Finite Group Databasebeta

← #13119826

Subgroups — #13119826

Order 1664.

540 conjugacy classes of subgroups; only the 177 normal subgroups are shown.

normal subgroups only

This group has 540 conjugacy classes of subgroups — too many to draw. Only its 177 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
1C2×#88198C211yesmaximal, characteristic
2C2×#88198C211yesmaximal, characteristic
3C2×#88141C211yesmaximal, characteristic
4C2×#88123C211yesmaximal, characteristic
5C13×#391C211yesmaximal, characteristic
6#11718635C211yesmaximal, characteristic
7C4×#6101C211yesmaximal, characteristic
8#11718318C214yesmaximal
9#11718308C214yesmaximal
10C22×Q8×C13C2211yescharacteristic
11C22×Dic26C2211yescharacteristic
12C22×Dic26C2211yescharacteristic
13C2×C13×C4⋊C4C2211yescharacteristic
14C2×C42×C13C2211yescharacteristic
15#88198—24no—
16#88198—24no—
17C2×C4⋊Dic13C2214yes—
18C2×#6101C2212yes—
19C2×#6101C2212yes—
20C2×#6101C2214yes—
21C2×#6101C2212yes—
22C2×#6101C2212yes—
23C2×C4×Dic13C2212yes—
24C2×C4×Dic13C2211yescharacteristic
25C2×C4×Dic13C2211yescharacteristic
26#88141—24no—
27#88123—24no—
28C13×#95C2214yes—
29#88071C2214yes—
30#88071C2212yes—
31C2×Q8×C13—22no—
32C2×Q8×C13—22no—
33C2×Q8×C13—22no—
34C22×C4×C13C2312yes—
35C22×C4×C13C2312yes—
36C22×C4×C13C2312yes—
37C22×C4×C13C2311yescharacteristic
38C22×Dic13C2312yes—
39C22×Dic13C2311yescharacteristic
40C22×Dic13C2312yes—
41C22×Dic13C2312yes—
42C22×Dic13C2311yescharacteristic
43C2×Dic26—22no—
44C2×Dic26—22no—
45C2×Dic26—22no—
46C2×Dic26—22no—
47C2×Dic26—22no—
48C2×Dic26D414yes—
49C13×C4⋊C4—22no—
50C42×C13—22no—
51C4⋊Dic13—28no—
52#6101—24no—
53#6101—28no—
54#6101—24no—
55#6101—24no—
56#6101Q818yescomplemented
57C4×Dic13—22no—
58C4×Dic13—24no—
59C4×Dic13D414yes—
60#2546—131nomaximal, Sylow
61C23×C13C2411yescharacteristic
62Q8×C13—44no—
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×C13—24no—
70C2×C4×C13C2×D412yes—
71C2×C4×C13C2×D412yes—
72C2×C4×C13C2×Q814yes—
73C2×C4×C13#4112yes—
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×Dic13C2×D412yes—
83C2×Dic13C2×D414yes—
84C2×Dic13C2×D412yes—
85C2×Dic13C2×Q814yes—
86C2×Dic13C2×Q814yes—
87Dic26—28no—
88Dic26—44no—
89C2×C4⋊Q8—131no—
90C2×C4⋊Q8—131no—
91C2×C4⋊Q8—131no—
92C2×C4×Q8—131no—
93#398—134no—
94#391—131no—
95#391D1311yescharacteristic
96#389—134no—
97C4×C4⋊C4—131no—
98C22×C13C22×D411yescharacteristic
99C22×C13C22×D411yescharacteristic
100C22×C13C22×Q812yes—
101C22×C13C2×#4111yescharacteristic
102C22×C132−1+412yes—
103C4×C13—24no—
104C4×C13—42no—
105C4×C13—42no—
106C4×C13#12114yes—
107Dic13—24no—
108Dic13—22no—
109Dic13—24no—
110Dic13—42no—
111Dic13C4⋊Q814yescomplemented
112C22×Q8—131no—
113C22×Q8—131no—
114C22×Q8C2×D1311yescharacteristic
115C4⋊Q8—264no—
116C4⋊Q8—264no—
117C4⋊Q8—264no—
118C4×Q8—264no—
119C2×C4⋊C4—132no—
120C2×C4⋊C4—132no—
121C2×C4⋊C4—132no—
122C2×C4⋊C4—134no—
123C2×C4⋊C4—132no—
124C2×C4⋊C4—134no—
125C2×C4⋊C4C2×D1311yescharacteristic
126C2×C42—131no—
127C2×C42—132no—
128C2×C42—131no—
129C2×C42C2×D1311yescharacteristic
130#95—132no—
131#95—134no—
132#95C2×D1314yes—
133C2×C13C2×#12111yescharacteristic
134C2×C13C2×C4⋊Q811yescharacteristic
135C2×C13#53611yescharacteristic
136C2×C13D4×Q812yes—
137C2×C13#55712yes—
138C2×Q8—22no—
139C2×Q8—22no—
140C2×Q8—22no—
141C2×Q8—134no—
142C2×Q8—262no—
143C2×Q8—262no—
144C2×Q8—262no—
145C2×Q8—262no—
146C2×Q8—262no—
147C22×C4—131no—
148C22×C4—132no—
149C22×C4—131no—
150C22×C4—132no—
151C22×C4—132no—
152C22×C4C22×D1312yes—
153C22×C4C22×D1312yes—
154C22×C4C22×D1312yes—
155C22×C4C22×D1311yescharacteristic
156C4⋊C4—22no—
157C4⋊C4—138no—
158C4⋊C4—264no—
159C4⋊C4—264no—
160C4⋊C4—264no—
161C4⋊C4—268no—
162C4⋊C4—268no—
163C42—22no—
164C42—134no—
165C42—264no—
166C42—262no—
167C13#254611yescharacteristic, complemented, Sylow
168C23C23×D1311yescharacteristic
169Q8—44no—
170Q8—268no—
171Q8—524no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—24no—
179C2×C4—132no—
180C2×C4—134no—
181C2×C4—132no—
182C2×C4—134no—
183C2×C4—134no—
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#612712yes—
193C2×C4D4×D1312yes—
194C2×C4D4×D1312yes—
195C2×C4Q8×D1314yes—
196C22C2×#612711yescharacteristic
197C22C2×D4×D1311yescharacteristic
198C22C2×D4×D1311yescharacteristic
199C22C2×Q8×D1312yes—
200C22#8825712yes—
201C4—24no—
202C4—42no—
203C4—42no—
204C4—134no—
205C4—264no—
206C4—264no—
207C4—262no—
208C4—522no—
209C4#8813814yes—
210C2C2×#8813811yescharacteristic
211C2#1171927212yes—
212C2#1171933712yes—
213C2#1171938011yescharacteristic
214C2D13×C4⋊Q811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, prime radical, cosocleC23×C13C24
FittingC13×#391C2
hypercenter#391D13
hypocenterC13#2546
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
56. #6101Q8semidirect
111. Dic13C4⋊Q8semidirect
167. C13#2546semidirect

Maximal subgroups

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

subgroupindex
C2×#881982
C2×#881412
C2×#881232
C13×#3912
#117186352
C4×#61012
#117183182
#117183082
#254613