Finite Group Databasebeta

← #19136233

Subgroups — #19136233

Order 5504.

264 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 55 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#14583405C211yesmaximal, characteristic
2#14582880C211yesmaximal, characteristic, complemented
3#14582871C211yesmaximal, characteristic, complemented
4#14582690C211yesmaximal, characteristic, complemented
5#14582688C211yesmaximal, characteristic, complemented
6#14582686C211yesmaximal, characteristic, complemented
7C43×AΣL(1,𝔽16)C211yesmaximal, characteristic, complemented
8C2×#10621900C2211yescharacteristic
9C23×Dic43C411yescharacteristic, complemented
10M16×D43—21no—
11#13063309C411yescharacteristic, complemented
12#13063306C2211yescharacteristic
13#13063302—21no—
14#13063297—21no—
15#13063294C411yescharacteristic, complemented
16D4×Dic43—21no—
17(C22⋊D43)⋊C4—21no—
18#13063281—21no—
19#13063281C411yescharacteristic, complemented
20#13063243—21no—
21#13063242C2211yescharacteristic
22#13063240C2211yescharacteristic
23#13063239—21no—
24#120×C43C2211yescharacteristic
25#100×C43C2211yescharacteristic
26#99×C43C2211yescharacteristic
27C24×C43C2×C411yescharacteristic
28C2×D4×C43—21no—
29C2×D4×C43C2311yescharacteristic
30C2×C22⋊D43—21no—
31C2×C22⋊D43C2×C411yescharacteristic
32C2×C22⋊D43D411yescharacteristic
33C22×Dic43—21no—
34C22×Dic43—21no—
35C22×Dic43—41no—
36C22×Dic43—41no—
37C22×Dic43C2×C411yescharacteristic
38C22×Dic43C2×C411yescharacteristic
39C22×Dic43D411yescharacteristic
40#10621900—41no—
41#10621900—41no—
42C2×C4×D43D411yescharacteristic
43C2×Dic86D411yescharacteristic
44M16×C43—21no—
45C22⋊C4×C43—21no—
46C22⋊C4×C43—21no—
47C22⋊C4×C43C2×C411yescharacteristic
48C22⋊Dic43—21no—
49C22⋊Dic43—21no—
50C22⋊Dic43—21no—
51C22⋊Dic43C2×C411yescharacteristic
52(C2×D43)⋊C4—21no—
53C4⋊Dic43—21no—
54Dic43⋊C4—21no—
55Dic43⋊C4—21no—
56Dic43⋊C4—41no—
57C4×Dic43—21no—
58C4×Dic43—41no—
59#10621877—21no—
60#10621872—41no—
61C8×D43—41no—
62C23×C43—21no—
63C23×C43—41no—
64C23×C43—42no—
65C23×C43C22×C411yescharacteristic
66C23×C43C2×D411yescharacteristic
67C22×D43C22⋊C411yescharacteristic
68D4×C43—41no—
69D4×C43—42no—
70C2×C4×C43—21no—
71C2×C4×C43—41no—
72C2×C4×C43C2×D411yescharacteristic
73C22⋊D43—41no—
74C22⋊D43—41no—
75C22⋊D43—42no—
76C2×Dic43—21no—
77C2×Dic43—21no—
78C2×Dic43—21no—
79C2×Dic43—21no—
80C2×Dic43—21no—
81C2×Dic43—21no—
82C2×Dic43—42no—
83C2×Dic43—41no—
84C2×Dic43—41no—
85C2×Dic43—41no—
86C2×Dic43—41no—
87C2×Dic43C22⋊C411yescharacteristic
88C2×Dic43C22⋊C411yescharacteristic
89C2×Dic43C22⋊C411yescharacteristic
90C4×D43—21no—
91C4×D43—21no—
92Dic86—41no—
93C8×C43—41no—
94C43⋊C8—41no—
95C22×C43—22no—
96C22×C43—21no—
97C22×C43—21no—
98C22×C43—41no—
99C22×C43—41no—
100C22×C43—41no—
101C22×C43—42no—
102C22×C43—42no—
103C22×C43—41no—
104C22×C43C2×C22⋊C411yescharacteristic
105C2×D43—21no—
106C2×D43—41no—
107C4×C43—21no—
108C4×C43—41no—
109C4×C43—81no—
110Dic43—21no—
111Dic43—21no—
112Dic43—41no—
113Dic43—41no—
114Dic43—81no—
