Finite Group Databasebeta

← #13127016

Subgroups — #13127016

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×#555C211yesmaximal, characteristic, complemented
2#11719257C211yesmaximal, characteristic, complemented
3#11718755C211yesmaximal, characteristic, complemented
4#11718750C211yesmaximal, characteristic, complemented
5#11718702C211yesmaximal, characteristic, complemented
6#11718701C211yesmaximal, characteristic, complemented
7#11718700C211yesmaximal, characteristic, complemented
8#11718698C211yesmaximal, characteristic, complemented
9#11718679C211yesmaximal, characteristic, complemented
10#11718677C211yesmaximal, characteristic, complemented
11#11718672C211yesmaximal, characteristic, complemented
12#11718665C211yesmaximal, characteristic, complemented
13#11718664C211yesmaximal, characteristic, complemented
14#11718663C211yesmaximal, characteristic, complemented
15#11718657C211yesmaximal, characteristic, complemented
16C2×#6127C2211yescharacteristic
17C22×Dic26C2211yescharacteristic
18C13×C4⋊Q8C2211yescharacteristic
19C13×#124—21no—
20C13×#124—21no—
21C13×#121—21no—
22C13×#121C2211yescharacteristic
23C13×#121C2211yescharacteristic
24C4×D4×C13C2211yescharacteristic
25C4×D4×C13C2211yescharacteristic
26C13×#117—21no—
27C13×#117C2211yescharacteristic
28C13×#117C2211yescharacteristic
29#88193—21no—
30C2×#6105C2211yescharacteristic
31C2×#6105C2211yescharacteristic
32C2×#6104C2211yescharacteristic
33#88184C2211yescharacteristic
34#88178C2211yescharacteristic
35C2×#6099C2211yescharacteristic
36C22×#1055C2211yescharacteristic
37#88150—21no—
38#88139—21no—
39#88135—21no—
40#88129C2211yescharacteristic
41C4×Dic26C2211yescharacteristic
42#88072C2211yescharacteristic
43C22⋊#1055C2211yescharacteristic
44C22⋊#1055C2211yescharacteristic
45#88050C2211yescharacteristic
46#88050C2211yescharacteristic
47#88050C2211yescharacteristic
48#88050C2211yescharacteristic
49#88050C2211yescharacteristic
50#88050C2211yescharacteristic
51#88049C2211yescharacteristic
52#88049C2211yescharacteristic
53#88049C2211yescharacteristic
54#88048C2211yescharacteristic
55#88048C2211yescharacteristic
56#88047C2211yescharacteristic
57C4⋊#1055C2211yescharacteristic
58#88043C2211yescharacteristic
59C2×Q8×C13—21no—
60C2×D4×C13—21no—
61C2×D4×C13—21no—
62C2×D4×C13D411yescharacteristic
63C2×D4×C13C2311yescharacteristic
64C22×C4×C13—21no—
65C22×C4×C13C2311yescharacteristic
66C22×C4×C13C2311yescharacteristic
67C2×C22⋊D13—21no—
68C2×C22⋊D13—21no—
69C22×Dic13—21no—
70#6127—22no—
71#6127—41no—
72C2×D52C2311yescharacteristic
73C2×C4×D13—21no—
74C2×Dic26—22no—
75C2×Dic26—21no—
76C2×Dic26—41no—
77C2×Dic26C2311yescharacteristic
78C2×Dic26C2311yescharacteristic
79C13×C4⋊C4—21no—
80C13×C4⋊C4D411yescharacteristic
81C13×C4⋊C4C2311yescharacteristic
82C13×C4⋊C4C2311yescharacteristic
83C13×C4⋊C4C2311yescharacteristic
84C13×C22⋊C4—21no—
85C13×C22⋊C4—21no—
86C13×C22⋊C4—21no—
87C13×C22⋊C4—21no—
88C13×C22⋊C4—21no—
89C13×C22⋊C4D411yescharacteristic
90C13×C22⋊C4D411yescharacteristic
91C42×C13—21no—
92C42×C13—21no—
93C42×C13C2311yescharacteristic
94C22⋊Dic13—21no—
95#6105—22no—
96#6105—41no—
97#6104—41no—
98#6103—21no—
99#6103—21no—
100#6103—21no—
101C4⋊Dic13C2311yescharacteristic
102#6101—21no—
103#6101—21no—
104C4×Dic13—21no—
105#6099—41no—
106C2×#1055—41no—
107C2×#1055C2311yescharacteristic
108C2×#1055C2311yescharacteristic
109C2×#1055C2311yescharacteristic
110C2×#1055C2311yescharacteristic
111#3321—131nomaximal, Sylow
112C23×C13—21no—
113C23×C13C2×D411yescharacteristic
114C23×C13C2×D411yescharacteristic
115C22×D13—21no—
116Q8×C13—81no—
117D4×C13—21no—
118D4×C13—21no—
119D4×C13—41no—
120D4×C13—81no—
121D4×C13—81no—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13—21no—
125C2×C4×C13—21no—
126C2×C4×C13—21no—
127C2×C4×C13—21no—
128C2×C4×C13—21no—
129C2×C4×C13—42no—
130C2×C4×C13C2×D411yescharacteristic
131C2×C4×C13C2×D411yescharacteristic
132C2×C4×C13C2×D411yescharacteristic
133C2×C4×C13C2×D411yescharacteristic
134C2×C4×C13C2411yescharacteristic
135C22⋊D13—42no—
136C22⋊D13—42no—
137C2×Dic13—21no—
138C2×Dic13—21no—
139C2×Dic13—21no—
140C2×Dic13—42no—
141D52—21no—
142D52—21no—
143C4×D13—42no—
144Dic26—21no—
145Dic26—21no—
146Dic26—21no—
147Dic26—42no—
148Dic26#4112yes—
149#1055—21no—
150#1055—21no—
151#1055—21no—
