Finite Group Databasebeta

← #13130809

Subgroups — #13130809

Order 1664.

432 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 118 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
1C23×#1057C211yesmaximal, characteristic, complemented
2C2×D4×Dic13C211yesmaximal, characteristic
3C2×C22⋊#1057C211yesmaximal, characteristic, complemented
4C2×C22⋊#1057C212yesmaximal, complemented
5#11718290C212yesmaximal, complemented
6C22×D4×C13C411yescharacteristic
7C23×Dic13C2211yescharacteristic
8C23×Dic13C2211yescharacteristic
9C22×#1057—22no—
10C22×#1057—24no—
11C22×#1057C2212yes—
12C22×#1057C2212yes—
13C2×C22⋊Dic13C411yescharacteristic
14C2×C22⋊Dic13C411yescharacteristic
15D4×Dic13—22no—
16D4×Dic13—22no—
17C2×C4⋊Dic13C411yescharacteristic
18C2×C4×Dic13C2211yescharacteristic
19C22⋊#1057—22no—
20C22⋊#1057—24no—
21C24×C13C2×C411yescharacteristic
22C24×C13C2×C411yescharacteristic
23C2×D4×C13—22no—
24C2×D4×C13—22no—
25C2×D4×C13C814yescomplemented
26C22×C4×C13C2×C411yescharacteristic
27C22×Dic13—22no—
28C22×Dic13—22no—
29C22×Dic13—22no—
30C22×Dic13—21no—
31C22×Dic13—21no—
32C22×Dic13—22no—
33C22×Dic13C2×C411yescharacteristic
34C22×Dic13C2×C411yescharacteristic
35C22×Dic13C2×C411yescharacteristic
36C22×Dic13D412yes—
37C22×Dic13D412yes—
38C22×Dic13C2311yescharacteristic
39C2×#1057—28no—
40C2×#1057—22no—
41C2×#1057—22no—
42C2×#1057—22no—
43C2×#1057—22no—
44C2×#1057—22no—
45C2×#1057D414yescomplemented
46C22⋊Dic13—22no—
47C22⋊Dic13—22no—
48C4⋊Dic13—22no—
49C4×Dic13—21no—
50C4×Dic13—21no—
51#1869—131nomaximal, Sylow
52C23×C13—22no—
53C23×C13—22no—
54C23×C13—21no—
55C23×C13—22no—
56C23×C13—21no—
57C23×C13—22no—
58C23×C13C22⋊C412yes—
59C23×C13C2×C812yes—
60C23×C13C2×C812yescomplemented
61C23×C13M1612yes—
62C23×C13C22×C411yescharacteristic
63D4×C13—28no—
64C2×C4×C13—21no—
65C2×C4×C13—21no—
66C2×C4×C13C2×C812yescomplemented
67C2×Dic13—22no—
68C2×Dic13—22no—
69C2×Dic13—24no—
70C2×Dic13—22no—
71C2×Dic13—21no—
72C2×Dic13—21no—
73C2×Dic13—22no—
74C2×Dic13—22no—
75C2×Dic13—41no—
76C2×Dic13—42no—
77C2×Dic13—41no—
78C2×Dic13C22⋊C412yes—
79C2×Dic13C2×D412yes—
80C2×Dic13C2×D411yescharacteristic
81C2×Dic13C2×D411yescharacteristic
82C2×Dic13#4112yes—
83#1057—24no—
84#1057—42no—
85C23×C8—131no—
86C2×C4×D4—131no—
87C2×C22⋊C8—132no—
88C2×C22⋊C8—131no—
89#336—132no—
90C22×C13—22no—
91C22×C13—22no—
92C22×C13—24no—
93C22×C13—24no—
94C22×C13—22no—
95C22×C13—24no—
96C22×C13—41no—
97C22×C13—41no—
98C22×C13—42no—
99C22×C13C22⋊C814yescomplemented
100C22×C13C2×C22⋊C411yescharacteristic
101C22×C13C4×D412yes—
102C22×C13C22×C811yescharacteristic
103C22×C13C2×M1611yescharacteristic
104C22×C13#13112yes—
105C4×C13—22no—
106Dic13—22no—
107Dic13—41no—
108Dic13—41no—
109Dic13#12011yescharacteristic
110Dic13#12112yes—
111Dic13#12311yescharacteristic
112C22×D4#26111yescharacteristic
113C23×C4—131no—
114C23×C4—131no—
115C22×C8—132no—
116C22×C8—132no—
