Finite Group Databasebeta

← #15760719

Subgroups — #15760719

Order 3328.

958 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 958 conjugacy classes of subgroups — too many to draw. Only its 115 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#13117189C211yesmaximal, characteristic, complemented
2#13114780C212yesmaximal, complemented
3#13113163C211yesmaximal, characteristic, complemented
4#13112688C212yesmaximal, complemented
5C13×#2404C211yesmaximal, characteristic
6C22×C13×#41C2211yescharacteristic
7C2×C13×#120—21no—
8C22×C13×C22⋊C4C2211yescharacteristic
9C22×C22⋊Dic13—21no—
10C13×#393C412yescomplemented
11C13×#392C412yescomplemented
12C13×#386—21no—
13C13×#386—22no—
14C13×#381C2211yescharacteristic
15C2×#88077—24no—
16C4×C22⋊Dic13—21no—
17C4×C22⋊Dic13C2212yes—
18#11718868C2212yes—
19C22⋊C4×Dic13—24no—
20#11718117—22no—
21C25×C13D411yescharacteristic
22C2×C13×#41—22no—
23C2×C13×#41—22no—
24C2×C13×#41—44no—
25C22×Q8×C13C2×C411yescharacteristic, complemented
26C22×D4×C13—21no—
27C22×D4×C13—22no—
28C22×D4×C13C2×C411yescharacteristic, complemented
29C23×C4×C13—21no—
30C23×C4×C13D411yescharacteristic
31C23×C4×C13C2311yescharacteristic
32C23×Dic13—22no—
33C13×#120—44no—
34C2×C13×C22⋊C4—22no—
35C2×C13×C22⋊C4—22no—
36C2×C13×C22⋊C4—22no—
37C2×C13×C22⋊C4—21no—
38C2×C13×C22⋊C4—22no—
39C2×C13×C22⋊C4C2×C412yes—
40C2×C13×C22⋊C4D412yes—
41C2×C22⋊Dic13—28no—
42C2×C22⋊Dic13—22no—
43C2×C22⋊Dic13—22no—
44C2×C4×Dic13—22no—
45C2×C4×Dic13D414yescomplemented
46C2×#6099—22no—
47C13×#95—22no—
48C13×#95—21no—
49C13×#95C2×C412yescomplemented
50#88077—48no—
51#88071—22no—
52#88071—22no—
53C22⋊#1055—22no—
54C22⋊#1055—22no—
55#9475—131nomaximal, Sylow
56C24×C13—21no—
57C24×C13—24no—
58C24×C13—21no—
59C24×C13—21no—
60C24×C13—42no—
61C24×C13—81no—
62C24×C13C22⋊C412yes—
63C24×C13C2×D411yescharacteristic
64C13×#41—28no—
65C13×#41—44no—
66C13×#41—44no—
67C13×#41—44no—
68C2×Q8×C13—22no—
69C2×Q8×C13—42no—
70C2×D4×C13—24no—
71C2×D4×C13—22no—
72C2×D4×C13—42no—
73C2×D4×C13—42no—
74C2×D4×C13—41no—
75C2×D4×C13—41no—
76C2×D4×C13—44no—
77C2×D4×C13—44no—
78C2×D4×C13—82no—
79C22×C4×C13—21no—
80C22×C4×C13—21no—
81C22×C4×C13—21no—
82C22×C4×C13—22no—
83C22×C4×C13—42no—
84C22×C4×C13—42no—
85C22×C4×C13—42no—
86C22×C4×C13—42no—
87C22×C4×C13—81no—
88C22×C4×C13C22⋊C412yes—
89C22×C4×C13C22×C411yescharacteristic
90C22×C4×C13C2×D412yes—
91C22×C4×C13C2×D411yescharacteristic
92C22×C4×C13#4112yes—
93C22×Dic13—24no—
94C22×Dic13—28no—
95C22×Dic13—82no—
96C22×Dic13—82no—
97C13×C22⋊C4—24no—
98C13×C22⋊C4—24no—
99C13×C22⋊C4—44no—
100C13×C22⋊C4—42no—
101C13×C22⋊C4—82no—
102C22⋊Dic13—28no—
103C22⋊Dic13—28no—
104C4×Dic13—44no—
105C4×Dic13—82no—
106#6099—44no—
107C2×#1055—42no—
108#2404D1311yescharacteristic
109#2273—131no—
110#1789—132no—
111#1462—131no—
112#1284—132no—
113C23×C13—22no—
114C23×C13—22no—
115C23×C13—24no—
116C23×C13—22no—
117C23×C13—22no—
118C23×C13—22no—
119C23×C13—22no—
120C23×C13—22no—
121C23×C13—41no—
122C23×C13—42no—
123C23×C13—42no—
