Finite Group Databasebeta

← #16019076

Subgroups — #16019076

Order 3328.

466 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13125406C211yesmaximal, characteristic
2#13117112C212yesmaximal, complemented
3#13117070C212yesmaximal, complemented
4#13117044C212yesmaximal, complemented
5#13117027C212yesmaximal
6#13116985C211yesmaximal, characteristic, complemented
7#13116980C211yesmaximal, characteristic, complemented
8#13116975C211yesmaximal, characteristic, complemented
9#13116970C211yesmaximal, characteristic, complemented
10#13116635C211yesmaximal, characteristic, complemented
11C13×#3160C211yesmaximal, characteristic, complemented
12C13×#533—21no—
13#11719184—21no—
14C13×#500C2211yescharacteristic
15C13×#500C2211yescharacteristic
16C13×#499—21no—
17C13×#499C2212yes—
18C13×#498—21no—
19C13×#427—21no—
20C13×#427C2212yes—
21C2×C4×C8×C13C2211yescharacteristic
22#11718777C2211yescharacteristic
23#11718776C2211yescharacteristic
24#11718775—21no—
25C4×Dic52C2211yescharacteristic
26#11718358—21no—
27#11718357C2211yescharacteristic
28C4×D104C2211yescharacteristic
29C4×#6095—21no—
30#11718344C2211yescharacteristic
31C22⋊#6090C2212yes—
32#11718084C2212yes—
33#11718084C2212yes—
34#11718083C2212yes—
35#11718083C2212yes—
36#11718082C2212yes—
37#11718082C2212yes—
38#11718081C2212yes—
39#11718081C2212yes—
40C4⋊#6090C2211yescharacteristic
41C4⋊#6090C2211yescharacteristic
42C4×#6090C2212yes—
43C22×C8×C13D411yescharacteristic
44C22×C8×C13C2311yescharacteristic
45C13×C4⋊Q8—21no—
46C13×C4⋊Q8—21no—
47C13×#125—22no—
48C13×C22⋊Q8—41no—
49C13×C22⋊Q8—41no—
50C4×Q8×C13—41no—
51C4×Q8×C13—41no—
52C13×#117—22no—
53C2×C42×C13D411yescharacteristic
54#88184—21no—
55#88183—41no—
56C4×C22⋊D13—41no—
57#88178—21no—
58C2×Dic52C2311yescharacteristic
59C2×D104C2311yescharacteristic
60C2×#6095—21no—
61#88130—41no—
62#88129—21no—
63C4×D52—21no—
64#88126—41no—
65#88124—21no—
66C4×Dic26—21no—
67C13×#107—21no—
68C13×#107—21no—
69C13×#107C2312yes—
70C13×#107C2312yes—
71C13×#106—22no—
72C13×#106—22no—
73C4×C8×C13D411yescharacteristic
74C4×C8×C13D411yescharacteristic
75C4×C8×C13C2311yescharacteristic
76C4×C8×C13C2311yescharacteristic
77#88061—21no—
78#88061—21no—
79#88058C2311yescharacteristic
80#88058C2311yescharacteristic
81#88057—21no—
82#88056—21no—
83#88056—21no—
84C2×#6090C2312yes—
85C2×#6090C2312yes—
86#33799—131nomaximal, Sylow
87C2×Q8×C13—41no—
88C2×Q8×C13—41no—
89C22×C4×C13D811yescharacteristic
90C22×C4×C13D811yescharacteristic
91C22×C4×C13C2×D411yescharacteristic
92C2×C22⋊D13—41no—
93C2×D52—21no—
94C2×C4×D13—41no—
95C2×Dic26—21no—
96C2×C8×C13—22no—
97C2×C8×C13—21no—
98C2×C8×C13—21no—
99C2×C8×C13C2×D411yescharacteristic
100C2×C8×C13C2×D411yescharacteristic
101C2×C8×C13C2×D411yescharacteristic
102C2×C8×C13C2411yescharacteristic
103C13×C4⋊C4—22no—
104C13×C4⋊C4—22no—
105C13×C4⋊C4—42no—
106C13×C4⋊C4—42no—
107C13×C4⋊C4—41no—
108C13×C4⋊C4—41no—
109C13×C22⋊C4—42no—
110C42×C13—42no—
111C42×C13D811yescharacteristic
112C42×C13D811yescharacteristic
113C42×C13C2×D411yescharacteristic
