Group #32985485 — subgroups

Subgroups — #32985485

Order 18688.

454 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 454 conjugacy classes of subgroups — too many to draw. Only its 127 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	#22610069	C₂	1	1	yes	maximal, characteristic
2	#22608603	C₂	1	4	yes	maximal
3	#22608223	C₂	1	1	yes	maximal, characteristic
4	C₂×#494×C₇₃	C₂	1	1	yes	maximal, characteristic
5	#17988640	C₂²	1	2	yes	—
6	#17988611	C₂²	1	2	yes	—
7	#17988352	—	2	2	no	—
8	#17988333	—	2	8	no	—
9	#17988309	—	2	2	no	—
10	C₂²×Q₁₆×C₇₃	—	2	2	no	—
11	C₂×C₄⋊Q₈×C₇₃	C₂²	1	2	yes	—
12	#494×C₇₃	—	2	2	no	—
13	#494×C₇₃	C₄	1	4	yes	—
14	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
15	C₂×#11924012	—	2	2	no	—
16	C₄⋊#10596831	—	2	4	no	—
17	C₄⋊#10596831	D₄	1	4	yes	—
18	C₂²⋊#10596831	—	2	2	no	—
19	C₄×#10596831	—	2	2	no	—
20	C₂²×Q₈×C₇₃	—	2	2	no	—
21	C₂×Q₁₆×C₇₃	—	2	8	no	—
22	C₂×Q₁₆×C₇₃	—	4	8	no	—
23	C₂²×C₈×C₇₃	D₄	1	2	yes	—
24	C₄⋊Q₈×C₇₃	—	2	4	no	—
25	C₄⋊Q₈×C₇₃	—	2	2	no	—
26	C₄⋊Q₈×C₇₃	C₂×C₄	1	4	yes	—
27	C₂×C₄⋊C₄×C₇₃	—	2	4	no	—
28	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
29	C₄×C₈×C₇₃	C₂×C₄	1	2	yes	—
30	C₄×C₈×C₇₃	D₄	1	2	yes	—
31	#11924012	—	4	4	no	—
32	C₂×#10596831	—	2	4	no	—
33	C₂×#10596831	—	4	2	no	—
34	C₂×Q₈×C₇₃	—	2	4	no	—
35	C₂×Q₈×C₇₃	—	4	2	no	—
36	C₂×Q₈×C₇₃	—	4	8	no	—
37	C₂²×C₄×C₇₃	—	4	2	no	—
38	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
39	C₂²×C₄×C₇₃	#41	1	2	yes	—
40	Q₁₆×C₇₃	—	4	16	no	—
41	C₂×C₈×C₇₃	—	2	4	no	—
42	C₂×C₈×C₇₃	C₂²⋊C₄	1	4	yes	—
43	C₄⋊C₄×C₇₃	—	2	8	no	—
44	C₄⋊C₄×C₇₃	—	4	4	no	—
45	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
46	C₄²×C₇₃	C₂×D₄	1	2	yes	—
47	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
48	C₂³×C₇₃	#124	1	1	yes	characteristic
49	Q₈×C₇₃	—	4	8	no	—
50	Q₈×C₇₃	—	8	4	no	—
51	C₂×C₄×C₇₃	—	2	4	no	—
52	C₂×C₄×C₇₃	—	4	4	no	—
53	C₂×C₄×C₇₃	—	8	4	no	—
54	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
55	C₂×C₄×C₇₃	C₄×D₄	1	2	yes	—
56	C₂×C₄×C₇₃	#121	1	2	yes	—
57	C₂×C₄×C₇₃	#127	1	1	yes	characteristic
58	C₂×C₄×C₇₃	AGL(1,ℤ/8)	1	4	yes	—
59	C₈×C₇₃	—	2	4	no	—
60	#10596831	—	4	4	no	—
61	#10596831	—	8	2	no	—
62	C₂²×C₇₃	—	2	2	no	—
63	C₂²×C₇₃	#390	1	1	yes	characteristic
64	C₂²×C₇₃	#490	1	2	yes	—
65	C₄×C₇₃	—	2	2	no	—
66	C₄×C₇₃	—	8	4	no	—
67	C₄×C₇₃	#418	1	2	yes	—
68	C₄×C₇₃	#473	1	4	yes	—
69	C₄×C₇₃	#496	1	2	yes	—
70	#9779	—	73	1	no	maximal, Sylow
71	C₂×C₇₃	—	2	2	no	—
72	C₂×C₇₃	#1961	1	1	yes	characteristic
73	C₂×C₇₃	#1979	1	2	yes	—
74	C₂×#494	D₇₃	1	1	yes	characteristic
75	#1837	—	73	1	no	—
76	#1546	—	73	4	no	—
77	#1452	—	73	1	no	—
78	C₇₃	#9779	1	1	yes	characteristic, complemented, Sylow
79	C₂²×Q₁₆	—	2	2	no	—
80	C₂×C₄⋊Q₈	C₂×D₇₃	1	2	yes	—
81	#494	—	2	2	no	—
82	#494	Dic₇₃	1	4	yes	—
83	#431	—	73	2	no	—
84	#423	—	73	2	no	—
85	C₂×C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
86	#341	—	146	2	no	—
87	#332	—	146	8	no	—
88	#322	—	146	2	no	—
89	C₂²×Q₈	—	2	2	no	—
90	C₂×Q₁₆	—	2	8	no	—
91	C₂×Q₁₆	—	4	8	no	—
92	C₂×M₁₆	—	146	2	no	—
93	C₂²×C₈	C₂²⋊D₇₃	1	2	yes	—
94	C₄⋊Q₈	—	2	4	no	—
95	C₄⋊Q₈	—	2	2	no	—
96	C₄⋊Q₈	C₂×Dic₇₃	1	4	yes	—
97	C₂×C₄⋊C₄	—	2	4	no	—
98	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
99	C₄⋊C₈	—	73	4	no	—
100	C₄⋊C₈	—	146	4	no	—
101	C₂²⋊C₈	—	146	2	no	—
102	C₄×C₈	—	146	2	no	—
103	C₄×C₈	C₂×Dic₇₃	1	2	yes	—
104	C₄×C₈	C₂²⋊D₇₃	1	2	yes	—
105	C₂×Q₈	—	2	4	no	—
106	C₂×Q₈	—	4	2	no	—
107	C₂×Q₈	—	4	8	no	—
108	C₂²×C₄	—	4	2	no	—
109	C₂²×C₄	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
110	C₂²×C₄	#11924027	1	2	yes	—
111	Q₁₆	—	4	16	no	—
112	M₁₆	—	292	4	no	—
113	C₂×C₈	—	2	4	no	—
114	C₂×C₈	—	292	2	no	—
115	C₂×C₈	—	146	4	no	—
116	C₂×C₈	C₂²⋊Dic₇₃	1	4	yes	—
117	C₄⋊C₄	—	2	8	no	—
118	C₄⋊C₄	—	4	4	no	—
119	C₄²	C₂²×Dic₇₃	1	1	yes	characteristic
120	C₄²	D₄×D₇₃	1	2	yes	—
121	C₄²	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
122	C₂³	#14556578	1	1	yes	characteristic
123	Q₈	—	4	8	no	—
124	Q₈	—	8	4	no	—
125	C₂×C₄	—	2	4	no	—
126	C₂×C₄	—	4	4	no	—
127	C₂×C₄	—	8	4	no	—
128	C₂×C₄	C₂×C₂²⋊Dic₇₃	1	1	yes	characteristic
129	C₂×C₄	D₄×Dic₇₃	1	2	yes	—
130	C₂×C₄	#14556562	1	2	yes	—
131	C₂×C₄	#14556587	1	1	yes	characteristic
132	C₂×C₄	#14556617	1	4	yes	—
133	C₈	—	2	4	no	—
134	C₈	—	292	4	no	—
135	C₈	—	584	2	no	—
136	C₂²	—	2	2	no	—
137	C₂²	#17988490	1	1	yes	characteristic
138	C₂²	#17988951	1	2	yes	—
139	C₄	—	2	2	no	—
140	C₄	—	8	4	no	—
141	C₄	#17988592	1	2	yes	—
142	C₄	#17988859	1	4	yes	—
143	C₄	#17988974	1	2	yes	—
144	C₂	—	2	2	no	—
145	C₂	#22610756	1	1	yes	characteristic
146	C₂	#22610847	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#22610069

