Finite Group Databasebeta

← #15861976

Subgroups — #15861976

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×#11718685C211yesmaximal, characteristic
2C2×Q8×#1055C211yesmaximal, characteristic
3#13114711C212yesmaximal
4#13114705C211yesmaximal, characteristic
5C4⋊C4×#1055C211yesmaximal, characteristic
6C4⋊C4×#1055C212yesmaximal
7#13114693C212yesmaximal
8C4×C4⋊#1055C211yesmaximal, characteristic
9#13114588C212yesmaximal
10#13114582C211yesmaximal, characteristic
11C13×#2295C211yesmaximal, characteristic
12C2×C4×Q8×C13C2211yescharacteristic
13C13×#391C412yes—
14C13×#389C412yes—
15C13×#387C414yes—
16C4×C13×C4⋊C4C2211yescharacteristic
17C4×C13×C4⋊C4C2212yes—
18C13×#376C2212yes—
19C43×C13C2211yescharacteristic
20#11718685C418yescomplemented
21Q8×#1055C418yescomplemented
22C2×C4⋊#1055C2211yescharacteristic
23C2×C4⋊#1055C2211yescharacteristic
24C2×C4⋊#1055C2212yes—
25C2×C4⋊#1055C2212yes—
26C2×#88043C2212yes—
27C2×#88043C2212yes—
28C2×C4×#1055C2212yes—
29C2×C4×#1055C2212yes—
30C2×C4×#1055C2212yes—
31C2×C4×#1055C2211yescharacteristic
32C2×C4×#1055C2211yescharacteristic
33#11718116C2212yes—
34#11718116C2211yescharacteristic
35#11718116C2211yescharacteristic
36#11718116C2212yes—
37#11718116C2212yes—
38#11718116C2211yescharacteristic
39#11718116C2211yescharacteristic
40C22×Q8×C13C2×C411yescharacteristic
41C4×Q8×C13C2×C414yes—
42C4×Q8×C13C2×C414yes—
43C2×C13×C4⋊C4C2×C414yes—
44C2×C13×C4⋊C4C2×C412yes—
45C2×C13×C4⋊C4C2×C412yes—
46C2×C13×C4⋊C4C2×C411yescharacteristic
47C2×C42×C13C2×C412yes—
48C2×C42×C13C2×C412yes—
49C2×C42×C13C2311yescharacteristic
50C2×C42×C13C2312yes—
51C2×C42×C13C2311yescharacteristic
52C2×C42×C13C2311yescharacteristic
53C2×C42×C13C2312yes—
54C22×#1055C2312yes—
55C22×#1055C2311yescharacteristic
56C22×#1055C2311yescharacteristic
57C22×#1055C2312yes—
58C22×#1055C2311yescharacteristic
59C22×#1055C2311yescharacteristic
60C13×#95C2×C412yes—
61C13×#95C2×C414yes—
62C13×#95C2×C414yes—
63C13×#95C2×C414yes—
64C4⋊#1055C2×C414yes—
65C4⋊#1055C2×C418yes—
66C4⋊#1055C2×C418yes—
67C4⋊#1055C2×C414yes—
68#88043—42no—
69#88043C2×C418yes—
70C4×#1055—42no—
71C4×#1055—42no—
72C4×#1055C2×C418yes—
73C4×#1055C2×C414yes—
74C4×#1055C2×C414yes—
75#20571—131nomaximal, Sylow
76C2×Q8×C13—24no—
77C2×Q8×C13C4214yes—
78C22×C4×C13C22×C412yes—
79C22×C4×C13C22×C414yes—
80C22×C4×C13C22×C412yes—
81C22×C4×C13C22×C411yescharacteristic
82C22×C4×C13C22×C412yes—
83C22×C4×C13C22×C412yes—
84C22×C4×C13C22×C411yescharacteristic
85C22×C4×C13C2411yescharacteristic
86C13×C4⋊C4—28no—
87C13×C4⋊C4—24no—
88C13×C4⋊C4C4218yes—
89C13×C4⋊C4C4214yes—
90C42×C13—24no—
91C42×C13—24no—
92C42×C13—21no—
93C42×C13—22no—
94C42×C13—21no—
95C42×C13—21no—
96C42×C13—21no—
97C42×C13—22no—
98C42×C13C22×C414yes—
99C42×C13C22×C412yes—
