Finite Group Databasebeta

← #13128643

Subgroups — #13128643

Order 1664.

964 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#557C211yesmaximal, characteristic, complemented
2#11719434C213yesmaximal
3#11719427C213yesmaximal, complemented
4#11719394C213yesmaximal
5#11719393C213yesmaximal
6#11719390C213yesmaximal, complemented
7#11719390C213yesmaximal, complemented
8#11719283C213yesmaximal
9#11719277C211yesmaximal, characteristic
10#11719277C211yesmaximal, characteristic
11C4×Q8×D13C211yesmaximal, characteristic
12#11719274C211yesmaximal, characteristic, complemented
13#11719274C211yesmaximal, characteristic, complemented
14#11719272C213yesmaximal, complemented
15Q8×Dic26C211yesmaximal, characteristic, complemented
16C2×Q8×D13C2211yescharacteristic
17C13×C4⋊Q8C2213yes—
18C13×#125C2213yes—
19C13×#125C2213yes—
20C4×Q8×C13C2211yescharacteristic
21C4×Q8×C13C2213yes—
22C4×Q8×C13C2211yescharacteristic
23C4×Q8×C13C2211yescharacteristic
24#88200C2213yes—
25Q8×Dic13C2211yescharacteristic
26Q8×Dic13C2211yescharacteristic
27Q8×Dic13C2211yescharacteristic
28#88198C2213yes—
29#88198C2216yes—
30#88151C2213yes—
31#88150C2216yes—
32#88150C2211yescharacteristic
33#88150C2213yes—
34#88146C2213yes—
35#88146C2213yes—
36C4⋊C4×D13C2213yes—
37#88144C2213yes—
38#88144C2213yes—
39#88143C2216yes—
40#88143C2213yes—
41#88143C2216yes—
42#88143C2213yes—
43#88142C2213yes—
44#88142C2213yes—
45#88142C2216yes—
46#88142C2213yes—
47#88142C2213yes—
48#88142C2213yes—
49#88141C2213yes—
50#88141C2213yes—
51#88141C2216yes—
52#88141C2216yes—
53#88141C2213yes—
54#88126C2213yes—
55#88126C2213yes—
56C42×D13C2213yes—
57#88124C2213yes—
58#88124C2213yes—
59#88123C2213yes—
60C4×Dic26C2213yes—
61C4×Dic26C2213yes—
62C4×Dic26C2213yes—
63C4×Dic26C2213yes—
64C4×Dic26C2213yes—
65C4×Dic26C2213yes—
66C2×Q8×C13C2313yes—
67C2×Q8×C13C2311yescharacteristic
68Q8×D13Q818yescomplemented
69C2×C4×D13C2311yescharacteristic
70C2×C4×D13C2313yes—
71C2×C4×D13C2313yes—
72C2×Dic26C2311yescharacteristic
73C2×Dic26C2313yes—
74C2×Dic26C2313yes—
75C2×Dic26C2316yes—
76C2×Dic26C2313yes—
77C13×C4⋊C4C2313yes—
78C13×C4⋊C4C2313yes—
79C13×C4⋊C4C2316yes—
80C13×C4⋊C4C2313yes—
81C13×C4⋊C4C2313yes—
82C13×C4⋊C4C2313yes—
83C13×C4⋊C4C2311yescharacteristic
84C42×C13C2313yes—
85C42×C13C2313yes—
86C42×C13C2313yes—
87#6103C2311yescharacteristic
88#6103C2311yescharacteristic
89#6103C2313yes—
90#6103C2313yes—
91C4⋊Dic13C2313yes—
92C4⋊Dic13C2313yes—
93C4⋊Dic13C2313yes—
94C4⋊Dic13C2313yes—
95C4⋊Dic13C2313yes—
96C4⋊Dic13C2313yes—
97#6101C2311yescharacteristic
98#6101C2311yescharacteristic
