Finite Group Databasebeta

← #13124972

Subgroups — #13124972

Order 1664.

450 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719262C211yesmaximal, characteristic, complemented
2C4×D4×D13C211yesmaximal, characteristic, complemented
3C13×#442C211yesmaximal, characteristic, complemented
4#11718817C211yesmaximal, characteristic
5#11718814C211yesmaximal, characteristic, complemented
6#11718679C211yesmaximal, characteristic, complemented
7#11718675C211yesmaximal, characteristic, complemented
8#11718532C211yesmaximal, characteristic, complemented
9#11718523C211yesmaximal, characteristic, complemented
10#11718448C211yesmaximal, characteristic, complemented
11#11718437C211yesmaximal, characteristic, complemented
12#11718435C211yesmaximal, characteristic, complemented
13#11718427C211yesmaximal, characteristic, complemented
14#11718371C211yesmaximal, characteristic, complemented
15#11718366C211yesmaximal, characteristic, complemented
16C2×D4×D13C2211yescharacteristic
17C22×C4×D13—21no—
18C2×C13×D8C2211yescharacteristic
19C4×D4×C13C2211yescharacteristic
20C4×D4×C13C2211yescharacteristic, complemented
21#88192C2211yescharacteristic
22#88190C2211yescharacteristic, complemented
23D4×Dic13C2211yescharacteristic
24C2×#6105C2211yescharacteristic
25C2×#6104C2211yescharacteristic
26C4×C22⋊D13—21no—
27C4×C22⋊D13—21no—
28#88180—21no—
29C2×#6095C2211yescharacteristic
30#88151C2211yescharacteristic
31#88147C2211yescharacteristic
32C4⋊C4×D13C2211yescharacteristic
33#88144C2211yescharacteristic, complemented
34#88137—21no—
35#88135—21no—
36C22⋊C4×D13—21no—
37#88133—21no—
38C4×D52C2211yescharacteristic
39C42×D13C2211yescharacteristic
40C4×Dic26C2211yescharacteristic, complemented
41C13×#106C2211yescharacteristic, complemented
42C13×#102C2211yescharacteristic
43C13×#102C2211yescharacteristic, complemented
44C13×#97C2211yescharacteristic, complemented
45#88072C2211yescharacteristic
46#88072C2211yescharacteristic, complemented
47#88061C2211yescharacteristic
48#88060C2211yescharacteristic
49#88060C2211yescharacteristic
50#88058C2211yescharacteristic, complemented
51#88056C2211yescharacteristic, complemented
52#88054C2211yescharacteristic, complemented
53#88054C2211yescharacteristic, complemented
54#88050C2211yescharacteristic, complemented
55#88049C2211yescharacteristic
56#88048C2211yescharacteristic, complemented
57#88047C2211yescharacteristic, complemented
58#88043C2211yescharacteristic, complemented
59C23×D13—21no—
60C2×D4×C13C2311yescharacteristic
61C2×D4×C13C2311yescharacteristic
62C22×C4×C13—21no—
63C22×C4×C13—21no—
64C2×C22⋊D13—21no—
65C2×C22⋊D13—21no—
66C22×Dic13—21no—
67D4×D13—22no—
68D4×D13—22no—
69C2×D52C2311yescharacteristic
70C2×C4×D13—21no—
71C2×C4×D13—21no—
72C2×C4×D13—21no—
73C2×C4×D13—44no—
74C2×C4×D13D411yescharacteristic
75C2×C4×D13D411yescharacteristic
76C2×C4×D13C2311yescharacteristic
77C2×Dic26C2311yescharacteristic
78C13×D8—22no—
79C2×C8×C13C2311yescharacteristic
80C2×C8×C13C2311yescharacteristic
81C13×C4⋊C4C2311yescharacteristic
82C13×C4⋊C4C2311yescharacteristic
83C13×C22⋊C4—21no—
84C13×C22⋊C4—21no—
85C42×C13C2311yescharacteristic
86C22⋊Dic13—21no—
87C22⋊Dic13—21no—
88C22⋊Dic13—21no—
89C22⋊Dic13—21no—
90#6105—22no—
91#6104—22no—
92#6103—21no—
93#6103—21no—
94#6103—21no—
95C4⋊Dic13—21no—
