Finite Group Databasebeta

← #13126729

Subgroups — #13126729

Order 1664.

386 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719347C211yesmaximal, characteristic, complemented
2#11719303C211yesmaximal, characteristic
3C13×#465C211yesmaximal, characteristic, complemented
4#11718834C211yesmaximal, characteristic, complemented
5#11718827C211yesmaximal, characteristic, complemented
6C8×C22⋊D13C211yesmaximal, characteristic, complemented
7C2×#88056C211yesmaximal, characteristic, complemented
8#11718711C211yesmaximal, characteristic, complemented
9#11718694C211yesmaximal, characteristic, complemented
10#11718528C211yesmaximal, characteristic, complemented
11#11718518C211yesmaximal, characteristic, complemented
12#11718474C211yesmaximal, characteristic, complemented
13#11718451C211yesmaximal, characteristic, complemented
14#11718433C211yesmaximal, characteristic, complemented
15#11718429C211yesmaximal, characteristic, complemented
16C2×#6129C2211yescharacteristic
17C22×Dic26C2211yescharacteristic
18C2×C13×SD16C2211yescharacteristic
19C22×C8×C13C2211yescharacteristic
20C13×C22⋊Q8C2211yescharacteristic
21C13×#121C2211yescharacteristic
22#88200C2211yescharacteristic
23Q8×Dic13C2211yescharacteristic
24C2×#6107C2211yescharacteristic
25C2×#6107C2211yescharacteristic
26#88193—21no—
27#88190C2211yescharacteristic
28D4×Dic13—21no—
29C4×C22⋊D13C2211yescharacteristic
30C2×C4⋊Dic13C2211yescharacteristic
31C2×C8×D13C2211yescharacteristic
32#88152—21no—
33#88151C2211yescharacteristic
34#88146C2211yescharacteristic
35#88144—21no—
36#88144C2211yescharacteristic
37#88141C2211yescharacteristic
38#88140—21no—
39#88139—21no—
40#88132—21no—
41#88131—21no—
42C13×#106C2211yescharacteristic
43C13×#103C2211yescharacteristic
44C13×#102C2211yescharacteristic
45#88072C2211yescharacteristic
46#88072C2211yescharacteristic
47C22⋊#1055C2211yescharacteristic
48#88060C2211yescharacteristic
49#88056C2211yescharacteristic
50#88056C2211yescharacteristic
51#88056C2211yescharacteristic
52#88056C2211yescharacteristic
53#88054C2211yescharacteristic
54C8×Dic13C2211yescharacteristic
55#88050C2211yescharacteristic
56#88050C2211yescharacteristic
57#88047C2211yescharacteristic
58#88047C2211yescharacteristic
59C2×Q8×C13C2311yescharacteristic
60C2×D4×C13—21no—
61C2×D4×C13C2311yescharacteristic
62C22×C4×C13C2311yescharacteristic
63C2×C22⋊D13—21no—
64C2×C22⋊D13D411yescharacteristic
65C22×Dic13—21no—
66C22×Dic13—21no—
67C22×Dic13—21no—
68#6129—22no—
69#6129—41no—
70C2×C4×D13C2311yescharacteristic
71C2×Dic26—22no—
72C2×Dic26—21no—
73C2×Dic26—41no—
74C2×Dic26C2311yescharacteristic
75C2×Dic26C2311yescharacteristic
76C13×SD16—41no—
77C2×C8×C13—41no—
78C2×C8×C13C2311yescharacteristic
79C2×C8×C13C2311yescharacteristic
80C13×C4⋊C4—21no—
81C13×C4⋊C4C2311yescharacteristic
82C13×C4⋊C4C2311yescharacteristic
83C13×C22⋊C4—21no—
84C13×C22⋊C4—21no—
85C22⋊Dic13—21no—
86C22⋊Dic13—21no—
87C22⋊Dic13D411yescharacteristic
