Finite Group Databasebeta

← #13127191

Subgroups — #13127191

Order 1664.

388 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719316C211yesmaximal, characteristic
2#11719216C211yesmaximal, characteristic, complemented
3C13×#481C211yesmaximal, characteristic, complemented
4#11718702C211yesmaximal, characteristic, complemented
5C2×#88048C211yesmaximal, characteristic, complemented
6#11718523C211yesmaximal, characteristic, complemented
7D13×#106C211yesmaximal, characteristic, complemented
8#11718516C211yesmaximal, characteristic, complemented
9#11718515C211yesmaximal, characteristic, complemented
10#11718439C211yesmaximal, characteristic, complemented
11#11718438C211yesmaximal, characteristic, complemented
12#11718422C211yesmaximal, characteristic, complemented
13#11718419C211yesmaximal, characteristic, complemented
14#11718386C211yesmaximal, characteristic, complemented
15#11718382C211yesmaximal, characteristic, complemented
16C2×#6129—21no—
17C13×#121C2211yescharacteristic
18C2×C13×C4⋊C4C2211yescharacteristic
19#88192C2211yescharacteristic
20#88189—21no—
21D4×Dic13C2211yescharacteristic
22C2×#6105C2211yescharacteristic
23C4×C22⋊D13—21no—
24C4×C22⋊D13C2211yescharacteristic
25C2×C4⋊Dic13C2211yescharacteristic
26#88178—21no—
27#88178C2211yescharacteristic
28C22×#1055C2211yescharacteristic
29C2×C8×D13C2211yescharacteristic
30#88151C2211yescharacteristic
31#88150—21no—
32C4⋊C4×D13C2211yescharacteristic
33C4⋊C4×D13C2211yescharacteristic
34#88143—21no—
35#88142C2211yescharacteristic
36#88142C2211yescharacteristic
37#88141C2211yescharacteristic
38#88137—21no—
39#88132—21no—
40C13×#106C2211yescharacteristic
41C13×#106C2211yescharacteristic
42C13×#102C2211yescharacteristic
43C13×#102C2211yescharacteristic
44C13×C22⋊C8C2211yescharacteristic
45#88072C2211yescharacteristic
46#88060C2211yescharacteristic
47#88057C2211yescharacteristic
48#88057C2211yescharacteristic
49#88056C2211yescharacteristic
50#88056C2211yescharacteristic
51#88054C2211yescharacteristic
52C8×Dic13C2211yescharacteristic
53#88050C2211yescharacteristic
54#88048C2211yescharacteristic
55#88048C2211yescharacteristic
56#88048C2211yescharacteristic
57#88048C2211yescharacteristic
58#88048C2211yescharacteristic
59C2×D4×C13—21no—
60C2×D4×C13C2311yescharacteristic
61C22×C4×C13—21no—
62C22×C4×C13C2311yescharacteristic
63C2×C22⋊D13—21no—
64C2×C22⋊D13D411yescharacteristic
65C22×Dic13—21no—
66C22×Dic13—21no—
67#6129—44no—
68C2×C4×D13—21no—
69C2×C4×D13—21no—
70C2×C4×D13C2311yescharacteristic
71C2×Dic26—21no—
72C2×Dic26—21no—
73C2×Dic26C2311yescharacteristic
74C2×C8×C13C2311yescharacteristic
75C2×C8×C13C2311yescharacteristic
76C13×C4⋊C4—21no—
77C13×C4⋊C4C2311yescharacteristic
78C13×C4⋊C4C2311yescharacteristic
79C13×C4⋊C4C2311yescharacteristic
80C13×C22⋊C4—21no—
81C22⋊Dic13—21no—
82C22⋊Dic13—21no—
83C22⋊Dic13—21no—
84C22⋊Dic13D411yescharacteristic
85#6105—22no—
86#6103—21no—
87#6103D411yescharacteristic
