Finite Group Databasebeta

← #13126956

Subgroups — #13126956

Order 1664.

392 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#552C211yesmaximal, characteristic, complemented
2#11719258C211yesmaximal, characteristic
3#11718728C211yesmaximal, characteristic, complemented
4#11718724C211yesmaximal, characteristic, complemented
5#11718710C211yesmaximal, characteristic, complemented
6#11718709C211yesmaximal, characteristic, complemented
7#11718708C211yesmaximal, characteristic, complemented
8#11718708C211yesmaximal, characteristic, complemented
9#11718691C211yesmaximal, characteristic, complemented
10#11718688C211yesmaximal, characteristic, complemented
11#11718672C211yesmaximal, characteristic, complemented
12#11718664C211yesmaximal, characteristic, complemented
13#11718663C211yesmaximal, characteristic, complemented
14#11718629C211yesmaximal, characteristic, complemented
15#11718627C211yesmaximal, characteristic, complemented
16C2×#6127C2211yescharacteristic
17C2×#6127C2211yescharacteristic
18C13×#126—21no—
19C13×#125—21no—
20C13×#125C2211yescharacteristic
21C13×#123—21no—
22C13×C22⋊Q8C2211yescharacteristic
23C13×C22⋊Q8C2211yescharacteristic
24C4×Q8×C13C2211yescharacteristic
25C4×D4×C13C2211yescharacteristic
26C13×#117—21no—
27C13×#117C2211yescharacteristic
28C2×C13×C4⋊C4C2211yescharacteristic
29C2×#6107C2211yescharacteristic
30C2×#6106C2211yescharacteristic
31C2×#6106C2211yescharacteristic
32#88194—21no—
33#88184C2211yescharacteristic
34#88184C2211yescharacteristic
35C2×#6099C2211yescharacteristic
36C22×#1055C2211yescharacteristic
37#88147—21no—
38#88138—21no—
39#88138—21no—
40#88128C2211yescharacteristic
41C4×Dic26C2211yescharacteristic
42#88075C2211yescharacteristic
43C22⋊#1055C2211yescharacteristic
44C22⋊#1055C2211yescharacteristic
45#88050C2211yescharacteristic
46#88050C2211yescharacteristic
47#88050C2211yescharacteristic
48#88049C2211yescharacteristic
49#88049C2211yescharacteristic
50#88049C2211yescharacteristic
51#88049C2211yescharacteristic
52#88049C2211yescharacteristic
53#88049C2211yescharacteristic
54#88048C2211yescharacteristic
55#88048C2211yescharacteristic
56#88047C2211yescharacteristic
57C4⋊#1055C2211yescharacteristic
58#88043C2211yescharacteristic
59C2×Q8×C13C2311yescharacteristic
60C2×D4×C13D411yescharacteristic
61C22×C4×C13—21no—
62C22×C4×C13C2311yescharacteristic
63C22×C4×C13C2311yescharacteristic
64C2×C22⋊D13—21no—
65C2×C22⋊D13—21no—
66C2×C22⋊D13—21no—
67C2×C22⋊D13—21no—
68#6127—22no—
69#6127—22no—
70#6127—41no—
71#6127—41no—
72C2×D52—21no—
73C2×D52—21no—
74C2×D52C2311yescharacteristic
75C2×D52C2311yescharacteristic
76C2×C4×D13—21no—
77C2×C4×D13—21no—
78C2×Dic26C2311yescharacteristic
79C13×C4⋊C4—21no—
80C13×C4⋊C4—21no—
81C13×C4⋊C4—21no—
82C13×C4⋊C4—21no—
83C13×C4⋊C4—21no—
84C13×C4⋊C4—21no—
85C13×C4⋊C4D411yescharacteristic
86C13×C4⋊C4C2311yescharacteristic
87C13×C4⋊C4C2311yescharacteristic
88C13×C4⋊C4C2311yescharacteristic
89C13×C22⋊C4—21no—
90C13×C22⋊C4—21no—
91C13×C22⋊C4—21no—
92C13×C22⋊C4D411yescharacteristic
