Finite Group Databasebeta

← #13119151

Subgroups — #13119151

Order 1664.

584 conjugacy classes of subgroups.

The subgroup lattice has 320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊C4×D13C211yesmaximal, characteristic, complemented
2C2×C4×D52C211yesmaximal, characteristic
3C13×#389C211yesmaximal, characteristic, complemented
4#11718653C212yesmaximal, complemented
5#11718650C212yesmaximal, complemented
6#11718648C211yesmaximal, characteristic, complemented
7#11718648C211yesmaximal, characteristic, complemented
8#11718648C211yesmaximal, characteristic, complemented
9#11718589C211yesmaximal, characteristic, complemented
10#11718326C212yesmaximal
11#11718321C212yesmaximal, complemented
12C22×D52C2211yescharacteristic
13C22×C4×D13C2211yescharacteristic
14C22×C4×D13C2211yescharacteristic
15C22×C4×D13C2212yes—
16C2×C13×C4⋊C4C2211yescharacteristic
17C2×C13×C4⋊C4C2211yescharacteristic
18C2×C13×C4⋊C4C2212yes—
19C2×C42×C13C2211yescharacteristic
20C2×#6103C2211yescharacteristic
21C2×#6103C2211yescharacteristic
22C2×#6103C2212yes—
23C2×#6103C2212yes—
24C2×#6103C2212yes—
25C2×C4⋊Dic13C2211yescharacteristic
26C2×C4⋊Dic13C2211yescharacteristic
27C2×C4⋊Dic13C2211yescharacteristic
28C2×#6101C2212yes—
29C2×#6101C2212yes—
30C4⋊C4×D13—24no—
31C4×D52—24no—
32C13×#95C2212yes—
33#88071C2212yes—
34#88071C2212yes—
35#88071C2212yes—
36#88071C2212yes—
37C23×D13C2311yescharacteristic
38C23×D13C2311yescharacteristic
39C22×C4×C13C2312yes—
40C22×C4×C13C2312yes—
41C22×C4×C13C2311yescharacteristic
42C22×C4×C13C2311yescharacteristic
43C22×C4×C13C2311yescharacteristic
44C22×Dic13C2311yescharacteristic
45C22×Dic13C2312yes—
46C22×Dic13C2312yes—
47C22×Dic13C2311yescharacteristic
48C2×D52—22no—
49C2×D52—22no—
50C2×D52Q814yes—
51C2×C4×D13—22no—
52C2×C4×D13—22no—
53C2×C4×D13—24no—
54C2×C4×D13—22no—
55C2×C4×D13—22no—
56C2×C4×D13—22no—
57C2×C4×D13—42no—
58C2×C4×D13—42no—
59C2×C4×D13D414yes—
60C13×C4⋊C4—22no—
61C13×C4⋊C4—22no—
62C13×C4⋊C4—42no—
63C42×C13—22no—
64#6103—22no—
65#6103—24no—
66#6103—22no—
67#6103—42no—
68#6103—42no—
69C4⋊Dic13—22no—
70C4⋊Dic13—22no—
71C4⋊Dic13—22no—
72#6101—24no—
73#6101—42no—
74#2487—131nomaximal, Sylow
75C23×C13C2411yescharacteristic
76C22×D13—21no—
77C22×D13—21no—
78C22×D13—21no—
79C22×D13—21no—
80C22×D13—21no—
81C22×D13—21no—
82C22×D13—21no—
83C22×D13—21no—
84C22×D13—21no—
85C22×D13—21no—
86C22×D13C2×D412yes—
87C22×D13C2×Q812yes—
88C22×D13C2×Q812yes—
89C22×D13#4112yes—
90C2×C4×C13—21no—
91C2×C4×C13—21no—
92C2×C4×C13—22no—
93C2×C4×C13—21no—
94C2×C4×C13—22no—
95C2×C4×C13—22no—
96C2×C4×C13—21no—
97C2×C4×C13—22no—
98C2×C4×C13—22no—
99C2×C4×C13—21no—
100C2×C4×C13—22no—
101C2×C4×C13C2×D412yes—
102C2×C4×C13C2×Q812yes—
103C2×C4×C13#4112yes—
104C2×C4×C13#4112yes—
105C2×Dic13—21no—
106C2×Dic13—21no—
107C2×Dic13—22no—
108C2×Dic13—21no—
109C2×Dic13—22no—
110C2×Dic13—22no—
111C2×Dic13—21no—
112C2×Dic13—21no—
113C2×Dic13—22no—
114C2×Dic13—22no—
115C2×Dic13—22no—
116C2×Dic13C2×D412yes—
117D52—28no—
118C4×D13—28no—
119C4×D13—48no—
120C4×D13—44no—
121C2×C4×D4—131no—
122C22×C4⋊C4—131no—
123#400—132no—
124#399—132no—
125#389—131no—
126#389D1311yescharacteristic, complemented
127#386—132no—
128#385—132no—
129#380—131no—
130#380—131no—
131#380—131no—
132C22×C13C22×D411yescharacteristic
133C22×C13C22×Q811yescharacteristic
134C22×C13C2×#4111yescharacteristic
135C22×C13C2×#4111yescharacteristic
136C22×C13C2×#4111yescharacteristic
137C22×C13H(5,𝔽2)11yescharacteristic
138C22×C13H(5,𝔽2)11yescharacteristic
139C2×D13—22no—
140C2×D13—22no—
141C2×D13—22no—
142C2×D13—22no—
143C2×D13—22no—
144C2×D13—22no—
145C2×D13—22no—
146C2×D13—22no—
147C2×D13—22no—
148C2×D13—41no—
149C2×D13—41no—
150C2×D13—41no—
151C2×D13—41no—
152C2×D13C22⋊Q814yes—
153C4×C13—22no—
154C4×C13—42no—
155C4×C13—41no—
156C4×C13—42no—
