Finite Group Databasebeta

← #13130961

Subgroups — #13130961

Order 1664.

384 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 92 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×#88135C211yesmaximal, characteristic
2C2×C22⋊#1057C212yesmaximal, complemented
3C2×#88111C212yesmaximal, complemented
4C2×#88110C211yesmaximal, characteristic, complemented
5C2×C4⋊#1057C211yesmaximal, characteristic, complemented
6C22×C22⋊D13C411yescharacteristic
7C23×Dic13C2211yescharacteristic
8C22×C4×D13C2211yescharacteristic
9C22×#1057C2212yes—
10C22×#1057C2212yes—
11C2×C13×C22⋊C4C411yescharacteristic
12C2×#6103C411yescharacteristic
13C2×#6101C411yescharacteristic
14C2×C4×Dic13C2211yescharacteristic
15#88135—22no—
16#88135—22no—
17C22⋊#1057—24no—
18#88111—24no—
19#88110—22no—
20C4⋊#1057—22no—
21C24×C13C2×C411yescharacteristic
22C23×D13C2×C411yescharacteristic
23C22×C4×C13C2×C411yescharacteristic
24C22×C4×C13C2×C411yescharacteristic
25C2×C22⋊D13—22no—
26C2×C22⋊D13—22no—
27C2×C22⋊D13—22no—
28C22×Dic13—22no—
29C22×Dic13—21no—
30C22×Dic13—21no—
31C22×Dic13—22no—
32C22×Dic13C2×C411yescharacteristic
33C22×Dic13C2×C411yescharacteristic
34C22×Dic13C2311yescharacteristic
35C2×C4×D13—22no—
36C2×C4×D13—21no—
37C2×C4×D13—21no—
38C2×C4×D13—22no—
39C2×#1057—22no—
40C2×#1057—22no—
41C2×#1057—22no—
42C2×#1057—22no—
43C2×#1057—22no—
44C2×#1057D414yescomplemented
45C13×C22⋊C4—22no—
46#6103—22no—
47#6101—22no—
48C4×Dic13D412yes—
49C4×Dic13D412yes—
50#1955—131nomaximal, Sylow
51C23×C13—21no—
52C23×C13—22no—
53C23×C13—21no—
54C23×C13—22no—
55C23×C13M1612yes—
56C23×C13C22×C411yescharacteristic
57C22×D13—21no—
58C22×D13—22no—
59C22×D13—21no—
60C22×D13—22no—
61C22×D13M1612yes—
62C2×C4×C13—22no—
63C2×C4×C13—21no—
64C2×C4×C13—22no—
65C2×C4×C13C22⋊C412yes—
66C22⋊D13—28no—
67C2×Dic13—21no—
68C2×Dic13—21no—
69C2×Dic13—21no—
70C2×Dic13—22no—
71C2×Dic13—42no—
72C2×Dic13—41no—
73C2×Dic13—41no—
74C2×Dic13C22⋊C412yes—
75C2×Dic13C2×D411yescharacteristic
76C2×Dic13C2×D412yes—
77C2×Dic13C2×D411yescharacteristic
78C2×Dic13#4112yes—
79C4×D13—42no—
80C4×D13—41no—
81C4×D13—41no—
82#1057—24no—
83#1057—42no—
84C2×C4×D4—131no—
85C2×C4⋊C8—131no—
86C2×C22⋊C8—132no—
87C2×C22⋊C8—132no—
88C2×#97—131no—
89C22×C13—22no—
90C22×C13—24no—
91C22×C13—41no—
92C22×C13—41no—
93C22×C13—42no—
94C22×C13C2×C22⋊C411yescharacteristic
95C22×C13C4×D412yes—
96C22×C13C2×M1611yescharacteristic
97C22×C13C2×M1611yescharacteristic
98C22×C13#13112yes—
99C2×D13—22no—
100C2×D13—24no—
101C2×D13—41no—
102C2×D13—41no—
103C2×D13—42no—
104C4×C13—22no—
105C4×C13—41no—
106Dic13—22no—
107Dic13—41no—
108Dic13#12112yes—
109Dic13#12411yescharacteristic
110Dic13#12711yescharacteristic
