Finite Group Databasebeta

← #15753963

Subgroups — #15753963

Order 3328.

392 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13114587C211yesmaximal, characteristic, complemented
2#13113424C211yesmaximal, characteristic
3#13113322C211yesmaximal, characteristic
4#13113125C211yesmaximal, characteristic, complemented
5#13112734C211yesmaximal, characteristic, complemented
6#13112728C211yesmaximal, characteristic, complemented
7C13×#2966C211yesmaximal, characteristic
8C13×#529C2211yescharacteristic
9C13×#446C411yescharacteristic, complemented
10C8×Q8×C13C411yescharacteristic, complemented
11C13×#436C411yescharacteristic, complemented
12C13×#435—21no—
13C8×D4×C13—21no—
14C8×D4×C13C411yescharacteristic, complemented
15C13×#433—21no—
16C13×#432C2211yescharacteristic
17C13×#405—21no—
18C2×C4×C8×C13C2211yescharacteristic
19#11718593C2211yescharacteristic
20#11718586C2211yescharacteristic
21C4×#6099C2211yescharacteristic
22C2×#88043C2211yescharacteristic
23#11718142—21no—
24#11718142—21no—
25#11718135C412yescomplemented
26#11718132C412yescomplemented
27#11718130C412yes—
28#11718129C412yes—
29#11718047—21no—
30#11718046—21no—
31C2×C13×M16—21no—
32C22×C8×C13—21no—
33C22×C8×C13D411yescharacteristic
34C22×C8×C13D411yescharacteristic
35C13×#126—21no—
36C13×#125C2×C411yescharacteristic
37C13×#124C2×C411yescharacteristic
38C13×#123—21no—
39C13×C22⋊Q8C2×C411yescharacteristic
40C13×#121C2×C411yescharacteristic
41C4×Q8×C13C2×C411yescharacteristic
42C4×D4×C13—21no—
43C4×D4×C13C2×C411yescharacteristic
44C13×#117—21no—
45C2×C42×C13C2311yescharacteristic
46C2×C4×Dic13—21no—
47C2×#6099—21no—
48C22×#1055—21no—
49C13×C4⋊C8—21no—
50C13×C4⋊C8—21no—
51C13×C4⋊C8C2×C411yescharacteristic
52C13×C4⋊C8C2×C411yescharacteristic
53C13×C22⋊C8—21no—
54C13×C22⋊C8—21no—
55C13×C22⋊C8—21no—
56C13×#97—21no—
57C13×#97—21no—
58C4×C8×C13—21no—
59C4×C8×C13C2×C411yescharacteristic
60C4×C8×C13C2×C411yescharacteristic
61C4×C8×C13D411yescharacteristic
62C4×C8×C13D411yescharacteristic
63#88071—21no—
64#88071C2×C412yes—
65C22⋊#1055C2×C412yes—
66C4⋊#1055—21no—
67#88043—21no—
68#88043C2×C412yes—
69#88043C2×C412yes—
70C4×#1055—21no—
71C4×#1055—21no—
72#8248—131nomaximal, Sylow
73C2×Q8×C13C4211yescharacteristic
74C2×D4×C13—21no—
75C2×D4×C13C4211yescharacteristic
76C22×C4×C13—21no—
77C22×C4×C13C22×C411yescharacteristic
78C22×C4×C13C2×D411yescharacteristic
79C22×C4×C13#4111yescharacteristic
80C22×Dic13—22no—
81C13×M16—42no—
82C2×C8×C13—21no—
83C2×C8×C13—21no—
84C2×C8×C13—41no—
85C2×C8×C13—41no—
86C2×C8×C13—42no—
87C2×C8×C13C22⋊C411yescharacteristic
88C2×C8×C13C22⋊C411yescharacteristic
89C2×C8×C13C22⋊C411yescharacteristic
90C2×C8×C13C22⋊C411yescharacteristic
91C13×C4⋊C4—21no—
92C13×C4⋊C4—21no—
93C13×C4⋊C4—21no—
94C13×C4⋊C4—21no—
95C13×C4⋊C4C4211yescharacteristic
96C13×C4⋊C4C4211yescharacteristic
97C13×C22⋊C4—21no—
98C13×C22⋊C4—21no—
99C13×C22⋊C4—21no—
100C13×C22⋊C4—21no—
101C13×C22⋊C4—21no—
102C42×C13—21no—
103C42×C13C22×C411yescharacteristic
