Finite Group Databasebeta

← #13122795

Subgroups — #13122795

Order 1664.

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

normal subgroups only

This group has 392 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
1C13×#391C211yesmaximal, characteristic
2#11718890C212yesmaximal
3#11718633C212yesmaximal
4#11718590C211yesmaximal, characteristic
5#11718589C211yesmaximal, characteristic
6#11718318C212yesmaximal
7#11718318C212yesmaximal
8#11718314C212yesmaximal
9#11718307C212yesmaximal
10C22×Q8×C13C2211yescharacteristic
11C22×Dic26C2211yescharacteristic
12C2×C13×C4⋊C4C2211yescharacteristic
13C2×C42×C13C2211yescharacteristic
14C2×C4⋊Dic13C2211yescharacteristic
15C2×C4⋊Dic13C2211yescharacteristic
16C2×C4⋊Dic13C2211yescharacteristic
17C2×#6101C2212yes—
18C2×#6101C2212yes—
19C2×#6101C2212yes—
20C2×#6101C2212yes—
21C2×#6101C2212yes—
22C2×C4×Dic13C2212yes—
23C13×#95C2212yes—
24C13×#95C2212yes—
25#88071C2212yes—
26#88071C2212yes—
27#88071C2212yes—
28#88071C2212yes—
29#88071C2212yes—
30#88071C2212yes—
31C2×Q8×C13—22no—
32C2×Q8×C13—41no—
33C2×Q8×C13—41no—
34C22×C4×C13C2312yes—
35C22×C4×C13C2312yes—
36C22×C4×C13C2311yescharacteristic
37C22×C4×C13C2311yescharacteristic
38C22×C4×C13C2311yescharacteristic
39C22×Dic13C2312yes—
40C22×Dic13C2312yes—
41C22×Dic13C2312yes—
42C22×Dic13C2312yes—
43C2×Dic26—41no—
44C2×Dic26—41no—
45C2×Dic26Q814yescomplemented
46C13×C4⋊C4—41no—
47C42×C13—41no—
48C4⋊Dic13—41no—
49C4⋊Dic13—41no—
50C4⋊Dic13Q814yescomplemented
51#6101—24no—
52#6101—42no—
53#6101—42no—
54#6101—42no—
55#6101—42no—
56C4×Dic13—42no—
57#2806—131nomaximal, Sylow
58C23×C13C2411yescharacteristic
59Q8×C13—44no—
60C2×C4×C13—21no—
61C2×C4×C13—21no—
62C2×C4×C13—21no—
63C2×C4×C13—21no—
64C2×C4×C13—21no—
65C2×C4×C13—21no—
66C2×C4×C13—22no—
67C2×C4×C13—22no—
68C2×C4×C13—22no—
69C2×C4×C13—22no—
70C2×C4×C13—22no—
71C2×C4×C13—22no—
72C2×C4×C13C2×Q812yes—
73C2×C4×C13C2×Q812yes—
74C2×C4×C13#4112yes—
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×Dic13C2×Q814yes—
86C2×Dic13C2×Q814yes—
87Dic26—44no—
88#398—132no—
89#398—132no—
90#395—132no—
91#391—131no—
92#391—132no—
93#391D1311yescharacteristic
94#389—132no—
95#389—131no—
96#387—132no—
97C22×C13C22×Q811yescharacteristic
98C22×C13C22×Q811yescharacteristic
99C22×C13C2×#4111yescharacteristic
100C22×C13H(5,𝔽2)11yescharacteristic
101C22×C13H(5,𝔽2)11yescharacteristic
102C22×C13H(5,𝔽2)11yescharacteristic
103C22×C132−1+411yescharacteristic
104C4×C13—22no—
105C4×C13—22no—
106C4×C13—22no—
107C4×C13—42no—
108C4×C13—42no—
109Dic13—24no—
110Dic13—24no—
111Dic13—42no—
112Dic13—42no—
113C22×Q8—131no—
114C22×Q8C2×D1311yescharacteristic
115C2×C4⋊C4—131no—
116C2×C4⋊C4—132no—
117C2×C4⋊C4—132no—
118C2×C4⋊C4—132no—
119C2×C4⋊C4—132no—
120C2×C4⋊C4—132no—
121C2×C4⋊C4—131no—
122C2×C4⋊C4—131no—
123C2×C4⋊C4C2×D1311yescharacteristic
124C2×C42—132no—
125C2×C42C2×D1311yescharacteristic
126#95—132no—
127#95—132no—
128#95—132no—
129#95—132no—
130#95—132no—
131#95—132no—
132#95C2×D1312yes—
133#95C2×D1312yes—
134C2×C13#53811yescharacteristic
135C2×C13#54311yescharacteristic
136C2×C13#54411yescharacteristic
137C2×C13#55411yescharacteristic
138C2×C13#55711yescharacteristic
139C2×C13Q8211yescharacteristic
140C2×C13#56211yescharacteristic
141C2×Q8—22no—
142C2×Q8—41no—
143C2×Q8—41no—
144C2×Q8—134no—
145C2×Q8—521no—
146C2×Q8—521no—
147C22×C4—132no—
148C22×C4—132no—
149C22×C4—132no—
150C22×C4—132no—
151C22×C4C22×D1312yes—
152C22×C4C22×D1312yes—
153C22×C4C22×D1311yescharacteristic
154C22×C4C22×D1311yescharacteristic
155C22×C4C22×D1311yescharacteristic
156C4⋊C4—41no—
157C4⋊C4—134no—
158C4⋊C4—264no—
159C4⋊C4—522no—
160C4⋊C4—522no—
161C4⋊C4—522no—
162C4⋊C4—522no—
163C4⋊C4—521no—
164C4⋊C4—521no—
165C42—41no—
166C42—522no—
167C13#280611yescharacteristic, complemented, Sylow
168C23C23×D1311yescharacteristic
169Q8—44no—
170Q8—524no—
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—21no—
174C2×C4—21no—
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—134no—
184C2×C4—134no—
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#612712yes—
196C2×C4Q8×D1312yes—
197C2×C4Q8×D1312yes—
198C22C2×#612711yescharacteristic
199C22#8825111yescharacteristic
200C22#8825111yescharacteristic
201C22C2×Q8×D1311yescharacteristic
202C22C2×Q8×D1311yescharacteristic
203C22#8825611yescharacteristic
204C22#8825711yescharacteristic
205C4—22no—
206C4—22no—
207C4—22no—
208C4—42no—
209C4—42no—
210C4—264no—
211C4—264no—
212C4—522no—
213C4—522no—
214C2#1171919911yescharacteristic
215C2#1171927211yescharacteristic
216C2#1171928411yescharacteristic
217C2#1171932811yescharacteristic
218C2#1171933911yescharacteristic
219C2#1171938911yescharacteristic
220C2#1171942711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, prime radical, cosocleC23×C13C24
FittingC13×#391C2
hypercenter#391D13
hypocenterC13#2806
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
45. C2×Dic26Q8semidirect
50. C4⋊Dic13Q8semidirect
167. C13#2806semidirect

Maximal subgroups

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

subgroupindex
C13×#3912
#117188902
#117186332
#117185902
#117185892
#117183182
#117183142
#117183072
#280613