Finite Group Databasebeta

← #15760260

Subgroups — #15760260

Order 3328.

532 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 532 conjugacy classes of subgroups — too many to draw. Only its 111 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#13123255C211yesmaximal, characteristic
2#13113438C212yesmaximal, complemented
3#13113170C211yesmaximal, characteristic
4#13112729C212yesmaximal, complemented
5C13×#2611C211yesmaximal, characteristic
6C2×C13×#125C2211yescharacteristic
7C2×C13×#117C2211yescharacteristic
8C22×#6099—21no—
9C13×#400C411yescharacteristic
10C13×#399C411yescharacteristic
11C13×#398C411yescharacteristic
12C13×#397C411yescharacteristic
13C13×#389—21no—
14C13×#388—21no—
15C13×#387—21no—
16C13×#385—21no—
17C13×#376C2211yescharacteristic
18#11718658—24no—
19#11718587C2212yes—
20C4×#6099—21no—
21C4×#6099C2212yes—
22#11718135—24no—
23#11718120—21no—
24#11718117—21no—
25C23×C4×C13D411yescharacteristic
26C13×#125—22no—
27C13×#125—22no—
28C13×#117—22no—
29C13×#117—22no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4—21no—
34C2×C13×C4⋊C4C2×C411yescharacteristic
35C2×C13×C4⋊C4C2×C411yescharacteristic
36C2×C13×C4⋊C4C2×C411yescharacteristic
37C2×C13×C4⋊C4D411yescharacteristic
38C2×C13×C22⋊C4—21no—
39C2×C13×C22⋊C4—21no—
40C2×C13×C22⋊C4C2×C411yescharacteristic
41C2×C13×C22⋊C4D411yescharacteristic
42C2×C42×C13—21no—
43C2×C42×C13D411yescharacteristic
44C2×C42×C13C2311yescharacteristic
45C2×#6099—22no—
46C2×#6099—24no—
47C2×#6099—24no—
48C2×#6099—22no—
49C22×#1055—22no—
50C13×#95—21no—
51C13×#95—21no—
52C13×#95—21no—
53C13×#95—21no—
54C13×#95—21no—
55C13×#95C2×C411yescharacteristic
56C13×#95C2×C411yescharacteristic
57C22⋊#1055—22no—
58C4⋊#1055—22no—
59#88043—22no—
60#88043—22no—
61#88043D414yes—
62C4×#1055—22no—
63C4×#1055—22no—
64#9388—131nomaximal, Sylow
65C24×C13C22⋊C411yescharacteristic
66C22×C4×C13—22no—
67C22×C4×C13—22no—
68C22×C4×C13—21no—
69C22×C4×C13—21no—
70C22×C4×C13—21no—
71C22×C4×C13—21no—
72C22×C4×C13—21no—
73C22×C4×C13—21no—
74C22×C4×C13C22⋊C411yescharacteristic
75C22×C4×C13C22⋊C411yescharacteristic
76C22×C4×C13C22⋊C411yescharacteristic
77C22×C4×C13C22×C411yescharacteristic
78C22×C4×C13C2×D411yescharacteristic
79C22×C4×C13C2×D411yescharacteristic
80C13×C4⋊C4—22no—
81C13×C4⋊C4—22no—
82C13×C4⋊C4—22no—
83C13×C4⋊C4—22no—
84C13×C4⋊C4—42no—
85C13×C4⋊C4—42no—
86C13×C4⋊C4—41no—
87C13×C4⋊C4—42no—
88C13×C4⋊C4—41no—
89C13×C22⋊C4—22no—
90C13×C22⋊C4—22no—
91C13×C22⋊C4—42no—
92C13×C22⋊C4—42no—
93C42×C13—21no—
94C42×C13—21no—
95C42×C13—42no—
96C42×C13C2×D412yes—
97C42×C13#4112yes—
98#6099—28no—
99#6099—24no—
100#6099—24no—
101C2×#1055—28no—
102C2×#1055—24no—
103C2×#1055—42no—
104#2873—131no—
105#2611D1311yescharacteristic
106#1528—132no—
107#1464—131no—
108#1300—132no—
109C23×C13—21no—
110C23×C13—21no—
111C23×C13—41no—
112C23×C13—41no—
113C23×C13#10412yes—
114C23×C13C2×C22⋊C411yescharacteristic
115C2×C4×C13—22no—
116C2×C4×C13—22no—
117C2×C4×C13—24no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—22no—
123C2×C4×C13—21no—
124C2×C4×C13—21no—
125C2×C4×C13—41no—
126C2×C4×C13—41no—
127C2×C4×C13—41no—
128C2×C4×C13—41no—
129C2×C4×C13—41no—
130C2×C4×C13—41no—
131C2×C4×C13—41no—
132C2×C4×C13—41no—
133C2×C4×C13—41no—
134C2×C4×C13—41no—
135C2×C4×C13—41no—
136C2×C4×C13—41no—
137C2×C4×C13—41no—
138C2×C4×C13—41no—
139C2×C4×C13—41no—
140C2×C4×C13#10412yes—
141C2×C4×C13C4×D412yes—
142C2×C4×C13#12011yescharacteristic
143C2×C4×C13#12112yes—
144C2×C4×C13#12311yescharacteristic
145#1055—28no—
146#1055—82no—
147C22×M16—261no—
148C2×#125C2×D1311yescharacteristic
149C2×#117C2×D1311yescharacteristic
150#432—132no—
151#405—264no—
152C4×M16—132no—
153C4×M16—261no—
154#400Dic1311yescharacteristic
155#399Dic1311yescharacteristic
156#398Dic1311yescharacteristic
