Finite Group Databasebeta

← #16797296

Subgroups — #16797296

Order 3328.

990 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719054C211yesmaximal, characteristic
2C2×C4×D13⋊C8C211yesmaximal, characteristic
3#13130632C212yesmaximal, complemented
4C4⋊C4×#1057C212yesmaximal, complemented
5#13130574C212yesmaximal
6#13130570C212yesmaximal
7#13130555C212yesmaximal, complemented
8#13130493C212yesmaximal, complemented
9#13117229C211yesmaximal, characteristic
10C22×D13⋊C8C2211yescharacteristic
11C22×D13⋊C8C2211yescharacteristic
12C2×C42×D13C2211yescharacteristic
13C2×#88111C2212yes—
14C2×#88110C2214yes—
15C2×#88110C2212yes—
16C2×C4⋊#1057C2212yes—
17C2×C4×#1057C2214yes—
18C2×C4×#1057C2211yescharacteristic
19C2×C4×#1057C2211yescharacteristic
20C2×C4×#1057C2211yescharacteristic
21C2×C4×#1057C2211yescharacteristic
22#11719054C418yescomplemented
23C4×D13⋊C8C418yescomplemented
24C13×#382C411yescharacteristic
25#11718648C412yes—
26C4⋊C4×Dic13C2212yes—
27#11718597C411yescharacteristic
28#11718327C2212yes—
29#11718325C412yes—
30#11718312C412yes—
31#11718309C2212yes—
32#11718290C2214yes—
33#11718290C2214yes—
34C22×C4×D13C2×C411yescharacteristic
35C22×C4×D13C2×C411yescharacteristic
36C22×C4×D13C2311yescharacteristic
37C22×#1057C2311yescharacteristic
38C22×#1057C2311yescharacteristic
39C22×#1057C2314yes—
40C22×#1057C2311yescharacteristic
41C22×#1057C2311yescharacteristic
42C2×D13⋊C8—24no—
43C2×D13⋊C8—24no—
44C2×D13⋊C8C2×C414yes—
45C2×D13⋊C8C2×C414yes—
46C2×C13×C4⋊C4C2×C412yes—
47C2×C42×C13C2×C411yescharacteristic
48C2×#6103C2×C414yes—
49C2×C4⋊Dic13C2×C412yes—
50C2×C4×Dic13C2×C411yescharacteristic
51C2×C4×Dic13C2314yes—
52C2×C4×Dic13C2311yescharacteristic
53C2×C4×Dic13C2311yescharacteristic
54C42×D13C2×C414yes—
55C42×D13C2×C414yes—
56#88111C2×C418yes—
57#88110—28no—
58#88110C2×C418yes—
59C4⋊#1057C2×C418yes—
60C4×#1057—28no—
61C4×#1057C2×C414yes—
62C4×#1057C2×C414yes—
63C4×#1057C2×C414yes—
64C4×#1057C2×C414yes—
65C13×#95C2×C412yes—
66C13×#95C2×C412yes—
67#88071C2×C414yes—
68#88071C2×C412yes—
69#88071C2×C414yes—
70#88071C2×C412yes—
71#20476—131nomaximal, Sylow
72C23×D13C22×C411yescharacteristic
73C22×C4×C13C22×C414yes—
74C22×C4×C13C22×C411yescharacteristic
75C22×C4×C13C22×C411yescharacteristic
76C22×C4×C13C22×C411yescharacteristic
77C22×Dic13C22×C414yes—
78C22×Dic13C22×C411yescharacteristic
79C22×Dic13C22×C411yescharacteristic
80C22×Dic13C2411yescharacteristic
81C2×C4×D13—24no—
82C2×C4×D13—22no—
83C2×C4×D13—22no—
84C2×C4×D13—22no—
85C2×C4×D13—22no—
86C2×C4×D13C4214yes—
87C2×C4×D13C4214yes—
88C2×C4×D13C22×C412yes—
89C2×C4×D13C22×C412yes—
90C2×#1057—24no—
91C2×#1057—24no—
92C2×#1057—22no—
93C2×#1057—22no—
94C2×#1057C22×C412yes—
95C2×#1057C22×C412yes—
96C2×#1057C22×C418yes—
97C2×#1057C22×C412yes—
98C2×#1057C22×C412yes—
99C2×#1057#4114yes—
100C2×#1057#4114yes—
