Finite Group Databasebeta

← #15751411

Subgroups — #15751411

Order 3328.

410 conjugacy classes of subgroups.

The subgroup lattice has 310 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123218C211yesmaximal, characteristic
2C4×C4⋊#1055C211yesmaximal, characteristic
3#13112661C212yesmaximal
4#13112658C212yesmaximal
5C13×#1767C211yesmaximal, characteristic
6C2×C13×C4⋊C8—21no—
7C2×C13×#97—21no—
8C43×C13C2211yescharacteristic
9#11718598—21no—
10#11718594—21no—
11#11718594—21no—
12#11718594—21no—
13#11718590C411yescharacteristic
14#11718590C411yescharacteristic
15#11718590C2211yescharacteristic
16#11718589C411yescharacteristic
17#11718589C411yescharacteristic
18#11718589C2211yescharacteristic
19C2×C4⋊#1055—21no—
20C2×C4×#1055—21no—
21C13×#336C2212yes—
22#11718116C2212yes—
23C22×Dic26C2×C411yescharacteristic
24C22×C8×C13—22no—
25C2×C42×C13C2×C411yescharacteristic
26C2×C42×C13C2×C411yescharacteristic
27C2×C42×C13D411yescharacteristic
28C2×C42×C13D411yescharacteristic
29C2×C42×C13D411yescharacteristic
30C2×C42×C13D411yescharacteristic
31C2×C42×C13C2311yescharacteristic
32C2×C4⋊Dic13C2×C411yescharacteristic
33C2×C4⋊Dic13C2×C411yescharacteristic
34C2×C4⋊Dic13C2×C411yescharacteristic
35C2×#6101—21no—
36C2×#6101—21no—
37C2×#6101—21no—
38C22×#1055—22no—
39C13×C4⋊C8—24no—
40C13×#97—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—
49#88071—21no—
50C4⋊#1055—24no—
51C4×#1055—42no—
52#7689—131nomaximal, Sylow
53C22×C4×C13C22⋊C411yescharacteristic
54C22×C4×C13C22⋊C411yescharacteristic
55C22×C4×C13C22⋊C411yescharacteristic
56C22×C4×C13C22⋊C411yescharacteristic
57C22×C4×C13C22×C411yescharacteristic
58C22×C4×C13C2×D411yescharacteristic
59C22×C4×C13C2×D411yescharacteristic
60C22×Dic13—21no—
61C22×Dic13—21no—
62C22×Dic13—21no—
63C22×Dic13—21no—
64C2×Dic26—22no—
65C2×Dic26—41no—
66C2×Dic26—41no—
67C2×C8×C13—24no—
68C2×C8×C13—42no—
69C2×C8×C13—42no—
70C42×C13—22no—
71C42×C13—22no—
72C42×C13—22no—
73C42×C13—21no—
74C42×C13—21no—
75C42×C13—41no—
76C42×C13—41no—
77C42×C13SD1612yes—
78C42×C13Q1612yes—
79C4⋊Dic13—22no—
80C4⋊Dic13—41no—
81C4⋊Dic13—41no—
82#6101—42no—
83#6101—42no—
84#6101—41no—
85#6101—41no—
86C2×#1055—24no—
87C2×#1055—42no—
88C2×#1055—42no—
89#2863—131no—
90#1767D1311yescharacteristic
91C4×C4⋊C8—131no—
92#1272—132no—
93#1271—132no—
94C23×C13C2×C22⋊C411yescharacteristic
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#10312yes—
110C2×C4×C13#10312yes—
111C2×C4×C13#10412yes—
112C2×C4×C13#10412yes—
113C2×C4×C13#13112yes—
114C2×C4×C13C2×SD1611yescharacteristic
115C2×C4×C13C2×Q1611yescharacteristic
116C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
117C2×C4×C13#13711yescharacteristic
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—
129C2×Dic13—41no—
130Dic26—82no—
131C8×C13—44no—
132#1055—44no—
133C2×C4⋊C8—21no—
134C2×C4⋊C8—261no—
135C2×#97—21no—
136C2×C4×C8—261no—
137#391—131no—
138#391—131no—
139#391—131no—
140#389—131no—
141#389—131no—
142#389—131no—
143#387—261no—
144#387—261no—
145#387—261no—
146#383—261no—
147C43C2×D1311yescharacteristic
148#336—132no—
149#336C2×D1312yes—
150C22×C13#40811yescharacteristic
151C22×C13#41011yescharacteristic
152C22×C13#41311yescharacteristic
153C22×C13C2×#10311yescharacteristic
154C22×C13#41711yescharacteristic
155C22×C13C2×#10411yescharacteristic
156C22×C13C2×#10411yescharacteristic
157C4×C13—22no—
158C4×C13—22no—
159C4×C13—22no—
160C4×C13—22no—
