Finite Group Databasebeta

← #16780204

Subgroups — #16780204

Order 3328.

562 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13131512C211yesmaximal, characteristic
2#13131512C211yesmaximal, characteristic
3#13129739C214yesmaximal
4#13117230C211yesmaximal, characteristic
5C22×C4×Dic13C2211yescharacteristic
6#11719169C2212yes—
7#11719169C2212yes—
8#11719130—21no—
9#11719130C412yescomplemented
10#11719129—21no—
11#11719129—21no—
12#11719128—21no—
13#11719128C412yescomplemented
14#11719125—21no—
15#11719125C412yescomplemented
16C4×#6122—21no—
17C4×#6122—21no—
18#11719119—21no—
19#11719119C412yescomplemented
20C4×C13×C22⋊C4C411yescharacteristic
21C4×C22⋊Dic13C411yescharacteristic
22#11718604C2212yes—
23#11718603C412yes—
24#11718593—21no—
25C4×#6101—21no—
26#11718312—21no—
27#11718311—21no—
28C23×C4×C13C2×C411yescharacteristic
29C23×Dic13C2×C411yescharacteristic
30C23×Dic13C2311yescharacteristic
31C2×#6122—22no—
32C2×#6122—22no—
33C2×C13×C22⋊C4C2×C412yes—
34C2×C42×C13—21no—
35C2×C22⋊Dic13C2×C412yes—
36C2×#6101—22no—
37C2×C4×Dic13—21no—
38C2×C4×Dic13C2×C411yescharacteristic
39C2×C4×Dic13C2×C411yescharacteristic
40C2×C4×Dic13C2×C411yescharacteristic
41C2×C4×Dic13C2×C411yescharacteristic
42C2×C4×Dic13D411yescharacteristic
43C2×C4×Dic13D411yescharacteristic
44C2×C4×Dic13D411yescharacteristic
45C2×C4×Dic13D411yescharacteristic
46C2×C4×Dic13D411yescharacteristic
47C2×C4×Dic13D411yescharacteristic
48C2×C4×Dic13Q811yescharacteristic
49C2×C4×Dic13Q811yescharacteristic
50C22⋊#1057—22no—
51C22⋊#1057—22no—
52C22⋊#1057C2×C414yes—
53C22⋊#1057C2×C414yes—
54#88112—22no—
55#88112—22no—
56#88110—22no—
57#88110—22no—
58C4⋊#1057—22no—
59C4⋊#1057—22no—
60C4×#1057—22no—
61C4×#1057—22no—
62C13×#95—21no—
63#88071—21no—
64#88071—22no—
65#88071—22no—
66#88071—22no—
67#8113—131nomaximal, Sylow
68C24×C13C22×C411yescharacteristic
69C22×C4×C13—22no—
70C22×C4×C13—42no—
71C22×C4×C13C4211yescharacteristic
72C22×C4×C13C4211yescharacteristic
73C22×C4×C13C22⋊C411yescharacteristic
74C22×C4×C13C22⋊C411yescharacteristic
75C22×C4×C13C4⋊C411yescharacteristic
76C22×C4×C13C4⋊C411yescharacteristic
77C22×Dic13—22no—
78C22×Dic13—42no—
79C22×Dic13—42no—
80C22×Dic13C4211yescharacteristic
81C22×Dic13C4211yescharacteristic
82C22×Dic13C22⋊C411yescharacteristic
83C22×Dic13C22⋊C411yescharacteristic
84C22×Dic13C4⋊C411yescharacteristic
85C22×Dic13C4⋊C411yescharacteristic
86C22×Dic13C22×C411yescharacteristic
87C22×Dic13C22×C411yescharacteristic
88C22×Dic13C2×D411yescharacteristic
89C22×Dic13C2×D411yescharacteristic
90C22×Dic13C2×D411yescharacteristic
91C22×Dic13C2×Q811yescharacteristic
92#6122—44no—
93#6122—44no—
94C2×#1057—24no—
95C2×#1057—24no—
96C13×C22⋊C4—42no—
97C42×C13—42no—
98C22⋊Dic13—42no—
99#6101—44no—
100C4×Dic13—42no—
101C4×Dic13C22⋊C411yescharacteristic
102C4×Dic13C22⋊C411yescharacteristic
103C4×Dic13C22⋊C411yescharacteristic
104C4×Dic13C22⋊C411yescharacteristic
105C4×Dic13C22⋊C411yescharacteristic
106C4×Dic13C22⋊C411yescharacteristic
