Finite Group Databasebeta

← #13128661

Subgroups — #13128661

Order 1664.

988 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#557C211yesmaximal, characteristic, complemented
2#11719435C213yesmaximal, complemented
3#11719434C213yesmaximal, complemented
4#11719395C213yesmaximal, complemented
5#11719395C213yesmaximal, complemented
6#11719394C213yesmaximal, complemented
7D13×#125C213yesmaximal, complemented
8#11719284C213yesmaximal, complemented
9#11719283C213yesmaximal, complemented
10#11719279C211yesmaximal, characteristic
11#11719279C211yesmaximal, characteristic
12C4×#6131C211yesmaximal, characteristic
13#11719275C211yesmaximal, characteristic, complemented
14#11719274C211yesmaximal, characteristic, complemented
15#11719274C211yesmaximal, characteristic, complemented
16C2×#6131C2211yescharacteristic
17C13×C4⋊Q8C2213yes—
18C13×#125C2213yes—
19C13×#125C2213yes—
20C4×Q8×C13C2211yescharacteristic
21C4×Q8×C13C2211yescharacteristic
22C4×Q8×C13C2211yescharacteristic
23C4×Q8×C13C2213yes—
24#88200C2216yes—
25#88200C2213yes—
26Q8×Dic13C2211yescharacteristic
27Q8×Dic13C2211yescharacteristic
28Q8×Dic13C2211yescharacteristic
29#88198C2213yes—
30#88151C2216yes—
31#88151C2213yes—
32#88150C2216yes—
33#88150C2213yes—
34#88150C2213yes—
35#88150C2216yes—
36#88147C2213yes—
37#88147C2213yes—
38#88147C2213yes—
39#88146C2213yes—
40C4⋊C4×D13C2213yes—
41C4⋊C4×D13C2216yes—
42C4⋊C4×D13C2213yes—
43C4⋊C4×D13C2216yes—
44#88144C2213yes—
45#88144C2213yes—
46#88144C2213yes—
47#88144C2213yes—
48#88143C2216yes—
49#88143C2211yescharacteristic
50#88143C2213yes—
51#88142C2213yes—
52#88142C2213yes—
53#88142C2213yes—
54C4×D52C2213yes—
55C4×D52C2213yes—
56C4×D52C2213yes—
57#88126C2213yes—
58#88126C2213yes—
59C42×D13C2213yes—
60#88124C2213yes—
61#88124C2213yes—
62#88123C2213yes—
63C4×Dic26C2213yes—
64C4×Dic26C2213yes—
65C4×Dic26C2213yes—
66C2×Q8×C13C2313yes—
67C2×Q8×C13C2311yescharacteristic
68#6131Q818yescomplemented
69C2×D52C2313yes—
70C2×C4×D13C2313yes—
71C2×C4×D13C2313yes—
72C2×C4×D13C2316yes—
73C2×C4×D13C2316yes—
74C2×C4×D13C2313yes—
75C2×Dic26C2313yes—
76C2×Dic26C2313yes—
77C2×Dic26C2313yes—
78C13×C4⋊C4C2313yes—
79C13×C4⋊C4C2313yes—
80C13×C4⋊C4C2313yes—
81C13×C4⋊C4C2313yes—
82C13×C4⋊C4C2316yes—
83C13×C4⋊C4C2311yescharacteristic
84C13×C4⋊C4C2313yes—
85C42×C13C2313yes—
86C42×C13C2313yes—
87C42×C13C2313yes—
88#6103C2313yes—
89#6103C2313yes—
90#6103C2313yes—
91#6103C2313yes—
92#6103C2316yes—
93C4⋊Dic13C2311yescharacteristic
94C4⋊Dic13C2313yes—
95C4⋊Dic13C2313yes—
96C4⋊Dic13C2313yes—
97C4⋊Dic13C2313yes—
98C4⋊Dic13C2316yes—
99C4⋊Dic13C2313yes—
100#6101C2311yescharacteristic
101#6101C2311yescharacteristic
