Finite Group Databasebeta

← #16019065

Subgroups — #16019065

Order 3328.

468 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#13117112C212yesmaximal, complemented
3#13117070C212yesmaximal, complemented
4#13117038C211yesmaximal, characteristic, complemented
5#13117033C211yesmaximal, characteristic, complemented
6#13117021C211yesmaximal, characteristic
7#13117016C211yesmaximal, characteristic
8#13116997C212yesmaximal, complemented
9#13116990C212yesmaximal, complemented
10#13116635C211yesmaximal, characteristic, complemented
11C2×C13×#499C211yesmaximal, characteristic, complemented
12C2×C13×#125—21no—
13#11719184—21no—
14C13×#499—21no—
15C13×#499—21no—
16C13×#499C2212yes—
17C13×#499C2212yes—
18C2×C13×#107C2211yescharacteristic
19C2×C13×#107C2211yescharacteristic
20C2×C13×#106—21no—
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⋊#6090C2211yescharacteristic
32C22⋊#6090C2211yescharacteristic
33#11718084C2212yes—
34#11718084C2212yes—
35#11718083C2212yes—
36#11718083C2212yes—
37#11718082C2212yes—
38#11718082C2212yes—
39#11718081C2212yes—
40#11718081C2212yes—
41C4⋊#6090C2212yes—
42C4×#6090C2212yes—
43C22×C8×C13D411yescharacteristic
44C22×C8×C13C2311yescharacteristic
45C13×#125—22no—
46C13×#125—22no—
47C13×#125—41no—
48C13×#125—41no—
49C2×C13×C4⋊C4—21no—
50C2×C13×C4⋊C4—21no—
51C2×C13×C4⋊C4—41no—
52C2×C13×C4⋊C4—41no—
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#33798—131nomaximal, Sylow
87C22×C4×C13—41no—
88C22×C4×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—41no—
105C13×C4⋊C4—41no—
106C13×C4⋊C4—42no—
107C13×C4⋊C4—42no—
108C13×C4⋊C4—42no—
109C13×C4⋊C4—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—
132C2×#499D1311yescharacteristic, complemented
133#2253—132no—
134#2242—132no—
135#2236—131no—
136#2235—131no—
137#2233—131no—
138#2232—131no—
139#2229—132no—
140#2228—132no—
141#2162—131no—
142C23×C13C2×D811yescharacteristic
143C22×D13—41no—
144C2×C4×C13—22no—
145C2×C4×C13—21no—
146C2×C4×C13—21no—
147C2×C4×C13—41no—
148C2×C4×C13—42no—
149C2×C4×C13—42no—
150C2×C4×C13—82no—
151C2×C4×C13—82no—
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#529—261no—
172C2×#125—21no—
173#499—21no—
174#499—21no—
175#499—131no—
176#499C2×D1312yes—
177#499C2×D1312yes—
178#495—131no—
179#488—261no—
180#467—131no—
181#466—131no—
182#465—261no—
183C4×Q16—131no—
184C4×SD16—261no—
185C4×D8—131no—
186C2×#107C2×D1311yescharacteristic
187C2×#107C2×D1311yescharacteristic
188C2×#106—21no—
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—131no—
200C22⋊C16—131no—
201C4×C16—132no—
202C22×C13—21no—
203C22×C13—21no—
204C22×C13#50812yes—
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
226#126—521no—
227#125—22no—
228#125—22no—
229#125—41no—
230#125—41no—
231#125—261no—
232#124—261no—
233#123—521no—
234C22⋊Q8—261no—
235#121—261no—
236C4×Q8—261no—
237C4×D4—261no—
238C4×D4—521no—
239#117—521no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—41no—
243C2×C4⋊C4—41no—
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—22no—
265C2×C13#322611yescharacteristic
266C2×C13C2×#50811yescharacteristic
267C2×C13#341411yescharacteristic
268D13—161no—
269C2×Q8—261no—
270C2×D4—261no—
271C2×D4—521no—
272C22×C4—41no—
273C22×C4—41no—
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—41no—
290C4⋊C4—41no—
291C4⋊C4—42no—
292C4⋊C4—42no—
293C4⋊C4—42no—
294C4⋊C4—42no—
295C4⋊C4—261no—
296C4⋊C4—261no—
297C4⋊C4—521no—
298C4⋊C4—521no—
299C4⋊C4—521no—
300C4⋊C4—521no—
301C22⋊C4—521no—
302C22⋊C4—521no—
303C22⋊C4—521no—
304C22⋊C4—521no—
305C22⋊C4—521no—
306C42—521no—
307C42#610411yescharacteristic
308C42#610411yescharacteristic
309C42C2×C22⋊D1311yescharacteristic
310C42C2×C22⋊D1311yescharacteristic
311C16—262no—
312C16—262no—
313C13#3379811yescharacteristic, complemented, Sylow
314C23—521no—
315C23C2×#610411yescharacteristic
316Q8—521no—
317Q8—521no—
318D4—521no—
319D4—521no—
320D4—1042no—
321C2×C4—22no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—41no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—82no—
328C2×C4—82no—
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—1041no—
346C22—1041no—
347C22—1041no—
348C22#1171885512yes—
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—22no—
363C2—2081no—
364C2#1312595711yescharacteristic
365C2C2×#1171885511yescharacteristic
366C2#1312797011yescharacteristic
subgroupG/H
centerC22C22×#6104
commutator, cosocleC2×C8×C13C24
FrattiniC2×C8C23×D13
FittingC2×C13×#499C2
socleC22×C13C22×D8
prime radical#11718776C22
hypercenterC2×#499D13
hypocenterC13#33798
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×C8 ◁ C2×#499

Complements

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

NH ≅ G/Ntype
2. #13117112C2semidirect
3. #13117070C2semidirect
4. #13117038C2semidirect
5. #13117033C2semidirect
8. #13116997C2semidirect
9. #13116990C2semidirect
10. #13116635C2semidirect
11. C2×C13×#499C2semidirect
132. C2×#499D13semidirect
313. C13#33798semidirect

Maximal subgroups

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

subgroupindex
#131254062
#131171122
#131170702
#131170382
#131170332
#131170212
#131170162
#131169972
#131169902
#131166352
C2×C13×#4992
#3379813