Finite Group Databasebeta

← #13078124

Subgroups — #13078124

Order 1408.

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

normal subgroups only

This group has 494 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
1C11×#536C211yesmaximal, characteristic, complemented
2C2×#67002C211yesmaximal, characteristic
3C22×#4325C211yesmaximal, characteristic, complemented
4#10623052C211yesmaximal, characteristic, complemented
5#10622846C211yesmaximal, characteristic, complemented
6#10622838C211yesmaximal, characteristic, complemented
7#10622696C214yesmaximal, complemented
8#10622670C214yesmaximal, complemented
9#10622612C211yesmaximal, characteristic, complemented
10C2×C11×#41C2211yescharacteristic
11C22×Q8×C11C2211yescharacteristic
12C22×D44C2211yescharacteristic
13C11×C4⋊Q8C2212yescomplemented
14C11×#124C2212yescomplemented
15C11×#123—22no—
16C11×C22⋊Q8—22no—
17C11×#117C2211yescharacteristic
18#67002—24no—
19C2×#4325—24no—
20C2×#4325C2214yes—
21C2×#4325C2212yes—
22C2×#4323C2212yes—
23#66979C2211yescharacteristic
24C2×#4318C2211yescharacteristic
25C22×C11⋊C8C2211yescharacteristic
26#66946—22no—
27C22⋊C4×D11—22no—
28C4×D44C2214yes—
29#66899C2214yescomplemented
30#66899C2212yescomplemented
31#66896C2212yescomplemented
32C4⋊(C11⋊C8)C2214yescomplemented
33C23×D11—21no—
34C11×#41—22no—
35C11×#41—22no—
36C2×Q8×C11—21no—
37C2×Q8×C11—22no—
38C2×Q8×C11—22no—
39C2×Q8×C11C2312yes—
40C2×Q8×C11C2311yescharacteristic
41C2×D4×C11—21no—
42C2×D4×C11C2311yescharacteristic
43C22×C4×C11—21no—
44C22×C4×C11—21no—
45C22×C4×C11C2311yescharacteristic
46C2×D44—21no—
47C2×D44—22no—
48C2×D44D414yes—
49C2×D44C2312yes—
50C2×C4×D11—24no—
51C11×C4⋊C4—24no—
52C11×C4⋊C4D412yes—
53C11×C22⋊C4—24no—
54C11×C22⋊C4D412yes—
55C42×C11C2312yes—
56C22⋊Dic11—21no—
57#4325—28no—
58#4325—24no—
59#4323—24no—
60(C2×D11)⋊C4—24no—
61C4⋊Dic11C2312yes—
62C4×Dic11—21no—
63#4318—22no—
64C2×C11⋊C8—22no—
65C2×C11⋊C8C2312yes—
66C2×C11⋊C8C2312yes—
67#3042—111nomaximal, Sylow
68C23×C11—21no—
69C23×C11C2×D411yescharacteristic
70C22×D11—22no—
71C22×D11—24no—
72C22×D11—82no—
73Q8×C11—22no—
74Q8×C11—21no—
75Q8×C11—22no—
76Q8×C11—21no—
77Q8×C11—42no—
78D4×C11—21no—
79D4×C11—21no—
80D4×C11—42no—
81C2×C4×C11—22no—
82C2×C4×C11—21no—
83C2×C4×C11—42no—
84C2×C4×C11—42no—
85C2×C4×C11C2×D412yes—
86C2×C4×C11C2×D414yes—
87C2×C4×C11C2×D411yescharacteristic
88C2×C4×C11#4112yes—
89C2×C4×C11C2411yescharacteristic
90C2×Dic11—22no—
91D44—24no—
92D44—22no—
93D44C2×D414yes—
94C4×D11—84no—
95C11⋊C8—22no—
96C11⋊C8—22no—
97C2×AGL(1,ℤ/8)—111no—
98C22×SD16—111no—
99#536D1111yescharacteristic, complemented
100#518—111no—
101#463—114no—
102#461—114no—
103#424—111no—
104#419—111no—
105#416—111no—
106C22×C11—22no—
107C22×C11—41no—
108C22×C11—42no—
109C22×C11#12112yes—
110C22×C11C22×D411yescharacteristic
111C2×D11—24no—
112C2×D11—44no—
113C2×D11—84no—
114C4×C11—24no—
115C4×C11—41no—
116C4×C11—42no—
117C4×C11#12112yes—
118C4×C11C22×D411yescharacteristic
119C4×C11C2×#4111yescharacteristic
120Dic11—42no—
121C2×#41C2×D1111yescharacteristic
