Finite Group Databasebeta

← #13127381

Subgroups — #13127381

Order 1664.

348 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#556C211yesmaximal, characteristic, complemented
2#11719270C211yesmaximal, characteristic
3#11718745C211yesmaximal, characteristic, complemented
4#11718741C211yesmaximal, characteristic, complemented
5#11718710C211yesmaximal, characteristic, complemented
6#11718709C211yesmaximal, characteristic, complemented
7#11718706C211yesmaximal, characteristic, complemented
8#11718704C211yesmaximal, characteristic, complemented
9#11718687C211yesmaximal, characteristic, complemented
10#11718683C211yesmaximal, characteristic, complemented
11#11718672C211yesmaximal, characteristic, complemented
12#11718664C211yesmaximal, characteristic, complemented
13#11718664C211yesmaximal, characteristic, complemented
14#11718659C211yesmaximal, characteristic, complemented
15#11718656C211yesmaximal, characteristic, complemented
16C13×C4⋊Q8C2211yescharacteristic
17C13×#126—21no—
18C13×#126—21no—
19C13×#124—21no—
20C13×C22⋊Q8C2211yescharacteristic
21C13×C22⋊Q8C2211yescharacteristic
22C4×Q8×C13—21no—
23C4×Q8×C13C2211yescharacteristic
24C4×D4×C13C2211yescharacteristic
25C13×#117C2211yescharacteristic
26C13×#117C2211yescharacteristic
27C2×#6106C2211yescharacteristic
28#88193—21no—
29#88184C2211yescharacteristic
30#88184C2211yescharacteristic
31#88180C2211yescharacteristic
32C2×C4⋊Dic13C2211yescharacteristic
33C2×#6099C2211yescharacteristic
34C22×#1055C2211yescharacteristic
35#88152—21no—
36#88137—21no—
37#88135—21no—
38C4×D52C2211yescharacteristic
39#88124C2211yescharacteristic
40#88075C2211yescharacteristic
41#88075C2211yescharacteristic
42#88075C2211yescharacteristic
43C22⋊#1055C2211yescharacteristic
44C22⋊#1055C2211yescharacteristic
45#88049C2211yescharacteristic
46#88049C2211yescharacteristic
47#88049C2211yescharacteristic
48#88048C2211yescharacteristic
49#88048C2211yescharacteristic
50#88048C2211yescharacteristic
51#88048C2211yescharacteristic
52#88048C2211yescharacteristic
53#88047C2211yescharacteristic
54#88047C2211yescharacteristic
55#88047C2211yescharacteristic
56#88047C2211yescharacteristic
57C4⋊#1055C2211yescharacteristic
58#88043C2211yescharacteristic
59C2×Q8×C13—21no—
60C2×Q8×C13C2311yescharacteristic
61C2×D4×C13D411yescharacteristic
62C22×C4×C13C2311yescharacteristic
63C22×C4×C13C2311yescharacteristic
64C2×C22⋊D13—21no—
65C2×C22⋊D13—21no—
66C22×Dic13—21no—
67C2×D52C2311yescharacteristic
68C2×C4×D13—21no—
69C13×C4⋊C4—21no—
70C13×C4⋊C4—21no—
71C13×C4⋊C4—21no—
72C13×C4⋊C4—21no—
73C13×C4⋊C4D411yescharacteristic
74C13×C4⋊C4C2311yescharacteristic
75C13×C4⋊C4C2311yescharacteristic
76C13×C4⋊C4C2311yescharacteristic
77C13×C22⋊C4—21no—
78C13×C22⋊C4—21no—
79C13×C22⋊C4—21no—
80C13×C22⋊C4—21no—
81C13×C22⋊C4D411yescharacteristic
82C13×C22⋊C4D411yescharacteristic
83C42×C13—21no—
