Finite Group Databasebeta

← #15772496

Subgroups — #15772496

Order 3328.

440 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 83 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#13119324C211yesmaximal, characteristic
2C2×#11718120C211yesmaximal, characteristic, complemented
3#13112779C212yesmaximal, complemented
4#13112767C212yesmaximal, complemented
5C13×#1463C211yesmaximal, characteristic, complemented
6C22×C13×C4⋊C4C2211yescharacteristic
7C2×#88184C411yescharacteristic
8C13×#407—21no—
9#11718874—21no—
10#11718874—21no—
11C4×C22⋊Dic13C411yescharacteristic
12C2×C22⋊#1055—21no—
13#11718654—21no—
14#11718654—21no—
15#11718649C411yescharacteristic
16#11718649C2211yescharacteristic
17#11718638C411yescharacteristic
18#11718638C2211yescharacteristic
19C13×#324—21no—
20C13×#324C2212yes—
21#11718120—21no—
22#11718120C2212yes—
23C23×C4×C13C2×C411yescharacteristic
24C23×C4×C13D411yescharacteristic
25C23×C4×C13D411yescharacteristic
26C22×C22⋊D13—21no—
27C22×D52C2×C411yescharacteristic
28C2×C13×M16—41no—
29C2×C13×C4⋊C4—41no—
30C2×C13×C4⋊C4—41no—
31C2×C13×C4⋊C4C2×C411yescharacteristic
32C2×C13×C4⋊C4D411yescharacteristic
33C2×C13×C4⋊C4D411yescharacteristic
34C2×C13×C4⋊C4C2311yescharacteristic
35C2×C22⋊Dic13—21no—
36#88184—41no—
37#88184—41no—
38C2×#6103—21no—
39C2×#6103—21no—
40C2×#6103—21no—
41C2×#6103—21no—
42C2×#6103—21no—
43C2×C4⋊Dic13C2×C411yescharacteristic
44C2×C4×Dic13C2×C411yescharacteristic
45C2×C4×Dic13C2×C411yescharacteristic
46C22×#1055—41no—
47C13×C22⋊C8—22no—
48C13×C22⋊C8—41no—
49#88071—21no—
50#88071—21no—
51#88071—21no—
52#88071—21no—
53#88071—21no—
54C22⋊#1055—22no—
55C22⋊#1055—41no—
56#11553—131nomaximal, Sylow
57C24×C13C22⋊C411yescharacteristic
58C23×D13—21no—
59C22×C4×C13—21no—
60C22×C4×C13—21no—
61C22×C4×C13—21no—
62C22×C4×C13—21no—
63C22×C4×C13—21no—
64C22×C4×C13—21no—
65C22×C4×C13—22no—
66C22×C4×C13—41no—
67C22×C4×C13—81no—
68C22×C4×C13—81no—
69C22×C4×C13C22⋊C411yescharacteristic
70C22×C4×C13C22⋊C411yescharacteristic
71C22×C4×C13C22⋊C411yescharacteristic
72C22×C4×C13C22×C411yescharacteristic
73C22×C4×C13C2×D411yescharacteristic
74C22×C4×C13C2×D411yescharacteristic
75C2×C22⋊D13—42no—
76C2×C22⋊D13—42no—
77C2×C22⋊D13—41no—
78C2×C22⋊D13—41no—
79C22×Dic13—21no—
80C22×Dic13—21no—
81C22×Dic13—21no—
82C2×D52—22no—
83C2×D52—41no—
84C2×D52—41no—
85C13×M16—82no—
86C2×C8×C13—42no—
87C13×C4⋊C4—41no—
88C13×C4⋊C4—41no—
89C13×C4⋊C4—41no—
90C13×C4⋊C4—41no—
91C22⋊Dic13—42no—
92#6103—42no—
93#6103—81no—
94#6103—81no—
95#6103—81no—
96#6103—81no—
97C4⋊Dic13—41no—
98C4×Dic13—22no—
99C4×Dic13—41no—
100C2×#1055—42no—
101C2×#1055—82no—
102#2504—131no—
103#1463D1311yescharacteristic, complemented
104C2×#324—131no—
105#1324—132no—
106#1318—132no—
