Finite Group Databasebeta

← #16829415

Subgroups — #16829415

Order 3712.

458 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 141 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#14271498C212yesmaximal, complemented
3#14271493C212yesmaximal, complemented
4#14271481C212yesmaximal, complemented
5#14271476C212yesmaximal, complemented
6#14271203C212yesmaximal, complemented
7#14271162C212yesmaximal, complemented
8#14271127C211yesmaximal, characteristic, complemented
9C22×C4⋊C4×C29C211yesmaximal, characteristic, complemented
10C23×C4×C29—21no—
11C23×C4×C29C2211yescharacteristic
12C2×#90805C2211yescharacteristic
13C2×C4⋊C4×C29—21no—
14C2×C4⋊C4×C29—21no—
15C2×C4⋊C4×C29—21no—
16C2×C4⋊C4×C29C2212yes—
17C2×C4⋊C4×C29C2212yes—
18C2×C4⋊C4×C29C2212yes—
19#11745315—21no—
20#11745292C2211yescharacteristic
21#11745292C2211yescharacteristic
22#11745291—21no—
23C4×C22⋊D29—21no—
24C4×C22⋊D29—21no—
25#11745288C2211yescharacteristic
26#11745286C2211yescharacteristic
27#11745286C2211yescharacteristic
28C2×#90777C2212yes—
29C22⋊#6597C2212yes—
30C22⋊#6597C2212yes—
31#11745158C2214yescomplemented
32#11745157C2214yescomplemented
33#11745156C2214yescomplemented
34#11745155C2214yescomplemented
35C24×C29D411yescharacteristic
36C22×C4×C29—24no—
37C22×C4×C29—22no—
38C22×C4×C29—22no—
39C22×C4×C29—22no—
40C22×C4×C29—44no—
41C22×C4×C29D411yescharacteristic
42C22×C4×C29D411yescharacteristic
43C22×C4×C29D411yescharacteristic
44C22×C4×C29C2311yescharacteristic
45C22×C4×C29C2311yescharacteristic
46C22×C4×C29C2311yescharacteristic
47C2×C22⋊D29—21no—
48C2×C22⋊D29—21no—
49C2×C22⋊D29—21no—
50#90805—24no—
51C2×D116C2311yescharacteristic
52C2×C4×D29—21no—
53C2×Dic58C2311yescharacteristic
54C4⋊C4×C29—22no—
55C4⋊C4×C29—22no—
56C4⋊C4×C29—22no—
57C4⋊C4×C29C2314yes—
58C22⋊Dic29—21no—
59C22⋊Dic29—21no—
60C22⋊Dic29—21no—
61#90781—21no—
62#90781—21no—
63C4⋊Dic29C2311yescharacteristic
64C4⋊Dic29C2311yescharacteristic
65#90779—21no—
66#90779—21no—
67C4×Dic29—21no—
68#90777—24no—
69C2×#6597C2314yes—
70C23×C29—22no—
71C23×C29—22no—
72C23×C29—22no—
73C23×C29C2×D411yescharacteristic
74C23×C29C2×D411yescharacteristic
75C23×C29C2×D411yescharacteristic
76C22×D29—21no—
77C2×C4×C29—22no—
78C2×C4×C29—22no—
79C2×C4×C29—22no—
80C2×C4×C29—22no—
81C2×C4×C29—22no—
82C2×C4×C29—24no—
83C2×C4×C29—44no—
84C2×C4×C29—44no—
85C2×C4×C29—44no—
86C2×C4×C29C2×D411yescharacteristic
87C2×C4×C29C2×D411yescharacteristic
88C2×C4×C29C2×D411yescharacteristic
89C2×C4×C29#4114yes—
90C2×C4×C29C2411yescharacteristic
91C22⋊D29—42no—
92C22⋊D29—42no—
93C22⋊D29—42no—
94C2×Dic29—21no—
95C2×Dic29—21no—
96C2×Dic29—21no—
97D116—22no—
98C4×D29—42no—
99Dic58—22no—
100#6597—24no—
101#3092—291nomaximal, Sylow
102C22×C29—28no—
103C22×C29—21no—
104C22×C29—21no—
105C22×C29—21no—
106C22×C29—21no—
107C22×C29—21no—
108C22×C29—21no—
109C22×C29#12312yes—
110C22×C29AGL(1,ℤ/8)12yes—
111C22×C29#13712yes—
112C22×C29C22×D411yescharacteristic
113C2×D29—41no—
114C2×D29—41no—
115C2×D29—41no—
116C4×C29—21no—
117C4×C29—21no—
118C4×C29—44no—
119C4×C29#12312yes—
120C4×C29C2×#4112yes—
121Dic29—41no—
122Dic29—41no—
123Dic29—41no—
124#525—291no—
125C22×C4⋊C4D2911yescharacteristic, complemented
126#484—292no—
127#483—292no—
128#481—292no—
129#480—292no—
130#428—292no—
131#417—292no—
