Finite Group Databasebeta

← #13118266

Subgroups — #13118266

Order 1664.

604 conjugacy classes of subgroups.

The subgroup lattice has 326 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×C22⋊Q8C211yesmaximal, characteristic, complemented
2C2×#88200C211yesmaximal, characteristic, complemented
3C2×C4×C22⋊D13C211yesmaximal, characteristic
4C2×#88180C211yesmaximal, characteristic, complemented
5#11718891C211yesmaximal, characteristic, complemented
6#11718651C212yesmaximal, complemented
7#11718648C211yesmaximal, characteristic, complemented
8#11718634C211yesmaximal, characteristic, complemented
9#11718633C212yesmaximal, complemented
10#11718620C212yesmaximal
11#11718613C212yesmaximal, complemented
12C22×Q8×C13C2211yescharacteristic
13C23×C4×C13C2211yescharacteristic
14C22×C22⋊D13C2211yescharacteristic
15C22×C4×D13C2211yescharacteristic
16C13×C22⋊Q8—24no—
17C2×C13×C4⋊C4C2212yes—
18C2×C13×C4⋊C4C2211yescharacteristic
19C2×C13×C22⋊C4C2212yes—
20C2×C22⋊Dic13C2212yes—
21C2×C22⋊Dic13C2211yescharacteristic
22#88200—24no—
23C4×C22⋊D13—24no—
24C2×#6103C2211yescharacteristic
25C2×#6103C2212yes—
26C2×#6103C2212yes—
27#88180—24no—
28C2×C4⋊Dic13C2211yescharacteristic
29C2×C4⋊Dic13C2211yescharacteristic
30C2×#6101C2211yescharacteristic
31C2×#6101C2212yes—
32C2×#6101C2212yes—
33C2×C4×Dic13C2212yes—
34C2×C4×Dic13C2211yescharacteristic
35#88071C2212yes—
36#88071C2212yes—
37#88071C2212yes—
38#88071C2212yes—
39C24×C13C2311yescharacteristic
40C23×D13C2311yescharacteristic
41C2×Q8×C13—22no—
42C2×Q8×C13—22no—
43C2×Q8×C13—22no—
44C22×C4×C13—22no—
45C22×C4×C13—22no—
46C22×C4×C13D414yes—
47C22×C4×C13C2312yes—
48C22×C4×C13C2312yes—
49C22×C4×C13C2311yescharacteristic
50C22×C4×C13C2311yescharacteristic
51C2×C22⋊D13—22no—
52C2×C22⋊D13—22no—
53C2×C22⋊D13—22no—
54C22×Dic13C2311yescharacteristic
55C22×Dic13C2312yes—
56C22×Dic13C2311yescharacteristic
57C22×Dic13C2312yes—
58C22×Dic13C2311yescharacteristic
59C2×C4×D13—22no—
60C2×C4×D13—22no—
61C2×C4×D13—22no—
62C13×C4⋊C4—22no—
63C13×C4⋊C4—24no—
64C13×C22⋊C4—24no—
65C22⋊Dic13—22no—
66C22⋊Dic13—24no—
67#6103—24no—
68#6103—22no—
69#6103—24no—
70C4⋊Dic13—22no—
71C4⋊Dic13D414yescomplemented
72#6101—22no—
73#6101—24no—
74#6101—24no—
75C4×Dic13—22no—
76C4×Dic13—24no—
77#2415—131nomaximal, Sylow
78C23×C13—21no—
79C23×C13—21no—
80C23×C13—21no—
81C23×C13—21no—
82C23×C13—21no—
83C23×C13—21no—
84C23×C13C2×D412yes—
85C23×C13C2411yescharacteristic
86C22×D13—21no—
87C22×D13—21no—
88C22×D13—21no—
89C22×D13—21no—
90C22×D13—21no—
91C22×D13—21no—
92C22×D13#4112yes—
93Q8×C13—44no—
94C2×C4×C13—21no—
95C2×C4×C13—21no—
96C2×C4×C13—28no—
