Finite Group Databasebeta

← #13078140

Subgroups — #13078140

Order 1408.

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

normal subgroups only

This group has 490 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#10623361C211yesmaximal, characteristic
2C2×#67004C211yesmaximal, characteristic, complemented
3C22×#4314C211yesmaximal, characteristic, complemented
4#10623047C211yesmaximal, characteristic, complemented
5C11×#416C211yesmaximal, characteristic, complemented
6#10622715C211yesmaximal, characteristic, complemented
7#10622614C211yesmaximal, characteristic, complemented
8#10622411C214yesmaximal, complemented
9#10622375C214yesmaximal, complemented
10C2×C11×#41C2211yescharacteristic
11C22×D44C2211yescharacteristic
12C22×Dic22C2211yescharacteristic
13C22×C8×C11C2211yescharacteristic
14C11×#117C2211yescharacteristic
15#67004—24no—
16#67000C2212yes—
17C2×#4326C2212yescomplemented
18#66993C2212yes—
19#66990—22no—
20C2×#4324C2212yescomplemented
21#66983—22no—
22#66979C2211yescharacteristic
23C2×#4318C2211yescharacteristic
24C2×#4314—24no—
25C2×#4314C2214yes—
26#66940C2214yescomplemented
27#66930—22no—
28C4×Dic22—22no—
29C11×#103C2212yescomplemented
30C11×#102C2212yescomplemented
31Dic11⋊C8C2214yescomplemented
32#66873C2214yes—
33C23×D11—21no—
34C11×#41—22no—
35C11×#41—22no—
36C2×Q8×C11C2311yescharacteristic
37C2×D4×C11—21no—
38C2×D4×C11C2311yescharacteristic
39C22×C4×C11—21no—
40C22×C4×C11C2311yescharacteristic
41C2×C22⋊D11—24no—
42C22×Dic11—21no—
43C2×D44—21no—
44C2×D44—22no—
45C2×D44—22no—
46C2×D44C2312yes—
47C2×Dic22—21no—
48C2×Dic22—22no—
49C2×Dic22D414yescomplemented
50C2×Dic22C2312yes—
51C2×C8×C11—22no—
52C2×C8×C11C2312yes—
53C11×C4⋊C4C2312yes—
54C11×C22⋊C4—21no—
55C42×C11—21no—
56C22⋊Dic11D412yes—
57#4326—24no—
58#4324—24no—
59(C2×D11)⋊C4—24no—
60C4⋊Dic11D412yes—
61Dic11⋊C4—24no—
62C4×Dic11—24no—
63C4×Dic11C2312yes—
64#4318—22no—
65C2×C11⋊C8C2312yes—
66#4314—28no—
67#3043—111nomaximal, Sylow
68C23×C11—21no—
69C23×C11C2×D411yescharacteristic
70C22×D11—22no—
71C22×D11—42no—
72C22×D11—82no—
73Q8×C11—21no—
74Q8×C11—21no—
75D4×C11—21no—
76D4×C11—21no—
77D4×C11—42no—
78C2×C4×C11—22no—
79C2×C4×C11—21no—
80C2×C4×C11—42no—
81C2×C4×C11C2×D411yescharacteristic
82C2×C4×C11C2×D412yes—
83C2×C4×C11#4112yes—
84C2×C4×C11C2411yescharacteristic
85C22⋊D11—84no—
86C2×Dic11—24no—
87C2×Dic11—22no—
88C2×Dic11C2×D414yes—
89D44—22no—
90D44—22no—
91D44—42no—
92Dic22—24no—
93Dic22—22no—
94Dic22C2×D414yes—
95C8×C11—22no—
96C11⋊C8—22no—
97C2×#137—111no—
98C22×SD16—111no—
99#535—111no—
100#519—111no—
101#464—114no—
102#460—114no—
103#424—111no—
104#418—111no—
105#416D1111yescharacteristic, complemented
106C22×C11—22no—
107C22×C11—41no—
108C22×C11—42no—
109C22×C11#12112yes—
110C22×C11C22×D411yescharacteristic
111C2×D11—42no—
112C2×D11—44no—
113C2×D11—84no—
114C4×C11—41no—
115C4×C11—42no—
116C4×C11#12112yes—
117C4×C11C22×D411yescharacteristic
118C4×C11C2×#4111yescharacteristic
