Finite Group Databasebeta

← #19140403

Subgroups — #19140403

Order 5504.

668 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 668 conjugacy classes of subgroups — too many to draw. Only its 157 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
1C2×#13063304C211yesmaximal, characteristic, complemented
2C22×(C2×D43)⋊C4C211yesmaximal, characteristic
3#14582836C212yesmaximal, complemented
4#14582821C214yesmaximal, complemented
5#14582812C212yesmaximal, complemented
6#14582774C212yesmaximal, complemented
7#14582754C212yesmaximal
8C43×#380C211yesmaximal, characteristic, complemented
9C24×D43C2211yescharacteristic
10C22×Dic86C2211yescharacteristic, complemented
11C23×Dic43C2211yescharacteristic
12#13063304—24no—
13C2×C4⋊Dic43C2211yescharacteristic, complemented
14C2×C4⋊Dic43C2214yescomplemented
15C2×Dic43⋊C4C2212yescomplemented
16C2×C22⋊Dic43C2212yes—
17C2×(C2×D43)⋊C4—24no—
18C2×(C2×D43)⋊C4C2212yes—
19C2×(C2×D43)⋊C4C2212yes—
20C2×(C2×D43)⋊C4C2214yes—
21C2×(C2×D43)⋊C4C2214yes—
22C43⋊#95C2214yescomplemented
23C23×C4×C43C2211yescharacteristic
24C2×C4⋊C4×C43C2212yescomplemented
25C2×C22⋊C4×C43C2212yes—
26#95×C43C2212yescomplemented
27C24×C43C2311yescharacteristic
28C23×D43—22no—
29C23×D43—22no—
30C23×D43—42no—
31C23×D43—42no—
32C23×D43Q814yescomplemented
33C23×D43C2312yes—
34C22×C4×C43—42no—
35C22×C4×C43D414yes—
36C22×C4×C43C2314yes—
37C22×C4×C43C2311yescharacteristic
38C22×C4×C43C2311yescharacteristic
39C22×Dic43—22no—
40C22×Dic43—42no—
41C22×Dic43C2312yes—
42C22×Dic43C2312yes—
43C22×Dic43C2312yes—
44C2×Dic86—22no—
45C2×Dic86—42no—
46C4⋊C4×C43—42no—
47C22⋊C4×C43—24no—
48C22⋊Dic43—24no—
49(C2×D43)⋊C4—24no—
50(C2×D43)⋊C4—24no—
51(C2×D43)⋊C4—44no—
52(C2×D43)⋊C4—44no—
53C4⋊Dic43—22no—
54C4⋊Dic43—44no—
55Dic43⋊C4—24no—
56C23×C43—22no—
57C23×C43—22no—
58C23×C43C2×D412yes—
59C23×C43C2×Q812yes—
60C23×C43#4112yes—
61C23×C43C2411yescharacteristic
62C22×D43—28no—
63C22×D43—22no—
64C22×D43—22no—
65C22×D43—24no—
66C22×D43—24no—
67C22×D43—48no—
68C22×D43—44no—
69C22×D43—44no—
70C22×D43—48no—
71C22×D43C2×Q814yes—
72C2×C4×C43—22no—
73C2×C4×C43—22no—
74C2×C4×C43—24no—
75C2×C4×C43—24no—
76C2×C4×C43—24no—
77C2×C4×C43—44no—
78C2×C4×C43C2×D412yes—
79C2×C4×C43C2×D412yes—
80C2×Dic43—22no—
81C2×Dic43—22no—
82C2×Dic43—22no—
83C2×Dic43—24no—
84C2×Dic43—24no—
85C2×Dic43—24no—
86C2×Dic43—44no—
87Dic86—44no—
88C22×C43—22no—
89C22×C43—22no—
90C22×C43—24no—
91C22×C43—24no—
92C22×C43C22⋊Q814yes—
93C22×C43C22×D411yescharacteristic
94C22×C43C22×Q811yescharacteristic
95C22×C43C2×#4111yescharacteristic
96C22×C43H(5,𝔽2)12yes—
97C22×C43H(5,𝔽2)12yes—
98C2×D43—24no—
99C2×D43—28no—
100C2×D43—416no—
101C2×D43—42no—
102C2×D43—42no—
103C2×D43—44no—
104C4×C43—22no—
105C4×C43—22no—
106C4×C43—44no—
107Dic43—42no—
108Dic43—42no—
109Dic43—42no—
110#2626—431nomaximal, Sylow
111C2×C43—24no—
112C2×C43C2×C22⋊Q811yescharacteristic
113C2×C43#53411yescharacteristic
114C2×C43#53511yescharacteristic
115C2×C43#53812yes—
116C2×C43#54312yes—
117D43—44no—
