Finite Group Databasebeta

← #15756378

Subgroups — #15756378

Order 3328.

622 conjugacy classes of subgroups; only the 155 normal subgroups are shown.

normal subgroups only

This group has 622 conjugacy classes of subgroups — too many to draw. Only its 155 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
1C2×#11718117C212yesmaximal
2#13112684C214yesmaximal, complemented
3C13×#2273C211yesmaximal, characteristic
4C22×C13×C22⋊C4C411yescharacteristic
5C22×C13×C22⋊C4C411yescharacteristic
6C22×C13×C22⋊C4C2211yescharacteristic
7C4×C13×C22⋊C4—22no—
8C4×C13×C22⋊C4—22no—
9C4×C13×C22⋊C4C412yes—
10C4×C13×C22⋊C4C2212yes—
11C2×C22⋊#1055C2214yes—
12#11718117—22no—
13#11718117—22no—
14C25×C13C2×C411yescharacteristic
15C23×C4×C13—21no—
16C23×C4×C13—21no—
17C23×C4×C13C2×C411yescharacteristic
18C23×C4×C13C2311yescharacteristic
19C2×C13×C22⋊C4—21no—
20C2×C13×C22⋊C4—21no—
21C2×C13×C22⋊C4—22no—
22C2×C13×C22⋊C4—24no—
23C2×C13×C22⋊C4—24no—
24C2×C13×C22⋊C4C814yescomplemented
25C2×C13×C22⋊C4C2×C412yes—
26C2×C13×C22⋊C4C2×C412yes—
27C2×C13×C22⋊C4D412yes—
28C2×C13×C22⋊C4D412yes—
29C2×C42×C13—22no—
30C2×C42×C13—22no—
31C22×#1055—24no—
32C13×#95—22no—
33C13×#95—22no—
34C22⋊#1055—24no—
35C22⋊#1055—24no—
36#8734—131nomaximal, Sylow
37C24×C13—22no—
38C24×C13—22no—
39C24×C13—81no—
40C24×C13—81no—
41C24×C13C22⋊C411yescharacteristic
42C24×C13C22⋊C411yescharacteristic
43C24×C13C2×C812yes—
44C24×C13M1612yes—
45C24×C13C22×C411yescharacteristic
46C22×C4×C13—22no—
47C22×C4×C13—22no—
48C22×C4×C13—24no—
49C22×C4×C13—24no—
50C22×C4×C13—22no—
51C22×C4×C13—81no—
52C22×C4×C13—81no—
53C22×C4×C13—81no—
54C22×C4×C13—81no—
55C22×C4×C13—81no—
56C22×C4×C13—81no—
57C22×C4×C13C22⋊C412yes—
58C22×C4×C13C2×D412yes—
59C22×C4×C13#4114yes—
60C13×C22⋊C4—24no—
61C13×C22⋊C4—24no—
62C13×C22⋊C4—22no—
63C13×C22⋊C4—22no—
64C13×C22⋊C4—24no—
65C13×C22⋊C4—24no—
66C13×C22⋊C4C2×C814yes—
67C13×C22⋊C4M1614yes—
68C42×C13—82no—
69C42×C13—82no—
70C2×#1055—44no—
71C2×#1055—84no—
72#2273D1311yescharacteristic
73C2×#323—132no—
74#1282—134no—
75C23×C13—21no—
76C23×C13—21no—
77C23×C13—21no—
78C23×C13—21no—
79C23×C13—24no—
80C23×C13—24no—
81C23×C13—41no—
82C23×C13—41no—
83C23×C13—41no—
84C23×C13—41no—
85C23×C13—41no—
86C23×C13—41no—
87C23×C13—82no—
88C23×C13—82no—
89C23×C13—84no—
90C23×C13—82no—
91C23×C13—82no—
92C23×C13C22⋊C812yes—
93C23×C13C22⋊C812yes—
94C23×C13C2×C22⋊C411yescharacteristic
95C23×C13#11712yes—
96C23×C13C22×C811yescharacteristic
97C23×C13C2×M1611yescharacteristic
98C23×C13C2×M1612yes—
99C2×C4×C13—22no—
100C2×C4×C13—24no—
101C2×C4×C13—24no—
102C2×C4×C13—44no—
103C2×C4×C13—42no—
104C2×C4×C13—42no—
105C2×C4×C13—42no—
106C2×C4×C13—42no—
107C2×C4×C13—42no—
108C2×C4×C13—42no—
109C2×C4×C13—82no—
110C2×C4×C13—84no—
111C2×C4×C13—84no—
112C2×C4×C13#12314yes—
113#1055—84no—
114C22×C22⋊C4Dic1311yescharacteristic
115C22×C22⋊C4Dic1311yescharacteristic
116C22×C22⋊C4C2×D1311yescharacteristic
117C2×C22⋊C8—134no—
118C4×C22⋊C4—22no—
119C4×C22⋊C4—22no—
120C4×C22⋊C4Dic1312yes—
121C4×C22⋊C4C2×D1312yes—
122#323—262no—
123#323—262no—
124C22×C13—21no—
125C22×C13—22no—
126C22×C13—21no—
127C22×C13—22no—
128C22×C13—22no—
129C22×C13—22no—
130C22×C13—41no—
131C22×C13—41no—
132C22×C13—42no—
133C22×C13—42no—
134C22×C13—42no—
135C22×C13—42no—
136C22×C13—42no—
137C22×C13—41no—
138C22×C13—41no—
139C22×C13—41no—
140C22×C13—41no—
141C22×C13—84no—
142C22×C13—84no—
143C22×C13#38111yescharacteristic
