Finite Group Databasebeta

← #16018486

Subgroups — #16018486

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#13125406C211yesmaximal, characteristic, complemented
2#13117119C211yesmaximal, characteristic, complemented
3#13117100C211yesmaximal, characteristic, complemented
4#13117077C211yesmaximal, characteristic, complemented
5#13117075C211yesmaximal, characteristic, complemented
6#13116947C212yesmaximal, complemented
7#13116937C212yesmaximal, complemented
8C4×#88067C212yesmaximal, complemented
9C4×#88066C212yesmaximal, complemented
10C4×#88052C211yesmaximal, characteristic, complemented
11C13×#3169C211yesmaximal, characteristic, complemented
12C13×#532—21no—
13#11719184—21no—
14C13×#500C2211yescharacteristic
15C13×#493C2211yescharacteristic
16C13×#486—21no—
17C13×#466—21no—
18C13×#466C2212yes—
19C4×C13×D8—21no—
20C4×C13×D8C2212yes—
21C2×C4×C8×C13C2211yescharacteristic
22C2×#88067C2212yes—
23C2×#88066C2212yes—
24#11718777C2211yescharacteristic
25#11718776C2211yescharacteristic
26#11718775—21no—
27C2×#88052C2212yes—
28C4×Dic52C2211yescharacteristic
29#11718358—21no—
30#11718357C2211yescharacteristic
31C4×D104C2211yescharacteristic
32C4×#6095—21no—
33#11718344C2211yescharacteristic
34#11718154C2212yes—
35#11718154C2212yes—
36#11718084C2212yes—
37#11718083C2212yes—
38#11718082C2212yes—
39#11718081C2212yes—
40#11718053C2211yescharacteristic
41#11718053C2211yescharacteristic
42C4×#6090C2212yes—
43C2×C13×#41—41no—
44C2×C13×D8—21no—
45C2×C13×D8C2312yes—
46C22×C8×C13D411yescharacteristic
47C22×C8×C13C2311yescharacteristic
48C13×C4⋊Q8—21no—
49C13×#127—21no—
50C13×#124—41no—
51C13×#121—22no—
52C13×#121—41no—
53C4×D4×C13—22no—
54C4×D4×C13—41no—
55C2×C42×C13D411yescharacteristic
56#88184—21no—
57#88183—41no—
58C4×C22⋊D13—41no—
59#88178—21no—
60C2×Dic52C2311yescharacteristic
61C2×D104C2311yescharacteristic
62C2×#6095—21no—
63#88130—41no—
64#88129—21no—
65C4×D52—21no—
66#88126—41no—
67#88124—21no—
68C4×Dic26—21no—
69C13×#107—21no—
70C13×#107C2312yes—
71C13×#102—22no—
72C13×#102—22no—
73C4×C8×C13D411yescharacteristic
74C4×C8×C13D411yescharacteristic
75C4×C8×C13C2311yescharacteristic
76C4×C8×C13C2311yescharacteristic
77#88067—24no—
78#88066—24no—
79#88061—21no—
80#88061—21no—
81#88058C2311yescharacteristic
82#88058C2311yescharacteristic
83#88057—21no—
84#88056—21no—
85#88056—21no—
86#88052—24no—
87C2×#6090C2312yes—
88C2×#6090C2312yes—
89#33737—131nomaximal, Sylow
90C13×#41—84no—
91C2×Q8×C13—41no—
92C2×D4×C13—22no—
93C2×D4×C13—42no—
94C2×D4×C13—41no—
95C2×D4×C13—41no—
96C22×C4×C13—42no—
97C22×C4×C13D811yescharacteristic
98C22×C4×C13D811yescharacteristic
99C22×C4×C13C2×D411yescharacteristic
100C2×C22⋊D13—41no—
101C2×D52—21no—
102C2×C4×D13—41no—
103C2×Dic26—21no—
104C13×D8—22no—
105C13×D8—22no—
106C13×D8—42no—
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—22no—
114C13×C4⋊C4—41no—
115C13×C22⋊C4—42no—
116C13×C22⋊C4—42no—
