Finite Group Databasebeta

← #13126519

Subgroups — #13126519

Order 1664.

526 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719534C211yesmaximal, characteristic, complemented
2C2×#88204C211yesmaximal, characteristic, complemented
3C2×D8×D13C211yesmaximal, characteristic, complemented
4#11719317C211yesmaximal, characteristic, complemented
5C13×#449C211yesmaximal, characteristic, complemented
6#11718830C211yesmaximal, characteristic, complemented
7#11718829C211yesmaximal, characteristic, complemented
8#11718814C211yesmaximal, characteristic, complemented
9#11718699C211yesmaximal, characteristic, complemented
10#11718480C211yesmaximal, characteristic, complemented
11#11718474C211yesmaximal, characteristic, complemented
12#11718437C211yesmaximal, characteristic, complemented
13#11718417C211yesmaximal, characteristic, complemented
14#11718395C211yesmaximal, characteristic, complemented
15#11718386C211yesmaximal, characteristic, complemented
16C2×C13×#41C2211yescharacteristic, complemented
17C2×D4×D13C2211yescharacteristic
18C2×D4×D13C2211yescharacteristic
19C2×#6127C2211yescharacteristic, complemented
20C2×C13×SD16C2211yescharacteristic, complemented
21C2×C13×D8C2211yescharacteristic
22C13×#121C2211yescharacteristic, complemented
23#88204—24no—
24#88201C2211yescharacteristic, complemented
25#88200C2211yescharacteristic
26C2×#6107C2211yescharacteristic, complemented
27C2×#6106C2211yescharacteristic, complemented
28#88193—21no—
29#88192—21no—
30#88191—21no—
31#88191—21no—
32#88190C2211yescharacteristic, complemented
33D4×Dic13C2211yescharacteristic, complemented
34C2×#6105C2211yescharacteristic, complemented
35C2×#6104C2211yescharacteristic
36C2×#6104C2211yescharacteristic
37#88184C2211yescharacteristic, complemented
38#88183—21no—
39C4×C22⋊D13C2211yescharacteristic
40C2×#6103—21no—
41C22×#1055C2211yescharacteristic, complemented
42D8×D13—24no—
43C2×D104C2211yescharacteristic
44C2×#6095C2211yescharacteristic, complemented
45C2×C8×D13C2211yescharacteristic
46#88151C2211yescharacteristic
47#88147C2211yescharacteristic, complemented
48#88137—21no—
49C22⋊C4×D13—21no—
50C13×#103C2211yescharacteristic, complemented
51C13×#102C2211yescharacteristic, complemented
52C13×C22⋊C8C2211yescharacteristic, complemented
53#88072C2211yescharacteristic, complemented
54#88061C2211yescharacteristic, complemented
55#88060C2211yescharacteristic
56#88056C2211yescharacteristic, complemented
57#88054C2211yescharacteristic, complemented
58C8×Dic13C2211yescharacteristic, complemented
59#88049C2211yescharacteristic, complemented
60#88047C2211yescharacteristic, complemented
61C23×D13—21no—
62C23×D13—21no—
63C13×#41—22no—
64C13×#41—41no—
65C2×Q8×C13C2311yescharacteristic
66C2×D4×C13—21no—
67C2×D4×C13—21no—
68C2×D4×C13C2311yescharacteristic
69C2×D4×C13C2311yescharacteristic
