Group #34014766 — subgroups

Subgroups — #34014766

Order 18688.

1246 conjugacy classes of subgroups; only the 288 normal subgroups are shown.

normal subgroups only

This group has 1246 conjugacy classes of subgroups — too many to draw. Only its 288 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	#22625118	C₂	1	8	yes	maximal
2	C₄×(C₂×#64408)⋊C₄	C₂	1	6	yes	maximal
3	#376×D₇₃	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₄×#64408	C₂²	1	4	yes	—
5	C₂×(C₂×#64408)⋊C₄	C₂²	1	24	yes	—
6	C₂×C₄²×D₇₃	C₂²	1	3	yes	—
7	#17988433	C₄	1	3	yes	complemented
8	#17988432	C₄	1	4	yes	complemented
9	#95×D₇₃	C₂²	1	4	yes	—
10	#376×C₇₃	C₄	1	1	yes	characteristic, complemented
11	C₂³×#64408	C₂³	1	8	yes	—
12	C₂×C₄×#64408	—	2	24	no	—
13	(C₂×#64408)⋊C₄	—	2	48	no	—
14	C₂²×C₄×D₇₃	C₂³	1	6	yes	—
15	C₂²×C₄×D₇₃	C₂³	1	1	yes	characteristic
16	C₂×C₄×Dic₇₃	C₂×C₄	1	6	yes	—
17	C₂×C₄×Dic₇₃	C₂×C₄	1	3	yes	—
18	C₄²×D₇₃	—	2	12	no	—
19	#14556498	C₂×C₄	1	12	yes	—
20	C₂×C₄²×C₇₃	C₂×C₄	1	3	yes	—
21	#95×C₇₃	C₂×C₄	1	4	yes	—
22	C₂²×#64408	—	2	24	no	—
23	C₂²×#64408	—	2	24	no	—
24	C₂²×#64408	#41	1	16	yes	—
25	C₄×#64408	—	4	16	no	—
26	C₂³×D₇₃	C₂⁴	1	1	yes	characteristic
27	C₂²×Dic₇₃	C₂²×C₄	1	6	yes	—
28	C₂²×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
29	C₂×C₄×D₇₃	—	2	12	no	—
30	C₂×C₄×D₇₃	—	2	24	no	—
31	C₂×C₄×D₇₃	#41	1	12	yes	—
32	C₄×Dic₇₃	—	2	6	no	—
33	C₄×Dic₇₃	—	2	12	no	—
34	C₂²×C₄×C₇₃	C₂²×C₄	1	6	yes	—
35	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
36	C₄²×C₇₃	—	2	6	no	—
37	C₂³×C₇₃	C₂³×C₄	1	1	yes	characteristic
38	C₂²×D₇₃	C₂×#41	1	6	yes	—
39	C₂²×D₇₃	C₂×#41	1	8	yes	—
40	C₂×#64408	—	2	48	no	—
41	C₂×#64408	—	4	8	no	—
42	C₂×#64408	—	4	24	no	—
43	C₂×C₄×C₇₃	—	2	6	no	—
44	C₂×C₄×C₇₃	—	2	12	no	—
45	C₂×C₄×C₇₃	#117	1	6	yes	—
46	C₂×Dic₇₃	—	2	6	no	—
47	C₂×Dic₇₃	—	2	12	no	—
48	C₂×Dic₇₃	#117	1	6	yes	—
49	C₄×D₇₃	—	4	24	no	—
50	C₄×D₇₃	#126	1	16	yes	—
51	C₂²×C₇₃	C₂×#117	1	3	yes	—
52	C₂²×C₇₃	C₄×#41	1	4	yes	—
