Finite Group Databasebeta

← #13074186

Subgroups — #13074186

Order 1408.

492 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 139 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×Q8×Dic11C211yesmaximal, characteristic, complemented
2C2×#66930C211yesmaximal, characteristic
3C11×#393C211yesmaximal, characteristic
4#10622842C211yesmaximal, characteristic, complemented
5#10622566C211yesmaximal, characteristic
6#10622563C212yesmaximal
7#10622558C212yesmaximal
8#10622274C211yesmaximal, characteristic, complemented
9#10622268C212yesmaximal, complemented
10#10622267C212yesmaximal, complemented
11#10622264C211yesmaximal, characteristic, complemented
12C22×Q8×C11C2211yescharacteristic
13C23×Dic11C2211yescharacteristic
14C2×C11×C22⋊C4C2211yescharacteristic
15C2×C11×C22⋊C4C2212yes—
16C2×C22⋊Dic11C2211yescharacteristic
17C2×C22⋊Dic11C2212yes—
18Q8×Dic11—24no—
19C2×C4⋊Dic11C2212yes—
20C2×C4⋊Dic11C2212yes—
21C2×C4⋊Dic11C2211yescharacteristic
22C2×Dic11⋊C4C2211yescharacteristic
23C2×Dic11⋊C4C2211yescharacteristic
24C2×Dic11⋊C4C2212yes—
25C2×C4×Dic11C2211yescharacteristic
26C2×C4×Dic11C2212yes—
27C2×C4×Dic11C2211yescharacteristic
28#66930—24no—
29C11×#95C2211yescharacteristic
30C11×#95C2212yes—
31C11⋊#95C2212yes—
32C11⋊#95C2212yes—
33C11⋊#95C2211yescharacteristic
34C11⋊#95C2212yes—
35C11⋊#95C2212yes—
36C11⋊#95C2212yes—
37C24×C11C2311yescharacteristic
38C2×Q8×C11—22no—
39C2×Q8×C11—24no—
40C22×C4×C11C2312yes—
41C22×C4×C11C2311yescharacteristic
42C22×C4×C11C2311yescharacteristic
43C22×C4×C11C2312yes—
44C22×Dic11—22no—
45C22×Dic11—22no—
46C22×Dic11—22no—
47C22×Dic11C2312yes—
48C22×Dic11C2311yescharacteristic
49C22×Dic11C2312yes—
50C22×Dic11C2311yescharacteristic
51C22×Dic11C2311yescharacteristic
52C22×Dic11C2311yescharacteristic
53C11×C22⋊C4—22no—
54C11×C22⋊C4—24no—
55C22⋊Dic11—22no—
56C22⋊Dic11—24no—
57C4⋊Dic11—24no—
58C4⋊Dic11—24no—
59C4⋊Dic11—22no—
60Dic11⋊C4—22no—
61Dic11⋊C4—22no—
62Dic11⋊C4—24no—
63C4×Dic11—22no—
64C4×Dic11—24no—
65C4×Dic11D414yes—
66#2599—111nomaximal, Sylow
67C23×C11—21no—
68C23×C11—22no—
69C23×C11—21no—
70C23×C11—22no—
71C23×C11#4112yes—
72C23×C11C2411yescharacteristic
73Q8×C11—28no—
74C2×C4×C11—22no—
75C2×C4×C11—22no—
76C2×C4×C11—22no—
77C2×C4×C11—21no—
78C2×C4×C11—22no—
79C2×C4×C11—22no—
80C2×C4×C11—22no—
81C2×C4×C11—22no—
82C2×C4×C11C2×D412yes—
83C2×C4×C11#4114yes—
84C2×Dic11—28no—
85C2×Dic11—21no—
86C2×Dic11—21no—
87C2×Dic11—21no—
88C2×Dic11—21no—
89C2×Dic11—22no—
90C2×Dic11—21no—
91C2×Dic11—22no—
92C2×Dic11—22no—
93C2×Dic11—22no—
94C2×Dic11—22no—
95C2×Dic11—22no—
96C2×Dic11—22no—
97C2×Dic11—22no—
98C2×Dic11C2×D412yes—
99C2×Dic11C2×D412yes—
100C2×Dic11#4112yes—
101C2×C4×Q8—111no—
102C2×#117—111no—
103#398—111no—
104#397—111no—
105#395—111no—
106#393D1111yescharacteristic
107#388—112no—
108#387—112no—
109#387—112no—
110#385—112no—
111#383—111no—
112C22×C11—22no—
113C22×C11—24no—
114C22×C11—41no—
115C22×C11—41no—
116C22×C11—42no—
117C22×C11C22×D411yescharacteristic
118C22×C11C2×#4112yes—
119C22×C11C2×#4111yescharacteristic
120C22×C11C2×#4111yescharacteristic