97C2×C4×C13—22no—
98C2×C4×C13—22no—
99C2×C4×C13—22no—
100C2×C4×C13—22no—
101C2×C4×C13—22no—
102C2×C4×C13—22no—
103C2×C4×C13C2×D412yes—
104C2×C4×C13C2×D412yes—
105C2×C4×C13C2×D412yes—
106C2×C4×C13#4112yes—
107C22⋊D13—28no—
108C2×Dic13—21no—
109C2×Dic13—22no—
110C2×Dic13—21no—
111C2×Dic13—22no—
112C2×Dic13—22no—
113C2×Dic13—21no—
114C2×Dic13—21no—
115C2×Dic13—21no—
116C2×Dic13—22no—
117C2×Dic13—21no—
118C2×Dic13—21no—
119C2×Dic13—21no—
120C2×Dic13—22no—
121C2×Dic13C2×D414yes—
122C2×Dic13#4112yes—
123C4×D13—44no—
124C2×C22⋊Q8—131no—
125C2×C22⋊Q8D1311yescharacteristic, complemented
126C2×C4×D4—131no—
127C2×#117—131no—
128#397—132no—
129#394—132no—
130#391—131no—
131#389—132no—
132#389—131no—
133#388—132no—
134#380—131no—
135C22×C13—22no—
136C22×C13—22no—
137C22×C13—22no—
138C22×C13—41no—
139C22×C13—41no—
140C22×C13—41no—
141C22×C13—41no—
142C22×C13C22×D411yescharacteristic
143C22×C13C22×D411yescharacteristic
144C22×C13C2×#4111yescharacteristic
145C22×C13C2×#4111yescharacteristic
146C22×C13C2×#4111yescharacteristic
147C22×C132−1+411yescharacteristic
148C22×C132−1+411yescharacteristic
149C2×D13—22no—
150C2×D13—22no—
151C2×D13—22no—
152C2×D13—41no—
153C2×D13—41no—
154C2×D13—41no—
155C2×D13—41no—
156C4×C13—22no—
157C4×C13—42no—
158C4×C13—42no—
159C4×C13#12114yes—
160Dic13—22no—
161Dic13—24no—
162Dic13—41no—
163Dic13—41no—
164Dic13—42no—
165C22×Q8C2×D1311yescharacteristic
166C22×D4—131no—
167C23×C4—131no—
168C23×C4C2×D1311yescharacteristic
169C22⋊Q8—24no—
170C22⋊Q8—264no—
171C4×D4—264no—
172#117—264no—
173C2×C4⋊C4—131no—
174C2×C4⋊C4—131no—
175C2×C4⋊C4—131no—
176C2×C4⋊C4—132no—
177C2×C4⋊C4—132no—
178C2×C4⋊C4C2×D1311yescharacteristic
179C2×C4⋊C4C2×D1312yes—
180C2×C22⋊C4—132no—
181C2×C22⋊C4—131no—
182C2×C22⋊C4—131no—
183C2×C22⋊C4—132no—
184C2×C22⋊C4—132no—
185C2×C22⋊C4C2×D1312yes—
186C2×C42—132no—
187C2×C42—131no—
188#95—132no—
189#95—132no—
190#95—132no—
191#95—132no—
192C2×C13—42no—
193C2×C13C2×#12111yescharacteristic
194C2×C13#52511yescharacteristic
195C2×C13#53611yescharacteristic
196C2×C13#54711yescharacteristic
197C2×C13#54811yescharacteristic
198C2×C13#55211yescharacteristic
199C2×C13#55611yescharacteristic
200D13—42no—
201C24—131no—
202C24C22×D1311yescharacteristic
203C2×Q8—22no—
204C2×Q8—22no—
205C2×Q8—22no—
206C2×D4—262no—
207C2×D4—262no—
208C2×D4—262no—
209C22×C4—22no—
210C22×C4—22no—
211C22×C4—131no—
212C22×C4—132no—
213C22×C4—131no—
214C22×C4—132no—
215C22×C4—131no—
216C22×C4—262no—
217C22×C4—262no—
218C22×C4—262no—
219C22×C4C22⋊D1314yes—
220C22×C4C22×D1312yes—
221C22×C4C22×D1312yes—
222C22×C4C22×D1311yescharacteristic
