Finite Group Databasebeta

← #13080942

Subgroups — #13080942

Order 1408.

430 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 430 conjugacy classes of subgroups — too many to draw. Only its 115 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#10623257C211yesmaximal, characteristic, complemented
2#10623249C211yesmaximal, characteristic, complemented
3C11×#486C211yesmaximal, characteristic, complemented
4#10622707C211yesmaximal, characteristic, complemented
5#10622685C211yesmaximal, characteristic, complemented
6#10622395C212yesmaximal, complemented
7#10622394C212yesmaximal, complemented
8#10622390C212yesmaximal, complemented
9#10622384C212yesmaximal, complemented
10C4×#4314C211yesmaximal, characteristic, complemented
11#10622301C211yesmaximal, characteristic, complemented
12C2×#4343—21no—
13C2×#4341C2212yes—
14C11×C4⋊Q8C2211yescharacteristic
15C11×#127C2211yescharacteristic
16#66999—21no—
17#66993—21no—
18#66992—22no—
19#66991C2212yes—
20D4×Dic11—21no—
21C2×#4323C2212yes—
22C2×#4314C2211yescharacteristic
23C2×#4313C2212yes—
24#66948C2212yes—
25#66947—22no—
26C4⋊C4×D11C2212yes—
27C4×D44C2211yescharacteristic
28C4×D44C2211yescharacteristic
29C4×Dic22C2211yescharacteristic
30C11×#102C2212yes—
31C11×#102C2212yes—
32C4×C8×C11C2211yescharacteristic
33#66896C2212yes—
34#66885C2211yescharacteristic
35(C2×D11)⋊C8C2212yes—
36#66881C2211yescharacteristic
37#66880C2211yescharacteristic
38#66874C2212yes—
39#66872C2212yes—
40C4⋊(C11⋊C8)C2211yescharacteristic
41C2×Q8×C11—21no—
42C2×D4×C11—21no—
43C2×D4×C11—21no—
44C2×D4×C11C2312yes—
45C2×C22⋊D11—22no—
46C2×C22⋊D11—22no—
47C22×Dic11—22no—
48#4343—44no—
49#4341—24no—
50#4341—42no—
51C2×D44—22no—
52C2×D44D411yescharacteristic
53C2×D44C2311yescharacteristic
54C2×C4×D11—22no—
55C2×C4×D11—21no—
56C2×C4×D11C2312yes—
57C2×Dic22C2311yescharacteristic
58C2×C8×C11C2311yescharacteristic
59C2×C8×C11C2311yescharacteristic
60C11×C4⋊C4—21no—
61C11×C4⋊C4C2312yes—
62C42×C11C2311yescharacteristic
63C22⋊Dic11—22no—
64#4323—42no—
65(C2×D11)⋊C4—22no—
66(C2×D11)⋊C4—21no—
67(C2×D11)⋊C4D412yes—
68C4⋊Dic11D411yescharacteristic
69C4⋊Dic11C2311yescharacteristic
70C4⋊Dic11C2311yescharacteristic
71Dic11⋊C4—22no—
72Dic11⋊C4—21no—
73C4×Dic11—21no—
74C2×C11⋊C8C2312yes—
75#4314—22no—
76#4313—42no—
77#3332—111nomaximal, Sylow
78C23×C11—22no—
79C22×D11—21no—
80C22×D11C2×D412yes—
81Q8×C11—42no—
82D4×C11—22no—
83D4×C11—22no—
84D4×C11—42no—
85D4×C11—81no—
86C2×C4×C11—22no—
87C2×C4×C11C2×D411yescharacteristic
88C2×C4×C11C2×D411yescharacteristic
89C2×C4×C11C2411yescharacteristic
90C22⋊D11—44no—
91C22⋊D11—82no—
92C2×Dic11—21no—
93C2×Dic11—21no—
94C2×Dic11—21no—
95C2×Dic11—44no—
96C2×Dic11C2×D412yes—
97D44—22no—
98D44—21no—
99D44—21no—
100D44—44no—
101C4×D11—22no—
102C4×D11—22no—
103C4×D11—44no—
104C4×D11—42no—
105Dic22—21no—
106Dic22#4112yescomplemented
107C8×C11—21no—
108C8×C11—21no—
109C11⋊C8—22no—
110#550—111no—
111#547—111no—
112#486D1111yescharacteristic, complemented
113#481—112no—
114#475—111no—
115#469—112no—
116#459—111no—
117#449—112no—
118C4×SD16—111no—
119#436—111no—
120#417—112no—
121C22×C11—42no—
122C22×C11—42no—
123C22×C11—42no—
124C22×C11C22×D411yescharacteristic
125C2×D11—22no—
126C2×D11—22no—
127C2×D11—22no—
128C2×D11—41no—
129C2×D11—41no—
130C2×D11—41no—
