Finite Group Databasebeta

← #13120538

Subgroups — #13120538

Order 1664.

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

normal subgroups only

This group has 388 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×#395C211yesmaximal, characteristic
2#11718891C212yesmaximal
3#11718647C211yesmaximal, characteristic
4#11718646C212yesmaximal
5#11718639C212yesmaximal
6#11718638C211yesmaximal, characteristic
7#11718322C212yesmaximal
8#11718314C212yesmaximal
9#11718309C212yesmaximal
10C22×Q8×C13C2211yescharacteristic
11C2×C13×C4⋊C4C2212yes—
12C2×C13×C4⋊C4C2211yescharacteristic
13C2×C4⋊Dic13C2212yes—
14C2×C4⋊Dic13C2211yescharacteristic
15C2×C4⋊Dic13C2212yes—
16C2×C4⋊Dic13C2211yescharacteristic
17C2×#6101C2212yes—
18C2×C4×Dic13C2212yes—
19C2×C4×Dic13C2212yes—
20C2×C4×Dic13C2211yescharacteristic
21C13×#95C2212yes—
22C13×#95C2211yescharacteristic
23#88071C2212yes—
24#88071C2212yes—
25#88071C2212yes—
26#88071C2212yes—
27#88071C2212yes—
28#88071C2212yes—
29#88071C2212yes—
30#88071C2211yescharacteristic
31C2×Q8×C13—24no—
32C2×Q8×C13—41no—
33C22×C4×C13C2311yescharacteristic
34C22×C4×C13C2311yescharacteristic
35C22×C4×C13C2311yescharacteristic
36C22×C4×C13C2312yes—
37C22×C4×C13C2312yes—
38C22×Dic13C2312yes—
39C22×Dic13C2312yes—
40C22×Dic13C2312yes—
41C22×Dic13C2312yes—
42C13×C4⋊C4—24no—
43C13×C4⋊C4—41no—
44C4⋊Dic13—24no—
45C4⋊Dic13—41no—
46C4⋊Dic13—42no—
47C4⋊Dic13—41no—
48#6101—24no—
49C4×Dic13—24no—
50C4×Dic13—24no—
51C4×Dic13Q814yescomplemented
52#2612—131nomaximal, Sylow
53C23×C13C2411yescharacteristic
54Q8×C13—44no—
55C2×C4×C13—22no—
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—21no—
64C2×C4×C13—21no—
65C2×C4×C13C2×Q812yes—
66C2×C4×C13#4114yes—
67C2×C4×C13#4114yes—
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×Dic13—22no—
77C2×Dic13—22no—
78C2×Dic13—22no—
79C2×Dic13C2×Q814yes—
80#400—131no—
81#398—132no—
82#395D1311yescharacteristic
83#391—132no—
84#389—132no—
85#387—132no—
86#387—132no—
87#382—131no—
88#376—132no—
89C22×C13C22×Q811yescharacteristic
90C22×C13C2×#4112yes—
91C22×C13C2×#4112yes—
92C22×C13H(5,𝔽2)11yescharacteristic
93C22×C132−1+411yescharacteristic
94C4×C13—22no—
95C4×C13—24no—
96C4×C13—24no—
97C4×C13—41no—
98C4×C13—41no—
99Dic13—24no—
100Dic13—42no—
101Dic13—42no—
102Dic13—42no—
103C22×Q8C2×D1311yescharacteristic
104C2×C4⋊C4—132no—
105C2×C4⋊C4—132no—
106C2×C4⋊C4—131no—
107C2×C4⋊C4—131no—
108C2×C4⋊C4—132no—
109C2×C4⋊C4C2×D1312yes—
110C2×C4⋊C4C2×D1311yescharacteristic
111C2×C42—131no—
112C2×C42—132no—
113C2×C42—132no—
114#95—132no—
115#95—132no—
116#95—132no—
117#95—132no—
118#95—132no—
119#95—131no—
120#95—132no—
121#95—132no—
122#95C2×D1312yes—
123#95C2×D1311yescharacteristic
124C2×C13#53312yes—
125C2×C13#54411yescharacteristic
126C2×C13#55111yescharacteristic
127C2×C13#55212yes—
128C2×C13#55511yescharacteristic
129C2×Q8—24no—
130C2×Q8—41no—
131C22×C4—132no—
132C22×C4—132no—
133C22×C4—132no—
134C22×C4—132no—
135C22×C4C22×D1311yescharacteristic
136C22×C4C22×D1311yescharacteristic
137C22×C4C22×D1312yes—
138C22×C4C22×D1311yescharacteristic
139C22×C4C22×D1312yes—
140C4⋊C4—24no—
141C4⋊C4—41no—
142C4⋊C4—264no—
143C4⋊C4—264no—
144C4⋊C4—521no—
145C4⋊C4—522no—
146C4⋊C4—521no—
147C42—134no—
148C42—264no—
149C42—264no—
150C13#261211yescharacteristic, complemented, Sylow
151C23C23×D1311yescharacteristic
152Q8—44no—
153C2×C4—22no—
154C2×C4—22no—
155C2×C4—21no—
156C2×C4—22no—
157C2×C4—21no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—21no—
162C2×C4—21no—
163C2×C4—134no—
164C2×C4—262no—
165C2×C4—262no—
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×C4#612914yes—
176C2×C4Q8×D1312yes—
177C2×C4#613114yes—
178C22C2×#612912yes—
179C22#8825111yescharacteristic
180C22C2×Q8×D1311yescharacteristic
181C22C2×#613112yes—
182C22#8825711yescharacteristic
183C4—24no—
184C4—22no—
185C4—24no—
186C4—41no—
187C4—41no—
188C4—264no—
189C4—522no—
190C4—522no—
191C4—522no—
192C2#1171929211yescharacteristic
193C2#1171932811yescharacteristic
194C2#1171934712yes—
195C2#1171943312yes—
196C2#1171943911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, prime radical, cosocleC23×C13C24
FittingC13×#395C2
hypercenter#395D13
hypocenterC13#2612
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
51. C4×Dic13Q8semidirect
150. C13#2612semidirect

Maximal subgroups

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

subgroupindex
C13×#3952
#117188912
#117186472
#117186462
#117186392
#117186382
#117183222
#117183142
#117183092
#261213