Group #32976442 — subgroups

Subgroups — #32976442

Order 18688.

294 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 294 conjugacy classes of subgroups — too many to draw. Only its 131 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	#22609682	C₂	1	1	yes	maximal, characteristic
2	#22608214	C₂	1	1	yes	maximal, characteristic
3	#22607761	C₂	1	2	yes	maximal
4	#22607759	C₂	1	2	yes	maximal
5	C₇₃×#1452	C₂	1	1	yes	maximal, characteristic
6	#17988640	C₂²	1	2	yes	—
7	C₂×#14556502	C₂²	1	1	yes	characteristic
8	#17988433	C₂²	1	1	yes	characteristic
9	#17988341	C₄	1	4	yes	—
10	#17988308	C₄	1	2	yes	complemented
11	C₈×#10596831	C₄	1	2	yes	complemented
12	#431×C₇₃	C₂²	1	2	yes	—
13	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
14	#322×C₇₃	C₄	1	4	yes	complemented
15	C₂²×#10596831	C₂×C₄	1	2	yes	—
16	C₂×C₄×Dic₇₃	C₂×C₄	1	2	yes	—
17	C₄⋊#10596831	—	2	2	no	—
18	C₂²⋊#10596831	—	2	2	no	—
19	#14556502	—	2	2	no	—
20	C₄×#10596831	C₂×C₄	1	4	yes	—
21	#14556498	—	2	2	no	—
22	C₂²×C₈×C₇₃	C₂×C₄	1	2	yes	—
23	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
24	C₄⋊C₈×C₇₃	—	2	2	no	—
25	C₂²⋊C₈×C₇₃	—	2	2	no	—
26	C₄×C₈×C₇₃	C₂×C₄	1	4	yes	—
27	C₄×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
28	C₄×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
29	C₄×C₈×C₇₃	C₂×C₄	1	2	yes	—
30	C₂²×Dic₇₃	—	2	2	no	—
31	C₂×#10596831	—	2	4	no	—
32	C₂×#10596831	—	2	2	no	—
33	C₂×#10596831	—	2	4	no	—
34	C₄×Dic₇₃	—	2	4	no	—
35	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
36	C₂²×C₄×C₇₃	#41	1	2	yes	—
37	C₂×C₈×C₇₃	—	2	4	no	—
38	C₂×C₈×C₇₃	—	2	4	no	—
39	C₂×C₈×C₇₃	C₄²	1	2	yes	—
40	C₂×C₈×C₇₃	C₄²	1	2	yes	—
41	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
42	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
43	C₄²×C₇₃	#41	1	2	yes	—
44	C₂³×C₇₃	#117	1	1	yes	characteristic
45	C₂×C₄×C₇₃	—	4	2	no	—
46	C₂×C₄×C₇₃	C₂×C₄²	1	1	yes	characteristic
47	C₂×C₄×C₇₃	#117	1	2	yes	—
48	C₂×C₄×C₇₃	#117	1	1	yes	characteristic
49	C₂×C₄×C₇₃	#117	1	2	yes	—
50	C₂×C₄×C₇₃	#131	1	4	yes	—
51	C₂×Dic₇₃	—	4	4	no	—
52	C₂×Dic₇₃	—	4	2	no	—
53	C₈×C₇₃	—	2	2	no	—
54	C₈×C₇₃	—	2	2	no	—
55	C₈×C₇₃	—	4	4	no	—
56	#10596831	—	4	4	no	—
57	#10596831	—	4	2	no	—
58	C₂²×C₇₃	—	2	2	no	—
59	C₂²×C₇₃	#376	1	1	yes	characteristic
60	C₂²×C₇₃	#433	1	2	yes	—
