Finite Group Databasebeta

← #15756413

Subgroups — #15756413

Order 3328.

384 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 91 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#13117334C211yesmaximal, characteristic
2#13113170C211yesmaximal, characteristic
3#13112693C212yesmaximal, complemented
4#13112691C212yesmaximal, complemented
5C13×#1464C211yesmaximal, characteristic
6C2×C13×#117C2211yescharacteristic
7C13×#432C2212yes—
8C4×C22⋊Dic13C411yescharacteristic
9C4×C22⋊Dic13C411yescharacteristic
10#11718642—21no—
11#11718642—21no—
12#11718612—21no—
13#11718612—21no—
14C4×C4⋊Dic13C2211yescharacteristic
15C4×C4⋊Dic13C2211yescharacteristic
16#11718593C411yescharacteristic
17C42×Dic13C411yescharacteristic
18#11718587C2212yes—
19C13×#324—21no—
20C13×#323—21no—
21#11718120—21no—
22#11718117—21no—
23C23×C4×C13C2×C411yescharacteristic
24C13×#117—22no—
25C13×#117—22no—
26C2×C13×C4⋊C4D411yescharacteristic
27C2×C13×C4⋊C4D411yescharacteristic
28C2×C13×C22⋊C4D411yescharacteristic
29C2×C13×C22⋊C4D411yescharacteristic
30C2×C42×C13C2×C411yescharacteristic
31C2×C42×C13C2311yescharacteristic
32C2×C22⋊Dic13—21no—
33C2×C22⋊Dic13—21no—
34C2×C4⋊Dic13—21no—
35C2×C4⋊Dic13—21no—
36C2×C4×Dic13—21no—
37C2×C4×Dic13—21no—
38C2×C4×Dic13C2×C411yescharacteristic
39C2×C4×Dic13C2×C411yescharacteristic
40C2×C4×Dic13C2×C411yescharacteristic
41C2×C4×Dic13C2×C411yescharacteristic
42C13×C4⋊C8—22no—
43C13×C22⋊C8—22no—
44C13×#97—22no—
45#88071—21no—
46#88071—21no—
47#88071—21no—
48#88071—21no—
49#88071—21no—
50#88071—21no—
51C22⋊#1055—22no—
52C4⋊#1055—22no—
53#88043—22no—
54#8745—131nomaximal, Sylow
55C24×C13C22⋊C411yescharacteristic
56C22×C4×C13—21no—
57C22×C4×C13—21no—
58C22×C4×C13—41no—
59C22×C4×C13—41no—
60C22×C4×C13C22⋊C411yescharacteristic
61C22×C4×C13C22⋊C411yescharacteristic
62C22×C4×C13C22⋊C411yescharacteristic
63C22×C4×C13C22×C411yescharacteristic
64C22×C4×C13C2×D411yescharacteristic
65C22×C4×C13C2×D411yescharacteristic
66C22×Dic13—21no—
67C22×Dic13—21no—
68C22×Dic13—21no—
69C22×Dic13—21no—
70C2×C8×C13—42no—
71C13×C4⋊C4—22no—
72C13×C4⋊C4—22no—
73C13×C22⋊C4—22no—
74C13×C22⋊C4—22no—
75C42×C13—21no—
76C42×C13—21no—
77C42×C13#4112yes—
78C42×C13#4112yes—
79C22⋊Dic13—42no—
80C22⋊Dic13—42no—
81C4⋊Dic13—42no—
82C4⋊Dic13—42no—
83C4×Dic13—42no—
84C4×Dic13—42no—
85C4×Dic13—41no—
86C4×Dic13—41no—
87C4×Dic13—41no—
88C4×Dic13—41no—
89C2×#1055—42no—
90#2298—131no—
91#1464—131no—
92#1464D1311yescharacteristic
93#1285—132no—
94#1285—132no—
95C23×C13—21no—
96C23×C13—21no—
97C23×C13—21no—
98C23×C13—41no—
99C23×C13—41no—
100C23×C13C2×C22⋊C411yescharacteristic
101C2×C4×C13—21no—
102C2×C4×C13—21no—
103C2×C4×C13—21no—
104C2×C4×C13—21no—
105C2×C4×C13—21no—
106C2×C4×C13—21no—
107C2×C4×C13—21no—
108C2×C4×C13—41no—
109C2×C4×C13—41no—
110C2×C4×C13—42no—
111C2×C4×C13—42no—
112C2×C4×C13—41no—
113C2×C4×C13—41no—
114C2×C4×C13#11711yescharacteristic
115C2×C4×C13#11711yescharacteristic
116C2×C4×C13#12312yes—
117C2×C4×C13#12312yes—
118C2×Dic13—22no—
119C2×Dic13—22no—
120C2×Dic13—41no—
121C2×Dic13—41no—
122C2×Dic13—41no—
123C2×Dic13—41no—
124C2×Dic13—41no—
125C2×Dic13—41no—
126C2×Dic13—41no—
127C2×Dic13—41no—
128C2×Dic13—41no—
129C2×Dic13—41no—
130C8×C13—82no—
131#1055—82no—
132C2×#117C2×D1311yescharacteristic
133#432—132no—
134#432C2×D1312yes—
135#388—261no—
136#388—261no—
137#387—261no—
138#387—261no—
139C4×C4⋊C4—131no—
140C4×C4⋊C4—131no—
141C4×C22⋊C4—131no—
142C4×C22⋊C4—131no—
143#376—131no—
144C43—131no—
145#324—21no—
146#324—261no—
147#323—21no—
148#323—261no—
