Finite Group Databasebeta

← #13127157

Subgroups — #13127157

Order 1664.

430 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 430 conjugacy classes of subgroups — too many to draw. Only its 123 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
1C13×#547C211yesmaximal, characteristic, complemented
2#11719258C211yesmaximal, characteristic, complemented
3#11718755C211yesmaximal, characteristic, complemented
4#11718749C211yesmaximal, characteristic, complemented
5#11718700C212yesmaximal, complemented
6#11718698C212yesmaximal, complemented
7C4×#6105C211yesmaximal, characteristic, complemented
8#11718676C211yesmaximal, characteristic, complemented
9#11718673C211yesmaximal, characteristic, complemented
10#11718629C212yesmaximal, complemented
11#11718627C212yesmaximal, complemented
12C2×C13×#41—21no—
13C2×#6127C2212yes—
14C13×C4⋊Q8C2211yescharacteristic
15C13×#123—22no—
16C13×C22⋊Q8—21no—
17C13×#121C2212yes—
18C4×D4×C13C2211yescharacteristic
19C4×D4×C13C2211yescharacteristic
20C2×C13×C4⋊C4C2212yes—
21#88194—21no—
22C2×#6105C2211yescharacteristic
23C2×#6104C2212yes—
24#88184C2212yes—
25C2×#6099C2212yes—
26#88147—21no—
27#88138—22no—
28#88128C2211yescharacteristic
29C4×Dic26C2211yescharacteristic
30#88072C2211yescharacteristic
31C22⋊#1055C2212yes—
32#88050C2211yescharacteristic
33#88050C2212yes—
34#88049C2212yes—
35#88049C2212yes—
36#88049C2212yes—
37#88048C2211yescharacteristic
38#88048C2212yes—
39C4⋊#1055C2211yescharacteristic
40C4×#1055C2211yescharacteristic
41C13×#41—44no—
42C2×Q8×C13—21no—
43C2×D4×C13—22no—
44C2×D4×C13D411yescharacteristic
45C2×D4×C13C2311yescharacteristic
46C22×C4×C13—22no—
47C22×C4×C13—21no—
48C22×C4×C13C2312yes—
49C2×C22⋊D13—22no—
50C2×C22⋊D13—22no—
51#6127—24no—
52#6127—42no—
53C2×D52—21no—
54C2×D52—21no—
55C2×D52C2312yes—
56C2×C4×D13—22no—
57C2×Dic26C2311yescharacteristic
58C13×C4⋊C4—22no—
59C13×C4⋊C4—21no—
60C13×C4⋊C4D411yescharacteristic
61C13×C4⋊C4C2311yescharacteristic
62C13×C4⋊C4C2312yes—
63C13×C22⋊C4—21no—
64C13×C22⋊C4—22no—
65C13×C22⋊C4D412yes—
66C42×C13C2311yescharacteristic
67#6105—22no—
68#6104—42no—
69#6103—22no—
70C4⋊Dic13C2311yescharacteristic
71#6101—21no—
72C4×Dic13—21no—
73#6099—42no—
74C2×#1055C2311yescharacteristic
75C2×#1055C2312yes—
76C2×#1055C2311yescharacteristic
77#3332—131nomaximal, Sylow
78C23×C13—21no—
79C23×C13C2×D412yes—
80C22×D13—22no—
81Q8×C13—42no—
82D4×C13—22no—
83D4×C13—21no—
84D4×C13—21no—
85D4×C13—44no—
86C2×C4×C13—22no—
87C2×C4×C13—22no—
88C2×C4×C13—21no—
89C2×C4×C13—22no—
90C2×C4×C13—44no—
91C2×C4×C13—42no—
92C2×C4×C13C2×D411yescharacteristic
93C2×C4×C13C2×D412yes—
94C2×C4×C13C2×D411yescharacteristic
95C2×C4×C13C2411yescharacteristic
96C22⋊D13—44no—
97C22⋊D13—82no—
98C2×Dic13—21no—
99C2×Dic13—21no—
100D52—22no—
101D52—22no—
102D52—42no—
103D52—81no—
104C4×D13—44no—
105Dic26—21no—
106Dic26#4112yescomplemented
107#1055—21no—
108#1055—21no—
109#1055—22no—
110#550—131no—
111#547D1311yescharacteristic, complemented
112#486—131no—
113#481—132no—
114#475—131no—
115#469—132no—
116#459—131no—
117#449—132no—
118C4×SD16—131no—
119#436—131no—
120#417—132no—
121C22×C13—22no—
122C22×C13—22no—
123C22×C13—22no—
124C22×C13—41no—
125C22×C13—41no—
126C22×C13—41no—
127C22×C13C22×D411yescharacteristic
128C2×D13—42no—
129C2×D13—42no—
130C2×D13—42no—
131C4×C13—22no—
132C4×C13—21no—
133C4×C13—41no—
134C4×C13—42no—
135C4×C13AGL(1,ℤ/8)12yes—
