Finite Group Databasebeta

← #13074990

Subgroups — #13074990

Order 1408.

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

normal subgroups only

This group has 592 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×#66999C212yesmaximal, complemented
2C2×#66949C212yesmaximal, complemented
3C11×#395C211yesmaximal, characteristic, complemented
4#10622607C212yesmaximal, complemented
5#10622601C211yesmaximal, characteristic
6#10622592C211yesmaximal, characteristic, complemented
7#10622289C212yesmaximal, complemented
8#10622278C212yesmaximal
9#10622260C212yesmaximal, complemented
10C22×Q8×C11C2211yescharacteristic
11C22×D44C2211yescharacteristic
12C22×C4×D11C2212yes—
13C22×Dic22C2211yescharacteristic
14C2×C11×C4⋊C4C2212yes—
15C2×C11×C4⋊C4C2211yescharacteristic
16#66999—28no—
17C2×(C2×D11)⋊C4C2212yes—
18C2×(C2×D11)⋊C4C2212yes—
19C2×(C2×D11)⋊C4C2212yes—
20C2×(C2×D11)⋊C4C2212yes—
21C2×(C2×D11)⋊C4C2212yes—
22C2×C4⋊Dic11C2212yes—
23C2×Dic11⋊C4C2212yes—
24C2×Dic11⋊C4C2212yes—
25C2×Dic11⋊C4C2212yes—
26C2×Dic11⋊C4C2212yes—
27C2×C4×Dic11C2211yescharacteristic
28#66949—28no—
29C11×#95C2212yes—
30C11×#95C2211yescharacteristic
31C11⋊#95C2212yes—
32C11⋊#95C2211yescharacteristic
33C23×D11C2312yes—
34C2×Q8×C11—24no—
35C2×Q8×C11—41no—
36C22×C4×C11C2311yescharacteristic
37C22×C4×C11C2312yes—
38C22×C4×C11C2311yescharacteristic
39C22×C4×C11C2312yes—
40C22×C4×C11C2311yescharacteristic
41C22×Dic11C2312yes—
42C22×Dic11C2312yes—
43C22×Dic11C2312yes—
44C2×D44—41no—
45C2×D44—41no—
46C2×D44Q814yescomplemented
47C2×C4×D11—24no—
48C2×C4×D11—24no—
49C2×C4×D11—42no—
50C2×Dic22—24no—
51C2×Dic22—41no—
52C11×C4⋊C4—24no—
53C11×C4⋊C4—41no—
54(C2×D11)⋊C4—24no—
55(C2×D11)⋊C4—24no—
56(C2×D11)⋊C4—24no—
57(C2×D11)⋊C4—24no—
58(C2×D11)⋊C4—42no—
59C4⋊Dic11—24no—
60Dic11⋊C4—24no—
61Dic11⋊C4—24no—
62Dic11⋊C4—42no—
63Dic11⋊C4D418yescomplemented
64C4×Dic11—41no—
65#2683—111nomaximal, Sylow
66C23×C11C2411yescharacteristic
67C22×D11—22no—
68C22×D11—22no—
69C22×D11—22no—
70C22×D11—22no—
71C22×D11—22no—
72C22×D11—22no—
73C22×D11C2×Q814yes—
74Q8×C11—44no—
75C2×C4×C11—22no—
76C2×C4×C11—21no—
77C2×C4×C11—21no—
78C2×C4×C11—22no—
79C2×C4×C11—22no—
80C2×C4×C11—22no—
81C2×C4×C11—22no—
82C2×C4×C11—22no—
83C2×C4×C11—21no—
84C2×C4×C11—21no—
85C2×C4×C11—22no—
86C2×C4×C11C2×D414yes—
87C2×C4×C11C2×Q812yes—
88C2×Dic11—22no—
89C2×Dic11—22no—
90C2×Dic11—22no—
91C2×Dic11—22no—
92C2×Dic11—22no—
93C2×Dic11—22no—
94C2×Dic11—22no—
95C2×Dic11C2×D414yes—
96C2×Dic11C2×D414yes—
97D44—44no—
98C4×D11—48no—
99Dic22—44no—
100C2×C22⋊Q8—112no—
101C2×C22⋊Q8—112no—
102#396—112no—
103#396—112no—
104#395—111no—
105#395D1111yescharacteristic, complemented
106#390—111no—
107#389—112no—
108#386—112no—
109C22×C11C22×D412yes—
110C22×C11C22×Q811yescharacteristic
111C22×C11H(5,𝔽2)11yescharacteristic
112C22×C11H(5,𝔽2)11yescharacteristic
113C22×C112−1+412yes—
114C2×D11—24no—
115C2×D11—24no—
116C2×D11—24no—
117C2×D11—42no—
118C2×D11—42no—
119C2×D11—42no—
120C2×D11—42no—
121C4×C11—22no—
