Finite Group Databasebeta

← #13127436

Subgroups — #13127436

Order 1664.

360 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#553C211yesmaximal, characteristic, complemented
2#11719270C211yesmaximal, characteristic, complemented
3#11718727C211yesmaximal, characteristic, complemented
4#11718725C211yesmaximal, characteristic, complemented
5#11718700C211yesmaximal, characteristic, complemented
6#11718700C211yesmaximal, characteristic, complemented
7#11718696C211yesmaximal, characteristic, complemented
8#11718694C211yesmaximal, characteristic, complemented
9C4×#6104C211yesmaximal, characteristic, complemented
10#11718673C211yesmaximal, characteristic, complemented
11#11718670C211yesmaximal, characteristic, complemented
12#11718664C211yesmaximal, characteristic, complemented
13#11718656C211yesmaximal, characteristic, complemented
14#11718628C211yesmaximal, characteristic, complemented
15#11718625C211yesmaximal, characteristic, complemented
16C13×#126—21no—
17C13×#125C2211yescharacteristic
18C13×#123—21no—
19C13×#121—21no—
20C13×#121C2211yescharacteristic
21C13×#121C2211yescharacteristic
22C4×D4×C13—21no—
23C4×D4×C13C2211yescharacteristic
24C4×D4×C13C2211yescharacteristic
25C13×#117C2211yescharacteristic
26C2×C13×C4⋊C4C2211yescharacteristic
27#88193—21no—
28C2×#6104C2211yescharacteristic
29#88184C2211yescharacteristic
30#88184C2211yescharacteristic
31#88180C2211yescharacteristic
32C2×C4⋊Dic13C2211yescharacteristic
33C2×#6099C2211yescharacteristic
34C2×#6099C2211yescharacteristic
35#88152—21no—
36#88137—21no—
37#88135—21no—
38C4×D52C2211yescharacteristic
39#88124C2211yescharacteristic
40#88072C2211yescharacteristic
41#88072C2211yescharacteristic
42#88072C2211yescharacteristic
43C22⋊#1055C2211yescharacteristic
44C22⋊#1055C2211yescharacteristic
45#88049C2211yescharacteristic
46#88049C2211yescharacteristic
47#88049C2211yescharacteristic
48#88048C2211yescharacteristic
49#88048C2211yescharacteristic
50#88048C2211yescharacteristic
51#88048C2211yescharacteristic
52#88047C2211yescharacteristic
53#88047C2211yescharacteristic
54#88047C2211yescharacteristic
55#88047C2211yescharacteristic
56#88047C2211yescharacteristic
57C4⋊#1055C2211yescharacteristic
58C4×#1055C2211yescharacteristic
59C2×D4×C13—21no—
60C2×D4×C13—21no—
61C2×D4×C13D411yescharacteristic
62C2×D4×C13C2311yescharacteristic
63C22×C4×C13—21no—
64C22×C4×C13—21no—
65C22×C4×C13C2311yescharacteristic
66C22×C4×C13C2311yescharacteristic
67C2×C22⋊D13—21no—
68C2×C22⋊D13—21no—
69C22×Dic13—21no—
70C2×D52C2311yescharacteristic
71C2×C4×D13—21no—
72C13×C4⋊C4—21no—
73C13×C4⋊C4—21no—
74C13×C4⋊C4—21no—
75C13×C4⋊C4D411yescharacteristic
76C13×C4⋊C4C2311yescharacteristic
77C13×C4⋊C4C2311yescharacteristic
78C13×C4⋊C4C2311yescharacteristic
79C13×C22⋊C4—21no—
80C13×C22⋊C4—21no—
81C13×C22⋊C4—21no—
82C13×C22⋊C4—21no—
83C13×C22⋊C4D411yescharacteristic
84C13×C22⋊C4D411yescharacteristic
