Group #32975327 — subgroups

Subgroups — #32975327

Order 18688.

414 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 95 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	#22611469	C₂	1	3	yes	maximal
2	#22607757	C₂	1	3	yes	maximal
3	C₇₃×#2811	C₂	1	1	yes	maximal, characteristic
4	C₂×#14556524	—	2	3	no	—
5	C₂×#14556515	—	2	3	no	—
6	#17988457	C₂²	1	1	yes	characteristic
7	#17988342	C₂²	1	3	yes	—
8	#395×C₇₃	—	2	3	no	—
9	#391×C₇₃	—	2	3	no	—
10	#391×C₇₃	C₂²	1	3	yes	—
11	C₂²×#10596831	—	2	3	no	—
12	C₂×C₄⋊Dic₇₃	—	2	3	no	—
13	#14556524	—	4	6	no	—
14	#14556515	—	4	6	no	—
15	C₂²×Q₈×C₇₃	—	2	1	no	—
16	C₂²×Q₈×C₇₃	D₄	1	3	yes	—
17	C₂×C₄⋊C₄×C₇₃	—	2	3	no	—
18	C₂×C₄⋊C₄×C₇₃	D₄	1	3	yes	—
19	C₂×C₄²×C₇₃	—	2	1	no	—
20	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
21	#95×C₇₃	—	2	3	no	—
22	#95×C₇₃	—	2	6	no	—
23	C₂²×Dic₇₃	—	4	1	no	—
24	C₂×#10596831	—	2	6	no	—
25	C₂×#10596831	—	4	3	no	—
26	C₂×#10596831	—	4	3	no	—
27	C₄⋊Dic₇₃	—	4	3	no	—
28	C₄⋊Dic₇₃	—	4	3	no	—
29	C₂×Q₈×C₇₃	—	2	3	no	—
30	C₂×Q₈×C₇₃	—	4	3	no	—
31	C₂×Q₈×C₇₃	—	4	3	no	—
32	C₂×Q₈×C₇₃	—	8	3	no	—
33	C₂×Q₈×C₇₃	Q₁₆	1	6	yes	—
34	C₂²×C₄×C₇₃	—	2	3	no	—
35	C₂²×C₄×C₇₃	—	2	3	no	—
36	C₂²×C₄×C₇₃	C₂×D₄	1	3	yes	—
37	C₄⋊C₄×C₇₃	—	4	3	no	—
38	C₄⋊C₄×C₇₃	—	8	3	no	—
39	C₄²×C₇₃	—	4	1	no	—
40	C₄²×C₇₃	—	8	1	no	—
41	C₂³×C₇₃	#120	1	1	yes	characteristic
42	Q₈×C₇₃	—	4	6	no	—
43	Q₈×C₇₃	—	8	3	no	—
44	Q₈×C₇₃	—	8	4	no	—
45	C₂×C₄×C₇₃	—	2	3	no	—
46	C₂×C₄×C₇₃	—	2	3	no	—
47	C₂×C₄×C₇₃	—	2	6	no	—
48	C₂×C₄×C₇₃	—	4	3	no	—
49	C₂×C₄×C₇₃	—	4	3	no	—
50	C₂×C₄×C₇₃	—	4	3	no	—
51	C₂×C₄×C₇₃	—	4	6	no	—
52	C₂×C₄×C₇₃	C₂×Q₁₆	1	3	yes	—
53	C₂×C₄×C₇₃	#137	1	3	yes	—
54	C₂×Dic₇₃	—	8	3	no	—
55	#10596831	—	4	6	no	—
56	C₂²×C₇₃	#451	1	3	yes	—
57	C₂²×C₇₃	#453	1	3	yes	—
58	C₂²×C₇₃	#458	1	1	yes	characteristic
59	C₄×C₇₃	—	2	3	no	—
60	C₄×C₇₃	—	2	3	no	—
61	C₄×C₇₃	—	4	6	no	—
62	C₄×C₇₃	—	8	3	no	—
