Finite Group Databasebeta

← #13126016

Subgroups — #13126016

Order 1664.

332 conjugacy classes of subgroups.

The subgroup lattice has 320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719396C211yesmaximal, characteristic
2#11719393C211yesmaximal, characteristic, complemented
3C13×#499C211yesmaximal, characteristic, complemented
4#11718729C211yesmaximal, characteristic, complemented
5#11718725C211yesmaximal, characteristic, complemented
6#11718551C211yesmaximal, characteristic, complemented
7#11718549C211yesmaximal, characteristic, complemented
8#11718546C211yesmaximal, characteristic
9#11718536C211yesmaximal, characteristic, complemented
10#11718531C211yesmaximal, characteristic, complemented
11#11718528C211yesmaximal, characteristic, complemented
12#11718527C211yesmaximal, characteristic
13#11718515C211yesmaximal, characteristic, complemented
14#11718358C211yesmaximal, characteristic, complemented
15#11718346C211yesmaximal, characteristic, complemented
16C13×#125C2211yescharacteristic
17C13×#125C2211yescharacteristic
18#88152—21no—
19#88151C2211yescharacteristic
20#88150—21no—
21#88150—21no—
22#88149C2211yescharacteristic
23#88148—21no—
24#88147—21no—
25#88147C2211yescharacteristic
26#88146—21no—
27#88146C2211yescharacteristic
28#88146C2211yescharacteristic
29#88142C2211yescharacteristic
30#88142C2211yescharacteristic
31#88141—21no—
32#88141—21no—
33#88141C2211yescharacteristic
34#88129C2211yescharacteristic
35C42×D13C2211yescharacteristic
36#88124C2211yescharacteristic
37C13×#107C2211yescharacteristic
38C13×#107C2211yescharacteristic
39C13×#106C2211yescharacteristic
40C13×#106C2211yescharacteristic
41C4×C8×C13C2211yescharacteristic
42#88061C2211yescharacteristic
43#88061C2211yescharacteristic
44#88060C2211yescharacteristic
45#88060C2211yescharacteristic
46#88056C2211yescharacteristic
47#88056C2211yescharacteristic
48#88054C2211yescharacteristic
49#88054C2211yescharacteristic
50#88050C2211yescharacteristic
51#88050C2211yescharacteristic
52#88049C2211yescharacteristic
53#88049C2211yescharacteristic
54#88048C2211yescharacteristic
55#88048C2211yescharacteristic
56#88047C2211yescharacteristic
57#88047C2211yescharacteristic
58C4×#1055C2211yescharacteristic
59C2×D52—21no—
60C2×D52C2311yescharacteristic
61C2×C4×D13—21no—
62C2×C4×D13D411yescharacteristic
63C2×C4×D13D411yescharacteristic
64C2×C4×D13C2311yescharacteristic
65C2×Dic26—21no—
66C2×Dic26—21no—
67C2×Dic26C2311yescharacteristic
68C2×C8×C13C2311yescharacteristic
69C2×C8×C13C2311yescharacteristic
70C13×C4⋊C4—21no—
71C13×C4⋊C4—21no—
72C13×C4⋊C4—21no—
73C13×C4⋊C4—21no—
74C13×C4⋊C4C2311yescharacteristic
75C13×C4⋊C4C2311yescharacteristic
76C13×C4⋊C4C2311yescharacteristic
77C13×C4⋊C4C2311yescharacteristic
78C42×C13C2311yescharacteristic
79#6103—21no—
80#6103—21no—
81#6103—21no—
82#6103—21no—
83#6103—21no—
84#6103—21no—
85#6103—21no—
86C4⋊Dic13—21no—
87C4⋊Dic13C2311yescharacteristic
88C4⋊Dic13C2311yescharacteristic
89#6101—21no—
90#6101—21no—
91#6101—21no—
92#6101—21no—
93#6101—21no—
94C4×Dic13—21no—
95C4×Dic13—21no—
96C4×Dic13—21no—
97C4×Dic13D411yescharacteristic
98C4×Dic13D411yescharacteristic
99C4×Dic13C2311yescharacteristic
100C2×#1055C2311yescharacteristic
101C2×#1055C2311yescharacteristic
102#3233—131nomaximal, Sylow
103C22×D13—21no—
104C22×D13C2×D411yescharacteristic
105C2×C4×C13—21no—
106C2×C4×C13—21no—
107C2×C4×C13—21no—
108C2×C4×C13—21no—
109C2×C4×C13C2×D411yescharacteristic
110C2×C4×C13C2×D411yescharacteristic
111C2×C4×C13C2411yescharacteristic
112C2×Dic13—21no—
113C2×Dic13—21no—
114C2×Dic13—21no—
115C2×Dic13C2×D411yescharacteristic
116C2×Dic13C2×D411yescharacteristic
117C2×Dic13C2×D411yescharacteristic
118D52—21no—
119D52—21no—
120D52—42no—
121C4×D13—21no—
122C4×D13—21no—
123C4×D13—22no—
124C4×D13—41no—
125C4×D13—42no—
126Dic26—21no—
127Dic26—21no—
128Dic26—42no—
129Dic26—42no—
130C8×C13—21no—
131C8×C13—21no—
132#1055—21no—
133#1055—21no—
134#533—131no—
135#529—131no—
136#499—131no—
137#499D1311yescharacteristic, complemented
138#488—131no—
139#488—131no—
140#485—131no—
141#485—131no—
142#482—131no—
143#482—131no—
144#477—131no—
