Finite Group Databasebeta

← #13078263

Subgroups — #13078263

Order 1408.

524 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 524 conjugacy classes of subgroups — too many to draw. Only its 133 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#10623336C211yesmaximal, characteristic, complemented
2C22×#4323C211yesmaximal, characteristic, complemented
3C2×#66960C211yesmaximal, characteristic, complemented
4#10623056C211yesmaximal, characteristic, complemented
5C11×#418C211yesmaximal, characteristic, complemented
6#10622744C211yesmaximal, characteristic, complemented
7#10622611C211yesmaximal, characteristic, complemented
8#10622395C214yesmaximal, complemented
9#10622388C214yesmaximal, complemented
10C22×D4×C11C2211yescharacteristic
11C2×#4339C2211yescharacteristic
12C22×D44C2211yescharacteristic
13C2×C11×M16C2211yescharacteristic
14C11×#117C2211yescharacteristic
15#67006—22no—
16#66993—21no—
17#66991C2214yescomplemented
18#66989—21no—
19C2×#4323—24no—
20C2×#4323C2212yes—
21C2×#4323C2212yes—
22#66979C2211yescharacteristic
23C22×C11⋊C8C2211yescharacteristic
24#66960—24no—
25C2×#4313C2212yescomplemented
26C2×C8×D11C2212yescomplemented
27#66948C2214yescomplemented
28#66935—22no—
29#66928—21no—
30#66927—21no—
31C11×#102C2214yescomplemented
32#66885C2214yescomplemented
33#66872C2212yescomplemented
34#66871C2212yescomplemented
35C24×C11—21no—
36C23×D11—21no—
37C2×D4×C11—22no—
38C2×D4×C11—21no—
39C2×D4×C11—22no—
40C2×D4×C11C2312yes—
41C22×C4×C11C2311yescharacteristic
42C2×C22⋊D11—24no—
43C2×C22⋊D11D412yes—
44#4339—22no—
45#4339—22no—
46C2×D44—24no—
47C2×D44—21no—
48C2×D44—22no—
49C2×D44—22no—
50C2×D44D411yescharacteristic
51C2×D44C2312yes—
52C2×C4×D11C2312yes—
53C2×Dic22D411yescharacteristic
54C11×M16—22no—
55C2×C8×C11C2312yes—
56C11×C4⋊C4C2312yes—
57C11×C22⋊C4—21no—
58C42×C11—21no—
59C22⋊Dic11—24no—
60C22⋊Dic11—21no—
61#4323—24no—
62#4323—24no—
63(C2×D11)⋊C4—24no—
64C4⋊Dic11C2312yes—
65C4×Dic11—21no—
66C2×C11⋊C8D414yescomplemented
67C2×C11⋊C8C2311yescharacteristic
68C2×C11⋊C8C2311yescharacteristic
69#4313—24no—
70C8×D11—24no—
71#3058—111nomaximal, Sylow
72C23×C11—22no—
73C23×C11—42no—
74C23×C11—82no—
75C23×C11C2×D411yescharacteristic
76C22×D11—22no—
77C22×D11—42no—
78C22×D11—82no—
79C22×D11C2×D412yes—
80D4×C11—22no—
81D4×C11—22no—
82D4×C11—42no—
83C2×C4×C11—22no—
84C2×C4×C11C2×D411yescharacteristic
85C2×C4×C11C2×D412yes—
86C2×C4×C11#4112yes—
87C2×C4×C11C2411yescharacteristic
88C22⋊D11—24no—
89C22⋊D11—84no—
90C2×Dic11—22no—
91C2×Dic11C2×D412yes—
92D44—22no—
93D44—22no—
94D44—22no—
95D44—42no—
96D44—84no—
97C4×D11—22no—
98C4×D11—22no—
99Dic22—22no—
100C8×C11—22no—
101C11⋊C8C2×D412yes—
102C11⋊C8C2×D412yes—
103C22×D8—111no—
104C2×#131—111no—
105#535—111no—
106#535—111no—
107#469—114no—
108#466—114no—
109#427—111no—
110#418—111no—
111#418D1111yescharacteristic, complemented
112C22×C11—22no—
113C22×C11—42no—
114C22×C11—44no—
115C22×C11—84no—
116C22×C11#12112yes—
117C22×C11C22×D411yescharacteristic
118C2×D11—22no—
119C2×D11—24no—
120C2×D11—42no—
121C2×D11—44no—
122C2×D11—84no—
123C4×C11—42no—
124C4×C11#12112yes—
125C4×C11C22×D411yescharacteristic
