Finite Group Databasebeta

← #13125753

Subgroups — #13125753

Order 1664.

532 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 532 conjugacy classes of subgroups — too many to draw. Only its 123 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D13×#127C211yesmaximal, characteristic, complemented
2#11719253C211yesmaximal, characteristic, complemented
3C13×#459C211yesmaximal, characteristic, complemented
4#11718817C212yesmaximal, complemented
5#11718812C212yesmaximal, complemented
6#11718733C211yesmaximal, characteristic, complemented
7#11718676C211yesmaximal, characteristic, complemented
8#11718504C211yesmaximal, characteristic, complemented
9#11718494C211yesmaximal, characteristic, complemented
10#11718434C212yesmaximal, complemented
11#11718421C212yesmaximal, complemented
12C2×D4×D13—21no—
13C2×D4×D13—21no—
14C2×D4×D13C2212yes—
15C2×#6127—21no—
16C2×C13×D8C2212yescomplemented
17C13×#127C2211yescharacteristic
18C4×D4×C13C2211yescharacteristic, complemented
19#88194—21no—
20#88194—21no—
21#88194C2212yes—
22#88194C2211yescharacteristic, complemented
23#88192C2211yescharacteristic
24C2×#6104C2212yescomplemented
25C2×#6104C2212yescomplemented
26C4×C22⋊D13—21no—
27C2×D104C2212yescomplemented
28#88149C2211yescharacteristic
29#88142C2211yescharacteristic, complemented
30#88139—21no—
31#88138—21no—
32#88128C2211yescharacteristic
33C4×D52C2211yescharacteristic, complemented
34C42×D13C2211yescharacteristic
35C13×C4⋊C8C2211yescharacteristic, complemented
36C13×#102C2212yescomplemented
37#88072C2212yescomplemented
38#88061C2212yescomplemented
39#88060C2212yes—
40C8×Dic13C2212yescomplemented
41#88049C2212yescomplemented
42C4⋊#1055C2211yescharacteristic, complemented
43C23×D13—22no—
44C2×D4×C13—21no—
45C2×D4×C13—21no—
46C2×D4×C13C2312yes—
47C2×D4×C13C2311yescharacteristic
48C22×C4×C13—21no—
49C2×C22⋊D13—21no—
50C2×C22⋊D13—21no—
51C2×C22⋊D13—21no—
52C2×C22⋊D13—22no—
53C2×C22⋊D13—22no—
54C2×C22⋊D13—22no—
55D4×D13—42no—
56D4×D13—42no—
57D4×D13—44no—
58D4×D13—44no—
59#6127—44no—
60C2×D52—21no—
61C2×D52—21no—
62C2×D52—21no—
63C2×D52C2311yescharacteristic
64C2×D52C2312yes—
65C2×C4×D13—21no—
66C2×C4×D13D411yescharacteristic
67C2×C4×D13D411yescharacteristic
68C2×C4×D13C2311yescharacteristic
69C2×Dic26—21no—
70C13×D8—42no—
71C2×C8×C13C2312yes—
72C13×C4⋊C4C2311yescharacteristic
73C13×C22⋊C4—21no—
74C42×C13C2311yescharacteristic
75C22⋊Dic13—21no—
76#6104—42no—
77#6104—42no—
78#6103—21no—
79#6103—21no—
80C4⋊Dic13C2311yescharacteristic
81#6101—21no—
82C4×Dic13D411yescharacteristic
83C4×Dic13D411yescharacteristic
84C4×Dic13C2311yescharacteristic
85C2×#1055C2312yes—
86D104—42no—
87#3205—131nomaximal, Sylow
88C23×C13—21no—
89C23×C13—22no—
90C22×D13—21no—
91C22×D13—22no—
92C22×D13—44no—
93C22×D13—44no—
