₄×C₇₃

C₂×C₄⋊C₄

yes

—

C₂×Dic₇₃

—

C₂×Dic₇₃

C₂×C₄⋊C₄

yes

—

C₂×Dic₇₃

C₂²×D₄

yes

—

C₂×Dic₇₃

C₂²×Q₈

yes

—

C₄×D₇₃

—

C₄×D₇₃

#127

yes

—

C₄×D₇₃

C₄⋊Q₈

yes

—

#10596833

—

C₂²×C₇₃

C₂²×C₄⋊C₄

yes

—

C₂²×C₇₃

C₂×#131

yes

—

C₂×D₇₃

#384

yes

—

C₂×D₇₃

#424

yes

—

C₄×C₇₃

—

C₄×C₇₃

#384

yes

—

Dic₇₃

—

Dic₇₃

C₂×#127

yes

characteristic

Dic₇₃

C₂×C₄⋊Q₈

yes

—

—

C₂×C₇₃

yes

C₂×C₇₃

yes

—

D₇₃

#1843

yes

complemented

C₂²×C₄⋊C₈

—

C₂×#376

—

#1843

—

C₇₃

C₂×#1843

yes

characteristic, complemented, Sylow

C₂³×C₈

—

C₂²×C₄²

—

C₂×C₄⋊C₈

—

C₂×C₄⋊C₈

—

C₂×C₄⋊C₈

—

146

—

—

—

yes

C₂×#95

—

C₂³×C₄

—

C₂³×C₄

—

C₂²×C₈

—

C₂²×C₈

—

146

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂×#64408

yes

—

C₄⋊C₈

—

146

—

C₄⋊C₈

—

146

—

#95

—

#95

C₂×#64408

yes

—

C₂⁴

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

100

C₂²×C₄

—

146

—

101

C₂²×C₄

C₂²×#64408

yes

—

102

C₂²×C₄

C₂²×#64408

yes

characteristic

103

C₂×C₈

—

292

—

104

C₂×C₈

—

146

—

105

C₄²

—

106

C₄²

—

107

C₄²

—

108

C₄²

C₄⋊#64408

yes

—

109

C₂³

—

110

C₂³

—

111

C₂³

C₂³×#64408

yes

characteristic

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

146

—

119

C₂×C₄

—

146

—

120

C₂×C₄

C₂×C₄⋊#64408

yes

—

121

C₂×C₄

C₂×C₄⋊#64408

yes

—

122

C₈

—

292

—

123

C₂²

—

124

C₂²

—

125

C₂²

C₂²×C₄⋊#64408

yes

—

126

C₂²

D₇₃⋊#131

yes

—

127

C₄

—

128

C₄

—

129

C₄

—

130

C₄

—

146

—

131

C₄

#17989533

yes

—

132

C₂

—

133

C₂

C₂×#17989533

yes

characteristic

134

C₂

D₇₃⋊#424

yes

—

	subgroup	G/H
center	C₂²×C₄	C₂²×#64408
commutator, socle	C₂³×C₇₃	C₂³×C₄
Frattini	C₂³	C₂³×#64408
Fitting	#376×C₇₃	C₄
prime radical	C₂³×D₇₃	C₂²×C₄
cosocle	C₂²×Dic₇₃	C₂⁴
hypercenter	#376	#64408
hypocenter	C₇₃	C₂×#1843
LCS	G ▷ C₂³×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂²×C₄ ◁ #376

subgroup

G/H

center

C₂²×C₄

C₂²×#64408

commutator, socle

C₂³×C₇₃

C₂³×C₄

Frattini

C₂³

C₂³×#64408

Fitting

#376×C₇₃

C₄

prime radical

C₂³×D₇₃

C₂²×C₄

cosocle

C₂²×Dic₇₃

C₂⁴

C₇₃

G ▷ C₂³×C₇₃ ▷ C₇₃

C₁ ◁ C₂²×C₄ ◁ #376

N	H ≅ G/N	type
2. #22625865	C₂	semidirect
67. D₇₃	#1843	semidirect
71. C₇₃	C₂×#1843	semidirect

H ≅ G/N

type

2. #22625865

C₂

semidirect

67. D₇₃

#1843

semidirect

71. C₇₃

C₂×#1843

semidirect

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

subgroup	index
C₂×#17989588	2
#22625865	2
#376×D₇₃	2
C₂×#1843	73

subgroup

index

C₂×#17989588

#22625865

#376×D₇₃

C₂×#1843

Subgroups — D₇₃⋊#1843 #34021322

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D73⋊#1843 #34021322

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₇₃⋊#1843 #34021322