Finite Group Databasebeta

← #15773584

Subgroups — #15773584

Order 3328.

486 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 486 conjugacy classes of subgroups — too many to draw. Only its 87 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#13114913C211yesmaximal, characteristic, complemented
2#13113170C211yesmaximal, characteristic, complemented
3#13112836C212yesmaximal, complemented
4#13112833C212yesmaximal
5C13×#2392C211yesmaximal, characteristic
6C2×C4×D4×C13—21no—
7C2×C4×D4×C13C411yescharacteristic, complemented
8C2×C13×#117C2211yescharacteristic
9C13×#398C411yescharacteristic, complemented
10C13×#397C2211yescharacteristic
11C13×#396—21no—
12C13×#394—21no—
13C13×#394C411yescharacteristic, complemented
14C13×#392C2211yescharacteristic
15C4×C13×C4⋊C4C411yescharacteristic, complemented
16C4×C13×C22⋊C4—21no—
17#11718872—21no—
18#11718587—21no—
19#11718120—21no—
20#11718118—21no—
21#11718118C2212yes—
22#11718117C2212yes—
23C22×D4×C13—21no—
24C22×D4×C13C2×C411yescharacteristic
25C23×C4×C13—21no—
26C23×C4×C13D411yescharacteristic
27C4×D4×C13—41no—
28C4×D4×C13—41no—
29C4×D4×C13—44no—
30C13×#117—41no—
31C13×#117—41no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4—21no—
34C2×C13×C4⋊C4C2×C411yescharacteristic
35C2×C13×C4⋊C4C2×C411yescharacteristic
36C2×C13×C4⋊C4D411yescharacteristic
37C2×C13×C22⋊C4—21no—
38C2×C13×C22⋊C4—21no—
39C2×C13×C22⋊C4—21no—
40C2×C13×C22⋊C4—21no—
41C2×C13×C22⋊C4—21no—
42C2×C13×C22⋊C4D411yescharacteristic
43C2×C13×C22⋊C4C2311yescharacteristic
44C2×C42×C13—21no—
45C2×C42×C13C2×C411yescharacteristic
46C2×C42×C13D411yescharacteristic
47C2×C22⋊Dic13—22no—
48C13×#95—21no—
49C13×#95—21no—
50C13×#95C2×C411yescharacteristic
51C13×#95C2×C411yescharacteristic
52#88071—41no—
53#88071—41no—
54C22⋊#1055—22no—
55C4⋊#1055—41no—
56#88043—41no—
57#11798—131nomaximal, Sylow
58C24×C13—21no—
59C24×C13C2×D411yescharacteristic
60C2×D4×C13—41no—
61C2×D4×C13—42no—
62C2×D4×C13—42no—
63C2×D4×C13—42no—
64C2×D4×C13—42no—
65C22×C4×C13—21no—
66C22×C4×C13—22no—
67C22×C4×C13—21no—
68C22×C4×C13—21no—
69C22×C4×C13—21no—
70C22×C4×C13—21no—
71C22×C4×C13—41no—
72C22×C4×C13—42no—
73C22×C4×C13—42no—
74C22×C4×C13—41no—
75C22×C4×C13—41no—
76C22×C4×C13C22⋊C411yescharacteristic
77C22×C4×C13C22⋊C411yescharacteristic
78C22×C4×C13C22⋊C411yescharacteristic
79C22×C4×C13C22⋊C411yescharacteristic
80C22×C4×C13C22×C411yescharacteristic
81C22×C4×C13C2×D411yescharacteristic
82C22×Dic13—42no—
83C13×C4⋊C4—41no—
84C13×C4⋊C4—41no—
85C13×C4⋊C4—41no—
86C13×C4⋊C4—42no—
87C13×C4⋊C4—42no—
88C13×C22⋊C4—41no—
89C13×C22⋊C4—41no—
90C13×C22⋊C4—42no—
91C13×C22⋊C4—42no—
92C13×C22⋊C4—42no—
93C13×C22⋊C4—42no—
94C13×C22⋊C4—42no—
95C42×C13—21no—
96C42×C13—21no—
97C42×C13—21no—
98C42×C13—21no—
99C42×C13—42no—
100C22⋊Dic13—42no—
101C22⋊Dic13—42no—
102C2×#1055—42no—
103#2392D1311yescharacteristic
104#1820—131no—
105#1464—131no—
