Finite Group Databasebeta

← #13069639

Subgroups — #13069639

Order 1408.

382 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 73 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×#66989C211yesmaximal, characteristic, complemented
2C2×#66985C211yesmaximal, characteristic
3#10623057C211yesmaximal, characteristic, complemented
4C11×#418C211yesmaximal, characteristic, complemented
5C2×#66889C211yesmaximal, characteristic, complemented
6C2×#66888C211yesmaximal, characteristic, complemented
7#10622170C211yesmaximal, characteristic, complemented
8C22×D4×C11C2211yescharacteristic
9C2×#4339C2211yescharacteristic
10C22×Dic22C2211yescharacteristic
11C2×C11×M16C2211yescharacteristic
12C11×#117C2211yescharacteristic
13C2×C22⋊Dic11—22no—
14#66989—22no—
15#66989—22no—
16C2×#4324—21no—
17#66985—22no—
18#66985—22no—
19C2×#4323—21no—
20C2×C4×Dic11C2211yescharacteristic
21C2×#4318C2211yescharacteristic
22#66950—22no—
23#66939—22no—
24#66928—21no—
25#66922—21no—
26C11×#102—22no—
27#66889—22no—
28#66888—22no—
29C24×C11—21no—
30C2×D4×C11—21no—
31C2×D4×C11—21no—
32C2×D4×C11—21no—
33C2×D4×C11—21no—
34C2×D4×C11—21no—
35C2×D4×C11D412yes—
36C22×C4×C11C2311yescharacteristic
37C2×C22⋊D11—21no—
38C22×Dic11—21no—
39C22×Dic11D412yes—
40#4339—21no—
41#4339—21no—
42#4339—21no—
43#4339—21no—
44C2×D44D411yescharacteristic
45C2×C4×D11—21no—
46C2×Dic22—21no—
47C2×Dic22—21no—
48C2×Dic22—21no—
49C2×Dic22—21no—
50C2×Dic22—21no—
51C2×Dic22—21no—
52C2×Dic22D411yescharacteristic
53C11×M16—21no—
54C11×M16—21no—
55C2×C8×C11—21no—
56C11×C4⋊C4D412yes—
57C11×C22⋊C4—21no—
58C42×C11—21no—
59C22⋊Dic11—28no—
60#4324—24no—
61#4323—24no—
62(C2×D11)⋊C4—24no—
63C4⋊Dic11—24no—
64C4×Dic11—21no—
65C4×Dic11D412yes—
66#4318—21no—
67#4318D412yes—
68C2×C11⋊C8—21no—
69#2003—111nomaximal, Sylow
70C23×C11—22no—
71C23×C11—44no—
72C23×C11—41no—
73C23×C11—41no—
74C23×C11C2×D411yescharacteristic
75C22×D11—21no—
76D4×C11—22no—
77D4×C11—22no—
78D4×C11—41no—
79D4×C11—41no—
80C2×C4×C11—22no—
81C2×C4×C11C2×D411yescharacteristic
82C2×C4×C11C2×D411yescharacteristic
83C2×C4×C11C2×D411yescharacteristic
84C2×C4×C11C2×D411yescharacteristic
85C2×C4×C11C2×D411yescharacteristic
86C2×C4×C11#4111yescharacteristic
87C22⋊D11—41no—
88C22⋊D11—41no—
89C2×Dic11—22no—
90C2×Dic11—21no—
91C2×Dic11—22no—
92C2×Dic11—22no—
93C2×Dic11—22no—
94C2×Dic11—42no—
95D44—21no—
96D44—21no—
97C4×D11—41no—
98C4×D11—41no—
99Dic22—21no—
100Dic22—21no—
101Dic22—41no—
102Dic22—41no—
103Dic22—41no—
104Dic22—41no—
105C8×C11—41no—
106C11⋊C8—22no—
107C2×AGL(1,ℤ/8)—111no—
108#536—111no—
109C2×#124—111no—
110C2×#104—111no—
111#418D1111yescharacteristic, complemented
112C2×#101—111no—
113#339—111no—
114C22×C11—22no—
115C22×C11—44no—
116C22×C11—42no—
117C22×C11—82no—
118C22×C11—82no—
119C22×C11#12011yescharacteristic
120C22×C11#12011yescharacteristic
121C22×C11#12111yescharacteristic
122C2×D11—41no—
123C2×D11—42no—
124C4×C11—42no—
125C4×C11#12011yescharacteristic
126C4×C11#12111yescharacteristic
127C4×C11#12111yescharacteristic