111C22×D4—131no—
112C23×C4—131no—
113C23×C4—131no—
114C22×C8—132no—
115C22×C8—132no—
116C4×D4—262no—
117C4×D4—262no—
118C2×C4⋊C4—131no—
119C2×C22⋊C4—131no—
120C2×C22⋊C4#26111yescharacteristic
121C2×C42—131no—
122C4⋊C8—262no—
123C22⋊C8—264no—
124C22⋊C8—264no—
125#97—262no—
126C2×C13—42no—
127C2×C13#39011yescharacteristic
128C2×C13#40711yescharacteristic
129C2×C13#40811yescharacteristic
130C2×C13#43512yes—
131C2×C13#43512yes—
132D13—42no—
133C24—131no—
134C24C2×#26111yescharacteristic
135C2×D4—262no—
136C2×D4—262no—
137C2×D4—262no—
138C22×C4—131no—
139C22×C4—131no—
140C22×C4—131no—
141C22×C4—262no—
142C22×C4—261no—
143C22×C4—261no—
144C22×C4—262no—
145C22×C4—262no—
146C22×C4—261no—
147C22×C4—261no—
148C22×C4—262no—
149C22×C4C2×#26111yescharacteristic
150C22×C4C2×#26111yescharacteristic
151C2×C8—134no—
152C2×C8—262no—
153C2×C8—262no—
154C2×C8—262no—
155C2×C8—262no—
156C2×C8—262no—
157C4⋊C4—262no—
158C22⋊C4—22no—
159C22⋊C4—262no—
160C42—132no—
161C42—132no—
162C13#195511yescharacteristic, complemented, Sylow
163C23—21no—
164C23—22no—
165C23—22no—
166C23—21no—
167C23—132no—
168C23—261no—
169C23—262no—
170C23—262no—
171C23—261no—
172C23#611812yes—
173C23C22×#26111yescharacteristic
174D4—268no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—21no—
178C2×C4—132no—
179C2×C4—132no—
180C2×C4—131no—
181C2×C4—131no—
182C2×C4—132no—
183C2×C4—261no—
184C2×C4—261no—
185C2×C4—262no—
186C2×C4—261no—
187C2×C4—522no—
188C2×C4—521no—
189C2×C4—521no—
190C2×C4—522no—
191C2×C4—521no—
192C2×C4—521no—
193C2×C4C22⋊#26112yes—
194C8—264no—
195C8—522no—
196C22—24no—
197C22—22no—
198C22—42no—
199C22—41no—
200C22—41no—
201C22—264no—
202C22—262no—
203C22—522no—
204C22—521no—
205C22—521no—
206C22C2×#611811yescharacteristic
207C22D13⋊M1611yescharacteristic
208C22#8823812yes—
209C22D4×#26112yes—
210C22C2×C22⋊#26111yescharacteristic
211C4—22no—
212C4—41no—
213C4—132no—
214C4—131no—
215C4—131no—
216C4—262no—
217C4—521no—
218C2—42no—
219C2—522no—
220C2#1171906412yes—
221C2#1171906512yes—
222C2#1171912711yescharacteristic
223C2#1171914611yescharacteristic
224C2#1171915111yescharacteristic
subgroupG/H
center, FrattiniC23C22×#261
commutator, socleC23×C13C22×C4
FittingC2×C13×C22⋊C4C4
prime radicalC22×C22⋊D13C4
cosocleC22×Dic13C23
hypercenterC2×C22⋊C4#261
hypocenterC13#1955
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C22⋊#1057C2semidirect
3. C2×#88111C2semidirect
4. C2×#88110C2semidirect
5. C2×C4⋊#1057C2semidirect
44. C2×#1057D4semidirect
162. C13#1955semidirect

Maximal subgroups

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

subgroupindex
C2×#881352
C2×C22⋊#10572
C2×#881112
C2×#881102
C2×C4⋊#10572
#195513