114C42×C13C2×D411yescharacteristic
115C22⋊Dic13—41no—
116#6103—41no—
117#6103—41no—
118#6103—41no—
119#6103—41no—
120C4⋊Dic13—21no—
121C4⋊Dic13—21no—
122#6101—41no—
123#6101—41no—
124#6101—41no—
125#6101—41no—
126C4×Dic13—41no—
127Dic52—21no—
128Dic52—21no—
129D104—21no—
130D104—21no—
131#6095—42no—
132#6090—22no—
133#6090—22no—
134#3168—131no—
135#3160D1311yescharacteristic, complemented
136#2253—132no—
137#2242—132no—
138#2237—132no—
139#2234—132no—
140#2227—131no—
141#2226—131no—
142#2225—131no—
143#2224—131no—
144#2162—131no—
145C23×C13C2×D811yescharacteristic
146C22×D13—41no—
147Q8×C13—82no—
148Q8×C13—82no—
149C2×C4×C13—21no—
150C2×C4×C13—21no—
151C2×C4×C13—22no—
152C2×C4×C13—41no—
153C2×C4×C13—42no—
154C2×C4×C13—42no—
155C2×C4×C13C2×D811yescharacteristic
156C2×C4×C13C2×D811yescharacteristic
157C2×C4×C13C2×D811yescharacteristic
158C2×C4×C13C2×D811yescharacteristic
159C2×C4×C13C2×D811yescharacteristic
160C2×C4×C13C22×D411yescharacteristic
161C22⋊D13—82no—
162C2×Dic13—41no—
163C2×Dic13—41no—
164C2×Dic13—41no—
165D52—41no—
166D52—41no—
167C4×D13—82no—
168Dic26—41no—
169Dic26—41no—
170C8×C13—21no—
171C8×C13—21no—
172C8×C13#13712yes—
173C8×C132−1+411yescharacteristic
174C8×C132−1+411yescharacteristic
175#533—21no—
176#529—261no—
177#500C2×D1311yescharacteristic
178#500C2×D1311yescharacteristic
179#499—21no—
180#499—131no—
181#499C2×D1312yes—
182#498—21no—
183#495—131no—
184#488—261no—
185#467—131no—
186#466—131no—
187#465—261no—
188C4×Q16—131no—
189C4×SD16—261no—
190C4×D8—131no—
191#427—21no—
192#427C2×D1312yes—
193C2×C4×C8C2×D1311yescharacteristic
194#367—132no—
195#367—132no—
196#366—132no—
197#366—132no—
198C4⋊C16—131no—
199C4⋊C16—131no—
200#358—132no—
201#358—132no—
202#357—132no—
203#357—132no—
204C22⋊C16—132no—
205C4×C16—132no—
206C22×C13—21no—
207C22×C13—21no—
208C22×C13—21no—
209C22×C13C22×D811yescharacteristic
210C2×D13—81no—
211C2×D13—81no—
212C2×D13—81no—
213C4×C13—21no—
214C4×C13—21no—
215C4×C13—21no—
216C4×C13—21no—
217C4×C13—82no—
218C4×C13—82no—
219C4×C13#50812yes—
220C4×C13#53611yescharacteristic
221C4×C13C2×#13711yescharacteristic
222Dic13—81no—
223Dic13—81no—
224Dic13—81no—
225C2×Q16—131no—
226C2×SD16—261no—
227C2×D8—131no—
228C22×C8C22⋊D1311yescharacteristic
229C22×C8C22×D1311yescharacteristic
230C4⋊Q8—21no—
231C4⋊Q8—21no—
232#126—521no—
233#125—22no—
234#125—261no—
235#124—261no—
236#123—521no—
237C22⋊Q8—41no—
238C22⋊Q8—41no—
239C22⋊Q8—261no—
240#121—261no—
241C4×Q8—41no—
242C4×Q8—41no—
243C4×Q8—261no—
244C4×D4—261no—
245C4×D4—521no—
246#117—22no—
247#117—521no—
248C2×C42C22⋊D1311yescharacteristic
249C2×C16—132no—
250C2×C16—132no—
251#107—21no—
252#107—21no—
253#107—131no—
254#107—131no—
255#107C22×D1312yes—
256#107C22×D1312yes—
257#106—22no—
258#106—22no—
259#106—261no—
260#103—261no—
261#103—261no—
262#102—261no—
263#102—261no—
264C4×C8C22⋊D1311yescharacteristic
265C4×C8C22⋊D1311yescharacteristic
266C4×C8C22×D1311yescharacteristic
267C4×C8C22×D1311yescharacteristic
268C2×C13—41no—
269C2×C13#322611yescharacteristic
