Finite Group Databasebeta

← #16018493

Subgroups — #16018493

Order 3328.

554 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13125415C211yesmaximal, characteristic, complemented
2#13117123C211yesmaximal, characteristic, complemented
3#13117103C211yesmaximal, characteristic, complemented
4#13117079C211yesmaximal, characteristic, complemented
5#13117072C211yesmaximal, characteristic, complemented
6#13116951C212yesmaximal, complemented
7#13116937C212yesmaximal, complemented
8C4×#88068C212yesmaximal, complemented
9C4×#88066C212yesmaximal, complemented
10C4×#88052C211yesmaximal, characteristic, complemented
11C13×#3168C211yesmaximal, characteristic, complemented
12C13×#529—21no—
13#11719182—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
24C2×#88068C2212yes—
25C2×#88066C2212yes—
26#11718776—21no—
27#11718776C2212yes—
28C2×#88052C2212yes—
29#11718356C2211yescharacteristic
30#11718355—21no—
31C4×D104—21no—
32C4×D104C2212yes—
33#11718343C2211yescharacteristic
34#11718156C2212yes—
35#11718154C2212yes—
36#11718083C2212yes—
37#11718083C2212yes—
38#11718082C2212yes—
39#11718081C2212yes—
40#11718053C2211yescharacteristic
41#11718053C2211yescharacteristic
42C4×#6090C2212yes—
43C2×#6127—41no—
44C2×C13×Q16C2311yescharacteristic
45C2×C13×SD16—21no—
46C2×C13×D8C2311yescharacteristic
47C22×C8×C13D411yescharacteristic
48C22×C8×C13C2311yescharacteristic
49C13×#126—41no—
50C13×#125—21no—
51C13×#124—21no—
52C13×#123—41no—
53C13×C22⋊Q8—21no—
54C13×#121—21no—
55C4×Q8×C13—21no—
56C4×D4×C13—21no—
57C4×D4×C13—41no—
58C13×#117—41no—
59C2×C42×C13D411yescharacteristic
60#88184—22no—
61#88184—41no—
62C2×D104—21no—
63C2×D104C2312yes—
64#88129—41no—
65#88128—21no—
66C4×D52—22no—
67C4×D52—41no—
68#88123—21no—
69C13×#107C2311yescharacteristic
70C13×#107C2311yescharacteristic
71C13×#106—21no—
72C13×#103—21no—
73C13×#103—21no—
74C13×#102—21no—
75C13×#102—21no—
76C4×C8×C13D411yescharacteristic
77C4×C8×C13D411yescharacteristic
78C4×C8×C13C2311yescharacteristic
79C4×C8×C13C2311yescharacteristic
80#88068—24no—
81#88066—24no—
82#88061—22no—
83#88061—22no—
84#88058—21no—
85#88058C2312yes—
86#88052—24no—
87C2×#6090C2312yes—
88C2×#6090C2312yes—
89#33737—131nomaximal, Sylow
90C2×Q8×C13—21no—
91C2×D4×C13—21no—
92C2×D4×C13—41no—
93C22×C4×C13—41no—
94C22×C4×C13D811yescharacteristic
95C22×C4×C13D811yescharacteristic
96C22×C4×C13C2×D411yescharacteristic
97C2×C22⋊D13—42no—
98#6127—84no—
99C2×D52—22no—
100C2×D52—41no—
101C2×D52—41no—
102C2×C4×D13—42no—
103C2×Dic26—41no—
104C13×Q16—22no—
105C13×SD16—42no—
106C13×D8—22no—
107C2×C8×C13—22no—
108C2×C8×C13—22no—
109C2×C8×C13C2×D411yescharacteristic
110C2×C8×C13C2×D411yescharacteristic
111C2×C8×C13C2×D411yescharacteristic
112C2×C8×C13C2411yescharacteristic
113C13×C4⋊C4—21no—
114C13×C4⋊C4—21no—
115C13×C4⋊C4—41no—
116C13×C4⋊C4—41no—
117C13×C4⋊C4—41no—
118C13×C4⋊C4—41no—
119C13×C22⋊C4—41no—
120C13×C22⋊C4—41no—
121C13×C22⋊C4—41no—
122C13×C22⋊C4—41no—
123C13×C22⋊C4—41no—
124C42×C13—41no—
125C42×C13D811yescharacteristic
126C42×C13D811yescharacteristic
127C42×C13C2×D411yescharacteristic
128C42×C13C2×D411yescharacteristic
