Finite Group Databasebeta

← #19142589

Subgroups — #19142589

Order 5504.

712 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 712 conjugacy classes of subgroups — too many to draw. Only its 125 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×#13063293C212yesmaximal, complemented
2#14582828C212yesmaximal, complemented
3#14582824C211yesmaximal, characteristic, complemented
4#14582815C212yesmaximal, complemented
5#14582814C212yesmaximal, complemented
6#14582813C212yesmaximal, complemented
7#14582807C212yesmaximal, complemented
8#14582754C211yesmaximal, characteristic, complemented
9C43×#392C211yesmaximal, characteristic, complemented
10C24×D43C2211yescharacteristic
11C22×C22⋊D43C2212yes—
12C22×C22⋊D43C2212yes—
13#13063293—28no—
14C2×C4⋊Dic43C2211yescharacteristic, complemented
15C2×Dic43⋊C4C2212yescomplemented
16C2×C22⋊Dic43C2212yes—
17C2×C22⋊Dic43C2211yescharacteristic
18C2×C22⋊Dic43C2212yescomplemented
19C2×C22⋊Dic43C2212yescomplemented
20C2×(C2×D43)⋊C4C2212yes—
21C2×(C2×D43)⋊C4C2212yes—
22C2×(C2×D43)⋊C4C2212yes—
23C2×(C2×D43)⋊C4C2212yes—
24C43⋊#95C2212yescomplemented
25C43⋊#95C2212yescomplemented
26C43⋊#95C2211yescharacteristic, complemented
27C22×D4×C43C2212yes—
28C22×D4×C43C2211yescharacteristic, complemented
29C2×C22⋊C4×C43C2211yescharacteristic
30C2×C22⋊C4×C43C2212yescomplemented
31#95×C43C2211yescharacteristic, complemented
32C24×C43C2312yes—
33C24×C43C2311yescharacteristic
34C23×D43—42no—
35C23×D43—42no—
36C23×D43—41no—
37C23×D43—41no—
38C23×D43D414yescomplemented
39C23×D43C2312yes—
40C2×D4×C43—24no—
41C2×D4×C43—42no—
42C2×D4×C43—42no—
43C2×D4×C43—41no—
44C2×D4×C43—42no—
45C22×C4×C43C2311yescharacteristic
46C22×C4×C43C2312yes—
47C22×C4×C43C2311yescharacteristic
48C2×C22⋊D43—24no—
49C2×C22⋊D43—24no—
50C2×C22⋊D43—42no—
51C2×C22⋊D43—42no—
52C2×C22⋊D43—42no—
53C2×C22⋊D43—42no—
54C22×Dic43C2312yes—
55C22×Dic43C2312yes—
56C22×Dic43C2312yes—
57C22⋊C4×C43—41no—
58C22⋊C4×C43—42no—
59C22⋊Dic43—24no—
60C22⋊Dic43—41no—
61C22⋊Dic43—42no—
62C22⋊Dic43—42no—
63(C2×D43)⋊C4—24no—
64(C2×D43)⋊C4—24no—
65(C2×D43)⋊C4—42no—
66(C2×D43)⋊C4—42no—
67C4⋊Dic43—41no—
68Dic43⋊C4—42no—
69C23×C43—21no—
70C23×C43—21no—
71C23×C43—22no—
72C23×C43—22no—
73C23×C43—22no—
74C23×C43—22no—
75C23×C43—22no—
76C23×C43—22no—
77C23×C43—22no—
78C23×C43—22no—
79C23×C43—22no—
80C23×C43C2×D412yes—
81C23×C43C2411yescharacteristic
82C22×D43—22no—
83C22×D43—22no—
84C22×D43—22no—
85C22×D43—22no—
86C22×D43—22no—
87C22×D43—22no—
88C22×D43—48no—
89C22×D43—44no—
90C22×D43—44no—
91C22×D43—48no—
92C22×D43—44no—
93C22×D43C2×D414yes—
94D4×C43—48no—
95D4×C43—44no—
96C2×C4×C43—22no—
97C2×C4×C43—22no—
98C2×C4×C43—21no—
99C2×C4×C43—22no—
100C2×C4×C43—22no—
101C2×C4×C43—22no—
102C2×C4×C43—21no—
103C22⋊D43—48no—
104C22⋊D43—48no—
105C2×Dic43—22no—
106C2×Dic43—22no—
107C2×Dic43—22no—
108C2×Dic43—22no—
109C2×Dic43—22no—
110C2×Dic43—22no—
111C2×Dic43—22no—
112C2×Dic43—22no—
113C2×Dic43—22no—
114C22×C43—22no—
115C22×C43—24no—
116C22×C43—41no—
117C22×C43—42no—
118C22×C43—41no—
119C22×C43—42no—
120C22×C43—42no—
121C22×C43—42no—
122C22×C43—42no—
123C22×C43—42no—
124C22×C43—42no—
125C22×C43—42no—
126C22×C43C22×D411yescharacteristic
127C22×C43H(5,𝔽2)12yes—
128C22×C43H(5,𝔽2)11yescharacteristic
129C22×C43H(5,𝔽2)12yes—
130C22×C43H(5,𝔽2)11yescharacteristic
131C2×D43—24no—
132C2×D43—24no—
133C2×D43—24no—
134C2×D43—416no—
135C2×D43—42no—
136C2×D43—42no—
137C2×D43—42no—
138C2×D43—42no—
139C4×C43—42no—
140C4×C43—41no—
141C4×C43—41no—
142Dic43—42no—
143Dic43—42no—
144Dic43—42no—
145#2812—431nomaximal, Sylow
146C2×C43—42no—
147C2×C43—82no—
148C2×C43#53411yescharacteristic
149C2×C43#53412yes—
