Finite Group Databasebeta

← #13079680

Subgroups — #13079680

Order 1408.

388 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 109 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#10623229C211yesmaximal, characteristic, complemented
2#10623206C211yesmaximal, characteristic, complemented
3C11×#488C211yesmaximal, characteristic, complemented
4#10622682C211yesmaximal, characteristic, complemented
5#10622671C211yesmaximal, characteristic, complemented
6#10622431C212yesmaximal, complemented
7#10622419C212yesmaximal, complemented
8#10622400C212yesmaximal, complemented
9#10622394C212yesmaximal, complemented
10#10622306C211yesmaximal, characteristic, complemented
11#10622303C211yesmaximal, characteristic, complemented
12C2×Q8×D11C2211yescharacteristic
13C2×#4341C2211yescharacteristic
14C11×#125C2211yescharacteristic
15C11×#124C2211yescharacteristic
16#66997C2211yescharacteristic
17C2×#4325C2212yes—
18#66989C2211yescharacteristic
19C2×#4323C2212yes—
20C2×#4314C2212yes—
21C2×#4314C2212yes—
22#66948—22no—
23#66948C2212yes—
24#66947—22no—
25#66946C2212yes—
26#66936—22no—
27#66931—22no—
28#66927C2211yescharacteristic
29#66925C2211yescharacteristic
30#66922C2211yescharacteristic
31C11×#103C2212yes—
32C11×#102C2212yes—
33C4×C8×C11C2211yescharacteristic
34(C2×D11)⋊C8C2212yes—
35Dic11⋊C8C2212yes—
36#66874C2212yes—
37#66874C2212yes—
38#66867C2211yescharacteristic
39C2×Q8×C11C2311yescharacteristic
40C2×D4×C11C2311yescharacteristic
41C2×C22⋊D11—21no—
42C22×Dic11—21no—
43Q8×D11—42no—
44#4341—42no—
45C2×D44—22no—
46C2×D44—22no—
47C2×D44C2312yes—
48C2×C4×D11—22no—
49C2×C4×D11—21no—
50C2×C4×D11C2311yescharacteristic
51C2×Dic22—21no—
52C2×Dic22C2311yescharacteristic
53C2×Dic22C2311yescharacteristic
54C2×C8×C11C2312yes—
55C11×C4⋊C4—22no—
56C11×C4⋊C4C2312yes—
57C11×C22⋊C4—22no—
58C42×C11C2311yescharacteristic
59C22⋊Dic11—22no—
60#4325—42no—
61#4323—42no—
62(C2×D11)⋊C4—22no—
63(C2×D11)⋊C4—22no—
64(C2×D11)⋊C4D412yes—
65C4⋊Dic11—22no—
66Dic11⋊C4—22no—
67Dic11⋊C4D412yes—
68C4×Dic11C2311yescharacteristic
69C2×C11⋊C8C2312yes—
70#4314—42no—
71#4314—42no—
72#3221—111nomaximal, Sylow
73C23×C11—21no—
74C22×D11—22no—
75C22×D11C2×D411yescharacteristic
76Q8×C11—22no—
77D4×C11—22no—
78C2×C4×C11—21no—
79C2×C4×C11—22no—
80C2×C4×C11C2×D412yes—
81C2×C4×C11C2411yescharacteristic
82C22⋊D11—42no—
83C2×Dic11—21no—
84C2×Dic11—21no—
85C2×Dic11—42no—
86C2×Dic11C2×D412yes—
87C2×Dic11C2×D411yescharacteristic
88D44—22no—
89D44—22no—
90D44—82no—
91D44—82no—
92C4×D11—22no—
93C4×D11—42no—
94C4×D11—82no—
95Dic22—22no—
96Dic22—22no—
97Dic22—42no—
98C8×C11—22no—
99C11⋊C8—22no—
100#540—111no—
101#536—111no—
102#496—111no—
103#492—111no—
104#491—111no—
105#488D1111yescharacteristic, complemented
106#463—112no—
107#461—112no—
108#449—112no—
109#448—112no—
110#433—111no—
111C22×C11—41no—
112C22×C11—42no—
113C22×C11C22×D411yescharacteristic
114C2×D11—21no—
115C2×D11—22no—
116C2×D11—42no—
117C2×D11—42no—