106#1344—132no—
107#1343—132no—
108C23×C13—21no—
109C23×C13—21no—
110C23×C13—22no—
111C23×C13—41no—
112C23×C13—41no—
113C23×C13—41no—
114C23×C13—41no—
115C23×C13—41no—
116C23×C13—41no—
117C23×C13—41no—
118C23×C13—41no—
119C23×C13C2×C22⋊C411yescharacteristic
120C23×C13AGL(1,ℤ/8)12yes—
121D4×C13—48no—
122D4×C13—42no—
123D4×C13—42no—
124C2×C4×C13—21no—
125C2×C4×C13—21no—
126C2×C4×C13—22no—
127C2×C4×C13—21no—
128C2×C4×C13—21no—
129C2×C4×C13—21no—
130C2×C4×C13—21no—
131C2×C4×C13—21no—
132C2×C4×C13—21no—
133C2×C4×C13—21no—
134C2×C4×C13—42no—
135C2×C4×C13—42no—
136C2×C4×C13—41no—
137C2×C4×C13—41no—
138C2×C4×C13—41no—
139C2×C4×C13—41no—
140C2×C4×C13—41no—
141C2×C4×C13—41no—
142C2×C4×C13—41no—
143C2×C4×C13—41no—
144C2×C4×C13—41no—
145C2×C4×C13—41no—
146C2×C4×C13—41no—
147C2×C4×C13—41no—
148C2×C4×C13—82no—
149C2×C4×C13—82no—
150C2×C4×C13#9911yescharacteristic
151C2×C4×C13#9911yescharacteristic
152C2×Dic13—82no—
153C2×Dic13—82no—
154C2×Dic13—82no—
155#1055—82no—
156C2×C4×D4—21no—
157C2×C4×D4Dic1311yescharacteristic, complemented
158C2×#117C2×D1311yescharacteristic
159#432—261no—
160#398Dic1311yescharacteristic, complemented
161#397C2×D1311yescharacteristic
162#396—21no—
163#394—21no—
164#394Dic1311yescharacteristic, complemented
165#392C2×D1311yescharacteristic
166#381—261no—
167C4×C4⋊C4Dic1311yescharacteristic, complemented
168C4×C22⋊C4—21no—
169#342—132no—
170#342—261no—
171#324—261no—
172#323—132no—
173C22×C13—21no—
174C22×C13—21no—
175C22×C13—22no—
176C22×C13—42no—
177C22×C13—42no—
178C22×C13—42no—
179C22×C13—41no—
180C22×C13—41no—
181C22×C13—42no—
182C22×C13—81no—
183C22×C13—81no—
184C22×C13—81no—
185C22×C13—81no—
186C22×C13—81no—
187C22×C13C2×#9911yescharacteristic
188C22×C13#41811yescharacteristic
189C22×C13#42111yescharacteristic
190C4×C13—21no—
191C4×C13—21no—
192C4×C13—42no—
193C4×C13—41no—
194C4×C13—41no—
195C4×C13—41no—
196C4×C13—41no—
197C4×C13—41no—
198C4×C13—81no—
199C4×C13—81no—
200Dic13—162no—
201C22×D4—21no—
202C22×D4C2×Dic1311yescharacteristic
203C23×C4—21no—
204C23×C4C22⋊D1311yescharacteristic
205C4×D4—41no—
206C4×D4—41no—
207C4×D4—44no—
208#117—41no—
209#117—41no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4C2×Dic1311yescharacteristic
213C2×C4⋊C4C2×Dic1311yescharacteristic
214C2×C4⋊C4C22⋊D1311yescharacteristic
215C2×C22⋊C4—21no—
216C2×C22⋊C4—21no—
217C2×C22⋊C4—21no—
218C2×C22⋊C4—21no—
219C2×C22⋊C4—21no—
220C2×C22⋊C4—262no—
221C2×C22⋊C4C22⋊D1311yescharacteristic
222C2×C22⋊C4C22×D1311yescharacteristic
223C2×C42—21no—
224C2×C42C2×Dic1311yescharacteristic
225C2×C42C22⋊D1311yescharacteristic
226C4⋊C8—521no—
227C22⋊C8—262no—
228#97—521no—
229#95—21no—
230#95—21no—
231#95—521no—
232#95—521no—
233#95C2×Dic1311yescharacteristic
234#95C2×Dic1311yescharacteristic
235C2×C13—21no—
236C2×C13—21no—
237C2×C13—42no—
238C2×C13—82no—
239C2×C13#151011yescharacteristic
240C2×C13#212011yescharacteristic
