Finite Group Databasebeta

← #15753836

Subgroups — #15753836

Order 3328.

532 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 532 conjugacy classes of subgroups — too many to draw. Only its 141 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
1#13117391C211yesmaximal, characteristic
2#97×Dic13C212yesmaximal
3C2×#11718057C212yesmaximal
4#13112717C211yesmaximal, characteristic
5C13×#1295C211yesmaximal, characteristic
6C2×#88124C2211yescharacteristic
7C2×C13×#97C2212yes—
8C13×#382C2211yescharacteristic
9C2×#88055—22no—
10C2×C8×Dic13—22no—
11C4⋊C4×Dic13C412yes—
12#11718634C412yes—
13C42×Dic13C2211yescharacteristic
14C2×#88043C2212yes—
15#11718313—22no—
16#11718310—22no—
17#11718057C418yescomplemented
18C22×C8×C13—22no—
19C2×C13×C4⋊C4C2×C412yes—
20C2×C42×C13C2311yescharacteristic
21C2×C4⋊Dic13C2×C412yes—
22C2×#6101—22no—
23C2×#6101—22no—
24C2×C4×Dic13—22no—
25C2×C4×Dic13C2×C411yescharacteristic
26C2×C4×Dic13C2×C411yescharacteristic
27C2×C4×Dic13D412yes—
28C2×C4×Dic13D412yes—
29C22×#1055—22no—
30#88124—21no—
31#88124—21no—
32#88124C2×C414yes—
33C13×#97—22no—
34C13×#97C2×C414yes—
35C13×#95—22no—
36#88071—22no—
37#88071—22no—
38#88055—28no—
39C8×Dic13—28no—
40#88043—22no—
41#88043C2×C414yes—
42C4×#330—131nomaximal, Sylow
43C22×C4×C13—22no—
44C22×C4×C13C22×C411yescharacteristic
45C22×C4×C13C2×D412yes—
46C22×Dic13—22no—
47C22×Dic13C22⋊C411yescharacteristic
48C22×Dic13C22⋊C412yes—
49C22×Dic13C22⋊C411yescharacteristic
50C2×C8×C13—24no—
51C2×C8×C13—24no—
52C2×C8×C13—24no—
53C13×C4⋊C4—42no—
54C42×C13C22×C412yes—
55C42×C13#4111yescharacteristic
56C42×C13#4111yescharacteristic
57C4⋊Dic13—22no—
58C4⋊Dic13C4214yes—
59#6101—24no—
60#6101—24no—
61#6101—44no—
62C4×Dic13—22no—
63C4×Dic13—24no—
64C4×Dic13—24no—
65C4×Dic13—41no—
66C4×Dic13—44no—
67C2×#1055—24no—
68C2×#1055—24no—
69C2×#1055—24no—
70C4×#125—131no—
71C4×#97—132no—
72C2×#330—132no—
73#1295—131no—
74#1295D1311yescharacteristic
75C23×C13C2×C22⋊C411yescharacteristic
76C2×C4×C13—21no—
77C2×C4×C13—21no—
78C2×C4×C13—22no—
79C2×C4×C13—22no—
80C2×C4×C13—42no—
81C2×C4×C13—42no—
82C2×C4×C13—42no—
83C2×C4×C13C2×C4211yescharacteristic
84C2×C4×C13#11711yescharacteristic
85C2×C4×C13C4×D412yes—
86C2×C4×C13C4×D412yes—
87C2×Dic13—22no—
88C2×Dic13—22no—
89C2×Dic13—24no—
90C2×Dic13—21no—
91C2×Dic13—22no—
92C2×Dic13—42no—
93C2×Dic13—42no—
94C2×Dic13#10112yes—
95C2×Dic13#10414yes—
96C2×Dic13#10414yes—
97C8×C13—28no—
98#1055—28no—
99C2×#125—131no—
100C2×#97—132no—
101C2×#97—262no—
102C2×#97C2×D1312yes—
103C2×C4×C8—262no—
104#389—132no—
105#387—262no—
106#382C2×D1311yescharacteristic
107C4×C4⋊C4—132no—
108C4×C4⋊C4—262no—
109C43—131no—
110#330—138no—
111C22×C13C4×C22⋊C411yescharacteristic
112C22×C13C2×#10111yescharacteristic
