Finite Group Databasebeta

← #13125776

Subgroups — #13125776

Order 1664.

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

normal subgroups only

This group has 488 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
2#11719283C211yesmaximal, characteristic, complemented
3C13×#460C211yesmaximal, characteristic, complemented
4#11718836C212yesmaximal, complemented
5#11718830C212yesmaximal, complemented
6#11718736C211yesmaximal, characteristic, complemented
7#11718688C211yesmaximal, characteristic, complemented
8#11718509C211yesmaximal, characteristic, complemented
9#11718494C211yesmaximal, characteristic, complemented
10#11718437C212yesmaximal, complemented
11#11718421C212yesmaximal, complemented
12C2×D4×D13—21no—
13C2×D4×D13—21no—
14C2×D4×D13C2212yes—
15C2×C13×SD16C2212yescomplemented
16C13×#127C2211yescharacteristic
17C4×Q8×C13C2211yescharacteristic, complemented
18#88200C2211yescharacteristic
19#88198C2211yescharacteristic, complemented
20C2×#6106C2212yescomplemented
21#88194—21no—
22#88194—21no—
23#88194C2212yes—
24C2×#6105C2212yescomplemented
25C2×#6095C2212yescomplemented
26#88151C2211yescharacteristic
27#88150—21no—
28#88143—21no—
29#88142C2211yescharacteristic, complemented
30#88128C2211yescharacteristic
31#88126—21no—
32C42×D13C2211yescharacteristic
33C4×Dic26—21no—
34C4×Dic26C2211yescharacteristic, complemented
35C13×C4⋊C8C2211yescharacteristic, complemented
36C13×#102C2212yescomplemented
37#88072C2212yescomplemented
38#88061C2212yescomplemented
39#88060C2212yes—
40C8×Dic13C2212yescomplemented
41#88049C2212yescomplemented
42C4⋊#1055C2211yescharacteristic, complemented
43C23×D13—22no—
44C2×Q8×C13C2311yescharacteristic
45C2×D4×C13—21no—
46C2×D4×C13—21no—
47C2×D4×C13C2312yes—
48C2×C22⋊D13—22no—
49C2×C22⋊D13—22no—
50C2×C22⋊D13—22no—
51D4×D13—42no—
52D4×D13—42no—
53D4×D13—44no—
54D4×D13—44no—
55C2×D52—21no—
56C2×D52—21no—
57C2×D52C2312yes—
58C2×C4×D13D411yescharacteristic
59C2×C4×D13D411yescharacteristic
60C2×C4×D13C2311yescharacteristic
61C2×Dic26—21no—
62C2×Dic26C2311yescharacteristic
63C13×SD16—42no—
64C2×C8×C13C2312yes—
65C13×C4⋊C4—21no—
66C13×C4⋊C4C2311yescharacteristic
67C42×C13—21no—
68C42×C13C2311yescharacteristic
69#6106—42no—
70#6105—42no—
71#6103—21no—
72#6103—21no—
73C4⋊Dic13—21no—
74C4⋊Dic13C2311yescharacteristic
75#6101—21no—
76#6101—21no—
77#6101—21no—
78#6101—21no—
79#6101—21no—
80C4×Dic13—21no—
81C4×Dic13D411yescharacteristic
82C4×Dic13D411yescharacteristic
83C4×Dic13C2311yescharacteristic
84C2×#1055C2312yes—
85#6095—42no—
86#3208—131nomaximal, Sylow
87C23×C13—22no—
88C22×D13—22no—
89C22×D13—44no—
90C22×D13—44no—
91C22×D13—44no—
92C22×D13C2×D411yescharacteristic
93Q8×C13—21no—
94Q8×C13—21no—
95D4×C13—22no—
96D4×C13—22no—
97D4×C13—42no—
98D4×C13—42no—
99C2×C4×C13—21no—
100C2×C4×C13—21no—
101C2×C4×C13C2×D411yescharacteristic
102C2×C4×C13C2×D411yescharacteristic
103C2×C4×C13C2411yescharacteristic
104C22⋊D13—44no—
105C22⋊D13—44no—
106C22⋊D13—44no—
107C2×Dic13—21no—
108C2×Dic13—21no—
109C2×Dic13C2×D411yescharacteristic
110C2×Dic13C2×D411yescharacteristic
111C2×Dic13C2×D411yescharacteristic
112D52—22no—
113D52—22no—
114D52—42no—
115D52—42no—
116C4×D13—21no—
117C4×D13—21no—
118C4×D13—22no—
119C4×D13SD1614yescomplemented
120Dic26—21no—
121Dic26—21no—
122Dic26—42no—
123C8×C13—22no—
124#1055—22no—
125#533—131no—
126C2×#127—131no—
127#492—132no—
128#486—132no—
129#460—131no—
130#460—131no—
131#460—131no—
132#460D1311yescharacteristic, complemented
133#450—132no—
134#450—132no—
135#431—131no—
136C22×C13—42no—
137C22×C13—42no—
138C22×C13—42no—
139C22×C13C22×D411yescharacteristic
140C2×D13—21no—
141C2×D13—21no—
142C2×D13—42no—
143C2×D13—42no—
144C2×D13—42no—
145C2×D13—88no—
146C2×D13C2×SD1612yes—
147C4×C13—21no—
148C4×C13—41no—
149C4×C13—41no—
150C4×C13C2×SD1612yes—
151C4×C13H(5,𝔽2)11yescharacteristic
152C4×C13H(5,𝔽2)11yescharacteristic
153Dic13—21no—
154Dic13—41no—
155Dic13—41no—
156Dic13C2×SD1612yes—
