Finite Group Databasebeta

← #13125187

Subgroups — #13125187

Order 1664.

404 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719434C211yesmaximal, characteristic, complemented
2#11719379C211yesmaximal, characteristic
3C13×#489C211yesmaximal, characteristic, complemented
4#11718749C211yesmaximal, characteristic, complemented
5#11718717C211yesmaximal, characteristic, complemented
6#11718465C211yesmaximal, characteristic, complemented
7#11718464C211yesmaximal, characteristic, complemented
8#11718461C211yesmaximal, characteristic, complemented
9#11718456C211yesmaximal, characteristic, complemented
10#11718431C211yesmaximal, characteristic, complemented
11D13×#102C211yesmaximal, characteristic, complemented
12#11718425C211yesmaximal, characteristic, complemented
13#11718421C211yesmaximal, characteristic, complemented
14#11718374C211yesmaximal, characteristic, complemented
15#11718369C211yesmaximal, characteristic, complemented
16C2×#6131C2211yescharacteristic
17C2×D4×D13C2211yescharacteristic
18C13×C4⋊Q8C2211yescharacteristic, complemented
19C13×#124C2211yescharacteristic
20#88201C2211yescharacteristic
21#88200—21no—
22#88198—21no—
23#88194C2211yescharacteristic
24C2×#6094C2211yescharacteristic
25C2×C8×D13C2211yescharacteristic
26#88150—21no—
27#88146C2211yescharacteristic
28C4⋊C4×D13C2211yescharacteristic
29#88144C2211yescharacteristic, complemented
30#88143—21no—
31#88142C2211yescharacteristic, complemented
32#88138—21no—
33#88138—21no—
34#88136—21no—
35#88136—21no—
36#88128C2211yescharacteristic
37#88126C2211yescharacteristic
38#88124C2211yescharacteristic, complemented
39C13×#103C2211yescharacteristic, complemented
40C13×#103C2211yescharacteristic, complemented
41C13×#102C2211yescharacteristic
42C13×#102C2211yescharacteristic
43C13×#97C2211yescharacteristic, complemented
44#88075C2211yescharacteristic, complemented
45#88075C2211yescharacteristic, complemented
46#88072C2211yescharacteristic
47#88072C2211yescharacteristic
48#88061C2211yescharacteristic
49#88061C2211yescharacteristic
50#88061C2211yescharacteristic, complemented
51#88061C2211yescharacteristic, complemented
52#88055C2211yescharacteristic, complemented
53C8×Dic13C2211yescharacteristic, complemented
54#88049C2211yescharacteristic
55#88049C2211yescharacteristic
56#88049C2211yescharacteristic, complemented
57#88049C2211yescharacteristic, complemented
58C4×#1055C2211yescharacteristic, complemented
59C23×D13—21no—
60C2×Q8×C13—21no—
61C2×Q8×C13C2311yescharacteristic
62C2×D4×C13C2311yescharacteristic
63C2×C22⋊D13—21no—
64C2×C22⋊D13—21no—
65C2×C22⋊D13—21no—
66#6131—22no—
67#6131—22no—
68D4×D13—22no—
69D4×D13—22no—
70C2×D52—21no—
71C2×D52—21no—
72C2×D52—21no—
73C2×D52C2311yescharacteristic
74C2×D52C2311yescharacteristic
75C2×C4×D13—21no—
76C2×C4×D13—21no—
77C2×C4×D13C2311yescharacteristic
78C2×Dic26—21no—
79C2×C8×C13C2311yescharacteristic
80C2×C8×C13C2311yescharacteristic
81C13×C4⋊C4—21no—
82C13×C4⋊C4C2311yescharacteristic
83C13×C4⋊C4C2311yescharacteristic
84C13×C22⋊C4—21no—
85C13×C22⋊C4—21no—
86C42×C13C2311yescharacteristic
87#6103—21no—
88#6103—21no—
89#6103—21no—
90#6103D411yescharacteristic
91#6103D411yescharacteristic
92C4⋊Dic13—21no—
93C4⋊Dic13C2311yescharacteristic
