Finite Group Databasebeta

← #15759667

Subgroups — #15759667

Order 3328.

480 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13125964C211yesmaximal, characteristic
2#13115668C211yesmaximal, characteristic
3#13113521C211yesmaximal, characteristic, complemented
4#13113395C211yesmaximal, characteristic
5#13112694C211yesmaximal, characteristic, complemented
6#13112665C211yesmaximal, characteristic, complemented
7C13×#2331C211yesmaximal, characteristic, complemented
8C2×C13×C4⋊Q8C2211yescharacteristic
9#11719182C2211yescharacteristic
10C13×#391—22no—
11C13×#389—21no—
12C13×#387—22no—
13C13×#382C2211yescharacteristic
14C4×C13×C4⋊C4—21no—
15C13×#376C2211yescharacteristic
16#11718749C412yescomplemented
17#11718745—22no—
18#11718740C412yescomplemented
19#11718629—22no—
20C2×#88045—21no—
21C2×#88045—21no—
22#11718586C2211yescharacteristic
23#11718586C2211yescharacteristic
24#11718585C2211yescharacteristic
25#11718139—22no—
26#11718043—22no—
27C22×Q8×C13—21no—
28C2×#6127—21no—
29C13×C4⋊Q8—21no—
30C13×C4⋊Q8—21no—
31C13×C4⋊Q8C2×C412yes—
32C13×C4⋊Q8D412yes—
33C2×C13×C4⋊C4—21no—
34C2×C13×C4⋊C4—21no—
35C2×C13×C4⋊C4—22no—
36C2×C13×C4⋊C4D412yes—
37C2×C42×C13—22no—
38C2×C42×C13D411yescharacteristic
39C2×C42×C13D411yescharacteristic
40C2×C42×C13C2311yescharacteristic
41#88184—21no—
42#88184—21no—
43C2×#6099—21no—
44#88129—21no—
45#88128C2×C411yescharacteristic
46C4×D52—21no—
47C4×D52—21no—
48#88123C2×C411yescharacteristic
49C13×#95—22no—
50C13×#95—22no—
51C13×#95—21no—
52C13×#95—21no—
53C13×#95—21no—
54C13×#95D412yes—
55C22⋊#1055—21no—
56C22⋊#1055—21no—
57#88049—24no—
58#88048—24no—
59#88045—42no—
60#88045—42no—
61C4⋊#1055—21no—
62C4⋊#1055—21no—
63C4⋊#1055—21no—
64C4⋊#1055—21no—
65C4×#1055—21no—
66C4×#1055C2×C412yes—
67#9302—131nomaximal, Sylow
68C2×Q8×C13—22no—
69C2×Q8×C13—22no—
70C2×Q8×C13—82no—
71C22×C4×C13—21no—
72C22×C4×C13—22no—
73C22×C4×C13—21no—
74C22×C4×C13—22no—
75C22×C4×C13C2×D411yescharacteristic
76C22×C4×C13C2×D411yescharacteristic
77C22×C4×C13C2×D411yescharacteristic
78C2×C22⋊D13—41no—
79#6127—41no—
80#6127—41no—
81#6127—41no—
82#6127—41no—
83C2×D52—21no—
84C2×D52—21no—
85C2×D52—21no—
86C2×C4×D13—41no—
87C2×Dic26—21no—
88C13×C4⋊C4—22no—
89C13×C4⋊C4—22no—
90C13×C4⋊C4—22no—
91C13×C4⋊C4—41no—
92C13×C4⋊C4—41no—
93C13×C4⋊C4—82no—
94C13×C4⋊C4C22⋊C414yes—
95C42×C13—21no—
96C42×C13—21no—
97C42×C13—21no—
98C42×C13—82no—
99C42×C13SD1612yes—
100C42×C13C22×C411yescharacteristic
101C42×C13C2×D411yescharacteristic
102C42×C13#4111yescharacteristic
103C42×C13#4111yescharacteristic
104#6103—41no—
105#6103—41no—
106C4⋊Dic13—21no—
107C4⋊Dic13—21no—
108#6099—41no—
109#6099—41no—
110C2×#1055—22no—
111C2×#1055—41no—
112C2×#1055—41no—
113#3227—131no—
114#2331D1311yescharacteristic, complemented
115#1963—131no—
116#1549—131no—
117#1517—131no—
118#1286—131no—
119#1274—131no—