84C42×C13—21no—
85C42×C13—21no—
86C42×C13C2311yescharacteristic
87C22⋊Dic13—21no—
88#6106—22no—
89#6103—21no—
90#6103—21no—
91#6103—21no—
92C4⋊Dic13—21no—
93C4⋊Dic13C2311yescharacteristic
94C4⋊Dic13C2311yescharacteristic
95C4⋊Dic13C2311yescharacteristic
96#6101—21no—
97#6101—21no—
98C4×Dic13—21no—
99#6099—22no—
100C2×#1055—22no—
101C2×#1055C2311yescharacteristic
102C2×#1055C2311yescharacteristic
103C2×#1055C2311yescharacteristic
104C2×#1055C2311yescharacteristic
105#3350—131nomaximal, Sylow
106C23×C13C2×D411yescharacteristic
107C23×C13C2×D411yescharacteristic
108C22×D13—21no—
109Q8×C13—21no—
110Q8×C13—21no—
111Q8×C13—42no—
112D4×C13—41no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13C2×D411yescharacteristic
122C2×C4×C13C2×D411yescharacteristic
123C2×C4×C13C2×D411yescharacteristic
124C2×C4×C13C2×D411yescharacteristic
125C2×C4×C13C2411yescharacteristic
126C22⋊D13—42no—
127C22⋊D13—81no—
128C2×Dic13—21no—
129C2×Dic13—21no—
130C2×Dic13—21no—
131C2×Dic13—81no—
132D52—21no—
133D52—21no—
134C4×D13—81no—
135#1055—21no—
136#1055—21no—
137#1055—21no—
138#1055#4112yes—
139#556D1311yescharacteristic, complemented
140#553—131no—
141#501—131no—
142#485—131no—
143#483—131no—
144#482—131no—
145#482—131no—
146#479—131no—
147#476—131no—
148#468—131no—
149#465—131no—
150#440—131no—
151#435—131no—
152#428—131no—
153#427—131no—
154C22×C13—21no—
155C22×C13—21no—
156C22×C13—21no—
157C22×C13—21no—
158C22×C13—21no—
159C22×C13—21no—
160C22×C13C22×D411yescharacteristic
161C2×D13—41no—
162C2×D13—41no—
163C2×D13—41no—
164C4×C13—21no—
165C4×C13—21no—
166C4×C13—21no—
167C4×C13—21no—
168C4×C13—41no—
169C4×C13—41no—
170C4×C13—41no—
171C4×C13—41no—
172C4×C13C2×#4111yescharacteristic
173C4×C132−1+411yescharacteristic
174Dic13—41no—
175Dic13—41no—
176Dic13—41no—
177C2×SD16—131no—
178C2×M16—131no—
179C22×C8—131no—
180C4⋊Q8C2×D1311yescharacteristic
181#126—21no—
182#126—21no—
183#126—261no—
184#125—131no—
185#124—21no—
186#123—261no—
187C22⋊Q8C2×D1311yescharacteristic
188C22⋊Q8C2×D1311yescharacteristic
189#121—131no—
190#121—131no—
191#121—261no—
192C4×Q8—21no—
193C4×Q8C2×D1311yescharacteristic
194C4×D4—131no—
195C4×D4—261no—
196C4×D4C2×D1311yescharacteristic
197#117—131no—
198#117C2×D1311yescharacteristic
199#117C2×D1311yescharacteristic
200C2×C4⋊C4—131no—
201#107—131no—
202#107—131no—
203#107—131no—
204#107—131no—
205#106—131no—
206#106—131no—
207#106—131no—
208#106—131no—
209#106—131no—
210C4⋊C8—131no—
211#103—131no—
212#103—131no—
213#103—131no—
214#102—131no—
215#102—131no—
216#102—131no—
217C22⋊C8—131no—
218C22⋊C8—131no—
219#97—131no—
220C2×C13—41no—
221C2×C13—41no—
222C2×C13#54711yescharacteristic
223C2×C13#57511yescharacteristic
224C2×C13#57711yescharacteristic
225D13—81no—
226C2×Q8—21no—
227C2×Q8C22×D1311yescharacteristic
228C2×D4—131no—
229C2×D4—261no—
230C2×D4—261no—
231C2×D4C22⋊D1311yescharacteristic
