Finite Group Databasebeta

← #15751448

Subgroups — #15751448

Order 3328.

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

normal subgroups only

This group has 378 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#13123223C211yesmaximal, characteristic
2#13114689C211yesmaximal, characteristic
3#13112660C212yesmaximal
4#13112658C212yesmaximal
5C13×#1831C211yesmaximal, characteristic
6C2×C13×C4⋊C8—21no—
7C43×C13C2211yescharacteristic
8#11718597C411yescharacteristic
9#11718597C411yescharacteristic
10#11718594—21no—
11#11718594—21no—
12#11718594—21no—
13#11718594—21no—
14#11718589C411yescharacteristic
15#11718589C411yescharacteristic
16#11718589C2211yescharacteristic
17#11718589C2211yescharacteristic
18C2×C4⋊#1055—21no—
19C2×#88043—21no—
20C13×#336—21no—
21C13×#336C2212yes—
22#11718116C2212yes—
23C22×C8×C13—22no—
24C2×C42×C13C2×C411yescharacteristic
25C2×C42×C13C2×C411yescharacteristic
26C2×C42×C13D411yescharacteristic
27C2×C42×C13D411yescharacteristic
28C2×C42×C13D411yescharacteristic
29C2×C42×C13D411yescharacteristic
30C2×C42×C13C2311yescharacteristic
31C2×C4⋊Dic13C2×C411yescharacteristic
32C2×C4⋊Dic13C2×C411yescharacteristic
33C2×C4⋊Dic13C2×C411yescharacteristic
34C2×C4⋊Dic13C2×C411yescharacteristic
35C2×#6101—21no—
36C2×#6101—21no—
37C2×#6101—21no—
38C2×#6101—21no—
39C22×#1055—22no—
40C13×C4⋊C8—42no—
41#88071—21no—
42#88071—21no—
43#88071—21no—
44#88071—21no—
45#88071—21no—
46#88071—21no—
47#88071—21no—
48#88071—21no—
49C4⋊#1055—24no—
50#88043—42no—
51#7697—131nomaximal, Sylow
52C22×C4×C13C22⋊C411yescharacteristic
53C22×C4×C13C22⋊C411yescharacteristic
54C22×C4×C13C22⋊C411yescharacteristic
55C22×C4×C13C22⋊C411yescharacteristic
56C22×C4×C13C22×C411yescharacteristic
57C22×C4×C13C2×D411yescharacteristic
58C22×C4×C13C2×D411yescharacteristic
59C22×Dic13—21no—
60C22×Dic13—21no—
61C22×Dic13—21no—
62C22×Dic13—21no—
63C2×C8×C13—42no—
64C2×C8×C13—42no—
65C2×C8×C13—42no—
66C42×C13—22no—
67C42×C13—22no—
68C42×C13—22no—
69C42×C13—21no—
70C42×C13—21no—
71C42×C13—21no—
72C42×C13—21no—
73C42×C13—41no—
74C42×C13—41no—
75C4⋊Dic13—22no—
76C4⋊Dic13—22no—
77C4⋊Dic13—41no—
78C4⋊Dic13—41no—
79#6101—42no—
80#6101—42no—
81#6101—41no—
82#6101—41no—
83#6101—41no—
84#6101—41no—
85C2×#1055—24no—
86C2×#1055—42no—
87C2×#1055—42no—
88#2864—131no—
89#1831D1311yescharacteristic
90#1767—131no—
91#1271—132no—
92#1271—132no—
93C23×C13C2×C22⋊C411yescharacteristic
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—21no—
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—21no—
109C2×C4×C13—21no—
110C2×C4×C13#10112yes—
111C2×C4×C13#10412yes—
112C2×C4×C13#13112yes—
113C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
114C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
115C2×C4×C13#13711yescharacteristic
116C2×C4×C13#13711yescharacteristic
117C2×Dic13—41no—
118C2×Dic13—41no—
119C2×Dic13—41no—
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—
129C8×C13—82no—
130#1055—44no—
131C2×C4⋊C8—21no—
132C2×C4⋊C8—261no—
133C2×#97—261no—
134#389—131no—
135#389—131no—
136#389—131no—
137#389—131no—
138#387—261no—
139#387—261no—
140#387—261no—
141#387—261no—
142#382—131no—
143#382—131no—
144C43C2×D1311yescharacteristic
145#336—21no—
146#336—132no—
147#336C2×D1312yes—
148C22×C13#40811yescharacteristic
149C22×C13#41011yescharacteristic
150C22×C13C2×#10111yescharacteristic
151C22×C13#41711yescharacteristic
152C22×C13#41711yescharacteristic
153C22×C13C2×#10411yescharacteristic
154C22×C13#42111yescharacteristic