131C4×C11—21no—
132C4×C11—42no—
133C4×C11AGL(1,ℤ/8)12yes—
134C4×C11C2×#4111yescharacteristic
135C4×C11H(5,𝔽2)11yescharacteristic
136Dic11—22no—
137Dic11—22no—
138Dic11—41no—
139Dic11—41no—
140C2×#41—112no—
141C2×#41—221no—
142C2×SD16—111no—
143C2×D8—112no—
144C2×M16—112no—
145C4⋊Q8C2×D1111yescharacteristic
146#127—221no—
147#127C2×D1111yescharacteristic
148#123—222no—
149C22⋊Q8—221no—
150#121—112no—
151#121—112no—
152#121—222no—
153C4×Q8—111no—
154C4×D4—111no—
155C4×D4—111no—
156C4×D4—221no—
157C2×C4⋊C4—112no—
158#106—111no—
159#106—112no—
160C4⋊C8—111no—
161#103—111no—
162#103—112no—
163#102—112no—
164#102—111no—
165#102C2×D1112yes—
166#102C2×D1112yes—
167C22⋊C8—112no—
168C4×C8C2×D1111yescharacteristic
169C2×C11—82no—
170C2×C11#54611yescharacteristic
171C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
172C2×C11#57711yescharacteristic
173D11—42no—
174D11—81no—
175#41—224no—
176#41—442no—
177#41—444no—
178C2×Q8—21no—
179C2×Q8—111no—
180C2×D4—21no—
181C2×D4—21no—
182C2×D4—111no—
183C2×D4—111no—
184C2×D4—222no—
185C2×D4—222no—
186C2×D4—222no—
187C2×D4C22×D1112yes—
188C22×C4—112no—
189C22×C4—222no—
190C22×C4—222no—
191C22×C4—221no—
192SD16—222no—
193D8—442no—
194M16—442no—
195C2×C8—112no—
196C2×C8C22×D1111yescharacteristic
197C2×C8C22×D1111yescharacteristic
198C4⋊C4—21no—
199C4⋊C4—111no—
200C4⋊C4—111no—
201C4⋊C4—111no—
202C4⋊C4—222no—
203C4⋊C4—221no—
204C4⋊C4C22×D1112yes—
205C22⋊C4—112no—
206C22⋊C4—222no—
207C22⋊C4—222no—
208C22⋊C4—221no—
209C42—221no—
210C42C22×D1111yescharacteristic
211C11#333211yescharacteristic, complemented, Sylow
212C23—22no—
213C23—112no—
214C23—221no—
215Q8—42no—
216Q8—112no—
217Q8—221no—
218D4—22no—
219D4—22no—
220D4—42no—
221D4—81no—
222D4—222no—
223D4—221no—
224D4—221no—
225D4—444no—
226D4—444no—
227D4—882no—
228C2×C4—22no—
229C2×C4—112no—
230C2×C4—221no—
231C2×C4—222no—
232C2×C4—222no—
233C2×C4—221no—
234C2×C4—221no—
235C2×C4—444no—
236C2×C4—444no—
237C2×C4—442no—
238C2×C4D4×D1111yescharacteristic
239C2×C4D4×D1111yescharacteristic
240C2×C4C23×D1111yescharacteristic
241C8—21no—
242C8—21no—
243C8—222no—
244C22—42no—
245C22—42no—
246C22—42no—
247C22—222no—
248C22—222no—
249C22—222no—
250C22—441no—
251C22—441no—
252C22—441no—
253C22C2×D4×D1111yescharacteristic
254C4—21no—
255C4—42no—
256C4—222no—
257C4—222no—
258C4—441no—
259C4—441no—
260C4#6696412yes—
261C4#41×D1111yescharacteristic
262C4#6704211yescharacteristic
263C2—82no—
264C2—442no—
265C2—881no—
266C2#1062320711yescharacteristic
267C2C2×#6696411yescharacteristic
268C2#1062329311yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#486C2
socleC22×C11C22×D4
hypercenter#486D11
hypocenterC11#3332
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. #10623257C2semidirect
2. #10623249C2semidirect
3. C11×#486C2semidirect
4. #10622707C2semidirect
5. #10622685C2semidirect
6. #10622395C2semidirect
7. #10622394C2semidirect
8. #10622390C2semidirect
9. #10622384C2semidirect
10. C4×#4314C2semidirect
11. #10622301C2semidirect
106. Dic22#41semidirect
112. #486D11semidirect
211. C11#3332semidirect

Maximal subgroups

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

subgroupindex
#106232572
#106232492
C11×#4862
#106227072
#106226852
#106223952
#106223942
#106223902
#106223842
C4×#43142
#106223012
#333211