Finite Group Databasebeta

← #13124517

Subgroups — #13124517

Order 1664.

504 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 141 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×#88162C211yesmaximal, characteristic, complemented
2C2×#88161C211yesmaximal, characteristic, complemented
3#11719230C211yesmaximal, characteristic, complemented
4#11719215C211yesmaximal, characteristic, complemented
5C13×#428C211yesmaximal, characteristic, complemented
6#11718663C211yesmaximal, characteristic, complemented
7C2×#88049C211yesmaximal, characteristic, complemented
8#11718547C212yesmaximal, complemented
9#11718544C212yesmaximal, complemented
10#11718526C212yesmaximal, complemented
11#11718525C212yesmaximal, complemented
12C2×#6127C2211yescharacteristic
13C2×#6127C2211yescharacteristic
14C22×D52C2211yescharacteristic
15C2×C13×M16C2211yescharacteristic
16C13×#117C2211yescharacteristic
17C2×C13×C4⋊C4C2211yescharacteristic
18#88184—22no—
19C22×#1055C2211yescharacteristic
20#88162—24no—
21#88161—24no—
22C2×D104C2212yes—
23C2×#6095C2212yes—
24C2×#6094C2212yescomplemented
25C2×C8×D13C2212yescomplemented
26#88151—21no—
27#88151C2212yescomplemented
28#88149—21no—
29#88149C2212yes—
30#88149C2212yes—
31#88149C2212yescomplemented
32#88136—22no—
33#88129—21no—
34#88128—21no—
35C13×#107C2212yescomplemented
36C13×#106C2212yescomplemented
37#88050C2211yescharacteristic, complemented
38#88050C2211yescharacteristic, complemented
39#88049C2212yes—
40#88049C2212yes—
41#88049C2211yescharacteristic, complemented
42#88049C2211yescharacteristic, complemented
43C23×D13—21no—
44C22×C4×C13—21no—
45C22×C4×C13C2311yescharacteristic
46C2×C22⋊D13—21no—
47C2×C22⋊D13D412yes—
48#6127—22no—
49#6127—22no—
50#6127—22no—
51#6127—22no—
52C2×D52—22no—
53C2×D52—22no—
54C2×D52—21no—
55C2×D52—22no—
56C2×D52—22no—
57C2×D52—22no—
58C2×D52D411yescharacteristic
59C2×D52C2312yes—
60C2×D52C2311yescharacteristic
61C2×C4×D13—21no—
62C2×C4×D13C2312yes—
63C2×Dic26D411yescharacteristic
64C2×Dic26C2311yescharacteristic
65C13×M16D414yescomplemented
66C2×C8×C13C2312yes—
67C13×C4⋊C4—21no—
68C13×C4⋊C4C2311yescharacteristic
69C13×C4⋊C4C2312yes—
70C13×C4⋊C4C2311yescharacteristic
71C13×C22⋊C4—21no—
72C42×C13—21no—
73#6103—22no—
74#6103—22no—
75#6103—22no—
76#6103—22no—
77C4⋊Dic13—22no—
78C2×#1055—22no—
79C2×#1055C2311yescharacteristic
80C2×#1055C2311yescharacteristic
81D104—24no—
82#6095—24no—
83#6094—24no—
84C8×D13—24no—
85#3062—131nomaximal, Sylow
86C23×C13C2×D411yescharacteristic
87C22×D13—21no—
88C22×D13—22no—
89C22×D13—42no—
90C22×D13—81no—
91C22×D13—81no—
92C22×D13C2×D412yes—
93C2×C4×C13—22no—
94C2×C4×C13—21no—
95C2×C4×C13—21no—
96C2×C4×C13—81no—
97C2×C4×C13C2×D411yescharacteristic
98C2×C4×C13C2×D412yes—
99C2×C4×C13#4112yes—
100C2×C4×C13C2411yescharacteristic
101C22⋊D13—24no—
102C22⋊D13—42no—
103C2×Dic13—21no—
104C2×Dic13C2×D412yes—
105D52—22no—
106D52—22no—
107D52—21no—
108D52—22no—
109D52—21no—
110D52—42no—
111D52—82no—
112D52—82no—
113D52—82no—
114C4×D13—22no—
115C4×D13—22no—
116C4×D13—42no—
117Dic26—22no—
118Dic26—21no—
119Dic26—21no—
120C8×C13C2×D414yes—
121#1055—21no—
122#1055—21no—
123C2×AGL(1,ℤ/8)—131no—
124C2×#131—131no—
125#537—131no—
126#535—131no—
127#469—132no—
128#468—132no—
129#466—132no—
130#465—132no—
131#428D1311yescharacteristic, complemented
132#416—131no—
133C2×#102—131no—
134C22×C13—21no—
135C22×C13—21no—
136C22×C13#12112yes—
137C22×C13C22×D411yescharacteristic
138C2×D13—22no—
139C2×D13—22no—
140C2×D13—22no—
141C2×D13—41no—
142C2×D13—42no—
143C2×D13—41no—
144C2×D13—42no—
145C2×D13—42no—
146C2×D13—41no—
147C2×D13—84no—
148C4×C13—41no—
149C4×C13—42no—
150C4×C13—41no—
151C4×C13#12112yes—
152C4×C13C22×D411yescharacteristic
153C4×C13C2×#4111yescharacteristic
154Dic13—22no—
