Finite Group Databasebeta

← #16822763

Subgroups — #16822763

Order 3712.

528 conjugacy classes of subgroups; only the 159 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 159 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×Q8×Dic29C211yesmaximal, characteristic, complemented
2C2×#11745254C211yesmaximal, characteristic
3#14271102C211yesmaximal, characteristic, complemented
4#14271100C211yesmaximal, characteristic
5#14271095C212yesmaximal, complemented
6#14271085C212yesmaximal
7#14271074C211yesmaximal, characteristic
8C4⋊C4×Dic29C212yesmaximal, complemented
9#14271014C211yesmaximal, characteristic, complemented
10#14271010C212yesmaximal
11C29×#395C211yesmaximal, characteristic, complemented
12C22×Q8×C29C2211yescharacteristic
13C22×C4×D29C2211yescharacteristic
14C2×C4⋊C4×C29C2212yes—
15C2×C4⋊C4×C29C2211yescharacteristic
16Q8×Dic29—24no—
17C2×#90781C2212yes—
18C2×#90781C2212yes—
19C2×#90781C2211yescharacteristic
20C2×#90781C2211yescharacteristic
21C2×C4⋊Dic29C2212yes—
22C2×C4⋊Dic29C2212yes—
23C2×C4⋊Dic29C2211yescharacteristic
24C2×C4⋊Dic29C2211yescharacteristic
25C2×#90779C2212yes—
26C2×C4×Dic29C2212yes—
27C2×C4×Dic29C2212yes—
28C2×C4×Dic29C2211yescharacteristic
29C2×C4×Dic29C2211yescharacteristic
30#11745254—24no—
31C29×#95C2212yes—
32C29×#95C2211yescharacteristic
33#11745179C2212yes—
34#11745179C2211yescharacteristic
35#11745179C2212yes—
36#11745179C2212yes—
37C23×D29C2311yescharacteristic
38C2×Q8×C29—22no—
39C2×Q8×C29—24no—
40C22×C4×C29C2311yescharacteristic
41C22×C4×C29C2311yescharacteristic
42C22×C4×C29C2311yescharacteristic
43C22×C4×C29C2312yes—
44C22×C4×C29C2312yes—
45C22×Dic29C2312yes—
46C22×Dic29C2312yes—
47C22×Dic29C2311yescharacteristic
48C22×Dic29C2311yescharacteristic
49C22×Dic29C2311yescharacteristic
50C2×C4×D29—22no—
51C2×C4×D29—22no—
52C2×C4×D29Q814yescomplemented
53C4⋊C4×C29—22no—
54C4⋊C4×C29—24no—
55#90781—22no—
56#90781—24no—
57#90781—24no—
58#90781—22no—
59C4⋊Dic29—22no—
60C4⋊Dic29—24no—
61C4⋊Dic29—24no—
62C4⋊Dic29—22no—
63#90779—24no—
64C4×Dic29—24no—
65C4×Dic29—22no—
66C4×Dic29—24no—
67C4×Dic29D414yes—
68C23×C29C2411yescharacteristic
69C22×D29—21no—
70C22×D29—22no—
71C22×D29—22no—
72C22×D29—21no—
73C22×D29C2×Q812yes—
74Q8×C29—28no—
75C2×C4×C29—22no—
76C2×C4×C29—21no—
77C2×C4×C29—22no—
78C2×C4×C29—22no—
79C2×C4×C29—21no—
80C2×C4×C29—22no—
81C2×C4×C29—22no—
82C2×C4×C29—21no—
83C2×C4×C29—22no—
84C2×C4×C29C2×D412yes—
85C2×C4×C29C2×Q812yes—
86C2×C4×C29#4114yes—
87C2×C4×C29#4114yes—
88C2×Dic29—22no—
89C2×Dic29—22no—
90C2×Dic29—21no—
91C2×Dic29—22no—
92C2×Dic29—22no—
93C2×Dic29—22no—
94C2×Dic29—22no—
95C2×Dic29—22no—
96C2×Dic29—22no—
97C2×Dic29C2×D412yes—
98C2×Dic29C2×D412yes—
99C2×Dic29C2×Q812yes—
100C2×Dic29#4112yes—
101C4×D29—28no—
102#2396—291nomaximal, Sylow
103C22×C29C22×D411yescharacteristic
104C22×C29C22×Q811yescharacteristic
105C22×C29C2×#4112yes—
106C22×C29C2×#4112yes—
107C22×C29C2×#4111yescharacteristic
108C2×D29—22no—
109C2×D29—24no—
110C2×D29—41no—
111C2×D29—42no—
112C2×D29—41no—
113C4×C29—22no—
114C4×C29—22no—
115C4×C29—24no—
116C4×C29—24no—
117C4×C29—41no—
118Dic29—22no—
119Dic29—42no—
120Dic29—42no—
121Dic29—41no—
122Dic29C22⋊Q814yes—