126C4×C11C2×#4111yescharacteristic
127Dic11—22no—
128Dic11—42no—
129C2×#41—111no—
130C22×D4—111no—
131C22×D4C2×D1111yescharacteristic
132C2×D8—112no—
133C2×D8—112no—
134C2×D8—224no—
135#131—224no—
136C2×M16—112no—
137C2×M16C2×D1111yescharacteristic
138C22×C8—111no—
139C22×C8—112no—
140#127—221no—
141#127—221no—
142#124—221no—
143#124—221no—
144#121—114no—
145#121—114no—
146#120—222no—
147#120—222no—
148#117—111no—
149#117C2×D1111yescharacteristic
150#107—112no—
151#106—112no—
152#102—114no—
153#102C2×D1114yescomplemented
154C2×C11—22no—
155C2×C11—82no—
156C2×C11C2×#12111yescharacteristic
157C2×C11#57612yes—
158D11—42no—
159D11—82no—
160C24—21no—
161C24—221no—
162#41—222no—
163#41—222no—
164C2×Q8—111no—
165C2×D4—22no—
166C2×D4—22no—
167C2×D4—21no—
168C2×D4—112no—
169C2×D4—111no—
170C2×D4—112no—
171C2×D4—224no—
172C2×D4—224no—
173C2×D4—222no—
174C2×D4—222no—
175C2×D4—221no—
176C2×D4C22×D1112yes—
177C22×C4—112no—
178C22×C4C22×D1111yescharacteristic
179D8—224no—
180D8—224no—
181M16—22no—
182M16—224no—
183C2×C8—114no—
184C2×C8—111no—
185C2×C8—111no—
186C2×C8—224no—
187C2×C8C22×D1112yes—
188C4⋊C4—112no—
189C4⋊C4C22×D1112yes—
190C22⋊C4—21no—
191C22⋊C4—224no—
192C22⋊C4—224no—
193C22⋊C4—221no—
194C42—21no—
195C42—221no—
196C11#305811yescharacteristic, complemented, Sylow
197C23—22no—
198C23—42no—
199C23—82no—
200C23—112no—
201C23—222no—
202C23—442no—
203C23—882no—
204C23D4×D1111yescharacteristic
205Q8—222no—
206D4—22no—
207D4—22no—
208D4—42no—
209D4—224no—
210D4—222no—
211D4—222no—
212D4—222no—
213D4—442no—
214D4—884no—
215D4—884no—
216C2×C4—22no—
217C2×C4—112no—
218C2×C4—222no—
219C2×C4—222no—
220C2×C4—222no—
221C2×C4#433912yes—
222C2×C4D4×D1111yescharacteristic
223C2×C4D4×D1112yes—
224C2×C4C23×D1111yescharacteristic
225C8—22no—
226C8—112no—
227C8—112no—
228C22—22no—
229C22—42no—
230C22—44no—
231C22—84no—
232C22—222no—
233C22—224no—
234C22—442no—
235C22—444no—
236C22—884no—
237C22#6693712yes—
238C22C2×D4×D1111yescharacteristic
239C4—42no—
240C4—222no—
241C4—442no—
242C4#6693712yes—
243C4C2×#433911yescharacteristic
244C4C2×D4×D1111yescharacteristic
245C2—22no—
246C2—82no—
247C2—442no—
248C2—882no—
249C2C2×#6693711yescharacteristic
250C2#1062330512yes—
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#418C2
socleC22×C11C22×D4
hypercenter#418D11
hypocenterC11#3058
LCSG ▷ C2×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. #10623336C2semidirect
2. C22×#4323C2semidirect
3. C2×#66960C2semidirect
4. #10623056C2semidirect
5. C11×#418C2semidirect
6. #10622744C2semidirect
7. #10622611C2semidirect
8. #10622395C2semidirect
9. #10622388C2semidirect
17. #66991C22semidirect
25. C2×#4313C22semidirect
26. C2×C8×D11C22semidirect
27. #66948C22semidirect
31. C11×#102C22semidirect
32. #66885C22semidirect
33. #66872C22semidirect
34. #66871C22semidirect
66. C2×C11⋊C8D4semidirect
111. #418D11semidirect
153. #102C2×D11semidirect
196. C11#3058semidirect

Maximal subgroups

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

subgroupindex
#106233362
C22×#43232
C2×#669602
#106230562
C11×#4182
#106227442
#106226112
#106223952
#106223882
#305811