Finite Group Databasebeta

← #13122822

Subgroups — #13122822

Order 1664.

368 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 137 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#11718891C211yesmaximal, characteristic
3#11718891C211yesmaximal, characteristic
4#11718645C212yesmaximal
5#11718594C212yesmaximal
6#11718321C212yesmaximal
7#11718318C212yesmaximal
8#11718315C212yesmaximal
9#11718308C212yesmaximal
10C22×Q8×C13C2211yescharacteristic
11C2×C13×C4⋊C4C2211yescharacteristic
12C2×C42×C13C2211yescharacteristic
13C2×C4⋊Dic13C2212yes—
14C2×C4⋊Dic13C2211yescharacteristic
15C2×C4⋊Dic13C2211yescharacteristic
16C2×#6101C2212yes—
17C2×#6101C2212yes—
18C2×#6101C2212yes—
19C2×#6101C2212yes—
20C2×C4×Dic13C2211yescharacteristic
21C2×C4×Dic13C2211yescharacteristic
22C13×#95C2212yes—
23C13×#95C2212yes—
24#88071C2212yes—
25#88071C2212yes—
26#88071C2212yes—
27#88071C2212yes—
28#88071C2212yes—
29#88071C2212yes—
30#88071C2212yes—
31C2×Q8×C13—41no—
32C2×Q8×C13—41no—
33C2×Q8×C13Q814yes—
34C22×C4×C13C2312yes—
35C22×C4×C13C2312yes—
36C22×C4×C13C2311yescharacteristic
37C22×C4×C13C2311yescharacteristic
38C22×C4×C13C2311yescharacteristic
39C22×Dic13C2312yes—
40C22×Dic13C2312yes—
41C22×Dic13C2312yes—
42C22×Dic13C2312yes—
43C13×C4⋊C4—41no—
44C42×C13—41no—
45C4⋊Dic13—24no—
46C4⋊Dic13—41no—
47C4⋊Dic13—41no—
48#6101—24no—
49#6101—24no—
50#6101—42no—
51#6101—42no—
52C4×Dic13—41no—
53C4×Dic13—41no—
54#2809—131nomaximal, Sylow
55C23×C13C2411yescharacteristic
56Q8×C13—44no—
57C2×C4×C13—21no—
58C2×C4×C13—21no—
59C2×C4×C13—21no—
60C2×C4×C13—21no—
61C2×C4×C13—21no—
62C2×C4×C13—21no—
63C2×C4×C13—22no—
64C2×C4×C13—22no—
65C2×C4×C13—22no—
66C2×C4×C13—22no—
67C2×C4×C13—22no—
68C2×C4×C13—22no—
69C2×C4×C13C2×Q812yes—
70C2×C4×C13C2×Q812yes—
71C2×C4×C13C2×Q812yes—
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—24no—
82C2×Dic13#4114yes—
83#400—132no—
84#398—132no—
85#398—132no—
86#391—131no—
87#391—131no—
88#391D1311yescharacteristic
89#389—132no—
90#387—132no—
91#387—132no—
92C22×C13C22×Q811yescharacteristic
93C22×C13C2×#4112yes—
94C22×C13H(5,𝔽2)11yescharacteristic
95C22×C13H(5,𝔽2)11yescharacteristic
96C22×C132−1+412yes—
97C4×C13—22no—
98C4×C13—22no—
99C4×C13—22no—
100C4×C13—42no—
101C4×C13—42no—
102Dic13—24no—
103Dic13—42no—
104Dic13—42no—
105Dic13—42no—
106C22×Q8C2×D1311yescharacteristic
107C2×C4⋊C4—132no—
108C2×C4⋊C4—132no—
109C2×C4⋊C4—132no—
110C2×C4⋊C4—132no—
111C2×C4⋊C4—132no—
112C2×C4⋊C4—131no—
113C2×C4⋊C4—131no—
114C2×C4⋊C4C2×D1311yescharacteristic
115C2×C42—131no—
116C2×C42—131no—
117C2×C42C2×D1311yescharacteristic
118#95—132no—
119#95—132no—
120#95—132no—
121#95—132no—
122#95—132no—
123#95—132no—
124#95—132no—
125#95C2×D1312yes—
126#95C2×D1312yes—
127C2×C13#53912yes—
128C2×C13#54311yescharacteristic
129C2×C13#55511yescharacteristic
130C2×C13#55712yes—
131C2×C13#56311yescharacteristic
132C2×Q8—41no—
133C2×Q8—41no—
134C2×Q8Dic2614yes—
135C22×C4—132no—
136C22×C4—132no—
137C22×C4—132no—
138C22×C4—132no—
139C22×C4C22×D1312yes—
140C22×C4C22×D1312yes—
141C22×C4C22×D1311yescharacteristic
142C22×C4C22×D1311yescharacteristic
143C22×C4C22×D1311yescharacteristic
144C4⋊C4—41no—
145C4⋊C4—264no—
146C4⋊C4—264no—
147C4⋊C4—264no—
148C4⋊C4—522no—
149C4⋊C4—522no—
150C4⋊C4—521no—
151C4⋊C4—521no—
152C42—41no—
153C42—521no—
154C42—521no—
155C13#280911yescharacteristic, complemented, Sylow
156C23C23×D1311yescharacteristic
157Q8—44no—
158C2×C4—21no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—21no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—22no—
165C2×C4—22no—
166C2×C4—22no—
167C2×C4—22no—
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—134no—
171C2×C4—262no—
172C2×C4—262no—
173C2×C4—262no—
174C2×C4—262no—
175C2×C4—262no—
176C2×C4—264no—
177C2×C4—262no—
178C2×C4—262no—
179C2×C4—262no—
180C2×C4—262no—
181C2×C4C2×Dic2612yes—
182C2×C4C2×Dic2612yes—
183C2×C4C2×Dic2612yes—
184C22C22×Dic2611yescharacteristic
185C22#8825111yescharacteristic
186C22#8825111yescharacteristic
187C22#8825412yes—
188C22#41×D1312yes—
189C4—22no—
190C4—22no—
191C4—22no—
192C4—42no—
193C4—42no—
194C4—264no—
195C4—522no—
196C4—522no—
197C4—522no—
198C2#1171918811yescharacteristic
199C2#1171927412yes—
200C2#1171934312yes—
201C2#1171937511yescharacteristic
202C2#1171944011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, prime radical, cosocleC23×C13C24
FittingC13×#391C2
hypercenter#391D13
hypocenterC13#2809
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
155. C13#2809semidirect

Maximal subgroups

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

subgroupindex
C13×#3912
#117188912
#117186452
#117185942
#117183212
#117183182
#117183152
#117183082
#280913