Finite Group Databasebeta

← #13127164

Subgroups — #13127164

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
1#11719260C211yesmaximal, characteristic, complemented
2#11719258C211yesmaximal, characteristic, complemented
3C13×#436C211yesmaximal, characteristic, complemented
4#11718796C212yesmaximal, complemented
5#11718794C212yesmaximal, complemented
6#11718512C211yesmaximal, characteristic, complemented
7#11718504C211yesmaximal, characteristic, complemented
8#11718396C212yesmaximal, complemented
9#11718395C212yesmaximal, complemented
10#11718355C211yesmaximal, characteristic, complemented
11C4×#6095C211yesmaximal, characteristic, complemented
12C2×#6129—21no—
13C2×#6127C2212yes—
14C2×C13×M16C2212yes—
15C4×D4×C13C2211yescharacteristic
16#88194—21no—
17#88184C2212yes—
18#88184C2212yes—
19C2×C4⋊Dic13C2212yes—
20C2×D104C2212yes—
21C2×#6095C2211yescharacteristic
22#88151—21no—
23#88147—21no—
24#88140—22no—
25#88138—22no—
26#88128C2211yescharacteristic
27C4×D52C2211yescharacteristic
28#88123C2211yescharacteristic
29C4×Dic26C2211yescharacteristic
30C13×C4⋊C8C2211yescharacteristic
31C13×C22⋊C8C2212yes—
32C4×C8×C13C2211yescharacteristic
33#88061C2212yes—
34#88061C2212yes—
35#88061C2211yescharacteristic
36#88061C2212yes—
37#88057C2212yes—
38#88057C2211yescharacteristic
39#88056C2212yes—
40#88056C2211yescharacteristic
41C2×D4×C13D411yescharacteristic
42C22×C4×C13C2312yes—
43C2×C22⋊D13—22no—
44C2×C22⋊D13—22no—
45C2×C22⋊D13—22no—
46C22×Dic13—22no—
47#6129—44no—
48#6127—24no—
49#6127—42no—
50C2×D52—21no—
51C2×D52—21no—
52C2×D52C2311yescharacteristic
53C2×D52C2312yes—
54C2×C4×D13—21no—
55C2×C4×D13—22no—
56C2×Dic26—21no—
57C2×Dic26C2311yescharacteristic
58C13×M16—42no—
59C2×C8×C13C2311yescharacteristic
60C2×C8×C13C2311yescharacteristic
61C2×C8×C13C2312yes—
62C13×C4⋊C4D411yescharacteristic
63C13×C22⋊C4D412yes—
64C42×C13C2311yescharacteristic
65#6103—21no—
66#6103—22no—
67#6103—22no—
68C4⋊Dic13—21no—
69C4⋊Dic13—22no—
70C4⋊Dic13C2311yescharacteristic
71C4⋊Dic13C2312yes—
72C4⋊Dic13C2311yescharacteristic
73#6101—21no—
74C4×Dic13—21no—
75D104—42no—
76#6095—22no—
77#3332—131nomaximal, Sylow
78C23×C13C2×D412yes—
79C22×D13—21no—
80C22×D13—22no—
81D4×C13—22no—
82C2×C4×C13—22no—
83C2×C4×C13—22no—
84C2×C4×C13C2×D411yescharacteristic
85C2×C4×C13C2×D412yes—
86C2×C4×C13C2×D411yescharacteristic
87C2×C4×C13C2411yescharacteristic
88C22⋊D13—44no—
89C22⋊D13—44no—
90C22⋊D13—82no—
91C2×Dic13—21no—
92C2×Dic13—21no—
93C2×Dic13—22no—
94C2×Dic13—21no—
95C2×Dic13—44no—
96D52—21no—
97D52—22no—
98D52—21no—
99D52—22no—
100D52—42no—
101D52—81no—
102C4×D13—44no—
103C4×D13—42no—
104Dic26—21no—
105Dic26—42no—
106Dic26#4112yescomplemented
107C8×C13—21no—
108C8×C13—22no—
109C8×C13—21no—
110#550—131no—
111#547—131no—
112#486—131no—
113#481—132no—
114#475—131no—
115#469—132no—
116#459—131no—
117#449—132no—
118C4×SD16—131no—
119#436D1311yescharacteristic, complemented
120#417—132no—
121C22×C13—22no—
122C22×C13—22no—
123C22×C13—22no—
124C22×C13C22×D411yescharacteristic
125C2×D13—42no—
126C2×D13—41no—
127C2×D13—41no—
128C2×D13—42no—
129C2×D13—42no—
130C2×D13—41no—
131C4×C13—22no—
132C4×C13—21no—
133C4×C13AGL(1,ℤ/8)12yes—
134C4×C13C2×#4111yescharacteristic
135C4×C13H(5,𝔽2)11yescharacteristic
136Dic13—22no—
137Dic13—42no—
138Dic13—41no—
139Dic13—41no—
