Finite Group Databasebeta

← #16782123

Subgroups — #16782123

Order 3328.

642 conjugacy classes of subgroups; only the 144 normal subgroups are shown.

normal subgroups only

This group has 642 conjugacy classes of subgroups — too many to draw. Only its 144 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#13130726C212yesmaximal
2#13129674C214yesmaximal
3C2×C4⋊C4×Dic13C211yesmaximal, characteristic
4C22×C13×C4⋊C4C411yescharacteristic
5C22×C4⋊Dic13C411yescharacteristic
6C22×C4×Dic13C412yes—
7C22×C4×Dic13C2211yescharacteristic
8C2×C22⋊#1057C2214yes—
9C2×#88071C2212yes—
10C4⋊C4×Dic13—22no—
11C4⋊C4×Dic13—22no—
12#11718290—22no—
13#11718290—22no—
14C23×C4×C13C2×C412yes—
15C23×C4×C13C2×C411yescharacteristic
16C23×Dic13C2×C411yescharacteristic
17C23×Dic13C2×C412yes—
18C23×Dic13C2311yescharacteristic
19C22×#1057—24no—
20C2×C13×C4⋊C4—22no—
21C2×C13×C4⋊C4—22no—
22C2×C13×C4⋊C4C814yescomplemented
23C2×C4⋊Dic13—22no—
24C2×C4⋊Dic13—24no—
25C2×C4×Dic13—24no—
26C2×C4×Dic13—22no—
27C2×C4×Dic13—22no—
28C2×C4×Dic13—44no—
29C2×C4×Dic13D412yes—
30C2×C4×Dic13D412yes—
31C22⋊#1057—28no—
32#88071—24no—
33#8701—131nomaximal, Sylow
34C24×C13C22×C411yescharacteristic
35C22×C4×C13—22no—
36C22×C4×C13—22no—
37C22×C4×C13—22no—
38C22×C4×C13—22no—
39C22×C4×C13—42no—
40C22×C4×C13—42no—
41C22×C4×C13C22⋊C412yes—
42C22×C4×C13C2×C812yes—
43C22×C4×C13C2×C814yes—
44C22×C4×C13M1612yes—
45C22×Dic13—22no—
46C22×Dic13—22no—
47C22×Dic13—22no—
48C22×Dic13—22no—
49C22×Dic13—22no—
50C22×Dic13—41no—
51C22×Dic13—41no—
52C22×Dic13—42no—
53C22×Dic13—42no—
54C22×Dic13C22⋊C411yescharacteristic
55C22×Dic13C22⋊C411yescharacteristic
56C22×Dic13M1614yes—
57C22×Dic13C2×D412yes—
58C22×Dic13#4114yes—
59C2×#1057—44no—
60C2×#1057—44no—
61C2×#1057—44no—
62C13×C4⋊C4—28no—
63C4⋊Dic13—28no—
64C4×Dic13—24no—
65C4×Dic13—24no—
66C4×Dic13—44no—
67C4×Dic13—44no—
68C2×C4×C4⋊C4—131no—
69#1817—132no—
70#1280—134no—
71C23×C13—21no—
72C23×C13—21no—
73C23×C13—21no—
74C23×C13—21no—
75C23×C13C2×C22⋊C411yescharacteristic
76C23×C13#11712yes—
77C23×C13C22×C811yescharacteristic
78C23×C13C2×M1611yescharacteristic
79C23×C13C2×M1612yes—
80C2×C4×C13—22no—
81C2×C4×C13—22no—
82C2×C4×C13—24no—
83C2×C4×C13—24no—
84C2×C4×C13—24no—
85C2×C4×C13—44no—
86C2×C4×C13—42no—
87C2×C4×C13—42no—
88C2×C4×C13—44no—
89C2×C4×C13C22⋊C814yes—
90C2×Dic13—28no—
91C2×Dic13—21no—
92C2×Dic13—21no—
93C2×Dic13—22no—
94C2×Dic13—22no—
95C2×Dic13—21no—
96C2×Dic13—21no—
97C2×Dic13—24no—
98C2×Dic13—44no—
99C2×Dic13—44no—
100C2×Dic13—42no—
101C2×Dic13—42no—
102C2×Dic13—44no—
103C2×Dic13#10012yes—
104C2×Dic13#10112yes—
105C2×Dic13#12314yes—
106#1057—84no—
107C22×C4⋊C4—131no—
108C22×C4⋊C4#26111yescharacteristic
109C22×C42—131no—
110C22×C42—132no—
111C2×C22⋊C8—134no—
112C4×C4⋊C4—262no—
113C4×C4⋊C4—262no—
114C2×#95—132no—
115#336—262no—
116#336—262no—
117C22×C13—22no—
118C22×C13—22no—
119C22×C13—21no—
120C22×C13—21no—
121C22×C13—21no—
122C22×C13—21no—
123C22×C13—22no—
124C22×C13—22no—
125C22×C13#38111yescharacteristic
126C22×C13C2×C22⋊C811yescharacteristic
127C22×C13#40711yescharacteristic
128C22×C13#41011yescharacteristic
129C22×C13#41011yescharacteristic
130C22×C13C2×#10011yescharacteristic
131C22×C13C2×#10111yescharacteristic
132C22×C13#43112yes—
133C22×C13#43212yes—
