Finite Group Databasebeta

← #13126079

Subgroups — #13126079

Order 1664.

328 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 328 conjugacy classes of subgroups — too many to draw. Only its 109 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#11719433C211yesmaximal, characteristic, complemented
2#11719396C211yesmaximal, characteristic
3C13×#501C211yesmaximal, characteristic, complemented
4#11718750C211yesmaximal, characteristic, complemented
5#11718726C211yesmaximal, characteristic, complemented
6#11718546C212yesmaximal
7#11718538C212yesmaximal, complemented
8#11718532C212yesmaximal, complemented
9#11718528C212yesmaximal, complemented
10#11718375C211yesmaximal, characteristic, complemented
11#11718366C211yesmaximal, characteristic, complemented
12C13×C4⋊Q8C2211yescharacteristic
13C13×#125C2211yescharacteristic
14#88200—21no—
15Q8×Dic13—21no—
16#88152—21no—
17#88151—21no—
18#88151C2211yescharacteristic
19#88149C2211yescharacteristic
20#88148—21no—
21#88147—21no—
22#88147C2211yescharacteristic
23#88146—21no—
24#88146C2212yes—
25#88144C2212yes—
26#88141—21no—
27#88141C2211yescharacteristic
28#88129C2211yescharacteristic
29C42×D13C2211yescharacteristic
30#88123C2211yescharacteristic
31C13×#107C2212yes—
32C13×#106C2212yes—
33C13×#97C2211yescharacteristic
34#88061C2212yes—
35#88060C2212yes—
36#88056C2212yes—
37#88054C2212yes—
38#88050C2212yes—
39#88049C2212yes—
40#88048C2212yes—
41#88047C2212yes—
42#88043C2211yescharacteristic
43C2×Q8×C13—21no—
44C2×D52—21no—
45C2×D52C2311yescharacteristic
46C2×C4×D13—21no—
47C2×C4×D13D411yescharacteristic
48C2×C4×D13D411yescharacteristic
49C2×C4×D13C2311yescharacteristic
50C2×Dic26—21no—
51C2×Dic26C2311yescharacteristic
52C2×C8×C13C2312yes—
53C13×C4⋊C4—21no—
54C13×C4⋊C4—21no—
55C13×C4⋊C4—21no—
56C13×C4⋊C4C2311yescharacteristic
57C13×C4⋊C4C2312yes—
58C13×C4⋊C4C2311yescharacteristic
59C42×C13C2311yescharacteristic
60#6103—22no—
61#6103—21no—
62#6103—21no—
63#6103—21no—
64#6103—21no—
65#6103—21no—
66C4⋊Dic13—21no—
67C4⋊Dic13—22no—
68C4⋊Dic13—21no—
69C4⋊Dic13C2312yes—
70#6101—22no—
71#6101—21no—
72C4×Dic13—22no—
73C4×Dic13—21no—
74C4×Dic13D411yescharacteristic
75C4×Dic13D411yescharacteristic
76C4×Dic13C2311yescharacteristic
77C2×#1055C2312yes—
78#3240—131nomaximal, Sylow
79C22×D13—21no—
80C22×D13C2×D411yescharacteristic
81Q8×C13—42no—
82C2×C4×C13—22no—
83C2×C4×C13—21no—
84C2×C4×C13—21no—
85C2×C4×C13C2×D411yescharacteristic
86C2×C4×C13C2×D411yescharacteristic
87C2×C4×C13C2411yescharacteristic
88C2×Dic13—22no—
89C2×Dic13—21no—
90C2×Dic13C2×D411yescharacteristic
91C2×Dic13C2×D411yescharacteristic
92C2×Dic13C2×D411yescharacteristic
93D52—22no—
94D52—42no—
95C4×D13—22no—
96C4×D13—41no—
97C4×D13—41no—
98C4×D13—42no—
99Dic26—22no—
100Dic26—42no—
101C8×C13—22no—
102#1055—22no—
103#533—131no—
104#529—131no—
105#501—131no—
106#501D1311yescharacteristic, complemented
107#489—131no—
108#489—131no—
109#485—132no—
110#482—132no—
111#479—132no—
112#478—132no—
113#432—131no—
