Finite Group Databasebeta

← #13126718

Subgroups — #13126718

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#11719344C211yesmaximal, characteristic, complemented
2#11719338C211yesmaximal, characteristic
3C13×#467C211yesmaximal, characteristic, complemented
4#11718847C211yesmaximal, characteristic, complemented
5#11718846C211yesmaximal, characteristic, complemented
6#11718774C211yesmaximal, characteristic, complemented
7C8×C22⋊D13C211yesmaximal, characteristic, complemented
8#11718708C211yesmaximal, characteristic, complemented
9#11718706C211yesmaximal, characteristic, complemented
10#11718543C211yesmaximal, characteristic, complemented
11#11718538C211yesmaximal, characteristic, complemented
12#11718468C211yesmaximal, characteristic, complemented
13D13×#103C211yesmaximal, characteristic, complemented
14#11718461C211yesmaximal, characteristic, complemented
15#11718451C211yesmaximal, characteristic, complemented
16C2×Q8×D13C2211yescharacteristic
17C2×#6127C2211yescharacteristic
18C2×C13×Q16C2211yescharacteristic
19C22×C8×C13C2211yescharacteristic
20C13×C22⋊Q8C2211yescharacteristic
21C13×C22⋊Q8C2211yescharacteristic
22#88201C2211yescharacteristic
23#88200C2211yescharacteristic
24Q8×Dic13C2211yescharacteristic
25C2×#6107C2211yescharacteristic
26C2×#6106C2211yescharacteristic
27C4×C22⋊D13C2211yescharacteristic
28#88180C2211yescharacteristic
29C2×C8×D13C2211yescharacteristic
30#88150—21no—
31#88149C2211yescharacteristic
32#88147—21no—
33#88146—21no—
34C4⋊C4×D13C2211yescharacteristic
35#88144C2211yescharacteristic
36#88143—21no—
37#88141C2211yescharacteristic
38#88139—21no—
39#88138—21no—
40#88137—21no—
41#88133—21no—
42C13×#107C2211yescharacteristic
43C13×#103C2211yescharacteristic
44C13×#103C2211yescharacteristic
45#88075C2211yescharacteristic
46#88075C2211yescharacteristic
47C22⋊#1055C2211yescharacteristic
48#88061C2211yescharacteristic
49#88061C2211yescharacteristic
50#88060C2211yescharacteristic
51#88056C2211yescharacteristic
52#88056C2211yescharacteristic
53#88054C2211yescharacteristic
54C8×Dic13C2211yescharacteristic
55#88050C2211yescharacteristic
56#88049C2211yescharacteristic
57#88048C2211yescharacteristic
58#88047C2211yescharacteristic
59C2×Q8×C13C2311yescharacteristic
60C2×Q8×C13C2311yescharacteristic
61C22×C4×C13C2311yescharacteristic
62C2×C22⋊D13—21no—
63C2×C22⋊D13D411yescharacteristic
64Q8×D13—22no—
65Q8×D13—41no—
66#6127—22no—
67#6127—41no—
68C2×D52—21no—
69C2×D52C2311yescharacteristic
70C2×C4×D13—21no—
71C2×C4×D13—21no—
72C2×C4×D13—21no—
73C2×C4×D13C2311yescharacteristic
74C2×Dic26—21no—
75C2×Dic26C2311yescharacteristic
76C13×Q16—41no—
77C2×C8×C13—41no—
78C2×C8×C13C2311yescharacteristic
79C2×C8×C13C2311yescharacteristic
80C13×C4⋊C4—21no—
81C13×C4⋊C4—21no—
82C13×C4⋊C4C2311yescharacteristic
83C13×C4⋊C4C2311yescharacteristic
84C13×C22⋊C4—21no—
85C13×C22⋊C4—21no—
86C22⋊Dic13—21no—
87C22⋊Dic13D411yescharacteristic
88#6107—22no—
89#6106—41no—
90#6103—21no—
91#6103—21no—
92#6103—21no—
93#6103—21no—
94#6103D411yescharacteristic
95C4⋊Dic13—21no—
96C4⋊Dic13—21no—
97C4⋊Dic13C2311yescharacteristic
98C4⋊Dic13C2311yescharacteristic
99#6101—21no—
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×C13C2×D411yescharacteristic
113C22×D13—21no—
114C22×D13C2×D411yescharacteristic
115Q8×C13—21no—
116Q8×C13—21no—
117Q8×C13—21no—
118Q8×C13—21no—
119C2×C4×C13—21no—
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×Dic13C2×D411yescharacteristic
133C2×Dic13C2×D411yescharacteristic
134C2×Dic13C2×D411yescharacteristic
135D52—21no—
136D52—21no—
137D52—42no—
138C4×D13—21no—
139C4×D13—21no—
140C4×D13—42no—
141C4×D13—42no—
142C4×D13—42no—
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#467D1311yescharacteristic, complemented
