Finite Group Databasebeta

← #16019072

Subgroups — #16019072

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#13125350C211yesmaximal, characteristic, complemented
2#13117112C212yesmaximal, complemented
3#13117067C212yesmaximal, complemented
4#13117041C212yesmaximal, complemented
5#13117024C212yesmaximal
6#13116988C211yesmaximal, characteristic, complemented
7#13116983C211yesmaximal, characteristic, complemented
8#13116978C211yesmaximal, characteristic, complemented
9#13116973C211yesmaximal, characteristic, complemented
10#13116635C211yesmaximal, characteristic, complemented
11C13×#3168C211yesmaximal, characteristic
12C13×#529—21no—
13#11719175—21no—
14C13×#499C2211yescharacteristic
15C13×#495C2211yescharacteristic
16C13×#488—21no—
17C13×#467C2211yescharacteristic
18C13×#466C2211yescharacteristic
19C13×#465—21no—
20C4×C13×Q16C2211yescharacteristic
21C4×C13×SD16—21no—
22C4×C13×D8C2211yescharacteristic
23C2×C4×C8×C13C2211yescharacteristic
24#11718767—21no—
25#11718767C2212yes—
26#11718344—21no—
27#11718344C2212yes—
28#11718343C2211yescharacteristic
29#11718343C2211yescharacteristic
30#11718341—21no—
31#11718156C2212yes—
32#11718156C2212yes—
33#11718154C2212yes—
34#11718154C2212yes—
35C22⋊#6090C2212yes—
36#11718082C2212yes—
37#11718082C2212yes—
38#11718081C2212yes—
39#11718081C2212yes—
40C4⋊#6090C2211yescharacteristic
41C4⋊#6090C2211yescharacteristic
42C4×#6090C2212yes—
43C2×C13×Q16C2311yescharacteristic
44C2×C13×SD16—21no—
45C2×C13×D8C2311yescharacteristic
46C22×C8×C13D411yescharacteristic
47C22×C8×C13C2311yescharacteristic
48C13×#126—41no—
49C13×#125—21no—
50C13×#124—21no—
51C13×#123—41no—
52C13×C22⋊Q8—21no—
53C13×#121—21no—
54C4×Q8×C13—21no—
55C4×D4×C13—21no—
56C4×D4×C13—41no—
57C13×#117—41no—
58C2×C42×C13D411yescharacteristic
59#88180—22no—
60#88178—41no—
61#88178—41no—
62#88124—22no—
63#88123—21no—
64#88123—21no—
65C4×Dic26—41no—
66C4×Dic26—41no—
67C13×#107C2311yescharacteristic
68C13×#107C2311yescharacteristic
69C13×#106—21no—
70C13×#103—21no—
71C13×#103—21no—
72C13×#102—21no—
73C13×#102—21no—
74C4×C8×C13D411yescharacteristic
75C4×C8×C13D411yescharacteristic
76C4×C8×C13C2311yescharacteristic
77C4×C8×C13C2311yescharacteristic
78#88058—21no—
79#88058—21no—
80#88058C2312yes—
81#88058C2312yes—
82#88057—22no—
83#88057—22no—
84C2×#6090C2312yes—
85C2×#6090C2312yes—
86#33799—131nomaximal, Sylow
87C2×Q8×C13—21no—
88C2×D4×C13—21no—
89C2×D4×C13—41no—
90C22×C4×C13—41no—
91C22×C4×C13D811yescharacteristic
92C22×C4×C13D811yescharacteristic
93C22×C4×C13C2×D411yescharacteristic
94C2×Dic26—41no—
95C2×Dic26—41no—
96C13×Q16—21no—
97C13×Q16—21no—
98C13×SD16—42no—
99C13×D8—21no—
100C13×D8—21no—
101C2×C8×C13—22no—
102C2×C8×C13—21no—
103C2×C8×C13—21no—
104C2×C8×C13C2×D411yescharacteristic
105C2×C8×C13C2×D411yescharacteristic
106C2×C8×C13C2×D411yescharacteristic
107C2×C8×C13C2411yescharacteristic
108C13×C4⋊C4—21no—
109C13×C4⋊C4—21no—
