Finite Group Databasebeta

← #16780187

Subgroups — #16780187

Order 3328.

606 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13131512C211yesmaximal, characteristic
2#13131512C211yesmaximal, characteristic
3#13129737C214yesmaximal
4#13117238C211yesmaximal, characteristic
5C22×C4×Dic13C2211yescharacteristic
6C2×#88131C412yes—
7#11719169C2212yes—
8#11719169C2212yes—
9#11719130—21no—
10#11719130—21no—
11#11719129—21no—
12#11719129C412yescomplemented
13#11719128—21no—
14#11719128C412yescomplemented
15#11719125—21no—
16#11719125—21no—
17C4×#6122—21no—
18C4×#6122C412yescomplemented
19#11719119—21no—
20#11719119C412yescomplemented
21C13×#380C411yescharacteristic
22#11718873C411yescharacteristic
23#11718637—21no—
24C4⋊C4×Dic13—21no—
25#11718603C2212yes—
26#11718311—21no—
27#11718310—21no—
28C23×C4×C13C2×C411yescharacteristic
29C23×Dic13C2×C411yescharacteristic
30C23×Dic13C2311yescharacteristic
31C2×#6122—22no—
32C2×#6122C2×C414yes—
33C2×C13×C4⋊C4—21no—
34C2×C13×C22⋊C4C2×C412yes—
35C2×C22⋊Dic13C2×C412yes—
36C2×C4⋊Dic13—21no—
37C2×#6101—22no—
38C2×#6101—22no—
39C2×C4×Dic13—22no—
40C2×C4×Dic13C2×C411yescharacteristic
41C2×C4×Dic13C2×C411yescharacteristic
42C2×C4×Dic13C2×C411yescharacteristic
43C2×C4×Dic13C2×C411yescharacteristic
44C2×C4×Dic13D411yescharacteristic
45C2×C4×Dic13D411yescharacteristic
46C2×C4×Dic13D411yescharacteristic
47C2×C4×Dic13D411yescharacteristic
48C2×C4×Dic13D411yescharacteristic
49C2×C4×Dic13D411yescharacteristic
50C2×C4×Dic13Q811yescharacteristic
51C2×C4×Dic13Q811yescharacteristic
52#88131—44no—
53C22⋊#1057—22no—
54C22⋊#1057—22no—
55C22⋊#1057—22no—
56C22⋊#1057C2×C414yes—
57#88112—22no—
58#88112—22no—
59#88110—22no—
60#88110—22no—
61C4⋊#1057—22no—
62C4⋊#1057—22no—
63C4×#1057—22no—
64C4×#1057—22no—
65C13×#95—21no—
66#88071—21no—
67#88071—22no—
68#8109—131nomaximal, Sylow
69C24×C13C22×C411yescharacteristic
70C22×C4×C13—22no—
71C22×C4×C13—42no—
72C22×C4×C13C4211yescharacteristic
73C22×C4×C13C4211yescharacteristic
74C22×C4×C13C22⋊C411yescharacteristic
75C22×C4×C13C22⋊C411yescharacteristic
76C22×C4×C13C4⋊C411yescharacteristic
77C22×C4×C13C4⋊C411yescharacteristic
78C22×Dic13—22no—
79C22×Dic13—22no—
80C22×Dic13—22no—
81C22×Dic13—42no—
82C22×Dic13C4211yescharacteristic
83C22×Dic13C4211yescharacteristic
84C22×Dic13C22⋊C411yescharacteristic
85C22×Dic13C22⋊C411yescharacteristic
86C22×Dic13C4⋊C411yescharacteristic
87C22×Dic13C4⋊C411yescharacteristic
88C22×Dic13C22×C411yescharacteristic
89C22×Dic13C22×C411yescharacteristic
90C22×Dic13C2×D411yescharacteristic
91C22×Dic13C2×D411yescharacteristic
92C22×Dic13C2×D411yescharacteristic
93C22×Dic13C2×Q811yescharacteristic
94#6122—44no—
95#6122—44no—
96C2×#1057—24no—
97C2×#1057—24no—
98C13×C4⋊C4—42no—
99C13×C22⋊C4—42no—
100C22⋊Dic13—42no—
101C4⋊Dic13—42no—
102#6101—44no—
103#6101—44no—
104C4×Dic13—44no—
105C4×Dic13C22⋊C411yescharacteristic
106C4×Dic13C22⋊C411yescharacteristic
107C4×Dic13C22⋊C411yescharacteristic
108C4×Dic13C22⋊C411yescharacteristic
109C4×Dic13C22⋊C411yescharacteristic
110C4×Dic13C22⋊C411yescharacteristic
111C4×Dic13C22⋊C411yescharacteristic
112C4×Dic13C22⋊C411yescharacteristic