124C23×C13—42no—
125C23×C13—42no—
126C23×C13—41no—
127C23×C13—42no—
128C23×C13—41no—
129C23×C13—42no—
130C23×C13—81no—
131C23×C13—81no—
132C23×C13—88no—
133C23×C13#10414yescomplemented
134C23×C13C2×C22⋊C411yescharacteristic
135C23×C13#12011yescharacteristic
136C23×C13#12311yescharacteristic
137Q8×C13—24no—
138Q8×C13—42no—
139D4×C13—24no—
140D4×C13—42no—
141D4×C13—44no—
142D4×C13—44no—
143D4×C13—88no—
144C2×C4×C13—24no—
145C2×C4×C13—22no—
146C2×C4×C13—22no—
147C2×C4×C13—41no—
148C2×C4×C13—41no—
149C2×C4×C13—42no—
150C2×C4×C13—48no—
151C2×C4×C13—42no—
152C2×C4×C13—41no—
153C2×C4×C13—41no—
154C2×C4×C13—42no—
155C2×C4×C13—42no—
156C2×C4×C13—42no—
157C2×C4×C13—42no—
158C2×C4×C13—81no—
159C2×C4×C13C4×D412yes—
160C2×C4×C13#12112yes—
161C2×Dic13—28no—
162C2×Dic13—44no—
163C2×Dic13—44no—
164C2×Dic13—88no—
165#1055—82no—
166C22×#41C2×D1311yescharacteristic
167C2×#120—21no—
168C22×C22⋊C4—261no—
169C22×C22⋊C4C2×D1311yescharacteristic
170C2×#104—264no—
171#407—132no—
172#393Dic1312yescomplemented
173#392Dic1312yescomplemented
174#386—21no—
175#386—22no—
176#381C2×D1311yescharacteristic
177C4×C22⋊C4—132no—
178C4×C22⋊C4—264no—
179C4×C22⋊C4—261no—
180#323—262no—
181C22×C13—21no—
182C22×C13—21no—
183C22×C13—21no—
184C22×C13—21no—
185C22×C13—21no—
186C22×C13—24no—
187C22×C13—21no—
188C22×C13—21no—
189C22×C13—44no—
190C22×C13—44no—
191C22×C13—44no—
192C22×C13—44no—
193C22×C13—44no—
194C22×C13—42no—
195C22×C13—42no—
196C22×C13—42no—
197C22×C13—82no—
198C22×C13—82no—
199C22×C13—84no—
200C22×C13—81no—
201C22×C13—81no—
202C22×C13#38611yescharacteristic
203C22×C13C2×#10412yes—
204C22×C13B(4,𝔽2)12yes—
205C4×C13—22no—
206C4×C13—22no—
207C4×C13—42no—
208C4×C13—42no—
209C4×C13—82no—
210Dic13—48no—
211C25C22⋊D1311yescharacteristic
212C2×#41—22no—
213C2×#41—22no—
214C2×#41—44no—
215C22×Q8C2×Dic1311yescharacteristic, complemented
216C22×D4—21no—
217C22×D4—22no—
218C22×D4C2×Dic1311yescharacteristic, complemented
219C23×C4—21no—
220C23×C4—262no—
221C23×C4C22⋊D1311yescharacteristic
222C23×C4C22×D1311yescharacteristic
223C2×M16—262no—
224#120—44no—
225C2×C22⋊C4—22no—
226C2×C22⋊C4—22no—
227C2×C22⋊C4—22no—
228C2×C22⋊C4—21no—
229C2×C22⋊C4—22no—
230C2×C22⋊C4—262no—
231C2×C22⋊C4—268no—
232C2×C22⋊C4—262no—
233C2×C22⋊C4C2×Dic1312yes—
234C2×C22⋊C4C22⋊D1312yes—
235C2×C42—134no—
236C2×C42—262no—
237#104—528no—
238C22⋊C8—262no—
239C22⋊C8—262no—
240#95—22no—
241#95—21no—
242#95—262no—
243#95—262no—
244#95C2×Dic1312yescomplemented
245C2×C13—22no—
246C2×C13—22no—
247C2×C13—41no—
248C2×C13—44no—
249C2×C13—82no—
250C2×C13#188911yescharacteristic
251C2×C13#189611yescharacteristic
252C2×C13#191111yescharacteristic
253C24—21no—
254C24—24no—
255C24—21no—
256C24—21no—
257C24—42no—
258C24—81no—
259C24C22⋊Dic1312yes—
260C24C2×C22⋊D1311yescharacteristic
261#41—28no—
262#41—44no—
263#41—44no—
264#41—44no—
265C2×Q8—22no—
266C2×Q8—42no—
267C2×D4—24no—
268C2×D4—22no—
269C2×D4—42no—
270C2×D4—42no—
271C2×D4—41no—
272C2×D4—41no—
273C2×D4—44no—
274C2×D4—44no—