114C22×C13C22×D411yescharacteristic
115C2×D13—21no—
116C2×D13—21no—
117C2×D13—21no—
118C2×D13—41no—
119C2×D13—41no—
120C2×D13—41no—
121C4×C13—21no—
122C4×C13—21no—
123C4×C13—41no—
124C4×C13—41no—
125C4×C13—42no—
126C4×C132−1+412yes—
127Dic13—21no—
128Dic13—21no—
129Dic13—21no—
130Dic13—41no—
131Dic13—42no—
132C4⋊Q8—131no—
133C4⋊Q8C2×D1311yescharacteristic
134#126—261no—
135#125—132no—
136#125C2×D1311yescharacteristic
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×C42—131no—
151#107—132no—
152#107C2×D1312yes—
153#106—132no—
154#106C2×D1312yes—
155C4⋊C8—132no—
156#103—132no—
157#103—132no—
158#102—132no—
159#102—132no—
160C22⋊C8—132no—
161#97—131no—
162#97C2×D1311yescharacteristic
163C2×C13#53611yescharacteristic
164C2×C13#57511yescharacteristic
165C2×C13#57511yescharacteristic
166D13—41no—
167D13—81no—
168C2×Q8—21no—
169C2×Q8—131no—
170C2×Q8—261no—
171C2×D4—131no—
172C2×D4—261no—
173C22×C4—131no—
174C22×C4—131no—
175C22×C4—131no—
176C22×C4—261no—
177C2×C8—132no—
178C2×C8C22×D1312yes—
179C4⋊C4—21no—
180C4⋊C4—21no—
181C4⋊C4—21no—
182C4⋊C4—132no—
183C4⋊C4—261no—
184C4⋊C4—261no—
185C4⋊C4—262no—
186C4⋊C4—262no—
187C4⋊C4—261no—
188C4⋊C4C22×D1312yes—
189C4⋊C4C22×D1311yescharacteristic
190C4⋊C4C22×D1311yescharacteristic
191C22⋊C4—261no—
192C22⋊C4—261no—
193C22⋊C4—262no—
194C22⋊C4—261no—
195C22⋊C4—261no—
196C22⋊C4—261no—
197C42—131no—
198C42—131no—
199C42—131no—
200C42—262no—
201C42—261no—
202C42C22×D1311yescharacteristic
203C13#324011yescharacteristic, complemented, Sylow
204C23—131no—
205C23—261no—
206Q8—42no—
207Q8—262no—
208Q8—522no—
209D4—262no—
210D4—522no—
211C2×C4—21no—
212C2×C4—22no—
213C2×C4—21no—
214C2×C4—131no—
215C2×C4—131no—
216C2×C4—131no—
217C2×C4—262no—
218C2×C4—261no—
219C2×C4—262no—
220C2×C4—521no—
221C2×C4—521no—
222C2×C4—522no—
223C2×C4D4×D1311yescharacteristic
224C2×C4D4×D1311yescharacteristic
225C2×C4C23×D1311yescharacteristic
226C8—22no—
227C8—262no—
228C22—261no—
229C22—261no—
230C22—261no—
231C22—521no—
232C22—521no—
233C22—521no—
234C22C2×D4×D1311yescharacteristic
235C4—21no—
236C4—21no—
237C4—41no—
238C4—42no—
239C4—41no—
240C4—261no—
241C4—261no—
242C4—261no—
243C4—521no—
244C4—522no—
245C4#8825412yes—
246C2—521no—
247C2—1041no—
248C2#1171942911yescharacteristic
249C2#1171947811yescharacteristic
250C2#1171948211yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#501C2
socleC22×C13C22×D4
prime radical#88149C22
hypercenter#501D13
hypocenterC13#3240
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
1. #11719433C2semidirect
3. C13×#501C2semidirect
4. #11718750C2semidirect
5. #11718726C2semidirect
7. #11718538C2semidirect
8. #11718532C2semidirect
9. #11718528C2semidirect
10. #11718375C2semidirect
11. #11718366C2semidirect
106. #501D13semidirect
203. C13#3240semidirect

Maximal subgroups

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

subgroupindex
#117194332
#117193962
C13×#5012
#117187502
#117187262
#117185462
#117185382
#117185322
#117185282
#117183752
#117183662
#324013