Finite Group Databasebeta

← #13073096

Subgroups — #13073096

Order 1408.

512 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 141 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×#66949C211yesmaximal, characteristic
2C2×C4⋊C4×D11C211yesmaximal, characteristic
3C11×#400C211yesmaximal, characteristic, complemented
4#10622599C211yesmaximal, characteristic, complemented
5#10622595C211yesmaximal, characteristic, complemented
6#10622279C211yesmaximal, characteristic
7#10622277C212yesmaximal
8#10622277C212yesmaximal
9#10622272C211yesmaximal, characteristic, complemented
10#10622263C212yesmaximal, complemented
11#10622259C212yesmaximal, complemented
12C22×C4×D11C2212yes—
13C22×C4×D11C2211yescharacteristic
14C22×Dic22C2211yescharacteristic
15C2×C11×C4⋊C4C2211yescharacteristic
16C2×C11×C4⋊C4C2211yescharacteristic
17C2×(C2×D11)⋊C4C2211yescharacteristic
18C2×(C2×D11)⋊C4C2211yescharacteristic
19C2×(C2×D11)⋊C4C2212yes—
20C2×C4⋊Dic11C2211yescharacteristic
21C2×Dic11⋊C4C2212yes—
22C2×Dic11⋊C4C2211yescharacteristic
23C2×Dic11⋊C4C2211yescharacteristic
24C2×C4×Dic11C2212yes—
25#66949—24no—
26C4⋊C4×D11—24no—
27C11×#95C2212yes—
28C11×#95C2212yes—
29C11×#95C2211yescharacteristic
30C11⋊#95C2212yes—
31C11⋊#95C2212yes—
32C11⋊#95C2212yes—
33C11⋊#95C2212yes—
34C11⋊#95C2212yes—
35C11⋊#95C2212yes—
36C11⋊#95C2211yescharacteristic
37C23×D11C2311yescharacteristic
38C22×C4×C11C2312yes—
39C22×C4×C11C2311yescharacteristic
40C22×C4×C11C2312yes—
41C22×C4×C11C2311yescharacteristic
42C22×C4×C11C2311yescharacteristic
43C22×Dic11C2312yes—
44C22×Dic11C2311yescharacteristic
45C22×Dic11C2312yes—
46C22×Dic11C2311yescharacteristic
47C22×Dic11C2311yescharacteristic
48C2×C4×D11—24no—
49C2×C4×D11—24no—
50C2×C4×D11—28no—
51C2×C4×D11D414yes—
52C2×Dic22—22no—
53C2×Dic22—24no—
54C11×C4⋊C4—22no—
55C11×C4⋊C4—22no—
56(C2×D11)⋊C4—22no—
57(C2×D11)⋊C4—22no—
58(C2×D11)⋊C4—24no—
59C4⋊Dic11—22no—
60Dic11⋊C4—24no—
61Dic11⋊C4—22no—
62Dic11⋊C4—22no—
63C4×Dic11—24no—
64#2503—111nomaximal, Sylow
65C23×C11C2411yescharacteristic
66C22×D11—22no—
67C22×D11—21no—
68C22×D11—21no—
69C22×D11C2×D412yes—
70C22×D11#4114yes—
71C2×C4×C11—22no—
72C2×C4×C11—21no—
73C2×C4×C11—22no—
74C2×C4×C11—21no—
75C2×C4×C11—22no—
76C2×C4×C11—22no—
77C2×C4×C11—22no—
78C2×C4×C11—24no—
79C2×C4×C11—21no—
80C2×C4×C11—21no—
81C2×C4×C11—22no—
82C2×C4×C11C2×D412yes—
83C2×Dic11—21no—
84C2×Dic11—22no—
85C2×Dic11—21no—
86C2×Dic11—22no—
87C2×Dic11—22no—
88C2×Dic11—22no—
89C2×Dic11—24no—
90C2×Dic11—21no—
91C2×Dic11—22no—
92C2×Dic11—21no—
93C2×Dic11C2×D412yes—
94C2×Dic11#4114yes—
95C4×D11—28no—
96C4×D11—48no—
97Dic22—44no—
98C2×C22⋊Q8—111no—
99C22×C4⋊C4—111no—
100#400—111no—
101#400—111no—
102#400—111no—
103#400D1111yescharacteristic, complemented
104#391—112no—
105#382—112no—
106#381—112no—
107#381—112no—
108C4×C22⋊C4—111no—
109C22×C11C22×D411yescharacteristic
110C22×C11C2×#4112yes—
111C22×C11C2×#4112yes—
112C22×C112−1+411yescharacteristic
113C22×C112−1+411yescharacteristic
114C2×D11—22no—
115C2×D11—22no—
116C2×D11—24no—
117C2×D11—24no—
118C2×D11#12414yes—
