Finite Group Databasebeta

← #13069901

Subgroups — #13069901

Order 1408.

266 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 266 conjugacy classes of subgroups — too many to draw. Only its 63 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
1#10623353C211yesmaximal, characteristic
2C11×#413C211yesmaximal, characteristic, complemented
3C2×#66901C211yesmaximal, characteristic, complemented
4C2×#66889C211yesmaximal, characteristic, complemented
5#10622745C211yesmaximal, characteristic, complemented
6#10622731C211yesmaximal, characteristic, complemented
7C11⋊#338C211yesmaximal, characteristic, complemented
8C2×C11×#41C2211yescharacteristic
9C2×#4339C2211yescharacteristic
10C2×C11×M16C2211yescharacteristic
11C2×C11×M16C2211yescharacteristic
12#67004—21no—
13#67003—22no—
14#67002—21no—
15#66995—21no—
16#66985—21no—
17C2×C4×Dic11C2211yescharacteristic
18C2×#4318C2211yescharacteristic
19C2×#4318C2211yescharacteristic
20C11×#101—21no—
21C11×#100—21no—
22#66901—21no—
23#66901—21no—
24#66889—21no—
25#66889—21no—
26#66888—21no—
27#66887—21no—
28Dic11⋊C8—22no—
29C11×#41—21no—
30C11×#41—21no—
31C11×#41—21no—
32C11×#41—21no—
33C2×Q8×C11D411yescharacteristic
34C2×D4×C11—21no—
35C2×D4×C11D411yescharacteristic
36C22×C4×C11—21no—
37C22×C4×C11C2311yescharacteristic
38C2×C22⋊D11—21no—
39C22×Dic11—21no—
40#4339—21no—
41#4339—21no—
42#4339—21no—
43#4339—21no—
44C2×D44D411yescharacteristic
45C2×C4×D11—21no—
46C2×Dic22D411yescharacteristic
47C11×M16—21no—
48C11×M16—21no—
49C11×M16—21no—
50C11×M16—21no—
51C2×C8×C11—21no—
52C2×C8×C11—21no—
53#4326—22no—
54#4325—22no—
55#4324—22no—
56#4323—22no—
57C4×Dic11—21no—
58C4×Dic11D411yescharacteristic
59C4×Dic11D411yescharacteristic
60#4318—21no—
61#4318—21no—
62#4318—21no—
63#4318—21no—
64C2×C11⋊C8—21no—
65C2×C11⋊C8D412yes—
66#2050—111nomaximal, Sylow
67C23×C11—21no—
68C23×C11#4111yescharacteristic
69C22×D11—21no—
70Q8×C11—21no—
71Q8×C11—21no—
72D4×C11—21no—
73D4×C11—21no—
74D4×C11—41no—
75D4×C11—41no—
76C2×C4×C11—21no—
77C2×C4×C11—41no—
78C2×C4×C11—41no—
79C2×C4×C11C2×D411yescharacteristic
80C2×C4×C11C2×D411yescharacteristic
81C2×C4×C11C2×D411yescharacteristic
82C2×C4×C11C2×D411yescharacteristic
83C2×C4×C11#4111yescharacteristic
84C2×C4×C11#4111yescharacteristic
85C22⋊D11—41no—
86C22⋊D11—41no—
87C2×Dic11—21no—
88C2×Dic11—21no—
89C2×Dic11—21no—
90C2×Dic11—42no—
91D44—21no—
92D44—21no—
93C4×D11—41no—
94C4×D11—41no—
95Dic22—21no—
96Dic22—21no—
97C8×C11—41no—
98C8×C11—41no—
99C11⋊C8—22no—
100C11⋊C8—41no—
101#575—111no—
102#423—111no—
103C2×#104—111no—
104C2×#104—111no—
105#413—111no—
106#413D1111yescharacteristic, complemented
107#338—111no—
108C22×C11—41no—
109C22×C11—41no—
110C22×C11—81no—
111C22×C11#12111yescharacteristic
112C22×C11#12311yescharacteristic
113C22×C11#12311yescharacteristic
114C2×D11—41no—
115C2×D11—81no—
116C4×C11—41no—
117C4×C11#12011yescharacteristic
118C4×C11#12111yescharacteristic
119C4×C11#12111yescharacteristic
120C4×C11#12411yescharacteristic
