Finite Group Databasebeta

← #16829405

Subgroups — #16829405

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
2#14271504C212yesmaximal, complemented
3#14271498C211yesmaximal, characteristic, complemented
4#14271493C211yesmaximal, characteristic, complemented
5#14271487C212yesmaximal, complemented
6#14271481C211yesmaximal, characteristic, complemented
7#14271476C211yesmaximal, characteristic, complemented
8#14271199C212yesmaximal, complemented
9#14271157C212yesmaximal, complemented
10C2×C22⋊#6597C211yesmaximal, characteristic, complemented
11C2×C29×#117C211yesmaximal, characteristic, complemented
12C23×C4×C29C2211yescharacteristic
13C2×#90805C2211yescharacteristic
14C29×#117—21no—
15C29×#117—21no—
16C29×#117C2212yes—
17C29×#117C2212yes—
18C2×C4⋊C4×C29C2211yescharacteristic
19C2×C4⋊C4×C29C2211yescharacteristic
20C2×C22⋊C4×C29—21no—
21C2×C42×C29—21no—
22#11745315—21no—
23#11745292C2211yescharacteristic
24#11745292C2211yescharacteristic
25#11745291—21no—
26C4×C22⋊D29—21no—
27C4×C22⋊D29—21no—
28#11745288C2211yescharacteristic
29#11745286C2211yescharacteristic
30#11745286C2211yescharacteristic
31C22×#6597C2212yes—
32C22⋊#6597C2211yescharacteristic
33C22⋊#6597C2211yescharacteristic
34C22⋊#6597C2212yes—
35#11745158C2212yescomplemented
36#11745158C2212yescomplemented
37#11745157C2212yescomplemented
38#11745157C2212yescomplemented
39#11745156C2212yescomplemented
40#11745156C2212yescomplemented
41#11745155C2212yescomplemented
42#11745155C2212yescomplemented
43C24×C29D411yescharacteristic
44C22×C4×C29—24no—
45C22×C4×C29—21no—
46C22×C4×C29—21no—
47C22×C4×C29D411yescharacteristic
48C22×C4×C29D411yescharacteristic
49C22×C4×C29D411yescharacteristic
50C22×C4×C29C2311yescharacteristic
51C22×C4×C29C2311yescharacteristic
52C22×C4×C29C2311yescharacteristic
53C2×C22⋊D29—21no—
54C2×C22⋊D29—21no—
55C2×C22⋊D29—21no—
56#90805—24no—
57C2×D116C2311yescharacteristic
58C2×C4×D29—21no—
59C2×Dic58C2311yescharacteristic
60C4⋊C4×C29—21no—
61C4⋊C4×C29—21no—
62C4⋊C4×C29C2312yes—
63C4⋊C4×C29C2312yes—
64C22⋊C4×C29—22no—
65C22⋊C4×C29—22no—
66C42×C29—22no—
67C42×C29—22no—
68C22⋊Dic29—21no—
69C22⋊Dic29—21no—
70C22⋊Dic29—21no—
71#90781—21no—
72#90781—21no—
73C4⋊Dic29C2311yescharacteristic
74C4⋊Dic29C2311yescharacteristic
75#90779—21no—
76#90779—21no—
77C4×Dic29—21no—
78C2×#6597—24no—
79C2×#6597C2312yes—
80C2×#6597C2312yes—
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×C29—22no—
94C2×C4×C29—22no—
95C2×C4×C29—42no—
96C2×C4×C29—42no—
97C2×C4×C29C2×D411yescharacteristic
98C2×C4×C29C2×D411yescharacteristic
99C2×C4×C29C2×D411yescharacteristic
100C2×C4×C29#4114yes—
101C2×C4×C29C2411yescharacteristic
102C22⋊D29—42no—
103C22⋊D29—42no—
104C22⋊D29—42no—
105C2×Dic29—21no—
106C2×Dic29—21no—
107C2×Dic29—21no—
108D116—22no—
109C4×D29—42no—
110Dic58—22no—
111#6597—22no—
112#6597—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—42no—
131C4×C29—42no—
132C4×C29#12312yes—
133C4×C29C2×#4112yes—
134Dic29—41no—
135Dic29—41no—
136Dic29—41no—
137#525—291no—
138C2×#117D2911yescharacteristic, complemented
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⋊C8—291no—
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×C8—292no—