88C4⋊Dic13—21no—
89C4⋊Dic13—21no—
90C4⋊Dic13C2311yescharacteristic
91C4⋊Dic13C2311yescharacteristic
92C4⋊Dic13C2311yescharacteristic
93#6101—21no—
94#6101—21no—
95#6101—21no—
96#6101—21no—
97#6101—21no—
98#6101—21no—
99#6101D411yescharacteristic
100C4×Dic13—21no—
101C4×Dic13C2311yescharacteristic
102C2×#1055—22no—
103C2×#1055C2311yescharacteristic
104C2×#1055C2311yescharacteristic
105C8×D13—22no—
106#3335—131nomaximal, Sylow
107C23×C13—21no—
108C23×C13C2×D411yescharacteristic
109C22×D13C2×D411yescharacteristic
110D4×C13—21no—
111D4×C13—21no—
112D4×C13—42no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—81no—
119C2×C4×C13C2×D411yescharacteristic
120C2×C4×C13C2411yescharacteristic
121C22⋊D13—42no—
122C22⋊D13SD1614yescomplemented
123C2×Dic13—21no—
124C2×Dic13—21no—
125C2×Dic13—21no—
126C2×Dic13—21no—
127C2×Dic13—42no—
128C2×Dic13—42no—
129C2×Dic13C2×D411yescharacteristic
130C2×Dic13C2×D411yescharacteristic
131C2×Dic13C2×D411yescharacteristic
132C4×D13—21no—
133C4×D13—21no—
134C4×D13—42no—
135C4×D13—81no—
136Dic26—21no—
137Dic26—21no—
138Dic26—42no—
139Dic26—81no—
140C8×C13—21no—
141C8×C13—21no—
142#1055—21no—
143#1055#4112yescomplemented
144#554—131no—
145#547—131no—
146#498—131no—
147#483—131no—
148#483—131no—
149#481—131no—
150#481D1311yescharacteristic, complemented
151#476—131no—
152#475—131no—
153#465—131no—
154#465—131no—
155C4×SD16—131no—
156C8×D4—131no—
157C2×#106—131no—
158C2×#106—131no—
159C22×C13—21no—
160C22×C13—21no—
161C22×C13—41no—
162C22×C13—41no—
163C22×C13—41no—
164C22×C13C2×SD1612yes—
165C22×C13C22×D411yescharacteristic
166C2×D13—21no—
167C2×D13—21no—
168C2×D13C2×SD1612yes—
169C4×C13—21no—
170C4×C13—41no—
171C4×C13—41no—
172C4×C13—41no—
173C4×C13C2×#4111yescharacteristic
174C4×C132−1+411yescharacteristic
175Dic13—21no—
176Dic13—21no—
177Dic13—41no—
178Dic13—41no—
179Dic13—41no—
180Dic13—41no—
181Dic13C2×SD1612yes—
182C2×#41—261no—
183C2×SD16—131no—
184C22×C8—131no—
185C22×C8—131no—
186C4⋊Q8—131no—
187C4⋊Q8—131no—
188#125—261no—
189#123—261no—
190#123—261no—
191C22⋊Q8—131no—
192C22⋊Q8—131no—
193C22⋊Q8—261no—
194C22⋊Q8—261no—
195C22⋊Q8—261no—
196#121—131no—
197#121C2×D1311yescharacteristic
198C4×Q8—131no—
199C4×D4—131no—
200C4×D4—131no—
201C4×D4—261no—
202C2×C4⋊C4—131no—
203C2×C4⋊C4—131no—
204C2×C4⋊C4—131no—
205C2×C4⋊C4C2×D1311yescharacteristic
206#106—131no—
207#106—131no—
208#106—131no—
209#106—131no—
210#106—131no—
211#106—131no—
212#106—131no—
213#106C2×D1311yescharacteristic
214#106C2×D1311yescharacteristic
215C4⋊C8—131no—
216#103—131no—
217#103—131no—
218#103—131no—
219#102—131no—
220#102C2×D1311yescharacteristic
221#102C2×D1311yescharacteristic
222C22⋊C8—131no—
223C22⋊C8C2×D1311yescharacteristic
224C4×C8—131no—
225C2×C13—22no—
226C2×C13—81no—
227C2×C13#54711yescharacteristic
228C2×C13C22×SD1611yescharacteristic
229C2×C13#57711yescharacteristic
230D13—22no—
231#41—524no—
232C2×Q8—131no—
233C2×Q8—261no—
234C2×Q8—261no—
235C2×D4—21no—
