Finite Group Databasebeta

← #13125855

Subgroups — #13125855

Order 1664.

490 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 113 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#11719396C211yesmaximal, characteristic, complemented
3C13×#490C211yesmaximal, characteristic, complemented
4#11718735C211yesmaximal, characteristic, complemented
5#11718728C211yesmaximal, characteristic, complemented
6#11718447C212yesmaximal, complemented
7#11718437C212yesmaximal, complemented
8#11718434C212yesmaximal, complemented
9#11718423C212yesmaximal, complemented
10#11718373C211yesmaximal, characteristic, complemented
11#11718366C211yesmaximal, characteristic, complemented
12C2×D4×D13—21no—
13C2×D4×D13—21no—
14C2×D4×D13C2212yes—
15C13×#127C2211yescharacteristic
16C13×#125C2211yescharacteristic, complemented
17#88194—21no—
18#88194—21no—
19#88194C2212yes—
20C2×#6105C2212yescomplemented
21C2×#6104C2212yescomplemented
22C2×D104C2212yescomplemented
23C2×#6095C2212yescomplemented
24#88152—21no—
25#88151C2211yescharacteristic
26#88149C2211yescharacteristic
27#88148—21no—
28#88147—21no—
29#88147C2211yescharacteristic, complemented
30#88146—21no—
31#88141C2211yescharacteristic, complemented
32#88129C2211yescharacteristic, complemented
33#88128C2211yescharacteristic
34C42×D13C2211yescharacteristic
35C13×#102C2212yescomplemented
36C13×#102C2212yescomplemented
37C13×#97C2211yescharacteristic, complemented
38#88060C2212yes—
39#88054C2212yescomplemented
40#88049C2212yescomplemented
41#88049C2212yescomplemented
42#88043C2211yescharacteristic, complemented
43C23×D13—22no—
44C2×D4×C13—21no—
45C2×D4×C13—21no—
46C2×D4×C13C2312yes—
47C2×C22⋊D13—22no—
48C2×C22⋊D13—22no—
49C2×C22⋊D13—22no—
50D4×D13—42no—
51D4×D13—42no—
52D4×D13—44no—
53D4×D13—44no—
54C2×D52—21no—
55C2×D52—21no—
56C2×D52—21no—
57C2×D52C2312yes—
58C2×D52C2311yescharacteristic
59C2×C4×D13—21no—
60C2×C4×D13D411yescharacteristic
61C2×C4×D13D411yescharacteristic
62C2×C4×D13C2311yescharacteristic
63C2×Dic26C2311yescharacteristic
64C2×C8×C13C2312yes—
65C13×C4⋊C4—21no—
66C13×C4⋊C4—21no—
67C13×C4⋊C4C2311yescharacteristic
68C13×C4⋊C4C2311yescharacteristic
69C42×C13C2311yescharacteristic
70#6105—42no—
71#6104—42no—
72#6103—21no—
73#6103—21no—
74#6103—21no—
75#6103—21no—
76#6103—21no—
77C4⋊Dic13—21no—
78#6101—21no—
79C4×Dic13—21no—
80C4×Dic13D411yescharacteristic
81C4×Dic13D411yescharacteristic
82C4×Dic13C2311yescharacteristic
83C2×#1055C2312yes—
84D104—42no—
85#6095—42no—
86#3217—131nomaximal, Sylow
87C23×C13—22no—
88C22×D13—21no—
89C22×D13—22no—
90C22×D13—44no—
91C22×D13—44no—
92C22×D13—44no—
93C22×D13C2×D411yescharacteristic
94D4×C13—22no—
95D4×C13—22no—
96D4×C13—42no—
97D4×C13—42no—
98C2×C4×C13—21no—
99C2×C4×C13—21no—
100C2×C4×C13C2×D411yescharacteristic
101C2×C4×C13C2×D411yescharacteristic
102C2×C4×C13C2411yescharacteristic
103C22⋊D13—44no—
104C22⋊D13—44no—
105C22⋊D13—44no—
106C2×Dic13—21no—
107C2×Dic13C2×D411yescharacteristic
108C2×Dic13C2×D411yescharacteristic
109C2×Dic13C2×D411yescharacteristic
110D52—22no—
111D52—22no—
112D52—22no—
113D52—42no—
114D52—42no—
115D52—42no—
116C4×D13—22no—
117C4×D13—22no—
118C4×D13—22no—
119C4×D13—42no—
120Dic26—22no—
121C8×C13—22no—
122#1055—22no—
123C2×#127—131no—
124#529—131no—
125#496—131no—
126#496—131no—
127#490—131no—
128#490D1311yescharacteristic, complemented
129#460—132no—
130#459—132no—
131#450—132no—
132#447—132no—
133#432—131no—
134C22×C13—42no—
135C22×C13—42no—
136C22×C13—42no—
137C22×C13C22×D411yescharacteristic
138C2×D13—21no—
139C2×D13—21no—
140C2×D13—42no—
141C2×D13—41no—
142C2×D13—41no—
143C2×D13—42no—
144C2×D13—42no—
145C2×D13—41no—
146C2×D13—88no—
147C2×D13AGL(1,ℤ/8)12yes—
148C4×C13—21no—
149C4×C13—21no—
150C4×C13—41no—
151C4×C13—41no—
152C4×C13H(5,𝔽2)12yes—
153Dic13—21no—
154Dic13—21no—
155Dic13—41no—
156Dic13AGL(1,ℤ/8)12yes—
157C22×D4—132no—
