Finite Group Databasebeta

← #13126078

Subgroups — #13126078

Order 1664.

328 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 328 conjugacy classes of subgroups — too many to draw. Only its 117 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#11719184C211yesmaximal, characteristic
2#11719175C211yesmaximal, characteristic, complemented
3C13×#432C211yesmaximal, characteristic, complemented
4#11718508C212yesmaximal, complemented
5#11718490C212yesmaximal, complemented
6#11718398C212yesmaximal
7#11718384C212yesmaximal, complemented
8#11718375C211yesmaximal, characteristic, complemented
9#11718375C211yesmaximal, characteristic, complemented
10#11718363C211yesmaximal, characteristic, complemented
11#11718363C211yesmaximal, characteristic, complemented
12C2×C42×C13C2211yescharacteristic
13#88184C2211yescharacteristic
14#88183—21no—
15C4×C22⋊D13—21no—
16#88180C2212yes—
17#88178—21no—
18#88178—21no—
19#88178C2211yescharacteristic
20#88130—21no—
21#88129C2211yescharacteristic
22C4×D52C2211yescharacteristic
23#88126—21no—
24#88124C2212yes—
25#88124C2211yescharacteristic
26#88123C2211yescharacteristic
27#88123C2211yescharacteristic
28C4×Dic26—21no—
29C4×Dic26—21no—
30C4×Dic26C2211yescharacteristic
31C13×C4⋊C8C2212yes—
32C13×C22⋊C8C2212yes—
33C13×#97C2211yescharacteristic
34C13×#97C2211yescharacteristic
35#88061C2212yes—
36#88061C2212yes—
37#88058C2212yes—
38#88058C2212yes—
39#88057C2212yes—
40#88057C2212yes—
41#88056C2212yes—
42#88056C2212yes—
43C22×C4×C13D411yescharacteristic
44C22×C4×C13D411yescharacteristic
45C22×C4×C13C2311yescharacteristic
46C2×C22⋊D13—21no—
47C2×D52C2311yescharacteristic
48C2×C4×D13—21no—
49C2×Dic26—21no—
50C2×Dic26—21no—
51C2×Dic26C2311yescharacteristic
52C2×C8×C13C2312yes—
53C2×C8×C13C2312yes—
54C42×C13D411yescharacteristic
55C42×C13D411yescharacteristic
56C42×C13C2311yescharacteristic
57C42×C13C2311yescharacteristic
58C22⋊Dic13—22no—
59C22⋊Dic13—21no—
60#6103—21no—
61#6103—21no—
62#6103—21no—
63#6103—21no—
64C4⋊Dic13—21no—
65C4⋊Dic13—21no—
66C4⋊Dic13C2311yescharacteristic
67C4⋊Dic13C2312yes—
68C4⋊Dic13C2312yes—
69C4⋊Dic13C2311yescharacteristic
70#6101—22no—
71#6101—22no—
72#6101—21no—
73#6101—21no—
74#6101—21no—
75#6101—21no—
76C4×Dic13—22no—
77C4×Dic13—21no—
78#3240—131nomaximal, Sylow
79C23×C13C2×D411yescharacteristic
80C22×D13—21no—
81C2×C4×C13—22no—
82C2×C4×C13—41no—
83C2×C4×C13—41no—
84C2×C4×C13C2×D411yescharacteristic
85C2×C4×C13C2×D411yescharacteristic
86C2×C4×C13C2×D411yescharacteristic
87C2×C4×C13C2×D411yescharacteristic
88C2×C4×C13C2×D411yescharacteristic
89C2×C4×C13C2411yescharacteristic
90C22⋊D13—42no—
91C2×Dic13—21no—
92C2×Dic13—22no—
93C2×Dic13—22no—
94C2×Dic13—21no—
95C2×Dic13—21no—
96D52—22no—
97C4×D13—42no—
98Dic26—22no—
99Dic26—42no—
100Dic26—42no—
101C8×C13—22no—
102C8×C13—22no—
103#533—131no—
104#529—131no—
105#501—131no—
106#501—131no—
107#489—131no—
108#489—131no—
109#485—132no—
110#482—132no—
111#479—132no—
112#478—132no—
113#432D1311yescharacteristic, complemented
114C22×C13—21no—
115C22×C13—21no—
116C22×C13—21no—
117C22×C13C22×D411yescharacteristic
118C2×D13—41no—
119C2×D13—41no—
120C2×D13—41no—
121C4×C13—21no—
122C4×C13—21no—
