Finite Group Databasebeta

← #16782186

Subgroups — #16782186

Order 3328.

526 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 100 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#13130563C211yesmaximal, characteristic
2#13130563C211yesmaximal, characteristic
3#13129712C214yesmaximal, complemented
4#13117241C211yesmaximal, characteristic
5C2×#88146C412yes—
6C2×C42×D13C2211yescharacteristic
7C2×#88111—21no—
8C2×#88111—21no—
9C2×#88110C2212yes—
10C2×#88110C2212yes—
11C13×#384C411yescharacteristic
12#11718648—21no—
13#11718648—21no—
14#11718638C2212yes—
15C4⋊C4×Dic13—21no—
16C4⋊C4×Dic13—21no—
17#11718596C411yescharacteristic
18#11718290—21no—
19#11718290—21no—
20C22×C4×D13C2×C411yescharacteristic
21C22×C4×D13D411yescharacteristic
22C22×C4×D13D411yescharacteristic
23C22×#1057—22no—
24C22×#1057—22no—
25C2×C13×C4⋊C4—21no—
26C2×C13×C4⋊C4—21no—
27C2×C13×C4⋊C4C2×C412yes—
28C2×C42×C13C2×C411yescharacteristic
29C2×#6103—22no—
30C2×C4⋊Dic13—21no—
31C2×C4⋊Dic13—21no—
32C2×C4⋊Dic13C2×C412yes—
33C2×C4×Dic13—22no—
34C2×C4×Dic13D411yescharacteristic
35C2×C4×Dic13D411yescharacteristic
36C2×C4×Dic13C2311yescharacteristic
37#88146—44no—
38C42×D13—24no—
39#88111—24no—
40#88111—24no—
41#88110—24no—
42#88110—24no—
43#88071—22no—
44#88071—22no—
45#8722—131nomaximal, Sylow
46C23×D13C22⋊C411yescharacteristic
47C22×C4×C13—22no—
48C22×C4×C13C22⋊C411yescharacteristic
49C22×C4×C13C22⋊C411yescharacteristic
50C22×C4×C13C22×C411yescharacteristic
51C22×Dic13—22no—
52C22×Dic13C22⋊C411yescharacteristic
53C22×Dic13C2×D411yescharacteristic
54C22×Dic13C2×D411yescharacteristic
55C2×C4×D13—22no—
56C2×C4×D13—22no—
57C2×C4×D13—22no—
58C2×C4×D13—22no—
59C2×C4×D13—22no—
60C2×C4×D13—22no—
61C2×C4×D13—22no—
62C2×C4×D13—41no—
63C2×C4×D13—41no—
64C2×#1057—24no—
65C2×#1057—24no—
66C2×#1057—42no—
67C2×#1057—42no—
68C2×#1057—42no—
69C2×#1057—42no—
70C13×C4⋊C4—42no—
71C13×C4⋊C4—42no—
72C13×C4⋊C4—42no—
73C42×C13—22no—
74#6103—44no—
75C4⋊Dic13—42no—
76C4⋊Dic13—42no—
77C4⋊Dic13—42no—
78C4×Dic13—22no—
79C4×Dic13—22no—
80C4×Dic13—44no—
81C4×Dic13#4114yes—
82#2285—131no—
83#1749—131no—
84#1749—131no—
85#1295—134no—
86C23×C13C2×C22⋊C411yescharacteristic
87C22×D13—21no—
88C22×D13—21no—
89C22×D13—21no—
90C22×D13—21no—
91C22×D13—21no—
92C22×D13—21no—
93C22×D13#10012yes—
94C2×C4×C13—21no—
95C2×C4×C13—21no—
96C2×C4×C13—21no—
97C2×C4×C13—21no—
98C2×C4×C13—21no—
99C2×C4×C13—21no—
100C2×C4×C13—42no—
101C2×C4×C13—42no—
102C2×C4×C13—42no—
103C2×C4×C13#10412yes—
104C2×C4×C13#10412yes—
105C2×C4×C13#11712yes—
106C2×Dic13—21no—
107C2×Dic13—21no—
108C2×Dic13—21no—
109C2×Dic13—21no—
110C2×Dic13—21no—
111C2×Dic13—21no—
112C2×Dic13—42no—
113C2×Dic13—42no—
114C2×Dic13—42no—
115C2×Dic13#10112yes—
116C2×Dic13#12312yes—
117C2×Dic13#12312yes—
118C4×D13—28no—
119C4×D13—44no—
120C4×D13—44no—
121#1057—44no—
122#1057—44no—
123C2×#117—132no—
124C22×C42—131no—
125C2×C22⋊C8—261no—
126C2×C22⋊C8—261no—
127C2×#97—132no—
128C2×#97—132no—
129#384—131no—
130#384#26111yescharacteristic
131#382—132no—
132#380—261no—
133#380—261no—
134C4×C4⋊C4—261no—
135C4×C4⋊C4—261no—
136#336—261no—
137#336—261no—
138C22×C13#38111yescharacteristic
139C22×C13C2×#10011yescharacteristic
140C22×C13C2×#10111yescharacteristic
141C22×C13C2×#10411yescharacteristic
142C22×C13C2×#10411yescharacteristic
143C22×C13#42111yescharacteristic