61	C₄×C₇₃	—	2	2	no	—
62	C₄×C₇₃	—	2	2	no	—
63	C₄×C₇₃	#405	1	2	yes	—
64	C₄×C₇₃	#433	1	2	yes	—
65	Dic₇₃	—	8	2	no	—
66	#8141	—	73	1	no	maximal, Sylow
67	C₂×C₇₃	—	2	2	no	—
68	C₂×C₇₃	#1746	1	1	yes	characteristic
69	C₂×C₇₃	#1747	1	2	yes	—
70	#1746	—	73	1	no	—
71	#1452	D₇₃	1	1	yes	characteristic
72	#1450	—	73	1	no	—
73	#1275	—	73	2	no	—
74	#1274	—	73	2	no	—
75	C₇₃	#8141	1	1	yes	characteristic, complemented, Sylow
76	#431	—	73	2	no	—
77	#431	C₂×D₇₃	1	2	yes	—
78	C₂×#97	—	73	1	no	—
79	C₂×C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
80	#376	—	73	1	no	—
81	#336	—	73	4	no	—
82	#322	—	73	2	no	—
83	#322	Dic₇₃	1	4	yes	complemented
84	C₈²	—	73	2	no	—
85	C₂²×C₈	—	73	2	no	—
86	C₂²×C₈	C₄×D₇₃	1	2	yes	—
87	C₂×C₄²	—	73	2	no	—
88	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
89	C₄⋊C₈	—	2	2	no	—
90	C₄⋊C₈	—	146	2	no	—
91	C₂²⋊C₈	—	2	2	no	—
92	C₂²⋊C₈	—	146	2	no	—
93	#97	—	146	2	no	—
94	C₄×C₈	—	73	4	no	—
95	C₄×C₈	C₄×D₇₃	1	1	yes	characteristic
96	C₄×C₈	C₄×D₇₃	1	1	yes	characteristic
97	C₄×C₈	C₂×Dic₇₃	1	4	yes	—
98	C₄×C₈	C₂×Dic₇₃	1	2	yes	—
99	#95	—	146	2	no	—
100	C₂²×C₄	—	146	2	no	—
101	C₂²×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
102	C₂²×C₄	#11924028	1	2	yes	—
103	C₂×C₈	—	2	4	no	—
104	C₂×C₈	—	2	4	no	—
105	C₂×C₈	—	146	4	no	—
106	C₂×C₈	—	146	2	no	—
107	C₂×C₈	—	146	4	no	—
108	C₂×C₈	C₄×Dic₇₃	1	2	yes	—
109	C₂×C₈	C₄×Dic₇₃	1	2	yes	—
110	C₄²	—	146	4	no	—
111	C₄²	C₂×C₄×D₇₃	1	1	yes	characteristic
112	C₄²	C₂²×Dic₇₃	1	1	yes	characteristic
113	C₄²	#11924028	1	2	yes	—
114	C₂³	#14556548	1	1	yes	characteristic
115	C₂×C₄	—	4	2	no	—
116	C₂×C₄	—	292	4	no	—
117	C₂×C₄	—	292	2	no	—
118	C₂×C₄	C₂×C₄×Dic₇₃	1	1	yes	characteristic
119	C₂×C₄	#14556548	1	2	yes	—
120	C₂×C₄	#14556548	1	1	yes	characteristic
121	C₂×C₄	#14556550	1	2	yes	—
122	C₂×C₄	#14556599	1	4	yes	—
123	C₈	—	2	2	no	—
124	C₈	—	2	2	no	—
125	C₈	—	4	4	no	—
126	C₈	—	292	4	no	—
127	C₈	—	292	2	no	—
128	C₂²	—	2	2	no	—
129	C₂²	#17988433	1	1	yes	characteristic
130	C₂²	#17988649	1	2	yes	—
131	C₄	—	2	2	no	—
132	C₄	—	2	2	no	—
133	C₄	—	584	2	no	—
134	C₄	#17988545	1	2	yes	—
135	C₄	#17988649	1	2	yes	—
136	C₂	—	2	2	no	—
137	C₂	#22609684	1	1	yes	characteristic
138	C₂	#22609686	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#22609682

