Finite Group Databasebeta

← #15760270

Subgroups — #15760270

Order 3328.

446 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 446 conjugacy classes of subgroups — too many to draw. Only its 103 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#13123474C211yesmaximal, characteristic
2#13113438C212yesmaximal, complemented
3#13113170C211yesmaximal, characteristic
4#13112729C212yesmaximal, complemented
5C13×#2611C211yesmaximal, characteristic
6C2×C13×#125C2211yescharacteristic
7C2×C13×#117C2211yescharacteristic
8C13×#400C411yescharacteristic
9C13×#399C411yescharacteristic
10C13×#398C411yescharacteristic
11C13×#397C411yescharacteristic
12C13×#389—21no—
13C13×#388—21no—
14C13×#387—21no—
15C13×#385—21no—
16C13×#376C2211yescharacteristic
17#11718868—21no—
18#11718661—24no—
19#11718587C2212yes—
20#11718585—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—
46C13×#95—21no—
47C13×#95—21no—
48C13×#95—21no—
49C13×#95—21no—
50C13×#95—21no—
51C13×#95C2×C411yescharacteristic
52C13×#95C2×C411yescharacteristic
53C22⋊#1055—24no—
54C22⋊#1055—22no—
55C4⋊#1055—24no—
56C4⋊#1055—22no—
57#88043—22no—
58#88043D414yes—
59C4×#1055—22no—
60#9390—131nomaximal, Sylow
61C24×C13C22⋊C411yescharacteristic
62C22×C4×C13—21no—
63C22×C4×C13—21no—
64C22×C4×C13—21no—
65C22×C4×C13—21no—
66C22×C4×C13—21no—
67C22×C4×C13—21no—
68C22×C4×C13—41no—
69C22×C4×C13—41no—
70C22×C4×C13C22⋊C411yescharacteristic
71C22×C4×C13C22⋊C411yescharacteristic
72C22×C4×C13C22⋊C411yescharacteristic
73C22×C4×C13C22×C411yescharacteristic
74C22×C4×C13C2×D411yescharacteristic
75C22×C4×C13C2×D411yescharacteristic
76C13×C4⋊C4—22no—
77C13×C4⋊C4—22no—
78C13×C4⋊C4—22no—
79C13×C4⋊C4—22no—
80C13×C4⋊C4—42no—
81C13×C4⋊C4—42no—
82C13×C4⋊C4—41no—
83C13×C4⋊C4—42no—
84C13×C4⋊C4—41no—
85C13×C22⋊C4—22no—
86C13×C22⋊C4—22no—
87C13×C22⋊C4—42no—
88C13×C22⋊C4—42no—
89C42×C13—21no—
90C42×C13—21no—
91C42×C13—42no—
92C42×C13C2×D412yes—
93C42×C13#4112yes—
94#6099—42no—
95#6099—42no—
96C2×#1055—24no—
97C2×#1055—42no—
98#2921—131no—
99#2611D1311yescharacteristic
100#1528—132no—
101#1464—131no—
102#1300—132no—
103C23×C13—21no—
104C23×C13—21no—
105C23×C13—21no—
106C23×C13—41no—
107C23×C13—41no—
108C23×C13C2×C22⋊C411yescharacteristic
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—22no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—41no—
118C2×C4×C13—41no—
119C2×C4×C13—42no—
120C2×C4×C13—42no—
121C2×C4×C13—41no—
122C2×C4×C13—41no—
123C2×C4×C13—41no—
124C2×C4×C13—41no—
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×C13C4×D412yes—
135C2×C4×C13#12011yescharacteristic
136C2×C4×C13#12112yes—
137C2×C4×C13#12311yescharacteristic
138#1055—44no—
139#1055—82no—
140C2×#125C2×D1311yescharacteristic
141C2×#117C2×D1311yescharacteristic
142#433—264no—
143#432—132no—
144#423—261no—
145#407—261no—
146C4×M16—132no—
147#400Dic1311yescharacteristic
148#399Dic1311yescharacteristic
149#398Dic1311yescharacteristic
150#397Dic1311yescharacteristic
151#389—21no—
152#388—21no—
153#387—21no—
154#385—21no—
155#376C2×D1311yescharacteristic
156#330—264no—
157#324—261no—
158#323—261no—
159C22×C13—21no—
160C22×C13—21no—
161C22×C13—42no—
162C22×C13—41no—
163C22×C13—41no—
