Finite Group Databasebeta

← #16829407

Subgroups — #16829407

Order 3712.

420 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 137 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
1#14271674C211yesmaximal, characteristic
2C2×#11745288C211yesmaximal, characteristic, complemented
3#14271505C212yesmaximal, complemented
4#14271499C211yesmaximal, characteristic, complemented
5#14271494C211yesmaximal, characteristic, complemented
6#14271488C212yesmaximal, complemented
7#14271482C211yesmaximal, characteristic, complemented
8#14271477C211yesmaximal, characteristic, complemented
9#14271201C212yesmaximal, complemented
10#14271160C212yesmaximal, complemented
11C2×C29×C22⋊C8C211yesmaximal, characteristic, complemented
12C23×C4×C29C2211yescharacteristic
13C2×#90805C2211yescharacteristic
14C22×C8×C29C2212yes—
15#11745315—21no—
16C2×C22⋊Dic29—21no—
17#11745292C2211yescharacteristic
18#11745292C2211yescharacteristic
19#11745291—21no—
20C4×C22⋊D29—21no—
21C4×C22⋊D29—21no—
22#11745288—21no—
23#11745288—21no—
24#11745288C2212yes—
25#11745288C2212yes—
26#11745288C2211yescharacteristic
27C2×C4⋊Dic29C2211yescharacteristic
28C2×C4⋊Dic29C2211yescharacteristic
29#11745286C2211yescharacteristic
30#11745286C2211yescharacteristic
31C2×C4×Dic29—21no—
32C29×C22⋊C8C2212yes—
33C29×C22⋊C8C2211yescharacteristic
34C29×C22⋊C8C2211yescharacteristic
35#11745169C2212yescomplemented
36#11745169C2212yescomplemented
37#11745166C2212yescomplemented
38#11745166C2212yescomplemented
39#11745165C2212yescomplemented
40#11745165C2212yescomplemented
41#11745164C2212yescomplemented
42#11745164C2212yescomplemented
43C24×C29D411yescharacteristic
44C22×C4×C29—24no—
45C22×C4×C29D411yescharacteristic
46C22×C4×C29D411yescharacteristic
47C22×C4×C29D411yescharacteristic
48C22×C4×C29C2311yescharacteristic
49C22×C4×C29C2311yescharacteristic
50C22×C4×C29C2311yescharacteristic
51C2×C22⋊D29—21no—
52C2×C22⋊D29—21no—
53C2×C22⋊D29—21no—
54C22×Dic29—21no—
55C22×Dic29—21no—
56#90805—24no—
57C2×D116C2311yescharacteristic
58C2×C4×D29—21no—
59C2×Dic58C2311yescharacteristic
60C2×C8×C29—24no—
61C2×C8×C29C2312yes—
62C2×C8×C29C2312yes—
63C22⋊Dic29—21no—
64C22⋊Dic29—21no—
65C22⋊Dic29—22no—
66C22⋊Dic29—22no—
67C22⋊Dic29—21no—
68#90781—21no—
69#90781—21no—
70C4⋊Dic29—21no—
71C4⋊Dic29—21no—
72C4⋊Dic29C2311yescharacteristic
73C4⋊Dic29C2311yescharacteristic
74C4⋊Dic29C2312yes—
75C4⋊Dic29C2312yes—
76#90779—21no—
77#90779—21no—
78C4×Dic29—22no—
79C4×Dic29—22no—
80C4×Dic29—21no—
81C23×C29—22no—
82C23×C29—22no—
83C23×C29—41no—
84C23×C29C2×D411yescharacteristic
85C23×C29C2×D411yescharacteristic
86C23×C29C2×D411yescharacteristic
87C22×D29—21no—
88C2×C4×C29—22no—
89C2×C4×C29—22no—
90C2×C4×C29—22no—
91C2×C4×C29—22no—
92C2×C4×C29—22no—
93C2×C4×C29C2×D411yescharacteristic
94C2×C4×C29C2×D411yescharacteristic
95C2×C4×C29C2×D411yescharacteristic
96C2×C4×C29#4114yes—
97C2×C4×C29C2411yescharacteristic
98C22⋊D29—42no—
99C22⋊D29—42no—
100C22⋊D29—42no—
101C2×Dic29—22no—
102C2×Dic29—22no—
103C2×Dic29—21no—
104C2×Dic29—21no—
105C2×Dic29—21no—
106C2×Dic29—42no—
107C2×Dic29—42no—
108D116—22no—
109C4×D29—42no—
110Dic58—22no—
111C8×C29—22no—
112C8×C29—22no—
113#3091—291nomaximal, Sylow
114C22×C29—21no—
115C22×C29—21no—
116C22×C29—21no—
117C22×C29—21no—
118C22×C29—21no—
119C22×C29—21no—
120C22×C29—21no—
121C22×C29—44no—
122C22×C29#12312yes—
123C22×C29#13512yes—
124C22×C29C22×D411yescharacteristic
125C2×D29—41no—
126C2×D29—41no—
127C2×D29—41no—
128C4×C29—21no—
129C4×C29—21no—
130C4×C29#12312yes—
131C4×C29C2×#4112yes—
132Dic29—41no—
133Dic29—42no—
134Dic29—41no—
135Dic29—42no—
136Dic29—41no—
137#525—291no—
138C2×#117—291no—
139#485—292no—
140#484—291no—
141#483—291no—
142#482—292no—
143#481—291no—
144#480—291no—
145#427—292no—
