Finite Group Databasebeta

← #13079569

Subgroups — #13079569

Order 1408.

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

normal subgroups only

This group has 394 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#10623259C211yesmaximal, characteristic, complemented
2#10623256C211yesmaximal, characteristic
3C11×#494C211yesmaximal, characteristic, complemented
4#10622800C214yesmaximal, complemented
5#10622798C214yesmaximal, complemented
6#10622698C211yesmaximal, characteristic, complemented
7#10622694C211yesmaximal, characteristic, complemented
8#10622307C211yesmaximal, characteristic, complemented
9#10622298C211yesmaximal, characteristic, complemented
10C2×#4343C2212yes—
11C2×C11×Q16C2214yes—
12C11×C4⋊Q8C2211yescharacteristic
13C11×C4⋊Q8C2211yescharacteristic
14#67000C2212yes—
15#66999C2212yes—
16Q8×Dic11C2212yes—
17C2×#4325C2214yes—
18#66950—21no—
19#66948—21no—
20#66948—21no—
21#66946—21no—
22#66946—21no—
23#66945—21no—
24#66943—21no—
25#66940—21no—
26#66927C2211yescharacteristic
27C42×D11C2211yescharacteristic
28#66922C2211yescharacteristic
29C4×C8×C11C2211yescharacteristic
30#66899C2214yes—
31#66885C2214yes—
32(C2×D11)⋊C8C2212yes—
33Dic11⋊C8C2212yes—
34C4×C11⋊C8C2211yescharacteristic
35C2×Q8×C11C2312yes—
36C2×Q8×C11C2312yes—
37#4343—44no—
38C2×D44—22no—
39C2×D44—21no—
40C2×D44—21no—
41C2×D44C2312yes—
42C2×C4×D11—22no—
43C2×C4×D11D411yescharacteristic
44C2×C4×D11D411yescharacteristic
45C2×C4×D11C2311yescharacteristic
46C2×Dic22—21no—
47C11×Q16—44no—
48C2×C8×C11C2312yes—
49C11×C4⋊C4—21no—
50C11×C4⋊C4—21no—
51C11×C4⋊C4—21no—
52C11×C4⋊C4—21no—
53C42×C11C2311yescharacteristic
54#4325—44no—
55(C2×D11)⋊C4—22no—
56(C2×D11)⋊C4—22no—
57(C2×D11)⋊C4—22no—
58C4⋊Dic11—22no—
59C4⋊Dic11—21no—
60C4⋊Dic11C2312yes—
61Dic11⋊C4—22no—
62C4×Dic11—22no—
63C4×Dic11D411yescharacteristic
64C4×Dic11D411yescharacteristic
65C4×Dic11C2311yescharacteristic
66C2×C11⋊C8C2312yes—
67#3210—111nomaximal, Sylow
68C22×D11—22no—
69C22×D11C2×D411yescharacteristic
70Q8×C11—24no—
71Q8×C11—24no—
72C2×C4×C11—22no—
73C2×C4×C11—22no—
74C2×C4×C11C2×D411yescharacteristic
75C2×C4×C11C2×D411yescharacteristic
76C2×C4×C11C2411yescharacteristic
77C2×Dic11—22no—
78C2×Dic11C2×D411yescharacteristic
79C2×Dic11C2×D411yescharacteristic
80C2×Dic11C2×D411yescharacteristic
81D44—24no—
82D44—44no—
83D44—42no—
84D44—42no—
85C4×D11—22no—
86C4×D11—22no—
87C4×D11—22no—
88C4×D11—44no—
89Dic22—42no—
90C8×C11—22no—
91C11⋊C8—22no—
92#533—111no—
93#532—111no—
94#494D1111yescharacteristic, complemented
95#492—111no—
96#487—111no—
97#486—111no—
98#464—114no—
99#452—114no—
100#431—111no—
101C22×C11C22×D411yescharacteristic
102C2×D11—21no—
103C2×D11—21no—
104C2×D11—21no—
105C2×D11—42no—
106C2×D11—42no—
107C2×D11—42no—
108C4×C11—42no—
109C4×C11—42no—
110C4×C11#13512yes—
