Finite Group Databasebeta

← #13080940

Subgroups — #13080940

Order 1408.

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

normal subgroups only

This group has 430 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#10623257C211yesmaximal, characteristic, complemented
2#10623108C211yesmaximal, characteristic, complemented
3C11×#475C211yesmaximal, characteristic, complemented
4#10622701C211yesmaximal, characteristic, complemented
5C4×#4325C211yesmaximal, characteristic, complemented
6#10622478C212yesmaximal, complemented
7#10622476C212yesmaximal, complemented
8#10622456C211yesmaximal, characteristic, complemented
9#10622451C211yesmaximal, characteristic, complemented
10#10622424C212yesmaximal, complemented
11#10622416C212yesmaximal, complemented
12C2×#4343—21no—
13C2×#4343C2212yes—
14C11×C4⋊Q8C2211yescharacteristic
15C4×Q8×C11C2211yescharacteristic
16#66999—21no—
17C2×#4325C2211yescharacteristic
18C2×D88C2212yes—
19C2×#4313C2212yes—
20#66948—22no—
21#66948C2212yes—
22#66948C2212yes—
23#66947—22no—
24C4⋊C4×D11C2212yes—
25#66927—21no—
26#66927C2211yescharacteristic
27C4×D44—21no—
28C4×D44C2211yescharacteristic
29C4×D44C2211yescharacteristic
30C11×#106C2212yes—
31C11×C4⋊C8C2211yescharacteristic
32C11×#103C2212yes—
33#66899C2211yescharacteristic
34#66885C2212yes—
35(C2×D11)⋊C8C2212yes—
36#66873C2212yes—
37#66873C2211yescharacteristic
38#66873C2212yes—
39#66872C2211yescharacteristic
40C4×C11⋊C8C2211yescharacteristic
41C2×Q8×C11—21no—
42C2×Q8×C11C2311yescharacteristic
43#4343—24no—
44#4343—42no—
45#4343—44no—
46C2×D44—22no—
47C2×D44—22no—
48C2×D44—22no—
49C2×D44—21no—
50C2×D44—21no—
51C2×D44D411yescharacteristic
52C2×D44C2312yes—
53C2×D44C2311yescharacteristic
54C2×C4×D11—22no—
55C2×C4×D11—22no—
56C2×C4×D11—21no—
57C2×C4×D11C2312yes—
58C2×C8×C11C2312yes—
59C11×C4⋊C4—21no—
60C11×C4⋊C4—21no—
61C11×C4⋊C4C2311yescharacteristic
62C11×C4⋊C4C2312yes—
63C42×C11—21no—
64C42×C11C2311yescharacteristic
65#4325—22no—
66(C2×D11)⋊C4—22no—
67(C2×D11)⋊C4—22no—
68(C2×D11)⋊C4—21no—
69(C2×D11)⋊C4D412yes—
70C4⋊Dic11D411yescharacteristic
71C4⋊Dic11C2311yescharacteristic
72Dic11⋊C4—22no—
73C2×C11⋊C8C2311yescharacteristic
74C2×C11⋊C8C2311yescharacteristic
75D88—42no—
76#4313—42no—
77#3332—111nomaximal, Sylow
78C22×D11—21no—
79C22×D11—22no—
80C22×D11C2×D412yes—
81Q8×C11—21no—
82Q8×C11—42no—
83Q8×C11#4112yescomplemented
84C2×C4×C11—21no—
85C2×C4×C11—22no—
86C2×C4×C11—21no—
87C2×C4×C11C2×D411yescharacteristic
88C2×C4×C11C2×D411yescharacteristic
89C2×C4×C11C2411yescharacteristic
90C2×Dic11—21no—
91C2×Dic11C2×D412yes—
92D44—22no—
93D44—21no—
94D44—22no—
95D44—21no—
96D44—22no—
97D44—44no—
98D44—44no—
99D44—42no—
100D44—81no—
101D44—82no—
102C4×D11—22no—
103C4×D11—22no—
104C4×D11—44no—
105C4×D11—44no—
106C4×D11—42no—
107C8×C11—22no—
108C11⋊C8—21no—
109C11⋊C8—21no—
110#550—111no—
111#547—111no—
112#486—111no—
113#481—112no—
114#475D1111yescharacteristic, complemented
115#469—112no—
116#459—111no—
117#449—112no—
118C4×SD16—111no—
119#436—111no—
120#417—112no—
121C22×C11C22×D411yescharacteristic
122C2×D11—22no—
123C2×D11—22no—
124C2×D11—22no—
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×C11—42no—
134C4×C11—41no—
135C4×C11AGL(1,ℤ/8)12yes—