102#6101C2313yes—
103#6101C2313yes—
104#6101C2313yes—
105#6101C2313yes—
106#6101C2316yes—
107#6101C2316yes—
108#6101C2311yescharacteristic
109#6101C2311yescharacteristic
110#6101C2313yes—
111#6101C2313yes—
112C4×Dic13C2313yes—
113C4×Dic13C2313yes—
114C4×Dic13C2313yes—
115C4×Dic13C2311yescharacteristic
116C4×Dic13C2313yes—
117#3504—131nomaximal, Sylow
118C22×D13C2413yes—
119Q8×C13—43no—
120Q8×C13C2×Q814yes—
121C2×C4×C13C2411yescharacteristic
122C2×C4×C13C2413yes—
123C2×C4×C13C2411yescharacteristic
124C2×C4×C13C2413yes—
125C2×C4×C13C2413yes—
126C2×C4×C13C2411yescharacteristic
127C2×C4×C13C2413yes—
128C2×Dic13C2411yescharacteristic
129C2×Dic13C2411yescharacteristic
130C2×Dic13C2411yescharacteristic
131C2×Dic13C2413yes—
132C2×Dic13C2413yes—
133C2×Dic13C2413yes—
134C2×Dic13C2411yescharacteristic
135D52C2×Q8112yes—
136C4×D13—43no—
137C4×D13—46no—
138C4×D13—46no—
139C4×D13—43no—
140C4×D13C2×Q8112yes—
141Dic26—43no—
142Dic26—43no—
143Dic26—43no—
144#557—131no—
145#557—131no—
146#557—131no—
147#557D1311yescharacteristic, complemented
148#554—133no—
149#554—133no—
150#554—133no—
151#554—133no—
152#544—133no—
153#544—133no—
154#533—133no—
155C2×#125—133no—
156#520—131no—
157#520—131no—
158C4×#41—131no—
159C22×C13C2511yescharacteristic
160C2×D13—23no—
161C2×D13—23no—
162C2×D13C22×Q816yes—
163C4×C13—21no—
164C4×C13—23no—
165C4×C13—23no—
166C4×C13—21no—
167C4×C13—23no—
168C4×C13—21no—
169C4×C13C22×Q816yes—
170Dic13—21no—
171Dic13—21no—
172Dic13—23no—
173Dic13—23no—
174Dic13—23no—
175Dic13—21no—
176Dic13C22×Q812yes—
177C2×#41—131no—
178C4⋊Q8—133no—
179C4⋊Q8—133no—
180C4⋊Q8—133no—
181C4⋊Q8—133no—
182C4⋊Q8—133no—
183C4⋊Q8C2×D1313yes—
184#125—133no—
185#125—136no—
186#125—133no—
187#125—133no—
188#125—131no—
189#125—133no—
190#125—133no—
191#125—133no—
192#125—133no—
193#125C2×D1313yes—
194#125C2×D1313yes—
195C22⋊Q8—133no—
196C22⋊Q8—136no—
197C22⋊Q8—133no—
198C22⋊Q8—133no—
199C22⋊Q8—133no—
200C22⋊Q8—136no—
201C22⋊Q8—136no—
202C22⋊Q8—136no—
203C4×Q8—131no—
204C4×Q8—131no—
205C4×Q8—131no—
206C4×Q8—133no—
207C4×Q8—133no—
208C4×Q8—133no—
209C4×Q8C2×D1311yescharacteristic
210C4×Q8C2×D1311yescharacteristic
211C4×Q8C2×D1311yescharacteristic
212C4×Q8C2×D1313yes—
213C4×D4—133no—
214C4×D4—133no—
215C4×D4—133no—
216C4×D4—133no—
217C4×D4—133no—
218C4×D4—133no—
219#117—133no—
220#117—133no—
221#117—133no—
222C2×C4⋊C4—133no—
223C2×C4⋊C4—133no—
224C2×C4⋊C4—136no—
225C2×C4⋊C4—136no—
226C2×C42—133no—
227C2×C13C23×Q811yescharacteristic
228C2×C13#58511yescharacteristic
229C2×C13#58511yescharacteristic
230D13—26no—
231#41—138no—
232C2×Q8—133no—
233C2×Q8—133no—
234C2×Q8—133no—
235C2×Q8C22×D1313yes—