101D13⋊C8—28no—
102D13⋊C8—28no—
103C13×C4⋊C4—24no—
104C42×C13C4214yes—
105#6103—28no—
106C4⋊Dic13—24no—
107C4×Dic13—24no—
108C4×Dic13—24no—
109C4×Dic13C4214yes—
110C4×Dic13C22×C412yes—
111C4×Dic13C22×C412yes—
112C4×Dic13C22×C412yes—
113C4×Dic13C22×C412yes—
114C2×#432—131no—
115C22×C4×C8—131no—
116#2283—131no—
117#1770—132no—
118C8×C4⋊C4—132no—
119#1752—132no—
120C8×C22⋊C4—132no—
121#1746—132no—
122#1726—132no—
123C23×C13C23×C411yescharacteristic
124C22×D13—22no—
125C22×D13—21no—
126C22×D13—21no—
127C22×D13C2×C4212yes—
128C22×D13#13114yes—
129C2×C4×C13—22no—
130C2×C4×C13—22no—
131C2×C4×C13—24no—
132C2×C4×C13—24no—
133C2×C4×C13—24no—
134C2×C4×C13C2×C4212yes—
135C2×C4×C13C2×C4212yes—
136C2×C4×C13C2×C4212yes—
137C2×C4×C13#13112yes—
138C2×C4×C13#13112yes—
139C2×Dic13—21no—
140C2×Dic13—21no—
141C2×Dic13—22no—
142C2×Dic13—24no—
143C2×Dic13—24no—
144C2×Dic13—24no—
145C2×Dic13C2×C4212yes—
146C2×Dic13C2×C4212yes—
147C2×Dic13C23×C411yescharacteristic
148C2×Dic13C23×C411yescharacteristic
149C2×Dic13C2×#4112yes—
150C2×Dic13C2×#4112yes—
151C4×D13—28no—
152C4×D13—28no—
153C4×D13—22no—
154C4×D13—22no—
155C4×D13—24no—
156#1057—22no—
157#1057—22no—
158#1057—28no—
159#1057#11714yes—
160#1057#11714yes—
161C23×C8—131no—
162C23×C8—131no—
163C22×C42—131no—
164#432—138no—
165C2×C4⋊C8—132no—
166C2×C22⋊C8—132no—
167C2×#97—132no—
168C2×#97—134no—
169C2×C4×C8—138no—
170C2×C4×C8—131no—
171C2×C4×C8—131no—
172C2×C4×C8—131no—
173C2×C4×C8—131no—
174C2×C4×C8—134no—
175#383—132no—
176#382—131no—
177#382#26111yescharacteristic
178#381—132no—
179#380—132no—
180C4×C4⋊C4—132no—
181C4×C22⋊C4—132no—
182#376—132no—
183#336—134no—
184#336—134no—
185C22×C13C22×C4211yescharacteristic
186C22×C13C4×#4112yes—
187C22×C13C2×#13111yescharacteristic
188C22×C13C2×#13111yescharacteristic
189C22×C13C2×#13112yes—
190C2×D13—22no—
191C2×D13—24no—
192C2×D13—24no—
193C2×D13—22no—
194C2×D13#40514yes—
195C4×C13—22no—
196C4×C13—22no—
197C4×C13—44no—
198C4×C13#40514yes—
199Dic13—22no—
200Dic13—22no—
201Dic13—44no—
202Dic13C2×#11711yescharacteristic
203Dic13C2×#11711yescharacteristic
204Dic13C4×#4112yes—
205C23×C4—131no—
206C23×C4—131no—
207C23×C4—131no—
208C22×C8—131no—
209C22×C8—131no—
210C22×C8—131no—
211C22×C8—131no—
212C22×C8—134no—
213C22×C8—134no—
214C22×C8—134no—
215C22×C8—264no—
216C22×C8—264no—
217C2×C4⋊C4—132no—
218C2×C4⋊C4C2×#26112yes—
219C2×C22⋊C4—134no—
220C2×C42—131no—
221C2×C42—131no—
222C2×C42—131no—
223C2×C42—134no—
224C2×C42—134no—
225C2×C42—134no—
226C2×C42C2×#26111yescharacteristic
227C4⋊C8—138no—
228C22⋊C8—138no—
229#97—138no—
230#97—268no—
231C4×C8—134no—
232C4×C8—134no—
233C4×C8—134no—
234C4×C8—134no—
235C4×C8—268no—
236#95—134no—
237#95—132no—
238#95—132no—
239#95—134no—
240#95C2×#26112yes—
241#95C2×#26112yes—
242C2×C13C4×#11711yescharacteristic
