Finite Group Databasebeta

← #16018014

Subgroups — #16018014

Order 3328.

548 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13125406C211yesmaximal, characteristic
2#13117038C211yesmaximal, characteristic, complemented
3#13117021C211yesmaximal, characteristic
4#13117000C212yesmaximal, complemented
5#13116898C212yesmaximal, complemented
6#13116770C211yesmaximal, characteristic, complemented
7#13116753C211yesmaximal, characteristic
8#13116705C212yesmaximal, complemented
9#13116698C212yesmaximal, complemented
10#13116639C211yesmaximal, characteristic, complemented
11C2×C4×C13×Q16C211yesmaximal, characteristic, complemented
12C22×C13×Q16C2211yescharacteristic
13C2×C4×Q8×C13—21no—
14#11719184—21no—
15C4×C13×Q16—21no—
16C4×C13×Q16—21no—
17C4×C13×Q16C2212yes—
18C4×C13×Q16C2212yes—
19C2×C13×#107C2211yescharacteristic
20C2×C13×#103—21no—
21C2×C4×C8×C13C2211yescharacteristic
22C2×#88069C2212yes—
23C2×#88068C2212yes—
24#11718777C2211yescharacteristic
25#11718776C2211yescharacteristic
26#11718775—21no—
27C4×Dic52C2211yescharacteristic
28#11718358—21no—
29#11718357C2211yescharacteristic
30C4×D104C2211yescharacteristic
31C4×#6095—21no—
32#11718344C2211yescharacteristic
33#11718156C2212yes—
34#11718156C2212yes—
35C22⋊#6090C2211yescharacteristic
36C22⋊#6090C2211yescharacteristic
37#11718084C2212yes—
38#11718083C2212yes—
39#11718082C2212yes—
40#11718081C2212yes—
41C4⋊#6090C2212yes—
42#11718053C2212yes—
43C22×Q8×C13—21no—
44C2×C13×Q16—24no—
45C2×C13×Q16—21no—
46C2×C13×Q16C2312yes—
47C22×C8×C13D411yescharacteristic
48C22×C8×C13C2311yescharacteristic
49C4×Q8×C13—22no—
50C4×Q8×C13—22no—
51C4×Q8×C13—41no—
52C4×Q8×C13—41no—
53C2×C13×C4⋊C4—21no—
54C2×C13×C4⋊C4—41no—
55C2×C42×C13—41no—
56C2×C42×C13D411yescharacteristic
57#88184—21no—
58#88183—41no—
59C4×C22⋊D13—41no—
60#88178—21no—
61C2×Dic52C2311yescharacteristic
62C2×D104C2311yescharacteristic
63C2×#6095—21no—
64#88130—41no—
65#88129—21no—
66C4×D52—21no—
67#88126—41no—
68#88124—21no—
69C4×Dic26—21no—
70C13×#107—21no—
71C13×#107C2312yes—
72C13×#103—22no—
73C13×#103—22no—
74C4×C8×C13D411yescharacteristic
75C4×C8×C13D411yescharacteristic
76C4×C8×C13C2311yescharacteristic
77C4×C8×C13C2311yescharacteristic
78#88069—24no—
79#88068—24no—
80#88061—21no—
81#88061—21no—
82#88058C2311yescharacteristic
83#88058C2311yescharacteristic
84#88057—21no—
85#88056—21no—
86#88056—21no—
87C2×#6090C2312yes—
88C2×#6090C2312yes—
89#33677—131nomaximal, Sylow
90C2×Q8×C13—24no—
91C2×Q8×C13—22no—
92C2×Q8×C13—42no—
93C2×Q8×C13—41no—
94C22×C4×C13—41no—
95C22×C4×C13—41no—
96C22×C4×C13D811yescharacteristic
97C22×C4×C13D811yescharacteristic
98C22×C4×C13C2×D411yescharacteristic
99C2×C22⋊D13—41no—
100C2×D52—21no—
101C2×C4×D13—41no—
102C2×Dic26—21no—
103C13×Q16—24no—
104C13×Q16—22no—
105C13×Q16#4114yes—
106C2×C8×C13—22no—
107C2×C8×C13—41no—
108C2×C8×C13C2×D411yescharacteristic
109C2×C8×C13C2×D411yescharacteristic
110C2×C8×C13C2×D411yescharacteristic
111C2×C8×C13C2411yescharacteristic
112C13×C4⋊C4—22no—
113C13×C4⋊C4—41no—
114C13×C4⋊C4—42no—
115C13×C4⋊C4—42no—
116C42×C13—42no—
117C42×C13—42no—
118C42×C13D811yescharacteristic