88#6107—22no—
89#6107—41no—
90#6103—21no—
91#6103—21no—
92#6103—21no—
93#6103D411yescharacteristic
94C4⋊Dic13—21no—
95C4⋊Dic13—21no—
96C4⋊Dic13—21no—
97C4⋊Dic13—21no—
98C4⋊Dic13C2311yescharacteristic
99C4⋊Dic13C2311yescharacteristic
100#6101—21no—
101#6101—21no—
102#6101—21no—
103#6101D411yescharacteristic
104C4×Dic13—21no—
105C4×Dic13—21no—
106C4×Dic13—21no—
107C4×Dic13C2311yescharacteristic
108C2×#1055C2311yescharacteristic
109C2×#1055C2311yescharacteristic
110C8×D13—41no—
111#3300—131nomaximal, Sylow
112C23×C13—21no—
113C23×C13C2×D411yescharacteristic
114C22×D13C2×D411yescharacteristic
115Q8×C13—21no—
116Q8×C13—21no—
117D4×C13—21no—
118D4×C13—21no—
119D4×C13—42no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13—21no—
125C2×C4×C13C2×D411yescharacteristic
126C2×C4×C13C2411yescharacteristic
127C22⋊D13—22no—
128C22⋊D13—42no—
129C2×Dic13—21no—
130C2×Dic13—21no—
131C2×Dic13—21no—
132C2×Dic13—21no—
133C2×Dic13—42no—
134C2×Dic13—42no—
135C2×Dic13—42no—
136C2×Dic13C2×D411yescharacteristic
137C2×Dic13C2×D411yescharacteristic
138C2×Dic13C2×D411yescharacteristic
139C4×D13—21no—
140C4×D13—21no—
141Dic26—21no—
142Dic26—21no—
143Dic26—21no—
144Dic26—42no—
145Dic26#4112yes—
146C8×C13—21no—
147C8×C13—21no—
148#1055—21no—
149#1055—21no—
150#552—131no—
151#548—131no—
152#488—131no—
153#485—131no—
154#480—131no—
155#479—131no—
156#467—131no—
157#465D1311yescharacteristic, complemented
158#464—131no—
159#452—131no—
160#451—131no—
161C4×Q16—131no—
162C8×D4—131no—
163#416—131no—
164C2×#103—131no—
165C22×C13—21no—
166C22×C13—21no—
167C22×C13—41no—
168C22×C13—41no—
169C22×C13—41no—
170C22×C13#13512yes—
171C22×C13C22×D411yescharacteristic
172C2×D13—21no—
173C2×D13—21no—
174C2×D13—21no—
175C4×C13—21no—
176C4×C13—41no—
177C4×C13—41no—
178C4×C13—41no—
179C4×C13C2×#4111yescharacteristic
180C4×C13H(5,𝔽2)11yescharacteristic
181Dic13—22no—
182Dic13—21no—
183Dic13—21no—
184Dic13—21no—
185Dic13—41no—
186Dic13—41no—
187Dic13—41no—
188C2×#41—131no—
189C22×Q8—131no—
190C2×Q16—131no—
191C2×Q16—131no—
192C2×SD16C2×D1311yescharacteristic
193C22×C8—131no—
194C22×C8C2×D1311yescharacteristic
195#126—261no—
196#125—131no—
197#125—261no—
198#124—131no—
199#124—261no—
200#123—261no—
201C22⋊Q8—131no—
202C22⋊Q8—131no—
203C22⋊Q8—261no—
204C22⋊Q8C2×D1311yescharacteristic
205#121—261no—
206#121C2×D1311yescharacteristic
207C4×Q8—131no—
208C4×Q8—131no—
209C4×D4—131no—
210C4×D4—261no—
211#117—131no—
212#117—261no—
213C2×C4⋊C4—131no—
214#107—131no—
215#107—131no—
216#106C2×D1311yescharacteristic
217C4⋊C8—131no—
218#103—131no—
219#103—131no—
220#103—131no—
221#103—131no—
222#103—131no—
223#103—131no—
224#103C2×D1311yescharacteristic
225#102—131no—
226#102—131no—
227#102C2×D1311yescharacteristic
228C22⋊C8—131no—
229C22⋊C8—131no—
230C4×C8—131no—
231C2×C13—22no—
232C2×C13—81no—
233C2×C13#54611yescharacteristic
234C2×C13C2×#13511yescharacteristic
235C2×C13#57811yescharacteristic
236D13—41no—
237#41—262no—
238#41—521no—