243C2×C13C2×#40511yescharacteristic
244C2×C13C2×#40511yescharacteristic
245C2×C13#296612yes—
246C2×C13#296612yes—
247D13—24no—
248C24—131no—
249C22×C4—131no—
250C22×C4—131no—
251C22×C4—131no—
252C22×C4—132no—
253C22×C4—132no—
254C22×C4—134no—
255C22×C4—134no—
256C22×C4—134no—
257C22×C4—262no—
258C22×C4—262no—
259C22×C4—264no—
260C22×C4—262no—
261C22×C4—262no—
262C22×C4C22×#26114yes—
263C22×C4C22×#26111yescharacteristic
264C22×C4C22×#26111yescharacteristic
265C22×C4C22×#26111yescharacteristic
266C2×C8—132no—
267C2×C8—132no—
268C2×C8—134no—
269C2×C8—134no—
270C2×C8—132no—
271C2×C8—132no—
272C2×C8—138no—
273C2×C8—268no—
274C2×C8—268no—
275C2×C8—264no—
276C2×C8—264no—
277C2×C8—262no—
278C2×C8—262no—
279C4⋊C4—24no—
280C4⋊C4—264no—
281C22⋊C4—268no—
282C42—132no—
283C42—132no—
284C42—132no—
285C42—132no—
286C42—134no—
287C42—264no—
288C42—264no—
289C42C4×#26114yes—
290C13#2047611yescharacteristic, complemented, Sylow
291C23—132no—
292C23—134no—
293C23—261no—
294C23—261no—
295C23—262no—
296C23C23×#26111yescharacteristic
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—24no—
300C2×C4—24no—
301C2×C4—24no—
302C2×C4—131no—
303C2×C4—131no—
304C2×C4—132no—
305C2×C4—132no—
306C2×C4—132no—
307C2×C4—132no—
308C2×C4—262no—
309C2×C4—262no—
310C2×C4—264no—
311C2×C4—268no—
312C2×C4—261no—
313C2×C4—261no—
314C2×C4—262no—
315C2×C4—268no—
316C2×C4—264no—
317C2×C4—264no—
318C2×C4—264no—
319C2×C4C2×C4×#26112yes—
320C2×C4C2×C4×#26112yes—
321C2×C4C2×C4×#26112yes—
322C2×C4#8823812yes—
323C2×C4#8824012yes—
324C8—134no—
325C8—134no—
326C8—262no—
327C8—262no—
328C8—268no—
329C22—134no—
330C22—262no—
331C22—264no—
332C22—262no—
333C22—264no—
334C22C22×C4×#26111yescharacteristic
335C22C2×#8823811yescharacteristic
336C22C2×#8824011yescharacteristic
337C22D13⋊#13112yes—
338C22#41×#26112yes—
339C4—22no—
340C4—22no—
341C4—44no—
342C4—131no—
343C4—131no—
344C4—132no—
345C4—262no—
346C4—262no—
347C4—524no—
348C4#1171907214yes—
349C2—264no—
350C2#117×#26111yescharacteristic
351C2#1313139611yescharacteristic
352C2C2×#1171907211yescharacteristic
353C2#1313165012yes—
354C2#1313165312yes—
subgroupG/H
center, FrattiniC23C23×#261
commutatorC22×C13C22×C42
FittingC13×#382C4
socleC23×C13C23×C4
prime radicalC23×D13C22×C4
cosocleC22×Dic13C24
hypercenter#382#261
hypocenterC13#20476
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ #382

Complements

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

NH ≅ G/Ntype
3. #13130632C2semidirect
4. C4⋊C4×#1057C2semidirect
7. #13130555C2semidirect
8. #13130493C2semidirect
22. #11719054C4semidirect
23. C4×D13⋊C8C4semidirect
290. C13#20476semidirect

Maximal subgroups

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

subgroupindex
C2×#117190542
C2×C4×D13⋊C82
#131306322
C4⋊C4×#10572
#131305742
#131305702
#131305552
#131304932
#131172292
#2047613