94C22×D13—44no—
95C22×D13C2×D411yescharacteristic
96D4×C13—21no—
97D4×C13—22no—
98D4×C13—21no—
99D4×C13—22no—
100D4×C13—42no—
101D4×C13—42no—
102C2×C4×C13—21no—
103C2×C4×C13—42no—
104C2×C4×C13C2×D411yescharacteristic
105C2×C4×C13C2×D411yescharacteristic
106C2×C4×C13C2411yescharacteristic
107C22⋊D13—44no—
108C22⋊D13—42no—
109C22⋊D13—42no—
110C22⋊D13—44no—
111C22⋊D13—44no—
112C22⋊D13—42no—
113C2×Dic13—21no—
114C2×Dic13C2×D411yescharacteristic
115C2×Dic13C2×D411yescharacteristic
116C2×Dic13C2×D411yescharacteristic
117D52—21no—
118D52—22no—
119D52—21no—
120D52—22no—
121D52—42no—
122D52—42no—
123D52—42no—
124C4×D13—21no—
125C4×D13—21no—
126C4×D13—22no—
127C4×D13—42no—
128C4×D13D814yescomplemented
129Dic26—42no—
130C8×C13—22no—
131#1055—22no—
132#532—131no—
133C2×#127—131no—
134#493—132no—
135#486—132no—
136#459—131no—
137#459—131no—
138#459—131no—
139#459D1311yescharacteristic, complemented
140#447—132no—
141#447—132no—
142#431—131no—
143C22×C13—42no—
144C22×C13—41no—
145C22×C13—41no—
146C22×C13—42no—
147C22×C13—42no—
148C22×C13—41no—
149C22×C13C22×D411yescharacteristic
150C2×D13—21no—
151C2×D13—21no—
152C2×D13—42no—
153C2×D13—41no—
154C2×D13—41no—
155C2×D13—42no—
156C2×D13—42no—
157C2×D13—41no—
158C2×D13—88no—
159C2×D13C2×D812yes—
160C4×C13—21no—
161C4×C13—41no—
162C4×C13C2×D812yes—
163C4×C13H(5,𝔽2)11yescharacteristic
164C4×C13H(5,𝔽2)11yescharacteristic
165Dic13—21no—
166Dic13—41no—
167Dic13C2×D812yes—
168Dic13AGL(1,ℤ/8)12yes—
169C2×#41—261no—
170C22×D4—132no—
171C22×D4—261no—
172C22×D4—261no—
173C2×D8—132no—
174C2×D8—132no—
175C2×D8—132no—
176C2×D8C2×D1312yescomplemented
177C4⋊Q8—131no—
178#127—132no—
179#127—131no—
180#127—131no—
181#127—261no—
182#127—261no—
183#127C2×D1311yescharacteristic
184#124—261no—
185#121—131no—
186#121—131no—
187#121—261no—
188C4×D4—131no—
189C4×D4—261no—
190C4×D4C2×D1311yescharacteristic, complemented
191C2×C42—131no—
192C4⋊C8—131no—
193C4⋊C8C2×D1311yescharacteristic, complemented
194#102—132no—
195#102—132no—
196#102—132no—
197#102C2×D1312yescomplemented
198C22⋊C8—132no—
199C4×C8—132no—
200C2×C13—82no—
201C2×C13—81no—
202C2×C13#53511yescharacteristic
203C2×C13C22×D811yescharacteristic
204C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
205D13—22no—
206D13—81no—
207D13—82no—
208C24—262no—
209#41—524no—
210C2×Q8—261no—
211C2×D4—21no—
212C2×D4—21no—
213C2×D4—132no—
214C2×D4—131no—
215C2×D4—261no—
216C2×D4—261no—
217C2×D4—261no—
218C2×D4—262no—
219C2×D4—262no—
220C2×D4—262no—
221C2×D4—261no—
222C2×D4—261no—
223C2×D4—261no—
224C2×D4—524no—
225C2×D4—522no—
226C2×D4—522no—
227C2×D4—524no—
228C2×D4C22×D1312yes—
229C2×D4C22×D1311yescharacteristic
230C22×C4—21no—
231C22×C4—131no—
232C22×C4—131no—
233C22×C4—131no—
234C22×C4—261no—
235D8—42no—
236D8—522no—
237D8—522no—
238D8—522no—