129#6103—42no—
130#6103—42no—
131C4⋊Dic13—22no—
132C4⋊Dic13—41no—
133D104—22no—
134D104—22no—
135D104—42no—
136#6090—22no—
137#6090#4114yescomplemented
138#3169—131no—
139#3168D1311yescharacteristic, complemented
140#2255—131no—
141#2250—131no—
142#2244—131no—
143#2243—131no—
144#2220—132no—
145#2218—132no—
146C4×SD32—132no—
147C4×D16—132no—
148C4×M32—131no—
149C23×C13—41no—
150C23×C13C2×D811yescharacteristic
151C22×D13—42no—
152Q8×C13—41no—
153Q8×C13—41no—
154D4×C13—41no—
155D4×C13—41no—
156D4×C13—82no—
157C2×C4×C13—21no—
158C2×C4×C13—21no—
159C2×C4×C13—22no—
160C2×C4×C13—41no—
161C2×C4×C13—41no—
162C2×C4×C13—41no—
163C2×C4×C13—41no—
164C2×C4×C13—82no—
165C2×C4×C13C2×D811yescharacteristic
166C2×C4×C13C2×D811yescharacteristic
167C2×C4×C13C2×D811yescharacteristic
168C2×C4×C13C2×D811yescharacteristic
169C2×C4×C13C2×D811yescharacteristic
170C2×C4×C13C22×D411yescharacteristic
171C22⋊D13—84no—
172C2×Dic13—42no—
173D52—42no—
174D52—42no—
175D52—82no—
176D52—82no—
177C4×D13—84no—
178Dic26—82no—
179C8×C13—21no—
180C8×C13—21no—
181C8×C13#13512yes—
182C8×C13C2×#4112yes—
183#532—261no—
184#529—21no—
185C2×SD32—132no—
186C2×D16—132no—
187C2×M32—132no—
188#500—131no—
189#499C2×D1311yescharacteristic
190#495C2×D1311yescharacteristic
191#493—131no—
192#488—21no—
193#486—261no—
194#467C2×D1311yescharacteristic
195#466—132no—
196#466—261no—
197#466C2×D1311yescharacteristic
198#465—21no—
199C4×Q16C2×D1311yescharacteristic
200C4×SD16—21no—
201C4×D8—132no—
202C4×D8—261no—
203C4×D8C2×D1311yescharacteristic
204C2×C4×C8C2×D1311yescharacteristic
205#367—132no—
206#366—132no—
207#358—132no—
208#357—132no—
209#357—132no—
210#357—132no—
211#346—131no—
212#346—131no—
213C4×C16—132no—
214C22×C13—21no—
215C22×C13—21no—
216C22×C13—21no—
217C22×C13—81no—
218C22×C13—81no—
219C22×C13—81no—
220C22×C13C22×D811yescharacteristic
221C2×D13—82no—
222C2×D13—82no—
223C2×D13—82no—
224C4×C13—21no—
225C4×C13—21no—
226C4×C13—21no—
227C4×C13—21no—
228C4×C13—81no—
229C4×C13—81no—
230C4×C13—81no—
231C4×C13#50912yes—
232C4×C13#53211yescharacteristic
233C4×C13C2×#13511yescharacteristic
234Dic13—82no—
235C2×#41—521no—
236C2×Q16C22×D1311yescharacteristic
237C2×SD16—21no—
238C2×D8—132no—
239C2×D8—261no—
240C2×D8C22×D1311yescharacteristic
241C22×C8C22⋊D1311yescharacteristic
242C22×C8C22×D1311yescharacteristic
243C4⋊Q8—261no—
244#127—261no—
245#126—41no—
246#125—21no—
247#124—21no—
248#124—521no—
249#123—41no—
250C22⋊Q8—21no—
251#121—21no—
252#121—262no—
253#121—521no—
254C4×Q8—21no—
255C4×D4—21no—
256C4×D4—41no—
257C4×D4—262no—
258C4×D4—521no—
259#117—41no—
260C2×C42C22⋊D1311yescharacteristic
261SD32—264no—
262D16—264no—
263M32—264no—
264C2×C16—132no—
265C2×C16—132no—
266#107—132no—
267#107—261no—
268#107C22×D1311yescharacteristic
269#107C22×D1311yescharacteristic
270#106—21no—
271#103—21no—
272#103—21no—
273#102—21no—
274#102—21no—
275#102—262no—
276#102—262no—
277C4×C8C22⋊D1311yescharacteristic
278C4×C8C22⋊D1311yescharacteristic
279C4×C8C22×D1311yescharacteristic
280C4×C8C22×D1311yescharacteristic
281C2×C13—41no—
282C2×C13—161no—
283C2×C13#316911yescharacteristic
