Finite Group Databasebeta

← #13079004

Subgroups — #13079004

Order 1408.

400 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 125 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
2#10623048C211yesmaximal, characteristic, complemented
3C11×#419C211yesmaximal, characteristic, complemented
4#10622838C211yesmaximal, characteristic, complemented
5#10622744C211yesmaximal, characteristic
6M16×Dic11C211yesmaximal, characteristic, complemented
7#10622614C211yesmaximal, characteristic
8#10622413C214yesmaximal, complemented
9#10622408C214yesmaximal, complemented
10C22×Q8×C11C2211yescharacteristic
11C22×D44C2211yescharacteristic
12C2×C11×M16C2211yescharacteristic
13C11×#117C2211yescharacteristic
14#67000—22no—
15#67000C2212yes—
16#67000C2212yes—
17C2×(C2×D11)⋊C4—22no—
18#66979C2211yescharacteristic
19C2×C4×Dic11C2211yescharacteristic
20C2×#4318C2211yescharacteristic
21#66943C2212yescomplemented
22#66941C2212yescomplemented
23#66931—22no—
24C4×Dic22—22no—
25C11×#103C2214yescomplemented
26#66899C2214yescomplemented
27#66885C2214yes—
28#66879C2212yescomplemented
29C8×Dic11C2212yescomplemented
30#66873C2214yes—
31C23×D11—21no—
32C2×Q8×C11—21no—
33C2×Q8×C11—22no—
34C2×Q8×C11—22no—
35C2×Q8×C11C2312yes—
36C22×C4×C11—21no—
37C22×C4×C11C2311yescharacteristic
38C22×Dic11D412yes—
39C2×D44—21no—
40C2×D44—22no—
41C2×D44—22no—
42C2×D44C2312yes—
43C2×Dic22—22no—
44C11×M16—22no—
45C2×C8×C11C2312yes—
46C11×C4⋊C4C2312yes—
47C11×C22⋊C4—21no—
48C42×C11—21no—
49C22⋊Dic11—21no—
50(C2×D11)⋊C4—24no—
51(C2×D11)⋊C4—24no—
52C4⋊Dic11—22no—
53C4⋊Dic11C2312yes—
54Dic11⋊C4—22no—
55Dic11⋊C4—22no—
56C4×Dic11—21no—
57C4×Dic11D412yes—
58C4×Dic11C2311yescharacteristic
59C4×Dic11C2311yescharacteristic
60#4318—22no—
61C2×C11⋊C8C2312yes—
62#3140—111nomaximal, Sylow
63C23×C11C2×D411yescharacteristic
64C22×D11—22no—
65C22×D11—44no—
66C22×D11—42no—
67Q8×C11—22no—
68Q8×C11—22no—
69Q8×C11—42no—
70C2×C4×C11—22no—
71C2×C4×C11—22no—
72C2×C4×C11—42no—
73C2×C4×C11C2×D411yescharacteristic
74C2×C4×C11#4112yes—
75C2×C4×C11#4112yes—
76C2×C4×C11C2411yescharacteristic
77C2×Dic11—22no—
78C2×Dic11—42no—
79C2×Dic11C2×D412yes—
80C2×Dic11C2×D412yes—
81D44—22no—
82D44—22no—
83D44—42no—
84Dic22—44no—
85C8×C11—22no—
86C11⋊C8—22no—
87#533—111no—
88C2×#124—111no—
89#489—114no—
90#488—114no—
91#419—111no—
92#419D1111yescharacteristic, complemented
93#418—111no—
94#418—111no—
95C4×M16—111no—
96C22×C11—22no—
97C22×C11#12412yes—
98C22×C11C22×D411yescharacteristic
99C2×D11—42no—
100C2×D11—44no—
101C2×D11—84no—
102C4×C11—42no—
103C4×C11—42no—
104C4×C11#12412yes—
105C4×C11C2×#4111yescharacteristic
106C4×C11C2×#4111yescharacteristic
107Dic11—22no—
108Dic11—22no—
109Dic11—42no—
110C22×Q8C2×D1111yescharacteristic
111C22×D4—111no—
112C2×M16—111no—
113C2×M16C2×D1111yescharacteristic
114C4⋊Q8—112no—
115#125—112no—
116#124—112no—
117#124—112no—
118#124—222no—
119C22⋊Q8—222no—
120C4×Q8—222no—
121#117—111no—
122#117C2×D1111yescharacteristic
123C2×C22⋊C4—222no—
124C2×C42—111no—
125#103—114no—
126#103C2×D1114yescomplemented
127#102—114no—
128#102—114no—
129#97—112no—
130C4×C8—112no—
131C2×C11—22no—
132C2×C11C2×#12411yescharacteristic
133C2×C11#57512yes—
134D11—82no—
135C24—221no—
136C2×Q8—21no—
137C2×Q8—22no—
138C2×Q8—22no—
139C2×Q8—222no—
140C2×Q8C22×D1112yes—
141C2×D4—112no—
142C2×D4—222no—
143C2×D4—221no—
144C2×D4—222no—
145C22×C4—21no—
146C22×C4—112no—
147C22×C4C22×D1111yescharacteristic
148M16—22no—
149M16—222no—
150C2×C8—112no—
151C2×C8C22×D1112yes—
152C4⋊C4—112no—
153C4⋊C4—222no—
154C4⋊C4—222no—
155C4⋊C4—222no—
156C4⋊C4C22×D1112yes—
157C22⋊C4—21no—
158C22⋊C4—224no—
159C22⋊C4—224no—
160C22⋊C4—221no—
161C42—21no—
162C42—112no—
163C42—111no—
164C42—111no—
165C42—221no—
166C11#314011yescharacteristic, complemented, Sylow
167C23—222no—
168C23—444no—
169C23—442no—
170C23D4×D1111yescharacteristic
171Q8—22no—
172Q8—22no—
173Q8—42no—
174Q8—444no—
175D4—222no—
176D4—222no—
177D4—442no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—42no—
181C2×C4—112no—
182C2×C4—112no—
183C2×C4—222no—
184C2×C4—442no—
185C2×C4#433912yes—
186C2×C4D4×D1111yescharacteristic
187C2×C4#434112yes—
188C2×C4C23×D1111yescharacteristic
189C8—22no—
190C8—222no—
191C22—22no—
192C22—442no—
193C22—444no—
194C22—884no—
195C22#6693812yes—
196C22C2×D4×D1111yescharacteristic
197C4—42no—
198C4—42no—
199C4—222no—
200C4—222no—
201C4—442no—
202C4#6693812yes—
203C4C2×#433911yescharacteristic
204C4C2×#434111yescharacteristic
205C2—22no—
206C2—882no—
207C2C2×#6693811yescharacteristic
208C2#1062330812yes—
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#419C2
socleC22×C11C22×D4
prime radicalC22×D44C22
hypercenter#419D11
hypocenterC11#3140
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
2. #10623048C2semidirect
3. C11×#419C2semidirect
4. #10622838C2semidirect
6. M16×Dic11C2semidirect
8. #10622413C2semidirect
9. #10622408C2semidirect
21. #66943C22semidirect
22. #66941C22semidirect
25. C11×#103C22semidirect
26. #66899C22semidirect
28. #66879C22semidirect
29. C8×Dic11C22semidirect
92. #419D11semidirect
126. #103C2×D11semidirect
166. C11#3140semidirect

Maximal subgroups

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

subgroupindex
C2×#670002
#106230482
C11×#4192
#106228382
#106227442
M16×Dic112
#106226142
#106224132
#106224082
#314011