111C4×C11#13712yes—
112C4×C11H(5,𝔽2)12yes—
113Dic11—21no—
114Dic11—21no—
115Dic11—21no—
116Dic11—42no—
117C2×#41—112no—
118C2×Q16C2×D1114yes—
119C2×SD16—114no—
120C4⋊Q8—111no—
121C4⋊Q8C2×D1111yescharacteristic
122C4⋊Q8C2×D1111yescharacteristic
123#127—111no—
124#125—221no—
125#124—112no—
126C22⋊Q8—112no—
127C22⋊Q8—221no—
128#121—221no—
129#121—221no—
130C4×Q8—112no—
131C4×Q8—221no—
132C4×D4—221no—
133C4×D4—221no—
134#117—221no—
135C2×C42—111no—
136C4⋊C8—112no—
137#103—114no—
138#102—114no—
139C22⋊C8—112no—
140C4×C8—111no—
141C4×C8C2×D1111yescharacteristic
142C2×C11#53511yescharacteristic
143C2×C11C2×#13511yescharacteristic
144C2×C11C2×#13711yescharacteristic
145D11—41no—
146D11—82no—
147#41—444no—
148C2×Q8—221no—
149C2×Q8C22×D1112yes—
150C2×Q8C22×D1112yes—
151C2×D4—112no—
152C2×D4—222no—
153C2×D4—221no—
154C2×D4—221no—
155C22×C4—111no—
156C22×C4—111no—
157C22×C4—111no—
158C22×C4—222no—
159Q16—44no—
160SD16—444no—
161C2×C8—112no—
162C2×C8C22×D1112yes—
163C4⋊C4—21no—
164C4⋊C4—21no—
165C4⋊C4—21no—
166C4⋊C4—21no—
167C4⋊C4—112no—
168C4⋊C4—222no—
169C4⋊C4—222no—
170C4⋊C4—221no—
171C22⋊C4—222no—
172C22⋊C4—222no—
173C22⋊C4—222no—
174C42—111no—
175C42—111no—
176C42—111no—
177C42—222no—
178C42C22×D1111yescharacteristic
179C11#321011yescharacteristic, complemented, Sylow
180C23—111no—
181C23—222no—
182Q8—24no—
183Q8—24no—
184Q8—442no—
185D4—224no—
186D4—444no—
187D4—442no—
188D4—442no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—111no—
192C2×C4—111no—
193C2×C4—111no—
194C2×C4—222no—
195C2×C4—222no—
196C2×C4—222no—
197C2×C4—222no—
198C2×C4—444no—
199C2×C4D4×D1111yescharacteristic
200C2×C4D4×D1111yescharacteristic
201C2×C4C23×D1111yescharacteristic
202C8—22no—
203C8—222no—
204C22—221no—
205C22—221no—
206C22—221no—
207C22—442no—
208C22—442no—
209C22—442no—
210C22C2×D4×D1111yescharacteristic
211C4—42no—
212C4—42no—
213C4—221no—
214C4—221no—
215C4—221no—
216C4—442no—
217C4#6697112yes—
218C4#6697212yes—
219C4#6703712yes—
220C2—441no—
221C2—882no—
222C2#1062324611yescharacteristic
223C2C2×#6697111yescharacteristic
224C2C2×#6697211yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#494C2
socleC22×C11C22×D4
prime radical#10623256C2
hypercenter#494D11
hypocenterC11#3210
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #494

Complements

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

NH ≅ G/Ntype
1. #10623259C2semidirect
3. C11×#494C2semidirect
4. #10622800C2semidirect
5. #10622798C2semidirect
6. #10622698C2semidirect
7. #10622694C2semidirect
8. #10622307C2semidirect
9. #10622298C2semidirect
94. #494D11semidirect
179. C11#3210semidirect

Maximal subgroups

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

subgroupindex
#106232592
#106232562
C11×#4942
#106228002
#106227982
#106226982
#106226942
#106223072
#106222982
#321011