145#476—131no—
146#475—131no—
147#474—131no—
148#431—131no—
149C22×C13C22×D411yescharacteristic
150C2×D13—21no—
151C2×D13—21no—
152C2×D13—21no—
153C2×D13—41no—
154C2×D13—41no—
155C2×D13—41no—
156C4×C13—21no—
157C4×C13—21no—
158C4×C13—41no—
159C4×C13—41no—
160C4×C13—41no—
161C4×C13—41no—
162C4×C132−1+411yescharacteristic
163C4×C132−1+411yescharacteristic
164Dic13—21no—
165Dic13—21no—
166Dic13—41no—
167Dic13—41no—
168Dic13—41no—
169Dic13#13512yes—
170C4⋊Q8—131no—
171C4⋊Q8—131no—
172#126—261no—
173#125—131no—
174#125C2×D1311yescharacteristic
175#125C2×D1311yescharacteristic
176#124—131no—
177#123—261no—
178C22⋊Q8—131no—
179C22⋊Q8—261no—
180C22⋊Q8—261no—
181#121—131no—
182C4×Q8—131no—
183C4×Q8—261no—
184C4×Q8—261no—
185C4×D4—131no—
186C4×D4—261no—
187#117—131no—
188#117—131no—
189#117—261no—
190C2×C42—131no—
191#107—131no—
192#107—131no—
193#107C2×D1311yescharacteristic
194#107C2×D1311yescharacteristic
195#106—131no—
196#106—131no—
197#106C2×D1311yescharacteristic
198#106C2×D1311yescharacteristic
199C4⋊C8—131no—
200C4⋊C8—131no—
201#103—131no—
202#103—131no—
203#103—131no—
204#103—131no—
205#102—131no—
206#102—131no—
207#102—131no—
208#102—131no—
209C22⋊C8—131no—
210C22⋊C8—131no—
211C4×C8—131no—
212C4×C8C2×D1311yescharacteristic
213C2×C13#53611yescharacteristic
214C2×C13C2×#13511yescharacteristic
215C2×C13#57511yescharacteristic
216D13—41no—
217D13—81no—
218C2×Q8—131no—
219C2×Q8—261no—
220C2×Q8—261no—
221C2×D4—131no—
222C2×D4—261no—
223C22×C4—131no—
224C22×C4—131no—
225C22×C4—131no—
226C22×C4—261no—
227C2×C8—131no—
228C2×C8—131no—
229C2×C8C22×D1311yescharacteristic
230C2×C8C22×D1311yescharacteristic
231C4⋊C4—21no—
232C4⋊C4—21no—
233C4⋊C4—21no—
234C4⋊C4—21no—
235C4⋊C4—131no—
236C4⋊C4—131no—
237C4⋊C4—261no—
238C4⋊C4—261no—
239C4⋊C4—261no—
240C4⋊C4—261no—
241C4⋊C4—261no—
242C4⋊C4—261no—
243C4⋊C4C22×D1311yescharacteristic
244C4⋊C4C22×D1311yescharacteristic
245C4⋊C4C22×D1311yescharacteristic
246C4⋊C4C22×D1311yescharacteristic
247C22⋊C4—261no—
248C22⋊C4—261no—
249C22⋊C4—261no—
250C22⋊C4—261no—
251C22⋊C4—261no—
252C22⋊C4—261no—
253C22⋊C4—261no—
254C42—131no—
255C42—131no—
256C42—131no—
257C42—261no—
258C42—261no—
259C42—261no—
260C42C22×D1311yescharacteristic
261C13#323311yescharacteristic, complemented, Sylow
262C23—131no—
263C23—261no—
264Q8—261no—
265Q8—261no—
266Q8—522no—
267Q8—522no—
268D4—261no—
269D4—261no—
270D4—522no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—131no—
276C2×C4—131no—
277C2×C4—131no—
278C2×C4—262no—
279C2×C4—261no—
280C2×C4—261no—
281C2×C4—261no—
282C2×C4—261no—
283C2×C4—261no—
284C2×C4—521no—
285C2×C4—522no—
286C2×C4D4×D1311yescharacteristic
287C2×C4D4×D1311yescharacteristic
288C2×C4C23×D1311yescharacteristic
289C8—21no—
290C8—21no—
291C8—261no—
292C8—261no—
293C22—261no—
294C22—261no—
295C22—261no—
296C22—521no—
297C22—521no—
298C22—521no—
299C22C2×D4×D1311yescharacteristic
300C4—21no—
301C4—21no—
302C4—41no—
303C4—41no—
304C4—41no—
305C4—41no—
306C4—132no—
307C4—261no—
308C4—261no—
309C4—521no—
310C4—521no—
311C4—521no—
312C4#8825411yescharacteristic
313C4#8825411yescharacteristic
314C2—521no—
315C2—1041no—
316C2#1171942911yescharacteristic
317C2D13×#13511yescharacteristic
318C2#1171947311yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#499C2
socleC22×C13C22×D4
prime radical#88149C22
hypercenter#499D13
hypocenterC13#3233
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #499

Complements

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

NH ≅ G/Ntype
2. #11719393C2semidirect
3. C13×#499C2semidirect
4. #11718729C2semidirect
5. #11718725C2semidirect
6. #11718551C2semidirect
7. #11718549C2semidirect
9. #11718536C2semidirect
10. #11718531C2semidirect
11. #11718528C2semidirect
13. #11718515C2semidirect
14. #11718358C2semidirect
15. #11718346C2semidirect
137. #499D13semidirect
261. C13#3233semidirect

Maximal subgroups

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

subgroupindex
#117193962
#117193932
C13×#4992
#117187292
#117187252
#117185512
#117185492
#117185462
#117185362
#117185312
#117185282
#117185272
#117185152
#117183582
#117183462
#323313