Finite Group Databasebeta

← #13128489

Subgroups — #13128489

Order 1664.

1536 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×#88257C211yesmaximal, characteristic, complemented
2C2×#41×D13C211yesmaximal, characteristic, complemented
3C13×#550C211yesmaximal, characteristic, complemented
4#11719539C211yesmaximal, characteristic, complemented
5#11719536C211yesmaximal, characteristic, complemented
6#11719423C213yesmaximal, complemented
7#11719420C213yesmaximal, complemented
8#11719312C213yesmaximal, complemented
9#11719311C213yesmaximal, complemented
10#11719304C213yesmaximal, complemented
11#11719303C213yesmaximal, complemented
12#11719281C211yesmaximal, characteristic, complemented
13#11719277C211yesmaximal, characteristic, complemented
14#11719257C213yesmaximal, complemented
15#11719252C213yesmaximal, complemented
16C2×C13×#41C2211yescharacteristic
17C2×C13×#41C2211yescharacteristic, complemented
18#88257—28no—
19#41×D13—28no—
20C2×#6131C2211yescharacteristic
21C2×Q8×D13C2211yescharacteristic
22C2×Q8×D13C2211yescharacteristic, complemented
23C2×#6129C2213yes—
24C2×#6129C2213yes—
25C2×#6129C2213yescomplemented
26C2×D4×D13C2213yes—
27C2×#6127C2213yes—
28C2×#6127C2213yes—
29C22×C4×D13C2213yes—
30C22×Dic26C2213yescomplemented
31C13×#127C2213yescomplemented
32C13×#121C2213yescomplemented
33C13×#121C2213yescomplemented
34C4×Q8×C13C2211yescharacteristic, complemented
35C4×D4×C13C2213yescomplemented
36Q8×Dic13C2211yescharacteristic, complemented
37#88194C2213yescomplemented
38#88194C2216yescomplemented
39#88193C2213yescomplemented
40#88193C2216yescomplemented
41#88193C2216yescomplemented
42#88192C2213yescomplemented
43#88192C2213yescomplemented
44#88191C2213yes—
45#88191C2216yes—
46#88190C2213yescomplemented
47D4×Dic13C2216yescomplemented
48#88184C2213yescomplemented
49C4×C22⋊D13C2213yescomplemented
50C4×C22⋊D13C2213yescomplemented
51#88178C2213yescomplemented
52#88151C2213yescomplemented
53#88150C2213yescomplemented
54#88149C2213yescomplemented
55#88148C2211yescharacteristic
56#88146C2213yes—
57#88141C2213yescomplemented
58#88139C2216yescomplemented
59#88138C2213yescomplemented
60#88137C2213yes—
61#88136C2213yes—
62#88135C2216yescomplemented
63#88132C2213yescomplemented
64#88129C2213yescomplemented
65C4×D52C2213yescomplemented
66#88126C2213yes—
67C4×Dic26C2213yescomplemented
68C23×D13C2313yes—
69C13×#41—24no—
70C13×#41—24no—
71C2×Q8×C13C2311yescharacteristic
72C2×D4×C13C2313yes—
73C2×D4×C13C2313yes—
74C2×D4×C13C2316yes—
75C2×D4×C13C2313yes—
76C22×C4×C13C2313yes—
77C22×C4×C13C2313yes—
78C2×C22⋊D13C2313yes—
79C2×C22⋊D13C2313yes—
80C2×C22⋊D13C2316yes—
81C2×C22⋊D13C2316yes—
82C2×C22⋊D13C2313yes—
83C2×C22⋊D13C2313yes—
84C22×Dic13C2313yes—
85C22×Dic13C2316yes—
86#6131—24no—
87Q8×D13—24no—
88Q8×D13D418yescomplemented
89#6129—212no—
90#6129—212no—
91#6129—212no—
92D4×D13—212no—
93#6127—212no—
94#6127—212no—
95C2×D52C2313yes—
96C2×D52C2311yescharacteristic
97C2×D52C2313yes—
98C2×C4×D13—212no—
99C2×C4×D13C2313yes—
100C2×C4×D13C2313yes—
101C2×C4×D13C2313yes—
102C2×C4×D13C2311yescharacteristic
