Finite Group Databasebeta

← #15760365

Subgroups — #15760365

Order 3328.

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

normal subgroups only

This group has 840 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#13113352C212yesmaximal, complemented
3#13113163C211yesmaximal, characteristic, complemented
4#13112722C212yesmaximal, complemented
5C13×#2539C211yesmaximal, characteristic
6C2×C13×#123—21no—
7C2×C13×#121C2211yescharacteristic
8C2×C13×#120—21no—
9C22×C13×C22⋊C4C2211yescharacteristic
10C22×C22⋊Dic13—21no—
11C13×#399C412yescomplemented
12C13×#392C412yescomplemented
13C13×#390—22no—
14C4×C13×C22⋊C4C2211yescharacteristic
15C4×C22⋊Dic13—21no—
16C4×C22⋊Dic13C2212yes—
17#11718868C2212yes—
18C22⋊C4×Dic13—24no—
19#11718129—24no—
20#11718117—22no—
21C25×C13D411yescharacteristic
22C22×D4×C13—21no—
23C22×D4×C13—22no—
24C22×D4×C13C2×C411yescharacteristic, complemented
25C23×C4×C13D411yescharacteristic
26C23×C4×C13C2311yescharacteristic
27C23×Dic13—22no—
28C13×#123—44no—
29C13×#121—22no—
30C13×#121—22no—
31C13×#120—44no—
32C2×C13×C4⋊C4—22no—
33C2×C13×C4⋊C4C2×C411yescharacteristic, complemented
34C2×C13×C22⋊C4—21no—
35C2×C13×C22⋊C4—22no—
36C2×C13×C22⋊C4—22no—
37C2×C13×C22⋊C4—22no—
38C2×C13×C22⋊C4—22no—
39C2×C13×C22⋊C4—21no—
40C2×C13×C22⋊C4C2×C412yes—
41C2×C13×C22⋊C4D412yes—
42C2×C42×C13—21no—
43C2×C22⋊Dic13—28no—
44C2×C22⋊Dic13—22no—
45C2×C22⋊Dic13—22no—
46C2×C4×Dic13—22no—
47C2×C4×Dic13—22no—
48C2×#6099—22no—
49C13×#95C2×C412yescomplemented
50#88071—22no—
51#88071D414yescomplemented
52C22⋊#1055—22no—
53C22⋊#1055—22no—
54#9409—131nomaximal, Sylow
55C24×C13—21no—
56C24×C13—24no—
57C24×C13—21no—
58C24×C13—21no—
59C24×C13—42no—
60C24×C13—81no—
61C24×C13C22⋊C412yes—
62C24×C13C2×D411yescharacteristic
63C2×D4×C13—22no—
64C2×D4×C13—44no—
65C2×D4×C13—42no—
66C2×D4×C13—42no—
67C2×D4×C13—44no—
68C2×D4×C13—41no—
69C2×D4×C13—41no—
70C2×D4×C13—82no—
71C2×D4×C13—81no—
72C22×C4×C13—22no—
73C22×C4×C13—21no—
74C22×C4×C13—21no—
75C22×C4×C13—21no—
76C22×C4×C13—42no—
77C22×C4×C13—81no—
78C22×C4×C13C22⋊C412yes—
79C22×C4×C13C22×C411yescharacteristic
80C22×C4×C13C2×D412yes—
81C22×C4×C13C2×D411yescharacteristic
82C22×C4×C13#4112yes—
83C22×Dic13—24no—
84C22×Dic13—28no—
85C22×Dic13—82no—
86C22×Dic13—82no—
87C13×C4⋊C4—22no—
88C13×C4⋊C4—44no—
89C13×C22⋊C4—24no—
90C13×C22⋊C4—24no—
91C13×C22⋊C4—24no—
92C13×C22⋊C4—44no—
93C13×C22⋊C4—44no—
94C13×C22⋊C4—42no—
95C42×C13—81no—
96C22⋊Dic13—28no—
97C22⋊Dic13—28no—
98C4×Dic13—82no—
99C4×Dic13—82no—
100#6099—82no—
101C2×#1055—42no—
102#2539D1311yescharacteristic
103#2273—131no—
104#1507—132no—
105#1462—131no—
106#1297—132no—
107C23×C13—22no—
108C23×C13—22no—
109C23×C13—24no—
110C23×C13—22no—
111C23×C13—22no—
112C23×C13—22no—
113C23×C13—22no—
114C23×C13—41no—
115C23×C13—42no—
116C23×C13—42no—
117C23×C13—42no—
118C23×C13—41no—
