Finite Group Databasebeta

← #16787001

Subgroups — #16787001

Order 3328.

598 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 598 conjugacy classes of subgroups — too many to draw. Only its 88 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#13130084C212yesmaximal
2#13129766C214yesmaximal, complemented
3C2×#11718891C211yesmaximal, characteristic
4C23×Q8×C13C411yescharacteristic
5C22×C4⋊Dic13C2211yescharacteristic
6C22×C4×Dic13C411yescharacteristic
7#11719169—22no—
8#11718891—22no—
9#11718891C412yes—
10#11718891C2212yes—
11C2×#88071—22no—
12#11718285—22no—
13#11718285C2214yes—
14C22×Q8×C13—24no—
15C22×Q8×C13—21no—
16C22×Q8×C13—42no—
17C22×Q8×C13—41no—
18C22×Q8×C13—41no—
19C22×Q8×C13C2×C412yes—
20C23×C4×C13—21no—
21C23×C4×C13C2×C411yescharacteristic
22C23×Dic13—21no—
23C23×Dic13D412yes—
24C2×#6122—42no—
25C2×C4⋊Dic13—41no—
26C2×C4⋊Dic13—41no—
27C2×C4⋊Dic13C2×C411yescharacteristic
28C2×C4⋊Dic13D412yes—
29C2×C4⋊Dic13C2311yescharacteristic
30C2×C4×Dic13—21no—
31C2×C4×Dic13—42no—
32C2×C4×Dic13C2×C412yes—
33C22⋊#1057—24no—
34C22⋊#1057—42no—
35#88071—24no—
36#88071—24no—
37#11506—131nomaximal, Sylow
38C24×C13C22⋊C411yescharacteristic
39C2×Q8×C13—24no—
40C2×Q8×C13—22no—
41C2×Q8×C13—48no—
42C2×Q8×C13—48no—
43C2×Q8×C13—42no—
44C2×Q8×C13—42no—
45C2×Q8×C13—42no—
46C2×Q8×C13—42no—
47C2×Q8×C13M1614yescomplemented
48C22×C4×C13—21no—
49C22×C4×C13—21no—
50C22×C4×C13—22no—
51C22×C4×C13—22no—
52C22×C4×C13—24no—
53C22×C4×C13—22no—
54C22×C4×C13—42no—
55C22×C4×C13—41no—
56C22×C4×C13—41no—
57C22×C4×C13C22⋊C411yescharacteristic
58C22×C4×C13C22×C411yescharacteristic
59C22×Dic13—24no—
60C22×Dic13—22no—
61C22×Dic13—22no—
62C22×Dic13—22no—
63C22×Dic13—42no—
64C22×Dic13—42no—
65C22×Dic13—44no—
66C22×Dic13C22⋊C412yes—
67C22×Dic13C2×D412yes—
68#6122—84no—
69C2×#1057—44no—
70C4⋊Dic13—41no—
71C4⋊Dic13—42no—
72C4⋊Dic13—41no—
73C4×Dic13—42no—
74C4×Dic13—42no—
75C2×#391—131no—
76#1463—132no—
77#1319—134no—
78C23×C13—22no—
79C23×C13—22no—
80C23×C13—21no—
81C23×C13—21no—
82C23×C13#9911yescharacteristic
83C23×C13#9911yescharacteristic
84C23×C13C2×C22⋊C411yescharacteristic
85Q8×C13—48no—
86Q8×C13—44no—
87Q8×C13—44no—
88C2×C4×C13—24no—
89C2×C4×C13—24no—
90C2×C4×C13—21no—
91C2×C4×C13—21no—
92C2×C4×C13—21no—
93C2×C4×C13—21no—
94C2×C4×C13—24no—
95C2×C4×C13—44no—
96C2×C4×C13—44no—
97C2×C4×C13—42no—
98C2×C4×C13—42no—
99C2×C4×C13#10012yes—
100C2×C4×C13C2×M1612yes—
101C2×Dic13—24no—
102C2×Dic13—22no—
103C2×Dic13—22no—
104C2×Dic13—48no—
105C2×Dic13—42no—
106C2×Dic13—44no—
107C2×Dic13—42no—
108C2×Dic13—42no—
109C2×Dic13—42no—
110C2×Dic13—82no—
111#1057—84no—
112C23×Q8#26111yescharacteristic
113C22×C4⋊C4—131no—
114C22×C42—131no—
115#407—262no—
116#391—132no—
117#391—132no—
118#391—262no—
119C2×#95—262no—
120#324—134no—
121#324—262no—
122C22×C13—24no—
123C22×C13—24no—
124C22×C13—21no—
125C22×C13—21no—
126C22×C13—21no—
127C22×C13—21no—
128C22×C13—21no—
129C22×C13—21no—
130C22×C13#35412yes—
131C22×C13#35612yes—
132C22×C13#40711yescharacteristic
133C22×C13C2×#9911yescharacteristic
134C22×C13C2×#10011yescharacteristic
