Finite Group Databasebeta

← #13120217

Subgroups — #13120217

Order 1664.

544 conjugacy classes of subgroups; only the 169 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 169 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×C13×C22⋊Q8C211yesmaximal, characteristic
2C22×#6101C211yesmaximal, characteristic
3#11718890C212yesmaximal, complemented
4C4×C22⋊Dic13C211yesmaximal, characteristic
5#11718641C212yesmaximal, complemented
6#11718633C214yesmaximal, complemented
7#11718607C212yesmaximal
8#11718607C212yesmaximal
9C22×Q8×C13C2211yescharacteristic
10C23×C4×C13C2211yescharacteristic
11C23×Dic13C2211yescharacteristic
12C23×Dic13C2211yescharacteristic
13C13×C22⋊Q8—24no—
14C2×C13×C4⋊C4C2212yes—
15C2×C13×C4⋊C4C2211yescharacteristic
16C2×C13×C22⋊C4C2212yes—
17C2×C22⋊Dic13C2212yes—
18C2×#6101—24no—
19C2×#6101C2212yes—
20C2×#6101C2212yes—
21C2×#6101C2214yes—
22C2×#6101C2214yes—
23C2×C4×Dic13C2212yes—
24#88071C2214yes—
25#88071C2214yes—
26#88071C2212yes—
27C24×C13C2311yescharacteristic
28C2×Q8×C13—22no—
29C2×Q8×C13—42no—
30C22×C4×C13—42no—
31C22×C4×C13D414yes—
32C22×C4×C13C2312yes—
33C22×C4×C13C2312yes—
34C22×C4×C13C2311yescharacteristic
35C22×C4×C13C2311yescharacteristic
36C22×Dic13—22no—
37C22×Dic13—24no—
38C22×Dic13—22no—
39C22×Dic13—42no—
40C22×Dic13C2312yes—
41C22×Dic13C2314yes—
42C22×Dic13C2312yes—
43C13×C4⋊C4—22no—
44C13×C4⋊C4—24no—
45C13×C22⋊C4—24no—
46C22⋊Dic13Q818yescomplemented
47#6101—24no—
48#6101—24no—
49#6101—28no—
50#6101—44no—
51C4×Dic13—42no—
52#2583—131nomaximal, Sylow
53C23×C13—22no—
54C23×C13—22no—
55C23×C13C2×D412yes—
56C23×C13C2×Q814yes—
57C23×C13C2411yescharacteristic
58Q8×C13—44no—
59C2×C4×C13—22no—
60C2×C4×C13—22no—
61C2×C4×C13—22no—
62C2×C4×C13—22no—
63C2×C4×C13—24no—
64C2×C4×C13—24no—
65C2×C4×C13—44no—
66C2×C4×C13C2×D412yes—
67C2×C4×C13C2×D412yes—
68C2×Dic13—28no—
69C2×Dic13—22no—
70C2×Dic13—24no—
71C2×Dic13—22no—
72C2×Dic13—24no—
73C2×Dic13—22no—
74C2×Dic13—24no—
75C2×Dic13—44no—
76C2×Dic13C2×Q818yes—
77C2×Dic13#4114yes—
78C2×C22⋊Q8D1311yescharacteristic
79C22×C4⋊C4—131no—
80#398—132no—
81#395—132no—
82#389—134no—
83#385—132no—
84#385—132no—
85C4×C22⋊C4—131no—
86C22×C13—22no—
87C22×C13—22no—
88C22×C13—28no—
89C22×C13C4⋊Q814yes—
90C22×C13C22×D411yescharacteristic
91C22×C13C22×Q812yes—
92C22×C13C2×#4112yes—
93C22×C13H(5,𝔽2)12yes—
94C4×C13—22no—
95C4×C13—22no—
96C4×C13—42no—
97C4×C13—42no—
98Dic13—24no—
99Dic13—28no—
100Dic13—42no—
101C22×Q8C2×D1311yescharacteristic
102C23×C4—131no—
103C23×C4—131no—
104C23×C4C2×D1311yescharacteristic
105C22⋊Q8—24no—
106C2×C4⋊C4—132no—
107C2×C4⋊C4—132no—
108C2×C4⋊C4—134no—
109C2×C4⋊C4—134no—
110C2×C4⋊C4—264no—
111C2×C4⋊C4C2×D1312yes—
112C2×C4⋊C4C2×D1311yescharacteristic
113C2×C22⋊C4—132no—
114C2×C22⋊C4C2×D1312yes—
115C2×C42—132no—
116#95—132no—
117#95—134no—
118#95—134no—
119C2×C13—24no—
120C2×C13#52511yescharacteristic
121C2×C13C2×C4⋊Q811yescharacteristic
122C2×C13#53411yescharacteristic
123C2×C13#55414yes—
124C24C22×D1311yescharacteristic
125C2×Q8—22no—
126C2×Q8—42no—
127C22×C4—42no—
128C22×C4—134no—
129C22×C4—132no—
130C22×C4—132no—
131C22×C4—264no—
132C22×C4—262no—
133C22×C4—262no—
134C22×C4—522no—
135C22×C4C22⋊D1314yes—
136C22×C4C22×D1312yes—
137C22×C4C22×D1312yes—
138C22×C4C22×D1311yescharacteristic
139C22×C4C22×D1311yescharacteristic
140C4⋊C4—22no—
141C4⋊C4—24no—
142C4⋊C4—268no—
143C4⋊C4—264no—
144C4⋊C4—264no—
145C4⋊C4—524no—
146C22⋊C4—24no—
147C22⋊C4—138no—
148C42—522no—
149C13#258311yescharacteristic, complemented, Sylow
150C23—22no—
151C23—22no—
152C23Q8×D1314yes—
153C23C2×C22⋊D1312yes—
154C23C23×D1311yescharacteristic
155Q8—44no—
156C2×C4—22no—
157C2×C4—22no—
158C2×C4—24no—
159C2×C4—24no—
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—44no—
163C2×C4—138no—
164C2×C4—134no—
165C2×C4—268no—
166C2×C4—264no—
167C2×C4—264no—
168C2×C4—262no—
169C2×C4—262no—
170C2×C4—264no—
171C2×C4—262no—
172C2×C4—524no—
173C2×C4C2×C22⋊D1312yes—
174C2×C4C2×C22⋊D1312yes—
175C22—22no—
176C22—22no—
177C22—28no—
178C22#8819814yes—
179C22#8825112yes—
180C22C2×Q8×D1312yes—
181C22#41×D1312yes—
182C22C22×C22⋊D1311yescharacteristic
183C4—22no—
184C4—22no—
185C4—42no—
186C4—42no—
187C4—264no—
188C4—268no—
189C4—522no—
190C2—24no—
191C2#1171934114yes—
192C2#1171950911yescharacteristic
193C2C2×#8819811yescharacteristic
194C2#1171953311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC2×C13×C22⋊Q8C2
prime radicalC24×C13C23
hypercenterC2×C22⋊Q8D13
hypocenterC13#2583
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
3. #11718890C2semidirect
5. #11718641C2semidirect
6. #11718633C2semidirect
46. C22⋊Dic13Q8semidirect
149. C13#2583semidirect

Maximal subgroups

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

subgroupindex
C2×C13×C22⋊Q82
C22×#61012
#117188902
C4×C22⋊Dic132
#117186412
#117186332
#117186072
#258313