Finite Group Databasebeta

← #13127415

Subgroups — #13127415

Order 1664.

374 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#11719346C211yesmaximal, characteristic, complemented
2#11719316C211yesmaximal, characteristic
3C13×#468C211yesmaximal, characteristic, complemented
4#11718835C211yesmaximal, characteristic, complemented
5SD16×Dic13C211yesmaximal, characteristic, complemented
6#11718789C211yesmaximal, characteristic, complemented
7#11718782C211yesmaximal, characteristic, complemented
8#11718705C211yesmaximal, characteristic, complemented
9#11718696C211yesmaximal, characteristic, complemented
10#11718542C211yesmaximal, characteristic, complemented
11#11718535C211yesmaximal, characteristic, complemented
12#11718470C211yesmaximal, characteristic, complemented
13#11718452C211yesmaximal, characteristic, complemented
14#11718440C211yesmaximal, characteristic, complemented
15#11718420C211yesmaximal, characteristic, complemented
16C2×#6129—21no—
17C2×C13×SD16C2211yescharacteristic
18C2×C13×M16C2211yescharacteristic
19C13×C22⋊Q8C2211yescharacteristic
20C13×#121C2211yescharacteristic
21#88200C2211yescharacteristic
22Q8×Dic13C2211yescharacteristic
23#88192C2211yescharacteristic
24#88189—21no—
25D4×Dic13C2211yescharacteristic
26C4×C22⋊D13C2211yescharacteristic
27#88180C2211yescharacteristic
28C2×C4⋊Dic13C2211yescharacteristic
29C2×#6094C2211yescharacteristic
30#88152—21no—
31#88146C2211yescharacteristic
32C4⋊C4×D13C2211yescharacteristic
33#88142C2211yescharacteristic
34#88142C2211yescharacteristic
35#88141—21no—
36#88139—21no—
37#88137—21no—
38#88133—21no—
39#88132—21no—
40C13×#107C2211yescharacteristic
41C13×#103C2211yescharacteristic
42C13×#102C2211yescharacteristic
43#88075C2211yescharacteristic
44#88075C2211yescharacteristic
45#88072C2211yescharacteristic
46#88072C2211yescharacteristic
47C22⋊#1055C2211yescharacteristic
48#88060C2211yescharacteristic
49#88058C2211yescharacteristic
50#88058C2211yescharacteristic
51#88057C2211yescharacteristic
52#88057C2211yescharacteristic
53#88054C2211yescharacteristic
54C8×Dic13C2211yescharacteristic
55#88048C2211yescharacteristic
56#88047C2211yescharacteristic
57#88047C2211yescharacteristic
58#88047C2211yescharacteristic
59C2×Q8×C13C2311yescharacteristic
60C2×D4×C13—21no—
61C2×D4×C13C2311yescharacteristic
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×Dic26—21no—
72C13×SD16—22no—
73C13×M16—22no—
74C2×C8×C13C2311yescharacteristic
75C2×C8×C13C2311yescharacteristic
76C13×C4⋊C4—21no—
77C13×C4⋊C4C2311yescharacteristic
78C13×C4⋊C4C2311yescharacteristic
79C13×C22⋊C4—21no—
80C13×C22⋊C4—21no—
81C22⋊Dic13—21no—
82C22⋊Dic13—21no—
83C22⋊Dic13—21no—
84C22⋊Dic13D411yescharacteristic
85#6103—21no—
86#6103—21no—
87#6103D411yescharacteristic
88C4⋊Dic13—21no—
89C4⋊Dic13—21no—
90C4⋊Dic13C2311yescharacteristic
91C4⋊Dic13C2311yescharacteristic
92C4⋊Dic13C2311yescharacteristic
93C4⋊Dic13C2311yescharacteristic
94#6101—21no—
95#6101—21no—
96#6101—21no—
97#6101—21no—
98#6101D411yescharacteristic
99C4×Dic13—21no—
100C4×Dic13—21no—
101C4×Dic13—21no—
102C4×Dic13C2311yescharacteristic
103C2×#1055C2311yescharacteristic
104C2×#1055C2311yescharacteristic
105#6094—22no—
106#3353—131nomaximal, Sylow
107C23×C13—21no—
108C23×C13C2×D411yescharacteristic
109C22×D13C2×D411yescharacteristic
110Q8×C13—21no—
111Q8×C13—21no—
112D4×C13—21no—
113D4×C13—21no—
114D4×C13—42no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13C2×D411yescharacteristic
121C2×C4×C13C2411yescharacteristic
122C22⋊D13—22no—
123C22⋊D13—42no—
124C2×Dic13—21no—
125C2×Dic13—21no—
126C2×Dic13—21no—
127C2×Dic13—21no—
128C2×Dic13—42no—
129C2×Dic13—42no—
130C2×Dic13C2×D411yescharacteristic
131C2×Dic13C2×D411yescharacteristic
132C2×Dic13C2×D411yescharacteristic
133C4×D13—21no—
134C4×D13—21no—
135C4×D13—42no—
136Dic26—42no—
137Dic26—42no—
138C8×C13—21no—
139C8×C13#4112yescomplemented
140#1055—21no—
141#1055—21no—
142#556—131no—
143#547—131no—
144#500—131no—
145#484—131no—
146#484—131no—
147#482—131no—
148#482—131no—
149#475—131no—
150#474—131no—