232C22×C4—261no—
233C22×C4—261no—
234C22×C4C22×D1311yescharacteristic
235C22×C4C22×D1311yescharacteristic
236SD16—262no—
237M16—262no—
238C2×C8—131no—
239C2×C8—131no—
240C2×C8—131no—
241C2×C8—131no—
242C2×C8—262no—
243C4⋊C4—21no—
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—21no—
247C4⋊C4—131no—
248C4⋊C4—131no—
249C4⋊C4—131no—
250C4⋊C4—261no—
251C4⋊C4—261no—
252C4⋊C4—261no—
253C4⋊C4C22⋊D1311yescharacteristic
254C4⋊C4C22×D1311yescharacteristic
255C4⋊C4C22×D1311yescharacteristic
256C4⋊C4C22×D1311yescharacteristic
257C22⋊C4—21no—
258C22⋊C4—21no—
259C22⋊C4—21no—
260C22⋊C4—21no—
261C22⋊C4—261no—
262C22⋊C4—261no—
263C22⋊C4—261no—
264C22⋊C4—261no—
265C22⋊C4C22⋊D1311yescharacteristic
266C22⋊C4C22⋊D1311yescharacteristic
267C42—21no—
268C42—21no—
269C42—21no—
270C42—261no—
271C42C22×D1311yescharacteristic
272C13#335011yescharacteristic, complemented, Sylow
273C23—261no—
274C23C2×C22⋊D1311yescharacteristic
275C23C2×C22⋊D1311yescharacteristic
276Q8—21no—
277Q8—21no—
278Q8—42no—
279D4—41no—
280D4—261no—
281D4—261no—
282D4—522no—
283D4—1041no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—261no—
293C2×C4—261no—
294C2×C4—261no—
295C2×C4—1041no—
296C2×C4—1041no—
297C2×C4C2×C22⋊D1311yescharacteristic
298C2×C4C2×C22⋊D1311yescharacteristic
299C2×C4C2×C22⋊D1311yescharacteristic
300C2×C4C2×C22⋊D1311yescharacteristic
301C2×C4C23×D1311yescharacteristic
302C8—132no—
303C8—261no—
304C8—261no—
305C8—261no—
306C22—21no—
307C22—21no—
308C22—21no—
309C22—21no—
310C22—21no—
311C22—21no—
312C22—521no—
313C22—521no—
314C22—521no—
315C22C22×C22⋊D1311yescharacteristic
316C4—21no—
317C4—21no—
318C4—21no—
319C4—21no—
320C4—41no—
321C4—41no—
322C4—41no—
323C4—41no—
324C4—521no—
325C4—521no—
326C4—521no—
327C4#41×D1311yescharacteristic
328C4#8825711yescharacteristic
329C2—41no—
330C2—41no—
331C2—1041no—
332C2#1171952711yescharacteristic
333C2#1171952911yescharacteristic
334C2#1171954211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#556C2
socleC22×C13C22×D4
prime radical#11719270C2
hypercenter#556D13
hypocenterC13#3350
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C4×D4 ◁ #556

Complements

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

NH ≅ G/Ntype
1. C13×#556C2semidirect
3. #11718745C2semidirect
4. #11718741C2semidirect
5. #11718710C2semidirect
6. #11718709C2semidirect
7. #11718706C2semidirect
8. #11718704C2semidirect
9. #11718687C2semidirect
10. #11718683C2semidirect
11. #11718672C2semidirect
12. #11718664C2semidirect
13. #11718664C2semidirect
14. #11718659C2semidirect
15. #11718656C2semidirect
139. #556D13semidirect
272. C13#3350semidirect

Maximal subgroups

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

subgroupindex
C13×#5562
#117192702
#117187452
#117187412
#117187102
#117187092
#117187062
#117187042
#117186872
#117186832
#117186722
#117186642
#117186592
#117186562
#335013