Finite Group Databasebeta

← #13124773

Subgroups — #13124773

Order 1664.

462 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 121 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×#121C211yesmaximal, characteristic
2C2×#88146C211yesmaximal, characteristic, complemented
3C13×#481C211yesmaximal, characteristic, complemented
4#11718694C211yesmaximal, characteristic, complemented
5#11718629C211yesmaximal, characteristic, complemented
6#11718527C212yesmaximal, complemented
7#11718522C212yesmaximal, complemented
8#11718445C212yesmaximal, complemented
9#11718431C212yesmaximal, complemented
10#11718397C211yesmaximal, characteristic, complemented
11#11718387C211yesmaximal, characteristic, complemented
12C2×D4×D13—21no—
13C2×D4×D13C2211yescharacteristic
14C22×C4×D13C2211yescharacteristic
15C13×#121C2211yescharacteristic
16C2×C13×C4⋊C4C2211yescharacteristic, complemented
17#88193—21no—
18#88192C2211yescharacteristic
19#88184C2211yescharacteristic
20C2×#6103—21no—
21C2×C4⋊Dic13C2211yescharacteristic, complemented
22C2×C4×Dic13—21no—
23C2×#6094C2212yes—
24#88149C2211yescharacteristic
25#88146—21no—
26#88146—21no—
27#88146C2212yes—
28#88146C2212yescomplemented
29C4⋊C4×D13C2211yescharacteristic
30#88138—21no—
31C22⋊C4×D13—21no—
32C13×#106C2212yescomplemented
33C13×#102C2212yescomplemented
34C13×C22⋊C8C2211yescharacteristic, complemented
35#88072C2212yescomplemented
36C22⋊#1055C2211yescharacteristic, complemented
37#88061C2212yescomplemented
38#88060C2212yescomplemented
39#88058C2212yescomplemented
40#88049C2212yescomplemented
41#88048C2212yescomplemented
42#88047C2212yescomplemented
43C23×D13—21no—
44C23×D13D411yescharacteristic
45C2×D4×C13—21no—
46C2×D4×C13C2311yescharacteristic
47C22×C4×C13—21no—
48C22×C4×C13C2311yescharacteristic
49C2×C22⋊D13—21no—
50C2×C22⋊D13—21no—
51C2×C22⋊D13—21no—
52C22×Dic13—21no—
53C22×Dic13D411yescharacteristic
54D4×D13—24no—
55D4×D13—44no—
56C2×D52—21no—
57C2×D52C2311yescharacteristic
58C2×C4×D13—24no—
59C2×C4×D13—21no—
60C2×C4×D13D411yescharacteristic
61C2×C4×D13D411yescharacteristic
62C2×C4×D13C2311yescharacteristic
63C2×C4×D13C2311yescharacteristic
64C2×C8×C13C2312yes—
65C13×C4⋊C4—21no—
66C13×C4⋊C4C2312yes—
67C13×C4⋊C4C2311yescharacteristic
68C13×C22⋊C4—21no—
69C22⋊Dic13—21no—
70#6103—22no—
71#6103—22no—
72#6103—21no—
73#6103—21no—
74C4⋊Dic13—21no—
75C4⋊Dic13C2312yes—
76C4⋊Dic13C2311yescharacteristic
77#6101—21no—
78C4×Dic13—22no—
79C4×Dic13—22no—
80C2×#1055C2312yes—
81#6094—24no—
82#3094—131nomaximal, Sylow
83C23×C13—21no—
84C23×C13C2×D411yescharacteristic
85C22×D13—22no—
86C22×D13—22no—
87C22×D13—21no—
88C22×D13—41no—
89C22×D13—42no—
90C22×D13—42no—
91C22×D13—42no—
92C22×D13C2×D411yescharacteristic
93C22×D13C2×D411yescharacteristic
94D4×C13—22no—
95D4×C13—42no—
96C2×C4×C13—22no—
97C2×C4×C13—22no—
98C2×C4×C13—21no—
99C2×C4×C13—42no—
100C2×C4×C13C2×D411yescharacteristic
101C2×C4×C13C2411yescharacteristic
102C22⋊D13—42no—
103C22⋊D13—42no—
104C22⋊D13—42no—
105C2×Dic13—22no—
106C2×Dic13—22no—
107C2×Dic13—21no—
108C2×Dic13—42no—
109C2×Dic13C2×D411yescharacteristic
110C2×Dic13C2×D411yescharacteristic
111D52—22no—
112D52—42no—
113C4×D13—22no—
114C4×D13—22no—
115C4×D13—22no—
116C4×D13—42no—
117C4×D13#4114yes—
118C8×C13—22no—
119#1055—22no—
120C2×#121—131no—
121C2×#117—131no—
122#482—132no—
123#482—132no—
124#481—131no—
125#481D1311yescharacteristic, complemented
126#480—131no—
127#480—131no—
128#428—132no—
129#418—132no—
130#407—131no—
131C22×C13—21no—
132C22×C13—21no—
133C22×C13—41no—
134C22×C13—41no—
135C22×C13—41no—
136C22×C13AGL(1,ℤ/8)12yes—
137C22×C13C22×D411yescharacteristic
138C2×D13—21no—
139C2×D13—21no—
140C2×D13—21no—
141C2×D13—21no—
142C2×D13—21no—
143C2×D13—44no—
144C2×D13—41no—
145C2×D13—41no—
146C2×D13—41no—
147C2×D13—84no—
148C2×D13#12312yes—
149C4×C13—21no—
150C4×C13—41no—
151C4×C13—42no—
152C4×C13C2×#4112yes—
153Dic13—21no—
154Dic13—41no—
155Dic13—42no—
156Dic13#12312yes—
157C22×D4—131no—
158C22×D4—261no—
159C23×C4—131no—
160C2×M16—132no—
161#121—131no—
162#121—131no—
163#121—131no—
164#121—261no—
165#121—261no—
166#121C2×D1311yescharacteristic
167#117—132no—
168#117—132no—
169#117—261no—
170#117—261no—
171C2×C4⋊C4—131no—
172C2×C4⋊C4—131no—
173C2×C4⋊C4C2×D1311yescharacteristic, complemented
174C2×C22⋊C4—261no—
175C2×C22⋊C4—261no—
176C2×C42—261no—
177#107—132no—
178#107—132no—
179#106—132no—
180#106C2×D1312yescomplemented
181#102—132no—
182#102—132no—
183#102—132no—
184#102C2×D1312yescomplemented
185C22⋊C8—131no—
186C22⋊C8—132no—
187C22⋊C8C2×D1311yescharacteristic, complemented
188C2×C13—22no—
189C2×C13—81no—
190C2×C13C2×#12311yescharacteristic
191C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
192C2×C13#57511yescharacteristic
193D13—22no—
194D13—41no—
195D13—81no—
196C24—131no—
197C24—261no—
198C2×D4—21no—
199C2×D4—131no—
200C2×D4—261no—
201C2×D4—264no—
202C2×D4—261no—
203C2×D4—261no—
204C2×D4—261no—
205C2×D4—524no—
206C2×D4C22×D1311yescharacteristic
207C22×C4—21no—
208C22×C4—131no—
209C22×C4—131no—
210C22×C4—131no—
211C22×C4—131no—
212C22×C4—131no—
213C22×C4—264no—
214C22×C4—261no—
215C22×C4—261no—
216C22×C4C22×D1311yescharacteristic
217M16—264no—
218C2×C8—132no—
219C2×C8C22×D1312yes—
220C4⋊C4—21no—
221C4⋊C4—132no—
222C4⋊C4—131no—
223C4⋊C4—261no—
224C4⋊C4—261no—
225C4⋊C4C22×D1312yes—
226C4⋊C4C22×D1311yescharacteristic
227C22⋊C4—21no—
228C22⋊C4—261no—
229C22⋊C4—262no—
230C22⋊C4—262no—
231C22⋊C4—261no—
232C22⋊C4—261no—
233C42—262no—
234C42—262no—
235C13#309411yescharacteristic, complemented, Sylow
236C23—21no—
237C23—131no—
238C23—131no—
239C23—262no—
240C23—262no—
241C23—261no—
242C23—521no—
243C23—522no—
244C23—522no—
245C23—522no—
246C23D4×D1311yescharacteristic
247D4—22no—
248D4—42no—
249D4—262no—
250D4—522no—
251D4—522no—
252D4—522no—
253D4—522no—
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—21no—
257C2×C4—42no—
258C2×C4—131no—
259C2×C4—134no—
260C2×C4—131no—
261C2×C4—262no—
262C2×C4—262no—
263C2×C4—262no—
264C2×C4—262no—
265C2×C4—262no—
266C2×C4—261no—
267C2×C4—522no—
268C2×C4—522no—
269C2×C4D4×D1311yescharacteristic
270C2×C4C23×D1311yescharacteristic
271C8—22no—
272C8—262no—
273C22—21no—
274C22—21no—
275C22—41no—
276C22—41no—
277C22—41no—
278C22—132no—
279C22—261no—
280C22—261no—
281C22—261no—
282C22—261no—
283C22—261no—
284C22—524no—
285C22—521no—
286C22—521no—
287C22—521no—
288C22—1044no—
289C22#8816812yes—
290C22C2×D4×D1311yescharacteristic
291C4—21no—
292C4—41no—
293C4—42no—
294C4—132no—
295C4—261no—
296C4—522no—
297C4—521no—
298C4#41×D1312yes—
299C2—22no—
300C2—81no—
301C2—262no—
302C2—521no—
303C2—1041no—
304C2D13×#12311yescharacteristic
305C2C2×#8816811yescharacteristic
306C2#1171947811yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#481C2
socleC22×C13C22×D4
prime radicalD13×#121C2
hypercenter#481D13
hypocenterC13#3094
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #481