C₂

yes

maximal, characteristic

#22608603

C₂

yes

maximal

#22608223

C₂

yes

maximal, characteristic

C₂×#494×C₇₃

C₂

yes

maximal, characteristic

#17988640

C₂²

yes

—

#17988611

C₂²

yes

—

#17988352

—

#17988333

—

#17988309

—

C₂²×Q₁₆×C₇₃

—

C₂×C₄⋊Q₈×C₇₃

C₂²

yes

—

#494×C₇₃

—

#494×C₇₃

C₄

yes

—

C₂×C₄×C₈×C₇₃

C₂²

yes

—

—

D₄

yes

—

C₂²⋊#10596831

—

C₄×#10596831

—

C₂²×Q₈×C₇₃

—

C₂×Q₁₆×C₇₃

—

C₂×Q₁₆×C₇₃

—

C₂²×C₈×C₇₃

D₄

yes

—

C₄⋊Q₈×C₇₃

—

C₄⋊Q₈×C₇₃

—

C₄⋊Q₈×C₇₃

C₂×C₄

yes

—

C₂×C₄⋊C₄×C₇₃

—

C₂×C₄²×C₇₃

C₂³

yes

characteristic

C₄×C₈×C₇₃

C₂×C₄

yes

—

C₄×C₈×C₇₃

D₄

yes

—

#11924012

—

C₂×#10596831

—

C₂×#10596831

—

C₂×Q₈×C₇₃

—

C₂×Q₈×C₇₃

—

C₂×Q₈×C₇₃

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₇₃

#41

yes

—

Q₁₆×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

C₂²⋊C₄

yes

—

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄²×C₇₃

C₂²×C₄

yes

characteristic

C₄²×C₇₃

C₂×D₄

yes

—

C₄²×C₇₃

C₂×D₄

yes

characteristic

C₂³×C₇₃

#124

yes

characteristic

Q₈×C₇₃

—

Q₈×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₃

C₄×D₄

yes

—

C₂×C₄×C₇₃

#121

yes

—

C₂×C₄×C₇₃

#127

yes

characteristic

C₂×C₄×C₇₃

AGL(1,ℤ/8)

