Group #34021256 — subgroups

Subgroups — #34021256

Order 18688.

830 conjugacy classes of subgroups; only the 232 normal subgroups are shown.

normal subgroups only

This group has 830 conjugacy classes of subgroups — too many to draw. Only its 232 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	#22625860	C₂	1	8	yes	maximal, complemented
2	#22625594	C₂	1	6	yes	maximal
3	C₂×#17988432	C₂	1	1	yes	maximal, characteristic
4	C₂²×#11924037	C₂²	1	4	yes	—
5	#17989453	C₂²	1	24	yes	—
6	C₂²×C₄×Dic₇₃	C₂²	1	3	yes	—
7	#17988432	C₄	1	4	yes	—
8	#17988432	C₂²	1	4	yes	—
9	C₂×#14556498	C₄	1	3	yes	—
10	C₂×#95×C₇₃	C₄	1	1	yes	characteristic
11	C₂×#11924037	—	2	24	no	—
12	C₂²×#10596833	C₂³	1	8	yes	—
13	C₂³×Dic₇₃	C₂×C₄	1	3	yes	—
14	C₂³×Dic₇₃	C₂³	1	1	yes	characteristic
15	C₂×C₄×Dic₇₃	—	2	12	no	—
16	C₂×C₄×Dic₇₃	C₂×C₄	1	6	yes	—
17	C₂×C₄×Dic₇₃	C₂³	1	6	yes	—
18	#14556498	C₂×C₄	1	12	yes	—
19	C₂³×C₄×C₇₃	C₂×C₄	1	3	yes	—
20	#95×C₇₃	C₂×C₄	1	4	yes	—
21	#11924037	—	4	16	no	—
22	C₂×#10596833	—	2	24	no	—
23	C₂²×Dic₇₃	—	2	6	no	—
24	C₂²×Dic₇₃	—	4	3	no	—
25	C₂²×Dic₇₃	—	4	3	no	—
26	C₂²×Dic₇₃	C₂²×C₄	1	6	yes	—
27	C₂²×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
28	C₂²×Dic₇₃	#41	1	12	yes	—
29	C₂²×Dic₇₃	C₂⁴	1	1	yes	characteristic
30	C₄×Dic₇₃	—	2	12	no	—
31	C₄×Dic₇₃	—	2	12	no	—
32	C₂⁴×C₇₃	C₂²×C₄	1	1	yes	characteristic
33	C₂²×C₄×C₇₃	—	2	6	no	—
34	C₂²×C₄×C₇₃	—	4	6	no	—
35	C₂²×C₄×C₇₃	C₂²×C₄	1	6	yes	—
36	C₂³×C₇₃	—	2	3	no	—
37	C₂³×C₇₃	—	2	1	no	—
38	C₂³×C₇₃	#117	1	6	yes	—
39	C₂³×C₇₃	C₂³×C₄	1	1	yes	characteristic
40	C₂×C₄×C₇₃	—	2	6	no	—
41	C₂×C₄×C₇₃	—	2	12	no	—
42	C₂×C₄×C₇₃	—	4	12	no	—
43	C₂×Dic₇₃	—	2	6	no	—
44	C₂×Dic₇₃	—	2	6	no	—
45	C₂×Dic₇₃	—	2	6	no	—
46	C₂×Dic₇₃	—	4	12	no	—
47	C₂×Dic₇₃	#117	1	6	yes	—
48	C₂×Dic₇₃	#126	1	16	yes	—
49	C₂×Dic₇₃	C₂×#41	1	6	yes	—
50	#10596833	—	4	8	no	—
51	C₂²×C₇₃	—	2	6	no	—
52	C₂²×C₇₃	—	2	6	no	—
53	C₂²×C₇₃	#383	1	4	yes	—
54	C₂²×C₇₃	C₂×#117	1	3	yes	—
55	C₂²×C₇₃	#568	1	3	yes	—