149C22×C13—21no—
150C22×C13—21no—
151C22×C13—41no—
152C22×C13—41no—
153C22×C13—41no—
154C22×C13—81no—
155C22×C13—81no—
156C22×C13#38111yescharacteristic
157C22×C13#41311yescharacteristic
158C22×C13#41311yescharacteristic
159C4×C13—21no—
160C4×C13—21no—
161C4×C13—22no—
162C4×C13—22no—
163C4×C13—41no—
164C4×C13—41no—
165C4×C13—41no—
166Dic13—42no—
167Dic13—42no—
168Dic13—81no—
169Dic13—81no—
170C23×C4C4×D1311yescharacteristic
171#117—22no—
172#117—22no—
173C2×C4⋊C4—261no—
174C2×C4⋊C4—261no—
175C2×C4⋊C4D5211yescharacteristic
176C2×C4⋊C4C22⋊D1311yescharacteristic
177C2×C22⋊C4—261no—
178C2×C22⋊C4—261no—
179C2×C22⋊C4D5211yescharacteristic
180C2×C22⋊C4C22⋊D1311yescharacteristic
181C2×C42—131no—
182C2×C42—131no—
183C2×C42—131no—
184C2×C42—131no—
185C2×C42—261no—
186C2×C42—261no—
187C2×C42C4×D1311yescharacteristic
188C2×C42C22×D1311yescharacteristic
189C4⋊C8—22no—
190C4⋊C8—262no—
191C22⋊C8—22no—
192C22⋊C8—262no—
193#97—22no—
194#97—262no—
195#95—261no—
196#95—261no—
197#95—261no—
198#95—261no—
199#95—261no—
200#95—261no—
201C2×C13—21no—
202C2×C13—21no—
203C2×C13—81no—
204C2×C13#182211yescharacteristic
205C2×C13#182711yescharacteristic
206C2×C13#182711yescharacteristic
207C24#610311yescharacteristic
208C22×C4—21no—
209C22×C4—21no—
210C22×C4—41no—
211C22×C4—41no—
212C22×C4—261no—
213C22×C4—261no—
214C22×C4—261no—
215C22×C4—261no—
216C22×C4#610311yescharacteristic
217C22×C4#610311yescharacteristic
218C22×C4#610311yescharacteristic
219C22×C4C2×C4×D1311yescharacteristic
220C22×C4C2×D5211yescharacteristic
221C22×C4C2×C22⋊D1311yescharacteristic
222C2×C8—42no—
223C2×C8—522no—
224C4⋊C4—22no—
225C4⋊C4—22no—
226C4⋊C4—522no—
227C4⋊C4—522no—
228C22⋊C4—22no—
229C22⋊C4—22no—
230C22⋊C4—522no—
231C22⋊C4—522no—
232C42—21no—
233C42—21no—
234C42—521no—
235C42—521no—
236C42—521no—
237C42—521no—
238C42—522no—
239C42—522no—
240C42#612912yes—
241C42#612912yes—
242C13#874511yescharacteristic, complemented, Sylow
243C23—21no—
244C23—21no—
245C23—21no—
246C23—41no—
247C23—41no—
248C23C2×#610311yescharacteristic
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—42no—
259C2×C4—42no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—262no—
263C2×C4—262no—
264C2×C4—521no—
265C2×C4—521no—
266C2×C4—521no—
267C2×C4—521no—
268C2×C4—521no—
269C2×C4—521no—
270C2×C4—521no—
271C2×C4—521no—
272C2×C4—521no—
273C2×C4—521no—
274C2×C4#8813111yescharacteristic
275C2×C4#8813111yescharacteristic
276C2×C4#8814012yes—
277C2×C4#8818912yes—
278C8—82no—
279C8—1042no—
280C22—21no—
281C22—21no—
282C22—41no—
283C22—41no—
284C22—41no—
285C22—81no—
286C22—81no—
287C22#1171860411yescharacteristic
288C22#1171879311yescharacteristic
289C22#1171879311yescharacteristic
290C4—21no—
291C4—21no—
292C4—22no—
293C4—22no—
294C4—41no—
295C4—41no—
296C4—41no—
297C4—522no—
298C4—522no—
299C4—1041no—
300C4—1041no—
301C2—21no—
302C2—21no—
303C2—81no—
304C2#1311491711yescharacteristic
305C2#1311493711yescharacteristic
306C2#1311494111yescharacteristic
subgroupG/H
centerC22#11718604
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1464C2
socleC22×C13#381
prime radicalC24×C13C22⋊C4
cosocleC2×C42×C13C23
hypercenter#1464D13
hypocenterC13#8745
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1464

Complements

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

NH ≅ G/Ntype
3. #13112693C2semidirect
4. #13112691C2semidirect
242. C13#8745semidirect

Maximal subgroups

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

subgroupindex
#131173342
#131131702
#131126932
#131126912
C13×#14642
#874513