yes

—

C₈×C₇₃

—

#10596831

—

#10596831

—

C₂²×C₇₃

—

C₂²×C₇₃

#390

yes

characteristic

C₂²×C₇₃

#490

yes

—

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

#418

yes

—

C₄×C₇₃

#473

yes

—

C₄×C₇₃

#496

yes

—

#9779

—

maximal, Sylow

C₂×C₇₃

—

C₂×C₇₃

#1961

yes

characteristic

C₂×C₇₃

#1979

yes

—

C₂×#494

D₇₃

yes

—

—

—

C₇₃

#9779

yes

characteristic, complemented, Sylow

C₂²×Q₁₆

—

C₂×C₄⋊Q₈

C₂×D₇₃

yes

—

#494

—

#494

Dic₇₃

yes

—

#431

—

#423

—

C₂×C₄×C₈

C₂×D₇₃

yes

characteristic

#341

—

146

—

#332

—

146

—

#322

—

146

—

C₂²×Q₈

—

C₂×Q₁₆

—

C₂×Q₁₆

—

C₂×M₁₆

—

146

—

C₂²×C₈

C₂²⋊D₇₃

yes

—

C₄⋊Q₈

—

C₄⋊Q₈

—

C₄⋊Q₈

C₂×Dic₇₃

yes

—

C₂×C₄⋊C₄

—

C₂×C₄²

C₂²×D₇₃

yes

characteristic

C₄⋊C₈

—

100

C₄⋊C₈

—

146

—

101

C₂²⋊C₈

—

146

—

102

C₄×C₈

—

146

—

103

C₄×C₈

C₂×Dic₇₃

yes

—

104

C₄×C₈

C₂²⋊D₇₃

yes

—

105

C₂×Q₈

—

106

C₂×Q₈

—

107

C₂×Q₈

—

108

C₂²×C₄

—

109

C₂²×C₄

C₂×C₂²⋊D₇₃

yes

characteristic

110

C₂²×C₄

#11924027

yes

—

111

Q₁₆

—

112

M₁₆

—

292

—

113

C₂×C₈

—

114

C₂×C₈

—

292

—

115

C₂×C₈

—

146

—

116

C₂×C₈

C₂²⋊Dic₇₃

yes

—

117

C₄⋊C₄

—

118

C₄⋊C₄

—

119

C₄²

C₂²×Dic₇₃

yes

characteristic

120

C₄²

D₄×D₇₃

yes

—

121

C₄²

C₂×C₂²⋊D₇₃

yes

characteristic

122

C₂³

#14556578

yes

characteristic

123

Q₈

—

124

Q₈

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

C₂×C₂²⋊Dic₇₃

yes

characteristic

129

C₂×C₄

D₄×Dic₇₃

yes

—

130

C₂×C₄

#14556562

yes

—

131

C₂×C₄

#14556587

yes

characteristic

132

C₂×C₄

#14556617

yes

—

133

C₈

—

134

C₈

—

292

—

135

C₈

—

584

—

136

C₂²

—

137

C₂²

#17988490

yes

characteristic

138

C₂²

#17988951

yes

—

139

C₄

—

140

C₄

—

141

C₄

#17988592

yes

—

142

C₄

#17988859

yes

—

143

C₄

#17988974

yes

—

144

C₂

—

145

C₂

#22610756

yes

characteristic

146

C₂

#22610847

yes

—

	subgroup	G/H
center	C₂²	#17988490
commutator	C₄²×C₇₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₇₃
Fitting	C₂×#494×C₇₃	C₂
socle	C₂²×C₇₃	#390
prime radical	C₂³×C₇₃	#124
cosocle	C₂×C₄²×C₇₃	C₂³
hypercenter	C₂×#494	D₇₃
hypocenter	C₇₃	#9779
LCS	G ▷ C₄²×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×#494

subgroup

G/H

center

C₂²

#17988490

commutator

C₄²×C₇₃

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₇₃

Fitting

C₂×#494×C₇₃

C₂

C₂²×C₇₃

C₂³×C₇₃

C₂×C₄²×C₇₃

C₂³

D₇₃

C₇₃

G ▷ C₄²×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×#494

N	H ≅ G/N	type
78. C₇₃	#9779	semidirect

H ≅ G/N

type

78. C₇₃

#9779

semidirect

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

subgroup	index
#22610069	2
#22608603	2
#22608223	2
C₂×#494×C₇₃	2
#9779	73

subgroup

index

C₂×#494×C₇₃

Subgroups — #32985485

Conjugacy classes of subgroups

Complements

Maximal subgroups