Finite Group Databasebeta

← #13078127

Subgroups — #13078127

Order 1408.

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

normal subgroups only

This group has 494 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#10623347C211yesmaximal, characteristic, complemented
2C22×#4325C211yesmaximal, characteristic, complemented
3C2×#66961C211yesmaximal, characteristic
4#10623052C211yesmaximal, characteristic, complemented
5C11×#419C211yesmaximal, characteristic, complemented
6#10622732C211yesmaximal, characteristic, complemented
7#10622615C211yesmaximal, characteristic, complemented
8#10622432C214yesmaximal, complemented
9#10622431C214yesmaximal, complemented
10C22×Q8×C11C2211yescharacteristic
11C2×#4339C2211yescharacteristic
12C22×D44C2211yescharacteristic
13C2×C11×M16C2211yescharacteristic
14C11×#117C2211yescharacteristic
15#67000C2212yescomplemented
16#66999—22no—
17#66997C2212yescomplemented
18C2×#4325—24no—
19C2×#4325C2214yes—
20#66982—22no—
21#66979C2211yescharacteristic
22C22×C11⋊C8C2211yescharacteristic
23#66961—24no—
24C2×D88C2212yes—
25C2×#4314C2212yes—
26#66946C2214yes—
27C22⋊C4×D11—22no—
28C4×D44—22no—
29C11×#103C2214yescomplemented
30Dic11⋊C8C2214yescomplemented
31#66874C2212yescomplemented
32#66873C2212yescomplemented
33C23×D11—21no—
34C2×Q8×C11—21no—
35C2×Q8×C11—22no—
36C2×Q8×C11—22no—
37C2×Q8×C11C2312yes—
38C22×C4×C11—21no—
39C22×C4×C11C2311yescharacteristic
40C2×C22⋊D11—21no—
41#4339—22no—
42#4339—22no—
43C2×D44—21no—
44C2×D44—22no—
45C2×D44D414yes—
46C2×D44C2311yescharacteristic
47C2×D44C2312yes—
48C2×C4×D11—24no—
49C2×C4×D11—21no—
50C2×Dic22C2311yescharacteristic
51C11×M16—22no—
52C2×C8×C11C2312yes—
53C11×C4⋊C4C2312yes—
54C11×C22⋊C4—21no—
55C42×C11—21no—
56C22⋊Dic11D412yes—
57#4325—28no—
58(C2×D11)⋊C4—24no—
59(C2×D11)⋊C4—24no—
60C4⋊Dic11D412yes—
61Dic11⋊C4—24no—
62C4×Dic11C2312yes—
63C2×C11⋊C8—22no—
64C2×C11⋊C8C2312yes—
65D88—24no—
66#4314—24no—
67#3042—111nomaximal, Sylow
68C23×C11C2×D411yescharacteristic
69C22×D11—22no—
70C22×D11—24no—
71C22×D11—21no—
72C22×D11—82no—
73Q8×C11—22no—
74Q8×C11—22no—
75Q8×C11—42no—
76C2×C4×C11—22no—
77C2×C4×C11—22no—
78C2×C4×C11—42no—
79C2×C4×C11C2×D411yescharacteristic
80C2×C4×C11C2×D412yes—
81C2×C4×C11#4112yes—
82C2×C4×C11C2411yescharacteristic
83C22⋊D11—42no—
84C2×Dic11—21no—
85C2×Dic11C2×D414yes—
86D44—24no—
87D44—21no—
88D44—22no—
89D44—21no—
90D44C2×D414yes—
91C4×D11—42no—
92C4×D11—84no—
93Dic22—21no—
94Dic22—21no—
95C8×C11—22no—
96C11⋊C8—22no—
97C2×AGL(1,ℤ/8)—111no—
98C22×SD16—111no—
99#536—111no—
100#518—111no—
101#463—114no—
102#461—114no—
103#424—111no—
104#419D1111yescharacteristic, complemented
105#416—111no—
106C22×C11—22no—
107C22×C11#12112yes—
108C22×C11C22×D411yescharacteristic
109C2×D11—24no—
110C2×D11—44no—
111C2×D11—41no—
112C2×D11—42no—
113C2×D11—84no—
114C4×C11—42no—
115C4×C11—42no—
116C4×C11#12112yes—
117C4×C11C22×D411yescharacteristic