151#468—131no—
152#468D1311yescharacteristic, complemented
153C4×SD16—131no—
154#436—131no—
155#428—131no—
156#428—131no—
157C22×C13—21no—
158C22×C13—21no—
159C22×C13—21no—
160C22×C13—41no—
161C22×C13—41no—
162C22×C13—41no—
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—41no—
176Dic13—41no—
177Dic13—41no—
178Dic13—41no—
179Dic13AGL(1,ℤ/8)12yes—
180C2×#41—261no—
181C2×SD16C2×D1311yescharacteristic
182C2×M16—131no—
183C2×M16C2×D1311yescharacteristic
184C4⋊Q8—131no—
185C4⋊Q8—131no—
186#126—261no—
187#126—261no—
188#124—261no—
189#123—261no—
190#123—261no—
191C22⋊Q8—131no—
192C22⋊Q8—261no—
193C22⋊Q8C2×D1311yescharacteristic
194#121—131no—
195#121C2×D1311yescharacteristic
196C4×Q8—131no—
197C4×Q8—261no—
198C4×D4—131no—
199C4×D4—131no—
200#117—131no—
201#117—131no—
202C2×C4⋊C4—131no—
203C2×C4⋊C4—131no—
204#107—131no—
205#107—131no—
206#107—131no—
207#107—131no—
208#107—131no—
209#107C2×D1311yescharacteristic
210#106—131no—
211#106—131no—
212#106—131no—
213C4⋊C8—131no—
214#103—131no—
215#103—131no—
216#103C2×D1311yescharacteristic
217#102—131no—
218#102—131no—
219#102C2×D1311yescharacteristic
220C22⋊C8—131no—
221C22⋊C8—131no—
222C4×C8—131no—
223C2×C13—41no—
224C2×C13—81no—
225C2×C13#54711yescharacteristic
226C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
227C2×C13#57811yescharacteristic
228D13—41no—
229#41—524no—
230C2×Q8—261no—
231C2×Q8—261no—
232C2×Q8C22×D1311yescharacteristic
233C2×D4—21no—
234C2×D4—131no—
235C2×D4—261no—
236C2×D4C22×D1311yescharacteristic
237C22×C4—131no—
238C22×C4—261no—
239C22×C4—261no—
240C22×C4—261no—
241C22×C4C22×D1311yescharacteristic
242SD16—22no—
243M16—22no—
244M16—262no—
245C2×C8—131no—
246C2×C8—131no—
247C2×C8C22×D1311yescharacteristic
248C2×C8C22×D1311yescharacteristic
249C4⋊C4—21no—
250C4⋊C4—131no—
251C4⋊C4—131no—
252C4⋊C4—131no—
253C4⋊C4—131no—
254C4⋊C4—131no—
255C4⋊C4—261no—
256C4⋊C4—261no—
257C4⋊C4—261no—
258C4⋊C4—261no—
259C4⋊C4—261no—
260C4⋊C4—261no—
261C4⋊C4C22×D1311yescharacteristic
262C4⋊C4C22×D1311yescharacteristic
263C22⋊C4—21no—
264C22⋊C4—21no—
265C22⋊C4—131no—
266C22⋊C4—131no—
267C22⋊C4—261no—
268C22⋊C4—261no—
269C22⋊C4—261no—
270C22⋊C4—261no—
271C22⋊C4—261no—
272C42—131no—
273C42—261no—
274C42—261no—
275C42—261no—
276C13#335311yescharacteristic, complemented, Sylow
277C23—21no—
278C23—131no—
279C23D4×D1311yescharacteristic
280Q8—21no—
281Q8—21no—
282Q8—522no—
283Q8—522no—
284D4—21no—
285D4—21no—
286D4—42no—
287D4—262no—
288D4—522no—
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—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—261no—
310C8—261no—
311C8#612912yescomplemented
312C22—21no—
313C22—21no—
314C22—21no—
315C22—41no—
316C22—41no—
317C22—41no—
318C22—261no—
319C22—261no—
320C22—261no—
321C22C2×D4×D1311yescharacteristic
322C4—21no—
323C4—41no—
324C4—41no—
325C4—41no—
326C4—132no—
327C4—261no—
328C4—261no—
329C4—521no—
330C4—521no—
331C4—521no—
332C4—521no—
333C4C2×#612911yescharacteristic
334C4#8825711yescharacteristic
335C2—41no—
336C2—81no—
337C2—521no—
338C2#1171931611yescharacteristic
339C2D13×AGL(1,ℤ/8)11yescharacteristic
340C2#1171948411yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#468C2
socleC22×C13C22×D4
prime radical#11719316C2
hypercenter#468D13
hypocenterC13#3353
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. #11719346C2semidirect
3. C13×#468C2semidirect
4. #11718835C2semidirect
5. SD16×Dic13C2semidirect
6. #11718789C2semidirect
7. #11718782C2semidirect
8. #11718705C2semidirect
9. #11718696C2semidirect
10. #11718542C2semidirect
11. #11718535C2semidirect
12. #11718470C2semidirect
13. #11718452C2semidirect
14. #11718440C2semidirect
15. #11718420C2semidirect
139. C8×C13#41semidirect
152. #468D13semidirect
276. C13#3353semidirect
311. C8#6129semidirect

Maximal subgroups

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

subgroupindex
#117193462
#117193162
C13×#4682
#117188352
SD16×Dic132
#117187892
#117187822
#117187052
#117186962
#117185422
#117185352
#117184702
#117184522
#117184402
#117184202
#335313