157#397Dic1311yescharacteristic
158#389—21no—
159#388—21no—
160#387—21no—
161#385—21no—
162#376C2×D1311yescharacteristic
163#330—264no—
164#324—261no—
165#323—261no—
166C22×C13—21no—
167C22×C13—21no—
168C22×C13—22no—
169C22×C13—42no—
170C22×C13—41no—
171C22×C13—41no—
172C22×C13—81no—
173C22×C13#38611yescharacteristic
174C22×C13C2×#10411yescharacteristic
175C22×C13C2×#10411yescharacteristic
176C4×C13—22no—
177C4×C13—21no—
178C4×C13—22no—
179C4×C13—21no—
180C4×C13—22no—
181C4×C13—42no—
182C4×C13—41no—
183C4×C13—41no—
184C4×C13—81no—
185C4×C13—81no—
186C4×C13—81no—
187C23×C4C22⋊D1311yescharacteristic
188C2×M16—264no—
189C2×M16—264no—
190C2×M16—262no—
191C2×M16—262no—
192C22×C8—262no—
193#125—22no—
194#125—22no—
195#117—22no—
196#117—22no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4C2×Dic1311yescharacteristic
202C2×C4⋊C4C2×Dic1311yescharacteristic
203C2×C4⋊C4C2×Dic1311yescharacteristic
204C2×C4⋊C4C22⋊D1311yescharacteristic
205C2×C22⋊C4—21no—
206C2×C22⋊C4—21no—
207C2×C22⋊C4C2×Dic1311yescharacteristic
208C2×C22⋊C4C22⋊D1311yescharacteristic
209C2×C42—21no—
210C2×C42C22⋊D1311yescharacteristic
211C2×C42C22×D1311yescharacteristic
212C4⋊C8—262no—
213C22⋊C8—262no—
214#97—134no—
215#97—262no—
216#97—262no—
217C4×C8—262no—
218C4×C8—262no—
219#95—21no—
220#95—21no—
221#95—21no—
222#95—21no—
223#95—21no—
224#95C2×Dic1311yescharacteristic
225#95C2×Dic1311yescharacteristic
226C2×C13—21no—
227C2×C13—21no—
228C2×C13—42no—
229C2×C13#188411yescharacteristic
230C2×C13#189611yescharacteristic
231C2×C13#191511yescharacteristic
232C24C22⋊Dic1311yescharacteristic
233C22×C4—22no—
234C22×C4—22no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4C22⋊Dic1311yescharacteristic
242C22×C4C22⋊Dic1311yescharacteristic
243C22×C4C22⋊Dic1311yescharacteristic
244C22×C4C22×Dic1311yescharacteristic
245C22×C4C2×C22⋊D1311yescharacteristic
246C22×C4C2×C22⋊D1311yescharacteristic
247M16—268no—
248M16—264no—
249M16—264no—
250C2×C8—268no—
251C2×C8—264no—
252C2×C8—522no—
253C4⋊C4—22no—
254C4⋊C4—22no—
255C4⋊C4—22no—
256C4⋊C4—22no—
257C4⋊C4—42no—
258C4⋊C4—42no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—42no—
262C22⋊C4—22no—
263C22⋊C4—22no—
264C22⋊C4—42no—
265C22⋊C4—42no—
266C42—21no—
267C42—21no—
268C42—42no—
269C42D4×D1312yes—
270C42#612912yes—
271C13#938811yescharacteristic, complemented, Sylow
272C23—21no—
273C23—21no—
274C23—41no—
275C23—41no—
276C23#8807712yes—
277C23C2×C22⋊Dic1311yescharacteristic
278C2×C4—22no—
279C2×C4—22no—
280C2×C4—24no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—22no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4#8807712yes—
304C2×C4D4×Dic1312yes—
305C2×C4#8818911yescharacteristic
306C2×C4#8819111yescharacteristic
307C2×C4#8819312yes—
308C8—268no—
309C8—1042no—
310C22—21no—
311C22—21no—
312C22—22no—
313C22—42no—
314C22—41no—
315C22—41no—
316C22—81no—
317C22#1171888111yescharacteristic
318C22C2×#8807711yescharacteristic
319C22C2×#8807711yescharacteristic
320C4—22no—
321C4—21no—
322C4—22no—
323C4—21no—
324C4—22no—
325C4—42no—
326C4—41no—
327C4—41no—
328C4—81no—
329C4—81no—
330C4—81no—
331C2—21no—
332C2—21no—
333C2—42no—
334C2#1311522011yescharacteristic
335C2#1311528011yescharacteristic
336C2#1311538911yescharacteristic
subgroupG/H
centerC22#11718881
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#2611C2
socleC22×C13#386
prime radicalC24×C13C22⋊C4
cosocleC2×C42×C13C23
hypercenter#2611D13
hypocenterC13#9388
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2611

Complements

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

NH ≅ G/Ntype
2. #13113438C2semidirect
4. #13112729C2semidirect
271. C13#9388semidirect

Maximal subgroups

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

subgroupindex
#131232552
#131134382
#131131702
#131127292
C13×#26112
#938813