Finite Group Databasebeta

← #15760245

Subgroups — #15760245

Order 3328.

548 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 548 conjugacy classes of subgroups — too many to draw. Only its 119 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#13123865C211yesmaximal, characteristic
2#13114824C211yesmaximal, characteristic
3#13113408C212yesmaximal, complemented
4#13112715C212yesmaximal, complemented
5C13×#2564C211yesmaximal, characteristic
6C2×C13×C22⋊Q8C2211yescharacteristic
7C2×C4×D4×C13C2211yescharacteristic
8C13×#400C411yescharacteristic, complemented
9C13×#399C411yescharacteristic, complemented
10C13×#395C411yescharacteristic, complemented
11C13×#393C411yescharacteristic, complemented
12C13×#387—21no—
13C13×#386—21no—
14C13×#385—21no—
15C13×#380—21no—
16C2×C13×#95C2211yescharacteristic
17C2×#88074—21no—
18#11718873C2212yes—
19#11718868—21no—
20C2×C22⋊#1055C2212yes—
21#11718672—24no—
22#11718587—21no—
23#11718130—24no—
24#11718118—21no—
25C22×Q8×C13C2×C411yescharacteristic
26C22×D4×C13D411yescharacteristic
27C23×C4×C13—21no—
28C23×C4×C13D411yescharacteristic
29C23×C4×C13C2311yescharacteristic
30C13×C22⋊Q8—22no—
31C13×C22⋊Q8—22no—
32C4×D4×C13—22no—
33C4×D4×C13—22no—
34C2×C13×C4⋊C4—21no—
35C2×C13×C4⋊C4—21no—
36C2×C13×C4⋊C4—21no—
37C2×C13×C4⋊C4C2×C411yescharacteristic
38C2×C13×C4⋊C4C2×C411yescharacteristic
39C2×C13×C22⋊C4—21no—
40C2×C13×C22⋊C4—21no—
41C2×C13×C22⋊C4—21no—
42C2×C13×C22⋊C4C2×C411yescharacteristic
43C2×C13×C22⋊C4D411yescharacteristic
44C2×C42×C13D411yescharacteristic
45C2×C22⋊Dic13—22no—
46C2×C4⋊Dic13—22no—
47C2×#6099—22no—
48C22×#1055—22no—
49C13×#95—21no—
50C13×#95—21no—
51C13×#95—21no—
52C13×#95—21no—
53C13×#95—21no—
54C13×#95C2×C411yescharacteristic
55C13×#95C2×C411yescharacteristic
56#88074—42no—
57#88071—22no—
58C22⋊#1055—22no—
59C22⋊#1055—22no—
60C22⋊#1055D414yes—
61C4⋊#1055—22no—
62#88043—22no—
63#9385—131nomaximal, Sylow
64C24×C13C22⋊C411yescharacteristic
65C24×C13C2×D411yescharacteristic
66C2×Q8×C13—22no—
67C2×Q8×C13—81no—
68C2×D4×C13—22no—
69C2×D4×C13—21no—
70C2×D4×C13—22no—
71C2×D4×C13—21no—
72C22×C4×C13—21no—
73C22×C4×C13—21no—
74C22×C4×C13—21no—
75C22×C4×C13—21no—
76C22×C4×C13—21no—
77C22×C4×C13—21no—
78C22×C4×C13—42no—
79C22×C4×C13—41no—
80C22×C4×C13—41no—
81C22×C4×C13—81no—
82C22×C4×C13—81no—
83C22×C4×C13—81no—
84C22×C4×C13C22⋊C411yescharacteristic
85C22×C4×C13C22⋊C411yescharacteristic
86C22×C4×C13C22⋊C411yescharacteristic
87C22×C4×C13C22×C411yescharacteristic
88C22×C4×C13C2×D412yes—
89C22×C4×C13C2×D411yescharacteristic
90C22×C4×C13#4112yes—
91C22×Dic13—42no—
92C13×C4⋊C4—22no—
93C13×C4⋊C4—22no—
94C13×C4⋊C4—42no—
95C13×C4⋊C4—41no—
96C13×C4⋊C4—41no—
97C13×C4⋊C4—81no—
98C13×C22⋊C4—22no—
99C13×C22⋊C4—22no—
100C13×C22⋊C4—42no—
101C13×C22⋊C4—42no—
102C13×C22⋊C4—81no—
103C42×C13—21no—
104C42×C13—21no—
105C22⋊Dic13—42no—
106C22⋊Dic13—42no—
107C4⋊Dic13—82no—
108#6099—82no—
109C2×#1055—24no—
110C2×#1055—82no—
111#2973—131no—
