Finite Group Databasebeta

← #13124452

Subgroups — #13124452

Order 1664.

548 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88165C211yesmaximal, characteristic, complemented
2C22×#6094C211yesmaximal, characteristic, complemented
3#11719311C211yesmaximal, characteristic, complemented
4D13×#121C211yesmaximal, characteristic, complemented
5C13×#466C211yesmaximal, characteristic, complemented
6#11718820C211yesmaximal, characteristic, complemented
7#11718775C211yesmaximal, characteristic, complemented
8#11718702C211yesmaximal, characteristic, complemented
9#11718699C211yesmaximal, characteristic, complemented
10#11718547C211yesmaximal, characteristic, complemented
11#11718542C211yesmaximal, characteristic, complemented
12#11718443C211yesmaximal, characteristic, complemented
13#11718441C211yesmaximal, characteristic, complemented
14#11718432C211yesmaximal, characteristic, complemented
15#11718431C211yesmaximal, characteristic, complemented
16C2×#6129C2211yescharacteristic
17C2×D4×D13—21no—
18C2×D4×D13C2211yescharacteristic
19C22×C4×D13C2211yescharacteristic
20C2×C13×D8C2211yescharacteristic, complemented
21C22×C8×C13C2211yescharacteristic, complemented
22C13×#121C2211yescharacteristic
23C13×#121C2211yescharacteristic, complemented
24#88193—21no—
25#88192C2211yescharacteristic
26#88192C2211yescharacteristic, complemented
27#88191—21no—
28D4×Dic13—21no—
29C2×#6105C2211yescharacteristic, complemented
30C2×#6104C2211yescharacteristic, complemented
31#88184C2211yescharacteristic
32#88178C2211yescharacteristic, complemented
33C22×#1055C2211yescharacteristic, complemented
34#88165—24no—
35C2×#6095C2211yescharacteristic, complemented
36C2×#6094—24no—
37C2×#6094C2211yescharacteristic
38C2×#6094C2211yescharacteristic
39C2×#6094C2211yescharacteristic, complemented
40C2×#6094C2211yescharacteristic, complemented
41#88151C2211yescharacteristic, complemented
42#88149C2211yescharacteristic
43#88146C2211yescharacteristic
44C4⋊C4×D13C2211yescharacteristic
45#88138—21no—
46#88137—21no—
47#88135—21no—
48C22⋊C4×D13—21no—
49C13×#107C2211yescharacteristic, complemented
50C13×#102C2211yescharacteristic, complemented
51C13×#102C2211yescharacteristic, complemented
52#88072C2211yescharacteristic, complemented
53#88072C2211yescharacteristic, complemented
54#88061C2211yescharacteristic, complemented
55#88057C2211yescharacteristic, complemented
56#88056C2211yescharacteristic, complemented
57#88050C2211yescharacteristic, complemented
58#88049C2211yescharacteristic, complemented
59#88048C2211yescharacteristic, complemented
60#88047C2211yescharacteristic, complemented
61C23×D13—21no—
62C23×D13D411yescharacteristic
63C2×D4×C13—21no—
64C2×D4×C13—21no—
65C2×D4×C13C2311yescharacteristic
66C2×D4×C13C2311yescharacteristic
67C22×C4×C13C2311yescharacteristic
68C2×C22⋊D13—21no—
69C2×C22⋊D13—21no—
70C2×C22⋊D13—21no—
71C2×C22⋊D13—21no—
72C2×C22⋊D13—21no—
73C22×Dic13—21no—
74C22×Dic13D411yescharacteristic
75#6129—22no—
76#6129—22no—
77D4×D13—22no—
78D4×D13—22no—
79D4×D13—44no—
80C2×D52—21no—
81C2×D52C2311yescharacteristic
82C2×C4×D13—22no—
83C2×C4×D13—22no—
84C2×C4×D13—21no—
85C2×C4×D13D411yescharacteristic
86C2×C4×D13D411yescharacteristic
87C2×C4×D13C2311yescharacteristic
88C2×C4×D13C2311yescharacteristic
89C2×Dic26C2311yescharacteristic
