Finite Group Databasebeta

← #13126911

Subgroups — #13126911

Order 1664.

410 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#554C211yesmaximal, characteristic, complemented
2#11719255C211yesmaximal, characteristic
3#11718750C211yesmaximal, characteristic, complemented
4#11718748C211yesmaximal, characteristic, complemented
5#11718712C211yesmaximal, characteristic, complemented
6#11718710C211yesmaximal, characteristic, complemented
7#11718708C211yesmaximal, characteristic, complemented
8#11718707C211yesmaximal, characteristic, complemented
9#11718689C211yesmaximal, characteristic, complemented
10#11718687C211yesmaximal, characteristic, complemented
11#11718672C211yesmaximal, characteristic, complemented
12#11718631C211yesmaximal, characteristic, complemented
13#11718628C211yesmaximal, characteristic, complemented
14#11718627C211yesmaximal, characteristic, complemented
15C2×#88049C211yesmaximal, characteristic, complemented
16C2×#6127C2211yescharacteristic
17C22×D52C2211yescharacteristic
18C13×C4⋊Q8C2211yescharacteristic, complemented
19C13×#125—21no—
20C13×C22⋊Q8—21no—
21C13×C22⋊Q8—21no—
22C13×C22⋊Q8C2211yescharacteristic
23C13×C22⋊Q8C2211yescharacteristic, complemented
24C4×Q8×C13C2211yescharacteristic, complemented
25C4×D4×C13—21no—
26C4×D4×C13C2211yescharacteristic
27C2×C13×C4⋊C4C2211yescharacteristic
28C2×C13×C4⋊C4C2211yescharacteristic, complemented
29C2×#6107C2211yescharacteristic, complemented
30C2×#6106C2211yescharacteristic
31C2×#6106C2211yescharacteristic
32#88191—21no—
33#88184C2211yescharacteristic
34#88178C2211yescharacteristic
35C2×#6099C2211yescharacteristic, complemented
36C22×#1055C2211yescharacteristic
37#88148—21no—
38#88138—21no—
39C22⋊C4×D13—21no—
40#88129C2211yescharacteristic
41C4×D52C2211yescharacteristic
42#88075C2211yescharacteristic, complemented
43C22⋊#1055C2211yescharacteristic
44C22⋊#1055C2211yescharacteristic, complemented
45#88050C2211yescharacteristic, complemented
46#88050C2211yescharacteristic, complemented
47#88050C2211yescharacteristic, complemented
48#88049C2211yescharacteristic
49#88049C2211yescharacteristic
50#88049C2211yescharacteristic
51#88049C2211yescharacteristic
52#88049C2211yescharacteristic
53#88049C2211yescharacteristic
54#88047C2211yescharacteristic, complemented
55#88047C2211yescharacteristic, complemented
56#88047C2211yescharacteristic, complemented
57C4⋊#1055C2211yescharacteristic, complemented
58#88043C2211yescharacteristic, complemented
59C23×D13—21no—
60C2×Q8×C13—21no—
61C2×Q8×C13C2311yescharacteristic
62C2×D4×C13D411yescharacteristic
63C22×C4×C13—21no—
64C22×C4×C13—21no—
65C22×C4×C13C2311yescharacteristic
66C22×C4×C13C2311yescharacteristic
67C2×C22⋊D13—21no—
68C2×C22⋊D13—21no—
69#6127—22no—
70#6127—41no—
71C2×D52—22no—
72C2×D52—21no—
73C2×D52—41no—
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⋊C4D411yescharacteristic
92C13×C22⋊C4D411yescharacteristic
93C42×C13—21no—
94C42×C13C2311yescharacteristic
95C22⋊Dic13—21no—
96#6107—41no—
97#6106—22no—
98#6106—41no—
99#6103—21no—
100#6103—21no—
101#6103—21no—
102#6103—21no—
103C4⋊Dic13C2311yescharacteristic
104#6101—21no—
105#6099—41no—
106C2×#1055—41no—
107C2×#1055C2311yescharacteristic
