Finite Group Databasebeta

← #13080944

Subgroups — #13080944

Order 1408.

430 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 430 conjugacy classes of subgroups — too many to draw. Only its 123 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#10623086C211yesmaximal, characteristic, complemented
2#10623084C211yesmaximal, characteristic, complemented
3C11×#436C211yesmaximal, characteristic, complemented
4#10622748C212yesmaximal, complemented
5#10622746C212yesmaximal, complemented
6#10622464C211yesmaximal, characteristic, complemented
7#10622456C211yesmaximal, characteristic, complemented
8#10622348C212yesmaximal, complemented
9#10622347C212yesmaximal, complemented
10#10622307C211yesmaximal, characteristic, complemented
11C4×#4314C211yesmaximal, characteristic, complemented
12C2×#4341—21no—
13C2×#4339C2212yes—
14C2×C11×M16C2212yes—
15C4×D4×C11C2211yescharacteristic
16#66993—21no—
17#66983C2212yes—
18#66983C2212yes—
19C2×C4⋊Dic11C2212yes—
20C2×D88C2212yes—
21C2×#4314C2211yescharacteristic
22#66950—21no—
23#66946—21no—
24#66939—22no—
25#66937—22no—
26#66927C2211yescharacteristic
27C4×D44C2211yescharacteristic
28#66922C2211yescharacteristic
29C4×Dic22C2211yescharacteristic
30C11×C4⋊C8C2211yescharacteristic
31C11×C22⋊C8C2212yes—
32C4×C8×C11C2211yescharacteristic
33#66885C2212yes—
34#66885C2212yes—
35#66885C2211yescharacteristic
36#66885C2212yes—
37#66881C2212yes—
38#66881C2211yescharacteristic
39#66880C2212yes—
40#66880C2211yescharacteristic
41C2×D4×C11D411yescharacteristic
42C22×C4×C11C2312yes—
43C2×C22⋊D11—22no—
44C2×C22⋊D11—22no—
45C2×C22⋊D11—22no—
46C22×Dic11—22no—
47#4341—44no—
48#4339—24no—
49#4339—42no—
50C2×D44—21no—
51C2×D44—21no—
52C2×D44C2312yes—
53C2×D44C2311yescharacteristic
54C2×C4×D11—21no—
55C2×C4×D11—22no—
56C2×Dic22—21no—
57C2×Dic22C2311yescharacteristic
58C11×M16—42no—
59C2×C8×C11C2312yes—
60C2×C8×C11C2311yescharacteristic
61C2×C8×C11C2311yescharacteristic
62C11×C4⋊C4D411yescharacteristic
63C11×C22⋊C4D412yes—
64C42×C11C2311yescharacteristic
65(C2×D11)⋊C4—21no—
66(C2×D11)⋊C4—22no—
67(C2×D11)⋊C4—22no—
68C4⋊Dic11—21no—
69C4⋊Dic11—22no—
70C4⋊Dic11C2312yes—
71C4⋊Dic11C2311yescharacteristic
72C4⋊Dic11C2311yescharacteristic
73Dic11⋊C4—21no—
74C4×Dic11—21no—
75D88—42no—
76#4314—22no—
77#3332—111nomaximal, Sylow
78C23×C11C2×D412yes—
79C22×D11—21no—
80C22×D11—22no—
81D4×C11—22no—
82C2×C4×C11—22no—
83C2×C4×C11—22no—
84C2×C4×C11C2×D411yescharacteristic
85C2×C4×C11C2×D412yes—
86C2×C4×C11C2×D411yescharacteristic
87C2×C4×C11C2411yescharacteristic
88C22⋊D11—44no—
89C22⋊D11—44no—
90C22⋊D11—82no—
91C2×Dic11—21no—
92C2×Dic11—21no—
93C2×Dic11—22no—
94C2×Dic11—21no—
95C2×Dic11—44no—
96D44—21no—
97D44—22no—
98D44—21no—
99D44—22no—
100D44—42no—
101D44—81no—
102C4×D11—44no—
103C4×D11—42no—
104Dic22—21no—
105Dic22—42no—
106Dic22#4112yescomplemented
107C8×C11—21no—
108C8×C11—22no—
109C8×C11—21no—
110#550—111no—
111#547—111no—
112#486—111no—
113#481—112no—
114#475—111no—
115#469—112no—
116#459—111no—
117#449—112no—
118C4×SD16—111no—
119#436D1111yescharacteristic, complemented
120#417—112no—
121C22×C11—22no—
122C22×C11—22no—
123C22×C11—22no—
124C22×C11C22×D411yescharacteristic
125C2×D11—42no—
126C2×D11—41no—
127C2×D11—41no—
128C2×D11—42no—
129C2×D11—41no—
130C2×D11—42no—
131C4×C11—22no—
132C4×C11—21no—
133C4×C11AGL(1,ℤ/8)12yes—
134C4×C11C2×#4111yescharacteristic
