Finite Group Databasebeta

← #13126455

Subgroups — #13126455

Order 1664.

556 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 556 conjugacy classes of subgroups — too many to draw. Only its 125 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×#88165C212yesmaximal, complemented
2#11719423C211yesmaximal, characteristic, complemented
3#11719422C211yesmaximal, characteristic, complemented
4C13×#493C211yesmaximal, characteristic, complemented
5#11718820C212yesmaximal, complemented
6#11718819C212yesmaximal, complemented
7#11718817C212yesmaximal, complemented
8#11718736C211yesmaximal, characteristic, complemented
9#11718733C211yesmaximal, characteristic, complemented
10C4×#6095C211yesmaximal, characteristic, complemented
11#11718349C211yesmaximal, characteristic, complemented
12C2×#6129C2212yescomplemented
13C2×D4×D13—21no—
14C2×D4×D13C2212yes—
15C2×C13×D8C2212yescomplemented
16C2×C13×D8C2212yescomplemented
17C13×#127C2211yescharacteristic
18C13×#127C2211yescharacteristic, complemented
19#88194—21no—
20#88193—22no—
21#88192—21no—
22#88192C2212yes—
23#88192C2212yescomplemented
24#88191—22no—
25D4×Dic13—21no—
26C2×#6105C2212yescomplemented
27C2×#6104C2212yes—
28#88165—28no—
29C2×#6095C2211yescharacteristic
30C2×#6094C2212yescomplemented
31C4×D52C2211yescharacteristic
32C4×D52C2211yescharacteristic
33C4×Dic26C2211yescharacteristic, complemented
34C4×C8×C13C2211yescharacteristic, complemented
35#88072C2212yescomplemented
36#88072C2212yescomplemented
37#88061C2211yescharacteristic
38#88060C2212yescomplemented
39#88057C2211yescharacteristic, complemented
40#88056C2211yescharacteristic, complemented
41C4⋊#1055C2211yescharacteristic, complemented
42C23×D13—22no—
43C2×D4×C13—21no—
44C2×D4×C13—21no—
45C2×D4×C13—21no—
46C2×D4×C13—21no—
47C2×D4×C13C2312yes—
48C2×D4×C13C2312yes—
49C2×C22⋊D13—22no—
50C2×C22⋊D13—22no—
51C2×C22⋊D13—22no—
52C2×C22⋊D13—22no—
53C22×Dic13—22no—
54#6129—24no—
55#6129—42no—
56D4×D13—24no—
57D4×D13—42no—
58D4×D13—44no—
59C2×D52D411yescharacteristic
60C2×D52C2311yescharacteristic
61C2×C4×D13—21no—
62C2×C4×D13C2312yes—
63C2×Dic26C2311yescharacteristic
64C13×D8—24no—
65C13×D8—42no—
66C2×C8×C13C2311yescharacteristic
67C2×C8×C13C2311yescharacteristic
68C42×C13C2311yescharacteristic
69C22⋊Dic13—22no—
70C22⋊Dic13—22no—
71#6105—24no—
72#6104—24no—
73#6103—21no—
74#6103D412yes—
75C4⋊Dic13D411yescharacteristic
76C4⋊Dic13C2311yescharacteristic
77C4⋊Dic13C2311yescharacteristic
78#6101—21no—
79C4×Dic13—21no—
80C2×#1055C2312yes—
81#6095D414yescomplemented
82#6094—24no—
83#3274—131nomaximal, Sylow
84C23×C13—22no—
85C23×C13—22no—
86C22×D13—21no—
87C22×D13—44no—
88C22×D13—44no—
89C22×D13—82no—
90C22×D13C2×D412yes—
91D4×C13—22no—
92D4×C13—22no—
93D4×C13—22no—
94D4×C13—22no—
95D4×C13—42no—
96D4×C13—42no—
97D4×C13—81no—
98D4×C13—81no—
99C2×C4×C13C2×D411yescharacteristic
100C2×C4×C13C2×D411yescharacteristic
101C2×C4×C13C2411yescharacteristic
102C22⋊D13—44no—
103C22⋊D13—44no—
104C22⋊D13—44no—
105C22⋊D13—82no—
106C2×Dic13—21no—
107C2×Dic13—21no—
108C2×Dic13—21no—
109C2×Dic13—44no—
110C2×Dic13C2×D412yes—
111D52—22no—
112D52—21no—
113D52C2×D412yes—
114C4×D13—22no—
115C4×D13—22no—
116C4×D13—42no—
117Dic26—21no—
118Dic26C2×D412yescomplemented
119C8×C13—21no—
120C8×C13C2×D412yescomplemented
121#1055—22no—
122C2×AGL(1,ℤ/8)—132no—
123#550—131no—
124D42—131no—
125#493D1311yescharacteristic, complemented
126#469—132no—
127#460—131no—
128#459—131no—
129#449—132no—
130#447—132no—
131C4×SD16—131no—
132#436—131no—
133C22×C13—42no—
134C22×C13—42no—
135C22×C13—42no—
136C22×C13—42no—
137C22×C13—42no—
138C22×C13—42no—
139C22×C13C22×D411yescharacteristic
140C2×D13—22no—
141C2×D13—22no—
142C2×D13—22no—
143C2×D13—22no—
144C2×D13—41no—
145C2×D13—41no—
146C2×D13—88no—
147C4×C13—21no—
148C4×C13AGL(1,ℤ/8)12yescomplemented
149C4×C13C22×D411yescharacteristic
150C4×C13H(5,𝔽2)11yescharacteristic
151Dic13—22no—
152Dic13—22no—
153Dic13—41no—
154Dic13—41no—
155C2×#41—132no—
156C22×D4—132no—
157C22×D4—261no—
158AGL(1,ℤ/8)—268no—
159C2×SD16—132no—
160C2×SD16—131no—
161C2×D8—132no—
162C2×D8C2×D1312yescomplemented
163C2×D8C2×D1312yescomplemented
164C2×M16—132no—
165#127—261no—
166#127C2×D1311yescharacteristic
167#127C2×D1311yescharacteristic, complemented
168#121—132no—
169#121—132no—
170#121—262no—
171#121—261no—
172#120—262no—
173C4×Q8—131no—
174C4×D4—131no—
175C4×D4—131no—
176C4×D4—261no—
177#106—131no—
178C4⋊C8—131no—
179#103—131no—
180#102—132no—
181#102—132no—
182#102—131no—
183C22⋊C8—132no—
184C4×C8C2×D1311yescharacteristic, complemented
185C2×C13—82no—
186C2×C13—82no—
187C2×C13D4211yescharacteristic
188C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
189C2×C13#57611yescharacteristic
190D13—42no—
191D13—42no—
192C24—262no—
193#41—264no—
194#41—522no—
195C2×Q8—131no—
196C2×D4—21no—
197C2×D4—21no—
198C2×D4—21no—
199C2×D4—21no—
200C2×D4—131no—
201C2×D4—131no—
202C2×D4—262no—
203C2×D4—264no—
204C2×D4—262no—
205C2×D4—262no—
206C2×D4—262no—
207C2×D4—522no—
208C2×D4—524no—
209C2×D4C22×D1312yes—
210C2×D4C22×D1312yes—
211C22×C4—132no—
212C22×C4—262no—
213C22×C4—261no—
214SD16—134no—
215SD16—264no—
216D8—24no—
217D8—42no—
218D8—264no—
219M16—264no—
220C2×C8—132no—
221C2×C8C22×D1311yescharacteristic
222C2×C8C22×D1311yescharacteristic
223C4⋊C4—131no—
224C4⋊C4—131no—
225C4⋊C4—131no—
226C4⋊C4—261no—
227C22⋊C4—132no—
228C22⋊C4—262no—
229C22⋊C4—262no—
230C22⋊C4—261no—
231C42—261no—
232C42C22×D1311yescharacteristic
233C13#327411yescharacteristic, complemented, Sylow
234C23—22no—
235C23—22no—
236C23—132no—
237C23—261no—
238C23—524no—
239C23—524no—
240C23—1042no—
241Q8—132no—
242Q8—261no—
243D4—22no—
244D4—22no—
245D4—22no—
246D4—22no—
247D4—42no—
248D4—42no—
249D4—81no—
250D4—81no—
251D4—132no—
252D4—262no—
253D4—261no—
254D4—524no—
255D4—524no—
256D4—524no—
257D4—1042no—
258C2×C4—132no—
259C2×C4—261no—
260C2×C4—262no—
261C2×C4—262no—
262C2×C4—261no—
263C2×C4—261no—
264C2×C4—524no—
265C2×C4—522no—
266C2×C4D4×D1311yescharacteristic
267C2×C4D4×D1311yescharacteristic
268C2×C4C23×D1311yescharacteristic
269C8—21no—
270C8—262no—
271C8D4×D1312yescomplemented
272C22—42no—
273C22—42no—
274C22—42no—
275C22—42no—
276C22—42no—
277C22—42no—
278C22—262no—
279C22—262no—
280C22—262no—
281C22—262no—
282C22—521no—
283C22—521no—
284C22—1048no—
285C22C2×D4×D1311yescharacteristic
286C4—21no—
287C4—262no—
288C4—262no—
289C4—521no—
290C4—521no—
291C4#8816512yescomplemented
292C4C2×D4×D1311yescharacteristic
293C4#8825111yescharacteristic
294C2—82no—
295C2—82no—
296C2—522no—
297C2—522no—
298C2#1171942211yescharacteristic
299C2C2×#8816511yescharacteristic
300C2#1171946211yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#493C2
socleC22×C13C22×D4
hypercenter#493D13
hypocenterC13#3274
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #493

