Finite Group Databasebeta

← #15774047

Subgroups — #15774047

Order 3328.

452 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 452 conjugacy classes of subgroups — too many to draw. Only its 107 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#13114824C211yesmaximal, characteristic
2#13113157C211yesmaximal, characteristic
3#13112860C214yesmaximal, complemented
4C13×#2487C211yesmaximal, characteristic
5C2×C4×D4×C13C2211yescharacteristic
6C22×C13×C4⋊C4C411yescharacteristic, complemented
7C13×#400C412yescomplemented
8C13×#399C2212yes—
9C13×#389—21no—
10C13×#386—21no—
11C13×#385—21no—
12C13×#380—21no—
13C13×#380C411yescharacteristic, complemented
14C2×#88074—21no—
15#11718873—21no—
16#11718586—21no—
17#11718118C2212yes—
18#11718117—21no—
19#11718117C2212yes—
20C22×D4×C13D411yescharacteristic
21C23×C4×C13—21no—
22C23×C4×C13C2×C411yescharacteristic
23C23×C4×C13D411yescharacteristic
24C4×D4×C13—41no—
25C4×D4×C13—41no—
26C2×C13×C4⋊C4—21no—
27C2×C13×C4⋊C4—21no—
28C2×C13×C4⋊C4—22no—
29C2×C13×C4⋊C4—41no—
30C2×C13×C4⋊C4—41no—
31C2×C13×C4⋊C4C2×C412yes—
32C2×C13×C4⋊C4C2×C411yescharacteristic
33C2×C13×C22⋊C4—21no—
34C2×C13×C22⋊C4—22no—
35C2×C13×C22⋊C4D411yescharacteristic
36C2×C13×C22⋊C4C2311yescharacteristic
37C2×C42×C13D411yescharacteristic
38C2×C22⋊Dic13—22no—
39C2×C4⋊Dic13—41no—
40C13×#95—22no—
41C13×#95—22no—
42C13×#95C2×C412yes—
43#88074—42no—
44#88071—41no—
45C22⋊#1055—22no—
46C4⋊#1055—41no—
47C4×#1055—41no—
48#11899—131nomaximal, Sylow
49C24×C13C22⋊C411yescharacteristic
50C24×C13C2×D411yescharacteristic
51C2×D4×C13—41no—
52C2×D4×C13—41no—
53C2×D4×C13SD1612yes—
54C2×D4×C13Q1612yes—
55C22×C4×C13—21no—
56C22×C4×C13—21no—
57C22×C4×C13—21no—
58C22×C4×C13—21no—
59C22×C4×C13—22no—
60C22×C4×C13—22no—
61C22×C4×C13—42no—
62C22×C4×C13—42no—
63C22×C4×C13—42no—
64C22×C4×C13—82no—
65C22×C4×C13C22⋊C411yescharacteristic
66C22×C4×C13C22⋊C411yescharacteristic
67C22×C4×C13C22⋊C411yescharacteristic
68C22×C4×C13C22×C411yescharacteristic
69C22×C4×C13C2×D411yescharacteristic
70C22×Dic13—42no—
71C13×C4⋊C4—41no—
72C13×C4⋊C4—42no—
73C13×C4⋊C4—42no—
74C13×C4⋊C4—41no—
75C13×C4⋊C4—41no—
76C13×C4⋊C4—82no—
77C13×C22⋊C4—41no—
78C13×C22⋊C4—41no—
79C13×C22⋊C4—42no—
80C13×C22⋊C4—82no—
81C42×C13—21no—
82C42×C13—21no—
83C22⋊Dic13—42no—
84C22⋊Dic13—42no—
85C4⋊Dic13—82no—
86C2×#1055—42no—
87#2487D1311yescharacteristic
88#1799—131no—
89#1460—131no—
90#1352—134no—
91C23×C13—21no—
92C23×C13—21no—
93C23×C13—21no—
94C23×C13—21no—
95C23×C13—41no—
96C23×C13—41no—
97C23×C13—41no—
98C23×C13—41no—
99C23×C13#10312yes—
100C23×C13C2×C22⋊C411yescharacteristic
