Finite Group Databasebeta

← #13128627

Subgroups — #13128627

Order 1664.

1540 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88256C211yesmaximal, characteristic, complemented
2C2×#88254C211yesmaximal, characteristic, complemented
3C13×#548C211yesmaximal, characteristic, complemented
4#11719536C211yesmaximal, characteristic, complemented
5#11719522C211yesmaximal, characteristic, complemented
6#11719381C213yesmaximal, complemented
7D13×#124C213yesmaximal, complemented
8#11719335C213yesmaximal, complemented
9#11719333C213yesmaximal, complemented
10#11719317C213yesmaximal, complemented
11#11719312C213yesmaximal, complemented
12#11719281C211yesmaximal, characteristic, complemented
13C4×#6131C211yesmaximal, characteristic, complemented
14#11719255C213yesmaximal, complemented
15#11719253C213yesmaximal, complemented
16C2×C13×#41C2211yescharacteristic
17C22×Q8×C13C2211yescharacteristic, complemented
18#88256—28no—
19#88254—28no—
20C2×#6131C2211yescharacteristic
21C2×#6131C2211yescharacteristic
22C2×#6131C2213yescomplemented
23C2×Q8×D13C2211yescharacteristic, complemented
24C2×Q8×D13C2213yescomplemented
25C2×D4×D13C2213yes—
26C2×D4×D13C2213yes—
27C2×#6127C2213yes—
28C2×#6127C2213yescomplemented
29C2×#6127C2213yescomplemented
30C22×D52C2213yes—
31C13×#124C2213yescomplemented
32C13×C22⋊Q8C2213yescomplemented
33C13×#121C2213yescomplemented
34C4×Q8×C13C2211yescharacteristic, complemented
35C4×D4×C13C2213yescomplemented
36#88201C2213yescomplemented
37#88200C2213yescomplemented
38Q8×Dic13C2211yescharacteristic, complemented
39#88194C2213yescomplemented
40#88192C2213yescomplemented
41#88192C2213yescomplemented
42#88191C2216yescomplemented
43#88190C2213yescomplemented
44#88184C2213yescomplemented
45C4×C22⋊D13C2213yescomplemented
46C4×C22⋊D13C2213yescomplemented
47#88178C2213yescomplemented
48#88151C2213yescomplemented
49#88149C2213yescomplemented
50#88149C2213yescomplemented
51#88148C2216yescomplemented
52#88147C2213yescomplemented
53#88146C2213yescomplemented
54#88142C2213yescomplemented
55#88139C2211yescharacteristic, complemented
56#88139C2213yescomplemented
57#88139C2216yescomplemented
58#88138C2213yescomplemented
59#88138C2213yescomplemented
60#88137C2216yescomplemented
61#88136C2216yescomplemented
62C22⋊C4×D13C2216yescomplemented
63C22⋊C4×D13C2216yescomplemented
64#88129C2213yescomplemented
65C4×D52C2213yescomplemented
66C4×D52C2213yescomplemented
67C42×D13C2213yescomplemented
68C23×D13C2316yes—
69C13×#41—24no—
70C2×Q8×C13—24no—
71C2×Q8×C13C2313yes—
72C2×Q8×C13C2311yescharacteristic
73C2×D4×C13C2313yes—
74C2×D4×C13C2313yes—
75C22×C4×C13C2313yes—
76C22×C4×C13C2313yes—
77C2×C22⋊D13C2313yes—
78C2×C22⋊D13C2313yes—
79C2×C22⋊D13C2313yes—
80C2×C22⋊D13C2311yescharacteristic
81C2×C22⋊D13C2313yes—
82C2×C22⋊D13C2313yes—
83#6131—24no—
84#6131—212no—
85#6131D418yescomplemented
86Q8×D13—24no—
87Q8×D13—212no—
88D4×D13—212no—
89D4×D13—212no—
90#6127—212no—
91#6127—212no—
92#6127—212no—
93C2×D52—212no—
94C2×D52C2313yes—
95C2×D52C2313yes—
96C2×D52C2313yes—
97C2×D52C2313yes—
98C2×D52C2313yes—
99C2×C4×D13C2313yes—
100C2×C4×D13C2313yes—
