Finite Group Databasebeta

← #16780186

Subgroups — #16780186

Order 3328.

606 conjugacy classes of subgroups.

The subgroup lattice has 408 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#13117239C211yesmaximal, characteristic
5C2×C13×#117C411yescharacteristic
6C2×#88180C411yescharacteristic
7C22×C4×Dic13C2211yescharacteristic
8#11719169C2212yes—
9#11719169C2212yes—
10#11719130—21no—
11#11719130C412yescomplemented
12#11719129—21no—
13#11719129C412yescomplemented
14#11719128—21no—
15#11719128—21no—
16#11719125—21no—
17#11719125C412yescomplemented
18C4×#6122—21no—
19C4×#6122C412yescomplemented
20#11719119—21no—
21#11719119—21no—
22#11718638—21no—
23#11718637—21no—
24#11718603C412yes—
25#11718603C2212yes—
26C4×#6101—21no—
27C4×#6101—21no—
28C23×C4×C13C2×C411yescharacteristic
29C23×Dic13C2×C411yescharacteristic
30C23×Dic13C2311yescharacteristic
31C2×#6122—22no—
32C2×#6122C2×C414yes—
33C13×#117—42no—
34C2×C13×C4⋊C4—21no—
35C2×C13×C22⋊C4C2×C412yes—
36C2×C42×C13—21no—
37C2×C22⋊Dic13C2×C412yes—
38#88180—42no—
39C2×C4⋊Dic13—21no—
40C2×#6101—22no—
41C2×#6101—22no—
42C2×C4×Dic13—21no—
43C2×C4×Dic13C2×C411yescharacteristic
44C2×C4×Dic13C2×C411yescharacteristic
45C2×C4×Dic13C2×C411yescharacteristic
46C2×C4×Dic13C2×C411yescharacteristic
47C2×C4×Dic13D411yescharacteristic
48C2×C4×Dic13D411yescharacteristic
49C2×C4×Dic13D411yescharacteristic
50C2×C4×Dic13D411yescharacteristic
51C2×C4×Dic13D411yescharacteristic
52C2×C4×Dic13D411yescharacteristic
53C2×C4×Dic13Q811yescharacteristic
54C2×C4×Dic13Q811yescharacteristic
55C22⋊#1057—22no—
56C22⋊#1057—22no—
57C22⋊#1057—22no—
58C22⋊#1057C2×C414yes—
59#88112—22no—
60#88112—22no—
61#88110—22no—
62#88110—22no—
63C4⋊#1057—22no—
64C4⋊#1057—22no—
65C4×#1057—22no—
66C4×#1057—22no—
67#88071—22no—
68#88071—22no—
69#8109—131nomaximal, Sylow
70C24×C13C22×C411yescharacteristic
71C22×C4×C13—22no—
72C22×C4×C13—22no—
73C22×C4×C13—22no—
74C22×C4×C13C4211yescharacteristic
75C22×C4×C13C4211yescharacteristic
76C22×C4×C13C22⋊C411yescharacteristic
77C22×C4×C13C22⋊C411yescharacteristic
78C22×C4×C13C4⋊C411yescharacteristic
79C22×C4×C13C4⋊C411yescharacteristic
80C22×Dic13—22no—
81C22×Dic13—42no—
82C22×Dic13—42no—
83C22×Dic13C4211yescharacteristic
84C22×Dic13C4211yescharacteristic
85C22×Dic13C22⋊C411yescharacteristic
86C22×Dic13C22⋊C411yescharacteristic
87C22×Dic13C4⋊C411yescharacteristic
88C22×Dic13C4⋊C411yescharacteristic
89C22×Dic13C22×C411yescharacteristic
90C22×Dic13C22×C411yescharacteristic
91C22×Dic13C2×D411yescharacteristic
92C22×Dic13C2×D411yescharacteristic
93C22×Dic13C2×D411yescharacteristic
94C22×Dic13C2×Q811yescharacteristic
95#6122—44no—
96#6122—44no—
97C2×#1057—24no—
98C2×#1057—24no—
99C13×C4⋊C4—42no—
100C13×C22⋊C4—42no—
101C42×C13—42no—
102C22⋊Dic13—42no—
103C4⋊Dic13—42no—
104#6101—44no—
105#6101—44no—
106C4×Dic13—42no—
107C4×Dic13C22⋊C411yescharacteristic
108C4×Dic13C22⋊C411yescharacteristic
109C4×Dic13C22⋊C411yescharacteristic
110C4×Dic13C22⋊C411yescharacteristic
111C4×Dic13C22⋊C411yescharacteristic
112C4×Dic13C22⋊C411yescharacteristic