120C23×C13#12011yescharacteristic
121C22×D13—41no—
122Q8×C13—82no—
123Q8×C13—82no—
124C2×C4×C13—24no—
125C2×C4×C13—22no—
126C2×C4×C13—41no—
127C2×C4×C13—41no—
128C2×C4×C13—41no—
129C2×C4×C13—42no—
130C2×C4×C13—42no—
131C2×C4×C13—41no—
132C2×C4×C13—42no—
133C2×C4×C13—41no—
134C2×C4×C13—41no—
135C2×C4×C13—42no—
136C2×C4×C13—41no—
137C2×C4×C13—42no—
138C2×C4×C13C2×C22⋊C411yescharacteristic
139C2×C4×C13C4×D411yescharacteristic
140C2×C4×C13C4×D411yescharacteristic
141C2×C4×C13#12111yescharacteristic
142C2×C4×C13#12111yescharacteristic
143C2×C4×C13#12311yescharacteristic
144C2×C4×C13C2×SD1611yescharacteristic
145C2×C4×C13#13511yescharacteristic
146C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
147C2×C4×C13#13711yescharacteristic
148C22⋊D13—81no—
149C22⋊D13—81no—
150C2×Dic13—41no—
151D52—42no—
152D52—41no—
153D52—41no—
154D52—81no—
155C4×D13—81no—
156C4×D13—81no—
157Dic26—41no—
158Dic26—41no—
159#1055—42no—
160#1055—81no—
161#1055—81no—
162#532—131no—
163C2×C4⋊Q8C2×D1311yescharacteristic
164#498—132no—
165#486—132no—
166#481—262no—
167#476—262no—
168#431—131no—
169#431—131no—
170#423—131no—
171C2×#104—261no—
172C2×#104—261no—
173#391—22no—
174#389—21no—
175#387—22no—
176#382C2×D1311yescharacteristic
177C4×C4⋊C4—21no—
178#376C2×D1311yescharacteristic
179#332—262no—
180#327—262no—
181C22×C13—21no—
182C22×C13—21no—
183C22×C13#38611yescharacteristic
184C22×C13#44811yescharacteristic
185C22×C13#44911yescharacteristic
186C2×D13—81no—
187C2×D13—81no—
188C2×D13—81no—
189C4×C13—21no—
190C4×C13—21no—
191C4×C13—21no—
192C4×C13—21no—
193C4×C13—42no—
194C4×C13—44no—
195C4×C13—82no—
196C4×C13—81no—
197C4×C13C4×SD1611yescharacteristic
198C4×C13#44011yescharacteristic
199C4×C13#46011yescharacteristic
200C4×C13#46411yescharacteristic
201Dic13—81no—
202C2×#41—261no—
203C22×Q8—21no—
204C2×M16—261no—
205C4⋊Q8—21no—
206C4⋊Q8—21no—
207C4⋊Q8—131no—
208C4⋊Q8C4×D1312yes—
209C4⋊Q8D5212yes—
210#127—131no—
211#124—261no—
212#121—261no—
213#121—261no—
214C4×D4—261no—
215C4×D4—261no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—22no—
219C2×C4⋊C4C22⋊D1312yes—
220C2×C42—22no—
221C2×C42C22⋊D1311yescharacteristic
222C2×C42C22⋊D1311yescharacteristic
223C2×C42C22×D1311yescharacteristic
224#106—264no—
225C4⋊C8—261no—
226C4⋊C8—261no—
227C4⋊C8—261no—
228C4⋊C8—261no—
229#104—522no—
230#104—522no—
231#102—264no—
232C22⋊C8—261no—
233C22⋊C8—261no—
234C4×C8—132no—
235C4×C8—261no—
236#95—22no—
237#95—22no—
238#95—21no—
239#95—21no—
240#95—21no—
241#95C22⋊D1312yes—
242C2×C13—21no—
243C2×C13—21no—
244C2×C13#188011yescharacteristic
245C2×C13#190411yescharacteristic
246C2×C13#191211yescharacteristic
247D13—161no—
248#41—521no—
249#41—521no—
250#41—521no—
251#41—521no—
252C2×Q8—22no—
253C2×Q8—22no—
254C2×Q8—82no—
255C2×Q8—261no—
256C2×D4—261no—
257C2×D4—261no—
258C2×D4—261no—
259C2×D4—521no—
