Finite Group Databasebeta

← #16822761

Subgroups — #16822761

Order 3712.

528 conjugacy classes of subgroups; only the 155 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 155 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×#11745249C211yesmaximal, characteristic, complemented
2C2×#11745239C211yesmaximal, characteristic
3#14271101C211yesmaximal, characteristic, complemented
4#14271094C212yesmaximal, complemented
5#14271086C212yesmaximal
6#14271084C211yesmaximal, characteristic, complemented
7#14271075C211yesmaximal, characteristic
8C4⋊C4×Dic29C212yesmaximal, complemented
9#14271014C211yesmaximal, characteristic, complemented
10C22⋊C4×Dic29C212yesmaximal
11C29×#399C211yesmaximal, characteristic
12C23×Dic29C2211yescharacteristic
13C22×Dic58C2211yescharacteristic
14C2×C4⋊C4×C29C2212yes—
15C2×C4⋊C4×C29C2211yescharacteristic
16C2×C22⋊C4×C29C2212yes—
17C2×C22⋊C4×C29C2211yescharacteristic
18C2×C22⋊Dic29C2212yes—
19C2×C22⋊Dic29C2211yescharacteristic
20C2×C4⋊Dic29C2212yes—
21C2×#90779C2212yes—
22C2×#90779C2211yescharacteristic
23C2×#90779C2212yes—
24C2×#90779C2211yescharacteristic
25C2×C4×Dic29C2212yes—
26C2×C4×Dic29C2212yes—
27C2×C4×Dic29C2211yescharacteristic
28C2×C4×Dic29C2211yescharacteristic
29#11745249—24no—
30#11745239—24no—
31C29×#95C2211yescharacteristic
32#11745179C2212yes—
33#11745179C2212yes—
34#11745179C2211yescharacteristic
35#11745179C2212yes—
36#11745179C2212yes—
37C24×C29C2311yescharacteristic
38C22×C4×C29C2311yescharacteristic
39C22×C4×C29C2312yes—
40C22×C4×C29C2311yescharacteristic
41C22×C4×C29C2312yes—
42C22×Dic29—22no—
43C22×Dic29—22no—
44C22×Dic29Q814yescomplemented
45C22×Dic29C2311yescharacteristic
46C22×Dic29C2312yes—
47C22×Dic29C2311yescharacteristic
48C22×Dic29C2311yescharacteristic
49C22×Dic29C2312yes—
50C22×Dic29C2311yescharacteristic
51C2×Dic58—22no—
52C2×Dic58—24no—
53C4⋊C4×C29—22no—
54C4⋊C4×C29—24no—
55C22⋊C4×C29—22no—
56C22⋊C4×C29—24no—
57C22⋊Dic29—22no—
58C22⋊Dic29—24no—
59C4⋊Dic29—24no—
60#90779—22no—
61#90779—24no—
62#90779—22no—
63#90779—24no—
64C4×Dic29—22no—
65C4×Dic29—24no—
66C4×Dic29—24no—
67C4×Dic29D414yes—
68C23×C29—21no—
69C23×C29—22no—
70C23×C29—22no—
71C23×C29—21no—
72C23×C29C2×Q812yes—
73C23×C29C2411yescharacteristic
74C2×C4×C29—22no—
75C2×C4×C29—22no—
76C2×C4×C29—22no—
77C2×C4×C29—21no—
78C2×C4×C29—22no—
79C2×C4×C29—22no—
80C2×C4×C29—22no—
81C2×C4×C29—22no—
82C2×C4×C29C2×D412yes—
83C2×C4×C29#4114yes—
84C2×Dic29—22no—
85C2×Dic29—21no—
86C2×Dic29—22no—
87C2×Dic29—22no—
88C2×Dic29—21no—
89C2×Dic29—28no—
90C2×Dic29—21no—
91C2×Dic29—22no—
92C2×Dic29—22no—
93C2×Dic29—22no—
94C2×Dic29—22no—
95C2×Dic29C2×D412yes—
96C2×Dic29C2×D412yes—
97C2×Dic29C2×Q812yes—
98C2×Dic29C2×Q812yes—
99C2×Dic29#4114yes—
100C2×Dic29#4112yes—
101Dic58—28no—
102#2396—291nomaximal, Sylow
103C22×C29—22no—
104C22×C29—24no—
105C22×C29—41no—
106C22×C29—42no—
107C22×C29—41no—
108C22×C29C22×D411yescharacteristic
109C22×C29C22×Q811yescharacteristic
110C22×C29C2×#4112yes—
111C22×C29C2×#4111yescharacteristic
112C22×C29C2×#4112yes—
113C4×C29—22no—
114C4×C29—24no—
115C4×C29—41no—
116C4×C29—42no—
117Dic29—22no—
118Dic29—24no—
119Dic29—22no—
120Dic29—41no—