63	Dic₇₃	—	16	1	no	—
64	#7837	—	73	1	no	maximal, Sylow
65	C₂×C₇₃	#1614	1	3	yes	—
66	C₂×C₇₃	#1633	1	3	yes	—
67	C₂×C₇₃	#1655	1	1	yes	characteristic
68	#2811	D₇₃	1	1	yes	characteristic
69	#2095	—	73	3	no	—
70	#1272	—	73	3	no	—
71	C₇₃	#7837	1	1	yes	characteristic, complemented, Sylow
72	C₂×#107	—	146	3	no	—
73	C₂×#103	—	146	3	no	—
74	#395	—	2	3	no	—
75	#391	—	2	3	no	—
76	#391	C₂×D₇₃	1	3	yes	—
77	#384	—	73	1	no	—
78	#336	—	73	3	no	—
79	C₂²×Q₈	—	2	1	no	—
80	C₂²×Q₈	C₂²⋊D₇₃	1	3	yes	—
81	C₂²×C₈	—	146	3	no	—
82	C₂×C₄⋊C₄	—	2	3	no	—
83	C₂×C₄⋊C₄	—	146	3	no	—
84	C₂×C₄⋊C₄	C₂²⋊D₇₃	1	3	yes	—
85	C₂×C₄²	—	2	1	no	—
86	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
87	#107	—	292	6	no	—
88	#103	—	292	6	no	—
89	#95	—	2	3	no	—
90	#95	—	2	6	no	—
91	C₂×Q₈	—	2	3	no	—
92	C₂×Q₈	—	4	3	no	—
93	C₂×Q₈	—	4	3	no	—
94	C₂×Q₈	—	8	3	no	—
95	C₂×Q₈	#11924018	1	6	yes	—
96	C₂²×C₄	—	2	3	no	—
97	C₂²×C₄	—	2	3	no	—
98	C₂²×C₄	—	292	1	no	—
99	C₂²×C₄	C₂×C₂²⋊D₇₃	1	3	yes	—
100	C₂×C₈	—	292	3	no	—
101	C₂×C₈	—	292	3	no	—
102	C₂×C₈	—	146	6	no	—
103	C₄⋊C₄	—	4	3	no	—
104	C₄⋊C₄	—	8	3	no	—
105	C₄⋊C₄	—	292	3	no	—
106	C₄⋊C₄	—	292	3	no	—
107	C₄²	—	4	1	no	—
108	C₄²	—	8	1	no	—
109	C₂³	#14556560	1	1	yes	characteristic
110	Q₈	—	4	6	no	—
111	Q₈	—	8	3	no	—
112	Q₈	—	8	4	no	—
113	C₂×C₄	—	2	3	no	—
114	C₂×C₄	—	2	3	no	—
115	C₂×C₄	—	2	6	no	—
116	C₂×C₄	—	4	3	no	—
117	C₂×C₄	—	4	3	no	—
118	C₂×C₄	—	4	3	no	—
119	C₂×C₄	—	4	6	no	—
120	C₂×C₄	—	584	3	no	—
121	C₂×C₄	C₂×#11924018	1	3	yes	—
122	C₂×C₄	#14556622	1	3	yes	—
123	C₈	—	292	6	no	—
124	C₂²	#17988743	1	3	yes	—
125	C₂²	#17988755	1	3	yes	—
126	C₂²	#17988777	1	1	yes	characteristic
127	C₄	—	2	3	no	—
128	C₄	—	2	3	no	—
129	C₄	—	4	6	no	—
130	C₄	—	8	3	no	—
131	C₄	—	1168	1	no	—
132	C₂	#22608956	1	3	yes	—
133	C₂	#22609071	1	3	yes	—
134	C₂	#22609220	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#22611469