136C4×C13C2×#4111yescharacteristic
137C4×C13H(5,𝔽2)11yescharacteristic
138Dic13—22no—
139Dic13—41no—
140C2×#41—21no—
141C2×#41—132no—
142C2×SD16—131no—
143C2×D8—132no—
144C2×M16—132no—
145C4⋊Q8C2×D1311yescharacteristic
146#127—131no—
147#127—261no—
148#123—22no—
149C22⋊Q8—21no—
150#121—132no—
151#121—262no—
152#121C2×D1312yes—
153C4×Q8—131no—
154C4×D4—261no—
155C4×D4C2×D1311yescharacteristic
156C4×D4C2×D1311yescharacteristic
157C2×C4⋊C4C2×D1312yes—
158#106—131no—
159#106—132no—
160C4⋊C8—131no—
161#103—131no—
162#103—132no—
163#102—131no—
164#102—132no—
165#102—132no—
166#102—132no—
167C22⋊C8—132no—
168C4×C8—131no—
169C2×C13—42no—
170C2×C13—81no—
171C2×C13#54611yescharacteristic
172C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
173C2×C13#57711yescharacteristic
174D13—82no—
175#41—44no—
176#41—264no—
177#41—522no—
178C2×Q8—21no—
179C2×Q8—131no—
180C2×D4—22no—
181C2×D4—132no—
182C2×D4—262no—
183C2×D4—262no—
184C2×D4—261no—
185C2×D4—261no—
186C2×D4C22⋊D1311yescharacteristic
187C2×D4C22×D1311yescharacteristic
188C22×C4—22no—
189C22×C4—21no—
190C22×C4—262no—
191C22×C4C22×D1312yes—
192SD16—262no—
193D8—522no—
194M16—522no—
195C2×C8—131no—
196C2×C8—131no—
197C2×C8—132no—
198C4⋊C4—22no—
199C4⋊C4—21no—
200C4⋊C4—131no—
201C4⋊C4—261no—
202C4⋊C4C22⋊D1311yescharacteristic
203C4⋊C4C22×D1311yescharacteristic
204C4⋊C4C22×D1312yes—
205C22⋊C4—21no—
206C22⋊C4—22no—
207C22⋊C4—262no—
208C22⋊C4C22⋊D1312yes—
209C42—261no—
210C42C22×D1311yescharacteristic
211C13#333211yescharacteristic, complemented, Sylow
212C23—21no—
213C23—262no—
214C23C2×C22⋊D1312yes—
215Q8—42no—
216Q8—132no—
217Q8—261no—
218D4—22no—
219D4—21no—
220D4—21no—
221D4—44no—
222D4—262no—
223D4—262no—
224D4—524no—
225D4—522no—
226D4—1041no—
227D4—1042no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—21no—
231C2×C4—22no—
232C2×C4—44no—
233C2×C4—42no—
234C2×C4—261no—
235C2×C4—261no—
236C2×C4—524no—
237C2×C4C2×C22⋊D1311yescharacteristic
238C2×C4C2×C22⋊D1312yes—
239C2×C4C2×C22⋊D1311yescharacteristic
240C2×C4C23×D1311yescharacteristic
241C8—261no—
242C8—261no—
243C8—262no—
244C22—22no—
245C22—22no—
246C22—22no—
247C22—41no—
248C22—41no—
249C22—41no—
250C22—522no—
251C22—522no—
252C22—522no—
253C22C22×C22⋊D1311yescharacteristic
254C4—22no—
255C4—21no—
256C4—41no—
257C4—42no—
258C4—262no—
259C4—521no—
260C4#8818612yes—
261C4#41×D1311yescharacteristic
262C4#8825611yescharacteristic
263C2—42no—
264C2—81no—
265C2—1042no—
266C2C2×#8818611yescharacteristic
267C2#1171953411yescharacteristic
268C2#1171954211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#547C2
socleC22×C13C22×D4
hypercenter#547D13
hypocenterC13#3332
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C4×D4 ◁ #547

Complements

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

NH ≅ G/Ntype
1. C13×#547C2semidirect
2. #11719258C2semidirect
3. #11718755C2semidirect
4. #11718749C2semidirect
5. #11718700C2semidirect
6. #11718698C2semidirect
7. C4×#6105C2semidirect
8. #11718676C2semidirect
9. #11718673C2semidirect
10. #11718629C2semidirect
11. #11718627C2semidirect
106. Dic26#41semidirect
111. #547D13semidirect
211. C13#3332semidirect

Maximal subgroups

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

subgroupindex
C13×#5472
#117192582
#117187552
#117187492
#117187002
#117186982
C4×#61052
#117186762
#117186732
#117186292
#117186272
#333213