117C42×C13D811yescharacteristic
118C42×C13D811yescharacteristic
119C42×C13C2×D411yescharacteristic
120C42×C13C2×D411yescharacteristic
121C22⋊Dic13—41no—
122#6103—41no—
123#6103—41no—
124#6103—41no—
125#6103—41no—
126C4⋊Dic13—21no—
127C4⋊Dic13—21no—
128#6101—41no—
129#6101—41no—
130#6101—41no—
131#6101—41no—
132C4×Dic13—41no—
133Dic52—22no—
134D104—22no—
135#6095—42no—
136#6090—22no—
137#6090#4114yescomplemented
138#3169D1311yescharacteristic, complemented
139#3168—131no—
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—42no—
150C23×C13C2×D811yescharacteristic
151C22×D13—41no—
152Q8×C13—82no—
153D4×C13—42no—
154D4×C13—42no—
155D4×C13—82no—
156D4×C13—82no—
157D4×C13—84no—
158C2×C4×C13—21no—
159C2×C4×C13—21no—
160C2×C4×C13—22no—
161C2×C4×C13—41no—
162C2×C4×C13—42no—
163C2×C4×C13—84no—
164C2×C4×C13C2×D811yescharacteristic
165C2×C4×C13C2×D811yescharacteristic
166C2×C4×C13C2×D811yescharacteristic
167C2×C4×C13C2×D811yescharacteristic
168C2×C4×C13C2×D811yescharacteristic
169C2×C4×C13C22×D411yescharacteristic
170C22⋊D13—82no—
171C2×Dic13—41no—
172C2×Dic13—41no—
173C2×Dic13—41no—
174D52—41no—
175D52—41no—
176C4×D13—82no—
177Dic26—41no—
178Dic26—41no—
179C8×C13—21no—
180C8×C13—21no—
181C8×C13#13512yes—
182C8×C13C2×#4112yes—
183#532—21no—
184#529—261no—
185C2×SD32—132no—
186C2×D16—132no—
187C2×M32—132no—
188#500C2×D1311yescharacteristic
189#499—131no—
190#495—131no—
191#493C2×D1311yescharacteristic
192#488—261no—
193#486—21no—
194#467—131no—
195#466—21no—
196#466—131no—
197#466C2×D1312yes—
198#465—261no—
199C4×Q16—131no—
200C4×SD16—261no—
201C4×D8—21no—
202C4×D8—131no—
203C4×D8C2×D1312yes—
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—82no—
218C22×C13—82no—
219C22×C13—82no—
220C22×C13C22×D811yescharacteristic
221C2×D13—81no—
222C2×D13—81no—
223C2×D13—81no—
224C4×C13—21no—
225C4×C13—21no—
226C4×C13—21no—
227C4×C13—21no—
228C4×C13—82no—
229C4×C13#50912yes—
230C4×C13#53211yescharacteristic
231C4×C13C2×#13511yescharacteristic
232Dic13—81no—
233Dic13—81no—
234Dic13—81no—
235C2×#41—41no—
236C2×Q16—131no—
237C2×SD16—261no—
238C2×D8—21no—
239C2×D8—131no—
240C2×D8C22×D1312yes—
241C22×C8C22⋊D1311yescharacteristic
242C22×C8C22×D1311yescharacteristic
243C4⋊Q8—21no—
244#127—21no—
245#126—521no—
246#125—261no—
247#124—41no—
248#124—261no—
249#123—521no—
250C22⋊Q8—261no—
251#121—22no—
252#121—41no—
253#121—261no—
254C4×Q8—261no—
255C4×D4—22no—
256C4×D4—41no—
257C4×D4—261no—
258C4×D4—521no—
259#117—521no—
260C2×C42C22⋊D1311yescharacteristic
261SD32—264no—
262D16—264no—
263M32—264no—
264C2×C16—132no—
265C2×C16—132no—
266#107—21no—
267#107—131no—
268#107—131no—
269#107C22×D1312yes—
270#106—261no—
271#103—261no—
272#103—261no—
273#102—22no—
274#102—22no—
275#102—261no—
276#102—261no—
277C4×C8C22⋊D1311yescharacteristic
278C4×C8C22⋊D1311yescharacteristic
279C4×C8C22×D1311yescharacteristic
280C4×C8C22×D1311yescharacteristic
281C2×C13—41no—
282C2×C13—162no—