118C2×D11—42no—
119C4×C11—22no—
120C4×C11—41no—
121C4×C11—42no—
122C4×C11H(5,𝔽2)12yes—
123Dic11—21no—
124Dic11—22no—
125Dic11—41no—
126Dic11—41no—
127C2×#41—111no—
128C22×Q8—111no—
129C2×SD16—112no—
130C2×SD16—112no—
131C2×SD16—112no—
132C2×D8—112no—
133C4⋊Q8—111no—
134C4⋊Q8—111no—
135#127—111no—
136#125C2×D1111yescharacteristic
137#124—111no—
138#124C2×D1111yescharacteristic
139#123—222no—
140#123—222no—
141C22⋊Q8—222no—
142#121—112no—
143#121—222no—
144C4×D4—112no—
145#117—111no—
146C4⋊C8—112no—
147#103—112no—
148#103—112no—
149#103C2×D1112yes—
150#102C2×D1112yes—
151C22⋊C8—112no—
152#97—111no—
153C4×C8C2×D1111yescharacteristic
154C2×C11—81no—
155C2×C11#53511yescharacteristic
156C2×C11#57712yes—
157D11—41no—
158D11—82no—
159#41—442no—
160C2×Q8—111no—
161C2×Q8—111no—
162C2×Q8—221no—
163C2×Q8—442no—
164C2×Q8C22×D1111yescharacteristic
165C2×D4—112no—
166C2×D4—222no—
167C2×D4—221no—
168C2×D4—222no—
169C2×D4C22×D1111yescharacteristic
170C22×C4—111no—
171C22×C4—222no—
172C22×C4—221no—
173C22×C4—221no—
174SD16—442no—
175SD16—442no—
176SD16—442no—
177D8—442no—
178C2×C8—112no—
179C2×C8C22×D1112yes—
180C4⋊C4—22no—
181C4⋊C4—112no—
182C4⋊C4—222no—
183C4⋊C4—222no—
184C4⋊C4C22×D1112yes—
185C22⋊C4—22no—
186C22⋊C4—112no—
187C22⋊C4—222no—
188C22⋊C4—222no—
189C22⋊C4—222no—
190C42—111no—
191C42C22×D1111yescharacteristic
192C11#322111yescharacteristic, complemented, Sylow
193C23—21no—
194C23—111no—
195C23—222no—
196Q8—22no—
197Q8—222no—
198Q8—222no—
199Q8—442no—
200D4—22no—
201D4—222no—
202D4—222no—
203D4—442no—
204D4—882no—
205D4—882no—
206C2×C4—21no—
207C2×C4—22no—
208C2×C4—112no—
209C2×C4—111no—
210C2×C4—222no—
211C2×C4—221no—
212C2×C4—221no—
213C2×C4—442no—
214C2×C4—442no—
215C2×C4—882no—
216C2×C4D4×D1112yes—
217C2×C4C23×D1111yescharacteristic
218C8—22no—
219C8—222no—
220C22—42no—
221C22—41no—
222C22—222no—
223C22—221no—
224C22—442no—
225C22—442no—
226C22—442no—
227C22C2×D4×D1111yescharacteristic
228C4—22no—
229C4—42no—
230C4—41no—
231C4—222no—
232C4—221no—
233C4—441no—
234C4—441no—
235C4#6704212yes—
236C2—81no—
237C2—441no—
238C2—882no—
239C2#1062320511yescharacteristic
240C2#1062330112yes—
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#488C2
socleC22×C11C22×D4
hypercenter#488D11
hypocenterC11#3221
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #488

Complements

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

NH ≅ G/Ntype
1. #10623229C2semidirect
2. #10623206C2semidirect
3. C11×#488C2semidirect
4. #10622682C2semidirect
5. #10622671C2semidirect
6. #10622431C2semidirect
7. #10622419C2semidirect
8. #10622400C2semidirect
9. #10622394C2semidirect
10. #10622306C2semidirect
11. #10622303C2semidirect
105. #488D11semidirect
192. C11#3221semidirect

Maximal subgroups

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

subgroupindex
#106232292
#106232062
C11×#4882
#106226822
#106226712
#106224312
#106224192
#106224002
#106223942
#106223062
#106223032
#322111