Finite Group Databasebeta

← #13124473

Subgroups — #13124473

Order 1664.

492 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×SD16×D13C211yesmaximal, characteristic, complemented
2C2×#88161C211yesmaximal, characteristic, complemented
3#11719333C211yesmaximal, characteristic, complemented
4#11719312C211yesmaximal, characteristic
5C13×#468C211yesmaximal, characteristic, complemented
6#11718835C211yesmaximal, characteristic, complemented
7#11718795C211yesmaximal, characteristic, complemented
8#11718709C211yesmaximal, characteristic, complemented
9#11718702C211yesmaximal, characteristic, complemented
10#11718547C211yesmaximal, characteristic, complemented
11#11718541C211yesmaximal, characteristic, complemented
12#11718468C211yesmaximal, characteristic, complemented
13#11718463C211yesmaximal, characteristic, complemented
14#11718439C211yesmaximal, characteristic, complemented
15#11718431C211yesmaximal, characteristic, complemented
16C2×Q8×D13C2211yescharacteristic
17C2×D4×D13C2211yescharacteristic
18C2×#6127C2211yescharacteristic
19C2×C13×SD16C2211yescharacteristic
20C2×C13×M16C2211yescharacteristic, complemented
21C13×C22⋊Q8C2211yescharacteristic, complemented
22C13×#121C2211yescharacteristic
23#88200C2211yescharacteristic, complemented
24C2×#6106C2211yescharacteristic
25#88194—21no—
26#88192C2211yescharacteristic
27#88191—21no—
28C2×#6105C2211yescharacteristic
29#88184C2211yescharacteristic
30#88178C2211yescharacteristic, complemented
31C22×#1055C2211yescharacteristic, complemented
32SD16×D13—24no—
33#88161—24no—
34C2×#6095C2211yescharacteristic
35C2×#6094C2211yescharacteristic
36C2×#6094C2211yescharacteristic, complemented
37C2×C8×D13C2211yescharacteristic
38C2×C8×D13C2211yescharacteristic, complemented
39#88151C2211yescharacteristic, complemented
40#88149C2211yescharacteristic
41#88148—21no—
42#88146C2211yescharacteristic
43#88146C2211yescharacteristic
44#88142—21no—
45#88139—21no—
46#88139—21no—
47#88137—21no—
48#88136—21no—
49C13×#107C2211yescharacteristic, complemented
50C13×#103C2211yescharacteristic, complemented
51C13×#102C2211yescharacteristic
52#88075C2211yescharacteristic, complemented
53#88072C2211yescharacteristic
54#88061C2211yescharacteristic
55#88058C2211yescharacteristic, complemented
56#88056C2211yescharacteristic, complemented
57#88050C2211yescharacteristic, complemented
58#88049C2211yescharacteristic
59#88048C2211yescharacteristic, complemented
60#88048C2211yescharacteristic, complemented
61C23×D13—21no—
62C2×Q8×C13C2311yescharacteristic
63C2×D4×C13—21no—
64C2×D4×C13C2311yescharacteristic
65C22×C4×C13C2311yescharacteristic
66C2×C22⋊D13—21no—
67C2×C22⋊D13—21no—
68C2×C22⋊D13—21no—
69C2×C22⋊D13D411yescharacteristic
70C2×C22⋊D13D411yescharacteristic
71Q8×D13—22no—
72Q8×D13—22no—
73D4×D13—22no—
74D4×D13—22no—
75#6127—22no—
76#6127—22no—
77C2×D52—21no—
78C2×D52D411yescharacteristic
79C2×D52C2311yescharacteristic
80C2×C4×D13—21no—
81C2×C4×D13C2311yescharacteristic
82C2×C4×D13C2311yescharacteristic
83C2×Dic26—21no—
84C2×Dic26D411yescharacteristic
85C2×Dic26C2311yescharacteristic
86C13×SD16—22no—
87C13×M16—22no—
88C2×C8×C13C2311yescharacteristic
89C2×C8×C13C2311yescharacteristic
90C13×C4⋊C4—21no—
91C13×C4⋊C4C2311yescharacteristic
92C13×C4⋊C4C2311yescharacteristic
93C13×C22⋊C4—21no—
94C13×C22⋊C4—21no—
95C22⋊Dic13—21no—
96C22⋊Dic13—21no—
97#6106—22no—
98#6105—22no—
99#6103—21no—
100#6103—21no—
101#6103—21no—
102#6103—21no—
103#6103—21no—