121Dic29—42no—
122Dic29C22⋊Q814yes—
123C2×C4×Q8—291no—
124C2×#117—291no—
125#400—291no—
126#399D2911yescharacteristic
127#398—292no—
128#396—292no—
129#395—291no—
130#393—291no—
131C4×C4⋊C4—292no—
132C4×C4⋊C4—291no—
133C4×C22⋊C4—292no—
134C2×C29—42no—
135C2×C29C2×C22⋊Q811yescharacteristic
136C2×C29#52511yescharacteristic
137C2×C29#52912yes—
138C2×C29#53211yescharacteristic
139C2×C29#53312yes—
140C22×Q8—291no—
141C23×C4—291no—
142C4×Q8—584no—
143#117—584no—
144C2×C4⋊C4—291no—
145C2×C4⋊C4—291no—
146C2×C4⋊C4—292no—
147C2×C4⋊C4—292no—
148C2×C4⋊C4—292no—
149C2×C4⋊C4C2×D2911yescharacteristic
150C2×C4⋊C4C2×D2912yes—
151C2×C22⋊C4—291no—
152C2×C22⋊C4—292no—
153C2×C22⋊C4C2×D2911yescharacteristic
154C2×C22⋊C4C2×D2912yes—
155C2×C42—291no—
156C2×C42—291no—
157C2×C42—292no—
158C2×C42—292no—
159#95—292no—
160#95—292no—
161#95—292no—
162#95—291no—
163#95—292no—
164#95C2×D2911yescharacteristic
165C29#239611yescharacteristic, complemented, Sylow
166C24C22×D2911yescharacteristic
167C2×Q8—584no—
168C2×Q8—582no—
169C22×C4—291no—
170C22×C4—294no—
171C22×C4—291no—
172C22×C4—292no—
173C22×C4—291no—
174C22×C4—292no—
175C22×C4—291no—
176C22×C4—582no—
177C22×C4—582no—
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—584no—
187C4⋊C4—582no—
188C4⋊C4—584no—
189C22⋊C4—22no—
190C22⋊C4—24no—
191C22⋊C4—582no—
192C22⋊C4—584no—
193C42—294no—
194C42—582no—
195C42—584no—
196C42—584no—
197C23—21no—
198C23—22no—
199C23—22no—
200C23—21no—
201C23Q8×D2912yes—
202C23C23×D2911yescharacteristic
203Q8—588no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—21no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—292no—
213C2×C4—292no—
214C2×C4—292no—
215C2×C4—292no—
216C2×C4—292no—
217C2×C4—294no—
218C2×C4—588no—
219C2×C4—582no—
220C2×C4—581no—
221C2×C4—582no—
222C2×C4—581no—
223C2×C4—582no—
224C2×C4—581no—
225C2×C4—582no—
226C2×C4—582no—
227C2×C4—582no—
228C2×C4—582no—
229C2×C4D4×D2912yes—
230C2×C4#9080714yes—
231C22—22no—
232C22—24no—
233C22—41no—
234C22—42no—
235C22—41no—
236C22C2×D4×D2911yescharacteristic
237C22C2×#9080712yes—
238C22C2×Q8×D2911yescharacteristic
239C22#41×D2911yescharacteristic
240C22#41×D2912yes—
241C4—22no—
242C4—24no—
243C4—41no—
244C4—42no—
245C4—294no—
246C4—582no—
247C4—584no—
248C4—582no—
249C4—1161no—
250C4—1162no—
251C2—42no—
252C2C22⋊Q8×D2911yescharacteristic
253C2#1427167111yescharacteristic
254C2#1427169012yes—
255C2#1427171111yescharacteristic
256C2#1427171512yes—
subgroupG/H
center, FrattiniC23C23×D29
commutator, socle, cosocleC23×C29C24
FittingC29×#399C2
prime radicalC24×C29C23
hypercenter#399D29
hypocenterC29#2396
LCSG ▷ C23×C29 ▷ C29
UCSC1 ◁ C23 ◁ #399

Complements

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

NH ≅ G/Ntype
1. C2×#11745249C2semidirect
3. #14271101C2semidirect
4. #14271094C2semidirect
6. #14271084C2semidirect
8. C4⋊C4×Dic29C2semidirect
9. #14271014C2semidirect
44. C22×Dic29Q8semidirect
165. C29#2396semidirect

Maximal subgroups

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

subgroupindex
C2×#117452492
C2×#117452392
#142711012
#142710942
#142710862
#142710842
#142710752
C4⋊C4×Dic292
#142710142
C22⋊C4×Dic292
C29×#3992
#239629