260C22×C4—21no—
261C22×C4—22no—
262C22×C4—21no—
263C22×C4—22no—
264C22×C4—521no—
265C22×C4C2×C22⋊D1311yescharacteristic
266C22×C4C2×C22⋊D1311yescharacteristic
267C22×C4C2×C22⋊D1311yescharacteristic
268M16—521no—
269M16—521no—
270C2×C8—262no—
271C2×C8—521no—
272C2×C8—521no—
273C4⋊C4—22no—
274C4⋊C4—22no—
275C4⋊C4—22no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C4⋊C4—82no—
279C4⋊C4—261no—
280C4⋊C4—261no—
281C4⋊C4#610314yes—
282C22⋊C4—521no—
283C22⋊C4—521no—
284C42—21no—
285C42—21no—
286C42—21no—
287C42—82no—
288C42#610612yes—
289C42C2×C4×D1311yescharacteristic
290C42C2×D5211yescharacteristic
291C42#612711yescharacteristic
292C42#612711yescharacteristic
293C13#930211yescharacteristic, complemented, Sylow
294C23—521no—
295C23#8820711yescharacteristic
296Q8—82no—
297Q8—82no—
298Q8—521no—
299Q8—521no—
300D4—522no—
301D4—521no—
302D4—521no—
303D4—1041no—
304D4—1041no—
305D4—1041no—
306C2×C4—24no—
307C2×C4—22no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—41no—
314C2×C4—42no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—42no—
318C2×C4—41no—
319C2×C4—42no—
320C2×C4—521no—
321C2×C4—1041no—
322C2×C4—1041no—
323C2×C4C2×#610311yescharacteristic
324C2×C4C4×C22⋊D1311yescharacteristic
325C2×C4C4×C22⋊D1311yescharacteristic
326C2×C4#8818311yescharacteristic
327C2×C4#8818411yescharacteristic
328C2×C4#8818411yescharacteristic
329C2×C4C2×#610611yescharacteristic
330C2×C4#8819611yescharacteristic
331C2×C4#8820311yescharacteristic
332C2×C4#8820411yescharacteristic
333C8—522no—
334C8—1041no—
335C8—1041no—
336C22—21no—
337C22—21no—
338C22—1041no—
339C22—1041no—
340C22—1041no—
341C22#1171887411yescharacteristic
342C22#1171888811yescharacteristic
343C22#1171889911yescharacteristic
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—42no—
349C4—44no—
350C4—82no—
351C4—81no—
352C4—1041no—
353C4C4×#610611yescharacteristic
354C4#1171868711yescharacteristic
355C4#1171868811yescharacteristic
356C4#1171868911yescharacteristic
357C2—21no—
358C2—21no—
359C2—2081no—
360C2#1311519111yescharacteristic
361C2#1311532311yescharacteristic
362C2#1311537311yescharacteristic
subgroupG/H
centerC22#11718874
commutatorC42×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#2331C2
socleC22×C13#386
prime radical#11719182C22
cosocleC2×C42×C13C23
hypercenter#2331D13
hypocenterC13#9302
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2331

Complements

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

NH ≅ G/Ntype
3. #13113521C2semidirect
5. #13112694C2semidirect
6. #13112665C2semidirect
7. C13×#2331C2semidirect
16. #11718749C4semidirect
18. #11718740C4semidirect
114. #2331D13semidirect
293. C13#9302semidirect

Maximal subgroups

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

subgroupindex
#131259642
#131156682
#131135212
#131133952
#131126942
#131126652
C13×#23312
#930213