123C4×C13—21no—
124C4×C13—21no—
125C4×C13—21no—
126C4×C132−1+412yes—
127Dic13—41no—
128Dic13—42no—
129Dic13—42no—
130Dic13—41no—
131Dic13—41no—
132C4⋊Q8—131no—
133C4⋊Q8—131no—
134#126—261no—
135#125—131no—
136#125—132no—
137#124—131no—
138#123—261no—
139C22⋊Q8—131no—
140C22⋊Q8—261no—
141C22⋊Q8—261no—
142#121—131no—
143C4×Q8—131no—
144C4×Q8—261no—
145C4×Q8—261no—
146C4×D4—131no—
147C4×D4—261no—
148#117—132no—
149#117—261no—
150C2×C42C2×D1311yescharacteristic
151#107—132no—
152#107—132no—
153#106—132no—
154#106—132no—
155C4⋊C8C2×D1312yes—
156#103—132no—
157#103—132no—
158#102—132no—
159#102—132no—
160C22⋊C8C2×D1312yes—
161#97C2×D1311yescharacteristic
162#97C2×D1311yescharacteristic
163C2×C13—41no—
164C2×C13#53611yescharacteristic
165C2×C13#57511yescharacteristic
166C2×C13#57511yescharacteristic
167D13—81no—
168C2×Q8—131no—
169C2×Q8—261no—
170C2×Q8—261no—
171C2×D4—131no—
172C2×D4—261no—
173C22×C4—261no—
174C22×C4D5211yescharacteristic
175C22×C4D5211yescharacteristic
176C22×C4C22×D1311yescharacteristic
177C2×C8C22×D1312yes—
178C2×C8C22×D1312yes—
179C4⋊C4—132no—
180C4⋊C4—132no—
181C4⋊C4—131no—
182C4⋊C4—131no—
183C4⋊C4—261no—
184C4⋊C4—261no—
185C4⋊C4—261no—
186C4⋊C4—261no—
187C4⋊C4—262no—
188C4⋊C4—262no—
189C4⋊C4—261no—
190C4⋊C4—261no—
191C22⋊C4—262no—
192C22⋊C4—261no—
193C22⋊C4—261no—
194C22⋊C4—261no—
195C22⋊C4—261no—
196C22⋊C4—261no—
197C42—262no—
198C42—261no—
199C42D5211yescharacteristic
200C42D5211yescharacteristic
201C42C22×D1311yescharacteristic
202C42C22×D1311yescharacteristic
203C13#324011yescharacteristic, complemented, Sylow
204C23—261no—
205C23C2×D5211yescharacteristic
206Q8—262no—
207Q8—522no—
208Q8—522no—
209D4—262no—
210D4—522no—
211C2×C4—22no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—261no—
215C2×C4—261no—
216C2×C4—262no—
217C2×C4—262no—
218C2×C4—261no—
219C2×C4—522no—
220C2×C4C2×D5211yescharacteristic
221C2×C4C2×D5211yescharacteristic
222C2×C4C2×D5211yescharacteristic
223C2×C4C2×D5211yescharacteristic
224C2×C4C2×D5211yescharacteristic
225C2×C4C23×D1311yescharacteristic
226C8—22no—
227C8—22no—
228C22—21no—
229C22—21no—
230C22—21no—
231C22—521no—
232C22—521no—
233C22—521no—
234C22C22×D5211yescharacteristic
235C4—21no—
236C4—21no—
237C4—21no—
238C4—21no—
239C4—21no—
240C4—521no—
241C4—521no—
242C4—522no—
243C4—522no—
244C4—521no—
245C4#8825712yes—
246C2—41no—
247C2—1041no—
248C2#1171923111yescharacteristic
249C2#1171945311yescharacteristic
250C2#1171945311yescharacteristic
subgroupG/H
centerC22C22×D52
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#432C2
socleC22×C13C22×D4
prime radical#88184C22
hypercenter#432D13
hypocenterC13#3240
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
2. #11719175C2semidirect
3. C13×#432C2semidirect
4. #11718508C2semidirect
5. #11718490C2semidirect
7. #11718384C2semidirect
8. #11718375C2semidirect
9. #11718375C2semidirect
10. #11718363C2semidirect
11. #11718363C2semidirect
113. #432D13semidirect
203. C13#3240semidirect

Maximal subgroups

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

subgroupindex
#117191842
#117191752
C13×#4322
#117185082
#117184902
#117183982
#117183842
#117183752
#117183632
#324013