Finite Group Databasebeta

← #15760934

Subgroups — #15760934

Order 3328.

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

normal subgroups only

This group has 518 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#13123877C211yesmaximal, characteristic
2#13113174C211yesmaximal, characteristic
3#13113166C212yesmaximal, complemented
4#13112742C212yesmaximal, complemented
5C13×#2579C211yesmaximal, characteristic
6C2×C4×D4×C13C2211yescharacteristic
7C22×C13×C4⋊C4C2211yescharacteristic
8C13×#398—21no—
9C13×#396—21no—
10C13×#387—21no—
11C13×#386C411yescharacteristic
12C13×#386C411yescharacteristic
13C13×#385—21no—
14C13×#385C411yescharacteristic
15C13×#385C411yescharacteristic
16C13×#380C2211yescharacteristic
17#11718868—21no—
18#11718868C2212yes—
19#11718868C2212yes—
20#11718673—24no—
21#11718586—21no—
22#11718120—21no—
23#11718120—24no—
24#11718117—21no—
25C22×D4×C13C2×C411yescharacteristic
26C23×C4×C13C2×C411yescharacteristic
27C23×C4×C13C2×C411yescharacteristic
28C23×C4×C13D411yescharacteristic
29C23×C4×C13C2311yescharacteristic
30C4×D4×C13—22no—
31C4×D4×C13—22no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4—21no—
34C2×C13×C4⋊C4—21no—
35C2×C13×C4⋊C4—22no—
36C2×C13×C4⋊C4—22no—
37C2×C13×C4⋊C4—21no—
38C2×C13×C4⋊C4—21no—
39C2×C13×C4⋊C4D411yescharacteristic
40C2×C13×C22⋊C4—21no—
41C2×C13×C22⋊C4—21no—
42C2×C13×C22⋊C4C2×C411yescharacteristic
43C2×C13×C22⋊C4C2×C411yescharacteristic
44C2×C13×C22⋊C4C2×C411yescharacteristic
45C2×C13×C22⋊C4D411yescharacteristic
46C2×C42×C13D411yescharacteristic
47C2×#6099—22no—
48C2×#6099—22no—
49C2×#6099—22no—
50C13×#95—21no—
51C13×#95—21no—
52C13×#95—21no—
53C13×#95—21no—
54C13×#95—21no—
55C22⋊#1055—22no—
56C22⋊#1055—22no—
57C22⋊#1055—22no—
58C22⋊#1055—22no—
59C22⋊#1055D414yes—
60C4⋊#1055—22no—
61C4×#1055—22no—
62#9518—131nomaximal, Sylow
63C24×C13C22⋊C411yescharacteristic
64C24×C13C22×C411yescharacteristic
65C2×D4×C13—22no—
66C2×D4×C13—22no—
67C2×D4×C13—41no—
68C22×C4×C13—21no—
69C22×C4×C13—22no—
70C22×C4×C13—21no—
71C22×C4×C13—21no—
72C22×C4×C13—21no—
73C22×C4×C13—21no—
74C22×C4×C13—21no—
75C22×C4×C13—22no—
76C22×C4×C13—42no—
77C22×C4×C13—81no—
78C22×C4×C13—81no—
79C22×C4×C13—81no—
80C22×C4×C13C22⋊C411yescharacteristic
81C22×C4×C13C22⋊C411yescharacteristic
82C22×C4×C13C22⋊C411yescharacteristic
83C22×C4×C13C2×D412yes—
84C22×C4×C13C2×D411yescharacteristic
85C22×C4×C13C2×D411yescharacteristic
86C22×C4×C13#4112yes—
87C13×C4⋊C4—22no—
88C13×C4⋊C4—42no—
89C13×C4⋊C4—41no—
90C13×C4⋊C4—42no—
91C13×C4⋊C4—41no—
92C13×C4⋊C4—81no—
93C13×C4⋊C4—81no—
94C13×C22⋊C4—22no—
95C13×C22⋊C4—22no—
96C13×C22⋊C4—42no—
97C13×C22⋊C4—41no—
98C13×C22⋊C4—41no—
99C13×C22⋊C4—81no—
100C42×C13—21no—
101C42×C13—21no—
102#6099—82no—
103#6099—82no—