164C22×C13—41no—
165C22×C13—81no—
166C22×C13#38611yescharacteristic
167C22×C13#42111yescharacteristic
168C22×C13#42111yescharacteristic
169C4×C13—22no—
170C4×C13—21no—
171C4×C13—21no—
172C4×C13—22no—
173C4×C13—42no—
174C4×C13—41no—
175C4×C13—41no—
176C4×C13—41no—
177C4×C13—81no—
178C4×C13—81no—
179C4×C13—81no—
180C23×C4C22⋊D1311yescharacteristic
181C2×M16—262no—
182#125—22no—
183#125—22no—
184#117—22no—
185#117—22no—
186C2×C4⋊C4—21no—
187C2×C4⋊C4—21no—
188C2×C4⋊C4—21no—
189C2×C4⋊C4—21no—
190C2×C4⋊C4C2×Dic1311yescharacteristic
191C2×C4⋊C4C2×Dic1311yescharacteristic
192C2×C4⋊C4C2×Dic1311yescharacteristic
193C2×C4⋊C4C22⋊D1311yescharacteristic
194C2×C22⋊C4—21no—
195C2×C22⋊C4—21no—
196C2×C22⋊C4C2×Dic1311yescharacteristic
197C2×C22⋊C4C22⋊D1311yescharacteristic
198C2×C42—21no—
199C2×C42C22⋊D1311yescharacteristic
200C2×C42C22×D1311yescharacteristic
201C4⋊C8—264no—
202C4⋊C8—262no—
203C22⋊C8—264no—
204C22⋊C8—262no—
205#97—134no—
206#97—262no—
207C4×C8—262no—
208#95—21no—
209#95—21no—
210#95—21no—
211#95—21no—
212#95—21no—
213#95C2×Dic1311yescharacteristic
214#95C2×Dic1311yescharacteristic
215C2×C13—21no—
216C2×C13—21no—
217C2×C13—81no—
218C2×C13#188411yescharacteristic
219C2×C13#189711yescharacteristic
220C2×C13#191511yescharacteristic
221C24C22⋊Dic1311yescharacteristic
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—41no—
229C22×C4—41no—
230C22×C4C22⋊Dic1311yescharacteristic
231C22×C4C22⋊Dic1311yescharacteristic
232C22×C4C22⋊Dic1311yescharacteristic
233C22×C4C22×Dic1311yescharacteristic
234C22×C4C2×C22⋊D1311yescharacteristic
235C22×C4C2×C22⋊D1311yescharacteristic
236M16—522no—
237M16—522no—
238C2×C8—264no—
239C2×C8—522no—
240C4⋊C4—22no—
241C4⋊C4—22no—
242C4⋊C4—22no—
243C4⋊C4—22no—
244C4⋊C4—42no—
245C4⋊C4—42no—
246C4⋊C4—41no—
247C4⋊C4—41no—
248C4⋊C4—42no—
249C22⋊C4—22no—
250C22⋊C4—22no—
251C22⋊C4—42no—
252C22⋊C4—42no—
253C42—21no—
254C42—21no—
255C42—42no—
256C42D4×D1312yes—
257C42#612912yes—
258C13#939011yescharacteristic, complemented, Sylow
259C23—21no—
260C23—21no—
261C23—21no—
262C23—41no—
263C23—41no—
264C23C2×C22⋊Dic1311yescharacteristic
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—22no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—42no—
276C2×C4—42no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4D4×Dic1312yes—
291C2×C4#8818911yescharacteristic
292C2×C4#8819111yescharacteristic
293C2×C4#8819312yes—
294C8—524no—
295C8—1042no—
296C22—21no—
297C22—21no—
298C22—42no—
299C22—41no—
300C22—41no—
301C22—41no—
302C22—81no—
303C22#1171888111yescharacteristic
304C22#1171889711yescharacteristic
305C22#1171889711yescharacteristic
306C4—22no—
307C4—21no—
308C4—21no—
309C4—22no—
310C4—42no—
311C4—41no—
312C4—41no—
313C4—41no—
314C4—81no—
315C4—81no—
316C4—81no—
317C2—21no—
318C2—21no—
319C2—81no—
320C2#1311522011yescharacteristic
321C2#1311528511yescharacteristic
322C2#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#9390
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
258. C13#9390semidirect

Maximal subgroups

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

subgroupindex
#131234742
#131134382
#131131702
#131127292
C13×#26112
#939013