Finite Group Databasebeta

← #15759669

Subgroups — #15759669

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#13117585C211yesmaximal, characteristic, complemented
2#13115669C211yesmaximal, characteristic
3#13113521C211yesmaximal, characteristic, complemented
4#13113396C211yesmaximal, characteristic
5#13112695C211yesmaximal, characteristic, complemented
6#13112664C211yesmaximal, characteristic, complemented
7C13×#3227C211yesmaximal, characteristic
8C13×#532C2211yescharacteristic
9C2×C13×C4⋊Q8C2211yescharacteristic
10C13×#498C412yescomplemented
11C13×#486C412yescomplemented
12C13×#481—22no—
13C13×#476—22no—
14C13×#431C2211yescharacteristic
15C2×#88077—21no—
16C2×#88077—21no—
17#11718891—22no—
18#11718646—21no—
19#11718642—22no—
20C4⋊C4×Dic13—21no—
21#11718597C2211yescharacteristic
22#11718593C2211yescharacteristic
23#11718586C2211yescharacteristic
24#11718585C2211yescharacteristic
25#11718139—22no—
26#11718129—22no—
27C2×C13×#41—21no—
28C22×Q8×C13—21no—
29C13×C4⋊Q8—21no—
30C13×C4⋊Q8—21no—
31C13×C4⋊Q8C2×C411yescharacteristic
32C13×C4⋊Q8C2×C412yes—
33C13×C4⋊Q8D412yes—
34C13×#127C2×C411yescharacteristic
35C13×#124—21no—
36C13×#121—21no—
37C13×#121—21no—
38C4×D4×C13—21no—
39C4×D4×C13—21no—
40C2×C13×C4⋊C4—21no—
41C2×C13×C4⋊C4D412yes—
42C2×C42×C13C2311yescharacteristic
43C2×C4⋊Dic13—21no—
44C2×C4⋊Dic13—22no—
45C2×C4×Dic13—22no—
46C2×C4×Dic13D411yescharacteristic
47C2×C4×Dic13D411yescharacteristic
48C2×#6099—21no—
49C13×#106—24no—
50C13×C4⋊C8—21no—
51C13×#102—24no—
52C13×C22⋊C8—21no—
53C4×C8×C13C2×C412yes—
54#88077—42no—
55#88077—42no—
56#88071—22no—
57#88071—22no—
58#88071—21no—
59#88071—21no—
60#88071—21no—
61#88071D412yes—
62C22⋊#1055—21no—
63C4⋊#1055—21no—
64C4⋊#1055—21no—
65C4⋊#1055—21no—
66C4×#1055—21no—
67#9302—131nomaximal, Sylow
68C13×#41—41no—
69C13×#41—41no—
70C13×#41—41no—
71C13×#41—41no—
72C2×Q8×C13—22no—
73C2×Q8×C13—22no—
74C2×Q8×C13—21no—
75C2×Q8×C13—82no—
76C2×D4×C13—21no—
77C2×D4×C13—21no—
78C2×D4×C13—21no—
79C2×D4×C13—41no—
80C22×C4×C13—22no—
81C22×C4×C13—41no—
82C22×C4×C13C2×D411yescharacteristic
83C22×C4×C13C2×D411yescharacteristic
84C22×C4×C13C2×D411yescharacteristic
85C22×Dic13—21no—
86C22×Dic13—21no—
87C22×Dic13—22no—
88C2×C8×C13—22no—
89C13×C4⋊C4—22no—
90C13×C4⋊C4—22no—
91C13×C4⋊C4—22no—
92C13×C4⋊C4—21no—
93C13×C4⋊C4—21no—
94C13×C4⋊C4C22⋊C414yes—
95C13×C22⋊C4—41no—
96C13×C22⋊C4—41no—
97C42×C13C22×C411yescharacteristic
98C42×C13C2×D411yescharacteristic
99C42×C13#4111yescharacteristic
100C42×C13#4111yescharacteristic
101C4⋊Dic13—41no—
102C4⋊Dic13—41no—
103C4⋊Dic13—82no—
104C4×Dic13—21no—
105C4×Dic13—21no—
106C4×Dic13—21no—
107C4×Dic13—82no—
108C4×Dic13SD1612yes—
109#6099—41no—
110#6099—41no—
111C2×#1055—41no—
112C2×#1055—41no—
113#3227D1311yescharacteristic
114#2331—131no—
115#1963—131no—
116#1549—131no—
117#1517—131no—
118#1286—131no—
119#1274—131no—
120C23×C13—41no—
