Finite Group Databasebeta

← #19137175

Subgroups — #19137175

Order 5504.

1104 conjugacy classes of subgroups; only the 269 normal subgroups are shown.

normal subgroups only

This group has 1104 conjugacy classes of subgroups — too many to draw. Only its 269 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×D172C211yesmaximal, characteristic
2C2×#13063284C211yesmaximal, characteristic, complemented
3#14582801C214yesmaximal, complemented
4#14582800C214yesmaximal, complemented
5#14582754C214yesmaximal, complemented
6C2×#117×C43C211yesmaximal, characteristic, complemented
7C24×D43C2212yes—
8C22×D172—24no—
9C22×D172—24no—
10C22×D172C418yescomplemented
11C22×D172C2212yes—
12C22×D172C2212yes—
13#13063284—24no—
14C2×C4⋊Dic43C2212yescomplemented
15C2×C22⋊Dic43C2212yes—
16C2×(C2×D43)⋊C4C22116yescomplemented
17C2×C4×Dic43C2212yescomplemented
18C23×C4×C43C2211yescharacteristic
19#117×C43—24no—
20C2×C4⋊C4×C43C2212yescomplemented
21C2×C22⋊C4×C43C2212yes—
22C2×C42×C43C2212yescomplemented
23C24×C43C2311yescharacteristic
24C23×D43—24no—
25C23×D43—24no—
26C23×D43—48no—
27C23×D43C2×C418yes—
28C23×D43C2314yes—
29C22×C4×C43C2×C414yes—
30C22×C4×C43D414yes—
31C22×C4×C43D414yes—
32C22×C4×C43C2314yes—
33C22×C4×C43C2311yescharacteristic
34C22×C4×C43C2311yescharacteristic
35C22×Dic43C2314yes—
36C2×D172—232no—
37C2×D172—24no—
38C2×D172—24no—
39C2×D172—24no—
40C2×D172—24no—
41C2×D172C2×C418yes—
42C2×D172C2×C418yes—
43C4⋊C4×C43—24no—
44C22⋊C4×C43—24no—
45C42×C43—24no—
46C22⋊Dic43—24no—
47(C2×D43)⋊C4—416no—
48C4⋊Dic43—24no—
49C4×Dic43—24no—
50C23×C43—24no—
51C23×C43C22×C412yes—
52C23×C43C2×D412yes—
53C23×C43C2×D412yes—
54C23×C43C2411yescharacteristic
55C22×D43—216no—
56C22×D43—24no—
57C22×D43—24no—
58C22×D43—216no—
59C22×D43—416no—
60C22×D43—416no—
61C22×D43—416no—
62C22×D43C22×C418yes—
63C2×C4×C43—24no—
64C2×C4×C43—28no—
65C2×C4×C43C22⋊C4116yescomplemented
66C2×C4×C43C22×C412yes—
67C2×C4×C43C22×C412yes—
68C2×C4×C43C2×D412yes—
69C2×C4×C43C2×D412yes—
70C2×C4×C43C2×D412yes—
71C2×C4×C43C2×D412yes—
72C2×Dic43—24no—
73C2×Dic43—28no—
74D172—216no—
75D172—216no—
76C22×C43—24no—
77C22×C43—24no—
78C22×C43—24no—
79C22×C43C2×C22⋊C414yes—
80C22×C43C23×C411yescharacteristic
81C22×C43C22×D411yescharacteristic
82C22×C43C22×D411yescharacteristic
83C22×C43H(5,𝔽2)14yes—
84C2×D43—28no—
85C2×D43—216no—
86C2×D43—432no—
87C2×D43—48no—
88C2×D43—48no—
89C4×C43—44no—
90C4×C43C2×C22⋊C414yes—
91C4×C43C2×C22⋊C414yes—
92Dic43—44no—
93#2309—431nomaximal, Sylow
94C2×C43—24no—
95C2×C43C22×C22⋊C411yescharacteristic
96C2×C43#51812yes—
97C2×C43#53512yes—
98C2×C43#53512yes—
99D43—48no—
100C23×D4—431no—
101C2×#117—431no—
102C2×#117D4311yescharacteristic, complemented
