Finite Group Databasebeta

← #19145415

Subgroups — #19145415

Order 5504.

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

normal subgroups only

This group has 410 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
1C22⋊Q8×D43C212yesmaximal
2#14583231C212yesmaximal, complemented
3#14583228C212yesmaximal, complemented
4#14583157C211yesmaximal, characteristic, complemented
5#14583155C212yesmaximal, complemented
6#14583056C212yesmaximal, complemented
7#14583053C212yesmaximal, complemented
8#14582862C211yesmaximal, characteristic
9C43×#470C211yesmaximal, characteristic, complemented
10C2×Q8×D43C2212yes—
11C22×C4×D43C2211yescharacteristic
12C2×Dic172C2211yescharacteristic, complemented
13C2×#10621885C2212yescomplemented
14C2×#10621877C2211yescharacteristic
15#13063305C2212yes—
16#13063304C2212yes—
17#13063303—22no—
18#13063302—22no—
19#13063301C2212yes—
20C4⋊C4×D43—22no—
21C4⋊C4×D43C2212yes—
22C22⋊C4×D43—22no—
23#13063257C2211yescharacteristic, complemented
24#13063256C2212yescomplemented
25#13063250C2212yescomplemented
26#13063249C2212yescomplemented
27#13063248C2212yescomplemented
28(C2×D43)⋊C8C2212yes—
29(C2×D43)⋊C8C2212yes—
30C2×Q16×C43C2211yescharacteristic, complemented
31C2×M16×C43C2211yescharacteristic
32C22⋊Q8×C43C2212yes—
33#106×C43C2211yescharacteristic, complemented
34#103×C43C2212yescomplemented
35C23×D43D411yescharacteristic
36C2×Q8×C43C2312yes—
37C22×C4×C43C2311yescharacteristic
38C22×Dic43D411yescharacteristic
39Q8×D43—42no—
40Q8×D43—42no—
41C2×C4×D43—22no—
42C2×C4×D43—22no—
43C2×C4×D43—41no—
44C2×C4×D43—41no—
45C2×C4×D43D412yes—
46C2×C4×D43C2312yes—
47C2×Dic86—22no—
48C2×Dic86C2312yes—
49Q16×C43—41no—
50M16×C43—41no—
51C2×C8×C43C2311yescharacteristic
52C2×C8×C43C2311yescharacteristic
53C4⋊C4×C43—22no—
54C4⋊C4×C43C2312yes—
55C22⋊C4×C43—22no—
56C22⋊Dic43—22no—
57#10621885—42no—
58(C2×D43)⋊C4—22no—
59(C2×D43)⋊C4—22no—
60C4⋊Dic43—22no—
61C4⋊Dic43C2312yes—
62Dic43⋊C4—22no—
63Dic43⋊C4—22no—
64Dic43⋊C4—22no—
65#10621877—41no—
66C2×C43⋊C8C2312yes—
67Dic172—41no—
68C23×C43C2×D411yescharacteristic
69C22×D43—24no—
70C22×D43—41no—
71C22×D43C2×D412yes—
72Q8×C43—22no—
73Q8×C43—22no—
74C2×C4×C43—21no—
75C2×C4×C43—21no—
76C2×C4×C43—22no—
77C2×C4×C43—22no—
78C2×C4×C43C2×D411yescharacteristic
79C2×C4×C43C2411yescharacteristic
80C2×Dic43—22no—
81C2×Dic43—22no—
82C2×Dic43—41no—
83C2×Dic43C2×D412yes—
84C4×D43—22no—
85C4×D43—22no—
86C4×D43—42no—
87C4×D43—44no—
88C4×D43—44no—
89Dic86—22no—
90Dic86—22no—
91Dic86—44no—
92C8×C43—21no—
93C8×C43—21no—
94C43⋊C8—22no—
95C22×C43—21no—
96C22×C43—22no—
97C22×C43C22×D411yescharacteristic
98C2×D43—22no—
99C2×D43—22no—
100C2×D43—44no—
101C2×D43#13714yes—
102C4×C43—21no—
103C4×C43—42no—
104C4×C43—42no—
105C4×C43H(5,𝔽2)11yescharacteristic
106C4×C43H(5,𝔽2)11yescharacteristic
107Dic43—22no—
108Dic43—42no—
109Dic43—42no—
110#3195—431nomaximal, Sylow
111C2×C43—41no—
112C2×C43#53411yescharacteristic
113C2×C43C2×#13712yes—
114D43—24no—
115C2×C22⋊Q8—432no—
