Finite Group Databasebeta

← #13121006

Subgroups — #13121006

Order 1664.

424 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 141 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
1C4×C13×C22⋊C4C211yesmaximal, characteristic
2#11718873C211yesmaximal, characteristic
3#11718872C211yesmaximal, characteristic
4#11718609C212yesmaximal
5#11718608C212yesmaximal
6#11718594C212yesmaximal, complemented
7#11718590C212yesmaximal, complemented
8#11718321C212yesmaximal, complemented
9#11718317C212yesmaximal, complemented
10C23×C4×C13C2211yescharacteristic
11C22×Dic26C2212yes—
12C2×C13×C22⋊C4C2212yes—
13C2×C42×C13C2212yes—
14C2×C22⋊Dic13C2211yescharacteristic
15C2×C22⋊Dic13C2212yes—
16C2×C22⋊Dic13C2211yescharacteristic
17C2×C4⋊Dic13C2212yes—
18C2×C4⋊Dic13C2212yes—
19C2×#6101C2212yes—
20C2×#6101C2212yes—
21C13×#95C2211yescharacteristic
22C13×#95C2211yescharacteristic
23#88071C2212yes—
24#88071C2212yes—
25#88071C2212yes—
26#88071C2212yes—
27#88071C2212yes—
28#88071C2211yescharacteristic
29#88071C2212yes—
30#88071C2211yescharacteristic
31C24×C13C2311yescharacteristic
32C22×C4×C13—42no—
33C22×C4×C13Q814yescomplemented
34C22×C4×C13C2312yes—
35C22×C4×C13C2311yescharacteristic
36C22×C4×C13C2311yescharacteristic
37C22×C4×C13C2312yes—
38C22×Dic13C2312yes—
39C22×Dic13C2312yes—
40C22×Dic13C2312yes—
41C22×Dic13C2312yes—
42C2×Dic26—24no—
43C2×Dic26—42no—
44C2×Dic26—42no—
45C13×C22⋊C4—24no—
46C42×C13—42no—
47C22⋊Dic13—42no—
48C22⋊Dic13—41no—
49C22⋊Dic13—41no—
50C4⋊Dic13—42no—
51C4⋊Dic13—42no—
52#6101—24no—
53#6101—42no—
54#2665—131nomaximal, Sylow
55C23×C13—22no—
56C23×C13—21no—
57C23×C13—22no—
58C23×C13—21no—
59C23×C13C2×Q812yes—
60C23×C13C2411yescharacteristic
61C2×C4×C13—22no—
62C2×C4×C13—22no—
63C2×C4×C13—22no—
64C2×C4×C13—22no—
65C2×C4×C13—22no—
66C2×C4×C13—22no—
67C2×C4×C13—22no—
68C2×C4×C13—44no—
69C2×C4×C13C2×Q812yes—
70C2×C4×C13C2×Q812yes—
71C2×C4×C13#4114yes—
72C2×Dic13—22no—
73C2×Dic13—22no—
74C2×Dic13—22no—
75C2×Dic13—22no—
76C2×Dic13—22no—
77C2×Dic13—22no—
78C2×Dic13—22no—
79C2×Dic13—22no—
80C2×Dic13—22no—
81C2×Dic13—22no—
82C2×Dic13—22no—
83C2×Dic13—22no—
84Dic26—48no—
85#400—132no—
86#396—132no—
87#395—132no—
88#393—132no—
89#391—132no—
90#387—132no—
91#381—131no—
92#380—131no—
93C4×C22⋊C4D1311yescharacteristic
94C22×C13—22no—
95C22×C13—22no—
96C22×C13—22no—
97C22×C13—42no—
98C22×C13—42no—
99C22×C13C22×Q811yescharacteristic
100C22×C13C2×#4112yes—
101C22×C13H(5,𝔽2)12yes—
102C22×C13H(5,𝔽2)11yescharacteristic
103C22×C132−1+411yescharacteristic
104C4×C13—24no—
105C4×C13—22no—
106C4×C13—22no—
107C4×C13—42no—
108Dic13—42no—
109Dic13—42no—