236C2×Q8C22×D1311yescharacteristic
237C2×D4—133no—
238C22×C4—133no—
239C22×C4—133no—
240C22×C4—133no—
241C22×C4—136no—
242C22×C4—136no—
243C4⋊C4—133no—
244C4⋊C4—133no—
245C4⋊C4—133no—
246C4⋊C4—133no—
247C4⋊C4—133no—
248C4⋊C4—133no—
249C4⋊C4—133no—
250C4⋊C4—136no—
251C4⋊C4—136no—
252C4⋊C4—136no—
253C4⋊C4—131no—
254C4⋊C4—131no—
255C4⋊C4—133no—
256C4⋊C4—131no—
257C4⋊C4—131no—
258C4⋊C4—131no—
259C4⋊C4—133no—
260C4⋊C4—133no—
261C4⋊C4—133no—
262C4⋊C4C22×D1313yes—
263C4⋊C4C22×D1313yes—
264C4⋊C4C22×D1313yes—
265C4⋊C4C22×D1316yes—
266C4⋊C4C22×D1313yes—
267C4⋊C4C22×D1311yescharacteristic
268C4⋊C4C22×D1313yes—
269C22⋊C4—133no—
270C22⋊C4—133no—
271C22⋊C4—136no—
272C22⋊C4—133no—
273C22⋊C4—133no—
274C42—131no—
275C42—133no—
276C42—133no—
277C42—133no—
278C42—133no—
279C42C22×D1313yes—
280C42C22×D1313yes—
281C42C22×D1313yes—
282C13#350411yescharacteristic, complemented, Sylow
283C23—133no—
284Q8—43no—
285Q8—523no—
286Q8—523no—
287Q8—523no—
288Q8Q8×D1314yes—
289D4—1312no—
290C2×C4—131no—
291C2×C4—1312no—
292C2×C4—131no—
293C2×C4—131no—
294C2×C4—131no—
295C2×C4—133no—
296C2×C4—133no—
297C2×C4—133no—
298C2×C4—526no—
299C2×C4—523no—
300C2×C4—523no—
301C2×C4—526no—
302C2×C4C23×D1311yescharacteristic
303C2×C4C23×D1313yes—
304C2×C4C23×D1311yescharacteristic
305C2×C4C23×D1311yescharacteristic
306C2×C4C23×D1313yes—
307C2×C4C23×D1313yes—
308C2×C4C23×D1313yes—
309C22—136no—
310C22—263no—
311C22—263no—
312C22C24×D1311yescharacteristic
313C4—23no—
314C4—23no—
315C4—21no—
316C4—21no—
317C4—23no—
318C4—21no—
319C4—132no—
320C4—261no—
321C4—263no—
322C4—261no—
323C4—263no—
324C4—263no—
325C4—261no—
326C4C2×Q8×D1316yes—
327C2—266no—
328C2C22×Q8×D1311yescharacteristic
329C2#1171964811yescharacteristic
330C2#1171965211yescharacteristic
subgroupG/H
center, FrattiniC22C24×D13
commutator, socle, cosocleC22×C13C25
FittingC13×#557C2
prime radicalC2×#6131C22
hypercenter#557D13
hypocenterC13#3504
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ #557

Complements

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

NH ≅ G/Ntype
1. C13×#557C2semidirect
2. #11719435C2semidirect
3. #11719434C2semidirect
4. #11719395C2semidirect
5. #11719395C2semidirect
6. #11719394C2semidirect
7. D13×#125C2semidirect
8. #11719284C2semidirect
9. #11719283C2semidirect
13. #11719275C2semidirect
14. #11719274C2semidirect
15. #11719274C2semidirect
68. #6131Q8semidirect
147. #557D13semidirect
282. C13#3504semidirect

Maximal subgroups

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

subgroupindex
C13×#5572
#117194352
#117194342
#117193952
#117193942
D13×#1252
#117192842
#117192832
#117192792
C4×#61312
#117192752
#117192742
#350413