Finite Group Databasebeta

← #16822879

Subgroups — #16822879

Order 3712.

786 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 786 conjugacy classes of subgroups — too many to draw. Only its 157 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×#11745248C211yesmaximal, characteristic, complemented
2C2×#11745315C211yesmaximal, characteristic
3C2×#11745239C211yesmaximal, characteristic, complemented
4C22×C22⋊Dic29C211yesmaximal, characteristic, complemented
5#14271086C212yesmaximal, complemented
6#14271078C212yesmaximal, complemented
7#14271063C212yesmaximal, complemented
8#14271056C212yesmaximal, complemented
9#14271040C211yesmaximal, characteristic, complemented
10#14271035C211yesmaximal, characteristic, complemented
11C29×#379C211yesmaximal, characteristic, complemented
12C25×C29C2211yescharacteristic
13C22×C22⋊D29C2211yescharacteristic
14C22×C22⋊D29C2212yes—
15C23×Dic29C2211yescharacteristic
16C23×Dic29C2211yescharacteristic
17C2×C22⋊C4×C29C2211yescharacteristic
18C2×C22⋊C4×C29C2211yescharacteristic
19C2×C22⋊C4×C29C2212yes—
20C2×C22⋊C4×C29C2212yes—
21#11745315—24no—
22C2×C22⋊Dic29—24no—
23C2×C22⋊Dic29C2212yes—
24C2×C22⋊Dic29C2212yes—
25C2×C22⋊Dic29C2212yes—
26C2×C22⋊Dic29C2211yescharacteristic
27C2×#90781C2211yescharacteristic, complemented
28C2×#90781C2211yescharacteristic, complemented
29C2×#90781C2212yescomplemented
30C2×C4⋊Dic29C2211yescharacteristic, complemented
31C2×C4⋊Dic29C2211yescharacteristic, complemented
32C2×#90779C2212yescomplemented
33C2×#90779C2212yescomplemented
34C2×C4×Dic29C2212yescomplemented
35#11745248—24no—
36#11745239—24no—
37#11745179C2212yescomplemented
38#11745179C2212yescomplemented
39C24×C29—22no—
40C24×C29—24no—
41C24×C29—22no—
42C24×C29—22no—
43C24×C29—42no—
44C24×C29C2312yes—
45C24×C29C2311yescharacteristic
46C23×D29C2311yescharacteristic
47C22×C4×C29C2312yes—
48C22×C4×C29C2311yescharacteristic
49C22×C4×C29C2311yescharacteristic
50C2×C22⋊D29—22no—
51C2×C22⋊D29—22no—
52C2×C22⋊D29—22no—
53C2×C22⋊D29—24no—
54C2×C22⋊D29—24no—
55C2×C22⋊D29—42no—
56C22×Dic29—22no—
57C22×Dic29—22no—
58C22×Dic29—22no—
59C22×Dic29—42no—
60C22×Dic29D414yescomplemented
61C22×Dic29C2312yes—
62C22×Dic29C2311yescharacteristic
63C22×Dic29C2311yescharacteristic
64C22×Dic29C2312yes—
65C22×Dic29C2311yescharacteristic
66C22⋊C4×C29—22no—
67C22⋊C4×C29—22no—
68C22⋊C4×C29—24no—
69C22⋊C4×C29—42no—
70C22⋊Dic29—24no—
71C22⋊Dic29—24no—
72C22⋊Dic29—24no—
73C22⋊Dic29D414yes—
74#90781—22no—
75#90781—22no—
76#90781—42no—
77C4⋊Dic29—22no—
78C4⋊Dic29—22no—
79#90779—24no—
80#90779—42no—
81C4×Dic29—24no—
82C23×C29—22no—
83C23×C29—22no—
84C23×C29—28no—
85C23×C29—22no—
86C23×C29—22no—
87C23×C29—22no—
88C23×C29—22no—
89C23×C29—22no—
90C23×C29—22no—
91C23×C29—48no—
92C23×C29—48no—
93C23×C29—44no—
94C23×C29—44no—
95C23×C29C2×D412yes—
96C23×C29C2×D412yes—