113C22×C13#41311yescharacteristic
114C22×C13C2×#10412yes—
115C22×C13C2×#10412yes—
116C4×C13—21no—
117C4×C13—21no—
118C4×C13—22no—
119C4×C13—22no—
120C4×C13—82no—
121Dic13—24no—
122Dic13—44no—
123Dic13—41no—
124Dic13#33014yescomplemented
125C22×C8—22no—
126C22×C8—262no—
127#125—134no—
128#125—261no—
129#125—261no—
130C2×C4⋊C4—132no—
131C2×C4⋊C4—262no—
132C2×C4⋊C4—262no—
133C2×C4⋊C4C4×D1312yes—
134C2×C42—131no—
135C2×C42—132no—
136C2×C42—132no—
137C2×C42—131no—
138C2×C42—262no—
139C2×C42C22×D1311yescharacteristic
140#97—22no—
141#97—134no—
142#97—268no—
143#97—262no—
144#97C4×D1314yes—
145C4×C8—268no—
146#95—22no—
147#95—262no—
148#95—262no—
149C2×C13C2×#33011yescharacteristic
150C2×C13#152412yes—
151C2×C13#152611yescharacteristic
152C2×C13C4×#10111yescharacteristic
153C2×C13C4×#10412yes—
154C22×C4—22no—
155C22×C4—131no—
156C22×C4—132no—
157C22×C4—131no—
158C22×C4—262no—
159C22×C4C2×C4×D1311yescharacteristic
160C22×C4D4×D1312yes—
161C2×C8—24no—
162C2×C8—24no—
163C2×C8—24no—
164C2×C8—264no—
165C2×C8—264no—
166C2×C8—264no—
167C4⋊C4—42no—
168C4⋊C4—134no—
169C4⋊C4—264no—
170C4⋊C4—262no—
171C4⋊C4—264no—
172C4⋊C4—524no—
173C42—264no—
174C42—264no—
175C42—262no—
176C42—521no—
177C42—524no—
178C42C2×C4×D1312yes—
179C42#612911yescharacteristic
180C42#613111yescharacteristic
181C13C4×#33011yescharacteristic, complemented, Sylow
182C23C22⋊C4×D1311yescharacteristic
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—42no—
188C2×C4—42no—
189C2×C4—42no—
190C2×C4—132no—
191C2×C4—134no—
192C2×C4—134no—
193C2×C4—262no—
194C2×C4—262no—
195C2×C4—261no—
196C2×C4—262no—
197C2×C4—264no—
198C2×C4—522no—
199C2×C4—522no—
200C2×C4C42×D1311yescharacteristic
201C2×C4#8813512yes—
202C2×C4#8814611yescharacteristic
203C2×C4#8814712yes—
204C8—28no—
205C8—268no—
206C22#1171832711yescharacteristic
207C22#1171840611yescharacteristic
208C22D13×#10111yescharacteristic
209C22D13×#10412yes—
210C22D13×#10412yes—
211C4—21no—
212C4—21no—
213C4—22no—
214C4—22no—
215C4—82no—
216C4—134no—
217C4—264no—
218C4—524no—
219C4—521no—
220C2D13×#33011yescharacteristic
221C2#1311342112yes—
222C2#1311342911yescharacteristic
223C2#1311463111yescharacteristic
224C2#1311464012yes—
subgroupG/H
centerC23C22⋊C4×D13
commutatorC2×C4×C13C2×C42
FrattiniC2×C42C22×D13
FittingC13×#1295C2
socle, prime radicalC23×C13C2×C22⋊C4
cosocleC2×C42×C13C23
hypercenter#1295D13
hypocenterC13C4×#330
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1295

Complements

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

NH ≅ G/Ntype
17. #11718057C4semidirect
124. Dic13#330semidirect
181. C13C4×#330semidirect

Maximal subgroups

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

subgroupindex
#131173912
#97×Dic132
C2×#117180572
#131127172
C13×#12952
C4×#33013