122C4×C11—24no—
123C4×C11—42no—
124C4×C11—41no—
125C4×C11—41no—
126Dic11—24no—
127Dic11—24no—
128Dic11—42no—
129C22×Q8—111no—
130C22×Q8C2×D1111yescharacteristic
131C22×D4—111no—
132C23×C4—112no—
133C22⋊Q8—228no—
134C22⋊Q8—228no—
135C2×C4⋊C4—112no—
136C2×C4⋊C4—112no—
137C2×C4⋊C4—112no—
138C2×C4⋊C4—112no—
139C2×C4⋊C4—112no—
140C2×C4⋊C4C2×D1112yes—
141C2×C4⋊C4C2×D1111yescharacteristic
142C2×C22⋊C4—112no—
143C2×C22⋊C4—112no—
144C2×C22⋊C4—112no—
145C2×C22⋊C4—112no—
146C2×C22⋊C4—112no—
147C2×C42—111no—
148#95—112no—
149#95—111no—
150#95C2×D1112yes—
151#95C2×D1111yescharacteristic
152C2×C11#53712yes—
153C2×C11#54311yescharacteristic
154C2×C11D4211yescharacteristic
155C2×C11D4×Q812yes—
156C2×C11#56311yescharacteristic
157D11—44no—
158C24—112no—
159C2×Q8—24no—
160C2×Q8—41no—
161C2×Q8—224no—
162C2×Q8—441no—
163C2×D4—114no—
164C2×D4—441no—
165C2×D4—441no—
166C22×C4—112no—
167C22×C4—112no—
168C22×C4—112no—
169C22×C4—224no—
170C22×C4—224no—
171C22×C4—442no—
172C22×C4C22×D1111yescharacteristic
173C22×C4C22×D1112yes—
174C22×C4C22×D1111yescharacteristic
175C22×C4C22×D1112yes—
176C22×C4C22×D1111yescharacteristic
177C4⋊C4—24no—
178C4⋊C4—41no—
179C4⋊C4—118no—
180C4⋊C4—224no—
181C4⋊C4—224no—
182C4⋊C4—224no—
183C4⋊C4—442no—
184C22⋊C4—224no—
185C22⋊C4—224no—
186C22⋊C4—224no—
187C22⋊C4—224no—
188C22⋊C4—442no—
189C42—441no—
190C11#268311yescharacteristic, complemented, Sylow
191C23—114no—
192C23—222no—
193C23—222no—
194C23—222no—
195C23—222no—
196C23—222no—
197C23—222no—
198C23C23×D1111yescharacteristic
199Q8—44no—
200Q8—444no—
201D4—444no—
202C2×C4—22no—
203C2×C4—21no—
204C2×C4—22no—
205C2×C4—21no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—114no—
214C2×C4—114no—
215C2×C4—222no—
216C2×C4—222no—
217C2×C4—222no—
218C2×C4—222no—
219C2×C4—222no—
220C2×C4—222no—
221C2×C4—222no—
222C2×C4—448no—
223C2×C4D4×D1114yes—
224C2×C4Q8×D1112yes—
225C22—224no—
226C22—224no—
227C22—224no—
228C22—442no—
229C22—442no—
230C22—442no—
231C22—442no—
232C22C2×D4×D1112yes—
233C22#6703711yescharacteristic
234C22C2×Q8×D1111yescharacteristic
235C22#6704012yes—
236C22#6704211yescharacteristic
237C4—24no—
238C4—22no—
239C4—41no—
240C4—41no—
241C4—42no—
242C4—224no—
243C4—224no—
244C4—442no—
245C2—444no—
246C2#1062312111yescharacteristic
247C2#1062316012yes—
248C2#1062316511yescharacteristic
249C2#1062325812yes—
250C2#1062326611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#395C2
prime radicalC22×D44C22
hypercenter#395D11
hypocenterC11#2683
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
1. C2×#66999C2semidirect
2. C2×#66949C2semidirect
3. C11×#395C2semidirect
4. #10622607C2semidirect
6. #10622592C2semidirect
7. #10622289C2semidirect
9. #10622260C2semidirect
46. C2×D44Q8semidirect
63. Dic11⋊C4D4semidirect
105. #395D11semidirect
190. C11#2683semidirect

Maximal subgroups

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

subgroupindex
C2×#669992
C2×#669492
C11×#3952
#106226072
#106226012
#106225922
#106222892
#106222782
#106222602
#268311