90C13×D8—22no—
91C2×C8×C13—22no—
92C2×C8×C13C2311yescharacteristic
93C2×C8×C13C2311yescharacteristic
94C13×C4⋊C4C2311yescharacteristic
95C13×C4⋊C4C2311yescharacteristic
96C13×C22⋊C4—21no—
97C13×C22⋊C4—21no—
98C22⋊Dic13—21no—
99C22⋊Dic13—21no—
100C22⋊Dic13—21no—
101#6105—22no—
102#6104—22no—
103#6103—21no—
104#6103—21no—
105#6103—21no—
106#6103—21no—
107C4⋊Dic13—21no—
108C4⋊Dic13C2311yescharacteristic
109C4⋊Dic13C2311yescharacteristic
110#6101—21no—
111#6101—21no—
112C4×Dic13—21no—
113C2×#1055—22no—
114C2×#1055C2311yescharacteristic
115C2×#1055C2311yescharacteristic
116#6095—22no—
117#6094—22no—
118#6094—22no—
119#6094—22no—
120#6094D414yescomplemented
121#3055—131nomaximal, Sylow
122C23×C13—21no—
123C23×C13—21no—
124C23×C13C2×D411yescharacteristic
125C22×D13—22no—
126C22×D13—22no—
127C22×D13—21no—
128C22×D13—41no—
129C22×D13—42no—
130C22×D13—42no—
131C22×D13—42no—
132C22×D13C2×D411yescharacteristic
133C22×D13C2×D411yescharacteristic
134D4×C13—21no—
135D4×C13—21no—
136D4×C13—21no—
137D4×C13—21no—
138D4×C13—42no—
139D4×C13—42no—
140C2×C4×C13—21no—
141C2×C4×C13—21no—
142C2×C4×C13—21no—
143C2×C4×C13—21no—
144C2×C4×C13C2×D411yescharacteristic
145C2×C4×C13C2411yescharacteristic
146C22⋊D13—42no—
147C22⋊D13—42no—
148C22⋊D13—42no—
149C22⋊D13—42no—
150C22⋊D13—42no—
151C2×Dic13—22no—
152C2×Dic13—21no—
153C2×Dic13—21no—
154C2×Dic13—21no—
155C2×Dic13—42no—
156C2×Dic13C2×D411yescharacteristic
157C2×Dic13C2×D411yescharacteristic
158D52—21no—
159D52—21no—
160D52—42no—
161C4×D13—22no—
162C4×D13—21no—
163C4×D13—21no—
164C4×D13—22no—
165C4×D13—42no—
166C4×D13C2×D412yes—
167C4×D13#4112yes—
168Dic26—21no—
169Dic26—21no—
170C8×C13—21no—
171C8×C13C2×D412yescomplemented
172#1055—21no—
173#1055C2×D412yescomplemented
174C2×AGL(1,ℤ/8)—131no—
175C22×M16—131no—
176#525—131no—
177C2×#121—131no—
178#469—131no—
179#469—131no—
180#468—131no—
181#468—131no—
182#466—131no—
183#466D1311yescharacteristic, complemented
184#465—131no—
185#465—131no—
186#428—131no—
187#418—131no—
188#417—131no—
189C22×C13—21no—
190C22×C13—21no—
191C22×C13—41no—
192C22×C13—41no—
193C22×C13—41no—
194C22×C13—41no—
195C22×C13—41no—
196C22×C13—41no—
197C22×C13AGL(1,ℤ/8)12yescomplemented
198C22×C13C22×D411yescharacteristic
199C2×D13—21no—
200C2×D13—21no—
201C2×D13—21no—
202C2×D13—21no—
203C2×D13—21no—
204C2×D13—44no—
205C2×D13—41no—
206C2×D13—41no—
207C2×D13—41no—
208C2×D13—84no—
209C2×D13#12112yes—
210C4×C13—21no—
211C4×C13—41no—
212C4×C13—41no—
213C4×C13C22×D411yescharacteristic
214C4×C13C2×#4111yescharacteristic
215Dic13—21no—
216Dic13—41no—
217Dic13—41no—
218Dic13—41no—
219Dic13#12112yes—
220C2×#41—131no—
221C22×D4—131no—
222C22×D4—261no—
223C23×C4—131no—
224AGL(1,ℤ/8)—264no—
225C2×SD16—131no—
226C2×SD16—131no—
227C2×D8—131no—
228C2×D8C2×D1311yescharacteristic, complemented
229C2×M16—131no—
230C2×M16—131no—
231C2×M16—131no—
232C2×M16—131no—
233C2×M16—264no—
234C22×C8—131no—
235C22×C8C2×D1311yescharacteristic, complemented
236#123—261no—
237C22⋊Q8—131no—
238C22⋊Q8—131no—
239#121—131no—
240#121—131no—
241#121—131no—
242#121—131no—
243#121—261no—
244#121—261no—
245#121C2×D1311yescharacteristic
246#121C2×D1311yescharacteristic, complemented
247#120—261no—
248C4×D4—261no—
249C4×D4—261no—
250#117—131no—
251C2×C4⋊C4—131no—
252C2×C22⋊C4—261no—
