Finite Group Databasebeta

← #15861978

Subgroups — #15861978

Order 3328.

826 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q8×#1055C211yesmaximal, characteristic
2#13117314C211yesmaximal, characteristic
3#13114708C212yesmaximal
4#13114706C211yesmaximal, characteristic
5#13114701C212yesmaximal
6C8×C4⋊Dic13C211yesmaximal, characteristic
7#13114695C212yesmaximal
8C4⋊C8×Dic13C211yesmaximal, characteristic
9#13114589C212yesmaximal
10#13114581C211yesmaximal, characteristic
11C2×C13×#446C211yesmaximal, characteristic
12C2×C4×Q8×C13C2211yescharacteristic
13C13×#446C418yescomplemented
14C2×C13×C4⋊C8C2211yescharacteristic
15C2×C13×C4⋊C8C2212yes—
16C2×C13×#97C2212yes—
17C2×C4×C8×C13C2211yescharacteristic
18#11718891C412yes—
19C2×#88055C2212yes—
20C2×C8×Dic13C2212yes—
21C2×C8×Dic13C2212yes—
22Q8×#1055C418yescomplemented
23#11718646C412yes—
24#11718642C414yes—
25C4×C4⋊Dic13C2211yescharacteristic
26C4×C4⋊Dic13C2212yes—
27#11718593C2212yes—
28C42×Dic13C2211yescharacteristic
29C2×C4⋊#1055C2211yescharacteristic
30C2×C4⋊#1055C2212yes—
31C2×C4×#1055C2212yes—
32C2×C4×#1055C2211yescharacteristic
33#11718142C2212yes—
34#11718142C2211yescharacteristic
35#11718142C2212yes—
36#11718142C2211yescharacteristic
37#11718142C2212yes—
38#11718142C2211yescharacteristic
39#11718142C2211yescharacteristic
40C22×Q8×C13C2×C411yescharacteristic
41C22×C8×C13C2311yescharacteristic
42C22×C8×C13C2311yescharacteristic
43C22×C8×C13C2312yes—
44C4×Q8×C13C2×C414yes—
45C4×Q8×C13C2×C414yes—
46C2×C13×C4⋊C4C2×C412yes—
47C2×C13×C4⋊C4C2×C411yescharacteristic
48C2×C42×C13C2311yescharacteristic
49C2×C42×C13C2312yes—
50C2×C4⋊Dic13C2×C412yes—
51C2×C4⋊Dic13C2×C414yes—
52C2×C4×Dic13C2×C412yes—
53C2×C4×Dic13C2×C412yes—
54C2×C4×Dic13C2311yescharacteristic
55C2×C4×Dic13C2312yes—
56C2×C4×Dic13C2311yescharacteristic
57C22×#1055C2312yes—
58C22×#1055C2311yescharacteristic
59C22×#1055C2311yescharacteristic
60C13×C4⋊C8C2×C414yes—
61C13×C4⋊C8C2×C418yes—
62C13×#97C2×C418yes—
63C4×C8×C13C2×C414yes—
64#88071C2×C414yes—
65#88071C2×C414yes—
66#88071C2×C414yes—
67#88071C2×C412yes—
68#88055—42no—
69C8×Dic13—42no—
70C8×Dic13—42no—
71C4⋊#1055C2×C414yes—
72C4⋊#1055C2×C418yes—
73C4×#1055C2×C418yes—
74C4×#1055C2×C414yes—
75#20571—131nomaximal, Sylow
76C2×Q8×C13—24no—
77C2×Q8×C13C4214yes—
78C22×C4×C13C22×C412yes—
79C22×C4×C13C22×C411yescharacteristic
80C22×C4×C13C22×C412yes—
81C22×C4×C13C22×C411yescharacteristic
82C22×C4×C13C2411yescharacteristic
83C22×Dic13C22×C412yes—
84C22×Dic13C22×C414yes—
85C22×Dic13C22×C412yes—
86C2×C8×C13—21no—
87C2×C8×C13—22no—
88C2×C8×C13—21no—
89C2×C8×C13—21no—
90C2×C8×C13—21no—
91C2×C8×C13—22no—
92C2×C8×C13C22×C412yes—
93C2×C8×C13C22×C412yes—
94C2×C8×C13C22×C414yes—
95C13×C4⋊C4C4218yes—
96C13×C4⋊C4C4214yes—
97C42×C13C22×C414yes—
98C42×C13C22×C412yes—
99C42×C13C22×C412yes—
100C42×C13C22×C414yes—
101C4⋊Dic13—24no—
102C4⋊Dic13—28no—
103C4×Dic13—24no—