113C4×Dic13C22⋊C411yescharacteristic
114C4×Dic13C22⋊C411yescharacteristic
115C4×Dic13C4⋊C411yescharacteristic
116C4×Dic13C4⋊C411yescharacteristic
117C4×Dic13C4⋊C411yescharacteristic
118C4×Dic13C4⋊C411yescharacteristic
119C4×Dic13C4⋊C411yescharacteristic
120C4×Dic13C4⋊C411yescharacteristic
121C4×Dic13C4⋊C411yescharacteristic
122C4×Dic13C4⋊C411yescharacteristic
123#2920—131no—
124#2920—131no—
125#2285—131no—
126#1305—134no—
127C23×C13—21no—
128C23×C13—21no—
129C23×C13—41no—
130C23×C13—41no—
131C23×C13C2×C4211yescharacteristic
132C23×C13C2×C22⋊C411yescharacteristic
133C23×C13C2×C4⋊C411yescharacteristic
134C2×C4×C13—21no—
135C2×C4×C13—21no—
136C2×C4×C13—22no—
137C2×C4×C13—22no—
138C2×C4×C13—22no—
139C2×C4×C13—22no—
140C2×C4×C13—42no—
141C2×C4×C13—42no—
142C2×C4×C13—42no—
143C2×C4×C13#9511yescharacteristic
144C2×C4×C13#9511yescharacteristic
145C2×C4×C13#9511yescharacteristic
146C2×C4×C13#9511yescharacteristic
147C2×C4×C13#10012yes—
148C2×C4×C13#10112yes—
149C2×Dic13—22no—
150C2×Dic13—22no—
151C2×Dic13—22no—
152C2×Dic13—22no—
153C2×Dic13—22no—
154C2×Dic13—22no—
155C2×Dic13—41no—
156C2×Dic13—41no—
157C2×Dic13—41no—
158C2×Dic13—41no—
159C2×Dic13—41no—
160C2×Dic13—41no—
161C2×Dic13—42no—
162C2×Dic13—42no—
163C2×Dic13—42no—
164C2×Dic13#9511yescharacteristic
165C2×Dic13#9511yescharacteristic
166C2×Dic13#9511yescharacteristic
167C2×Dic13#9511yescharacteristic
168C2×Dic13C2×C22⋊C411yescharacteristic
169C2×Dic13C2×C22⋊C411yescharacteristic
170C2×Dic13C2×C4⋊C411yescharacteristic
171C2×Dic13C2×C4⋊C411yescharacteristic
172#1057—44no—
173#1057—44no—
174C2×#117—131no—
175C2×#117#26111yescharacteristic
176C22×C42—131no—
177#432—132no—
178#432—261no—
179#432—261no—
180#432—261no—
181#431—132no—
182#431—261no—
183#431—261no—
184#431—261no—
185#423—132no—
186#423—261no—
187#407—132no—
188#407—132no—
189C4×M16—132no—
190C4×M16—261no—
191#384—261no—
192#382—261no—
193#380—132no—
194#380—132no—
195C4×C4⋊C4—261no—
196C4×C4⋊C4—261no—
197C22×C13—21no—
198C22×C13—21no—
199C22×C13—21no—
200C22×C13—21no—
201C22×C13—21no—
202C22×C13—21no—
203C22×C13—21no—
204C22×C13—21no—
205C22×C13—42no—
206C22×C13—42no—
207C22×C13C2×#9511yescharacteristic
208C22×C13C2×#10011yescharacteristic
209C22×C13C2×#10111yescharacteristic
210C4×C13—21no—
211C4×C13—21no—
212C4×C13—82no—
213C4×C13#34312yes—
214C4×C13#34312yes—
215Dic13—21no—
216Dic13—21no—
217Dic13—21no—
218Dic13—21no—
219Dic13—21no—
220Dic13—21no—
221Dic13—82no—
222Dic13#34412yes—
223Dic13#41012yes—
224C23×C4—131no—
225C23×C4—131no—
226C23×C4C2×#26111yescharacteristic
227C2×M16—134no—
228C2×M16—262no—
229#117—42no—
230#117—522no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—262no—
233C2×C4⋊C4—262no—
234C2×C4⋊C4—261no—
235C2×C22⋊C4—132no—
236C2×C22⋊C4C2×#26112yes—
237C2×C42—21no—
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—131no—
247C2×C42—131no—
248C2×C42—131no—
249C2×C42—131no—
250C2×C42—261no—
251C4⋊C8—262no—
252C4⋊C8—262no—
253C4⋊C8—262no—
254C4⋊C8—262no—
255C22⋊C8—134no—
256C22⋊C8—262no—
257C22⋊C8—262no—
258C22⋊C8—262no—
259#97—262no—
260#97—262no—
