Finite Group Databasebeta

← #13125485

Subgroups — #13125485

Order 1664.

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

normal subgroups only

This group has 386 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, complemented
2#11719403C211yesmaximal, characteristic, complemented
3C13×#490C211yesmaximal, characteristic, complemented
4#11718734C211yesmaximal, characteristic, complemented
5#11718725C211yesmaximal, characteristic, complemented
6#11718446C212yesmaximal, complemented
7#11718443C212yesmaximal, complemented
8#11718436C212yesmaximal, complemented
9#11718417C212yesmaximal, complemented
10#11718374C211yesmaximal, characteristic, complemented
11#11718369C211yesmaximal, characteristic, complemented
12C13×#127C2211yescharacteristic
13C13×#125C2211yescharacteristic
14#88193—22no—
15#88192C2212yes—
16#88189—22no—
17D4×Dic13C2212yes—
18C2×#6104C2212yes—
19C2×#6104C2212yes—
20C2×#6094C2211yescharacteristic
21C2×C8×D13C2211yescharacteristic
22#88149—22no—
23#88149C2212yes—
24#88148—22no—
25#88147C2212yes—
26#88128C2211yescharacteristic
27#88126C2211yescharacteristic
28#88124C2211yescharacteristic
29C13×#102C2212yes—
30C13×#102C2212yes—
31C13×#97C2211yescharacteristic
32#88061C2212yes—
33#88061C2212yes—
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×D52—22no—
44C2×D52—22no—
45C2×D52C2312yes—
46C2×C4×D13—22no—
47C2×C4×D13C2311yescharacteristic
48C2×C8×C13C2311yescharacteristic
49C2×C8×C13C2311yescharacteristic
50C13×C4⋊C4—22no—
51C13×C4⋊C4C2312yes—
52C42×C13C2311yescharacteristic
53C22⋊Dic13—22no—
54C22⋊Dic13—22no—
55#6104—24no—
56#6104—24no—
57#6103—22no—
58#6103—22no—
59#6103D412yes—
60C4⋊Dic13C2312yes—
61#6101—22no—
62#6101D412yes—
63C4×Dic13C2311yescharacteristic
64C2×#1055C2311yescharacteristic
65C2×#1055C2311yescharacteristic
66#6094—22no—
67C8×D13—22no—
68#3176—131nomaximal, Sylow
69C23×C13—22no—
70C22×D13—22no—
71C22×D13C2×D411yescharacteristic
72D4×C13—22no—
73D4×C13—22no—
74D4×C13—82no—
75C2×C4×C13—22no—
76C2×C4×C13C2×D412yes—
77C2×C4×C13C2411yescharacteristic
78C22⋊D13—82no—
79C2×Dic13—22no—
80C2×Dic13—82no—
81C2×Dic13C2×D412yes—
82C2×Dic13C2×D411yescharacteristic
83D52—22no—
84D52—22no—
85D52—82no—
86D52—82no—
87C4×D13—21no—
88C4×D13—21no—
89C4×D13—82no—
90C8×C13—21no—
91C8×C13—21no—
92#1055#4112yes—
93#1055#4112yes—
94#540—131no—
95#540—131no—
96#499—131no—
97#493—131no—
98#490—131no—
99#490D1311yescharacteristic, complemented
100#469—132no—
101#466—132no—
102#442—132no—
103C4×D8—132no—
104#405—131no—
105C22×C13—42no—
106C22×C13—42no—
107C22×C13—42no—
108C22×C13C22×D411yescharacteristic
109C2×D13—21no—
110C2×D13—22no—
111C2×D13—42no—
112C2×D13—42no—
113C2×D13—42no—
114C4×C13—22no—
115C4×C13—42no—
116C4×C13C2×#4111yescharacteristic
117C4×C13C2×#4111yescharacteristic
118Dic13—21no—
119Dic13—22no—
120Dic13—42no—
121C2×D8—132no—
122C2×D8—132no—
123C2×M16—131no—
124C22×C8—131no—
125#127—131no—
126#127C2×D1311yescharacteristic
127#125—131no—
128#125C2×D1311yescharacteristic
129#123—262no—
130#123—262no—
131#121—132no—
132#121—132no—
133#121—262no—
134#121—262no—
135C4×D4—132no—
136C4×D4—132no—
137#117—131no—
138#107—132no—
139#106—132no—
140#102—132no—
141#102—132no—
142#102C2×D1312yes—
143#102C2×D1312yes—
144#97—131no—
145#97C2×D1311yescharacteristic
146C4×C8—131no—
147C4×C8—131no—
148C2×C13—82no—
149C2×C13#53211yescharacteristic
150C2×C13#57612yes—
151D13—41no—
152D13—82no—
153C2×D4—22no—
154C2×D4—132no—
155C2×D4—262no—
156C2×D4—262no—
157C2×D4—262no—
158C2×D4C22×D1312yes—
159C22×C4—131no—
160C22×C4—262no—
161C22×C4—262no—
162D8—264no—
163D8—264no—
164M16—262no—
165C2×C8—131no—
166C2×C8—131no—
167C2×C8—262no—
168C2×C8C22×D1311yescharacteristic
169C2×C8C22×D1311yescharacteristic
170C4⋊C4—22no—
171C4⋊C4—132no—
172C4⋊C4—132no—
173C4⋊C4—262no—
174C4⋊C4C22×D1312yes—
175C22⋊C4—132no—
176C22⋊C4—262no—
177C22⋊C4—262no—
178C22⋊C4—262no—
179C22⋊C4—262no—
180C42—131no—
181C42C22×D1311yescharacteristic
182C13#317611yescharacteristic, complemented, Sylow
183C23—22no—
184C23—131no—
185C23—262no—
186D4—22no—
187D4—22no—
188D4—82no—
189D4—262no—
190D4—262no—
191D4—1042no—
192D4—1042no—
193D4—1042no—
194C2×C4—22no—
195C2×C4—132no—
196C2×C4—131no—
197C2×C4—261no—
198C2×C4—261no—
199C2×C4—262no—
200C2×C4—1042no—
201C2×C4—1042no—
202C2×C4D4×D1312yes—
203C2×C4C23×D1311yescharacteristic
204C8—21no—
205C8—21no—
206C8—132no—
207C8—132no—
208C22—42no—
209C22—42no—
210C22—42no—
211C22—262no—
212C22—261no—
213C22—522no—
214C22—522no—
215C22—522no—
216C22C2×D4×D1311yescharacteristic
217C4—22no—
218C4—42no—
219C4—262no—
220C4—261no—
221C4—522no—
222C4#41×D1311yescharacteristic
223C4#41×D1311yescharacteristic
224C2—82no—
225C2—521no—
226C2—1042no—
227C2#1171937311yescharacteristic
228C2#1171947912yes—
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#490C2
socleC22×C13C22×D4
hypercenter#490D13
hypocenterC13#3176
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
1. #11719424C2semidirect
2. #11719403C2semidirect
3. C13×#490C2semidirect
4. #11718734C2semidirect
5. #11718725C2semidirect
6. #11718446C2semidirect
7. #11718443C2semidirect
8. #11718436C2semidirect
9. #11718417C2semidirect
10. #11718374C2semidirect
11. #11718369C2semidirect
99. #490D13semidirect
182. C13#3176semidirect

Maximal subgroups

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

subgroupindex
#117194242
#117194032
C13×#4902
#117187342
#117187252
#117184462
#117184432
#117184362
#117184172
#117183742
#117183692
#317613