119C4×C11—22no—
120C4×C11—41no—
121C4×C11—42no—
122C4×C11—41no—
123C4×C11—42no—
124Dic11—41no—
125Dic11—42no—
126Dic11—41no—
127Dic11—42no—
128Dic11#12314yes—
129C22×Q8—111no—
130C23×C4—111no—
131C23×C4—112no—
132C22⋊Q8—224no—
133C2×C4⋊C4—112no—
134C2×C4⋊C4—111no—
135C2×C4⋊C4—111no—
136C2×C4⋊C4—111no—
137C2×C4⋊C4—224no—
138C2×C4⋊C4C2×D1111yescharacteristic
139C2×C4⋊C4C2×D1111yescharacteristic
140C2×C22⋊C4—111no—
141C2×C22⋊C4—111no—
142C2×C22⋊C4—112no—
143C2×C42—112no—
144#95—111no—
145#95—112no—
146#95—112no—
147#95—112no—
148#95—112no—
149#95—112no—
150#95—112no—
151#95C2×D1111yescharacteristic
152#95C2×D1112yes—
153#95C2×D1112yes—
154C2×C11C2×#12311yescharacteristic
155C2×C11C2×#12411yescharacteristic
156C2×C11#53611yescharacteristic
157C2×C11#55212yes—
158C2×C11#55212yes—
159D11—24no—
160C24—111no—
161C2×Q8—222no—
162C2×Q8—224no—
163C22×C4—111no—
164C22×C4—114no—
165C22×C4—112no—
166C22×C4—111no—
167C22×C4—111no—
168C22×C4—112no—
169C22×C4—224no—
170C22×C4—224no—
171C22×C4—228no—
172C22×C4C22×D1112yes—
173C22×C4C22×D1111yescharacteristic
174C22×C4C22×D1111yescharacteristic
175C22×C4C22×D1112yes—
176C22×C4C22×D1111yescharacteristic
177C4⋊C4—22no—
178C4⋊C4—22no—
179C4⋊C4—224no—
180C4⋊C4—222no—
181C4⋊C4—222no—
182C4⋊C4—222no—
183C22⋊C4—222no—
184C22⋊C4—222no—
185C22⋊C4—224no—
186C42—224no—
187C11#250311yescharacteristic, complemented, Sylow
188C23—112no—
189C23—114no—
190C23—221no—
191C23—222no—
192C23—221no—
193C23C23×D1111yescharacteristic
194Q8—444no—
195C2×C4—22no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—22no—
199C2×C4—21no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—24no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—21no—
206C2×C4—112no—
207C2×C4—114no—
208C2×C4—228no—
209C2×C4—221no—
210C2×C4—221no—
211C2×C4—222no—
212C2×C4—221no—
213C2×C4—222no—
214C2×C4—222no—
215C2×C4—222no—
216C2×C4—224no—
217C2×C4—222no—
218C2×C4—221no—
219C2×C4—448no—
220C2×C4D4×D1112yes—
221C22—114no—
222C22—224no—
223C22—222no—
224C22—222no—
225C22—224no—
226C22C2×D4×D1111yescharacteristic
227C22#6704011yescharacteristic
228C22#41×D1112yes—
229C22#41×D1112yes—
230C22#6704311yescharacteristic
231C4—22no—
232C4—42no—
233C4—41no—
234C4—41no—
235C4—42no—
236C4—114no—
237C4—441no—
238C4—441no—
239C4—442no—
240C4—442no—
241C2—224no—
242C2#1062315911yescharacteristic
243C2D11×#12311yescharacteristic
244C2D11×#12411yescharacteristic
245C2#1062322412yes—
246C2#1062323912yes—
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#400C2
prime radicalC23×D11C23
hypercenter#400D11
hypocenterC11#2503
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
3. C11×#400C2semidirect
4. #10622599C2semidirect
5. #10622595C2semidirect
9. #10622272C2semidirect
10. #10622263C2semidirect
11. #10622259C2semidirect
103. #400D11semidirect
187. C11#2503semidirect

Maximal subgroups

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

subgroupindex
C2×#669492
C2×C4⋊C4×D112
C11×#4002
#106225992
#106225952
#106222792
#106222772
#106222722
#106222632
#106222592
#250311