157C4×C13#12314yes—
158Dic13—22no—
159Dic13—41no—
160Dic13—42no—
161Dic13—42no—
162C22×D4—131no—
163C23×C4—131no—
164C23×C4—131no—
165C23×C4—132no—
166C4×D4—264no—
167C2×C4⋊C4—132no—
168C2×C4⋊C4—131no—
169C2×C4⋊C4—131no—
170C2×C4⋊C4—131no—
171C2×C4⋊C4—132no—
172C2×C4⋊C4—264no—
173C2×C4⋊C4C2×D1311yescharacteristic
174C2×C4⋊C4C2×D1311yescharacteristic
175C2×C4⋊C4C2×D1312yes—
176C2×C22⋊C4—131no—
177C2×C22⋊C4—131no—
178C2×C22⋊C4—132no—
179C2×C22⋊C4—132no—
180C2×C22⋊C4—132no—
181C2×C42C2×D1311yescharacteristic
182#95—132no—
183#95—132no—
184#95—132no—
185#95—132no—
186#95C2×D1312yes—
187C2×C13C2×C22⋊Q811yescharacteristic
188C2×C13C2×#12311yescharacteristic
189C2×C13#53511yescharacteristic
190C2×C13#55311yescharacteristic
191C2×C13#55311yescharacteristic
192C2×C13#55411yescharacteristic
193C2×C13#55411yescharacteristic
194D13—24no—
195D13—42no—
196C24—131no—
197C24—131no—
198C2×D4—134no—
199C2×D4—262no—
200C2×D4—262no—
201C22×C4—131no—
202C22×C4—134no—
203C22×C4—131no—
204C22×C4—132no—
205C22×C4—132no—
206C22×C4—264no—
207C22×C4—262no—
208C22×C4—262no—
209C22×C4—262no—
210C22×C4—262no—
211C22×C4—262no—
212C22×C4—522no—
213C22×C4—522no—
214C22×C4C22×D1312yes—
215C22×C4C22×D1312yes—
216C22×C4C22×D1311yescharacteristic
217C22×C4C22×D1311yescharacteristic
218C22×C4C22×D1311yescharacteristic
219C4⋊C4—22no—
220C4⋊C4—22no—
221C4⋊C4—42no—
222C4⋊C4—264no—
223C4⋊C4—262no—
224C4⋊C4—262no—
225C4⋊C4—262no—
226C4⋊C4—522no—
227C22⋊C4—262no—
228C22⋊C4—262no—
229C22⋊C4—264no—
230C22⋊C4—522no—
231C22⋊C4—522no—
232C42—22no—
233C13#248711yescharacteristic, complemented, Sylow
234C23—132no—
235C23—132no—
236C23—132no—
237C23—132no—
238C23—261no—
239C23—261no—
240C23—261no—
241C23—261no—
242C23—261no—
243C23—261no—
244C23—261no—
245C23—261no—
246C23—261no—
247C23—261no—
248C23C23×D1311yescharacteristic
249D4—268no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—22no—
253C2×C4—21no—
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—21no—
257C2×C4—22no—
258C2×C4—22no—
259C2×C4—22no—
260C2×C4—21no—
261C2×C4—132no—
262C2×C4—261no—
263C2×C4—261no—
264C2×C4—268no—
265C2×C4—261no—
266C2×C4—261no—
267C2×C4—262no—
268C2×C4—262no—
269C2×C4—262no—
270C2×C4—261no—
271C2×C4—262no—
272C2×C4—262no—
273C2×C4—262no—
274C2×C4—528no—
275C2×C4—524no—
276C2×C4#612712yes—
277C2×C4D4×D1312yes—
278C2×C4Q8×D1312yes—
279C2×C4#613112yes—
280C22—134no—
281C22—262no—
282C22—262no—
283C22—262no—
284C22—262no—
285C22—262no—
286C22—262no—
287C22—262no—
288C22—262no—
289C22—262no—
290C22—521no—
291C22—521no—
292C22—521no—
293C22—521no—
294C22C2×#612711yescharacteristic
295C22C2×D4×D1311yescharacteristic
296C22#8825111yescharacteristic
297C22C2×Q8×D1311yescharacteristic
298C22C2×#613111yescharacteristic
299C22#41×D1311yescharacteristic
300C22#8825611yescharacteristic
301C4—22no—
302C4—42no—
303C4—41no—
304C4—42no—
305C4—262no—
306C4—521no—
307C4—522no—
308C4—522no—
309C4#8814814yes—
310C2—264no—
311C2—522no—
312C2C2×#8814811yescharacteristic
313C2#1171926311yescharacteristic
314C2#1171928411yescharacteristic
315C2#1171931211yescharacteristic
316C2D13×C22⋊Q811yescharacteristic
317C2#1171940011yescharacteristic
318C2#1171943511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#389C2
prime radicalC22×D52C22
hypercenter#389D13
hypocenterC13#2487
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
1. C2×C4⋊C4×D13C2semidirect
3. C13×#389C2semidirect
4. #11718653C2semidirect
5. #11718650C2semidirect
6. #11718648C2semidirect
7. #11718648C2semidirect
8. #11718648C2semidirect
9. #11718589C2semidirect
11. #11718321C2semidirect
126. #389D13semidirect
233. C13#2487semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊C4×D132
C2×C4×D522
C13×#3892
#117186532
#117186502
#117186482
#117185892
#117183262
#117183212
#248713