Finite Group Databasebeta

← #16797295

Subgroups — #16797295

Order 3328.

990 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719130C211yesmaximal, characteristic
2C22×C4×#1057C211yesmaximal, characteristic
3#13130632C212yesmaximal, complemented
4C4⋊C4×#1057C212yesmaximal, complemented
5#13130573C212yesmaximal
6C22⋊C4×#1057C212yesmaximal
7#13130555C212yesmaximal, complemented
8#13130493C212yesmaximal, complemented
9#13117231C211yesmaximal, characteristic
10C23×#1057C2211yescharacteristic
11C23×#1057C2211yescharacteristic
12C22×C4×Dic13C2211yescharacteristic
13C2×C22⋊#1057C2212yes—
14#11719130C418yescomplemented
15C2×#88110C2214yes—
16C2×#88110C2212yes—
17C2×C4⋊#1057C2212yes—
18C2×C4×#1057C418yescomplemented
19C2×C4×#1057C2214yes—
20C2×C4×#1057C2211yescharacteristic
21C2×C4×#1057C2211yescharacteristic
22C2×C4×#1057C2211yescharacteristic
23C2×C4×#1057C2211yescharacteristic
24C13×#380C411yescharacteristic
25#11718873C411yescharacteristic
26#11718638C412yes—
27C4⋊C4×Dic13C2212yes—
28#11718604C412yes—
29C22⋊C4×Dic13C2212yes—
30#11718312C412yes—
31#11718309C2212yes—
32#11718290C2214yes—
33#11718290C2214yes—
34C23×C4×C13C2×C411yescharacteristic
35C23×Dic13C2×C411yescharacteristic
36C23×Dic13C2311yescharacteristic
37C22×#1057—24no—
38C22×#1057—24no—
39C22×#1057C2×C414yes—
40C22×#1057C2×C414yes—
41C22×#1057C2314yes—
42C22×#1057C2311yescharacteristic
43C22×#1057C2311yescharacteristic
44C22×#1057C2311yescharacteristic
45C22×#1057C2311yescharacteristic
46C2×C13×C4⋊C4C2×C412yes—
47C2×C13×C22⋊C4C2×C412yes—
48C2×C22⋊Dic13C2×C412yes—
49C2×C4⋊Dic13C2×C412yes—
50C2×C4×Dic13C2×C411yescharacteristic
51C2×C4×Dic13C2×C411yescharacteristic
52C2×C4×Dic13C2×C414yes—
53C2×C4×Dic13C2×C414yes—
54C2×C4×Dic13C2314yes—
55C2×C4×Dic13C2311yescharacteristic
56C2×C4×Dic13C2311yescharacteristic
57C22⋊#1057C2×C418yes—
58#88110—28no—
59#88110C2×C418yes—
60C4⋊#1057C2×C418yes—
61C4×#1057—28no—
62C4×#1057C2×C414yes—
63C4×#1057C2×C414yes—
64C4×#1057C2×C414yes—
65C4×#1057C2×C414yes—
66C13×#95C2×C412yes—
67#88071C2×C412yes—
68#88071C2×C414yes—
69#88071C2×C414yes—
70#88071C2×C414yes—
71#20476—131nomaximal, Sylow
72C24×C13C22×C411yescharacteristic
73C22×C4×C13—24no—
74C22×C4×C13C4214yes—
75C22×C4×C13C22×C414yes—
76C22×C4×C13C22×C411yescharacteristic
77C22×C4×C13C22×C411yescharacteristic
78C22×Dic13—22no—
79C22×Dic13—22no—
80C22×Dic13—22no—
81C22×Dic13—22no—
82C22×Dic13C4214yes—
83C22×Dic13C22×C414yes—
84C22×Dic13C22×C411yescharacteristic
85C22×Dic13C22×C411yescharacteristic
86C22×Dic13C22×C411yescharacteristic
87C22×Dic13C22×C412yes—
88C22×Dic13C22×C412yes—
89C22×Dic13C2411yescharacteristic
90C2×#1057—24no—
91C2×#1057—24no—
92C2×#1057—22no—
93C2×#1057—22no—
94C2×#1057—28no—
95C2×#1057—28no—
96C2×#1057C22×C412yes—
97C2×#1057C22×C412yes—
98C2×#1057C22×C418yes—
99C2×#1057C22×C412yes—
100C2×#1057C22×C412yes—