128C4×C11#12711yescharacteristic
129Dic11—42no—
130Dic11—41no—
131Dic11—42no—
132C2×#41—111no—
133C22×Q8—111no—
134C22×D4C2×D1111yescharacteristic
135AGL(1,ℤ/8)—222no—
136AGL(1,ℤ/8)—222no—
137C2×SD16—221no—
138C2×D8—221no—
139C2×M16—111no—
140C2×M16C2×D1111yescharacteristic
141C4⋊Q8—221no—
142#124—221no—
143#124—222no—
144#124—222no—
145#123—222no—
146C22⋊Q8—222no—
147#117C2×D1111yescharacteristic
148C2×C22⋊C4—222no—
149C2×C42—111no—
150#104—222no—
151#102—22no—
152#101—222no—
153C2×C11—21no—
154C2×C11—21no—
155C2×C11—82no—
156C2×C11#39211yescharacteristic
157C2×C11#45412yes—
158D11—81no—
159C24—21no—
160#41—221no—
161#41—221no—
162#41—221no—
163#41—221no—
164C2×Q8—111no—
165C2×Q8—221no—
166C2×Q8—221no—
167C2×Q8—221no—
168C2×Q8—221no—
169C2×Q8—221no—
170C2×Q8—221no—
171C2×D4—21no—
172C2×D4—21no—
173C2×D4—21no—
174C2×D4—21no—
175C2×D4—21no—
176C2×D4—111no—
177C2×D4—221no—
178C2×D4D4412yes—
179C22×C4—112no—
180C22×C4—221no—
181C22×C4—221no—
182C22×C4C22×D1111yescharacteristic
183SD16—224no—
184D8—224no—
185M16—21no—
186M16—21no—
187M16—112no—
188M16—221no—
189C2×C8—21no—
190C2×C8—221no—
191C4⋊C4—224no—
192C4⋊C4C22⋊D1112yes—
193C22⋊C4—21no—
194C22⋊C4—224no—
195C22⋊C4—228no—
196C42—21no—
197C42—112no—
198C42—221no—
199C11#200311yescharacteristic, complemented, Sylow
200C23—22no—
201C23—44no—
202C23—41no—
203C23—41no—
204C23—221no—
205C23D4×D1111yescharacteristic
206Q8—221no—
207Q8—221no—
208Q8—441no—
209Q8—441no—
210Q8—441no—
211Q8—441no—
212D4—22no—
213D4—22no—
214D4—41no—
215D4—41no—
216D4—221no—
217D4—221no—
218D4—441no—
219D4—441no—
220C2×C4—22no—
221C2×C4—222no—
222C2×C4—222no—
223C2×C4—222no—
224C2×C4—222no—
225C2×C4—221no—
226C2×C4—442no—
227C2×C4—441no—
228C2×C4—441no—
229C2×C4C2×D4411yescharacteristic
230C2×C4#433911yescharacteristic
231C2×C4D4×D1111yescharacteristic
232C2×C4D4×D1111yescharacteristic
233C2×C4D4×D1111yescharacteristic
234C2×C4C2×C22⋊D1111yescharacteristic
235C8—41no—
236C8—222no—
237C22—22no—
238C22—44no—
239C22—42no—
240C22—82no—
241C22—82no—
242C22—442no—
243C22—441no—
244C22#6693511yescharacteristic
245C22#6693711yescharacteristic
246C22#6699011yescharacteristic
247C4—42no—
248C4—442no—
249C4—442no—
250C4—441no—
251C4#6693511yescharacteristic
252C4#6693711yescharacteristic
253C4#6698311yescharacteristic
254C4#6699311yescharacteristic
255C2—21no—
256C2—21no—
257C2—82no—
258C2—881no—
259C2#1062257311yescharacteristic
260C2#1062281412yes—
subgroupG/H
centerC22#66990
commutator, cosocleC22×C4×C11C23
FrattiniC22×C4C22×D11
FittingC11×#418C2
socleC22×C11#120
prime radicalC2×#66985C2
hypercenter#418D11
hypocenterC11#2003
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
1. C2×#66989C2semidirect
3. #10623057C2semidirect
4. C11×#418C2semidirect
5. C2×#66889C2semidirect
6. C2×#66888C2semidirect
7. #10622170C2semidirect
111. #418D11semidirect
199. C11#2003semidirect

Maximal subgroups

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

subgroupindex
C2×#669892
C2×#669852
#106230572
C11×#4182
C2×#668892
C2×#668882
#106221702
#200311