144C22×C13#42111yescharacteristic
145C2×D13—22no—
146C2×D13—22no—
147C2×D13—22no—
148C2×D13—41no—
149C2×D13—41no—
150C2×D13—41no—
151C2×D13—41no—
152C4×C13—22no—
153C4×C13—22no—
154C4×C13—22no—
155C4×C13—82no—
156Dic13—22no—
157Dic13—22no—
158Dic13—22no—
159Dic13—82no—
160C23×C4—131no—
161C23×C4—131no—
162C23×C4—131no—
163C22×C8—262no—
164C22×C8—262no—
165#117—524no—
166C2×C4⋊C4—21no—
167C2×C4⋊C4—21no—
168C2×C4⋊C4—132no—
169C2×C4⋊C4—261no—
170C2×C4⋊C4—261no—
171C2×C4⋊C4C2×#26112yes—
172C2×C22⋊C4—262no—
173C2×C42—131no—
174C2×C42—131no—
175C2×C42—131no—
176C2×C42—264no—
177C2×C42—262no—
178C2×C42C2×#26111yescharacteristic
179C22⋊C8—264no—
180C22⋊C8—264no—
181#97—264no—
182#97—264no—
183#95—262no—
184#95—262no—
185C2×C13#152611yescharacteristic
186C2×C13#153011yescharacteristic
187C2×C13#153011yescharacteristic
188C2×C13#153711yescharacteristic
189C2×C13#182111yescharacteristic
190C2×C13#182611yescharacteristic
191C2×C13#182611yescharacteristic
192D13—42no—
193C24—131no—
194C22×C4—22no—
195C22×C4—131no—
196C22×C4—131no—
197C22×C4—131no—
198C22×C4—262no—
199C22×C4—262no—
200C22×C4—262no—
201C22×C4—262no—
202C22×C4—262no—
203C22×C4—262no—
204C22×C4—262no—
205C22×C4—262no—
206C22×C4—521no—
207C22×C4—521no—
208C22×C4C22⋊#26111yescharacteristic
209C22×C4C22⋊#26111yescharacteristic
210C22×C4C22×#26111yescharacteristic
211C2×C8—264no—
212C2×C8—264no—
213C2×C8—522no—
214C2×C8—522no—
215C2×C8—522no—
216C2×C8—522no—
217C4⋊C4—42no—
218C4⋊C4—42no—
219C4⋊C4—42no—
220C4⋊C4—522no—
221C4⋊C4—522no—
222C4⋊C4—522no—
223C22⋊C4—524no—
224C42—22no—
225C42—134no—
226C42—262no—
227C42—262no—
228C42—524no—
229C13#872211yescharacteristic, complemented, Sylow
230C23—132no—
231C23—261no—
232C23—261no—
233C23—261no—
234C23—261no—
235C23—261no—
236C23—261no—
237C23C2×C22⋊#26111yescharacteristic
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—42no—
245C2×C4—42no—
246C2×C4—42no—
247C2×C4—132no—
248C2×C4—132no—
249C2×C4—132no—
250C2×C4—268no—
251C2×C4—261no—
252C2×C4—261no—
253C2×C4—261no—
254C2×C4—261no—
255C2×C4—261no—
256C2×C4—261no—
257C2×C4—524no—
258C2×C4—524no—
259C2×C4—522no—
260C2×C4—522no—
261C2×C4—522no—
262C2×C4#8811612yes—
263C2×C4#8811812yes—
264C2×C4#8823712yes—
265C8—524no—
266C8—524no—
267C22—262no—
268C22—262no—
269C22—262no—
270C22—521no—
271C22—521no—
272C22—521no—
273C22—521no—
274C22#1171913511yescharacteristic
275C22C2×#8811611yescharacteristic
276C22#1171914011yescharacteristic
277C22D13⋊#10011yescharacteristic
278C22C2×#8811811yescharacteristic
279C22#1171915511yescharacteristic
280C22D13⋊#10111yescharacteristic
281C4—22no—
282C4—22no—
283C4—22no—
284C4—82no—
285C4—262no—
286C4—262no—
287C4—262no—
288C4—1042no—
289C2—522no—
290C2#1313029411yescharacteristic
291C2#1313030611yescharacteristic
292C2#1313030711yescharacteristic
293C2#1313032811yescharacteristic
294C2#1313073611yescharacteristic
295C2#1313074211yescharacteristic
296C2#1313074311yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC13×#384C4
socleC23×C13C2×C22⋊C4
prime radicalC23×D13C22⋊C4
cosocleC2×C4×Dic13C23
hypercenter#384#261
hypocenterC13#8722
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
3. #13129712C2semidirect
229. C13#8722semidirect

Maximal subgroups

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

subgroupindex
#131305632
#131297122
#131172412
#872213