101C2×#1057#4114yes—
102C2×#1057#4114yes—
103C13×C4⋊C4—24no—
104C13×C22⋊C4—24no—
105C22⋊Dic13—24no—
106C4⋊Dic13—24no—
107C4×Dic13—24no—
108C4×Dic13—24no—
109C4×Dic13C4214yes—
110C4×Dic13C4214yes—
111C4×Dic13C22×C412yes—
112C4×Dic13C22×C412yes—
113C4×Dic13C22×C412yes—
114C4×Dic13C22×C412yes—
115C2×#432—131no—
116C22×C4×C8—131no—
117#2283—131no—
118#1770—132no—
119C8×C4⋊C4—132no—
120#1752—132no—
121C8×C22⋊C4—132no—
122#1746—132no—
123#1726—132no—
124C23×C13—22no—
125C23×C13—22no—
126C23×C13C2×C4212yes—
127C23×C13#13112yes—
128C23×C13#13112yes—
129C23×C13C23×C411yescharacteristic
130C2×C4×C13—22no—
131C2×C4×C13—28no—
132C2×C4×C13—24no—
133C2×C4×C13—24no—
134C2×C4×C13—24no—
135C2×C4×C13C2×C4212yes—
136C2×C4×C13C2×C4212yes—
137C2×C4×C13#13114yes—
138C2×Dic13—22no—
139C2×Dic13—21no—
140C2×Dic13—21no—
141C2×Dic13—21no—
142C2×Dic13—21no—
143C2×Dic13—28no—
144C2×Dic13—22no—
145C2×Dic13—22no—
146C2×Dic13—24no—
147C2×Dic13—24no—
148C2×Dic13—24no—
149C2×Dic13—24no—
150C2×Dic13C2×C4212yes—
151C2×Dic13C2×C4212yes—
152C2×Dic13C2×C4212yes—
153C2×Dic13C23×C411yescharacteristic
154C2×Dic13C23×C411yescharacteristic
155C2×Dic13C2×#4112yes—
156C2×Dic13C2×#4112yes—
157#1057—22no—
158#1057—22no—
159#1057—28no—
160#1057#11714yes—
161#1057#11714yes—
162C23×C8—131no—
163C23×C8—131no—
164C22×C42—131no—
165#432—138no—
166C2×C4⋊C8—132no—
167C2×C22⋊C8—132no—
168C2×#97—132no—
169C2×#97—134no—
170C2×C4×C8—131no—
171C2×C4×C8—138no—
172C2×C4×C8—131no—
173C2×C4×C8—131no—
174C2×C4×C8—131no—
175C2×C4×C8—134no—
176#383—132no—
177#382—132no—
178#381—132no—
179#380—131no—
180#380#26111yescharacteristic
181C4×C4⋊C4—132no—
182C4×C22⋊C4—132no—
183#376—132no—
184#336—134no—
185#336—134no—
186C22×C13—22no—
187C22×C13—24no—
188C22×C13—24no—
189C22×C13—22no—
190C22×C13#40514yes—
191C22×C13C22×C4211yescharacteristic
192C22×C13C4×#4112yes—
193C22×C13C2×#13111yescharacteristic
194C22×C13C2×#13112yes—
195C22×C13C2×#13111yescharacteristic
196C4×C13—22no—
197C4×C13—44no—
198C4×C13#40514yes—
199Dic13—22no—
200Dic13—22no—
201Dic13—22no—
202Dic13—44no—
203Dic13C2×#11711yescharacteristic
204Dic13C2×#11711yescharacteristic
205Dic13C4×#4112yes—
206C23×C4—131no—
207C23×C4—131no—
208C23×C4C2×#26111yescharacteristic
209C22×C8—131no—
210C22×C8—131no—
211C22×C8—131no—
212C22×C8—131no—
213C22×C8—134no—
214C22×C8—134no—
215C22×C8—134no—
216C22×C8—264no—
217C22×C8—264no—
218C2×C4⋊C4—132no—
219C2×C4⋊C4C2×#26112yes—
220C2×C22⋊C4—132no—
221C2×C22⋊C4C2×#26112yes—
222C2×C42—134no—
223C2×C42—134no—
224C2×C42—131no—
225C2×C42—131no—
226C2×C42—131no—
227C2×C42—131no—
228C2×C42—134no—
229C4⋊C8—138no—
230C22⋊C8—138no—
231#97—138no—
232#97—268no—
233C4×C8—134no—
234C4×C8—134no—
235C4×C8—134no—
236C4×C8—134no—
237C4×C8—268no—
238#95—132no—
239#95—134no—
240#95—134no—
241#95—134no—
242#95C2×#26112yes—
243C2×C13—24no—
244C2×C13C4×#11711yescharacteristic
