Finite Group Databasebeta

← #19136243

Subgroups — #19136243

Order 5504.

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

normal subgroups only

This group has 266 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#14583464C211yesmaximal, characteristic
2#14582880C211yesmaximal, characteristic, complemented
3#14582871C211yesmaximal, characteristic, complemented
4#14582687C211yesmaximal, characteristic, complemented
5#14582686C211yesmaximal, characteristic, complemented
6#14582685C211yesmaximal, characteristic, complemented
7C43×AΣL(1,𝔽16)C211yesmaximal, characteristic, complemented
8C2×#10621900C2211yescharacteristic
9C22×C22⋊D43C411yescharacteristic, complemented
10M16×D43—21no—
11#13063321—21no—
12#13063311—21no—
13#13063298—21no—
14#13063297—21no—
15#13063295C411yescharacteristic, complemented
16#13063294C411yescharacteristic, complemented
17#13063293C2211yescharacteristic
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
28C23×D43C2×C411yescharacteristic
29C2×D4×C43—21no—
30C2×D4×C43C2311yescharacteristic
31C2×C22⋊D43—21no—
32C2×C22⋊D43—21no—
33C2×C22⋊D43—21no—
34C2×C22⋊D43—21no—
35C2×C22⋊D43—41no—
36C2×C22⋊D43—41no—
37C2×C22⋊D43C2×C411yescharacteristic
38C2×C22⋊D43D411yescharacteristic
39C22×Dic43C2×C411yescharacteristic
40C22×Dic43D411yescharacteristic
41#10621900—41no—
42#10621900—41no—
43C2×D172—21no—
44C2×C4×D43D411yescharacteristic
45C2×Dic86D411yescharacteristic
46M16×C43—21no—
47C22⋊C4×C43—21no—
48C22⋊C4×C43—21no—
49C22⋊C4×C43C2×C411yescharacteristic
50C22⋊Dic43—21no—
51C22⋊Dic43—21no—
52C22⋊Dic43C2×C411yescharacteristic
53(C2×D43)⋊C4—21no—
54(C2×D43)⋊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—81no—
65C23×C43C22×C411yescharacteristic
66C23×C43C2×D411yescharacteristic
67C22×D43—21no—
68C22×D43—41no—
69C22×D43—81no—
70C22×D43C22⋊C411yescharacteristic
71D4×C43—41no—
72D4×C43—81no—
73C2×C4×C43—21no—
74C2×C4×C43—41no—
75C2×C4×C43C2×D411yescharacteristic
76C22⋊D43—41no—
77C22⋊D43—41no—
78C22⋊D43—42no—
79C22⋊D43—41no—
80C22⋊D43—41no—
81C22⋊D43—81no—
82C22⋊D43—81no—
83C2×Dic43—21no—
84C2×Dic43—21no—
85C2×Dic43—21no—
86C2×Dic43—21no—
87C2×Dic43—21no—
88C2×Dic43—41no—
89C2×Dic43C22⋊C411yescharacteristic
90C2×Dic43C22⋊C411yescharacteristic
91C2×Dic43C22⋊C411yescharacteristic
92D172—81no—
93C4×D43—21no—
94C4×D43—21no—
95Dic86—41no—
96C8×C43—41no—
97C43⋊C8—41no—
98C22×C43—21no—
99C22×C43—21no—
100C22×C43—41no—
101C22×C43—41no—
102C22×C43—41no—
103C22×C43—41no—
104C22×C43—41no—
105C22×C43—82no—
106C22×C43C2×C22⋊C411yescharacteristic
107C2×D43—21no—
108C2×D43—41no—
109C2×D43—41no—
110C2×D43—41no—
111C2×D43—41no—
112C2×D43—82no—
113C4×C43—21no—
114C4×C43—41no—
115C4×C43—81no—
116Dic43—21no—
117Dic43—21no—
118Dic43—41no—
119Dic43—81no—
120Dic43#9911yescharacteristic