104#6103—21no—
105C4⋊Dic13—21no—
106C4⋊Dic13C2311yescharacteristic
107C4⋊Dic13C2311yescharacteristic
108#6101—21no—
109#6101—21no—
110C4×Dic13—21no—
111C4×Dic13—21no—
112C2×#1055—22no—
113C2×#1055C2311yescharacteristic
114C2×#1055C2311yescharacteristic
115#6095—22no—
116#6094—22no—
117#6094—22no—
118C8×D13—22no—
119C8×D13D414yescomplemented
120#3057—131nomaximal, Sylow
121C23×C13—21no—
122C23×C13C2×D411yescharacteristic
123C22×D13—21no—
124C22×D13—42no—
125C22×D13—81no—
126C22×D13—81no—
127C22×D13C2×D411yescharacteristic
128C22×D13C2×D411yescharacteristic
129Q8×C13—21no—
130Q8×C13—21no—
131D4×C13—21no—
132D4×C13—21no—
133D4×C13—81no—
134C2×C4×C13—21no—
135C2×C4×C13—21no—
136C2×C4×C13—21no—
137C2×C4×C13—21no—
138C2×C4×C13—21no—
139C2×C4×C13C2×D411yescharacteristic
140C2×C4×C13C2411yescharacteristic
141C22⋊D13—22no—
142C22⋊D13—22no—
143C22⋊D13—42no—
144C22⋊D13—81no—
145C22⋊D13—81no—
146C2×Dic13—21no—
147C2×Dic13—21no—
148C2×Dic13—21no—
149C2×Dic13C2×D411yescharacteristic
150C2×Dic13C2×D411yescharacteristic
151D52—22no—
152D52—21no—
153D52—21no—
154D52—81no—
155C4×D13—21no—
156C4×D13—21no—
157C4×D13—42no—
158C4×D13C2×D412yes—
159C4×D13#4112yes—
160Dic26—22no—
161Dic26—21no—
162Dic26—21no—
163Dic26—42no—
164C8×C13—21no—
165C8×C13C2×D412yes—
166#1055—21no—
167#1055C2×D412yes—
168C22×SD16—131no—
169C2×#131—131no—
170#536—131no—
171#535—131no—
172#468—131no—
173#468—131no—
174#468—131no—
175#468D1311yescharacteristic, complemented
176#465—131no—
177#465—131no—
178#465—131no—
179#465—131no—
180#427—131no—
181#419—131no—
182#418—131no—
183C22×C13—21no—
184C22×C13—21no—
185C22×C13—21no—
186C22×C13—41no—
187C22×C13—41no—
188C22×C13—41no—
189C22×C13C22×D411yescharacteristic
190C2×D13—21no—
191C2×D13—21no—
192C2×D13—21no—
193C2×D13—21no—
194C2×D13—21no—
195C2×D13—41no—
196C2×D13—41no—
197C2×D13—41no—
198C2×D13—84no—
199C2×D13#12112yes—
200C4×C13—21no—
201C4×C13—41no—
202C4×C13—41no—
203C4×C13—41no—
204C4×C13C22×D411yescharacteristic
205C4×C13C2×#4111yescharacteristic
206Dic13—21no—
207Dic13—41no—
208Dic13—41no—
209Dic13—41no—
210Dic13#12112yes—
211C2×#41—131no—
212C22×Q8—131no—
213C22×D4—131no—
214C2×SD16—131no—
215C2×SD16—131no—
216C2×SD16—131no—
217C2×SD16—264no—
218C2×SD16C2×D1311yescharacteristic
219#131—264no—
220C2×M16—131no—
221C2×M16—131no—
222C2×M16C2×D1311yescharacteristic, complemented
223C22×C8—131no—
224C22×C8—131no—
225C22×C8—131no—
226C4⋊Q8—261no—
227#127—261no—
228#124—261no—
229#124—261no—
230#123—261no—
231#123—261no—
232C22⋊Q8—131no—
233C22⋊Q8—131no—
234C22⋊Q8—131no—
235C22⋊Q8C2×D1311yescharacteristic, complemented
236#121—131no—
237#121—131no—
238#121—131no—
239#121C2×D1311yescharacteristic
240#120—261no—
241#120—261no—
242#117—131no—
243#117—131no—
244#107—131no—
245#107C2×D1311yescharacteristic, complemented
246#106—131no—
247#106—131no—
248#103—131no—
249#103—131no—
250#103—131no—
251#103C2×D1311yescharacteristic, complemented
252#102—131no—
253#102—131no—
254#102—131no—
255#102C2×D1311yescharacteristic
256C2×C13—41no—
257C2×C13—81no—
258C2×C13C2×#12111yescharacteristic
259C2×C13#57711yescharacteristic
260C2×C13#57711yescharacteristic
261D13—22no—
262D13—41no—
263D13—81no—
264C24—261no—
265#41—262no—
266#41—262no—
267C2×Q8—131no—
268C2×Q8—131no—
269C2×Q8—261no—
270C2×Q8—262no—
271C2×Q8—262no—
272C2×Q8C22×D1311yescharacteristic
273C2×D4—21no—
274C2×D4—131no—
275C2×D4—131no—
276C2×D4—131no—
277C2×D4—131no—
278C2×D4—261no—
279C2×D4—262no—
280C2×D4—262no—