70C22×C4×C13—21no—
71C22×C4×C13C2311yescharacteristic
72C2×C22⋊D13—21no—
73C2×C22⋊D13—21no—
74C2×C22⋊D13—21no—
75C2×C22⋊D13—21no—
76C2×C22⋊D13D411yescharacteristic
77C22×Dic13—21no—
78D4×D13—22no—
79D4×D13—22no—
80D4×D13—41no—
81D4×D13—41no—
82#6127—22no—
83#6127—41no—
84C2×D52C2311yescharacteristic
85C2×D52C2311yescharacteristic
86C2×C4×D13—21no—
87C2×C4×D13—21no—
88C2×C4×D13C2311yescharacteristic
89C2×Dic26C2311yescharacteristic
90C13×SD16—41no—
91C13×D8—22no—
92C2×C8×C13C2311yescharacteristic
93C2×C8×C13C2311yescharacteristic
94C13×C4⋊C4C2311yescharacteristic
95C13×C22⋊C4—21no—
96C22⋊Dic13—21no—
97C22⋊Dic13—21no—
98C22⋊Dic13—21no—
99C22⋊Dic13D411yescharacteristic
100#6107—22no—
101#6106—22no—
102#6105—22no—
103#6104—22no—
104#6104D414yescomplemented
105#6103—21no—
106#6103—21no—
107#6103—21no—
108#6103—21no—
109#6103—21no—
110#6103—21no—
111#6103D411yescharacteristic
112C4⋊Dic13—21no—
113C4⋊Dic13C2311yescharacteristic
114#6101—21no—
115#6101D411yescharacteristic
116C4×Dic13C2311yescharacteristic
117C2×#1055—22no—
118C2×#1055C2311yescharacteristic
119C2×#1055C2311yescharacteristic
120D104—22no—
121#6095—41no—
122C8×D13—22no—
123#3280—131nomaximal, Sylow
124C23×C13—21no—
125C23×C13—21no—
126C23×C13C2×D411yescharacteristic
127C22×D13—21no—
128C22×D13—21no—
129C22×D13—42no—
130C22×D13—42no—
131C22×D13—42no—
132C22×D13—42no—
133C22×D13—81no—
134C22×D13—81no—
135C22×D13C2×D411yescharacteristic
136Q8×C13—21no—
137Q8×C13—21no—
138D4×C13—21no—
139D4×C13—21no—
140D4×C13—21no—
141D4×C13—42no—
142D4×C13—81no—
143D4×C13C2×D412yes—
144C2×C4×C13—21no—
145C2×C4×C13—21no—
146C2×C4×C13—21no—
147C2×C4×C13—21no—
148C2×C4×C13—42no—
149C2×C4×C13C2×D411yescharacteristic
150C2×C4×C13C2411yescharacteristic
151C22⋊D13—22no—
152C22⋊D13—42no—
153C22⋊D13—42no—
154C22⋊D13—42no—
155C22⋊D13—81no—
156C2×Dic13—21no—
157C2×Dic13—21no—
158C2×Dic13—81no—
159C2×Dic13C2×D411yescharacteristic
160C2×Dic13C2×D411yescharacteristic
161C2×Dic13C2×D411yescharacteristic
162D52—21no—
163D52—21no—
164D52—21no—
165D52C2×D412yes—
166C4×D13—21no—
167C4×D13—21no—
168C4×D13—42no—
169C4×D13—81no—
170Dic26—21no—
171Dic26—21no—
172C8×C13—21no—
173C8×C13—21no—
174#1055—21no—
175#1055C2×D412yes—
176C2×#135—131no—
177C22×D8—131no—
178#546—131no—
179#546—131no—
180#495—131no—
181#467—131no—
182#466—131no—
183#463—131no—
184#463—131no—
185#450—131no—
186#450—131no—
187#449—131no—
188#449D1311yescharacteristic, complemented
189C4×D8—131no—
190C8×D4—131no—
191C22×C13—21no—
192C22×C13—22no—
193C22×C13—21no—
194C22×C13—21no—
195C22×C13—41no—
196C22×C13—41no—
197C22×C13—41no—
198C22×C13—41no—
199C22×C13—41no—
200C22×C13C22×D411yescharacteristic
201C2×D13—21no—
202C2×D13—21no—
203C2×D13—22no—
204C2×D13—41no—
205C2×D13—41no—
206C2×D13—41no—
207C2×D13—41no—
208C2×D13—41no—
209C2×D13—84no—
210C2×D13—84no—
