Finite Group Databasebeta

← #13127275

Subgroups — #13127275

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#11719431C211yesmaximal, characteristic
2#11719399C211yesmaximal, characteristic, complemented
3C13×#501C211yesmaximal, characteristic, complemented
4#11718752C211yesmaximal, characteristic, complemented
5#11718727C211yesmaximal, characteristic, complemented
6#11718547C211yesmaximal, characteristic, complemented
7#11718545C211yesmaximal, characteristic, complemented
8#11718543C211yesmaximal, characteristic, complemented
9D13×#107C211yesmaximal, characteristic, complemented
10#11718527C211yesmaximal, characteristic, complemented
11#11718525C211yesmaximal, characteristic, complemented
12#11718523C211yesmaximal, characteristic, complemented
13#11718522C211yesmaximal, characteristic, complemented
14#11718371C211yesmaximal, characteristic, complemented
15#11718367C211yesmaximal, characteristic, complemented
16C2×#6131—21no—
17C13×C4⋊Q8C2211yescharacteristic
18C13×#125C2211yescharacteristic
19#88200—21no—
20C2×#6095C2211yescharacteristic
21C2×#6094C2211yescharacteristic
22C2×C8×D13C2211yescharacteristic
23#88152—21no—
24#88151C2211yescharacteristic
25#88151C2211yescharacteristic
26#88149C2211yescharacteristic
27#88149C2211yescharacteristic
28#88148—21no—
29#88148—21no—
30#88148—21no—
31#88146—21no—
32#88146C2211yescharacteristic
33C4⋊C4×D13C2211yescharacteristic
34C4⋊C4×D13C2211yescharacteristic
35C4⋊C4×D13C2211yescharacteristic
36#88144—21no—
37C4×D52C2211yescharacteristic
38C4×D52C2211yescharacteristic
39C4×Dic26C2211yescharacteristic
40C13×#107C2211yescharacteristic
41C13×#107C2211yescharacteristic
42C13×#106C2211yescharacteristic
43C13×#106C2211yescharacteristic
44C13×#97C2211yescharacteristic
45#88061C2211yescharacteristic
46#88060C2211yescharacteristic
47#88060C2211yescharacteristic
48#88058C2211yescharacteristic
49#88056C2211yescharacteristic
50#88050C2211yescharacteristic
51#88050C2211yescharacteristic
52#88049C2211yescharacteristic
53#88049C2211yescharacteristic
54#88048C2211yescharacteristic
55#88047C2211yescharacteristic
56#88047C2211yescharacteristic
57#88047C2211yescharacteristic
58C4⋊#1055C2211yescharacteristic
59C2×Q8×C13—21no—
60#6131—44no—
61C2×D52—21no—
62C2×D52—21no—
63C2×D52D411yescharacteristic
64C2×D52C2311yescharacteristic
65C2×C4×D13—21no—
66C2×C4×D13—21no—
67C2×C4×D13—21no—
68C2×C4×D13—21no—
69C2×C4×D13C2311yescharacteristic
70C2×C4×D13C2311yescharacteristic
71C2×Dic26C2311yescharacteristic
72C2×C8×C13C2311yescharacteristic
73C2×C8×C13C2311yescharacteristic
74C13×C4⋊C4—21no—
75C13×C4⋊C4—21no—
76C13×C4⋊C4—21no—
77C13×C4⋊C4C2311yescharacteristic
78C13×C4⋊C4C2311yescharacteristic
79C13×C4⋊C4C2311yescharacteristic
80C13×C4⋊C4C2311yescharacteristic
81C42×C13C2311yescharacteristic
82#6103—21no—
83#6103—21no—
84#6103—21no—
85#6103—21no—
86#6103—21no—
87#6103—21no—
88#6103D411yescharacteristic
89#6103D411yescharacteristic
90C4⋊Dic13—21no—
91C4⋊Dic13—21no—
92C4⋊Dic13D411yescharacteristic
93C4⋊Dic13C2311yescharacteristic
94C4⋊Dic13C2311yescharacteristic
95#6101—21no—
96#6101—21no—
97#6101—21no—
98#6101—21no—
99C4×Dic13—21no—
100C4×Dic13—21no—
101C2×#1055C2311yescharacteristic
102C2×#1055C2311yescharacteristic
103#6095—22no—
104#6094—22no—
105C8×D13—22no—
106#3343—131nomaximal, Sylow
107C22×D13—21no—
108C22×D13C2×D411yescharacteristic
109C22×D13C2×D411yescharacteristic
110Q8×C13—42no—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13C2×D411yescharacteristic
116C2×C4×C13C2×D411yescharacteristic
117C2×C4×C13C2411yescharacteristic
118C2×Dic13—21no—
119C2×Dic13—21no—
120C2×Dic13—21no—
121C2×Dic13C2×D411yescharacteristic
122C2×Dic13C2×D411yescharacteristic
123D52—22no—
124D52—21no—
125D52—21no—
126D52—42no—
127D52—42no—
128C4×D13—21no—
129C4×D13—21no—
130C4×D13—21no—
131C4×D13—21no—
132C4×D13—42no—
133C4×D13—42no—
134C4×D13—42no—
135C4×D13—42no—
136Dic26—21no—
137Dic26—21no—