108C2×#1055C2311yescharacteristic
109C2×#1055C2311yescharacteristic
110C2×#1055C2311yescharacteristic
111#3314—131nomaximal, Sylow
112C23×C13C2×D411yescharacteristic
113C23×C13C2×D411yescharacteristic
114C22×D13—21no—
115C22×D13—21no—
116C22×D13—42no—
117C22×D13—42no—
118C22×D13—81no—
119Q8×C13—21no—
120Q8×C13—21no—
121Q8×C13—81no—
122D4×C13—22no—
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—21no—
130C2×C4×C13—21no—
131C2×C4×C13—81no—
132C2×C4×C13—81no—
133C2×C4×C13C2×D411yescharacteristic
134C2×C4×C13C2×D411yescharacteristic
135C2×C4×C13C2×D411yescharacteristic
136C2×C4×C13C2×D411yescharacteristic
137C2×C4×C13C2411yescharacteristic
138C22⋊D13—42no—
139C22⋊D13—81no—
140C2×Dic13—21no—
141C2×Dic13—21no—
142D52—21no—
143D52—21no—
144D52—21no—
145D52—42no—
146D52#4112yes—
147C4×D13—42no—
148C4×D13—81no—
149Dic26—21no—
150Dic26—21no—
151#1055—21no—
152#1055—21no—
153#1055—21no—
154#1055—21no—
155#554D1311yescharacteristic, complemented
156#546—131no—
157#489—131no—
158#484—131no—
159#480—131no—
160#474—131no—
161#468—131no—
162#467—131no—
163#464—131no—
164#452—131no—
165#450—131no—
166#440—131no—
167#435—131no—
168#417—131no—
169C2×#102—131no—
170C22×C13—21no—
171C22×C13—21no—
172C22×C13—21no—
173C22×C13—21no—
174C22×C13—21no—
175C22×C13#13712yes—
176C22×C13C22×D411yescharacteristic
177C2×D13—22no—
178C2×D13—41no—
179C2×D13—41no—
180C2×D13—41no—
181C2×D13—41no—
182C2×D13—41no—
183C2×D13—84no—
184C4×C13—21no—
185C4×C13—21no—
186C4×C13—21no—
187C4×C13—21no—
188C4×C13—41no—
189C4×C13—41no—
190C4×C13—41no—
191C4×C13—41no—
192C4×C13C2×#4111yescharacteristic
193C4×C13H(5,𝔽2)11yescharacteristic
194Dic13—41no—
195Dic13—41no—
196C2×#41—131no—
197C22×D4—131no—
198C2×Q16—131no—
199C2×SD16—131no—
200C2×SD16—131no—
201C2×M16—131no—
202C22×C8—131no—
203C4⋊Q8C2×D1311yescharacteristic, complemented
204#125—21no—
205#124—131no—
206#123—261no—
207C22⋊Q8—21no—
208C22⋊Q8—21no—
209C22⋊Q8—131no—
210C22⋊Q8C2×D1311yescharacteristic
211C22⋊Q8C2×D1311yescharacteristic, complemented
212#121—131no—
213#121—261no—
214#120—261no—
215C4×Q8C2×D1311yescharacteristic, complemented
216C4×D4—21no—
217C4×D4—131no—
218C4×D4C2×D1311yescharacteristic
219C2×C4⋊C4C2×D1311yescharacteristic
220C2×C4⋊C4C2×D1311yescharacteristic, complemented
221C2×C22⋊C4—261no—
222#107—131no—
223#107—131no—
224#107—131no—
225C4⋊C8—131no—
226#103—131no—
227#103—131no—
228#103—131no—
229#103—131no—
230#102—131no—
231#102—131no—
232#102—131no—
233#102—131no—
234#102—131no—
235#102—131no—
236C22⋊C8—131no—
237C22⋊C8—131no—
238#97—131no—
239C2×C13—22no—
240C2×C13—41no—
241C2×C13#54611yescharacteristic
242C2×C13C2×#13711yescharacteristic
243C2×C13#57611yescharacteristic
244D13—42no—
245D13—81no—
246C24—261no—
247#41—262no—
248#41—521no—
249C2×Q8—21no—
250C2×Q8—131no—
251C2×Q8C22×D1311yescharacteristic
252C2×D4—131no—
253C2×D4—131no—
254C2×D4—262no—
255C2×D4—261no—
256C2×D4—261no—
257C2×D4—261no—
258C2×D4—521no—
259C2×D4C22⋊D1311yescharacteristic
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—261no—
263C22×C4—261no—
264C22×C4C22×D1311yescharacteristic
265C22×C4C22×D1311yescharacteristic
266Q16—521no—
267SD16—262no—
268SD16—521no—
269M16—521no—
270C2×C8—131no—
271C2×C8—131no—