132#407—291no—
133C2×C29—22no—
134C2×C29—22no—
135C2×C29—22no—
136C2×C29C2×#12311yescharacteristic
137C2×C29C2×AGL(1,ℤ/8)11yescharacteristic
138C2×C29C2×#13711yescharacteristic
139D29—81no—
140C2×#41—291no—
141C23×C4—21no—
142C23×C4C2×D2911yescharacteristic
143C2×M16—292no—
144#123—581no—
145C22⋊Q8—291no—
146C22⋊Q8—291no—
147#121—291no—
148#121—291no—
149#120—581no—
150C4×D4—581no—
151C4×D4—581no—
152#117—291no—
153C2×C4⋊C4—21no—
154C2×C4⋊C4—21no—
155C2×C4⋊C4—21no—
156C2×C4⋊C4C2×D2912yes—
157C2×C4⋊C4C2×D2912yes—
158C2×C4⋊C4C2×D2912yes—
159#107—294no—
160#106—294no—
161#103—294no—
162#102—294no—
163C22⋊C8—292no—
164C22⋊C8—292no—
165C29#309211yescharacteristic, complemented, Sylow
166C24C22⋊D2911yescharacteristic
167#41—584no—
168C2×Q8—291no—
169C2×D4—291no—
170C2×D4—581no—
171C2×D4—581no—
172C2×D4—581no—
173C22×C4—24no—
174C22×C4—22no—
175C22×C4—22no—
176C22×C4—22no—
177C22×C4—44no—
178C22×C4—581no—
179C22×C4C22⋊D2911yescharacteristic
180C22×C4C22⋊D2911yescharacteristic
181C22×C4C22⋊D2911yescharacteristic
182C22×C4C22×D2911yescharacteristic
183C22×C4C22×D2911yescharacteristic
184C22×C4C22×D2911yescharacteristic
185M16—584no—
186C2×C8—294no—
187C4⋊C4—22no—
188C4⋊C4—22no—
189C4⋊C4—22no—
190C4⋊C4—291no—
191C4⋊C4—291no—
192C4⋊C4—581no—
193C4⋊C4—581no—
194C4⋊C4C22×D2914yes—
195C22⋊C4—581no—
196C22⋊C4—581no—
197C22⋊C4—581no—
198C22⋊C4—581no—
199C22⋊C4—581no—
200C42—581no—
201C23—22no—
202C23—22no—
203C23—22no—
204C23—581no—
205C23C2×C22⋊D2911yescharacteristic
206C23C2×C22⋊D2911yescharacteristic
207C23C2×C22⋊D2911yescharacteristic
208Q8—582no—
209D4—582no—
210D4—1162no—
211D4—1162no—
212D4—1162no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—24no—
219C2×C4—44no—
220C2×C4—44no—
221C2×C4—44no—
222C2×C4—581no—
223C2×C4—581no—
224C2×C4—581no—
225C2×C4—1162no—
226C2×C4#9080514yes—
227C2×C4C2×C22⋊D2911yescharacteristic
228C2×C4C2×C22⋊D2911yescharacteristic
229C2×C4C2×C22⋊D2911yescharacteristic
230C2×C4C23×D2911yescharacteristic
231C8—584no—
232C22—28no—
233C22—21no—
234C22—21no—
235C22—21no—
236C22—21no—
237C22—21no—
238C22—21no—
239C22—1161no—
240C22—1161no—
241C22—1161no—
242C22#1174529112yes—
243C22#1174529412yes—
244C22#1174530412yes—
245C22C22×C22⋊D2911yescharacteristic
246C4—21no—
247C4—21no—
248C4—44no—
249C4—1161no—
250C4—1161no—
251C4—1161no—
252C4#1174529112yes—
253C4C2×#9080512yes—
254C2—22no—
255C2—22no—
256C2—22no—
257C2—2321no—
258C2C2×#1174529111yescharacteristic
259C2C2×#1174529411yescharacteristic
260C2C2×#1174530411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC22×C4⋊C4×C29C2
socleC22×C29C22×D4
prime radical#14271674C2
hypercenterC22×C4⋊C4D29
hypocenterC29#3092
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #14271498C2semidirect
3. #14271493C2semidirect
4. #14271481C2semidirect
5. #14271476C2semidirect
6. #14271203C2semidirect
7. #14271162C2semidirect
8. #14271127C2semidirect
9. C22×C4⋊C4×C29C2semidirect
31. #11745158C22semidirect
32. #11745157C22semidirect
33. #11745156C22semidirect
34. #11745155C22semidirect
125. C22×C4⋊C4D29semidirect
165. C29#3092semidirect

Maximal subgroups

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

subgroupindex
#142716742
#142714982
#142714932
#142714812
#142714762
#142712032
#142711622
#142711272
C22×C4⋊C4×C292
#309229