56	C₂²×C₇₃	#568	1	1	yes	characteristic
57	C₄×C₇₃	—	4	6	no	—
58	Dic₇₃	—	4	6	no	—
59	Dic₇₃	#383	1	4	yes	—
60	Dic₇₃	C₂×#126	1	4	yes	—
61	#20773	—	73	1	no	maximal, Sylow
62	C₂×C₇₃	—	2	4	no	—
63	C₂×C₇₃	C₂×#383	1	1	yes	characteristic
64	C₂×C₇₃	#2921	1	3	yes	—
65	C₂×C₇₃	#2921	1	3	yes	—
66	C₂×#376	—	73	1	no	—
67	#1840	—	73	8	no	—
68	#1728	—	73	6	no	—
69	C₇₃	#20773	1	1	yes	characteristic, complemented, Sylow
70	C₂²×M₁₆	—	73	4	no	—
71	C₂²×C₄²	—	73	3	no	—
72	#376	—	73	4	no	—
73	#376	—	73	4	no	—
74	C₂×#95	—	73	3	no	—
75	C₂×#95	#64408	1	1	yes	characteristic
76	#336	—	73	24	no	—
77	C₂³×C₄	—	73	3	no	—
78	C₂³×C₄	—	73	1	no	—
79	C₂³×C₄	C₂×#64408	1	3	yes	—
80	C₂×M₁₆	—	146	24	no	—
81	C₂²×C₈	—	73	8	no	—
82	C₂×C₄²	—	73	6	no	—
83	C₂×C₄²	—	73	6	no	—
84	C₂×C₄²	—	146	12	no	—
85	#95	—	73	12	no	—
86	#95	C₂×#64408	1	4	yes	—
87	C₂⁴	C₂²×#64408	1	1	yes	characteristic
88	C₂²×C₄	—	2	6	no	—
89	C₂²×C₄	—	4	6	no	—
90	C₂²×C₄	—	292	3	no	—
91	C₂²×C₄	—	292	3	no	—
92	C₂²×C₄	—	73	1	no	—
93	C₂²×C₄	—	73	1	no	—
94	C₂²×C₄	—	73	12	no	—
95	C₂²×C₄	—	73	6	no	—
96	C₂²×C₄	—	146	6	no	—
97	C₂²×C₄	C₂²×#64408	1	6	yes	—
98	M₁₆	—	292	16	no	—
99	C₂×C₈	—	146	24	no	—
100	C₄²	—	146	12	no	—
101	C₄²	—	146	12	no	—
102	C₂³	—	2	3	no	—
103	C₂³	—	2	1	no	—
104	C₂³	#14556670	1	6	yes	—
105	C₂³	C₂³×#64408	1	1	yes	characteristic
106	C₂×C₄	—	2	6	no	—
107	C₂×C₄	—	2	12	no	—
108	C₂×C₄	—	4	12	no	—
109	C₂×C₄	—	292	12	no	—
110	C₂×C₄	—	73	6	no	—
111	C₂×C₄	—	73	6	no	—
112	C₂×C₄	—	73	16	no	—
113	C₂×C₄	—	146	6	no	—
114	C₂×C₄	—	146	6	no	—
115	C₂×C₄	—	146	6	no	—
116	C₈	—	292	8	no	—
117	C₂²	—	2	6	no	—
118	C₂²	—	2	6	no	—
119	C₂²	#17989532	1	4	yes	—
120	C₂²	C₂×#14556670	1	3	yes	—
121	C₂²	#17989665	1	3	yes	—
122	C₂²	#17989667	1	1	yes	characteristic
123	C₄	—	4	6	no	—
124	C₄	—	292	6	no	—
125	C₄	—	73	4	no	—
126	C₄	—	73	4	no	—
127	C₂	—	2	4	no	—
128	C₂	C₂×#17989532	1	1	yes	characteristic
129	C₂	#22626611	1	3	yes	—
130	C₂	#22626613	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#22625860

