Finite Group Databasebeta

← #15756082

Subgroups — #15756082

Order 3328.

454 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123792C211yesmaximal, characteristic
2#13114857C211yesmaximal, characteristic
3#13114853C211yesmaximal, characteristic
4C4×#88048C211yesmaximal, characteristic, complemented
5#13113591C211yesmaximal, characteristic, complemented
6#13112738C211yesmaximal, characteristic, complemented
7C13×#1303C211yesmaximal, characteristic, complemented
8C4×#6127C2211yescharacteristic
9C13×#431C2211yescharacteristic
10C13×#423C2211yescharacteristic
11C4×C13×C4⋊C4C2211yescharacteristic
12C2×#88065—21no—
13C2×#88048—21no—
14C4×C4⋊Dic13C2211yescharacteristic
15C2×#88045—21no—
16#11718585C2211yescharacteristic
17C2×C4×#1055C2211yescharacteristic
18#11718495C411yescharacteristic, complemented
19#11718495C411yescharacteristic, complemented
20#11718491C411yescharacteristic, complemented
21#11718491C411yescharacteristic, complemented
22#11718386—21no—
23#11718386—21no—
24#11718346—21no—
25C4×C8×D13—21no—
26#11718147—21no—
27#11718121—21no—
28#11718115—21no—
29#11718072—21no—
30#11718072—21no—
31C2×#6127D411yescharacteristic
32C2×C13×M16—21no—
33C2×C13×C4⋊C4—21no—
34C2×C42×C13—21no—
35C2×C42×C13C2311yescharacteristic
36C4×C22⋊D13—21no—
37C4×C22⋊D13—21no—
38#88180D411yescharacteristic
39C2×C4⋊Dic13—21no—
40C2×C4×Dic13—21no—
41C2×#6099—21no—
42C22×#1055D411yescharacteristic
43C22×#1055D411yescharacteristic
44C2×C8×D13—21no—
45C2×C8×D13—21no—
46C4×D52C2×C411yescharacteristic
47C4×D52Q811yescharacteristic
48#88126—21no—
49C42×D13—21no—
50C4×Dic26C2×C411yescharacteristic
51C4×Dic26Q811yescharacteristic
52C13×C4⋊C8—21no—
53C13×C4⋊C8—21no—
54C13×C4⋊C8C2×C411yescharacteristic
55C13×C4⋊C8C2×C411yescharacteristic
56C13×C22⋊C8—21no—
57C4×C8×C13—21no—
58C13×#95—21no—
59#88071—21no—
60#88065—42no—
61#88060—21no—
62#88060—21no—
63#88054—21no—
64#88054—21no—
65C8×Dic13—21no—
66C8×Dic13—21no—
67#88048—24no—
68#88045—42no—
69C4⋊#1055—21no—
70C4⋊#1055—21no—
71C4×#1055C2×C411yescharacteristic
72C4×#1055C2×C411yescharacteristic
73C4×#1055D411yescharacteristic
74C4×#1055D411yescharacteristic
75#8666—131nomaximal, Sylow
76C22×C4×C13—41no—
77C22×C4×C13C2×D411yescharacteristic
78C22×C4×C13C2×D411yescharacteristic
79C22×C4×C13#4111yescharacteristic
80C2×C22⋊D13—21no—
81C22×Dic13—41no—
82#6127—21no—
83#6127—21no—
84#6127SD1612yes—
85#6127SD1612yes—
86C2×D52C4⋊C411yescharacteristic
87C2×C4×D13—21no—
88C2×C4×D13—21no—
89C2×C4×D13—21no—
90C2×Dic26C4⋊C411yescharacteristic
91C13×M16—41no—
92C13×M16—41no—
93C2×C8×C13—21no—
94C2×C8×C13—21no—
95C2×C8×C13—41no—
96C13×C4⋊C4—22no—
97C13×C4⋊C4—41no—
98C42×C13—41no—
99C42×C13—41no—
100C42×C13C22×C411yescharacteristic
101C42×C13C2×D411yescharacteristic
102C42×C13C2×Q811yescharacteristic
103C42×C13#4111yescharacteristic
104C22⋊Dic13—21no—
105#6103—21no—
106#6103—21no—
107C4⋊Dic13—22no—
108C4⋊Dic13—41no—
109C4⋊Dic13C4⋊C411yescharacteristic
110C4⋊Dic13C4⋊C411yescharacteristic
111#6101—21no—
112#6101—21no—
113C4×Dic13—21no—
114C4×Dic13—21no—
115C4×Dic13—21no—
116C4×Dic13—41no—
117C4×Dic13—41no—
118#6099—41no—
119#6099—41no—
120C2×#1055—22no—
121C2×#1055—41no—
122C2×#1055—41no—
123C2×#1055C22⋊C411yescharacteristic
124C2×#1055C22⋊C411yescharacteristic