157Dic13AGL(1,ℤ/8)12yes—
158C22×D4—132no—
159C22×D4—261no—
160C22×D4—261no—
161C2×SD16—132no—
162C2×SD16—132no—
163C2×SD16—132no—
164C2×SD16C2×D1312yescomplemented
165C4⋊Q8—131no—
166C4⋊Q8—131no—
167#127—132no—
168#127—131no—
169#127—261no—
170#127—261no—
171#127C2×D1311yescharacteristic
172#125—261no—
173C22⋊Q8—131no—
174C22⋊Q8—131no—
175C22⋊Q8—261no—
176C4×Q8—131no—
177C4×Q8—261no—
178C4×Q8C2×D1311yescharacteristic, complemented
179#117—261no—
180C2×C42—131no—
181C4⋊C8—131no—
182C4⋊C8C2×D1311yescharacteristic, complemented
183#102—132no—
184#102—132no—
185#102—132no—
186#102C2×D1312yescomplemented
187C22⋊C8—132no—
188C4×C8—132no—
189C2×C13—82no—
190C2×C13#53511yescharacteristic
191C2×C13C22×SD1611yescharacteristic
192C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
193D13—22no—
194D13—82no—
195C24—262no—
196C2×Q8—131no—
197C2×Q8—261no—
198C2×Q8C22×D1311yescharacteristic
199C2×D4—21no—
200C2×D4—21no—
201C2×D4—132no—
202C2×D4—262no—
203C2×D4—262no—
204C2×D4—262no—
205C2×D4—261no—
206C2×D4—261no—
207C2×D4—524no—
208C2×D4—522no—
209C2×D4—522no—
210C2×D4—524no—
211C2×D4C22×D1312yes—
212C22×C4—131no—
213C22×C4—131no—
214C22×C4—131no—
215SD16—42no—
216SD16—522no—
217SD16—522no—
218SD16—522no—
219C2×C8—132no—
220C2×C8C22×D1312yes—
221C4⋊C4—21no—
222C4⋊C4—131no—
223C4⋊C4—261no—
224C4⋊C4—261no—
225C4⋊C4—261no—
226C4⋊C4—261no—
227C4⋊C4—261no—
228C4⋊C4—261no—
229C4⋊C4C22×D1311yescharacteristic
230C22⋊C4—261no—
231C22⋊C4—261no—
232C42—21no—
233C42—131no—
234C42—131no—
235C42—131no—
236C42—261no—
237C42C22×D1311yescharacteristic
238C13#320811yescharacteristic, complemented, Sylow
239C23—22no—
240C23—131no—
241C23—262no—
242C23—524no—
243C23—524no—
244C23—524no—
245Q8—21no—
246Q8—21no—
247Q8—261no—
248Q8—261no—
249Q8—522no—
250D4—22no—
251D4—22no—
252D4—42no—
253D4—42no—
254D4—262no—
255D4—262no—
256D4—522no—
257D4—524no—
258D4—524no—
259D4—524no—
260D4—522no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—131no—
264C2×C4—131no—
265C2×C4—134no—
266C2×C4—131no—
267C2×C4—262no—
268C2×C4—261no—
269C2×C4—261no—
270C2×C4—261no—
271C2×C4—261no—
272C2×C4D4×D1311yescharacteristic
273C2×C4D4×D1311yescharacteristic
274C2×C4C23×D1311yescharacteristic
275C8—22no—
276C8—262no—
277C22—42no—
278C22—42no—
279C22—42no—
280C22—132no—
281C22—261no—
282C22—261no—
283C22—522no—
284C22—522no—
285C22—522no—
286C22—1048no—
287C22C2×D4×D1311yescharacteristic
288C4—21no—
289C4—41no—
290C4—41no—
291C4—132no—
292C4—132no—
293C4—261no—
294C4—521no—
295C4—521no—
296C4SD16×D1312yes—
297C4#8825111yescharacteristic
298C4#8825611yescharacteristic
299C2—82no—
300C2—262no—
301C2—1042no—
302C2#1171931211yescharacteristic
303C2C2×SD16×D1311yescharacteristic
304C2D13×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#460C2
socleC22×C13C22×D4
prime radicalD13×#127C2
hypercenter#460D13
hypocenterC13#3208
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
2. #11719283C2semidirect
3. C13×#460C2semidirect
4. #11718836C2semidirect
5. #11718830C2semidirect
6. #11718736C2semidirect
7. #11718688C2semidirect
8. #11718509C2semidirect
9. #11718494C2semidirect
10. #11718437C2semidirect
11. #11718421C2semidirect
15. C2×C13×SD16C22semidirect
17. C4×Q8×C13C22semidirect
19. #88198C22semidirect
20. C2×#6106C22semidirect
24. C2×#6105C22semidirect
25. C2×#6095C22semidirect
29. #88142C22semidirect
34. C4×Dic26C22semidirect
35. C13×C4⋊C8C22semidirect
36. C13×#102C22semidirect
37. #88072C22semidirect
38. #88061C22semidirect
40. C8×Dic13C22semidirect
41. #88049C22semidirect
42. C4⋊#1055C22semidirect
119. C4×D13SD16semidirect
132. #460D13semidirect
164. C2×SD16C2×D13semidirect
178. C4×Q8C2×D13semidirect
182. C4⋊C8C2×D13semidirect
186. #102C2×D13semidirect
238. C13#3208semidirect

Maximal subgroups

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

subgroupindex
D13×#1272
#117192832
C13×#4602
#117188362
#117188302
#117187362
#117186882
#117185092
#117184942
#117184372
#117184212
#320813