C₂

yes

maximal, complemented

#22625594

C₂

yes

maximal

C₂×#17988432

C₂

yes

maximal, characteristic

C₂²×#11924037

C₂²

yes

—

#17989453

C₂²

yes

—

C₂²×C₄×Dic₇₃

C₂²

yes

—

#17988432

C₄

yes

—

#17988432

C₂²

yes

—

C₂×#14556498

C₄

yes

—

C₂×#95×C₇₃

C₄

yes

characteristic

C₂×#11924037

—

C₂²×#10596833

C₂³

yes

—

C₂³×Dic₇₃

C₂×C₄

yes

—

C₂³×Dic₇₃

C₂³

yes

characteristic

C₂×C₄×Dic₇₃

—

C₂×C₄×Dic₇₃

C₂×C₄

yes

—

C₂×C₄×Dic₇₃

C₂³

yes

—

#14556498

C₂×C₄

yes

—

C₂³×C₄×C₇₃

C₂×C₄

yes

—

#95×C₇₃

C₂×C₄

yes

—

#11924037

—

C₂×#10596833

—

C₂²×Dic₇₃

—

C₂²×Dic₇₃

—

C₂²×Dic₇₃

—

C₂²×Dic₇₃

C₂²×C₄

yes

—

C₂²×Dic₇₃

C₂²×C₄

yes

characteristic

C₂²×Dic₇₃

#41

yes

—

C₂²×Dic₇₃

C₂⁴

yes

characteristic

C₄×Dic₇₃

—

C₄×Dic₇₃

—

C₂⁴×C₇₃

C₂²×C₄

yes

characteristic

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

C₂²×C₄

yes

—

C₂³×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

#117

yes

—

C₂³×C₇₃

C₂³×C₄

yes

characteristic

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

#117

yes

—

C₂×Dic₇₃

#126

yes

—

C₂×Dic₇₃

C₂×#41

yes

—

#10596833

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

#383

yes

—

C₂²×C₇₃

C₂×#117

yes

—

C₂²×C₇₃

#568

yes

—

C₂²×C₇₃

#568

yes

characteristic

C₄×C₇₃

—

Dic₇₃

—

Dic₇₃

#383

yes

—

Dic₇₃

C₂×#126

yes

—

#20773

—

maximal, Sylow

C₂×C₇₃

—

C₂×C₇₃

C₂×#383

yes

characteristic

C₂×C₇₃

#2921

yes

—

C₂×C₇₃

#2921

yes

—

C₂×#376

—

#1840

—

#1728

—

C₇₃

#20773

yes

characteristic, complemented, Sylow

C₂²×M₁₆

—

C₂²×C₄²

—

#376

—

#376

—

C₂×#95

—

C₂×#95

#64408

yes

characteristic

#336

—

C₂³×C₄

—

C₂³×C₄

—

C₂³×C₄

C₂×#64408

yes

—

C₂×M₁₆

—

146

—

C₂²×C₈

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

146

—

#95

—

#95

C₂×#64408

yes

—

C₂⁴

C₂²×#64408

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

292

—

C₂²×C₄

—

292

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

146

—

C₂²×C₄

C₂²×#64408

yes

—

M₁₆

—

292

—

C₂×C₈

—

146

—

100

C₄²

—

146

—

101

C₄²

—

146

—

102

C₂³

—

103

C₂³

—

104

C₂³

#14556670

yes

—

105

C₂³

C₂³×#64408

yes

characteristic

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

—

292

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

—

146

—

114

C₂×C₄

—

146

—

115

C₂×C₄

—

146

—

116

C₈

—

292

—

117

C₂²

—

118

C₂²

—

119

C₂²

#17989532

yes

—

120

C₂²

C₂×#14556670

yes

—

121

C₂²

#17989665

yes

—

122

C₂²

#17989667

yes

characteristic

123

C₄

—

124

C₄

—

292

—

125

C₄

—

126

C₄

—

127

C₂

—

128

C₂

C₂×#17989532

yes

characteristic

129

C₂

#22626611

yes

—

130

C₂

#22626613

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×#64408
commutator, socle	C₂³×C₇₃	C₂³×C₄
Fitting	C₂×#95×C₇₃	C₄
prime radical	C₂⁴×C₇₃	C₂²×C₄
cosocle	C₂²×Dic₇₃	C₂⁴
hypercenter	C₂×#95	#64408
hypocenter	C₇₃	#20773
LCS	G ▷ C₂³×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂³ ◁ C₂×#95

subgroup

G/H

center, Frattini

C₂³

C₂³×#64408

commutator, socle

C₂³×C₇₃

C₂³×C₄

Fitting

C₂×#95×C₇₃

C₄

prime radical

C₂⁴×C₇₃

C₂²×C₄

cosocle

C₂²×Dic₇₃

C₂⁴

C₂×#95

C₇₃

G ▷ C₂³×C₇₃ ▷ C₇₃

C₁ ◁ C₂³ ◁ C₂×#95

N	H ≅ G/N	type
1. #22625860	C₂	semidirect
69. C₇₃	#20773	semidirect

H ≅ G/N

type

1. #22625860

C₂

semidirect

69. C₇₃

#20773

semidirect

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

subgroup	index
#22625860	2
#22625594	2
C₂×#17988432	2
#20773	73

subgroup

index

Subgroups — #34021256

Conjugacy classes of subgroups

Complements

Maximal subgroups