Finite Group Databasebeta

← #13123093

Subgroups — #13123093

Order 1664.

396 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 133 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
1C13×#381C211yesmaximal, characteristic
2#11718873C212yesmaximal
3#11718610C211yesmaximal, characteristic
4#11718609C212yesmaximal
5#11718608C211yesmaximal, characteristic
6#11718322C212yesmaximal, complemented
7#11718321C212yesmaximal, complemented
8#11718318C212yesmaximal, complemented
9#11718317C212yesmaximal, complemented
10C23×C4×C13C2211yescharacteristic
11C22×Dic26C2211yescharacteristic
12C2×C13×C22⋊C4C2211yescharacteristic
13C2×C13×C22⋊C4C2211yescharacteristic
14C2×C22⋊Dic13C2212yes—
15C2×C22⋊Dic13C2212yes—
16C2×C4⋊Dic13C2212yes—
17C2×C4⋊Dic13C2212yes—
18C2×C4⋊Dic13C2212yes—
19C2×C4⋊Dic13C2211yescharacteristic
20C2×#6101C2212yes—
21C2×#6101C2212yes—
22C2×#6101C2212yes—
23C13×#95C2212yes—
24C13×#95C2212yes—
25#88071C2212yes—
26#88071C2212yes—
27#88071C2211yescharacteristic
28#88071C2212yes—
29#88071C2211yescharacteristic
30#88071C2212yes—
31C24×C13C2311yescharacteristic
32C22×C4×C13—41no—
33C22×C4×C13—41no—
34C22×C4×C13Q814yescomplemented
35C22×C4×C13C2311yescharacteristic
36C22×C4×C13C2312yes—
37C22×C4×C13C2311yescharacteristic
38C22×C4×C13C2312yes—
39C22×Dic13C2312yes—
40C22×Dic13C2312yes—
41C22×Dic13C2312yes—
42C22×Dic13C2312yes—
43C2×Dic26—41no—
44C2×Dic26—42no—
45C13×C22⋊C4—41no—
46C13×C22⋊C4—41no—
47C22⋊Dic13—42no—
48C22⋊Dic13—42no—
49C4⋊Dic13—42no—
50C4⋊Dic13—41no—
51C4⋊Dic13—42no—
52C4⋊Dic13—42no—
53#6101—42no—
54#6101—42no—
55#6101—42no—
56#2841—131nomaximal, Sylow
57C23×C13—22no—
58C23×C13—21no—
59C23×C13—21no—
60C23×C13—22no—
61C23×C13C2×Q812yes—
62C23×C13C2411yescharacteristic
63C2×C4×C13—22no—
64C2×C4×C13—22no—
65C2×C4×C13—22no—
66C2×C4×C13—22no—
67C2×C4×C13—22no—
68C2×C4×C13—21no—
69C2×C4×C13—21no—
70C2×C4×C13—22no—
71C2×C4×C13—22no—
72C2×C4×C13—44no—
73C2×C4×C13C2×Q814yes—
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—
84C2×Dic13—22no—
85C2×Dic13—22no—
86Dic26—44no—
87#400—132no—
88#399—131no—
89#398—132no—
90#398—132no—
91#396—132no—
92#395—132no—
93#393—131no—
94#381D1311yescharacteristic
95#380—132no—
96C22×C13—22no—
97C22×C13—24no—
98C22×C13—41no—
99C22×C13—42no—
100C22×C13—41no—
101C22×C13C22×Q811yescharacteristic
102C22×C13H(5,𝔽2)11yescharacteristic
103C22×C13H(5,𝔽2)11yescharacteristic
104C22×C13H(5,𝔽2)12yes—
105C22×C132−1+412yes—
106C4×C13—24no—
107C4×C13—41no—
108C4×C13—42no—
109C4×C13—41no—
110Dic13—42no—
111Dic13—42no—
112Dic13—42no—
113Dic13—42no—
114C22×Q8—131no—
115C23×C4C2×D1311yescharacteristic
116C2×C4⋊C4—132no—
117C2×C4⋊C4—132no—
118C2×C4⋊C4—132no—
119C2×C4⋊C4—132no—
120C2×C4⋊C4—132no—
121C2×C4⋊C4—132no—
122C2×C4⋊C4—131no—
123C2×C22⋊C4—132no—
124C2×C22⋊C4—132no—
125C2×C22⋊C4C2×D1311yescharacteristic
126C2×C22⋊C4C2×D1311yescharacteristic
127#95—132no—
128#95—132no—
129#95—131no—
130#95—132no—
131#95—132no—
132#95—131no—
133#95C2×D1312yes—
134#95C2×D1312yes—
135C2×C13—42no—
136C2×C13#54311yescharacteristic
137C2×C13#54412yes—
138C2×C13#56011yescharacteristic
139C2×C13#56212yes—
140C2×C13#56311yescharacteristic
141C24C22×D1311yescharacteristic
142C2×Q8—521no—
143C2×Q8—522no—
144C22×C4—41no—
145C22×C4—41no—
146C22×C4—132no—
147C22×C4—132no—
148C22×C4—132no—
149C22×C4—132no—
150C22×C4Dic2614yescomplemented
151C22×C4C22×D1311yescharacteristic
152C22×C4C22×D1312yes—
153C22×C4C22×D1311yescharacteristic
154C22×C4C22×D1312yes—
155C4⋊C4—522no—
156C4⋊C4—522no—
157C4⋊C4—522no—
158C4⋊C4—522no—
159C4⋊C4—522no—
160C4⋊C4—521no—
161C4⋊C4—522no—
162C22⋊C4—41no—
163C22⋊C4—41no—
164C22⋊C4—522no—
165C22⋊C4—522no—
166C13#284111yescharacteristic, complemented, Sylow
167C23—21no—
168C23—21no—
169C23—22no—
170C23—22no—
171C23C2×Dic2612yes—
172C23C23×D1311yescharacteristic
173Q8—524no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—21no—
177C2×C4—22no—
178C2×C4—21no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—44no—
184C2×C4—262no—
185C2×C4—262no—
186C2×C4—262no—
187C2×C4—262no—
188C2×C4—262no—
189C2×C4—262no—
190C2×C4—262no—
191C2×C4—262no—
192C2×C4—262no—
193C2×C4—262no—
194C2×C4—262no—
195C2×C4—262no—
196C2×C4C2×Dic2614yes—
197C22—22no—
198C22—24no—
199C22—41no—
200C22—41no—
201C22—42no—
202C22C22×Dic2611yescharacteristic
203C22#8825111yescharacteristic
204C22#8825111yescharacteristic
205C22#8825612yes—
206C22#8825712yes—
207C4—24no—
208C4—41no—
209C4—41no—
210C4—42no—
211C4—522no—
212C4—522no—
213C4—522no—
214C4—522no—
215C2—42no—
216C2#1171918811yescharacteristic
217C2#1171922412yes—
218C2#1171935611yescharacteristic
219C2#1171937111yescharacteristic
220C2#1171937212yes—
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#381C2
prime radicalC24×C13C23
hypercenter#381D13
hypocenterC13#2841
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
6. #11718322C2semidirect
7. #11718321C2semidirect
8. #11718318C2semidirect
9. #11718317C2semidirect
34. C22×C4×C13Q8semidirect
150. C22×C4Dic26semidirect
166. C13#2841semidirect

Maximal subgroups

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

subgroupindex
C13×#3812
#117188732
#117186102
#117186092
#117186082
#117183222
#117183212
#117183182
#117183172
#284113