Finite Group Databasebeta

← #13126460

Subgroups — #13126460

Order 1664.

498 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719536C211yesmaximal, characteristic, complemented
2C2×#88203C211yesmaximal, characteristic, complemented
3C2×#88172C211yesmaximal, characteristic, complemented
4#11719335C211yesmaximal, characteristic, complemented
5C13×#452C211yesmaximal, characteristic, complemented
6#11718846C211yesmaximal, characteristic, complemented
7#11718833C211yesmaximal, characteristic, complemented
8#11718829C211yesmaximal, characteristic, complemented
9#11718713C211yesmaximal, characteristic, complemented
10#11718467C211yesmaximal, characteristic, complemented
11#11718449C211yesmaximal, characteristic, complemented
12#11718448C211yesmaximal, characteristic, complemented
13#11718443C211yesmaximal, characteristic, complemented
14#11718392C211yesmaximal, characteristic, complemented
15#11718390C211yesmaximal, characteristic, complemented
16C2×C13×#41C2211yescharacteristic
17C2×#6131C2211yescharacteristic
18C2×Q8×D13C2211yescharacteristic, complemented
19C22×D52C2211yescharacteristic
20C2×C13×Q16C2211yescharacteristic, complemented
21C2×C13×SD16C2211yescharacteristic, complemented
22C13×C22⋊Q8C2211yescharacteristic
23#88203—24no—
24#88201C2211yescharacteristic
25Q8×Dic13C2211yescharacteristic, complemented
26C2×#6107C2211yescharacteristic, complemented
27C2×#6106C2211yescharacteristic
28C2×#6106C2211yescharacteristic
29#88192—21no—
30#88192C2211yescharacteristic, complemented
31#88190—21no—
32#88190C2211yescharacteristic, complemented
33C2×#6104C2211yescharacteristic
34C2×#6104C2211yescharacteristic
35C4×C22⋊D13—21no—
36C4×C22⋊D13C2211yescharacteristic
37#88178—21no—
38#88178C2211yescharacteristic
39C2×#6099C2211yescharacteristic
40#88172—24no—
41C2×#6095C2211yescharacteristic
42C2×#6095C2211yescharacteristic
43C2×#6094C2211yescharacteristic, complemented
44#88149—21no—
45#88149C2211yescharacteristic
46#88148—21no—
47#88147C2211yescharacteristic
48#88136—21no—
49C22⋊C4×D13—21no—
50C13×#103C2211yescharacteristic, complemented
51C13×#102C2211yescharacteristic, complemented
52C13×C22⋊C8C2211yescharacteristic
53#88075C2211yescharacteristic, complemented
54#88061C2211yescharacteristic
55#88061C2211yescharacteristic
56#88060C2211yescharacteristic, complemented
57#88054C2211yescharacteristic, complemented
58C8×Dic13C2211yescharacteristic, complemented
59#88050C2211yescharacteristic, complemented
60#88048C2211yescharacteristic, complemented
61C23×D13—21no—
62C13×#41—22no—
63C13×#41—41no—
64C2×Q8×C13C2311yescharacteristic
65C2×Q8×C13C2311yescharacteristic
66C2×D4×C13—21no—
67C2×D4×C13C2311yescharacteristic
68C22×C4×C13—21no—
69C22×C4×C13C2311yescharacteristic
70C2×C22⋊D13—21no—
71C2×C22⋊D13D411yescharacteristic
72#6131—22no—
73#6131—41no—
74Q8×D13—22no—
75Q8×D13—41no—
76C2×D52—22no—
77C2×D52—21no—
78C2×D52—21no—
79C2×D52—21no—
80C2×D52—41no—
81C2×D52C2311yescharacteristic
82C2×D52C2311yescharacteristic
83C2×C4×D13—21no—
84C2×C4×D13—21no—
85C2×C4×D13—21no—
86C2×C4×D13C2311yescharacteristic
87C2×Dic26—21no—
88C2×Dic26C2311yescharacteristic
89C13×Q16—22no—
90C13×SD16—41no—
91C2×C8×C13C2311yescharacteristic
92C2×C8×C13C2311yescharacteristic
93C13×C4⋊C4—21no—
94C13×C4⋊C4C2311yescharacteristic
95C13×C22⋊C4—21no—
96C22⋊Dic13—21no—
97C22⋊Dic13—21no—
98C22⋊Dic13—21no—
99C22⋊Dic13—21no—
100C22⋊Dic13D411yescharacteristic
101#6107—22no—
102#6106—22no—
103#6106D414yescomplemented
104#6104—22no—
105#6104—22no—
106#6103—21no—
107#6103—21no—
