Finite Group Databasebeta

← #16019137

Subgroups — #16019137

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#13125406C211yesmaximal, characteristic
2#13117119C211yesmaximal, characteristic, complemented
3#13117119C211yesmaximal, characteristic, complemented
4#13117075C211yesmaximal, characteristic, complemented
5#13117075C211yesmaximal, characteristic, complemented
6#13117044C212yesmaximal, complemented
7#13117027C212yesmaximal
8#13116997C212yesmaximal, complemented
9#13116990C212yesmaximal, complemented
10#13116639C211yesmaximal, 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⋊#6090C2212yes—
41#11718053C2211yescharacteristic
42#11718053C2211yescharacteristic
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#33806—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—22no—
98C2×C8×C13C2×D411yescharacteristic
99C2×C8×C13C2×D411yescharacteristic
100C2×C8×C13C2×D411yescharacteristic
101C2×C8×C13C2411yescharacteristic
102C13×C4⋊C4—22no—
103C13×C4⋊C4—22no—
104C13×C4⋊C4—42no—
105C13×C4⋊C4—42no—
106C13×C4⋊C4—41no—
107C13×C4⋊C4—41no—
108C13×C22⋊C4—42no—
109C42×C13—42no—
110C42×C13D811yescharacteristic
111C42×C13D811yescharacteristic
112C42×C13C2×D411yescharacteristic
113C42×C13C2×D411yescharacteristic
114C22⋊Dic13—41no—
115#6103—41no—
116#6103—41no—
117#6103—41no—
118#6103—41no—
119C4⋊Dic13—21no—
120C4⋊Dic13—21no—
121#6101—41no—
122#6101—41no—
123#6101—41no—
124#6101—41no—
125C4×Dic13—41no—
126Dic52—22no—
127D104—22no—
128#6095—42no—
129#6090—22no—
130#6090—22no—
131#3168—131no—
132#3160D1311yescharacteristic, complemented
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×C13C2×D811yescharacteristic
143C22×D13—41no—
144Q8×C13—82no—
145Q8×C13—82no—
146C2×C4×C13—21no—
147C2×C4×C13—21no—
148C2×C4×C13—41no—
149C2×C4×C13—41no—
150C2×C4×C13—42no—
151C2×C4×C13—42no—
152C2×C4×C13C2×D811yescharacteristic
153C2×C4×C13C2×D811yescharacteristic
154C2×C4×C13C2×D811yescharacteristic
155C2×C4×C13C2×D811yescharacteristic
156C2×C4×C13C2×D811yescharacteristic
157C2×C4×C13C22×D411yescharacteristic
158C22⋊D13—82no—
159C2×Dic13—41no—
160C2×Dic13—41no—
161C2×Dic13—41no—
162D52—41no—
163D52—41no—
164C4×D13—82no—
165Dic26—41no—
166Dic26—41no—
167C8×C13—21no—
168C8×C13—21no—
169C8×C13#13712yes—
170C8×C132−1+412yes—
171#533—21no—
172#529—261no—
173#500C2×D1311yescharacteristic
174#500C2×D1311yescharacteristic
175#499—21no—
176#499—131no—
177#499C2×D1312yes—
178#498—21no—
179#495—131no—
180#488—261no—
181#467—131no—
182#466—131no—
183#465—261no—
184C4×Q16—131no—
185C4×SD16—261no—
186C4×D8—131no—
187#427—21no—
188#427C2×D1312yes—
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×C13C22×D811yescharacteristic
206C2×D13—81no—
207C2×D13—81no—
208C2×D13—81no—
209C4×C13—21no—
210C4×C13—21no—
211C4×C13—21no—
212C4×C13—21no—
213C4×C13—21no—
214C4×C13—82no—
215C4×C13—82no—
216C4×C13#53611yescharacteristic
217C4×C13C2×#13711yescharacteristic
218Dic13—81no—
219Dic13—81no—
220Dic13—81no—
221C2×Q16—131no—
222C2×SD16—261no—
223C2×D8—131no—
224C22×C8C22⋊D1311yescharacteristic
225C22×C8C22×D1311yescharacteristic
226C4⋊Q8—21no—
227C4⋊Q8—21no—
228#126—521no—
229#125—22no—
230#125—261no—
231#124—261no—
232#123—521no—
233C22⋊Q8—41no—
234C22⋊Q8—41no—
235C22⋊Q8—261no—
236#121—261no—
237C4×Q8—41no—
238C4×Q8—41no—
239C4×Q8—261no—
