Finite Group Databasebeta

← #13127280

Subgroups — #13127280

Order 1664.

376 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719316C211yesmaximal, characteristic
2#11719218C211yesmaximal, characteristic, complemented
3C13×#480C211yesmaximal, characteristic, complemented
4#11718702C211yesmaximal, characteristic, complemented
5C2×#88047C211yesmaximal, characteristic, complemented
6#11718545C211yesmaximal, characteristic, complemented
7#11718542C211yesmaximal, characteristic, complemented
8#11718537C211yesmaximal, characteristic, complemented
9#11718536C211yesmaximal, characteristic, complemented
10#11718441C211yesmaximal, characteristic, complemented
11#11718440C211yesmaximal, characteristic, complemented
12#11718424C211yesmaximal, characteristic, complemented
13#11718418C211yesmaximal, characteristic, complemented
14#11718391C211yesmaximal, characteristic, complemented
15#11718382C211yesmaximal, characteristic, complemented
16C2×#6129—21no—
17C13×#121C2211yescharacteristic
18C2×C13×C4⋊C4C2211yescharacteristic
19#88192C2211yescharacteristic
20#88189—21no—
21D4×Dic13C2211yescharacteristic
22C2×#6105C2211yescharacteristic
23#88183—21no—
24C4×C22⋊D13C2211yescharacteristic
25#88180—21no—
26C2×C4⋊Dic13C2211yescharacteristic
27#88178C2211yescharacteristic
28C22×#1055C2211yescharacteristic
29C2×#6094C2211yescharacteristic
30#88152—21no—
31#88151C2211yescharacteristic
32#88146C2211yescharacteristic
33C4⋊C4×D13C2211yescharacteristic
34#88144C2211yescharacteristic
35#88143—21no—
36#88142C2211yescharacteristic
37#88141C2211yescharacteristic
38#88137—21no—
39#88132—21no—
40C13×#107C2211yescharacteristic
41C13×#107C2211yescharacteristic
42C13×#102C2211yescharacteristic
43C13×#102C2211yescharacteristic
44C13×C22⋊C8C2211yescharacteristic
45#88072C2211yescharacteristic
46#88060C2211yescharacteristic
47#88057C2211yescharacteristic
48#88057C2211yescharacteristic
49#88056C2211yescharacteristic
50#88056C2211yescharacteristic
51#88055C2211yescharacteristic
52#88054C2211yescharacteristic
53#88050C2211yescharacteristic
54#88048C2211yescharacteristic
55#88047C2211yescharacteristic
56#88047C2211yescharacteristic
57#88047C2211yescharacteristic
58#88047C2211yescharacteristic
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×D13C2311yescharacteristic
70C2×Dic26—21no—
71C2×Dic26C2311yescharacteristic
72C2×C8×C13C2311yescharacteristic
73C2×C8×C13C2311yescharacteristic
74C13×C4⋊C4—21no—
75C13×C4⋊C4C2311yescharacteristic
76C13×C4⋊C4C2311yescharacteristic
77C13×C4⋊C4C2311yescharacteristic
78C13×C22⋊C4—21no—
79C22⋊Dic13—21no—
80C22⋊Dic13—21no—
81C22⋊Dic13—21no—
82C22⋊Dic13D411yescharacteristic
83#6105—22no—
84#6103—21no—
85#6103—21no—
86#6103D411yescharacteristic
87C4⋊Dic13—21no—
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#6101D411yescharacteristic
99C4×Dic13—21no—
100C4×Dic13—21no—
101C4×Dic13C2311yescharacteristic
102C2×#1055—22no—
103C2×#1055C2311yescharacteristic
104C2×#1055C2311yescharacteristic
105#6094—22no—
106#3343—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—42no—
119C2×C4×C13C2×D411yescharacteristic
120C2×C4×C13C2411yescharacteristic
121C22⋊D13—22no—
122C22⋊D13—42no—
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—
135Dic26—21no—
136Dic26—21no—
137Dic26—42no—
138C8×C13—21no—
139C8×C13—21no—
140#1055—21no—
141#1055#4112yescomplemented
142#552—131no—
143#547—131no—
144#501—131no—
145#484—131no—
146#483—131no—
147#482—131no—
148#480D1311yescharacteristic, complemented
149#478—131no—
150#477—131no—
151#468—131no—
152#465—131no—
153#440—131no—
154#435—131no—
155#428—131no—
156C2×#107—131no—
157C22×C13—21no—
158C22×C13—21no—
159C22×C13—41no—
160C22×C13—41no—
161C22×C13—41no—
162C22×C13AGL(1,ℤ/8)12yes—
163C22×C13C22×D411yescharacteristic
164C2×D13—21no—
165C2×D13—21no—
166C2×D13—21no—
167C4×C13—21no—
168C4×C13—41no—
169C4×C13—41no—
170C4×C13—41no—
171C4×C13C2×#4111yescharacteristic
172C4×C132−1+411yescharacteristic
173Dic13—21no—
