Finite Group Databasebeta

← #13124078

Subgroups — #13124078

Order 1664.

758 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 758 conjugacy classes of subgroups — too many to draw. Only its 165 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
1C22×C13×#41C211yesmaximal, characteristic, complemented
2C2×#88196C211yesmaximal, characteristic, complemented
3C2×#88186C211yesmaximal, characteristic, complemented
4#11719496C211yesmaximal, characteristic, complemented
5#11718900C214yesmaximal, complemented
6#11718899C214yesmaximal, complemented
7#11718886C211yesmaximal, characteristic, complemented
8#11718876C211yesmaximal, characteristic, complemented
9#11718868C211yesmaximal, characteristic, complemented
10C2×C13×#41—24no—
11C2×C13×#41—24no—
12C2×C13×#41—22no—
13C2×C13×#41C2214yes—
14C22×Q8×C13C2211yescharacteristic
15C22×D4×C13—21no—
16C22×D4×C13C2211yescharacteristic
17C23×C4×C13—21no—
18C23×C4×C13C2211yescharacteristic
19C2×#6127C2211yescharacteristic
20#88207—21no—
21C2×#6107C2212yescomplemented
22#88196—24no—
23C2×#6106C2212yescomplemented
24C2×#6105C2212yescomplemented
25#88186—24no—
26C2×#6104C2212yescomplemented
27#88184C2212yescomplemented
28#88183—21no—
29C4×C22⋊D13—22no—
30#88180C2211yescharacteristic
31#88178C2212yescomplemented
32C2×#6099C2211yescharacteristic
33C2×#6099C2211yescharacteristic
34#88075C2214yescomplemented
35#88072C2214yescomplemented
36C22⋊#1055C2214yescomplemented
37C24×C13—21no—
38C24×C13D411yescharacteristic
39C13×#41—216no—
40C13×#41—28no—
41C13×#41—28no—
42C2×Q8×C13—22no—
43C2×Q8×C13—21no—
44C2×Q8×C13D414yescomplemented
45C2×Q8×C13C2312yes—
46C2×D4×C13—28no—
47C2×D4×C13—24no—
48C2×D4×C13—21no—
49C2×D4×C13—22no—
50C2×D4×C13D414yescomplemented
51C2×D4×C13C2312yes—
52C22×C4×C13—28no—
53C22×C4×C13—21no—
54C22×C4×C13—24no—
55C22×C4×C13—22no—
56C22×C4×C13—22no—
57C22×C4×C13D412yes—
58C22×C4×C13D411yescharacteristic
59C22×C4×C13C2312yes—
60C22×C4×C13C2311yescharacteristic
61C2×C22⋊D13—22no—
62C2×C22⋊D13—21no—
63#6127—22no—
64#6127—22no—
65C2×D52C2311yescharacteristic
66C2×C4×D13—21no—
67C2×Dic26C2311yescharacteristic
68C22⋊Dic13—22no—
69C22⋊Dic13—21no—
70#6107—24no—
71#6106—24no—
72#6105—24no—
73#6104—24no—
74#6103—22no—
75C4⋊Dic13C2312yes—
76#6101—22no—
77C4×Dic13—21no—
78#6099—22no—
79#6099—22no—
80C2×#1055C2312yes—
81C2×#1055C2312yes—
82#3005—131nomaximal, Sylow
83C23×C13—22no—
84C23×C13—24no—
85C23×C13—22no—
86C23×C13—42no—
87C23×C13—44no—
88C23×C13C2×D412yes—
89C23×C13C2×D411yescharacteristic
90C22×D13—21no—
91Q8×C13—24no—
92Q8×C13—22no—
93Q8×C13C2×D414yes—
94D4×C13—216no—
95D4×C13—24no—
96D4×C13—22no—
97D4×C13C2×D414yes—
98C2×C4×C13—216no—
99C2×C4×C13—22no—
100C2×C4×C13—24no—
101C2×C4×C13—22no—
102C2×C4×C13—24no—
103C2×C4×C13—22no—
104C2×C4×C13—22no—
105C2×C4×C13C2×D412yes—
106C2×C4×C13C2×D411yescharacteristic
107C2×C4×C13C2×D412yes—
108C2×C4×C13C2×D412yes—
109C2×C4×C13C2411yescharacteristic
110C22⋊D13—44no—
111C22⋊D13—42no—
112C2×Dic13—22no—
113C2×Dic13—21no—
114D52—21no—
115D52—21no—
116C4×D13—42no—
117Dic26—21no—
118Dic26—21no—
119#1055—22no—
120#1055—22no—
121C22×#41D1311yescharacteristic, complemented
122C2×#137—131no—
123C2×AGL(1,ℤ/8)—131no—
124#525—131no—
125#452—134no—
126#449—134no—
127#419—131no—
128#418—131no—
129#407—131no—
130C22×C13—22no—
131C22×C13—22no—
132C22×C13—24no—
133C22×C13—22no—
134C22×C13—22no—
135C22×C13—44no—
136C22×C13—48no—
137C22×C13—44no—
138C22×C13#12012yes—
139C22×C13C22×D411yescharacteristic
140C2×D13—41no—
141C2×D13—42no—
142C4×C13—22no—
143C4×C13—24no—
144C4×C13#12012yes—
145C4×C13C22×D411yescharacteristic
146C4×C13C22×D411yescharacteristic
147Dic13—41no—
148Dic13—42no—
149C2×#41—24no—