101C23×C13C2×SD1611yescharacteristic
102C23×C13C2×Q1611yescharacteristic
103D4×C13—42no—
104D4×C13—42no—
105C2×C4×C13—21no—
106C2×C4×C13—21no—
107C2×C4×C13—22no—
108C2×C4×C13—21no—
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—42no—
112C2×C4×C13—42no—
113C2×C4×C13—42no—
114C2×C4×C13—41no—
115C2×C4×C13—41no—
116C2×C4×C13—41no—
117C2×C4×C13—42no—
118C2×C4×C13—42no—
119C2×C4×C13—42no—
120C2×C4×C13—42no—
121C2×C4×C13—42no—
122C2×C4×C13—42no—
123C2×C4×C13—81no—
124C2×C4×C13—84no—
125C2×C4×C13#9911yescharacteristic
126C2×C4×C13#9911yescharacteristic
127C2×C4×C13#10312yes—
128C2×Dic13—82no—
129C2×Dic13—82no—
130C2×Dic13—82no—
131#1055—82no—
132C2×C4×D4C2×D1311yescharacteristic
133C22×C4⋊C4Dic1311yescharacteristic, complemented
134#431—261no—
135C2×#99—261no—
136#400Dic1312yescomplemented
137#399C2×D1312yes—
138#389—21no—
139#386—21no—
140#385—21no—
141#380—21no—
142#380—261no—
143#380Dic1311yescharacteristic, complemented
144#342—132no—
145#323—132no—
146#323—261no—
147C22×C13—21no—
148C22×C13—21no—
149C22×C13—21no—
150C22×C13—22no—
151C22×C13—21no—
152C22×C13—42no—
153C22×C13—41no—
154C22×C13—41no—
155C22×C13—42no—
156C22×C13—41no—
157C22×C13—41no—
158C22×C13—41no—
159C22×C13—41no—
160C22×C13—81no—
161C22×C13C2×#9911yescharacteristic
162C22×C13C2×#10311yescharacteristic
163C22×C13#42111yescharacteristic
164C4×C13—21no—
165C4×C13—22no—
166C4×C13—41no—
167C4×C13—41no—
168C4×C13—41no—
169C4×C13—82no—
170C4×C13—82no—
171C4×C13#35212yes—
172Dic13—162no—
173C22×D4C22⋊D1311yescharacteristic
174C23×C4—21no—
175C23×C4C2×Dic1311yescharacteristic
176C23×C4C22⋊D1311yescharacteristic
177C4×D4—41no—
178C4×D4—41no—
179C2×C4⋊C4—21no—
180C2×C4⋊C4—21no—
181C2×C4⋊C4—22no—
182C2×C4⋊C4—41no—
183C2×C4⋊C4—41no—
184C2×C4⋊C4—521no—
185C2×C4⋊C4C2×Dic1312yes—
186C2×C4⋊C4C2×Dic1311yescharacteristic
187C2×C22⋊C4—21no—
188C2×C22⋊C4—22no—
189C2×C22⋊C4—262no—
190C2×C22⋊C4C22⋊D1311yescharacteristic
191C2×C22⋊C4C22×D1311yescharacteristic
192C2×C42C22⋊D1311yescharacteristic
193C4⋊C8—521no—
194#99—522no—
195C22⋊C8—262no—
196C4×C8—521no—
197#95—22no—
198#95—22no—
199#95—521no—
200#95C2×Dic1312yes—
201C2×C13—21no—
202C2×C13—21no—
203C2×C13—41no—
204C2×C13—42no—
205C2×C13—41no—
206C2×C13#152011yescharacteristic
207C2×C13C2×#35211yescharacteristic
208C2×C13#212811yescharacteristic
209C24C22⋊Dic1311yescharacteristic
210C24C2×C22⋊D1311yescharacteristic
211C2×D4—41no—
212C2×D4—41no—
213C2×D4#610612yes—
214C2×D4#610712yes—
215C22×C4—21no—
216C22×C4—21no—
217C22×C4—21no—
218C22×C4—21no—
219C22×C4—22no—
220C22×C4—22no—
221C22×C4—42no—
