Finite Group Databasebeta

← #13127413

Subgroups — #13127413

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#11719212C211yesmaximal, characteristic
3C13×#484C211yesmaximal, characteristic, complemented
4#11718710C211yesmaximal, characteristic, complemented
5#11718625C211yesmaximal, characteristic, complemented
6#11718551C211yesmaximal, characteristic, complemented
7#11718546C211yesmaximal, characteristic, complemented
8#11718542C211yesmaximal, characteristic, complemented
9#11718535C211yesmaximal, characteristic, complemented
10#11718473C211yesmaximal, characteristic, complemented
11#11718470C211yesmaximal, characteristic, complemented
12#11718452C211yesmaximal, characteristic, complemented
13#11718449C211yesmaximal, characteristic, complemented
14#11718398C211yesmaximal, characteristic, complemented
15#11718390C211yesmaximal, characteristic, complemented
16C2×#6127—21no—
17C13×C22⋊Q8C2211yescharacteristic
18C2×C13×C4⋊C4C2211yescharacteristic
19#88200C2211yescharacteristic
20Q8×Dic13C2211yescharacteristic
21C2×#6106C2211yescharacteristic
22#88184C2211yescharacteristic
23#88183—21no—
24C4×C22⋊D13C2211yescharacteristic
25#88180C2211yescharacteristic
26C2×#6099C2211yescharacteristic
27C2×#6094C2211yescharacteristic
28#88152—21no—
29#88150—21no—
30#88149C2211yescharacteristic
31#88148—21no—
32#88147C2211yescharacteristic
33#88146C2211yescharacteristic
34C4⋊C4×D13C2211yescharacteristic
35#88142C2211yescharacteristic
36#88142C2211yescharacteristic
37#88141—21no—
38#88139—21no—
39#88133—21no—
40C13×#107C2211yescharacteristic
41C13×#107C2211yescharacteristic
42C13×#103C2211yescharacteristic
43C13×#103C2211yescharacteristic
44C13×C22⋊C8C2211yescharacteristic
45#88075C2211yescharacteristic
46#88061C2211yescharacteristic
47#88061C2211yescharacteristic
48#88060C2211yescharacteristic
49#88058C2211yescharacteristic
50#88057C2211yescharacteristic
51#88054C2211yescharacteristic
52C8×Dic13C2211yescharacteristic
53#88049C2211yescharacteristic
54#88048C2211yescharacteristic
55#88048C2211yescharacteristic
56#88047C2211yescharacteristic
57#88047C2211yescharacteristic
58#88047C2211yescharacteristic
59C2×Q8×C13C2311yescharacteristic
60C22×C4×C13—21no—
61C22×C4×C13C2311yescharacteristic
62C2×C22⋊D13—21no—
63C2×C22⋊D13D411yescharacteristic
64#6127—44no—
65C2×D52—21no—
66C2×D52C2311yescharacteristic
67C2×C4×D13—21no—
68C2×C4×D13—21no—
69C2×C4×D13C2311yescharacteristic
70C2×Dic26—21no—
71C2×Dic26—21no—
72C2×C8×C13C2311yescharacteristic
73C2×C8×C13C2311yescharacteristic
74C13×C4⋊C4—21no—
75C13×C4⋊C4—21no—
76C13×C4⋊C4C2311yescharacteristic
77C13×C4⋊C4C2311yescharacteristic
78C13×C4⋊C4C2311yescharacteristic
79C13×C22⋊C4—21no—
80C22⋊Dic13—21no—
81C22⋊Dic13D411yescharacteristic
82#6106—22no—
83#6103—21no—
84#6103—21no—
85#6103—21no—
86#6103—21no—
87#6103—21no—
88#6103D411yescharacteristic
89C4⋊Dic13—21no—
90C4⋊Dic13C2311yescharacteristic
91C4⋊Dic13C2311yescharacteristic
92C4⋊Dic13C2311yescharacteristic
93#6101—21no—
94#6101—21no—
95#6101—21no—
96#6101—21no—
97#6101D411yescharacteristic
98C4×Dic13—21no—
99C4×Dic13—21no—
100C4×Dic13—21no—
101C4×Dic13C2311yescharacteristic
102#6099—22no—
103C2×#1055C2311yescharacteristic
104C2×#1055C2311yescharacteristic
105#6094—22no—
106#3353—131nomaximal, Sylow
107C23×C13C2×D411yescharacteristic
108C22×D13—21no—
109C22×D13C2×D411yescharacteristic
110Q8×C13—21no—
111Q8×C13—21no—
112C2×C4×C13—21no—
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×Dic13C2×D411yescharacteristic
127C2×Dic13C2×D411yescharacteristic
128C2×Dic13C2×D411yescharacteristic
129D52—21no—
130D52—21no—
131D52—42no—
132C4×D13—21no—
133C4×D13—21no—
134C4×D13—42no—
135C4×D13—42no—
136Dic26—42no—
137Dic26—42no—
138C8×C13—21no—
139C8×C13—21no—
140#1055—21no—
141#1055#4112yescomplemented
