Finite Group Databasebeta

← #16786995

Subgroups — #16786995

Order 3328.

510 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 510 conjugacy classes of subgroups — too many to draw. Only its 80 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#13130087C212yesmaximal
2#13129762C214yesmaximal
3#13117422C211yesmaximal, characteristic
4C23×Q8×C13C411yescharacteristic
5C2×#88180C411yescharacteristic
6C2×#88180C2211yescharacteristic
7#11719128—22no—
8#11718891—22no—
9#11718891—22no—
10#11718872C412yes—
11#11718872C2212yes—
12#11718305C2214yes—
13#11718285—22no—
14C22×Q8×C13—21no—
15C22×Q8×C13—21no—
16C22×Q8×C13—24no—
17C22×Q8×C13—41no—
18C22×Q8×C13—41no—
19C22×Q8×C13—42no—
20C23×C4×C13C2×C412yes—
21C23×C4×C13C2×C411yescharacteristic
22C2×C22⋊Dic13C2×C412yes—
23C2×C22⋊Dic13C2×C411yescharacteristic
24C2×C22⋊Dic13C2311yescharacteristic
25#88180—41no—
26#88180—41no—
27#88180—42no—
28C2×C4⋊Dic13—21no—
29C2×C4⋊Dic13D412yes—
30C2×C4×Dic13—21no—
31C2×C4×Dic13D412yes—
32C22⋊#1057—24no—
33#88112—42no—
34#88110—42no—
35#88071—24no—
36#88071—24no—
37#11504—131nomaximal, Sylow
38C24×C13C22×C411yescharacteristic
39C2×Q8×C13—24no—
40C2×Q8×C13—24no—
41C2×Q8×C13—48no—
42C2×Q8×C13—48no—
43C2×Q8×C13—42no—
44C2×Q8×C13—42no—
45C2×Q8×C13—41no—
46C2×Q8×C13—41no—
47C2×Q8×C13—42no—
48C22×C4×C13—22no—
49C22×C4×C13—21no—
50C22×C4×C13—21no—
51C22×C4×C13—22no—
52C22×C4×C13—22no—
53C22×C4×C13—22no—
54C22×C4×C13—42no—
55C22×C4×C13—42no—
56C22×C4×C13C22⋊C411yescharacteristic
57C22×C4×C13C22⋊C411yescharacteristic
58C22×C4×C13M1614yes—
59C22×Dic13—22no—
60C22×Dic13C22⋊C412yes—
61C22×Dic13C2×D412yes—
62C2×#1057—44no—
63C22⋊Dic13—41no—
64C22⋊Dic13—41no—
65C22⋊Dic13—42no—
66C4⋊Dic13—42no—
67C4⋊Dic13—42no—
68C4×Dic13—22no—
69C4×Dic13—22no—
70C4×Dic13—42no—
71#2310—131no—
72#1464—132no—
73#1317—134no—
74C23×C13—21no—
75C23×C13—21no—
76C23×C13—42no—
77C23×C13C2×C22⋊C411yescharacteristic
78C23×C13C2×M1612yes—
79Q8×C13—44no—
80Q8×C13—44no—
81Q8×C13—48no—
82C2×C4×C13—24no—
83C2×C4×C13—24no—
84C2×C4×C13—21no—
85C2×C4×C13—21no—
86C2×C4×C13—21no—
87C2×C4×C13—21no—
88C2×C4×C13—24no—
89C2×C4×C13—44no—
90C2×C4×C13—42no—
91C2×C4×C13—42no—
92C2×C4×C13—44no—
93C2×C4×C13#9911yescharacteristic
94C2×C4×C13#9911yescharacteristic
95C2×C4×C13#10012yes—
96C2×Dic13—22no—
97C2×Dic13—22no—
98C2×Dic13—42no—
99C2×Dic13—42no—
100C2×Dic13—44no—
101C2×Dic13—42no—
102#1057—84no—
103C23×Q8#26111yescharacteristic
104C2×#117—131no—
105C2×#117—131no—
106#432—262no—
107#391—262no—
108#391—262no—
109#381—132no—
110#381—132no—
111#324—262no—
112#323—134no—
113C22×C13—22no—
114C22×C13—22no—
115C22×C13—42no—
116C22×C13—42no—
117C22×C13—42no—
118C22×C13#40711yescharacteristic