284C2×C13C2×#50911yescharacteristic
285C2×C13#341411yescharacteristic
286D13—162no—
287#41—1044no—
288C2×Q8—21no—
289C2×Q8—521no—
290C2×D4—21no—
291C2×D4—41no—
292C2×D4—262no—
293C2×D4—522no—
294C2×D4—521no—
295C2×D4—521no—
296C22×C4—41no—
297C22×C4—522no—
298C22×C4#610411yescharacteristic
299C22×C4#610411yescharacteristic
300C22×C4C2×C22⋊D1311yescharacteristic
301Q16—22no—
302SD16—42no—
303D8—22no—
304D8—262no—
305D8—262no—
306D8—522no—
307C2×C8—22no—
308C2×C8—22no—
309C2×C8C2×C22⋊D1311yescharacteristic
310C2×C8C2×C22⋊D1311yescharacteristic
311C2×C8C2×C22⋊D1311yescharacteristic
312C2×C8C23×D1311yescharacteristic
313C4⋊C4—21no—
314C4⋊C4—21no—
315C4⋊C4—41no—
316C4⋊C4—41no—
317C4⋊C4—41no—
318C4⋊C4—41no—
319C4⋊C4—262no—
320C4⋊C4—521no—
321C22⋊C4—41no—
322C22⋊C4—41no—
323C22⋊C4—41no—
324C22⋊C4—41no—
325C22⋊C4—41no—
326C22⋊C4—522no—
327C22⋊C4—522no—
328C42—41no—
329C42#610411yescharacteristic
330C42#610411yescharacteristic
331C42C2×C22⋊D1311yescharacteristic
332C42C2×C22⋊D1311yescharacteristic
333C16—134no—
334C16—262no—
335C13#3373711yescharacteristic, complemented, Sylow
336C23—41no—
337C23—522no—
338C23C2×#610411yescharacteristic
339Q8—41no—
340Q8—41no—
341Q8—1042no—
342D4—41no—
343D4—41no—
344D4—82no—
345D4—522no—
346D4—522no—
347D4—1042no—
348D4—1042no—
349D4—1044no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—22no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—82no—
358C2×C4—522no—
359C2×C4—1044no—
360C2×C4C2×#610411yescharacteristic
361C2×C4C2×#610411yescharacteristic
362C2×C4C2×#610411yescharacteristic
363C2×C4C2×#610411yescharacteristic
364C2×C4C2×#610411yescharacteristic
365C2×C4C22×C22⋊D1311yescharacteristic
366C8—21no—
367C8—21no—
368C8#8820412yes—
369C8#41×D1312yes—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—81no—
374C22—81no—
375C22—81no—
376C22—1042no—
377C22—1042no—
378C22—1042no—
379C22C22×#610411yescharacteristic
380C4—21no—
381C4—21no—
382C4—21no—
383C4—21no—
384C4—81no—
385C4—81no—
386C4—81no—
387C4—1042no—
388C4#1171885412yes—
389C4C2×#8820411yescharacteristic
390C4#1171953711yescharacteristic
391C2—41no—
392C2—161no—
393C2—2082no—
394C2#1312541111yescharacteristic
395C2C2×#1171885411yescharacteristic
396C2#1312797011yescharacteristic
subgroupG/H
centerC2×C4C2×#6104
commutator, cosocleC2×C8×C13C24
FrattiniC2×C8C23×D13
FittingC13×#3168C2
socleC22×C13C22×D8
hypercenter#3168D13
hypocenterC13#33737
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×C8 ◁ #3168

Complements

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

NH ≅ G/Ntype
1. #13125415C2semidirect
2. #13117123C2semidirect
3. #13117103C2semidirect
4. #13117079C2semidirect
5. #13117072C2semidirect
6. #13116951C2semidirect
7. #13116937C2semidirect
8. C4×#88068C2semidirect
9. C4×#88066C2semidirect
10. C4×#88052C2semidirect
11. C13×#3168C2semidirect
137. #6090#41semidirect
139. #3168D13semidirect
335. C13#33737semidirect

Maximal subgroups

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

subgroupindex
#131254152
#131171232
#131171032
#131170792
#131170722
#131169512
#131169372
C4×#880682
C4×#880662
C4×#880522
C13×#31682
#3373713