Finite Group Databasebeta

← #13127315

Subgroups — #13127315

Order 1664.

356 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#554C211yesmaximal, characteristic, complemented
2#11719270C211yesmaximal, characteristic
3#11718748C211yesmaximal, characteristic, complemented
4#11718741C211yesmaximal, characteristic, complemented
5#11718710C211yesmaximal, characteristic, complemented
6#11718709C211yesmaximal, characteristic, complemented
7#11718706C211yesmaximal, characteristic, complemented
8#11718705C211yesmaximal, characteristic, complemented
9#11718687C211yesmaximal, characteristic, complemented
10#11718683C211yesmaximal, characteristic, complemented
11#11718672C211yesmaximal, characteristic, complemented
12#11718629C211yesmaximal, characteristic, complemented
13#11718628C211yesmaximal, characteristic, complemented
14#11718625C211yesmaximal, characteristic, complemented
15C2×#88047C211yesmaximal, characteristic, complemented
16C13×C4⋊Q8C2211yescharacteristic
17C13×#125—21no—
18C13×C22⋊Q8—21no—
19C13×C22⋊Q8—21no—
20C13×C22⋊Q8C2211yescharacteristic
21C13×C22⋊Q8C2211yescharacteristic
22C4×Q8×C13C2211yescharacteristic
23C4×D4×C13—21no—
24C4×D4×C13C2211yescharacteristic
25C2×C13×C4⋊C4C2211yescharacteristic
26C2×C13×C4⋊C4C2211yescharacteristic
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#88047C2211yescharacteristic
52#88047C2211yescharacteristic
53#88047C2211yescharacteristic
54#88047C2211yescharacteristic
55#88047C2211yescharacteristic
56#88047C2211yescharacteristic
57C4⋊#1055C2211yescharacteristic
58#88043C2211yescharacteristic
59C2×Q8×C13—21no—
60C2×Q8×C13C2311yescharacteristic
61C2×D4×C13D411yescharacteristic
62C22×C4×C13—21no—
63C22×C4×C13—21no—
64C22×C4×C13C2311yescharacteristic
65C22×C4×C13C2311yescharacteristic
66C2×C22⋊D13—21no—
67C2×C22⋊D13—21no—
68C22×Dic13—21no—
69C2×D52C2311yescharacteristic
70C2×C4×D13—21no—
71C13×C4⋊C4—21no—
72C13×C4⋊C4—21no—
73C13×C4⋊C4—21no—
74C13×C4⋊C4—21no—
75C13×C4⋊C4—21no—
76C13×C4⋊C4—21no—
77C13×C4⋊C4D411yescharacteristic
78C13×C4⋊C4C2311yescharacteristic
79C13×C4⋊C4C2311yescharacteristic
80C13×C4⋊C4C2311yescharacteristic
81C13×C22⋊C4—21no—
82C13×C22⋊C4—21no—
83C13×C22⋊C4D411yescharacteristic
84C13×C22⋊C4D411yescharacteristic
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#3346—131nomaximal, Sylow
106C23×C13C2×D411yescharacteristic
107C23×C13C2×D411yescharacteristic
108C22×D13—21no—
109Q8×C13—21no—
110Q8×C13—21no—
111Q8×C13—81no—
112D4×C13—22no—
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×C13—81no—
122C2×C4×C13—81no—
123C2×C4×C13C2×D411yescharacteristic
124C2×C4×C13C2×D411yescharacteristic
125C2×C4×C13C2×D411yescharacteristic
126C2×C4×C13C2×D411yescharacteristic
127C2×C4×C13C2411yescharacteristic
128C22⋊D13—42no—
129C22⋊D13—81no—
130C2×Dic13—21no—
131C2×Dic13—21no—
132C2×Dic13—21no—
133C2×Dic13—81no—
134D52—21no—
135D52—21no—
136C4×D13—81no—
137#1055—21no—
138#1055—21no—
139#1055—21no—
140#1055#4112yes—
141#554D1311yescharacteristic, complemented
142#553—131no—
143#501—131no—
144#485—131no—
145#484—131no—
146#481—131no—
147#480—131no—
148#479—131no—
149#474—131no—
150#468—131no—
151#465—131no—
152#440—131no—
153#435—131no—
154#428—131no—
155C2×#107—131no—
156C22×C13—21no—
157C22×C13—21no—
158C22×C13—21no—
159C22×C13—21no—
160C22×C13—21no—
161C22×C13#13712yes—
162C22×C13C22×D411yescharacteristic
163C2×D13—41no—
164C2×D13—41no—
165C2×D13—41no—
166C4×C13—21no—
167C4×C13—21no—
168C4×C13—21no—
169C4×C13—21no—
170C4×C13—41no—
171C4×C13—41no—
172C4×C13—41no—
173C4×C13—41no—
174C4×C13C2×#4111yescharacteristic
175C4×C132−1+411yescharacteristic
176Dic13—41no—
177Dic13—41no—
178Dic13—41no—
179C2×SD16—131no—
180C2×M16—131no—
181C22×C8—131no—
182C4⋊Q8C2×D1311yescharacteristic
183#126—261no—
184#125—21no—
185#125—131no—
186#123—261no—
187C22⋊Q8—21no—
188C22⋊Q8—21no—
