Finite Group Databasebeta

← #19138864

Subgroups — #19138864

Order 5504.

672 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 672 conjugacy classes of subgroups — too many to draw. Only its 139 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×#13063283C211yesmaximal, characteristic, complemented
2C2×C22⋊C4×D43C211yesmaximal, characteristic
3#14582836C211yesmaximal, characteristic, complemented
4#14582835C211yesmaximal, characteristic, complemented
5#14582825C211yesmaximal, characteristic, complemented
6#14582792C212yesmaximal, complemented
7#14582788C212yesmaximal, complemented
8#14582773C212yesmaximal, complemented
9#14582761C211yesmaximal, characteristic, complemented
10#14582754C212yesmaximal
11C43×#397C211yesmaximal, characteristic, complemented
12C24×D43C2211yescharacteristic
13C22×C4×D43C2211yescharacteristic
14C22×C4×D43C2211yescharacteristic
15#13063283—24no—
16C2×C4⋊Dic43C2211yescharacteristic, complemented
17C2×C4⋊Dic43C2212yescomplemented
18C2×Dic43⋊C4C2212yescomplemented
19C2×C22⋊Dic43C2211yescharacteristic
20C2×C22⋊Dic43C2212yes—
21C2×(C2×D43)⋊C4C2211yescharacteristic
22C2×(C2×D43)⋊C4C2212yes—
23C2×(C2×D43)⋊C4C2211yescharacteristic
24C2×(C2×D43)⋊C4C2212yes—
25C2×(C2×D43)⋊C4C2212yes—
26C2×(C2×D43)⋊C4C2212yes—
27C22⋊C4×D43—24no—
28C2×C4×Dic43C2212yescomplemented
29C43⋊#95C2212yescomplemented
30C43⋊#95C2212yescomplemented
31C43⋊#95C2211yescharacteristic, complemented
32C2×C4⋊C4×C43C2211yescharacteristic, complemented
33C2×C22⋊C4×C43C2212yes—
34C2×C22⋊C4×C43C2211yescharacteristic
35#95×C43C2212yescomplemented
36#95×C43C2211yescharacteristic, complemented
37C24×C43C2311yescharacteristic
38C23×D43—22no—
39C23×D43—22no—
40C23×D43—22no—
41C23×D43—24no—
42C23×D43—42no—
43C23×D43C2311yescharacteristic
44C23×D43C2311yescharacteristic
45C22×C4×C43C2312yes—
46C22×C4×C43C2311yescharacteristic
47C22×C4×C43C2312yes—
48C22×C4×C43C2311yescharacteristic
49C22×Dic43C2312yes—
50C22×Dic43C2311yescharacteristic
51C22×Dic43C2312yes—
52C22×Dic43C2311yescharacteristic
53C2×C4×D43—22no—
54C2×C4×D43—24no—
55C2×C4×D43—42no—
56C2×C4×D43D414yes—
57C4⋊C4×C43—22no—
58C22⋊C4×C43—22no—
59C22⋊C4×C43—24no—
60C22⋊Dic43—22no—
61C22⋊Dic43—42no—
62(C2×D43)⋊C4—22no—
63(C2×D43)⋊C4—22no—
64(C2×D43)⋊C4—24no—
65(C2×D43)⋊C4—24no—
66(C2×D43)⋊C4—24no—
67(C2×D43)⋊C4—42no—
68C4⋊Dic43—22no—
69C4⋊Dic43—42no—
70Dic43⋊C4—42no—
71C4×Dic43—24no—
72C23×C43—21no—
73C23×C43—21no—
74C23×C43—22no—
75C23×C43—22no—
76C23×C43#4112yes—
77C23×C43C2411yescharacteristic
78C22×D43—21no—
79C22×D43—21no—
80C22×D43—22no—
81C22×D43—28no—
82C22×D43—21no—
83C22×D43—22no—
84C22×D43—21no—
85C22×D43—22no—
86C22×D43—48no—
87C22×D43—48no—
88C22×D43—44no—
89C22×D43—44no—
90C22×D43C2×D412yes—
91C22×D43#4112yes—
92C22×D43#4114yes—
93C2×C4×C43—22no—
94C2×C4×C43—22no—
95C2×C4×C43—21no—
96C2×C4×C43—22no—
97C2×C4×C43—22no—
98C2×C4×C43—22no—
99C2×C4×C43—22no—
100C2×C4×C43—22no—
101C2×C4×C43—22no—
102C2×C4×C43C2×D412yes—
103C2×Dic43—22no—
104C2×Dic43—22no—
105C2×Dic43—21no—
106C2×Dic43—22no—
107C2×Dic43—22no—
108C2×Dic43—22no—
109C2×Dic43—22no—
110C2×Dic43—22no—
111C2×Dic43—22no—
112C2×Dic43C2×D412yes—
113C4×D43—28no—
114C4×D43—44no—
115C22×C43—22no—
116C22×C43—24no—
117C22×C43—41no—
118C22×C43—41no—
119C22×C43—42no—
120C22×C43C22×D411yescharacteristic
121C22×C43C2×#4112yes—
122C22×C43C2×#4111yescharacteristic
123C22×C43C2×#4111yescharacteristic
124C22×C43H(5,𝔽2)12yes—
125C2×D43—22no—
126C2×D43—22no—
127C2×D43—24no—
128C2×D43—24no—
129C2×D43—22no—
130C2×D43—24no—
131C2×D43—416no—
132C2×D43—41no—
133C2×D43—41no—
134C2×D43—42no—
135C2×D43#12314yes—
136C4×C43—22no—
137C4×C43—42no—
138C4×C43—41no—
139C4×C43—42no—
140Dic43—22no—
141Dic43—41no—
142Dic43—42no—
143Dic43—42no—
144#2482—431nomaximal, Sylow