118C2×C22⋊Q8—431no—
119C22×C22⋊C4—431no—
120#399—432no—
121#396—434no—
122#393—432no—
123#385—432no—
124#380D4311yescharacteristic, complemented
125#379—432no—
126C43#262611yescharacteristic, complemented, Sylow
127C25—431no—
128C22×Q8—431no—
129C23×C4—431no—
130C23×C4C2×D4311yescharacteristic
131C22⋊Q8—864no—
132C2×C4⋊C4—432no—
133C2×C4⋊C4—431no—
134C2×C4⋊C4—434no—
135C2×C4⋊C4C2×D4312yescomplemented
136C2×C22⋊C4—432no—
137C2×C22⋊C4—432no—
138C2×C22⋊C4—432no—
139C2×C22⋊C4—434no—
140C2×C22⋊C4—434no—
141C2×C22⋊C4—864no—
142C2×C22⋊C4C2×D4312yes—
143#95—434no—
144#95C2×D4312yescomplemented
145C24—432no—
146C24—434no—
147C24—862no—
148C24—862no—
149C24—1722no—
150C24—1722no—
151C24C22×D4311yescharacteristic
152C2×Q8—862no—
153C2×Q8—1722no—
154C22×C4—42no—
155C22×C4—432no—
156C22×C4—432no—
157C22×C4—432no—
158C22×C4—862no—
159C22×C4—1722no—
160C22×C4D17214yes—
161C22×C4C22×D4314yes—
162C22×C4C22×D4311yescharacteristic
163C22×C4C22×D4311yescharacteristic
164C4⋊C4—42no—
165C4⋊C4—864no—
166C4⋊C4—862no—
167C4⋊C4—1724no—
168C22⋊C4—24no—
169C22⋊C4—864no—
170C22⋊C4—864no—
171C22⋊C4—864no—
172C22⋊C4—1724no—
173C22⋊C4—1724no—
174C23—22no—
175C23—22no—
176C23—434no—
177C23—868no—
178C23—862no—
179C23—862no—
180C23—864no—
181C23—864no—
182C23—1728no—
183C23—1724no—
184C23—1724no—
185C23—1728no—
186C23C2×D17212yes—
187C23#1062190012yes—
188C23Q8×D4312yes—
189C23C23×D4311yescharacteristic
190Q8—1724no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—24no—
194C2×C4—24no—
195C2×C4—24no—
196C2×C4—44no—
197C2×C4—862no—
198C2×C4—862no—
199C2×C4—862no—
200C2×C4—864no—
201C2×C4—864no—
202C2×C4—864no—
203C2×C4—1724no—
204C2×C4C2×D17212yes—
205C2×C4C2×D17212yes—
206C22—22no—
207C22—22no—
208C22—24no—
209C22—24no—
210C22—864no—
211C22—868no—
212C22—17216no—
213C22—1722no—
214C22—1722no—
215C22—1724no—
216C22#1306330514yes—
217C22C22×D17211yescharacteristic
218C22C2×Q8×D4311yescharacteristic
219C22C2×#1062190011yescharacteristic
220C22#1306337012yes—
221C22#1306337112yes—
222C4—22no—
223C4—22no—
224C4—44no—
225C4—1722no—
226C4—1722no—
227C4—1722no—
228C2—24no—
229C2—1724no—
230C2C2×#1306330511yescharacteristic
231C2#1458346111yescharacteristic
232C2#1458346811yescharacteristic
233C2#1458348612yes—
234C2#1458352412yes—
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#380C2
hypercenter#380D43
hypocenterC43#2626
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #380

Complements

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

NH ≅ G/Ntype
1. C2×#13063304C2semidirect
3. #14582836C2semidirect
4. #14582821C2semidirect
5. #14582812C2semidirect
6. #14582774C2semidirect
8. C43×#380C2semidirect
10. C22×Dic86C22semidirect
13. C2×C4⋊Dic43C22semidirect
14. C2×C4⋊Dic43C22semidirect
15. C2×Dic43⋊C4C22semidirect
22. C43⋊#95C22semidirect
24. C2×C4⋊C4×C43C22semidirect
26. #95×C43C22semidirect
32. C23×D43Q8semidirect
124. #380D43semidirect
126. C43#2626semidirect
135. C2×C4⋊C4C2×D43semidirect
144. #95C2×D43semidirect