Finite Group Databasebeta

← #15773129

Subgroups — #15773129

Order 3328.

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

normal subgroups only

This group has 552 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#13120586C211yesmaximal, characteristic
2#13113150C211yesmaximal, characteristic, complemented
3#13112838C214yesmaximal, complemented
4C13×#1742C211yesmaximal, characteristic, complemented
5C22×C13×M16—21no—
6C2×C13×#117C2211yescharacteristic
7C2×#88184—21no—
8C2×#88128C411yescharacteristic
9#11718652—21no—
10#11718652C2212yes—
11#11718621—21no—
12#11718621C412yes—
13#11718600—21no—
14#11718597C411yescharacteristic
15#11718586—21no—
16C13×#343—21no—
17C13×#343C2212yes—
18#11718120C2212yes—
19#11718117—21no—
20C23×C4×C13D411yescharacteristic
21C22×C22⋊D13—22no—
22C22×D52—21no—
23C22×D52—21no—
24C22×D52C2×C412yes—
25C2×C13×M16—24no—
26C2×C13×M16—22no—
27C2×C13×M16—41no—
28C2×C13×M16—42no—
29C22×C8×C13—41no—
30C13×#117—41no—
31C13×#117—41no—
32C2×C13×C4⋊C4D411yescharacteristic
33C2×C13×C4⋊C4C2311yescharacteristic
34C2×C13×C22⋊C4C2×C411yescharacteristic
35C2×C13×C22⋊C4D411yescharacteristic
36C2×C42×C13C2×C411yescharacteristic
37C2×C42×C13D411yescharacteristic
38#88184—42no—
39#88184—42no—
40C2×#6103—22no—
41C2×#6103—22no—
42C2×#6103—22no—
43C2×C4⋊Dic13—21no—
44#88128—41no—
45#88128—41no—
46#88071—21no—
47#88071C2×C412yes—
48C22⋊#1055—22no—
49C4⋊#1055—41no—
50C4×#1055—41no—
51#11699—131nomaximal, Sylow
52C24×C13C22⋊C411yescharacteristic
53C23×D13—22no—
54C22×C4×C13—21no—
55C22×C4×C13—21no—
56C22×C4×C13—22no—
57C22×C4×C13C22⋊C411yescharacteristic
58C22×C4×C13C22⋊C411yescharacteristic
59C22×C4×C13C22⋊C411yescharacteristic
60C22×C4×C13D812yes—
61C22×C4×C13SD1612yes—
62C22×C4×C13C22×C411yescharacteristic
63C22×C4×C13C2×D411yescharacteristic
64C22×C4×C13C2×D411yescharacteristic
65C2×C22⋊D13—44no—
66C2×C22⋊D13—82no—
67C2×C22⋊D13—82no—
68C22×Dic13—22no—
69C2×D52—42no—
70C2×D52—42no—
71C2×D52—41no—
72C2×D52—41no—
73C2×D52—42no—
74C2×D52—42no—
75C2×D52—82no—
76C2×D52—82no—
77C13×M16—24no—
78C13×M16—44no—
79C13×M16—42no—
80C2×C8×C13—42no—
81C2×C8×C13—44no—
82C13×C4⋊C4—41no—
83C13×C4⋊C4—41no—
84C13×C22⋊C4—41no—
85C13×C22⋊C4—41no—
86C42×C13—21no—
87C42×C13—21no—
88C42×C13—21no—
89C42×C13—21no—
90#6103—42no—
91#6103—42no—
92#6103—82no—
93#6103—82no—
94C4⋊Dic13—42no—
95C2×#1055—42no—
96#2619—131no—
97#1742D1311yescharacteristic, complemented
98#1458—131no—
99#1345—134no—
100C23×C13—21no—
101C23×C13—21no—
102C23×C13—41no—
103C23×C13—41no—
104C23×C13#10212yes—
105C23×C13C2×C22⋊C411yescharacteristic
106C22×D13—42no—
107C22×D13—42no—
108C22×D13—42no—
109C22×D13—42no—
110C22×D13—42no—
111C22×D13—42no—
112C22×D13—42no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—22no—
116C2×C4×C13—22no—
117C2×C4×C13—22no—
118C2×C4×C13—22no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—41no—
124C2×C4×C13—41no—
125C2×C4×C13—41no—
126C2×C4×C13—41no—
127C2×C4×C13#9911yescharacteristic
128C2×C4×C13#9911yescharacteristic
129C2×C4×C13#10212yes—
130C2×C4×C13#10412yes—
131C2×C4×C13C2×D811yescharacteristic
132C2×C4×C13C2×SD1611yescharacteristic
133C22⋊D13—88no—
134C2×Dic13—42no—
135C2×Dic13—42no—
136C2×Dic13—42no—
137D52—84no—
138D52—84no—
139D52—82no—
140D52—82no—
141C8×C13—44no—
142#1055—82no—
143C22×M16—21no—
144C2×#127—131no—
145C2×#121—261no—
146C2×#117C2×D1311yescharacteristic
147#431—261no—
148#394—132no—
149#394—261no—
150#392—132no—
151#392—261no—
152#390—261no—
153#382—131no—
154#343—21no—
155#343C2×D1312yes—
156#324—132no—
157#323—261no—
158C22×C13—21no—
159C22×C13—21no—
160C22×C13—22no—
161C22×C13—42no—
162C22×C13—41no—
163C22×C13—41no—
164C22×C13—81no—
165C22×C13C2×#9911yescharacteristic
166C22×C13C2×#10211yescharacteristic
167C22×C13C2×#10411yescharacteristic
168C2×D13—82no—
169C2×D13—82no—
170C2×D13—82no—
171C2×D13—82no—