94C4⋊Dic13C2311yescharacteristic
95#6101—21no—
96#6101—21no—
97#6101—21no—
98#6101—21no—
99#6101—21no—
100#6101D411yescharacteristic
101#6101D411yescharacteristic
102C4×Dic13—21no—
103C4×Dic13C2311yescharacteristic
104C2×#1055C2311yescharacteristic
105C2×#1055C2311yescharacteristic
106#6094—22no—
107C8×D13—22no—
108#3136—131nomaximal, Sylow
109C23×C13—21no—
110C22×D13—21no—
111C22×D13—21no—
112C22×D13—42no—
113C22×D13—81no—
114C22×D13—81no—
115C22×D13C2×D411yescharacteristic
116Q8×C13—21no—
117Q8×C13—21no—
118Q8×C13—81no—
119D4×C13—21no—
120D4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13C2×D411yescharacteristic
125C2×C4×C13C2×D411yescharacteristic
126C2×C4×C13C2411yescharacteristic
127C22⋊D13—42no—
128C22⋊D13—81no—
129C22⋊D13—81no—
130C2×Dic13—21no—
131C2×Dic13—21no—
132C2×Dic13C2×D411yescharacteristic
133C2×Dic13C2×D411yescharacteristic
134C2×Dic13C2×D411yescharacteristic
135D52—21no—
136D52—21no—
137D52—21no—
138D52—21no—
139D52—42no—
140D52—81no—
141D52—81no—
142C4×D13—42no—
143C4×D13—81no—
144C4×D13#4112yes—
145C4×D13#4112yes—
146Dic26—81no—
147C8×C13—21no—
148C8×C13—21no—
149#1055—21no—
150#1055—21no—
151#544—131no—
152#535—131no—
153#490—131no—
154#490—131no—
155#489—131no—
156#489D1311yescharacteristic, complemented
157#488—131no—
158#488—131no—
159#486—131no—
160#486—131no—
161#418—131no—
162#417—131no—
163#416—131no—
164C2×#102—131no—
165#405—131no—
166C22×C13—41no—
167C22×C13—41no—
168C22×C13—41no—
169C22×C13C22×D411yescharacteristic
170C2×D13—21no—
171C2×D13—21no—
172C2×D13—41no—
173C2×D13—41no—
174C2×D13—41no—
175C2×D13—41no—
176C2×D13—41no—
177C2×D13—41no—
178C2×D13—84no—
179C2×D13#12412yes—
180C4×C13—21no—
181C4×C13—21no—
182C4×C13—41no—
183C4×C13—41no—
184C4×C13—41no—
185C4×C13C2×#4111yescharacteristic
186C4×C13C2×#4111yescharacteristic
187Dic13—21no—
188Dic13—21no—
189Dic13—41no—
190Dic13—41no—
191Dic13#12412yes—
192C2×#41—131no—
193C22×D4—131no—
194C2×M16—131no—
195C22×C8—131no—
196C4⋊Q8—131no—
197C4⋊Q8—261no—
198C4⋊Q8C2×D1311yescharacteristic, complemented
199#127—131no—
200#127—131no—
201#125—131no—
202#125—131no—
203#125—261no—
204#124—131no—
205#124C2×D1311yescharacteristic
206C22⋊Q8—261no—
207C22⋊Q8—261no—
208#121—261no—
209#121—261no—
210#120—261no—
211#120—261no—
212#117—131no—
213#117—131no—
214C2×C4⋊C4—131no—
215#103—131no—
216#103—131no—
217#103C2×D1311yescharacteristic, complemented
218#103C2×D1311yescharacteristic, complemented
219#102—131no—
220#102—131no—
221#102—131no—
222#102—131no—
223#102—131no—
224#102—131no—
225#102—131no—
226#102—131no—
227#102—131no—
228#102—131no—
229#102C2×D1311yescharacteristic
230#102C2×D1311yescharacteristic
231#97—131no—
232#97C2×D1311yescharacteristic, complemented
233C4×C8—131no—
234C4×C8—131no—
235C2×C13—81no—
236C2×C13C2×#12411yescharacteristic
237C2×C13#57611yescharacteristic
238C2×C13#57711yescharacteristic
239D13—22no—
240D13—81no—
241D13—81no—
242C24—261no—
243#41—262no—
244#41—262no—
245C2×Q8—21no—
246C2×Q8—261no—
247C2×Q8C22×D1311yescharacteristic
248C2×D4—131no—
249C2×D4—131no—
250C2×D4—261no—
251C2×D4—262no—
252C2×D4—262no—
253C2×D4—261no—
254C2×D4—261no—
255C2×D4—261no—
256C2×D4—261no—
257C2×D4—261no—
258C2×D4C22×D1311yescharacteristic
259C22×C4—131no—