145C2×C43—42no—
146C2×C43C2×#12311yescharacteristic
147C2×C43#52511yescharacteristic
148C2×C43#53511yescharacteristic
149C2×C43#55112yes—
150C2×C43#55112yes—
151D43—24no—
152D43—42no—
153C2×#117—431no—
154C22×C22⋊C4—431no—
155#399—431no—
156#399—431no—
157#397—431no—
158#397D4311yescharacteristic, complemented
159#388—432no—
160#388—432no—
161#385—432no—
162#381—431no—
163#379—432no—
164C43#248211yescharacteristic, complemented, Sylow
165C25—431no—
166C23×C4—431no—
167C23×C4—431no—
168#117—864no—
169C2×C4⋊C4—431no—
170C2×C4⋊C4—432no—
171C2×C4⋊C4—432no—
172C2×C4⋊C4C2×D4311yescharacteristic, complemented
173C2×C22⋊C4—431no—
174C2×C22⋊C4—431no—
175C2×C22⋊C4—431no—
176C2×C22⋊C4—432no—
177C2×C22⋊C4—432no—
178C2×C22⋊C4—432no—
179C2×C22⋊C4—432no—
180C2×C22⋊C4—432no—
181C2×C22⋊C4—864no—
182C2×C22⋊C4C2×D4311yescharacteristic
183C2×C22⋊C4C2×D4312yes—
184C2×C42—432no—
185#95—432no—
186#95—431no—
187#95—432no—
188#95C2×D4311yescharacteristic, complemented
189#95C2×D4312yescomplemented
190C24—431no—
191C24—431no—
192C24—862no—
193C24—862no—
194C24—864no—
195C24—862no—
196C24—1722no—
197C24C22×D4311yescharacteristic
198C22×C4—431no—
199C22×C4—434no—
200C22×C4—432no—
201C22×C4—431no—
202C22×C4—432no—
203C22×C4—864no—
204C22×C4—862no—
205C22×C4—1722no—
206C22×C4C22×D4312yes—
207C22×C4C22×D4312yes—
208C22×C4C22×D4311yescharacteristic
209C22×C4C22×D4311yescharacteristic
210C4⋊C4—22no—
211C4⋊C4—862no—
212C4⋊C4—1722no—
213C4⋊C4—1722no—
214C22⋊C4—24no—
215C22⋊C4—22no—
216C22⋊C4—862no—
217C22⋊C4—864no—
218C22⋊C4—864no—
219C22⋊C4—864no—
220C22⋊C4—862no—
221C22⋊C4—862no—
222C22⋊C4—1722no—
223C22⋊C4—1722no—
224C42—864no—
225C23—21no—
226C23—22no—
227C23—21no—
228C23—22no—
229C23—432no—
230C23—434no—
231C23—432no—
232C23—868no—
233C23—861no—
234C23—861no—
235C23—862no—
236C23—861no—
237C23—862no—
238C23—861no—
239C23—862no—
240C23—1728no—
241C23—1724no—
242C23—1728no—
243C23—1724no—
244C23#1062190012yes—
245C23C23×D4311yescharacteristic
246C2×C4—22no—
247C2×C4—22no—
248C2×C4—21no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—432no—
256C2×C4—868no—
257C2×C4—862no—
258C2×C4—862no—
259C2×C4—861no—
260C2×C4—862no—
261C2×C4—862no—
262C2×C4—862no—
263C2×C4—862no—
264C2×C4—862no—
265C2×C4—862no—
266C2×C4—1724no—
267C2×C4D4×D4312yes—
268C22—24no—
269C22—22no—
270C22—42no—
271C22—41no—
272C22—41no—
273C22—434no—
274C22—864no—
275C22—864no—
276C22—862no—
277C22—862no—
278C22—864no—
279C22—862no—
280C22—17216no—
281C22—1722no—
282C22—1721no—
283C22—1721no—
284C22C2×D4×D4311yescharacteristic
285C22#41×D4312yes—
286C22#41×D4311yescharacteristic
287C22C2×#1062190011yescharacteristic
288C22#1306337112yes—
289C4—22no—
290C4—42no—
291C4—42no—
292C4—41no—
293C4—862no—
294C4—1722no—
295C4—1721no—
296C4—1722no—
297C2—42no—
298C2—864no—
299C2—1722no—
300C2#123×D4311yescharacteristic
301C2#1458340911yescharacteristic
302C2#1458346711yescharacteristic
303C2#1458357212yes—
304C2#1458357412yes—
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#397C2
hypercenter#397D43
hypocenterC43#2482
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
1. C2×#13063283C2semidirect
3. #14582836C2semidirect
4. #14582835C2semidirect
5. #14582825C2semidirect
6. #14582792C2semidirect
7. #14582788C2semidirect
8. #14582773C2semidirect
9. #14582761C2semidirect
11. C43×#397C2semidirect
16. C2×C4⋊Dic43C22semidirect
17. C2×C4⋊Dic43C22semidirect
18. C2×Dic43⋊C4C22semidirect
28. C2×C4×Dic43C22semidirect
29. C43⋊#95C22semidirect
30. C43⋊#95C22semidirect
31. C43⋊#95C22semidirect
32. C2×C4⋊C4×C43C22semidirect
35. #95×C43C22semidirect
36. #95×C43C22semidirect
158. #397D43semidirect
164. C43#2482semidirect
172. C2×C4⋊C4C2×D43semidirect
188. #95C2×D43semidirect
189. #95C2×D43semidirect