103C2×C4×D13C2313yes—
104C2×Dic26—212no—
105C2×Dic26C2313yes—
106C2×Dic26C2313yes—
107C2×Dic26C2313yes—
108C13×C4⋊C4C2313yes—
109C13×C4⋊C4C2311yescharacteristic
110C13×C22⋊C4C2313yes—
111C13×C22⋊C4C2313yes—
112C42×C13C2313yes—
113C22⋊Dic13C2313yes—
114C22⋊Dic13C2313yes—
115C22⋊Dic13C2316yes—
116#6103C2311yescharacteristic
117#6103C2313yes—
118#6103C2311yescharacteristic
119#6103C2313yes—
120#6103C2316yes—
121#6103C2313yes—
122#6103C2311yescharacteristic
123C4⋊Dic13C2313yes—
124C4⋊Dic13C2313yes—
125#6101C2313yes—
126#6101C2313yes—
127#6101C2311yescharacteristic
128#6101C2313yes—
129C4×Dic13C2316yes—
130C4×Dic13C2313yes—
131#3487—131nomaximal, Sylow
132C23×C13C2413yes—
133C23×C13C2413yes—
134C22×D13—26no—
135C22×D13—43no—
136C22×D13—43no—
137C22×D13C2413yes—
138C22×D13C2411yescharacteristic
139C22×D13C2411yescharacteristic
140Q8×C13C2×D414yes—
141D4×C13—26no—
142D4×C13—26no—
143D4×C13—46no—
144D4×C13—43no—
145C2×C4×C13—26no—
146C2×C4×C13—26no—
147C2×C4×C13C2413yes—
148C2×C4×C13C2411yescharacteristic
149C2×C4×C13C2411yescharacteristic
150C2×C4×C13C2411yescharacteristic
151C2×C4×C13C2413yes—
152C22⋊D13—26no—
153C22⋊D13—212no—
154C22⋊D13—26no—
155C22⋊D13—43no—
156C22⋊D13—43no—
157C22⋊D13—46no—
158C2×Dic13—212no—
159C2×Dic13—26no—
160C2×Dic13C2411yescharacteristic
161C2×Dic13C2413yes—
162C2×Dic13C2411yescharacteristic
163C2×Dic13C2413yes—
164C2×Dic13C2413yes—
165D52—22no—
166D52—26no—
167D52—43no—
168C4×D13—22no—
169C4×D13—26no—
170C4×D13—26no—
171C4×D13—26no—
172C4×D13C2×D4112yes—
173Dic26—26no—
174Dic26—26no—
175Dic26C2×D4112yes—
176C2×2−1+4—131no—
177C22×#41—131no—
178#550—131no—
179#550—133no—
180#550—133no—
181#550D1311yescharacteristic, complemented
182#548—131no—
183#548—133no—
184#548—131no—
185#548—133no—
186#535—133no—
187#535—133no—
188#525—133no—
189#525—133no—
190#519—131no—
191C22×C13—23no—
192C22×C13—23no—
193C22×C13—23no—
194C22×C13—23no—
195C22×C13—23no—
196C22×C13—23no—
197C22×C13C2511yescharacteristic
198C2×D13—21no—
199C2×D13—21no—
200C2×D13—21no—
201C2×D13—23no—
202C2×D13—21no—
203C2×D13—23no—
204C2×D13—21no—
205C2×D13—23no—
206C2×D13—412no—
207C2×D13C22×D412yes—
208C4×C13—21no—
209C4×C13—21no—
210C4×C13—23no—
211C4×C13—21no—
212C4×C13C22×D416yes—
213Dic13—23no—
214Dic13—21no—
215Dic13—23no—
216Dic13—21no—
217Dic13C22×D416yes—
2182−1+4—268no—
219C2×#41—131no—
220C2×#41—133no—
221C2×#41—133no—
222C2×#41—133no—
223C2×#41—133no—
224C2×#41—133no—
225C2×#41—268no—
226C2×#41C2×D1311yescharacteristic
227C2×#41C2×D1311yescharacteristic, complemented
228C22×Q8—131no—
229C22×Q8—131no—
230C22×Q8—133no—
231C22×D4—133no—
232C23×C4—133no—
233#127—136no—
234#127—133no—
235#127C2×D1313yescomplemented
236#124—133no—
237#124—136no—
238#124—133no—
239#123—131no—
240#123—133no—
241C22⋊Q8—133no—
242C22⋊Q8—133no—
243C22⋊Q8—133no—
244C22⋊Q8—133no—
245#121—133no—
246#121—133no—
247#121—133no—
248#121—136no—
249#121—136no—
250#121—133no—
251#121—133no—
252#121—133no—
253#121C2×D1313yescomplemented
254#121C2×D1313yescomplemented
255#120—136no—
256#120—133no—
257#120—133no—
