Finite Group Databasebeta

← #15830746

Subgroups — #15830746

Order 3328.

974 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123877C211yesmaximal, characteristic
2#13117809C211yesmaximal, characteristic
3#13113400C212yesmaximal, complemented
4#13113369C214yesmaximal, complemented
5#13113356C214yesmaximal, complemented
6#13113335C212yesmaximal, complemented
7C13×#3501C211yesmaximal, characteristic
8C13×#554—24no—
9C13×#554C414yescomplemented
10D4×Q8×C13C414yescomplemented
11C13×#544—21no—
12C13×#543—22no—
13C13×#533C2212yes—
14C2×C13×C22⋊Q8C2214yes—
15C13×#518—21no—
16C2×C4×D4×C13C2211yescharacteristic
17#11718882—21no—
18#11718872C2212yes—
19C4×C22⋊Dic13C2212yes—
20#11718868C2214yes—
21#11718673—24no—
22C4⋊C4×Dic13—21no—
23#11718612—22no—
24#11718597C2211yescharacteristic
25C4×C4⋊Dic13C2211yescharacteristic
26#11718586C2212yes—
27#11718130C2214yes—
28#11718130C2218yes—
29#11718130C2214yes—
30C22×Q8×C13C2×C414yes—
31C22×D4×C13D411yescharacteristic
32C23×C4×C13C2312yes—
33C13×C4⋊Q8—24no—
34C13×C4⋊Q8C2×C412yes—
35C13×C4⋊Q8C2×C412yes—
36C13×#125—24no—
37C13×#125—22no—
38C13×C22⋊Q8—24no—
39C13×C22⋊Q8—24no—
40C13×C22⋊Q8—22no—
41C13×C22⋊Q8—28no—
42C13×C22⋊Q8—28no—
43C13×C22⋊Q8C2×C418yes—
44C13×C22⋊Q8C2314yes—
45C4×Q8×C13—22no—
46C4×Q8×C13C2×C414yes—
47C4×D4×C13—24no—
48C4×D4×C13—24no—
49C4×D4×C13C2×C414yes—
50C4×D4×C13D414yes—
51C13×#117—22no—
52C2×C13×C4⋊C4—24no—
53C2×C13×C4⋊C4C2×C414yes—
54C2×C13×C4⋊C4D411yescharacteristic
55C2×C13×C22⋊C4—24no—
56C2×C13×C22⋊C4D412yes—
57C2×C42×C13C2311yescharacteristic
58C2×C22⋊Dic13—22no—
59C2×C22⋊Dic13—22no—
60C2×C4⋊Dic13—21no—
61C2×C4⋊Dic13—21no—
62C2×C4×Dic13—21no—
63C2×C4×Dic13—22no—
64C2×#6099—24no—
65#88071—21no—
66#88071—22no—
67#88071C2311yescharacteristic
68#88071C2311yescharacteristic
69#88071C2312yes—
70C22⋊#1055—24no—
71C22⋊#1055C2314yes—
72C4⋊#1055—22no—
73C4×#1055—22no—
74#17627—131nomaximal, Sylow
75C24×C13C2×D412yes—
76C2×Q8×C13—22no—
77C2×Q8×C13—24no—
78C2×Q8×C13—84no—
79C2×Q8×C13C22×C414yes—
80C2×D4×C13—22no—
81C2×D4×C13—22no—
82C2×D4×C13C22⋊C414yes—
83C22×C4×C13—24no—
84C22×C4×C13—24no—
85C22×C4×C13—82no—
86C22×C4×C13C22×C414yes—
87C22×C4×C13C2×D412yes—
88C22×C4×C13C2×D411yescharacteristic
89C22×C4×C13C2×D414yes—
90C22×C4×C13C2×D411yescharacteristic
91C22×C4×C13C2411yescharacteristic
92C22×Dic13—21no—
93C22×Dic13—22no—
94C22×Dic13—21no—
95C13×C4⋊C4—28no—
96C13×C4⋊C4—24no—
97C13×C4⋊C4—22no—
98C13×C4⋊C4—22no—
99C13×C4⋊C4—22no—
100C13×C4⋊C4—24no—
101C13×C4⋊C4—24no—
102C13×C4⋊C4C22⋊C414yes—
103C13×C4⋊C4C22×C414yes—
104C13×C22⋊C4—28no—
105C13×C22⋊C4—24no—
106C13×C22⋊C4C22⋊C418yes—
107C42×C13—24no—
108C42×C13C22×C412yes—
109C42×C13C2×D412yes—
110C22⋊Dic13—44no—
111C22⋊Dic13—82no—
112C4⋊Dic13—42no—
113C4⋊Dic13—42no—
114C4×Dic13—42no—
115C4×Dic13—82no—
