Finite Group Databasebeta

← #13113808

Subgroups — #13113808

Order 1664.

238 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 51 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
1#11719328C211yesmaximal, characteristic
2C13×#451C211yesmaximal, characteristic
3#11718890C211yesmaximal, characteristic
4#11718889C211yesmaximal, characteristic
5#11718130C211yesmaximal, characteristic
6#11718061C211yesmaximal, characteristic
7#11718059C211yesmaximal, characteristic
8C22×Q8×C13C2211yescharacteristic
9C2×C13×Q16—21no—
10C13×C22⋊Q8C2211yescharacteristic
11#88198—21no—
12C2×#6107—21no—
13#88178C2211yescharacteristic
14C2×#6101—21no—
15C2×#6101C2211yescharacteristic
16#88143—21no—
17#88143—21no—
18#88142—21no—
19#88132—21no—
20#88131—21no—
21C13×#103—21no—
22C13×C22⋊C8C2211yescharacteristic
23#88075—21no—
24#88071—21no—
25#88071C2211yescharacteristic
26C22⋊#1055C2211yescharacteristic
27C2×Q8×C13—21no—
28C2×Q8×C13—21no—
29C2×Q8×C13—42no—
30C2×Q8×C13D411yescharacteristic
31C22×C4×C13—21no—
32C22×C4×C13C2311yescharacteristic
33C22×Dic13—21no—
34C22×Dic13D411yescharacteristic
35C22×Dic13D411yescharacteristic
36C2×Dic26—21no—
37C2×Dic26D411yescharacteristic
38C13×Q16—42no—
39C2×C8×C13—21no—
40C13×C4⋊C4—21no—
41C13×C4⋊C4D411yescharacteristic
42C13×C22⋊C4—21no—
43C22⋊Dic13—21no—
44#6107—42no—
45C4⋊Dic13—21no—
46C4⋊Dic13D411yescharacteristic
47#6101—21no—
48#6101—21no—
49#6101—21no—
50#6101—21no—
51#6101—21no—
52#6101—21no—
53#6101—21no—
54#6101—42no—
55C4×Dic13—21no—
56C4×Dic13—21no—
57C2×#1055—21no—
58#1605—131nomaximal, Sylow
59C23×C13C2×D411yescharacteristic
60Q8×C13—22no—
61Q8×C13—22no—
62Q8×C13—41no—
63Q8×C13—41no—
64Q8×C13—41no—
65C2×C4×C13—22no—
66C2×C4×C13—21no—
67C2×C4×C13—21no—
68C2×C4×C13—41no—
69C2×C4×C13—41no—
70C2×C4×C13—41no—
71C2×C4×C13C2×D411yescharacteristic
72C2×C4×C13C2×D411yescharacteristic
73C2×Dic13—21no—
74C2×Dic13—21no—
75C2×Dic13—22no—
76C2×Dic13—21no—
77C2×Dic13—21no—
78C2×Dic13—21no—
79C2×Dic13—41no—
80C2×Dic13—41no—
81C2×Dic13—41no—
82C2×Dic13Q1612yescomplemented
83Dic26—41no—
84Dic26—81no—
85C8×C13—41no—
86#1055—41no—
87#544—131no—
88#451—131no—
89#451D1311yescharacteristic
90#395—131no—
91#328—131no—
92#328—131no—
93#324—131no—
94C22×C13—21no—
95C22×C13—21no—
96C22×C13#12011yescharacteristic
97C22×C13C2×Q1611yescharacteristic
98C22×C13#13711yescharacteristic
99C4×C13—21no—
100C4×C13—21no—
101C4×C13—41no—
102C4×C13—41no—
103C4×C13—42no—
104Dic13—22no—
105Dic13—42no—
106Dic13—41no—
107Dic13—41no—
108Dic13—41no—
109C22×Q8C2×D1311yescharacteristic
110C2×Q16—21no—
111C2×Q16—261no—
112C4⋊Q8—261no—
113C4⋊Q8—261no—
114#125—261no—
115#125—261no—
116C22⋊Q8—131no—
117C22⋊Q8—261no—
118C22⋊Q8C2×D1311yescharacteristic
119#117—261no—
120C2×C4⋊C4—131no—
121C2×C4⋊C4—261no—
122#103—21no—
123#103—261no—
124C22⋊C8—131no—
125C22⋊C8C2×D1311yescharacteristic
126#95—131no—
127#95—261no—
128C2×C13—21no—
129C2×C13—21no—
130C2×C13#45111yescharacteristic
131C2×C13#45611yescharacteristic
132C2×C13B(4,𝔽2)11yescharacteristic
133C2×Q8—21no—
134C2×Q8—21no—
135C2×Q8—42no—
136C2×Q8—131no—
137C2×Q8—261no—
138C2×Q8C22⋊D1311yescharacteristic
139C22×C4—21no—
140C22×C4—131no—
141C22×C4—131no—
142C22×C4—261no—
143C22×C4C22×D1311yescharacteristic
144Q16—42no—
145Q16—522no—
146C2×C8—21no—
147C2×C8—261no—
148C4⋊C4—21no—
149C4⋊C4—131no—
150C4⋊C4—261no—
151C4⋊C4—261no—
152C4⋊C4—261no—
153C4⋊C4—261no—
154C4⋊C4—261no—
155C4⋊C4—261no—
156C4⋊C4—261no—
157C4⋊C4—261no—
158C4⋊C4—522no—
159C4⋊C4C22⋊D1311yescharacteristic
160C22⋊C4—21no—
161C22⋊C4—261no—
162C42—261no—
163C42—261no—
164C13#160511yescharacteristic, complemented, Sylow
165C23D4×D1311yescharacteristic
166Q8—22no—
167Q8—22no—
168Q8—41no—
169Q8—41no—
170Q8—41no—
171Q8—521no—
172Q8—1041no—
173C2×C4—22no—
174C2×C4—21no—
175C2×C4—21no—
176C2×C4—41no—
177C2×C4—41no—
178C2×C4—41no—
179C2×C4—132no—
180C2×C4—261no—
181C2×C4—261no—
182C2×C4—262no—
183C2×C4—261no—
184C2×C4—261no—
185C2×C4—261no—
186C2×C4—521no—
187C2×C4—521no—
188C2×C4—521no—
189C2×C4D4×D1311yescharacteristic
190C2×C4C2×C22⋊D1311yescharacteristic
191C8—41no—
192C8—521no—
193C22—21no—
194C22—21no—
195C22Q16×D1311yescharacteristic
196C22#8817211yescharacteristic
197C22#8819111yescharacteristic
198C4—21no—
199C4—21no—
200C4—42no—
201C4—41no—
202C4—41no—
203C4—262no—
204C4—522no—
205C4—521no—
206C4—521no—
207C4—521no—
208C2—21no—
209C2—21no—
210C2#1171869311yescharacteristic
211C2#1171884711yescharacteristic
212C2#1171886611yescharacteristic
subgroupG/H
centerC22#88191
commutator, cosocleC22×C4×C13C23
FrattiniC22×C4C22×D13
FittingC13×#451C2
socleC22×C13#120
prime radicalC23×C13C2×D4
hypercenter#451D13
hypocenterC13#1605
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
82. C2×Dic13Q16semidirect
164. C13#1605semidirect

Maximal subgroups

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

subgroupindex
#117193282
C13×#4512
#117188902
#117188892
#117181302
#117180612
#117180592
#160513