Finite Group Databasebeta

← #13119830

Subgroups — #13119830

Order 1664.

604 conjugacy classes of subgroups.

The subgroup lattice has 322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C22⋊D13C211yesmaximal, characteristic
2C2×#88142C211yesmaximal, characteristic, complemented
3C2×#88139C212yesmaximal
4C13×#380C211yesmaximal, characteristic, complemented
5#11718873C211yesmaximal, characteristic, complemented
6#11718648C211yesmaximal, characteristic, complemented
7#11718648C211yesmaximal, characteristic, complemented
8C4⋊C4×Dic13C211yesmaximal, characteristic, complemented
9#11718613C212yesmaximal, complemented
10#11718336C212yesmaximal, complemented
11#11718307C212yesmaximal, complemented
12C23×C4×C13C2211yescharacteristic
13C22×C22⋊D13C2211yescharacteristic
14C22×C4×D13C2211yescharacteristic
15C22×Dic26C2212yes—
16C2×C13×C4⋊C4C2211yescharacteristic
17C2×C13×C4⋊C4C2211yescharacteristic
18C2×C13×C22⋊C4C2212yes—
19C2×C22⋊Dic13C2212yes—
20C2×C22⋊Dic13C2211yescharacteristic
21C4×C22⋊D13—24no—
22C2×#6103C2212yes—
23C2×#6103C2212yes—
24C2×#6103C2211yescharacteristic
25C2×C4⋊Dic13C2211yescharacteristic
26C2×C4⋊Dic13C2211yescharacteristic
27C2×#6101C2212yes—
28C2×#6101C2211yescharacteristic
29C2×C4×Dic13C2212yes—
30C2×C4×Dic13C2211yescharacteristic
31#88142—24no—
32#88139—28no—
33C13×#95C2212yes—
34#88071C2212yes—
35#88071C2212yes—
36#88071C2212yes—
37#88071C2212yes—
38C24×C13C2311yescharacteristic
39C23×D13C2311yescharacteristic
40C22×C4×C13—22no—
41C22×C4×C13—22no—
42C22×C4×C13—22no—
43C22×C4×C13C2311yescharacteristic
44C22×C4×C13C2312yes—
45C22×C4×C13C2312yes—
46C22×C4×C13C2311yescharacteristic
47C2×C22⋊D13—22no—
48C2×C22⋊D13—22no—
49C2×C22⋊D13D414yes—
50C22×Dic13C2311yescharacteristic
51C22×Dic13C2312yes—
52C22×Dic13C2312yes—
53C22×Dic13C2311yescharacteristic
54C22×Dic13C2311yescharacteristic
55C2×C4×D13—22no—
56C2×C4×D13—22no—
57C2×C4×D13—22no—
58C2×Dic26—24no—
59C2×Dic26—24no—
60C2×Dic26—24no—
61C13×C4⋊C4—22no—
62C13×C4⋊C4—22no—
63C13×C22⋊C4—24no—
64C22⋊Dic13—24no—
65C22⋊Dic13—22no—
66#6103—24no—
67#6103—24no—
68#6103—22no—
69C4⋊Dic13—22no—
70C4⋊Dic13—22no—
71#6101—24no—
72#6101—22no—
73C4×Dic13—24no—
74C4×Dic13D414yes—
75#2547—131nomaximal, Sylow
76C23×C13—21no—
77C23×C13—21no—
78C23×C13—21no—
79C23×C13—21no—
80C23×C13—21no—
81C23×C13—21no—
82C23×C13C2×D412yes—
83C23×C13C2411yescharacteristic
84C22×D13—21no—
85C22×D13—21no—
86C22×D13—21no—
87C22×D13—21no—
88C22×D13—21no—
89C22×D13—21no—
90C22×D13C2×D412yes—
91C2×C4×C13—22no—
92C2×C4×C13—21no—
93C2×C4×C13—22no—
94C2×C4×C13—22no—
95C2×C4×C13—22no—
96C2×C4×C13—22no—