239C2×Q8—131no—
240C2×Q8—131no—
241C2×Q8—262no—
242C2×Q8—261no—
243C2×Q8—521no—
244C2×Q8C22×D1311yescharacteristic
245C2×D4—21no—
246C2×D4—131no—
247C2×D4—261no—
248C2×D4C22×D1311yescharacteristic
249C22×C4—131no—
250C22×C4—261no—
251C22×C4—261no—
252C22×C4—261no—
253C22×C4C22×D1311yescharacteristic
254Q16—262no—
255Q16—521no—
256SD16—41no—
257C2×C8—41no—
258C2×C8—131no—
259C2×C8—131no—
260C2×C8—521no—
261C2×C8C22×D1311yescharacteristic
262C2×C8C22×D1311yescharacteristic
263C4⋊C4—21no—
264C4⋊C4—131no—
265C4⋊C4—131no—
266C4⋊C4—131no—
267C4⋊C4—261no—
268C4⋊C4—261no—
269C4⋊C4—261no—
270C4⋊C4—261no—
271C4⋊C4—261no—
272C4⋊C4—261no—
273C4⋊C4—261no—
274C4⋊C4C22×D1311yescharacteristic
275C4⋊C4C22×D1311yescharacteristic
276C22⋊C4—21no—
277C22⋊C4—21no—
278C22⋊C4—131no—
279C22⋊C4—131no—
280C22⋊C4—261no—
281C22⋊C4—261no—
282C22⋊C4—261no—
283C22⋊C4—261no—
284C22⋊C4—261no—
285C42—131no—
286C42—261no—
287C42—261no—
288C42—261no—
289C13#330011yescharacteristic, complemented, Sylow
290C23—21no—
291C23—131no—
292C23D4×D1311yescharacteristic
293Q8—21no—
294Q8—21no—
295Q8—132no—
296Q8—261no—
297Q8—261no—
298Q8—261no—
299Q8—522no—
300D4—21no—
301D4—21no—
302D4—42no—
303D4—262no—
304D4—522no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—131no—
311C2×C4—131no—
312C2×C4—131no—
313C2×C4—261no—
314C2×C4—261no—
315C2×C4—261no—
316C2×C4—261no—
317C2×C4—261no—
318C2×C4—261no—
319C2×C4—522no—
320C2×C4—522no—
321C2×C4—522no—
322C2×C4D4×D1311yescharacteristic
323C2×C4C23×D1311yescharacteristic
324C8—21no—
325C8—21no—
326C8—261no—
327C8—261no—
328C22—21no—
329C22—21no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—261no—
334C22—261no—
335C22—261no—
336C22#8817012yes—
337C22C2×D4×D1311yescharacteristic
338C4—21no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—261no—
343C4—261no—
344C4—261no—
345C4—262no—
346C4—521no—
347C4—521no—
348C4—521no—
349C4#8825111yescharacteristic
350C4#41×D1311yescharacteristic
351C2—22no—
352C2—81no—
353C2—521no—
354C2#1171931511yescharacteristic
355C2C2×#8817011yescharacteristic
356C2#1171947611yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#465C2
socleC22×C13C22×D4
prime radical#11719303C2
hypercenter#465D13
hypocenterC13#3300
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. #11719347C2semidirect
3. C13×#465C2semidirect
4. #11718834C2semidirect
5. #11718827C2semidirect
6. C8×C22⋊D13C2semidirect
7. C2×#88056C2semidirect
8. #11718711C2semidirect
9. #11718694C2semidirect
10. #11718528C2semidirect
11. #11718518C2semidirect
12. #11718474C2semidirect
13. #11718451C2semidirect
14. #11718433C2semidirect
15. #11718429C2semidirect
157. #465D13semidirect
289. C13#3300semidirect

Maximal subgroups

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

subgroupindex
#117193472
#117193032
C13×#4652
#117188342
#117188272
C8×C22⋊D132
C2×#880562
#117187112
#117186942
#117185282
#117185182
#117184742
#117184512
#117184332
#117184292
#330013