119C23×C13—41no—
120C23×C13—42no—
121C23×C13—42no—
122C23×C13—41no—
123C23×C13—42no—
124C23×C13—81no—
125C23×C13—81no—
126C23×C13—88no—
127C23×C13#10414yes—
128C23×C13C2×C22⋊C411yescharacteristic
129C23×C13#12011yescharacteristic
130C23×C13#12311yescharacteristic
131D4×C13—82no—
132D4×C13—88no—
133D4×C13—82no—
134D4×C13—82no—
135C2×C4×C13—24no—
136C2×C4×C13—22no—
137C2×C4×C13—42no—
138C2×C4×C13—42no—
139C2×C4×C13—41no—
140C2×C4×C13—41no—
141C2×C4×C13—42no—
142C2×C4×C13—42no—
143C2×C4×C13—42no—
144C2×C4×C13—42no—
145C2×C4×C13—41no—
146C2×C4×C13—41no—
147C2×C4×C13—41no—
148C2×C4×C13—81no—
149C2×C4×C13C4×D412yes—
150C2×C4×C13#12112yes—
151C2×Dic13—28no—
152C2×Dic13—44no—
153C2×Dic13—44no—
154C2×Dic13—88no—
155#1055—82no—
156C2×#123—21no—
157C2×#121C2×D1311yescharacteristic
158C2×#120—21no—
159C22×C22⋊C4—261no—
160C22×C22⋊C4C2×D1311yescharacteristic
161#407—132no—
162#399Dic1312yescomplemented
163#392Dic1312yescomplemented
164#390—22no—
165C4×C22⋊C4—132no—
166C4×C22⋊C4—264no—
167C4×C22⋊C4—261no—
168C4×C22⋊C4C2×D1311yescharacteristic
169#327—264no—
170#323—262no—
171C22×C13—21no—
172C22×C13—21no—
173C22×C13—21no—
174C22×C13—21no—
175C22×C13—21no—
176C22×C13—24no—
177C22×C13—21no—
178C22×C13—21no—
179C22×C13—44no—
180C22×C13—44no—
181C22×C13—44no—
182C22×C13—44no—
183C22×C13—42no—
184C22×C13—42no—
185C22×C13—82no—
186C22×C13—82no—
187C22×C13—82no—
188C22×C13—84no—
189C22×C13—81no—
190C22×C13—81no—
191C22×C13—81no—
192C22×C13#38611yescharacteristic
193C22×C13C2×#10412yes—
194C22×C13#45312yes—
195C4×C13—22no—
196C4×C13—22no—
197C4×C13—44no—
198C4×C13—42no—
199C4×C13—81no—
200Dic13—48no—
201C25C22⋊D1311yescharacteristic
202C22×D4—21no—
203C22×D4—22no—
204C22×D4C2×Dic1311yescharacteristic, complemented
205C23×C4—262no—
206C23×C4C22⋊D1311yescharacteristic
207C23×C4C22×D1311yescharacteristic
208C2×M16—262no—
209#123—44no—
210#121—22no—
211#121—22no—
212#120—44no—
213C2×C4⋊C4—22no—
214C2×C4⋊C4C2×Dic1311yescharacteristic, complemented
215C2×C22⋊C4—21no—
216C2×C22⋊C4—22no—
217C2×C22⋊C4—22no—
218C2×C22⋊C4—22no—
219C2×C22⋊C4—22no—
220C2×C22⋊C4—21no—
221C2×C22⋊C4—262no—
222C2×C22⋊C4—268no—
223C2×C22⋊C4—262no—
224C2×C22⋊C4C2×Dic1312yes—
225C2×C22⋊C4C22⋊D1312yes—
226C2×C42—21no—
227C2×C42—262no—
228C2×C42—262no—
229C22⋊C8—262no—
230C22⋊C8—262no—
231#95—134no—
232#95—262no—
233#95C2×Dic1312yescomplemented
234C2×C13—22no—
235C2×C13—22no—
236C2×C13—41no—
237C2×C13—44no—
238C2×C13—161no—
239C2×C13#188711yescharacteristic
240C2×C13#189611yescharacteristic
241C2×C13#191311yescharacteristic
242C24—21no—
243C24—24no—
244C24—21no—
245C24—21no—
246C24—42no—
247C24—81no—
248C24C22⋊Dic1312yes—
249C24C2×C22⋊D1311yescharacteristic
250C2×D4—22no—
251C2×D4—44no—
252C2×D4—42no—
253C2×D4—42no—
254C2×D4—44no—
255C2×D4—41no—
256C2×D4—41no—
257C2×D4—82no—
258C2×D4—81no—
259C22×C4—21no—
