Finite Group Databasebeta

← #13125017

Subgroups — #13125017

Order 1664.

406 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719387C211yesmaximal, characteristic, complemented
2#11719250C211yesmaximal, characteristic, complemented
3C13×#463C211yesmaximal, characteristic, complemented
4#11718830C211yesmaximal, characteristic, complemented
5#11718825C211yesmaximal, characteristic, complemented
6#11718817C211yesmaximal, characteristic
7D8×Dic13C211yesmaximal, characteristic, complemented
8#11718718C211yesmaximal, characteristic, complemented
9#11718669C211yesmaximal, characteristic, complemented
10#11718507C211yesmaximal, characteristic, complemented
11#11718501C211yesmaximal, characteristic, complemented
12#11718475C211yesmaximal, characteristic, complemented
13#11718449C211yesmaximal, characteristic, complemented
14#11718446C211yesmaximal, characteristic, complemented
15#11718445C211yesmaximal, characteristic, complemented
16C2×D4×D13C2211yescharacteristic
17C2×C13×SD16C2211yescharacteristic
18C2×C13×D8C2211yescharacteristic
19C13×#124C2211yescharacteristic, complemented
20C4×D4×C13C2211yescharacteristic
21#88200C2211yescharacteristic
22Q8×Dic13C2211yescharacteristic, complemented
23C2×#6106C2211yescharacteristic
24#88192C2211yescharacteristic
25D4×Dic13C2211yescharacteristic
26D4×Dic13C2211yescharacteristic, complemented
27C2×#6104C2211yescharacteristic
28C4×C22⋊D13—21no—
29C2×#6103—21no—
30#88147C2211yescharacteristic
31#88146C2211yescharacteristic
32#88140—21no—
33#88139—21no—
34#88135—21no—
35C22⋊C4×D13—21no—
36#88133—21no—
37#88132—21no—
38C4×D52C2211yescharacteristic
39#88126C2211yescharacteristic
40#88123C2211yescharacteristic, complemented
41C13×C4⋊C8C2211yescharacteristic, complemented
42C13×#103C2211yescharacteristic, complemented
43C13×#102C2211yescharacteristic, complemented
44#88075C2211yescharacteristic, complemented
45#88072C2211yescharacteristic
46#88072C2211yescharacteristic
47#88072C2211yescharacteristic, complemented
48#88061C2211yescharacteristic
49#88061C2211yescharacteristic
50#88060C2211yescharacteristic
51#88060C2211yescharacteristic
52#88058C2211yescharacteristic, complemented
53#88058C2211yescharacteristic, complemented
54#88055C2211yescharacteristic, complemented
55C8×Dic13C2211yescharacteristic, complemented
56#88048C2211yescharacteristic, complemented
57#88048C2211yescharacteristic, complemented
58C4⋊#1055C2211yescharacteristic, complemented
59C23×D13—21no—
60C2×Q8×C13C2311yescharacteristic
61C2×D4×C13C2311yescharacteristic
62C2×D4×C13C2311yescharacteristic
63C22×C4×C13—21no—
64C2×C22⋊D13—21no—
65C2×C22⋊D13—21no—
66C22×Dic13—21no—
67C22×Dic13—21no—
68D4×D13—22no—
69D4×D13—22no—
70C2×D52C2311yescharacteristic
71C2×C4×D13—21no—
72C2×C4×D13—21no—
73C2×C4×D13C2311yescharacteristic
74C2×Dic26—21no—
75C13×SD16—22no—
76C13×D8—22no—
77C2×C8×C13C2311yescharacteristic
78C2×C8×C13C2311yescharacteristic
79C13×C4⋊C4C2311yescharacteristic
80C13×C22⋊C4—21no—
81C13×C22⋊C4—21no—
82C13×C22⋊C4—21no—
83C42×C13C2311yescharacteristic
84C22⋊Dic13—21no—
85C22⋊Dic13—21no—
86C22⋊Dic13—21no—
87#6106—22no—
88#6104—22no—
89#6103—21no—
90#6103—21no—
91#6103—21no—
92#6103—21no—
93#6103D411yescharacteristic
94#6103D411yescharacteristic
95C4⋊Dic13—21no—
