Finite Group Databasebeta

← #13120074

Subgroups — #13120074

Order 1664.

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

normal subgroups only

This group has 380 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×#400C211yesmaximal, characteristic
2#11718647C211yesmaximal, characteristic
3#11718637C211yesmaximal, characteristic
4#11718633C212yesmaximal
5#11718321C212yesmaximal
6#11718311C212yesmaximal
7#11718311C212yesmaximal
8#11718310C212yesmaximal
9#11718308C212yesmaximal
10C2×C13×C4⋊C4C2211yescharacteristic
11C2×C13×C4⋊C4C2211yescharacteristic
12C2×C4⋊Dic13C2211yescharacteristic
13C2×C4⋊Dic13C2211yescharacteristic
14C2×#6101C2212yes—
15C2×#6101C2212yes—
16C2×#6101C2212yes—
17C2×#6101C2212yes—
18C2×#6101C2212yes—
19C2×C4×Dic13C2212yes—
20C2×C4×Dic13C2212yes—
21C2×C4×Dic13C2211yescharacteristic
22C13×#95C2212yes—
23C13×#95C2212yes—
24C13×#95C2211yescharacteristic
25#88071C2212yes—
26#88071C2212yes—
27#88071C2212yes—
28#88071C2211yescharacteristic
29#88071C2212yes—
30#88071C2212yes—
31C22×C4×C13C2312yes—
32C22×C4×C13C2311yescharacteristic
33C22×C4×C13C2312yes—
34C22×C4×C13C2311yescharacteristic
35C22×C4×C13C2311yescharacteristic
36C22×Dic13C2312yes—
37C22×Dic13C2312yes—
38C22×Dic13C2312yes—
39C22×Dic13C2312yes—
40C13×C4⋊C4—41no—
41C13×C4⋊C4—41no—
42C4⋊Dic13—41no—
43C4⋊Dic13—41no—
44#6101—24no—
45#6101—24no—
46#6101—24no—
47#6101—24no—
48#6101—42no—
49C4×Dic13—24no—
50C4×Dic13—24no—
51C4×Dic13Q814yes—
52#2571—131nomaximal, Sylow
53C23×C13C2411yescharacteristic
54C2×C4×C13—21no—
55C2×C4×C13—21no—
56C2×C4×C13—22no—
57C2×C4×C13—22no—
58C2×C4×C13—22no—
59C2×C4×C13—22no—
60C2×C4×C13—22no—
61C2×C4×C13—22no—
62C2×C4×C13—22no—
63C2×C4×C13—21no—
64C2×C4×C13—21no—
65C2×C4×C13—22no—
66C2×C4×C13C2×Q812yes—
67C2×Dic13—22no—
68C2×Dic13—22no—
69C2×Dic13—22no—
70C2×Dic13—22no—
71C2×Dic13—22no—
72C2×Dic13—22no—
73C2×Dic13—22no—
74C2×Dic13—22no—
75C2×Dic13—22no—
76C2×Dic13C2×Q814yes—
77C2×Dic13#4114yes—
78C2×Dic13#4114yes—
79#400—131no—
80#400—132no—
81#400D1311yescharacteristic
82#389—132no—
83#389—132no—
84#384—131no—
85#382—132no—
86#382—132no—
87C4×C4⋊C4—132no—
88C22×C13C22×Q811yescharacteristic
89C22×C13C2×#4112yes—
90C22×C13C2×#4112yes—
91C22×C13H(5,𝔽2)11yescharacteristic
92C22×C132−1+411yescharacteristic
93C4×C13—22no—
94C4×C13—42no—
95C4×C13—42no—
96C4×C13—41no—
97C4×C13—41no—
98Dic13—42no—
99Dic13—42no—
100Dic13—42no—
101Dic13#12518yes—
102C2×C4⋊C4—132no—
103C2×C4⋊C4—132no—
104C2×C4⋊C4—132no—
105C2×C4⋊C4—132no—
106C2×C4⋊C4—132no—
107C2×C4⋊C4—131no—
108C2×C4⋊C4—131no—
109C2×C4⋊C4C2×D1311yescharacteristic
110C2×C4⋊C4C2×D1311yescharacteristic
111C2×C42—131no—
112C2×C42—132no—
113C2×C42—132no—
114#95—132no—
115#95—131no—
116#95—132no—
117#95—132no—
118#95—132no—
119#95—132no—
120#95C2×D1312yes—
121#95C2×D1311yescharacteristic
122#95C2×D1312yes—
123C2×C13C2×#12512yes—
124C2×C13#54411yescharacteristic
125C2×C13#55511yescharacteristic
126C2×C13#55612yes—
127C2×C13#55911yescharacteristic
128C22×C4—132no—
129C22×C4—132no—
130C22×C4—132no—
131C22×C4—132no—
132C22×C4C22×D1312yes—
133C22×C4C22×D1311yescharacteristic
134C22×C4C22×D1312yes—
135C22×C4C22×D1311yescharacteristic
136C22×C4C22×D1311yescharacteristic
137C4⋊C4—41no—
138C4⋊C4—41no—
139C4⋊C4—264no—
140C4⋊C4—264no—
141C4⋊C4—264no—
142C4⋊C4—264no—
143C4⋊C4—522no—
144C4⋊C4—521no—
145C4⋊C4—521no—
146C42—134no—
147C42—264no—
148C42—264no—
149C13#257111yescharacteristic, complemented, Sylow
150C23C23×D1311yescharacteristic
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—22no—
156C2×C4—22no—
157C2×C4—22no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—22no—
163C2×C4—134no—
164C2×C4—134no—
165C2×C4—134no—
166C2×C4—262no—
167C2×C4—262no—
168C2×C4—262no—
169C2×C4—262no—
170C2×C4—262no—
171C2×C4—262no—
172C2×C4—262no—
173C2×C4—262no—
174C2×C4—262no—
175C2×C4Q8×D1312yes—
176C22#8825111yescharacteristic
177C22C2×Q8×D1311yescharacteristic
178C22#41×D1312yes—
179C22#41×D1312yes—
180C22#8825711yescharacteristic
181C4—22no—
182C4—41no—
183C4—41no—
184C4—42no—
185C4—42no—
186C4—138no—
187C4—522no—
188C4—522no—
189C4—522no—
190C2#1171932811yescharacteristic
191C2#1171936911yescharacteristic
192C2#1171937511yescharacteristic
193C2D13×#12512yes—
194C2#1171940712yes—
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, prime radical, cosocleC23×C13C24
FittingC13×#400C2
hypercenter#400D13
hypocenterC13#2571
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
149. C13#2571semidirect

Maximal subgroups

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

subgroupindex
C13×#4002
#117186472
#117186372
#117186332
#117183212
#117183112
#117183102
#117183082
#257113