119C22×C13C2×#9911yescharacteristic
120C22×C13C2×#10011yescharacteristic
121C4×C13—21no—
122C4×C13—21no—
123C4×C13—22no—
124C4×C13—44no—
125Dic13—42no—
126Dic13—42no—
127Dic13—82no—
128C22×Q8—24no—
129C22×Q8—21no—
130C22×Q8—21no—
131C22×Q8—41no—
132C22×Q8—41no—
133C22×Q8—42no—
134C23×C4C2×#26112yes—
135C23×C4C2×#26111yescharacteristic
136#117—521no—
137#117—521no—
138#117—522no—
139C2×C4⋊C4—132no—
140C2×C4⋊C4—261no—
141C2×C22⋊C4—131no—
142C2×C22⋊C4—131no—
143C2×C22⋊C4—132no—
144C2×C42—132no—
145C2×C42—261no—
146C4⋊C8—522no—
147C22⋊C8—264no—
148#97—522no—
149#95—264no—
150#95—264no—
151C2×C13—21no—
152C2×C13—21no—
153C2×C13—42no—
154C2×C13#146211yescharacteristic
155C2×C13#212312yes—
156C24C22×#26111yescharacteristic
157C2×Q8—24no—
158C2×Q8—24no—
159C2×Q8—48no—
160C2×Q8—48no—
161C2×Q8—42no—
162C2×Q8—42no—
163C2×Q8—41no—
164C2×Q8—41no—
165C2×Q8—42no—
166C22×C4—22no—
167C22×C4—21no—
168C22×C4—21no—
169C22×C4—22no—
170C22×C4—22no—
171C22×C4—22no—
172C22×C4—42no—
173C22×C4—42no—
174C22×C4—132no—
175C22×C4—132no—
176C22×C4—262no—
177C22×C4#612214yes—
178C22×C4C22⋊#26111yescharacteristic
179C22×C4C22⋊#26111yescharacteristic
180C2×C8—524no—
181C4⋊C4—522no—
182C4⋊C4—522no—
183C22⋊C4—521no—
184C22⋊C4—521no—
185C22⋊C4—522no—
186C42—262no—
187C42—262no—
188C42—522no—
189C13#1150411yescharacteristic, complemented, Sylow
190C23—21no—
191C23—21no—
192C23—42no—
193C23C2×#612212yes—
194C23C2×C22⋊#26111yescharacteristic
195Q8—44no—
196Q8—44no—
197Q8—48no—
198C2×C4—24no—
199C2×C4—24no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—24no—
205C2×C4—44no—
206C2×C4—42no—
207C2×C4—42no—
208C2×C4—44no—
209C2×C4—262no—
210C2×C4—262no—
211C2×C4—522no—
212C2×C4—522no—
213C2×C4—524no—
214C2×C4—522no—
215C2×C4#8811911yescharacteristic
216C2×C4#8811911yescharacteristic
217C2×C4#8812112yes—
218C8—1044no—
219C22—22no—
220C22—22no—
221C22—42no—
222C22—42no—
223C22—42no—
224C22C2×#8811911yescharacteristic
225C22#1171916911yescharacteristic
226C22C2×#8812111yescharacteristic
227C4—21no—
228C4—21no—
229C4—22no—
230C4—44no—
231C4—522no—
232C4—522no—
233C4—1042no—
234C2—21no—
235C2—21no—
236C2—42no—
237C2#1313008111yescharacteristic
238C2#1313109812yes—
subgroupG/H
centerC22C2×#88119
commutator, prime radicalC24×C13C22×C4
FrattiniC24C22×#261
FittingC23×Q8×C13C4
socleC22×C13C2×#99
cosocleC2×C22⋊Dic13C23
hypercenterC23×Q8#261
hypocenterC13#11504
LCSG ▷ C24×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C23×C4 ◁ C23×Q8

Complements

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

NH ≅ G/Ntype
189. C13#11504semidirect

Maximal subgroups

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

subgroupindex
#131300872
#131297622
#131174222
#1150413