119C42×C13D811yescharacteristic
120C42×C13C2×D411yescharacteristic
121C42×C13C2×D411yescharacteristic
122C22⋊Dic13—41no—
123#6103—41no—
124#6103—41no—
125#6103—41no—
126#6103—41no—
127C4⋊Dic13—21no—
128C4⋊Dic13—21no—
129#6101—41no—
130#6101—41no—
131#6101—41no—
132#6101—41no—
133C4×Dic13—41no—
134Dic52—22no—
135D104—22no—
136#6095—42no—
137#6090—22no—
138#6090—22no—
139#3168—131no—
140C2×C4×Q16D1311yescharacteristic, complemented
141#2236—131no—
142#2233—131no—
143#2229—132no—
144#2211—132no—
145#2188—131no—
146#2185—131no—
147#2176—132no—
148#2175—132no—
149#2163—131no—
150C23×C13C2×D811yescharacteristic
151C22×D13—41no—
152Q8×C13—24no—
153Q8×C13—44no—
154Q8×C13—42no—
155C2×C4×C13—22no—
156C2×C4×C13—21no—
157C2×C4×C13—21no—
158C2×C4×C13—41no—
159C2×C4×C13—44no—
160C2×C4×C13—42no—
161C2×C4×C13—42no—
162C2×C4×C13—82no—
163C2×C4×C13C2×D811yescharacteristic
164C2×C4×C13C2×D811yescharacteristic
165C2×C4×C13C2×D811yescharacteristic
166C2×C4×C13C2×D811yescharacteristic
167C2×C4×C13C2×D811yescharacteristic
168C2×C4×C13C22×D411yescharacteristic
169C22⋊D13—82no—
170C2×Dic13—41no—
171C2×Dic13—41no—
172C2×Dic13—41no—
173D52—41no—
174D52—41no—
175C4×D13—82no—
176Dic26—41no—
177Dic26—41no—
178C8×C13—21no—
179C8×C13—21no—
180C8×C13—21no—
181C8×C13C2×#4112yes—
182C22×Q16C2×D1311yescharacteristic
183#529—261no—
184C2×C4×Q8—21no—
185C2×Q32—132no—
186C2×SD32—132no—
187#499—131no—
188#495—131no—
189#488—261no—
190#467—131no—
191#466—131no—
192#465—261no—
193C4×Q16—21no—
194C4×Q16—21no—
195C4×Q16—131no—
196C4×Q16C2×D1312yes—
197C4×Q16C2×D1312yes—
198C4×SD16—261no—
199C4×D8—131no—
200C2×#107C2×D1311yescharacteristic
201C2×#103—21no—
202C2×C4×C8C2×D1311yescharacteristic
203#367—132no—
204#366—132no—
205C4⋊C16—132no—
206#358—132no—
207#358—132no—
208#358—132no—
209#357—132no—
210C22⋊C16—131no—
211C22⋊C16—131no—
212#346—132no—
213C22×C13—21no—
214C22×C13—21no—
215C22×C13#51012yes—
216C22×C13C22×D811yescharacteristic
217C2×D13—81no—
218C2×D13—81no—
219C2×D13—81no—
220C4×C13—21no—
221C4×C13—21no—
222C4×C13—21no—
223C4×C13—21no—
224C4×C13—21no—
225C4×C13—44no—
226C4×C13—82no—
227C4×C13#52511yescharacteristic
228C4×C13#57511yescharacteristic
229Dic13—81no—
230Dic13—81no—
231Dic13—81no—
232C22×Q8—21no—
233C2×Q16—24no—
234C2×Q16—21no—
235C2×Q16—131no—
236C2×Q16C22×D1312yes—
237C2×SD16—261no—
238C2×D8—131no—
239C22×C8C22⋊D1311yescharacteristic
240C22×C8C22×D1311yescharacteristic
241#126—521no—
242#125—261no—
243#124—261no—
244#123—521no—
245C22⋊Q8—261no—
246#121—261no—
247C4×Q8—22no—
248C4×Q8—22no—
249C4×Q8—41no—
250C4×Q8—41no—
251C4×Q8—261no—
252C4×D4—261no—
253C4×D4—521no—
254#117—521no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—41no—
257C2×C42—41no—
258C2×C42C22⋊D1311yescharacteristic
259Q32—264no—
260SD32—264no—
261C2×C16—132no—
262C2×C16—132no—
263#107—21no—
264#107—131no—
265#107—131no—
266#107C22×D1312yes—
267#106—261no—
268#103—22no—
269#103—22no—
270#103—261no—
271#103—261no—
272#102—261no—
273#102—261no—
274C4×C8C22⋊D1311yescharacteristic
275C4×C8C22⋊D1311yescharacteristic
276C4×C8C22×D1311yescharacteristic
277C4×C8C22×D1311yescharacteristic
