Finite Group Databasebeta

← #13127708

Subgroups — #13127708

Order 1664.

338 conjugacy classes of subgroups.

The subgroup lattice has 312 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719395C211yesmaximal, characteristic
2#11719390C211yesmaximal, characteristic, complemented
3C13×#499C211yesmaximal, characteristic, complemented
4#11718727C211yesmaximal, characteristic
5#11718724C211yesmaximal, characteristic, complemented
6#11718552C211yesmaximal, characteristic
7#11718551C211yesmaximal, characteristic
8#11718538C211yesmaximal, characteristic, complemented
9#11718536C211yesmaximal, characteristic, complemented
10#11718519C211yesmaximal, characteristic, complemented
11#11718516C211yesmaximal, characteristic, complemented
12#11718513C211yesmaximal, characteristic
13#11718513C211yesmaximal, characteristic
14C4×#6095C211yesmaximal, characteristic
15C8×Dic26C211yesmaximal, characteristic, complemented
16C13×#125C2211yescharacteristic
17C13×#125C2211yescharacteristic
18C2×#6095C2211yescharacteristic
19#88151—21no—
20#88150—21no—
21#88150—21no—
22#88147C2211yescharacteristic
23#88147C2211yescharacteristic
24C4⋊C4×D13—21no—
25#88144C2211yescharacteristic
26#88144C2211yescharacteristic
27#88143—21no—
28#88143—21no—
29#88142—21no—
30#88142C2211yescharacteristic
31#88142C2211yescharacteristic
32#88141—21no—
33#88141C2211yescharacteristic
34#88141C2211yescharacteristic
35C4×D52C2211yescharacteristic
36C4×Dic26C2211yescharacteristic
37C4×Dic26C2211yescharacteristic
38C13×#107C2211yescharacteristic
39C13×#107C2211yescharacteristic
40C13×#106C2211yescharacteristic
41C13×#106C2211yescharacteristic
42C4×C8×C13C2211yescharacteristic
43#88061C2211yescharacteristic
44#88057C2211yescharacteristic
45#88056C2211yescharacteristic
46#88054C2211yescharacteristic
47#88054C2211yescharacteristic
48C8×Dic13C2211yescharacteristic
49C8×Dic13C2211yescharacteristic
50#88050C2211yescharacteristic
51#88050C2211yescharacteristic
52#88049C2211yescharacteristic
53#88049C2211yescharacteristic
54#88048C2211yescharacteristic
55#88048C2211yescharacteristic
56#88047C2211yescharacteristic
57#88047C2211yescharacteristic
58C4⋊#1055C2211yescharacteristic
59C2×D52C2311yescharacteristic
60C2×C4×D13—21no—
61C2×C4×D13—21no—
62C2×C4×D13—21no—
63C2×Dic26—21no—
64C2×Dic26—21no—
65C2×Dic26D411yescharacteristic
66C2×Dic26C2311yescharacteristic
67C2×C8×C13C2311yescharacteristic
68C2×C8×C13C2311yescharacteristic
69C13×C4⋊C4—21no—
70C13×C4⋊C4—21no—
71C13×C4⋊C4—21no—
72C13×C4⋊C4—21no—
73C13×C4⋊C4C2311yescharacteristic
74C13×C4⋊C4C2311yescharacteristic
75C13×C4⋊C4C2311yescharacteristic
76C13×C4⋊C4C2311yescharacteristic
77C42×C13C2311yescharacteristic
78#6103—21no—
79#6103—21no—
80#6103—21no—
81C4⋊Dic13—21no—
82C4⋊Dic13—21no—
83C4⋊Dic13D411yescharacteristic
84C4⋊Dic13C2311yescharacteristic
85C4⋊Dic13C2311yescharacteristic
86#6101—21no—
87#6101—21no—
88#6101—21no—
89#6101—21no—
90#6101—21no—
91#6101—21no—
92#6101—21no—
93#6101D411yescharacteristic
94#6101D411yescharacteristic
95C4×Dic13—21no—
96C4×Dic13—21no—
97C4×Dic13—21no—
98C4×Dic13C2311yescharacteristic
99C4×Dic13C2311yescharacteristic
100C2×#1055C2311yescharacteristic
101C2×#1055C2311yescharacteristic
102#6095Q814yescomplemented
103#3381—131nomaximal, Sylow
104C22×D13—21no—
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
118C2×Dic13C2×D411yescharacteristic
119D52—21no—
120D52C2×Q812yes—
121C4×D13—42no—
122C4×D13—81no—
123C4×D13—81no—
124Dic26—21no—
125Dic26—22no—
126Dic26—42no—
127Dic26—81no—
128Dic26C2×Q812yes—
129C8×C13—21no—
130C8×C13C2×Q812yes—
131#1055—21no—
132#1055—21no—
133#557—131no—
134#554—131no—
135#499—131no—
136#499D1311yescharacteristic, complemented
137#498—131no—
138#479—131no—
139#479—131no—
140#478—131no—
141#478—131no—
142#477—131no—
143#474—131no—
144C8×Q8—131no—
145C4×SD16—131no—