117C22×C8—264no—
118C22×C8—262no—
119C4×D4—262no—
120C4×D4—262no—
121C2×C4⋊C4—131no—
122C2×C22⋊C4—131no—
123C2×C22⋊C4—131no—
124C2×C42—131no—
125C22⋊C8—264no—
126C22⋊C8—262no—
127C2×C13—24no—
128C2×C13—42no—
129C2×C13#38611yescharacteristic
130C2×C13C2×C22⋊C811yescharacteristic
131C2×C13#40811yescharacteristic
132C2×C13C8×D412yes—
133C2×C13#43512yes—
134C24C2×#26111yescharacteristic
135C24C2×#26111yescharacteristic
136C2×D4—22no—
137C2×D4—22no—
138C2×D4#105714yescomplemented
139C22×C4—131no—
140C22×C4—132no—
141C22×C4—132no—
142C22×C4—131no—
143C22×C4—131no—
144C22×C4—131no—
145C22×C4—262no—
146C22×C4—262no—
147C22×C4—262no—
148C22×C4—261no—
149C22×C4—261no—
150C22×C4—262no—
151C22×C4C2×#26111yescharacteristic
152C2×C8—134no—
153C2×C8—262no—
154C2×C8—262no—
155C2×C8—268no—
156C2×C8—262no—
157C2×C8—262no—
158C2×C8—262no—
159C4⋊C4—262no—
160C22⋊C4—262no—
161C22⋊C4—262no—
162C42—261no—
163C42—261no—
164C13#186911yescharacteristic, complemented, Sylow
165C23—22no—
166C23—22no—
167C23—22no—
168C23—22no—
169C23—21no—
170C23—21no—
171C23C2×#105712yes—
172C23C2×#105712yescomplemented
173C23#612212yes—
174C23C22⋊#26112yes—
175C23C22×#26111yescharacteristic
176D4—28no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—132no—
180C2×C4—132no—
181C2×C4—131no—
182C2×C4—131no—
183C2×C4—132no—
184C2×C4—262no—
185C2×C4—264no—
186C2×C4—262no—
187C2×C4—262no—
188C2×C4—262no—
189C2×C4—262no—
190C2×C4—261no—
191C2×C4—261no—
192C2×C4—521no—
193C2×C4—522no—
194C2×C4—521no—
195C2×C4C2×#105712yescomplemented
196C8—264no—
197C8—522no—
198C22—24no—
199C22—24no—
200C22—22no—
201C22—22no—
202C22—22no—
203C22—24no—
204C22—42no—
205C22—41no—
206C22—41no—
207C22C22⋊#105714yescomplemented
208C22#8823812yes—
209C22D4×#26112yes—
210C22C22×#105711yescharacteristic
211C22C2×#612211yescharacteristic
212C22C2×C22⋊#26111yescharacteristic
213C4—22no—
214C4—131no—
215C4—132no—
216C4—131no—
217C4—262no—
218C4—521no—
219C4—521no—
220C2—24no—
221C2—42no—
222C2D4×#105712yes—
223C2#1171914412yes—
224C2#1171914611yescharacteristic
225C2#1171915011yescharacteristic
226C2C2×C22⋊#105711yescharacteristic
subgroupG/H
center, FrattiniC23C22×#261
commutatorC22×C13C22×C8
Fitting, prime radicalC22×D4×C13C4
socleC23×C13C22×C4
cosocleC22×Dic13C23
hypercenterC22×D4#261
hypocenterC13#1869
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C23×#1057C2semidirect
3. C2×C22⋊#1057C2semidirect
4. C2×C22⋊#1057C2semidirect
5. #11718290C2semidirect
25. C2×D4×C13C8semidirect
45. C2×#1057D4semidirect
60. C23×C13C2×C8semidirect
66. C2×C4×C13C2×C8semidirect
99. C22×C13C22⋊C8semidirect
138. C2×D4#1057semidirect
164. C13#1869semidirect
172. C23C2×#1057semidirect
195. C2×C4C2×#1057semidirect
207. C22C22⋊#1057semidirect

Maximal subgroups

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

subgroupindex
C23×#10572
C2×D4×Dic132
C2×C22⋊#10572
#117182902
#186913