Finite Group Databasebeta

← #19139749

Subgroups — #19139749

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×#13063301C211yesmaximal, characteristic, complemented
2C2×C22⋊C4×D43C211yesmaximal, characteristic
3#14582826C211yesmaximal, characteristic, complemented
4#14582824C211yesmaximal, characteristic, complemented
5#14582810C211yesmaximal, characteristic, complemented
6#14582788C212yesmaximal, complemented
7#14582787C212yesmaximal, complemented
8#14582761C212yesmaximal, complemented
9#14582754C212yesmaximal
10#14582746C211yesmaximal, characteristic, complemented
11C43×#393C211yesmaximal, characteristic, complemented
12C24×D43C2211yescharacteristic
13C22×C4×D43C2211yescharacteristic
14C22×C4×D43C2211yescharacteristic
15#13063301—24no—
16C2×C4⋊Dic43C2211yescharacteristic, complemented
17C2×Dic43⋊C4C2212yescomplemented
18C2×C22⋊Dic43C2211yescharacteristic
19C2×C22⋊Dic43C2212yes—
20C2×(C2×D43)⋊C4C2211yescharacteristic
21C2×(C2×D43)⋊C4C2212yes—
22C2×(C2×D43)⋊C4C2211yescharacteristic
23C2×(C2×D43)⋊C4C2212yes—
24C2×(C2×D43)⋊C4C2212yes—
25C2×(C2×D43)⋊C4C2212yes—
26C22⋊C4×D43—24no—
27C2×C4×Dic43C2212yescomplemented
28C43⋊#95C2212yescomplemented
29C43⋊#95C2212yescomplemented
30C43⋊#95C2212yescomplemented
31C43⋊#95C2211yescharacteristic, complemented
32C22×Q8×C43C2211yescharacteristic, complemented
33C2×C22⋊C4×C43C2211yescharacteristic
34C2×C22⋊C4×C43C2212yes—
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
45C2×Q8×C43—22no—
46C2×Q8×C43—42no—
47C22×C4×C43C2311yescharacteristic
48C22×C4×C43C2312yes—
49C22×C4×C43C2312yes—
50C22×C4×C43C2311yescharacteristic
51C22×Dic43C2311yescharacteristic
52C22×Dic43C2312yes—
53C22×Dic43C2312yes—
54C22×Dic43C2311yescharacteristic
55C2×C4×D43—22no—
56C2×C4×D43—24no—
57C2×C4×D43—42no—
58C2×C4×D43D414yes—
59C22⋊C4×C43—22no—
60C22⋊C4×C43—42no—
61C22⋊Dic43—22no—
62C22⋊Dic43—24no—
63(C2×D43)⋊C4—22no—
64(C2×D43)⋊C4—22no—
65(C2×D43)⋊C4—24no—
66(C2×D43)⋊C4—24no—
67(C2×D43)⋊C4—24no—
68(C2×D43)⋊C4—42no—
69C4⋊Dic43—22no—
70Dic43⋊C4—24no—
71C4×Dic43—42no—
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—
93Q8×C43—44no—
94C2×C4×C43—22no—
95C2×C4×C43—22no—
96C2×C4×C43—21no—
97C2×C4×C43—22no—
98C2×C4×C43—22no—
99C2×C4×C43—22no—
100C2×C4×C43—22no—
101C2×C4×C43—22no—
102C2×C4×C43—22no—
103C2×C4×C43C2×D412yes—
104C2×Dic43—22no—
105C2×Dic43—22no—
106C2×Dic43—21no—
107C2×Dic43—22no—
108C2×Dic43—22no—
109C2×Dic43—22no—
110C2×Dic43—22no—
111C2×Dic43—22no—
112C2×Dic43—22no—
113C2×Dic43C2×D412yes—
114C4×D43—44no—
115C4×D43—44no—
116C22×C43—22no—
117C22×C43—24no—
118C22×C43—41no—
119C22×C43—41no—
120C22×C43—42no—
121C22×C43C22×D411yescharacteristic
122C22×C43C2×#4111yescharacteristic
123C22×C43C2×#4112yes—
124C22×C43C2×#4111yescharacteristic
125C22×C43H(5,𝔽2)12yes—
126C2×D43—22no—
127C2×D43—22no—
128C2×D43—24no—
129C2×D43—24no—
130C2×D43—22no—
131C2×D43—24no—
132C2×D43—416no—
133C2×D43—41no—
134C2×D43—41no—
135C2×D43—42no—
136C2×D43#12414yes—
137C4×C43—22no—
138C4×C43—41no—
139C4×C43—42no—
140C4×C43—42no—
141Dic43—22no—
142Dic43—42no—
143Dic43—41no—
144Dic43—42no—
145#2561—431nomaximal, Sylow
146C2×C43—42no—
147C2×C43#52511yescharacteristic
148C2×C43C2×#12411yescharacteristic
149C2×C43#53411yescharacteristic
150C2×C43#55112yes—
151C2×C43#55112yes—
152D43—24no—
153D43—42no—
154C2×C22⋊Q8—431no—
155C22×C22⋊C4—431no—
156#397—431no—