113C4×Dic13C4⋊C411yescharacteristic
114C4×Dic13C4⋊C411yescharacteristic
115C4×Dic13C4⋊C411yescharacteristic
116C4×Dic13C4⋊C411yescharacteristic
117C4×Dic13C4⋊C411yescharacteristic
118C4×Dic13C4⋊C411yescharacteristic
119C4×Dic13C4⋊C411yescharacteristic
120C4×Dic13C4⋊C411yescharacteristic
121#2920—131no—
122#2920—131no—
123#2285—131no—
124#1305—134no—
125C23×C13—21no—
126C23×C13—21no—
127C23×C13—41no—
128C23×C13—41no—
129C23×C13C2×C4211yescharacteristic
130C23×C13C2×C22⋊C411yescharacteristic
131C23×C13C2×C4⋊C411yescharacteristic
132C2×C4×C13—22no—
133C2×C4×C13—22no—
134C2×C4×C13—22no—
135C2×C4×C13—41no—
136C2×C4×C13—41no—
137C2×C4×C13—41no—
138C2×C4×C13—42no—
139C2×C4×C13—42no—
140C2×C4×C13—42no—
141C2×C4×C13#9511yescharacteristic
142C2×C4×C13#9511yescharacteristic
143C2×C4×C13#9511yescharacteristic
144C2×C4×C13#9511yescharacteristic
145C2×Dic13—21no—
146C2×Dic13—21no—
147C2×Dic13—22no—
148C2×Dic13—22no—
149C2×Dic13—22no—
150C2×Dic13—22no—
151C2×Dic13—22no—
152C2×Dic13—22no—
153C2×Dic13—22no—
154C2×Dic13—41no—
155C2×Dic13—41no—
156C2×Dic13—41no—
157C2×Dic13—42no—
158C2×Dic13—42no—
159C2×Dic13—42no—
160C2×Dic13#9511yescharacteristic
161C2×Dic13#9511yescharacteristic
162C2×Dic13#9511yescharacteristic
163C2×Dic13#9511yescharacteristic
164C2×Dic13#10012yes—
165C2×Dic13#10112yes—
166C2×Dic13C2×C22⋊C411yescharacteristic
167C2×Dic13C2×C22⋊C411yescharacteristic
168C2×Dic13C2×C4⋊C411yescharacteristic
169C2×Dic13C2×C4⋊C411yescharacteristic
170#1057—44no—
171#1057—44no—
172C2×#117—132no—
173C22×C42—131no—
174#432—132no—
175#432—261no—
176#432—261no—
177#432—261no—
178#431—132no—
179#431—261no—
180#431—261no—
181#431—261no—
182#423—132no—
183#423—261no—
184#407—132no—
185#407—132no—
186C4×M16—132no—
187C4×M16—261no—
188#384—261no—
189#382—261no—
190#380—131no—
191#380—132no—
192#380#26111yescharacteristic
193C4×C4⋊C4—261no—
194C4×C4⋊C4—261no—
195C22×C13—21no—
196C22×C13—21no—
197C22×C13—21no—
198C22×C13—21no—
199C22×C13—21no—
200C22×C13—21no—
201C22×C13—21no—
202C22×C13—21no—
203C22×C13—42no—
204C22×C13—42no—
205C22×C13C2×#9511yescharacteristic
206C22×C13C2×#10011yescharacteristic
207C22×C13C2×#10111yescharacteristic
208C4×C13—21no—
209C4×C13—21no—
210C4×C13—21no—
211C4×C13—82no—
212C4×C13#34412yes—
213Dic13—21no—
214Dic13—21no—
215Dic13—21no—
216Dic13—21no—
217Dic13—21no—
218Dic13—82no—
219Dic13#34312yes—
220Dic13#34312yes—
221Dic13#41012yes—
222C23×C4—131no—
223C23×C4—131no—
224C23×C4C2×#26111yescharacteristic
225C2×M16—134no—
226C2×M16—262no—
227#117—524no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—262no—
230C2×C4⋊C4—262no—
231C2×C4⋊C4—261no—
232C2×C22⋊C4—132no—
233C2×C22⋊C4C2×#26112yes—
234C2×C42—131no—
235C2×C42—131no—
236C2×C42—131no—
237C2×C42—131no—
238C2×C42—131no—
239C2×C42—131no—
240C2×C42—131no—
241C2×C42—131no—
242C2×C42—131no—
243C2×C42—131no—
244C2×C42—131no—
245C2×C42—131no—
246C2×C42—262no—
247C4⋊C8—262no—
248C4⋊C8—262no—
249C4⋊C8—262no—
250C4⋊C8—262no—
251C22⋊C8—134no—
252C22⋊C8—262no—
253C22⋊C8—262no—
254C22⋊C8—262no—
255#97—262no—
256#97—262no—
257C4×C8—262no—
258C4×C8—262no—
259#95—21no—
260#95—262no—