107C4×Dic13C22⋊C411yescharacteristic
108C4×Dic13C22⋊C411yescharacteristic
109C4×Dic13C4⋊C411yescharacteristic
110C4×Dic13C4⋊C411yescharacteristic
111C4×Dic13C4⋊C411yescharacteristic
112C4×Dic13C4⋊C411yescharacteristic
113C4×Dic13C4⋊C411yescharacteristic
114C4×Dic13C4⋊C411yescharacteristic
115C4×Dic13C4⋊C411yescharacteristic
116C4×Dic13C4⋊C411yescharacteristic
117#2920—131no—
118#2920—131no—
119#2283—131no—
120#1306—134no—
121C23×C13—22no—
122C23×C13—41no—
123C23×C13—41no—
124C23×C13C2×C4211yescharacteristic
125C23×C13C2×C22⋊C411yescharacteristic
126C23×C13C2×C4⋊C411yescharacteristic
127C2×C4×C13—22no—
128C2×C4×C13—22no—
129C2×C4×C13—22no—
130C2×C4×C13—41no—
131C2×C4×C13—41no—
132C2×C4×C13—41no—
133C2×C4×C13—42no—
134C2×C4×C13—42no—
135C2×C4×C13—42no—
136C2×C4×C13#9511yescharacteristic
137C2×C4×C13#9511yescharacteristic
138C2×C4×C13#9511yescharacteristic
139C2×C4×C13#9511yescharacteristic
140C2×Dic13—22no—
141C2×Dic13—22no—
142C2×Dic13—22no—
143C2×Dic13—22no—
144C2×Dic13—22no—
145C2×Dic13—41no—
146C2×Dic13—41no—
147C2×Dic13—41no—
148C2×Dic13—41no—
149C2×Dic13—41no—
150C2×Dic13—41no—
151C2×Dic13—41no—
152C2×Dic13—42no—
153C2×Dic13—42no—
154C2×Dic13—42no—
155C2×Dic13#9511yescharacteristic
156C2×Dic13#9511yescharacteristic
157C2×Dic13#9511yescharacteristic
158C2×Dic13#9511yescharacteristic
159C2×Dic13C2×C22⋊C411yescharacteristic
160C2×Dic13C2×C22⋊C411yescharacteristic
161C2×Dic13C2×C4⋊C411yescharacteristic
162C2×Dic13C2×C4⋊C411yescharacteristic
163#1057—44no—
164#1057—44no—
165C22×C42—131no—
166#432—132no—
167#432—132no—
168#432—261no—
169#432—261no—
170#431—132no—
171#431—132no—
172#431—261no—
173#431—261no—
174#423—261no—
175#423—261no—
176#407—132no—
177#407—132no—
178C4×M16—261no—
179C4×M16—261no—
180#383—261no—
181#382—261no—
182#381—132no—
183#380—132no—
184C4×C4⋊C4—261no—
185C4×C22⋊C4—131no—
186C4×C22⋊C4#26111yescharacteristic
187#376—261no—
188C22×C13—21no—
189C22×C13—21no—
190C22×C13—21no—
191C22×C13—21no—
192C22×C13—21no—
193C22×C13—21no—
194C22×C13—21no—
195C22×C13—21no—
196C22×C13—44no—
197C22×C13C2×#9511yescharacteristic
198C22×C13#41012yes—
199C4×C13—21no—
200C4×C13—21no—
201C4×C13—21no—
202C4×C13—82no—
203C4×C13#34412yes—
204Dic13—21no—
205Dic13—21no—
206Dic13—21no—
207Dic13—21no—
208Dic13—21no—
209Dic13—21no—
210Dic13—21no—
211Dic13—82no—
212Dic13#34412yes—
213C23×C4—131no—
214C23×C4—131no—
215C23×C4C2×#26111yescharacteristic
216C2×M16—262no—
217C2×M16—262no—
218C2×C4⋊C4—262no—
219C2×C22⋊C4—132no—
220C2×C22⋊C4C2×#26112yes—
221C2×C42—21no—
222C2×C42—131no—
223C2×C42—131no—
224C2×C42—131no—
225C2×C42—131no—
226C2×C42—131no—
227C2×C42—131no—
228C2×C42—131no—
229C2×C42—131no—
230C2×C42—131no—
231C2×C42—131no—
232C2×C42—131no—
233C2×C42—131no—
234C2×C42—261no—
235C4⋊C8—262no—
236C4⋊C8—262no—
237C4⋊C8—262no—
238C4⋊C8—262no—
239C22⋊C8—134no—
240C22⋊C8—134no—
241C22⋊C8—262no—
242C22⋊C8—262no—
243#97—262no—
244#97—262no—
245C4×C8—262no—
246C4×C8—262no—
247#95—21no—
248#95—262no—