116#483—432no—
117#483—432no—
118#470—431no—
119#470—432no—
120#470D4311yescharacteristic, complemented
121#451—432no—
122#451—432no—
123#407—431no—
124C43#319511yescharacteristic, complemented, Sylow
125C22×Q8—432no—
126C23×C4—431no—
127C2×Q16—432no—
128C2×Q16—431no—
129C2×Q16C2×D4311yescharacteristic, complemented
130C2×M16—431no—
131C2×M16C2×D4311yescharacteristic
132C22⋊Q8—432no—
133C22⋊Q8—432no—
134C22⋊Q8—432no—
135C22⋊Q8—862no—
136C22⋊Q8—862no—
137C22⋊Q8C2×D4312yes—
138C2×C4⋊C4—432no—
139C2×C4⋊C4—862no—
140C2×C22⋊C4—862no—
141#106—431no—
142#106—432no—
143#106C2×D4311yescharacteristic, complemented
144#103—432no—
145#103—432no—
146#103—432no—
147#103C2×D4312yescomplemented
148C22⋊C8—432no—
149C22⋊C8—432no—
150C24—431no—
151C2×Q8—432no—
152C2×Q8—862no—
153C2×Q8—1722no—
154C2×Q8—1722no—
155C2×Q8C22×D4312yes—
156C22×C4—431no—
157C22×C4—432no—
158C22×C4—432no—
159C22×C4—862no—
160C22×C4—862no—
161C22×C4—1721no—
162C22×C4—1721no—
163C22×C4C22×D4311yescharacteristic
164Q16—41no—
165Q16—1721no—
166Q16—1722no—
167M16—41no—
168M16—1721no—
169C2×C8—432no—
170C2×C8C22×D4311yescharacteristic
171C2×C8C22×D4311yescharacteristic
172C4⋊C4—22no—
173C4⋊C4—432no—
174C4⋊C4—862no—
175C4⋊C4—862no—
176C4⋊C4—862no—
177C4⋊C4—862no—
178C4⋊C4C22×D4312yes—
179C22⋊C4—22no—
180C22⋊C4—862no—
181C22⋊C4—862no—
182C22⋊C4—862no—
183C23—432no—
184C23—864no—
185C23—1721no—
186C23D4×D4311yescharacteristic
187Q8—22no—
188Q8—22no—
189Q8—862no—
190Q8—862no—
191Q8—1724no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—432no—
197C2×C4—862no—
198C2×C4—862no—
199C2×C4—862no—
200C2×C4—862no—
201C2×C4—1722no—
202C2×C4—1724no—
203C2×C4—1724no—
204C2×C4—1721no—
205C2×C4D4×D4311yescharacteristic
206C2×C4C23×D4311yescharacteristic
207C8—21no—
208C8—21no—
209C8—862no—
210C22—22no—
211C22—21no—
212C22—434no—
213C22—862no—
214C22—862no—
215C22—1724no—
216C22C2×D4×D4311yescharacteristic
217C4—21no—
218C4—42no—
219C4—42no—
220C4—862no—
221C4—1722no—
222C4—1722no—
223C4#1306337011yescharacteristic
224C4#1306337111yescharacteristic
225C2—41no—
226C2—864no—
227C2#1458345711yescharacteristic
228C2#137×D4312yes—
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#470C2
socleC22×C43C22×D4
hypercenter#470D43
hypocenterC43#3195
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #470

Complements

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

NH ≅ G/Ntype
2. #14583231C2semidirect
3. #14583228C2semidirect
4. #14583157C2semidirect
5. #14583155C2semidirect
6. #14583056C2semidirect
7. #14583053C2semidirect
9. C43×#470C2semidirect
12. C2×Dic172C22semidirect
13. C2×#10621885C22semidirect
23. #13063257C22semidirect
24. #13063256C22semidirect
25. #13063250C22semidirect
26. #13063249C22semidirect
27. #13063248C22semidirect
30. C2×Q16×C43C22semidirect
33. #106×C43C22semidirect
34. #103×C43C22semidirect
120. #470D43semidirect
124. C43#3195semidirect
129. C2×Q16C2×D43semidirect
143. #106C2×D43semidirect
147. #103C2×D43semidirect