142#556—131no—
143#547—131no—
144#500—131no—
145#484—131no—
146#484D1311yescharacteristic, complemented
147#482—131no—
148#482—131no—
149#475—131no—
150#474—131no—
151#468—131no—
152#468—131no—
153C4×SD16—131no—
154#436—131no—
155#428—131no—
156#428—131no—
157C22×C13—21no—
158C22×C13—21no—
159C22×C13—21no—
160C22×C13C22×D411yescharacteristic
161C2×D13—21no—
162C2×D13—21no—
163C2×D13—21no—
164C2×D13—41no—
165C2×D13—41no—
166C2×D13—41no—
167C4×C13—21no—
168C4×C13—41no—
169C4×C13—41no—
170C4×C13—41no—
171C4×C13—41no—
172C4×C13C2×#4111yescharacteristic
173C4×C132−1+411yescharacteristic
174Dic13—21no—
175Dic13—21no—
176Dic13—41no—
177Dic13—41no—
178Dic13—41no—
179Dic13AGL(1,ℤ/8)12yes—
180C2×#41—261no—
181C2×SD16—131no—
182C2×M16—131no—
183C2×M16—131no—
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#121—131no—
196C4×Q8—131no—
197C4×Q8—261no—
198C4×D4—131no—
199C4×D4—131no—
200#117—131no—
201#117—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#103C2×D1311yescharacteristic
216#103C2×D1311yescharacteristic
217#102—131no—
218#102—131no—
219#102—131no—
220C22⋊C8—131no—
221C22⋊C8C2×D1311yescharacteristic
222C4×C8—131no—
223C2×C13—41no—
224C2×C13#54711yescharacteristic
225C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
226C2×C13#57811yescharacteristic
227D13—41no—
228D13—81no—
229#41—524no—
230C2×Q8—261no—
231C2×Q8—261no—
232C2×Q8C22×D1311yescharacteristic
233C2×D4—131no—
234C2×D4—131no—
235C2×D4—261no—
236C2×D4—261no—
237C22×C4—21no—
238C22×C4—131no—
239C22×C4—261no—
240C22×C4—261no—
241C22×C4C22×D1311yescharacteristic
242SD16—262no—
243M16—262no—
244M16—262no—
245C2×C8—131no—
246C2×C8—131no—
247C2×C8C22×D1311yescharacteristic
248C2×C8C22×D1311yescharacteristic
249C4⋊C4—21no—
250C4⋊C4—21no—
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⋊C4C22×D1311yescharacteristic
261C4⋊C4C22×D1311yescharacteristic
262C4⋊C4C22×D1311yescharacteristic
263C22⋊C4—21no—
264C22⋊C4—131no—
265C22⋊C4—131no—
266C22⋊C4—261no—
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—131no—
278C23—261no—
279C23D4×D1311yescharacteristic
280Q8—21no—
281Q8—21no—
282Q8—522no—
283Q8—522no—
284D4—262no—
285D4—261no—
286D4—261no—
287D4—522no—
288D4—522no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—42no—
296C2×C4—131no—
297C2×C4—131no—
298C2×C4—131no—
299C2×C4—261no—
300C2×C4—261no—
301C2×C4—261no—
302C2×C4—261no—
303C2×C4—261no—
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—21no—
315C22—261no—
316C22—261no—
317C22—261no—
318C22—521no—
319C22—521no—
320C22—521no—
321C22C2×D4×D1311yescharacteristic
322C4—21no—
323C4—41no—
324C4—41no—
325C4—41no—
326C4—41no—
327C4—132no—
328C4—261no—
329C4—261no—
330C4—521no—
331C4—521no—
332C4—521no—
333C4#41×D1311yescharacteristic
334C4#8825711yescharacteristic
335C2—41no—
336C2—521no—
337C2—1041no—
338C2#1171936011yescharacteristic
339C2#1171947111yescharacteristic
340C2D13×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#484C2
socleC22×C13C22×D4
prime radical#11719212C2
hypercenter#484D13
hypocenterC13#3353
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
1. #11719346C2semidirect
3. C13×#484C2semidirect
4. #11718710C2semidirect
5. #11718625C2semidirect
6. #11718551C2semidirect
7. #11718546C2semidirect
8. #11718542C2semidirect
9. #11718535C2semidirect
10. #11718473C2semidirect
11. #11718470C2semidirect
12. #11718452C2semidirect
13. #11718449C2semidirect
14. #11718398C2semidirect
15. #11718390C2semidirect
141. #1055#41semidirect
146. #484D13semidirect
276. C13#3353semidirect

Maximal subgroups

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

subgroupindex
#117193462
#117192122
C13×#4842
#117187102
#117186252
#117185512
#117185462
#117185422
#117185352
#117184732
#117184702
#117184522
#117184492
#117183982
#117183902
#335313