249#95—262no—
250#95—262no—
251#95—261no—
252C2×C13—22no—
253C2×C13—41no—
254C2×C13—41no—
255C2×C13#174011yescharacteristic
256C2×C13C2×#34411yescharacteristic
257C2×C13C2×#34411yescharacteristic
258C24C22×#26111yescharacteristic
259C22×C4—22no—
260C22×C4—42no—
261C22×C4—131no—
262C22×C4—131no—
263C22×C4—131no—
264C22×C4—131no—
265C22×C4—131no—
266C22×C4—131no—
267C22×C4—131no—
268C22×C4—131no—
269C22×C4—131no—
270C22×C4—131no—
271C22×C4—131no—
272C22×C4—131no—
273C22×C4—262no—
274C22×C4—522no—
275C22×C4—522no—
276C22×C4C4×#26111yescharacteristic
277C22×C4C4×#26111yescharacteristic
278C22×C4C4⋊#26111yescharacteristic
279C22×C4C4⋊#26111yescharacteristic
280C22×C4C22⋊#26111yescharacteristic
281C22×C4C22⋊#26111yescharacteristic
282M16—524no—
283M16—524no—
284C2×C8—264no—
285C2×C8—264no—
286C4⋊C4—524no—
287C22⋊C4—42no—
288C22⋊C4—522no—
289C42—42no—
290C42—131no—
291C42—131no—
292C42—131no—
293C42—131no—
294C42—131no—
295C42—131no—
296C42—131no—
297C42—131no—
298C42—131no—
299C42—131no—
300C42—131no—
301C42—131no—
302C42—131no—
303C42—131no—
304C42—131no—
305C42—131no—
306C42—522no—
307C13#811311yescharacteristic, complemented, Sylow
308C23—22no—
309C23—41no—
310C23—41no—
311C23C2×C4×#26111yescharacteristic
312C23C2×C4⋊#26111yescharacteristic
313C23C2×C22⋊#26111yescharacteristic
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—42no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—131no—
324C2×C4—131no—
325C2×C4—131no—
326C2×C4—131no—
327C2×C4—131no—
328C2×C4—131no—
329C2×C4—131no—
330C2×C4—131no—
331C2×C4—262no—
332C2×C4—262no—
333C2×C4—262no—
334C2×C4—262no—
335C2×C4—262no—
336C2×C4—521no—
337C2×C4—521no—
338C2×C4—521no—
339C2×C4—521no—
340C2×C4—521no—
341C2×C4—521no—
342C2×C4—521no—
343C2×C4—522no—
344C2×C4—522no—
345C2×C4—522no—
346C2×C4(C2×#261)⋊C411yescharacteristic
347C2×C4(C2×#261)⋊C411yescharacteristic
348C2×C4(C2×#261)⋊C411yescharacteristic
349C2×C4(C2×#261)⋊C411yescharacteristic
350C8—524no—
351C8—524no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—44no—
361C22#1171911612yes—
362C22C2×(C2×#261)⋊C411yescharacteristic
363C4—21no—
364C4—21no—
365C4—21no—
366C4—82no—
367C4—132no—
368C4—261no—
369C4—261no—
370C4—261no—
371C4—261no—
372C4—261no—
373C4—261no—
374C4—261no—
375C4—1042no—
376C4#1171823912yes—
377C2—22no—
378C2—41no—
379C2—41no—
380C2#1313053511yescharacteristic
381C2C2×#1171823911yescharacteristic
382C2#1313054411yescharacteristic
subgroupG/H
centerC2×C4(C2×#261)⋊C4
commutatorC23×C13C2×C42
FrattiniC24C22×#261
FittingC4×C13×C22⋊C4C4
socleC22×C13C2×#95
prime radicalC24×C13C22×C4
cosocleC23×Dic13C23
hypercenterC4×C22⋊C4#261
hypocenterC13#8113
LCSG ▷ C23×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
9. #11719130C4semidirect
13. #11719128C4semidirect
15. #11719125C4semidirect
19. #11719119C4semidirect
307. C13#8113semidirect

Maximal subgroups

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

subgroupindex
#131315122
#131297392
#131172302
#811313