108#6103—21no—
109#6103—21no—
110#6103D411yescharacteristic
111C4⋊Dic13—21no—
112C4⋊Dic13C2311yescharacteristic
113#6101—21no—
114#6101D411yescharacteristic
115C4×Dic13—21no—
116C4×Dic13C2311yescharacteristic
117#6099—22no—
118C2×#1055C2311yescharacteristic
119C2×#1055C2311yescharacteristic
120#6095—22no—
121#6095—41no—
122#6094—22no—
123#3275—131nomaximal, Sylow
124C23×C13—21no—
125C23×C13C2×D411yescharacteristic
126C22×D13—21no—
127C22×D13—21no—
128C22×D13—42no—
129C22×D13—42no—
130C22×D13—81no—
131C22×D13C2×D411yescharacteristic
132Q8×C13—21no—
133Q8×C13—21no—
134Q8×C13—21no—
135Q8×C13C2×D412yes—
136D4×C13—21no—
137D4×C13—21no—
138D4×C13—42no—
139C2×C4×C13—21no—
140C2×C4×C13—21no—
141C2×C4×C13—21no—
142C2×C4×C13—21no—
143C2×C4×C13—21no—
144C2×C4×C13—42no—
145C2×C4×C13C2×D411yescharacteristic
146C2×C4×C13C2411yescharacteristic
147C22⋊D13—41no—
148C22⋊D13—42no—
149C2×Dic13—21no—
150C2×Dic13—21no—
151C2×Dic13C2×D411yescharacteristic
152C2×Dic13C2×D411yescharacteristic
153C2×Dic13C2×D411yescharacteristic
154D52—21no—
155D52—21no—
156D52—21no—
157D52—42no—
158D52—42no—
159D52—81no—
160D52C2×D412yes—
161C4×D13—21no—
162C4×D13—21no—
163C4×D13—42no—
164C4×D13—42no—
165C4×D13—81no—
166Dic26—21no—
167Dic26—21no—
168Dic26—42no—
169C8×C13—21no—
170C8×C13—21no—
171#1055—21no—
172#1055C2×D412yes—
173C2×#137—131no—
174C2×AGL(1,ℤ/8)—131no—
175#548—131no—
176#546—131no—
177#495—131no—
178#470—131no—
179#469—131no—
180#464—131no—
181#463—131no—
182#452D1311yescharacteristic, complemented
183#450—131no—
184#449—131no—
185#448—131no—
186C4×SD16—131no—
187#436—131no—
188C22×C13—21no—
189C22×C13—21no—
190C22×C13—21no—
191C22×C13—41no—
192C22×C13—41no—
193C22×C13—41no—
194C22×C13C22×D411yescharacteristic
195C2×D13—21no—
196C2×D13—22no—
197C2×D13—21no—
198C2×D13—21no—
199C2×D13—41no—
200C2×D13—41no—
201C2×D13—41no—
202C2×D13—41no—
203C2×D13—41no—
204C2×D13—84no—
205C4×C13—22no—
206C4×C13—21no—
207C4×C13—41no—
208C4×C13—41no—
209C4×C13C22×D411yescharacteristic
210C4×C13H(5,𝔽2)11yescharacteristic
211Dic13—21no—
212Dic13—21no—
213Dic13—21no—
214Dic13—41no—
215Dic13—41no—
216C2×#41—131no—
217C2×#41C2×D1311yescharacteristic
218C22×Q8—131no—
219C22×D4—131no—
220#137—264no—
221AGL(1,ℤ/8)—264no—
222C2×Q16—131no—
223C2×Q16C2×D1311yescharacteristic, complemented
224C2×SD16—131no—
225C2×SD16—131no—
226C2×SD16—131no—
227C2×SD16—131no—
228C2×SD16C2×D1311yescharacteristic, complemented
229C2×D8—131no—
230C2×D8—131no—
231C2×M16—131no—
232C2×M16—131no—
233#124—131no—
234#124—131no—
235#124—261no—
236#123—261no—
237C22⋊Q8—131no—
238C22⋊Q8—261no—
239C22⋊Q8C2×D1311yescharacteristic
240#121—131no—
241#121—131no—
242#121—261no—
243#121—261no—
244#120—261no—
245C4×Q8—131no—
246C4×D4—131no—
247C4×D4—131no—
248C4×D4—261no—
249C2×C22⋊C4—261no—
250#106—131no—
251C4⋊C8—131no—
252#103—131no—
253#103—131no—
254#103C2×D1311yescharacteristic, complemented
255#102—131no—
256#102—131no—
257#102C2×D1311yescharacteristic, complemented
258C22⋊C8—131no—
259C22⋊C8C2×D1311yescharacteristic
260C4×C8—131no—
261C2×C13—41no—
262C2×C13—81no—
263C2×C13D4211yescharacteristic
264C2×C13#57511yescharacteristic
265C2×C13#57711yescharacteristic
266D13—41no—
267D13—42no—
268D13—81no—
269C24—261no—
270#41—22no—
271#41—41no—
272#41—262no—
273#41—521no—
274C2×Q8—131no—
275C2×Q8—261no—
276C2×Q8—262no—
277C2×Q8—521no—
278C2×Q8C22×D1311yescharacteristic
279C2×Q8C22×D1311yescharacteristic
280C2×D4—21no—
281C2×D4—131no—
282C2×D4—131no—
283C2×D4—131no—
284C2×D4—262no—
285C2×D4—261no—
286C2×D4—261no—
287C2×D4—261no—
