Finite Group Databasebeta

← #15758963

Subgroups — #15758963

Order 3328.

684 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 684 conjugacy classes of subgroups — too many to draw. Only its 135 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#13117450C211yesmaximal, characteristic
2#13113408C212yesmaximal, complemented
3C2×#11718117C211yesmaximal, characteristic
4#13112703C212yesmaximal, complemented
5C13×#2626C211yesmaximal, characteristic
6C2×C13×C22⋊Q8C2211yescharacteristic
7C22×C13×C22⋊C4C2211yescharacteristic
8C22×C22⋊Dic13—21no—
9C13×#399C412yescomplemented
10C13×#396—22no—
11C13×#393C412yescomplemented
12C13×#385—21no—
13C13×#380C2211yescharacteristic
14C13×#379—21no—
15#11718873—21no—
16#11718873C2212yes—
17C2×C22⋊#1055C2212yes—
18#11718611—24no—
19#11718130—24no—
20#11718117—22no—
21C25×C13D411yescharacteristic
22C22×Q8×C13C2×C411yescharacteristic, complemented
23C23×C4×C13D411yescharacteristic
24C23×C4×C13C2311yescharacteristic
25C23×Dic13—22no—
26C13×C22⋊Q8—22no—
27C13×C22⋊Q8—22no—
28C2×C13×C4⋊C4—21no—
29C2×C13×C4⋊C4—22no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4C2×C411yescharacteristic, complemented
32C2×C13×C22⋊C4—22no—
33C2×C13×C22⋊C4—22no—
34C2×C13×C22⋊C4—21no—
35C2×C13×C22⋊C4—21no—
36C2×C13×C22⋊C4—22no—
37C2×C13×C22⋊C4—22no—
38C2×C13×C22⋊C4C2×C412yes—
39C2×C13×C22⋊C4D412yes—
40C2×C22⋊Dic13—22no—
41C2×C22⋊Dic13—22no—
42C2×C22⋊Dic13—42no—
43C2×C22⋊Dic13—42no—
44C2×C4⋊Dic13—22no—
45C2×C4⋊Dic13—22no—
46C22×#1055—22no—
47C13×#95—22no—
48C13×#95C2×C412yescomplemented
49#88071—22no—
50#88071D414yes—
51C22⋊#1055—22no—
52C22⋊#1055—22no—
53#9199—131nomaximal, Sylow
54C24×C13—21no—
55C24×C13—21no—
56C24×C13—21no—
57C24×C13—21no—
58C24×C13—81no—
59C24×C13—81no—
60C24×C13C22⋊C412yes—
61C24×C13SD1612yes—
62C24×C13Q1612yes—
63C24×C13C2×D411yescharacteristic
64C2×Q8×C13—22no—
65C2×Q8×C13—81no—
66C22×C4×C13—21no—
67C22×C4×C13—21no—
68C22×C4×C13—21no—
69C22×C4×C13—22no—
70C22×C4×C13—21no—
71C22×C4×C13—81no—
72C22×C4×C13—81no—
73C22×C4×C13C22⋊C412yes—
74C22×C4×C13C22×C411yescharacteristic
75C22×C4×C13C2×D412yes—
76C22×C4×C13C2×D411yescharacteristic
77C22×C4×C13#4112yes—
78C22×Dic13—24no—
79C22×Dic13—44no—
80C22×Dic13—82no—
81C22×Dic13—82no—
82C13×C4⋊C4—22no—
83C13×C4⋊C4—42no—
84C13×C4⋊C4—81no—
85C13×C4⋊C4—82no—
86C13×C22⋊C4—24no—
87C13×C22⋊C4—24no—
88C13×C22⋊C4—41no—
89C13×C22⋊C4—41no—
90C13×C22⋊C4—41no—
91C13×C22⋊C4—41no—
92C13×C22⋊C4—82no—
93C13×C22⋊C4—82no—
94C22⋊Dic13—44no—
95C22⋊Dic13—42no—
96C22⋊Dic13—42no—
97C4⋊Dic13—82no—
98C4⋊Dic13—82no—
99C2×#1055—42no—
100C2×#1055—82no—
101#2626D1311yescharacteristic
102#2315—131no—
103#1520—132no—
104C2×#323—131no—
105#1289—132no—
106C23×C13—22no—
107C23×C13—22no—
108C23×C13—22no—
109C23×C13—22no—
110C23×C13—22no—
111C23×C13—22no—
112C23×C13—41no—
113C23×C13—41no—
114C23×C13—42no—
115C23×C13—42no—
116C23×C13—42no—
117C23×C13—42no—
118C23×C13—81no—
119C23×C13—81no—
120C23×C13—82no—
121C23×C13—82no—
122C23×C13—82no—
123C23×C13—82no—
124C23×C13#10314yes—
