Finite Group Databasebeta

← #19142883

Subgroups — #19142883

Order 5504.

1068 conjugacy classes of subgroups; only the 201 normal subgroups are shown.

normal subgroups only

This group has 1068 conjugacy classes of subgroups — too many to draw. Only its 201 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×C4×D43C211yesmaximal, characteristic
2C2×#13063305C212yesmaximal, complemented
3C2×#13063304C211yesmaximal, characteristic, complemented
4#14582774C212yesmaximal, complemented
5#14582773C214yesmaximal, complemented
6#14582756C212yesmaximal, complemented
7#14582754C212yesmaximal
8C43×#380C211yesmaximal, characteristic, complemented
9C24×D43C2211yescharacteristic
10C22×Dic86C2211yescharacteristic, complemented
11C23×Dic43C2211yescharacteristic
12C22×C4×D43—24no—
13C22×C4×D43—28no—
14C22×C4×D43C2212yes—
15C22×C4×D43C2212yes—
16#13063305—28no—
17#13063304—24no—
18C2×C4⋊Dic43C2211yescharacteristic, complemented
19C2×C4⋊Dic43C2214yescomplemented
20C2×Dic43⋊C4C2212yescomplemented
21C2×C22⋊Dic43C2212yes—
22C2×(C2×D43)⋊C4C2214yes—
23C2×(C2×D43)⋊C4C2214yes—
24C43⋊#95C2214yescomplemented
25C23×C4×C43C2211yescharacteristic
26C2×C4⋊C4×C43C2212yescomplemented
27C2×C22⋊C4×C43C2212yes—
28#95×C43C2212yescomplemented
29C24×C43C2311yescharacteristic
30C23×D43—22no—
31C23×D43—22no—
32C23×D43—24no—
33C23×D43—24no—
34C23×D43Q814yescomplemented
35C23×D43C2312yes—
36C22×C4×C43—24no—
37C22×C4×C43D414yes—
38C22×C4×C43C2314yes—
39C22×C4×C43C2311yescharacteristic
40C22×C4×C43C2311yescharacteristic
41C22×Dic43—24no—
42C22×Dic43—22no—
43C22×Dic43C2312yes—
44C22×Dic43C2312yes—
45C22×Dic43C2312yes—
46C2×C4×D43—232no—
47C2×C4×D43—24no—
48C2×C4×D43—24no—
49C2×C4×D43—24no—
50C2×C4×D43—24no—
51C2×C4×D43—24no—
52C2×C4×D43D418yes—
53C2×Dic86—22no—
54C2×Dic86—24no—
55C4⋊C4×C43—24no—
56C22⋊C4×C43—24no—
57C22⋊Dic43—24no—
58(C2×D43)⋊C4—28no—
59(C2×D43)⋊C4—28no—
60C4⋊Dic43—22no—
61C4⋊Dic43—28no—
62Dic43⋊C4—24no—
63C23×C43—22no—
64C23×C43—22no—
65C23×C43C2×D412yes—
66C23×C43C2×Q812yes—
67C23×C43#4112yes—
68C23×C43C2411yescharacteristic
69C22×D43—28no—
70C22×D43—216no—
71C22×D43—28no—
72C22×D43—28no—
73C22×D43—22no—
74C22×D43—22no—
75C22×D43—22no—
76C22×D43—22no—
77C22×D43—216no—
78C22×D43C2×D414yes—
79C22×D43C2×Q814yes—
80C22×D43#4114yes—
81C2×C4×C43—22no—
82C2×C4×C43—28no—
83C2×C4×C43—24no—
84C2×C4×C43—24no—
85C2×C4×C43—24no—
86C2×C4×C43C2×D412yes—
87C2×C4×C43C2×D412yes—
88C2×C4×C43C2×D414yes—
89C2×Dic43—28no—
90C2×Dic43—22no—
91C2×Dic43—22no—
92C2×Dic43—22no—
93C2×Dic43—22no—
94C2×Dic43—24no—
95C2×Dic43—24no—
96C2×Dic43C2×D414yes—
97C4×D43—216no—
98C4×D43—216no—
99Dic86—44no—
100C22×C43—22no—
101C22×C43—24no—
102C22×C43—22no—
103C22×C43—24no—
104C22×C43C22⋊Q814yescomplemented
105C22×C43C22×D412yes—
106C22×C43C22×D411yescharacteristic
107C22×C43C22×Q811yescharacteristic
108C22×C43C2×#4112yes—
109C22×C43C2×#4111yescharacteristic
110C2×D43—232no—
111C2×D43—24no—
112C2×D43—24no—
113C2×D43—24no—
114C2×D43—24no—
115C2×D43—24no—
116C2×D43—24no—
117C2×D43C22⋊Q818yescomplemented
118C4×C43—22no—
119C4×C43—44no—
120C4×C43#12014yes—
121Dic43—24no—
122Dic43—42no—
123Dic43—42no—
124#2848—431nomaximal, Sylow
125C2×C43—24no—
126C2×C43C2×#12011yescharacteristic
127C2×C43C2×C22⋊Q812yes—
128C2×C43C2×C22⋊Q811yescharacteristic
129C2×C43#52512yes—