122C22×Q8C2×D1111yescharacteristic
123C22×D4—111no—
124AGL(1,ℤ/8)—224no—
125C2×SD16—114no—
126C2×SD16—112no—
127C2×SD16—224no—
128C2×D8—112no—
129C2×M16—111no—
130C22×C8—111no—
131C4⋊Q8C2×D1112yescomplemented
132#124C2×D1112yescomplemented
133#123—22no—
134C22⋊Q8—22no—
135C4×D4—114no—
136C4×D4—222no—
137#117—111no—
138#117C2×D1111yescharacteristic
139C2×C22⋊C4—222no—
140C4⋊C8—114no—
141#103—112no—
142#103—114no—
143#102—112no—
144C2×C11—22no—
145C2×C11—81no—
146C2×C11C2×#12111yescharacteristic
147C2×C11#57712yes—
148D11—44no—
149C24—221no—
150#41—22no—
151#41—22no—
152C2×Q8—21no—
153C2×Q8—22no—
154C2×Q8—22no—
155C2×Q8C22×D1112yes—
156C2×Q8C22×D1111yescharacteristic
157C2×D4—21no—
158C2×D4—114no—
159C2×D4—112no—
160C2×D4—222no—
161C2×D4—221no—
162C2×D4C22×D1111yescharacteristic
163C22×C4—21no—
164C22×C4—21no—
165C22×C4—224no—
166C22×C4C22×D1111yescharacteristic
167SD16—228no—
168SD16—224no—
169D8—224no—
170M16—222no—
171C2×C8—112no—
172C2×C8—112no—
173C2×C8—222no—
174C4⋊C4—24no—
175C4⋊C4—112no—
176C4⋊C4C22⋊D1112yes—
177C22⋊C4—24no—
178C22⋊C4—221no—
179C22⋊C4—224no—
180C22⋊C4C22⋊D1112yes—
181C42—221no—
182C42C22×D1112yes—
183C11#304211yescharacteristic, complemented, Sylow
184C23—21no—
185C23—222no—
186C23—224no—
187C23—882no—
188C23C2×C22⋊D1111yescharacteristic
189Q8—22no—
190Q8—21no—
191Q8—22no—
192Q8—21no—
193Q8—42no—
194D4—21no—
195D4—21no—
196D4—42no—
197D4—114no—
198D4—224no—
199D4—222no—
200C2×C4—22no—
201C2×C4—21no—
202C2×C4—42no—
203C2×C4—42no—
204C2×C4—222no—
205C2×C4—884no—
206C2×C4D4×D1112yes—
207C2×C4#434112yes—
208C2×C4C2×C22⋊D1114yes—
209C2×C4C2×C22⋊D1111yescharacteristic
210C2×C4C23×D1111yescharacteristic
211C8—222no—
212C8—222no—
213C22—22no—
214C22—41no—
215C22—42no—
216C22—224no—
217C22—444no—
218C22—884no—
219C22#6699112yes—
220C22C22×C22⋊D1111yescharacteristic
221C4—24no—
222C4—41no—
223C4—42no—
224C4—442no—
225C4#6699112yes—
226C4C2×D4×D1111yescharacteristic
227C4C2×#434111yescharacteristic
228C2—22no—
229C2—81no—
230C2—444no—
231C2C2×#6699111yescharacteristic
232C2#1062336812yes—
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#536C2
socleC22×C11C22×D4
prime radicalC2×#67002C2
hypercenter#536D11
hypocenterC11#3042
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ #117 ◁ #536

Complements

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

NH ≅ G/Ntype
1. C11×#536C2semidirect
3. C22×#4325C2semidirect
4. #10623052C2semidirect
5. #10622846C2semidirect
6. #10622838C2semidirect
7. #10622696C2semidirect
8. #10622670C2semidirect
9. #10622612C2semidirect
13. C11×C4⋊Q8C22semidirect
14. C11×#124C22semidirect
29. #66899C22semidirect
30. #66899C22semidirect
31. #66896C22semidirect
32. C4⋊(C11⋊C8)C22semidirect
99. #536D11semidirect
131. C4⋊Q8C2×D11semidirect
132. #124C2×D11semidirect
183. C11#3042semidirect

Maximal subgroups

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

subgroupindex
C11×#5362
C2×#670022
C22×#43252
#106230522
#106228462
#106228382
#106226962
#106226702
#106226122
#304211