Finite Group Databasebeta

← #16827829

Subgroups — #16827829

Order 3712.

564 conjugacy classes of subgroups; only the 169 normal subgroups are shown.

normal subgroups only

This group has 564 conjugacy classes of subgroups — too many to draw. Only its 169 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×#11745240C211yesmaximal, characteristic
2C22×C4×Dic29C211yesmaximal, characteristic
3#14271067C212yesmaximal, complemented
4#14271060C212yesmaximal, complemented
5#14271050C212yesmaximal, complemented
6#14271046C212yesmaximal, complemented
7#14271038C211yesmaximal, characteristic
8#14271035C211yesmaximal, characteristic
9#14271026C211yesmaximal, characteristic
10#14271021C211yesmaximal, characteristic
11C29×#381C211yesmaximal, characteristic
12C23×C4×C29C2211yescharacteristic
13C23×Dic29C2211yescharacteristic
14C23×Dic29C2211yescharacteristic
15C22×Dic58C2211yescharacteristic
16C2×C22⋊C4×C29C2211yescharacteristic
17C2×C22⋊C4×C29C2211yescharacteristic
18C2×C22⋊Dic29C2211yescharacteristic
19C2×C22⋊Dic29C2211yescharacteristic
20C2×C4⋊Dic29C2212yes—
21C2×C4⋊Dic29C2211yescharacteristic
22C2×#90779C2212yes—
23C2×#90779C2212yes—
24C2×#90779C2211yescharacteristic
25C2×#90779C2211yescharacteristic
26C2×C4×Dic29—24no—
27C2×C4×Dic29C2212yes—
28C2×C4×Dic29C2212yes—
29#11745240—24no—
30C29×#95C2212yes—
31C29×#95C2212yes—
32#11745179C2212yes—
33#11745179C2212yes—
34#11745179C2212yes—
35#11745179C2212yes—
36#11745179C2212yes—
37C24×C29C2311yescharacteristic
38C22×C4×C29—22no—
39C22×C4×C29—22no—
40C22×C4×C29Q814yescomplemented
41C22×C4×C29C2311yescharacteristic
42C22×C4×C29C2312yes—
43C22×C4×C29C2311yescharacteristic
44C22×C4×C29C2312yes—
45C22×Dic29—22no—
46C22×Dic29—24no—
47C22×Dic29—24no—
48C22×Dic29D414yes—
49C22×Dic29C2311yescharacteristic
50C22×Dic29C2312yes—
51C22×Dic29C2311yescharacteristic
52C22×Dic29C2311yescharacteristic
53C22×Dic29C2312yes—
54C22×Dic29C2311yescharacteristic
55C2×Dic58—22no—
56C2×Dic58—24no—
57C22⋊C4×C29—22no—
58C22⋊C4×C29—22no—
59C22⋊Dic29—22no—
60C22⋊Dic29—22no—
61C4⋊Dic29—22no—
62C4⋊Dic29—24no—
63#90779—22no—
64#90779—22no—
65#90779—24no—
66#90779—24no—
67C4×Dic29—24no—
68C4×Dic29—24no—
69C23×C29—22no—
70C23×C29—22no—
71C23×C29C2×D412yes—
72C23×C29C2×Q812yes—
73C23×C29#4112yes—
74C23×C29C2411yescharacteristic
75C2×C4×C29—28no—
76C2×C4×C29—22no—
77C2×C4×C29—22no—
78C2×C4×C29—21no—
79C2×C4×C29—21no—
80C2×C4×C29—22no—
81C2×C4×C29—22no—
82C2×C4×C29—22no—
83C2×C4×C29—22no—
84C2×C4×C29—22no—
85C2×C4×C29C2×Q814yes—
86C2×Dic29—28no—
87C2×Dic29—22no—
88C2×Dic29—22no—
89C2×Dic29—22no—
90C2×Dic29—28no—
91C2×Dic29—21no—
92C2×Dic29—21no—
93C2×Dic29—22no—
94C2×Dic29—22no—
95C2×Dic29—22no—
96C2×Dic29—22no—
97C2×Dic29—22no—
98C2×Dic29C2×D412yes—
99C2×Dic29C2×D412yes—
100C2×Dic29#4114yes—
101C2×Dic29#4114yes—
102Dic58—44no—
103#2855—291nomaximal, Sylow
104C22×C29—22no—
105C22×C29—22no—
106C22×C29—24no—
107C22×C29—24no—
108C22×C29C22⋊Q814yes—
109C22×C29C22×D411yescharacteristic
110C22×C29C22×Q811yescharacteristic
111C22×C29C2×#4111yescharacteristic
112C22×C29C2×#4112yes—
113C22×C29C2×#4112yes—
114C4×C29—24no—
115C4×C29—41no—
116C4×C29—41no—
117C4×C29—42no—
118Dic29—22no—
119Dic29—24no—
120Dic29—41no—
121Dic29—41no—
