Finite Group Databasebeta

← #16822784

Subgroups — #16822784

Order 3712.

504 conjugacy classes of subgroups; only the 163 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 163 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
2C2×#11745249C211yesmaximal, characteristic
3#14271097C212yesmaximal
4#14271094C211yesmaximal, characteristic
5#14271084C211yesmaximal, characteristic
6#14271083C212yesmaximal
7#14271083C211yesmaximal, characteristic
8C4⋊C4×Dic29C212yesmaximal
9#14271014C212yesmaximal
10#14271008C211yesmaximal, characteristic
11C29×#398C211yesmaximal, characteristic
12C22×Dic58C2211yescharacteristic
13C22×Dic58C2211yescharacteristic
14C2×C4⋊C4×C29C2212yes—
15C2×C4⋊C4×C29C2211yescharacteristic
16C2×C4⋊C4×C29C2211yescharacteristic
17C2×C4⋊Dic29C2212yes—
18C2×#90779C2212yes—
19C2×#90779C2212yes—
20C2×#90779C2212yes—
21C2×#90779C2211yescharacteristic
22C2×#90779C2211yescharacteristic
23C2×C4×Dic29C2211yescharacteristic
24C2×C4×Dic29C2212yes—
25C2×C4×Dic29C2211yescharacteristic
26C2×C4×Dic29C2211yescharacteristic
27C2×C4×Dic29C2212yes—
28#11745249—24no—
29#11745249—24no—
30C29×#95C2211yescharacteristic
31C29×#95C2212yes—
32#11745179C2211yescharacteristic
33#11745179C2212yes—
34#11745179C2212yes—
35#11745179C2212yes—
36#11745179C2212yes—
37C22×C4×C29C2311yescharacteristic
38C22×C4×C29C2312yes—
39C22×C4×C29C2311yescharacteristic
40C22×C4×C29C2312yes—
41C22×C4×C29C2311yescharacteristic
42C22×Dic29C2311yescharacteristic
43C22×Dic29C2311yescharacteristic
44C22×Dic29C2312yes—
45C22×Dic29C2311yescharacteristic
46C22×Dic29C2312yes—
47C22×Dic29C2311yescharacteristic
48C2×Dic58—22no—
49C2×Dic58—22no—
50C2×Dic58—22no—
51C2×Dic58—22no—
52C2×Dic58—24no—
53C4⋊C4×C29—22no—
54C4⋊C4×C29—22no—
55C4⋊C4×C29—24no—
56C4⋊Dic29—24no—
57#90779—22no—
58#90779—24no—
59#90779—22no—
60#90779—24no—
61#90779—24no—
62C4×Dic29—22no—
63C4×Dic29—24no—
64C4×Dic29—22no—
65C4×Dic29D414yes—
66C4×Dic29Q818yescomplemented
67C23×C29C2411yescharacteristic
68C2×C4×C29—21no—
69C2×C4×C29—22no—
70C2×C4×C29—22no—
71C2×C4×C29—22no—
72C2×C4×C29—21no—
73C2×C4×C29—21no—
74C2×C4×C29—22no—
75C2×C4×C29—22no—
76C2×C4×C29—22no—
77C2×C4×C29—22no—
78C2×C4×C29C2×D412yes—
79C2×C4×C29C2×Q814yes—
80C2×C4×C29#4112yes—
81C2×Dic29—21no—
82C2×Dic29—22no—
83C2×Dic29—22no—
84C2×Dic29—22no—
85C2×Dic29—21no—
86C2×Dic29—21no—
87C2×Dic29—21no—
88C2×Dic29—22no—
89C2×Dic29—21no—
90C2×Dic29—22no—
91C2×Dic29C2×D412yes—
92C2×Dic29C2×D412yes—
93C2×Dic29C2×Q814yes—
94C2×Dic29C2×Q814yes—
95C2×Dic29#4112yes—
96C2×Dic29#4114yes—
97Dic58—28no—
98Dic58—28no—
99#2399—291nomaximal, Sylow
100C22×C29C22×D411yescharacteristic
101C22×C29C22×Q812yes—
102C22×C29C2×#4111yescharacteristic
103C22×C29C2×#4112yes—
104C22×C29C2×#4111yescharacteristic
105C4×C29—22no—
106C4×C29—22no—
107C4×C29—24no—
108C4×C29—41no—
109C4×C29—42no—
110Dic29—22no—
111Dic29—24no—
112Dic29—22no—
113Dic29—24no—
