Finite Group Databasebeta

← #13130863

Subgroups — #13130863

Order 1664.

338 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 74 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
1C22×#6122C211yesmaximal, characteristic
2C2×#88132C211yesmaximal, characteristic
3#11719169C211yesmaximal, characteristic
4C2×#88113C212yesmaximal, complemented
5#11718291C212yesmaximal, complemented
6C23×Dic13C2211yescharacteristic
7C22×Dic26C2211yescharacteristic
8C2×#6122—21no—
9C2×#6122—24no—
10C2×#6122C2212yes—
11C2×#6122C2212yes—
12C22×#1057—21no—
13C2×C13×C22⋊C4C411yescharacteristic
14C2×C22⋊Dic13C411yescharacteristic
15C2×C4⋊Dic13C411yescharacteristic
16C2×#6101C411yescharacteristic
17C2×#6101C2211yescharacteristic
18#88132—21no—
19#88132—21no—
20#88132—21no—
21#88132—21no—
22C22⋊#1057—21no—
23C22⋊#1057—21no—
24#88113—24no—
25C24×C13C2×C411yescharacteristic
26C22×C4×C13C2×C411yescharacteristic
27C22×C4×C13C2×C411yescharacteristic
28C22×Dic13—22no—
29C22×Dic13—22no—
30C22×Dic13C2×C411yescharacteristic
31C22×Dic13C2×C411yescharacteristic
32C22×Dic13C2×C411yescharacteristic
33C22×Dic13D411yescharacteristic
34C22×Dic13D411yescharacteristic
35C22×Dic13D411yescharacteristic
36C22×Dic13D411yescharacteristic
37C22×Dic13C2311yescharacteristic
38C2×Dic26—22no—
39C2×Dic26—21no—
40C2×Dic26—21no—
41C2×Dic26—22no—
42#6122—24no—
43#6122—22no—
44#6122—22no—
45#6122—22no—
46#6122D414yes—
47C2×#1057—24no—
48C2×#1057—22no—
49C2×#1057—22no—
50C13×C22⋊C4—21no—
51C13×C22⋊C4—21no—
52C22⋊Dic13—21no—
53C22⋊Dic13—21no—
54C4⋊Dic13—21no—
55C4⋊Dic13—21no—
56#6101—21no—
57#6101—21no—
58#6101—21no—
59#6101—21no—
60#1901—131nomaximal, Sylow
61C23×C13—22no—
62C23×C13—22no—
63C23×C13—41no—
64C23×C13C22⋊C411yescharacteristic
65C23×C13C22⋊C411yescharacteristic
66C23×C13C22×C411yescharacteristic
67C2×C4×C13—21no—
68C2×C4×C13—21no—
69C2×C4×C13—22no—
70C2×C4×C13—41no—
71C2×Dic13—22no—
72C2×Dic13—21no—
73C2×Dic13—21no—
74C2×Dic13—22no—
75C2×Dic13—22no—
76C2×Dic13—21no—
77C2×Dic13—21no—
78C2×Dic13—21no—
79C2×Dic13—21no—
80C2×Dic13—22no—
81C2×Dic13—41no—
82C2×Dic13C22⋊C411yescharacteristic
83C2×Dic13C22⋊C411yescharacteristic
84C2×Dic13C2×D412yes—
85C2×Dic13C2×D411yescharacteristic
86C2×Dic13C2×D411yescharacteristic
87C2×Dic13#4112yes—
88Dic26—41no—
89Dic26—42no—
90Dic26—41no—
91#1057—24no—
92#1057—42no—
93C22×M16—131no—
94C2×C22⋊Q8—131no—
95C2×#101—132no—
96#407—131no—
97#343—132no—
98C22×C13—21no—
99C22×C13—21no—
100C22×C13—21no—
101C22×C13—21no—
102C22×C13—21no—
103C22×C13—21no—
104C22×C13—21no—
105C22×C13—44no—
106C22×C13#10112yescomplemented
107C22×C13C2×C22⋊C411yescharacteristic
108C22×C13C4×D412yes—
109C4×C13—41no—
110C4×C13—41no—
111Dic13—21no—
112Dic13—21no—
113Dic13—41no—
114Dic13—41no—
115Dic13#12011yescharacteristic
116Dic13#12112yes—
117Dic13#12311yescharacteristic
