Finite Group Databasebeta

← #19136240

Subgroups — #19136240

Order 5504.

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

normal subgroups only

This group has 280 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#14583460C211yesmaximal, characteristic
2#100×D43C211yesmaximal, characteristic, complemented
3#99×D43C211yesmaximal, characteristic, complemented
4#14582689C211yesmaximal, characteristic, complemented
5#14582687C211yesmaximal, characteristic, complemented
6#14582685C211yesmaximal, characteristic, complemented
7C43×#352C211yesmaximal, characteristic, complemented
8C22×D172C411yescharacteristic, complemented
9C2×D4×D43C2211yescharacteristic
10M16×D43—21no—
11#13063310—21no—
12#13063308C411yescharacteristic, complemented
13#13063300—21no—
14#13063298—21no—
15#13063295—21no—
16#13063295C411yescharacteristic, complemented
17#13063293C2211yescharacteristic
18C22⋊C4×D43—21no—
19C22⋊C4×D43C411yescharacteristic, complemented
20#13063242C2211yescharacteristic
21#13063241—21no—
22#13063240C2211yescharacteristic
23#13063239—21no—
24#123×C43C2211yescharacteristic
25#100×C43C2211yescharacteristic
26#99×C43C2211yescharacteristic
27C23×D43C2×C411yescharacteristic
28C23×D43C2×C411yescharacteristic, complemented
29C23×D43D411yescharacteristic
30C2×D4×C43C2311yescharacteristic
31C22×C4×C43C2×C411yescharacteristic, complemented
32C2×C22⋊D43—21no—
33C2×C22⋊D43C2×C411yescharacteristic
34C2×C22⋊D43D411yescharacteristic
35D4×D43—41no—
36D4×D43—41no—
37C2×D172—21no—
38C2×D172—21no—
39C2×D172—21no—
40C2×D172—41no—
41C2×D172—41no—
42C2×D172D411yescharacteristic
43C2×C4×D43—21no—
44C2×C4×D43—41no—
45C2×C4×D43D411yescharacteristic
46M16×C43—21no—
47C4⋊C4×C43—21no—
48C22⋊C4×C43—21no—
49C22⋊C4×C43—21no—
50C22⋊C4×C43C2×C411yescharacteristic, complemented
51C22⋊Dic43—21no—
52C22⋊Dic43C2×C411yescharacteristic, complemented
53(C2×D43)⋊C4—21no—
54(C2×D43)⋊C4—21no—
55(C2×D43)⋊C4—21no—
56(C2×D43)⋊C4—21no—
57(C2×D43)⋊C4—41no—
58Dic43⋊C4—21no—
59#10621877—21no—
60#10621872—41no—
61C8×D43—41no—
62C23×C43C22×C411yescharacteristic
63C23×C43C2×D411yescharacteristic
64C22×D43—21no—
65C22×D43—21no—
66C22×D43—21no—
67C22×D43—21no—
68C22×D43—21no—
69C22×D43—41no—
70C22×D43—81no—
71C22×D43—81no—
72C22×D43—81no—
73C22×D43C22⋊C411yescharacteristic
74C22×D43C22⋊C411yescharacteristic
75C22×D43C22⋊C411yescharacteristic
76D4×C43—41no—
77C2×C4×C43—21no—
78C2×C4×C43—21no—
79C2×C4×C43—41no—
80C2×C4×C43—41no—
81C2×C4×C43C2×D411yescharacteristic
82C22⋊D43—41no—
83C22⋊D43—41no—
84C22⋊D43—81no—
85C2×Dic43—21no—
86C2×Dic43—41no—
87C2×Dic43C22⋊C411yescharacteristic
88D172—41no—
89D172—42no—
90D172—41no—
91D172—41no—
92D172—81no—
93C4×D43—21no—
94C4×D43—21no—
95C4×D43—81no—
96C4×D43—82no—
97C8×C43—41no—
98C43⋊C8—41no—
99C22×C43—21no—
100C22×C43—21no—
101C22×C43—41no—
102C22×C43—41no—
103C22×C43C2×C22⋊C411yescharacteristic
104C2×D43—21no—
105C2×D43—21no—
106C2×D43—41no—
107C2×D43—42no—
108C2×D43—41no—
109C2×D43—41no—
110C2×D43—41no—
111C2×D43—41no—
112C2×D43—41no—
113C2×D43—81no—
114C2×D43—81no—
115C2×D43—81no—
116C2×D43—82no—
117C2×D43#9911yescharacteristic
118C2×D43#9911yescharacteristic
119C4×C43—21no—
120C4×C43—41no—
121C4×C43—41no—
122C4×C43—81no—
123Dic43—21no—
124Dic43—41no—
125Dic43—81no—
126#2121—431nomaximal, Sylow
127C2×C43—21no—