85C42×C13—21no—
86C42×C13C2311yescharacteristic
87C22⋊Dic13—21no—
88#6104—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—
100#6099—22no—
101C2×#1055C2311yescharacteristic
102C2×#1055C2311yescharacteristic
103C2×#1055C2311yescharacteristic
104C2×#1055C2311yescharacteristic
105#3355—131nomaximal, Sylow
106C23×C13—21no—
107C23×C13C2×D411yescharacteristic
108C23×C13C2×D411yescharacteristic
109C22×D13—21no—
110D4×C13—21no—
111D4×C13—21no—
112D4×C13—41no—
113D4×C13—42no—
114D4×C13—81no—
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—21no—
122C2×C4×C13—81no—
123C2×C4×C13—81no—
124C2×C4×C13C2×D411yescharacteristic
125C2×C4×C13C2×D411yescharacteristic
126C2×C4×C13C2×D411yescharacteristic
127C2×C4×C13C2×D411yescharacteristic
128C2×C4×C13C2411yescharacteristic
129C22⋊D13—42no—
130C22⋊D13—81no—
131C2×Dic13—21no—
132C2×Dic13—21no—
133C2×Dic13—21no—
134C2×Dic13—81no—
135D52—21no—
136D52—21no—
137C4×D13—81no—
138#1055—21no—
139#1055—21no—
140#1055—21no—
141#1055#4112yes—
142#553—131no—
143#553D1311yescharacteristic, complemented
144#499—131no—
145#482—131no—
146#482—131no—
147#480—131no—
148#480—131no—
149#478—131no—
150#478—131no—
151#469—131no—
152#469—131no—
153C4×D8—131no—
154#436—131no—
155#428—131no—
156#428—131no—
157C22×C13—21no—
158C22×C13—21no—
159C22×C13—21no—
160C22×C13—21no—
161C22×C13—21no—
162C22×C13—21no—
163C22×C13—41no—
164C22×C13—41no—
165C22×C13—41no—
166C22×C13C22×D411yescharacteristic
167C2×D13—41no—
168C2×D13—41no—
169C2×D13—41no—
170C4×C13—21no—
171C4×C13—21no—
172C4×C13—21no—
173C4×C13—21no—
174C4×C13—41no—
175C4×C13—41no—
176C4×C13—41no—
177C4×C13C2×#4111yescharacteristic
178C4×C132−1+411yescharacteristic
179Dic13—41no—
180Dic13—41no—
181Dic13—41no—
182C2×D8—131no—
183C2×M16—131no—
184C2×M16—131no—
185#126—21no—
186#126—261no—
187#125—131no—
188#125C2×D1311yescharacteristic
189#123—21no—
190#123—261no—
191#121—21no—
192#121—131no—
193#121—131no—
194#121—261no—
195#121C2×D1311yescharacteristic
196#121C2×D1311yescharacteristic
197C4×D4—21no—
198C4×D4—131no—
199C4×D4—261no—
200C4×D4C2×D1311yescharacteristic
201C4×D4C2×D1311yescharacteristic
202#117—131no—
203#117C2×D1311yescharacteristic
204C2×C4⋊C4—131no—
205C2×C4⋊C4C2×D1311yescharacteristic
206#107—131no—
207#107—131no—
208#107—131no—
209#107—131no—
210#107—131no—
211#106—131no—
212#106—131no—
213#106—131no—
214#106—131no—
215C4⋊C8—131no—
216#102—131no—
217#102—131no—
218#102—131no—
219#102—131no—
220#102—131no—
221#102—131no—
222C22⋊C8—131no—
223C22⋊C8—131no—
224C4×C8—131no—
225C2×C13—41no—
226C2×C13—41no—
227C2×C13—81no—
228C2×C13#54711yescharacteristic
229C2×C13#57511yescharacteristic
230C2×C13#57611yescharacteristic
231D13—81no—
232C2×D4—21no—
233C2×D4—21no—
234C2×D4—131no—
235C2×D4—261no—
236C2×D4—261no—
237C2×D4C22⋊D1311yescharacteristic
238C2×D4C22×D1311yescharacteristic
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—261no—
242C22×C4—261no—