222C22×C4—42no—
223C22×C4—42no—
224C22×C4—82no—
225C22×C4—522no—
226C22×C4C22⋊Dic1311yescharacteristic
227C22×C4C22⋊Dic1311yescharacteristic
228C22×C4C22⋊Dic1311yescharacteristic
229C22×C4C22×Dic1311yescharacteristic
230C22×C4C2×C22⋊D1311yescharacteristic
231C2×C8—522no—
232C4⋊C4—41no—
233C4⋊C4—42no—
234C4⋊C4—42no—
235C4⋊C4—41no—
236C4⋊C4—41no—
237C4⋊C4—82no—
238C4⋊C4—1042no—
239C22⋊C4—41no—
240C22⋊C4—41no—
241C22⋊C4—42no—
242C22⋊C4—82no—
243C22⋊C4—522no—
244C22⋊C4—522no—
245C42—21no—
246C42—21no—
247C13#1189911yescharacteristic, complemented, Sylow
248C23—21no—
249C23—21no—
250C23—21no—
251C23—21no—
252C23—41no—
253C23—41no—
254C23—41no—
255C23—41no—
256C23#8807512yes—
257C23C2×#610611yescharacteristic
258C23C2×#610711yescharacteristic
259C23C2×C22⋊Dic1311yescharacteristic
260D4—42no—
261D4—42no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—22no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—42no—
269C2×C4—42no—
270C2×C4—42no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—42no—
275C2×C4—42no—
276C2×C4—42no—
277C2×C4—42no—
278C2×C4—42no—
279C2×C4—42no—
280C2×C4—81no—
281C2×C4—84no—
282C2×C4—1042no—
283C2×C4—1042no—
284C2×C4—1042no—
285C2×C4#8807411yescharacteristic
286C2×C4#8807411yescharacteristic
287C2×C4#8807512yes—
288C8—1042no—
289C22—21no—
290C22—21no—
291C22—21no—
292C22—22no—
293C22—21no—
294C22—42no—
295C22—41no—
296C22—41no—
297C22—42no—
298C22—41no—
299C22—41no—
300C22—41no—
301C22—41no—
302C22—81no—
303C22C2×#8807411yescharacteristic
304C22C2×#8807511yescharacteristic
305C22#1171889711yescharacteristic
306C4—21no—
307C4—22no—
308C4—41no—
309C4—41no—
310C4—41no—
311C4—82no—
312C4—82no—
313C4—2082no—
314C4#1171813112yes—
315C2—21no—
316C2—21no—
317C2—41no—
318C2—42no—
319C2—41no—
320C2#1311340811yescharacteristic
321C2C2×#1171813111yescharacteristic
322C2#1311650811yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC22×C4×C13C22×C4
FrattiniC2×C22⋊C4C22×D13
FittingC13×#2487C2
socleC22×C13C2×#99
prime radicalC22×D4×C13D4
cosocleC2×C13×C22⋊C4C23
hypercenter#2487D13
hypocenterC13#11899
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2487

Complements

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

NH ≅ G/Ntype
3. #13112860C2semidirect
6. C22×C13×C4⋊C4C4semidirect
7. C13×#400C4semidirect
13. C13×#380C4semidirect
133. C22×C4⋊C4Dic13semidirect
136. #400Dic13semidirect
143. #380Dic13semidirect
247. C13#11899semidirect

Maximal subgroups

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

subgroupindex
#131148242
#131131572
#131128602
C13×#24872
#1189913