125C23×C13C2×C22⋊C411yescharacteristic
126C23×C13#12011yescharacteristic
127C23×C13#12311yescharacteristic
128C23×C13C2×SD1611yescharacteristic
129C23×C13C2×Q1611yescharacteristic
130C23×C13AGL(1,ℤ/8)11yescharacteristic
131C23×C13#13711yescharacteristic
132Q8×C13—82no—
133C2×C4×C13—22no—
134C2×C4×C13—42no—
135C2×C4×C13—42no—
136C2×C4×C13—41no—
137C2×C4×C13—41no—
138C2×C4×C13—42no—
139C2×C4×C13—42no—
140C2×C4×C13—42no—
141C2×C4×C13—42no—
142C2×C4×C13—42no—
143C2×C4×C13—42no—
144C2×C4×C13—41no—
145C2×C4×C13—41no—
146C2×C4×C13—42no—
147C2×C4×C13—81no—
148C2×C4×C13C4×D412yes—
149C2×C4×C13#12112yes—
150C2×Dic13—44no—
151C2×Dic13—44no—
152C2×Dic13—44no—
153C2×Dic13—88no—
154#1055—82no—
155C2×C22⋊Q8C2×D1311yescharacteristic
156C22×C22⋊C4—261no—
157C22×C22⋊C4C2×D1311yescharacteristic
158C2×C22⋊C8—132no—
159#399Dic1312yescomplemented
160#396—22no—
161#393Dic1312yescomplemented
162#385—21no—
163#385—264no—
164#380—132no—
165#380—261no—
166#380C2×D1311yescharacteristic
167#379—21no—
168#328—264no—
169#323—262no—
170C22×C13—21no—
171C22×C13—21no—
172C22×C13—21no—
173C22×C13—21no—
174C22×C13—21no—
175C22×C13—21no—
176C22×C13—24no—
177C22×C13—41no—
178C22×C13—41no—
179C22×C13—41no—
180C22×C13—41no—
181C22×C13—44no—
182C22×C13—44no—
183C22×C13—44no—
184C22×C13—42no—
185C22×C13—42no—
186C22×C13—82no—
187C22×C13—82no—
188C22×C13—82no—
189C22×C13#38611yescharacteristic
190C22×C13C2×#10311yescharacteristic
191C22×C13#41711yescharacteristic
192C22×C13#45011yescharacteristic
193C22×C13#45111yescharacteristic
194C22×C13#48311yescharacteristic
195C22×C13#48411yescharacteristic
196C4×C13—22no—
197C4×C13—22no—
198C4×C13—42no—
199C4×C13—82no—
200C4×C13—81no—
201C4×C13—81no—
202Dic13—84no—
203C25C22⋊D1311yescharacteristic
204C22×Q8C2×Dic1311yescharacteristic, complemented
205C23×C4—262no—
206C23×C4C22⋊D1311yescharacteristic
207C23×C4C22×D1311yescharacteristic
208C22×C8—262no—
209C22⋊Q8—22no—
210C22⋊Q8—22no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4—22no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4—262no—
215C2×C4⋊C4—262no—
216C2×C4⋊C4C2×Dic1311yescharacteristic, complemented
217C2×C22⋊C4—22no—
218C2×C22⋊C4—22no—
219C2×C22⋊C4—21no—
220C2×C22⋊C4—21no—
221C2×C22⋊C4—22no—
222C2×C22⋊C4—22no—
223C2×C22⋊C4—262no—
224C2×C22⋊C4—262no—
225C2×C22⋊C4—522no—
226C2×C22⋊C4—522no—
227C2×C22⋊C4C2×Dic1312yes—
228C2×C22⋊C4C22⋊D1312yes—
229C22⋊C8—262no—
230C22⋊C8—262no—
231#95—22no—
232#95—134no—
233#95—262no—
234#95C2×Dic1312yescomplemented
235C2×C13—21no—
236C2×C13—21no—
237C2×C13—21no—
238C2×C13—21no—
239C2×C13—21no—
240C2×C13—21no—
241C2×C13—44no—
242C2×C13#187211yescharacteristic
243C2×C13#191111yescharacteristic
244C2×C13#191311yescharacteristic
245C24—21no—
246C24—21no—
247C24—21no—
248C24—21no—
249C24—81no—
250C24—81no—
251C24#610612yes—
252C24#610712yes—
253C24C22⋊Dic1312yes—
254C24C2×C22⋊D1311yescharacteristic
255C2×Q8—22no—
256C2×Q8—81no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—22no—
261C22×C4—21no—
262C22×C4—81no—
263C22×C4—81no—