110Dic13—42no—
111Dic13—42no—
112C22×Q8—132no—
113C23×C4C2×D1311yescharacteristic
114C2×C4⋊C4—132no—
115C2×C4⋊C4—132no—
116C2×C4⋊C4—132no—
117C2×C4⋊C4—132no—
118C2×C22⋊C4—131no—
119C2×C22⋊C4—131no—
120C2×C22⋊C4—132no—
121C2×C22⋊C4C2×D1312yes—
122C2×C42C2×D1312yes—
123#95—132no—
124#95—131no—
125#95—131no—
126#95—132no—
127#95—132no—
128#95—132no—
129#95—132no—
130#95—132no—
131#95C2×D1311yescharacteristic
132#95C2×D1311yescharacteristic
133C2×C13—42no—
134C2×C13#53311yescharacteristic
135C2×C13#53812yes—
136C2×C13#54212yes—
137C2×C13#54311yescharacteristic
138C2×C13#54411yescharacteristic
139C24C22×D1311yescharacteristic
140C2×Q8—264no—
141C2×Q8—522no—
142C2×Q8—522no—
143C22×C4—42no—
144C22×C4—132no—
145C22×C4—132no—
146C22×C4—132no—
147C22×C4—132no—
148C22×C4Dic2614yescomplemented
149C22×C4C22×D1312yes—
150C22×C4C22×D1311yescharacteristic
151C22×C4C22×D1311yescharacteristic
152C22×C4C22×D1312yes—
153C4⋊C4—264no—
154C4⋊C4—522no—
155C4⋊C4—522no—
156C4⋊C4—522no—
157C22⋊C4—24no—
158C22⋊C4—522no—
159C22⋊C4—521no—
160C22⋊C4—521no—
161C42—42no—
162C13#266511yescharacteristic, complemented, Sylow
163C23—22no—
164C23—22no—
165C23—21no—
166C23—21no—
167C23C2×Dic2612yes—
168C23C23×D1311yescharacteristic
169Q8—528no—
170C2×C4—22no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—44no—
178C2×C4—262no—
179C2×C4—262no—
180C2×C4—262no—
181C2×C4—262no—
182C2×C4—262no—
183C2×C4—262no—
184C2×C4—262no—
185C2×C4—262no—
186C2×C4—262no—
187C2×C4—262no—
188C2×C4—262no—
189C2×C4—262no—
190C2×C4C2×Dic2612yes—
191C2×C4C2×Dic2612yes—
192C2×C4#612714yes—
193C22—22no—
194C22—22no—
195C22—22no—
196C22—42no—
197C22—42no—
198C22C22×Dic2611yescharacteristic
199C22C2×#612712yes—
200C22#8825112yes—
201C22#8825611yescharacteristic
202C22#8825711yescharacteristic
203C4—22no—
204C4—22no—
205C4—24no—
206C4—42no—
207C4—522no—
208C4—522no—
209C4—522no—
210C4—522no—
211C2—42no—
212C2#1171917511yescharacteristic
213C2#1171918811yescharacteristic
214C2#1171922411yescharacteristic
215C2#1171926512yes—
216C2#1171926612yes—
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC4×C13×C22⋊C4C2
prime radicalC24×C13C23
hypercenterC4×C22⋊C4D13
hypocenterC13#2665
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
6. #11718594C2semidirect
7. #11718590C2semidirect
8. #11718321C2semidirect
9. #11718317C2semidirect
33. C22×C4×C13Q8semidirect
148. C22×C4Dic26semidirect
162. C13#2665semidirect

Maximal subgroups

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

subgroupindex
C4×C13×C22⋊C42
#117188732
#117188722
#117186092
#117186082
#117185942
#117185902
#117183212
#117183172
#266513