107C23×C13—22no—
108C23×C13—21no—
109C23×C13—21no—
110C23×C13—41no—
111C23×C13#9911yescharacteristic
112C23×C13#9911yescharacteristic
113C23×C13C2×C22⋊C411yescharacteristic
114C22×D13—41no—
115C22×D13—41no—
116C22×D13—41no—
117C22×D13—41no—
118C22×D13—41no—
119C22×D13—41no—
120C22×D13—41no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13—21no—
125C2×C4×C13—21no—
126C2×C4×C13—21no—
127C2×C4×C13—21no—
128C2×C4×C13—21no—
129C2×C4×C13—21no—
130C2×C4×C13—42no—
131C2×C4×C13—42no—
132C2×C4×C13—42no—
133C2×C4×C13—42no—
134C2×C4×C13—41no—
135C2×C4×C13—41no—
136C2×C4×C13—41no—
137C2×C4×C13—41no—
138C2×C4×C13—81no—
139C2×C4×C13—81no—
140C2×C4×C13#13112yes—
141C22⋊D13—82no—
142C22⋊D13—82no—
143C2×Dic13—41no—
144C2×Dic13—41no—
145C2×Dic13—41no—
146C2×Dic13—41no—
147C2×Dic13—41no—
148C2×Dic13—41no—
149C2×Dic13—41no—
150C2×Dic13—41no—
151C2×Dic13—41no—
152D52—82no—
153C8×C13—82no—
154#1055—82no—
155C2×#121—131no—
156C22×C4⋊C4C2×D1311yescharacteristic
157#407—21no—
158C2×C22⋊C8—261no—
159#397—261no—
160#397—261no—
161#390—131no—
162#390—131no—
163#386—261no—
164#386—261no—
165#382—131no—
166#382—131no—
167C4×C22⋊C4—131no—
168#324—21no—
169#324—132no—
170#324—261no—
171#324C2×D1312yes—
172C22×C13—21no—
173C22×C13—21no—
174C22×C13—21no—
175C22×C13—21no—
176C22×C13—21no—
177C22×C13—21no—
178C22×C13—21no—
179C22×C13—42no—
180C22×C13—42no—
181C22×C13#35512yes—
182C22×C13#40811yescharacteristic
183C22×C13C2×#9911yescharacteristic
184C22×C13#41311yescharacteristic
185C2×D13—81no—
186C2×D13—81no—
187C2×D13—81no—
188C2×D13—81no—
189C2×D13—81no—
190C2×D13—81no—
191C2×D13—81no—
192C4×C13—22no—
193C4×C13—41no—
194C4×C13—41no—
195C4×C13—41no—
196C4×C13—41no—
197C4×C13—41no—
198Dic13—81no—
199Dic13—81no—
200Dic13—81no—
201C22×D4—131no—
202C22×D4—261no—
203C23×C4C4×D1311yescharacteristic
204C23×C4D5211yescharacteristic
205C23×C4C22⋊D1311yescharacteristic
206C2×M16—41no—
207C22×C8—521no—
208#121—521no—
209#121—521no—
210C2×C4⋊C4—41no—
211C2×C4⋊C4—41no—
212C2×C4⋊C4—131no—
213C2×C4⋊C4C4×D1311yescharacteristic
214C2×C4⋊C4D5211yescharacteristic
215C2×C4⋊C4C22⋊D1311yescharacteristic
216C2×C4⋊C4C22×D1311yescharacteristic
217C2×C22⋊C4—261no—
218C2×C22⋊C4—261no—
219C2×C22⋊C4—261no—
220C2×C22⋊C4—261no—
221C2×C22⋊C4—261no—
222C2×C22⋊C4—261no—
223C2×C42—131no—
224C2×C42—131no—
225C22⋊C8—22no—
226C22⋊C8—41no—
227C22⋊C8—262no—
228C22⋊C8—521no—
229#95—261no—
230#95—261no—
231#95—261no—
232#95—261no—
233#95—261no—
234C2×C13—21no—
235C2×C13—21no—
236C2×C13—22no—
237C2×C13—41no—
238C2×C13#146811yescharacteristic
239C2×C13#212711yescharacteristic
240C2×C13C2×#35511yescharacteristic
241D13—161no—
242C24—261no—
243C24#610311yescharacteristic
244C2×D4—262no—
245C2×D4—521no—