245C2×C13C2×#40511yescharacteristic
246C2×C13C2×#40511yescharacteristic
247C2×C13#296612yes—
248C2×C13#296612yes—
249C24C22×#26111yescharacteristic
250C22×C4—24no—
251C22×C4—131no—
252C22×C4—132no—
253C22×C4—132no—
254C22×C4—134no—
255C22×C4—131no—
256C22×C4—131no—
257C22×C4—131no—
258C22×C4—134no—
259C22×C4—262no—
260C22×C4—262no—
261C22×C4—262no—
262C22×C4—262no—
263C22×C4C4×#26114yes—
264C22×C4C22×#26114yes—
265C22×C4C22×#26111yescharacteristic
266C22×C4C22×#26111yescharacteristic
267C2×C8—132no—
268C2×C8—132no—
269C2×C8—134no—
270C2×C8—134no—
271C2×C8—132no—
272C2×C8—132no—
273C2×C8—138no—
274C2×C8—268no—
275C2×C8—268no—
276C2×C8—264no—
277C2×C8—264no—
278C2×C8—262no—
279C2×C8—262no—
280C4⋊C4—24no—
281C4⋊C4—264no—
282C22⋊C4—24no—
283C22⋊C4—264no—
284C42—132no—
285C42—132no—
286C42—132no—
287C42—132no—
288C42—134no—
289C42—134no—
290C42—264no—
291C42—264no—
292C13#2047611yescharacteristic, complemented, Sylow
293C23—22no—
294C23—22no—
295C23C2×C4×#26112yes—
296C23#8823812yes—
297C23#8824012yes—
298C23C23×#26111yescharacteristic
299C2×C4—22no—
300C2×C4—28no—
301C2×C4—24no—
302C2×C4—24no—
303C2×C4—24no—
304C2×C4—131no—
305C2×C4—131no—
306C2×C4—132no—
307C2×C4—132no—
308C2×C4—132no—
309C2×C4—132no—
310C2×C4—132no—
311C2×C4—262no—
312C2×C4—262no—
313C2×C4—264no—
314C2×C4—268no—
315C2×C4—261no—
316C2×C4—261no—
317C2×C4—261no—
318C2×C4—261no—
319C2×C4—262no—
320C2×C4—264no—
321C2×C4—264no—
322C2×C4—264no—
323C2×C4C2×C4×#26112yes—
324C2×C4C2×C4×#26112yes—
325C2×C4#8823814yes—
326C8—134no—
327C8—134no—
328C8—262no—
329C8—262no—
330C8—268no—
331C22—22no—
332C22—24no—
333C22—22no—
334C22—24no—
335C22#1171907214yes—
336C22C22×C4×#26111yescharacteristic
337C22C2×#8823811yescharacteristic
338C22C2×#8823812yes—
339C22C2×#8824011yescharacteristic
340C22#41×#26112yes—
341C4—22no—
342C4—44no—
343C4—131no—
344C4—131no—
345C4—132no—
346C4—262no—
347C4—262no—
348C4—262no—
349C4—524no—
350C4#1171906214yes—
351C2—24no—
352C2#117×#26111yescharacteristic
353C2C2×#1171906211yescharacteristic
354C2C2×#1171907211yescharacteristic
355C2#1313164912yes—
356C2#1313165212yes—
subgroupG/H
center, FrattiniC23C23×#261
commutatorC22×C13C22×C42
FittingC13×#380C4
socleC23×C13C23×C4
prime radicalC24×C13C22×C4
cosocleC22×Dic13C24
hypercenter#380#261
hypocenterC13#20476
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ #380

Complements

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

NH ≅ G/Ntype
3. #13130632C2semidirect
4. C4⋊C4×#1057C2semidirect
7. #13130555C2semidirect
8. #13130493C2semidirect
14. #11719130C4semidirect
18. C2×C4×#1057C4semidirect
292. C13#20476semidirect

Maximal subgroups

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

subgroupindex
C2×#117191302
C22×C4×#10572
#131306322
C4⋊C4×#10572
#131305732
C22⋊C4×#10572
#131305552
#131304932
#131172312
#2047613