104#6099—82no—
105C2×#1055—24no—
106C2×#1055—42no—
107#2975—131no—
108#2579D1311yescharacteristic
109#1465—131no—
110#1463—132no—
111#1305—132no—
112C23×C13—21no—
113C23×C13—21no—
114C23×C13—21no—
115C23×C13—21no—
116C23×C13—21no—
117C23×C13—41no—
118C23×C13—41no—
119C23×C13—41no—
120C23×C13—41no—
121C23×C13C2×C22⋊C411yescharacteristic
122C23×C13C4×D412yes—
123D4×C13—44no—
124C2×C4×C13—21no—
125C2×C4×C13—21no—
126C2×C4×C13—22no—
127C2×C4×C13—24no—
128C2×C4×C13—21no—
129C2×C4×C13—21no—
130C2×C4×C13—42no—
131C2×C4×C13—42no—
132C2×C4×C13—41no—
133C2×C4×C13—41no—
134C2×C4×C13—42no—
135C2×C4×C13—41no—
136C2×C4×C13—42no—
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—41no—
149C2×C4×C13—81no—
150C2×C4×C13—82no—
151C2×C4×C13#10112yes—
152C2×C4×C13#12011yescharacteristic
153C2×C4×C13#12112yes—
154C2×C4×C13#12311yescharacteristic
155#1055—44no—
156#1055—82no—
157C2×C4×D4C2×D1311yescharacteristic
158C22×C4⋊C4C2×D1311yescharacteristic
159#436—264no—
160#431—261no—
161#407—132no—
162#407—132no—
163#407—261no—
164#398—21no—
165#396—21no—
166#387—21no—
167#386Dic1311yescharacteristic
168#386Dic1311yescharacteristic
169#385—21no—
170#385Dic1311yescharacteristic
171#385Dic1311yescharacteristic
172#380C2×D1311yescharacteristic
173#324—264no—
174#324—261no—
175#323—261no—
176C22×C13—21no—
177C22×C13—21no—
178C22×C13—22no—
179C22×C13—22no—
180C22×C13—22no—
181C22×C13—42no—
182C22×C13—42no—
183C22×C13—42no—
184C22×C13—41no—
185C22×C13—41no—
186C22×C13—41no—
187C22×C13—81no—
188C22×C13#38611yescharacteristic
189C22×C13C2×#10111yescharacteristic
190C22×C13#41311yescharacteristic
191C4×C13—22no—
192C4×C13—21no—
193C4×C13—22no—
194C4×C13—21no—
195C4×C13—42no—
196C4×C13—41no—
197C4×C13—41no—
198C4×C13—81no—
199C4×C13—81no—
200C4×C13—81no—
201C22×D4C2×Dic1311yescharacteristic
202C23×C4C2×Dic1311yescharacteristic
203C23×C4C2×Dic1311yescharacteristic
204C23×C4C22⋊D1311yescharacteristic
205C23×C4C22×D1311yescharacteristic
206C2×M16—262no—
207C2×M16—262no—
208C2×M16—262no—
209C4×D4—22no—
210C4×D4—22no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4—22no—
213C2×C4⋊C4—22no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4C22⋊D1311yescharacteristic
219C2×C22⋊C4—21no—
220C2×C22⋊C4—21no—
221C2×C22⋊C4C2×Dic1311yescharacteristic
222C2×C22⋊C4C2×Dic1311yescharacteristic
223C2×C22⋊C4C2×Dic1311yescharacteristic
224C2×C22⋊C4C22⋊D1311yescharacteristic
225C2×C42C22⋊D1311yescharacteristic
226C4⋊C8—262no—
227C22⋊C8—134no—
228C22⋊C8—262no—
229C22⋊C8—262no—
230C22⋊C8—262no—
231C22⋊C8—262no—
232C4×C8—262no—
233#95—21no—
234#95—21no—
235#95—21no—
236#95—21no—
237#95—21no—
238C2×C13—21no—
239C2×C13—21no—
240C2×C13—42no—
241C2×C13—81no—
242C2×C13#189111yescharacteristic
