Finite Group Databasebeta

← #13125463

Subgroups — #13125463

Order 1664.

362 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 113 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#11719424C211yesmaximal, characteristic
2#11719402C211yesmaximal, characteristic, complemented
3C13×#490C211yesmaximal, characteristic, complemented
4#11718737C211yesmaximal, characteristic, complemented
5#11718725C211yesmaximal, characteristic, complemented
6#11718441C212yesmaximal, complemented
7#11718439C212yesmaximal, complemented
8#11718419C212yesmaximal, complemented
9#11718418C212yesmaximal, complemented
10#11718369C211yesmaximal, characteristic, complemented
11#11718364C211yesmaximal, characteristic, complemented
12C13×#127C2211yescharacteristic
13C13×#125C2211yescharacteristic
14#88193—22no—
15#88192C2212yes—
16#88189—22no—
17D4×Dic13C2212yes—
18C2×#6105C2212yes—
19C2×#6105C2212yes—
20C2×#6094C2211yescharacteristic
21C2×C8×D13C2211yescharacteristic
22#88152—22no—
23#88151C2212yes—
24#88144—22no—
25#88141C2212yes—
26#88126C2211yescharacteristic
27#88124C2211yescharacteristic
28#88123C2211yescharacteristic
29C13×#102C2212yes—
30C13×#102C2212yes—
31C13×#97C2211yescharacteristic
32#88056C2212yes—
33#88056C2212yes—
34#88055C2211yescharacteristic
35C8×Dic13C2211yescharacteristic
36#88048C2212yes—
37#88047C2212yes—
38C4×#1055C2211yescharacteristic
39C2×D4×C13—22no—
40C2×D4×C13C2312yes—
41C2×C22⋊D13—22no—
42C22×Dic13—22no—
43C2×C4×D13C2311yescharacteristic
44C2×Dic26C2312yes—
45C2×C8×C13C2311yescharacteristic
46C2×C8×C13C2311yescharacteristic
47C13×C4⋊C4—22no—
48C13×C4⋊C4C2312yes—
49C42×C13C2311yescharacteristic
50C22⋊Dic13—22no—
51C22⋊Dic13—22no—
52#6105—24no—
53#6105—24no—
54#6103—22no—
55#6103D412yes—
56C4⋊Dic13—22no—
57C4⋊Dic13—22no—
58C4⋊Dic13C2312yes—
59#6101—22no—
60#6101—22no—
61#6101D412yes—
62C4×Dic13—22no—
63C4×Dic13C2311yescharacteristic
64C2×#1055C2311yescharacteristic
65C2×#1055C2311yescharacteristic
66#6094—22no—
67C8×D13—22no—
68#3174—131nomaximal, Sylow
69C23×C13—22no—
70C22×D13C2×D411yescharacteristic
71D4×C13—22no—
72D4×C13—22no—
73D4×C13—82no—
74C2×C4×C13—22no—
75C2×C4×C13C2×D412yes—
76C2×C4×C13C2411yescharacteristic
77C22⋊D13—82no—
78C2×Dic13—22no—
79C2×Dic13—22no—
80C2×Dic13—82no—
81C2×Dic13C2×D412yes—
82C2×Dic13C2×D411yescharacteristic
83C4×D13—21no—
84C4×D13—21no—
85Dic26—22no—
86Dic26—22no—
87C8×C13—21no—
88C8×C13—21no—
89#1055#4112yes—
90#1055#4112yes—
91#541—131no—
92#540—131no—
93#499—131no—
94#492—131no—
95#491—131no—
96#490D1311yescharacteristic, complemented
97#468—132no—
98#465—132no—
99#440—132no—
100C4×SD16—132no—
101#405—131no—
102C22×C13—42no—
103C22×C13—42no—
104C22×C13—42no—
105C22×C13C22×D411yescharacteristic
106C2×D13—21no—
107C2×D13—22no—
108C4×C13—22no—
109C4×C13—42no—
110C4×C13C2×#4111yescharacteristic
111C4×C13C2×#4111yescharacteristic
112Dic13—21no—
113Dic13—22no—
114Dic13—42no—
115Dic13—42no—
116C2×SD16—132no—
117C2×SD16—132no—
118C2×M16—131no—
119C22×C8—131no—
120C4⋊Q8—131no—
121#127C2×D1311yescharacteristic
122#126—262no—
123#125—131no—
124#125—262no—
125#125C2×D1311yescharacteristic
126#123—262no—
127C22⋊Q8—132no—
128#121—132no—
129#121—262no—
130C4×Q8—132no—
131C4×D4—132no—
132#117—131no—
133#107—132no—
134#106—132no—
135#103—132no—
136#103—132no—
137#102C2×D1312yes—
138#102C2×D1312yes—
139#97—131no—
140#97C2×D1311yescharacteristic
141C4×C8—131no—
142C4×C8—131no—
143C2×C13—82no—
144C2×C13#53211yescharacteristic
145C2×C13#57712yes—
146D13—41no—
147C2×Q8—132no—
148C2×D4—22no—
149C2×D4—262no—
150C2×D4C22×D1312yes—
151C22×C4—131no—
152C22×C4—262no—
153SD16—264no—
154SD16—264no—
155M16—262no—
156C2×C8—131no—
157C2×C8—131no—
158C2×C8—262no—
159C2×C8C22×D1311yescharacteristic
160C2×C8C22×D1311yescharacteristic
161C4⋊C4—22no—
162C4⋊C4—132no—
163C4⋊C4—132no—
164C4⋊C4—262no—
165C4⋊C4—262no—
166C4⋊C4—262no—
167C4⋊C4—262no—
168C4⋊C4C22×D1312yes—
169C22⋊C4—132no—
170C22⋊C4—262no—
171C22⋊C4—262no—
172C22⋊C4—262no—
173C42—131no—
174C42—262no—
175C42C22×D1311yescharacteristic
176C13#317411yescharacteristic, complemented, Sylow
177C23—22no—
178C23—131no—
179Q8—262no—
180Q8—262no—
181D4—22no—
182D4—22no—
183D4—82no—
184D4—1042no—
185C2×C4—22no—
186C2×C4—132no—
187C2×C4—131no—
188C2×C4—261no—
189C2×C4—261no—
190C2×C4—262no—
191C2×C4—262no—
192C2×C4—1042no—
193C2×C4D4×D1312yes—
194C2×C4C23×D1311yescharacteristic
195C8—21no—
196C8—21no—
197C8—132no—
198C8—132no—
199C22—42no—
200C22—42no—
201C22—42no—
202C22—262no—
203C22—261no—
204C22C2×D4×D1311yescharacteristic
205C4—22no—
206C4—42no—
207C4—262no—
208C4—261no—
209C4—522no—
210C4—522no—
211C4#41×D1311yescharacteristic
212C4#41×D1311yescharacteristic
213C2—82no—
214C2—521no—
215C2#1171937311yescharacteristic
216C2#1171948012yes—
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#490C2
socleC22×C13C22×D4
prime radical#11719424C2
hypercenter#490D13
hypocenterC13#3174
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
2. #11719402C2semidirect
3. C13×#490C2semidirect
4. #11718737C2semidirect
5. #11718725C2semidirect
6. #11718441C2semidirect
7. #11718439C2semidirect
8. #11718419C2semidirect
9. #11718418C2semidirect
10. #11718369C2semidirect
11. #11718364C2semidirect
96. #490D13semidirect
176. C13#3174semidirect

Maximal subgroups

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

subgroupindex
#117194242
#117194022
C13×#4902
#117187372
#117187252
#117184412
#117184392
#117184192
#117184182
#117183692
#117183642
#317413