130C2×C43#52511yescharacteristic
131D43—28no—
132C24×C4—431no—
133C2×C22⋊Q8—431no—
134C2×C22⋊Q8—432no—
135#385—432no—
136#385—434no—
137#380—432no—
138#380D4311yescharacteristic, complemented
139#379—432no—
140C43#284811yescharacteristic, complemented, Sylow
141C25—431no—
142C22×Q8—431no—
143C23×C4—432no—
144C23×C4—431no—
145C23×C4—432no—
146C23×C4—868no—
147C23×C4—864no—
148C23×C4C2×D4311yescharacteristic
149C22⋊Q8—868no—
150C22⋊Q8—864no—
151C2×C4⋊C4—432no—
152C2×C4⋊C4—431no—
153C2×C4⋊C4—434no—
154C2×C4⋊C4C2×D4312yescomplemented
155C2×C22⋊C4—432no—
156C2×C22⋊C4—434no—
157C2×C22⋊C4—434no—
158C2×C22⋊C4C2×D4312yes—
159#95—434no—
160#95C2×D4312yescomplemented
161C24—432no—
162C24—434no—
163C24—864no—
164C24—864no—
165C24—862no—
166C24—862no—
167C24C22×D4311yescharacteristic
168C2×Q8—862no—
169C2×Q8—864no—
170C22×C4—24no—
171C22×C4—432no—
172C22×C4—438no—
173C22×C4—432no—
174C22×C4—432no—
175C22×C4—864no—
176C22×C4—864no—
177C22×C4—8632no—
178C22×C4—864no—
179C22×C4—862no—
180C22×C4—864no—
181C22×C4—864no—
182C22×C4—864no—
183C22×C4D17214yes—
184C22×C4C22×D4314yes—
185C22×C4C22×D4311yescharacteristic
186C22×C4C22×D4311yescharacteristic
187C4⋊C4—24no—
188C4⋊C4—868no—
189C4⋊C4—864no—
190C4⋊C4—862no—
191C22⋊C4—24no—
192C22⋊C4—868no—
193C22⋊C4—868no—
194C22⋊C4—864no—
195C23—22no—
196C23—22no—
197C23—434no—
198C23—434no—
199C23—434no—
200C23—8616no—
201C23—868no—
202C23—8616no—
203C23—868no—
204C23—868no—
205C23—862no—
206C23—862no—
207C23—862no—
208C23—862no—
209C23C2×D17212yes—
210C23#1062190012yes—
211C23Q8×D4312yes—
212C23C23×D4311yescharacteristic
213Q8—1724no—
214C2×C4—22no—
215C2×C4—28no—
216C2×C4—24no—
217C2×C4—24no—
218C2×C4—24no—
219C2×C4—434no—
220C2×C4—8616no—
221C2×C4—868no—
222C2×C4—862no—
223C2×C4—862no—
224C2×C4—8616no—
225C2×C4—864no—
226C2×C4—862no—
227C2×C4—862no—
228C2×C4—864no—
229C2×C4C2×D17212yes—
230C2×C4C2×D17212yes—
231C2×C4D4×D4314yes—
232C22—22no—
233C22—24no—
234C22—24no—
235C22—22no—
236C22—438no—
237C22—8632no—
238C22—864no—
239C22—864no—
240C22—864no—
241C22—864no—
242C22—864no—
243C22—864no—
244C22#1306330514yescomplemented
245C22C2×D4×D4312yes—
246C22C22×D17211yescharacteristic
247C22C2×Q8×D4311yescharacteristic
248C22#41×D4312yes—
249C22C2×#1062190011yescharacteristic
250C4—22no—
251C4—44no—
252C4—864no—
253C4—1722no—
254C4—1722no—
255C4#1306329514yes—
256C2—24no—
257C2—868no—
258C2C2×#1306329511yescharacteristic
259C2C22⋊Q8×D4312yes—
260C2C2×#1306330511yescharacteristic
261C2#1458340912yes—
262C2#1458341111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#380C2
hypercenter#380D43
hypocenterC43#2848
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #380

Complements

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

NH ≅ G/Ntype
2. C2×#13063305C2semidirect
3. C2×#13063304C2semidirect
4. #14582774C2semidirect
5. #14582773C2semidirect
6. #14582756C2semidirect
8. C43×#380C2semidirect
10. C22×Dic86C22semidirect
18. C2×C4⋊Dic43C22semidirect
19. C2×C4⋊Dic43C22semidirect
20. C2×Dic43⋊C4C22semidirect
24. C43⋊#95C22semidirect
26. C2×C4⋊C4×C43C22semidirect
28. #95×C43C22semidirect
34. C23×D43Q8semidirect
104. C22×C43C22⋊Q8semidirect
117. C2×D43C22⋊Q8semidirect
138. #380D43semidirect
140. C43#2848semidirect
154. C2×C4⋊C4C2×D43semidirect
160. #95C2×D43semidirect
244. C22#13063305semidirect