121C23×C13#12011yescharacteristic
122Q8×C13—41no—
123Q8×C13—41no—
124Q8×C13—82no—
125Q8×C13—82no—
126D4×C13—42no—
127D4×C13—41no—
128D4×C13—41no—
129D4×C13—81no—
130D4×C13—81no—
131D4×C13—81no—
132C2×C4×C13—24no—
133C2×C4×C13—41no—
134C2×C4×C13—41no—
135C2×C4×C13—42no—
136C2×C4×C13—42no—
137C2×C4×C13—41no—
138C2×C4×C13—81no—
139C2×C4×C13—81no—
140C2×C4×C13C2×C22⋊C411yescharacteristic
141C2×C4×C13C4×D411yescharacteristic
142C2×C4×C13C4×D411yescharacteristic
143C2×C4×C13#12111yescharacteristic
144C2×C4×C13#12111yescharacteristic
145C2×C4×C13#12311yescharacteristic
146C2×C4×C13C2×SD1611yescharacteristic
147C2×C4×C13#13511yescharacteristic
148C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
149C2×C4×C13#13711yescharacteristic
150C2×Dic13—22no—
151C2×Dic13—41no—
152C2×Dic13—41no—
153C2×Dic13—42no—
154C2×Dic13—41no—
155C2×Dic13—41no—
156C2×Dic13—42no—
157C2×Dic13—41no—
158C2×Dic13—42no—
159C8×C13—42no—
160#1055—81no—
161#1055—81no—
162#532C2×D1311yescharacteristic
163C2×C4⋊Q8C2×D1311yescharacteristic
164#498Dic1312yescomplemented
165#486Dic1312yescomplemented
166#481—22no—
167#476—22no—
168#431—131no—
169#431C2×D1311yescharacteristic
170#423—131no—
171C2×#104—261no—
172C2×#104—261no—
173#391—262no—
174#389—261no—
175#387—262no—
176#382—131no—
177C4×C4⋊C4—261no—
178#376—131no—
179#332—262no—
180#327—262no—
181C22×C13—21no—
182C22×C13—21no—
183C22×C13—81no—
184C22×C13—81no—
185C22×C13—81no—
186C22×C13#38611yescharacteristic
187C22×C13#44811yescharacteristic
188C22×C13#44911yescharacteristic
189C4×C13—21no—
190C4×C13—21no—
191C4×C13—21no—
192C4×C13—21no—
193C4×C13—44no—
194C4×C13—81no—
195C4×C13C4×SD1611yescharacteristic
196C4×C13#44011yescharacteristic
197C4×C13#46011yescharacteristic
198C4×C13#46411yescharacteristic
199Dic13—42no—
200Dic13—82no—
201Dic13—81no—
202C2×#41—21no—
203C22×Q8—21no—
204C2×M16—261no—
205C4⋊Q8—21no—
206C4⋊Q8—21no—
207C4⋊Q8C2×Dic1311yescharacteristic
208C4⋊Q8C2×Dic1312yes—
209C4⋊Q8C22⋊D1312yes—
210#127C2×Dic1311yescharacteristic
211#124—21no—
212#121—21no—
213#121—21no—
214C4×D4—21no—
215C4×D4—21no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4—261no—
218C2×C4⋊C4—262no—
219C2×C4⋊C4C22⋊D1312yes—
220C2×C42—131no—
221C2×C42—131no—
222C2×C42—262no—
223C2×C42C22×D1311yescharacteristic
224#106—24no—
225C4⋊C8—21no—
226C4⋊C8—261no—
227C4⋊C8—261no—
228C4⋊C8—261no—
229#104—522no—
230#104—522no—
231#102—24no—
232C22⋊C8—21no—
233C22⋊C8—261no—
234C4×C8—261no—
235C4×C8C2×Dic1312yes—
236#95—132no—
237#95—262no—
238#95—262no—
239#95—261no—
240#95—261no—
241#95—261no—
242C2×C13—21no—
243C2×C13—21no—
244C2×C13—161no—
245C2×C13#188011yescharacteristic
246C2×C13#190411yescharacteristic
247C2×C13#191211yescharacteristic
248#41—41no—
249#41—41no—
250#41—41no—
251#41—41no—
252C2×Q8—22no—
253C2×Q8—22no—
254C2×Q8—21no—
255C2×Q8—82no—
256C2×D4—21no—
257C2×D4—21no—
258C2×D4—21no—
259C2×D4—41no—