172C2×D13—82no—
173C2×D13—82no—
174C2×D13—82no—
175C4×C13—21no—
176C4×C13—21no—
177C4×C13—41no—
178C4×C13—41no—
179C4×C13—41no—
180C4×C13—41no—
181C4×C13#32712yes—
182C4×C13#32712yes—
183Dic13—82no—
184C22×D4—132no—
185C22×D4—262no—
186C22×D4—261no—
187C22×D4—261no—
188C23×C4C22⋊D1311yescharacteristic
189C2×M16—24no—
190C2×M16—22no—
191C2×M16—41no—
192C2×M16—42no—
193C22×C8—41no—
194#127—521no—
195#127—521no—
196#121—522no—
197#121—522no—
198#117—41no—
199#117—41no—
200C2×C4⋊C4—261no—
201C2×C4⋊C4C22⋊D1311yescharacteristic
202C2×C4⋊C4C22×D1311yescharacteristic
203C2×C22⋊C4—262no—
204C2×C22⋊C4—262no—
205C2×C22⋊C4—262no—
206C2×C22⋊C4C4×D1311yescharacteristic
207C2×C22⋊C4D5211yescharacteristic
208C2×C42C4×D1311yescharacteristic
209C2×C42D5211yescharacteristic
210C4⋊C8—521no—
211C22⋊C8—262no—
212C4×C8—521no—
213#95—132no—
214#95—261no—
215C2×C13—21no—
216C2×C13—21no—
217C2×C13—42no—
218C2×C13C2×#32711yescharacteristic
219C2×C13#212211yescharacteristic
220C2×C13#213411yescharacteristic
221D13—162no—
222C24—262no—
223C24#610311yescharacteristic
224C2×D4—522no—
225C2×D4—522no—
226C2×D4—524no—
227C2×D4—522no—
228C2×D4—521no—
229C2×D4—521no—
230C2×D4—522no—
231C2×D4—1042no—
232C2×D4—1042no—
233C2×D4—1042no—
234C2×D4—1042no—
235C22×C4—22no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—262no—
239C22×C4#610311yescharacteristic
240C22×C4#610311yescharacteristic
241C22×C4#610311yescharacteristic
242C22×C4#610412yes—
243C22×C4#610612yes—
244C22×C4C2×C4×D1311yescharacteristic
245C22×C4C2×D5211yescharacteristic
246C22×C4C2×C22⋊D1311yescharacteristic
247M16—24no—
248M16—44no—
249M16—42no—
250C2×C8—42no—
251C2×C8—44no—
252C2×C8—522no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—522no—
256C22⋊C4—41no—
257C22⋊C4—41no—
258C22⋊C4—522no—
259C22⋊C4—522no—
260C22⋊C4—1042no—
261C22⋊C4—1042no—
262C42—21no—
263C42—21no—
264C42—21no—
265C42—21no—
266C13#1169911yescharacteristic, complemented, Sylow
267C23—21no—
268C23—21no—
269C23—41no—
270C23—41no—
271C23—522no—
272C23—522no—
273C23—522no—
274C23—522no—
275C23—522no—
276C23—522no—
277C23—522no—
278C23#8804912yes—
279C23C2×#610311yescharacteristic
280D4—1044no—
281D4—1044no—
282D4—1048no—
283D4—1042no—
284D4—1042no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—22no—
288C2×C4—22no—
289C2×C4—22no—
290C2×C4—22no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—522no—
300C2×C4—522no—
301C2×C4—522no—
302C2×C4#8804512yes—
303C2×C4#8804611yescharacteristic
304C2×C4#8804611yescharacteristic
305C2×C4#8804912yes—
306C2×C4C2×#610411yescharacteristic
307C2×C4C2×#610611yescharacteristic
308C8—44no—
309C8—1042no—
310C22—21no—
311C22—21no—
312C22—22no—
313C22—42no—
314C22—41no—
315C22—41no—
316C22—81no—
317C22—1042no—
318C22—1042no—
319C22—1042no—
320C22—1042no—
321C22—1042no—
322C22—1042no—
323C22—1042no—
324C22C2×#8804511yescharacteristic
325C22C2×#8804611yescharacteristic
326C22C2×#8804911yescharacteristic
327C4—21no—
328C4—21no—
329C4—41no—
330C4—41no—
331C4—41no—
332C4—41no—
333C4—1042no—
334C4#1171804312yes—
335C4#1171804312yes—
336C2—21no—
337C2—21no—
338C2—42no—
339C2—2082no—
340C2C2×#1171804311yescharacteristic
341C2#1311648711yescharacteristic
342C2#1311652711yescharacteristic
subgroupG/H
centerC22C2×#88046
commutatorC22×C4×C13C22×C4
FrattiniC2×C4⋊C4C22×D13
FittingC13×#1742C2
socleC22×C13C2×#99
prime radical#13120586C2
cosocleC2×C13×C4⋊C4C23
hypercenter#1742D13
hypocenterC13#11699
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #1742

Complements

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

NH ≅ G/Ntype
2. #13113150C2semidirect
3. #13112838C2semidirect
4. C13×#1742C2semidirect
97. #1742D13semidirect
266. C13#11699semidirect

Maximal subgroups

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

subgroupindex
#131205862
#131131502
#131128382
C13×#17422
#1169913