278C2×C13—22no—
279C2×C13#310011yescharacteristic
280C2×C13C2×#51011yescharacteristic
281C2×C13#341411yescharacteristic
282D13—161no—
283C2×Q8—24no—
284C2×Q8—22no—
285C2×Q8—42no—
286C2×Q8—41no—
287C2×Q8—261no—
288C2×D4—261no—
289C2×D4—521no—
290C22×C4—41no—
291C22×C4—41no—
292C22×C4—521no—
293C22×C4#610411yescharacteristic
294C22×C4#610411yescharacteristic
295C22×C4C2×C22⋊D1311yescharacteristic
296Q16—24no—
297Q16—22no—
298Q16—262no—
299Q16#612714yes—
300SD16—522no—
301D8—262no—
302C2×C8—22no—
303C2×C8—41no—
304C2×C8C2×C22⋊D1311yescharacteristic
305C2×C8C2×C22⋊D1311yescharacteristic
306C2×C8C2×C22⋊D1311yescharacteristic
307C2×C8C23×D1311yescharacteristic
308C4⋊C4—22no—
309C4⋊C4—41no—
310C4⋊C4—42no—
311C4⋊C4—42no—
312C4⋊C4—261no—
313C4⋊C4—261no—
314C4⋊C4—521no—
315C4⋊C4—521no—
316C4⋊C4—521no—
317C4⋊C4—521no—
318C22⋊C4—521no—
319C22⋊C4—521no—
320C22⋊C4—521no—
321C22⋊C4—521no—
322C22⋊C4—521no—
323C42—42no—
324C42—42no—
325C42—521no—
326C42#610411yescharacteristic
327C42#610411yescharacteristic
328C42C2×C22⋊D1311yescharacteristic
329C42C2×C22⋊D1311yescharacteristic
330C16—262no—
331C16—262no—
332C13#3367711yescharacteristic, complemented, Sylow
333C23—521no—
334C23C2×#610411yescharacteristic
335Q8—24no—
336Q8—44no—
337Q8—42no—
338Q8—521no—
339Q8—521no—
340D4—521no—
341D4—521no—
342D4—1042no—
343C2×C4—22no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—41no—
347C2×C4—44no—
348C2×C4—42no—
349C2×C4—42no—
350C2×C4—82no—
351C2×C4—521no—
352C2×C4—521no—
353C2×C4—521no—
354C2×C4—1042no—
355C2×C4C2×#610411yescharacteristic
356C2×C4C2×#610411yescharacteristic
357C2×C4C2×#610411yescharacteristic
358C2×C4C2×#610411yescharacteristic
359C2×C4C2×#610411yescharacteristic
360C2×C4C22×C22⋊D1311yescharacteristic
361C8—21no—
362C8—21no—
363C8—21no—
364C8C2×#612712yes—
365C22—21no—
366C22—21no—
367C22—1041no—
368C22—1041no—
369C22—1041no—
370C22#1171884012yes—
371C22C22×#610411yescharacteristic
372C4—21no—
373C4—21no—
374C4—21no—
375C4—21no—
376C4—21no—
377C4—44no—
378C4—82no—
379C4—1041no—
380C4—1041no—
381C4—1041no—
382C4#1171949611yescharacteristic
383C4#1171952711yescharacteristic
384C2—22no—
385C2—2081no—
386C2#1312483611yescharacteristic
387C2C2×#1171884011yescharacteristic
388C2#1312797011yescharacteristic
subgroupG/H
centerC22C22×#6104
commutator, cosocleC2×C8×C13C24
FrattiniC2×C8C23×D13
FittingC2×C4×C13×Q16C2
socleC22×C13C22×D8
prime radical#11718776C22
hypercenterC2×C4×Q16D13
hypocenterC13#33677
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×C8 ◁ C2×C4×Q16

Complements

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

NH ≅ G/Ntype
2. #13117038C2semidirect
4. #13117000C2semidirect
5. #13116898C2semidirect
6. #13116770C2semidirect
8. #13116705C2semidirect
9. #13116698C2semidirect
10. #13116639C2semidirect
11. C2×C4×C13×Q16C2semidirect
140. C2×C4×Q16D13semidirect
332. C13#33677semidirect

Maximal subgroups

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

subgroupindex
#131254062
#131170382
#131170212
#131170002
#131168982
#131167702
#131167532
#131167052
#131166982
#131166392
C2×C4×C13×Q162
#3367713