112#2564D1311yescharacteristic
113#1799—131no—
114#1520—132no—
115#1294—132no—
116C23×C13—21no—
117C23×C13—21no—
118C23×C13—21no—
119C23×C13—41no—
120C23×C13—41no—
121C23×C13—41no—
122C23×C13—41no—
123C23×C13C2×C22⋊C411yescharacteristic
124C23×C13#12112yes—
125C23×C13AGL(1,ℤ/8)11yescharacteristic
126C23×C13#13711yescharacteristic
127C23×C13#13712yes—
128Q8×C13—82no—
129D4×C13—42no—
130D4×C13—42no—
131C2×C4×C13—22no—
132C2×C4×C13—21no—
133C2×C4×C13—21no—
134C2×C4×C13—21no—
135C2×C4×C13—21no—
136C2×C4×C13—21no—
137C2×C4×C13—42no—
138C2×C4×C13—42no—
139C2×C4×C13—41no—
140C2×C4×C13—41no—
141C2×C4×C13—42no—
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—41no—
150C2×C4×C13—41no—
151C2×C4×C13—41no—
152C2×C4×C13—41no—
153C2×C4×C13—41no—
154C2×C4×C13—41no—
155C2×C4×C13—81no—
156C2×C4×C13—82no—
157C2×C4×C13—82no—
158C2×C4×C13C4×D412yes—
159C2×C4×C13#12011yescharacteristic
160C2×C4×C13#12311yescharacteristic
161C2×Dic13—82no—
162C2×Dic13—82no—
163C2×Dic13—82no—
164#1055—44no—
165C2×C22⋊Q8C2×D1311yescharacteristic
166C2×C4×D4C2×D1311yescharacteristic
167#435—264no—
168#432—261no—
169C2×#99—261no—
170#407—261no—
171C2×C22⋊C8—132no—
172#400Dic1311yescharacteristic, complemented
173#399Dic1311yescharacteristic, complemented
174#395Dic1311yescharacteristic, complemented
175#393Dic1311yescharacteristic, complemented
176#387—21no—
177#386—21no—
178#385—21no—
179#380—21no—
180#380—132no—
181C2×#95C2×D1311yescharacteristic
182#342—261no—
183#328—264no—
184C22×C13—22no—
185C22×C13—21no—
186C22×C13—22no—
187C22×C13—21no—
188C22×C13—41no—
189C22×C13—41no—
190C22×C13—42no—
191C22×C13—42no—
192C22×C13—41no—
193C22×C13—41no—
194C22×C13—41no—
195C22×C13—81no—
196C22×C13#38611yescharacteristic
197C22×C13#41711yescharacteristic
198C22×C13#41911yescharacteristic
199C22×C13#46812yes—
200C22×C13#47012yes—
201C4×C13—21no—
202C4×C13—21no—
203C4×C13—22no—
204C4×C13—42no—
205C4×C13—41no—
206C4×C13—41no—
207C4×C13—41no—
208C4×C13—81no—
209C4×C13—81no—
210C4×C13—81no—
211Dic13—162no—
212C22×Q8C2×Dic1311yescharacteristic
213C22×D4C22⋊D1311yescharacteristic
214C23×C4—21no—
215C23×C4C22⋊D1311yescharacteristic
216C23×C4C22×D1311yescharacteristic
217C2×M16—262no—
218C22×C8—262no—
219C22⋊Q8—22no—
220C22⋊Q8—22no—
221C4×D4—22no—
222C4×D4—22no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—262no—
227C2×C4⋊C4C2×Dic1311yescharacteristic
228C2×C4⋊C4C2×Dic1311yescharacteristic
229C2×C22⋊C4—21no—
230C2×C22⋊C4—21no—
231C2×C22⋊C4—21no—
232C2×C22⋊C4—262no—
233C2×C22⋊C4C2×Dic1311yescharacteristic
234C2×C22⋊C4C22⋊D1311yescharacteristic
235C2×C42C22⋊D1311yescharacteristic
236C4⋊C8—262no—
237#99—522no—
238C22⋊C8—134no—
239C22⋊C8—262no—
240C22⋊C8—262no—
241#97—262no—
242#95—21no—
243#95—21no—
244#95—21no—
245#95—21no—
246#95—21no—
247#95—262no—
248#95C2×Dic1311yescharacteristic
249#95C2×Dic1311yescharacteristic
250C2×C13—22no—
251C2×C13—21no—
252C2×C13—21no—
253C2×C13—22no—
254C2×C13—81no—
255C2×C13#188411yescharacteristic