123C2×C4×Q8—291no—
124C2×#117—291no—
125#400—291no—
126#399—291no—
127#398—292no—
128#396—292no—
129#395D2911yescharacteristic, complemented
130#393—291no—
131C4×C4⋊C4—292no—
132C4×C4⋊C4—291no—
133C4×C22⋊C4—292no—
134C2×C29C2×C22⋊Q811yescharacteristic
135C2×C29#52511yescharacteristic
136C2×C29#52912yes—
137C2×C29#53211yescharacteristic
138C2×C29#53312yes—
139D29—42no—
140C22×Q8C2×D2911yescharacteristic
141C23×C4—291no—
142C4×Q8—584no—
143#117—584no—
144C2×C4⋊C4—291no—
145C2×C4⋊C4—292no—
146C2×C4⋊C4—291no—
147C2×C4⋊C4—292no—
148C2×C4⋊C4—292no—
149C2×C4⋊C4C2×D2911yescharacteristic
150C2×C4⋊C4C2×D2912yes—
151C2×C22⋊C4—291no—
152C2×C22⋊C4—291no—
153C2×C22⋊C4—292no—
154C2×C22⋊C4—292no—
155C2×C42—291no—
156C2×C42—291no—
157C2×C42—292no—
158C2×C42—292no—
159#95—292no—
160#95—292no—
161#95—291no—
162#95—292no—
163#95C2×D2912yes—
164#95C2×D2911yescharacteristic
165C29#239611yescharacteristic, complemented, Sylow
166C24—291no—
167C2×Q8—22no—
168C2×Q8—24no—
169C22×C4—291no—
170C22×C4—291no—
171C22×C4—294no—
172C22×C4—292no—
173C22×C4—291no—
174C22×C4—292no—
175C22×C4—582no—
176C22×C4—582no—
177C22×C4C22×D2911yescharacteristic
178C22×C4C22×D2911yescharacteristic
179C22×C4C22×D2912yes—
180C22×C4C22×D2911yescharacteristic
181C22×C4C22×D2912yes—
182C4⋊C4—22no—
183C4⋊C4—24no—
184C4⋊C4—582no—
185C4⋊C4—584no—
186C4⋊C4—582no—
187C4⋊C4—584no—
188C4⋊C4—584no—
189C22⋊C4—582no—
190C22⋊C4—582no—
191C22⋊C4—584no—
192C22⋊C4—584no—
193C42—294no—
194C42—582no—
195C42—584no—
196C42—584no—
197C23—292no—
198C23—581no—
199C23—582no—
200C23—582no—
201C23—581no—
202C23C23×D2911yescharacteristic
203Q8—28no—
204C2×C4—22no—
205C2×C4—21no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—22no—
213C2×C4—292no—
214C2×C4—292no—
215C2×C4—292no—
216C2×C4—292no—
217C2×C4—588no—
218C2×C4—582no—
219C2×C4—581no—
220C2×C4—582no—
221C2×C4—582no—
222C2×C4—582no—
223C2×C4—582no—
224C2×C4—582no—
225C2×C4—582no—
226C2×C4—582no—
227C2×C4D4×D2912yes—
228C2×C4#9080714yes—
229C2×C4Q8×D2912yes—
230C2×C4#9080914yes—
231C22—582no—
232C22—584no—
233C22—1161no—
234C22—1162no—
235C22—1161no—
236C22C2×D4×D2911yescharacteristic
237C22C2×#9080712yes—
238C22C2×Q8×D2911yescharacteristic
239C22C2×#9080912yes—
240C22#41×D2911yescharacteristic
241C4—22no—
242C4—22no—
243C4—24no—
244C4—24no—
245C4—41no—
246C4—294no—
247C4—582no—
248C4—1162no—
249C4—1161no—
250C4—1162no—
251C2—1162no—
252C2C22⋊Q8×D2911yescharacteristic
253C2#1427166911yescharacteristic
254C2#1427169912yes—
255C2#1427171411yescharacteristic
256C2#1427171812yes—
subgroupG/H
center, FrattiniC23C23×D29
commutator, socle, cosocleC23×C29C24
FittingC29×#395C2
prime radicalC23×D29C23
hypercenter#395D29
hypocenterC29#2396
LCSG ▷ C23×C29 ▷ C29
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
1. C2×Q8×Dic29C2semidirect
3. #14271102C2semidirect
5. #14271095C2semidirect
8. C4⋊C4×Dic29C2semidirect
9. #14271014C2semidirect
11. C29×#395C2semidirect
52. C2×C4×D29Q8semidirect
129. #395D29semidirect
165. C29#2396semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×Dic292
C2×#117452542
#142711022
#142711002
#142710952
#142710852
#142710742
C4⋊C4×Dic292
#142710142
#142710102
C29×#3952
#239629