Finite Group Databasebeta

← #16019133

Subgroups — #16019133

Order 3328.

462 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13125350C211yesmaximal, characteristic, complemented
2#13117123C211yesmaximal, characteristic, complemented
3#13117123C211yesmaximal, characteristic, complemented
4#13117072C211yesmaximal, characteristic, complemented
5#13117072C211yesmaximal, characteristic, complemented
6#13117041C212yesmaximal, complemented
7#13117024C212yesmaximal
8#13117000C212yesmaximal, complemented
9#13116993C212yesmaximal, complemented
10#13116639C211yesmaximal, 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⋊#6090C2212yes—
41#11718053C2211yescharacteristic
42#11718053C2211yescharacteristic
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#33806—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—22no—
97C13×SD16—42no—
98C13×D8—22no—
99C2×C8×C13—22no—
100C2×C8×C13—22no—
101C2×C8×C13C2×D411yescharacteristic
102C2×C8×C13C2×D411yescharacteristic
103C2×C8×C13C2×D411yescharacteristic
104C2×C8×C13C2411yescharacteristic
105C13×C4⋊C4—21no—
106C13×C4⋊C4—21no—
107C13×C4⋊C4—41no—
108C13×C4⋊C4—41no—
109C13×C4⋊C4—41no—
110C13×C4⋊C4—41no—
111C13×C22⋊C4—41no—
112C13×C22⋊C4—41no—
113C13×C22⋊C4—41no—
114C13×C22⋊C4—41no—
115C13×C22⋊C4—41no—
116C42×C13—41no—
117C42×C13D811yescharacteristic
118C42×C13D811yescharacteristic
119C42×C13C2×D411yescharacteristic
120C42×C13C2×D411yescharacteristic
121C22⋊Dic13—42no—
122C4⋊Dic13—22no—
123C4⋊Dic13—22no—
124C4⋊Dic13—41no—
125C4⋊Dic13—41no—
126#6101—42no—
127#6101—42no—
128C4×Dic13—42no—
129#6090—22no—
130#6090—22no—
131#3168D1311yescharacteristic
132#3160—131no—
133#2255—131no—
134#2255—131no—
135#2243—131no—
136#2243—131no—
137#2237—132no—
138#2234—132no—
139#2229—132no—
140#2228—132no—
141#2163—131no—
142C23×C13—41no—
143C23×C13C2×D811yescharacteristic
144Q8×C13—41no—
145Q8×C13—41no—
146D4×C13—41no—
147D4×C13—41no—
148D4×C13—82no—
149C2×C4×C13—21no—
150C2×C4×C13—21no—
151C2×C4×C13—41no—
152C2×C4×C13—41no—
153C2×C4×C13—41no—
154C2×C4×C13—41no—
155C2×C4×C13—41no—
156C2×C4×C13—82no—
157C2×C4×C13C2×D811yescharacteristic
158C2×C4×C13C2×D811yescharacteristic
159C2×C4×C13C2×D811yescharacteristic
160C2×C4×C13C2×D811yescharacteristic
161C2×C4×C13C2×D811yescharacteristic
162C2×C4×C13C22×D411yescharacteristic
163C2×Dic13—42no—
164C2×Dic13—42no—
165Dic26—82no—
166Dic26—82no—
167C8×C13—21no—
168C8×C13—21no—
169C8×C13#13712yes—
170C8×C132−1+412yes—
171#533—261no—
172#529—21no—
173#500—131no—
174#500—131no—
175#499—132no—
176#499—261no—
177#499C2×D1311yescharacteristic
178#498—261no—
179#495C2×D1311yescharacteristic
180#488—21no—
181#467C2×D1311yescharacteristic
182#466C2×D1311yescharacteristic
183#465—21no—
184C4×Q16C2×D1311yescharacteristic
185C4×SD16—21no—
186C4×D8C2×D1311yescharacteristic
187#427—132no—
188#427—261no—
189C2×C4×C8C2×D1311yescharacteristic
190#367—132no—
191#367—132no—
192#366—132no—
193#366—132no—
194C4⋊C16—132no—
195#358—132no—
196#358—132no—
197#357—132no—
198#357—132no—
199C22⋊C16—132no—
200#346—131no—
201#346—131no—
202C22×C13—21no—
203C22×C13—21no—
204C22×C13—21no—
205C22×C13—81no—
206C22×C13—81no—
207C22×C13—81no—
208C22×C13C22×D811yescharacteristic
209C4×C13—21no—
210C4×C13—21no—
211C4×C13—21no—
212C4×C13—21no—
213C4×C13—21no—
214C4×C13—81no—
215C4×C13—81no—
216C4×C13—81no—
217C4×C13#53611yescharacteristic
218C4×C13C2×#13711yescharacteristic
219Dic13—82no—
220Dic13—82no—
221C2×Q16C22×D1311yescharacteristic
222C2×SD16—21no—
223C2×D8C22×D1311yescharacteristic