155C4×C13—22no—
156C4×C13—22no—
157C4×C13—21no—
158C4×C13—21no—
159C4×C13—21no—
160C4×C13—21no—
161C4×C13—22no—
162C4×C13—41no—
163C4×C13—41no—
164Dic13—81no—
165Dic13—81no—
166Dic13—81no—
167Dic13—81no—
168C22×C8—22no—
169C22×C8—262no—
170C2×C4⋊C4—131no—
171C2×C4⋊C4—131no—
172C2×C4⋊C4—131no—
173C2×C4⋊C4—131no—
174C2×C4⋊C4—261no—
175C2×C4⋊C4—261no—
176C2×C4⋊C4—261no—
177C2×C4⋊C4—261no—
178C2×C42C4×D1311yescharacteristic
179C2×C42C4×D1311yescharacteristic
180C2×C42D5211yescharacteristic
181C2×C42D5211yescharacteristic
182C2×C42C22⋊D1311yescharacteristic
183C2×C42C22⋊D1311yescharacteristic
184C2×C42C22×D1311yescharacteristic
185C4⋊C8—42no—
186C4⋊C8—264no—
187#97—522no—
188#95—261no—
189#95—261no—
190#95—261no—
191#95—261no—
192#95—261no—
193#95—261no—
194#95—261no—
195#95—261no—
196C2×C13#147011yescharacteristic
197C2×C13#148311yescharacteristic
198C2×C13#149511yescharacteristic
199C2×C13#150911yescharacteristic
200C2×C13#151211yescharacteristic
201C2×C13#153111yescharacteristic
202C2×C13#156111yescharacteristic
203C22×C4—261no—
204C22×C4—261no—
205C22×C4—261no—
206C22×C4—261no—
207C22×C4#610311yescharacteristic
208C22×C4#610311yescharacteristic
209C22×C4#610311yescharacteristic
210C22×C4#610311yescharacteristic
211C22×C4C2×C4×D1311yescharacteristic
212C22×C4C2×D5211yescharacteristic
213C22×C4C2×C22⋊D1311yescharacteristic
214C2×C8—42no—
215C2×C8—42no—
216C2×C8—42no—
217C2×C8—264no—
218C2×C8—522no—
219C2×C8—522no—
220C4⋊C4—262no—
221C4⋊C4—262no—
222C4⋊C4—521no—
223C4⋊C4—521no—
224C4⋊C4—522no—
225C4⋊C4—522no—
226C4⋊C4—521no—
227C4⋊C4—521no—
228C4⋊C4—521no—
229C4⋊C4—521no—
230C42—22no—
231C42—22no—
232C42—22no—
233C42—21no—
234C42—21no—
235C42—21no—
236C42—21no—
237C42—41no—
238C42—41no—
239C13#769711yescharacteristic, complemented, Sylow
240C23C2×#610311yescharacteristic
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—521no—
258C2×C4—521no—
259C2×C4—521no—
260C2×C4—521no—
261C2×C4—521no—
262C2×C4—521no—
263C2×C4—521no—
264C2×C4—521no—
265C2×C4—521no—
266C2×C4—521no—
267C2×C4—521no—
268C2×C4—521no—
269C2×C4#8806412yes—
270C2×C4#8806512yes—
271C2×C4#8815512yes—
272C2×C4#8816211yescharacteristic
273C2×C4#8816311yescharacteristic
274C2×C4#8818611yescharacteristic
275C2×C4#8819611yescharacteristic
276C8—82no—
277C8—524no—
278C22#1171862711yescharacteristic
279C22#1171866611yescharacteristic
280C22#1171866711yescharacteristic
281C22#1171877111yescharacteristic
282C22#1171879411yescharacteristic
283C22C2×#8806411yescharacteristic
284C22C2×#8806511yescharacteristic
285C4—21no—
286C4—21no—
287C4—21no—
288C4—21no—
289C4—22no—
290C4—22no—
291C4—22no—
292C4—41no—
293C4—41no—
294C4—1041no—
295C4—1041no—
296C4—1041no—
297C4—1041no—
298C2#1311319111yescharacteristic
299C2#1311324711yescharacteristic
300C2#1311330211yescharacteristic
301C2#1311336211yescharacteristic
302C2#1311337211yescharacteristic
303C2#1311345211yescharacteristic
304C2#1311357311yescharacteristic
subgroupG/H
centerC23C2×#6103
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1831C2
socle, prime radicalC23×C13C2×C22⋊C4
cosocleC2×C42×C13C23
hypercenter#1831D13
hypocenterC13#7697
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C43 ◁ #1831

Complements

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

NH ≅ G/Ntype
239. C13#7697semidirect

Maximal subgroups

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

subgroupindex
#131232232
#131146892
#131126602
#131126582
C13×#18312
#769713