Finite Group Databasebeta

← #13125822

Subgroups — #13125822

Order 1664.

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

normal subgroups only

This group has 444 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
1C2×#88201C211yesmaximal, characteristic, complemented
2#11719301C211yesmaximal, characteristic, complemented
3C13×#448C211yesmaximal, characteristic, complemented
4#11718888C211yesmaximal, characteristic, complemented
5#11718837C212yesmaximal, complemented
6#11718826C212yesmaximal, complemented
7#11718697C211yesmaximal, characteristic, complemented
8#11718480C212yesmaximal, complemented
9#11718456C212yesmaximal, complemented
10#11718393C211yesmaximal, characteristic, complemented
11#11718380C211yesmaximal, characteristic, complemented
12C22×Q8×C13C2211yescharacteristic
13C2×#6129—21no—
14C22×D52C2211yescharacteristic
15C2×C13×SD16C2212yescomplemented
16C13×#121C2211yescharacteristic
17#88201—21no—
18#88201—21no—
19#88201C2212yes—
20#88201C2212yes—
21C2×#6106C2212yescomplemented
22#88194C2211yescharacteristic, complemented
23#88193—21no—
24D4×Dic13C2211yescharacteristic, complemented
25C2×#6104C2212yes—
26#88184C2211yescharacteristic
27C2×#6103—21no—
28C2×#6103—21no—
29C2×C4×Dic13C2211yescharacteristic
30C2×D104C2212yes—
31#88147C2211yescharacteristic, complemented
32#88142C2211yescharacteristic, complemented
33#88139—21no—
34#88135—21no—
35C13×#103C2212yescomplemented
36C13×C22⋊C8C2211yescharacteristic
37#88075C2212yescomplemented
38C22⋊#1055C2211yescharacteristic
39#88061C2212yes—
40#88055C2212yescomplemented
41#88054C2212yescomplemented
42#88049C2212yes—
43C23×D13—21no—
44C2×Q8×C13—21no—
45C2×Q8×C13—42no—
46C2×Q8×C13C2312yes—
47C2×D4×C13—21no—
48C2×D4×C13C2311yescharacteristic
49C22×C4×C13—21no—
50C22×C4×C13C2311yescharacteristic
51C2×C22⋊D13—21no—
52C2×C22⋊D13—21no—
53C2×C22⋊D13—21no—
54C22×Dic13—21no—
55C22×Dic13D411yescharacteristic
56C22×Dic13D411yescharacteristic
57#6129—44no—
58C2×D52—21no—
59C2×D52—42no—
60C2×D52C2311yescharacteristic
61C2×D52C2312yes—
62C2×C4×D13—21no—
63C2×Dic26—21no—
64C13×SD16—42no—
65C2×C8×C13C2312yes—
66C13×C4⋊C4C2311yescharacteristic
67C13×C22⋊C4—21no—
68C22⋊Dic13—21no—
69#6106—42no—
70#6104—42no—
71#6103—21no—
72#6103—21no—
73#6103—22no—
74#6103—22no—
75#6103—22no—
76#6103—22no—
77C4⋊Dic13C2311yescharacteristic
78#6101—21no—
79C4×Dic13D411yescharacteristic
80C4×Dic13D411yescharacteristic
81C4×Dic13C2311yescharacteristic
82C4×Dic13C2311yescharacteristic
83C2×#1055C2312yes—
84D104—42no—
85#3213—131nomaximal, Sylow
86C23×C13—21no—
87C23×C13C2×D411yescharacteristic
88C22×D13—22no—
89C22×D13—21no—
90C22×D13—42no—
91C22×D13—42no—
92C22×D13—42no—
93Q8×C13—22no—
94Q8×C13—22no—
95Q8×C13—42no—
96D4×C13—22no—
97D4×C13—42no—
98C2×C4×C13—22no—
99C2×C4×C13—21no—
100C2×C4×C13—22no—
101C2×C4×C13—42no—
102C2×C4×C13C2×D411yescharacteristic
103C2×C4×C13C2411yescharacteristic
104C22⋊D13—42no—
105C22⋊D13—42no—
106C22⋊D13—42no—
107C2×Dic13—22no—
108C2×Dic13—21no—
109C2×Dic13—41no—
110C2×Dic13—42no—
111C2×Dic13C2×D411yescharacteristic
112C2×Dic13C2×D411yescharacteristic
113C2×Dic13C2×D411yescharacteristic
114C2×Dic13C2×D411yescharacteristic
115D52—22no—
116D52—22no—
117D52—22no—
118D52—42no—
119C4×D13—42no—
120Dic26—42no—
121C8×C13—22no—
122#1055—22no—
123#532—131no—
124C2×#124—131no—
125#496—132no—
126#489—132no—
127#463—132no—
128#463—132no—
129#448—131no—
130#448D1311yescharacteristic, complemented
131#447—131no—
132#447—131no—
133#432—131no—
134C22×C13—21no—
135C22×C13—21no—
136C22×C13—41no—
137C22×C13—41no—
138C22×C13—41no—
139C22×C13AGL(1,ℤ/8)12yes—
140C22×C13C22×D411yescharacteristic
141C2×D13—42no—
142C2×D13—41no—
143C2×D13—41no—
144C2×D13—42no—
145C2×D13—41no—
146C2×D13—42no—
147C2×D13—84no—
148C4×C13—21no—
149C4×C13—42no—
150C4×C13—41no—
151C4×C13H(5,𝔽2)12yes—