155Dic13—41no—
156C2×#41—131no—
157C2×#41—131no—
158C22×D4—131no—
159AGL(1,ℤ/8)—264no—
160C2×SD16—132no—
161C2×D8—132no—
162#131—264no—
163C2×M16—132no—
164C2×M16C2×D1311yescharacteristic
165C22×C8—131no—
166C22×C8—132no—
167#127—261no—
168#124—261no—
169C22⋊Q8—132no—
170C22⋊Q8—261no—
171#121—132no—
172#121—132no—
173#121—132no—
174#121—261no—
175#121—262no—
176#120—262no—
177#117C2×D1311yescharacteristic
178C2×C4⋊C4C2×D1311yescharacteristic
179#107C2×D1312yescomplemented
180#106C2×D1312yescomplemented
181#103—131no—
182#103—131no—
183#102—132no—
184#102—132no—
185#102—131no—
186#102—131no—
187C2×C13—22no—
188C2×C13C2×#12111yescharacteristic
189C2×C13#57611yescharacteristic
190C2×C13#57711yescharacteristic
191D13—42no—
192D13—81no—
193D13—82no—
194C24—261no—
195#41—262no—
196#41—262no—
197#41—262no—
198#41—262no—
199C2×Q8—131no—
200C2×Q8—131no—
201C2×D4—132no—
202C2×D4—131no—
203C2×D4—131no—
204C2×D4—132no—
205C2×D4—262no—
206C2×D4—262no—
207C2×D4—262no—
208C2×D4—261no—
209C2×D4—262no—
210C2×D4—261no—
211C2×D4—262no—
212C22×C4—21no—
213C22×C4—132no—
214C22×C4—261no—
215C22×C4C22×D1311yescharacteristic
216SD16—264no—
217D8—264no—
218M16—264no—
219M16D5214yescomplemented
220C2×C8—131no—
221C2×C8—131no—
222C2×C8—262no—
223C2×C8—264no—
224C2×C8C22×D1312yes—
225C4⋊C4—21no—
226C4⋊C4—262no—
227C4⋊C4C22×D1312yes—
228C4⋊C4C22×D1311yescharacteristic
229C4⋊C4C22×D1311yescharacteristic
230C22⋊C4—21no—
231C22⋊C4—262no—
232C22⋊C4—262no—
233C22⋊C4—262no—
234C22⋊C4—262no—
235C42—21no—
236C13#306211yescharacteristic, complemented, Sylow
237C23—132no—
238C23—261no—
239C23—262no—
240C23—522no—
241C23—1041no—
242C23—1041no—
243C23D4×D1311yescharacteristic
244Q8—262no—
245Q8—261no—
246Q8—261no—
247D4—264no—
248D4—262no—
249D4—261no—
250D4—262no—
251D4—262no—
252D4—261no—
253D4—522no—
254D4—522no—
255D4—1042no—
256D4—1042no—
257D4—1042no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—22no—
261C2×C4—81no—
262C2×C4—132no—
263C2×C4—262no—
264C2×C4—262no—
265C2×C4—261no—
266C2×C4—522no—
267C2×C4C2×D5212yes—
268C2×C4D4×D1311yescharacteristic
269C2×C4#613112yes—
270C2×C4C23×D1311yescharacteristic
271C8—261no—
272C8—261no—
273C8C2×D5214yes—
274C22—21no—
275C22—21no—
276C22—262no—
277C22—262no—
278C22—262no—
279C22—521no—
280C22—522no—
281C22—521no—
282C22—522no—
283C22—522no—
284C22—521no—
285C22—1044no—
286C22#8814912yes—
287C22C2×D4×D1311yescharacteristic
288C4—42no—
289C4—41no—
290C4—41no—
291C4—262no—
292C4—521no—
293C4#8814912yes—
294C4C22×D5211yescharacteristic
295C4C2×#613111yescharacteristic
296C2—22no—
297C2—522no—
298C2—1042no—
299C2—1041no—
300C2C2×#8814911yescharacteristic
301C2#1171947911yescharacteristic
302C2#1171948311yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#428C2
socleC22×C13C22×D4
hypercenter#428D13
hypocenterC13#3062
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
1. C2×#88162C2semidirect
2. C2×#88161C2semidirect
3. #11719230C2semidirect
4. #11719215C2semidirect
5. C13×#428C2semidirect
6. #11718663C2semidirect
7. C2×#88049C2semidirect
8. #11718547C2semidirect
9. #11718544C2semidirect
10. #11718526C2semidirect
11. #11718525C2semidirect
24. C2×#6094C22semidirect
25. C2×C8×D13C22semidirect
27. #88151C22semidirect
31. #88149C22semidirect
35. C13×#107C22semidirect
36. C13×#106C22semidirect
37. #88050C22semidirect
38. #88050C22semidirect
41. #88049C22semidirect
42. #88049C22semidirect
65. C13×M16D4semidirect
131. #428D13semidirect
179. #107C2×D13semidirect
180. #106C2×D13semidirect
219. M16D52semidirect
236. C13#3062semidirect

Maximal subgroups

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

subgroupindex
C2×#881622
C2×#881612
#117192302
#117192152
C13×#4282
#117186632
C2×#880492
#117185472
#117185442
#117185262
#117185252
#306213