96C4⋊Dic13—21no—
97C4⋊Dic13C2311yescharacteristic
98C4⋊Dic13C2311yescharacteristic
99#6101—21no—
100#6101—21no—
101#6101—21no—
102C4×Dic13—21no—
103C4×Dic13D411yescharacteristic
104C4×Dic13D411yescharacteristic
105C4×Dic13C2311yescharacteristic
106C2×#1055C2311yescharacteristic
107C2×#1055C2311yescharacteristic
108#6095—22no—
109#3114—131nomaximal, Sylow
110C23×C13—21no—
111C23×C13—21no—
112C22×D13—24no—
113C22×D13—21no—
114C22×D13—42no—
115C22×D13—42no—
116C22×D13C2×D411yescharacteristic
117D4×C13—21no—
118D4×C13—21no—
119D4×C13—21no—
120D4×C13#4112yes—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—42no—
124C2×C4×C13—42no—
125C2×C4×C13C2×D411yescharacteristic
126C2×C4×C13C2×D411yescharacteristic
127C2×C4×C13C2411yescharacteristic
128C22⋊D13—24no—
129C22⋊D13—42no—
130C2×Dic13—21no—
131C2×Dic13—21no—
132C2×Dic13—21no—
133C2×Dic13—42no—
134C2×Dic13C2×D411yescharacteristic
135C2×Dic13C2×D411yescharacteristic
136C2×Dic13C2×D411yescharacteristic
137D52—21no—
138D52#4112yes—
139C4×D13—22no—
140C4×D13—21no—
141C4×D13—21no—
142C4×D13—41no—
143C4×D13—42no—
144C4×D13—42no—
145C4×D13—42no—
146Dic26—21no—
147Dic26—21no—
148C8×C13—21no—
149C8×C13—21no—
150#1055—21no—
151#1055—21no—
152#529—131no—
153C2×C4×D4—131no—
154#483—131no—
155#480—131no—
156#478—131no—
157#478—131no—
158#463—131no—
159#463—131no—
160#450—131no—
161#447—131no—
162#442—131no—
163#442D1311yescharacteristic, complemented
164#440—131no—
165#440—131no—
166#432—131no—
167C22×C13—22no—
168C22×C13—41no—
169C22×C13—41no—
170C22×C13—41no—
171C22×C13—41no—
172C22×C13—41no—
173C22×C13C22×D411yescharacteristic
174C2×D13—21no—
175C2×D13—21no—
176C2×D13—22no—
177C2×D13—48no—
178C2×D13—41no—
179C2×D13—41no—
180C2×D13AGL(1,ℤ/8)12yes—
181C4×C13—21no—
182C4×C13—21no—
183C4×C13—41no—
184C4×C13—41no—
185C4×C13C2×#4111yescharacteristic
186C4×C13C2×#4111yescharacteristic
187Dic13—21no—
188Dic13—21no—
189Dic13—21no—
190Dic13—41no—
191Dic13—41no—
192Dic13—41no—
193C22×D4—131no—
194C23×C4—261no—
195C2×SD16—131no—
196C2×SD16—131no—
197C2×D8—131no—
198C2×D8C2×D1311yescharacteristic
199#126—261no—
200#125—131no—
201#124—131no—
202#123—261no—
203C22⋊Q8—131no—
204#121—131no—
205C4×Q8—131no—
206C4×D4—131no—
207C4×D4—131no—
208C4×D4—131no—
209C4×D4—261no—
210C4×D4—261no—
211C4×D4—261no—
212C4×D4C2×D1311yescharacteristic
213C4×D4C2×D1311yescharacteristic, complemented
214#117—261no—
215C2×C4⋊C4—131no—
216C2×C22⋊C4—261no—
217C2×C42—131no—
218#107—131no—
219#107—131no—
220#106—131no—
221#106C2×D1311yescharacteristic, complemented
222C4⋊C8—131no—
223C4⋊C8—131no—
224#103—131no—
225#103—131no—
226#102—131no—
227#102—131no—
228#102—131no—
229#102—131no—
230#102C2×D1311yescharacteristic
231#102C2×D1311yescharacteristic, complemented
232C22⋊C8—131no—
233C22⋊C8—131no—
234#97—131no—
235#97C2×D1311yescharacteristic, complemented
236C2×C13—42no—
237C2×C13—81no—
238C2×C13#52511yescharacteristic
239C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
240C2×C13#57511yescharacteristic
241D13—22no—
242D13—42no—
243C24—261no—
244C2×Q8—131no—
245C2×D4—131no—
246C2×D4—261no—
247C2×D4—262no—
248C2×D4—262no—
249C2×D4—261no—
250C2×D4C22×D1311yescharacteristic
251C2×D4C22×D1311yescharacteristic
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—131no—
255C22×C4—131no—
256C22×C4—131no—
