Finite Group Databasebeta

← #13120247

Subgroups — #13120247

Order 1664.

412 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 145 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#11718644C211yesmaximal, characteristic
4#11718640C211yesmaximal, characteristic
5C4×#6101C212yesmaximal
6#11718313C212yesmaximal
7#11718313C212yesmaximal
8#11718308C212yesmaximal
9#11718307C212yesmaximal
10C22×Q8×C13C2211yescharacteristic
11C22×Dic26C2211yescharacteristic
12C2×C13×C4⋊C4C2211yescharacteristic
13C2×C42×C13C2211yescharacteristic
14C2×C4⋊Dic13C2211yescharacteristic
15C2×#6101C2212yes—
16C2×#6101C2212yes—
17C2×#6101C2212yes—
18C2×#6101C2212yes—
19C2×#6101C2212yes—
20C2×C4×Dic13C2212yes—
21C2×C4×Dic13C2212yes—
22C13×#95C2212yes—
23C13×#95C2212yes—
24#88071C2212yes—
25#88071C2212yes—
26#88071C2212yes—
27#88071C2212yes—
28#88071C2211yescharacteristic
29#88071C2211yescharacteristic
30#88071C2212yes—
31C2×Q8×C13—22no—
32C2×Q8×C13—41no—
33C2×Q8×C13—41no—
34C22×C4×C13C2311yescharacteristic
35C22×C4×C13C2312yes—
36C22×C4×C13C2311yescharacteristic
37C22×C4×C13C2312yes—
38C22×C4×C13C2311yescharacteristic
39C22×Dic13C2312yes—
40C22×Dic13C2312yes—
41C22×Dic13C2312yes—
42C22×Dic13C2312yes—
43C2×Dic26—24no—
44C2×Dic26—41no—
45C13×C4⋊C4—41no—
46C42×C13—41no—
47C4⋊Dic13—41no—
48#6101—24no—
49#6101—24no—
50#6101—42no—
51#6101—42no—
52#6101Q818yescomplemented
53C4×Dic13—24no—
54C4×Dic13—42no—
55#2586—131nomaximal, Sylow
56C23×C13C2411yescharacteristic
57Q8×C13—44no—
58C2×C4×C13—22no—
59C2×C4×C13—22no—
60C2×C4×C13—21no—
61C2×C4×C13—21no—
62C2×C4×C13—22no—
63C2×C4×C13—22no—
64C2×C4×C13—22no—
65C2×C4×C13—22no—
66C2×C4×C13—22no—
67C2×C4×C13—21no—
68C2×C4×C13—21no—
69C2×C4×C13C2×Q814yes—
70C2×C4×C13#4112yes—
71C2×Dic13—22no—
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×Dic13C2×Q814yes—
81C2×Dic13C2×Q814yes—
82C2×Dic13#4114yes—
83Dic26—44no—
84#398—131no—
85#395—132no—
86#395—131no—
87#391—132no—
88#391D1311yescharacteristic
89#389—132no—
90#387—132no—
91#387—132no—
92C4×C4⋊C4—132no—
93C22×C13C22×Q812yes—
94C22×C13C2×#4111yescharacteristic
95C22×C13C2×#4112yes—
96C22×C13H(5,𝔽2)11yescharacteristic
97C22×C13H(5,𝔽2)11yescharacteristic
98C4×C13—22no—
99C4×C13—24no—
100C4×C13—42no—
101C4×C13—41no—
102C4×C13—41no—
103Dic13—24no—
104Dic13—24no—
105Dic13—24no—
106Dic13—42no—
107C22×Q8—131no—
108C22×Q8C2×D1311yescharacteristic
109C2×C4⋊C4—132no—
110C2×C4⋊C4—132no—
111C2×C4⋊C4—132no—
112C2×C4⋊C4—132no—
113C2×C4⋊C4—132no—
114C2×C4⋊C4—131no—
115C2×C4⋊C4C2×D1311yescharacteristic
116C2×C42—132no—
117C2×C42—132no—
118C2×C42C2×D1311yescharacteristic
119#95—132no—
120#95—132no—
121#95—132no—
122#95—131no—
123#95—131no—
124#95—132no—
125#95—132no—
126#95C2×D1312yes—
127#95C2×D1312yes—
128C2×C13#53312yes—
129C2×C13#53811yescharacteristic
130C2×C13#55111yescharacteristic
131C2×C13#55412yes—
132C2×C13Q8211yescharacteristic
133C2×Q8—22no—
134C2×Q8—41no—
135C2×Q8—41no—
136C2×Q8—264no—
137C2×Q8—521no—
138C22×C4—132no—
139C22×C4—132no—
140C22×C4—132no—
141C22×C4—132no—
142C22×C4C22×D1311yescharacteristic
143C22×C4C22×D1312yes—
144C22×C4C22×D1311yescharacteristic
145C22×C4C22×D1311yescharacteristic
146C22×C4C22×D1312yes—
147C4⋊C4—41no—
148C4⋊C4—138no—
149C4⋊C4—264no—
150C4⋊C4—264no—
151C4⋊C4—522no—
152C4⋊C4—522no—
153C4⋊C4—521no—
154C42—41no—
155C42—264no—
156C42—522no—
157C13#258611yescharacteristic, complemented, Sylow
158C23C23×D1311yescharacteristic
159Q8—44no—
160Q8—524no—
161C2×C4—22no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—22no—
165C2×C4—22no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—22no—
172C2×C4—134no—
173C2×C4—134no—
174C2×C4—134no—
175C2×C4—262no—
176C2×C4—262no—
177C2×C4—262no—
178C2×C4—262no—
179C2×C4—262no—
180C2×C4—262no—
181C2×C4—262no—
182C2×C4—262no—
183C2×C4—262no—
184C2×C4#612712yes—
185C2×C4Q8×D1314yes—
186C22C2×#612711yescharacteristic
187C22#8825111yescharacteristic
188C22#8825111yescharacteristic
189C22C2×Q8×D1312yes—
190C22#41×D1312yes—
191C4—22no—
192C4—24no—
193C4—42no—
194C4—41no—
195C4—41no—
196C4—264no—
197C4—264no—
198C4—264no—
199C4—522no—
200C2#1171919911yescharacteristic
201C2#1171928312yes—
202C2#1171934112yes—
203C2#1171938411yescharacteristic
204C2#1171942711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, prime radical, cosocleC23×C13C24
FittingC13×#391C2
hypercenter#391D13
hypocenterC13#2586
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
52. #6101Q8semidirect
157. C13#2586semidirect

Maximal subgroups

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

subgroupindex
C13×#3912
#117188902
#117186442
#117186402
C4×#61012
#117183132
#117183082
#117183072
#258613