144C22×C13C2×C22⋊C811yescharacteristic
145C22×C13#40711yescharacteristic
146C22×C13#43112yes—
147C22×C13#43212yes—
148C4×C13—24no—
149C4×C13—44no—
150C4×C13—44no—
151C4×C13—42no—
152C25C2×Dic1311yescharacteristic
153C23×C4—21no—
154C23×C4—21no—
155C23×C4C2×Dic1311yescharacteristic
156C23×C4C22×D1311yescharacteristic
157C22×C8—264no—
158C2×C22⋊C4—22no—
159C2×C22⋊C4—21no—
160C2×C22⋊C4—21no—
161C2×C22⋊C4—24no—
162C2×C22⋊C4—24no—
163C2×C22⋊C4#105514yescomplemented
164C2×C22⋊C4C2×Dic1312yes—
165C2×C22⋊C4C2×Dic1312yes—
166C2×C22⋊C4C22⋊D1312yes—
167C2×C22⋊C4C22⋊D1312yes—
168C2×C42—22no—
169C2×C42—22no—
170C22⋊C8—264no—
171C22⋊C8—264no—
172#95—22no—
173#95—22no—
174C2×C13—21no—
175C2×C13—21no—
176C2×C13—22no—
177C2×C13—22no—
178C2×C13—42no—
179C2×C13—42no—
180C2×C13#181711yescharacteristic
181C2×C13#182811yescharacteristic
182C2×C13#182911yescharacteristic
183C24—22no—
184C24—22no—
185C24—81no—
186C24—81no—
187C24C2×#105512yes—
188C24#609912yes—
189C24C22⋊Dic1311yescharacteristic
190C24C22⋊Dic1311yescharacteristic
191C24C22×Dic1311yescharacteristic
192C22×C4—22no—
193C22×C4—22no—
194C22×C4—24no—
195C22×C4—24no—
196C22×C4—22no—
197C22×C4—81no—
198C22×C4—81no—
199C22×C4—81no—
200C22×C4—81no—
201C22×C4—81no—
202C22×C4—81no—
203C22×C4C22⋊Dic1312yes—
204C22×C4#612714yes—
205C22×C4C2×C22⋊D1312yes—
206C2×C8—524no—
207C2×C8—1044no—
208C22⋊C4—24no—
209C22⋊C4—24no—
210C22⋊C4—22no—
211C22⋊C4—22no—
212C22⋊C4—24no—
213C22⋊C4—24no—
214C22⋊C4C2×#105514yes—
215C22⋊C4#609914yes—
216C42—82no—
217C42—82no—
218C13#873411yescharacteristic, complemented, Sylow
219C23—21no—
220C23—21no—
221C23—21no—
222C23—21no—
223C23—24no—
224C23—24no—
225C23—41no—
226C23—41no—
227C23—41no—
228C23—41no—
229C23—41no—
230C23—41no—
231C23—82no—
232C23—82no—
233C23—82no—
234C23—82no—
235C23—84no—
236C23C22⋊#105512yes—
237C23C22⋊#105512yes—
238C23C22×#105511yescharacteristic
239C23C2×#609912yes—
240C23C2×#609911yescharacteristic
241C23#8818012yes—
242C23C2×C22⋊Dic1311yescharacteristic
243C2×C4—24no—
244C2×C4—24no—
245C2×C4—22no—
246C2×C4—42no—
247C2×C4—44no—
248C2×C4—42no—
249C2×C4—42no—
250C2×C4—42no—
251C2×C4—42no—
252C2×C4—42no—
253C2×C4—82no—
254C2×C4—84no—
255C2×C4—84no—
256C2×C4#8818314yes—
257C8—1044no—
258C22—21no—
259C22—22no—
260C22—21no—
261C22—22no—
262C22—22no—
263C22—22no—
264C22—41no—
265C22—41no—
266C22—42no—
267C22—42no—
268C22—42no—
269C22—42no—
270C22—42no—
271C22—41no—
272C22—41no—
273C22—41no—
274C22—41no—
275C22—84no—
276C22—84no—
277C22#1171858612yes—
278C22#1171858712yes—
279C22C2×C22⋊#105511yescharacteristic
280C22#1171886811yescharacteristic
281C22#1171887211yescharacteristic
282C4—24no—
283C4—44no—
284C4—44no—
285C4—42no—
286C2—21no—
287C2—21no—
288C2—22no—
289C2—22no—
290C2—42no—
291C2—42no—
292C2#1311490411yescharacteristic
293C2#1311494411yescharacteristic
294C2#1311494711yescharacteristic
subgroupG/H
centerC22#11718872
commutatorC23×C13C22×C8
FrattiniC23×C4C22×D13
FittingC13×#2273C2
socleC22×C13#381
prime radicalC25×C13C2×C4
cosocleC23×C4×C13C23
hypercenter#2273D13
hypocenterC13#8734
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2273

Complements

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

NH ≅ G/Ntype
2. #13112684C2semidirect
24. C2×C13×C22⋊C4C8semidirect
163. C2×C22⋊C4#1055semidirect
218. C13#8734semidirect

Maximal subgroups

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

subgroupindex
C2×#117181172
#131126842
C13×#22732
#873413