Finite Group Databasebeta

← #13078113

Subgroups — #13078113

Order 1408.

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

normal subgroups only

This group has 500 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
1C2×#67000C211yesmaximal, characteristic, complemented
2C2×#66995C211yesmaximal, characteristic, complemented
3C2×#66961C211yesmaximal, characteristic
4#10623053C211yesmaximal, characteristic, complemented
5C11×#419C211yesmaximal, characteristic, complemented
6#10622731C211yesmaximal, characteristic, complemented
7#10622614C211yesmaximal, characteristic, complemented
8#10622432C214yesmaximal, complemented
9#10622411C214yesmaximal, complemented
10C22×Q8×C11C2211yescharacteristic
11C2×#4339C2211yescharacteristic
12C22×D44C2211yescharacteristic
13C2×C11×M16C2211yescharacteristic
14C11×#117C2211yescharacteristic
15#67000—21no—
16#67000—21no—
17#67000C2214yes—
18C2×#4326C2212yescomplemented
19#66995—24no—
20C2×#4325C2212yescomplemented
21C2×(C2×D11)⋊C4—22no—
22C2×C4×Dic11C2211yescharacteristic
23C2×#4318C2211yescharacteristic
24#66961—24no—
25C2×D88C2212yes—
26C2×#4314C2212yes—
27#66946C2212yescomplemented
28#66940C2212yescomplemented
29(C22⋊D11)⋊C4—22no—
30#66925—21no—
31C42×D11—21no—
32C11×#103C2214yescomplemented
33Dic11⋊C8C2214yescomplemented
34#66873C2214yes—
35C23×D11—21no—
36C2×Q8×C11—21no—
37C2×Q8×C11—22no—
38C2×Q8×C11—22no—
39C2×Q8×C11C2312yes—
40C22×C4×C11—21no—
41C22×C4×C11C2311yescharacteristic
42C2×C22⋊D11—21no—
43C22×Dic11D412yes—
44#4339—22no—
45#4339D414yes—
46C2×D44—21no—
47C2×D44—22no—
48C2×D44—22no—
49C2×D44C2312yes—
50C2×D44C2311yescharacteristic
51C2×C4×D11—22no—
52C2×C4×D11—21no—
53C2×Dic22C2311yescharacteristic
54C11×M16—22no—
55C2×C8×C11C2312yes—
56C11×C4⋊C4C2312yes—
57C11×C22⋊C4—21no—
58C42×C11—21no—
59#4326—24no—
60#4325—24no—
61(C2×D11)⋊C4—22no—
62(C2×D11)⋊C4—24no—
63(C2×D11)⋊C4—24no—
64Dic11⋊C4—22no—
65C4×Dic11—22no—
66C4×Dic11D411yescharacteristic
67C4×Dic11D411yescharacteristic
68C4×Dic11C2312yes—
69#4318—22no—
70C2×C11⋊C8C2312yes—
71D88—24no—
72#4314—24no—
73#3040—111nomaximal, Sylow
74C23×C11C2×D411yescharacteristic
75C22×D11—21no—
76C22×D11—22no—
77C22×D11—44no—
78C22×D11—42no—
79Q8×C11—22no—
80Q8×C11—22no—
81Q8×C11—42no—
82C2×C4×C11—22no—
83C2×C4×C11—22no—
84C2×C4×C11—42no—
85C2×C4×C11C2×D411yescharacteristic
86C2×C4×C11C2×D412yes—
87C2×C4×C11#4112yes—
88C2×C4×C11C2411yescharacteristic
89C22⋊D11—24no—
90C2×Dic11—21no—
91C2×Dic11—42no—
92C2×Dic11C2×D412yes—
93C2×Dic11C2×D412yes—
94D44—22no—
95D44—21no—
96D44—22no—
97D44—42no—
98D44C2×D412yes—
99C4×D11—24no—
100C4×D11—44no—
101Dic22—21no—
102Dic22C2×D412yes—
103C8×C11—22no—
104C11⋊C8—22no—
105C2×#137—111no—
106C2×AGL(1,ℤ/8)—111no—
107C2×#124—111no—
108C4×#41—111no—
109#464—114no—
110#463—114no—
111#423—111no—
112#419D1111yescharacteristic, complemented
113#418—111no—
114C22×C11—22no—
115C22×C11#12112yes—
116C22×C11C22×D411yescharacteristic
117C2×D11—22no—
118C2×D11—42no—
119C2×D11—42no—
120C2×D11—44no—
121C2×D11—84no—
122C4×C11—42no—
123C4×C11—42no—
124C4×C11#12112yes—
125C4×C11C22×D411yescharacteristic
