Finite Group Databasebeta

← #13122632

Subgroups — #13122632

Order 1664.

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

normal subgroups only

This group has 384 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×#384C211yesmaximal, characteristic
2#11718645C212yesmaximal
3#11718644C211yesmaximal, characteristic
4#11718640C211yesmaximal, characteristic
5#11718640C212yesmaximal
6#11718639C212yesmaximal
7#11718633C212yesmaximal
8#11718633C212yesmaximal
9#11718594C212yesmaximal
10C22×Dic26C2211yescharacteristic
11C2×C13×C4⋊C4C2211yescharacteristic
12C2×C13×C4⋊C4C2212yes—
13C2×C13×C4⋊C4C2212yes—
14C2×C13×C4⋊C4C2211yescharacteristic
15C2×C42×C13C2211yescharacteristic
16C2×C4⋊Dic13C2211yescharacteristic
17C2×#6101C2212yes—
18C2×#6101C2212yes—
19C2×#6101C2212yes—
20C2×#6101C2212yes—
21C2×#6101C2212yes—
22C2×C4×Dic13C2212yes—
23#88071C2212yes—
24#88071C2212yes—
25#88071C2212yes—
26#88071C2212yes—
27#88071C2211yescharacteristic
28#88071C2212yes—
29#88071C2211yescharacteristic
30#88071C2212yes—
31C22×C4×C13C2311yescharacteristic
32C22×C4×C13C2312yes—
33C22×C4×C13C2311yescharacteristic
34C22×C4×C13C2312yes—
35C22×C4×C13C2311yescharacteristic
36C22×Dic13C2312yes—
37C22×Dic13C2312yes—
38C22×Dic13C2312yes—
39C22×Dic13C2312yes—
40C2×Dic26—41no—
41C2×Dic26—42no—
42C13×C4⋊C4—42no—
43C13×C4⋊C4—41no—
44C13×C4⋊C4—42no—
45C13×C4⋊C4—41no—
46C42×C13—22no—
47C4⋊Dic13—41no—
48#6101—24no—
49#6101—42no—
50#6101—42no—
51#6101—42no—
52#6101Q818yescomplemented
53C4×Dic13—42no—
54#2792—131nomaximal, Sylow
55C23×C13C2411yescharacteristic
56C2×C4×C13—22no—
57C2×C4×C13—21no—
58C2×C4×C13—22no—
59C2×C4×C13—21no—
60C2×C4×C13—22no—
61C2×C4×C13—22no—
62C2×C4×C13—22no—
63C2×C4×C13—22no—
64C2×C4×C13—21no—
65C2×C4×C13—21no—
66C2×C4×C13—22no—
67C2×C4×C13C2×Q814yes—
68C2×C4×C13#4112yes—
69C2×Dic13—22no—
70C2×Dic13—22no—
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×Dic13C2×Q814yes—
80C2×Dic13C2×Q814yes—
81Dic26—44no—
82#398—131no—
83#398—132no—
84#395—131no—
85#395—132no—
86#389—132no—
87#389—132no—
88#387—132no—
89#387—132no—
90#384D1311yescharacteristic
91C22×C13C22×Q812yes—
92C22×C13C2×#4111yescharacteristic
93C22×C13H(5,𝔽2)11yescharacteristic
94C22×C13H(5,𝔽2)12yes—
95C22×C132−1+411yescharacteristic
96C4×C13—22no—
97C4×C13—24no—
98C4×C13—41no—
99C4×C13—42no—
100C4×C13—41no—
101Dic13—24no—
102Dic13—24no—
103Dic13—42no—
104Dic13—42no—
105C22×Q8—131no—
106C2×C4⋊C4—132no—
107C2×C4⋊C4—132no—
108C2×C4⋊C4—132no—
109C2×C4⋊C4—132no—
110C2×C4⋊C4—132no—
111C2×C4⋊C4—131no—
112C2×C4⋊C4C2×D1312yes—
113C2×C4⋊C4C2×D1311yescharacteristic
114C2×C4⋊C4C2×D1312yes—
115C2×C4⋊C4C2×D1311yescharacteristic
116C2×C42—132no—
117C2×C42C2×D1311yescharacteristic
118#95—131no—
119#95—132no—
120#95—132no—
121#95—132no—
122#95—132no—
123#95—132no—
124#95—132no—
125#95—131no—
126C2×C13#53911yescharacteristic
127C2×C13#54412yes—
128C2×C13#55412yes—
129C2×C13Q8211yescharacteristic
130C2×C13#56011yescharacteristic
131C2×Q8—521no—
132C2×Q8—522no—
133C22×C4—132no—
134C22×C4—132no—
135C22×C4—132no—
136C22×C4—132no—
137C22×C4C22×D1311yescharacteristic
138C22×C4C22×D1312yes—
139C22×C4C22×D1311yescharacteristic
140C22×C4C22×D1311yescharacteristic
141C22×C4C22×D1312yes—
142C4⋊C4—42no—
143C4⋊C4—41no—
144C4⋊C4—42no—
145C4⋊C4—41no—
146C4⋊C4—138no—
147C4⋊C4—264no—
148C4⋊C4—522no—
149C4⋊C4—522no—
150C4⋊C4—522no—
151C4⋊C4—521no—
152C42—22no—
153C42—522no—
154C13#279211yescharacteristic, complemented, Sylow
155C23C23×D1311yescharacteristic
156Q8—524no—
157C2×C4—22no—
158C2×C4—22no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—22no—
162C2×C4—22no—
163C2×C4—21no—
164C2×C4—22no—
165C2×C4—22no—
166C2×C4—21no—
167C2×C4—22no—
168C2×C4—134no—
169C2×C4—134no—
170C2×C4—262no—
171C2×C4—262no—
172C2×C4—262no—
173C2×C4—262no—
174C2×C4—262no—
175C2×C4—262no—
176C2×C4—262no—
177C2×C4—262no—
178C2×C4—262no—
179C2×C4—262no—
180C2×C4#612712yes—
181C2×C4Q8×D1314yes—
182C22C2×#612711yescharacteristic
183C22#8825111yescharacteristic
184C22#8825112yes—
185C22C2×Q8×D1312yes—
186C22#8825411yescharacteristic
187C4—24no—
188C4—22no—
189C4—42no—
190C4—41no—
191C4—41no—
192C4—264no—
193C4—264no—
194C4—522no—
195C4—522no—
196C2#1171921612yes—
197C2#1171922011yescharacteristic
198C2#1171942511yescharacteristic
199C2#1171942711yescharacteristic
200C2#1171943412yes—
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, prime radical, cosocleC23×C13C24
FittingC13×#384C2
hypercenter#384D13
hypocenterC13#2792
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #384

Complements

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

NH ≅ G/Ntype
52. #6101Q8semidirect
154. C13#2792semidirect

Maximal subgroups

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

subgroupindex
C13×#3842
#117186452
#117186442
#117186402
#117186392
#117186332
#117185942
#279213