281C2×D4—261no—
282C2×D4—261no—
283C2×D4—261no—
284C2×D4C22×D1311yescharacteristic
285C22×C4—131no—
286C22×C4—131no—
287C22×C4—261no—
288C22×C4C22×D1311yescharacteristic
289SD16—22no—
290SD16—262no—
291SD16—262no—
292SD16—262no—
293M16—22no—
294M16—262no—
295M16—262no—
296C2×C8—131no—
297C2×C8—134no—
298C2×C8—131no—
299C2×C8—262no—
300C2×C8—262no—
301C2×C8C22×D1311yescharacteristic
302C2×C8C22×D1311yescharacteristic
303C4⋊C4—21no—
304C4⋊C4—131no—
305C4⋊C4—131no—
306C4⋊C4—261no—
307C4⋊C4—261no—
308C4⋊C4—261no—
309C4⋊C4C22×D1311yescharacteristic
310C4⋊C4C22×D1311yescharacteristic
311C22⋊C4—21no—
312C22⋊C4—21no—
313C22⋊C4—261no—
314C22⋊C4—261no—
315C22⋊C4—261no—
316C22⋊C4—261no—
317C22⋊C4—261no—
318C22⋊C4—261no—
319C22⋊C4—261no—
320C22⋊C4—261no—
321C42—261no—
322C42—261no—
323C13#305711yescharacteristic, complemented, Sylow
324C23—21no—
325C23—131no—
326C23—131no—
327C23—261no—
328C23—522no—
329C23—1041no—
330C23—1041no—
331C23D4×D1311yescharacteristic
332Q8—21no—
333Q8—21no—
334Q8—262no—
335Q8—261no—
336Q8—261no—
337Q8—522no—
338D4—21no—
339D4—21no—
340D4—81no—
341D4—262no—
342D4—262no—
343D4—262no—
344D4—261no—
345D4—261no—
346D4—522no—
347D4—1041no—
348D4—1041no—
349D4—1041no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—131no—
356C2×C4—132no—
357C2×C4—132no—
358C2×C4—131no—
359C2×C4—261no—
360C2×C4—261no—
361C2×C4—261no—
362C2×C4—261no—
363C2×C4—261no—
364C2×C4—522no—
365C2×C4D4×D1311yescharacteristic
366C2×C4C23×D1311yescharacteristic
367C8—21no—
368C8—132no—
369C8—261no—
370C8D4×D1312yes—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—132no—
378C22—261no—
379C22—261no—
380C22—261no—
381C22—261no—
382C22—261no—
383C22—521no—
384C22—521no—
385C22—521no—
386C22—1044no—
387C22C2×D4×D1311yescharacteristic
388C4—21no—
389C4—41no—
390C4—41no—
391C4—41no—
392C4—132no—
393C4—261no—
394C4—521no—
395C4—521no—
396C4—521no—
397C4C2×D4×D1311yescharacteristic
398C4#41×D1311yescharacteristic
399C2—41no—
400C2—81no—
401C2—262no—
402C2—521no—
403C2—1041no—
404C2D13×#12111yescharacteristic
405C2#1171948011yescharacteristic
406C2#1171948311yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#468C2
socleC22×C13C22×D4
prime radical#11719312C2
hypercenter#468D13
hypocenterC13#3057
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. C2×SD16×D13C2semidirect
2. C2×#88161C2semidirect
3. #11719333C2semidirect
5. C13×#468C2semidirect
6. #11718835C2semidirect
7. #11718795C2semidirect
8. #11718709C2semidirect
9. #11718702C2semidirect
10. #11718547C2semidirect
11. #11718541C2semidirect
12. #11718468C2semidirect
13. #11718463C2semidirect
14. #11718439C2semidirect
15. #11718431C2semidirect
20. C2×C13×M16C22semidirect
21. C13×C22⋊Q8C22semidirect
23. #88200C22semidirect
30. #88178C22semidirect
31. C22×#1055C22semidirect
36. C2×#6094C22semidirect
38. C2×C8×D13C22semidirect
39. #88151C22semidirect
49. C13×#107C22semidirect
50. C13×#103C22semidirect
52. #88075C22semidirect
55. #88058C22semidirect
56. #88056C22semidirect
57. #88050C22semidirect
59. #88048C22semidirect
60. #88048C22semidirect
119. C8×D13D4semidirect
175. #468D13semidirect
222. C2×M16C2×D13semidirect
235. C22⋊Q8C2×D13semidirect
245. #107C2×D13semidirect
251. #103C2×D13semidirect
323. C13#3057semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×D132
C2×#881612
#117193332
#117193122
C13×#4682
#117188352
#117187952
#117187092
#117187022
#117185472
#117185412
#117184682
#117184632
#117184392
#117184312
#305713