264C22×C4—264no—
265C22×C4—524no—
266C22×C4—1042no—
267C22×C4—1042no—
268C22×C4C22⋊Dic1312yes—
269C22×C4D4×D1312yes—
270C22×C4#612912yes—
271C22×C4C22×Dic1311yescharacteristic
272C22×C4C2×C22⋊D1311yescharacteristic
273C2×C8—522no—
274C2×C8—1042no—
275C4⋊C4—22no—
276C4⋊C4—42no—
277C4⋊C4—81no—
278C4⋊C4—82no—
279C4⋊C4—1042no—
280C4⋊C4—1042no—
281C22⋊C4—24no—
282C22⋊C4—24no—
283C22⋊C4—41no—
284C22⋊C4—41no—
285C22⋊C4—41no—
286C22⋊C4—41no—
287C22⋊C4—82no—
288C22⋊C4—82no—
289C22⋊C4—524no—
290C22⋊C4—522no—
291C22⋊C4—522no—
292C13#919911yescharacteristic, complemented, Sylow
293C23—22no—
294C23—22no—
295C23—22no—
296C23—22no—
297C23—22no—
298C23—22no—
299C23—41no—
300C23—41no—
301C23—42no—
302C23—42no—
303C23—42no—
304C23—42no—
305C23—81no—
306C23—81no—
307C23—82no—
308C23—82no—
309C23—82no—
310C23—82no—
311C23#8807514yes—
312C23#8818911yescharacteristic
313C23#8819111yescharacteristic
314C23C2×#610611yescharacteristic
315C23C2×#610711yescharacteristic
316C23#8820311yescharacteristic
317C23#8820511yescharacteristic
318C23C2×C22⋊Dic1311yescharacteristic
319Q8—82no—
320C2×C4—22no—
321C2×C4—41no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—41no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—42no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—42no—
334C2×C4—81no—
335C2×C4—524no—
336C2×C4—524no—
337C2×C4—524no—
338C2×C4—1048no—
339C2×C4D4×Dic1312yes—
340C2×C4#8819312yes—
341C8—1042no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22—24no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—44no—
354C22—44no—
355C22—44no—
356C22—42no—
357C22—42no—
358C22—82no—
359C22—82no—
360C22—82no—
361C22#1171870411yescharacteristic
362C22#1171870511yescharacteristic
363C22#1171870711yescharacteristic
364C22#1171871111yescharacteristic
365C22#1171888111yescharacteristic
366C22C2×#8807511yescharacteristic
367C22#1171889311yescharacteristic
368C4—22no—
369C4—22no—
370C4—42no—
371C4—82no—
372C4—81no—
373C4—81no—
374C4—1044no—
375C2—21no—
376C2—21no—
377C2—21no—
378C2—21no—
379C2—21no—
380C2—21no—
381C2—44no—
382C2#1311514411yescharacteristic
383C2#1311536911yescharacteristic
384C2#1311537911yescharacteristic
subgroupG/H
centerC22#11718881
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#2626C2
socleC22×C13#386
prime radicalC25×C13D4
cosocleC23×C4×C13C23
hypercenter#2626D13
hypocenterC13#9199
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2626

Complements

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

NH ≅ G/Ntype
2. #13113408C2semidirect
4. #13112703C2semidirect
9. C13×#399C4semidirect
11. C13×#393C4semidirect
22. C22×Q8×C13C2×C4semidirect
31. C2×C13×C4⋊C4C2×C4semidirect
48. C13×#95C2×C4semidirect
159. #399Dic13semidirect
161. #393Dic13semidirect
204. C22×Q8C2×Dic13semidirect
216. C2×C4⋊C4C2×Dic13semidirect
234. #95C2×Dic13semidirect
292. C13#9199semidirect

Maximal subgroups

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

subgroupindex
#131174502
#131134082
C2×#117181172
#131127032
C13×#26262
#919913