Finite Group Databasebeta

← #13070608

Subgroups — #13070608

Order 1408.

258 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 41 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#10623118C211yesmaximal, characteristic, complemented
2#10622645C211yesmaximal, characteristic
3#10622359C211yesmaximal, characteristic, complemented
4#10622355C211yesmaximal, characteristic, complemented
5C11×AΣL(1,𝔽16)C211yesmaximal, characteristic, complemented
6#10622114C211yesmaximal, characteristic, complemented
7#10622111C211yesmaximal, characteristic, complemented
8#67037C2211yescharacteristic
9C11×#120C2211yescharacteristic
10#67006—21no—
11C2×C22⋊Dic11—21no—
12#66989C2211yescharacteristic
13#66988—21no—
14#66988C2211yescharacteristic
15D4×Dic11—21no—
16#66962—21no—
17#66939—21no—
18#66932—21no—
19#66931—21no—
20#66930—21no—
21C11×#100C2211yescharacteristic
22C11×#99C2211yescharacteristic
23#66898C2211yescharacteristic
24#66889—21no—
25#66870—21no—
26#66870—21no—
27C24×C11D411yescharacteristic
28C2×D4×C11—21no—
29C2×D4×C11C2311yescharacteristic
30C2×C22⋊D11—21no—
31C2×C22⋊D11—21no—
32C2×C22⋊D11—41no—
33C22×Dic11—21no—
34C22×Dic11—21no—
35C22×Dic11D411yescharacteristic, complemented
36#4341—41no—
37D4×D11—41no—
38#4339—21no—
39C2×Dic22D411yescharacteristic, complemented
40C11×M16—21no—
41C11×C22⋊C4—21no—
42C11×C22⋊C4—21no—
43C11×C22⋊C4D411yescharacteristic
44C22⋊Dic11—21no—
45C22⋊Dic11—21no—
46C22⋊Dic11—21no—
47C22⋊Dic11—21no—
48C22⋊Dic11—21no—
49C22⋊Dic11—21no—
50C22⋊Dic11—41no—
51C22⋊Dic11D411yescharacteristic, complemented
52(C2×D11)⋊C4—41no—
53C4⋊Dic11—21no—
54C4⋊Dic11—41no—
55Dic11⋊C4—21no—
56Dic11⋊C4—21no—
57Dic11⋊C4—21no—
58C4×Dic11—21no—
59C4×Dic11D411yescharacteristic, complemented
60Dic44—41no—
61#4314—41no—
62#2197—111nomaximal, Sylow
63C23×C11—21no—
64C23×C11—41no—
65C23×C11—42no—
66C23×C11C2×D411yescharacteristic
67C23×C11C2×D411yescharacteristic
68C22×D11—21no—
69C22×D11—21no—
70D4×C11—41no—
71D4×C11—42no—
72C2×C4×C11—21no—
73C2×C4×C11—41no—
74C2×C4×C11C2×D411yescharacteristic
75C22⋊D11—41no—
76C22⋊D11—41no—
77C22⋊D11—41no—
78C22⋊D11—82no—
79C2×Dic11—21no—
80C2×Dic11—21no—
81C2×Dic11—21no—
82C2×Dic11—21no—
83C2×Dic11—21no—
84C2×Dic11—21no—
85C2×Dic11—42no—
86C2×Dic11—41no—
87C2×Dic11—41no—
88C2×Dic11—81no—
89D44—21no—
90C4×D11—41no—
91Dic22—21no—
92Dic22—41no—
93C8×C11—41no—
94#551—111no—
95#458—111no—
96B(4,𝔽2)—111no—
97#455—111no—
98#354—111no—
99#352—111no—
100AΣL(1,𝔽16)D1111yescharacteristic, complemented
101C22×C11—22no—
102C22×C11—21no—
103C22×C11—21no—
104C22×C11—41no—
105C22×C11—41no—
106C22×C11—41no—
107C22×C11—42no—
108C22×C11—41no—
109C22×C11—81no—
110C22×C11#12011yescharacteristic
111C2×D11—41no—
112C2×D11—81no—
113C2×D11—81no—
114C4×C11—21no—
115C4×C11—41no—
116C4×C11—81no—
117Dic11—41no—
118Dic11—41no—
119Dic11—41no—
120Dic11—41no—
121Dic11—41no—
122Dic11—81no—
123H(5,𝔽2)—111no—
