Finite Group Databasebeta

← #13127196

Subgroups — #13127196

Order 1664.

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

normal subgroups only

This group has 388 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#11719431C211yesmaximal, characteristic
2#11719284C211yesmaximal, characteristic, complemented
3C13×#475C211yesmaximal, characteristic, complemented
4#11718740C211yesmaximal, characteristic, complemented
5C4×#6106C211yesmaximal, characteristic, complemented
6#11718524C212yesmaximal, complemented
7D13×#106C212yesmaximal, complemented
8#11718503C211yesmaximal, characteristic, complemented
9#11718495C211yesmaximal, characteristic, complemented
10#11718468C212yesmaximal, complemented
11#11718466C212yesmaximal, complemented
12C2×#6131—21no—
13C13×C4⋊Q8C2211yescharacteristic
14C4×Q8×C13C2211yescharacteristic
15#88200—21no—
16#88200C2212yes—
17C2×#6106C2211yescharacteristic
18C2×C8×D13C2212yes—
19#88150—22no—
20#88149C2212yes—
21#88148—22no—
22C4⋊C4×D13C2212yes—
23C4⋊C4×D13C2212yes—
24C4×D52—21no—
25C4×D52C2211yescharacteristic
26C4×D52C2211yescharacteristic
27#88124—21no—
28#88123C2211yescharacteristic
29C13×#106C2212yes—
30C13×C4⋊C8C2211yescharacteristic
31C13×#103C2212yes—
32#88075C2211yescharacteristic
33#88061C2212yes—
34#88060C2212yes—
35#88057C2212yes—
36#88049C2211yescharacteristic
37#88048C2211yescharacteristic
38#88048C2212yes—
39#88048C2212yes—
40C4×#1055C2211yescharacteristic
41C2×Q8×C13—21no—
42C2×Q8×C13C2311yescharacteristic
43#6131—44no—
44C2×D52—22no—
45C2×D52D411yescharacteristic
46C2×D52C2311yescharacteristic
47C2×C4×D13—22no—
48C2×C4×D13—21no—
49C2×C4×D13—22no—
50C2×C4×D13C2312yes—
51C2×Dic26—21no—
52C2×C8×C13C2312yes—
53C13×C4⋊C4—21no—
54C13×C4⋊C4—21no—
55C13×C4⋊C4C2312yes—
56C13×C4⋊C4C2311yescharacteristic
57C42×C13—21no—
58C42×C13C2311yescharacteristic
59#6106—22no—
60#6103—22no—
61#6103—21no—
62#6103—22no—
63#6103D412yes—
64C4⋊Dic13—21no—
65C4⋊Dic13D411yescharacteristic
66C4⋊Dic13C2311yescharacteristic
67C4⋊Dic13C2312yes—
68#6101—22no—
69#6101—22no—
70#6101—22no—
71C2×#1055C2311yescharacteristic
72C2×#1055C2311yescharacteristic
73C8×D13—24no—
74#3335—131nomaximal, Sylow
75C22×D13—21no—
76C22×D13C2×D412yes—
77Q8×C13—21no—
78Q8×C13—21no—
79Q8×C13—42no—
80C2×C4×C13—21no—
81C2×C4×C13—21no—
82C2×C4×C13—22no—
83C2×C4×C13C2×D411yescharacteristic
84C2×C4×C13C2×D411yescharacteristic
85C2×C4×C13C2411yescharacteristic
86C2×Dic13—22no—
87C2×Dic13—21no—
88C2×Dic13C2×D412yes—
89D52—21no—
90D52—21no—
91D52—44no—
92D52SD1614yescomplemented
93C4×D13—22no—
94C4×D13—22no—
95C4×D13—44no—
96C4×D13—42no—
97C4×D13—82no—
98Dic26—81no—
99C8×C13—22no—
100#1055—21no—
101#1055#4112yescomplemented
102#554—131no—
103#547—131no—
104#498—131no—
105#483—132no—
106#481—132no—
107#476—131no—
108#475D1311yescharacteristic, complemented
109#465—132no—
110C4×SD16—131no—
111C8×D4—131no—
112C2×#106—132no—
113C22×C13C22×D411yescharacteristic
114C2×D13—22no—
115C2×D13—22no—
116C2×D13—41no—
117C2×D13—41no—
118C2×D13—41no—
119C2×D13C2×SD1614yes—
120C4×C13—21no—
121C4×C13—41no—
122C4×C13—42no—
123C4×C13—41no—
