Finite Group Databasebeta

← #16785125

Subgroups — #16785125

Order 3328.

424 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 102 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#13130621C211yesmaximal, characteristic
2#13130553C211yesmaximal, characteristic
3#13129712C214yesmaximal
4#13123197C211yesmaximal, characteristic
5C2×#88144C412yes—
6C2×#88112—21no—
7C2×#88110C2212yes—
8C2×#88110C2212yes—
9C13×#384C411yescharacteristic
10#11718646—21no—
11#11718646—21no—
12#11718638C2212yes—
13#11718634—21no—
14#11718634—21no—
15#11718596C411yescharacteristic
16C42×Dic13C2211yescharacteristic
17#11718290—21no—
18#11718290—21no—
19#11718290—21no—
20C22×#1057—22no—
21C22×#1057—22no—
22C2×C13×C4⋊C4—21no—
23C2×C13×C4⋊C4—21no—
24C2×C13×C4⋊C4C2×C412yes—
25C2×C42×C13C2×C411yescharacteristic
26C2×C4⋊Dic13—21no—
27C2×C4⋊Dic13—21no—
28C2×C4⋊Dic13—22no—
29C2×C4⋊Dic13C2×C412yes—
30C2×#6101—22no—
31C2×C4×Dic13C2×C411yescharacteristic
32C2×C4×Dic13D411yescharacteristic
33C2×C4×Dic13D411yescharacteristic
34C2×C4×Dic13D411yescharacteristic
35C2×C4×Dic13D411yescharacteristic
36C2×C4×Dic13C2311yescharacteristic
37#88144—44no—
38#88112—24no—
39#88110—22no—
40#88110—24no—
41#88110Q814yes—
42#88071—22no—
43#88071—22no—
44#9894—131nomaximal, Sylow
45C22×C4×C13—22no—
46C22×C4×C13C22⋊C411yescharacteristic
47C22×C4×C13C22⋊C411yescharacteristic
48C22×C4×C13C22×C411yescharacteristic
49C22×Dic13—22no—
50C22×Dic13C22⋊C411yescharacteristic
51C22×Dic13C22⋊C411yescharacteristic
52C22×Dic13C2×D411yescharacteristic
53C22×Dic13C2×D411yescharacteristic
54C2×#1057—24no—
55C2×#1057—24no—
56C2×#1057—42no—
57C2×#1057—42no—
58C2×#1057—42no—
59C2×#1057—42no—
60C13×C4⋊C4—42no—
61C13×C4⋊C4—42no—
62C13×C4⋊C4—42no—
63C42×C13—22no—
64C4⋊Dic13—42no—
65C4⋊Dic13—42no—
66C4⋊Dic13—44no—
67C4⋊Dic13—42no—
68#6101—44no—
69C4×Dic13—22no—
70C4×Dic13—22no—
71C4×Dic13—41no—
72C4×Dic13—41no—
73C4×Dic13—41no—
74C4×Dic13C2×Q812yes—
75C4×Dic13#4112yes—
76#2859—131no—
77#1767—131no—
78#1745—131no—
79#1295—134no—
80C23×C13C2×C22⋊C411yescharacteristic
81C2×C4×C13—21no—
82C2×C4×C13—21no—
83C2×C4×C13—21no—
84C2×C4×C13—21no—
85C2×C4×C13—21no—
86C2×C4×C13—21no—
87C2×C4×C13—42no—
88C2×C4×C13—42no—
89C2×C4×C13—42no—
90C2×C4×C13#10112yes—
91C2×C4×C13#10412yes—
92C2×C4×C13C4×Q812yes—
93C2×Dic13—21no—
94C2×Dic13—21no—
95C2×Dic13—21no—
96C2×Dic13—21no—
97C2×Dic13—21no—
98C2×Dic13—21no—
99C2×Dic13—21no—
100C2×Dic13—21no—
101C2×Dic13—21no—
102C2×Dic13—42no—
103C2×Dic13—42no—
104C2×Dic13—42no—
105C2×Dic13#10012yes—
106C2×Dic13C22⋊Q812yes—
107C2×Dic13#12411yescharacteristic
108C2×Dic13C4⋊Q811yescharacteristic
109#1057—44no—
110#1057—44no—
111C2×#125—132no—
112C2×C4⋊C8—261no—
113C2×#97—132no—
114C2×#97—132no—
115#389—261no—
116#389—261no—
117#389—261no—
118#389—261no—
119#384—131no—
120#384#26111yescharacteristic
121#382—132no—
122C43—131no—
123#336—261no—
124#336—261no—
125#336—261no—
126C22×C13#39111yescharacteristic
127C22×C13C2×#10011yescharacteristic
128C22×C13C2×#10111yescharacteristic
129C22×C13C2×#10411yescharacteristic
130C22×C13#42111yescharacteristic