174Dic13—21no—
175Dic13—21no—
176Dic13—41no—
177Dic13—41no—
178Dic13—41no—
179Dic13—41no—
180C2×#41—261no—
181C2×SD16—131no—
182C2×M16—131no—
183C22×C8—131no—
184C4⋊Q8—131no—
185#126—261no—
186#125—131no—
187#125—261no—
188#123—261no—
189#123—261no—
190#123—261no—
191C22⋊Q8—131no—
192C22⋊Q8—131no—
193C22⋊Q8—261no—
194#121—131no—
195#121C2×D1311yescharacteristic
196C4×Q8—131no—
197C4×D4—131no—
198C4×D4—131no—
199#117—131no—
200#117—261no—
201C2×C4⋊C4—131no—
202C2×C4⋊C4—131no—
203C2×C4⋊C4C2×D1311yescharacteristic
204#107—131no—
205#107—131no—
206#107—131no—
207#107—131no—
208#107C2×D1311yescharacteristic
209#107C2×D1311yescharacteristic
210#106—131no—
211#106—131no—
212#106—131no—
213C4⋊C8—131no—
214#103—131no—
215#103—131no—
216#103—131no—
217#102—131no—
218#102C2×D1311yescharacteristic
219#102C2×D1311yescharacteristic
220C22⋊C8—131no—
221C22⋊C8C2×D1311yescharacteristic
222#97—131no—
223C2×C13—22no—
224C2×C13—81no—
225C2×C13#54711yescharacteristic
226C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
227C2×C13#57811yescharacteristic
228D13—41no—
229#41—524no—
230C2×Q8—131no—
231C2×Q8—261no—
232C2×D4—21no—
233C2×D4—131no—
234C2×D4—261no—
235C2×D4C22×D1311yescharacteristic
236C22×C4—21no—
237C22×C4—131no—
238C22×C4—261no—
239C22×C4—261no—
240C22×C4—261no—
241C22×C4C22×D1311yescharacteristic
242SD16—262no—
243M16—262no—
244C2×C8—131no—
245C2×C8—131no—
246C2×C8—262no—
247C2×C8C22×D1311yescharacteristic
248C2×C8C22×D1311yescharacteristic
249C4⋊C4—21no—
250C4⋊C4—131no—
251C4⋊C4—131no—
252C4⋊C4—131no—
253C4⋊C4—131no—
254C4⋊C4—261no—
255C4⋊C4—261no—
256C4⋊C4—261no—
257C4⋊C4—261no—
258C4⋊C4—261no—
259C4⋊C4—261no—
260C4⋊C4—261no—
261C4⋊C4—261no—
262C4⋊C4C22×D1311yescharacteristic
263C4⋊C4C22×D1311yescharacteristic
264C4⋊C4C22×D1311yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—131no—
267C22⋊C4—131no—
268C22⋊C4—261no—
269C22⋊C4—261no—
270C22⋊C4—261no—
271C22⋊C4—261no—
272C22⋊C4—261no—
273C42—131no—
274C42—261no—
275C42—261no—
276C13#334311yescharacteristic, complemented, Sylow
277C23—21no—
278C23—131no—
279C23D4×D1311yescharacteristic
280Q8—261no—
281Q8—261no—
282Q8—522no—
283D4—21no—
284D4—21no—
285D4—42no—
286D4—262no—
287D4—522no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—42no—
294C2×C4—131no—
295C2×C4—131no—
296C2×C4—131no—
297C2×C4—261no—
298C2×C4—261no—
299C2×C4—261no—
300C2×C4—261no—
301C2×C4—261no—
302C2×C4—261no—
303C2×C4—522no—
304C2×C4—522no—
305C2×C4—522no—
306C2×C4D4×D1311yescharacteristic
307C2×C4C23×D1311yescharacteristic
308C8—21no—
309C8—21no—
310C8—132no—
311C8—261no—
312C22—21no—
313C22—21no—
314C22—41no—
315C22—41no—
316C22—41no—
317C22—261no—
318C22—261no—
319C22—261no—
320C22#8816512yes—
321C22C2×D4×D1311yescharacteristic
322C4—21no—
323C4—41no—
324C4—41no—
325C4—41no—
326C4—261no—
327C4—261no—
328C4—261no—
329C4—521no—
330C4—521no—
331C4—521no—
332C4—521no—
333C4#41×D1311yescharacteristic
334C4#8825711yescharacteristic
335C2—22no—
336C2—81no—
337C2—521no—
338C2#1171936011yescharacteristic
339C2C2×#8816511yescharacteristic
340C2#1171948411yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#480C2
socleC22×C13C22×D4
prime radical#11719316C2
hypercenter#480D13
hypocenterC13#3343
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
2. #11719218C2semidirect
3. C13×#480C2semidirect
4. #11718702C2semidirect
5. C2×#88047C2semidirect
6. #11718545C2semidirect
7. #11718542C2semidirect
8. #11718537C2semidirect
9. #11718536C2semidirect
10. #11718441C2semidirect
11. #11718440C2semidirect
12. #11718424C2semidirect
13. #11718418C2semidirect
14. #11718391C2semidirect
15. #11718382C2semidirect
141. #1055#41semidirect
148. #480D13semidirect
276. C13#3343semidirect

Maximal subgroups

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

subgroupindex
#117193162
#117192182
C13×#4802
#117187022
C2×#880472
#117185452
#117185422
#117185372
#117185362
#117184412
#117184402
#117184242
#117184182
#117183912
#117183822
#334313