Finite Group Databasebeta

← #13125906

Subgroups — #13125906

Order 1664.

396 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719535C211yesmaximal, characteristic
2#11719330C211yesmaximal, characteristic, complemented
3C13×#452C211yesmaximal, characteristic, complemented
4#11718900C211yesmaximal, characteristic, complemented
5#11718851C211yesmaximal, characteristic, complemented
6#11718846C211yesmaximal, characteristic, complemented
7#11718836C211yesmaximal, characteristic, complemented
8#11718824C211yesmaximal, characteristic, complemented
9#11718707C211yesmaximal, characteristic, complemented
10#11718461C211yesmaximal, characteristic, complemented
11#11718459C211yesmaximal, characteristic, complemented
12#11718425C211yesmaximal, characteristic, complemented
13#11718423C211yesmaximal, characteristic, complemented
14#11718392C211yesmaximal, characteristic, complemented
15#11718381C211yesmaximal, characteristic, complemented
16C2×C13×#41C2211yescharacteristic
17C22×D52C2211yescharacteristic
18C2×C13×Q16C2211yescharacteristic, complemented
19C2×C13×SD16C2211yescharacteristic, complemented
20C13×C22⋊Q8C2211yescharacteristic
21#88201C2211yescharacteristic
22#88201C2211yescharacteristic
23Q8×Dic13C2211yescharacteristic, complemented
24#88198C2211yescharacteristic, complemented
25C2×#6107C2211yescharacteristic, complemented
26C2×#6106C2211yescharacteristic
27C2×#6106C2211yescharacteristic
28#88194C2211yescharacteristic
29#88194C2211yescharacteristic
30#88191—21no—
31#88191—21no—
32C2×#6105C2211yescharacteristic, complemented
33#88184—21no—
34#88184—21no—
35#88180C2211yescharacteristic
36#88178C2211yescharacteristic
37C2×#6095C2211yescharacteristic
38C2×#6095C2211yescharacteristic
39#88144—21no—
40#88144C2211yescharacteristic, complemented
41#88143—21no—
42#88141C2211yescharacteristic, complemented
43#88133—21no—
44#88133—21no—
45C13×#103C2211yescharacteristic, complemented
46C13×#102C2211yescharacteristic, complemented
47C13×C22⋊C8C2211yescharacteristic
48#88075C2211yescharacteristic, complemented
49#88072C2211yescharacteristic, complemented
50C22⋊#1055C2211yescharacteristic
51#88061C2211yescharacteristic
52#88061C2211yescharacteristic
53#88055C2211yescharacteristic, complemented
54#88054C2211yescharacteristic, complemented
55#88054C2211yescharacteristic, complemented
56C8×Dic13C2211yescharacteristic, complemented
57#88049C2211yescharacteristic
58#88049C2211yescharacteristic
59C23×D13—21no—
60C13×#41—41no—
61C13×#41—41no—
62C2×Q8×C13C2311yescharacteristic
63C2×Q8×C13C2311yescharacteristic
64C2×D4×C13—21no—
65C2×D4×C13C2311yescharacteristic
66C22×C4×C13—21no—
67C22×C4×C13C2311yescharacteristic
68C2×C22⋊D13—21no—
69C2×C22⋊D13—21no—
70C2×C22⋊D13—21no—
71C2×C22⋊D13—21no—
72C2×D52—21no—
73C2×D52—41no—
74C2×D52—41no—
75C2×D52C2311yescharacteristic
76C2×D52C2311yescharacteristic
77C2×Dic26C2311yescharacteristic
78C13×Q16—41no—
79C13×SD16—41no—
80C2×C8×C13C2311yescharacteristic
81C2×C8×C13C2311yescharacteristic
82C13×C4⋊C4—21no—
83C13×C4⋊C4C2311yescharacteristic
84C13×C22⋊C4—21no—
85C22⋊Dic13—21no—
86C22⋊Dic13D411yescharacteristic
87C22⋊Dic13D411yescharacteristic
88#6107—41no—
89#6106—41no—
90#6106—41no—
91#6105—41no—
92#6103—21no—
93#6103—21no—
94#6103—21no—
95#6103—21no—
96C4⋊Dic13—21no—
97C4⋊Dic13—21no—