146#416—292no—
147C2×C22⋊C8D2911yescharacteristic, complemented
148C2×C29—22no—
149C2×C29—22no—
150C2×C29—41no—
151C2×C29C2×#12311yescharacteristic
152C2×C29C2×#13511yescharacteristic
153C2×C29#57511yescharacteristic
154D29—81no—
155C2×#41—291no—
156C23×C4C2×D2911yescharacteristic
157C22×C8C2×D2912yes—
158#123—581no—
159C22⋊Q8—291no—
160C22⋊Q8—291no—
161#121—291no—
162#121—291no—
163#120—581no—
164C4×D4—581no—
165C4×D4—581no—
166#117—292no—
167#117—292no—
168#117—291no—
169#117—581no—
170#117—581no—
171C2×C4⋊C4—291no—
172C2×C4⋊C4—291no—
173C2×C22⋊C4—581no—
174C2×C42—581no—
175#107—292no—
176#107—292no—
177#106—292no—
178#106—292no—
179#103—292no—
180#103—292no—
181#102—292no—
182#102—292no—
183C22⋊C8C2×D2911yescharacteristic
184C22⋊C8C2×D2911yescharacteristic
185C22⋊C8C2×D2912yes—
186C29#309111yescharacteristic, complemented, Sylow
187C24D11611yescharacteristic
188#41—584no—
189C2×Q8—291no—
190C2×D4—291no—
191C2×D4—581no—
192C2×D4—581no—
193C2×D4—581no—
194C22×C4—24no—
195C22×C4—581no—
196C22×C4—581no—
197C22×C4—581no—
198C22×C4D11611yescharacteristic
199C22×C4D11611yescharacteristic
200C22×C4D11611yescharacteristic
201C22×C4C22×D2911yescharacteristic
202C22×C4C22×D2911yescharacteristic
203C22×C4C22×D2911yescharacteristic
204C2×C8—24no—
205C2×C8C22×D2912yes—
206C2×C8C22×D2912yes—
207C4⋊C4—292no—
208C4⋊C4—292no—
209C4⋊C4—291no—
210C4⋊C4—291no—
211C4⋊C4—581no—
212C4⋊C4—581no—
213C4⋊C4—581no—
214C4⋊C4—581no—
215C22⋊C4—582no—
216C22⋊C4—582no—
217C22⋊C4—581no—
218C22⋊C4—581no—
219C22⋊C4—581no—
220C22⋊C4—581no—
221C22⋊C4—581no—
222C42—582no—
223C42—582no—
224C42—581no—
225C23—22no—
226C23—22no—
227C23—41no—
228C23—581no—
229C23C2×D11611yescharacteristic
230C23C2×D11611yescharacteristic
231C23C2×D11611yescharacteristic
232Q8—582no—
233D4—582no—
234D4—1162no—
235D4—1162no—
236D4—1162no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—22no—
241C2×C4—22no—
242C2×C4—582no—
243C2×C4—582no—
244C2×C4—581no—
245C2×C4—581no—
246C2×C4—581no—
247C2×C4—1162no—
248C2×C4—1162no—
249C2×C4—1162no—
250C2×C4C2×D11611yescharacteristic
251C2×C4C2×D11611yescharacteristic
252C2×C4C2×D11611yescharacteristic
253C2×C4#9080714yes—
254C2×C4C23×D2911yescharacteristic
255C8—22no—
256C8—22no—
257C22—21no—
258C22—21no—
259C22—21no—
260C22—21no—
261C22—21no—
262C22—21no—
263C22—21no—
264C22—44no—
265C22—1161no—
266C22—1161no—
267C22—1161no—
268C22#1174524812yes—
269C22#1174526612yes—
270C22C22×D11611yescharacteristic
271C4—21no—
272C4—21no—
273C4—1161no—
274C4—1162no—
275C4—1161no—
276C4—1162no—
277C4—1161no—
278C4#1174524812yes—
279C4C2×#9080712yes—
280C2—22no—
281C2—22no—
282C2—41no—
283C2—2321no—
284C2C2×#1174524811yescharacteristic
285C2C2×#1174526611yescharacteristic
286C2#1427196311yescharacteristic
subgroupG/H
centerC2×C4C2×D116
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC2×C29×C22⋊C8C2
socleC22×C29C22×D4
prime radical#14271674C2
hypercenterC2×C22⋊C8D29
hypocenterC29#3091
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×#11745288C2semidirect
3. #14271505C2semidirect
4. #14271499C2semidirect
5. #14271494C2semidirect
6. #14271488C2semidirect
7. #14271482C2semidirect
8. #14271477C2semidirect
9. #14271201C2semidirect
10. #14271160C2semidirect
11. C2×C29×C22⋊C8C2semidirect
35. #11745169C22semidirect
36. #11745169C22semidirect
37. #11745166C22semidirect
38. #11745166C22semidirect
39. #11745165C22semidirect
40. #11745165C22semidirect
41. #11745164C22semidirect
42. #11745164C22semidirect
147. C2×C22⋊C8D29semidirect
186. C29#3091semidirect

Maximal subgroups

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

subgroupindex
#142716742
C2×#117452882
#142715052
#142714992
#142714942
#142714882
#142714822
#142714772
#142712012
#142711602
C2×C29×C22⋊C82
#309129