128C2×C43—41no—
129C2×C43—41no—
130C2×C43C2×#9911yescharacteristic
131D43—21no—
132D43—21no—
133D43—41no—
134D43—41no—
135D43—81no—
136#534—431no—
137C2×#100—431no—
138C2×#99—431no—
139#352—431no—
140#352D4311yescharacteristic, complemented
141AΣL(1,𝔽16)—431no—
142AΣL(1,𝔽16)—431no—
143C43#212111yescharacteristic, complemented, Sylow
144C22×D4—431no—
145C22×D4—431no—
146C2×M16—861no—
147#123—431no—
148#123—861no—
149#123C2×D4311yescharacteristic
150#121—861no—
151#121—861no—
152#120—431no—
153#120—431no—
154#120—861no—
155C2×C22⋊C4—431no—
156C2×C22⋊C4—861no—
157#100—431no—
158#100—861no—
159#100C2×D4311yescharacteristic
160#99—431no—
161#99—861no—
162#99C2×D4311yescharacteristic
163C24—431no—
164C24—431no—
165C24—431no—
166C2×D4—431no—
167C2×D4—431no—
168C2×D4—431no—
169C2×D4—861no—
170C2×D4—861no—
171C2×D4—861no—
172C2×D4—861no—
173C2×D4—1721no—
174C2×D4—1721no—
175C2×D4—1721no—
176C2×D4—1721no—
177C2×D4C22×D4311yescharacteristic
178C22×C4—431no—
179C22×C4—861no—
180C22×C4—1721no—
181C22×C4C4×D4311yescharacteristic, complemented
182M16—21no—
183M16—861no—
184M16—1721no—
185C2×C8—1721no—
186C4⋊C4—21no—
187C4⋊C4—861no—
188C22⋊C4—21no—
189C22⋊C4—21no—
190C22⋊C4—431no—
191C22⋊C4—861no—
192C22⋊C4—861no—
193C22⋊C4—861no—
194C22⋊C4—861no—
195C22⋊C4—861no—
196C22⋊C4—1721no—
197C22⋊C4C4×D4311yescharacteristic, complemented
198C23—431no—
199C23—431no—
200C23—431no—
201C23—861no—
202C23—861no—
203C23—861no—
204C23—861no—
205C23—861no—
206C23—3441no—
207C23—3441no—
208C23—3441no—
209C23—1721no—
210C23C2×C4×D4311yescharacteristic
211C23D4×D4311yescharacteristic
212D4—41no—
213D4—3441no—
214D4—3441no—
215D4—1721no—
216D4—1721no—
217D4—1721no—
218D4—1722no—
219D4—1721no—
220D4—1721no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—41no—
224C2×C4—41no—
225C2×C4—431no—
226C2×C4—861no—
227C2×C4—861no—
228C2×C4—861no—
229C2×C4—3441no—
230C2×C4—3442no—
231C2×C4—1721no—
232C2×C4D4×D4311yescharacteristic
233C8—41no—
234C8—1721no—
235C22—21no—
236C22—21no—
237C22—41no—
238C22—41no—
239C22—431no—
240C22—431no—
241C22—861no—
242C22—861no—
243C22—3441no—
244C22—3441no—
245C22—3441no—
246C22—3442no—
247C22—1721no—
248C22—1721no—
249C22—1721no—
250C22—1721no—
251C22—1721no—
252C22—1722no—
253C22—1721no—
254C22C22⋊C4×D4311yescharacteristic
255C4—21no—
256C4—41no—
257C4—41no—
258C4—81no—
259C4—861no—
260C4—3441no—
261C4—1721no—
262C2—21no—
263C2—41no—
264C2—41no—
265C2—861no—
266C2—861no—
267C2—3441no—
268C2—1721no—
269C2—1721no—
270C2#99×D4311yescharacteristic
subgroupG/H
centerC2#99×D43
commutatorC23×C43C22×C4
FrattiniC2×D4C22×D43
FittingC43×#352C2
socleC2×C43C2×#99
hypercenter#352D43
hypocenterC43#2121
LCSG ▷ C23×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #352

Complements

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

NH ≅ G/Ntype
2. #100×D43C2semidirect
3. #99×D43C2semidirect
4. #14582689C2semidirect
5. #14582687C2semidirect
6. #14582685C2semidirect
7. C43×#352C2semidirect
8. C22×D172C4semidirect
12. #13063308C4semidirect
16. #13063295C4semidirect
19. C22⋊C4×D43C4semidirect
28. C23×D43C2×C4semidirect
31. C22×C4×C43C2×C4semidirect
50. C22⋊C4×C43C2×C4semidirect
52. C22⋊Dic43C2×C4semidirect
140. #352D43semidirect
143. C43#2121semidirect
181. C22×C4C4×D43semidirect
197. C22⋊C4C4×D43semidirect