Finite Group Databasebeta

← #16822842

Subgroups — #16822842

Order 3712.

1232 conjugacy classes of subgroups; only the 205 normal subgroups are shown.

normal subgroups only

This group has 1232 conjugacy classes of subgroups — too many to draw. Only its 205 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×#11745300C212yesmaximal, complemented
2C2×#11745315C212yesmaximal, complemented
3C2×C4×C22⋊D29C211yesmaximal, characteristic, complemented
4#14271077C212yesmaximal, complemented
5#14271071C212yesmaximal, complemented
6#14271066C212yesmaximal, complemented
7#14271023C211yesmaximal, characteristic, complemented
8#14271019C212yesmaximal, complemented
9C23×D4×C29C211yesmaximal, characteristic, complemented
10C25×C29C2212yes—
11C22×D4×C29—28no—
12C22×D4×C29—24no—
13C22×D4×C29C2212yes—
14C22×D4×C29C2212yes—
15C23×C4×C29C2211yescharacteristic
16C22×C22⋊D29C2211yescharacteristic
17C22×C22⋊D29C2214yescomplemented
18C22×C4×D29C2211yescharacteristic, complemented
19#11745315—28no—
20C2×C22⋊Dic29C2211yescharacteristic
21C2×C22⋊Dic29C2212yes—
22C2×C22⋊Dic29C2214yescomplemented
23C2×C22⋊Dic29C2214yescomplemented
24C2×C22⋊Dic29C2214yescomplemented
25#11745300—28no—
26C4×C22⋊D29—24no—
27C2×#90781C2211yescharacteristic, complemented
28C2×C4⋊Dic29C2212yescomplemented
29C2×#90779C2211yescharacteristic, complemented
30C2×C4×Dic29C2211yescharacteristic, complemented
31#11745179C2212yescomplemented
32C24×C29—28no—
33C24×C29—24no—
34C24×C29—24no—
35C24×C29—24no—
36C24×C29—44no—
37C24×C29C2314yes—
38C24×C29C2311yescharacteristic
39C23×D29C2311yescharacteristic
40C2×D4×C29—232no—
41C2×D4×C29—28no—
42C2×D4×C29—24no—
43C2×D4×C29—24no—
44C2×D4×C29—24no—
45C2×D4×C29D418yescomplemented
46C22×C4×C29—24no—
47C22×C4×C29D414yescomplemented
48C22×C4×C29C2311yescharacteristic
49C22×C4×C29C2311yescharacteristic
50C2×C22⋊D29—22no—
51C2×C22⋊D29—22no—
52C2×C22⋊D29—28no—
53C2×C22⋊D29—28no—
54C2×C22⋊D29—44no—
55C2×C22⋊D29D414yescomplemented
56C22×Dic29C2311yescharacteristic
57C22×Dic29C2311yescharacteristic
58C22×Dic29C2314yes—
59C22×Dic29C2311yescharacteristic
60C2×C4×D29—22no—
61C2×C4×D29—24no—
62C22⋊Dic29—22no—
63C22⋊Dic29—28no—
64C22⋊Dic29—24no—
65C22⋊Dic29—28no—
66C22⋊Dic29—44no—
67#90781—22no—
68C4⋊Dic29—24no—
69#90779—22no—
70C4×Dic29—22no—
71C23×C29—22no—
72C23×C29—22no—
73C23×C29—216no—
74C23×C29—24no—
75C23×C29—24no—
76C23×C29—24no—
77C23×C29—24no—
78C23×C29—24no—
79C23×C29—24no—
80C23×C29—416no—
81C23×C29—416no—
82C23×C29—48no—
83C23×C29—48no—
84C23×C29C2×D412yes—
85C23×C29C2×D418yes—
86C23×C29C2×D412yes—
87C23×C29#4112yes—
88C23×C29C2411yescharacteristic
89C22×D29—21no—
90C22×D29—22no—
91C22×D29—21no—
92C22×D29—22no—
93C22×D29C2×D412yescomplemented
94D4×C29—216no—
95D4×C29—216no—
96C2×C4×C29—22no—
97C2×C4×C29—28no—
98C2×C4×C29C2×D412yes—
99C2×C4×C29C2×D412yes—
100C2×C4×C29C2×D414yes—
101C22⋊D29—28no—
102C22⋊D29—416no—
103C2×Dic29—21no—
104C2×Dic29—21no—
105C2×Dic29—21no—
106C2×Dic29—21no—
107C2×Dic29—24no—
108C2×Dic29—22no—
109C2×Dic29—24no—
110C2×Dic29—22no—
111C2×Dic29—24no—
112C2×Dic29C2×D412yescomplemented
113C4×D29—44no—
114#2408—291nomaximal, Sylow
115C22×C29—22no—
116C22×C29—22no—
117C22×C29—24no—
118C22×C29—24no—
119C22×C29—28no—
120C22×C29—28no—
121C22×C29—28no—
122C22×C29—432no—
123C22×C29—44no—
124C22×C29—44no—
125C22×C29—44no—
126C22×C29—44no—
127C22×C29#12114yescomplemented
128C22×C29C22×D411yescharacteristic
129C22×C29C22×D411yescharacteristic
