Finite Group Databasebeta

← #13079552

Subgroups — #13079552

Order 1408.

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

normal subgroups only

This group has 438 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#10623256C211yesmaximal, characteristic, complemented
2#10623256C211yesmaximal, characteristic, complemented
3C11×#487C211yesmaximal, characteristic, complemented
4#10622701C211yesmaximal, characteristic, complemented
5#10622698C211yesmaximal, characteristic, complemented
6#10622432C214yesmaximal, complemented
7#10622424C214yesmaximal, complemented
8#10622308C211yesmaximal, characteristic, complemented
9#10622298C211yesmaximal, characteristic, complemented
10C2×#4343—21no—
11C2×#4343C2212yes—
12C11×C4⋊Q8C2211yescharacteristic
13C11×C4⋊Q8C2211yescharacteristic
14#67000—21no—
15#67000C2212yes—
16C2×#4325C2214yes—
17C2×D88C2214yes—
18#66948—21no—
19#66948—21no—
20#66948—21no—
21#66948C2212yes—
22#66946—21no—
23#66946—21no—
24#66946—21no—
25#66946C2212yes—
26#66927C2211yescharacteristic
27#66927C2211yescharacteristic
28C42×D11C2211yescharacteristic
29C11×#103C2214yes—
30C4×C8×C11C2211yescharacteristic
31(C2×D11)⋊C8C2212yes—
32Dic11⋊C8C2212yes—
33#66873C2214yes—
34C4×C11⋊C8C2211yescharacteristic
35C2×Q8×C11—21no—
36C2×Q8×C11C2312yes—
37#4343—44no—
38#4343—44no—
39C2×D44—22no—
40C2×D44—22no—
41C2×D44—21no—
42C2×D44—21no—
43C2×D44—21no—
44C2×D44—21no—
45C2×D44C2312yes—
46C2×D44C2312yes—
47C2×C4×D11—22no—
48C2×C4×D11—22no—
49C2×C4×D11D411yescharacteristic
50C2×C4×D11D411yescharacteristic
51C2×C4×D11C2311yescharacteristic
52C2×C8×C11C2312yes—
53C11×C4⋊C4—21no—
54C11×C4⋊C4—21no—
55C11×C4⋊C4—21no—
56C11×C4⋊C4C2312yes—
57C42×C11C2311yescharacteristic
58#4325—44no—
59(C2×D11)⋊C4—22no—
60(C2×D11)⋊C4—22no—
61(C2×D11)⋊C4—22no—
62(C2×D11)⋊C4—22no—
63C4×Dic11D411yescharacteristic
64C4×Dic11D411yescharacteristic
65C4×Dic11C2311yescharacteristic
66C2×C11⋊C8C2312yes—
67D88—44no—
68#3207—111nomaximal, Sylow
69C22×D11—22no—
70C22×D11—22no—
71C22×D11C2×D411yescharacteristic
72Q8×C11—24no—
73Q8×C11—42no—
74C2×C4×C11—22no—
75C2×C4×C11—22no—
76C2×C4×C11C2×D411yescharacteristic
77C2×C4×C11C2×D411yescharacteristic
78C2×C4×C11C2411yescharacteristic
79C2×Dic11C2×D411yescharacteristic
80C2×Dic11C2×D411yescharacteristic
81C2×Dic11C2×D411yescharacteristic
82D44—24no—
83D44—24no—
84D44—44no—
85D44—44no—
86D44—42no—
87D44—42no—
88D44—42no—
89D44—42no—
90C4×D11—22no—
91C4×D11—22no—
92C4×D11—22no—
93C4×D11—44no—
94C4×D11—44no—
95C8×C11—22no—
96C11⋊C8—22no—
97#532—111no—
98#532—111no—
99#493—111no—
100#492—111no—
101#487D1111yescharacteristic, complemented
102#486—111no—
103#463—114no—
104#449—114no—
105#431—111no—
106C22×C11C22×D411yescharacteristic
107C2×D11—21no—
108C2×D11—21no—
109C2×D11—21no—
110C2×D11—42no—
111C2×D11—42no—
112C2×D11—42no—
113C2×D11—42no—
114C2×D11—42no—
115C2×D11—42no—
116C4×C11—42no—
