Finite Group Databasebeta

← #13125924

Subgroups — #13125924

Order 1664.

408 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#542C211yesmaximal, characteristic, complemented
2#11719230C211yesmaximal, characteristic, complemented
3#11718750C211yesmaximal, characteristic, complemented
4#11718749C211yesmaximal, characteristic, complemented
5#11718720C211yesmaximal, characteristic, complemented
6#11718719C211yesmaximal, characteristic, complemented
7#11718708C211yesmaximal, characteristic, complemented
8#11718707C211yesmaximal, characteristic, complemented
9#11718698C211yesmaximal, characteristic, complemented
10#11718697C211yesmaximal, characteristic, complemented
11#11718689C211yesmaximal, characteristic, complemented
12#11718688C211yesmaximal, characteristic, complemented
13#11718677C211yesmaximal, characteristic, complemented
14#11718676C211yesmaximal, characteristic, complemented
15#11718661C211yesmaximal, characteristic, complemented
16C2×#6127C2211yescharacteristic
17C22×D52C2211yescharacteristic
18C13×C4⋊Q8C2211yescharacteristic, complemented
19C13×#126—21no—
20C13×#124—21no—
21C13×#124C2211yescharacteristic, complemented
22C13×#123—21no—
23C13×C22⋊Q8—21no—
24C13×C22⋊Q8C2211yescharacteristic
25C13×#121C2211yescharacteristic
26C4×Q8×C13C2211yescharacteristic, complemented
27C4×D4×C13C2211yescharacteristic, complemented
28C13×#117C2211yescharacteristic
29C2×#6107C2211yescharacteristic, complemented
30C2×#6106C2211yescharacteristic
31C2×#6106C2211yescharacteristic
32C2×#6106C2211yescharacteristic, complemented
33C2×#6105C2211yescharacteristic, complemented
34C2×#6104C2211yescharacteristic
35C2×#6104C2211yescharacteristic
36C2×#6104C2211yescharacteristic, complemented
37#88149—21no—
38#88149—21no—
39#88136—21no—
40#88136—21no—
41#88129C2211yescharacteristic
42#88129C2211yescharacteristic
43#88128C2211yescharacteristic
44#88128C2211yescharacteristic
45C22⋊#1055C2211yescharacteristic
46C22⋊#1055C2211yescharacteristic
47#88050C2211yescharacteristic, complemented
48#88050C2211yescharacteristic, complemented
49#88049C2211yescharacteristic
50#88049C2211yescharacteristic
51#88049C2211yescharacteristic
52#88049C2211yescharacteristic
53#88049C2211yescharacteristic, complemented
54#88049C2211yescharacteristic, complemented
55C4⋊#1055C2211yescharacteristic, complemented
56C4⋊#1055C2211yescharacteristic, complemented
57#88043C2211yescharacteristic, complemented
58C4×#1055C2211yescharacteristic, complemented
59C23×D13—21no—
60C2×Q8×C13—21no—
61C2×Q8×C13C2311yescharacteristic
62C2×D4×C13—21no—
63C2×D4×C13C2311yescharacteristic
64C22×C4×C13—21no—
65C22×C4×C13C2311yescharacteristic
66C2×C22⋊D13—21no—
67#6127—41no—
68#6127—41no—
69C2×D52—21no—
70C2×D52—21no—
71C2×D52—21no—
72C2×D52—21no—
73C2×D52—21no—
74C2×D52—41no—
75C2×D52—41no—
76C2×D52C2311yescharacteristic
77C2×D52C2311yescharacteristic
78C2×D52C2311yescharacteristic
79C2×C4×D13—21no—
80C2×Dic26C2311yescharacteristic
81C13×C4⋊C4—21no—
82C13×C4⋊C4—21no—
83C13×C4⋊C4—21no—
84C13×C4⋊C4D411yescharacteristic
85C13×C4⋊C4D411yescharacteristic
86C13×C4⋊C4C2311yescharacteristic
87C13×C4⋊C4C2311yescharacteristic
88C13×C22⋊C4—21no—
89C13×C22⋊C4—21no—
90C13×C22⋊C4—21no—
91C13×C22⋊C4—21no—
92C13×C22⋊C4—21no—
93C13×C22⋊C4D411yescharacteristic
94C13×C22⋊C4D411yescharacteristic
95C42×C13—21no—
96C42×C13C2311yescharacteristic
97C42×C13C2311yescharacteristic
98#6107—41no—
99#6106—41no—
100#6106—41no—
101#6106—41no—
102#6105—41no—
103#6104—41no—
104#6104—41no—
105#6104—41no—
106#6103—21no—
107#6103—21no—
108#6103—21no—
109#6103—21no—
110C2×#1055C2311yescharacteristic
111C2×#1055C2311yescharacteristic
112C2×#1055C2311yescharacteristic
113C2×#1055C2311yescharacteristic
114#3224—131nomaximal, Sylow
115C23×C13—21no—
116C23×C13C2×D411yescharacteristic
117C22×D13—21no—
118C22×D13—21no—
119C22×D13—21no—
120C22×D13—42no—
121C22×D13—81no—
122C22×D13—81no—
123Q8×C13—21no—
124Q8×C13—21no—
125Q8×C13—81no—
126D4×C13—21no—
127D4×C13—21no—
128D4×C13—81no—
129C2×C4×C13—21no—
130C2×C4×C13—21no—
131C2×C4×C13—21no—
132C2×C4×C13—21no—
133C2×C4×C13—21no—
134C2×C4×C13—81no—
135C2×C4×C13C2×D411yescharacteristic
136C2×C4×C13C2×D411yescharacteristic
137C2×C4×C13C2×D411yescharacteristic
138C2×C4×C13C2×D411yescharacteristic
139C2×C4×C13C2×D411yescharacteristic
140C2×C4×C13C2411yescharacteristic
141C22⋊D13—42no—
142C2×Dic13—21no—
143D52—21no—
144D52—21no—
145D52—21no—
146D52—21no—
147D52—21no—
148D52—21no—
149D52—42no—
150D52—81no—
151D52—81no—
152D52—81no—
153D52—81no—
154C4×D13—42no—
155Dic26—21no—