258C4×Q8—131no—
259C4×Q8—133no—
260C4×Q8—133no—
261C4×Q8C2×D1311yescharacteristic, complemented
262C4×D4—136no—
263C4×D4—133no—
264C4×D4—133no—
265C4×D4—136no—
266C4×D4—133no—
267C4×D4C2×D1313yescomplemented
268#117—133no—
269#117—133no—
270C2×C13—43no—
271C2×C13—43no—
272C2×C13C23×D411yescharacteristic
273C2×C13#58511yescharacteristic
274C2×C13#58511yescharacteristic
275D13—22no—
276D13—41no—
277D13—43no—
278C24—133no—
279#41—24no—
280#41—24no—
281#41—2612no—
282#41—2612no—
283#41—2612no—
284#41—2612no—
285#41—2612no—
286#41—264no—
287C2×Q8—138no—
288C2×Q8—133no—
289C2×Q8—133no—
290C2×Q8—133no—
291C2×Q8—2612no—
292C2×Q8—264no—
293C2×Q8C22×D1311yescharacteristic
294C2×D4—133no—
295C2×D4—136no—
296C2×D4—133no—
297C2×D4—133no—
298C2×D4—136no—
299C2×D4—133no—
300C2×D4—131no—
301C2×D4—133no—
302C2×D4—133no—
303C2×D4—2612no—
304C2×D4C22×D1313yes—
305C2×D4C22×D1313yes—
306C2×D4C22×D1316yes—
307C2×D4C22×D1313yes—
308C22×C4—133no—
309C22×C4—136no—
310C22×C4—133no—
311C22×C4—133no—
312C22×C4—133no—
313C22×C4—133no—
314C22×C4—131no—
315C22×C4—2612no—
316C22×C4C22×D1313yes—
317C22×C4C22×D1313yes—
318C4⋊C4—133no—
319C4⋊C4—133no—
320C4⋊C4—133no—
321C4⋊C4—133no—
322C4⋊C4—131no—
323C4⋊C4—133no—
324C4⋊C4C22×D1313yes—
325C4⋊C4C22×D1311yescharacteristic
326C22⋊C4—133no—
327C22⋊C4—136no—
328C22⋊C4—133no—
329C22⋊C4—133no—
330C22⋊C4—131no—
331C22⋊C4—131no—
332C22⋊C4—131no—
333C22⋊C4—133no—
334C22⋊C4—136no—
335C22⋊C4—133no—
336C22⋊C4C22×D1313yes—
337C22⋊C4C22×D1313yes—
338C42—136no—
339C42—133no—
340C42C22×D1313yes—
341C13#348711yescharacteristic, complemented, Sylow
342C23—131no—
343C23—133no—
344C23—131no—
345C23—266no—
346C23—523no—
347C23—523no—
348C23C23×D1313yes—
349C23C23×D1313yes—
350Q8—1312no—
351Q8—266no—
352Q8—266no—
353Q8D4×D1314yes—
354D4—26no—
355D4—26no—
356D4—43no—
357D4—46no—
358D4—262no—
359D4—2612no—
360D4—266no—
361D4—266no—
362D4—266no—
363D4—523no—
364D4—526no—
365D4—523no—
366D4—523no—
367C2×C4—26no—
368C2×C4—26no—
369C2×C4—133no—
370C2×C4—1312no—
371C2×C4—133no—
372C2×C4—131no—
373C2×C4—133no—
374C2×C4—131no—
375C2×C4—266no—
376C2×C4—262no—
377C2×C4—266no—
378C2×C4—2612no—
379C2×C4—266no—
380C2×C4—266no—
381C2×C4C23×D1313yes—
382C2×C4C23×D1311yescharacteristic
383C2×C4C23×D1311yescharacteristic
384C2×C4C23×D1311yescharacteristic
385C2×C4C23×D1313yes—
386C22—23no—
387C22—23no—
388C22—23no—
389C22—23no—
390C22—23no—
391C22—23no—
392C22—132no—
393C22—261no—
394C22—261no—
395C22—261no—
396C22—263no—
397C22—261no—
398C22—263no—
399C22—261no—
400C22—263no—
401C22—5212no—
402C22C24×D1311yescharacteristic
403C4—21no—
404C4—21no—
405C4—21no—
406C4—23no—
407C4—136no—
408C4—261no—
409C4—263no—
410C4—263no—
411C4—261no—
412C4C2×D4×D1316yes—
413C2—43no—
414C2—43no—
415C2—262no—
416C2—523no—
417C2—521no—
418C2C22×D4×D1311yescharacteristic
419C2#1171964811yescharacteristic
420C2#1171965011yescharacteristic
subgroupG/H
center, FrattiniC22C24×D13
commutator, socle, cosocleC22×C13C25
FittingC13×#550C2
hypercenter#550D13
hypocenterC13#3487
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ #550