283C2×C13#316911yescharacteristic
284C2×C13C2×#50911yescharacteristic
285C2×C13#341411yescharacteristic
286D13—161no—
287#41—84no—
288C2×Q8—41no—
289C2×Q8—261no—
290C2×D4—22no—
291C2×D4—42no—
292C2×D4—41no—
293C2×D4—41no—
294C2×D4—261no—
295C2×D4—521no—
296C22×C4—42no—
297C22×C4—521no—
298C22×C4#610411yescharacteristic
299C22×C4#610411yescharacteristic
300C22×C4C2×C22⋊D1311yescharacteristic
301Q16—262no—
302SD16—522no—
303D8—22no—
304D8—22no—
305D8—42no—
306D8—262no—
307C2×C8—22no—
308C2×C8—22no—
309C2×C8C2×C22⋊D1311yescharacteristic
310C2×C8C2×C22⋊D1311yescharacteristic
311C2×C8C2×C22⋊D1311yescharacteristic
312C2×C8C23×D1311yescharacteristic
313C4⋊C4—22no—
314C4⋊C4—41no—
315C4⋊C4—261no—
316C4⋊C4—261no—
317C4⋊C4—521no—
318C4⋊C4—521no—
319C4⋊C4—521no—
320C4⋊C4—521no—
321C22⋊C4—42no—
322C22⋊C4—42no—
323C22⋊C4—521no—
324C22⋊C4—521no—
325C22⋊C4—521no—
326C22⋊C4—521no—
327C22⋊C4—521no—
328C42—521no—
329C42#610411yescharacteristic
330C42#610411yescharacteristic
331C42C2×C22⋊D1311yescharacteristic
332C42C2×C22⋊D1311yescharacteristic
333C16—134no—
334C16—262no—
335C13#3373711yescharacteristic, complemented, Sylow
336C23—42no—
337C23—521no—
338C23C2×#610411yescharacteristic
339Q8—82no—
340Q8—521no—
341Q8—521no—
342D4—42no—
343D4—42no—
344D4—82no—
345D4—82no—
346D4—84no—
347D4—521no—
348D4—521no—
349D4—1042no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—22no—
353C2×C4—41no—
354C2×C4—42no—
355C2×C4—84no—
356C2×C4—521no—
357C2×C4—521no—
358C2×C4—521no—
359C2×C4—1042no—
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—82no—
374C22—82no—
375C22—82no—
376C22—1041no—
377C22—1041no—
378C22—1041no—
379C22C22×#610411yescharacteristic
380C4—21no—
381C4—21no—
382C4—21no—
383C4—21no—
384C4—82no—
385C4—1041no—
386C4—1041no—
387C4—1041no—
388C4#1171880812yes—
389C4C2×#8820411yescharacteristic
390C4#1171953711yescharacteristic
391C2—41no—
392C2—162no—
393C2—2081no—
394C2#1312541111yescharacteristic
395C2C2×#1171880811yescharacteristic
396C2#1312797011yescharacteristic
subgroupG/H
centerC2×C4C2×#6104
commutator, cosocleC2×C8×C13C24
FrattiniC2×C8C23×D13
FittingC13×#3169C2
socleC22×C13C22×D8
hypercenter#3169D13
hypocenterC13#33737
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×C8 ◁ #3169

Complements

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

NH ≅ G/Ntype
1. #13125406C2semidirect
2. #13117119C2semidirect
3. #13117100C2semidirect
4. #13117077C2semidirect
5. #13117075C2semidirect
6. #13116947C2semidirect
7. #13116937C2semidirect
8. C4×#88067C2semidirect
9. C4×#88066C2semidirect
10. C4×#88052C2semidirect
11. C13×#3169C2semidirect
137. #6090#41semidirect
138. #3169D13semidirect
335. C13#33737semidirect

Maximal subgroups

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

subgroupindex
#131254062
#131171192
#131171002
#131170772
#131170752
#131169472
#131169372
C4×#880672
C4×#880662
C4×#880522
C13×#31692
#3373713