156Dic26—21no—
157#1055—21no—
158#1055—21no—
159#1055—21no—
160#1055—21no—
161#542D1311yescharacteristic, complemented
162#535—131no—
163#496—131no—
164#495—131no—
165#489—131no—
166#486—131no—
167#464—131no—
168#463—131no—
169#460—131no—
170#459—131no—
171#452—131no—
172#450—131no—
173#449—131no—
174#447—131no—
175#433—131no—
176C22×C13—21no—
177C22×C13—21no—
178C22×C13—21no—
179C22×C13—41no—
180C22×C13—41no—
181C22×C13—41no—
182C22×C13C22×D411yescharacteristic
183C2×D13—41no—
184C2×D13—41no—
185C2×D13—41no—
186C2×D13—41no—
187C2×D13—41no—
188C2×D13—41no—
189C2×D13—41no—
190C2×D13—41no—
191C2×D13—41no—
192C2×D13—84no—
193C4×C13—21no—
194C4×C13—21no—
195C4×C13—21no—
196C4×C13—21no—
197C4×C13—21no—
198C4×C13—41no—
199C4×C13—41no—
200C4×C13—41no—
201C4×C13H(5,𝔽2)11yescharacteristic
202C4×C13H(5,𝔽2)11yescharacteristic
203Dic13—41no—
204C2×#41—131no—
205C22×D4—131no—
206C2×Q16—131no—
207C2×SD16—131no—
208C2×SD16—131no—
209C2×SD16—131no—
210C2×SD16—131no—
211C2×D8—131no—
212C2×D8—131no—
213C2×D8—131no—
214C4⋊Q8C2×D1311yescharacteristic, complemented
215#127—131no—
216#127—131no—
217#126—21no—
218#124—21no—
219#124—131no—
220#124—131no—
221#124C2×D1311yescharacteristic, complemented
222#123—21no—
223C22⋊Q8—21no—
224C22⋊Q8C2×D1311yescharacteristic
225#121—261no—
226#121—261no—
227#121C2×D1311yescharacteristic
228#120—261no—
229#120—261no—
230C4×Q8C2×D1311yescharacteristic, complemented
231C4×D4C2×D1311yescharacteristic, complemented
232#117C2×D1311yescharacteristic
233C4⋊C8—131no—
234C4⋊C8—131no—
235#103—131no—
236#103—131no—
237#102—131no—
238#102—131no—
239#102—131no—
240#102—131no—
241#102—131no—
242#102—131no—
243C22⋊C8—131no—
244C22⋊C8—131no—
245#97—131no—
246C4×C8—131no—
247C2×C13—41no—
248C2×C13—81no—
249C2×C13#53511yescharacteristic
250C2×C13#57611yescharacteristic
251C2×C13#57711yescharacteristic
252D13—81no—
253D13—81no—
254D13—81no—
255C24—261no—
256#41—521no—
257#41—521no—
258C2×Q8—21no—
259C2×Q8—131no—
260C2×Q8C22×D1311yescharacteristic
261C2×D4—21no—
262C2×D4—131no—
263C2×D4—131no—
264C2×D4—131no—
265C2×D4—261no—
266C2×D4—261no—
267C2×D4—261no—
268C2×D4—261no—
269C2×D4—261no—
270C2×D4—261no—
271C2×D4—521no—
272C2×D4—521no—
273C2×D4C22×D1311yescharacteristic
274C22×C4—21no—
275C22×C4—261no—
276C22×C4C22×D1311yescharacteristic
277Q16—521no—
278SD16—521no—
279SD16—521no—
280SD16—521no—
281SD16—521no—
282D8—521no—
283D8—521no—
284D8—521no—
285C2×C8—131no—
286C2×C8—131no—
287C2×C8—131no—
288C2×C8—131no—
289C4⋊C4—21no—
290C4⋊C4—21no—
291C4⋊C4—21no—
292C4⋊C4C22⋊D1311yescharacteristic
293C4⋊C4C22⋊D1311yescharacteristic
294C4⋊C4C22×D1311yescharacteristic
295C4⋊C4C22×D1311yescharacteristic
296C22⋊C4—21no—
297C22⋊C4—21no—
298C22⋊C4—21no—
299C22⋊C4—21no—
300C22⋊C4—21no—
301C22⋊C4—261no—
302C22⋊C4—261no—
303C22⋊C4—261no—
304C22⋊C4—261no—
305C22⋊C4C22⋊D1311yescharacteristic
306C22⋊C4C22⋊D1311yescharacteristic
307C42—21no—
308C42C22×D1311yescharacteristic
309C42C22×D1311yescharacteristic
310C13#322411yescharacteristic, complemented, Sylow
311C23—21no—
312C23—261no—
313C23—261no—
314C23—261no—
315C23—522no—
316C23—1041no—
317C23—1041no—
318C23C2×C22⋊D1311yescharacteristic
319Q8—21no—
320Q8—21no—
321Q8—81no—
322Q8—261no—
323Q8—261no—
324D4—21no—
325D4—21no—
326D4—81no—
327D4—261no—
328D4—261no—
329D4—261no—
330D4—261no—
331D4—261no—
332D4—261no—
333D4—522no—
334D4—522no—
335D4—1041no—
336D4—1041no—
337D4—1041no—
338D4—1041no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—81no—
345C2×C4—261no—
346C2×C4—522no—
347C2×C4C2×C22⋊D1311yescharacteristic
348C2×C4C2×C22⋊D1311yescharacteristic
349C2×C4C2×C22⋊D1311yescharacteristic
350C2×C4C2×C22⋊D1311yescharacteristic
351C2×C4C2×C22⋊D1311yescharacteristic
352C2×C4C23×D1311yescharacteristic
353C8—261no—
354C8—261no—
355C8—261no—
356C8—261no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—521no—
364C22—521no—
365C22—521no—
366C22—521no—
367C22—521no—
368C22—521no—
369C22—521no—
370C22—521no—
371C22—521no—
372C22—1044no—
373C22C22×C22⋊D1311yescharacteristic
374C4—21no—
375C4—21no—
376C4—21no—
377C4—21no—
378C4—21no—
379C4—41no—
380C4—41no—
381C4—41no—
382C4—521no—
383C4#8825611yescharacteristic
384C4#8825611yescharacteristic
385C2—41no—
386C2—81no—
387C2—1041no—
388C2—1041no—
389C2—1041no—
390C2#1171953511yescharacteristic
391C2#1171954011yescharacteristic
392C2#1171954211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#542C2
socleC22×C13C22×D4
hypercenter#542D13
hypocenterC13#3224
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ #117 ◁ #542