97C2×C4×C13—21no—
98C2×C4×C13—21no—
99C2×C4×C13—22no—
100C2×C4×C13—44no—
101C2×C4×C13C2×D412yes—
102C2×C4×C13#4112yes—
103C2×C4×C13#4112yes—
104C22⋊D13—28no—
105C2×Dic13—21no—
106C2×Dic13—21no—
107C2×Dic13—22no—
108C2×Dic13—22no—
109C2×Dic13—21no—
110C2×Dic13—22no—
111C2×Dic13—22no—
112C2×Dic13—22no—
113C2×Dic13—21no—
114C2×Dic13—21no—
115C2×Dic13—22no—
116C2×Dic13C2×D412yes—
117C2×Dic13C2×D412yes—
118C2×Dic13C2×D412yes—
119C2×Dic13#4112yes—
120C4×D13—44no—
121Dic26—48no—
122C2×C4⋊Q8—131no—
123C2×#124—132no—
124C2×C4×D4—131no—
125#397—132no—
126#397—132no—
127#391—132no—
128#380—131no—
129#380—131no—
130#380—131no—
131#380D1311yescharacteristic, complemented
132C4×C4⋊C4—131no—
133C22×C13—22no—
134C22×C13—22no—
135C22×C13—22no—
136C22×C13—41no—
137C22×C13—41no—
138C22×C13—41no—
139C22×C13—41no—
140C22×C13C22×D411yescharacteristic
141C22×C13C22×D411yescharacteristic
142C22×C13C2×#4111yescharacteristic
143C22×C13C2×#4111yescharacteristic
144C22×C13C2×#4111yescharacteristic
145C22×C132−1+411yescharacteristic
146C22×C132−1+411yescharacteristic
147C2×D13—22no—
148C2×D13—22no—
149C2×D13—22no—
150C2×D13—41no—
151C2×D13—41no—
152C2×D13—41no—
153C2×D13—41no—
154C4×C13—42no—
155C4×C13—41no—
156C4×C13—42no—
157C4×C13#12414yescomplemented
158Dic13—22no—
159Dic13—42no—
160Dic13—41no—
161Dic13—42no—
162Dic13#12114yes—
163C22×Q8—132no—
164C22×D4—131no—
165C23×C4—131no—
166C23×C4C2×D1311yescharacteristic
167C4⋊Q8—264no—
168#124—268no—
169C4×D4—264no—
170C2×C4⋊C4—131no—
171C2×C4⋊C4—132no—
172C2×C4⋊C4—131no—
173C2×C4⋊C4—131no—
174C2×C4⋊C4C2×D1311yescharacteristic
175C2×C4⋊C4C2×D1311yescharacteristic
176C2×C22⋊C4—131no—
177C2×C22⋊C4—132no—
178C2×C22⋊C4—131no—
179C2×C22⋊C4—132no—
180C2×C22⋊C4—132no—
181C2×C22⋊C4C2×D1312yes—
182C2×C42—131no—
183C2×C42—132no—
184#95—132no—
185#95—132no—
186#95—132no—
187#95—132no—
188#95C2×D1312yes—
189C2×C13—42no—
190C2×C13C2×#12111yescharacteristic
191C2×C13C2×#12411yescharacteristic
192C2×C13#53611yescharacteristic
193C2×C13#54711yescharacteristic
194C2×C13#54711yescharacteristic
195C2×C13#55611yescharacteristic
196C2×C13#55611yescharacteristic
197D13—42no—
198C24—131no—
199C24C22×D1311yescharacteristic
200C2×Q8—264no—
201C2×Q8—264no—
202C2×Q8—264no—
203C2×D4—134no—
204C2×D4—262no—
205C2×D4—262no—
206C22×C4—22no—
207C22×C4—22no—
208C22×C4—22no—
209C22×C4—131no—
210C22×C4—131no—
211C22×C4—131no—
212C22×C4—132no—
213C22×C4—132no—
214C22×C4—262no—
215C22×C4—262no—
216C22×C4—262no—
217C22×C4C22×D1311yescharacteristic
218C22×C4C22×D1312yes—
219C22×C4C22×D1312yes—
220C22×C4C22×D1311yescharacteristic