211C2×D13#13512yescomplemented
212C4×C13—21no—
213C4×C13—41no—
214C4×C13—41no—
215C4×C13C22×D411yescharacteristic
216C4×C13H(5,𝔽2)11yescharacteristic
217Dic13—21no—
218Dic13—21no—
219Dic13—21no—
220Dic13—41no—
221Dic13—41no—
222C2×#41—131no—
223C2×#41C2×D1311yescharacteristic, complemented
224C22×D4—131no—
225C22×D4—131no—
226#135—264no—
227C2×Q16—131no—
228C2×SD16—131no—
229C2×SD16—131no—
230C2×SD16—131no—
231C2×SD16C2×D1311yescharacteristic, complemented
232C2×D8—131no—
233C2×D8—131no—
234C2×D8—131no—
235C2×D8—264no—
236C2×D8C2×D1311yescharacteristic
237C22×C8—131no—
238C22×C8—131no—
239#124—131no—
240#124—131no—
241#123—261no—
242#123—261no—
243C22⋊Q8—131no—
244C22⋊Q8—131no—
245#121—131no—
246#121—261no—
247#121—261no—
248#121C2×D1311yescharacteristic, complemented
249#120—261no—
250#120—261no—
251C4×D4—131no—
252C4×D4—131no—
253C4×D4—131no—
254C2×C22⋊C4—261no—
255C2×C22⋊C4—261no—
256#107—131no—
257C4⋊C8—131no—
258#103—131no—
259#103C2×D1311yescharacteristic, complemented
260#102—131no—
261#102—131no—
262#102—131no—
263#102C2×D1311yescharacteristic, complemented
264C22⋊C8—131no—
265C22⋊C8C2×D1311yescharacteristic, complemented
266C4×C8—131no—
267C2×C13—42no—
268C2×C13—41no—
269C2×C13—81no—
270C2×C13D4211yescharacteristic
271C2×C13C2×#13511yescharacteristic
272C2×C13#57611yescharacteristic
273D13—22no—
274D13—42no—
275D13—81no—
276C24—261no—
277C24—261no—
278#41—22no—
279#41—41no—
280#41—262no—
281#41—521no—
282C2×Q8—131no—
283C2×Q8C22×D1311yescharacteristic
284C2×D4—21no—
285C2×D4—21no—
286C2×D4—131no—
287C2×D4—131no—
288C2×D4—131no—
289C2×D4—261no—
290C2×D4—261no—
291C2×D4—262no—
292C2×D4—262no—
293C2×D4—261no—
294C2×D4—261no—
295C2×D4—521no—
296C2×D4—521no—
297C2×D4C22×D1311yescharacteristic
298C2×D4C22×D1311yescharacteristic
299C22×C4—21no—
300C22×C4—131no—
301C22×C4—261no—
302C22×C4—261no—
303C22×C4—261no—
304C22×C4C22×D1311yescharacteristic
305Q16—262no—
306SD16—41no—
307SD16—262no—
308SD16—262no—
309SD16—521no—
310D8—22no—
311D8—134no—
312D8—262no—
313D8—262no—
314C2×C8—131no—
315C2×C8—131no—
316C2×C8—262no—
317C2×C8—262no—
318C2×C8C22×D1311yescharacteristic
319C2×C8C22×D1311yescharacteristic
320C4⋊C4—131no—
321C4⋊C4—131no—
322C4⋊C4—261no—
323C4⋊C4—261no—
324C4⋊C4C22×D1311yescharacteristic
325C22⋊C4—21no—
326C22⋊C4—131no—
327C22⋊C4—131no—
328C22⋊C4—261no—
329C22⋊C4—261no—
330C22⋊C4—261no—
331C22⋊C4—261no—
332C22⋊C4—261no—
333C22⋊C4—261no—
334C22⋊C4—261no—
335C22⋊C4—261no—
336C22⋊C4—261no—
337C42—131no—
338C13#328011yescharacteristic, complemented, Sylow
339C23—21no—
340C23—21no—
341C23—131no—
342C23—261no—
343C23—261no—
344C23—522no—
345C23—522no—
346C23—522no—
347C23—522no—
348C23—1041no—
349C23—1041no—
350C23D4×D1311yescharacteristic
351Q8—21no—
352Q8—21no—
353Q8—261no—
354Q8—261no—
355D4—21no—
356D4—21no—
357D4—21no—
358D4—42no—
359D4—81no—