152#1055—21no—
153#555D1311yescharacteristic, complemented
154#548—131no—
155#489—131no—
156#485—131no—
157#482—131no—
158#475—131no—
159#469—131no—
160#465—131no—
161#463—131no—
162#449—131no—
163#448—131no—
164#440—131no—
165#435—131no—
166#419—131no—
167#416—131no—
168C22×C13—21no—
169C22×C13—21no—
170C22×C13—21no—
171C22×C13—21no—
172C22×C13—21no—
173C22×C13—21no—
174C22×C13—41no—
175C22×C13—41no—
176C22×C13—41no—
177C22×C13C22×D411yescharacteristic
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×C13C2×#4111yescharacteristic
189C4×C13H(5,𝔽2)11yescharacteristic
190Dic13—22no—
191Dic13—41no—
192Dic13—41no—
193C2×#41—131no—
194C22×Q8—131no—
195C2×SD16—131no—
196C2×SD16—131no—
197C2×D8—131no—
198C2×M16—131no—
199C22×C8—131no—
200C4⋊Q8C2×D1311yescharacteristic
201#124—21no—
202#124—21no—
203#124—131no—
204#124—261no—
205C22⋊Q8—131no—
206C22⋊Q8—261no—
207#121—21no—
208#121—131no—
209#121—261no—
210#121C2×D1311yescharacteristic
211#121C2×D1311yescharacteristic
212C4×Q8—131no—
213C4×D4—261no—
214C4×D4C2×D1311yescharacteristic
215C4×D4C2×D1311yescharacteristic
216#117—21no—
217#117C2×D1311yescharacteristic
218#117C2×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#103—131no—
228#103—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—81no—
239C2×C13#54611yescharacteristic
240C2×C13#57511yescharacteristic
241C2×C13#57711yescharacteristic
242D13—81no—
243#41—262no—
244#41—521no—
245C2×Q8—21no—
246C2×Q8—131no—
247C2×Q8—131no—
248C2×Q8—262no—
249C2×Q8—261no—
250C2×Q8—521no—
251C2×D4—21no—
252C2×D4—21no—
253C2×D4—131no—
254C2×D4—261no—
255C2×D4—261no—
256C2×D4C22⋊D1311yescharacteristic
257C2×D4C22×D1311yescharacteristic
258C22×C4—21no—
259C22×C4—261no—
260C22×C4—261no—
261C22×C4C22×D1311yescharacteristic
262C22×C4C22×D1311yescharacteristic
263SD16—262no—
264SD16—521no—
265D8—521no—
266M16—521no—
267C2×C8—131no—
268C2×C8—131no—
269C2×C8—131no—
270C2×C8—131no—
271C2×C8—521no—
272C4⋊C4—21no—
273C4⋊C4—131no—
274C4⋊C4—261no—
275C4⋊C4—261no—
276C4⋊C4C22⋊D1311yescharacteristic
277C4⋊C4C22×D1311yescharacteristic
278C4⋊C4C22×D1311yescharacteristic
279C4⋊C4C22×D1311yescharacteristic
280C22⋊C4—21no—
281C22⋊C4—21no—
282C22⋊C4—21no—
283C22⋊C4—21no—
284C22⋊C4—21no—
285C22⋊C4—261no—
286C22⋊C4—261no—
287C22⋊C4—261no—
288C22⋊C4—261no—
289C22⋊C4C22⋊D1311yescharacteristic
290C22⋊C4C22⋊D1311yescharacteristic
291C42—21no—
292C42—21no—
293C42—261no—
294C42C22×D1311yescharacteristic
295C13#332111yescharacteristic, complemented, Sylow
296C23—21no—
297C23—261no—
298C23C2×C22⋊D1311yescharacteristic
299C23C2×C22⋊D1311yescharacteristic
300Q8—81no—
301Q8—132no—
302Q8—261no—
303Q8—261no—
304Q8—261no—
305Q8—522no—
306D4—21no—
307D4—21no—
308D4—41no—
309D4—81no—
310D4—81no—
311D4—261no—
312D4—261no—
313D4—522no—
314D4—522no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—42no—
323C2×C4—261no—
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—41no—
344C22—41no—
345C22—41no—
346C22—521no—
347C22—521no—
348C22—521no—
349C22C22×C22⋊D1311yescharacteristic
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—262no—
358C4—521no—
359C4—521no—
360C4#41×D1311yescharacteristic
361C4#8825611yescharacteristic
362C2—41no—
363C2—41no—
364C2—81no—
365C2—1041no—
366C2#1171952711yescharacteristic
367C2#1171953411yescharacteristic
368C2#1171954111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#555C2
socleC22×C13C22×D4
hypercenter#555D13
hypocenterC13#3321
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C4×D4 ◁ #555

Complements

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

NH ≅ G/Ntype
1. C13×#555C2semidirect
2. #11719257C2semidirect
3. #11718755C2semidirect
4. #11718750C2semidirect
5. #11718702C2semidirect
6. #11718701C2semidirect
7. #11718700C2semidirect
8. #11718698C2semidirect
9. #11718679C2semidirect
10. #11718677C2semidirect
11. #11718672C2semidirect
12. #11718665C2semidirect
13. #11718664C2semidirect
14. #11718663C2semidirect
15. #11718657C2semidirect
153. #555D13semidirect
295. C13#3321semidirect

Maximal subgroups

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

subgroupindex
C13×#5552
#117192572
#117187552
#117187502
#117187022
#117187012
#117187002
#117186982
#117186792
#117186772
#117186722
#117186652
#117186642
#117186632
#117186572
#332113