117C4×C11—42no—
118C4×C11#13512yes—
119C4×C11AGL(1,ℤ/8)12yes—
120C4×C11H(5,𝔽2)12yes—
121Dic11—21no—
122Dic11—21no—
123Dic11—21no—
124C2×#41—112no—
125C2×#41—221no—
126C2×SD16—114no—
127C2×D8—114no—
128C4⋊Q8C2×D1111yescharacteristic
129C4⋊Q8C2×D1111yescharacteristic
130#127—111no—
131#127—111no—
132#124—112no—
133#124—221no—
134#121—112no—
135#121—221no—
136#121—221no—
137#121—221no—
138C4×D4—112no—
139C4×D4—221no—
140C4×D4—221no—
141C4×D4—221no—
142C2×C42—111no—
143C4⋊C8—112no—
144#103C2×D1114yes—
145#102—114no—
146C22⋊C8—112no—
147C4×C8—111no—
148C4×C8C2×D1111yescharacteristic
149C2×C11#53511yescharacteristic
150C2×C11C2×#13511yescharacteristic
151C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
152D11—41no—
153D11—82no—
154D11—82no—
155#41—444no—
156#41—444no—
157C2×Q8—21no—
158C2×Q8C22×D1112yes—
159C2×D4—112no—
160C2×D4—112no—
161C2×D4—222no—
162C2×D4—222no—
163C2×D4—221no—
164C2×D4—221no—
165C2×D4—221no—
166C2×D4—221no—
167C22×C4—111no—
168C22×C4—111no—
169C22×C4—111no—
170C22×C4—222no—
171C22×C4—222no—
172SD16—444no—
173D8—444no—
174C2×C8—112no—
175C2×C8C22×D1112yes—
176C4⋊C4—21no—
177C4⋊C4—21no—
178C4⋊C4—21no—
179C4⋊C4C22×D1112yes—
180C22⋊C4—222no—
181C22⋊C4—222no—
182C22⋊C4—222no—
183C22⋊C4—222no—
184C42—111no—
185C42—111no—
186C42—111no—
187C42C22×D1111yescharacteristic
188C11#320711yescharacteristic, complemented, Sylow
189C23—111no—
190C23—222no—
191C23—222no—
192Q8—24no—
193Q8—42no—
194D4—224no—
195D4—224no—
196D4—444no—
197D4—444no—
198D4—442no—
199D4—442no—
200D4—442no—
201D4—442no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—111no—
205C2×C4—111no—
206C2×C4—111no—
207C2×C4—222no—
208C2×C4—222no—
209C2×C4—222no—
210C2×C4—444no—
211C2×C4—444no—
212C2×C4D4×D1111yescharacteristic
213C2×C4D4×D1111yescharacteristic
214C2×C4C23×D1111yescharacteristic
215C8—22no—
216C8—222no—
217C22—221no—
218C22—221no—
219C22—221no—
220C22—442no—
221C22—442no—
222C22—442no—
223C22—442no—
224C22—442no—
225C22—442no—
226C22C2×D4×D1111yescharacteristic
227C4—42no—
228C4—42no—
229C4—221no—
230C4—221no—
231C4—221no—
232C4#6696712yes—
233C4#6697212yes—
234C4#6704212yes—
235C2—441no—
236C2—882no—
237C2—882no—
238C2#1062320511yescharacteristic
239C2C2×#6696711yescharacteristic
240C2C2×#6697211yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#487C2
socleC22×C11C22×D4
hypercenter#487D11
hypocenterC11#3207
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
1. #10623256C2semidirect
2. #10623256C2semidirect
3. C11×#487C2semidirect
4. #10622701C2semidirect
5. #10622698C2semidirect
6. #10622432C2semidirect
7. #10622424C2semidirect
8. #10622308C2semidirect
9. #10622298C2semidirect
101. #487D11semidirect
188. C11#3207semidirect

Maximal subgroups

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

subgroupindex
#106232562
C11×#4872
#106227012
#106226982
#106224322
#106224242
#106223082
#106222982
#320711