257C22×C4—261no—
258C22×C4—261no—
259C22×C4—261no—
260C22×C4—261no—
261C22×C4—524no—
262SD16—262no—
263SD16—262no—
264D8—22no—
265D8—262no—
266C2×C8—131no—
267C2×C8—131no—
268C2×C8C22×D1311yescharacteristic
269C2×C8C22×D1311yescharacteristic
270C4⋊C4—131no—
271C4⋊C4—131no—
272C4⋊C4—261no—
273C4⋊C4—261no—
274C4⋊C4—261no—
275C4⋊C4—261no—
276C4⋊C4—261no—
277C4⋊C4C22×D1311yescharacteristic
278C4⋊C4C22×D1311yescharacteristic
279C22⋊C4—21no—
280C22⋊C4—21no—
281C22⋊C4—261no—
282C22⋊C4—261no—
283C22⋊C4—261no—
284C22⋊C4—261no—
285C22⋊C4—261no—
286C22⋊C4—261no—
287C22⋊C4—261no—
288C42—131no—
289C42—131no—
290C42—131no—
291C42—261no—
292C42C22×D1311yescharacteristic
293C13#311411yescharacteristic, complemented, Sylow
294C23—21no—
295C23—21no—
296C23—131no—
297C23—264no—
298C23—261no—
299C23—522no—
300C23—522no—
301Q8—261no—
302Q8—261no—
303D4—21no—
304D4—21no—
305D4—21no—
306D4—132no—
307D4—264no—
308D4—261no—
309D4—522no—
310D4#612712yes—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—131no—
316C2×C4—131no—
317C2×C4—131no—
318C2×C4—262no—
319C2×C4—261no—
320C2×C4—261no—
321C2×C4—261no—
322C2×C4—261no—
323C2×C4—261no—
324C2×C4—521no—
325C2×C4—522no—
326C2×C4—522no—
327C2×C4—522no—
328C2×C4—522no—
329C2×C4D4×D1311yescharacteristic
330C2×C4D4×D1311yescharacteristic
331C2×C4C23×D1311yescharacteristic
332C8—21no—
333C8—21no—
334C8—261no—
335C8—261no—
336C22—22no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—41no—
342C22—132no—
343C22—261no—
344C22—261no—
345C22—262no—
346C22—528no—
347C22—521no—
348C22—521no—
349C22C2×D4×D1311yescharacteristic
350C4—21no—
351C4—21no—
352C4—41no—
353C4—41no—
354C4—261no—
355C4—261no—
356C4—261no—
357C4—521no—
358C4—521no—
359C4—521no—
360C4C2×#612711yescharacteristic
361C4#41×D1311yescharacteristic
362C2—42no—
363C2—81no—
364C2—262no—
365C2—522no—
366C2#1171925211yescharacteristic
367C2D13×AGL(1,ℤ/8)11yescharacteristic
368C2#1171947811yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#442C2
socleC22×C13C22×D4
prime radical#11718817C2
hypercenter#442D13
hypocenterC13#3114
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
1. #11719262C2semidirect
2. C4×D4×D13C2semidirect
3. C13×#442C2semidirect
5. #11718814C2semidirect
6. #11718679C2semidirect
7. #11718675C2semidirect
8. #11718532C2semidirect
9. #11718523C2semidirect
10. #11718448C2semidirect
11. #11718437C2semidirect
12. #11718435C2semidirect
13. #11718427C2semidirect
14. #11718371C2semidirect
15. #11718366C2semidirect
20. C4×D4×C13C22semidirect
22. #88190C22semidirect
33. #88144C22semidirect
40. C4×Dic26C22semidirect
41. C13×#106C22semidirect
43. C13×#102C22semidirect
44. C13×#97C22semidirect
46. #88072C22semidirect
50. #88058C22semidirect
51. #88056C22semidirect
52. #88054C22semidirect
53. #88054C22semidirect
54. #88050C22semidirect
56. #88048C22semidirect
57. #88047C22semidirect
58. #88043C22semidirect
163. #442D13semidirect
213. C4×D4C2×D13semidirect
221. #106C2×D13semidirect
231. #102C2×D13semidirect
235. #97C2×D13semidirect
293. C13#3114semidirect

Maximal subgroups

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

subgroupindex
#117192622
C4×D4×D132
C13×#4422
#117188172
#117188142
#117186792
#117186752
#117185322
#117185232
#117184482
#117184372
#117184352
#117184272
#117183712
#117183662
#311413