124#137—221no—
125#126—221no—
126#124—111no—
127#123—111no—
128#123—221no—
129#123—221no—
130C22⋊Q8—221no—
131#120—221no—
132#120C2×D1111yescharacteristic
133C4×D4—221no—
134#117—221no—
135C2×C22⋊C4—221no—
136#104—221no—
137#100C2×D1111yescharacteristic
138#99—111no—
139#99—221no—
140#99—221no—
141#99C2×D1111yescharacteristic
142C2×C11—21no—
143C2×C11—41no—
144C2×C11—41no—
145C2×C11—42no—
146C2×C11B(4,𝔽2)11yescharacteristic
147D11—81no—
148C24D4411yescharacteristic
149#41—221no—
150#41—441no—
151C2×Q8—111no—
152C2×D4—21no—
153C2×D4—221no—
154C2×D4—221no—
155C2×D4—441no—
156C2×D4—441no—
157C2×D4C22×D1111yescharacteristic
158C22×C4—111no—
159C22×C4—221no—
160C22×C4—221no—
161Q16—441no—
162SD16—441no—
163M16—21no—
164C4⋊C4—221no—
165C4⋊C4—221no—
166C4⋊C4—221no—
167C4⋊C4—221no—
168C4⋊C4—441no—
169C22⋊C4—21no—
170C22⋊C4—21no—
171C22⋊C4—111no—
172C22⋊C4—221no—
173C22⋊C4—221no—
174C22⋊C4—221no—
175C22⋊C4—221no—
176C22⋊C4—221no—
177C22⋊C4—221no—
178C22⋊C4—441no—
179C22⋊C4—441no—
180C22⋊C4D4411yescharacteristic
181C42—111no—
182C42—221no—
183C11#219711yescharacteristic, complemented, Sylow
184C23—21no—
185C23—41no—
186C23—42no—
187C23—221no—
188C23—221no—
189C23C2×D4411yescharacteristic
190C23D4×D1111yescharacteristic
191Q8—221no—
192Q8—441no—
193D4—41no—
194D4—42no—
195D4—221no—
196D4—441no—
197D4—441no—
198D4—441no—
199D4—882no—
200C2×C4—21no—
201C2×C4—41no—
202C2×C4—221no—
203C2×C4—221no—
204C2×C4—221no—
205C2×C4—221no—
206C2×C4—221no—
207C2×C4—221no—
208C2×C4—441no—
209C2×C4—442no—
210C2×C4—441no—
211C2×C4—441no—
212C2×C4—881no—
213C2×C4D4×D1111yescharacteristic
214C8—41no—
215C22—22no—
216C22—21no—
217C22—21no—
218C22—41no—
219C22—41no—
220C22—41no—
221C22—42no—
222C22—41no—
223C22—81no—
224C22—441no—
225C22—881no—
226C22—881no—
227C22#6693511yescharacteristic
228C4—21no—
229C4—41no—
230C4—81no—
231C4—441no—
232C4—441no—
233C4—441no—
234C4—441no—
235C4—441no—
236C4—881no—
237C2—21no—
238C2—41no—
239C2—41no—
240C2—42no—
241C2—881no—
242C2#1062235411yescharacteristic
subgroupG/H
centerC2#10622354
commutator, cosocleC2×D4×C11C23
FrattiniC2×D4C22×D11
FittingC11×AΣL(1,𝔽16)C2
socleC2×C11B(4,𝔽2)
prime radical#10622645C2
hypercenterAΣL(1,𝔽16)D11
hypocenterC11#2197
LCSG ▷ C2×D4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ AΣL(1,𝔽16)

Complements

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

NH ≅ G/Ntype
1. #10623118C2semidirect
3. #10622359C2semidirect
4. #10622355C2semidirect
5. C11×AΣL(1,𝔽16)C2semidirect
6. #10622114C2semidirect
7. #10622111C2semidirect
35. C22×Dic11D4semidirect
39. C2×Dic22D4semidirect
51. C22⋊Dic11D4semidirect
59. C4×Dic11D4semidirect
100. AΣL(1,𝔽16)D11semidirect
183. C11#2197semidirect

Maximal subgroups

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

subgroupindex
#106231182
#106226452
#106223592
#106223552
C11×AΣL(1,𝔽16)2
#106221142
#106221112
#219711