126C4×C11C2×#4111yescharacteristic
127Dic11—22no—
128Dic11—22no—
129Dic11—22no—
130C2×#41—111no—
131C22×Q8C2×D1111yescharacteristic
132C22×D4—111no—
133#137—224no—
134AGL(1,ℤ/8)—224no—
135C2×Q16—112no—
136C2×SD16—112no—
137C2×SD16—112no—
138C2×D8—112no—
139C2×M16—111no—
140C2×M16C2×D1111yescharacteristic
141#124—114no—
142#124—221no—
143#124—221no—
144C4×Q8—112no—
145C4×D4—112no—
146C4×D4—222no—
147#117—221no—
148#117C2×D1111yescharacteristic
149C2×C22⋊C4—222no—
150C2×C42—111no—
151C2×C42—221no—
152C4⋊C8—114no—
153#103C2×D1114yescomplemented
154#102—114no—
155C2×C11—22no—
156C2×C11C2×#12111yescharacteristic
157C2×C11#57512yes—
158D11—42no—
159D11—82no—
160C24—221no—
161#41—114no—
162#41—222no—
163C2×Q8—21no—
164C2×Q8—22no—
165C2×Q8—22no—
166C2×Q8—111no—
167C2×Q8C22×D1112yes—
168C2×D4—111no—
169C2×D4—112no—
170C2×D4—221no—
171C2×D4—222no—
172C2×D4—222no—
173C2×D4—221no—
174C22×C4—21no—
175C22×C4—112no—
176C22×C4—222no—
177C22×C4—221no—
178C22×C4C22×D1111yescharacteristic
179Q16—224no—
180SD16—224no—
181SD16—224no—
182D8—224no—
183M16—22no—
184M16—222no—
185C2×C8—112no—
186C2×C8C22×D1112yes—
187C4⋊C4—222no—
188C4⋊C4C22×D1112yes—
189C22⋊C4—21no—
190C22⋊C4—224no—
191C22⋊C4—224no—
192C22⋊C4—222no—
193C42—21no—
194C42—111no—
195C42—111no—
196C42—112no—
197C42—222no—
198C11#304011yescharacteristic, complemented, Sylow
199C23—221no—
200C23—222no—
201C23—444no—
202C23—442no—
203C23D4×D1111yescharacteristic
204Q8—22no—
205Q8—22no—
206Q8—42no—
207Q8—112no—
208Q8—221no—
209D4—112no—
210D4—224no—
211D4—221no—
212D4—222no—
213D4—222no—
214D4—442no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—42no—
218C2×C4—112no—
219C2×C4—112no—
220C2×C4—221no—
221C2×C4—224no—
222C2×C4—444no—
223C2×C4—442no—
224C2×C4#433912yes—
225C2×C4D4×D1111yescharacteristic
226C2×C4D4×D1112yes—
227C2×C4C23×D1111yescharacteristic
228C8—22no—
229C8—222no—
230C22—22no—
231C22—222no—
232C22—442no—
233C22—442no—
234C22—444no—
235C22—884no—
236C22#6693712yes—
237C22C2×D4×D1111yescharacteristic
238C4—42no—
239C4—42no—
240C4—222no—
241C4—222no—
242C4—222no—
243C4#6693712yes—
244C4C2×#433911yescharacteristic
245C4C2×D4×D1111yescharacteristic
246C2—22no—
247C2—442no—
248C2—882no—
249C2C2×#6693711yescharacteristic
250C2#1062330812yes—
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#419C2
socleC22×C11C22×D4
prime radicalC2×#66961C2
hypercenter#419D11
hypocenterC11#3040
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. C2×#67000C2semidirect
2. C2×#66995C2semidirect
4. #10623053C2semidirect
5. C11×#419C2semidirect
6. #10622731C2semidirect
7. #10622614C2semidirect
8. #10622432C2semidirect
9. #10622411C2semidirect
18. C2×#4326C22semidirect
20. C2×#4325C22semidirect
27. #66946C22semidirect
28. #66940C22semidirect
32. C11×#103C22semidirect
33. Dic11⋊C8C22semidirect
112. #419D11semidirect
153. #103C2×D11semidirect
198. C11#3040semidirect

Maximal subgroups

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

subgroupindex
C2×#670002
C2×#669952
C2×#669612
#106230532
C11×#4192
#106227312
#106226142
#106224322
#106224112
#304011