101C2×C4×D13C2316yes—
102C2×C4×D13C2313yes—
103C2×C4×D13C2313yes—
104C2×C4×D13C2313yes—
105C2×Dic26C2313yes—
106C2×Dic26C2313yes—
107C2×Dic26C2311yescharacteristic
108C13×C4⋊C4C2313yes—
109C13×C4⋊C4C2313yes—
110C13×C22⋊C4C2313yes—
111C13×C22⋊C4C2316yes—
112C13×C22⋊C4C2311yescharacteristic
113C42×C13C2313yes—
114C22⋊Dic13C2313yes—
115C22⋊Dic13C2316yes—
116C22⋊Dic13C2311yescharacteristic
117#6103C2311yescharacteristic
118#6103C2313yes—
119#6103C2316yes—
120#6103C2316yes—
121#6103C2313yes—
122#6103C2316yes—
123#6103C2311yescharacteristic
124C4⋊Dic13C2313yes—
125C4⋊Dic13C2313yes—
126#6101C2313yes—
127#6101C2313yes—
128C4×Dic13C2311yescharacteristic
129C4×Dic13C2313yes—
130C4×Dic13C2313yes—
131#3500—131nomaximal, Sylow
132C23×C13C2413yes—
133C23×C13C2411yescharacteristic
134C22×D13—212no—
135C22×D13—46no—
136C22×D13—46no—
137C22×D13C2413yes—
138C22×D13C2411yescharacteristic
139C22×D13C2413yes—
140Q8×C13—26no—
141Q8×C13C2×D414yes—
142D4×C13—26no—
143D4×C13—43no—
144C2×C4×C13—26no—
145C2×C4×C13—26no—
146C2×C4×C13C2413yes—
147C2×C4×C13C2411yescharacteristic
148C2×C4×C13C2411yescharacteristic
149C2×C4×C13C2413yes—
150C2×C4×C13C2413yes—
151C22⋊D13—26no—
152C22⋊D13—26no—
153C22⋊D13—22no—
154C22⋊D13—26no—
155C22⋊D13—43no—
156C22⋊D13—43no—
157C2×Dic13C2411yescharacteristic
158C2×Dic13C2413yes—
159C2×Dic13C2411yescharacteristic
160C2×Dic13C2413yes—
161C2×Dic13C2411yescharacteristic
162D52—26no—
163D52—26no—
164D52—26no—
165D52—43no—
166D52C2×D4112yes—
167C4×D13—212no—
168C4×D13—26no—
169C4×D13—26no—
170C4×D13—43no—
171C4×D13—43no—
172C4×D13C2×D4112yes—
173Dic26—26no—
174Dic26—22no—
175Dic26—26no—
176C2×2−1+4—131no—
177C2×H(5,𝔽2)—131no—
178#548—131no—
179#548—131no—
180#548—131no—
181#548D1311yescharacteristic, complemented
182#546—133no—
183#546—133no—
184#546—133no—
185#546—133no—
186#536—133no—
187#535—133no—
188#532—133no—
189C2×#124—133no—
190C4×#41—131no—
191C22×C13—21no—
192C22×C13—23no—
193C22×C13—21no—
194C22×C13—23no—
195C22×C13—21no—
196C22×C13—23no—
197C22×C13C2511yescharacteristic
198C2×D13—23no—
199C2×D13—23no—
200C2×D13—21no—
201C2×D13—23no—
202C2×D13—21no—
203C2×D13—23no—
204C2×D13—21no—
205C2×D13—23no—
206C2×D13—812no—
207C2×D13C22×D416yes—
208C4×C13—23no—
209C4×C13—21no—
210C4×C13—21no—
211C4×C13—23no—
212C4×C13C22×D416yes—
213Dic13—23no—
214Dic13—21no—
215Dic13—21no—
216Dic13—23no—
217Dic13C22×D412yes—
2182−1+4—268no—
219H(5,𝔽2)—268no—
220C2×#41—131no—
221C2×#41—133no—
222C2×#41—131no—
223C2×#41—133no—
224C2×#41—133no—
225C2×#41—133no—
226C2×#41C2×D1311yescharacteristic
227C22×Q8—133no—
228C22×Q8—131no—
229C22×Q8C2×D1311yescharacteristic, complemented
230C22×D4—133no—
231C22×D4—133no—
232C22×D4—133no—
233C4⋊Q8—133no—
234#127—133no—
235#124—133no—
236#124—133no—
237#124—133no—
238#124—136no—
239#124—131no—
240#124—133no—
241#124C2×D1313yescomplemented
242#123—136no—
243#123—136no—
244C22⋊Q8—133no—
245C22⋊Q8—133no—
246C22⋊Q8—133no—
247C22⋊Q8C2×D1313yescomplemented
248#121—133no—
249#121—133no—
250#121—133no—
251#121—133no—
252#121—133no—
253#121—133no—
254#121—133no—
255#121C2×D1313yescomplemented
256#120—136no—