157#397—431no—
158#393—431no—
159#393D4311yescharacteristic, complemented
160#388—432no—
161#388—432no—
162#381—432no—
163#379—432no—
164C4×C22⋊C4—431no—
165C43#256111yescharacteristic, complemented, Sylow
166C25—431no—
167C22×Q8C2×D4311yescharacteristic, complemented
168C23×C4—431no—
169C23×C4—431no—
170C22⋊Q8—864no—
171C2×C4⋊C4—432no—
172C2×C4⋊C4—431no—
173C2×C22⋊C4—431no—
174C2×C22⋊C4—432no—
175C2×C22⋊C4—431no—
176C2×C22⋊C4—431no—
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—431no—
186#95—432no—
187#95—432no—
188#95—432no—
189#95C2×D4311yescharacteristic, complemented
190#95C2×D4312yescomplemented
191C24—431no—
192C24—431no—
193C24—862no—
194C24—862no—
195C24—864no—
196C24—862no—
197C24—1722no—
198C24C22×D4311yescharacteristic
199C2×Q8—22no—
200C2×Q8—42no—
201C22×C4—431no—
202C22×C4—434no—
203C22×C4—431no—
204C22×C4—432no—
205C22×C4—432no—
206C22×C4—862no—
207C22×C4—864no—
208C22×C4—1722no—
209C22×C4C22×D4311yescharacteristic
210C22×C4C22×D4312yes—
211C22×C4C22×D4312yes—
212C22×C4C22×D4311yescharacteristic
213C4⋊C4—864no—
214C4⋊C4—862no—
215C22⋊C4—22no—
216C22⋊C4—42no—
217C22⋊C4—862no—
218C22⋊C4—864no—
219C22⋊C4—864no—
220C22⋊C4—864no—
221C22⋊C4—862no—
222C22⋊C4—864no—
223C22⋊C4—862no—
224C22⋊C4—1722no—
225C42—1722no—
226C23—21no—
227C23—22no—
228C23—21no—
229C23—22no—
230C23—432no—
231C23—434no—
232C23—432no—
233C23—868no—
234C23—861no—
235C23—861no—
236C23—862no—
237C23—861no—
238C23—862no—
239C23—861no—
240C23—862no—
241C23—1728no—
242C23—1724no—
243C23—1728no—
244C23—1724no—
245C23#1062190212yes—
246C23C23×D4311yescharacteristic
247Q8—44no—
248C2×C4—22no—
249C2×C4—21no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—22no—
257C2×C4—432no—
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—862no—
267C2×C4—1724no—
268C2×C4—1724no—
269C2×C4D4×D4312yes—
270C22—24no—
271C22—22no—
272C22—42no—
273C22—41no—
274C22—41no—
275C22—434no—
276C22—864no—
277C22—864no—
278C22—862no—
279C22—862no—
280C22—864no—
281C22—862no—
282C22—17216no—
283C22—1722no—
284C22—1721no—
285C22—1721no—
286C22C2×D4×D4311yescharacteristic
287C22#41×D4312yes—
288C22#41×D4311yescharacteristic
289C22C2×#1062190211yescharacteristic
290C22#1306337012yes—
291C4—22no—
292C4—42no—
293C4—41no—
294C4—42no—
295C4—862no—
296C4—1722no—
297C4—1722no—
298C4—1721no—
299C2—42no—
300C2—864no—
301C2—1722no—
302C2#1458341211yescharacteristic
303C2#124×D4311yescharacteristic
304C2#1458345911yescharacteristic
305C2#1458357612yes—
306C2#1458357912yes—
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#393C2
hypercenter#393D43
hypocenterC43#2561
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #393

Complements

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

NH ≅ G/Ntype
1. C2×#13063301C2semidirect
3. #14582826C2semidirect
4. #14582824C2semidirect
5. #14582810C2semidirect
6. #14582788C2semidirect
7. #14582787C2semidirect
8. #14582761C2semidirect
10. #14582746C2semidirect
11. C43×#393C2semidirect
16. C2×C4⋊Dic43C22semidirect
17. C2×Dic43⋊C4C22semidirect
27. C2×C4×Dic43C22semidirect
28. C43⋊#95C22semidirect
29. C43⋊#95C22semidirect
30. C43⋊#95C22semidirect
31. C43⋊#95C22semidirect
32. C22×Q8×C43C22semidirect
35. #95×C43C22semidirect
36. #95×C43C22semidirect
159. #393D43semidirect
165. C43#2561semidirect
167. C22×Q8C2×D43semidirect
189. #95C2×D43semidirect
190. #95C2×D43semidirect