Finite Group Databasebeta

← #13076953

Subgroups — #13076953

Order 1408.

564 conjugacy classes of subgroups; only the 169 normal subgroups are shown.

normal subgroups only

This group has 564 conjugacy classes of subgroups — too many to draw. Only its 169 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
1C22×C4×Dic11C211yesmaximal, characteristic
2C2×#66931C211yesmaximal, characteristic
3C11×#381C211yesmaximal, characteristic
4#10622824C211yesmaximal, characteristic
5#10622563C211yesmaximal, characteristic
6#10622559C211yesmaximal, characteristic
7#10622555C211yesmaximal, characteristic
8#10622268C212yesmaximal, complemented
9#10622267C212yesmaximal, complemented
10#10622260C212yesmaximal, complemented
11#10622259C212yesmaximal, complemented
12C23×C4×C11C2211yescharacteristic
13C23×Dic11C2211yescharacteristic
14C23×Dic11C2211yescharacteristic
15C22×Dic22C2211yescharacteristic
16C2×C11×C22⋊C4C2211yescharacteristic
17C2×C11×C22⋊C4C2211yescharacteristic
18C2×C22⋊Dic11C2211yescharacteristic
19C2×C22⋊Dic11C2211yescharacteristic
20C2×C4⋊Dic11C2211yescharacteristic
21C2×C4⋊Dic11C2212yes—
22C2×Dic11⋊C4C2211yescharacteristic
23C2×Dic11⋊C4C2211yescharacteristic
24C2×Dic11⋊C4C2212yes—
25C2×Dic11⋊C4C2212yes—
26C2×C4×Dic11—24no—
27C2×C4×Dic11C2212yes—
28C2×C4×Dic11C2212yes—
29#66931—24no—
30C11×#95C2212yes—
31C11×#95C2212yes—
32C11⋊#95C2212yes—
33C11⋊#95C2212yes—
34C11⋊#95C2212yes—
35C11⋊#95C2212yes—
36C11⋊#95C2212yes—
37C24×C11C2311yescharacteristic
38C22×C4×C11—22no—
39C22×C4×C11—22no—
40C22×C4×C11Q814yescomplemented
41C22×C4×C11C2312yes—
42C22×C4×C11C2311yescharacteristic
43C22×C4×C11C2311yescharacteristic
44C22×C4×C11C2312yes—
45C22×Dic11—24no—
46C22×Dic11—24no—
47C22×Dic11—22no—
48C22×Dic11D414yes—
49C22×Dic11C2312yes—
50C22×Dic11C2311yescharacteristic
51C22×Dic11C2311yescharacteristic
52C22×Dic11C2311yescharacteristic
53C22×Dic11C2312yes—
54C22×Dic11C2311yescharacteristic
55C2×Dic22—22no—
56C2×Dic22—24no—
57C11×C22⋊C4—22no—
58C11×C22⋊C4—22no—
59C22⋊Dic11—22no—
60C22⋊Dic11—22no—
61C4⋊Dic11—22no—
62C4⋊Dic11—24no—
63Dic11⋊C4—22no—
64Dic11⋊C4—22no—
65Dic11⋊C4—24no—
66Dic11⋊C4—24no—
67C4×Dic11—24no—
68C4×Dic11—24no—
69#2855—111nomaximal, Sylow
70C23×C11—22no—
71C23×C11—22no—
72C23×C11C2×D412yes—
73C23×C11C2×Q812yes—
74C23×C11#4112yes—
75C23×C11C2411yescharacteristic
76C2×C4×C11—28no—
77C2×C4×C11—22no—
78C2×C4×C11—22no—
79C2×C4×C11—21no—
80C2×C4×C11—21no—
81C2×C4×C11—22no—
82C2×C4×C11—22no—
83C2×C4×C11—22no—
84C2×C4×C11—22no—
85C2×C4×C11—22no—
86C2×C4×C11C2×Q814yes—
87C2×Dic11—28no—
88C2×Dic11—22no—
89C2×Dic11—22no—
90C2×Dic11—22no—
91C2×Dic11—28no—
92C2×Dic11—21no—
93C2×Dic11—21no—
94C2×Dic11—22no—
95C2×Dic11—22no—
96C2×Dic11—22no—
97C2×Dic11—22no—
98C2×Dic11—22no—
99C2×Dic11C2×D412yes—
100C2×Dic11C2×D412yes—
101C2×Dic11#4114yes—
102C2×Dic11#4114yes—
103Dic22—44no—
104C2×C22⋊Q8—111no—
105C22×C42—111no—
106#391—112no—
107#389—112no—
108#387—112no—
109#387—112no—
110#385—111no—
111#385—111no—
112#381—111no—
113#381D1111yescharacteristic
114#380—111no—
115C22×C11—22no—
116C22×C11—22no—
117C22×C11—24no—
118C22×C11—24no—
119C22×C11C22⋊Q814yes—
120C22×C11C22×D411yescharacteristic