104C4×Dic13—21no—
105C4×Dic13—22no—
106C4×Dic13—21no—
107C4×Dic13—21no—
108C4×Dic13—22no—
109C4×Dic13—21no—
110C4×Dic13—24no—
111C2×#1055—22no—
112C2×#1055—21no—
113C2×#1055—21no—
114C2×#1055—21no—
115C2×#1055—22no—
116C2×#1055—21no—
117C2×#1055C22×C412yes—
118C2×#1055C22×C414yes—
119C2×#1055C22×C412yes—
120C2×#446D1311yescharacteristic
121C2×C8×Q8—131no—
122#2295—131no—
123#1771—132no—
124#1770—131no—
125C8×C4⋊C4—132no—
126C8×C4⋊C4—131no—
127#1768—132no—
128C4×C4⋊C8—131no—
129#1746—132no—
130#1744—131no—
131C23×C13C23×C411yescharacteristic
132Q8×C13—28no—
133C2×C4×C13—22no—
134C2×C4×C13—24no—
135C2×C4×C13—24no—
136C2×C4×C13C2×C4212yes—
137C2×C4×C13C2×C4214yes—
138C2×C4×C13C2×C4214yes—
139C2×C4×C13C2×C4212yes—
140C2×C4×C13#13114yes—
141C2×C4×C13C23×C411yescharacteristic
142C2×C4×C13C23×C411yescharacteristic
143C2×C4×C13H(5,𝔽2)11yescharacteristic
144C2×C4×C132−1+411yescharacteristic
145C2×C4×C132−1+411yescharacteristic
146C2×C4×C132−1+411yescharacteristic
147C2×Dic13—22no—
148C2×Dic13—22no—
149C2×Dic13—22no—
150C2×Dic13—24no—
151C2×Dic13—22no—
152C2×Dic13—22no—
153C2×Dic13—24no—
154C2×Dic13—24no—
155C2×Dic13#13114yes—
156C8×C13—22no—
157C8×C13—22no—
158C8×C13—24no—
159#1055—22no—
160#1055—24no—
161#1055—22no—
162C2×C4×Q8C2×D1311yescharacteristic
163#446Dic1318yescomplemented
164C8×Q8—138no—
165C2×C4⋊C8—131no—
166C2×C4⋊C8—132no—
167C2×C4⋊C8C2×D1311yescharacteristic
168C2×C4⋊C8C2×D1312yes—
169C2×#97—132no—
170C2×#97C2×D1312yes—
171C2×C4×C8—131no—
172C2×C4×C8—132no—
173C2×C4×C8—132no—
174C2×C4×C8—132no—
175C2×C4×C8C2×D1311yescharacteristic
176#391—132no—
177#389—132no—
178#387—134no—
179C4×C4⋊C4—131no—
180C4×C4⋊C4—132no—
181#376—132no—
182C43—131no—
183#336—131no—
184#336—131no—
185#336—131no—
186#336—131no—
187#336—132no—
188#336—132no—
189#336—132no—
190C22×C13C22×C4211yescharacteristic
191C22×C13#51911yescharacteristic
192C22×C13#52011yescharacteristic
193C22×C13C2×#13112yes—
194C22×C13C2×#13112yes—
195C4×C13—24no—
196C4×C13—22no—
197C4×C13—24no—
198C4×C13#40514yes—
199C4×C13#51911yescharacteristic
200C4×C13#51911yescharacteristic
201C4×C13#52011yescharacteristic
202C4×C13#52011yescharacteristic
203Dic13—24no—
204Dic13—42no—
205Dic13—44no—
206C22×Q8C4×D1311yescharacteristic
207C22×C8—131no—
208C22×C8—132no—
209C22×C8—131no—
210C22×C8C22×D1311yescharacteristic
211C22×C8C22×D1311yescharacteristic
212C22×C8C22×D1312yes—
213C4×Q8C4×D1314yes—
214C4×Q8C2×Dic1314yes—
215C2×C4⋊C4—134no—
216C2×C4⋊C4—132no—
217C2×C4⋊C4C4×D1312yes—
218C2×C4⋊C4C4×D1311yescharacteristic
219C2×C42—132no—
220C2×C42—132no—
221C2×C42—131no—
222C2×C42—131no—
223C2×C42—132no—
224C2×C42C22×D1311yescharacteristic
225C2×C42C22×D1312yes—
226C4⋊C8—134no—
227C4⋊C8—138no—
228C4⋊C8C2×Dic1314yes—
229C4⋊C8C2×Dic1318yes—
230#97—522no—
231#97C2×Dic1318yes—
232C4×C8—134no—
233C4×C8—138no—
234C4×C8—522no—
235C4×C8—522no—
236C4×C8C2×Dic1314yes—
237#95—134no—