150C2×C43#56011yescharacteristic
151C2×C43#56012yes—
152C2×C43H(3,𝔽4)11yescharacteristic
153D43—44no—
154C2×#120—432no—
155#397—431no—
156#397—432no—
157#394—432no—
158#394—432no—
159#394—432no—
160#392—432no—
161#392D4311yescharacteristic, complemented
162#379—431no—
163C43#281211yescharacteristic, complemented, Sylow
164C25—431no—
165C22×D4—432no—
166C22×D4—432no—
167C22×D4C2×D4312yes—
168C22×D4C2×D4311yescharacteristic, complemented
169#120—868no—
170C2×C4⋊C4—432no—
171C2×C4⋊C4—431no—
172C2×C22⋊C4—432no—
173C2×C22⋊C4—432no—
174C2×C22⋊C4—432no—
175C2×C22⋊C4—431no—
176C2×C22⋊C4—432no—
177C2×C22⋊C4—432no—
178C2×C22⋊C4—432no—
179C2×C22⋊C4—432no—
180C2×C22⋊C4C2×D4311yescharacteristic
181C2×C22⋊C4C2×D4312yescomplemented
182#95—432no—
183#95—431no—
184#95—432no—
185#95C2×D4311yescharacteristic, complemented
186C24—432no—
187C24—434no—
188C24—1721no—
189C24—1722no—
190C24—1722no—
191C24—1721no—
192C24C22×D4312yes—
193C24C22×D4311yescharacteristic
194C2×D4—24no—
195C2×D4—42no—
196C2×D4—42no—
197C2×D4—41no—
198C2×D4—42no—
199C2×D4—864no—
200C2×D4—864no—
201C2×D4—1722no—
202C2×D4—1722no—
203C2×D4—1722no—
204C2×D4—1722no—
205C22×C4—432no—
206C22×C4—432no—
207C22×C4—432no—
208C22×C4C22×D4311yescharacteristic
209C22×C4C22×D4312yes—
210C22×C4C22×D4311yescharacteristic
211C4⋊C4—1722no—
212C4⋊C4—1721no—
213C22⋊C4—41no—
214C22⋊C4—42no—
215C22⋊C4—864no—
216C22⋊C4—864no—
217C22⋊C4—864no—
218C22⋊C4—1722no—
219C22⋊C4—1722no—
220C22⋊C4—1722no—
221C22⋊C4—1721no—
222C22⋊C4—1722no—
223C23—21no—
224C23—22no—
225C23—22no—
226C23—21no—
227C23—22no—
228C23—22no—
229C23—22no—
230C23—22no—
231C23—22no—
232C23—22no—
233C23—22no—
234C23—434no—
235C23—862no—
236C23—862no—
237C23—862no—
238C23—862no—
239C23—862no—
240C23—862no—
241C23—1724no—
242C23—1728no—
243C23—1724no—
244C23—1728no—
245C23—1724no—
246C23D4×D4312yes—
247C23C23×D4311yescharacteristic
248D4—48no—
249D4—44no—
250D4—1728no—
251D4—1728no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—22no—
257C2×C4—22no—
258C2×C4—22no—
259C2×C4—862no—
260C2×C4—862no—
261C2×C4—862no—
262C2×C4—862no—
263C2×C4—862no—
264C2×C4—862no—
265C2×C4—862no—
266C2×C4—862no—
267C2×C4—862no—
268C22—22no—
269C22—24no—
270C22—41no—
271C22—42no—
272C22—41no—
273C22—42no—
274C22—42no—
275C22—42no—
276C22—42no—
277C22—42no—
278C22—42no—
279C22—42no—
280C22—864no—
281C22—864no—
282C22—864no—
283C22—17216no—
284C22—1722no—
285C22—1722no—
286C22—1722no—
287C22—1722no—
288C22C2×D4×D4311yescharacteristic
289C22#1306337012yes—
290C22#1306337011yescharacteristic
291C22#1306337012yes—
292C22#1306337111yescharacteristic
293C4—41no—
294C4—41no—
295C4—42no—
296C4—1722no—
297C4—1722no—
298C4—1722no—
299C2—42no—
300C2—82no—
301C2—1724no—
302C2#1458345711yescharacteristic
303C2#1458345912yes—
304C2#1458363611yescharacteristic
305C2#1458363712yes—
306C2#1458364211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#392C2
hypercenter#392D43
hypocenterC43#2812
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C2×#13063293C2semidirect
2. #14582828C2semidirect
3. #14582824C2semidirect
4. #14582815C2semidirect
5. #14582814C2semidirect
6. #14582813C2semidirect
7. #14582807C2semidirect
8. #14582754C2semidirect
9. C43×#392C2semidirect
14. C2×C4⋊Dic43C22semidirect
15. C2×Dic43⋊C4C22semidirect
18. C2×C22⋊Dic43C22semidirect
19. C2×C22⋊Dic43C22semidirect
24. C43⋊#95C22semidirect
25. C43⋊#95C22semidirect
26. C43⋊#95C22semidirect
28. C22×D4×C43C22semidirect
30. C2×C22⋊C4×C43C22semidirect
31. #95×C43C22semidirect
38. C23×D43D4semidirect
161. #392D43semidirect
163. C43#2812semidirect
168. C22×D4C2×D43semidirect
181. C2×C22⋊C4C2×D43semidirect
185. #95C2×D43semidirect