116#6099—84no—
117C2×#1055—24no—
118#3501D1311yescharacteristic
119#2975—131no—
120#2357—131no—
121#1518—132no—
122#1511—134no—
123#1508—134no—
124#1503—132no—
125C23×C13—22no—
126C23×C13—22no—
127C23×C13—42no—
128C23×C13—42no—
129C23×C13C2×C22⋊C414yes—
130C23×C13C22×D411yescharacteristic
131Q8×C13—44no—
132Q8×C13—82no—
133Q8×C13—84no—
134D4×C13—28no—
135C2×C4×C13—24no—
136C2×C4×C13—24no—
137C2×C4×C13—44no—
138C2×C4×C13—42no—
139C2×C4×C13—41no—
140C2×C4×C13—41no—
141C2×C4×C13—44no—
142C2×C4×C13—84no—
143C2×C4×C13—84no—
144C2×C4×C13C2×C22⋊C412yes—
145C2×C4×C13C2×C22⋊C414yes—
146C2×C4×C13C2×C22⋊C412yes—
147C2×C4×C13#13712yes—
148C2×C4×C13#13712yes—
149C2×C4×C13C23×C411yescharacteristic
150C2×C4×C13C22×D411yescharacteristic
151C2×Dic13—22no—
152C2×Dic13—41no—
153C2×Dic13—41no—
154C2×Dic13—42no—
155C2×Dic13—41no—
156C2×Dic13—42no—
157C2×Dic13—41no—
158C2×Dic13—41no—
159C2×Dic13—42no—
160#1055—44no—
161#554—24no—
162#554Dic1314yescomplemented
163D4×Q8Dic1314yescomplemented
164#544—21no—
165#543—22no—
166#533C2×D1312yes—
167C2×C22⋊Q8C2×D1314yes—
168#518—21no—
169C2×C4×D4C2×D1311yescharacteristic
170#436—264no—
171#431—132no—
172#407—134no—
173#390—261no—
174#388—262no—
175#382—131no—
176#381—132no—
177C4×C4⋊C4—131no—
178C4×C4⋊C4—261no—
179C4×C22⋊C4—132no—
180#328—134no—
181#328—134no—
182#328—138no—
183C22×C13—21no—
184C22×C13—21no—
185C22×C13—24no—
186C22×C13—24no—
187C22×C13—24no—
188C22×C13—82no—
189C22×C13—82no—
190C22×C13C22×C22⋊C411yescharacteristic
191C22×C13C2×#13711yescharacteristic
192C22×C13C2×#13711yescharacteristic
193C4×C13—21no—
194C4×C13—21no—
195C4×C13—24no—
196C4×C13—22no—
197C4×C13—44no—
198C4×C13—44no—
199C4×C13#41914yes—
200Dic13—42no—
201Dic13—81no—
202Dic13—82no—
203C22×Q8C2×Dic1314yes—
204C22×D4C22⋊D1311yescharacteristic
205C23×C4C22×D1312yes—
206C2×M16—264no—
207C4⋊Q8—24no—
208C4⋊Q8C2×Dic1312yes—
209C4⋊Q8C2×Dic1312yes—
210#125—24no—
211#125—22no—
212C22⋊Q8—24no—
213C22⋊Q8—24no—
214C22⋊Q8—22no—
215C22⋊Q8—28no—
216C22⋊Q8—28no—
217C22⋊Q8C2×Dic1318yes—
218C22⋊Q8C22×D1314yes—
219C4×Q8—22no—
220C4×Q8C2×Dic1314yes—
221C4×D4—24no—
222C4×D4—24no—
223C4×D4C2×Dic1314yes—
224C4×D4C22⋊D1314yes—
225#117—22no—
226C2×C4⋊C4—24no—
227C2×C4⋊C4—261no—
228C2×C4⋊C4—261no—
229C2×C4⋊C4C2×Dic1314yes—
230C2×C4⋊C4C22⋊D1311yescharacteristic
231C2×C22⋊C4—24no—
232C2×C22⋊C4—262no—
233C2×C22⋊C4—262no—
234C2×C22⋊C4C22⋊D1312yes—
235C2×C42—261no—
236C2×C42—262no—
237C2×C42C22×D1311yescharacteristic
238C4⋊C8—262no—
239C22⋊C8—134no—
240C22⋊C8—264no—
241C4×C8—262no—
242#95—131no—
243#95—132no—
244#95—131no—
245#95—262no—
246#95—261no—
247C2×C13—21no—
248C2×C13—21no—
249C2×C13—44no—
250C2×C13#288311yescharacteristic
251C2×C13C2×#41911yescharacteristic
252C2×C13#290111yescharacteristic
253C24C2×C22⋊D1312yes—