238#95—134no—
239#95—132no—
240#95—134no—
241C2×C13#227611yescharacteristic
242C2×C13C2×#40511yescharacteristic
243C2×C13C4×#13111yescharacteristic
244C2×C13#298612yes—
245C2×C13#299412yes—
246C2×Q8—24no—
247C2×Q8C4×Dic1314yes—
248C22×C4—132no—
249C22×C4—132no—
250C22×C4—134no—
251C22×C4C2×C4×D1312yes—
252C22×C4C2×C4×D1311yescharacteristic
253C22×C4C2×C4×D1312yes—
254C22×C4C2×C4×D1311yescharacteristic
255C22×C4C23×D1311yescharacteristic
256C2×C8—21no—
257C2×C8—21no—
258C2×C8—21no—
259C2×C8—22no—
260C2×C8—21no—
261C2×C8—22no—
262C2×C8—132no—
263C2×C8—134no—
264C2×C8—132no—
265C2×C8—261no—
266C2×C8—262no—
267C2×C8—261no—
268C2×C8—262no—
269C2×C8—261no—
270C2×C8—261no—
271C2×C8C22×Dic1312yes—
272C2×C8C22×Dic1312yes—
273C2×C8C22×Dic1314yes—
274C4⋊C4—268no—
275C4⋊C4—264no—
276C4⋊C4C4×Dic1318yes—
277C4⋊C4C4×Dic1314yes—
278C42—264no—
279C42—264no—
280C42—261no—
281C42—261no—
282C42—262no—
283C42—261no—
284C42—262no—
285C42—261no—
286C42C2×C4×D1314yes—
287C42C2×C4×D1312yes—
288C42C22×Dic1312yes—
289C42C22×Dic1314yes—
290C13#2057111yescharacteristic, complemented, Sylow
291C23C22×C4×D1311yescharacteristic
292Q8—28no—
293C2×C4—24no—
294C2×C4—22no—
295C2×C4—24no—
296C2×C4—134no—
297C2×C4—262no—
298C2×C4—262no—
299C2×C4—262no—
300C2×C4—264no—
301C2×C4—262no—
302C2×C4—264no—
303C2×C4—262no—
304C2×C4—264no—
305C2×C4#8816114yes—
306C2×C4C2×C4×Dic1312yes—
307C2×C4C2×C4×Dic1314yes—
308C2×C4C2×C4×Dic1314yes—
309C2×C4C2×C4×Dic1312yes—
310C2×C4C22×C4×D1311yescharacteristic
311C2×C4#8825411yescharacteristic
312C2×C4#8825411yescharacteristic
313C2×C4#8825611yescharacteristic
314C2×C4#8825711yescharacteristic
315C2×C4C23×Dic1311yescharacteristic
316C8—22no—
317C8—22no—
318C8—24no—
319C8—262no—
320C8—264no—
321C8—262no—
322C22#1171927711yescharacteristic
323C22#1171927911yescharacteristic
324C22C2×#8816112yes—
325C22D13×#13112yes—
326C22C22×C4×Dic1311yescharacteristic
327C4—24no—
328C4—22no—
329C4—24no—
330C4—264no—
331C4—522no—
332C4—524no—
333C4#1171878314yes—
334C4#1171927711yescharacteristic
335C4#1171927911yescharacteristic
336C4#1171951711yescharacteristic
337C4#1171953211yescharacteristic
338C2#1311720111yescharacteristic
339C2C2×#1171878311yescharacteristic
340C2#131×Dic1311yescharacteristic
341C2#1312393412yes—
342C2#1312399912yes—
subgroupG/H
center, FrattiniC22×C4C23×D13
commutatorC22×C13C22×C42
FittingC2×C13×#446C2
socle, prime radicalC23×C13C23×C4
cosocleC22×C4×C13C24
hypercenterC2×#446D13
hypocenterC13#20571
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C2×#446

Complements

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

NH ≅ G/Ntype
13. C13×#446C4semidirect
22. Q8×#1055C4semidirect
163. #446Dic13semidirect
290. C13#20571semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×#10552
#131173142
#131147082
#131147062
#131147012
C8×C4⋊Dic132
#131146952
C4⋊C8×Dic132
#131145892
#131145812
C2×C13×#4462
#2057113