236C2×D4—131no—
237C2×D4—261no—
238C2×D4C22×D1311yescharacteristic
239C22×C4—21no—
240C22×C4—131no—
241C22×C4—261no—
242C22×C4—261no—
243C22×C4—261no—
244C22×C4—261no—
245C22×C4C22×D1311yescharacteristic
246SD16—262no—
247C2×C8—131no—
248C2×C8—131no—
249C2×C8—262no—
250C2×C8—262no—
251C2×C8C22×D1311yescharacteristic
252C2×C8C22×D1311yescharacteristic
253C4⋊C4—21no—
254C4⋊C4—131no—
255C4⋊C4—131no—
256C4⋊C4—131no—
257C4⋊C4—131no—
258C4⋊C4—261no—
259C4⋊C4—261no—
260C4⋊C4—261no—
261C4⋊C4—261no—
262C4⋊C4—261no—
263C4⋊C4—261no—
264C4⋊C4—261no—
265C4⋊C4—261no—
266C4⋊C4C22×D1311yescharacteristic
267C4⋊C4C22×D1311yescharacteristic
268C4⋊C4C22×D1311yescharacteristic
269C22⋊C4—21no—
270C22⋊C4—131no—
271C22⋊C4—131no—
272C22⋊C4—261no—
273C22⋊C4—261no—
274C22⋊C4—261no—
275C22⋊C4—261no—
276C42—131no—
277C42—261no—
278C13#333511yescharacteristic, complemented, Sylow
279C23—21no—
280C23—131no—
281C23D4×D1311yescharacteristic
282Q8—261no—
283Q8—261no—
284Q8—522no—
285Q8—1041no—
286D4—21no—
287D4—21no—
288D4—42no—
289D4—134no—
290D4—522no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—81no—
297C2×C4—131no—
298C2×C4—131no—
299C2×C4—131no—
300C2×C4—261no—
301C2×C4—261no—
302C2×C4—261no—
303C2×C4—261no—
304C2×C4—261no—
305C2×C4—261no—
306C2×C4—522no—
307C2×C4—522no—
308C2×C4—522no—
309C2×C4—1041no—
310C2×C4D4×D1311yescharacteristic
311C2×C4C23×D1311yescharacteristic
312C8—21no—
313C8—21no—
314C8—132no—
315C8—261no—
316C22—21no—
317C22—21no—
318C22—41no—
319C22—41no—
320C22—41no—
321C22—132no—
322C22—261no—
323C22—261no—
324C22SD16×D1312yes—
325C22C2×D4×D1311yescharacteristic
326C4—21no—
327C4—41no—
328C4—41no—
329C4—41no—
330C4—132no—
331C4—261no—
332C4—261no—
333C4—521no—
334C4—521no—
335C4—521no—
336C4—521no—
337C4#41×D1311yescharacteristic
338C4#8825711yescharacteristic
339C2—22no—
340C2—81no—
341C2—262no—
342C2#1171936011yescharacteristic
343C2C2×SD16×D1311yescharacteristic
344C2#1171948011yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#481C2
socleC22×C13C22×D4
prime radical#11719316C2
hypercenter#481D13
hypocenterC13#3335
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #481

Complements

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

NH ≅ G/Ntype
2. #11719216C2semidirect
3. C13×#481C2semidirect
4. #11718702C2semidirect
5. C2×#88048C2semidirect
6. #11718523C2semidirect
7. D13×#106C2semidirect
8. #11718516C2semidirect
9. #11718515C2semidirect
10. #11718439C2semidirect
11. #11718438C2semidirect
12. #11718422C2semidirect
13. #11718419C2semidirect
14. #11718386C2semidirect
15. #11718382C2semidirect
122. C22⋊D13SD16semidirect
143. #1055#41semidirect
150. #481D13semidirect
278. C13#3335semidirect

Maximal subgroups

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

subgroupindex
#117193162
#117192162
C13×#4812
#117187022
C2×#880482
#117185232
D13×#1062
#117185162
#117185152
#117184392
#117184382
#117184222
#117184192
#117183862
#117183822
#333513