Finite Group Databasebeta

← #13125538

Subgroups — #13125538

Order 1664.

366 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719327C211yesmaximal, characteristic, complemented
2#11719305C211yesmaximal, characteristic
3C13×#465C211yesmaximal, characteristic
4#11718828C211yesmaximal, characteristic, complemented
5#11718825C211yesmaximal, characteristic, complemented
6#11718777C211yesmaximal, characteristic, complemented
7C2×#88055C211yesmaximal, characteristic, complemented
8#11718712C211yesmaximal, characteristic, complemented
9#11718702C211yesmaximal, characteristic
10#11718517C211yesmaximal, characteristic, complemented
11#11718514C211yesmaximal, characteristic, complemented
12#11718458C211yesmaximal, characteristic, complemented
13#11718450C211yesmaximal, characteristic, complemented
14#11718426C211yesmaximal, characteristic, complemented
15#11718418C211yesmaximal, characteristic, complemented
16C2×C13×SD16C2211yescharacteristic
17C22×C8×C13C2211yescharacteristic
18C13×C22⋊Q8C2211yescharacteristic
19C13×#121C2211yescharacteristic
20Q8×Dic13C2211yescharacteristic
21#88198C2211yescharacteristic
22C2×#6107C2211yescharacteristic
23#88190C2211yescharacteristic
24#88189—21no—
25D4×Dic13—21no—
26D4×Dic13C2211yescharacteristic
27C2×#6105C2211yescharacteristic
28#88178C2211yescharacteristic
29#88178C2211yescharacteristic
30C2×C4×Dic13C2211yescharacteristic
31C22×#1055C2211yescharacteristic
32C2×Dic52C2211yescharacteristic
33#88144C2211yescharacteristic
34#88143—21no—
35#88142C2211yescharacteristic
36#88141—21no—
37#88141C2211yescharacteristic
38#88141C2211yescharacteristic
39#88133—21no—
40#88132—21no—
41#88131—21no—
42#88131—21no—
43C13×#106C2211yescharacteristic
44C13×#103C2211yescharacteristic
45C13×#102C2211yescharacteristic
46#88075C2211yescharacteristic
47#88072C2211yescharacteristic
48#88058C2211yescharacteristic
49#88056C2211yescharacteristic
50#88056C2211yescharacteristic
51#88055C2211yescharacteristic
52#88055C2211yescharacteristic
53#88055C2211yescharacteristic
54#88055C2211yescharacteristic
55#88050C2211yescharacteristic
56#88050C2211yescharacteristic
57#88048C2211yescharacteristic
58#88047C2211yescharacteristic
59C2×Q8×C13C2311yescharacteristic
60C2×D4×C13—21no—
61C2×D4×C13C2311yescharacteristic
62C22×C4×C13C2311yescharacteristic
63C22×Dic13—21no—
64C22×Dic13D411yescharacteristic
65C22×Dic13D411yescharacteristic
66C2×Dic26—21no—
67C2×Dic26C2311yescharacteristic
68C2×Dic26C2311yescharacteristic
69C13×SD16—22no—
70C2×C8×C13—22no—
71C2×C8×C13C2311yescharacteristic
72C2×C8×C13C2311yescharacteristic
73C13×C4⋊C4—21no—
74C13×C4⋊C4C2311yescharacteristic
75C13×C4⋊C4C2311yescharacteristic
76C13×C22⋊C4—21no—
77C13×C22⋊C4—21no—
78C22⋊Dic13—21no—
79C22⋊Dic13—21no—
80C22⋊Dic13—21no—
81C22⋊Dic13—21no—