254C2×Q8—22no—
255C2×Q8—24no—
256C2×Q8—84no—
257C2×Q8C22×Dic1314yes—
258C2×D4—22no—
259C2×D4—22no—
260C2×D4C22⋊Dic1314yes—
261C22×C4—24no—
262C22×C4—24no—
263C22×C4—82no—
264C22×C4—261no—
265C22×C4—262no—
266C22×C4—261no—
267C22×C4C22×Dic1314yes—
268C22×C4C2×C22⋊D1312yes—
269C22×C4C2×C22⋊D1311yescharacteristic
270C22×C4C2×C22⋊D1314yes—
271C22×C4C2×C22⋊D1311yescharacteristic
272C22×C4C23×D1311yescharacteristic
273M16—1044no—
274C2×C8—264no—
275C4⋊C4—28no—
276C4⋊C4—24no—
277C4⋊C4—22no—
278C4⋊C4—22no—
279C4⋊C4—22no—
280C4⋊C4—24no—
281C4⋊C4—24no—
282C4⋊C4—522no—
283C4⋊C4—522no—
284C4⋊C4C22⋊Dic1314yes—
285C4⋊C4C22×Dic1314yes—
286C22⋊C4—28no—
287C22⋊C4—24no—
288C22⋊C4—524no—
289C22⋊C4—1042no—
290C22⋊C4C22⋊Dic1318yes—
291C42—24no—
292C42—522no—
293C42—1042no—
294C42C22×Dic1312yes—
295C42C2×C22⋊D1312yes—
296C13#1762711yescharacteristic, complemented, Sylow
297C23—22no—
298C23—22no—
299C23—42no—
300C23—42no—
301C23C2×C22⋊Dic1314yes—
302C23C22×C22⋊D1311yescharacteristic
303Q8—44no—
304Q8—84no—
305Q8—82no—
306D4—28no—
307C2×C4—24no—
308C2×C4—24no—
309C2×C4—42no—
310C2×C4—41no—
311C2×C4—44no—
312C2×C4—41no—
313C2×C4—44no—
314C2×C4—84no—
315C2×C4—84no—
316C2×C4—262no—
317C2×C4—521no—
318C2×C4—521no—
319C2×C4—522no—
320C2×C4—522no—
321C2×C4—521no—
322C2×C4—521no—
323C2×C4—521no—
324C2×C4—522no—
325C2×C4#8819612yes—
326C2×C4#8819612yes—
327C2×C4C2×C22⋊Dic1312yes—
328C2×C4C2×C22⋊Dic1314yes—
329C2×C4C2×C22⋊Dic1312yes—
330C2×C4C23×Dic1311yescharacteristic
331C2×C4C22×C22⋊D1311yescharacteristic
332C8—524no—
333C22—21no—
334C22—21no—
335C22—24no—
336C22—24no—
337C22—24no—
338C22—82no—
339C22—82no—
340C22C2×#8819611yescharacteristic
341C22C2×#8819611yescharacteristic
342C22C22×C22⋊Dic1311yescharacteristic
343C4—22no—
344C4—21no—
345C4—21no—
346C4—24no—
347C4—44no—
348C4—44no—
349C4—522no—
350C4—1041no—
351C4—1042no—
352C4#1171888614yes—
353C2—21no—
354C2—21no—
355C2—44no—
356C2#1312329711yescharacteristic
357C2C2×#1171888611yescharacteristic
358C2#1312338311yescharacteristic
subgroupG/H
centerC22C22×C22⋊Dic13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#3501C2
socleC22×C13C22×C22⋊C4
prime radicalC22×D4×C13D4
cosocleC22×C4×C13C24
hypercenter#3501D13
hypocenterC13#17627
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ #3501

Complements

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

NH ≅ G/Ntype
3. #13113400C2semidirect
4. #13113369C2semidirect
5. #13113356C2semidirect
6. #13113335C2semidirect
9. C13×#554C4semidirect
10. D4×Q8×C13C4semidirect
162. #554Dic13semidirect
163. D4×Q8Dic13semidirect
296. C13#17627semidirect

Maximal subgroups

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

subgroupindex
#131238772
#131178092
#131134002
#131133692
#131133562
#131133352
C13×#35012
#1762713