157#465—131no—
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—21no—
168C22×C13C22×D411yescharacteristic
169C2×D13—21no—
170C2×D13—21no—
171C2×D13—41no—
172C2×D13—41no—
173C2×D13—41no—
174C2×D13#13512yes—
175C4×C13—21no—
176C4×C13—41no—
177C4×C13—41no—
178C4×C13—41no—
179C4×C13—41no—
180C4×C13C2×#4111yescharacteristic
181C4×C13H(5,𝔽2)11yescharacteristic
182Dic13—22no—
183Dic13—21no—
184Dic13—21no—
185Dic13—21no—
186Dic13—41no—
187Dic13—41no—
188C2×#41—131no—
189C22×Q8—131no—
190C2×Q16—131no—
191C2×Q16C2×D1311yescharacteristic
192C2×SD16—131no—
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—261no—
203C22⋊Q8C2×D1311yescharacteristic
204C22⋊Q8C2×D1311yescharacteristic
205#121—131no—
206#121—261no—
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#107C2×D1311yescharacteristic
216#106—131no—
217C4⋊C8—131no—
218#103—131no—
219#103—131no—
220#103—131no—
221#103—131no—
222#103—131no—
223#103C2×D1311yescharacteristic
224#103C2×D1311yescharacteristic
225#102—131no—
226#102—131no—
227#102—131no—
228C22⋊C8—131no—
229C22⋊C8—131no—
230C4×C8—131no—
231C2×C13—41no—
232C2×C13#54611yescharacteristic
233C2×C13C2×#13511yescharacteristic
234C2×C13#57811yescharacteristic
235D13—22no—
236D13—81no—
237#41—262no—
238#41—521no—
239C2×Q8—131no—
240C2×Q8—261no—
241C2×Q8—262no—
242C2×Q8—521no—
243C2×Q8C22×D1311yescharacteristic
244C2×Q8C22×D1311yescharacteristic
245C2×D4—131no—
246C2×D4—131no—
247C2×D4—261no—
248C2×D4—261no—
249C22×C4—131no—
250C22×C4—261no—
251C22×C4—261no—
252C22×C4—261no—
253C22×C4C22×D1311yescharacteristic
254Q16—41no—
255Q16—262no—
256SD16—521no—
257C2×C8—41no—
258C2×C8—131no—
259C2×C8—131no—
260C2×C8—521no—
261C2×C8C22×D1311yescharacteristic
262C2×C8C22×D1311yescharacteristic
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4—131no—
266C4⋊C4—131no—
267C4⋊C4—131no—
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—131no—
291C23—261no—
292C23D4×D1311yescharacteristic
293Q8—21no—
294Q8—21no—
295Q8—21no—
296Q8—21no—
297Q8—132no—
298Q8—261no—
299Q8—522no—
300D4—262no—
301D4—261no—
302D4—261no—
303D4—522no—
304D4—522no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
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—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—21no—
331C22—132no—
332C22—261no—
333C22—261no—
334C22—521no—
335C22—521no—
336C22—521no—
337C22C2×D4×D1311yescharacteristic
338C4—21no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—261no—
344C4—261no—
345C4—261no—
346C4—262no—
347C4—521no—
348C4—521no—
349C4#8825111yescharacteristic
350C4#41×D1311yescharacteristic
351C2—41no—
352C2—262no—
353C2—1041no—
354C2#1171931511yescharacteristic
355C2#1171947111yescharacteristic
356C2D13×#13511yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#467C2
socleC22×C13C22×D4
prime radical#11719338C2
hypercenter#467D13
hypocenterC13#3300
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #467

Complements

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

NH ≅ G/Ntype
1. #11719344C2semidirect
3. C13×#467C2semidirect
4. #11718847C2semidirect
5. #11718846C2semidirect
6. #11718774C2semidirect
7. C8×C22⋊D13C2semidirect
8. #11718708C2semidirect
9. #11718706C2semidirect
10. #11718543C2semidirect
11. #11718538C2semidirect
12. #11718468C2semidirect
13. D13×#103C2semidirect
14. #11718461C2semidirect
15. #11718451C2semidirect
156. #467D13semidirect
289. C13#3300semidirect

Maximal subgroups

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

subgroupindex
#117193442
#117193382
C13×#4672
#117188472
#117188462
#117187742
C8×C22⋊D132
#117187082
#117187062
#117185432
#117185382
#117184682
D13×#1032
#117184612
#117184512
#330013