98C4⋊Dic13D411yescharacteristic
99C4⋊Dic13D411yescharacteristic
100C4⋊Dic13C2311yescharacteristic
101#6101—21no—
102#6101—21no—
103#6101—21no—
104#6101—21no—
105#6101—21no—
106C4×Dic13—21no—
107C4×Dic13—21no—
108C4×Dic13C2311yescharacteristic
109C4×Dic13C2311yescharacteristic
110C2×#1055C2311yescharacteristic
111C2×#1055C2311yescharacteristic
112#6095—41no—
113#6095—41no—
114#3222—131nomaximal, Sylow
115C23×C13—21no—
116C23×C13C2×D411yescharacteristic
117C22×D13—21no—
118C22×D13—21no—
119C22×D13—42no—
120C22×D13—81no—
121C22×D13—81no—
122Q8×C13—21no—
123Q8×C13—21no—
124Q8×C13—21no—
125Q8×C13—21no—
126D4×C13—21no—
127D4×C13—21no—
128D4×C13—42no—
129C2×C4×C13—21no—
130C2×C4×C13—21no—
131C2×C4×C13—21no—
132C2×C4×C13—21no—
133C2×C4×C13—21no—
134C2×C4×C13—42no—
135C2×C4×C13C2×D411yescharacteristic
136C2×C4×C13C2411yescharacteristic
137C22⋊D13—81no—
138C22⋊D13—81no—
139C22⋊D13—81no—
140C22⋊D13—81no—
141C2×Dic13—21no—
142C2×Dic13—21no—
143C2×Dic13C2×D411yescharacteristic
144C2×Dic13C2×D411yescharacteristic
145C2×Dic13C2×D411yescharacteristic
146C2×Dic13C2×D411yescharacteristic
147D52—21no—
148D52—21no—
149D52—21no—
150D52—21no—
151D52—42no—
152Dic26—21no—
153Dic26—21no—
154C8×C13—21no—
155C8×C13—21no—
156#1055—21no—
157#1055—21no—
158#541—131no—
159#535—131no—
160#497—131no—
161#492—131no—
162#490—131no—
163#488—131no—
164#464—131no—
165#464—131no—
166#460—131no—
167#460—131no—
168#452—131no—
169#452D1311yescharacteristic, complemented
170#450—131no—
171#450—131no—
172#433—131no—
173C22×C13—21no—
174C22×C13—21no—
175C22×C13—21no—
176C22×C13—41no—
177C22×C13—41no—
178C22×C13—41no—
179C22×C13C22×D411yescharacteristic
180C2×D13—41no—
181C2×D13—41no—
182C2×D13—41no—
183C2×D13—41no—
184C2×D13—41no—
185C2×D13—41no—
186C2×D13—84no—
187C4×C13—21no—
188C4×C13—41no—
189C4×C13—41no—
190C4×C13—41no—
191C4×C13H(5,𝔽2)11yescharacteristic
192C4×C13H(5,𝔽2)11yescharacteristic
193Dic13—21no—
194Dic13—21no—
195Dic13—21no—
196Dic13—21no—
197Dic13—41no—
198Dic13—41no—
199C2×#41C2×D1311yescharacteristic
200C22×D4—131no—
201C2×Q16—131no—
202C2×Q16C2×D1311yescharacteristic, complemented
203C2×SD16—131no—
204C2×SD16—131no—
205C2×SD16—131no—
206C2×SD16—131no—
207C2×SD16—131no—
208C2×SD16C2×D1311yescharacteristic, complemented
209C4⋊Q8—131no—
210#127—131no—
211#127—131no—
212#126—261no—
213#126—261no—
214#125—131no—
215#125—261no—
216#125—261no—
217#124—131no—
218#124—131no—
219C22⋊Q8—131no—
220C22⋊Q8C2×D1311yescharacteristic
221#121—261no—
222#121—261no—
223#120—261no—
224#120—261no—
225C4×Q8—131no—
226C4×Q8—131no—
227#117—131no—
228C4⋊C8—131no—
229C4⋊C8—131no—
230#103—131no—
231#103C2×D1311yescharacteristic, complemented
232#102—131no—
233#102—131no—
234#102—131no—
235#102—131no—
236#102—131no—
237#102C2×D1311yescharacteristic, complemented
238C22⋊C8—131no—
239C22⋊C8C2×D1311yescharacteristic
240#97—131no—
241C4×C8—131no—
242C2×C13—41no—
243C2×C13—81no—
244C2×C13#53511yescharacteristic
245C2×C13#57711yescharacteristic
246C2×C13#57711yescharacteristic
247D13—81no—
248D13—81no—
249C24—261no—
250#41—41no—
251#41—41no—
252C2×Q8—131no—
253C2×Q8C22×D1311yescharacteristic
254C2×Q8C22×D1311yescharacteristic
255C2×D4—21no—
256C2×D4—131no—
257C2×D4—131no—
258C2×D4—261no—
259C2×D4—261no—
260C2×D4—261no—
261C2×D4—261no—
262C2×D4—261no—
263C2×D4—521no—