125C2×#1055C22⋊C411yescharacteristic
126C2×#1055C22⋊C411yescharacteristic
127C8×D13—42no—
128C8×D13—42no—
129C8×#41—131no—
130#1806—131no—
131#1806—131no—
132C4×#106—131no—
133#1566—131no—
134#1303—131no—
135#1303D1311yescharacteristic, complemented
136C23×C13#12111yescharacteristic
137C22×D13—21no—
138C2×C4×C13—21no—
139C2×C4×C13—21no—
140C2×C4×C13—41no—
141C2×C4×C13—42no—
142C2×C4×C13—81no—
143C2×C4×C13—81no—
144C2×C4×C13C2×C22⋊C411yescharacteristic
145C2×C4×C13C2×C4⋊C411yescharacteristic
146C2×C4×C13#11711yescharacteristic
147C2×C4×C13#12111yescharacteristic
148C2×C4×C13C22⋊Q811yescharacteristic
149C2×C4×C13C22⋊Q811yescharacteristic
150C2×C4×C13C2×SD1611yescharacteristic
151C2×C4×C13C2×SD1611yescharacteristic
152C2×C4×C13#13511yescharacteristic
153C2×C4×C13#13511yescharacteristic
154C22⋊D13—22no—
155C22⋊D13—22no—
156C2×Dic13—21no—
157C2×Dic13—21no—
158C2×Dic13—21no—
159C2×Dic13—42no—
160C2×Dic13—81no—
161C2×Dic13—81no—
162D52—21no—
163D52#10612yescomplemented
164C4×D13—22no—
165C4×D13—22no—
166C4×D13—42no—
167C4×D13—41no—
168C4×D13—41no—
169Dic26—21no—
170Dic26#10612yescomplemented
171C8×C13—41no—
172C8×C13—41no—
173C8×C13—81no—
174#1055—21no—
175#1055—21no—
176#1055—21no—
177#1055—81no—
178#1055#10412yescomplemented
179C4×#41—131no—
180C8×Q8—131no—
181C8×Q8—131no—
182C8×D4—131no—
183C8×D4—131no—
184C8×D4—261no—
185C8×D4—261no—
186#431—261no—
187#431C2×D1311yescharacteristic
188C2×#106—261no—
189#423—131no—
190#423C2×D1311yescharacteristic
191C2×#104—261no—
192C2×#104—261no—
193C2×C4×C8—131no—
194C2×C4×C8—261no—
195C4×C4⋊C4—131no—
196C4×C4⋊C4C2×D1311yescharacteristic
197#340—261no—
198#339—261no—
199#339—261no—
200#334—261no—
201#334—261no—
202C22×C13—21no—
203C22×C13—21no—
204C22×C13#38011yescharacteristic
205C22×C13#46511yescharacteristic
206C22×C13#46511yescharacteristic
207C2×D13—22no—
208C2×D13—41no—
209C2×D13—41no—
210C4×C13—21no—
211C4×C13—21no—
212C4×C13—21no—
213C4×C13—82no—
214C4×C13C2×#10411yescharacteristic
215C4×C13#42111yescharacteristic
216C4×C13C2×#10611yescharacteristic
217C4×C13#42711yescharacteristic
218C4×C13#46511yescharacteristic
219C4×C13#46511yescharacteristic
220Dic13—22no—
221Dic13—41no—
222Dic13—41no—
223Dic13—82no—
224C2×#41—131no—
225C2×M16—21no—
226C2×M16—261no—
227C22×C8—131no—
228C22×C8—131no—
229C22×C8—261no—
230C22×C8—261no—
231C4×Q8—131no—
232C4×Q8—131no—
233C4×D4—131no—
234C4×D4—131no—
235C4×D4—261no—
236C4×D4—261no—
237#117—131no—
238#117—261no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—261no—
241C2×C42—21no—
242C2×C42—261no—
243C2×C42—261no—
244C2×C42C22×D1311yescharacteristic
245#106—264no—
246C4⋊C8—21no—
247C4⋊C8—21no—
248C4⋊C8—261no—
249C4⋊C8—261no—
250C4⋊C8—261no—
251C4⋊C8—261no—
252C4⋊C8C4×D1311yescharacteristic
253C4⋊C8C4×D1311yescharacteristic
254#104—522no—
255#104—522no—
256C22⋊C8—21no—
257C22⋊C8—261no—
258C22⋊C8—261no—
259C4×C8—21no—
260C4×C8—131no—
261C4×C8—131no—
262C4×C8—131no—
263C4×C8—131no—
264C4×C8—261no—
265C4×C8—261no—
266#95—21no—
267#95—261no—
268C2×C13—21no—
269C2×C13—21no—
270C2×C13#180611yescharacteristic
271C2×C13#180711yescharacteristic
272C2×C13#181411yescharacteristic
273D13—42no—
274#41—132no—
275#41—132no—
276#41—261no—
277#41—261no—
278C2×Q8—131no—
279C2×D4—131no—