257#120—136no—
258C4×Q8—131no—
259C4×Q8C2×D1311yescharacteristic, complemented
260C4×D4—133no—
261C4×D4—133no—
262C4×D4—133no—
263C4×D4—133no—
264C4×D4—133no—
265C4×D4C2×D1313yescomplemented
266#117—133no—
267C2×C22⋊C4—136no—
268C2×C22⋊C4—136no—
269C2×C42—133no—
270C2×C13—43no—
271C2×C13—41no—
272C2×C13C23×D411yescharacteristic
273C2×C13#58511yescharacteristic
274C2×C13#58511yescharacteristic
275D13—26no—
276D13—41no—
277D13—43no—
278C24—136no—
279#41—24no—
280#41—138no—
281#41—2612no—
282#41—2612no—
283#41—2612no—
284#41—2612no—
285#41—264no—
286C2×Q8—24no—
287C2×Q8—133no—
288C2×Q8—133no—
289C2×Q8—131no—
290C2×Q8—2612no—
291C2×Q8—264no—
292C2×Q8C22×D1313yes—
293C2×Q8C22×D1311yescharacteristic
294C2×D4—133no—
295C2×D4—133no—
296C2×D4—133no—
297C2×D4—131no—
298C2×D4—133no—
299C2×D4—133no—
300C2×D4—133no—
301C2×D4—133no—
302C2×D4—133no—
303C2×D4—133no—
304C2×D4—133no—
305C2×D4—2612no—
306C2×D4—2612no—
307C2×D4—2612no—
308C2×D4C22×D1313yes—
309C2×D4C22×D1313yes—
310C22×C4—133no—
311C22×C4—136no—
312C22×C4—133no—
313C22×C4—133no—
314C22×C4—133no—
315C22×C4—133no—
316C22×C4C22×D1313yes—
317C22×C4C22×D1313yes—
318C4⋊C4—133no—
319C4⋊C4—133no—
320C4⋊C4—133no—
321C4⋊C4—133no—
322C4⋊C4C22×D1313yes—
323C4⋊C4C22×D1313yes—
324C22⋊C4—133no—
325C22⋊C4—136no—
326C22⋊C4—131no—
327C22⋊C4—133no—
328C22⋊C4—133no—
329C22⋊C4—136no—
330C22⋊C4—136no—
331C22⋊C4—136no—
332C22⋊C4—131no—
333C22⋊C4—131no—
334C22⋊C4C22×D1313yes—
335C22⋊C4C22×D1316yes—
336C22⋊C4C22×D1311yescharacteristic
337C42—131no—
338C42—133no—
339C42—133no—
340C42C22×D1313yes—
341C13#350011yescharacteristic, complemented, Sylow
342C23—133no—
343C23—133no—
344C23—131no—
345C23—2612no—
346C23—526no—
347C23—526no—
348C23C23×D1313yes—
349C23C23×D1311yescharacteristic
350Q8—26no—
351Q8—266no—
352Q8—262no—
353Q8—266no—
354Q8D4×D1314yes—
355D4—26no—
356D4—43no—
357D4—1312no—
358D4—266no—
359D4—266no—
360D4—266no—
361D4—262no—
362D4—266no—
363D4—266no—
364D4—266no—
365D4—523no—
366D4—523no—
367D4—523no—
368C2×C4—26no—
369C2×C4—26no—
370C2×C4—131no—
371C2×C4—1312no—
372C2×C4—131no—
373C2×C4—133no—
374C2×C4—133no—
375C2×C4—131no—
376C2×C4—2612no—
377C2×C4—266no—
378C2×C4—266no—
379C2×C4—523no—
380C2×C4—523no—
381C2×C4C23×D1311yescharacteristic
382C2×C4C23×D1313yes—
383C2×C4C23×D1313yes—
384C2×C4C23×D1311yescharacteristic
385C2×C4C23×D1313yes—
386C22—21no—
387C22—23no—
388C22—21no—
389C22—23no—
390C22—21no—
391C22—23no—
392C22—136no—
393C22—263no—
394C22—263no—
395C22—261no—
396C22—263no—
397C22—261no—
398C22—263no—
399C22—261no—
400C22—263no—
401C22—10412no—
402C22C24×D1311yescharacteristic
403C4—21no—
404C4—23no—
405C4—23no—
406C4—21no—
407C4—132no—
408C4—261no—
409C4—263no—
410C4—261no—
411C4—263no—
412C4C2×D4×D1316yes—
413C2—43no—
414C2—41no—
415C2—266no—
416C2—523no—
417C2—521no—
418C2C22×D4×D1311yescharacteristic
419C2#1171964811yescharacteristic
420C2#1171965211yescharacteristic
subgroupG/H
center, FrattiniC22C24×D13
commutator, socle, cosocleC22×C13C25
FittingC13×#548C2
hypercenter#548D13
hypocenterC13#3500
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ #548