53	C₂×D₇₃	C₂×#126	1	4	yes	—
54	C₂×D₇₃	#529	1	24	yes	—
55	#64408	—	4	16	no	—
56	C₄×C₇₃	—	4	6	no	—
57	C₄×C₇₃	#383	1	4	yes	—
58	Dic₇₃	—	4	6	no	—
59	Dic₇₃	#383	1	4	yes	—
60	#13855	—	73	1	no	maximal, Sylow
61	C₂×C₇₃	C₂×#383	1	1	yes	characteristic
62	C₂×C₇₃	#2298	1	6	yes	—
63	D₇₃	#2401	1	8	yes	—
64	C₂×#376	—	73	1	no	—
65	#1443	—	73	8	no	—
66	C₄×#95	—	73	6	no	—
67	C₇₃	#13855	1	1	yes	characteristic, complemented, Sylow
68	C₂²×C₄²	—	73	3	no	—
69	C₂²×C₄²	—	73	4	no	—
70	#376	—	73	3	no	—
71	#376	—	73	4	no	—
72	#376	#64408	1	1	yes	characteristic, complemented
73	C₂×#95	—	73	4	no	—
74	C₂×#95	—	73	24	no	—
75	C₂³×C₄	—	73	1	no	—
76	C₂³×C₄	—	73	8	no	—
77	C₂³×C₄	—	73	6	no	—
78	C₂×C₄²	—	73	6	no	—
79	C₂×C₄²	—	73	3	no	—
80	C₂×C₄²	—	146	12	no	—
81	C₂×C₄²	—	146	24	no	—
82	C₂×C₄²	C₂×#64408	1	3	yes	—
83	#95	—	73	12	no	—
84	#95	—	146	48	no	—
85	#95	C₂×#64408	1	4	yes	—
86	C₂⁴	—	73	1	no	—
87	C₂²×C₄	—	73	1	no	—
88	C₂²×C₄	—	73	12	no	—
89	C₂²×C₄	—	73	16	no	—
90	C₂²×C₄	—	73	6	no	—
91	C₂²×C₄	—	146	24	no	—
92	C₂²×C₄	—	146	12	no	—
93	C₂²×C₄	—	146	24	no	—
94	C₂²×C₄	—	146	24	no	—
95	C₂²×C₄	C₂²×#64408	1	6	yes	—
96	C₂²×C₄	C₂²×#64408	1	1	yes	characteristic
97	C₄²	—	2	6	no	—
98	C₄²	—	292	16	no	—
99	C₄²	—	146	12	no	—
100	C₄²	—	146	6	no	—
101	C₂³	—	73	6	no	—
102	C₂³	—	73	8	no	—
103	C₂³	C₂³×#64408	1	1	yes	characteristic
104	C₂×C₄	—	2	6	no	—
105	C₂×C₄	—	2	12	no	—
106	C₂×C₄	—	292	24	no	—
107	C₂×C₄	—	292	8	no	—
108	C₂×C₄	—	292	24	no	—
109	C₂×C₄	—	73	6	no	—
110	C₂×C₄	—	73	16	no	—
111	C₂×C₄	—	146	48	no	—
112	C₂×C₄	—	146	6	no	—
113	C₂×C₄	—	146	12	no	—
114	C₂×C₄	#14556670	1	6	yes	—
115	C₂²	—	73	4	no	—
116	C₂²	—	73	24	no	—
117	C₂²	C₂×#14556670	1	3	yes	—
118	C₂²	#41×#64408	1	4	yes	—
119	C₄	—	4	6	no	—
120	C₄	—	292	16	no	—
121	C₄	—	292	6	no	—
122	C₄	—	73	4	no	—
123	C₄	#17989532	1	4	yes	—
124	C₂	—	73	8	no	—
125	C₂	C₂×#17989532	1	1	yes	characteristic
126	C₂	#22626393	1	6	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#22625118