280C2×D4—261no—
281C22×C4—41no—
282C22×C4—261no—
283C22×C4—261no—
284C22×C4—261no—
285C22×C4—521no—
286C22×C4#612711yescharacteristic
287C22×C4D4×D1311yescharacteristic
288C22×C4D4×D1311yescharacteristic
289M16—41no—
290M16—41no—
291M16—521no—
292M16—521no—
293C2×C8—21no—
294C2×C8—21no—
295C2×C8—41no—
296C2×C8—131no—
297C2×C8—131no—
298C2×C8—131no—
299C2×C8—131no—
300C2×C8—262no—
301C2×C8—522no—
302C2×C8—522no—
303C2×C8—521no—
304C2×C8—521no—
305C4⋊C4—22no—
306C4⋊C4—41no—
307C4⋊C4—131no—
308C4⋊C4—131no—
309C4⋊C4—262no—
310C4⋊C4—261no—
311C4⋊C4—261no—
312C4⋊C4—521no—
313C22⋊C4—261no—
314C22⋊C4—261no—
315C22⋊C4—261no—
316C42—41no—
317C42—41no—
318C42—261no—
319C42—261no—
320C42—261no—
321C42—521no—
322C42—521no—
323C42C2×C4×D1311yescharacteristic
324C42#612711yescharacteristic
325C42D4×D1311yescharacteristic
326C42Q8×D1311yescharacteristic
327C13#866611yescharacteristic, complemented, Sylow
328C23—261no—
329C23#8813811yescharacteristic
330Q8—132no—
331Q8—261no—
332D4—132no—
333D4—262no—
334D4—262no—
335D4—261no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—41no—
339C2×C4—42no—
340C2×C4—81no—
341C2×C4—81no—
342C2×C4—261no—
343C2×C4—262no—
344C2×C4—262no—
345C2×C4—261no—
346C2×C4—261no—
347C2×C4—522no—
348C2×C4—521no—
349C2×C4—521no—
350C2×C4—522no—
351C2×C4—1041no—
352C2×C4—1041no—
353C2×C4#8812611yescharacteristic
354C2×C4C22⋊C4×D1311yescharacteristic
355C2×C4#8813811yescharacteristic
356C2×C4C4⋊C4×D1311yescharacteristic
357C2×C4#8815011yescharacteristic
358C2×C4#8815011yescharacteristic
359C2×C4#8816611yescharacteristic
360C2×C4SD16×D1311yescharacteristic
361C2×C4SD16×D1311yescharacteristic
362C2×C4#8817311yescharacteristic
363C8—41no—
364C8—41no—
365C8—81no—
366C8—132no—
367C8—261no—
368C8—261no—
369C8—261no—
370C8—1041no—
371C22—21no—
372C22—21no—
373C22—262no—
374C22—521no—
375C22—521no—
376C22#1171832811yescharacteristic
377C22#1171843911yescharacteristic
378C22#1171846811yescharacteristic
379C4—21no—
380C4—21no—
381C4—21no—
382C4—82no—
383C4—262no—
384C4—521no—
385C4—521no—
386C4—1042no—
387C4#1171843911yescharacteristic
388C4#1171846811yescharacteristic
389C4D13×#10411yescharacteristic
390C4#1171848211yescharacteristic
391C4D13×#10611yescharacteristic
392C4#1171854111yescharacteristic
393C2—21no—
394C2—21no—
395C2—522no—
396C2#1311485511yescharacteristic
397C2#1311486011yescharacteristic
398C2#1311488911yescharacteristic
subgroupG/H
centerC2×C4#88138
commutatorC42×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1303C2
socleC22×C13#380
prime radicalC2×#6127D4
cosocleC2×C42×C13C23
hypercenter#1303D13
hypocenterC13#8666
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1303

Complements

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

NH ≅ G/Ntype
4. C4×#88048C2semidirect
5. #13113591C2semidirect
6. #13112738C2semidirect
7. C13×#1303C2semidirect
18. #11718495C4semidirect
19. #11718495C4semidirect
20. #11718491C4semidirect
21. #11718491C4semidirect
135. #1303D13semidirect
163. D52#106semidirect
170. Dic26#106semidirect
178. #1055#104semidirect
327. C13#8666semidirect

Maximal subgroups

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

subgroupindex
#131237922
#131148572
#131148532
C4×#880482
#131135912
#131127382
C13×#13032
#866613