260C22×C4—261no—
261C22×C4—261no—
262M16—262no—
263C2×C8—131no—
264C2×C8—131no—
265C2×C8—262no—
266C2×C8C22×D1311yescharacteristic
267C2×C8C22×D1311yescharacteristic
268C4⋊C4—21no—
269C4⋊C4—131no—
270C4⋊C4—131no—
271C4⋊C4—131no—
272C4⋊C4—131no—
273C4⋊C4—261no—
274C4⋊C4—261no—
275C4⋊C4—261no—
276C4⋊C4—261no—
277C4⋊C4—261no—
278C4⋊C4—261no—
279C4⋊C4C22×D1311yescharacteristic
280C4⋊C4C22×D1311yescharacteristic
281C22⋊C4—21no—
282C22⋊C4—21no—
283C22⋊C4—131no—
284C22⋊C4—131no—
285C22⋊C4—261no—
286C22⋊C4—261no—
287C22⋊C4—261no—
288C42—131no—
289C42—261no—
290C42C22×D1311yescharacteristic
291C13#313611yescharacteristic, complemented, Sylow
292C23—21no—
293C23—131no—
294C23—261no—
295C23—261no—
296C23—522no—
297C23—1041no—
298C23—1041no—
299Q8—21no—
300Q8—21no—
301Q8—81no—
302Q8—1041no—
303D4—21no—
304D4—21no—
305D4—261no—
306D4—261no—
307D4—261no—
308D4—261no—
309D4—522no—
310D4—522no—
311D4—1041no—
312D4—1041no—
313D4—1041no—
314D4—1041no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—131no—
319C2×C4—132no—
320C2×C4—132no—
321C2×C4—131no—
322C2×C4—131no—
323C2×C4—261no—
324C2×C4—261no—
325C2×C4—522no—
326C2×C4—1041no—
327C2×C4D4×D1311yescharacteristic
328C2×C4D4×D1311yescharacteristic
329C2×C4C23×D1311yescharacteristic
330C8—21no—
331C8—21no—
332C8—261no—
333C8—261no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—132no—
338C22—261no—
339C22—261no—
340C22—521no—
341C22—521no—
342C22—521no—
343C22—521no—
344C22—521no—
345C22—521no—
346C22—1044no—
347C22C2×D4×D1311yescharacteristic
348C4—21no—
349C4—21no—
350C4—41no—
351C4—41no—
352C4—41no—
353C4—132no—
354C4—261no—
355C4—261no—
356C4—521no—
357C4—521no—
358C4#41×D1311yescharacteristic
359C4#41×D1311yescharacteristic
360C2—81no—
361C2—262no—
362C2—1041no—
363C2—1041no—
364C2D13×#12411yescharacteristic
365C2#1171947911yescharacteristic
366C2#1171948311yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#489C2
socleC22×C13C22×D4
prime radical#11719379C2
hypercenter#489D13
hypocenterC13#3136
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
1. #11719434C2semidirect
3. C13×#489C2semidirect
4. #11718749C2semidirect
5. #11718717C2semidirect
6. #11718465C2semidirect
7. #11718464C2semidirect
8. #11718461C2semidirect
9. #11718456C2semidirect
10. #11718431C2semidirect
11. D13×#102C2semidirect
12. #11718425C2semidirect
13. #11718421C2semidirect
14. #11718374C2semidirect
15. #11718369C2semidirect
18. C13×C4⋊Q8C22semidirect
29. #88144C22semidirect
31. #88142C22semidirect
38. #88124C22semidirect
39. C13×#103C22semidirect
40. C13×#103C22semidirect
43. C13×#97C22semidirect
44. #88075C22semidirect
45. #88075C22semidirect
50. #88061C22semidirect
51. #88061C22semidirect
52. #88055C22semidirect
53. C8×Dic13C22semidirect
56. #88049C22semidirect
57. #88049C22semidirect
58. C4×#1055C22semidirect
156. #489D13semidirect
198. C4⋊Q8C2×D13semidirect
217. #103C2×D13semidirect
218. #103C2×D13semidirect
232. #97C2×D13semidirect
291. C13#3136semidirect

Maximal subgroups

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

subgroupindex
#117194342
#117193792
C13×#4892
#117187492
#117187172
#117184652
#117184642
#117184612
#117184562
#117184312
D13×#1022
#117184252
#117184212
#117183742
#117183692
#313613