103#390—434no—
104#390—434no—
105#379—434no—
106C43#230911yescharacteristic, complemented, Sylow
107C25—432no—
108C22×D4—432no—
109C22×D4—432no—
110C22×D4—438no—
111C22×D4—864no—
112C22×D4—864no—
113C23×C4C2×D4311yescharacteristic
114#117—24no—
115#117—864no—
116C2×C4⋊C4—432no—
117C2×C4⋊C4C2×D4312yescomplemented
118C2×C22⋊C4—432no—
119C2×C22⋊C4—4316no—
120C2×C22⋊C4C2×D4312yes—
121C2×C42—432no—
122C2×C42C2×D4312yescomplemented
123C24—434no—
124C24—438no—
125C24—864no—
126C24—864no—
127C24—1728no—
128C24C22×D4311yescharacteristic
129C2×D4—438no—
130C2×D4—438no—
131C2×D4—8632no—
132C2×D4—864no—
133C2×D4—864no—
134C2×D4—864no—
135C2×D4—864no—
136C22×C4—434no—
137C22×C4C4×D4314yes—
138C22×C4D17214yes—
139C22×C4C22⋊D4314yes—
140C22×C4C22×D4314yes—
141C22×C4C22×D4311yescharacteristic
142C22×C4C22×D4311yescharacteristic
143C4⋊C4—24no—
144C4⋊C4—864no—
145C22⋊C4—24no—
146C22⋊C4—864no—
147C22⋊C4—17216no—
148C42—24no—
149C42—864no—
150C23—24no—
151C23—438no—
152C23—8616no—
153C23—864no—
154C23—864no—
155C23—8616no—
156C23—17216no—
157C23—17216no—
158C23—17216no—
159C23C2×C4×D4312yes—
160C23C2×D17212yes—
161C23C2×C22⋊D4312yes—
162C23C23×D4311yescharacteristic
163D4—8616no—
164D4—8616no—
165C2×C4—24no—
166C2×C4—28no—
167C2×C4—864no—
168C2×C4—868no—
169C2×C4(C2×D43)⋊C4116yescomplemented
170C2×C4C2×C4×D4312yes—
171C2×C4C2×C4×D4312yes—
172C2×C4C2×D17212yes—
173C2×C4C2×D17212yes—
174C2×C4C2×C22⋊D4312yes—
175C2×C4C2×C22⋊D4312yes—
176C22—24no—
177C22—24no—
178C22—24no—
179C22—868no—
180C22—8616no—
181C22—17232no—
182C22—1728no—
183C22—1728no—
184C22C2×(C2×D43)⋊C414yes—
185C22C22×C4×D4311yescharacteristic
186C22C22×C22⋊D4311yescharacteristic
187C22C22×D17211yescharacteristic
188C22#1306337114yes—
189C4—44no—
190C4—1724no—
191C4C2×(C2×D43)⋊C414yes—
192C4C2×(C2×D43)⋊C414yes—
193C2—24no—
194C2—1728no—
195C2C22×(C2×D43)⋊C411yescharacteristic
196C2#1458337312yes—
197C2#1458346312yes—
198C2#1458346812yes—
subgroupG/H
center, FrattiniC23C23×D43
commutatorC22×C43C23×C4
FittingC2×#117×C43C2
socleC23×C43C24
hypercenterC2×#117D43
hypocenterC43#2309
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#117

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#13063284C2semidirect
3. #14582801C2semidirect
4. #14582800C2semidirect
5. #14582754C2semidirect
6. C2×#117×C43C2semidirect
10. C22×D172C4semidirect
14. C2×C4⋊Dic43C22semidirect
16. C2×(C2×D43)⋊C4C22semidirect
17. C2×C4×Dic43C22semidirect
20. C2×C4⋊C4×C43C22semidirect
22. C2×C42×C43C22semidirect
65. C2×C4×C43C22⋊C4semidirect
102. C2×#117D43semidirect
106. C43#2309semidirect
117. C2×C4⋊C4C2×D43semidirect
122. C2×C42C2×D43semidirect
169. C2×C4(C2×D43)⋊C4semidirect