93C13×C22⋊C4D411yescharacteristic
94C42×C13—21no—
95C42×C13—21no—
96C42×C13C2311yescharacteristic
97#6107—22no—
98#6106—41no—
99#6106—41no—
100#6103—21no—
101#6103—21no—
102C4⋊Dic13C2311yescharacteristic
103#6101—21no—
104C4×Dic13—21no—
105#6099—41no—
106C2×#1055—41no—
107C2×#1055C2311yescharacteristic
108C2×#1055C2311yescharacteristic
109C2×#1055C2311yescharacteristic
110C2×#1055C2311yescharacteristic
111#3317—131nomaximal, Sylow
112C23×C13C2×D411yescharacteristic
113C23×C13C2×D411yescharacteristic
114C22×D13—21no—
115C22×D13—21no—
116Q8×C13—21no—
117Q8×C13—21no—
118D4×C13—41no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13—21no—
125C2×C4×C13—21no—
126C2×C4×C13—21no—
127C2×C4×C13—42no—
128C2×C4×C13C2×D411yescharacteristic
129C2×C4×C13C2×D411yescharacteristic
130C2×C4×C13C2×D411yescharacteristic
131C2×C4×C13C2×D411yescharacteristic
132C2×C4×C13C2411yescharacteristic
133C22⋊D13—42no—
134C22⋊D13—42no—
135C22⋊D13—81no—
136C22⋊D13—81no—
137C2×Dic13—21no—
138C2×Dic13—21no—
139D52—21no—
140D52—21no—
141D52—21no—
142D52—21no—
143D52—42no—
144D52—81no—
145C4×D13—42no—
146C4×D13—42no—
147Dic26—21no—
148Dic26#4112yes—
149#1055—21no—
150#1055—21no—
151#1055—21no—
152#1055—21no—
153#552D1311yescharacteristic, complemented
154#550—131no—
155#490—131no—
156#482—131no—
157#481—131no—
158#479—131no—
159#468—131no—
160#465—131no—
161#460—131no—
162#452—131no—
163#452—131no—
164#441—131no—
165#435—131no—
166#417—131no—
167#416—131no—
168C22×C13—21no—
169C22×C13—21no—
170C22×C13—21no—
171C22×C13—21no—
172C22×C13—21no—
173C22×C13—21no—
174C22×C13C22×D411yescharacteristic
175C2×D13—41no—
176C2×D13—41no—
177C2×D13—41no—
178C2×D13—41no—
179C2×D13—41no—
180C2×D13—41no—
181C4×C13—21no—
182C4×C13—21no—
183C4×C13—21no—
184C4×C13—21no—
185C4×C13—41no—
186C4×C13—41no—
187C4×C13—41no—
188C4×C13—41no—
189C4×C13C2×#4111yescharacteristic
190C4×C13H(5,𝔽2)11yescharacteristic
191Dic13—22no—
192Dic13—41no—
193C2×#41—131no—
194C2×#41—131no—
195C2×Q16—131no—
196C2×SD16—131no—
197C2×SD16—131no—
198C2×M16—131no—
199C22×C8—131no—
200#127—131no—
201#127—261no—
202#126—21no—
203#125—21no—
204#125C2×D1311yescharacteristic
205#123—21no—
206C22⋊Q8C2×D1311yescharacteristic
207C22⋊Q8C2×D1311yescharacteristic
208#121—131no—
209#121—131no—
210#121—261no—
211#121—261no—
212C4×Q8—131no—
213C4×Q8C2×D1311yescharacteristic
214C4×D4—261no—
215C4×D4C2×D1311yescharacteristic
216#117—21no—
217#117C2×D1311yescharacteristic
218C2×C4⋊C4C2×D1311yescharacteristic
219#107—131no—
220#106—131no—
221#106—131no—
222C4⋊C8—131no—
223#103—131no—
224#103—131no—
225#103—131no—
226#103—131no—
227#102—131no—
228#102—131no—
229#102—131no—
230#102—131no—
231#102—131no—
232#102—131no—
233C22⋊C8—131no—
234C22⋊C8—131no—
235#97—131no—
236C2×C13—41no—
237C2×C13—41no—
238C2×C13#54611yescharacteristic
239C2×C13#57511yescharacteristic
240C2×C13#57711yescharacteristic
241D13—81no—
242D13—81no—
243#41—262no—
244#41—262no—
245#41—521no—
246#41—521no—
247C2×Q8—131no—
248C2×Q8C22×D1311yescharacteristic