104C42×C13C22×C411yescharacteristic
105C42×C13C2×D411yescharacteristic
106C42×C13#4111yescharacteristic
107C4×Dic13—41no—
108C4×Dic13—41no—
109#6099—42no—
110C2×#1055—22no—
111C2×#1055—22no—
112C2×#1055—22no—
113C2×#1055—41no—
114C2×#1055—41no—
115#2966D1311yescharacteristic
116#1746—131no—
117#1524—131no—
118#1500—131no—
119#1451—131no—
120#1302—131no—
121#1300—131no—
122C23×C13—21no—
123C23×C13C4×D411yescharacteristic
124Q8×C13—41no—
125D4×C13—41no—
126D4×C13—42no—
127C2×C4×C13—22no—
128C2×C4×C13—21no—
129C2×C4×C13—21no—
130C2×C4×C13—21no—
131C2×C4×C13—21no—
132C2×C4×C13—21no—
133C2×C4×C13—41no—
134C2×C4×C13—41no—
135C2×C4×C13—41no—
136C2×C4×C13C2×C4211yescharacteristic
137C2×C4×C13C2×C22⋊C411yescharacteristic
138C2×C4×C13#11711yescharacteristic
139C2×C4×C13C4×D411yescharacteristic
140C2×C4×C13C4×D411yescharacteristic
141C2×C4×C13C4×D411yescharacteristic
142C2×Dic13—42no—
143C2×Dic13—42no—
144C2×Dic13—42no—
145C8×C13—21no—
146C8×C13—21no—
147C8×C13—21no—
148C8×C13—21no—
149C8×C13—41no—
150C8×C13—41no—
151#1055—42no—
152#1055—42no—
153#1055—42no—
154#529C2×D1311yescharacteristic
155#446Dic1311yescharacteristic, complemented
156C8×Q8Dic1311yescharacteristic, complemented
157#436Dic1311yescharacteristic, complemented
158#435—21no—
159C8×D4—21no—
160C8×D4Dic1311yescharacteristic, complemented
161#433—21no—
162#432C2×D1311yescharacteristic
163#431—131no—
164#405—21no—
165C4×M16—131no—
166C2×#97—131no—
167C2×C4×C8C2×D1311yescharacteristic
168#376—131no—
169#336—261no—
170#336—261no—
171#330—132no—
172#329—132no—
173#328—132no—
174#327—132no—
175#322—261no—
176#322—261no—
177C22×C13—21no—
178C22×C13—21no—
179C22×C13—41no—
180C22×C13—41no—
181C22×C13—41no—
182C22×C13C4×C22⋊C411yescharacteristic
183C22×C13#44412yes—
184C4×C13—21no—
185C4×C13—21no—
186C4×C13—21no—
187C4×C13—21no—
188C4×C13—21no—
189C4×C13—41no—
190C4×C13—41no—
191C4×C13—41no—
192C4×C13#42111yescharacteristic
193C4×C13#42111yescharacteristic
194Dic13—82no—
195C2×M16—21no—
196C2×M16—261no—
197C22×C8—21no—
198C22×C8—261no—
199C22×C8C22⋊D1311yescharacteristic
200C22×C8C22⋊D1311yescharacteristic
201#126—21no—
202#125C4×D1311yescharacteristic
203#124C4×D1311yescharacteristic
204#123—21no—
205C22⋊Q8C4×D1311yescharacteristic
206#121C4×D1311yescharacteristic
207C4×Q8C2×Dic1311yescharacteristic
208C4×D4—21no—
209C4×D4C2×Dic1311yescharacteristic
210#117—21no—
211C2×C42—261no—
212C2×C42C22×D1311yescharacteristic
213C4⋊C8—21no—
214C4⋊C8—21no—
215C4⋊C8—261no—
216C4⋊C8C2×Dic1311yescharacteristic
217C4⋊C8C2×Dic1311yescharacteristic
218C22⋊C8—21no—
219C22⋊C8—21no—
220C22⋊C8—21no—
221C22⋊C8—132no—
222#97—21no—
223#97—21no—
224#97—132no—
225#97—132no—
226#97—261no—
227C4×C8—21no—
228C4×C8—261no—
229C4×C8—261no—
230C4×C8C2×Dic1311yescharacteristic
231C4×C8C2×Dic1311yescharacteristic
232C4×C8C22⋊D1311yescharacteristic
233C4×C8C22⋊D1311yescharacteristic
234#95—132no—
235#95—261no—
236C2×C13—22no—
237C2×C13—81no—
238C2×C13#175711yescharacteristic
