Finite Group Databasebeta

← #13125233

Subgroups — #13125233

Order 1664.

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

normal subgroups only

This group has 392 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
1D13×#125C211yesmaximal, characteristic, complemented
2#11719373C211yesmaximal, characteristic
3C13×#488C211yesmaximal, characteristic, complemented
4#11718729C211yesmaximal, characteristic, complemented
5#11718717C211yesmaximal, characteristic, complemented
6#11718464C212yesmaximal, complemented
7#11718458C212yesmaximal, complemented
8#11718432C212yesmaximal, complemented
9#11718425C212yesmaximal, complemented
10#11718358C211yesmaximal, characteristic, complemented
11C4×#6094C211yesmaximal, characteristic, complemented
12C2×#6131C2211yescharacteristic
13C2×#6129C2211yescharacteristic
14C13×#125C2211yescharacteristic
15C13×#124C2211yescharacteristic
16#88198C2211yescharacteristic
17#88194C2211yescharacteristic
18C2×#6094C2212yes—
19C4⋊C4×D13—22no—
20C4⋊C4×D13C2212yes—
21#88144C2212yes—
22#88143—22no—
23#88138—22no—
24#88135—22no—
25#88129C2211yescharacteristic
26C42×D13C2211yescharacteristic
27#88124C2211yescharacteristic
28C13×#103C2212yes—
29C13×#102C2212yes—
30C4×C8×C13C2211yescharacteristic
31#88075C2212yes—
32#88072C2212yes—
33#88061C2212yes—
34#88056C2212yes—
35#88055C2212yes—
36#88050C2212yes—
37#88049C2212yes—
38C4×#1055C2211yescharacteristic
39C2×Q8×C13C2311yescharacteristic
40C2×D4×C13C2311yescharacteristic
41C2×C22⋊D13—21no—
42C2×C22⋊D13—22no—
43C22×Dic13—21no—
44#6131—24no—
45#6129—24no—
46C2×D52—21no—
47C2×D52C2311yescharacteristic
48C2×C4×D13—22no—
49C2×C4×D13—21no—
50C2×C4×D13D412yes—
51C2×C4×D13C2311yescharacteristic
52C2×Dic26C2311yescharacteristic
53C2×C8×C13C2312yes—
54C13×C4⋊C4—22no—
55C13×C4⋊C4C2312yes—
56C13×C22⋊C4—22no—
57C42×C13C2311yescharacteristic
58#6103—22no—
59C4⋊Dic13—22no—
60C4⋊Dic13C2312yes—
61#6101—22no—
62#6101—22no—
63#6101—22no—
64#6101—22no—
65C4×Dic13D412yes—
66C4×Dic13C2311yescharacteristic
67C2×#1055C2312yes—
68#6094—24no—
69#3142—131nomaximal, Sylow
70C23×C13—21no—
71C22×D13—21no—
72C22×D13C2×D411yescharacteristic
73Q8×C13—22no—
74D4×C13—22no—
75C2×C4×C13—22no—
76C2×C4×C13—21no—
77C2×C4×C13C2×D412yes—
78C2×C4×C13C2411yescharacteristic
79C22⋊D13—44no—
80C22⋊D13—42no—
81C2×Dic13—22no—
82C2×Dic13—21no—
83C2×Dic13—42no—
84C2×Dic13C2×D412yes—
85C2×Dic13C2×D411yescharacteristic
86D52—22no—
87D52—42no—
88C4×D13—42no—
89C4×D13—44no—
90C4×D13—42no—
91C4×D13#4114yes—
92Dic26—22no—
93C8×C13—22no—
94#1055—22no—
95#532—131no—
96C2×#125—131no—
97#491—132no—
98#490—132no—
99#488—131no—
100#488—131no—
101#488—131no—
102#488D1311yescharacteristic, complemented
103#417—132no—
104#417—132no—
105C4×M16—131no—
106C22×C13—41no—
107C22×C13—42no—
108C22×C13C22×D411yescharacteristic
109C2×D13—22no—
110C2×D13—41no—
111C2×D13—42no—