249C2×D4—131no—
250C2×D4—131no—
251C2×D4—261no—
252C2×D4—261no—
253C2×D4—261no—
254C2×D4—261no—
255C2×D4—261no—
256C2×D4—261no—
257C2×D4C22⋊D1311yescharacteristic
258C22×C4—21no—
259C22×C4—261no—
260C22×C4—261no—
261C22×C4C22×D1311yescharacteristic
262C22×C4C22×D1311yescharacteristic
263Q16—262no—
264SD16—521no—
265SD16—521no—
266M16—521no—
267C2×C8—131no—
268C2×C8—131no—
269C2×C8—131no—
270C2×C8—131no—
271C2×C8—521no—
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4—21no—
278C4⋊C4—131no—
279C4⋊C4—261no—
280C4⋊C4C22⋊D1311yescharacteristic
281C4⋊C4C22×D1311yescharacteristic
282C4⋊C4C22×D1311yescharacteristic
283C4⋊C4C22×D1311yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—261no—
288C22⋊C4—261no—
289C22⋊C4C22⋊D1311yescharacteristic
290C22⋊C4C22⋊D1311yescharacteristic
291C42—21no—
292C42—21no—
293C42—261no—
294C42C22×D1311yescharacteristic
295C13#331711yescharacteristic, complemented, Sylow
296C23—261no—
297C23—261no—
298C23C2×C22⋊D1311yescharacteristic
299C23C2×C22⋊D1311yescharacteristic
300Q8—21no—
301Q8—21no—
302Q8—132no—
303Q8—261no—
304D4—41no—
305D4—261no—
306D4—261no—
307D4—261no—
308D4—261no—
309D4—522no—
310D4—522no—
311D4—522no—
312D4—1041no—
313D4—1041no—
314D4—1041no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—42no—
324C2×C4—261no—
325C2×C4—261no—
326C2×C4—522no—
327C2×C4—522no—
328C2×C4C2×C22⋊D1311yescharacteristic
329C2×C4C2×C22⋊D1311yescharacteristic
330C2×C4C2×C22⋊D1311yescharacteristic
331C2×C4C2×C22⋊D1311yescharacteristic
332C2×C4C23×D1311yescharacteristic
333C8—261no—
334C8—261no—
335C8—261no—
336C8—261no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—521no—
344C22—521no—
345C22—521no—
346C22—521no—
347C22—521no—
348C22—521no—
349C22C22×C22⋊D1311yescharacteristic
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—41no—
358C4—262no—
359C4—521no—
360C4#41×D1311yescharacteristic
361C4#8825611yescharacteristic
362C2—41no—
363C2—41no—
364C2—1041no—
365C2—1041no—
366C2#1171952711yescharacteristic
367C2#1171953411yescharacteristic
368C2#1171954211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#552C2
socleC22×C13C22×D4
prime radical#11719258C2
hypercenter#552D13
hypocenterC13#3317
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C4×D4 ◁ #552

Complements

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

NH ≅ G/Ntype
1. C13×#552C2semidirect
3. #11718728C2semidirect
4. #11718724C2semidirect
5. #11718710C2semidirect
6. #11718709C2semidirect
7. #11718708C2semidirect
8. #11718708C2semidirect
9. #11718691C2semidirect
10. #11718688C2semidirect
11. #11718672C2semidirect
12. #11718664C2semidirect
13. #11718663C2semidirect
14. #11718629C2semidirect
15. #11718627C2semidirect
153. #552D13semidirect
295. C13#3317semidirect

Maximal subgroups

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

subgroupindex
C13×#5522
#117192582
#117187282
#117187242
#117187102
#117187092
#117187082
#117186912
#117186882
#117186722
#117186642
#117186632
#117186292
#117186272
#331713