Complements

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

NH ≅ G/Ntype
1. C2×#88257C2semidirect
2. C2×#41×D13C2semidirect
3. C13×#550C2semidirect
4. #11719539C2semidirect
5. #11719536C2semidirect
6. #11719423C2semidirect
7. #11719420C2semidirect
8. #11719312C2semidirect
9. #11719311C2semidirect
10. #11719304C2semidirect
11. #11719303C2semidirect
12. #11719281C2semidirect
13. #11719277C2semidirect
14. #11719257C2semidirect
15. #11719252C2semidirect
17. C2×C13×#41C22semidirect
22. C2×Q8×D13C22semidirect
25. C2×#6129C22semidirect
30. C22×Dic26C22semidirect
31. C13×#127C22semidirect
32. C13×#121C22semidirect
33. C13×#121C22semidirect
34. C4×Q8×C13C22semidirect
35. C4×D4×C13C22semidirect
36. Q8×Dic13C22semidirect
37. #88194C22semidirect
38. #88194C22semidirect
39. #88193C22semidirect
40. #88193C22semidirect
41. #88193C22semidirect
42. #88192C22semidirect
43. #88192C22semidirect
46. #88190C22semidirect
47. D4×Dic13C22semidirect
48. #88184C22semidirect
49. C4×C22⋊D13C22semidirect
50. C4×C22⋊D13C22semidirect
51. #88178C22semidirect
52. #88151C22semidirect
53. #88150C22semidirect
54. #88149C22semidirect
57. #88141C22semidirect
58. #88139C22semidirect
59. #88138C22semidirect
62. #88135C22semidirect
63. #88132C22semidirect
64. #88129C22semidirect
65. C4×D52C22semidirect
67. C4×Dic26C22semidirect
88. Q8×D13D4semidirect
181. #550D13semidirect
227. C2×#41C2×D13semidirect
235. #127C2×D13semidirect
253. #121C2×D13semidirect
254. #121C2×D13semidirect
261. C4×Q8C2×D13semidirect
267. C4×D4C2×D13semidirect
341. C13#3487semidirect

Maximal subgroups

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

subgroupindex
C2×#882572
C2×#41×D132
C13×#5502
#117195392
#117195362
#117194232
#117194202
#117193122
#117193112
#117193042
#117193032
#117192812
#117192772
#117192572
#117192522
#348713