C₂

yes

maximal, characteristic

#22608214

C₂

yes

maximal, characteristic

#22607761

C₂

yes

maximal

#22607759

C₂

yes

maximal

C₇₃×#1452

C₂

yes

maximal, characteristic

#17988640

C₂²

yes

—

C₂×#14556502

C₂²

yes

characteristic

#17988433

C₂²

yes

characteristic

#17988341

C₄

yes

—

#17988308

C₄

yes

complemented

C₈×#10596831

C₄

yes

complemented

#431×C₇₃

C₂²

yes

—

C₂×C₄×C₈×C₇₃

C₂²

yes

characteristic

#322×C₇₃

C₄

yes

complemented

C₂²×#10596831

C₂×C₄

yes

—

C₂×C₄×Dic₇₃

C₂×C₄

yes

—

—

—

—

C₂×C₄

yes

—

#14556498

—

C₂²×C₈×C₇₃

C₂×C₄

yes

—

C₂×C₄²×C₇₃

C₂³

yes

characteristic

C₄⋊C₈×C₇₃

—

C₂²⋊C₈×C₇₃

—

C₄×C₈×C₇₃

C₂×C₄

yes

—

C₄×C₈×C₇₃

C₂×C₄

yes

characteristic

C₄×C₈×C₇₃

C₂×C₄

yes

characteristic

C₄×C₈×C₇₃

C₂×C₄

yes

—

C₂²×Dic₇₃

—

C₂×#10596831

—

C₂×#10596831

—

C₂×#10596831

—

C₄×Dic₇₃

—

C₂²×C₄×C₇₃

C₂²×C₄

yes

characteristic

C₂²×C₄×C₇₃

#41

yes

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

C₄²

yes

—

C₂×C₈×C₇₃

C₄²

yes

—

C₄²×C₇₃

C₂²×C₄

yes

characteristic

C₄²×C₇₃

C₂²×C₄

yes

characteristic

C₄²×C₇₃

#41

yes

—

C₂³×C₇₃

#117

yes

characteristic

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂×C₄²

yes

characteristic

C₂×C₄×C₇₃

#117

yes

—

C₂×C₄×C₇₃

#117

yes

characteristic

C₂×C₄×C₇₃

#117

yes

—

C₂×C₄×C₇₃

#131

yes

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₈×C₇₃

—

C₈×C₇₃

—

C₈×C₇₃

—

#10596831

—

#10596831

—

C₂²×C₇₃

—

C₂²×C₇₃

#376

yes

characteristic

C₂²×C₇₃

#433

yes

—

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

#405

yes

—

C₄×C₇₃

#433

yes

—

Dic₇₃

—

#8141

—

maximal, Sylow

C₂×C₇₃

—

C₂×C₇₃

#1746

yes

characteristic

C₂×C₇₃

#1747

yes

—

#1746

—

#1452

D₇₃

yes

—

—

—

C₇₃

#8141

yes

characteristic, complemented, Sylow

#431

—

#431

C₂×D₇₃

yes

—

C₂×#97

—

C₂×C₄×C₈

C₂×D₇₃

yes

—

—

—

Dic₇₃

yes

complemented

C₈²

—

C₂²×C₈

—

C₂²×C₈

C₄×D₇₃

yes

—

C₂×C₄²

—

C₂×C₄²

C₂²×D₇₃

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

146

—

C₂²⋊C₈

—

C₂²⋊C₈

—

146

—

#97

—

146

—

C₄×C₈

—

C₄×C₈

C₄×D₇₃

yes

characteristic

C₄×C₈

C₄×D₇₃

yes

characteristic

C₄×C₈

C₂×Dic₇₃

yes

—

C₄×C₈

C₂×Dic₇₃

yes

—

#95

—

146

—

100

C₂²×C₄

—

146

—

101

C₂²×C₄

C₂×C₄×D₇₃

yes

characteristic

102

C₂²×C₄

#11924028

yes

—

103

C₂×C₈

—

104

C₂×C₈

—

105

C₂×C₈

—

146

—

106

C₂×C₈

—

146

—

107

C₂×C₈

—

146

—

108

C₂×C₈

C₄×Dic₇₃

yes

—

109

C₂×C₈

C₄×Dic₇₃

yes

—

110

C₄²

—

146

—

111

C₄²

C₂×C₄×D₇₃

yes

characteristic

112

C₄²

C₂²×Dic₇₃

yes

characteristic

113

C₄²

#11924028

yes

—

114

C₂³

#14556548

yes

characteristic

115

C₂×C₄

—

116

C₂×C₄

—

292

—

117

C₂×C₄

—

292

—

118

C₂×C₄

C₂×C₄×Dic₇₃

yes

characteristic

119

C₂×C₄

#14556548

yes

—

120

C₂×C₄

#14556548

yes

characteristic

121

C₂×C₄

#14556550

yes

—

122

C₂×C₄

#14556599

yes

—

123

C₈

—

124

C₈

—

125

C₈

—

126

C₈

—

292

—

127

C₈

—

292

—

128

C₂²

—

129

C₂²

#17988433

yes

characteristic

130

C₂²

#17988649

yes

—

131

C₄

—

132

C₄

—

133

C₄

—

584

—

134

C₄

#17988545

yes

—

135

C₄

#17988649

yes

—

136

C₂

—

137

C₂

#22609684

yes

characteristic

138

C₂

#22609686

yes

—

	subgroup	G/H
center	C₂×C₄	C₂×C₄×Dic₇₃
commutator	C₂×C₄×C₇₃	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₇₃
Fitting	C₇₃×#1452	C₂
socle	C₂²×C₇₃	#376
prime radical	C₂³×C₇₃	#117
cosocle	C₂×C₄²×C₇₃	C₂³
hypercenter	#1452	D₇₃
hypocenter	C₇₃	#8141
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ #1452

subgroup

G/H

center

C₂×C₄

C₂×C₄×Dic₇₃

commutator

C₂×C₄×C₇₃

C₂×C₄²

Frattini

C₂×C₄²

C₂²×D₇₃

Fitting

C₇₃×#1452

C₂

C₂²×C₇₃

C₂³×C₇₃

C₂×C₄²×C₇₃

C₂³

D₇₃

C₇₃

G ▷ C₂×C₄×C₇₃ ▷ C₇₃

C₁ ◁ C₂×C₄ ◁ #1452

N	H ≅ G/N	type
10. #17988308	C₄	semidirect
11. C₈×#10596831	C₄	semidirect
14. #322×C₇₃	C₄	semidirect
75. C₇₃	#8141	semidirect
83. #322	Dic₇₃	semidirect

H ≅ G/N

type

10. #17988308

C₄

semidirect

11. C₈×#10596831

C₄

semidirect

14. #322×C₇₃

C₄

semidirect

75. C₇₃

#8141

semidirect

83. #322

Dic₇₃

semidirect

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

subgroup	index
#22609682	2
#22608214	2
#22607761	2
#22607759	2
C₇₃×#1452	2
#8141	73

subgroup

index

C₇₃×#1452

Subgroups — #32976442

Conjugacy classes of subgroups

Complements

Maximal subgroups