97C23×C29#4112yes—
98C23×C29#4114yes—
99C23×C29C2411yescharacteristic
100C22×D29—21no—
101C22×D29—21no—
102C22×D29—21no—
103C22×D29—22no—
104C22×D29—22no—
105C2×C4×C29—22no—
106C2×C4×C29—21no—
107C2×C4×C29—21no—
108C2×C4×C29—22no—
109C2×C4×C29—22no—
110C2×C4×C29—22no—
111C2×C4×C29—22no—
112C22⋊D29—48no—
113C22⋊D29—44no—
114C2×Dic29—28no—
115C2×Dic29—21no—
116C2×Dic29—21no—
117C2×Dic29—21no—
118C2×Dic29—21no—
119C2×Dic29—22no—
120C2×Dic29—22no—
121C2×Dic29—21no—
122C2×Dic29—22no—
123C2×Dic29—21no—
124C2×Dic29—21no—
125C2×Dic29—22no—
126C2×Dic29—22no—
127C2×Dic29—44no—
128C2×Dic29C2×D414yes—
129C2×Dic29C2×D412yes—
130C2×Dic29C2×D412yes—
131#2411—291nomaximal, Sylow
132C22×C29—22no—
133C22×C29—22no—
134C22×C29—24no—
135C22×C29—24no—
136C22×C29—24no—
137C22×C29—24no—
138C22×C29—24no—
139C22×C29—416no—
140C22×C29—42no—
141C22×C29—42no—
142C22×C29—42no—
143C22×C29—42no—
144C22×C29#12114yes—
145C22×C29C22×D411yescharacteristic
146C22×C29C22×D411yescharacteristic
147C22×C29C2×#4111yescharacteristic
148C22×C29C2×#4112yes—
149C22×C29H(5,𝔽2)12yes—
150C2×D29—41no—
151C2×D29—41no—
152C2×D29—41no—
153C2×D29—42no—
154C2×D29—42no—
155C4×C29—41no—
156C4×C29—41no—
157C4×C29—42no—
158Dic29—22no—
159Dic29—22no—
160Dic29—24no—
161Dic29—41no—
162Dic29—42no—
163C2×#123—291no—
164C2×#120—291no—
165C2×#117—291no—
166C22×C22⋊C4—291no—
167#396—292no—
168#394—292no—
169#390—292no—
170#388—292no—
171#386—291no—
172#385—291no—
173#379D2911yescharacteristic, complemented
174C2×C29—24no—
175C2×C29—44no—
176C2×C29C2×#12111yescharacteristic
177C2×C29#52511yescharacteristic
178C2×C29#53511yescharacteristic
179C2×C29#54612yes—
180C2×C29#55112yes—
181D29—81no—
182C25C2×D2911yescharacteristic
183C22×D4—291no—
184C22×D4—292no—
185C23×C4—291no—
186C23×C4—291no—
187#123—584no—
188#120—584no—
189#117—584no—
190C2×C4⋊C4—292no—
191C2×C4⋊C4—291no—
192C2×C4⋊C4—291no—
193C2×C4⋊C4—292no—
194C2×C22⋊C4—291no—
195C2×C22⋊C4—292no—
196C2×C22⋊C4—292no—
197C2×C22⋊C4—292no—
198C2×C22⋊C4—291no—
199C2×C22⋊C4—291no—
200C2×C22⋊C4—292no—
201C2×C22⋊C4—584no—
202C2×C22⋊C4C2×D2911yescharacteristic
203C2×C22⋊C4C2×D2911yescharacteristic
204C2×C22⋊C4C2×D2912yes—
205C2×C22⋊C4C2×D2912yes—
206C2×C42—292no—
207#95—292no—
208#95—292no—
209C29#241111yescharacteristic, complemented, Sylow
210C24—22no—
211C24—24no—
212C24—22no—
213C24—22no—
214C24—42no—
215C24—291no—
216C24C22×D2912yes—
217C24C22×D2911yescharacteristic
218C2×D4—584no—
219C2×D4—582no—
220C2×D4—582no—
221C2×D4—582no—
222C2×D4—584no—
223C2×D4—1162no—
224C22×C4—294no—
225C22×C4—292no—
226C22×C4—291no—
227C22×C4—291no—
228C22×C4—292no—
229C22×C4—291no—
230C22×C4—582no—
231C22×C4—582no—
232C22×C4—582no—
233C22×C4—1162no—
234C22×C4C22×D2911yescharacteristic
235C22×C4C22×D2912yes—
236C22×C4C22×D2911yescharacteristic
237C4⋊C4—584no—
238C4⋊C4—582no—
239C4⋊C4—582no—
