Finite Group Databasebeta

← #13120049

Subgroups — #13120049

Order 1664.

468 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 157 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×#88142C211yesmaximal, characteristic
2C2×#88141C211yesmaximal, characteristic
3C13×#382C211yesmaximal, characteristic
4#11718638C211yesmaximal, characteristic
5#11718635C211yesmaximal, characteristic
6C4×#6101C211yesmaximal, characteristic
7#11718590C211yesmaximal, characteristic
8#11718319C214yesmaximal
9#11718307C214yesmaximal
10C22×Dic26C2212yes—
11C22×Dic26C2211yescharacteristic
12C2×C13×C4⋊C4C2211yescharacteristic
13C2×C13×C4⋊C4C2211yescharacteristic
14C2×C42×C13C2211yescharacteristic
15C2×C4⋊Dic13C2211yescharacteristic
16C2×#6101C2212yes—
17C2×#6101C2212yes—
18C2×#6101C2212yes—
19C2×C4×Dic13C2212yes—
20C2×C4×Dic13C2211yescharacteristic
21C2×C4×Dic13C2211yescharacteristic
22#88142—24no—
23#88141—24no—
24C13×#95C2214yes—
25#88071C2214yes—
26#88071C2214yes—
27#88071C2214yes—
28#88071C2212yes—
29C22×C4×C13C2312yes—
30C22×C4×C13C2312yes—
31C22×C4×C13C2312yes—
32C22×C4×C13C2311yescharacteristic
33C22×Dic13C2312yes—
34C22×Dic13C2312yes—
35C22×Dic13C2311yescharacteristic
36C22×Dic13C2312yes—
37C22×Dic13C2311yescharacteristic
38C2×Dic26—22no—
39C2×Dic26—22no—
40C2×Dic26—24no—
41C2×Dic26—28no—
42C2×Dic26Q814yescomplemented
43C13×C4⋊C4—22no—
44C13×C4⋊C4—22no—
45C42×C13—22no—
46C4⋊Dic13—22no—
47#6101—24no—
48#6101—24no—
49#6101—24no—
50C4×Dic13—22no—
51C4×Dic13—24no—
52C4×Dic13D414yes—
53#2568—131nomaximal, Sylow
54C23×C13C2411yescharacteristic
55C2×C4×C13—22no—
56C2×C4×C13—22no—
57C2×C4×C13—22no—
58C2×C4×C13—22no—
59C2×C4×C13—24no—
60C2×C4×C13—24no—
61C2×C4×C13—22no—
62C2×C4×C13C2×D412yes—
63C2×C4×C13C2×Q812yes—
64C2×C4×C13#4112yes—
65C2×Dic13—22no—
66C2×Dic13—22no—
67C2×Dic13—22no—
68C2×Dic13—22no—
69C2×Dic13—22no—
70C2×Dic13—22no—
71C2×Dic13—24no—
72C2×Dic13—22no—
73C2×Dic13C2×D412yes—
74C2×Dic13C2×D412yes—
75C2×Dic13C2×Q814yes—
76C2×Dic13#4114yes—
77Dic26—28no—
78Dic26—48no—
79C2×C4⋊Q8—131no—
80C2×C4×Q8—131no—
81#400—134no—
82#391—131no—
83#391—131no—
84#391—134no—
85#382—131no—
86#382D1311yescharacteristic
87C4×C4⋊C4—131no—
88C22×C13C22×D411yescharacteristic
89C22×C13C22×Q811yescharacteristic
90C22×C13C2×#4111yescharacteristic
91C22×C13C2×#4112yes—
92C22×C132−1+412yes—
93C4×C13—42no—
94C4×C13—42no—
95C4×C13—42no—
96C4×C13C22⋊Q814yes—
97Dic13—24no—
98Dic13—22no—
99Dic13—42no—
100Dic13—42no—
101Dic13#12414yes—
102C22×Q8—131no—
103C22×Q8—132no—
104C4⋊Q8—264no—
105C4×Q8—264no—
106C2×C4⋊C4—132no—
107C2×C4⋊C4—132no—
108C2×C4⋊C4—131no—
109C2×C4⋊C4—132no—
110C2×C4⋊C4C2×D1311yescharacteristic
111C2×C4⋊C4C2×D1311yescharacteristic
112C2×C42—131no—
113C2×C42—132no—
114C2×C42—131no—
115C2×C42C2×D1311yescharacteristic
116#95—132no—
117#95—134no—
118#95—134no—
119#95—134no—
120#95C2×D1314yes—
121C2×C13C2×C22⋊Q811yescharacteristic
122C2×C13C2×#12411yescharacteristic
123C2×C13#53611yescharacteristic
124C2×C13#55612yes—
125C2×C13#55712yes—
126C2×Q8—134no—
127C2×Q8—264no—
128C2×Q8—268no—
129C2×Q8—262no—
130C2×Q8—262no—
131C22×C4—131no—
132C22×C4—132no—
133C22×C4—131no—
134C22×C4—132no—
135C22×C4—132no—
136C22×C4C22×D1312yes—
137C22×C4C22×D1312yes—
138C22×C4C22×D1312yes—
139C22×C4C22×D1311yescharacteristic
140C4⋊C4—22no—
141C4⋊C4—22no—
142C4⋊C4—264no—
143C4⋊C4—264no—
144C4⋊C4—264no—
145C4⋊C4—262no—
146C42—22no—
147C42—134no—
148C42—264no—
149C42—262no—
150C13#256811yescharacteristic, complemented, Sylow
151C23C23×D1311yescharacteristic
152Q8—268no—
153Q8—528no—
154C2×C4—22no—
155C2×C4—22no—
156C2×C4—22no—
157C2×C4—22no—
158C2×C4—24no—
159C2×C4—22no—
160C2×C4—24no—
161C2×C4—132no—
162C2×C4—134no—
163C2×C4—132no—
164C2×C4—134no—
165C2×C4—262no—
166C2×C4—262no—
167C2×C4—262no—
168C2×C4—262no—
169C2×C4—262no—
170C2×C4—262no—
171C2×C4—264no—
172C2×C4—262no—
173C2×C4#612712yes—
174C2×C4D4×D1312yes—
175C2×C4Q8×D1312yes—
176C22C2×#612711yescharacteristic
177C22C2×D4×D1311yescharacteristic
178C22C2×Q8×D1311yescharacteristic
179C22#41×D1312yes—
180C22#8825712yes—
181C4—42no—
182C4—42no—
183C4—42no—
184C4—134no—
185C4—264no—
186C4—262no—
187C4—522no—
188C4—522no—
189C4#8815014yes—
190C2C2×#8815011yescharacteristic
191C2#1171923812yes—
192C2D13×#12411yescharacteristic
193C2#1171938011yescharacteristic
194C2#1171939012yes—
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, prime radical, cosocleC23×C13C24
FittingC13×#382C2
hypercenter#382D13
hypocenterC13#2568
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #382

Complements

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

NH ≅ G/Ntype
42. C2×Dic26Q8semidirect
150. C13#2568semidirect

Maximal subgroups

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

subgroupindex
C2×#881422
C2×#881412
C13×#3822
#117186382
#117186352
C4×#61012
#117185902
#117183192
#117183072
#256813