Complements

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

NH ≅ G/Ntype
1. C13×#542C2semidirect
2. #11719230C2semidirect
3. #11718750C2semidirect
4. #11718749C2semidirect
5. #11718720C2semidirect
6. #11718719C2semidirect
7. #11718708C2semidirect
8. #11718707C2semidirect
9. #11718698C2semidirect
10. #11718697C2semidirect
11. #11718689C2semidirect
12. #11718688C2semidirect
13. #11718677C2semidirect
14. #11718676C2semidirect
15. #11718661C2semidirect
18. C13×C4⋊Q8C22semidirect
21. C13×#124C22semidirect
26. C4×Q8×C13C22semidirect
27. C4×D4×C13C22semidirect
29. C2×#6107C22semidirect
32. C2×#6106C22semidirect
33. C2×#6105C22semidirect
36. C2×#6104C22semidirect
47. #88050C22semidirect
48. #88050C22semidirect
53. #88049C22semidirect
54. #88049C22semidirect
55. C4⋊#1055C22semidirect
56. C4⋊#1055C22semidirect
57. #88043C22semidirect
58. C4×#1055C22semidirect
161. #542D13semidirect
214. C4⋊Q8C2×D13semidirect
221. #124C2×D13semidirect
230. C4×Q8C2×D13semidirect
231. C4×D4C2×D13semidirect
310. C13#3224semidirect

Maximal subgroups

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

subgroupindex
C13×#5422
#117192302
#117187502
#117187492
#117187202
#117187192
#117187082
#117187072
#117186982
#117186972
#117186892
#117186882
#117186772
#117186762
#117186612
#322413