110C13×C4⋊C4—41no—
111C13×C4⋊C4—41no—
112C13×C4⋊C4—41no—
113C13×C4⋊C4—41no—
114C13×C22⋊C4—41no—
115C13×C22⋊C4—41no—
116C13×C22⋊C4—41no—
117C13×C22⋊C4—41no—
118C13×C22⋊C4—41no—
119C42×C13—41no—
120C42×C13D811yescharacteristic
121C42×C13D811yescharacteristic
122C42×C13C2×D411yescharacteristic
123C42×C13C2×D411yescharacteristic
124C22⋊Dic13—42no—
125C4⋊Dic13—22no—
126C4⋊Dic13—22no—
127C4⋊Dic13—41no—
128C4⋊Dic13—41no—
129#6101—42no—
130#6101—42no—
131C4×Dic13—42no—
132#6090—22no—
133#6090—22no—
134#3168D1311yescharacteristic
135#3160—131no—
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×C13—41no—
146C23×C13C2×D811yescharacteristic
147Q8×C13—41no—
148Q8×C13—41no—
149D4×C13—41no—
150D4×C13—41no—
151D4×C13—82no—
152C2×C4×C13—21no—
153C2×C4×C13—21no—
154C2×C4×C13—22no—
155C2×C4×C13—41no—
156C2×C4×C13—41no—
157C2×C4×C13—41no—
158C2×C4×C13—41no—
159C2×C4×C13—82no—
160C2×C4×C13C2×D811yescharacteristic
161C2×C4×C13C2×D811yescharacteristic
162C2×C4×C13C2×D811yescharacteristic
163C2×C4×C13C2×D811yescharacteristic
164C2×C4×C13C2×D811yescharacteristic
165C2×C4×C13C22×D411yescharacteristic
166C2×Dic13—42no—
167C2×Dic13—42no—
168Dic26—82no—
169Dic26—82no—
170C8×C13—21no—
171C8×C13—21no—
172C8×C13#13712yes—
173C8×C132−1+411yescharacteristic
174C8×C132−1+411yescharacteristic
175#533—261no—
176#529—21no—
177#500—131no—
178#500—131no—
179#499—132no—
180#499—261no—
181#499C2×D1311yescharacteristic
182#498—261no—
183#495C2×D1311yescharacteristic
184#488—21no—
185#467C2×D1311yescharacteristic
186#466C2×D1311yescharacteristic
187#465—21no—
188C4×Q16C2×D1311yescharacteristic
189C4×SD16—21no—
190C4×D8C2×D1311yescharacteristic
191#427—132no—
192#427—261no—
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×C13—81no—
210C22×C13—81no—
211C22×C13—81no—
212C22×C13C22×D811yescharacteristic
213C4×C13—21no—
214C4×C13—21no—
215C4×C13—21no—
216C4×C13—21no—
217C4×C13—81no—
218C4×C13—81no—
219C4×C13—81no—
220C4×C13#50812yes—
221C4×C13#53611yescharacteristic
222C4×C13C2×#13711yescharacteristic
223Dic13—82no—
224Dic13—82no—
225C2×Q16C22×D1311yescharacteristic
226C2×SD16—21no—
227C2×D8C22×D1311yescharacteristic
228C22×C8C22⋊D1311yescharacteristic
229C22×C8C22×D1311yescharacteristic
230C4⋊Q8—261no—
231C4⋊Q8—261no—
232#126—41no—
233#125—21no—
234#125—262no—
235#124—21no—
236#123—41no—
237C22⋊Q8—21no—
238C22⋊Q8—521no—
239C22⋊Q8—521no—
240#121—21no—
241C4×Q8—21no—
242C4×Q8—521no—
243C4×Q8—521no—
244C4×D4—21no—
245C4×D4—41no—
246#117—41no—
247#117—262no—
248C2×C42C22⋊D1311yescharacteristic
249C2×C16—132no—
250C2×C16—132no—
251#107—132no—
252#107—132no—
253#107—261no—
254#107—261no—
255#107C22×D1311yescharacteristic
256#107C22×D1311yescharacteristic
257#106—21no—
258#106—262no—
259#106—262no—
260#103—21no—
261#103—21no—
262#102—21no—
263#102—21no—
264C4×C8C22⋊D1311yescharacteristic
265C4×C8C22⋊D1311yescharacteristic
266C4×C8C22×D1311yescharacteristic