C₂

yes

maximal

C₄×(C₂×#64408)⋊C₄

C₂

yes

maximal

#376×D₇₃

C₂

yes

maximal, characteristic

C₂²×C₄×#64408

C₂²

yes

—

C₂×(C₂×#64408)⋊C₄

C₂²

yes

—

C₂×C₄²×D₇₃

C₂²

yes

—

#17988433

C₄

yes

complemented

#17988432

C₄

yes

complemented

#95×D₇₃

C₂²

yes

—

#376×C₇₃

C₄

yes

characteristic, complemented

C₂³×#64408

C₂³

yes

—

C₂×C₄×#64408

—

(C₂×#64408)⋊C₄

—

C₂²×C₄×D₇₃

C₂³

yes

—

C₂²×C₄×D₇₃

C₂³

yes

characteristic

C₂×C₄×Dic₇₃

C₂×C₄

yes

—

C₂×C₄×Dic₇₃

C₂×C₄

yes

—

C₄²×D₇₃

—

#14556498

C₂×C₄

yes

—

C₂×C₄²×C₇₃

C₂×C₄

yes

—

#95×C₇₃

C₂×C₄

yes

—

C₂²×#64408

—

C₂²×#64408

—

C₂²×#64408

#41

yes

—

C₄×#64408

—

C₂³×D₇₃

C₂⁴

yes

characteristic

C₂²×Dic₇₃

C₂²×C₄

yes

—

C₂²×Dic₇₃

C₂²×C₄

yes

characteristic

C₂×C₄×D₇₃

—

C₂×C₄×D₇₃

—

C₂×C₄×D₇₃

#41

yes

—

C₄×Dic₇₃

—

C₄×Dic₇₃

—

C₂²×C₄×C₇₃

C₂²×C₄

yes

—

C₂²×C₄×C₇₃

C₂²×C₄

yes

characteristic

C₄²×C₇₃

—

C₂³×C₇₃

C₂³×C₄

yes

characteristic

C₂²×D₇₃

C₂×#41

yes

—

C₂²×D₇₃

C₂×#41

yes

—

C₂×#64408

—

C₂×#64408

—

C₂×#64408

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

#117

yes

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

#117

yes

—

C₄×D₇₃

—

C₄×D₇₃

#126

yes

—

C₂²×C₇₃

C₂×#117

yes

—

C₂²×C₇₃

C₄×#41

yes

—

C₂×D₇₃

C₂×#126

yes

—

C₂×D₇₃

#529

yes

—

#64408

—

C₄×C₇₃

—

C₄×C₇₃

#383

yes

—

Dic₇₃

—

Dic₇₃

#383

yes

—

—

C₂×C₇₃

yes

C₂×C₇₃

yes

—

D₇₃

#2401

yes

—

C₂×#376

—

#1443

—

C₄×#95

—

C₇₃

#13855

yes

characteristic, complemented, Sylow

C₂²×C₄²

—

C₂²×C₄²

—

—

—

yes

characteristic, complemented

C₂×#95

—

C₂×#95

—

C₂³×C₄

—

C₂³×C₄

—

C₂³×C₄

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

146

—

C₂×C₄²

—

146

—

C₂×C₄²

C₂×#64408

yes

—

#95

—

#95

—

146

—

#95

C₂×#64408

yes

—

C₂⁴

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

146

—

C₂²×C₄

—

146

—

C₂²×C₄

—

146

—

C₂²×C₄

—

146

—

C₂²×C₄

C₂²×#64408

yes

—

C₂²×C₄

C₂²×#64408

yes

characteristic

C₄²

—

C₄²

—

292

—

C₄²

—

146

—

100

C₄²

—

146

—

101

C₂³

—

102

C₂³

—

103

C₂³

C₂³×#64408

yes

characteristic

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

292

—

107

C₂×C₄

—

292

—

108

C₂×C₄

—

292

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

146

—

112

C₂×C₄

—

146

—

113

C₂×C₄

—

146

—

114

C₂×C₄

#14556670

yes

—

115

C₂²

—

116

C₂²

—

117

C₂²

C₂×#14556670

yes

—

118

C₂²

#41×#64408

yes

—

119

C₄

—

120

C₄

—

292

—

121

C₄

—

292

—

122

C₄

—

123

C₄

#17989532

yes

—

124

C₂

—

125

C₂

C₂×#17989532

yes

characteristic

126

C₂

#22626393

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, cosocle	C₂³×D₇₃	C₂⁴
hypercenter	#376	#64408
hypocenter	C₇₃	#13855
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, cosocle

C₂³×D₇₃

C₂⁴

C₇₃

G ▷ C₂³×C₇₃ ▷ C₇₃

C₁ ◁ C₂²×C₄ ◁ #376

N	H ≅ G/N	type
7. #17988433	C₄	semidirect
8. #17988432	C₄	semidirect
10. #376×C₇₃	C₄	semidirect
67. C₇₃	#13855	semidirect
72. #376	#64408	semidirect

H ≅ G/N

type

7. #17988433

C₄

semidirect

8. #17988432

C₄

semidirect

10. #376×C₇₃

C₄

semidirect

67. C₇₃

#13855

semidirect

72. #376

#64408

semidirect

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

subgroup	index
#22625118	2
C₄×(C₂×#64408)⋊C₄	2
#376×D₇₃	2
#13855	73

subgroup

index

#22625118

C₄×(C₂×#64408)⋊C₄

#376×D₇₃

#13855

Subgroups — #34014766

Conjugacy classes of subgroups

Complements

Maximal subgroups