223C22×C4C22×D1311yescharacteristic
224C4⋊C4—22no—
225C4⋊C4—24no—
226C4⋊C4—134no—
227C4⋊C4—264no—
228C4⋊C4—264no—
229C4⋊C4—262no—
230C4⋊C4—262no—
231C22⋊C4—24no—
232C22⋊C4—264no—
233C22⋊C4—264no—
234C22⋊C4—264no—
235C22⋊C4—262no—
236C22⋊C4—262no—
237C42—264no—
238C42—262no—
239C13#241511yescharacteristic, complemented, Sylow
240C23—21no—
241C23—21no—
242C23—21no—
243C23—21no—
244C23—21no—
245C23—21no—
246C23—132no—
247C23—261no—
248C23—261no—
249C23—261no—
250C23—261no—
251C23—261no—
252C23—261no—
253C23C2×C22⋊D1312yes—
254C23C23×D1311yescharacteristic
255Q8—44no—
256D4—268no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—28no—
260C2×C4—22no—
261C2×C4—22no—
262C2×C4—22no—
263C2×C4—22no—
264C2×C4—22no—
265C2×C4—22no—
266C2×C4—134no—
267C2×C4—132no—
268C2×C4—262no—
269C2×C4—262no—
270C2×C4—261no—
271C2×C4—261no—
272C2×C4—262no—
273C2×C4—261no—
274C2×C4—261no—
275C2×C4—261no—
276C2×C4—261no—
277C2×C4—262no—
278C2×C4—262no—
279C2×C4—261no—
280C2×C4—261no—
281C2×C4—524no—
282C2×C4D4×D1312yes—
283C2×C4#612912yes—
284C2×C4C2×C22⋊D1312yes—
285C2×C4C2×C22⋊D1312yes—
286C22—22no—
287C22—22no—
288C22—22no—
289C22—41no—
290C22—41no—
291C22—41no—
292C22—41no—
293C22—262no—
294C22—262no—
295C22—262no—
296C22—521no—
297C22—521no—
298C22—521no—
299C22—521no—
300C22C2×D4×D1311yescharacteristic
301C22C2×#612911yescharacteristic
302C22#8825411yescharacteristic
303C22#8825411yescharacteristic
304C22#41×D1311yescharacteristic
305C22#41×D1311yescharacteristic
306C22C22×C22⋊D1311yescharacteristic
307C4—22no—
308C4—42no—
309C4—42no—
310C4—262no—
311C4—264no—
312C4—521no—
313C4—521no—
314C4—522no—
315C4#8819314yes—
316C2—42no—
317C2—522no—
318C2#1171933611yescharacteristic
319C2#1171933811yescharacteristic
320C2#1171934411yescharacteristic
321C2#1171934611yescharacteristic
322C2C2×#8819311yescharacteristic
323C2#1171952111yescharacteristic
324C2#1171953311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC2×C13×C22⋊Q8C2
prime radicalC22×C22⋊D13C22
hypercenterC2×C22⋊Q8D13
hypocenterC13#2415
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×C13×C22⋊Q8C2semidirect
2. C2×#88200C2semidirect
4. C2×#88180C2semidirect
5. #11718891C2semidirect
6. #11718651C2semidirect
7. #11718648C2semidirect
8. #11718634C2semidirect
9. #11718633C2semidirect
11. #11718613C2semidirect
71. C4⋊Dic13D4semidirect
125. C2×C22⋊Q8D13semidirect
239. C13#2415semidirect

Maximal subgroups

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

subgroupindex
C2×C13×C22⋊Q82
C2×#882002
C2×C4×C22⋊D132
C2×#881802
#117188912
#117186512
#117186482
#117186342
#117186332
#117186202
#117186132
#241513