264C2×D4—521no—
265C2×D4C22×D1311yescharacteristic
266C22×C4—21no—
267C22×C4C22×D1311yescharacteristic
268Q16—41no—
269Q16—521no—
270SD16—41no—
271SD16—521no—
272SD16—521no—
273SD16—521no—
274SD16—521no—
275SD16—521no—
276C2×C8—131no—
277C2×C8—131no—
278C2×C8C22×D1311yescharacteristic
279C2×C8C22×D1311yescharacteristic
280C4⋊C4—21no—
281C4⋊C4—131no—
282C4⋊C4—131no—
283C4⋊C4—131no—
284C4⋊C4—261no—
285C4⋊C4—261no—
286C4⋊C4—261no—
287C4⋊C4—261no—
288C4⋊C4—261no—
289C4⋊C4—261no—
290C4⋊C4—261no—
291C4⋊C4C22×D1311yescharacteristic
292C22⋊C4—21no—
293C22⋊C4—131no—
294C22⋊C4—131no—
295C22⋊C4—261no—
296C22⋊C4—261no—
297C22⋊C4—261no—
298C22⋊C4—261no—
299C22⋊C4—261no—
300C42—131no—
301C42—131no—
302C42—261no—
303C42—261no—
304C13#322211yescharacteristic, complemented, Sylow
305C23—21no—
306C23—261no—
307C23—261no—
308C23—522no—
309C23—1041no—
310C23—1041no—
311C23D4×D1311yescharacteristic
312Q8—21no—
313Q8—21no—
314Q8—21no—
315Q8—21no—
316Q8—261no—
317Q8—261no—
318D4—21no—
319D4—21no—
320D4—42no—
321D4—261no—
322D4—261no—
323D4—261no—
324D4—261no—
325D4—522no—
326D4—1041no—
327D4—1041no—
328D4—1041no—
329D4—1041no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—42no—
336C2×C4—131no—
337C2×C4—131no—
338C2×C4—131no—
339C2×C4—131no—
340C2×C4—261no—
341C2×C4—261no—
342C2×C4D4×D1311yescharacteristic
343C2×C4C23×D1311yescharacteristic
344C8—21no—
345C8—21no—
346C8—261no—
347C8—261no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—521no—
355C22—521no—
356C22—521no—
357C22—521no—
358C22—521no—
359C22—521no—
360C22—1044no—
361C22C2×D4×D1311yescharacteristic
362C4—21no—
363C4—41no—
364C4—41no—
365C4—41no—
366C4—261no—
367C4—261no—
368C4—261no—
369C4—261no—
370C4—521no—
371C4—521no—
372C4#8825111yescharacteristic
373C4#8825111yescharacteristic
374C2—41no—
375C2—81no—
376C2—1041no—
377C2—1041no—
378C2#1171929711yescharacteristic
379C2#1171947511yescharacteristic
380C2#1171948311yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#452C2
socleC22×C13C22×D4
prime radical#11719535C2
hypercenter#452D13
hypocenterC13#3222
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
2. #11719330C2semidirect
3. C13×#452C2semidirect
4. #11718900C2semidirect
5. #11718851C2semidirect
6. #11718846C2semidirect
7. #11718836C2semidirect
8. #11718824C2semidirect
9. #11718707C2semidirect
10. #11718461C2semidirect
11. #11718459C2semidirect
12. #11718425C2semidirect
13. #11718423C2semidirect
14. #11718392C2semidirect
15. #11718381C2semidirect
18. C2×C13×Q16C22semidirect
19. C2×C13×SD16C22semidirect
23. Q8×Dic13C22semidirect
24. #88198C22semidirect
25. C2×#6107C22semidirect
32. C2×#6105C22semidirect
40. #88144C22semidirect
42. #88141C22semidirect
45. C13×#103C22semidirect
46. C13×#102C22semidirect
48. #88075C22semidirect
49. #88072C22semidirect
53. #88055C22semidirect
54. #88054C22semidirect
55. #88054C22semidirect
56. C8×Dic13C22semidirect
169. #452D13semidirect
202. C2×Q16C2×D13semidirect
208. C2×SD16C2×D13semidirect
231. #103C2×D13semidirect
237. #102C2×D13semidirect
304. C13#3222semidirect

Maximal subgroups

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

subgroupindex
#117195352
#117193302
C13×#4522
#117189002
#117188512
#117188462
#117188362
#117188242
#117187072
#117184612
#117184592
#117184252
#117184232
#117183922
#117183812
#322213