114Dic29—41no—
115Dic29C4⋊Q814yes—
116C2×C4×Q8—291no—
117C2×C4×Q8—291no—
118#398—291no—
119#398—292no—
120#398D2911yescharacteristic
121#395—292no—
122#395—291no—
123#395—291no—
124C4×C4⋊C4—292no—
125C4×C4⋊C4—292no—
126#376—291no—
127C2×C29#52511yescharacteristic
128C2×C29#52511yescharacteristic
129C2×C29C2×C4⋊Q811yescharacteristic
130C2×C29#53312yes—
131C2×C29#53312yes—
132C22×Q8—291no—
133C22×Q8—291no—
134C4×Q8—584no—
135C4×Q8—584no—
136C2×C4⋊C4—292no—
137C2×C4⋊C4—291no—
138C2×C4⋊C4—291no—
139C2×C4⋊C4—292no—
140C2×C4⋊C4—292no—
141C2×C4⋊C4—292no—
142C2×C4⋊C4C2×D2911yescharacteristic
143C2×C4⋊C4C2×D2911yescharacteristic
144C2×C4⋊C4C2×D2912yes—
145C2×C42—291no—
146C2×C42—292no—
147C2×C42—292no—
148C2×C42—291no—
149C2×C42—291no—
150#95—291no—
151#95—292no—
152#95—292no—
153#95—292no—
154#95—292no—
155#95C2×D2911yescharacteristic
156#95C2×D2912yes—
157C29#239911yescharacteristic, complemented, Sylow
158C2×Q8—582no—
159C2×Q8—584no—
160C2×Q8—582no—
161C2×Q8—582no—
162C2×Q8—582no—
163C22×C4—291no—
164C22×C4—292no—
165C22×C4—291no—
166C22×C4—291no—
167C22×C4—292no—
168C22×C4—291no—
169C22×C4C22×D2912yes—
170C22×C4C22×D2911yescharacteristic
171C22×C4C22×D2911yescharacteristic
172C22×C4C22×D2911yescharacteristic
173C22×C4C22×D2912yes—
174C4⋊C4—22no—
175C4⋊C4—22no—
176C4⋊C4—24no—
177C4⋊C4—584no—
178C4⋊C4—582no—
179C4⋊C4—584no—
180C4⋊C4—584no—
181C4⋊C4—584no—
182C4⋊C4—582no—
183C42—294no—
184C42—298no—
185C42—582no—
186C42—582no—
187C42—584no—
188C23C23×D2911yescharacteristic
189Q8—588no—
190Q8—588no—
191C2×C4—21no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—21no—
196C2×C4—21no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—292no—
202C2×C4—294no—
203C2×C4—292no—
204C2×C4—294no—
205C2×C4—294no—
206C2×C4—292no—
207C2×C4—582no—
208C2×C4—581no—
209C2×C4—581no—
210C2×C4—581no—
211C2×C4—582no—
212C2×C4—582no—
213C2×C4—582no—
214C2×C4—581no—
215C2×C4—581no—
216C2×C4—582no—
217C2×C4D4×D2912yes—
218C2×C4#9080712yes—
219C2×C4Q8×D2914yes—
220C22C2×D4×D2911yescharacteristic
221C22C2×#9080711yescharacteristic
222C22C2×Q8×D2912yes—
223C22#41×D2912yes—
224C22#41×D2911yescharacteristic
225C4—22no—
226C4—22no—
227C4—24no—
228C4—41no—
229C4—42no—
230C4—294no—
231C4—584no—
232C4—582no—
233C4—582no—
234C4—584no—
235C4—1161no—
236C2#1427167111yescharacteristic
237C2#1427167311yescharacteristic
238C2C4⋊Q8×D2911yescharacteristic
239C2#1427171512yes—
240C2#1427171912yes—
subgroupG/H
center, FrattiniC23C23×D29
commutator, socle, prime radical, cosocleC23×C29C24
FittingC29×#398C2
hypercenter#398D29
hypocenterC29#2399
LCSG ▷ C23×C29 ▷ C29
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
66. C4×Dic29Q8semidirect
157. C29#2399semidirect

Maximal subgroups

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

subgroupindex
C2×#117452492
#142710972
#142710942
#142710842
#142710832
C4⋊C4×Dic292
#142710142
#142710082
C29×#3982
#239929