Complements

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

NH ≅ G/Ntype
1. C2×#88256C2semidirect
2. C2×#88254C2semidirect
3. C13×#548C2semidirect
4. #11719536C2semidirect
5. #11719522C2semidirect
6. #11719381C2semidirect
7. D13×#124C2semidirect
8. #11719335C2semidirect
9. #11719333C2semidirect
10. #11719317C2semidirect
11. #11719312C2semidirect
12. #11719281C2semidirect
13. C4×#6131C2semidirect
14. #11719255C2semidirect
15. #11719253C2semidirect
17. C22×Q8×C13C22semidirect
22. C2×#6131C22semidirect
23. C2×Q8×D13C22semidirect
24. C2×Q8×D13C22semidirect
28. C2×#6127C22semidirect
29. C2×#6127C22semidirect
31. C13×#124C22semidirect
32. C13×C22⋊Q8C22semidirect
33. C13×#121C22semidirect
34. C4×Q8×C13C22semidirect
35. C4×D4×C13C22semidirect
36. #88201C22semidirect
37. #88200C22semidirect
38. Q8×Dic13C22semidirect
39. #88194C22semidirect
40. #88192C22semidirect
41. #88192C22semidirect
42. #88191C22semidirect
43. #88190C22semidirect
44. #88184C22semidirect
45. C4×C22⋊D13C22semidirect
46. C4×C22⋊D13C22semidirect
47. #88178C22semidirect
48. #88151C22semidirect
49. #88149C22semidirect
50. #88149C22semidirect
51. #88148C22semidirect
52. #88147C22semidirect
53. #88146C22semidirect
54. #88142C22semidirect
55. #88139C22semidirect
56. #88139C22semidirect
57. #88139C22semidirect
58. #88138C22semidirect
59. #88138C22semidirect
60. #88137C22semidirect
61. #88136C22semidirect
62. C22⋊C4×D13C22semidirect
63. C22⋊C4×D13C22semidirect
64. #88129C22semidirect
65. C4×D52C22semidirect
66. C4×D52C22semidirect
67. C42×D13C22semidirect
85. #6131D4semidirect
181. #548D13semidirect
229. C22×Q8C2×D13semidirect
241. #124C2×D13semidirect
247. C22⋊Q8C2×D13semidirect
255. #121C2×D13semidirect
259. C4×Q8C2×D13semidirect
265. C4×D4C2×D13semidirect
341. C13#3500semidirect

Maximal subgroups

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

subgroupindex
C2×#882562
C2×#882542
C13×#5482
#117195362
#117195222
#117193812
D13×#1242
#117193352
#117193332
#117193172
#117193122
#117192812
C4×#61312
#117192552
#117192532
#350013