118C4×C11C2×#4111yescharacteristic
119Dic11—24no—
120Dic11—41no—
121C2×#41—111no—
122C22×Q8C2×D1111yescharacteristic
123C22×D4—111no—
124AGL(1,ℤ/8)—224no—
125C2×SD16—114no—
126C2×SD16—112no—
127C2×SD16—224no—
128C2×D8—112no—
129C2×M16C2×D1111yescharacteristic
130C22×C8—111no—
131C4⋊Q8—112no—
132#124—112no—
133#123—222no—
134C22⋊Q8—222no—
135C4×D4—114no—
136C4×D4—222no—
137#117—111no—
138#117C2×D1111yescharacteristic
139C2×C22⋊C4—222no—
140C4⋊C8—114no—
141#103—112no—
142#103C2×D1114yescomplemented
143#102—112no—
144C2×C11—22no—
145C2×C11C2×#12111yescharacteristic
146C2×C11#57712yes—
147D11—44no—
148D11—81no—
149C24—221no—
150#41—222no—
151#41—222no—
152C2×Q8—21no—
153C2×Q8—22no—
154C2×Q8—22no—
155C2×Q8—111no—
156C2×Q8C22×D1112yes—
157C2×D4—114no—
158C2×D4—112no—
159C2×D4—111no—
160C2×D4—221no—
161C2×D4—222no—
162C2×D4—221no—
163C22×C4—21no—
164C22×C4—224no—
165C22×C4—221no—
166C22×C4C22×D1111yescharacteristic
167SD16—224no—
168SD16—228no—
169D8—224no—
170M16—22no—
171C2×C8—112no—
172C2×C8—222no—
173C2×C8C22×D1112yes—
174C4⋊C4—112no—
175C4⋊C4—224no—
176C4⋊C4C22×D1112yes—
177C22⋊C4—21no—
178C22⋊C4—112no—
179C22⋊C4—224no—
180C22⋊C4—224no—
181C42—21no—
182C42—112no—
183C11#304211yescharacteristic, complemented, Sylow
184C23—222no—
185C23—224no—
186C23—221no—
187C23—882no—
188C23D4×D1111yescharacteristic
189Q8—22no—
190Q8—22no—
191Q8—42no—
192Q8—221no—
193Q8—221no—
194D4—114no—
195D4—224no—
196D4—222no—
197D4—221no—
198D4—221no—
199D4—442no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—42no—
203C2×C4—114no—
204C2×C4—221no—
205C2×C4—442no—
206C2×C4—884no—
207C2×C4#433912yes—
208C2×C4D4×D1111yescharacteristic
209C2×C4D4×D1112yes—
210C2×C4C23×D1111yescharacteristic
211C8—22no—
212C8—222no—
213C22—22no—
214C22—224no—
215C22—444no—
216C22—441no—
217C22—442no—
218C22—884no—
219C22#6693712yes—
220C22C2×D4×D1111yescharacteristic
221C4—42no—
222C4—42no—
223C4—224no—
224C4—441no—
225C4#6693712yes—
226C4C2×#433911yescharacteristic
227C4C2×D4×D1111yescharacteristic
228C2—22no—
229C2—444no—
230C2—881no—
231C2C2×#6693711yescharacteristic
232C2#1062330912yes—
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#419C2
socleC22×C11C22×D4
prime radicalC2×#66961C2
hypercenter#419D11
hypocenterC11#3042
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
1. #10623347C2semidirect
2. C22×#4325C2semidirect
4. #10623052C2semidirect
5. C11×#419C2semidirect
6. #10622732C2semidirect
7. #10622615C2semidirect
8. #10622432C2semidirect
9. #10622431C2semidirect
15. #67000C22semidirect
17. #66997C22semidirect
29. C11×#103C22semidirect
30. Dic11⋊C8C22semidirect
31. #66874C22semidirect
32. #66873C22semidirect
104. #419D11semidirect
142. #103C2×D11semidirect
183. C11#3042semidirect

Maximal subgroups

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

subgroupindex
#106233472
C22×#43252
C2×#669612
#106230522
C11×#4192
#106227322
#106226152
#106224322
#106224312
#304211