Finite Group Databasebeta

← #16822749

Subgroups — #16822749

Order 3712.

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

normal subgroups only

This group has 560 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×C4×C22⋊D29C211yesmaximal, characteristic
2#14271101C211yesmaximal, characteristic, complemented
3#14271098C211yesmaximal, characteristic, complemented
4#14271094C211yesmaximal, characteristic, complemented
5#14271091C212yesmaximal, complemented
6#14271089C211yesmaximal, characteristic, complemented
7#14271078C212yesmaximal
8C4×#90779C212yesmaximal, complemented
9C4×#90781C212yesmaximal, complemented
10C4×C22⋊Dic29C211yesmaximal, characteristic, complemented
11C2×C29×#117C211yesmaximal, characteristic, complemented
12C23×C4×C29C2211yescharacteristic
13C22×C22⋊D29C2211yescharacteristic
14C22×C4×D29C2211yescharacteristic
15C29×#117—24no—
16C2×C4⋊C4×C29C2211yescharacteristic
17C2×C4⋊C4×C29C2211yescharacteristic
18C2×C22⋊C4×C29C2212yes—
19C2×C42×C29C2212yes—
20C2×C22⋊Dic29C2212yes—
21C2×C22⋊Dic29C2211yescharacteristic
22C4×C22⋊D29—24no—
23C2×#90781C2212yes—
24C2×#90781C2212yes—
25C2×#90781C2211yescharacteristic
26C2×#90779C2212yes—
27C2×#90779C2212yes—
28C2×#90779C2211yescharacteristic
29C2×C4×Dic29C2212yes—
30C2×C4×Dic29C2211yescharacteristic
31#11745179C2211yescharacteristic
32#11745179C2211yescharacteristic
33#11745179C2212yes—
34#11745179C2212yes—
35#11745179C2212yes—
36#11745179C2212yes—
37C24×C29C2311yescharacteristic
38C23×D29C2311yescharacteristic
39C22×C4×C29—24no—
40C22×C4×C29D414yes—
41C22×C4×C29C2312yes—
42C22×C4×C29C2312yes—
43C22×C4×C29C2311yescharacteristic
44C22×C4×C29C2311yescharacteristic
45C2×C22⋊D29—22no—
46C2×C22⋊D29—22no—
47C2×C22⋊D29—22no—
48C22×Dic29C2311yescharacteristic
49C22×Dic29C2312yes—
50C22×Dic29C2311yescharacteristic
51C22×Dic29C2311yescharacteristic
52C22×Dic29C2312yes—
53C2×C4×D29—22no—
54C2×C4×D29—24no—
55C4⋊C4×C29—22no—
56C4⋊C4×C29—22no—
57C22⋊C4×C29—24no—
58C42×C29—24no—
59C22⋊Dic29—22no—
60C22⋊Dic29—24no—
61#90781—24no—
62#90781—22no—
63#90781—24no—
64#90779—22no—
65#90779—24no—
66#90779—24no—
67C4×Dic29—22no—
68C4×Dic29—24no—
69C23×C29—22no—
70C23×C29—21no—
71C23×C29—21no—
72C23×C29—22no—
73C23×C29C2×D412yes—
74C23×C29C2411yescharacteristic
75C22×D29—21no—
76C22×D29—22no—
77C22×D29—22no—
78C22×D29—21no—
79C22×D29#4112yes—
80C2×C4×C29—22no—
81C2×C4×C29—28no—
82C2×C4×C29—22no—
83C2×C4×C29—22no—
84C2×C4×C29—22no—
85C2×C4×C29—22no—
86C2×C4×C29—22no—
87C2×C4×C29—22no—
88C2×C4×C29C2×D412yes—
89C2×C4×C29C2×D412yes—
90C2×C4×C29#4114yes—
91C22⋊D29—28no—
92C2×Dic29—21no—
93C2×Dic29—22no—
94C2×Dic29—22no—
95C2×Dic29—21no—
96C2×Dic29—21no—
97C2×Dic29—21no—
98C2×Dic29—22no—
99C2×Dic29—22no—
100C2×Dic29—22no—
101C2×Dic29—22no—
102C2×Dic29—22no—
103C2×Dic29#4112yes—
104C2×Dic29#4114yes—
105C4×D29—44no—
106#2395—291nomaximal, Sylow
107C22×C29—22no—
108C22×C29—22no—
109C22×C29—22no—
110C22×C29—42no—
111C22×C29—42no—
112C22×C29C22×D411yescharacteristic
113C22×C29C2×#4112yes—
114C22×C29C2×#4111yescharacteristic
115C22×C29C2×#4111yescharacteristic
116C22×C29C2×#4112yes—
117C2×D29—22no—
118C2×D29—24no—
119C2×D29—41no—
120C2×D29—42no—
121C2×D29—41no—
122C4×C29—22no—
123C4×C29—42no—
124C4×C29—42no—
125C4×C29#12314yes—
126Dic29—22no—
127Dic29—24no—
128Dic29—41no—
129Dic29—42no—
130Dic29—41no—
131C2×C4×D4—291no—
132C2×#117D2911yescharacteristic, complemented