161C4×C13—21no—
162C4×C13—21no—
163C4×C13—21no—
164C4×C13—21no—
165C4×C13—22no—
166Dic13—81no—
167Dic13—81no—
168Dic13—81no—
169Dic13—81no—
170C22×Q8—131no—
171C22×C8—22no—
172C22×C8—262no—
173C2×C4⋊C4—131no—
174C2×C4⋊C4—131no—
175C2×C4⋊C4—131no—
176C2×C4⋊C4—261no—
177C2×C4⋊C4—261no—
178C2×C4⋊C4—261no—
179C2×C42C4×D1311yescharacteristic
180C2×C42C4×D1311yescharacteristic
181C2×C42D5211yescharacteristic
182C2×C42D5211yescharacteristic
183C2×C42C22⋊D1311yescharacteristic
184C2×C42C22⋊D1311yescharacteristic
185C2×C42C22×D1311yescharacteristic
186C4⋊C8—24no—
187C4⋊C8—264no—
188#97—42no—
189C4×C8—522no—
190#95—261no—
191#95—261no—
192#95—261no—
193#95—261no—
194#95—261no—
195#95—261no—
196#95—261no—
197#95—261no—
198#95—261no—
199C2×C13#147311yescharacteristic
200C2×C13#148311yescharacteristic
201C2×C13#149311yescharacteristic
202C2×C13#150311yescharacteristic
203C2×C13#150911yescharacteristic
204C2×C13#152411yescharacteristic
205C2×C13#155011yescharacteristic
206C2×Q8—262no—
207C2×Q8—521no—
208C2×Q8—521no—
209C22×C4—261no—
210C22×C4—261no—
211C22×C4—261no—
212C22×C4—261no—
213C22×C4#610311yescharacteristic
214C22×C4#610311yescharacteristic
215C22×C4#610311yescharacteristic
216C22×C4#610311yescharacteristic
217C22×C4C2×C4×D1311yescharacteristic
218C22×C4C2×D5211yescharacteristic
219C22×C4C2×C22⋊D1311yescharacteristic
220C2×C8—24no—
221C2×C8—42no—
222C2×C8—42no—
223C2×C8—264no—
224C2×C8—522no—
225C2×C8—522no—
226C4⋊C4—262no—
227C4⋊C4—521no—
228C4⋊C4—521no—
229C4⋊C4—522no—
230C4⋊C4—521no—
231C4⋊C4—521no—
232C4⋊C4—522no—
233C42—22no—
234C42—22no—
235C42—21no—
236C42—21no—
237C42—22no—
238C42—41no—
239C42—41no—
240C42#610512yes—
241C42#610712yes—
242C13#768911yescharacteristic, complemented, Sylow
243C23C2×#610311yescharacteristic
244Q8—1042no—
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—21no—
258C2×C4—21no—
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—521no—
270C2×C4—521no—
271C2×C4#8804512yes—
272C2×C4#8805012yes—
273C2×C4#8805012yes—
274C2×C4#8806512yes—
275C2×C4#8816112yes—
276C2×C4#8816211yescharacteristic
277C2×C4#8816311yescharacteristic
278C2×C4C2×#610511yescharacteristic
279C2×C4C2×#610711yescharacteristic
280C8—44no—
281C8—524no—
282C22C2×#8804511yescharacteristic
283C22C2×#8805011yescharacteristic
284C22#1171866711yescharacteristic
285C22#1171879011yescharacteristic
286C22#1171879311yescharacteristic
287C22#1171879411yescharacteristic
288C22C2×#8806511yescharacteristic
289C4—21no—
290C4—21no—
291C4—22no—
292C4—22no—
293C4—22no—
294C4—22no—
295C4—22no—
296C4—21no—
297C4—21no—
298C4—1041no—
299C4—1041no—
300C4—1041no—
301C4—1041no—
302C2#1311320611yescharacteristic
303C2#1311325011yescharacteristic
304C2#1311329011yescharacteristic
305C2#1311333411yescharacteristic
306C2#1311336211yescharacteristic
307C2#1311342211yescharacteristic
308C2#1311352711yescharacteristic
subgroupG/H
centerC23C2×#6103
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1767C2
socle, prime radicalC23×C13C2×C22⋊C4
cosocleC2×C42×C13C23
hypercenter#1767D13
hypocenterC13#7689
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C43 ◁ #1767

Complements

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

NH ≅ G/Ntype
242. C13#7689semidirect

Maximal subgroups

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

subgroupindex
#131232182
C4×C4⋊#10552
#131126612
#131126582
C13×#17672
#768913