Finite Group Databasebeta

← #13079679

Subgroups — #13079679

Order 1408.

388 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 117 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#10623066C211yesmaximal, characteristic, complemented
2#10623057C211yesmaximal, characteristic, complemented
3C11×#433C211yesmaximal, characteristic, complemented
4#10622457C212yesmaximal, complemented
5#10622454C212yesmaximal, complemented
6#10622351C212yesmaximal, complemented
7#10622347C212yesmaximal, complemented
8#10622325C211yesmaximal, characteristic, complemented
9#10622316C211yesmaximal, characteristic, complemented
10#10622310C211yesmaximal, characteristic, complemented
11#10622306C211yesmaximal, characteristic, complemented
12C2×#4339C2211yescharacteristic
13C22×Dic22C2211yescharacteristic
14C11×#117C2211yescharacteristic
15#66983C2212yes—
16C2×D88C2212yes—
17C2×#4314C2212yes—
18C2×#4314C2212yes—
19C2×#4314C2212yes—
20#66950—22no—
21#66947—22no—
22#66939—22no—
23#66937—22no—
24#66928C2211yescharacteristic
25#66928C2211yescharacteristic
26#66927C2211yescharacteristic
27C4×D44C2212yes—
28#66923C2211yescharacteristic
29#66922C2211yescharacteristic
30#66922C2211yescharacteristic
31C11×C4⋊C8C2212yes—
32C11×C22⋊C8C2212yes—
33C11×#97C2211yescharacteristic
34C4×C8×C11C2211yescharacteristic
35#66885C2212yes—
36#66880C2212yes—
37#66880C2212yes—
38#66880C2212yes—
39C22×C4×C11C2311yescharacteristic
40C2×C22⋊D11—21no—
41C2×C22⋊D11—22no—
42C22×Dic11—21no—
43#4339—42no—
44C2×D44—22no—
45C2×D44C2311yescharacteristic
46C2×D44C2312yes—
47C2×C4×D11—21no—
48C2×C4×D11—22no—
49C2×Dic22—21no—
50C2×Dic22—42no—
51C2×Dic22C2311yescharacteristic
52C2×Dic22C2311yescharacteristic
53C2×Dic22C2311yescharacteristic
54C2×C8×C11C2312yes—
55C2×C8×C11C2312yes—
56C11×C4⋊C4D412yes—
57C11×C22⋊C4D412yes—
58C42×C11C2311yescharacteristic
59C42×C11C2311yescharacteristic
60(C2×D11)⋊C4—22no—
61(C2×D11)⋊C4—22no—
62(C2×D11)⋊C4—22no—
63(C2×D11)⋊C4—22no—
64C4⋊Dic11—22no—
65C4⋊Dic11—22no—
66C4⋊Dic11C2312yes—
67Dic11⋊C4—22no—
68D88—42no—
69#4314—42no—
70#4314—42no—
71#4314—42no—
72#3221—111nomaximal, Sylow
73C23×C11C2×D411yescharacteristic
74C22×D11—21no—
75C22×D11—22no—
76C2×C4×C11—22no—
77C2×C4×C11C2×D412yes—
78C2×C4×C11C2×D412yes—
79C2×C4×C11C2×D411yescharacteristic
80C2×C4×C11C2411yescharacteristic
81C22⋊D11—42no—
82C22⋊D11—82no—
83C2×Dic11—22no—
84C2×Dic11—21no—
85C2×Dic11—21no—
86C2×Dic11—21no—
87C2×Dic11—42no—
88D44—22no—
89D44—22no—
90D44—22no—
91D44—82no—
92C4×D11—42no—
93C4×D11—82no—
94Dic22—22no—
95Dic22—22no—
96Dic22—22no—
97Dic22—42no—
98C8×C11—22no—
99C8×C11—22no—
100#540—111no—
101#536—111no—
102#496—111no—
103#492—111no—
104#491—111no—
105#488—111no—
106#463—112no—
107#461—112no—
108#449—112no—
109#448—112no—
110#433D1111yescharacteristic, complemented
111C22×C11—21no—
112C22×C11—22no—
113C22×C11C22×D411yescharacteristic
114C2×D11—41no—