130C22×C29C22×D412yes—
131C22×C29C2×#4111yescharacteristic
132C22×C29H(5,𝔽2)12yes—
133C2×D29—22no—
134C2×D29—24no—
135C2×D29—41no—
136C2×D29—41no—
137C2×D29—42no—
138C4×C29—22no—
139C4×C29#12014yescomplemented
140Dic29—22no—
141Dic29—41no—
142Dic29—41no—
143Dic29—44no—
144C23×D4D2911yescharacteristic, complemented
145C2×#121—292no—
146C2×#120—292no—
147C2×C4×D4—291no—
148#394—292no—
149#392—292no—
150#390—292no—
151#380—291no—
152#379—292no—
153C2×C29—24no—
154C2×C29—48no—
155C2×C29C2×#12011yescharacteristic
156C2×C29C2×#12111yescharacteristic
157C2×C29#53511yescharacteristic
158C2×C29D4212yes—
159C2×C29#54612yes—
160D29—42no—
161C25C2×D2912yes—
162C22×D4—28no—
163C22×D4—24no—
164C22×D4—291no—
165C22×D4—294no—
166C22×D4C2×D2912yes—
167C22×D4C2×D2912yes—
168C23×C4—291no—
169C23×C4C2×D2911yescharacteristic
170#121—588no—
171#120—588no—
172C4×D4—584no—
173C2×C4⋊C4—291no—
174C2×C4⋊C4—292no—
175C2×C22⋊C4—291no—
176C2×C22⋊C4—292no—
177C2×C22⋊C4—294no—
178C2×C22⋊C4—294no—
179C2×C22⋊C4—291no—
180C2×C22⋊C4—294no—
181C2×C42—291no—
182#95—292no—
183C29#240811yescharacteristic, complemented, Sylow
184C24—28no—
185C24—24no—
186C24—24no—
187C24—24no—
188C24—44no—
189C24—291no—
190C24C22×D2914yes—
191C24C22×D2911yescharacteristic
192C2×D4—232no—
193C2×D4—28no—
194C2×D4—24no—
195C2×D4—24no—
196C2×D4—24no—
197C2×D4—294no—
198C2×D4—582no—
199C2×D4—582no—
200C2×D4—588no—
201C2×D4—588no—
202C2×D4—1164no—
203C2×D4C22⋊D2918yescomplemented
204C22×C4—24no—
205C22×C4—291no—
206C22×C4—294no—
207C22×C4—291no—
208C22×C4—291no—
209C22×C4—582no—
210C22×C4—584no—
211C22×C4C22⋊D2914yescomplemented
212C22×C4C22×D2911yescharacteristic
213C22×C4C22×D2911yescharacteristic
214C4⋊C4—582no—
215C4⋊C4—584no—
216C22⋊C4—588no—
217C22⋊C4—584no—
218C22⋊C4—582no—
219C22⋊C4—588no—
220C22⋊C4—582no—
221C22⋊C4—1164no—
222C42—582no—
223C23—22no—
224C23—22no—
225C23—216no—
226C23—24no—
227C23—24no—
228C23—24no—
229C23—24no—
230C23—24no—
231C23—24no—
232C23—416no—
233C23—416no—
234C23—48no—
235C23—48no—
236C23—292no—
237C23—581no—
238C23—582no—
239C23—581no—
240C23—582no—
241C23D4×D2912yes—
242C23#9080712yes—
243C23C2×C22⋊D2918yes—
244C23C2×C22⋊D2912yes—
245C23C23×D2911yescharacteristic
246D4—216no—
247D4—216no—
248D4—588no—
249D4—11616no—
250C2×C4—22no—
251C2×C4—28no—
252C2×C4—292no—
253C2×C4—581no—
254C2×C4—581no—
255C2×C4—584no—
256C2×C4—582no—
257C2×C4—584no—
258C2×C4—581no—
259C2×C4—582no—
260C2×C4—581no—
261C2×C4—584no—
262C2×C4—1164no—
263C2×C4C2×C22⋊D2912yes—
264C2×C4C2×C22⋊D2912yes—
265C2×C4C2×C22⋊D2914yes—
266C22—24no—
267C22—24no—
268C22—22no—
269C22—22no—
270C22—28no—
271C22—28no—
272C22—28no—
273C22—432no—
274C22—44no—
275C22—44no—
276C22—44no—
277C22—44no—
278C22—584no—
279C22—582no—
280C22—1162no—
281C22—1161no—
282C22—1161no—
283C22#1174530014yescomplemented
284C22C2×D4×D2911yescharacteristic
285C22C2×#9080711yescharacteristic
286C22#1174535912yes—
287C22C22×C22⋊D2912yes—
288C22C22×C22⋊D2911yescharacteristic
289C4—22no—
290C4—582no—
291C4—1164no—
292C4—1161no—
293C4—1161no—
294C4#1174531514yescomplemented
295C2—24no—
296C2—48no—
297C2—1162no—
298C2C2×#1174531511yescharacteristic
299C2C2×#1174530011yescharacteristic
300C2#1427173011yescharacteristic
301C2D4×C22⋊D2912yes—
302C2#1427180712yes—
subgroupG/H
center, FrattiniC23C23×D29
commutator, socle, cosocleC23×C29C24
FittingC23×D4×C29C2
hypercenterC23×D4D29
hypocenterC29#2408
LCSG ▷ C23×C29 ▷ C29
UCSC1 ◁ C23 ◁ C23×D4