275C2×D4—82no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—22no—
280C22×C4—42no—
281C22×C4—42no—
282C22×C4—42no—
283C22×C4—42no—
284C22×C4—81no—
285C22×C4—264no—
286C22×C4—268no—
287C22×C4—1042no—
288C22×C4—1042no—
289C22×C4C22⋊Dic1312yes—
290C22×C4D4×D1312yes—
291C22×C4#612912yes—
292C22×C4C22×Dic1311yescharacteristic
293C22×C4C2×C22⋊D1311yescharacteristic
294M16—524no—
295C2×C8—522no—
296C22⋊C4—24no—
297C22⋊C4—24no—
298C22⋊C4—44no—
299C22⋊C4—42no—
300C22⋊C4—82no—
301C22⋊C4—268no—
302C22⋊C4—268no—
303C42—524no—
304C42—1042no—
305C13#947511yescharacteristic, complemented, Sylow
306C23—22no—
307C23—22no—
308C23—24no—
309C23—22no—
310C23—22no—
311C23—22no—
312C23—22no—
313C23—22no—
314C23—41no—
315C23—42no—
316C23—42no—
317C23—42no—
318C23—42no—
319C23—41no—
320C23—42no—
321C23—41no—
322C23—42no—
323C23—81no—
324C23—81no—
325C23—88no—
326C23#8807714yescomplemented
327C23#8818911yescharacteristic
328C23#8819111yescharacteristic
329C23C2×C22⋊Dic1311yescharacteristic
330Q8—24no—
331Q8—42no—
332D4—24no—
333D4—42no—
334D4—44no—
335D4—44no—
336D4—88no—
337C2×C4—24no—
338C2×C4—22no—
339C2×C4—22no—
340C2×C4—41no—
341C2×C4—42no—
342C2×C4—41no—
343C2×C4—48no—
344C2×C4—42no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—42no—
348C2×C4—42no—
349C2×C4—42no—
350C2×C4—42no—
351C2×C4—81no—
352C2×C4—268no—
353C2×C4—524no—
354C2×C4—524no—
355C2×C4—1048no—
356C2×C4D4×Dic1312yes—
357C2×C4#8819312yes—
358C8—1042no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—24no—
365C22—21no—
366C22—21no—
367C22—44no—
368C22—44no—
369C22—44no—
370C22—44no—
371C22—44no—
372C22—42no—
373C22—42no—
374C22—42no—
375C22—82no—
376C22—82no—
377C22—84no—
378C22—81no—
379C22—81no—
380C22#1171869312yes—
381C22#1171888111yescharacteristic
382C22C2×#8807712yes—
383C4—22no—
384C4—22no—
385C4—42no—
386C4—42no—
387C4—82no—
388C4—528no—
389C2—22no—
390C2—22no—
391C2—41no—
392C2—44no—
393C2—82no—
394C2#1311524511yescharacteristic
395C2#1311528011yescharacteristic
396C2#1311536911yescharacteristic
subgroupG/H
centerC22#11718881
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
Fitting, prime radicalC13×#2404C2
socleC22×C13#386
cosocleC23×C4×C13C23
hypercenter#2404D13
hypocenterC13#9475
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2404

Complements

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

NH ≅ G/Ntype
1. #13117189C2semidirect
2. #13114780C2semidirect
3. #13113163C2semidirect
4. #13112688C2semidirect
10. C13×#393C4semidirect
11. C13×#392C4semidirect
25. C22×Q8×C13C2×C4semidirect
28. C22×D4×C13C2×C4semidirect
45. C2×C4×Dic13D4semidirect
49. C13×#95C2×C4semidirect
133. C23×C13#104semidirect
172. #393Dic13semidirect
173. #392Dic13semidirect
215. C22×Q8C2×Dic13semidirect
218. C22×D4C2×Dic13semidirect
244. #95C2×Dic13semidirect
305. C13#9475semidirect
326. C23#88077semidirect

Maximal subgroups

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

subgroupindex
#131171892
#131147802
#131131632
#131126882
C13×#24042
#947513