253#107—131no—
254#107C2×D1311yescharacteristic, complemented
255#106—131no—
256#106—131no—
257#103—131no—
258#103—131no—
259#102—131no—
260#102—131no—
261#102—131no—
262#102—131no—
263#102C2×D1311yescharacteristic, complemented
264#102C2×D1311yescharacteristic, complemented
265C2×C13—22no—
266C2×C13—81no—
267C2×C13—81no—
268C2×C13C2×#12111yescharacteristic
269C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
270C2×C13#57511yescharacteristic
271D13—22no—
272D13—41no—
273D13—81no—
274C24—131no—
275C24—261no—
276#41—262no—
277#41—262no—
278C2×Q8—131no—
279C2×D4—21no—
280C2×D4—21no—
281C2×D4—131no—
282C2×D4—261no—
283C2×D4—262no—
284C2×D4—262no—
285C2×D4—261no—
286C2×D4—261no—
287C2×D4—261no—
288C2×D4—261no—
289C2×D4—261no—
290C2×D4—524no—
291C2×D4C22×D1311yescharacteristic
292C2×D4C22×D1311yescharacteristic
293C22×C4—131no—
294C22×C4—131no—
295C22×C4—131no—
296C22×C4—131no—
297C22×C4—131no—
298C22×C4—262no—
299C22×C4—262no—
300C22×C4—261no—
301C22×C4—261no—
302C22×C4C22×D1311yescharacteristic
303SD16—262no—
304SD16—262no—
305D8—22no—
306D8—262no—
307M16—134no—
308M16—262no—
309M16—262no—
310M16—262no—
311C2×C8—22no—
312C2×C8—131no—
313C2×C8—131no—
314C2×C8—262no—
315C2×C8C22×D1311yescharacteristic
316C2×C8C22×D1311yescharacteristic
317C4⋊C4—131no—
318C4⋊C4—131no—
319C4⋊C4—261no—
320C4⋊C4—261no—
321C4⋊C4—261no—
322C4⋊C4C22×D1311yescharacteristic
323C4⋊C4C22×D1311yescharacteristic
324C22⋊C4—21no—
325C22⋊C4—21no—
326C22⋊C4—261no—
327C22⋊C4—261no—
328C22⋊C4—261no—
329C22⋊C4—261no—
330C22⋊C4—261no—
331C22⋊C4—261no—
332C22⋊C4—261no—
333C42—261no—
334C13#305511yescharacteristic, complemented, Sylow
335C23—21no—
336C23—21no—
337C23—131no—
338C23—131no—
339C23—262no—
340C23—262no—
341C23—261no—
342C23—521no—
343C23—522no—
344C23—522no—
345C23—522no—
346C23D4×D1311yescharacteristic
347Q8—261no—
348Q8—261no—
349D4—21no—
350D4—21no—
351D4—21no—
352D4—21no—
353D4—42no—
354D4—42no—
355D4—261no—
356D4—261no—
357D4—522no—
358D4—522no—
359D4—522no—
360D4—522no—
361D4—522no—
362D4—522no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—131no—
368C2×C4—132no—
369C2×C4—132no—
370C2×C4—131no—
371C2×C4—262no—
372C2×C4—262no—
373C2×C4—262no—
374C2×C4—261no—
375C2×C4—261no—
376C2×C4—261no—
377C2×C4—261no—
378C2×C4—261no—
379C2×C4—522no—
380C2×C4—522no—
381C2×C4D4×D1311yescharacteristic
382C2×C4C23×D1311yescharacteristic
383C8—21no—
384C8—132no—
385C8—261no—
386C8D4×D1312yescomplemented
387C22—21no—
388C22—21no—
389C22—41no—
390C22—41no—
391C22—41no—
392C22—41no—
393C22—41no—
394C22—41no—
395C22—132no—
396C22—261no—
397C22—261no—
398C22—261no—
399C22—261no—
400C22—261no—
401C22—524no—
402C22—521no—
403C22—521no—
404C22—521no—
405C22—1044no—
406C22#8816512yescomplemented
407C22C2×D4×D1311yescharacteristic
408C4—21no—
409C4—41no—
410C4—41no—
411C4—132no—
412C4—261no—
413C4—521no—
414C4—521no—
415C4—521no—
416C4C2×D4×D1311yescharacteristic
417C4#41×D1311yescharacteristic
418C2—22no—
419C2—81no—
420C2—81no—
421C2—262no—
422C2—521no—
423C2—1041no—
424C2D13×#12111yescharacteristic
425C2C2×#8816511yescharacteristic
426C2#1171947311yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#466C2
socleC22×C13C22×D4
hypercenter#466D13
hypocenterC13#3055
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #466

