Finite Group Databasebeta

← #13079682

Subgroups — #13079682

Order 1408.

396 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 117 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
1C11×#541C211yesmaximal, characteristic, complemented
2#10623056C211yesmaximal, characteristic
3#10622699C211yesmaximal, characteristic, complemented
4#10622698C211yesmaximal, characteristic, complemented
5#10622681C211yesmaximal, characteristic, complemented
6#10622680C211yesmaximal, characteristic, complemented
7#10622660C212yesmaximal, complemented
8#10622659C212yesmaximal, complemented
9#10622641C212yesmaximal, complemented
10#10622640C212yesmaximal, complemented
11#10622613C211yesmaximal, characteristic, complemented
12C2×#4339C2211yescharacteristic
13C22×D44C2211yescharacteristic
14C11×C4⋊Q8C2211yescharacteristic, complemented
15C11×#126—22no—
16C11×#125—22no—
17C11×#125C2211yescharacteristic, complemented
18C11×C22⋊Q8C2212yes—
19C4×Q8×C11C2212yescomplemented
20C11×#117C2211yescharacteristic
21C2×#4326C2212yescomplemented
22C2×#4325C2212yes—
23C2×#4325C2212yes—
24C2×#4325C2212yescomplemented
25#66948—22no—
26#66935—22no—
27#66928C2211yescharacteristic
28#66928C2211yescharacteristic
29#66927C2211yescharacteristic
30#66927C2211yescharacteristic
31C22⋊(C11⋊C8)C2212yes—
32#66874C2212yescomplemented
33#66873C2212yes—
34#66873C2212yes—
35#66873C2212yescomplemented
36C4⋊(C11⋊C8)C2212yescomplemented
37#66867C2211yescharacteristic, complemented
38C4×C11⋊C8C2211yescharacteristic, complemented
39C23×D11—21no—
40C2×Q8×C11C2312yes—
41C22×C4×C11C2311yescharacteristic
42C2×C22⋊D11—21no—
43#4339—42no—
44C2×D44—21no—
45C2×D44—22no—
46C2×D44—22no—
47C2×D44—42no—
48C2×D44C2311yescharacteristic
49C2×D44C2311yescharacteristic
50C2×D44C2311yescharacteristic
51C2×C4×D11—21no—
52C2×Dic22C2311yescharacteristic
53C11×C4⋊C4—22no—
54C11×C4⋊C4—22no—
55C11×C4⋊C4—22no—
56C11×C4⋊C4—22no—
57C11×C4⋊C4D412yes—
58C11×C4⋊C4C2312yes—
59C11×C22⋊C4—22no—
60C11×C22⋊C4D412yes—
61C42×C11—22no—
62C42×C11C2311yescharacteristic
63C42×C11C2311yescharacteristic
64#4326—42no—
65#4325—42no—
66#4325—42no—
67#4325—42no—
68(C2×D11)⋊C4—22no—
69(C2×D11)⋊C4—22no—
70C2×C11⋊C8C2312yes—
71C2×C11⋊C8C2312yes—
72#3222—111nomaximal, Sylow
73C23×C11C2×D411yescharacteristic
74C22×D11—21no—
75C22×D11—21no—
76C22×D11—21no—
77C22×D11—42no—
78C22×D11—82no—
79Q8×C11—22no—
80Q8×C11—22no—
81C2×C4×C11—22no—
82C2×C4×C11—22no—
83C2×C4×C11—22no—
84C2×C4×C11C2×D412yes—
85C2×C4×C11C2×D412yes—
86C2×C4×C11C2×D411yescharacteristic
87C2×C4×C11C2411yescharacteristic
88C22⋊D11—42no—
89C2×Dic11—21no—
90D44—22no—
91D44—22no—
92D44—22no—
93D44—42no—
94D44—82no—
95D44—82no—
96C4×D11—42no—
97Dic22—22no—
98C11⋊C8—22no—
99C11⋊C8—22no—
100#541D1111yescharacteristic, complemented
101#535—111no—
102#497—111no—
103#492—111no—
104#490—111no—
105#488—111no—
106#464—112no—
107#460—112no—
108#452—112no—
109#450—112no—
110#433—111no—
111C22×C11—21no—
112C22×C11—22no—
113C22×C11C22×D411yescharacteristic
114C2×D11—41no—
115C2×D11—41no—
116C2×D11—41no—
117C2×D11—42no—
118C2×D11—42no—
119C2×D11—42no—
120C2×D11—84no—
121C4×C11—21no—
122C4×C11—22no—
123C4×C11—22no—
124C4×C11—42no—
125C4×C11—42no—
126C4×C11H(5,𝔽2)12yes—
127Dic11—41no—
128C2×#41—111no—
129C22×D4—111no—