140C2×#41—132no—
141C2×#41—261no—
142C2×SD16—131no—
143C2×D8—132no—
144C2×M16C2×D1312yes—
145C4⋊Q8—131no—
146#127—131no—
147#127—261no—
148#123—262no—
149C22⋊Q8—261no—
150#121—132no—
151#121—132no—
152#121—262no—
153C4×Q8—131no—
154C4×D4—131no—
155C4×D4—261no—
156C4×D4C2×D1311yescharacteristic
157C2×C4⋊C4—132no—
158#106—131no—
159#106—132no—
160C4⋊C8C2×D1311yescharacteristic
161#103—131no—
162#103—132no—
163#102—132no—
164#102—132no—
165#102—131no—
166#102—132no—
167C22⋊C8C2×D1312yes—
168C4×C8C2×D1311yescharacteristic
169C2×C13—42no—
170C2×C13#54611yescharacteristic
171C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
172C2×C13#57711yescharacteristic
173D13—82no—
174D13—81no—
175#41—264no—
176#41—522no—
177#41—524no—
178C2×Q8—131no—
179C2×Q8—261no—
180C2×D4—132no—
181C2×D4—131no—
182C2×D4—262no—
183C2×D4—262no—
184C2×D4—262no—
185C2×D4—261no—
186C2×D4—261no—
187C2×D4D5211yescharacteristic
188C22×C4—262no—
189C22×C4—261no—
190C22×C4—262no—
191C22×C4C22×D1312yes—
192SD16—262no—
193D8—522no—
194M16—42no—
195C2×C8C22×D1311yescharacteristic
196C2×C8C22×D1311yescharacteristic
197C2×C8C22×D1312yes—
198C4⋊C4—131no—
199C4⋊C4—132no—
200C4⋊C4—131no—
201C4⋊C4—262no—
202C4⋊C4—261no—
203C4⋊C4—261no—
204C4⋊C4D5211yescharacteristic
205C22⋊C4—261no—
206C22⋊C4—262no—
207C22⋊C4—262no—
208C22⋊C4D5212yes—
209C42—261no—
210C42C22×D1311yescharacteristic
211C13#333211yescharacteristic, complemented, Sylow
212C23—261no—
213C23—262no—
214C23C2×D5212yes—
215Q8—132no—
216Q8—261no—
217Q8—522no—
218D4—22no—
219D4—261no—
220D4—262no—
221D4—261no—
222D4—262no—
223D4—524no—
224D4—524no—
225D4—522no—
226D4—1041no—
227D4—1042no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—261no—
231C2×C4—261no—
232C2×C4—261no—
233C2×C4—262no—
234C2×C4—524no—
235C2×C4—524no—
236C2×C4—522no—
237C2×C4C2×D5211yescharacteristic
238C2×C4C2×D5212yes—
239C2×C4C2×D5211yescharacteristic
240C2×C4C23×D1311yescharacteristic
241C8—21no—
242C8—22no—
243C8—21no—
244C22—22no—
245C22—22no—
246C22—22no—
247C22—521no—
248C22—522no—
249C22—522no—
250C22—521no—
251C22—522no—
252C22—521no—
253C22C22×D5211yescharacteristic
254C4—21no—
255C4—22no—
256C4—262no—
257C4—521no—
258C4—522no—
259C4—521no—
260C4#8816212yes—
261C4#8825111yescharacteristic
262C4#41×D1311yescharacteristic
263C2—42no—
264C2—1041no—
265C2—1042no—
266C2#1171925911yescharacteristic
267C2C2×#8816211yescharacteristic
268C2#1171945611yescharacteristic
subgroupG/H
centerC22C22×D52
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#436C2
socleC22×C13C22×D4
hypercenter#436D13
hypocenterC13#3332
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C4×D4 ◁ #436

Complements

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

NH ≅ G/Ntype
1. #11719260C2semidirect
2. #11719258C2semidirect
3. C13×#436C2semidirect
4. #11718796C2semidirect
5. #11718794C2semidirect
6. #11718512C2semidirect
7. #11718504C2semidirect
8. #11718396C2semidirect
9. #11718395C2semidirect
10. #11718355C2semidirect
11. C4×#6095C2semidirect
106. Dic26#41semidirect
119. #436D13semidirect
211. C13#3332semidirect

Maximal subgroups

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

subgroupindex
#117192602
#117192582
C13×#4362
#117187962
#117187942
#117185122
#117185042
#117183962
#117183952
#117183552
C4×#60952
#333213