256C2×C13#189411yescharacteristic
257C2×C13#191311yescharacteristic
258C24C22⋊Dic1311yescharacteristic
259C24C2×C22⋊D1311yescharacteristic
260C2×Q8—22no—
261C2×Q8—81no—
262C2×D4—22no—
263C2×D4—22no—
264C2×D4—21no—
265C2×D4—21no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—42no—
273C22×C4—41no—
274C22×C4—41no—
275C22×C4—81no—
276C22×C4—81no—
277C22×C4—81no—
278C22×C4—522no—
279C22×C4C22⋊Dic1311yescharacteristic
280C22×C4C22⋊Dic1311yescharacteristic
281C22×C4C22⋊Dic1311yescharacteristic
282C22×C4D4×D1312yes—
283C22×C4#612912yes—
284C22×C4C22×Dic1311yescharacteristic
285C22×C4C2×C22⋊D1311yescharacteristic
286M16—1042no—
287C2×C8—264no—
288C2×C8—1042no—
289C4⋊C4—22no—
290C4⋊C4—22no—
291C4⋊C4—42no—
292C4⋊C4—41no—
293C4⋊C4—41no—
294C4⋊C4—81no—
295C4⋊C4—1042no—
296C22⋊C4—22no—
297C22⋊C4—22no—
298C22⋊C4—42no—
299C22⋊C4—42no—
300C22⋊C4—81no—
301C22⋊C4—522no—
302C22⋊C4—522no—
303C42—21no—
304C42—21no—
305C13#938511yescharacteristic, complemented, Sylow
306C23—21no—
307C23—21no—
308C23—21no—
309C23—41no—
310C23—41no—
311C23—41no—
312C23—41no—
313C23#8819312yes—
314C23#8819612yes—
315C23#8820311yescharacteristic
316C23#8820511yescharacteristic
317C23C2×C22⋊Dic1311yescharacteristic
318Q8—82no—
319D4—42no—
320D4—42no—
321C2×C4—22no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—42no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—81no—
346C2×C4—82no—
347C2×C4—82no—
348C2×C4—1042no—
349C2×C4—1042no—
350C2×C4—1042no—
351C2×C4D4×Dic1312yes—
352C2×C4#8818911yescharacteristic
353C2×C4#8819111yescharacteristic
354C8—524no—
355C22—21no—
356C22—22no—
357C22—21no—
358C22—22no—
359C22—41no—
360C22—41no—
361C22—42no—
362C22—42no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—81no—
367C22#1171871012yes—
368C22#1171871312yes—
369C22#1171888111yescharacteristic
370C22#1171888611yescharacteristic
371C22#1171889311yescharacteristic
372C4—21no—
373C4—21no—
374C4—22no—
375C4—42no—
376C4—41no—
377C4—41no—
378C4—41no—
379C4—81no—
380C4—81no—
381C4—81no—
382C4—2082no—
383C2—21no—
384C2—22no—
385C2—21no—
386C2—22no—
387C2—81no—
388C2#1311522011yescharacteristic
389C2#1311527011yescharacteristic
390C2#1311537911yescharacteristic
subgroupG/H
centerC22#11718881
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#2564C2
socleC22×C13#386
prime radicalC22×D4×C13D4
cosocleC23×C4×C13C23
hypercenter#2564D13
hypocenterC13#9385
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2564

Complements

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

NH ≅ G/Ntype
3. #13113408C2semidirect
4. #13112715C2semidirect
8. C13×#400C4semidirect
9. C13×#399C4semidirect
10. C13×#395C4semidirect
11. C13×#393C4semidirect
172. #400Dic13semidirect
173. #399Dic13semidirect
174. #395Dic13semidirect
175. #393Dic13semidirect
305. C13#9385semidirect

Maximal subgroups

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

subgroupindex
#131238652
#131148242
#131134082
#131127152
C13×#25642
#938513