189C22⋊Q8C2×D1311yescharacteristic
190C22⋊Q8C2×D1311yescharacteristic
191#121—131no—
192#121—131no—
193#121—261no—
194C4×Q8C2×D1311yescharacteristic
195C4×D4—21no—
196C4×D4—131no—
197C4×D4—261no—
198C4×D4C2×D1311yescharacteristic
199#117—131no—
200C2×C4⋊C4—131no—
201C2×C4⋊C4C2×D1311yescharacteristic
202C2×C4⋊C4C2×D1311yescharacteristic
203#107—131no—
204#107—131no—
205#107—131no—
206#107—131no—
207#107—131no—
208#107—131no—
209#106—131no—
210#106—131no—
211#106—131no—
212C4⋊C8—131no—
213#103—131no—
214#103—131no—
215#103—131no—
216#102—131no—
217#102—131no—
218#102—131no—
219C22⋊C8—131no—
220C22⋊C8—131no—
221#97—131no—
222C2×C13—22no—
223C2×C13—41no—
224C2×C13#54711yescharacteristic
225C2×C13C2×#13711yescharacteristic
226C2×C13#57611yescharacteristic
227D13—81no—
228C2×Q8—21no—
229C2×Q8C22×D1311yescharacteristic
230C2×D4—131no—
231C2×D4—261no—
232C2×D4—261no—
233C2×D4C22⋊D1311yescharacteristic
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—261no—
237C22×C4—261no—
238C22×C4C22×D1311yescharacteristic
239C22×C4C22×D1311yescharacteristic
240SD16—262no—
241M16—262no—
242C2×C8—131no—
243C2×C8—131no—
244C2×C8—131no—
245C2×C8—131no—
246C2×C8—262no—
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—21no—
251C4⋊C4—21no—
252C4⋊C4—21no—
253C4⋊C4—131no—
254C4⋊C4—131no—
255C4⋊C4—131no—
256C4⋊C4—261no—
257C4⋊C4—261no—
258C4⋊C4—261no—
259C4⋊C4C22⋊D1311yescharacteristic
260C4⋊C4C22×D1311yescharacteristic
261C4⋊C4C22×D1311yescharacteristic
262C4⋊C4C22×D1311yescharacteristic
263C22⋊C4—21no—
264C22⋊C4—21no—
265C22⋊C4—261no—
266C22⋊C4—261no—
267C22⋊C4—261no—
268C22⋊C4—261no—
269C22⋊C4C22⋊D1311yescharacteristic
270C22⋊C4C22⋊D1311yescharacteristic
271C42—21no—
272C42—261no—
273C42C22×D1311yescharacteristic
274C13#334611yescharacteristic, complemented, Sylow
275C23—261no—
276C23C2×C22⋊D1311yescharacteristic
277C23C2×C22⋊D1311yescharacteristic
278Q8—21no—
279Q8—21no—
280Q8—81no—
281D4—22no—
282D4—261no—
283D4—261no—
284D4—522no—
285D4—1041no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—81no—
295C2×C4—81no—
296C2×C4—261no—
297C2×C4—261no—
298C2×C4—261no—
299C2×C4—1041no—
300C2×C4—1041no—
301C2×C4C2×C22⋊D1311yescharacteristic
302C2×C4C2×C22⋊D1311yescharacteristic
303C2×C4C2×C22⋊D1311yescharacteristic
304C2×C4C2×C22⋊D1311yescharacteristic
305C2×C4C23×D1311yescharacteristic
306C8—132no—
307C8—261no—
308C8—261no—
309C8—261no—
310C22—21no—
311C22—21no—
312C22—21no—
313C22—21no—
314C22—21no—
315C22—521no—
316C22—521no—
317C22—521no—
318C22#8819612yes—
319C22C22×C22⋊D1311yescharacteristic
320C4—21no—
321C4—21no—
322C4—21no—
323C4—21no—
324C4—41no—
325C4—41no—
326C4—41no—
327C4—41no—
328C4—521no—
329C4—521no—
330C4—521no—
331C4#41×D1311yescharacteristic
332C4#8825711yescharacteristic
333C2—22no—
334C2—41no—
335C2—1041no—
336C2C2×#8819611yescharacteristic
337C2#1171952911yescharacteristic
338C2#1171954011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#554C2
socleC22×C13C22×D4
prime radical#11719270C2
hypercenter#554D13
hypocenterC13#3346
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C4×D4 ◁ #554

Complements

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

NH ≅ G/Ntype
1. C13×#554C2semidirect
3. #11718748C2semidirect
4. #11718741C2semidirect
5. #11718710C2semidirect
6. #11718709C2semidirect
7. #11718706C2semidirect
8. #11718705C2semidirect
9. #11718687C2semidirect
10. #11718683C2semidirect
11. #11718672C2semidirect
12. #11718629C2semidirect
13. #11718628C2semidirect
14. #11718625C2semidirect
15. C2×#88047C2semidirect
141. #554D13semidirect
274. C13#3346semidirect

Maximal subgroups

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

subgroupindex
C13×#5542
#117192702
#117187482
#117187412
#117187102
#117187092
#117187062
#117187052
#117186872
#117186832
#117186722
#117186292
#117186282
#117186252
C2×#880472
#334613