241C2×C13#212611yescharacteristic
242C24—21no—
243C24C2×C22⋊D1311yescharacteristic
244C2×D4—41no—
245C2×D4—42no—
246C2×D4—42no—
247C2×D4—42no—
248C2×D4—42no—
249C22×C4—22no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—41no—
256C22×C4—42no—
257C22×C4—42no—
258C22×C4—41no—
259C22×C4—41no—
260C22×C4—522no—
261C22×C4C22⋊Dic1311yescharacteristic
262C22×C4C22⋊Dic1311yescharacteristic
263C22×C4C22⋊Dic1311yescharacteristic
264C22×C4C22⋊Dic1311yescharacteristic
265C22×C4C22×Dic1311yescharacteristic
266C22×C4C2×C22⋊D1311yescharacteristic
267C2×C8—522no—
268C4⋊C4—41no—
269C4⋊C4—41no—
270C4⋊C4—41no—
271C4⋊C4—42no—
272C4⋊C4—42no—
273C22⋊C4—41no—
274C22⋊C4—41no—
275C22⋊C4—42no—
276C22⋊C4—42no—
277C22⋊C4—42no—
278C22⋊C4—42no—
279C22⋊C4—42no—
280C22⋊C4—522no—
281C22⋊C4—522no—
282C42—21no—
283C42—21no—
284C42—21no—
285C42—21no—
286C42—42no—
287C13#1179811yescharacteristic, complemented, Sylow
288C23—21no—
289C23—21no—
290C23—22no—
291C23—41no—
292C23—41no—
293C23—41no—
294C23—41no—
295C23—41no—
296C23—41no—
297C23—41no—
298C23—41no—
299C23#8818612yes—
300C23C2×C22⋊Dic1311yescharacteristic
301D4—42no—
302D4—48no—
303D4—42no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—22no—
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—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—82no—
329C2×C4—82no—
330C2×C4—1042no—
331C2×C4—1042no—
332C2×C4—1042no—
333C2×C4#8807411yescharacteristic
334C2×C4#8807411yescharacteristic
335C8—1042no—
336C22—21no—
337C22—21no—
338C22—22no—
339C22—42no—
340C22—42no—
341C22—42no—
342C22—41no—
343C22—41no—
344C22—42no—
345C22—81no—
346C22—81no—
347C22—81no—
348C22—81no—
349C22—81no—
350C22#1171887611yescharacteristic
351C22C2×#8807411yescharacteristic
352C22#1171889711yescharacteristic
353C4—21no—
354C4—21no—
355C4—42no—
356C4—41no—
357C4—41no—
358C4—41no—
359C4—41no—
360C4—41no—
361C4—81no—
362C4—81no—
363C4—2082no—
364C2—21no—
365C2—21no—
366C2—42no—
367C2—82no—
368C2#1311336511yescharacteristic
369C2#1311647711yescharacteristic
370C2#1311650111yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC22×C4×C13C22×C4
FrattiniC2×C22⋊C4C22×D13
FittingC13×#2392C2
socleC22×C13C2×#99
prime radicalC13×#392C22
cosocleC2×C13×C22⋊C4C23
hypercenter#2392D13
hypocenterC13#11798
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #2392

Complements

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

NH ≅ G/Ntype
1. #13114913C2semidirect
2. #13113170C2semidirect
3. #13112836C2semidirect
7. C2×C4×D4×C13C4semidirect
9. C13×#398C4semidirect
13. C13×#394C4semidirect
15. C4×C13×C4⋊C4C4semidirect
157. C2×C4×D4Dic13semidirect
160. #398Dic13semidirect
164. #394Dic13semidirect
167. C4×C4⋊C4Dic13semidirect
287. C13#11798semidirect

Maximal subgroups

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

subgroupindex
#131149132
#131131702
#131128362
#131128332
C13×#23922
#1179813