270C2×C13C2×#50811yescharacteristic
271C2×C13#341411yescharacteristic
272D13—161no—
273C2×Q8—41no—
274C2×Q8—41no—
275C2×Q8—261no—
276C2×D4—261no—
277C2×D4—521no—
278C22×C4—521no—
279C22×C4#610411yescharacteristic
280C22×C4#610411yescharacteristic
281C22×C4C2×C22⋊D1311yescharacteristic
282Q16—261no—
283Q16—261no—
284SD16—522no—
285D8—261no—
286D8—261no—
287C2×C8—22no—
288C2×C8—21no—
289C2×C8—21no—
290C2×C8C2×C22⋊D1311yescharacteristic
291C2×C8C2×C22⋊D1311yescharacteristic
292C2×C8C2×C22⋊D1311yescharacteristic
293C2×C8C23×D1311yescharacteristic
294C4⋊C4—22no—
295C4⋊C4—22no—
296C4⋊C4—42no—
297C4⋊C4—42no—
298C4⋊C4—41no—
299C4⋊C4—41no—
300C4⋊C4—261no—
301C4⋊C4—261no—
302C4⋊C4—521no—
303C4⋊C4—521no—
304C4⋊C4—521no—
305C4⋊C4—521no—
306C22⋊C4—42no—
307C22⋊C4—521no—
308C22⋊C4—521no—
309C22⋊C4—521no—
310C22⋊C4—521no—
311C22⋊C4—521no—
312C42—42no—
313C42—521no—
314C42#610411yescharacteristic
315C42#610411yescharacteristic
316C42C2×C22⋊D1311yescharacteristic
317C42C2×C22⋊D1311yescharacteristic
318C16—262no—
319C16—262no—
320C13#3379911yescharacteristic, complemented, Sylow
321C23—521no—
322C23C2×#610411yescharacteristic
323Q8—82no—
324Q8—82no—
325Q8—521no—
326Q8—521no—
327D4—521no—
328D4—521no—
329D4—1042no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—22no—
333C2×C4—41no—
334C2×C4—42no—
335C2×C4—42no—
336C2×C4—521no—
337C2×C4—521no—
338C2×C4—521no—
339C2×C4—1042no—
340C2×C4C2×#610411yescharacteristic
341C2×C4C2×#610411yescharacteristic
342C2×C4C2×#610411yescharacteristic
343C2×C4C2×#610411yescharacteristic
344C2×C4C2×#610411yescharacteristic
345C2×C4C22×C22⋊D1311yescharacteristic
346C8—21no—
347C8—21no—
348C8#8819612yes—
349C8#8825411yescharacteristic
350C8#8825411yescharacteristic
351C22—21no—
352C22—21no—
353C22—21no—
354C22—1041no—
355C22—1041no—
356C22—1041no—
357C22C22×#610411yescharacteristic
358C4—21no—
359C4—21no—
360C4—21no—
361C4—21no—
362C4—82no—
363C4—82no—
364C4—1041no—
365C4—1041no—
366C4—1041no—
367C4#1171885512yes—
368C4C2×#8819611yescharacteristic
369C4#1171952111yescharacteristic
370C2—41no—
371C2—2081no—
372C2#1312595711yescharacteristic
373C2C2×#1171885511yescharacteristic
374C2#1312797011yescharacteristic
subgroupG/H
centerC22C22×#6104
commutator, cosocleC2×C8×C13C24
FrattiniC2×C8C23×D13
FittingC13×#3160C2
socleC22×C13C22×D8
prime radical#11718776C22
hypercenter#3160D13
hypocenterC13#33799
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×C8 ◁ #3160

Complements

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

NH ≅ G/Ntype
2. #13117112C2semidirect
3. #13117070C2semidirect
4. #13117044C2semidirect
6. #13116985C2semidirect
7. #13116980C2semidirect
8. #13116975C2semidirect
9. #13116970C2semidirect
10. #13116635C2semidirect
11. C13×#3160C2semidirect
135. #3160D13semidirect
320. C13#33799semidirect

Maximal subgroups

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

subgroupindex
#131254062
#131171122
#131170702
#131170442
#131170272
#131169852
#131169802
#131169752
#131169702
#131166352
C13×#31602
#3379913