146C4×SD16—131no—
147C4×SD16—131no—
148C22×C13C22×D411yescharacteristic
149C2×D13—22no—
150C2×D13—41no—
151C2×D13—41no—
152C4×C13—21no—
153C4×C13—21no—
154C4×C13—41no—
155C4×C13—41no—
156C4×C13—41no—
157C4×C13—41no—
158C4×C13C22×Q811yescharacteristic
159C4×C132−1+411yescharacteristic
160Dic13—22no—
161Dic13—21no—
162Dic13—21no—
163Dic13—21no—
164Dic13—41no—
165Dic13—41no—
166Dic13#13512yes—
167C2×SD16—131no—
168C4⋊Q8—131no—
169C4⋊Q8—131no—
170C4⋊Q8—261no—
171#125—131no—
172#125—131no—
173#125—261no—
174#125—261no—
175#125C2×D1311yescharacteristic
176#125C2×D1311yescharacteristic
177C22⋊Q8—261no—
178C22⋊Q8—261no—
179C22⋊Q8—261no—
180C4×Q8—131no—
181C4×Q8—131no—
182C4×Q8—131no—
183C4×Q8—131no—
184C4×Q8—261no—
185C4×D4—131no—
186C4×D4—131no—
187C4×D4—131no—
188C2×C4⋊C4—261no—
189#107—131no—
190#107—131no—
191#107C2×D1311yescharacteristic
192#107C2×D1311yescharacteristic
193#106—131no—
194#106—131no—
195#106—131no—
196#106C2×D1311yescharacteristic
197#106C2×D1311yescharacteristic
198C4⋊C8—131no—
199C4⋊C8—131no—
200C4⋊C8—131no—
201#103—131no—
202#103—131no—
203#103—131no—
204#102—131no—
205#102—131no—
206#102—131no—
207C4×C8—131no—
208C4×C8—131no—
209C4×C8C2×D1311yescharacteristic
210C2×C13D4×Q811yescharacteristic
211C2×C13C2×#13511yescharacteristic
212C2×C13#57711yescharacteristic
213D13—42no—
214C2×Q8—131no—
215C2×Q8—131no—
216C2×Q8—261no—
217C2×Q8—261no—
218C2×D4—131no—
219C22×C4—261no—
220C22×C4—261no—
221C22×C4—261no—
222SD16—134no—
223C2×C8—131no—
224C2×C8—131no—
225C2×C8C22×D1311yescharacteristic
226C2×C8C22×D1311yescharacteristic
227C4⋊C4—21no—
228C4⋊C4—21no—
229C4⋊C4—21no—
230C4⋊C4—21no—
231C4⋊C4—131no—
232C4⋊C4—131no—
233C4⋊C4—131no—
234C4⋊C4—131no—
235C4⋊C4—131no—
236C4⋊C4—261no—
237C4⋊C4—261no—
238C4⋊C4—261no—
239C4⋊C4—261no—
240C4⋊C4—261no—
241C4⋊C4—261no—
242C4⋊C4—261no—
243C4⋊C4—261no—
244C4⋊C4—261no—
245C4⋊C4C22×D1311yescharacteristic
246C4⋊C4C22×D1311yescharacteristic
247C4⋊C4C22×D1311yescharacteristic
248C4⋊C4C22×D1311yescharacteristic
249C22⋊C4—261no—
250C22⋊C4—261no—
251C22⋊C4—261no—
252C42—131no—
253C42—131no—
254C42—261no—
255C42—261no—
256C42—261no—
257C42C22×D1311yescharacteristic
258C13#338111yescharacteristic, complemented, Sylow
259C23—261no—
260Q8—132no—
261Q8—262no—
262Q8—261no—
263Q8—522no—
264Q8—1041no—
265D4—132no—
266D4—261no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—131no—
272C2×C4—131no—
273C2×C4—131no—
274C2×C4—131no—
275C2×C4—261no—
276C2×C4—261no—
277C2×C4—261no—
278C2×C4—522no—
279C2×C4—1041no—
280C2×C4—1041no—
281C2×C4D4×D1311yescharacteristic
282C2×C4D4×D1311yescharacteristic
283C2×C4C23×D1311yescharacteristic
284C8—21no—
285C8—261no—
286C8—261no—
287C8Q8×D1312yes—
288C22—262no—
289C22—521no—
290C22—521no—
291C22C2×D4×D1311yescharacteristic
292C4—21no—
293C4—21no—
294C4—41no—
295C4—41no—
296C4—41no—
297C4—41no—
298C4—132no—
299C4—262no—
300C4—261no—
301C4—261no—
302C4—261no—
303C4—521no—
304C4—521no—
305C4C2×Q8×D1311yescharacteristic
306C4#8825411yescharacteristic
307C2—522no—
308C2#1171943211yescharacteristic
309C2D13×#13511yescharacteristic
310C2#1171947511yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#499C2
socleC22×C13C22×D4
prime radicalC2×D52C23
hypercenter#499D13
hypocenterC13#3381
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. #11719390C2semidirect
3. C13×#499C2semidirect
5. #11718724C2semidirect
8. #11718538C2semidirect
9. #11718536C2semidirect
10. #11718519C2semidirect
11. #11718516C2semidirect
15. C8×Dic26C2semidirect
102. #6095Q8semidirect
136. #499D13semidirect
258. C13#3381semidirect

Maximal subgroups

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

subgroupindex
#117193952
#117193902
C13×#4992
#117187272
#117187242
#117185522
#117185512
#117185382
#117185362
#117185192
#117185162
#117185132
C4×#60952
C8×Dic262
#338113