224C22×C8C22⋊D1311yescharacteristic
225C22×C8C22×D1311yescharacteristic
226C4⋊Q8—261no—
227C4⋊Q8—261no—
228#126—41no—
229#125—21no—
230#125—262no—
231#124—21no—
232#123—41no—
233C22⋊Q8—21no—
234C22⋊Q8—521no—
235C22⋊Q8—521no—
236#121—21no—
237C4×Q8—21no—
238C4×Q8—521no—
239C4×Q8—521no—
240C4×D4—21no—
241C4×D4—41no—
242#117—41no—
243#117—262no—
244C2×C42C22⋊D1311yescharacteristic
245C2×C16—132no—
246C2×C16—132no—
247#107—132no—
248#107—132no—
249#107—261no—
250#107—261no—
251#107C22×D1311yescharacteristic
252#107C22×D1311yescharacteristic
253#106—21no—
254#106—262no—
255#106—262no—
256#103—21no—
257#103—21no—
258#102—21no—
259#102—21no—
260C4×C8C22⋊D1311yescharacteristic
261C4×C8C22⋊D1311yescharacteristic
262C4×C8C22×D1311yescharacteristic
263C4×C8C22×D1311yescharacteristic
264C2×C13—41no—
265C2×C13—161no—
266C2×C13#322611yescharacteristic
267C2×C13#341411yescharacteristic
268C2×C13#341411yescharacteristic
269C2×Q8—21no—
270C2×Q8—521no—
271C2×Q8—521no—
272C2×D4—21no—
273C2×D4—41no—
274C22×C4—41no—
275C22×C4#610411yescharacteristic
276C22×C4#610411yescharacteristic
277C22×C4C2×C22⋊D1311yescharacteristic
278Q16—22no—
279SD16—42no—
280D8—22no—
281C2×C8—22no—
282C2×C8—22no—
283C2×C8C2×C22⋊D1311yescharacteristic
284C2×C8C2×C22⋊D1311yescharacteristic
285C2×C8C2×C22⋊D1311yescharacteristic
286C2×C8C23×D1311yescharacteristic
287C4⋊C4—21no—
288C4⋊C4—21no—
289C4⋊C4—41no—
290C4⋊C4—41no—
291C4⋊C4—41no—
292C4⋊C4—41no—
293C4⋊C4—262no—
294C4⋊C4—262no—
295C4⋊C4—522no—
296C4⋊C4—522no—
297C4⋊C4—521no—
298C4⋊C4—521no—
299C22⋊C4—41no—
300C22⋊C4—41no—
301C22⋊C4—41no—
302C22⋊C4—41no—
303C22⋊C4—41no—
304C22⋊C4—522no—
305C42—41no—
306C42—522no—
307C42#610411yescharacteristic
308C42#610411yescharacteristic
309C42C2×C22⋊D1311yescharacteristic
310C42C2×C22⋊D1311yescharacteristic
311C16—262no—
312C16—262no—
313C13#3380611yescharacteristic, complemented, Sylow
314C23—41no—
315C23C2×#610411yescharacteristic
316Q8—41no—
317Q8—41no—
318Q8—1042no—
319Q8—1042no—
320D4—41no—
321D4—41no—
322D4—82no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—82no—
331C2×C4—522no—
332C2×C4—522no—
333C2×C4C2×#610411yescharacteristic
334C2×C4C2×#610411yescharacteristic
335C2×C4C2×#610411yescharacteristic
336C2×C4C2×#610411yescharacteristic
337C2×C4C2×#610411yescharacteristic
338C2×C4C22×C22⋊D1311yescharacteristic
339C8—21no—
340C8—21no—
341C8#8820512yes—
342C8#8825712yes—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—81no—
347C22—81no—
348C22—81no—
349C22C22×#610411yescharacteristic
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—21no—
355C4—81no—
356C4—81no—
357C4—81no—
358C4—1042no—
359C4—1042no—
360C4C2×#8820511yescharacteristic
361C4#1171953011yescharacteristic
362C2—41no—
363C2—161no—
364C2#1312595411yescharacteristic
365C2#1312797011yescharacteristic
366C2#1312797011yescharacteristic
subgroupG/H
centerC22C22×#6104
commutator, cosocleC2×C8×C13C24
FrattiniC2×C8C23×D13
FittingC13×#3168C2
socleC22×C13C22×D8
prime radicalC13×#466C22
hypercenter#3168D13
hypocenterC13#33806
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. #13117123C2semidirect
3. #13117123C2semidirect
4. #13117072C2semidirect
5. #13117072C2semidirect
6. #13117041C2semidirect
8. #13117000C2semidirect
9. #13116993C2semidirect
10. #13116639C2semidirect
313. C13#33806semidirect

Maximal subgroups

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

subgroupindex
#131253502
#131171232
#131170722
#131170412
#131170242
#131170002
#131169932
#131166392
C13×#31682
#3380613