131C22×C13#42111yescharacteristic
132C22×C13#42111yescharacteristic
133C4×C13—22no—
134C4×C13—22no—
135C4×C13—22no—
136C4×C13—82no—
137Dic13—21no—
138Dic13—21no—
139Dic13—22no—
140Dic13—22no—
141Dic13—41no—
142Dic13—82no—
143C22×C8—262no—
144C22×C8—262no—
145#125—524no—
146C2×C4⋊C4—21no—
147C2×C4⋊C4—21no—
148C2×C4⋊C4—132no—
149C2×C4⋊C4—262no—
150C2×C4⋊C4—262no—
151C2×C4⋊C4—261no—
152C2×C4⋊C4—261no—
153C2×C4⋊C4C2×#26112yes—
154C2×C42—131no—
155C2×C42—131no—
156C2×C42—131no—
157C2×C42—131no—
158C2×C42—131no—
159C2×C42—131no—
160C2×C42C2×#26111yescharacteristic
161C4⋊C8—264no—
162#97—134no—
163#97—262no—
164#97—264no—
165#95—262no—
166#95—262no—
167C2×C13#152811yescharacteristic
168C2×C13#153011yescharacteristic
169C2×C13#153411yescharacteristic
170C2×C13#153611yescharacteristic
171C2×C13#198611yescharacteristic
172C2×C13#199511yescharacteristic
173C2×C13#199711yescharacteristic
174C22×C4—22no—
175C22×C4—131no—
176C22×C4—131no—
177C22×C4—131no—
178C22×C4—131no—
179C22×C4—262no—
180C22×C4C22⋊#26111yescharacteristic
181C22×C4C22⋊#26111yescharacteristic
182C22×C4C22×#26111yescharacteristic
183C2×C8—264no—
184C2×C8—264no—
185C2×C8—522no—
186C2×C8—522no—
187C2×C8—522no—
188C2×C8—522no—
189C4⋊C4—42no—
190C4⋊C4—42no—
191C4⋊C4—42no—
192C4⋊C4—522no—
193C4⋊C4—522no—
194C4⋊C4—524no—
195C4⋊C4—524no—
196C4⋊C4—522no—
197C42—22no—
198C42—132no—
199C42—132no—
200C42—262no—
201C42—262no—
202C42—521no—
203C42—521no—
204C42—521no—
205C13#989411yescharacteristic, complemented, Sylow
206C23C2×C22⋊#26111yescharacteristic
207C2×C4—21no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—42no—
214C2×C4—42no—
215C2×C4—42no—
216C2×C4—132no—
217C2×C4—132no—
218C2×C4—131no—
219C2×C4—131no—
220C2×C4—261no—
221C2×C4—261no—
222C2×C4—261no—
223C2×C4—261no—
224C2×C4—261no—
225C2×C4—261no—
226C2×C4—261no—
227C2×C4—261no—
228C2×C4—261no—
229C2×C4—522no—
230C2×C4—522no—
231C2×C4—522no—
232C2×C4#8811312yes—
233C2×C4#8811812yes—
234C2×C4Q8×#26112yes—
235C8—524no—
236C8—524no—
237C22C2×#8811311yescharacteristic
238C22#1171914011yescharacteristic
239C22#1171914011yescharacteristic
240C22D13⋊#10011yescharacteristic
241C22C2×#8811811yescharacteristic
242C22#1171915511yescharacteristic
243C22(C2×#261)⋊Q811yescharacteristic
244C4—22no—
245C4—22no—
246C4—22no—
247C4—82no—
248C4—261no—
249C4—261no—
250C4—262no—
251C4—262no—
252C4—521no—
253C4—1042no—
254C2#1313030011yescharacteristic
255C2#1313030711yescharacteristic
256C2#1313031811yescharacteristic
257C2#1313032511yescharacteristic
258C2#1313101111yescharacteristic
259C2#1313102411yescharacteristic
260C2#1313102911yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC13×#384C4
socle, prime radicalC23×C13C2×C22⋊C4
cosocleC2×C4×Dic13C23
hypercenter#384#261
hypocenterC13#9894
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #384

Complements

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

NH ≅ G/Ntype
205. C13#9894semidirect

Maximal subgroups

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

subgroupindex
#131306212
#131305532
#131297122
#131231972
#989413