240C4×D4—261no—
241C4×D4—521no—
242#117—22no—
243#117—521no—
244C2×C42C22⋊D1311yescharacteristic
245C2×C16—132no—
246C2×C16—132no—
247#107—21no—
248#107—21no—
249#107—131no—
250#107—131no—
251#107C22×D1312yes—
252#107C22×D1312yes—
253#106—22no—
254#106—22no—
255#106—261no—
256#103—261no—
257#103—261no—
258#102—261no—
259#102—261no—
260C4×C8C22⋊D1311yescharacteristic
261C4×C8C22⋊D1311yescharacteristic
262C4×C8C22×D1311yescharacteristic
263C4×C8C22×D1311yescharacteristic
264C2×C13—41no—
265C2×C13#322611yescharacteristic
266C2×C13#341411yescharacteristic
267C2×C13#341411yescharacteristic
268D13—161no—
269C2×Q8—41no—
270C2×Q8—41no—
271C2×Q8—261no—
272C2×D4—261no—
273C2×D4—521no—
274C22×C4—521no—
275C22×C4#610411yescharacteristic
276C22×C4#610411yescharacteristic
277C22×C4C2×C22⋊D1311yescharacteristic
278Q16—262no—
279SD16—522no—
280D8—262no—
281C2×C8—22no—
282C2×C8—22no—
283C2×C8C2×C22⋊D1311yescharacteristic
284C2×C8C2×C22⋊D1311yescharacteristic
285C2×C8C2×C22⋊D1311yescharacteristic
286C2×C8C23×D1311yescharacteristic
287C4⋊C4—22no—
288C4⋊C4—22no—
289C4⋊C4—42no—
290C4⋊C4—42no—
291C4⋊C4—41no—
292C4⋊C4—41no—
293C4⋊C4—261no—
294C4⋊C4—261no—
295C4⋊C4—521no—
296C4⋊C4—521no—
297C4⋊C4—521no—
298C4⋊C4—521no—
299C22⋊C4—42no—
300C22⋊C4—521no—
301C22⋊C4—521no—
302C22⋊C4—521no—
303C22⋊C4—521no—
304C22⋊C4—521no—
305C42—42no—
306C42—521no—
307C42#610411yescharacteristic
308C42#610411yescharacteristic
309C42C2×C22⋊D1311yescharacteristic
310C42C2×C22⋊D1311yescharacteristic
311C16—262no—
312C16—262no—
313C13#3380611yescharacteristic, complemented, Sylow
314C23—521no—
315C23C2×#610411yescharacteristic
316Q8—82no—
317Q8—82no—
318Q8—521no—
319Q8—521no—
320D4—521no—
321D4—521no—
322D4—1042no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—521no—
330C2×C4—521no—
331C2×C4—521no—
332C2×C4—1042no—
333C2×C4C2×#610411yescharacteristic
334C2×C4C2×#610411yescharacteristic
335C2×C4C2×#610411yescharacteristic
336C2×C4C2×#610411yescharacteristic
337C2×C4C2×#610411yescharacteristic
338C2×C4C22×C22⋊D1311yescharacteristic
339C8—21no—
340C8—21no—
341C8#8819612yes—
342C8#8825412yes—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—1041no—
347C22—1041no—
348C22—1041no—
349C22C22×#610411yescharacteristic
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—21no—
355C4—82no—
356C4—82no—
357C4—1041no—
358C4—1041no—
359C4—1041no—
360C4C2×#8819611yescharacteristic
361C4#1171952111yescharacteristic
362C2—41no—
363C2—2081no—
364C2#1312595711yescharacteristic
365C2#1312797011yescharacteristic
366C2#1312797011yescharacteristic
subgroupG/H
centerC22C22×#6104
commutator, cosocleC2×C8×C13C24
FrattiniC2×C8C23×D13
FittingC13×#3160C2
socleC22×C13C22×D8
prime radical#11718776C22
hypercenter#3160D13
hypocenterC13#33806
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. #13117119C2semidirect
3. #13117119C2semidirect
4. #13117075C2semidirect
5. #13117075C2semidirect
6. #13117044C2semidirect
8. #13116997C2semidirect
9. #13116990C2semidirect
10. #13116639C2semidirect
11. C13×#3160C2semidirect
132. #3160D13semidirect
313. C13#33806semidirect

Maximal subgroups

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

subgroupindex
#131254062
#131171192
#131170752
#131170442
#131170272
#131169972
#131169902
#131166392
C13×#31602
#3380613