Complements

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

NH ≅ G/Ntype
1. C2×#11745300C2semidirect
2. C2×#11745315C2semidirect
3. C2×C4×C22⋊D29C2semidirect
4. #14271077C2semidirect
5. #14271071C2semidirect
6. #14271066C2semidirect
7. #14271023C2semidirect
8. #14271019C2semidirect
9. C23×D4×C29C2semidirect
17. C22×C22⋊D29C22semidirect
18. C22×C4×D29C22semidirect
22. C2×C22⋊Dic29C22semidirect
23. C2×C22⋊Dic29C22semidirect
24. C2×C22⋊Dic29C22semidirect
27. C2×#90781C22semidirect
28. C2×C4⋊Dic29C22semidirect
29. C2×#90779C22semidirect
30. C2×C4×Dic29C22semidirect
31. #11745179C22semidirect
45. C2×D4×C29D4semidirect
47. C22×C4×C29D4semidirect
55. C2×C22⋊D29D4semidirect
93. C22×D29C2×D4semidirect
112. C2×Dic29C2×D4semidirect
127. C22×C29#121semidirect
139. C4×C29#120semidirect
144. C23×D4D29semidirect
183. C29#2408semidirect
203. C2×D4C22⋊D29semidirect
211. C22×C4C22⋊D29semidirect
283. C22#11745300semidirect
294. C4#11745315semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#117453002
C2×#117453152
C2×C4×C22⋊D292
#142710772
#142710712
#142710662
#142710232
#142710192
C23×D4×C292
#240829