99#6101C2313yes—
100#6101C2313yes—
101#6101C2313yes—
102#6101C2313yes—
103#6101C2313yes—
104#6101C2316yes—
105#6101C2313yes—
106#6101C2316yes—
107#6101C2316yes—
108#6101C2313yes—
109#6101C2313yes—
110C4×Dic13C2313yes—
111C4×Dic13C2313yes—
112C4×Dic13C2313yes—
113C4×Dic13C2313yes—
114C4×Dic13C2316yes—
115C4×Dic13C2316yes—
116C4×Dic13C2313yes—
117#3502—131nomaximal, Sylow
118C22×D13C2411yescharacteristic
119Q8×C13—43no—
120Q8×C13C2×Q814yes—
121C2×C4×C13C2411yescharacteristic
122C2×C4×C13C2413yes—
123C2×C4×C13C2413yes—
124C2×C4×C13C2413yes—
125C2×C4×C13C2411yescharacteristic
126C2×C4×C13C2411yescharacteristic
127C2×C4×C13C2413yes—
128C2×Dic13C2411yescharacteristic
129C2×Dic13C2413yes—
130C2×Dic13C2411yescharacteristic
131C2×Dic13C2413yes—
132C2×Dic13C2413yes—
133C2×Dic13C2413yes—
134C2×Dic13C2411yescharacteristic
135C4×D13—22no—
136C4×D13—43no—
137C4×D13C2×Q8112yes—
138Dic26—22no—
139Dic26—26no—
140Dic26—43no—
141Dic26—46no—
142Dic26C2×Q8112yes—
143Q82—133no—
144Q82—131no—
145#557—133no—
146#557—133no—
147#557—133no—
148#557—131no—
149#557—131no—
150#557D1311yescharacteristic, complemented
151#544—133no—
152#544—133no—
153#533—133no—
154#533—133no—
155#519—131no—
156#519—131no—
157C2×C4×Q8—131no—
158C22×C13C2511yescharacteristic
159C2×D13—21no—
160C2×D13—21no—
161C2×D13C22×Q812yes—
162C4×C13—23no—
163C4×C13—21no—
164C4×C13—21no—
165C4×C13—23no—
166C4×C13—23no—
167C4×C13—21no—
168C4×C13C22×Q816yes—
169Dic13—21no—
170Dic13—23no—
171Dic13—21no—
172Dic13—23no—
173Dic13—23no—
174Dic13C22×Q816yes—
175Dic132−1+412yes—
176C22×Q8—131no—
177C4⋊Q8—133no—
178C4⋊Q8—136no—
179C4⋊Q8—133no—
180C4⋊Q8—133no—
181C4⋊Q8—133no—
182C4⋊Q8—136no—
183C4⋊Q8—133no—
184C4⋊Q8—133no—
185C4⋊Q8—133no—
186C4⋊Q8C2×D1313yes—
187#125—133no—
188#125—133no—
189#125—136no—
190#125—136no—
191#125—133no—
192#125—133no—
193#125—133no—
194#125—133no—
195#125C2×D1313yes—
196#125C2×D1313yes—
197C22⋊Q8—133no—
198C22⋊Q8—133no—
199C22⋊Q8—131no—
200C22⋊Q8—136no—
201C22⋊Q8—133no—
202C4×Q8—131no—
203C4×Q8—131no—
204C4×Q8—131no—
205C4×Q8—133no—
206C4×Q8—133no—
207C4×Q8—133no—
208C4×Q8—136no—
209C4×Q8—136no—
210C4×Q8—133no—
211C4×Q8—133no—
212C4×Q8—133no—
213C4×Q8—133no—
214C4×Q8—133no—
215C4×Q8—133no—
216C4×Q8C2×D1311yescharacteristic
217C4×Q8C2×D1311yescharacteristic
218C4×Q8C2×D1311yescharacteristic
219C4×Q8C2×D1313yes—
220#117—133no—
221#117—133no—
222#117—133no—
223#117—133no—
224C2×C4⋊C4—133no—
225C2×C42—133no—
226C2×C13C23×Q811yescharacteristic
227C2×C13C2×2−1+411yescharacteristic
228C2×C13#58511yescharacteristic
229D13—22no—
230C2×Q8—138no—
231C2×Q8—133no—