150C2×#41—24no—
151C2×#41—22no—
152C2×#41—131no—
153C2×#41C2×D1314yes—
154C22×Q8C2×D1311yescharacteristic
155C22×D4—21no—
156C22×D4C2×D1311yescharacteristic
157C23×C4—21no—
158C23×C4C2×D1311yescharacteristic
159#137—264no—
160AGL(1,ℤ/8)—264no—
161C2×Q16—132no—
162C2×SD16—132no—
163C2×SD16—132no—
164C2×D8—132no—
165C2×M16—131no—
166C2×M16—131no—
167#123—261no—
168C22⋊Q8—132no—
169#121—132no—
170#120—261no—
171C4×D4—262no—
172#117—131no—
173#103—134no—
174#102—134no—
175C22⋊C8—134no—
176C2×C13—22no—
177C2×C13—42no—
178C2×C13—44no—
179C2×C13C2×#12011yescharacteristic
180C2×C13#57512yes—
181D13—81no—
182C24—21no—
183C24C22⋊D1311yescharacteristic
184#41—216no—
185#41—28no—
186#41—28no—
187#41—262no—
188#41—262no—
189C2×Q8—22no—
190C2×Q8—21no—
191C2×Q8—131no—
192C2×Q8C22⋊D1314yescomplemented
193C2×Q8C22×D1312yes—
194C2×D4—28no—
195C2×D4—24no—
196C2×D4—21no—
197C2×D4—22no—
198C2×D4—131no—
199C2×D4—262no—
200C2×D4—261no—
201C2×D4C22⋊D1314yescomplemented
202C2×D4C22×D1312yes—
203C22×C4—28no—
204C22×C4—21no—
205C22×C4—24no—
206C22×C4—22no—
207C22×C4—22no—
208C22×C4—261no—
209C22×C4C22⋊D1312yes—
210C22×C4C22⋊D1311yescharacteristic
211C22×C4C22×D1312yes—
212C22×C4C22×D1311yescharacteristic
213Q16—264no—
214SD16—264no—
215SD16—264no—
216D8—264no—
217M16—262no—
218M16—262no—
219C2×C8—132no—
220C2×C8—132no—
221C4⋊C4—132no—
222C4⋊C4—262no—
223C22⋊C4—261no—
224C22⋊C4—262no—
225C22⋊C4—262no—
226C42—261no—
227C13#300511yescharacteristic, complemented, Sylow
228C23—22no—
229C23—24no—
230C23—22no—
231C23—42no—
232C23—44no—
233C23—261no—
234C23C2×C22⋊D1312yes—
235C23C2×C22⋊D1311yescharacteristic
236Q8—24no—
237Q8—22no—
238Q8—261no—
239Q8—261no—
240Q8C2×C22⋊D1314yes—
241D4—216no—
242D4—24no—
243D4—22no—
244D4—261no—
245D4—261no—
246D4—524no—
247D4—522no—
248D4C2×C22⋊D1314yes—
249C2×C4—216no—
250C2×C4—22no—
251C2×C4—24no—
252C2×C4—22no—
253C2×C4—24no—
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—262no—
257C2×C4—261no—
258C2×C4—522no—
259C2×C4C2×C22⋊D1312yes—
260C2×C4C2×C22⋊D1311yescharacteristic
261C2×C4C2×C22⋊D1312yes—
262C2×C4C2×C22⋊D1312yes—
263C2×C4C23×D1311yescharacteristic
264C8—262no—
265C8—262no—
266C22—22no—
267C22—22no—
268C22—22no—
269C22—22no—
270C22—24no—
271C22—44no—
272C22—48no—
273C22—44no—
274C22—522no—
275C22—521no—
276C22#8820712yes—
277C22C22×C22⋊D1311yescharacteristic
278C4—22no—
279C4—24no—
280C4—522no—
281C4—521no—
282C4#8820712yes—
283C4C22×C22⋊D1311yescharacteristic
284C4C22×C22⋊D1311yescharacteristic
285C2—22no—
286C2—42no—
287C2—44no—
288C2—1041no—
289C2#1171952712yes—
290C2C2×#8820711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC22×C13×#41C2
socleC22×C13C22×D4
hypercenterC22×#41D13
hypocenterC13#3005
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×#41

Complements

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

NH ≅ G/Ntype
1. C22×C13×#41C2semidirect
2. C2×#88196C2semidirect
3. C2×#88186C2semidirect
4. #11719496C2semidirect
5. #11718900C2semidirect
6. #11718899C2semidirect
7. #11718886C2semidirect
8. #11718876C2semidirect
9. #11718868C2semidirect
21. C2×#6107C22semidirect
23. C2×#6106C22semidirect
24. C2×#6105C22semidirect
26. C2×#6104C22semidirect
27. #88184C22semidirect
31. #88178C22semidirect
34. #88075C22semidirect
35. #88072C22semidirect
36. C22⋊#1055C22semidirect
44. C2×Q8×C13D4semidirect
50. C2×D4×C13D4semidirect
121. C22×#41D13semidirect
192. C2×Q8C22⋊D13semidirect
201. C2×D4C22⋊D13semidirect
227. C13#3005semidirect

Maximal subgroups

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

subgroupindex
C22×C13×#412
C2×#881962
C2×#881862
#117194962
#117189002
#117188992
#117188862
#117188762
#117188682
#300513