118C22×Q8—131no—
119C23×C4—131no—
120C2×M16—132no—
121C2×M16—132no—
122C2×M16—264no—
123C2×M16—261no—
124C22×C8—261no—
125C22⋊Q8—261no—
126C22⋊Q8—261no—
127C22⋊Q8—261no—
128C22⋊Q8—261no—
129C2×C4⋊C4—131no—
130C2×C4⋊C4—131no—
131C2×C4⋊C4—131no—
132C2×C22⋊C4—131no—
133C2×C22⋊C4#26111yescharacteristic
134#101—264no—
135C22⋊C8—261no—
136C22⋊C8—261no—
137C2×C13—22no—
138C2×C13—22no—
139C2×C13—41no—
140C2×C13#38611yescharacteristic
141C2×C13C2×#10111yescharacteristic
142C2×C13#41311yescharacteristic
143C24C2×#26111yescharacteristic
144C2×Q8—262no—
145C2×Q8—261no—
146C2×Q8—261no—
147C2×Q8—262no—
148C22×C4—131no—
149C22×C4—131no—
150C22×C4—131no—
151C22×C4—131no—
152C22×C4—131no—
153C22×C4—131no—
154C22×C4—131no—
155C22×C4—131no—
156C22×C4—262no—
157C22×C4—262no—
158C22×C4C2×#26111yescharacteristic
159C22×C4C2×#26111yescharacteristic
160M16—134no—
161M16—262no—
162M16—264no—
163M16—262no—
164M16—262no—
165C2×C8—262no—
166C2×C8—264no—
167C2×C8—262no—
168C4⋊C4—261no—
169C4⋊C4—261no—
170C4⋊C4—261no—
171C4⋊C4—261no—
172C4⋊C4—261no—
173C4⋊C4—261no—
174C22⋊C4—21no—
175C22⋊C4—21no—
176C22⋊C4—261no—
177C22⋊C4—261no—
178C13#190111yescharacteristic, complemented, Sylow
179C23—22no—
180C23—22no—
181C23—41no—
182C23C22⋊#26111yescharacteristic
183C23C22⋊#26111yescharacteristic
184C23C22×#26111yescharacteristic
185Q8—521no—
186Q8—522no—
187Q8—521no—
188C2×C4—22no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—41no—
192C2×C4—132no—
193C2×C4—132no—
194C2×C4—131no—
195C2×C4—131no—
196C2×C4—131no—
197C2×C4—131no—
198C2×C4—261no—
199C2×C4—261no—
200C2×C4—262no—
201C2×C4—262no—
202C2×C4—261no—
203C2×C4—261no—
204C2×C4—262no—
205C2×C4—262no—
206C2×C4—261no—
207C2×C4—261no—
208C2×C4—521no—
209C8—264no—
210C8—522no—
211C22—21no—
212C22—21no—
213C22—21no—
214C22—21no—
215C22—21no—
216C22—21no—
217C22—21no—
218C22—44no—
219C22#8811312yescomplemented
220C22D4×#26112yes—
221C22C2×C22⋊#26111yescharacteristic
222C4—41no—
223C4—41no—
224C4—131no—
225C4—132no—
226C4—131no—
227C4—261no—
228C4—261no—
229C4—521no—
230C4—521no—
231C2—22no—
232C2—22no—
233C2—41no—
234C2C2×#8811311yescharacteristic
235C2#1171914811yescharacteristic
236C2#1171915011yescharacteristic
subgroupG/H
centerC22C2×C22⋊#261
commutatorC23×C13C22×C4
FrattiniC23C22×#261
FittingC2×C13×C22⋊C4C4
socleC22×C13C2×C22⋊C4
prime radicalC24×C13C2×C4
cosocleC22×Dic13C23
hypercenterC2×C22⋊C4#261
hypocenterC13#1901
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C24 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
4. C2×#88113C2semidirect
5. #11718291C2semidirect
106. C22×C13#101semidirect
178. C13#1901semidirect
219. C22#88113semidirect

Maximal subgroups

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

subgroupindex
C22×#61222
C2×#881322
#117191692
C2×#881132
#117182912
#190113