239C2×C13#175911yescharacteristic
240C2×C13#176511yescharacteristic
241C2×Q8C4×Dic1311yescharacteristic
242C2×D4—21no—
243C2×D4C4×Dic1311yescharacteristic
244C22×C4—21no—
245C22×C4—262no—
246C22×C4C2×C4×D1311yescharacteristic
247C22×C4#612711yescharacteristic
248C22×C4C2×C22⋊D1311yescharacteristic
249M16—42no—
250M16—522no—
251C2×C8—21no—
252C2×C8—21no—
253C2×C8—41no—
254C2×C8—41no—
255C2×C8—42no—
256C2×C8—262no—
257C2×C8—262no—
258C2×C8—262no—
259C2×C8—521no—
260C2×C8—521no—
261C2×C8C22⋊Dic1311yescharacteristic
262C2×C8C22⋊Dic1311yescharacteristic
263C2×C8C22⋊Dic1311yescharacteristic
264C2×C8C22⋊Dic1311yescharacteristic
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4C4×Dic1311yescharacteristic
270C4⋊C4C4×Dic1311yescharacteristic
271C22⋊C4—21no—
272C22⋊C4—21no—
273C22⋊C4—21no—
274C22⋊C4—21no—
275C22⋊C4—21no—
276C42—21no—
277C42—521no—
278C42—521no—
279C42C2×C4×D1311yescharacteristic
280C42#612711yescharacteristic
281C42C22×Dic1311yescharacteristic
282C42C2×C22⋊D1311yescharacteristic
283C13#824811yescharacteristic, complemented, Sylow
284C23—21no—
285C23C4×C22⋊D1311yescharacteristic
286Q8—41no—
287D4—41no—
288D4—42no—
289C2×C4—22no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—522no—
299C2×C4—522no—
300C2×C4—522no—
301C2×C4C2×C4×Dic1311yescharacteristic
302C2×C4#8818011yescharacteristic
303C2×C4C4×C22⋊D1311yescharacteristic
304C2×C4C4×C22⋊D1311yescharacteristic
305C2×C4C4×C22⋊D1311yescharacteristic
306C2×C4C2×C22⋊Dic1311yescharacteristic
307C8—21no—
308C8—21no—
309C8—21no—
310C8—21no—
311C8—41no—
312C8—41no—
313C8—522no—
314C8—522no—
315C8—522no—
316C22—21no—
317C22—21no—
318C22—41no—
319C22—41no—
320C22—41no—
321C22#1171880612yes—
322C22C4×C22⋊Dic1311yescharacteristic
323C4—21no—
324C4—21no—
325C4—21no—
326C4—21no—
327C4—21no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—1042no—
332C4#1171889711yescharacteristic
333C4#1171889711yescharacteristic
334C2—22no—
335C2—81no—
336C2#1311463611yescharacteristic
337C2#1311464611yescharacteristic
338C2#1311467811yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊Dic13
commutatorC2×C4×C13C2×C42
FrattiniC2×C42C22×D13
FittingC13×#2966C2
socleC22×C13C4×C22⋊C4
prime radicalC13×#121C2×C4
cosocleC2×C42×C13C23
hypercenter#2966D13
hypocenterC13#8248
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C4×C8 ◁ #2966

Complements

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

NH ≅ G/Ntype
1. #13114587C2semidirect
4. #13113125C2semidirect
5. #13112734C2semidirect
6. #13112728C2semidirect
9. C13×#446C4semidirect
10. C8×Q8×C13C4semidirect
11. C13×#436C4semidirect
14. C8×D4×C13C4semidirect
25. #11718135C4semidirect
26. #11718132C4semidirect
155. #446Dic13semidirect
156. C8×Q8Dic13semidirect
157. #436Dic13semidirect
160. C8×D4Dic13semidirect
283. C13#8248semidirect

Maximal subgroups

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

subgroupindex
#131145872
#131134242
#131133222
#131131252
#131127342
#131127282
C13×#29662
#824813