Finite Group Databasebeta

← #13126040

Subgroups — #13126040

Order 1664.

324 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
1D13×#125C211yesmaximal, characteristic
2#11719283C211yesmaximal, characteristic
3C13×#479C211yesmaximal, characteristic, complemented
4#11718724C211yesmaximal, characteristic, complemented
5#11718683C211yesmaximal, characteristic, complemented
6#11718545C211yesmaximal, characteristic
7#11718537C211yesmaximal, characteristic, complemented
8#11718523C211yesmaximal, characteristic
9#11718517C211yesmaximal, characteristic, complemented
10#11718496C211yesmaximal, characteristic
11#11718490C211yesmaximal, characteristic, complemented
12#11718470C211yesmaximal, characteristic
13#11718466C211yesmaximal, characteristic
14#11718458C211yesmaximal, characteristic, complemented
15#11718458C211yesmaximal, characteristic, complemented
16C13×#125C2211yescharacteristic
17C4×Q8×C13C2211yescharacteristic
18#88200C2211yescharacteristic
19#88198C2211yescharacteristic
20#88151C2211yescharacteristic
21#88150—21no—
22C4⋊C4×D13—21no—
23C4⋊C4×D13—21no—
24C4⋊C4×D13C2211yescharacteristic
25C4⋊C4×D13C2211yescharacteristic
26#88144C2211yescharacteristic
27#88144C2211yescharacteristic
28#88143—21no—
29#88143—21no—
30#88143—21no—
31#88142C2211yescharacteristic
32#88126—21no—
33C42×D13C2211yescharacteristic
34#88124C2211yescharacteristic
35C4×Dic26—21no—
36C4×Dic26C2211yescharacteristic
37C13×#107C2211yescharacteristic
38C13×#106C2211yescharacteristic
39C13×C4⋊C8C2211yescharacteristic
40C13×#103C2211yescharacteristic
41C13×#103C2211yescharacteristic
42#88075C2211yescharacteristic
43#88075C2211yescharacteristic
44#88060C2211yescharacteristic
45#88060C2211yescharacteristic
46#88058C2211yescharacteristic
47#88057C2211yescharacteristic
48#88056C2211yescharacteristic
49#88056C2211yescharacteristic
50#88055C2211yescharacteristic
51#88055C2211yescharacteristic
52#88050C2211yescharacteristic
53#88050C2211yescharacteristic
54#88048C2211yescharacteristic
55#88048C2211yescharacteristic
56#88047C2211yescharacteristic
57#88047C2211yescharacteristic
58C4⋊#1055C2211yescharacteristic
59C2×Q8×C13C2311yescharacteristic
60C2×C4×D13—21no—
61C2×C4×D13—21no—
62C2×C4×D13D411yescharacteristic
63C2×C4×D13D411yescharacteristic
64C2×C4×D13C2311yescharacteristic
65C2×Dic26—21no—
66C2×Dic26C2311yescharacteristic
67C2×C8×C13C2311yescharacteristic
68C2×C8×C13C2311yescharacteristic
69C13×C4⋊C4—21no—
70C13×C4⋊C4—21no—
71C13×C4⋊C4—21no—
72C13×C4⋊C4C2311yescharacteristic
73C13×C4⋊C4C2311yescharacteristic
74C13×C4⋊C4C2311yescharacteristic
75C42×C13—21no—
76C42×C13C2311yescharacteristic
77#6103—21no—
78#6103—21no—
79C4⋊Dic13—21no—
80C4⋊Dic13—21no—
81C4⋊Dic13—21no—
82C4⋊Dic13C2311yescharacteristic
83C4⋊Dic13C2311yescharacteristic
84C4⋊Dic13C2311yescharacteristic
85#6101—21no—
86#6101—21no—
87#6101—21no—
88#6101—21no—
89#6101—21no—
90#6101—21no—
91#6101—21no—
92#6101—21no—
93#6101—21no—
94#6101—21no—
95#6101—21no—
96C4×Dic13—21no—
97C4×Dic13D411yescharacteristic
98C4×Dic13D411yescharacteristic
99C4×Dic13C2311yescharacteristic
100C2×#1055C2311yescharacteristic
101C2×#1055C2311yescharacteristic
102#3236—131nomaximal, Sylow
103C22×D13C2×D411yescharacteristic
104Q8×C13—21no—
105Q8×C13—21no—
106C2×C4×C13—21no—
107C2×C4×C13—21no—
108C2×C4×C13—21no—
109C2×C4×C13—21no—
110C2×C4×C13C2×D411yescharacteristic
111C2×C4×C13C2×D411yescharacteristic
112C2×C4×C13C2411yescharacteristic
113C2×Dic13—21no—
114C2×Dic13—21no—
115C2×Dic13—21no—
116C2×Dic13—21no—
117C2×Dic13C2×D411yescharacteristic
118C2×Dic13C2×D411yescharacteristic
119C2×Dic13C2×D411yescharacteristic
120C4×D13—22no—
121C4×D13—21no—
122C4×D13—21no—
123C4×D13—41no—
124C4×D13—42no—
125C4×D13—42no—
126Dic26—21no—
127Dic26—21no—
128Dic26—42no—
129C8×C13—21no—
130C8×C13—21no—
131#1055—21no—
132#1055—21no—
133#533—131no—
134C2×#125—131no—
135#501—131no—
136#501—131no—
137#491—131no—
138#491—131no—