133#400—291no—
134#399—291no—
135#398—291no—
136#397—291no—
137#397—292no—
138#394—292no—
139C4×C4⋊C4—292no—
140C4×C22⋊C4—291no—
141C4×C22⋊C4—292no—
142C2×C29—42no—
143C2×C29C2×#12311yescharacteristic
144C2×C29#52511yescharacteristic
145C2×C29#52912yes—
146C2×C29#52912yes—
147C2×C29#53211yescharacteristic
148D29—42no—
149C22×D4—291no—
150C23×C4—291no—
151C23×C4C2×D2911yescharacteristic
152C4×D4—584no—
153#117—24no—
154C2×C4⋊C4—291no—
155C2×C4⋊C4—292no—
156C2×C4⋊C4—292no—
157C2×C4⋊C4C2×D2911yescharacteristic
158C2×C4⋊C4C2×D2911yescharacteristic
159C2×C22⋊C4—291no—
160C2×C22⋊C4—292no—
161C2×C22⋊C4—291no—
162C2×C22⋊C4—292no—
163C2×C22⋊C4—292no—
164C2×C22⋊C4C2×D2912yes—
165C2×C42—291no—
166C2×C42—292no—
167C2×C42C2×D2912yes—
168#95—292no—
169#95—291no—
170#95—292no—
171#95—291no—
172#95—292no—
173#95—292no—
174C29#239511yescharacteristic, complemented, Sylow
175C24—291no—
176C24C22×D2911yescharacteristic
177C2×D4—582no—
178C2×D4—582no—
179C2×D4—582no—
180C22×C4—24no—
181C22×C4—292no—
182C22×C4—291no—
183C22×C4—292no—
184C22×C4—291no—
185C22×C4—291no—
186C22×C4—584no—
187C22×C4—582no—
188C22×C4C22⋊D2914yes—
189C22×C4C22×D2912yes—
190C22×C4C22×D2912yes—
191C22×C4C22×D2911yescharacteristic
192C22×C4C22×D2911yescharacteristic
193C4⋊C4—22no—
194C4⋊C4—22no—
195C4⋊C4—584no—
196C4⋊C4—584no—
197C4⋊C4—582no—
198C22⋊C4—24no—
199C22⋊C4—584no—
200C22⋊C4—584no—
201C22⋊C4—584no—
202C22⋊C4—582no—
203C22⋊C4—582no—
204C42—24no—
205C42—584no—
206C42—582no—
207C23—22no—
208C23—22no—
209C23—21no—
210C23—21no—
211C23—292no—
212C23—582no—
213C23—582no—
214C23—581no—
215C23—581no—
216C23C2×C22⋊D2912yes—
217C23C23×D2911yescharacteristic
218D4—588no—
219C2×C4—22no—
220C2×C4—28no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—294no—
228C2×C4—292no—
229C2×C4—582no—
230C2×C4—582no—
231C2×C4—581no—
232C2×C4—581no—
233C2×C4—582no—
234C2×C4—582no—
235C2×C4—582no—
236C2×C4—582no—
237C2×C4—582no—
238C2×C4—581no—
239C2×C4—581no—
240C2×C4—1164no—
241C2×C4#9080514yes—
242C2×C4C2×C22⋊D2912yes—
243C2×C4C2×C22⋊D2912yes—
244C22—22no—
245C22—22no—
246C22—22no—
247C22—42no—
248C22—42no—
249C22—582no—
250C22—584no—
251C22—1161no—
252C22—1162no—
253C22—1161no—
254C22C2×#9080512yes—
255C22#41×D2911yescharacteristic
256C22#41×D2911yescharacteristic
257C22#41×D2912yes—
258C22C22×C22⋊D2911yescharacteristic
259C4—22no—
260C4—42no—
261C4—42no—
262C4—582no—
263C4—584no—
264C4—1161no—
265C4—1162no—
266C4—1161no—
267C4#1174529114yes—
268C2—42no—
269C2—1162no—
270C2C2×#1174529111yescharacteristic
271C2#1427167011yescharacteristic
272C2#1427169112yes—
273C2#1427169112yes—
274C2#1427170911yescharacteristic
subgroupG/H
centerC22×C4C22×D29
commutator, socle, cosocleC23×C29C24
FrattiniC23C23×D29
FittingC2×C29×#117C2
prime radicalC22×C22⋊D29C22
hypercenterC2×#117D29
hypocenterC29#2395
LCSG ▷ C23×C29 ▷ C29
UCSC1 ◁ C22×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
2. #14271101C2semidirect
3. #14271098C2semidirect
4. #14271094C2semidirect
5. #14271091C2semidirect
6. #14271089C2semidirect
8. C4×#90779C2semidirect
9. C4×#90781C2semidirect
10. C4×C22⋊Dic29C2semidirect
11. C2×C29×#117C2semidirect
132. C2×#117D29semidirect
174. C29#2395semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C22⋊D292
#142711012
#142710982
#142710942
#142710912
#142710892
#142710782
C4×#907792
C4×#907812
C4×C22⋊Dic292
C2×C29×#1172
#239529