158C22×D4—261no—
159C22×D4—261no—
160C2×SD16—132no—
161C2×SD16—132no—
162C2×D8—132no—
163C2×D8—132no—
164#127—132no—
165#127—131no—
166#127—261no—
167#127—261no—
168#127C2×D1311yescharacteristic
169#126—261no—
170#125C2×D1311yescharacteristic, complemented
171#124—131no—
172#123—261no—
173C22⋊Q8—131no—
174#121—131no—
175C4×Q8—131no—
176C4×D4—131no—
177C4×D4—261no—
178#117—261no—
179C2×C42—131no—
180C4⋊C8—132no—
181#102—132no—
182#102—132no—
183#102C2×D1312yescomplemented
184#102C2×D1312yescomplemented
185C22⋊C8—132no—
186#97—131no—
187#97C2×D1311yescharacteristic, complemented
188C2×C13—82no—
189C2×C13#53511yescharacteristic
190C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
191C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
192D13—22no—
193D13—81no—
194D13—82no—
195C24—262no—
196C2×Q8—131no—
197C2×D4—21no—
198C2×D4—21no—
199C2×D4—132no—
200C2×D4—131no—
201C2×D4—261no—
202C2×D4—262no—
203C2×D4—262no—
204C2×D4—262no—
205C2×D4—261no—
206C2×D4—261no—
207C2×D4—522no—
208C2×D4—522no—
209C2×D4—524no—
210C2×D4—524no—
211C2×D4C22×D1312yes—
212C22×C4—131no—
213C22×C4—131no—
214C22×C4—131no—
215C22×C4—261no—
216SD16—522no—
217SD16—522no—
218D8—522no—
219D8—522no—
220C2×C8—132no—
221C2×C8C22×D1312yes—
222C4⋊C4—21no—
223C4⋊C4—21no—
224C4⋊C4—261no—
225C4⋊C4—261no—
226C4⋊C4C22×D1311yescharacteristic
227C4⋊C4C22×D1311yescharacteristic
228C22⋊C4—261no—
229C22⋊C4—261no—
230C22⋊C4—261no—
231C22⋊C4—261no—
232C22⋊C4—261no—
233C42—131no—
234C42—131no—
235C42—131no—
236C42—261no—
237C42C22×D1311yescharacteristic
238C13#321711yescharacteristic, complemented, Sylow
239C23—22no—
240C23—131no—
241C23—261no—
242C23—262no—
243C23—524no—
244C23—524no—
245C23—524no—
246Q8—262no—
247D4—22no—
248D4—22no—
249D4—42no—
250D4—42no—
251D4—262no—
252D4—262no—
253D4—262no—
254D4—522no—
255D4—522no—
256D4—522no—
257D4—524no—
258D4—524no—
259D4—524no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—131no—
263C2×C4—131no—
264C2×C4—131no—
265C2×C4—262no—
266C2×C4—262no—
267C2×C4—262no—
268C2×C4—261no—
269C2×C4—522no—
270C2×C4D4×D1311yescharacteristic
271C2×C4D4×D1311yescharacteristic
272C2×C4C23×D1311yescharacteristic
273C8—22no—
274C8—262no—
275C22—42no—
276C22—42no—
277C22—42no—
278C22—132no—
279C22—261no—
280C22—261no—
281C22—521no—
282C22—522no—
283C22—522no—
284C22—521no—
285C22—522no—
286C22—521no—
287C22—1048no—
288C22C2×D4×D1311yescharacteristic
289C4—21no—
290C4—21no—
291C4—41no—
292C4—41no—
293C4—132no—
294C4—261no—
295C4—261no—
296C4—521no—
297C4#8825612yes—
298C2—82no—
299C2—262no—
300C2—1042no—
301C2—1041no—
302C2#1171937911yescharacteristic
303C2D13×AGL(1,ℤ/8)11yescharacteristic
304C2D13×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#490C2
socleC22×C13C22×D4
hypercenter#490D13
hypocenterC13#3217
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
1. D13×#127C2semidirect
2. #11719396C2semidirect
3. C13×#490C2semidirect
4. #11718735C2semidirect
5. #11718728C2semidirect
6. #11718447C2semidirect
7. #11718437C2semidirect
8. #11718434C2semidirect
9. #11718423C2semidirect
10. #11718373C2semidirect
11. #11718366C2semidirect
16. C13×#125C22semidirect
20. C2×#6105C22semidirect
21. C2×#6104C22semidirect
22. C2×D104C22semidirect
23. C2×#6095C22semidirect
29. #88147C22semidirect
31. #88141C22semidirect
32. #88129C22semidirect
35. C13×#102C22semidirect
36. C13×#102C22semidirect
37. C13×#97C22semidirect
39. #88054C22semidirect
40. #88049C22semidirect
41. #88049C22semidirect
42. #88043C22semidirect
128. #490D13semidirect
170. #125C2×D13semidirect
183. #102C2×D13semidirect
184. #102C2×D13semidirect
187. #97C2×D13semidirect
238. C13#3217semidirect

Maximal subgroups

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

subgroupindex
D13×#1272
#117193962
C13×#4902
#117187352
#117187282
#117184472
#117184372
#117184342
#117184232
#117183732
#117183662
#321713