122Dic29—42no—
123Dic29#12314yes—
124C2×C22⋊Q8—291no—
125C22×C42—291no—
126#391—292no—
127#389—292no—
128#387—292no—
129#387—292no—
130#385—291no—
131#385—291no—
132#381—291no—
133#381D2911yescharacteristic
134#380—291no—
135C2×C29—24no—
136C2×C29C2×C22⋊Q811yescharacteristic
137C2×C29C2×#12311yescharacteristic
138C2×C29#52511yescharacteristic
139C2×C29#52912yes—
140C2×C29#53312yes—
141C22×Q8—291no—
142C23×C4—291no—
143C23×C4—291no—
144C23×C4C2×D2911yescharacteristic
145C22⋊Q8—584no—
146C2×C4⋊C4—291no—
147C2×C4⋊C4—291no—
148C2×C4⋊C4—292no—
149C2×C4⋊C4—292no—
150C2×C4⋊C4—291no—
151C2×C4⋊C4—292no—
152C2×C22⋊C4—291no—
153C2×C22⋊C4—291no—
154C2×C22⋊C4C2×D2911yescharacteristic
155C2×C22⋊C4C2×D2911yescharacteristic
156C2×C42—292no—
157C2×C42—292no—
158C2×C42—584no—
159#95—292no—
160#95—292no—
161#95—292no—
162#95—292no—
163#95—292no—
164#95C2×D2912yes—
165#95C2×D2912yes—
166C29#285511yescharacteristic, complemented, Sylow
167C24C22×D2911yescharacteristic
168C2×Q8—582no—
169C2×Q8—584no—
170C22×C4—22no—
171C22×C4—22no—
172C22×C4—291no—
173C22×C4—294no—
174C22×C4—291no—
175C22×C4—292no—
176C22×C4—292no—
177C22×C4—291no—
178C22×C4—291no—
179C22×C4—584no—
180C22×C4—584no—
181C22×C4—582no—
182C22×C4Dic5814yescomplemented
183C22×C4C22×D2912yes—
184C22×C4C22×D2911yescharacteristic
185C22×C4C22×D2911yescharacteristic
186C22×C4C22×D2912yes—
187C4⋊C4—582no—
188C4⋊C4—582no—
189C4⋊C4—582no—
190C4⋊C4—584no—
191C4⋊C4—584no—
192C4⋊C4—584no—
193C22⋊C4—22no—
194C22⋊C4—22no—
195C22⋊C4—582no—
196C22⋊C4—582no—
197C42—584no—
198C42—584no—
199C23—22no—
200C23—22no—
201C23C2×Dic5812yes—
202C23D4×D2912yes—
203C23#9080712yes—
204C23C23×D2911yescharacteristic
205Q8—1164no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—28no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—292no—
217C2×C4—294no—
218C2×C4—292no—
219C2×C4—294no—
220C2×C4—588no—
221C2×C4—588no—
222C2×C4—582no—
223C2×C4—582no—
224C2×C4—582no—
225C2×C4—581no—
226C2×C4—581no—
227C2×C4—582no—
228C2×C4—582no—
229C2×C4—582no—
230C2×C4—582no—
231C2×C4—582no—
232C2×C4C2×Dic5814yes—
233C22—22no—
234C22—22no—
235C22—24no—
236C22—24no—
237C22#1174524014yes—
238C22C22×Dic5811yescharacteristic
239C22C2×D4×D2911yescharacteristic
240C22C2×#9080711yescharacteristic
241C22#41×D2912yes—
242C22#41×D2912yes—
243C4—24no—
244C4—41no—
245C4—41no—
246C4—42no—
247C4—294no—
248C4—582no—
249C4—584no—
250C4—1161no—
251C4—1161no—
252C4—1162no—
253C2—24no—
254C2C2×#1174524011yescharacteristic
255C2#123×D2911yescharacteristic
256C2#1427167111yescharacteristic
257C2#1427169012yes—
258C2#1427171612yes—
subgroupG/H
center, FrattiniC23C23×D29
commutator, socle, cosocleC23×C29C24
FittingC29×#381C2
prime radicalC24×C29C23
hypercenter#381D29
hypocenterC29#2855
LCSG ▷ C23×C29 ▷ C29
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
3. #14271067C2semidirect
4. #14271060C2semidirect
5. #14271050C2semidirect
6. #14271046C2semidirect
40. C22×C4×C29Q8semidirect
166. C29#2855semidirect
182. C22×C4Dic58semidirect

Maximal subgroups

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

subgroupindex
C2×#117452402
C22×C4×Dic292
#142710672
#142710602
#142710502
#142710462
#142710382
#142710352
#142710262
#142710212
C29×#3812
#285529