Finite Group Databasebeta

← #13122598

Subgroups — #13122598

Order 1664.

352 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 352 conjugacy classes of subgroups — too many to draw. Only its 125 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#11718647C212yesmaximal
4#11718644C211yesmaximal, characteristic
5#11718642C212yesmaximal
6#11718638C211yesmaximal, characteristic
7C13⋊#401C212yesmaximal
8#11718316C212yesmaximal
9#11718314C212yesmaximal
10C22×Q8×C13C2211yescharacteristic
11C2×C13×C4⋊C4C2212yes—
12C2×C13×C4⋊C4C2211yescharacteristic
13C2×C4⋊Dic13C2212yes—
14C2×C4⋊Dic13C2211yescharacteristic
15C2×C4⋊Dic13C2211yescharacteristic
16C2×#6101C2212yes—
17C2×C4×Dic13C2211yescharacteristic
18C2×C4×Dic13C2212yes—
19C13×#95C2212yes—
20C13×#95C2211yescharacteristic
21#88071C2212yes—
22#88071C2212yes—
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×C13C2312yes—
34C22×C4×C13C2311yescharacteristic
35C22×C4×C13C2311yescharacteristic
36C22×C4×C13C2312yes—
37C22×C4×C13C2311yescharacteristic
38C22×Dic13C2312yes—
39C22×Dic13C2312yes—
40C22×Dic13C2312yes—
41C22×Dic13C2312yes—
42C13×C4⋊C4—24no—
43C13×C4⋊C4—41no—
44C4⋊Dic13—24no—
45C4⋊Dic13—41no—
46C4⋊Dic13—41no—
47#6101—24no—
48C4×Dic13—22no—
49C4×Dic13—42no—
50#2789—131nomaximal, Sylow
51C23×C13C2411yescharacteristic
52Q8×C13—44no—
53C2×C4×C13—22no—
54C2×C4×C13—22no—
55C2×C4×C13—21no—
56C2×C4×C13—21no—
57C2×C4×C13—22no—
58C2×C4×C13—22no—
59C2×C4×C13—22no—
60C2×C4×C13—21no—
61C2×C4×C13—21no—
62C2×C4×C13—22no—
63C2×C4×C13—22no—
64C2×C4×C13#4114yes—
65C2×C4×C13#4112yes—
66C2×Dic13—22no—
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×Dic13—24no—
77#401—132no—
78#400—132no—
79#398—131no—
80#395D1311yescharacteristic
81#391—132no—
82#387—132no—
83#387—132no—
84#387—132no—
85#382—131no—
86C22×C13C2×#4112yes—
87C22×C13C2×#4111yescharacteristic
88C22×C13H(5,𝔽2)11yescharacteristic
89C22×C132−1+412yes—
90C22×C132−1+411yescharacteristic
91C4×C13—22no—
92C4×C13—24no—
93C4×C13—42no—
94C4×C13—41no—
95C4×C13—41no—
96Dic13—42no—
97Dic13—42no—
98Dic13—42no—
99Dic13—42no—
100C22×Q8C2×D1311yescharacteristic
101C2×C4⋊C4—132no—
102C2×C4⋊C4—132no—
103C2×C4⋊C4—131no—
104C2×C4⋊C4—131no—
105C2×C4⋊C4C2×D1312yes—
106C2×C4⋊C4C2×D1311yescharacteristic
107C2×C42—131no—
108C2×C42—132no—
109#95—132no—
110#95—132no—
111#95—132no—
112#95—132no—
113#95—132no—
114#95—132no—
115#95—132no—
116#95—132no—
117#95—132no—
118#95—131no—
119#95C2×D1312yes—
120#95C2×D1311yescharacteristic
121C2×C13#53911yescharacteristic
122C2×C13#54112yes—
123C2×C13#55111yescharacteristic
124C2×C13#55612yes—
125C2×C13#56311yescharacteristic
126C2×Q8—24no—
127C2×Q8—41no—
128C22×C4—132no—
129C22×C4—132no—
130C22×C4—132no—
131C22×C4—132no—
132C22×C4C22×D1312yes—
133C22×C4C22×D1311yescharacteristic
134C22×C4C22×D1311yescharacteristic
135C22×C4C22×D1312yes—
136C22×C4C22×D1311yescharacteristic
137C4⋊C4—24no—
138C4⋊C4—41no—
139C4⋊C4—264no—
140C4⋊C4—264no—
141C4⋊C4—521no—
142C4⋊C4—521no—
143C42—262no—
144C42—522no—
145C13#278911yescharacteristic, complemented, Sylow
146C23C23×D1311yescharacteristic
147Q8—44no—
148C2×C4—22no—
149C2×C4—22no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—22no—
153C2×C4—22no—
154C2×C4—22no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—22no—
158C2×C4—22no—
159C2×C4—262no—
160C2×C4—262no—
161C2×C4—262no—
162C2×C4—262no—
163C2×C4—262no—
164C2×C4—262no—
165C2×C4—262no—
166C2×C4—262no—
167C2×C4—262no—
168C2×C4—264no—
169C2×C4—262no—
170C2×C4#612914yes—
171C2×C4#613112yes—
172C22C2×#612912yes—
173C22#8825111yescharacteristic
174C22C2×#613111yescharacteristic
175C22#8825412yes—
176C22#8825711yescharacteristic
177C4—24no—
178C4—22no—
179C4—41no—
180C4—41no—
181C4—42no—
182C4—522no—
183C4—522no—
184C4—522no—
185C4—522no—
186C2#1171929211yescharacteristic
187C2#1171933012yes—
188C2#1171935011yescharacteristic
189C2#1171943712yes—
190C2#1171944011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, prime radical, cosocleC23×C13C24
FittingC13×#395C2
hypercenter#395D13
hypocenterC13#2789
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
145. C13#2789semidirect

Maximal subgroups

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

subgroupindex
C13×#3952
#117188912
#117186472
#117186442
#117186422
#117186382
C13⋊#4012
#117183162
#117183142
#278913