246C2×D4—521no—
247C2×D4—522no—
248C2×D4—522no—
249C2×D4—521no—
250C2×D4—521no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—22no—
258C22×C4—41no—
259C22×C4—81no—
260C22×C4—81no—
261C22×C4—261no—
262C22×C4—261no—
263C22×C4—261no—
264C22×C4#610311yescharacteristic
265C22×C4#610311yescharacteristic
266C22×C4#610311yescharacteristic
267C22×C4C2×C4×D1311yescharacteristic
268C22×C4C2×D5211yescharacteristic
269C22×C4C2×C22⋊D1311yescharacteristic
270M16—82no—
271C2×C8—42no—
272C2×C8—522no—
273C2×C8—1042no—
274C4⋊C4—41no—
275C4⋊C4—41no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C4⋊C4—521no—
279C22⋊C4—522no—
280C22⋊C4—522no—
281C22⋊C4—1041no—
282C22⋊C4—1041no—
283C22⋊C4—1041no—
284C22⋊C4—1041no—
285C42—262no—
286C42—521no—
287C13#1155311yescharacteristic, complemented, Sylow
288C23—21no—
289C23—21no—
290C23—22no—
291C23—41no—
292C23—521no—
293C23—521no—
294C23—521no—
295C23—521no—
296C23—521no—
297C23—521no—
298C23—521no—
299C23#8804611yescharacteristic
300C23#8804611yescharacteristic
301C23C2×#610311yescharacteristic
302D4—1042no—
303D4—1042no—
304D4—1042no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—42no—
317C2×C4—42no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—81no—
323C2×C4—81no—
324C2×C4—521no—
325C2×C4—521no—
326C2×C4—521no—
327C2×C4—521no—
328C2×C4—521no—
329C2×C4—521no—
330C2×C4—521no—
331C2×C4—521no—
332C2×C4—521no—
333C2×C4#8816112yes—
334C8—82no—
335C8—1042no—
336C22—21no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—42no—
344C22—42no—
345C22—1041no—
346C22—1041no—
347C22—1041no—
348C22—1041no—
349C22—1041no—
350C22—1041no—
351C22—1041no—
352C22#1171806912yes—
353C22C2×#8804611yescharacteristic
354C22#1171879011yescharacteristic
355C22#1171879311yescharacteristic
356C4—22no—
357C4—41no—
358C4—41no—
359C4—41no—
360C4—41no—
361C4—41no—
362C4—1041no—
363C4—1041no—
364C4—1041no—
365C2—21no—
366C2—21no—
367C2—22no—
368C2—41no—
369C2—2081no—
370C2#1311318511yescharacteristic
371C2#1311650311yescharacteristic
372C2C2×#1171806911yescharacteristic
subgroupG/H
centerC22C2×#88046
commutatorC22×C4×C13C22×C4
FrattiniC2×C4⋊C4C22×D13
FittingC13×#1463C2
socleC22×C13C2×#99
prime radicalC2×#88184C4
cosocleC2×C13×C4⋊C4C23
hypercenter#1463D13
hypocenterC13#11553
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C24 ◁ C22×C4⋊C4 ◁ #1463

Complements

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

NH ≅ G/Ntype
2. C2×#11718120C2semidirect
3. #13112779C2semidirect
4. #13112767C2semidirect
5. C13×#1463C2semidirect
103. #1463D13semidirect
287. C13#11553semidirect

Maximal subgroups

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

subgroupindex
#131193242
C2×#117181202
#131127792
#131127672
C13×#14632
#1155313