96C4⋊Dic13—21no—
97C4⋊Dic13C2311yescharacteristic
98C4⋊Dic13C2311yescharacteristic
99C4⋊Dic13C2311yescharacteristic
100#6101—21no—
101#6101D411yescharacteristic
102#6101D411yescharacteristic
103C4×Dic13—21no—
104C4×Dic13—21no—
105C4×Dic13C2311yescharacteristic
106C2×#1055C2311yescharacteristic
107C2×#1055C2311yescharacteristic
108#3118—131nomaximal, Sylow
109C23×C13—21no—
110C23×C13—21no—
111C22×D13—21no—
112C22×D13—24no—
113C22×D13—81no—
114C22×D13—81no—
115C22×D13C2×D411yescharacteristic
116Q8×C13—21no—
117Q8×C13—21no—
118D4×C13—21no—
119D4×C13—21no—
120D4×C13—21no—
121D4×C13#4112yes—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13—81no—
125C2×C4×C13C2×D411yescharacteristic
126C2×C4×C13C2×D411yescharacteristic
127C2×C4×C13C2411yescharacteristic
128C22⋊D13—24no—
129C22⋊D13—81no—
130C2×Dic13—21no—
131C2×Dic13—21no—
132C2×Dic13—21no—
133C2×Dic13—81no—
134C2×Dic13—81no—
135C2×Dic13C2×D411yescharacteristic
136C2×Dic13C2×D411yescharacteristic
137C2×Dic13C2×D411yescharacteristic
138D52—21no—
139D52#4112yes—
140C4×D13—21no—
141C4×D13—21no—
142C4×D13—81no—
143C4×D13—81no—
144Dic26—81no—
145C8×C13—21no—
146C8×C13—21no—
147#1055—21no—
148#1055—21no—
149#542—131no—
150#518—131no—
151#485—131no—
152#482—131no—
153#476—131no—
154#474—131no—
155#463—131no—
156#463D1311yescharacteristic, complemented
157#450—131no—
158#447—131no—
159#442—131no—
160#440—131no—
161C4×SD16—131no—
162C4×D8—131no—
163#433—131no—
164C22×C13—22no—
165C22×C13—41no—
166C22×C13—41no—
167C22×C13—41no—
168C22×C13—41no—
169C22×C13—41no—
170C22×C13C22×D411yescharacteristic
171C2×D13—21no—
172C2×D13—22no—
173C2×D13—21no—
174C2×D13—21no—
175C2×D13—41no—
176C2×D13—41no—
177C2×D13—84no—
178C4×C13—21no—
179C4×C13—21no—
180C4×C13—41no—
181C4×C13—41no—
182C4×C13C2×#4111yescharacteristic
183C4×C13C2×#4111yescharacteristic
184Dic13—21no—
185Dic13—21no—
186Dic13—21no—
187Dic13—41no—
188Dic13—41no—
189Dic13—41no—
190C22×D4—131no—
191C2×SD16—131no—
192C2×SD16C2×D1311yescharacteristic
193C2×D8—131no—
194C2×D8C2×D1311yescharacteristic
195C4⋊Q8—131no—
196#126—261no—
197#124—261no—
198#124C2×D1311yescharacteristic, complemented
199#123—261no—
200C22⋊Q8—131no—
201C22⋊Q8—261no—
202#121—131no—
203C4×Q8—131no—
204C4×D4—131no—
205C4×D4—131no—
206C4×D4—131no—
207C4×D4—131no—
208C4×D4—261no—
209C4×D4—261no—
210C4×D4C2×D1311yescharacteristic
211#117—131no—
212#117—131no—
213C2×C22⋊C4—261no—
214C2×C22⋊C4—261no—
215#107—131no—
216#107—131no—
217#106—131no—
218#106—131no—
219C4⋊C8—131no—
220C4⋊C8C2×D1311yescharacteristic, complemented
221#103—131no—
222#103C2×D1311yescharacteristic, complemented
223#102—131no—
224#102—131no—
225#102—131no—
226#102—131no—
227#102—131no—
228#102C2×D1311yescharacteristic, complemented
229C22⋊C8—131no—
230C22⋊C8—131no—
231#97—131no—
232C4×C8—131no—
233C2×C13—42no—
234C2×C13—81no—
235C2×C13#52511yescharacteristic
236C2×C13#57611yescharacteristic
237C2×C13#57711yescharacteristic
238D13—41no—
239D13—42no—
240C24—261no—
241C2×Q8—261no—
242C2×Q8C22×D1311yescharacteristic
243C2×D4—131no—
244C2×D4—261no—
245C2×D4—262no—
246C2×D4—262no—
247C2×D4—261no—
248C2×D4C22×D1311yescharacteristic
249C2×D4C22×D1311yescharacteristic
250C22×C4—21no—
251C22×C4—131no—
252C22×C4—261no—
253C22×C4—261no—