139#484—131no—
140#484—131no—
141#483—131no—
142#483—131no—
143#479—131no—
144#479—131no—
145#479—131no—
146#479D1311yescharacteristic, complemented
147#432—131no—
148C22×C13C22×D411yescharacteristic
149C2×D13—21no—
150C2×D13—21no—
151C2×D13#13712yes—
152C4×C13—21no—
153C4×C13—21no—
154C4×C13—41no—
155C4×C13—41no—
156C4×C13—41no—
157C4×C13—41no—
158C4×C132−1+411yescharacteristic
159C4×C132−1+411yescharacteristic
160Dic13—21no—
161Dic13—21no—
162Dic13—21no—
163Dic13—41no—
164Dic13—41no—
165Dic13—41no—
166Dic13—41no—
167C4⋊Q8—131no—
168C4⋊Q8—131no—
169#125—131no—
170#125—131no—
171#125—131no—
172#125—261no—
173#125—261no—
174#125—261no—
175#125C2×D1311yescharacteristic
176C22⋊Q8—131no—
177C22⋊Q8—131no—
178C22⋊Q8—261no—
179C4×Q8—131no—
180C4×Q8—261no—
181C4×Q8C2×D1311yescharacteristic
182#117—261no—
183C2×C4⋊C4—131no—
184C2×C4⋊C4—131no—
185C2×C4⋊C4—261no—
186C2×C4⋊C4—261no—
187C2×C42—131no—
188#107—131no—
189#107—131no—
190#107—131no—
191#107C2×D1311yescharacteristic
192#106—131no—
193#106—131no—
194#106—131no—
195#106C2×D1311yescharacteristic
196C4⋊C8—131no—
197C4⋊C8C2×D1311yescharacteristic
198#103—131no—
199#103—131no—
200#103—131no—
201#103—131no—
202#103—131no—
203#103—131no—
204#103C2×D1311yescharacteristic
205#103C2×D1311yescharacteristic
206C22⋊C8—131no—
207C22⋊C8—131no—
208#97—131no—
209#97—131no—
210C2×C13#53611yescharacteristic
211C2×C13C2×#13711yescharacteristic
212C2×C13#57511yescharacteristic
213D13—22no—
214C2×Q8—131no—
215C2×Q8—261no—
216C2×Q8C22×D1311yescharacteristic
217C22×C4—131no—
218C22×C4—131no—
219C22×C4—131no—
220C22×C4—261no—
221C22×C4—261no—
222C2×C8—131no—
223C2×C8—131no—
224C2×C8C22×D1311yescharacteristic
225C2×C8C22×D1311yescharacteristic
226C4⋊C4—21no—
227C4⋊C4—21no—
228C4⋊C4—21no—
229C4⋊C4—131no—
230C4⋊C4—131no—
231C4⋊C4—131no—
232C4⋊C4—261no—
233C4⋊C4—261no—
234C4⋊C4—261no—
235C4⋊C4—261no—
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⋊C4—261no—
246C4⋊C4C22×D1311yescharacteristic
247C4⋊C4C22×D1311yescharacteristic
248C4⋊C4C22×D1311yescharacteristic
249C22⋊C4—261no—
250C22⋊C4—261no—
251C42—21no—
252C42—131no—
253C42—131no—
254C42—131no—
255C42—261no—
256C42C22×D1311yescharacteristic
257C13#323611yescharacteristic, complemented, Sylow
258C23—131no—
259Q8—21no—
260Q8—21no—
261Q8—261no—
262Q8—261no—
263Q8—522no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—131no—
269C2×C4—131no—
270C2×C4—131no—
271C2×C4—262no—
272C2×C4—261no—
273C2×C4—261no—
274C2×C4—261no—
275C2×C4—261no—
276C2×C4—261no—
277C2×C4—261no—
278C2×C4—521no—
279C2×C4—522no—
280C2×C4—522no—
281C2×C4D4×D1311yescharacteristic
282C2×C4D4×D1311yescharacteristic
283C2×C4C23×D1311yescharacteristic
284C8—21no—
285C8—21no—
286C8—261no—
287C8—261no—
288C22—132no—
289C22—261no—
290C22—261no—
291C22C2×D4×D1311yescharacteristic
292C4—21no—
293C4—21no—
294C4—41no—
295C4—41no—
296C4—41no—
297C4—41no—
298C4—261no—
299C4—261no—
300C4—261no—
301C4—521no—
302C4—521no—
303C4—521no—
304C4—521no—
305C4#8825411yescharacteristic
306C4#8825711yescharacteristic
307C2—262no—
308C2#1171933311yescharacteristic
309C2#1171947311yescharacteristic
310C2D13×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#479C2
socleC22×C13C22×D4
prime radicalC22×D13C2×D4
hypercenter#479D13
hypocenterC13#3236
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #479

Complements

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

NH ≅ G/Ntype
3. C13×#479C2semidirect
4. #11718724C2semidirect
5. #11718683C2semidirect
7. #11718537C2semidirect
9. #11718517C2semidirect
11. #11718490C2semidirect
14. #11718458C2semidirect
15. #11718458C2semidirect
146. #479D13semidirect
257. C13#3236semidirect

Maximal subgroups

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

subgroupindex
D13×#1252
#117192832
C13×#4792
#117187242
#117186832
#117185452
#117185372
#117185232
#117185172
#117184962
#117184902
#117184702
#117184662
#117184582
#323613