Finite Group Databasebeta

← #13075633

Subgroups — #13075633

Order 1408.

528 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 149 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×#66931C212yesmaximal, complemented
2C11×#390C211yesmaximal, characteristic
3#10622833C212yesmaximal
4#10622597C212yesmaximal, complemented
5#10622563C212yesmaximal, complemented
6#10622562C212yesmaximal, complemented
7#10622561C212yesmaximal, complemented
8#10622542C211yesmaximal, characteristic, complemented
9#10622541C211yesmaximal, characteristic, complemented
10C22×D4×C11C2211yescharacteristic
11C23×Dic11C2212yes—
12C22×Dic22C2211yescharacteristic
13C2×C11×C4⋊C4C2211yescharacteristic
14C2×C11×C22⋊C4C2212yes—
15C2×C11×C22⋊C4C2212yes—
16C2×C42×C11C2211yescharacteristic
17C2×C22⋊Dic11C2212yes—
18C2×C22⋊Dic11C2212yes—
19C2×C22⋊Dic11C2212yes—
20C2×C4⋊Dic11C2212yes—
21C2×C4⋊Dic11C2211yescharacteristic
22C2×C4⋊Dic11C2211yescharacteristic
23C2×C4⋊Dic11C2211yescharacteristic
24C2×Dic11⋊C4C2212yes—
25C2×Dic11⋊C4C2212yes—
26C2×Dic11⋊C4C2212yes—
27#66931—28no—
28C11⋊#95C2212yes—
29C11⋊#95C2212yes—
30C11⋊#95C2212yes—
31C11⋊#95C2212yes—
32C24×C11C2312yes—
33C2×D4×C11—41no—
34C2×D4×C11—41no—
35C2×D4×C11Q814yescomplemented
36C22×C4×C11C2312yes—
37C22×C4×C11C2311yescharacteristic
38C22×C4×C11C2311yescharacteristic
39C22×C4×C11C2311yescharacteristic
40C22×Dic11—24no—
41C22×Dic11—42no—
42C22×Dic11—42no—
43C22×Dic11C2312yes—
44C22×Dic11C2312yes—
45C22×Dic11C2312yes—
46C22×Dic11C2312yes—
47C2×Dic22—41no—
48C2×Dic22—41no—
49C2×Dic22D414yescomplemented
50C11×C4⋊C4—41no—
51C11×C22⋊C4—24no—
52C11×C22⋊C4—24no—
53C42×C11—41no—
54C22⋊Dic11—24no—
55C22⋊Dic11—42no—
56C22⋊Dic11—42no—
57C4⋊Dic11—24no—
58C4⋊Dic11—22no—
59C4⋊Dic11—41no—
60C4⋊Dic11—41no—
61Dic11⋊C4—24no—
62Dic11⋊C4—24no—
63Dic11⋊C4—42no—
64#2732—111nomaximal, Sylow
65C23×C11—22no—
66C23×C11—22no—
67C23×C11—22no—
68C23×C11—22no—
69C23×C11—22no—
70C23×C11—22no—
71C23×C11C2×Q814yes—
72C23×C11C2411yescharacteristic
73D4×C11—44no—
74C2×C4×C11—21no—
75C2×C4×C11—21no—
76C2×C4×C11—21no—
77C2×C4×C11—21no—
78C2×C4×C11—21no—
79C2×C4×C11—21no—
80C2×C4×C11—22no—
81C2×C4×C11—22no—
82C2×C4×C11—22no—
83C2×C4×C11C2×D412yes—
84C2×C4×C11C2×Q812yes—
85C2×C4×C11#4112yes—
86C2×Dic11—22no—
87C2×Dic11—22no—
88C2×Dic11—22no—
89C2×Dic11—22no—
90C2×Dic11—22no—
91C2×Dic11—22no—
92C2×Dic11—22no—
93C2×Dic11—22no—
94C2×Dic11—22no—
95C2×Dic11—22no—
96C2×Dic11—22no—
97C2×Dic11—48no—
98C2×Dic11C2×D414yes—
99Dic22—44no—
100C2×C22⋊Q8—112no—
101#399—112no—
102#398—112no—
103#396—112no—
104#391—111no—
105#390D1111yescharacteristic
106#389—111no—
107#386—112no—
108#385—112no—
109C22×C11—24no—
110C22×C11—24no—
111C22×C11—24no—
112C22×C11—42no—
113C22×C11—42no—
114C22×C11—42no—
115C22×C11—42no—
116C22×C11C22×D411yescharacteristic
117C22×C11C22×Q811yescharacteristic
118C22×C11C2×#4111yescharacteristic
119C22×C11H(5,𝔽2)11yescharacteristic
120C22×C11H(5,𝔽2)11yescharacteristic
121C22×C11H(5,𝔽2)11yescharacteristic
122C22×C112−1+411yescharacteristic
123C4×C11—22no—
124C4×C11—22no—
125C4×C11—22no—
126C4×C11—42no—
127Dic11—24no—
128Dic11—42no—
129Dic11—42no—
130Dic11—42no—
131C22×Q8—111no—