240C4⋊C4—1162no—
241C22⋊C4—22no—
242C22⋊C4—22no—
243C22⋊C4—24no—
244C22⋊C4—42no—
245C22⋊C4—294no—
246C22⋊C4—582no—
247C22⋊C4—582no—
248C22⋊C4—584no—
249C22⋊C4—584no—
250C22⋊C4—584no—
251C22⋊C4—1162no—
252C42—584no—
253C23—22no—
254C23—22no—
255C23—28no—
256C23—22no—
257C23—22no—
258C23—22no—
259C23—22no—
260C23—22no—
261C23—22no—
262C23—48no—
263C23—48no—
264C23—44no—
265C23—44no—
266C23—581no—
267C23—581no—
268C23—581no—
269C23—582no—
270C23—582no—
271C23#9080512yes—
272C23D4×D2912yes—
273C23D4×D2912yes—
274C23#9080714yes—
275C23C23×D2911yescharacteristic
276D4—1168no—
277D4—1164no—
278C2×C4—22no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—22no—
282C2×C4—22no—
283C2×C4—22no—
284C2×C4—22no—
285C2×C4—294no—
286C2×C4—292no—
287C2×C4—292no—
288C2×C4—581no—
289C2×C4—581no—
290C2×C4—581no—
291C2×C4—581no—
292C2×C4—582no—
293C2×C4—582no—
294C2×C4—588no—
295C2×C4—581no—
296C2×C4—582no—
297C2×C4—581no—
298C2×C4—581no—
299C2×C4—582no—
300C2×C4—582no—
301C2×C4—1164no—
302C22—24no—
303C22—24no—
304C22—22no—
305C22—22no—
306C22—24no—
307C22—24no—
308C22—24no—
309C22—416no—
310C22—42no—
311C22—42no—
312C22—42no—
313C22—42no—
314C22—1162no—
315C22—1162no—
316C22—1161no—
317C22—1161no—
318C22—1161no—
319C22#1174524614yes—
320C22C2×#9080511yescharacteristic
321C22C2×D4×D2911yescharacteristic
322C22C2×D4×D2911yescharacteristic
323C22C2×#9080712yes—
324C22#1174535912yes—
325C4—42no—
326C4—41no—
327C4—41no—
328C4—584no—
329C4—582no—
330C4—582no—
331C4—1161no—
332C4—1162no—
333C2—24no—
334C2—44no—
335C2—2321no—
336C2C2×#1174524611yescharacteristic
337C2#1427166911yescharacteristic
338C2#1427172811yescharacteristic
339C2#1427180012yes—
340C2#1427183912yes—
subgroupG/H
center, FrattiniC23C23×D29
commutator, socle, cosocleC23×C29C24
FittingC29×#379C2
prime radicalC2×#11745315C2
hypercenter#379D29
hypocenterC29#2411
LCSG ▷ C23×C29 ▷ C29
UCSC1 ◁ C23 ◁ #379

Complements

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

NH ≅ G/Ntype
1. C2×#11745248C2semidirect
3. C2×#11745239C2semidirect
4. C22×C22⋊Dic29C2semidirect
5. #14271086C2semidirect
6. #14271078C2semidirect
7. #14271063C2semidirect
8. #14271056C2semidirect
9. #14271040C2semidirect
10. #14271035C2semidirect
11. C29×#379C2semidirect
27. C2×#90781C22semidirect
28. C2×#90781C22semidirect
29. C2×#90781C22semidirect
30. C2×C4⋊Dic29C22semidirect
31. C2×C4⋊Dic29C22semidirect
32. C2×#90779C22semidirect
33. C2×#90779C22semidirect
34. C2×C4×Dic29C22semidirect
37. #11745179C22semidirect
38. #11745179C22semidirect
60. C22×Dic29D4semidirect
173. #379D29semidirect
209. C29#2411semidirect

Maximal subgroups

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

subgroupindex
C2×#117452482
C2×#117453152
C2×#117452392
C22×C22⋊Dic292
#142710862
#142710782
#142710632
#142710562
#142710402
#142710352
C29×#3792
#241129