121Dic43#9911yescharacteristic
122#2122—431nomaximal, Sylow
123C2×C43—21no—
124C2×C43—41no—
125C2×C43—41no—
126C2×C43—81no—
127C2×C43C2×#9911yescharacteristic
128D43—41no—
129D43—81no—
130#535—431no—
131#413—431no—
132#410—431no—
133AΣL(1,𝔽16)—431no—
134AΣL(1,𝔽16)—431no—
135AΣL(1,𝔽16)—431no—
136AΣL(1,𝔽16)D4311yescharacteristic, complemented
137C43#212211yescharacteristic, complemented, Sylow
138C2×#41—431no—
139C22×D4—431no—
140C2×M16—861no—
141#127—861no—
142#124—861no—
143#121—861no—
144#121—861no—
145#120—431no—
146#120—431no—
147#120—431no—
148#120C2×D4311yescharacteristic
149#117—431no—
150#117—861no—
151#101—861no—
152#100—431no—
153#100C2×D4311yescharacteristic
154#99—431no—
155#99—861no—
156#99C2×D4311yescharacteristic
157C24—431no—
158C24C4×D4311yescharacteristic
159#41—1721no—
160#41—1721no—
161C2×Q8—431no—
162C2×D4—21no—
163C2×D4—431no—
164C2×D4—431no—
165C2×D4—861no—
166C2×D4—861no—
167C2×D4—861no—
168C2×D4—861no—
169C2×D4—861no—
170C2×D4—1721no—
171C2×D4—1721no—
172C2×D4C22×D4311yescharacteristic
173C22×C4—431no—
174C22×C4—431no—
175C22×C4—431no—
176M16—21no—
177M16—861no—
178M16—1721no—
179C2×C8—1721no—
180C4⋊C4—861no—
181C4⋊C4—1721no—
182C22⋊C4—21no—
183C22⋊C4—21no—
184C22⋊C4—431no—
185C22⋊C4—861no—
186C22⋊C4—861no—
187C22⋊C4—861no—
188C22⋊C4—861no—
189C22⋊C4C4×D4311yescharacteristic
190C42—861no—
191C42—1721no—
192C23—21no—
193C23—41no—
194C23—81no—
195C23—431no—
196C23—861no—
197C23—3441no—
198C23—1721no—
199C23C2×C4×D4311yescharacteristic
200C23D4×D4311yescharacteristic
201Q8—1721no—
202D4—41no—
203D4—81no—
204D4—3441no—
205D4—3441no—
206D4—3441no—
207D4—1721no—
208D4—1721no—
209D4—1721no—
210D4—1721no—
211D4—1722no—
212C2×C4—21no—
213C2×C4—41no—
214C2×C4—431no—
215C2×C4—431no—
216C2×C4—431no—
217C2×C4—861no—
218C2×C4—861no—
219C2×C4—861no—
220C2×C4—861no—
221C2×C4—861no—
222C2×C4—861no—
223C2×C4—861no—
224C2×C4—1721no—
225C2×C4D4×D4311yescharacteristic
226C8—41no—
227C8—1721no—
228C22—21no—
229C22—21no—
230C22—41no—
231C22—41no—
232C22—41no—
233C22—41no—
234C22—41no—
235C22—82no—
236C22—861no—
237C22—3442no—
238C22—1721no—
239C22—1721no—
240C22—1721no—
241C22—1721no—
242C22C22⋊C4×D4311yescharacteristic
243C4—21no—
244C4—41no—
245C4—81no—
246C4—431no—
247C4—431no—
248C4—861no—
249C4—861no—
250C4—3441no—
251C4—1721no—
252C2—21no—
253C2—41no—
254C2—41no—
255C2—81no—
256C2—3441no—
257C2—1721no—
258C2#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#2122
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. #14582687C2semidirect
5. #14582686C2semidirect
6. #14582685C2semidirect
7. C43×AΣL(1,𝔽16)C2semidirect
9. C22×C22⋊D43C4semidirect
15. #13063295C4semidirect
16. #13063294C4semidirect
19. #13063281C4semidirect
136. AΣL(1,𝔽16)D43semidirect
137. C43#2122semidirect