254C22×C4—261no—
255C22×C4—261no—
256SD16—22no—
257SD16—262no—
258D8—22no—
259D8—262no—
260C2×C8—131no—
261C2×C8—131no—
262C2×C8C22×D1311yescharacteristic
263C2×C8C22×D1311yescharacteristic
264C4⋊C4—131no—
265C4⋊C4—131no—
266C4⋊C4—131no—
267C4⋊C4—131no—
268C4⋊C4—131no—
269C4⋊C4—261no—
270C4⋊C4—261no—
271C4⋊C4—261no—
272C4⋊C4C22×D1311yescharacteristic
273C22⋊C4—21no—
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—131no—
277C22⋊C4—131no—
278C22⋊C4—261no—
279C22⋊C4—261no—
280C22⋊C4—261no—
281C22⋊C4—261no—
282C22⋊C4—261no—
283C22⋊C4—261no—
284C22⋊C4—261no—
285C42—131no—
286C42—261no—
287C42—261no—
288C42C22×D1311yescharacteristic
289C13#311811yescharacteristic, complemented, Sylow
290C23—21no—
291C23—21no—
292C23—131no—
293C23—264no—
294C23—261no—
295C23—1041no—
296C23—1041no—
297Q8—21no—
298Q8—21no—
299Q8—1041no—
300D4—21no—
301D4—21no—
302D4—21no—
303D4—132no—
304D4—264no—
305D4—261no—
306D4—1041no—
307D4#612912yes—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—81no—
311C2×C4—131no—
312C2×C4—131no—
313C2×C4—131no—
314C2×C4—261no—
315C2×C4—261no—
316C2×C4—261no—
317C2×C4—261no—
318C2×C4—261no—
319C2×C4—1041no—
320C2×C4—1041no—
321C2×C4—1041no—
322C2×C4—1041no—
323C2×C4D4×D1311yescharacteristic
324C2×C4D4×D1311yescharacteristic
325C2×C4C23×D1311yescharacteristic
326C8—21no—
327C8—21no—
328C8—261no—
329C8—261no—
330C22—22no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—261no—
337C22—261no—
338C22—261no—
339C22—262no—
340C22—521no—
341C22—521no—
342C22—1044no—
343C22C2×D4×D1311yescharacteristic
344C4—21no—
345C4—21no—
346C4—41no—
347C4—41no—
348C4—261no—
349C4—261no—
350C4—261no—
351C4—521no—
352C4—521no—
353C4—521no—
354C4C2×#612911yescharacteristic
355C4#41×D1311yescharacteristic
356C2—42no—
357C2—81no—
358C2—521no—
359C2—522no—
360C2#1171931111yescharacteristic
361C2#1171947411yescharacteristic
362C2#1171948011yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#463C2
socleC22×C13C22×D4
prime radical#11718817C2
hypercenter#463D13
hypocenterC13#3118
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. #11719387C2semidirect
2. #11719250C2semidirect
3. C13×#463C2semidirect
4. #11718830C2semidirect
5. #11718825C2semidirect
7. D8×Dic13C2semidirect
8. #11718718C2semidirect
9. #11718669C2semidirect
10. #11718507C2semidirect
11. #11718501C2semidirect
12. #11718475C2semidirect
13. #11718449C2semidirect
14. #11718446C2semidirect
15. #11718445C2semidirect
19. C13×#124C22semidirect
22. Q8×Dic13C22semidirect
26. D4×Dic13C22semidirect
40. #88123C22semidirect
41. C13×C4⋊C8C22semidirect
42. C13×#103C22semidirect
43. C13×#102C22semidirect
44. #88075C22semidirect
47. #88072C22semidirect
52. #88058C22semidirect
53. #88058C22semidirect
54. #88055C22semidirect
55. C8×Dic13C22semidirect
56. #88048C22semidirect
57. #88048C22semidirect
58. C4⋊#1055C22semidirect
156. #463D13semidirect
198. #124C2×D13semidirect
220. C4⋊C8C2×D13semidirect
222. #103C2×D13semidirect
228. #102C2×D13semidirect
289. C13#3118semidirect

Maximal subgroups

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

subgroupindex
#117193872
#117192502
C13×#4632
#117188302
#117188252
#117188172
D8×Dic132
#117187182
#117186692
#117185072
#117185012
#117184752
#117184492
#117184462
#117184452
#311813