136C4×C11C2×#4111yescharacteristic
137C4×C11H(5,𝔽2)11yescharacteristic
138Dic11—22no—
139Dic11—41no—
140C2×#41—112no—
141C2×#41—221no—
142C2×SD16—111no—
143C2×D8—112no—
144C2×M16—112no—
145C4⋊Q8C2×D1111yescharacteristic
146#127—111no—
147#127—221no—
148#123—222no—
149C22⋊Q8—221no—
150#121—112no—
151#121—112no—
152#121—222no—
153C4×Q8C2×D1111yescharacteristic
154C4×D4—111no—
155C4×D4—111no—
156C4×D4—221no—
157C2×C4⋊C4—112no—
158#106—111no—
159#106C2×D1112yes—
160C4⋊C8C2×D1111yescharacteristic
161#103—111no—
162#103C2×D1112yes—
163#102—112no—
164#102—112no—
165#102—111no—
166#102—112no—
167C22⋊C8—112no—
168C4×C8—111no—
169C2×C11#54611yescharacteristic
170C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
171C2×C11#57711yescharacteristic
172D11—42no—
173D11—82no—
174D11—81no—
175#41—224no—
176#41—442no—
177#41—444no—
178C2×Q8—21no—
179C2×Q8C22×D1111yescharacteristic
180C2×D4—111no—
181C2×D4—112no—
182C2×D4—111no—
183C2×D4—222no—
184C2×D4—222no—
185C2×D4—222no—
186C2×D4—221no—
187C2×D4—221no—
188C22×C4—112no—
189C22×C4—222no—
190C22×C4—222no—
191C22×C4—221no—
192SD16—222no—
193D8—442no—
194M16—442no—
195C2×C8—111no—
196C2×C8—111no—
197C2×C8C22×D1112yes—
198C4⋊C4—21no—
199C4⋊C4—21no—
200C4⋊C4—111no—
201C4⋊C4—111no—
202C4⋊C4—222no—
203C4⋊C4C22×D1112yes—
204C4⋊C4C22×D1111yescharacteristic
205C22⋊C4—112no—
206C22⋊C4—222no—
207C22⋊C4—222no—
208C22⋊C4—221no—
209C42—21no—
210C42C22×D1111yescharacteristic
211C11#333211yescharacteristic, complemented, Sylow
212C23—112no—
213C23—221no—
214C23—222no—
215Q8—21no—
216Q8—42no—
217Q8#434312yescomplemented
218D4—222no—
219D4—221no—
220D4—222no—
221D4—221no—
222D4—222no—
223D4—444no—
224D4—444no—
225D4—442no—
226D4—881no—
227D4—882no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—22no—
231C2×C4—112no—
232C2×C4—222no—
233C2×C4—222no—
234C2×C4—221no—
235C2×C4—444no—
236C2×C4—444no—
237C2×C4—442no—
238C2×C4D4×D1111yescharacteristic
239C2×C4D4×D1111yescharacteristic
240C2×C4C23×D1111yescharacteristic
241C8—22no—
242C8—221no—
243C8—221no—
244C22—222no—
245C22—222no—
246C22—222no—
247C22—441no—
248C22—442no—
249C22—442no—
250C22—441no—
251C22—442no—
252C22—441no—
253C22C2×D4×D1111yescharacteristic
254C4—21no—
255C4—22no—
256C4—42no—
257C4—41no—
258C4—222no—
259C4—441no—
260C4#6696712yes—
261C4C2×#434311yescharacteristic
262C4#6704211yescharacteristic
263C2—442no—
264C2—881no—
265C2—882no—
266C2#1062316111yescharacteristic
267C2C2×#6696711yescharacteristic
268C2#1062330911yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#475C2
socleC22×C11C22×D4
hypercenter#475D11
hypocenterC11#3332
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
1. #10623257C2semidirect
2. #10623108C2semidirect
3. C11×#475C2semidirect
4. #10622701C2semidirect
5. C4×#4325C2semidirect
6. #10622478C2semidirect
7. #10622476C2semidirect
8. #10622456C2semidirect
9. #10622451C2semidirect
10. #10622424C2semidirect
11. #10622416C2semidirect
83. Q8×C11#41semidirect
114. #475D11semidirect
211. C11#3332semidirect
217. Q8#4343semidirect

Maximal subgroups

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

subgroupindex
#106232572
#106231082
C11×#4752
#106227012
C4×#43252
#106224782
#106224762
#106224562
#106224512
#106224242
#106224162
#333211