272C2×C8—131no—
273C2×C8—131no—
274C2×C8—521no—
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4—21no—
278C4⋊C4—21no—
279C4⋊C4—21no—
280C4⋊C4—21no—
281C4⋊C4—131no—
282C4⋊C4—261no—
283C4⋊C4C22⋊D1311yescharacteristic
284C4⋊C4C22×D1311yescharacteristic
285C4⋊C4C22×D1311yescharacteristic
286C4⋊C4C22×D1311yescharacteristic
287C22⋊C4—21no—
288C22⋊C4—21no—
289C22⋊C4—261no—
290C22⋊C4—261no—
291C22⋊C4—261no—
292C22⋊C4—261no—
293C22⋊C4—261no—
294C22⋊C4C22⋊D1311yescharacteristic
295C22⋊C4C22⋊D1311yescharacteristic
296C42—21no—
297C42C22×D1311yescharacteristic
298C13#331411yescharacteristic, complemented, Sylow
299C23—261no—
300C23—261no—
301C23—522no—
302C23—522no—
303C23—1041no—
304C23C2×C22⋊D1311yescharacteristic
305C23C2×C22⋊D1311yescharacteristic
306Q8—21no—
307Q8—21no—
308Q8—81no—
309Q8—261no—
310Q8—261no—
311D4—22no—
312D4—132no—
313D4—261no—
314D4—261no—
315D4—261no—
316D4—522no—
317D4—522no—
318D4—1041no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—81no—
328C2×C4—81no—
329C2×C4—261no—
330C2×C4—261no—
331C2×C4—522no—
332C2×C4—1041no—
333C2×C4C2×C22⋊D1311yescharacteristic
334C2×C4C2×C22⋊D1311yescharacteristic
335C2×C4C2×C22⋊D1311yescharacteristic
336C2×C4C2×C22⋊D1311yescharacteristic
337C2×C4C23×D1311yescharacteristic
338C8—261no—
339C8—261no—
340C8—261no—
341C8—261no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—262no—
348C22—521no—
349C22—521no—
350C22—521no—
351C22—521no—
352C22—521no—
353C22—1044no—
354C22#8819612yes—
355C22C22×C22⋊D1311yescharacteristic
356C4—21no—
357C4—21no—
358C4—21no—
359C4—21no—
360C4—41no—
361C4—41no—
362C4—41no—
363C4—41no—
364C4—521no—
365C4—521no—
366C4#41×D1311yescharacteristic
367C4#8825611yescharacteristic
368C2—22no—
369C2—41no—
370C2—522no—
371C2—1041no—
372C2C2×#8819611yescharacteristic
373C2#1171953411yescharacteristic
374C2#1171954011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#554C2
socleC22×C13C22×D4
prime radical#11719255C2
hypercenter#554D13
hypocenterC13#3314
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. #11718750C2semidirect
4. #11718748C2semidirect
5. #11718712C2semidirect
6. #11718710C2semidirect
7. #11718708C2semidirect
8. #11718707C2semidirect
9. #11718689C2semidirect
10. #11718687C2semidirect
11. #11718672C2semidirect
12. #11718631C2semidirect
13. #11718628C2semidirect
14. #11718627C2semidirect
15. C2×#88049C2semidirect
18. C13×C4⋊Q8C22semidirect
23. C13×C22⋊Q8C22semidirect
24. C4×Q8×C13C22semidirect
28. C2×C13×C4⋊C4C22semidirect
29. C2×#6107C22semidirect
35. C2×#6099C22semidirect
42. #88075C22semidirect
44. C22⋊#1055C22semidirect
45. #88050C22semidirect
46. #88050C22semidirect
47. #88050C22semidirect
54. #88047C22semidirect
55. #88047C22semidirect
56. #88047C22semidirect
57. C4⋊#1055C22semidirect
58. #88043C22semidirect
155. #554D13semidirect
203. C4⋊Q8C2×D13semidirect
211. C22⋊Q8C2×D13semidirect
215. C4×Q8C2×D13semidirect
220. C2×C4⋊C4C2×D13semidirect
298. C13#3314semidirect

Maximal subgroups

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

subgroupindex
C13×#5542
#117192552
#117187502
#117187482
#117187122
#117187102
#117187082
#117187072
#117186892
#117186872
#117186722
#117186312
#117186282
#117186272
C2×#880492
#331413