267C4×C8C22×D1311yescharacteristic
268C2×C13—41no—
269C2×C13—161no—
270C2×C13#322611yescharacteristic
271C2×C13C2×#50811yescharacteristic
272C2×C13#341411yescharacteristic
273C2×Q8—21no—
274C2×Q8—521no—
275C2×Q8—521no—
276C2×D4—21no—
277C2×D4—41no—
278C22×C4—41no—
279C22×C4#610411yescharacteristic
280C22×C4#610411yescharacteristic
281C22×C4C2×C22⋊D1311yescharacteristic
282Q16—21no—
283Q16—21no—
284SD16—42no—
285D8—21no—
286D8—21no—
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—21no—
295C4⋊C4—21no—
296C4⋊C4—41no—
297C4⋊C4—41no—
298C4⋊C4—41no—
299C4⋊C4—41no—
300C4⋊C4—262no—
301C4⋊C4—262no—
302C4⋊C4—522no—
303C4⋊C4—522no—
304C4⋊C4—521no—
305C4⋊C4—521no—
306C22⋊C4—41no—
307C22⋊C4—41no—
308C22⋊C4—41no—
309C22⋊C4—41no—
310C22⋊C4—41no—
311C22⋊C4—522no—
312C42—41no—
313C42—522no—
314C42#610411yescharacteristic
315C42#610411yescharacteristic
316C42C2×C22⋊D1311yescharacteristic
317C42C2×C22⋊D1311yescharacteristic
318C16—262no—
319C16—262no—
320C13#3379911yescharacteristic, complemented, Sylow
321C23—41no—
322C23C2×#610411yescharacteristic
323Q8—41no—
324Q8—41no—
325Q8—1042no—
326Q8—1042no—
327D4—41no—
328D4—41no—
329D4—82no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—22no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—82no—
338C2×C4—522no—
339C2×C4—522no—
340C2×C4C2×#610411yescharacteristic
341C2×C4C2×#610411yescharacteristic
342C2×C4C2×#610411yescharacteristic
343C2×C4C2×#610411yescharacteristic
344C2×C4C2×#610411yescharacteristic
345C2×C4C22×C22⋊D1311yescharacteristic
346C8—21no—
347C8—21no—
348C8#8820512yes—
349C8#8825711yescharacteristic
350C8#8825711yescharacteristic
351C22—21no—
352C22—21no—
353C22—21no—
354C22—81no—
355C22—81no—
356C22—81no—
357C22C22×#610411yescharacteristic
358C4—21no—
359C4—21no—
360C4—21no—
361C4—21no—
362C4—81no—
363C4—81no—
364C4—81no—
365C4—1042no—
366C4—1042no—
367C4#1171885512yes—
368C4C2×#8820511yescharacteristic
369C4#1171953011yescharacteristic
370C2—41no—
371C2—161no—
372C2#1312595411yescharacteristic
373C2C2×#1171885511yescharacteristic
374C2#1312797011yescharacteristic
subgroupG/H
centerC22C22×#6104
commutator, cosocleC2×C8×C13C24
FrattiniC2×C8C23×D13
FittingC13×#3168C2
socleC22×C13C22×D8
prime radicalC13×#466C22
hypercenter#3168D13
hypocenterC13#33799
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×C8 ◁ #3168

Complements

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

NH ≅ G/Ntype
1. #13125350C2semidirect
2. #13117112C2semidirect
3. #13117067C2semidirect
4. #13117041C2semidirect
6. #13116988C2semidirect
7. #13116983C2semidirect
8. #13116978C2semidirect
9. #13116973C2semidirect
10. #13116635C2semidirect
320. C13#33799semidirect

Maximal subgroups

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

subgroupindex
#131253502
#131171122
#131170672
#131170412
#131170242
#131169882
#131169832
#131169782
#131169732
#131166352
C13×#31682
#3379913