121C22×C11C22×Q811yescharacteristic
122C22×C11C2×#4111yescharacteristic
123C22×C11C2×#4112yes—
124C22×C11C2×#4112yes—
125C4×C11—24no—
126C4×C11—41no—
127C4×C11—41no—
128C4×C11—42no—
129Dic11—22no—
130Dic11—24no—
131Dic11—41no—
132Dic11—41no—
133Dic11—42no—
134Dic11#12314yes—
135C22×Q8—111no—
136C23×C4—111no—
137C23×C4—111no—
138C23×C4C2×D1111yescharacteristic
139C22⋊Q8—224no—
140C2×C4⋊C4—111no—
141C2×C4⋊C4—111no—
142C2×C4⋊C4—111no—
143C2×C4⋊C4—112no—
144C2×C4⋊C4—112no—
145C2×C4⋊C4—112no—
146C2×C22⋊C4—111no—
147C2×C22⋊C4—111no—
148C2×C22⋊C4C2×D1111yescharacteristic
149C2×C22⋊C4C2×D1111yescharacteristic
150C2×C42—112no—
151C2×C42—112no—
152C2×C42—224no—
153#95—112no—
154#95—112no—
155#95—112no—
156#95—112no—
157#95—112no—
158#95C2×D1112yes—
159#95C2×D1112yes—
160C2×C11—24no—
161C2×C11C2×C22⋊Q811yescharacteristic
162C2×C11C2×#12311yescharacteristic
163C2×C11#52511yescharacteristic
164C2×C11#52912yes—
165C2×C11#53312yes—
166C24C22×D1111yescharacteristic
167C2×Q8—222no—
168C2×Q8—224no—
169C22×C4—22no—
170C22×C4—22no—
171C22×C4—111no—
172C22×C4—114no—
173C22×C4—111no—
174C22×C4—112no—
175C22×C4—112no—
176C22×C4—111no—
177C22×C4—111no—
178C22×C4—224no—
179C22×C4—224no—
180C22×C4—222no—
181C22×C4Dic2214yescomplemented
182C22×C4C22×D1112yes—
183C22×C4C22×D1111yescharacteristic
184C22×C4C22×D1111yescharacteristic
185C22×C4C22×D1112yes—
186C4⋊C4—222no—
187C4⋊C4—222no—
188C4⋊C4—222no—
189C4⋊C4—224no—
190C4⋊C4—224no—
191C4⋊C4—224no—
192C22⋊C4—22no—
193C22⋊C4—22no—
194C22⋊C4—222no—
195C22⋊C4—222no—
196C42—224no—
197C42—224no—
198C11#285511yescharacteristic, complemented, Sylow
199C23—22no—
200C23—22no—
201C23C2×Dic2212yes—
202C23D4×D1112yes—
203C23#434112yes—
204C23C23×D1111yescharacteristic
205Q8—444no—
206C2×C4—28no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—112no—
217C2×C4—114no—
218C2×C4—112no—
219C2×C4—114no—
220C2×C4—228no—
221C2×C4—228no—
222C2×C4—222no—
223C2×C4—222no—
224C2×C4—222no—
225C2×C4—221no—
226C2×C4—221no—
227C2×C4—222no—
228C2×C4—222no—
229C2×C4—222no—
230C2×C4—222no—
231C2×C4—222no—
232C2×C4C2×Dic2214yes—
233C22—24no—
234C22—24no—
235C22—22no—
236C22—22no—
237C22#6693114yes—
238C22C22×Dic2211yescharacteristic
239C22C2×D4×D1111yescharacteristic
240C22C2×#434111yescharacteristic
241C22#41×D1112yes—
242C22#41×D1112yes—
243C4—24no—
244C4—42no—
245C4—41no—
246C4—41no—
247C4—114no—
248C4—222no—
249C4—224no—
250C4—442no—
251C4—441no—
252C4—441no—
253C2—24no—
254C2C2×#6693111yescharacteristic
255C2#1062304812yes—
256C2#1062318012yes—
257C2D11×#12311yescharacteristic
258C2#1062318711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#381C2
prime radicalC24×C11C23
hypercenter#381D11
hypocenterC11#2855
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
8. #10622268C2semidirect
9. #10622267C2semidirect
10. #10622260C2semidirect
11. #10622259C2semidirect
40. C22×C4×C11Q8semidirect
181. C22×C4Dic22semidirect
198. C11#2855semidirect

Maximal subgroups

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

subgroupindex
C22×C4×Dic112
C2×#669312
C11×#3812
#106228242
#106225632
#106225592
#106225552
#106222682
#106222672
#106222602
#106222592
#285511