243C22×C4C22×D1311yescharacteristic
244C22×C4C22×D1311yescharacteristic
245D8—262no—
246M16—262no—
247M16—262no—
248C2×C8—131no—
249C2×C8—131no—
250C2×C8—131no—
251C2×C8—131no—
252C4⋊C4—21no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—131no—
256C4⋊C4—131no—
257C4⋊C4—131no—
258C4⋊C4—261no—
259C4⋊C4—261no—
260C4⋊C4—261no—
261C4⋊C4C22⋊D1311yescharacteristic
262C4⋊C4C22×D1311yescharacteristic
263C4⋊C4C22×D1311yescharacteristic
264C4⋊C4C22×D1311yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—21no—
267C22⋊C4—21no—
268C22⋊C4—21no—
269C22⋊C4—261no—
270C22⋊C4—261no—
271C22⋊C4—261no—
272C22⋊C4—261no—
273C22⋊C4C22⋊D1311yescharacteristic
274C22⋊C4C22⋊D1311yescharacteristic
275C42—21no—
276C42—261no—
277C42C22×D1311yescharacteristic
278C13#335511yescharacteristic, complemented, Sylow
279C23—21no—
280C23—261no—
281C23C2×C22⋊D1311yescharacteristic
282C23C2×C22⋊D1311yescharacteristic
283D4—21no—
284D4—21no—
285D4—41no—
286D4—42no—
287D4—81no—
288D4—261no—
289D4—261no—
290D4—522no—
291D4—1041no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—81no—
300C2×C4—81no—
301C2×C4—261no—
302C2×C4—261no—
303C2×C4—261no—
304C2×C4—1041no—
305C2×C4—1041no—
306C2×C4C2×C22⋊D1311yescharacteristic
307C2×C4C2×C22⋊D1311yescharacteristic
308C2×C4C2×C22⋊D1311yescharacteristic
309C2×C4C2×C22⋊D1311yescharacteristic
310C2×C4C23×D1311yescharacteristic
311C8—132no—
312C8—261no—
313C8—261no—
314C8—261no—
315C22—21no—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—21no—
320C22—21no—
321C22—41no—
322C22—41no—
323C22—41no—
324C22—521no—
325C22—521no—
326C22—521no—
327C22C22×C22⋊D1311yescharacteristic
328C4—21no—
329C4—21no—
330C4—21no—
331C4—21no—
332C4—41no—
333C4—41no—
334C4—41no—
335C4—521no—
336C4—521no—
337C4—521no—
338C4#41×D1311yescharacteristic
339C4#8825711yescharacteristic
340C2—41no—
341C2—41no—
342C2—81no—
343C2—1041no—
344C2#1171952711yescharacteristic
345C2#1171952911yescharacteristic
346C2#1171954011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#553C2
socleC22×C13C22×D4
hypercenter#553D13
hypocenterC13#3355
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C4×D4 ◁ #553

Complements

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

NH ≅ G/Ntype
1. C13×#553C2semidirect
2. #11719270C2semidirect
3. #11718727C2semidirect
4. #11718725C2semidirect
5. #11718700C2semidirect
6. #11718700C2semidirect
7. #11718696C2semidirect
8. #11718694C2semidirect
9. C4×#6104C2semidirect
10. #11718673C2semidirect
11. #11718670C2semidirect
12. #11718664C2semidirect
13. #11718656C2semidirect
14. #11718628C2semidirect
15. #11718625C2semidirect
143. #553D13semidirect
278. C13#3355semidirect

Maximal subgroups

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

subgroupindex
C13×#5532
#117192702
#117187272
#117187252
#117187002
#117186962
#117186942
C4×#61042
#117186732
#117186702
#117186642
#117186562
#117186282
#117186252
#335513