Complements

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

NH ≅ G/Ntype
1. C2×#88165C2semidirect
2. #11719423C2semidirect
3. #11719422C2semidirect
4. C13×#493C2semidirect
5. #11718820C2semidirect
6. #11718819C2semidirect
7. #11718817C2semidirect
8. #11718736C2semidirect
9. #11718733C2semidirect
10. C4×#6095C2semidirect
11. #11718349C2semidirect
12. C2×#6129C22semidirect
15. C2×C13×D8C22semidirect
16. C2×C13×D8C22semidirect
18. C13×#127C22semidirect
23. #88192C22semidirect
26. C2×#6105C22semidirect
30. C2×#6094C22semidirect
33. C4×Dic26C22semidirect
34. C4×C8×C13C22semidirect
35. #88072C22semidirect
36. #88072C22semidirect
38. #88060C22semidirect
39. #88057C22semidirect
40. #88056C22semidirect
41. C4⋊#1055C22semidirect
81. #6095D4semidirect
118. Dic26C2×D4semidirect
120. C8×C13C2×D4semidirect
125. #493D13semidirect
148. C4×C13AGL(1,ℤ/8)semidirect
162. C2×D8C2×D13semidirect
163. C2×D8C2×D13semidirect
167. #127C2×D13semidirect
184. C4×C8C2×D13semidirect
233. C13#3274semidirect
271. C8D4×D13semidirect
291. C4#88165semidirect

Maximal subgroups

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

subgroupindex
C2×#881652
#117194232
#117194222
C13×#4932
#117188202
#117188192
#117188172
#117187362
#117187332
C4×#60952
#117183492
#327413