119Dic11—24no—
120Dic11—24no—
121C2×#41C2×D1111yescharacteristic
122C22×Q8—111no—
123C22×D4—111no—
124#137—224no—
125C2×Q16—112no—
126C2×SD16—112no—
127C2×SD16—114no—
128C2×SD16—224no—
129C2×M16—111no—
130C22×C8C2×D1111yescharacteristic
131#127—112no—
132#124—112no—
133#121—222no—
134#120—222no—
135C4×Q8—114no—
136C4×Q8—222no—
137#117—111no—
138#117—222no—
139#117C2×D1111yescharacteristic
140C4⋊C8—114no—
141#103C2×D1112yescomplemented
142#102—114no—
143#102C2×D1112yescomplemented
144C2×C11—22no—
145C2×C11—81no—
146C2×C11C2×#12111yescharacteristic
147C2×C11#57712yes—
148D11—82no—
149C24—221no—
150#41—22no—
151#41—22no—
152C2×Q8—114no—
153C2×Q8—112no—
154C2×Q8—222no—
155C2×Q8—221no—
156C2×Q8C22×D1111yescharacteristic
157C2×D4—21no—
158C2×D4—112no—
159C2×D4—224no—
160C2×D4—222no—
161C2×D4—222no—
162C2×D4—221no—
163C2×D4C22×D1111yescharacteristic
164C22×C4—21no—
165C22×C4—221no—
166C22×C4C22×D1111yescharacteristic
167Q16—224no—
168SD16—228no—
169SD16—224no—
170M16—222no—
171C2×C8—22no—
172C2×C8—112no—
173C2×C8C22×D1112yes—
174C4⋊C4—112no—
175C4⋊C4—224no—
176C4⋊C4C22×D1112yes—
177C22⋊C4—21no—
178C22⋊C4—112no—
179C22⋊C4—224no—
180C42—21no—
181C42—112no—
182C42—224no—
183C11#304311yescharacteristic, complemented, Sylow
184C23—21no—
185C23—222no—
186C23—442no—
187C23—882no—
188C23D4×D1111yescharacteristic
189Q8—21no—
190Q8—21no—
191Q8—114no—
192Q8—224no—
193Q8—222no—
194D4—21no—
195D4—21no—
196D4—42no—
197D4—222no—
198D4—222no—
199D4—442no—
200D4—884no—
201C2×C4—22no—
202C2×C4—21no—
203C2×C4—42no—
204C2×C4—114no—
205C2×C4—224no—
206C2×C4—222no—
207C2×C4#433912yes—
208C2×C4D4×D1111yescharacteristic
209C2×C4D4×D1112yes—
210C2×C4C23×D1111yescharacteristic
211C8—22no—
212C8—222no—
213C22—22no—
214C22—41no—
215C22—42no—
216C22—442no—
217C22—444no—
218C22—884no—
219C22#6693712yes—
220C22C2×D4×D1111yescharacteristic
221C4—41no—
222C4—42no—
223C4—224no—
224C4—224no—
225C4#6693712yes—
226C4C2×#433911yescharacteristic
227C4C2×D4×D1111yescharacteristic
228C2—22no—
229C2—81no—
230C2—882no—
231C2C2×#6693711yescharacteristic
232C2#1062330112yes—
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#416C2
socleC22×C11C22×D4
prime radical#10623361C2
hypercenter#416D11
hypocenterC11#3043
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
2. C2×#67004C2semidirect
3. C22×#4314C2semidirect
4. #10623047C2semidirect
5. C11×#416C2semidirect
6. #10622715C2semidirect
7. #10622614C2semidirect
8. #10622411C2semidirect
9. #10622375C2semidirect
17. C2×#4326C22semidirect
20. C2×#4324C22semidirect
26. #66940C22semidirect
29. C11×#103C22semidirect
30. C11×#102C22semidirect
31. Dic11⋊C8C22semidirect
49. C2×Dic22D4semidirect
105. #416D11semidirect
141. #103C2×D11semidirect
143. #102C2×D11semidirect
183. C11#3043semidirect

Maximal subgroups

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

subgroupindex
#106233612
C2×#670042
C22×#43142
#106230472
C11×#4162
#106227152
#106226142
#106224112
#106223752
#304311