130C2×Q16—112no—
131C2×SD16—112no—
132C2×SD16—112no—
133C2×SD16—112no—
134C4⋊Q8C2×D1111yescharacteristic, complemented
135#127—111no—
136#127—111no—
137#126—22no—
138#125—22no—
139#125C2×D1111yescharacteristic, complemented
140#124—111no—
141#124—111no—
142C22⋊Q8C2×D1112yes—
143#121—222no—
144#120—222no—
145C4×Q8C2×D1112yescomplemented
146#117C2×D1111yescharacteristic
147C4⋊C8—112no—
148#103—112no—
149#102—112no—
150#102—112no—
151#102—112no—
152C22⋊C8—112no—
153#97—111no—
154C4×C8—111no—
155C2×C11—41no—
156C2×C11#53511yescharacteristic
157C2×C11#57712yes—
158D11—81no—
159D11—81no—
160D11—81no—
161C24—221no—
162#41—442no—
163C2×Q8—111no—
164C2×Q8C22×D1112yes—
165C2×D4—111no—
166C2×D4—111no—
167C2×D4—111no—
168C2×D4—221no—
169C2×D4—221no—
170C2×D4—222no—
171C2×D4—222no—
172C2×D4—442no—
173C22×C4—221no—
174C22×C4C22×D1111yescharacteristic
175Q16—442no—
176SD16—442no—
177SD16—442no—
178SD16—442no—
179C2×C8—112no—
180C2×C8—112no—
181C4⋊C4—22no—
182C4⋊C4—22no—
183C4⋊C4—22no—
184C4⋊C4—22no—
185C4⋊C4C22⋊D1112yes—
186C4⋊C4C22×D1112yes—
187C22⋊C4—22no—
188C22⋊C4—222no—
189C22⋊C4—222no—
190C22⋊C4C22⋊D1112yes—
191C42—22no—
192C42C22×D1111yescharacteristic
193C42C22×D1111yescharacteristic
194C11#322211yescharacteristic, complemented, Sylow
195C23—221no—
196C23—221no—
197C23—221no—
198C23—442no—
199C23—882no—
200C23C2×C22⋊D1111yescharacteristic
201Q8—22no—
202Q8—22no—
203Q8—222no—
204D4—222no—
205D4—222no—
206D4—222no—
207D4—442no—
208D4—442no—
209D4—882no—
210D4—882no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—221no—
215C2×C4—442no—
216C2×C4C2×C22⋊D1112yes—
217C2×C4C2×C22⋊D1112yes—
218C2×C4C2×C22⋊D1111yescharacteristic
219C2×C4C23×D1111yescharacteristic
220C8—222no—
221C8—222no—
222C22—21no—
223C22—22no—
224C22—441no—
225C22—441no—
226C22—441no—
227C22—442no—
228C22—442no—
229C22—442no—
230C22—884no—
231C22C22×C22⋊D1111yescharacteristic
232C4—21no—
233C4—22no—
234C4—22no—
235C4—42no—
236C4—42no—
237C4—441no—
238C4#6704212yes—
239C2—41no—
240C2—881no—
241C2—881no—
242C2—881no—
243C2#1062336111yescharacteristic
244C2#1062336812yes—
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#541C2
socleC22×C11C22×D4
prime radical#10623056C2
hypercenter#541D11
hypocenterC11#3222
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ #117 ◁ #541

Complements

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

NH ≅ G/Ntype
1. C11×#541C2semidirect
3. #10622699C2semidirect
4. #10622698C2semidirect
5. #10622681C2semidirect
6. #10622680C2semidirect
7. #10622660C2semidirect
8. #10622659C2semidirect
9. #10622641C2semidirect
10. #10622640C2semidirect
11. #10622613C2semidirect
14. C11×C4⋊Q8C22semidirect
17. C11×#125C22semidirect
19. C4×Q8×C11C22semidirect
21. C2×#4326C22semidirect
24. C2×#4325C22semidirect
32. #66874C22semidirect
35. #66873C22semidirect
36. C4⋊(C11⋊C8)C22semidirect
37. #66867C22semidirect
38. C4×C11⋊C8C22semidirect
100. #541D11semidirect
134. C4⋊Q8C2×D11semidirect
139. #125C2×D11semidirect
145. C4×Q8C2×D11semidirect
194. C11#3222semidirect

Maximal subgroups

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

subgroupindex
C11×#5412
#106230562
#106226992
#106226982
#106226812
#106226802
#106226602
#106226592
#106226412
#106226402
#106226132
#322211