Finite Group Databasebeta

← #19145382

Subgroups — #19145382

Order 5504.

424 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 113 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#14583409C212yesmaximal, complemented
2#14583242C212yesmaximal, complemented
3#14583221C212yesmaximal, complemented
4#14583140C211yesmaximal, characteristic, complemented
5#14583126C212yesmaximal, complemented
6#14583062C212yesmaximal, complemented
7#14583041C212yesmaximal, complemented
8C2×(C2×D43)⋊C8C211yesmaximal, characteristic, complemented
9C43×#466C211yesmaximal, characteristic, complemented
10C2×#10621900C2212yes—
11C22×C4×D43C2211yescharacteristic
12C2×Dic172C2211yescharacteristic, complemented
13C2×#10621883C2212yescomplemented
14C22×C43⋊C8C2211yescharacteristic
15#13063307—22no—
16#13063305C2212yes—
17#13063304C2212yes—
18#13063296C2212yes—
19#13063293—22no—
20D4×Dic43—22no—
21(C22⋊D43)⋊C4—22no—
22#13063283C2212yes—
23#13063259C2211yescharacteristic, complemented
24#13063256C2212yescomplemented
25#13063250C2212yescomplemented
26#13063248C2212yescomplemented
27#13063246C2212yescomplemented
28(C2×D43)⋊C8C2212yes—
29(C2×D43)⋊C8C2212yes—
30C2×D8×C43C2211yescharacteristic, complemented
31C22×C8×C43C2211yescharacteristic
32#121×C43C2212yes—
33#107×C43C2211yescharacteristic, complemented
34#102×C43C2212yescomplemented
35C23×D43D411yescharacteristic
36C2×D4×C43—22no—
37C2×D4×C43C2312yes—
38C22×C4×C43C2311yescharacteristic
39C2×C22⋊D43—22no—
40C2×C22⋊D43—22no—
41C22×Dic43—22no—
42C22×Dic43D411yescharacteristic
43#10621900—42no—
44#10621900—42no—
45C2×C4×D43—41no—
46C2×C4×D43—41no—
47C2×C4×D43D412yes—
48C2×C4×D43C2312yes—
49C2×Dic86C2312yes—
50D8×C43—41no—
51C2×C8×C43—41no—
52C2×C8×C43C2311yescharacteristic
53C2×C8×C43C2311yescharacteristic
54C4⋊C4×C43C2312yes—
55C22⋊C4×C43—22no—
56C22⋊Dic43—22no—
57C22⋊Dic43—22no—
58#10621883—42no—
59(C2×D43)⋊C4—22no—
60(C2×D43)⋊C4—22no—
61C4⋊Dic43—22no—
62C4⋊Dic43C2312yes—
63Dic43⋊C4—22no—
64C4×Dic43—22no—
65C2×C43⋊C8—41no—
66C2×C43⋊C8C2312yes—
67Dic172—41no—
68C23×C43—22no—
69C23×C43C2×D411yescharacteristic
70C22×D43—22no—
71C22×D43—41no—
72C22×D43—41no—
73C22×D43C2×D412yes—
74D4×C43—22no—
75D4×C43—22no—
76D4×C43—44no—
77C2×C4×C43—21no—
78C2×C4×C43—21no—
79C2×C4×C43—22no—
80C2×C4×C43C2×D411yescharacteristic
81C2×C4×C43C2411yescharacteristic
82C22⋊D43—44no—
83C22⋊D43—44no—
84C2×Dic43—22no—
85C2×Dic43—22no—
86C2×Dic43—41no—
87C2×Dic43—44no—
88C2×Dic43C2×D412yes—
89C4×D43—22no—
90C4×D43—22no—
91C4×D43—42no—
92Dic86—22no—
93Dic86—22no—
94C8×C43—21no—
95C8×C43—21no—
96C43⋊C8—22no—
97C22×C43—21no—
98C22×C43—21no—
99C22×C43—42no—
100C22×C43—42no—
101C22×C43—42no—
102C22×C43#13512yes—
103C22×C43C22×D411yescharacteristic
104C2×D43—22no—
105C2×D43—22no—
106C2×D43—22no—
107C2×D43—44no—
108C4×C43—21no—
109C4×C43—42no—
110C4×C43H(5,𝔽2)11yescharacteristic
111C4×C43H(5,𝔽2)11yescharacteristic
112Dic43—22no—
113Dic43—42no—
114Dic43—42no—
115#3191—431nomaximal, Sylow
116C2×C43—22no—
117C2×C43—82no—
118C2×C43#53411yescharacteristic
119C2×C43C2×#13511yescharacteristic
120C2×C43#57511yescharacteristic
121D43—42no—
122#525—432no—
123#485—432no—