C₂

yes

maximal

#22607757

C₂

yes

maximal

C₇₃×#2811

C₂

yes

maximal, characteristic

C₂×#14556524

—

C₂×#14556515

—

#17988457

C₂²

yes

characteristic

#17988342

C₂²

yes

—

#395×C₇₃

—

#391×C₇₃

—

#391×C₇₃

C₂²

yes

—

C₂²×#10596831

—

C₂×C₄⋊Dic₇₃

—

#14556524

—

#14556515

—

C₂²×Q₈×C₇₃

—

C₂²×Q₈×C₇₃

D₄

yes

—

C₂×C₄⋊C₄×C₇₃

—

C₂×C₄⋊C₄×C₇₃

D₄

yes

—

C₂×C₄²×C₇₃

—

C₂×C₄²×C₇₃

C₂³

yes

characteristic

#95×C₇₃

—

#95×C₇₃

—

C₂²×Dic₇₃

—

C₂×#10596831

—

C₂×#10596831

—

C₂×#10596831

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

C₂×Q₈×C₇₃

—

C₂×Q₈×C₇₃

—

C₂×Q₈×C₇₃

—

C₂×Q₈×C₇₃

—

C₂×Q₈×C₇₃

Q₁₆

yes

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

C₂×D₄

yes

—

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄²×C₇₃

—

C₄²×C₇₃

—

C₂³×C₇₃

#120

yes

characteristic

Q₈×C₇₃

—

Q₈×C₇₃

—

Q₈×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂×Q₁₆

yes

—

C₂×C₄×C₇₃

#137

yes

—

C₂×Dic₇₃

—

#10596831

—

C₂²×C₇₃

#451

yes

—

C₂²×C₇₃

#453

yes

—

C₂²×C₇₃

#458

yes

characteristic

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

—

Dic₇₃

—

#7837

—

maximal, Sylow

C₂×C₇₃

#1614

yes

—

C₂×C₇₃

#1633

yes

—

C₂×C₇₃

#1655

yes

characteristic

#2811

D₇₃

yes

characteristic

#2095

—

#1272

—

C₇₃

#7837

yes

characteristic, complemented, Sylow

C₂×#107

—

146

—

C₂×#103

—

146

—

#395

—

#391

—

#391

C₂×D₇₃

yes

—

#384

—

#336

—

C₂²×Q₈

—

C₂²×Q₈

C₂²⋊D₇₃

yes

—

C₂²×C₈

—

146

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

146

—

C₂×C₄⋊C₄

C₂²⋊D₇₃

yes

—

C₂×C₄²

—

C₂×C₄²

C₂²×D₇₃

yes

characteristic

#107

—

292

—

#103

—

292

—

#95

—

#95

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

#11924018

yes

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

292

—

C₂²×C₄

C₂×C₂²⋊D₇₃

yes

—

100

C₂×C₈

—

292

—

101

C₂×C₈

—

292

—

102

C₂×C₈

—

146

—

103

C₄⋊C₄

—

104

C₄⋊C₄

—

105

C₄⋊C₄

—

292

—

106

C₄⋊C₄

—

292

—

107

C₄²

—

108

C₄²

—

109

C₂³

#14556560

yes

characteristic

110

Q₈

—

111

Q₈

—

112

Q₈

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

584

—

121

C₂×C₄

C₂×#11924018

yes

—

122

C₂×C₄

#14556622

yes

—

123

C₈

—

292

—

124

C₂²

#17988743

yes

—

125

C₂²

#17988755

yes

—

126

C₂²

#17988777

yes

characteristic

127

C₄

—

128

C₄

—

129

C₄

—

130

C₄

—

131

C₄

—

1168

—

132

C₂

#22608956

yes

—

133

C₂

#22609071

yes

—

134

C₂

#22609220

yes

characteristic

	subgroup	G/H
center	C₂³	#14556560
commutator, cosocle	C₂×C₄²×C₇₃	C₂³
Frattini	C₂×C₄²	C₂²×D₇₃
Fitting	C₇₃×#2811	C₂
socle, prime radical	C₂³×C₇₃	#120
hypercenter	#2811	D₇₃
hypocenter	C₇₃	#7837
LCS	G ▷ C₂×C₄²×C₇₃ ▷ C₂³×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #2811

subgroup

G/H

center

C₂³

#14556560

commutator, cosocle

C₂×C₄²×C₇₃

C₂³

Frattini

C₂×C₄²

C₂²×D₇₃

Fitting

C₇₃×#2811

C₂

C₂³×C₇₃

D₇₃

C₇₃

G ▷ C₂×C₄²×C₇₃ ▷ C₂³×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #2811

N	H ≅ G/N	type
71. C₇₃	#7837	semidirect

H ≅ G/N

type

71. C₇₃

#7837

semidirect

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

subgroup	index
#22611469	2
#22607757	2
C₇₃×#2811	2
#7837	73

subgroup

index

#22611469

#22607757

C₇₃×#2811

#7837

Subgroups — #32975327

Conjugacy classes of subgroups

Complements

Maximal subgroups