138C8×C13—21no—
139C8×C13#4112yescomplemented
140#1055—21no—
141#1055—21no—
142#552—131no—
143#547—131no—
144#501D1311yescharacteristic, complemented
145#484—131no—
146#483—131no—
147#482—131no—
148#480—131no—
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×C13C22×D411yescharacteristic
158C2×D13—21no—
159C2×D13—21no—
160C2×D13—21no—
161C2×D13—21no—
162C2×D13—21no—
163C2×D13—41no—
164C2×D13—41no—
165C2×D13—41no—
166C2×D13AGL(1,ℤ/8)12yes—
167C4×C13—21no—
168C4×C13—21no—
169C4×C13—41no—
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—
180C2×#41—261no—
181C2×SD16—131no—
182C2×M16—131no—
183C22×C8—131no—
184C4⋊Q8C2×D1311yescharacteristic
185#126—261no—
186#125—261no—
187#125C2×D1311yescharacteristic
188#123—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×D4—131no—
198C4×D4—131no—
199#117—131no—
200#117—261no—
201C2×C4⋊C4—131no—
202C2×C4⋊C4—131no—
203C2×C4⋊C4—131no—
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—
222#97C2×D1311yescharacteristic
223C2×C13#54711yescharacteristic
224C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
225C2×C13#57811yescharacteristic
226D13—22no—
227D13—41no—
228D13—81no—
229#41—524no—
230C2×Q8—21no—
231C2×Q8—131no—
232C2×D4—131no—
233C2×D4—131no—
234C2×D4—261no—
235C2×D4—261no—
236C22×C4—131no—
237C22×C4—131no—
238C22×C4—261no—
239C22×C4—261no—
240C22×C4—261no—
241C22×C4—261no—
242SD16—262no—
243M16—262no—
244C2×C8—131no—
245C2×C8—131no—
246C2×C8—262no—
247C2×C8C22×D1311yescharacteristic
248C2×C8C22×D1311yescharacteristic
249C4⋊C4—21no—
250C4⋊C4—21no—
251C4⋊C4—21no—
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
263C4⋊C4C22×D1311yescharacteristic
264C4⋊C4C22×D1311yescharacteristic
265C22⋊C4—131no—
266C22⋊C4—131no—
267C22⋊C4—261no—
268C22⋊C4—261no—
269C22⋊C4—261no—
270C22⋊C4—261no—
271C22⋊C4—261no—
272C22⋊C4—261no—
273C42—261no—
274C42—261no—
275C42C22×D1311yescharacteristic
276C13#334311yescharacteristic, complemented, Sylow
277C23—131no—
278C23—131no—
279C23—261no—
280Q8—42no—
281Q8—261no—
282Q8—261no—
283D4—262no—
284D4—261no—
285D4—261no—
286D4—522no—
287D4—522no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—131no—
293C2×C4—131no—
294C2×C4—261no—
295C2×C4—261no—
296C2×C4—261no—
297C2×C4—261no—
298C2×C4—261no—
299C2×C4—261no—
300C2×C4—261no—
301C2×C4—522no—
302C2×C4—522no—
303C2×C4—522no—
304C2×C4—522no—
305C2×C4D4×D1311yescharacteristic
306C2×C4D4×D1311yescharacteristic
307C2×C4C23×D1311yescharacteristic
308C8—21no—
309C8—261no—
310C8—261no—
311C8#613112yescomplemented
312C22—132no—
313C22—261no—
314C22—261no—
315C22—261no—
316C22—261no—
317C22—261no—
318C22—521no—
319C22—521no—
320C22—521no—
321C22C2×D4×D1311yescharacteristic
322C4—21no—
323C4—21no—
324C4—41no—
325C4—41no—
326C4—41no—
327C4—41no—
328C4—261no—
329C4—261no—
330C4—521no—
331C4—521no—
332C4—521no—
333C4C2×#613111yescharacteristic
334C4#8825411yescharacteristic
335C2—262no—
336C2—521no—
337C2—1041no—
338C2#1171943111yescharacteristic
339C2D13×AGL(1,ℤ/8)11yescharacteristic
340C2#1171948411yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#501C2
socleC22×C13C22×D4
prime radical#11719431C2
hypercenter#501D13
hypocenterC13#3343
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
2. #11719399C2semidirect
3. C13×#501C2semidirect
4. #11718752C2semidirect
5. #11718727C2semidirect
6. #11718547C2semidirect
7. #11718545C2semidirect
8. #11718543C2semidirect
9. D13×#107C2semidirect
10. #11718527C2semidirect
11. #11718525C2semidirect
12. #11718523C2semidirect
13. #11718522C2semidirect
14. #11718371C2semidirect
15. #11718367C2semidirect
139. C8×C13#41semidirect
144. #501D13semidirect
276. C13#3343semidirect
311. C8#6131semidirect

Maximal subgroups

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

subgroupindex
#117194312
#117193992
C13×#5012
#117187522
#117187272
#117185472
#117185452
#117185432
D13×#1072
#117185272
#117185252
#117185232
#117185222
#117183712
#117183672
#334313