Complements

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

NH ≅ G/Ntype
2. C2×#88146C2semidirect
3. C13×#481C2semidirect
4. #11718694C2semidirect
5. #11718629C2semidirect
6. #11718527C2semidirect
7. #11718522C2semidirect
8. #11718445C2semidirect
9. #11718431C2semidirect
10. #11718397C2semidirect
11. #11718387C2semidirect
16. C2×C13×C4⋊C4C22semidirect
21. C2×C4⋊Dic13C22semidirect
28. #88146C22semidirect
32. C13×#106C22semidirect
33. C13×#102C22semidirect
34. C13×C22⋊C8C22semidirect
35. #88072C22semidirect
36. C22⋊#1055C22semidirect
37. #88061C22semidirect
38. #88060C22semidirect
39. #88058C22semidirect
40. #88049C22semidirect
41. #88048C22semidirect
42. #88047C22semidirect
125. #481D13semidirect
173. C2×C4⋊C4C2×D13semidirect
180. #106C2×D13semidirect
184. #102C2×D13semidirect
187. C22⋊C8C2×D13semidirect
235. C13#3094semidirect

Maximal subgroups

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

subgroupindex
D13×#1212
C2×#881462
C13×#4812
#117186942
#117186292
#117185272
#117185222
#117184452
#117184312
#117183972
#117183872
#309413