134C4×C13—24no—
135C4×C13—44no—
136Dic13—24no—
137Dic13—22no—
138Dic13—22no—
139Dic13—44no—
140C23×C4—131no—
141C23×C4—131no—
142C23×C4—132no—
143C23×C4C2×#26112yes—
144C23×C4C2×#26111yescharacteristic
145C22×C8—264no—
146C2×C4⋊C4—22no—
147C2×C4⋊C4—22no—
148C2×C4⋊C4—264no—
149C2×C4⋊C4—262no—
150C2×C4⋊C4#105714yescomplemented
151C2×C42—132no—
152C2×C42—132no—
153C2×C42—264no—
154C2×C42—262no—
155C2×C42—262no—
156C2×C42—524no—
157C22⋊C8—268no—
158#95—264no—
159C2×C13—22no—
160C2×C13—22no—
161C2×C13#146011yescharacteristic
162C2×C13#146111yescharacteristic
163C2×C13#146611yescharacteristic
164C2×C13#146711yescharacteristic
165C2×C13#181711yescharacteristic
166C2×C13#182011yescharacteristic
167C2×C13#182111yescharacteristic
168C24C22×#26111yescharacteristic
169C22×C4—22no—
170C22×C4—22no—
171C22×C4—22no—
172C22×C4—22no—
173C22×C4—42no—
174C22×C4—42no—
175C22×C4—132no—
176C22×C4—131no—
177C22×C4—131no—
178C22×C4—134no—
179C22×C4—134no—
180C22×C4—262no—
181C22×C4—262no—
182C22×C4—262no—
183C22×C4—262no—
184C22×C4—262no—
185C22×C4—521no—
186C22×C4—521no—
187C22×C4—522no—
188C22×C4—522no—
189C22×C4C2×#105712yes—
190C22×C4C2×#105714yes—
191C22×C4#612212yes—
192C22×C4C22⋊#26112yes—
193C2×C8—524no—
194C2×C8—524no—
195C2×C8—524no—
196C4⋊C4—28no—
197C4⋊C4—268no—
198C42—264no—
199C42—264no—
200C42—524no—
201C42—524no—
202C13#870111yescharacteristic, complemented, Sylow
203C23—21no—
204C23—21no—
205C23—21no—
206C23—21no—
207C23D13⋊M1612yes—
208C23#8823712yes—
209C23C22×#105711yescharacteristic
210C23C2×#612211yescharacteristic
211C23C2×C22⋊#26111yescharacteristic
212C2×C4—24no—
213C2×C4—22no—
214C2×C4—24no—
215C2×C4—22no—
216C2×C4—24no—
217C2×C4—44no—
218C2×C4—42no—
219C2×C4—42no—
220C2×C4—44no—
221C2×C4—134no—
222C2×C4—132no—
223C2×C4—132no—
224C2×C4—268no—
225C2×C4—261no—
226C2×C4—261no—
227C2×C4—262no—
228C2×C4—261no—
229C2×C4—262no—
230C2×C4—261no—
231C2×C4—264no—
232C2×C4—524no—
233C2×C4—524no—
234C2×C4—522no—
235C2×C4—522no—
236C2×C4—524no—
237C2×C4C22⋊#105714yes—
238C8—1044no—
239C22—21no—
240C22—21no—
241C22—21no—
242C22—21no—
243C22—22no—
244C22—22no—
245C22—22no—
246C22—22no—
247C22#1171911912yes—
248C22#1171912611yescharacteristic
249C22#1171912812yes—
250C22#1171913511yescharacteristic
251C22#1171914211yescharacteristic
252C22D13⋊#10011yescharacteristic
253C22#1171915611yescharacteristic
254C22D13⋊#10111yescharacteristic
255C22C2×C22⋊#105711yescharacteristic
256C4—24no—
257C4—44no—
258C4—264no—
259C4—262no—
260C4—262no—
261C4—524no—
262C2—22no—
263C2—22no—
264C2#1313007611yescharacteristic
265C2#1313007911yescharacteristic
266C2#1313009711yescharacteristic
267C2#1313010011yescharacteristic
268C2#1313072611yescharacteristic
269C2#1313073411yescharacteristic
270C2#1313073611yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC23×C13C22×C8
FrattiniC24C22×#261
FittingC22×C13×C4⋊C4C4
socleC23×C13C2×C22⋊C4
prime radicalC24×C13C22×C4
cosocleC23×Dic13C23
hypercenterC22×C4⋊C4#261
hypocenterC13#8701
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
22. C2×C13×C4⋊C4C8semidirect
150. C2×C4⋊C4#1057semidirect
202. C13#8701semidirect

Maximal subgroups

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

subgroupindex
#131307262
#131296742
C2×C4⋊C4×Dic132
#870113