115C2×D11—42no—
116C2×D11—42no—
117C2×D11—42no—
118C2×D11—42no—
119C4×C11—21no—
120C4×C11—22no—
121C4×C11—22no—
122C4×C11H(5,𝔽2)12yes—
123Dic11—41no—
124Dic11—41no—
125Dic11—41no—
126Dic11—42no—
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#125—111no—
137#124—111no—
138#124—111no—
139#123—222no—
140#123—222no—
141C22⋊Q8—222no—
142#121—112no—
143#121—222no—
144C4×D4—112no—
145#117C2×D1111yescharacteristic
146C4⋊C8C2×D1112yes—
147#103—112no—
148#103—112no—
149#103—112no—
150#102—112no—
151C22⋊C8C2×D1112yes—
152#97C2×D1111yescharacteristic
153C4×C8C2×D1111yescharacteristic
154C2×C11—41no—
155C2×C11#53511yescharacteristic
156C2×C11#57712yes—
157D11—81no—
158D11—82no—
159#41—442no—
160C2×Q8—111no—
161C2×Q8—111no—
162C2×Q8—111no—
163C2×Q8—221no—
164C2×Q8—442no—
165C2×D4—111no—
166C2×D4—112no—
167C2×D4—221no—
168C2×D4—222no—
169C2×D4—222no—
170C22×C4—221no—
171C22×C4—221no—
172C22×C4—222no—
173C22×C4C22×D1111yescharacteristic
174SD16—442no—
175SD16—442no—
176SD16—442no—
177D8—442no—
178C2×C8C22×D1112yes—
179C2×C8C22×D1112yes—
180C4⋊C4—112no—
181C4⋊C4—222no—
182C4⋊C4—222no—
183C4⋊C4—222no—
184C4⋊C4D4412yes—
185C22⋊C4—222no—
186C22⋊C4—222no—
187C22⋊C4—222no—
188C22⋊C4—222no—
189C22⋊C4D4412yes—
190C42C22×D1111yescharacteristic
191C42C22×D1111yescharacteristic
192C11#322111yescharacteristic, complemented, Sylow
193C23—221no—
194C23—222no—
195C23C2×D4411yescharacteristic
196Q8—222no—
197Q8—222no—
198Q8—222no—
199Q8—442no—
200D4—222no—
201D4—222no—
202D4—222no—
203D4—442no—
204D4—882no—
205D4—882no—
206C2×C4—22no—
207C2×C4—222no—
208C2×C4—221no—
209C2×C4—221no—
210C2×C4—221no—
211C2×C4—442no—
212C2×C4—442no—
213C2×C4—882no—
214C2×C4C2×D4412yes—
215C2×C4C2×D4412yes—
216C2×C4C2×D4411yescharacteristic
217C2×C4C23×D1111yescharacteristic
218C8—22no—
219C8—22no—
220C22—22no—
221C22—21no—
222C22—442no—
223C22—442no—
224C22—442no—
225C22—441no—
226C22—442no—
227C22C22×D4411yescharacteristic
228C4—22no—
229C4—22no—
230C4—21no—
231C4—442no—
232C4—441no—
233C4—441no—
234C4—441no—
235C4#6704212yes—
236C2—41no—
237C2—882no—
238C2—881no—
239C2#1062305611yescharacteristic
240C2#1062328212yes—
subgroupG/H
centerC22C22×D44
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#433C2
socleC22×C11C22×D4
hypercenter#433D11
hypocenterC11#3221
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #10623066C2semidirect
2. #10623057C2semidirect
3. C11×#433C2semidirect
4. #10622457C2semidirect
5. #10622454C2semidirect
6. #10622351C2semidirect
7. #10622347C2semidirect
8. #10622325C2semidirect
9. #10622316C2semidirect
10. #10622310C2semidirect
11. #10622306C2semidirect
110. #433D11semidirect
192. C11#3221semidirect

Maximal subgroups

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

subgroupindex
#106230662
#106230572
C11×#4332
#106224572
#106224542
#106223512
#106223472
#106223252
#106223162
#106223102
#106223062
#322111