124#482—432no—
125#467—431no—
126#466D4311yescharacteristic, complemented
127#465—432no—
128#452—432no—
129#449—432no—
130C2×C22⋊C8—431no—
131C43#319111yescharacteristic, complemented, Sylow
132C2×#41—432no—
133C23×C4—431no—
134C2×Q16—431no—
135C2×SD16—432no—
136C2×D8C2×D4311yescharacteristic, complemented
137C22×C8—431no—
138C22×C8C2×D4311yescharacteristic
139#123—862no—
140C22⋊Q8—432no—
141C22⋊Q8—432no—
142#121—432no—
143#121C2×D4312yes—
144#120—862no—
145C4×D4—862no—
146C4×D4—862no—
147#117—432no—
148#107—431no—
149#107C2×D4311yescharacteristic, complemented
150#106—432no—
151#103—432no—
152#103—432no—
153#102—432no—
154#102C2×D4312yescomplemented
155C22⋊C8—432no—
156C22⋊C8—432no—
157C24—431no—
158#41—1722no—
159#41—1722no—
160C2×Q8—432no—
161C2×D4—22no—
162C2×D4—862no—
163C2×D4—862no—
164C2×D4C22×D4312yes—
165C22×C4—431no—
166C22×C4—432no—
167C22×C4—432no—
168C22×C4—862no—
169C22×C4—1721no—
170C22×C4—1721no—
171C22×C4C22×D4311yescharacteristic
172Q16—1721no—
173SD16—1722no—
174D8—41no—
175C2×C8—41no—
176C2×C8—432no—
177C2×C8—1721no—
178C2×C8C22×D4311yescharacteristic
179C2×C8C22×D4311yescharacteristic
180C4⋊C4—432no—
181C4⋊C4—862no—
182C4⋊C4—862no—
183C4⋊C4C22×D4312yes—
184C22⋊C4—22no—
185C22⋊C4—862no—
186C22⋊C4—862no—
187C22⋊C4—862no—
188C22⋊C4—862no—
189C42—862no—
190C23—22no—
191C23—432no—
192C23—862no—
193C23—1721no—
194C23—1721no—
195C23D4×D4311yescharacteristic
196Q8—862no—
197Q8—862no—
198D4—22no—
199D4—22no—
200D4—44no—
201D4—1724no—
202D4—1724no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—22no—
206C2×C4—432no—
207C2×C4—862no—
208C2×C4—862no—
209C2×C4—862no—
210C2×C4—862no—
211C2×C4—1722no—
212C2×C4—1721no—
213C2×C4—1724no—
214C2×C4D4×D4311yescharacteristic
215C2×C4C23×D4311yescharacteristic
216C8—21no—
217C8—21no—
218C8—862no—
219C22—21no—
220C22—21no—
221C22—42no—
222C22—42no—
223C22—42no—
224C22—862no—
225C22—862no—
226C22—862no—
227C22—1724no—
228C22#1306334412yes—
229C22C2×D4×D4311yescharacteristic
230C4—21no—
231C4—42no—
232C4—862no—
233C4—1722no—
234C4—1722no—
235C4#1306337011yescharacteristic
236C4#1306337111yescharacteristic
237C2—22no—
238C2—82no—
239C2—1722no—
240C2#1458345711yescharacteristic
241C2C2×#1306334411yescharacteristic
242C2#1458369611yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#466C2
socleC22×C43C22×D4
hypercenter#466D43
hypocenterC43#3191
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #466

Complements

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

NH ≅ G/Ntype
1. #14583409C2semidirect
2. #14583242C2semidirect
3. #14583221C2semidirect
4. #14583140C2semidirect
5. #14583126C2semidirect
6. #14583062C2semidirect
7. #14583041C2semidirect
8. C2×(C2×D43)⋊C8C2semidirect
9. C43×#466C2semidirect
12. C2×Dic172C22semidirect
13. C2×#10621883C22semidirect
23. #13063259C22semidirect
24. #13063256C22semidirect
25. #13063250C22semidirect
26. #13063248C22semidirect
27. #13063246C22semidirect
30. C2×D8×C43C22semidirect
33. #107×C43C22semidirect
34. #102×C43C22semidirect
126. #466D43semidirect
131. C43#3191semidirect
136. C2×D8C2×D43semidirect
149. #107C2×D43semidirect
154. #102C2×D43semidirect