261C4×C8—262no—
262C4×C8—262no—
263#95—262no—
264#95—262no—
265C2×C13—21no—
266C2×C13—21no—
267C2×C13—41no—
268C2×C13—41no—
269C2×C13#174011yescharacteristic
270C2×C13C2×#34311yescharacteristic
271C2×C13C2×#34411yescharacteristic
272C24C22×#26111yescharacteristic
273C22×C4—22no—
274C22×C4—22no—
275C22×C4—22no—
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—131no—
285C22×C4—131no—
286C22×C4—131no—
287C22×C4—131no—
288C22×C4—262no—
289C22×C4—522no—
290C22×C4—522no—
291C22×C4C4×#26111yescharacteristic
292C22×C4C4×#26111yescharacteristic
293C22×C4C4⋊#26111yescharacteristic
294C22×C4C4⋊#26111yescharacteristic
295C22×C4C22⋊#26111yescharacteristic
296C22×C4C22⋊#26111yescharacteristic
297M16—524no—
298M16—524no—
299C2×C8—264no—
300C2×C8—264no—
301C4⋊C4—42no—
302C4⋊C4—524no—
303C4⋊C4—524no—
304C4⋊C4—522no—
305C22⋊C4—42no—
306C22⋊C4—522no—
307C42—42no—
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—131no—
321C42—131no—
322C42—131no—
323C42—131no—
324C42—522no—
325C13#810911yescharacteristic, complemented, Sylow
326C23—21no—
327C23—21no—
328C23—41no—
329C23—41no—
330C23C2×C4×#26111yescharacteristic
331C23C2×C4⋊#26111yescharacteristic
332C23C2×C22⋊#26111yescharacteristic
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—22no—
336C2×C4—22no—
337C2×C4—22no—
338C2×C4—22no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4—131no—
343C2×C4—131no—
344C2×C4—131no—
345C2×C4—131no—
346C2×C4—131no—
347C2×C4—131no—
348C2×C4—131no—
349C2×C4—131no—
350C2×C4—262no—
351C2×C4—262no—
352C2×C4—262no—
353C2×C4—262no—
354C2×C4—262no—
355C2×C4—262no—
356C2×C4—521no—
357C2×C4—521no—
358C2×C4—521no—
359C2×C4—521no—
360C2×C4—521no—
361C2×C4—521no—
362C2×C4—522no—
363C2×C4—522no—
364C2×C4—522no—
365C2×C4#8811312yes—
366C2×C4(C2×#261)⋊C411yescharacteristic
367C2×C4(C2×#261)⋊C411yescharacteristic
368C2×C4(C2×#261)⋊C411yescharacteristic
369C2×C4(C2×#261)⋊C411yescharacteristic
370C2×C4#8812112yes—
371C8—524no—
372C8—524no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—21no—
380C22—21no—
381C22—42no—
382C22—42no—
383C22C2×#8811311yescharacteristic
384C22C2×(C2×#261)⋊C411yescharacteristic
385C22C2×#8812111yescharacteristic
386C4—21no—
387C4—21no—
388C4—82no—
389C4—132no—
390C4—132no—
391C4—261no—
392C4—261no—
393C4—261no—
394C4—261no—
395C4—261no—
396C4—261no—
397C4—1042no—
398C4#1171829112yes—
399C4#1171829112yes—
400C2—21no—
401C2—21no—
402C2—41no—
403C2—41no—
404C2#1313053411yescharacteristic
405C2C2×#1171829111yescharacteristic
406C2#1313054411yescharacteristic
subgroupG/H
centerC22C2×(C2×#261)⋊C4
commutatorC23×C13C2×C42
FrattiniC24C22×#261
FittingC2×C13×#117C4
socleC22×C13C2×#95
prime radicalC24×C13C22×C4
cosocleC23×Dic13C23
hypercenterC2×#117#261
hypocenterC13#8109
LCSG ▷ C23×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
11. #11719130C4semidirect
13. #11719129C4semidirect
17. #11719125C4semidirect
19. C4×#6122C4semidirect
325. C13#8109semidirect

Maximal subgroups

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

subgroupindex
#131315122
#131297372
#131172392
#810913