260C22×C4—22no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—42no—
264C22×C4—81no—
265C22×C4—264no—
266C22×C4—268no—
267C22×C4—1042no—
268C22×C4—1042no—
269C22×C4C22⋊Dic1312yes—
270C22×C4D4×D1312yes—
271C22×C4#612912yes—
272C22×C4C22×Dic1311yescharacteristic
273C22×C4C2×C22⋊D1311yescharacteristic
274M16—1042no—
275C2×C8—522no—
276C4⋊C4—22no—
277C4⋊C4—44no—
278C22⋊C4—24no—
279C22⋊C4—24no—
280C22⋊C4—24no—
281C22⋊C4—44no—
282C22⋊C4—44no—
283C22⋊C4—42no—
284C22⋊C4—268no—
285C22⋊C4—268no—
286C42—81no—
287C42—1042no—
288C42—1042no—
289C13#940911yescharacteristic, complemented, Sylow
290C23—22no—
291C23—22no—
292C23—24no—
293C23—22no—
294C23—22no—
295C23—22no—
296C23—22no—
297C23—41no—
298C23—42no—
299C23—42no—
300C23—42no—
301C23—41no—
302C23—41no—
303C23—42no—
304C23—42no—
305C23—41no—
306C23—42no—
307C23—81no—
308C23—81no—
309C23—88no—
310C23#8807714yes—
311C23#8818911yescharacteristic
312C23#8819111yescharacteristic
313C23C2×C22⋊Dic1311yescharacteristic
314D4—82no—
315D4—88no—
316D4—82no—
317D4—82no—
318C2×C4—24no—
319C2×C4—22no—
320C2×C4—41no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—41no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—81no—
332C2×C4—268no—
333C2×C4—524no—
334C2×C4—524no—
335C2×C4—1048no—
336C2×C4D4×Dic1312yes—
337C2×C4#8819312yes—
338C8—1042no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—24no—
345C22—21no—
346C22—21no—
347C22—44no—
348C22—44no—
349C22—44no—
350C22—44no—
351C22—42no—
352C22—42no—
353C22—82no—
354C22—82no—
355C22—82no—
356C22—84no—
357C22—81no—
358C22—81no—
359C22—81no—
360C22#1171873812yes—
361C22#1171888111yescharacteristic
362C22C2×#8807712yes—
363C4—22no—
364C4—22no—
365C4—44no—
366C4—42no—
367C4—81no—
368C4—528no—
369C2—22no—
370C2—22no—
371C2—41no—
372C2—44no—
373C2—161no—
374C2#1311523511yescharacteristic
375C2#1311528011yescharacteristic
376C2#1311537911yescharacteristic
subgroupG/H
centerC22#11718881
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
Fitting, prime radicalC13×#2539C2
socleC22×C13#386
cosocleC23×C4×C13C23
hypercenter#2539D13
hypocenterC13#9409
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2539

Complements

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

NH ≅ G/Ntype
1. #13117189C2semidirect
2. #13113352C2semidirect
3. #13113163C2semidirect
4. #13112722C2semidirect
11. C13×#399C4semidirect
12. C13×#392C4semidirect
24. C22×D4×C13C2×C4semidirect
33. C2×C13×C4⋊C4C2×C4semidirect
49. C13×#95C2×C4semidirect
51. #88071D4semidirect
162. #399Dic13semidirect
163. #392Dic13semidirect
204. C22×D4C2×Dic13semidirect
214. C2×C4⋊C4C2×Dic13semidirect
233. #95C2×Dic13semidirect
289. C13#9409semidirect

Maximal subgroups

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

subgroupindex
#131171892
#131133522
#131131632
#131127222
C13×#25392
#940913