135C4×C11H(5,𝔽2)11yescharacteristic
136Dic11—22no—
137Dic11—42no—
138Dic11—41no—
139Dic11—41no—
140C2×#41—112no—
141C2×#41—221no—
142C2×SD16—111no—
143C2×D8—112no—
144C2×M16C2×D1112yes—
145C4⋊Q8—111no—
146#127—111no—
147#127—221no—
148#123—222no—
149C22⋊Q8—221no—
150#121—112no—
151#121—112no—
152#121—222no—
153C4×Q8—111no—
154C4×D4—111no—
155C4×D4—221no—
156C4×D4C2×D1111yescharacteristic
157C2×C4⋊C4—112no—
158#106—111no—
159#106—112no—
160C4⋊C8C2×D1111yescharacteristic
161#103—111no—
162#103—112no—
163#102—112no—
164#102—112no—
165#102—111no—
166#102—112no—
167C22⋊C8C2×D1112yes—
168C4×C8C2×D1111yescharacteristic
169C2×C11—42no—
170C2×C11#54611yescharacteristic
171C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
172C2×C11#57711yescharacteristic
173D11—82no—
174D11—81no—
175#41—224no—
176#41—442no—
177#41—444no—
178C2×Q8—111no—
179C2×Q8—221no—
180C2×D4—112no—
181C2×D4—111no—
182C2×D4—222no—
183C2×D4—222no—
184C2×D4—222no—
185C2×D4—221no—
186C2×D4—221no—
187C2×D4D4411yescharacteristic
188C22×C4—222no—
189C22×C4—221no—
190C22×C4—222no—
191C22×C4C22×D1112yes—
192SD16—222no—
193D8—442no—
194M16—42no—
195C2×C8C22×D1111yescharacteristic
196C2×C8C22×D1111yescharacteristic
197C2×C8C22×D1112yes—
198C4⋊C4—111no—
199C4⋊C4—112no—
200C4⋊C4—111no—
201C4⋊C4—222no—
202C4⋊C4—221no—
203C4⋊C4—221no—
204C4⋊C4D4411yescharacteristic
205C22⋊C4—221no—
206C22⋊C4—222no—
207C22⋊C4—222no—
208C22⋊C4D4412yes—
209C42—221no—
210C42C22×D1111yescharacteristic
211C11#333211yescharacteristic, complemented, Sylow
212C23—221no—
213C23—222no—
214C23C2×D4412yes—
215Q8—112no—
216Q8—221no—
217Q8—442no—
218D4—22no—
219D4—221no—
220D4—222no—
221D4—221no—
222D4—222no—
223D4—444no—
224D4—444no—
225D4—442no—
226D4—881no—
227D4—882no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—221no—
231C2×C4—221no—
232C2×C4—221no—
233C2×C4—222no—
234C2×C4—444no—
235C2×C4—444no—
236C2×C4—442no—
237C2×C4C2×D4411yescharacteristic
238C2×C4C2×D4412yes—
239C2×C4C2×D4411yescharacteristic
240C2×C4C23×D1111yescharacteristic
241C8—21no—
242C8—22no—
243C8—21no—
244C22—22no—
245C22—22no—
246C22—22no—
247C22—441no—
248C22—442no—
249C22—442no—
250C22—441no—
251C22—442no—
252C22—441no—
253C22C22×D4411yescharacteristic
254C4—21no—
255C4—22no—
256C4—222no—
257C4—441no—
258C4—442no—
259C4—441no—
260C4#6696112yes—
261C4#6703711yescharacteristic
262C4#41×D1111yescharacteristic
263C2—42no—
264C2—881no—
265C2—882no—
266C2#1062308511yescharacteristic
267C2C2×#6696111yescharacteristic
268C2#1062328211yescharacteristic
subgroupG/H
centerC22C22×D44
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#436C2
socleC22×C11C22×D4
hypercenter#436D11
hypocenterC11#3332
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ #436

Complements

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

NH ≅ G/Ntype
1. #10623086C2semidirect
2. #10623084C2semidirect
3. C11×#436C2semidirect
4. #10622748C2semidirect
5. #10622746C2semidirect
6. #10622464C2semidirect
7. #10622456C2semidirect
8. #10622348C2semidirect
9. #10622347C2semidirect
10. #10622307C2semidirect
11. C4×#4314C2semidirect
106. Dic22#41semidirect
119. #436D11semidirect
211. C11#3332semidirect

Maximal subgroups

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

subgroupindex
#106230862
#106230842
C11×#4362
#106227482
#106227462
#106224642
#106224562
#106223482
#106223472
#106223072
C4×#43142
#333211