121Dic11—22no—
122Dic11—41no—
123Dic11—41no—
124C2×#41—111no—
125C2×#41C2×D1111yescharacteristic
126#137—221no—
127#137—221no—
128AGL(1,ℤ/8)—221no—
129AGL(1,ℤ/8)—221no—
130#135—222no—
131C2×M16—111no—
132C2×M16—111no—
133C2×M16C2×D1111yescharacteristic
134C2×M16C2×D1111yescharacteristic
135C2×C42—111no—
136C4⋊C8—222no—
137#104—221no—
138#104—221no—
139#104—221no—
140#104—221no—
141#101—21no—
142#101—221no—
143#100—21no—
144#100—221no—
145C2×C11—21no—
146C2×C11—21no—
147C2×C11—21no—
148C2×C11—81no—
149C2×C11#39411yescharacteristic
150D11—81no—
151#41—21no—
152#41—21no—
153#41—21no—
154#41—21no—
155#41—221no—
156#41—221no—
157#41—221no—
158#41—221no—
159C2×Q8—111no—
160C2×Q8C22⋊D1111yescharacteristic
161C2×D4—21no—
162C2×D4—111no—
163C2×D4—221no—
164C2×D4C22⋊D1111yescharacteristic
165C22×C4—21no—
166C22×C4—221no—
167C22×C4—221no—
168C22×C4C22×D1111yescharacteristic
169Q16—222no—
170SD16—222no—
171SD16—222no—
172D8—222no—
173M16—21no—
174M16—21no—
175M16—21no—
176M16—21no—
177M16—221no—
178M16—221no—
179M16—221no—
180M16—221no—
181C2×C8—21no—
182C2×C8—21no—
183C2×C8—112no—
184C2×C8—221no—
185C42—111no—
186C42—111no—
187C42—221no—
188C11#205011yescharacteristic, complemented, Sylow
189C23—21no—
190C23—221no—
191C23#433911yescharacteristic
192Q8—21no—
193Q8—21no—
194Q8—221no—
195Q8—221no—
196D4—21no—
197D4—21no—
198D4—41no—
199D4—41no—
200D4—221no—
201D4—221no—
202D4—441no—
203D4—441no—
204C2×C4—21no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—221no—
208C2×C4—221no—
209C2×C4—221no—
210C2×C4—442no—
211C2×C4—441no—
212C2×C4—441no—
213C2×C4#433911yescharacteristic
214C2×C4D4×D1111yescharacteristic
215C2×C4D4×D1111yescharacteristic
216C2×C4D4×D1111yescharacteristic
217C2×C4#434111yescharacteristic
218C2×C4C2×C22⋊D1111yescharacteristic
219C8—41no—
220C8—41no—
221C8—222no—
222C8—441no—
223C22—41no—
224C22—41no—
225C22—81no—
226C22—441no—
227C22—881no—
228C22#6693611yescharacteristic
229C22#6693711yescharacteristic
230C22#6698211yescharacteristic
231C4—41no—
232C4—222no—
233C4—441no—
234C4—441no—
235C4#6693711yescharacteristic
236C4#6693811yescharacteristic
237C4#6699011yescharacteristic
238C4#6699211yescharacteristic
239C2—21no—
240C2—21no—
241C2—21no—
242C2—81no—
243C2—881no—
244C2#1062257211yescharacteristic
subgroupG/H
centerC4#66938
commutator, cosocleC22×C4×C11C23
FrattiniC22×C4C22×D11
FittingC11×#413C2
socleC2×C11#394
prime radical#10623353C2
hypercenter#413D11
hypocenterC11#2050
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C22×C4 ◁ #413

Complements

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

NH ≅ G/Ntype
2. C11×#413C2semidirect
3. C2×#66901C2semidirect
4. C2×#66889C2semidirect
5. #10622745C2semidirect
6. #10622731C2semidirect
7. C11⋊#338C2semidirect
106. #413D11semidirect
188. C11#2050semidirect

Maximal subgroups

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

subgroupindex
#106233532
C11×#4132
C2×#669012
C2×#668892
#106227452
#106227312
C11⋊#3382
#205011