261#95—261no—
262C2×C13—21no—
263C2×C13—21no—
264C2×C13—41no—
265C2×C13—41no—
266C2×C13#174011yescharacteristic
267C2×C13C2×#34311yescharacteristic
268C2×C13C2×#34411yescharacteristic
269C24C22×#26111yescharacteristic
270C22×C4—22no—
271C22×C4—42no—
272C22×C4—131no—
273C22×C4—131no—
274C22×C4—131no—
275C22×C4—131no—
276C22×C4—131no—
277C22×C4—131no—
278C22×C4—131no—
279C22×C4—131no—
280C22×C4—131no—
281C22×C4—131no—
282C22×C4—131no—
283C22×C4—131no—
284C22×C4—262no—
285C22×C4—262no—
286C22×C4—262no—
287C22×C4—522no—
288C22×C4C4×#26111yescharacteristic
289C22×C4C4×#26111yescharacteristic
290C22×C4C4⋊#26111yescharacteristic
291C22×C4C4⋊#26111yescharacteristic
292C22×C4C22⋊#26111yescharacteristic
293C22×C4C22⋊#26111yescharacteristic
294M16—524no—
295M16—524no—
296C2×C8—264no—
297C2×C8—264no—
298C4⋊C4—42no—
299C4⋊C4—522no—
300C4⋊C4—524no—
301C4⋊C4—524no—
302C22⋊C4—42no—
303C22⋊C4—522no—
304C42—131no—
305C42—131no—
306C42—131no—
307C42—131no—
308C42—131no—
309C42—131no—
310C42—131no—
311C42—131no—
312C42—131no—
313C42—131no—
314C42—131no—
315C42—131no—
316C42—131no—
317C42—131no—
318C42—131no—
319C42—131no—
320C42—524no—
321C13#810911yescharacteristic, complemented, Sylow
322C23—21no—
323C23—21no—
324C23—41no—
325C23—41no—
326C23C2×C4×#26111yescharacteristic
327C23C2×C4⋊#26111yescharacteristic
328C23C2×C22⋊#26111yescharacteristic
329C2×C4—22no—
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—42no—
336C2×C4—42no—
337C2×C4—42no—
338C2×C4—131no—
339C2×C4—131no—
340C2×C4—131no—
341C2×C4—132no—
342C2×C4—132no—
343C2×C4—131no—
344C2×C4—131no—
345C2×C4—131no—
346C2×C4—131no—
347C2×C4—131no—
348C2×C4—262no—
349C2×C4—262no—
350C2×C4—262no—
351C2×C4—262no—
352C2×C4—262no—
353C2×C4—262no—
354C2×C4—262no—
355C2×C4—261no—
356C2×C4—261no—
357C2×C4—521no—
358C2×C4—521no—
359C2×C4—521no—
360C2×C4—522no—
361C2×C4—522no—
362C2×C4—522no—
363C2×C4(C2×#261)⋊C411yescharacteristic
364C2×C4(C2×#261)⋊C411yescharacteristic
365C2×C4(C2×#261)⋊C411yescharacteristic
366C2×C4(C2×#261)⋊C411yescharacteristic
367C8—524no—
368C8—524no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—42no—
378C22—42no—
379C22C2×(C2×#261)⋊C411yescharacteristic
380C22D13⋊#10011yescharacteristic
381C22D13⋊#10111yescharacteristic
382C4—21no—
383C4—21no—
384C4—21no—
385C4—82no—
386C4—132no—
387C4—132no—
388C4—132no—
389C4—261no—
390C4—261no—
391C4—261no—
392C4—261no—
393C4—261no—
394C4—1042no—
395C4#1171823912yes—
396C2—21no—
397C2—21no—
398C2—41no—
399C2—41no—
400C2#1313053411yescharacteristic
401C2#1313053911yescharacteristic
402C2C2×#1171823911yescharacteristic
subgroupG/H
centerC22C2×(C2×#261)⋊C4
commutatorC23×C13C2×C42
FrattiniC24C22×#261
FittingC13×#380C4
socleC22×C13C2×#95
prime radicalC24×C13C22×C4
cosocleC23×Dic13C23
hypercenter#380#261
hypocenterC13#8109
LCSG ▷ C23×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
12. #11719129C4semidirect
14. #11719128C4semidirect
18. C4×#6122C4semidirect
20. #11719119C4semidirect
321. C13#8109semidirect

Maximal subgroups

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

subgroupindex
#131315122
#131297372
#131172382
#810913