260C22×C4—22no—
261C22×C4—41no—
262C22×C4—261no—
263C22×C4—262no—
264C22×C4—261no—
265C22×C4D4×D1311yescharacteristic
266C22×C4D4×D1311yescharacteristic
267C22×C4C2×C22⋊D1311yescharacteristic
268M16—521no—
269M16—521no—
270C2×C8—22no—
271C2×C8—521no—
272C2×C8—521no—
273C4⋊C4—22no—
274C4⋊C4—22no—
275C4⋊C4—22no—
276C4⋊C4—21no—
277C4⋊C4—21no—
278C4⋊C4—521no—
279C4⋊C4—521no—
280C4⋊C4—1042no—
281C4⋊C4C22⋊Dic1314yes—
282C22⋊C4—41no—
283C22⋊C4—41no—
284C42—132no—
285C42—261no—
286C42—261no—
287C42—261no—
288C42—1042no—
289C42#612911yescharacteristic
290C42#612911yescharacteristic
291C42C22×Dic1311yescharacteristic
292C42C2×C22⋊D1311yescharacteristic
293C13#930211yescharacteristic, complemented, Sylow
294C23—41no—
295C23#8819111yescharacteristic
296Q8—41no—
297Q8—41no—
298Q8—82no—
299Q8—82no—
300D4—42no—
301D4—41no—
302D4—41no—
303D4—81no—
304D4—81no—
305D4—81no—
306C2×C4—24no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—42no—
310C2×C4—42no—
311C2×C4—41no—
312C2×C4—81no—
313C2×C4—81no—
314C2×C4—262no—
315C2×C4—521no—
316C2×C4—521no—
317C2×C4—522no—
318C2×C4—521no—
319C2×C4—522no—
320C2×C4—521no—
321C2×C4—521no—
322C2×C4—522no—
323C2×C4SD16×D1311yescharacteristic
324C2×C4#8816811yescharacteristic
325C2×C4#8816911yescharacteristic
326C2×C4#8817011yescharacteristic
327C2×C4D4×Dic1311yescharacteristic
328C2×C4D4×Dic1311yescharacteristic
329C2×C4#8818911yescharacteristic
330C2×C4#8819311yescharacteristic
331C2×C4#8819311yescharacteristic
332C2×C4C2×C22⋊Dic1311yescharacteristic
333C8—42no—
334C8—1041no—
335C8—1041no—
336C22—21no—
337C22—21no—
338C22—81no—
339C22—81no—
340C22—81no—
341C22#1171883111yescharacteristic
342C22#1171883311yescharacteristic
343C22#1171888111yescharacteristic
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—44no—
349C4—81no—
350C4—522no—
351C4—1042no—
352C4—1041no—
353C4SD16×Dic1311yescharacteristic
354C4#1171882411yescharacteristic
355C4#1171882511yescharacteristic
356C4#1171882711yescharacteristic
357C2—21no—
358C2—21no—
359C2—161no—
360C2#1311519311yescharacteristic
361C2#1311532511yescharacteristic
362C2#1311537411yescharacteristic
subgroupG/H
centerC22#11718881
commutatorC42×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#3227C2
socleC22×C13#386
prime radicalC13×#532C22
cosocleC2×C42×C13C23
hypercenter#3227D13
hypocenterC13#9302
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3227

Complements

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

NH ≅ G/Ntype
1. #13117585C2semidirect
3. #13113521C2semidirect
5. #13112695C2semidirect
6. #13112664C2semidirect
10. C13×#498C4semidirect
11. C13×#486C4semidirect
164. #498Dic13semidirect
165. #486Dic13semidirect
293. C13#9302semidirect

Maximal subgroups

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

subgroupindex
#131175852
#131156692
#131135212
#131133962
#131126952
#131126642
C13×#32272
#930213