221C4⋊C4—22no—
222C4⋊C4—22no—
223C4⋊C4—262no—
224C4⋊C4—264no—
225C4⋊C4—262no—
226C4⋊C4—262no—
227C22⋊C4—24no—
228C22⋊C4—262no—
229C22⋊C4—264no—
230C22⋊C4—264no—
231C22⋊C4—262no—
232C22⋊C4—264no—
233C42—134no—
234C42—264no—
235C13#254711yescharacteristic, complemented, Sylow
236C23—21no—
237C23—21no—
238C23—21no—
239C23—21no—
240C23—21no—
241C23—21no—
242C23—132no—
243C23—261no—
244C23—261no—
245C23—261no—
246C23—261no—
247C23—261no—
248C23—261no—
249C23D4×D1312yes—
250C23C23×D1311yescharacteristic
251Q8—528no—
252D4—268no—
253C2×C4—21no—
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—21no—
257C2×C4—22no—
258C2×C4—22no—
259C2×C4—21no—
260C2×C4—22no—
261C2×C4—22no—
262C2×C4—44no—
263C2×C4—132no—
264C2×C4—132no—
265C2×C4—132no—
266C2×C4—132no—
267C2×C4—261no—
268C2×C4—261no—
269C2×C4—262no—
270C2×C4—261no—
271C2×C4—262no—
272C2×C4—262no—
273C2×C4—261no—
274C2×C4—262no—
275C2×C4—261no—
276C2×C4—262no—
277C2×C4—262no—
278C2×C4—524no—
279C2×C4#612712yes—
280C2×C4D4×D1312yes—
281C2×C4#612912yes—
282C22—22no—
283C22—22no—
284C22—22no—
285C22—41no—
286C22—41no—
287C22—41no—
288C22—41no—
289C22—262no—
290C22—262no—
291C22—262no—
292C22—521no—
293C22—521no—
294C22—521no—
295C22—521no—
296C22C2×#612711yescharacteristic
297C22C2×D4×D1311yescharacteristic
298C22C2×D4×D1311yescharacteristic
299C22C2×#612911yescharacteristic
300C22#8825411yescharacteristic
301C22#41×D1311yescharacteristic
302C22#8825711yescharacteristic
303C4—41no—
304C4—42no—
305C4—42no—
306C4—134no—
307C4—262no—
308C4—521no—
309C4—522no—
310C4—522no—
311C4#8813914yescomplemented
312C2—42no—
313C2—522no—
314C2C2×#8813911yescharacteristic
315C2#1171921211yescharacteristic
316C2#1171923811yescharacteristic
317C2D13×#12111yescharacteristic
318C2#1171931611yescharacteristic
319C2#1171933311yescharacteristic
320C2#1171934611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#380C2
prime radicalC22×C22⋊D13C22
hypercenter#380D13
hypocenterC13#2547
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #380

Complements

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

NH ≅ G/Ntype
2. C2×#88142C2semidirect
4. C13×#380C2semidirect
5. #11718873C2semidirect
6. #11718648C2semidirect
7. #11718648C2semidirect
8. C4⋊C4×Dic13C2semidirect
9. #11718613C2semidirect
10. #11718336C2semidirect
11. #11718307C2semidirect
131. #380D13semidirect
157. C4×C13#124semidirect
235. C13#2547semidirect
311. C4#88139semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C22⋊D132
C2×#881422
C2×#881392
C13×#3802
#117188732
#117186482
C4⋊C4×Dic132
#117186132
#117183362
#117183072
#254713