152Dic13—21no—
153Dic13—21no—
154Dic13—21no—
155Dic13—21no—
156Dic13—41no—
157C2×#41—261no—
158C22×Q8C2×D1311yescharacteristic
159C22×D4—131no—
160C2×SD16—132no—
161C2×SD16C2×D1312yescomplemented
162C2×D8—132no—
163C2×D8—132no—
164C4⋊Q8—131no—
165#127—131no—
166#124—132no—
167#124—132no—
168#124—261no—
169#124—261no—
170#124—261no—
171#121—131no—
172#121—261no—
173#121C2×D1311yescharacteristic
174C4×D4—131no—
175C4×D4—131no—
176C4×D4—261no—
177C2×C22⋊C4—261no—
178C2×C22⋊C4—261no—
179C2×C42—131no—
180C4⋊C8—132no—
181#103—132no—
182#103C2×D1312yescomplemented
183#102—132no—
184#102—132no—
185C22⋊C8—131no—
186C22⋊C8C2×D1311yescharacteristic
187#97—132no—
188C2×C13—22no—
189C2×C13—81no—
190C2×C13#53511yescharacteristic
191C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
192C2×C13#57511yescharacteristic
193D13—81no—
194D13—82no—
195C24—261no—
196#41—524no—
197C2×Q8—21no—
198C2×Q8—42no—
199C2×Q8—261no—
200C2×Q8C22×D1312yes—
201C2×D4—21no—
202C2×D4—132no—
203C2×D4—131no—
204C2×D4—261no—
205C2×D4—261no—
206C2×D4—261no—
207C2×D4—261no—
208C2×D4—522no—
209C2×D4C22×D1311yescharacteristic
210C22×C4—21no—
211C22×C4—131no—
212C22×C4—131no—
213C22×C4—261no—
214C22×C4—261no—
215C22×C4C22×D1311yescharacteristic
216SD16—42no—
217SD16—522no—
218D8—522no—
219D8—522no—
220C2×C8—132no—
221C2×C8C22×D1312yes—
222C4⋊C4—131no—
223C4⋊C4—261no—
224C4⋊C4C22×D1311yescharacteristic
225C22⋊C4—21no—
226C22⋊C4—262no—
227C22⋊C4—262no—
228C22⋊C4—262no—
229C22⋊C4—262no—
230C22⋊C4—261no—
231C22⋊C4—261no—
232C22⋊C4—261no—
233C42—131no—
234C42—131no—
235C42—131no—
236C42—131no—
237C13#321311yescharacteristic, complemented, Sylow
238C23—21no—
239C23—262no—
240C23—261no—
241C23—522no—
242C23—522no—
243C23—522no—
244C23D4×D1311yescharacteristic
245Q8—22no—
246Q8—22no—
247Q8—42no—
248Q8—522no—
249D4—22no—
250D4—42no—
251D4—262no—
252D4—262no—
253D4—262no—
254D4—522no—
255D4—522no—
256D4—522no—
257D4—522no—
258C2×C4—22no—
259C2×C4—21no—
260C2×C4—22no—
261C2×C4—42no—
262C2×C4—131no—
263C2×C4—131no—
264C2×C4—131no—
265C2×C4—131no—
266C2×C4—262no—
267C2×C4—261no—
268C2×C4—522no—
269C2×C4—521no—
270C2×C4—522no—
271C2×C4D4×D1311yescharacteristic
272C2×C4C23×D1311yescharacteristic
273C8—22no—
274C8—262no—
275C22—21no—
276C22—21no—
277C22—41no—
278C22—41no—
279C22—41no—
280C22—521no—
281C22—522no—
282C22—521no—
283C22—522no—
284C22—522no—
285C22—521no—
286C22—1044no—
287C22#8816812yes—
288C22C2×D4×D1311yescharacteristic
289C4—21no—
290C4—41no—
291C4—42no—
292C4—261no—
293C4—261no—
294C4—261no—
295C4—261no—
296C4—521no—
297C4#8825112yes—
298C2—22no—
299C2—81no—
300C2—1042no—
301C2—1041no—
302C2#1171929711yescharacteristic
303C2C2×#8816811yescharacteristic
304C2#1171948211yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#448C2
socleC22×C13C22×D4
hypercenter#448D13
hypocenterC13#3213
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #448

Complements

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

NH ≅ G/Ntype
1. C2×#88201C2semidirect
2. #11719301C2semidirect
3. C13×#448C2semidirect
4. #11718888C2semidirect
5. #11718837C2semidirect
6. #11718826C2semidirect
7. #11718697C2semidirect
8. #11718480C2semidirect
9. #11718456C2semidirect
10. #11718393C2semidirect
11. #11718380C2semidirect
15. C2×C13×SD16C22semidirect
21. C2×#6106C22semidirect
22. #88194C22semidirect
24. D4×Dic13C22semidirect
31. #88147C22semidirect
32. #88142C22semidirect
35. C13×#103C22semidirect
37. #88075C22semidirect
40. #88055C22semidirect
41. #88054C22semidirect
130. #448D13semidirect
161. C2×SD16C2×D13semidirect
182. #103C2×D13semidirect
237. C13#3213semidirect

Maximal subgroups

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

subgroupindex
C2×#882012
#117193012
C13×#4482
#117188882
#117188372
#117188262
#117186972
#117184802
#117184562
#117183932
#117183802
#321313