112C2×D13#12412yes—
113C4×C13—22no—
114C4×C13—41no—
115C4×C13—42no—
116C4×C13C2×#4112yes—
117Dic13—22no—
118Dic13—41no—
119Dic13—42no—
120Dic13#12412yes—
121C2×#41—131no—
122C2×#41—131no—
123C2×M16—132no—
124C4⋊Q8—131no—
125#127—131no—
126#125—132no—
127#125—131no—
128#125—262no—
129#125C2×D1311yescharacteristic
130#124—131no—
131#124C2×D1311yescharacteristic
132#121—262no—
133C4×D4—262no—
134C2×C4⋊C4—132no—
135C2×C4⋊C4—262no—
136C2×C42—131no—
137#103—132no—
138#103—132no—
139#103—132no—
140#103C2×D1312yes—
141#102—132no—
142#102—132no—
143#102—132no—
144#102C2×D1312yes—
145#97—132no—
146C4×C8—131no—
147C4×C8C2×D1311yescharacteristic
148C2×C13—81no—
149C2×C13C2×#12411yescharacteristic
150C2×C13#57512yes—
151D13—22no—
152D13—81no—
153#41—264no—
154#41—264no—
155C2×Q8—131no—
156C2×Q8C22×D1311yescharacteristic
157C2×D4—131no—
158C2×D4—261no—
159C2×D4—262no—
160C2×D4—261no—
161C2×D4C22×D1311yescharacteristic
162C22×C4—131no—
163C22×C4—132no—
164C22×C4—261no—
165C22×C4—262no—
166C22×C4—261no—
167M16—264no—
168C2×C8—132no—
169C2×C8C22×D1312yes—
170C4⋊C4—22no—
171C4⋊C4—132no—
172C4⋊C4—262no—
173C4⋊C4—262no—
174C4⋊C4—262no—
175C4⋊C4—262no—
176C4⋊C4—262no—
177C4⋊C4C22×D1312yes—
178C22⋊C4—22no—
179C22⋊C4—262no—
180C42—132no—
181C42—131no—
182C42C22×D1311yescharacteristic
183C13#314211yescharacteristic, complemented, Sylow
184C23—21no—
185C23—131no—
186C23—261no—
187Q8—22no—
188Q8—262no—
189D4—22no—
190D4—262no—
191D4—522no—
192D4—524no—
193D4—522no—
194C2×C4—21no—
195C2×C4—22no—
196C2×C4—131no—
197C2×C4—134no—
198C2×C4—132no—
199C2×C4—261no—
200C2×C4—262no—
201C2×C4—522no—
202C2×C4—522no—
203C2×C4—524no—
204C2×C4—522no—
205C2×C4D4×D1312yes—
206C2×C4C23×D1311yescharacteristic
207C8—22no—
208C8—262no—
209C22—42no—
210C22—41no—
211C22—132no—
212C22—262no—
213C22—522no—
214C22—521no—
215C22C2×D4×D1311yescharacteristic
216C4—22no—
217C4—42no—
218C4—41no—
219C4—132no—
220C4—262no—
221C4—522no—
222C4—521no—
223C4#41×D1312yes—
224C2—81no—
225C2—262no—
226C2—1041no—
227C2D13×#12411yescharacteristic
228C2#1171947312yes—
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#488C2
socleC22×C13C22×D4
prime radical#11719373C2
hypercenter#488D13
hypocenterC13#3142
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #488

Complements

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

NH ≅ G/Ntype
1. D13×#125C2semidirect
3. C13×#488C2semidirect
4. #11718729C2semidirect
5. #11718717C2semidirect
6. #11718464C2semidirect
7. #11718458C2semidirect
8. #11718432C2semidirect
9. #11718425C2semidirect
10. #11718358C2semidirect
11. C4×#6094C2semidirect
102. #488D13semidirect
183. C13#3142semidirect

Maximal subgroups

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

subgroupindex
D13×#1252
#117193732
C13×#4882
#117187292
#117187172
#117184642
#117184582
#117184322
#117184252
#117183582
C4×#60942
#314213