121C22×C112−1+412yes—
122C4×C11—22no—
123C4×C11—24no—
124C4×C11—41no—
125C4×C11—42no—
126Dic11—22no—
127Dic11—22no—
128Dic11—22no—
129Dic11—41no—
130Dic11—42no—
131Dic11—42no—
132C22×Q8C2×D1111yescharacteristic
133C23×C4—111no—
134C4×Q8—224no—
135#117—224no—
136C2×C4⋊C4—111no—
137C2×C4⋊C4—111no—
138C2×C4⋊C4—112no—
139C2×C4⋊C4—111no—
140C2×C4⋊C4—112no—
141C2×C4⋊C4—112no—
142C2×C22⋊C4—111no—
143C2×C22⋊C4—112no—
144C2×C22⋊C4C2×D1111yescharacteristic
145C2×C22⋊C4C2×D1112yes—
146C2×C42—111no—
147C2×C42—111no—
148C2×C42—112no—
149#95—112no—
150#95—112no—
151#95—111no—
152#95—112no—
153#95—112no—
154#95—112no—
155#95C2×D1111yescharacteristic
156#95C2×D1112yes—
157C2×C11—42no—
158C2×C11#52511yescharacteristic
159C2×C11#52511yescharacteristic
160C2×C11#53611yescharacteristic
161C2×C11#55212yes—
162C2×C11#55612yes—
163C24C22×D1111yescharacteristic
164C2×Q8—22no—
165C2×Q8—24no—
166C22×C4—111no—
167C22×C4—111no—
168C22×C4—111no—
169C22×C4—112no—
170C22×C4—111no—
171C22×C4—112no—
172C22×C4—222no—
173C22×C4—222no—
174C22×C4—222no—
175C22×C4C22×D1112yes—
176C22×C4C22×D1111yescharacteristic
177C22×C4C22×D1111yescharacteristic
178C22×C4C22×D1112yes—
179C4⋊C4—222no—
180C4⋊C4—224no—
181C4⋊C4—224no—
182C4⋊C4—222no—
183C4⋊C4—222no—
184C4⋊C4—224no—
185C22⋊C4—22no—
186C22⋊C4—24no—
187C22⋊C4—222no—
188C22⋊C4—224no—
189C42—114no—
190C42—222no—
191C42—224no—
192C11#259911yescharacteristic, complemented, Sylow
193C23—21no—
194C23—22no—
195C23—21no—
196C23—22no—
197C23#434312yes—
198C23C23×D1111yescharacteristic
199Q8—28no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—21no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—112no—
209C2×C4—112no—
210C2×C4—112no—
211C2×C4—228no—
212C2×C4—221no—
213C2×C4—221no—
214C2×C4—221no—
215C2×C4—221no—
216C2×C4—222no—
217C2×C4—221no—
218C2×C4—222no—
219C2×C4—222no—
220C2×C4—222no—
221C2×C4—222no—
222C2×C4—222no—
223C2×C4—222no—
224C2×C4—222no—
225C2×C4D4×D1112yes—
226C2×C4#434114yes—
227C22—22no—
228C22—24no—
229C22—41no—
230C22—42no—
231C22—41no—
232C22C2×D4×D1111yescharacteristic
233C22C2×#434112yes—
234C22C2×#434311yescharacteristic
235C22#41×D1111yescharacteristic
236C22#6704312yes—
237C4—22no—
238C4—24no—
239C4—42no—
240C4—41no—
241C4—222no—
242C4—222no—
243C4—222no—
244C4—441no—
245C4—442no—
246C4—442no—
247C2—42no—
248C2#1062311711yescharacteristic
249C2#1062315811yescharacteristic
250C2#1062317312yes—
251C2#1062320212yes—
252C2#1062320611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#393C2
prime radicalC24×C11C23
hypercenter#393D11
hypocenterC11#2599
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #393

Complements

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

NH ≅ G/Ntype
1. C2×Q8×Dic11C2semidirect
4. #10622842C2semidirect
8. #10622274C2semidirect
9. #10622268C2semidirect
10. #10622267C2semidirect
11. #10622264C2semidirect
192. C11#2599semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×Dic112
C2×#669302
C11×#3932
#106228422
#106225662
#106225632
#106225582
#106222742
#106222682
#106222672
#106222642
#259911