Finite Group Databasebeta

← #13127416

Subgroups — #13127416

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#11719238C211yesmaximal, characteristic, complemented
2#11719212C211yesmaximal, characteristic
3C13×#428C211yesmaximal, characteristic, complemented
4#11718795C211yesmaximal, characteristic, complemented
5#11718789C211yesmaximal, characteristic, complemented
6#11718664C211yesmaximal, characteristic, complemented
7#11718631C211yesmaximal, characteristic, complemented
8#11718551C211yesmaximal, characteristic, complemented
9#11718547C211yesmaximal, characteristic, complemented
10#11718545C211yesmaximal, characteristic, complemented
11#11718535C211yesmaximal, characteristic, complemented
12#11718527C211yesmaximal, characteristic, complemented
13#11718522C211yesmaximal, characteristic, complemented
14#11718515C211yesmaximal, characteristic, complemented
15#11718513C211yesmaximal, characteristic, complemented
16C2×#6127—21no—
17C2×C13×M16C2211yescharacteristic
18C13×#117C2211yescharacteristic
19C2×C13×C4⋊C4C2211yescharacteristic
20#88184C2211yescharacteristic
21#88183—21no—
22C4×C22⋊D13C2211yescharacteristic
23#88178C2211yescharacteristic
24C2×#6095C2211yescharacteristic
25C2×#6094C2211yescharacteristic
26#88151C2211yescharacteristic
27#88150—21no—
28#88149C2211yescharacteristic
29#88148—21no—
30#88147C2211yescharacteristic
31#88146C2211yescharacteristic
32C4⋊C4×D13C2211yescharacteristic
33#88142C2211yescharacteristic
34#88142C2211yescharacteristic
35#88141C2211yescharacteristic
36#88139—21no—
37#88133—21no—
38#88130—21no—
39C4×Dic26—21no—
40C13×#107C2211yescharacteristic
41C13×#107C2211yescharacteristic
42C13×#106C2211yescharacteristic
43C13×#106C2211yescharacteristic
44C22⋊#1055C2211yescharacteristic
45#88061C2211yescharacteristic
46#88060C2211yescharacteristic
47#88058C2211yescharacteristic
48#88056C2211yescharacteristic
49#88054C2211yescharacteristic
50C8×Dic13C2211yescharacteristic
51#88050C2211yescharacteristic
52#88050C2211yescharacteristic
53#88049C2211yescharacteristic
54#88049C2211yescharacteristic
55#88048C2211yescharacteristic
56#88047C2211yescharacteristic
57#88047C2211yescharacteristic
58#88047C2211yescharacteristic
59C22×C4×C13—21no—
60C22×C4×C13C2311yescharacteristic
61C2×C22⋊D13—21no—
62C2×C22⋊D13D411yescharacteristic
63#6127—44no—
64C2×D52—21no—
65C2×D52C2311yescharacteristic
66C2×C4×D13—21no—
67C2×C4×D13—21no—
68C2×C4×D13C2311yescharacteristic
69C2×Dic26—21no—
70C2×Dic26—21no—
71C2×Dic26C2311yescharacteristic
72C13×M16—22no—
73C2×C8×C13C2311yescharacteristic
74C2×C8×C13C2311yescharacteristic
75C13×C4⋊C4—21no—
76C13×C4⋊C4C2311yescharacteristic
77C13×C4⋊C4C2311yescharacteristic
78C13×C4⋊C4C2311yescharacteristic
79C13×C4⋊C4C2311yescharacteristic
80C13×C22⋊C4—21no—
81C42×C13—21no—
82C22⋊Dic13—21no—
83C22⋊Dic13D411yescharacteristic
84#6103—21no—
85#6103—21no—
86#6103—21no—
87#6103—21no—
88#6103—21no—
89#6103D411yescharacteristic
90C4⋊Dic13—21no—
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×#1055C2311yescharacteristic
103C2×#1055C2311yescharacteristic
104#6095—22no—
105#6094—22no—
106#3353—131nomaximal, Sylow
107C23×C13C2×D411yescharacteristic
108C22×D13—21no—
109C22×D13C2×D411yescharacteristic
110C2×C4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—42no—
117C2×C4×C13C2×D411yescharacteristic
118C2×C4×C13C2411yescharacteristic
119C22⋊D13—22no—
120C22⋊D13—42no—
121C2×Dic13—21no—
122C2×Dic13—21no—
123C2×Dic13—21no—
124C2×Dic13C2×D411yescharacteristic
125C2×Dic13C2×D411yescharacteristic
126C2×Dic13C2×D411yescharacteristic
127D52—21no—
128D52—21no—
129D52—42no—
130C4×D13—21no—
131C4×D13—21no—
132C4×D13—42no—
133C4×D13—42no—
134Dic26—21no—
135Dic26—21no—
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#468—131no—
153C4×SD16—131no—
154#436—131no—
155#428—131no—
156#428D1311yescharacteristic, complemented
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×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—131no—
193C22⋊Q8—261no—
194#121—131no—
195#121—131no—
196C4×Q8—131no—
197C4×Q8—261no—
198C4×D4—131no—
199C4×D4—131no—
200#117—131no—
201#117C2×D1311yescharacteristic
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#106C2×D1311yescharacteristic
212#106C2×D1311yescharacteristic
213C4⋊C8—131no—
214#103—131no—
215#103—131no—
216#103—131no—
217#102—131no—
218#102—131no—
219#102—131no—
220C22⋊C8—131no—
221C22⋊C8—131no—
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—131no—
231C2×Q8—261no—
232C2×Q8—261no—
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—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—261no—
254C4⋊C4—261no—
255C4⋊C4—261no—
256C4⋊C4—261no—
257C4⋊C4—261no—
258C4⋊C4—261no—
259C4⋊C4C22×D1311yescharacteristic
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—21no—
273C42—131no—
274C42—261no—
275C42—261no—
276C13#335311yescharacteristic, complemented, Sylow
277C23—131no—
278C23—261no—
279C23D4×D1311yescharacteristic
280Q8—261no—
281Q8—261no—
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—261no—
310C8—261no—
311C8#612712yescomplemented
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—
333C4C2×#612711yescharacteristic
334C4#8825411yescharacteristic
335C2—41no—
336C2—521no—
337C2—1041no—
338C2#1171921211yescharacteristic
339C2D13×AGL(1,ℤ/8)11yescharacteristic
340C2#1171948411yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#428C2
socleC22×C13C22×D4
prime radical#11719212C2
hypercenter#428D13
hypocenterC13#3353
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
1. #11719238C2semidirect
3. C13×#428C2semidirect
4. #11718795C2semidirect
5. #11718789C2semidirect
6. #11718664C2semidirect
7. #11718631C2semidirect
8. #11718551C2semidirect
9. #11718547C2semidirect
10. #11718545C2semidirect
11. #11718535C2semidirect
12. #11718527C2semidirect
13. #11718522C2semidirect
14. #11718515C2semidirect
15. #11718513C2semidirect
139. C8×C13#41semidirect
156. #428D13semidirect
276. C13#3353semidirect
311. C8#6127semidirect

Maximal subgroups

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

subgroupindex
#117192382
#117192122
C13×#4282
#117187952
#117187892
#117186642
#117186312
#117185512
#117185472
#117185452
#117185352
#117185272
#117185222
#117185152
#117185132
#335313