82C22⋊Dic13—21no—
83#6107—22no—
84#6105—22no—
85C4⋊Dic13—21no—
86C4⋊Dic13—21no—
87C4⋊Dic13C2311yescharacteristic
88C4⋊Dic13C2311yescharacteristic
89#6101—21no—
90#6101—21no—
91#6101—21no—
92#6101—21no—
93#6101—21no—
94#6101—21no—
95#6101—21no—
96#6101—21no—
97C4×Dic13—21no—
98C4×Dic13—21no—
99C4×Dic13—21no—
100C4×Dic13D411yescharacteristic
101C4×Dic13D411yescharacteristic
102C4×Dic13C2311yescharacteristic
103C4×Dic13C2311yescharacteristic
104C2×#1055—22no—
105C2×#1055C2311yescharacteristic
106C2×#1055C2311yescharacteristic
107Dic52—22no—
108#3181—131nomaximal, Sylow
109C23×C13—21no—
110C23×C13C2×D411yescharacteristic
111Q8×C13—21no—
112Q8×C13—21no—
113D4×C13—21no—
114D4×C13—21no—
115D4×C13—42no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13C2×D411yescharacteristic
122C2×C4×C13C2411yescharacteristic
123C2×Dic13—22no—
124C2×Dic13—21no—
125C2×Dic13—21no—
126C2×Dic13—21no—
127C2×Dic13—21no—
128C2×Dic13—41no—
129C2×Dic13—42no—
130C2×Dic13C2×D411yescharacteristic
131C2×Dic13C2×D411yescharacteristic
132C2×Dic13C2×D411yescharacteristic
133C2×Dic13C2×D411yescharacteristic
134Dic26—21no—
135Dic26—21no—
136Dic26—21no—
137Dic26—21no—
138Dic26—42no—
139C8×C13—21no—
140C8×C13#4112yes—
141#1055—21no—
142#1055#4112yes—
143#533—131no—
144#529—131no—
145#501—131no—
146#497—131no—
147#491—131no—
148#489—131no—
149#467—131no—
150#467—131no—
151#465—131no—
152#465D1311yescharacteristic
153#441—131no—
154#441—131no—
155#440—131no—
156#440—131no—
157C2×#97—131no—
158C22×C13—21no—
159C22×C13—21no—
160C22×C13—41no—
161C22×C13—41no—
162C22×C13—41no—
163C22×C13#13712yes—
164C22×C13C22×D411yescharacteristic
165C4×C13—21no—
166C4×C13—41no—
167C4×C13—41no—
168C4×C13—41no—
169C4×C13C2×#4111yescharacteristic
170C4×C13C2×#4111yescharacteristic
171Dic13—21no—
172Dic13—21no—
173Dic13—21no—
174Dic13—21no—
175Dic13—41no—
176Dic13—41no—
177Dic13—41no—
178Dic13—41no—
179C2×Q16—131no—
180C2×Q16—131no—
181C2×SD16—131no—
182C2×SD16C2×D1311yescharacteristic
183C22×C8—131no—
184C22×C8C2×D1311yescharacteristic
185C4⋊Q8—131no—
186C4⋊Q8—131no—
187#126—261no—
188#125—131no—
189#125—261no—
190#124—131no—
191#123—261no—
192C22⋊Q8—131no—
193C22⋊Q8—131no—
194C22⋊Q8—261no—
195C22⋊Q8C2×D1311yescharacteristic
196#121C2×D1311yescharacteristic
197C4×Q8—131no—
198C4×Q8—131no—
199C4×Q8—131no—
200C4×Q8—261no—
201C4×D4—131no—
202C4×D4—261no—
203#117—261no—
204#117—261no—
205C2×C42—131no—
206#107—131no—
207#107—131no—
208#106—131no—
209#106C2×D1311yescharacteristic
210#103—131no—
211#103—131no—
212#103—131no—
213#103—131no—
214#103—131no—
215#103C2×D1311yescharacteristic
216#102—131no—
217#102C2×D1311yescharacteristic
218#97—131no—
219#97—131no—
220#97—131no—
221#97—131no—
222C2×C13—22no—
223C2×C13—81no—
224C2×C13#53211yescharacteristic