Complements

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

NH ≅ G/Ntype
1. C2×#88165C2semidirect
2. C22×#6094C2semidirect
3. #11719311C2semidirect
4. D13×#121C2semidirect
5. C13×#466C2semidirect
6. #11718820C2semidirect
7. #11718775C2semidirect
8. #11718702C2semidirect
9. #11718699C2semidirect
10. #11718547C2semidirect
11. #11718542C2semidirect
12. #11718443C2semidirect
13. #11718441C2semidirect
14. #11718432C2semidirect
15. #11718431C2semidirect
20. C2×C13×D8C22semidirect
21. C22×C8×C13C22semidirect
23. C13×#121C22semidirect
26. #88192C22semidirect
29. C2×#6105C22semidirect
30. C2×#6104C22semidirect
32. #88178C22semidirect
33. C22×#1055C22semidirect
35. C2×#6095C22semidirect
39. C2×#6094C22semidirect
40. C2×#6094C22semidirect
41. #88151C22semidirect
49. C13×#107C22semidirect
50. C13×#102C22semidirect
51. C13×#102C22semidirect
52. #88072C22semidirect
53. #88072C22semidirect
54. #88061C22semidirect
55. #88057C22semidirect
56. #88056C22semidirect
57. #88050C22semidirect
58. #88049C22semidirect
59. #88048C22semidirect
60. #88047C22semidirect
120. #6094D4semidirect
171. C8×C13C2×D4semidirect
173. #1055C2×D4semidirect
183. #466D13semidirect
197. C22×C13AGL(1,ℤ/8)semidirect
228. C2×D8C2×D13semidirect
235. C22×C8C2×D13semidirect
246. #121C2×D13semidirect
254. #107C2×D13semidirect
263. #102C2×D13semidirect
264. #102C2×D13semidirect
334. C13#3055semidirect
386. C8D4×D13semidirect
406. C22#88165semidirect

Maximal subgroups

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

subgroupindex
C2×#881652
C22×#60942
#117193112
D13×#1212
C13×#4662
#117188202
#117187752
#117187022
#117186992
#117185472
#117185422
#117184432
#117184412
#117184322
#117184312
#305513