135C4×C13—22no—
136C4×C13—22no—
137C4×C13—44no—
138Dic13—44no—
139Dic13—42no—
140Dic13—42no—
141C22×Q8—24no—
142C22×Q8—21no—
143C22×Q8—42no—
144C22×Q8—41no—
145C22×Q8—41no—
146C22×Q8C2×#26112yes—
147C23×C4—21no—
148C23×C4—132no—
149C23×C4—261no—
150C23×C4C2×#26111yescharacteristic
151C2×M16—522no—
152C2×C4⋊C4—132no—
153C2×C4⋊C4—131no—
154C2×C4⋊C4—131no—
155C2×C4⋊C4—521no—
156C2×C4⋊C4—521no—
157C2×C42—132no—
158C2×C42—261no—
159C2×C42—522no—
160C22⋊C8—264no—
161C22⋊C8—522no—
162#95—264no—
163#95—264no—
164C2×C13—21no—
165C2×C13—22no—
166C2×C13—22no—
167C2×C13—21no—
168C2×C13#146211yescharacteristic
169C2×C13C2×#35411yescharacteristic
170C2×C13C2×#35611yescharacteristic
171C24C22⋊#26111yescharacteristic
172C2×Q8—24no—
173C2×Q8—22no—
174C2×Q8—48no—
175C2×Q8—48no—
176C2×Q8—42no—
177C2×Q8—42no—
178C2×Q8—42no—
179C2×Q8—42no—
180C2×Q8#612214yescomplemented
181C22×C4—21no—
182C22×C4—21no—
183C22×C4—22no—
184C22×C4—22no—
185C22×C4—24no—
186C22×C4—22no—
187C22×C4—42no—
188C22×C4—41no—
189C22×C4—41no—
190C22×C4—132no—
191C22×C4—132no—
192C22×C4—264no—
193C22×C4—262no—
194C22×C4—262no—
195C22×C4—262no—
196C22×C4—522no—
197C22×C4—522no—
198C22×C4—524no—
199C22×C4C22⋊#26111yescharacteristic
200C22×C4C22×#26111yescharacteristic
201M16—1044no—
202C2×C8—524no—
203C4⋊C4—522no—
204C4⋊C4—521no—
205C4⋊C4—521no—
206C42—522no—
207C42—522no—
208C13#1150611yescharacteristic, complemented, Sylow
209C23—21no—
210C23—21no—
211C23—22no—
212C23—22no—
213C23#8811911yescharacteristic
214C23#8811911yescharacteristic
215C23C2×C22⋊#26111yescharacteristic
216Q8—44no—
217Q8—48no—
218Q8—44no—
219C2×C4—24no—
220C2×C4—24no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—24no—
226C2×C4—44no—
227C2×C4—44no—
228C2×C4—42no—
229C2×C4—42no—
230C2×C4—264no—
231C2×C4—262no—
232C2×C4—262no—
233C2×C4—528no—
234C2×C4—522no—
235C2×C4—522no—
236C2×C4—524no—
237C2×C4—522no—
238C2×C4—522no—
239C2×C4—1042no—
240C2×C4#8812112yes—
241C2×C4C2×#612212yes—
242C8—1044no—
243C22—24no—
244C22—24no—
245C22—21no—
246C22—21no—
247C22—21no—
248C22—21no—
249C22—21no—
250C22—21no—
251C22#1171830012yes—
252C22#1171830112yes—
253C22C2×#8811911yescharacteristic
254C22#1171916911yescharacteristic
255C22C2×#8812111yescharacteristic
256C4—22no—
257C4—22no—
258C4—44no—
259C4—524no—
260C4—522no—
261C4—522no—
262C2—21no—
263C2—21no—
264C2—22no—
265C2—22no—
266C2#1313008111yescharacteristic
267C2C2×#1171830011yescharacteristic
268C2C2×#1171830111yescharacteristic
subgroupG/H
centerC22C2×#88119
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC23×Q8×C13C4
socleC22×C13C2×#99
prime radicalC24×C13C22⋊C4
cosocleC2×C4⋊Dic13C23
hypercenterC23×Q8#261
hypocenterC13#11506
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C24 ◁ C23×C4 ◁ C23×Q8

Complements

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

NH ≅ G/Ntype
2. #13129766C2semidirect
47. C2×Q8×C13M16semidirect
180. C2×Q8#6122semidirect
208. C13#11506semidirect

Maximal subgroups

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

subgroupindex
#131300842
#131297662
C2×#117188912
#1150613