360D4—132no—
361D4—262no—
362D4—261no—
363D4—261no—
364D4—261no—
365D4—522no—
366D4—522no—
367D4—522no—
368D4—1041no—
369D4D4×D1312yes—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—42no—
375C2×C4—131no—
376C2×C4—131no—
377C2×C4—131no—
378C2×C4—261no—
379C2×C4—261no—
380C2×C4—261no—
381C2×C4—261no—
382C2×C4—522no—
383C2×C4—1041no—
384C2×C4—1041no—
385C2×C4D4×D1311yescharacteristic
386C2×C4C23×D1311yescharacteristic
387C8—21no—
388C8—21no—
389C8—132no—
390C8—261no—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—22no—
395C22—41no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—41no—
400C22—132no—
401C22—261no—
402C22—261no—
403C22—262no—
404C22—521no—
405C22—521no—
406C22—521no—
407C22—521no—
408C22—521no—
409C22—1044no—
410C22—1044no—
411C22C2×D4×D1311yescharacteristic
412C4—21no—
413C4—41no—
414C4—41no—
415C4—261no—
416C4—261no—
417C4—261no—
418C4—521no—
419C4—521no—
420C4C2×D4×D1311yescharacteristic
421C4#8825111yescharacteristic
422C2—41no—
423C2—42no—
424C2—81no—
425C2—262no—
426C2—522no—
427C2—1041no—
428C2#1171929511yescharacteristic
429C2D13×#13511yescharacteristic
430C2#1171947911yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#449C2
socleC22×C13C22×D4
hypercenter#449D13
hypocenterC13#3280
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #11719534C2semidirect
2. C2×#88204C2semidirect
3. C2×D8×D13C2semidirect
4. #11719317C2semidirect
5. C13×#449C2semidirect
6. #11718830C2semidirect
7. #11718829C2semidirect
8. #11718814C2semidirect
9. #11718699C2semidirect
10. #11718480C2semidirect
11. #11718474C2semidirect
12. #11718437C2semidirect
13. #11718417C2semidirect
14. #11718395C2semidirect
15. #11718386C2semidirect
16. C2×C13×#41C22semidirect
19. C2×#6127C22semidirect
20. C2×C13×SD16C22semidirect
22. C13×#121C22semidirect
24. #88201C22semidirect
26. C2×#6107C22semidirect
27. C2×#6106C22semidirect
32. #88190C22semidirect
33. D4×Dic13C22semidirect
34. C2×#6105C22semidirect
37. #88184C22semidirect
41. C22×#1055C22semidirect
44. C2×#6095C22semidirect
47. #88147C22semidirect
50. C13×#103C22semidirect
51. C13×#102C22semidirect
52. C13×C22⋊C8C22semidirect
53. #88072C22semidirect
54. #88061C22semidirect
56. #88056C22semidirect
57. #88054C22semidirect
58. C8×Dic13C22semidirect
59. #88049C22semidirect
60. #88047C22semidirect
104. #6104D4semidirect
188. #449D13semidirect
211. C2×D13#135semidirect
223. C2×#41C2×D13semidirect
231. C2×SD16C2×D13semidirect
248. #121C2×D13semidirect
259. #103C2×D13semidirect
263. #102C2×D13semidirect
265. C22⋊C8C2×D13semidirect
338. C13#3280semidirect

Maximal subgroups

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

subgroupindex
#117195342
C2×#882042
C2×D8×D132
#117193172
C13×#4492
#117188302
#117188292
#117188142
#117186992
#117184802
#117184742
#117184372
#117184172
#117183952
#117183862
#328013