232C2×Q8—133no—
233C2×Q8—131no—
234C2×Q8—133no—
235C2×Q8—136no—
236C2×Q8C22×D1313yes—
237C2×Q8C22×D1311yescharacteristic
238C22×C4—133no—
239C22×C4—131no—
240C22×C4—133no—
241C4⋊C4—136no—
242C4⋊C4—133no—
243C4⋊C4—133no—
244C4⋊C4—133no—
245C4⋊C4—133no—
246C4⋊C4—133no—
247C4⋊C4—133no—
248C4⋊C4—133no—
249C4⋊C4—133no—
250C4⋊C4—131no—
251C4⋊C4—133no—
252C4⋊C4—131no—
253C4⋊C4—136no—
254C4⋊C4—133no—
255C4⋊C4—136no—
256C4⋊C4—133no—
257C4⋊C4—133no—
258C4⋊C4—133no—
259C4⋊C4—133no—
260C4⋊C4C22×D1313yes—
261C4⋊C4C22×D1313yes—
262C4⋊C4C22×D1313yes—
263C4⋊C4C22×D1313yes—
264C4⋊C4C22×D1316yes—
265C4⋊C4C22×D1311yescharacteristic
266C4⋊C4C22×D1313yes—
267C22⋊C4—133no—
268C22⋊C4—131no—
269C22⋊C4—133no—
270C22⋊C4—131no—
271C42—133no—
272C42—133no—
273C42—133no—
274C42—136no—
275C42—136no—
276C42—133no—
277C42—133no—
278C42C22×D1313yes—
279C42C22×D1313yes—
280C42C22×D1313yes—
281C13#350211yescharacteristic, complemented, Sylow
282C23—131no—
283Q8—43no—
284Q8—1312no—
285Q8—266no—
286Q8—262no—
287Q8—523no—
288Q8—526no—
289Q8Q8×D1314yes—
290C2×C4—133no—
291C2×C4—131no—
292C2×C4—1312no—
293C2×C4—131no—
294C2×C4—133no—
295C2×C4—131no—
296C2×C4—133no—
297C2×C4—133no—
298C2×C4—262no—
299C2×C4—523no—
300C2×C4C23×D1311yescharacteristic
301C2×C4C23×D1313yes—
302C2×C4C23×D1313yes—
303C2×C4C23×D1313yes—
304C2×C4C23×D1311yescharacteristic
305C2×C4C23×D1311yescharacteristic
306C2×C4C23×D1313yes—
307C22—132no—
308C22—261no—
309C22—261no—
310C22C24×D1311yescharacteristic
311C4—23no—
312C4—21no—
313C4—23no—
314C4—21no—
315C4—23no—
316C4—21no—
317C4—136no—
318C4—132no—
319C4—263no—
320C4—261no—
321C4—263no—
322C4—261no—
323C4—263no—
324C4C2×Q8×D1316yes—
325C2—262no—
326C2C22×Q8×D1311yescharacteristic
327C2#1171964811yescharacteristic
328C2D13×2−1+411yescharacteristic
subgroupG/H
center, FrattiniC22C24×D13
commutator, socle, cosocleC22×C13C25
FittingC13×#557C2
prime radicalC22×D13C24
hypercenter#557D13
hypocenterC13#3502
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ #557

Complements

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

NH ≅ G/Ntype
1. C13×#557C2semidirect
3. #11719427C2semidirect
6. #11719390C2semidirect
7. #11719390C2semidirect
12. #11719274C2semidirect
13. #11719274C2semidirect
14. #11719272C2semidirect
15. Q8×Dic26C2semidirect
68. Q8×D13Q8semidirect
150. #557D13semidirect
281. C13#3502semidirect

Maximal subgroups

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

subgroupindex
C13×#5572
#117194342
#117194272
#117193942
#117193932
#117193902
#117192832
#117192772
C4×Q8×D132
#117192742
#117192722
Q8×Dic262
#350213