124C4×C13C2×SD1612yes—
125C4×C13C2×#4111yescharacteristic
126C4×C132−1+411yescharacteristic
127Dic13—22no—
128Dic13—41no—
129Dic13—42no—
130C2×#41—261no—
131C2×SD16—131no—
132C22×C8—132no—
133C4⋊Q8—131no—
134C4⋊Q8C2×D1311yescharacteristic
135#125—261no—
136#123—262no—
137C22⋊Q8—132no—
138C22⋊Q8—262no—
139C22⋊Q8—261no—
140#121—132no—
141C4×Q8C2×D1311yescharacteristic
142C4×D4—131no—
143C4×D4—131no—
144C4×D4—261no—
145C2×C4⋊C4—132no—
146C2×C4⋊C4—132no—
147#106—132no—
148#106—131no—
149#106—132no—
150#106—132no—
151#106C2×D1312yes—
152C4⋊C8C2×D1311yescharacteristic
153#103—131no—
154#103C2×D1312yes—
155#102—132no—
156#102—131no—
157C22⋊C8—132no—
158C4×C8—131no—
159C2×C13#54711yescharacteristic
160C2×C13C22×SD1611yescharacteristic
161C2×C13#57711yescharacteristic
162D13—24no—
163D13—81no—
164#41—524no—
165C2×Q8—21no—
166C2×Q8—261no—
167C2×Q8C22×D1311yescharacteristic
168C2×D4—131no—
169C2×D4—131no—
170C2×D4—262no—
171C22×C4—132no—
172C22×C4—262no—
173C22×C4—262no—
174C22×C4—261no—
175SD16—262no—
176C2×C8—131no—
177C2×C8—131no—
178C2×C8—264no—
179C2×C8C22×D1312yes—
180C4⋊C4—21no—
181C4⋊C4—21no—
182C4⋊C4—131no—
183C4⋊C4—132no—
184C4⋊C4—131no—
185C4⋊C4—262no—
186C4⋊C4—262no—
187C4⋊C4—262no—
188C4⋊C4—261no—
189C4⋊C4C22×D1311yescharacteristic
190C4⋊C4C22×D1312yes—
191C22⋊C4—132no—
192C22⋊C4—262no—
193C22⋊C4—262no—
194C22⋊C4—261no—
195C42—21no—
196C42C22×D1311yescharacteristic
197C13#333511yescharacteristic, complemented, Sylow
198C23—132no—
199C23—261no—
200Q8—21no—
201Q8—21no—
202Q8—42no—
203Q8—1041no—
204D4—134no—
205D4—261no—
206D4—261no—
207D4—524no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—22no—
211C2×C4—132no—
212C2×C4—262no—
213C2×C4—262no—
214C2×C4—262no—
215C2×C4—261no—
216C2×C4—524no—
217C2×C4—522no—
218C2×C4—1042no—
219C2×C4D4×D1311yescharacteristic
220C2×C4D4×D1311yescharacteristic
221C2×C4C23×D1311yescharacteristic
222C8—22no—
223C8—132no—
224C8—261no—
225C22—134no—
226C22—262no—
227C22—262no—
228C22—521no—
229C22—521no—
230C22—521no—
231C22C2×D4×D1311yescharacteristic
232C4—21no—
233C4—42no—
234C4—41no—
235C4—41no—
236C4—262no—
237C4—521no—
238C4—522no—
239C4SD16×D1312yes—
240C4#8825411yescharacteristic
241C4#41×D1311yescharacteristic
242C2—264no—
243C2—1041no—
244C2#1171933611yescharacteristic
245C2C2×SD16×D1311yescharacteristic
246C2#1171948311yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#475C2
socleC22×C13C22×D4
prime radical#11719431C2
hypercenter#475D13
hypocenterC13#3335
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
2. #11719284C2semidirect
3. C13×#475C2semidirect
4. #11718740C2semidirect
5. C4×#6106C2semidirect
6. #11718524C2semidirect
7. D13×#106C2semidirect
8. #11718503C2semidirect
9. #11718495C2semidirect
10. #11718468C2semidirect
11. #11718466C2semidirect
92. D52SD16semidirect
101. #1055#41semidirect
108. #475D13semidirect
197. C13#3335semidirect

Maximal subgroups

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

subgroupindex
#117194312
#117192842
C13×#4752
#117187402
C4×#61062
#117185242
D13×#1062
#117185032
#117184952
#117184682
#117184662
#333513