243C2×C13#190111yescharacteristic
244C2×C13#191311yescharacteristic
245C24C22⋊Dic1311yescharacteristic
246C24C22×Dic1311yescharacteristic
247C2×D4—22no—
248C2×D4—22no—
249C2×D4—41no—
250C22×C4—22no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—22no—
258C22×C4—42no—
259C22×C4—81no—
260C22×C4—81no—
261C22×C4—81no—
262C22×C4C22⋊Dic1311yescharacteristic
263C22×C4C22⋊Dic1311yescharacteristic
264C22×C4C22⋊Dic1311yescharacteristic
265C22×C4D4×D1312yes—
266C22×C4#612912yes—
267C22×C4C2×C22⋊D1311yescharacteristic
268C22×C4C2×C22⋊D1311yescharacteristic
269M16—1042no—
270M16—1042no—
271M16—1042no—
272C2×C8—264no—
273C2×C8—522no—
274C4⋊C4—22no—
275C4⋊C4—42no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C4⋊C4—42no—
279C4⋊C4—81no—
280C4⋊C4—81no—
281C22⋊C4—22no—
282C22⋊C4—22no—
283C22⋊C4—42no—
284C22⋊C4—41no—
285C22⋊C4—41no—
286C22⋊C4—81no—
287C42—21no—
288C42—21no—
289C13#951811yescharacteristic, complemented, Sylow
290C23—21no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23—21no—
295C23—41no—
296C23—41no—
297C23—41no—
298C23—41no—
299C23D4×Dic1312yes—
300C23C2×C22⋊Dic1311yescharacteristic
301D4—44no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—22no—
305C2×C4—24no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—41no—
309C2×C4—42no—
310C2×C4—42no—
311C2×C4—41no—
312C2×C4—42no—
313C2×C4—41no—
314C2×C4—42no—
315C2×C4—41no—
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—81no—
328C2×C4—82no—
329C2×C4#8807612yes—
330C2×C4#8818911yescharacteristic
331C2×C4#8819111yescharacteristic
332C2×C4#8819312yes—
333C8—524no—
334C8—1042no—
335C22—21no—
336C22—21no—
337C22—22no—
338C22—22no—
339C22—22no—
340C22—42no—
341C22—42no—
342C22—42no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—81no—
347C22#1171888111yescharacteristic
348C22C2×#8807611yescharacteristic
349C22#1171889811yescharacteristic
350C4—22no—
351C4—21no—
352C4—22no—
353C4—21no—
354C4—42no—
355C4—41no—
356C4—41no—
357C4—81no—
358C4—81no—
359C4—81no—
360C2—21no—
361C2—21no—
362C2—42no—
363C2—81no—
364C2#1311525511yescharacteristic
365C2#1311530511yescharacteristic
366C2#1311537911yescharacteristic
subgroupG/H
centerC22#11718881
commutatorC24×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#2579C2
socleC22×C13#386
prime radicalC22×D4×C13C2×C4
cosocleC23×C4×C13C23
hypercenter#2579D13
hypocenterC13#9518
LCSG ▷ C24×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2579

Complements

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

NH ≅ G/Ntype
3. #13113166C2semidirect
4. #13112742C2semidirect
289. C13#9518semidirect

Maximal subgroups

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

subgroupindex
#131238772
#131131742
#131131662
#131127422
C13×#25792
#951813