100C42×C13C22×C412yes—
101C42×C13C22×C414yes—
102C2×#1055—22no—
103C2×#1055—21no—
104C2×#1055—22no—
105C2×#1055—21no—
106C2×#1055—21no—
107C2×#1055—21no—
108C2×#1055—21no—
109C2×#1055—21no—
110C2×#1055—22no—
111C2×#1055—21no—
112C2×#1055—22no—
113C2×#1055—21no—
114C2×#1055C22×C412yes—
115C2×#1055C22×C412yes—
116C2×#1055C22×C414yes—
117C2×#1055C22×C412yes—
118C2×#1055C22×C412yes—
119C2×#1055C22×C414yes—
120C2×#446—131no—
121C2×C8×Q8—131no—
122#2295D1311yescharacteristic
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—22no—
135C2×C4×C13—22no—
136C2×C4×C13—24no—
137C2×C4×C13—24no—
138C2×C4×C13—22no—
139C2×C4×C13—24no—
140C2×C4×C13—22no—
141C2×C4×C13—22no—
142C2×C4×C13—24no—
143C2×C4×C13—24no—
144C2×C4×C13C2×C4212yes—
145C2×C4×C13C2×C4214yes—
146C2×C4×C13C2×C4214yes—
147C2×C4×C13C2×C4212yes—
148C2×C4×C13#13114yes—
149C2×C4×C13#13114yes—
150C2×C4×C13C23×C411yescharacteristic
151C2×C4×C13C23×C411yescharacteristic
152C2×C4×C13H(5,𝔽2)11yescharacteristic
153C2×C4×C132−1+411yescharacteristic
154C2×C4×C132−1+411yescharacteristic
155C2×C4×C132−1+411yescharacteristic
156#1055—22no—
157#1055—22no—
158#1055—24no—
159#1055—22no—
160#1055—24no—
161#1055—22no—
162C2×C4×Q8C2×D1311yescharacteristic
163#446—138no—
164C8×Q8—138no—
165C2×C4⋊C8—131no—
166C2×C4⋊C8—132no—
167C2×C4⋊C8—131no—
168C2×C4⋊C8—132no—
169C2×#97—132no—
170C2×#97—132no—
171C2×C4×C8—131no—
172C2×C4×C8—132no—
173C2×C4×C8—131no—
174C2×C4×C8—132no—
175C2×C4×C8—132no—
176#391Dic1312yes—
177#389Dic1312yes—
178#387Dic1314yes—
179C4×C4⋊C4C2×D1311yescharacteristic
180C4×C4⋊C4C2×D1312yes—
181#376C2×D1312yes—
182C43C2×D1311yescharacteristic
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—24no—
199C4×C13—42no—
200C4×C13—44no—
201C4×C13#40514yes—
202C4×C13#51911yescharacteristic
203C4×C13#51911yescharacteristic
204C4×C13#52011yescharacteristic
205C4×C13#52011yescharacteristic
206C22×Q8C2×Dic1311yescharacteristic
207C22×C8—131no—
208C22×C8—131no—
209C22×C8—131no—
210C22×C8—132no—
211C22×C8—131no—
212C22×C8—132no—
213C4×Q8C4×D1314yes—
214C4×Q8C4×D1314yes—
215C2×C4⋊C4C2×Dic1314yes—
216C2×C4⋊C4C2×Dic1312yes—
217C2×C4⋊C4C2×Dic1312yes—
218C2×C4⋊C4C2×Dic1311yescharacteristic
219C2×C42C2×Dic1312yes—
220C2×C42C2×Dic1312yes—
221C2×C42C22×D1311yescharacteristic
222C2×C42C22×D1311yescharacteristic
223C2×C42C22×D1312yes—
224C2×C42C22×D1311yescharacteristic
225C2×C42C22×D1312yes—
226C4⋊C8—134no—
227C4⋊C8—138no—
228C4⋊C8—134no—
229C4⋊C8—138no—
230#97—138no—
231#97—522no—
232C4×C8—134no—
233C4×C8—138no—
234C4×C8—134no—
235C4×C8—522no—
236C4×C8—522no—
237#95C2×Dic1314yes—
238#95C2×Dic1314yes—
239#95C2×Dic1312yes—
240#95C2×Dic1314yes—
241C2×C13#227611yescharacteristic
242C2×C13C2×#40511yescharacteristic
243C2×C13C4×#13111yescharacteristic