132C22×D4C2×D1111yescharacteristic
133C23×C4—112no—
134C22⋊Q8—228no—
135C2×C4⋊C4—112no—
136C2×C4⋊C4—112no—
137C2×C4⋊C4—112no—
138C2×C4⋊C4—111no—
139C2×C4⋊C4—111no—
140C2×C4⋊C4—111no—
141C2×C4⋊C4—112no—
142C2×C4⋊C4C2×D1111yescharacteristic
143C2×C22⋊C4—112no—
144C2×C22⋊C4—112no—
145C2×C22⋊C4—112no—
146C2×C22⋊C4C2×D1112yes—
147C2×C22⋊C4C2×D1112yes—
148C2×C42C2×D1111yescharacteristic
149#95—112no—
150#95—112no—
151#95—112no—
152#95—112no—
153C2×C11—44no—
154C2×C11#53411yescharacteristic
155C2×C11#53911yescharacteristic
156C2×C11#54311yescharacteristic
157C2×C11D4×Q811yescharacteristic
158C2×C11#55011yescharacteristic
159C2×C11#55411yescharacteristic
160C2×C11#56211yescharacteristic
161C24C22×D1112yes—
162C2×Q8—114no—
163C2×Q8—441no—
164C2×Q8—441no—
165C2×D4—41no—
166C2×D4—41no—
167C2×D4Dic2214yescomplemented
168C22×C4—112no—
169C22×C4—112no—
170C22×C4—112no—
171C22×C4—112no—
172C22×C4—224no—
173C22×C4—442no—
174C22×C4—442no—
175C22×C4C22×D1112yes—
176C22×C4C22×D1111yescharacteristic
177C22×C4C22×D1111yescharacteristic
178C22×C4C22×D1111yescharacteristic
179C4⋊C4—41no—
180C4⋊C4—224no—
181C4⋊C4—224no—
182C4⋊C4—224no—
183C4⋊C4—222no—
184C4⋊C4—442no—
185C4⋊C4—441no—
186C4⋊C4—441no—
187C22⋊C4—24no—
188C22⋊C4—24no—
189C22⋊C4—224no—
190C22⋊C4—442no—
191C22⋊C4—442no—
192C42—41no—
193C11#273211yescharacteristic, complemented, Sylow
194C23—22no—
195C23—22no—
196C23—22no—
197C23—22no—
198C23—22no—
199C23—22no—
200C23C2×Dic2214yes—
201C23C23×D1111yescharacteristic
202Q8—444no—
203D4—44no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—114no—
214C2×C4—222no—
215C2×C4—222no—
216C2×C4—222no—
217C2×C4—222no—
218C2×C4—222no—
219C2×C4—222no—
220C2×C4—222no—
221C2×C4—222no—
222C2×C4—222no—
223C2×C4—222no—
224C2×C4—222no—
225C2×C4—448no—
226C2×C4C2×Dic2212yes—
227C2×C4D4×D1112yes—
228C2×C4#434112yes—
229C22—24no—
230C22—24no—
231C22—24no—
232C22—42no—
233C22—42no—
234C22—42no—
235C22—42no—
236C22C22×Dic2211yescharacteristic
237C22C2×D4×D1111yescharacteristic
238C22C2×#434111yescharacteristic
239C22#6703711yescharacteristic
240C22#6703711yescharacteristic
241C22#6704211yescharacteristic
242C22#6704311yescharacteristic
243C4—22no—
244C4—22no—
245C4—22no—
246C4—42no—
247C4—224no—
248C4—442no—
249C4—442no—
250C4—442no—
251C2—44no—
252C2#1062301411yescharacteristic
253C2D4×Dic2211yescharacteristic
254C2#1062307411yescharacteristic
255C2#1062313311yescharacteristic
256C2#1062313611yescharacteristic
257C2#1062321511yescharacteristic
258C2#1062324911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#390C2
prime radicalC22×D4×C11C22
hypercenter#390D11
hypocenterC11#2732
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
1. C2×#66931C2semidirect
4. #10622597C2semidirect
5. #10622563C2semidirect
6. #10622562C2semidirect
7. #10622561C2semidirect
8. #10622542C2semidirect
9. #10622541C2semidirect
35. C2×D4×C11Q8semidirect
49. C2×Dic22D4semidirect
167. C2×D4Dic22semidirect
193. C11#2732semidirect

Maximal subgroups

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

subgroupindex
C2×#669312
C11×#3902
#106228332
#106225972
#106225632
#106225622
#106225612
#106225422
#106225412
#273211