225C2×C13C2×#13711yescharacteristic
226C2×C13#57511yescharacteristic
227C2×Q8—131no—
228C2×Q8—131no—
229C2×Q8—261no—
230C2×Q8C22×D1311yescharacteristic
231C2×D4—21no—
232C2×D4C22×D1311yescharacteristic
233C22×C4—131no—
234C22×C4—131no—
235C22×C4—261no—
236C22×C4C22×D1311yescharacteristic
237Q16—262no—
238Q16—262no—
239SD16—22no—
240SD16—262no—
241C2×C8—22no—
242C2×C8—131no—
243C2×C8—131no—
244C2×C8—262no—
245C2×C8C22×D1311yescharacteristic
246C2×C8C22×D1311yescharacteristic
247C4⋊C4—21no—
248C4⋊C4—131no—
249C4⋊C4—131no—
250C4⋊C4—261no—
251C4⋊C4—261no—
252C4⋊C4—261no—
253C4⋊C4—261no—
254C4⋊C4—261no—
255C4⋊C4—261no—
256C4⋊C4—261no—
257C4⋊C4—261no—
258C4⋊C4—261no—
259C4⋊C4—261no—
260C4⋊C4C22×D1311yescharacteristic
261C4⋊C4C22×D1311yescharacteristic
262C22⋊C4—21no—
263C22⋊C4—21no—
264C22⋊C4—261no—
265C22⋊C4—261no—
266C22⋊C4—261no—
267C22⋊C4—261no—
268C22⋊C4—261no—
269C42—131no—
270C42—131no—
271C42—131no—
272C42—131no—
273C42—261no—
274C42—261no—
275C42—261no—
276C13#318111yescharacteristic, complemented, Sylow
277C23—21no—
278C23D4×D1311yescharacteristic
279Q8—21no—
280Q8—21no—
281Q8—261no—
282Q8—261no—
283Q8—261no—
284Q8—261no—
285Q8—522no—
286D4—21no—
287D4—21no—
288D4—42no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—131no—
295C2×C4—131no—
296C2×C4—131no—
297C2×C4—131no—
298C2×C4—262no—
299C2×C4—261no—
300C2×C4—261no—
301C2×C4—261no—
302C2×C4—261no—
303C2×C4—521no—
304C2×C4—522no—
305C2×C4D4×D1311yescharacteristic
306C2×C4C23×D1311yescharacteristic
307C8—21no—
308C8—132no—
309C8—261no—
310C8#612912yes—
311C22—21no—
312C22—21no—
313C22—41no—
314C22—41no—
315C22—41no—
316C22#8816912yes—
317C22C2×D4×D1311yescharacteristic
318C4—21no—
319C4—41no—
320C4—41no—
321C4—41no—
322C4—261no—
323C4—261no—
324C4—261no—
325C4—261no—
326C4—521no—
327C4—521no—
328C4—521no—
329C4—521no—
330C4C2×#612911yescharacteristic
331C4#41×D1311yescharacteristic
332C2—22no—
333C2—81no—
334C2#1171930111yescharacteristic
335C2C2×#8816911yescharacteristic
336C2#1171947311yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#465C2
socleC22×C13C22×D4
prime radicalC13×#121C22
hypercenter#465D13
hypocenterC13#3181
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. #11719327C2semidirect
4. #11718828C2semidirect
5. #11718825C2semidirect
6. #11718777C2semidirect
7. C2×#88055C2semidirect
8. #11718712C2semidirect
10. #11718517C2semidirect
11. #11718514C2semidirect
12. #11718458C2semidirect
13. #11718450C2semidirect
14. #11718426C2semidirect
15. #11718418C2semidirect
276. C13#3181semidirect

Maximal subgroups

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

subgroupindex
#117193272
#117193052
C13×#4652
#117188282
#117188252
#117187772
C2×#880552
#117187122
#117187022
#117185172
#117185142
#117184582
#117184502
#117184262
#117184182
#318113