288C2×D4—261no—
289C2×D4—521no—
290C2×D4C22×D1311yescharacteristic
291C22×C4—21no—
292C22×C4—131no—
293C22×C4—261no—
294C22×C4—261no—
295C22×C4—261no—
296C22×C4C22×D1311yescharacteristic
297Q16—22no—
298Q16—262no—
299SD16—41no—
300SD16—134no—
301SD16—262no—
302SD16—262no—
303SD16—521no—
304D8—262no—
305D8—262no—
306M16—262no—
307M16—262no—
308C2×C8—131no—
309C2×C8—131no—
310C2×C8C22×D1311yescharacteristic
311C2×C8C22×D1311yescharacteristic
312C4⋊C4—21no—
313C4⋊C4—131no—
314C4⋊C4—131no—
315C4⋊C4—261no—
316C4⋊C4—261no—
317C4⋊C4C22×D1311yescharacteristic
318C22⋊C4—21no—
319C22⋊C4—131no—
320C22⋊C4—131no—
321C22⋊C4—261no—
322C22⋊C4—261no—
323C22⋊C4—261no—
324C22⋊C4—261no—
325C22⋊C4—261no—
326C22⋊C4—261no—
327C22⋊C4—261no—
328C22⋊C4—261no—
329C42—131no—
330C42—261no—
331C13#327511yescharacteristic, complemented, Sylow
332C23—21no—
333C23—131no—
334C23—261no—
335C23—261no—
336C23—522no—
337C23—522no—
338C23—1041no—
339C23D4×D1311yescharacteristic
340Q8—21no—
341Q8—21no—
342Q8—21no—
343Q8—261no—
344Q8—261no—
345Q8—522no—
346Q8D4×D1312yes—
347D4—21no—
348D4—21no—
349D4—42no—
350D4—132no—
351D4—261no—
352D4—261no—
353D4—261no—
354D4—522no—
355D4—522no—
356D4—521no—
357D4—522no—
358D4—1041no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—42no—
365C2×C4—131no—
366C2×C4—131no—
367C2×C4—131no—
368C2×C4—261no—
369C2×C4—261no—
370C2×C4—261no—
371C2×C4—261no—
372C2×C4—522no—
373C2×C4—522no—
374C2×C4—1041no—
375C2×C4D4×D1311yescharacteristic
376C2×C4C23×D1311yescharacteristic
377C8—21no—
378C8—21no—
379C8—132no—
380C8—261no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—261no—
388C22—261no—
389C22—261no—
390C22—262no—
391C22—521no—
392C22—521no—
393C22—521no—
394C22—521no—
395C22—521no—
396C22—1044no—
397C22C2×D4×D1311yescharacteristic
398C4—21no—
399C4—22no—
400C4—41no—
401C4—41no—
402C4—261no—
403C4—261no—
404C4—261no—
405C4—521no—
406C4—521no—
407C4C2×D4×D1311yescharacteristic
408C4#8825111yescharacteristic
409C2—41no—
410C2—81no—
411C2—521no—
412C2—522no—
413C2—1041no—
414C2#1171929511yescharacteristic
415C2#1171947511yescharacteristic
416C2#1171948211yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#452C2
socleC22×C13C22×D4
hypercenter#452D13
hypocenterC13#3275
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
1. #11719536C2semidirect
2. C2×#88203C2semidirect
3. C2×#88172C2semidirect
4. #11719335C2semidirect
5. C13×#452C2semidirect
6. #11718846C2semidirect
7. #11718833C2semidirect
8. #11718829C2semidirect
9. #11718713C2semidirect
10. #11718467C2semidirect
11. #11718449C2semidirect
12. #11718448C2semidirect
13. #11718443C2semidirect
14. #11718392C2semidirect
15. #11718390C2semidirect
18. C2×Q8×D13C22semidirect
20. C2×C13×Q16C22semidirect
21. C2×C13×SD16C22semidirect
25. Q8×Dic13C22semidirect
26. C2×#6107C22semidirect
30. #88192C22semidirect
32. #88190C22semidirect
43. C2×#6094C22semidirect
50. C13×#103C22semidirect
51. C13×#102C22semidirect
53. #88075C22semidirect
56. #88060C22semidirect
57. #88054C22semidirect
58. C8×Dic13C22semidirect
59. #88050C22semidirect
60. #88048C22semidirect
103. #6106D4semidirect
182. #452D13semidirect
223. C2×Q16C2×D13semidirect
228. C2×SD16C2×D13semidirect
254. #103C2×D13semidirect
257. #102C2×D13semidirect
331. C13#3275semidirect

Maximal subgroups

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

subgroupindex
#117195362
C2×#882032
C2×#881722
#117193352
C13×#4522
#117188462
#117188332
#117188292
#117187132
#117184672
#117184492
#117184482
#117184432
#117183922
#117183902
#327513