239C2×C8—132no—
240C2×C8C22×D1312yes—
241C4⋊C4—131no—
242C4⋊C4—261no—
243C4⋊C4C22×D1311yescharacteristic
244C22⋊C4—21no—
245C22⋊C4—261no—
246C22⋊C4—261no—
247C22⋊C4—261no—
248C42—131no—
249C42—131no—
250C42—131no—
251C42C22×D1311yescharacteristic
252C13#320511yescharacteristic, complemented, Sylow
253C23—21no—
254C23—22no—
255C23—131no—
256C23—261no—
257C23—262no—
258C23—524no—
259C23—524no—
260C23—524no—
261Q8—522no—
262D4—21no—
263D4—22no—
264D4—21no—
265D4—22no—
266D4—42no—
267D4—42no—
268D4—261no—
269D4—262no—
270D4—261no—
271D4—262no—
272D4—522no—
273D4—522no—
274D4—522no—
275D4—524no—
276D4—524no—
277D4—522no—
278D4—524no—
279D4—522no—
280D4—522no—
281C2×C4—21no—
282C2×C4—42no—
283C2×C4—131no—
284C2×C4—131no—
285C2×C4—134no—
286C2×C4—131no—
287C2×C4—262no—
288C2×C4—261no—
289C2×C4—261no—
290C2×C4—261no—
291C2×C4—522no—
292C2×C4D4×D1311yescharacteristic
293C2×C4D4×D1311yescharacteristic
294C2×C4C23×D1311yescharacteristic
295C8—22no—
296C8—262no—
297C22—41no—
298C22—42no—
299C22—42no—
300C22—41no—
301C22—42no—
302C22—41no—
303C22—132no—
304C22—261no—
305C22—261no—
306C22—521no—
307C22—522no—
308C22—522no—
309C22—521no—
310C22—522no—
311C22—521no—
312C22—1048no—
313C22C2×D4×D1311yescharacteristic
314C4—21no—
315C4—41no—
316C4—132no—
317C4—132no—
318C4—261no—
319C4—521no—
320C4D8×D1312yes—
321C4#8825111yescharacteristic
322C4#8825611yescharacteristic
323C2—82no—
324C2—81no—
325C2—262no—
326C2—1042no—
327C2—1041no—
328C2#1171931211yescharacteristic
329C2C2×D8×D1311yescharacteristic
330C2D13×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#459C2
socleC22×C13C22×D4
hypercenter#459D13
hypocenterC13#3205
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. D13×#127C2semidirect
2. #11719253C2semidirect
3. C13×#459C2semidirect
4. #11718817C2semidirect
5. #11718812C2semidirect
6. #11718733C2semidirect
7. #11718676C2semidirect
8. #11718504C2semidirect
9. #11718494C2semidirect
10. #11718434C2semidirect
11. #11718421C2semidirect
16. C2×C13×D8C22semidirect
18. C4×D4×C13C22semidirect
22. #88194C22semidirect
24. C2×#6104C22semidirect
25. C2×#6104C22semidirect
27. C2×D104C22semidirect
29. #88142C22semidirect
33. C4×D52C22semidirect
35. C13×C4⋊C8C22semidirect
36. C13×#102C22semidirect
37. #88072C22semidirect
38. #88061C22semidirect
40. C8×Dic13C22semidirect
41. #88049C22semidirect
42. C4⋊#1055C22semidirect
128. C4×D13D8semidirect
139. #459D13semidirect
176. C2×D8C2×D13semidirect
190. C4×D4C2×D13semidirect
193. C4⋊C8C2×D13semidirect
197. #102C2×D13semidirect
252. C13#3205semidirect

Maximal subgroups

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

subgroupindex
D13×#1272
#117192532
C13×#4592
#117188172
#117188122
#117187332
#117186762
#117185042
#117184942
#117184342
#117184212
#320513