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—21no—
167#117—21no—
168#117—291no—
169#117C2×D2912yes—
170#117C2×D2912yes—
171C2×C4⋊C4C2×D2911yescharacteristic
172C2×C4⋊C4C2×D2911yescharacteristic
173C2×C22⋊C4—21no—
174C2×C42—21no—
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⋊C8—291no—
184C22⋊C8—291no—
185C22⋊C8—292no—
186C29#309111yescharacteristic, complemented, Sylow
187C24C22⋊D2911yescharacteristic
188#41—584no—
189C2×Q8—291no—
190C2×D4—291no—
191C2×D4—581no—
192C2×D4—581no—
193C2×D4—581no—
194C22×C4—24no—
195C22×C4—21no—
196C22×C4—21no—
197C22×C4—581no—
198C22×C4C22⋊D2911yescharacteristic
199C22×C4C22⋊D2911yescharacteristic
200C22×C4C22⋊D2911yescharacteristic
201C22×C4C22×D2911yescharacteristic
202C22×C4C22×D2911yescharacteristic
203C22×C4C22×D2911yescharacteristic
204C2×C8—292no—
205C2×C8—292no—
206C2×C8—584no—
207C4⋊C4—21no—
208C4⋊C4—21no—
209C4⋊C4—291no—
210C4⋊C4—291no—
211C4⋊C4—581no—
212C4⋊C4—581no—
213C4⋊C4C22×D2912yes—
214C4⋊C4C22×D2912yes—
215C22⋊C4—22no—
216C22⋊C4—22no—
217C22⋊C4—581no—
218C22⋊C4—581no—
219C22⋊C4—581no—
220C22⋊C4—581no—
221C22⋊C4—581no—
222C42—22no—
223C42—22no—
224C42—581no—
225C23—22no—
226C23—22no—
227C23—41no—
228C23—581no—
229C23C2×C22⋊D2911yescharacteristic
230C23C2×C22⋊D2911yescharacteristic
231C23C2×C22⋊D2911yescharacteristic
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—22no—
243C2×C4—22no—
244C2×C4—42no—
245C2×C4—42no—
246C2×C4—581no—
247C2×C4—581no—
248C2×C4—581no—
249C2×C4—1162no—
250C2×C4#9080514yes—
251C2×C4C2×C22⋊D2911yescharacteristic
252C2×C4C2×C22⋊D2911yescharacteristic
253C2×C4C2×C22⋊D2911yescharacteristic
254C2×C4C23×D2911yescharacteristic
255C8—582no—
256C8—582no—
257C22—21no—
258C22—21no—
259C22—21no—
260C22—21no—
261C22—21no—
262C22—21no—
263C22—21no—
264C22—44no—
265C22—1161no—
266C22—1161no—
267C22—1161no—
268C22#1174529112yes—
269C22#1174531212yes—
270C22C22×C22⋊D2911yescharacteristic
271C4—21no—
272C4—21no—
273C4—42no—
274C4—42no—
275C4—1161no—
276C4—1161no—
277C4—1161no—
278C4#1174529112yes—
279C4C2×#9080512yes—
280C2—22no—
281C2—22no—
282C2—41no—
283C2—2321no—
284C2C2×#1174529111yescharacteristic
285C2C2×#1174531211yescharacteristic
286C2#1427196111yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC2×C29×#117C2
socleC22×C29C22×D4
prime radical#14271674C2
hypercenterC2×#117D29
hypocenterC29#3091
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
2. #14271504C2semidirect
3. #14271498C2semidirect
4. #14271493C2semidirect
5. #14271487C2semidirect
6. #14271481C2semidirect
7. #14271476C2semidirect
8. #14271199C2semidirect
9. #14271157C2semidirect
10. C2×C22⋊#6597C2semidirect
11. C2×C29×#117C2semidirect
35. #11745158C22semidirect
36. #11745158C22semidirect
37. #11745157C22semidirect
38. #11745157C22semidirect
39. #11745156C22semidirect
40. #11745156C22semidirect
41. #11745155C22semidirect
42. #11745155C22semidirect
138. C2×#117D29semidirect
186. C29#3091semidirect

Maximal subgroups

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

subgroupindex
#142716742
#142715042
#142714982
#142714932
#142714872
#142714812
#142714762
#142711992
#142711572
C2×C22⋊#65972
C2×C29×#1172
#309129