115Dic43#9911yescharacteristic
116Dic43#9911yescharacteristic
117#2120—431nomaximal, Sylow
118C2×C43—21no—
119C2×C43—41no—
120C2×C43—42no—
121C2×C43—41no—
122C2×C43C2×#9911yescharacteristic
123D43—41no—
124#525—431no—
125#413—431no—
126#410—431no—
127#352—431no—
128#352—431no—
129AΣL(1,𝔽16)—431no—
130AΣL(1,𝔽16)D4311yescharacteristic, complemented
131C43#212011yescharacteristic, complemented, Sylow
132C2×#41—431no—
133C23×C4—431no—
134C2×M16—861no—
135#123—431no—
136#123—431no—
137C22⋊Q8—861no—
138#121—861no—
139#120—431no—
140#120C2×D4311yescharacteristic
141C4×D4—861no—
142C4×D4—861no—
143#117—431no—
144#117—861no—
145#101—861no—
146#100—431no—
147#100C2×D4311yescharacteristic
148#99—431no—
149#99—861no—
150#99C2×D4311yescharacteristic
151C24C4×D4311yescharacteristic
152#41—1721no—
153#41—1721no—
154C2×Q8—431no—
155C2×D4—21no—
156C2×D4—431no—
157C2×D4—431no—
158C2×D4—861no—
159C2×D4C22×D4311yescharacteristic
160C22×C4—431no—
161C22×C4—431no—
162C22×C4—431no—
163C22×C4—431no—
164C22×C4—861no—
165C22×C4—861no—
166C22×C4—1721no—
167C22×C4—1721no—
168M16—21no—
169M16—861no—
170M16—1721no—
171C2×C8—1721no—
172C4⋊C4—861no—
173C4⋊C4—861no—
174C4⋊C4—861no—
175C4⋊C4—1721no—
176C22⋊C4—21no—
177C22⋊C4—21no—
178C22⋊C4—431no—
179C22⋊C4—861no—
180C22⋊C4—861no—
181C22⋊C4—861no—
182C22⋊C4—861no—
183C22⋊C4C4×D4311yescharacteristic
184C42—861no—
185C42—1721no—
186C23—21no—
187C23—41no—
188C23—42no—
189C23—431no—
190C23C2×C4×D4311yescharacteristic
191C23D4×D4311yescharacteristic
192Q8—1721no—
193D4—41no—
194D4—42no—
195D4—1721no—
196D4—1721no—
197D4—1722no—
198C2×C4—21no—
199C2×C4—41no—
200C2×C4—431no—
201C2×C4—431no—
202C2×C4—431no—
203C2×C4—861no—
204C2×C4—861no—
205C2×C4—861no—
206C2×C4—861no—
207C2×C4—861no—
208C2×C4—861no—
209C2×C4—861no—
210C2×C4—861no—
211C2×C4—1721no—
212C2×C4—1721no—
213C2×C4—1722no—
214C2×C4—1721no—
215C2×C4—1721no—
216C2×C4D4×D4311yescharacteristic
217C8—41no—
218C8—1721no—
219C22—22no—
220C22—21no—
221C22—21no—
222C22—41no—
223C22—41no—
224C22—41no—
225C22—42no—
226C22—42no—
227C22—41no—
228C22—861no—
229C22—1721no—
230C22C22⋊C4×D4311yescharacteristic
231C4—21no—
232C4—41no—
233C4—81no—
234C4—431no—
235C4—431no—
236C4—861no—
237C4—861no—
238C4—3441no—
239C4—1721no—
240C4—1721no—
241C2—21no—
242C2—41no—
243C2—42no—
244C2—41no—
245C2—1721no—
246C2#99×D4311yescharacteristic
subgroupG/H
centerC2#99×D43
commutatorC23×C43C22×C4
FrattiniC2×D4C22×D43
FittingC43×AΣL(1,𝔽16)C2
socleC2×C43C2×#99
hypercenterAΣL(1,𝔽16)D43
hypocenterC43#2120
LCSG ▷ C23×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ AΣL(1,𝔽16)

Complements

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

NH ≅ G/Ntype
2. #14582880C2semidirect
3. #14582871C2semidirect
4. #14582690C2semidirect
5. #14582688C2semidirect
6. #14582686C2semidirect
7. C43×AΣL(1,𝔽16)C2semidirect
9. C23×Dic43C4semidirect
11. #13063309C4semidirect
15. #13063294C4semidirect
19. #13063281C4semidirect
130. AΣL(1,𝔽16)D43semidirect
131. C43#2120semidirect