244C2×C13#298612yes—
245C2×C13#299412yes—
246C2×Q8—24no—
247C2×Q8C4×Dic1314yes—
248C22×C4C22×Dic1312yes—
249C22×C4C22×Dic1314yes—
250C22×C4C22×Dic1312yes—
251C22×C4C22×Dic1311yescharacteristic
252C22×C4C22×Dic1312yes—
253C22×C4C22×Dic1312yes—
254C22×C4C22×Dic1311yescharacteristic
255C22×C4C23×D1311yescharacteristic
256C2×C8—132no—
257C2×C8—132no—
258C2×C8—134no—
259C2×C8—132no—
260C2×C8—132no—
261C2×C8—134no—
262C2×C8—261no—
263C2×C8—261no—
264C2×C8—261no—
265C2×C8—262no—
266C2×C8—261no—
267C2×C8—262no—
268C2×C8—262no—
269C2×C8—261no—
270C2×C8—262no—
271C2×C8—261no—
272C2×C8—261no—
273C2×C8—261no—
274C4⋊C4—28no—
275C4⋊C4—24no—
276C4⋊C4C4×Dic1318yes—
277C4⋊C4C4×Dic1314yes—
278C42—24no—
279C42—24no—
280C42—21no—
281C42—21no—
282C42—21no—
283C42—22no—
284C42—21no—
285C42—22no—
286C42C2×C4×D1314yes—
287C42C2×C4×D1312yes—
288C42C2×C4×D1312yes—
289C42C2×C4×D1314yes—
290C13#2057111yescharacteristic, complemented, Sylow
291C23C23×Dic1311yescharacteristic
292Q8—28no—
293C2×C4—22no—
294C2×C4—22no—
295C2×C4—24no—
296C2×C4—24no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—22no—
300C2×C4—22no—
301C2×C4—24no—
302C2×C4—24no—
303C2×C4—24no—
304C2×C4C2×C4×Dic1312yes—
305C2×C4C2×C4×Dic1314yes—
306C2×C4C2×C4×Dic1314yes—
307C2×C4C2×C4×Dic1312yes—
308C2×C4#8820214yes—
309C2×C4#8820214yes—
310C2×C4C22×C4×D1311yescharacteristic
311C2×C4C22×C4×D1311yescharacteristic
312C2×C4#8825411yescharacteristic
313C2×C4#8825411yescharacteristic
314C2×C4#8825611yescharacteristic
315C2×C4#8825711yescharacteristic
316C8—262no—
317C8—262no—
318C8—264no—
319C8—262no—
320C8—262no—
321C8—264no—
322C22C22×C4×Dic1311yescharacteristic
323C22#1171951711yescharacteristic
324C22C2×#8820212yes—
325C22C2×#8820212yes—
326C22#1171953211yescharacteristic
327C4—24no—
328C4—24no—
329C4—22no—
330C4—24no—
331C4—42no—
332C4—44no—
333C4#1171865814yes—
334C4#1171927711yescharacteristic
335C4#1171927711yescharacteristic
336C4#1171927911yescharacteristic
337C4#1171927911yescharacteristic
338C2#1311720111yescharacteristic
339C2C2×#1171865811yescharacteristic
340C2C4×#8820211yescharacteristic
341C2#1312393812yes—
342C2#1312399612yes—
subgroupG/H
center, FrattiniC22×C4C23×D13
commutatorC22×C13C22×C42
FittingC13×#2295C2
socle, prime radicalC23×C13C23×C4
cosocleC22×C4×C13C24
hypercenter#2295D13
hypocenterC13#20571
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ #2295

Complements

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

NH ≅ G/Ntype
20. #11718685C4semidirect
21. Q8×#1055C4semidirect
290. C13#20571semidirect

Maximal subgroups

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

subgroupindex
C2×#117186852
C2×Q8×#10552
#131147112
#131147052
C4⋊C4×#10552
#131146932
C4×C4⋊#10552
#131145882
#131145822
C13×#22952
#2057113