Finite Group Databasebeta

← #19145366

Subgroups — #19145366

Order 5504.

416 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 121 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#14583236C212yesmaximal, complemented
3#14583233C212yesmaximal, complemented
4#14583140C211yesmaximal, characteristic, complemented
5#14583138C212yesmaximal, complemented
6#14583056C212yesmaximal, complemented
7#14583053C212yesmaximal, complemented
8C2×(C2×D43)⋊C8C211yesmaximal, characteristic
9C43×#467C211yesmaximal, characteristic, complemented
10C2×Q8×D43C2212yes—
11C22×C4×D43C2211yescharacteristic
12C2×Dic172C2211yescharacteristic, complemented
13C2×#10621885C2212yescomplemented
14C22×C43⋊C8C2211yescharacteristic
15#13063305C2212yes—
16#13063304C2212yes—
17#13063303—22no—
18#13063302—22no—
19#13063301C2212yes—
20C4⋊C4×D43—22no—
21C4⋊C4×D43C2212yes—
22C22⋊C4×D43—22no—
23#13063259C2211yescharacteristic, complemented
24#13063258C2212yescomplemented
25#13063250C2212yescomplemented
26#13063249C2212yescomplemented
27#13063248C2212yescomplemented
28(C2×D43)⋊C8C2212yes—
29(C2×D43)⋊C8C2212yes—
30C2×Q16×C43C2211yescharacteristic, complemented
31C22×C8×C43C2211yescharacteristic
32C22⋊Q8×C43C2212yes—
33#107×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—
50C2×C8×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—
65C2×C43⋊C8—41no—
66C2×C43⋊C8C2312yes—
67Dic172—41no—
68C23×C43C2×D411yescharacteristic
69C22×D43—41no—
70C22×D43—41no—
71C22×D43Q1614yescomplemented
72C22×D43C2×D412yes—
73Q8×C43—22no—
74Q8×C43—22no—
75C2×C4×C43—21no—
76C2×C4×C43—21no—
77C2×C4×C43—22no—
78C2×C4×C43—22no—
79C2×C4×C43C2×D411yescharacteristic
80C2×C4×C43C2411yescharacteristic
81C2×Dic43—22no—
82C2×Dic43—22no—
83C2×Dic43—41no—
84C2×Dic43C2×D412yes—
85C4×D43—22no—
86C4×D43—22no—
87C4×D43—42no—
88C4×D43—44no—
89C4×D43—44no—
90Dic86—22no—
91Dic86—22no—
92Dic86—44no—
93C8×C43—21no—
94C8×C43—21no—
95C43⋊C8—22no—
96C22×C43—21no—
97C22×C43—21no—
98C22×C43C2×Q1612yes—
99C22×C43C22×D411yescharacteristic
100C2×D43—22no—
101C2×D43—22no—
102C2×D43—44no—
103C2×D43C2×Q1614yes—
104C4×C43—21no—
105C4×C43—42no—
106C4×C43—42no—
107C4×C43H(5,𝔽2)11yescharacteristic
108C4×C43H(5,𝔽2)11yescharacteristic
109Dic43—22no—
110Dic43—42no—
111Dic43—42no—
112#3189—431nomaximal, Sylow
113C2×C43—22no—
114C2×C43#53411yescharacteristic
115C2×C43C22×Q1611yescharacteristic
116C2×C43#57511yescharacteristic
117D43—24no—
118C2×C22⋊Q8—432no—
119#484—432no—
120#484—432no—
121#467—431no—
122#467—432no—
123#467D4311yescharacteristic, complemented
124#451—432no—
125#451—432no—
126C2×C22⋊C8—431no—
127C43#318911yescharacteristic, complemented, Sylow
128C22×Q8—432no—
129C23×C4—431no—
130C2×Q16—432no—
131C2×Q16—431no—
132C2×Q16C2×D4311yescharacteristic, complemented
133C22×C8—431no—
134C22×C8C2×D4311yescharacteristic
135C22⋊Q8—432no—
136C22⋊Q8—432no—
137C22⋊Q8—432no—
138C22⋊Q8—862no—
139C22⋊Q8—862no—
140C22⋊Q8C2×D4312yes—
141C2×C4⋊C4—432no—
142C2×C4⋊C4—862no—
143C2×C22⋊C4—862no—
144#107—431no—
145#107—432no—
146#107C2×D4311yescharacteristic, complemented
147#103—432no—
148#103—432no—
149#103—432no—
150#103C2×D4312yescomplemented
151C22⋊C8—432no—
152C22⋊C8—432no—
153C24—431no—
154C2×Q8—432no—
155C2×Q8—862no—
156C2×Q8—1722no—
157C2×Q8—1722no—
158C2×Q8C22×D4312yes—
159C22×C4—431no—
160C22×C4—432no—
161C22×C4—432no—
162C22×C4—862no—
163C22×C4—862no—
164C22×C4—1721no—
165C22×C4—1721no—
166C22×C4C22×D4311yescharacteristic
167Q16—41no—
168Q16—1721no—
169Q16—1722no—
170C2×C8—41no—
171C2×C8—432no—
172C2×C8—1721no—
173C2×C8C22×D4311yescharacteristic
174C2×C8C22×D4311yescharacteristic
175C4⋊C4—22no—
176C4⋊C4—432no—
177C4⋊C4—862no—
178C4⋊C4—862no—
179C4⋊C4—862no—
180C4⋊C4—862no—
181C4⋊C4C22×D4312yes—
182C22⋊C4—22no—
183C22⋊C4—862no—
184C22⋊C4—862no—
185C22⋊C4—862no—
186C23—432no—
187C23—434no—
188C23—1721no—
189C23—1721no—
190C23D4×D4311yescharacteristic
191Q8—22no—
192Q8—22no—
193Q8—862no—
194Q8—862no—
195Q8—1724no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—432no—
201C2×C4—862no—
202C2×C4—862no—
203C2×C4—862no—
204C2×C4—862no—
205C2×C4—1722no—
206C2×C4—1724no—
207C2×C4—1724no—
208C2×C4—1721no—
209C2×C4D4×D4311yescharacteristic
210C2×C4C23×D4311yescharacteristic
211C8—21no—
212C8—21no—
213C8—862no—
214C22—21no—
215C22—21no—
216C22—434no—
217C22—862no—
218C22—862no—
219C22—1724no—
220C22Q16×D4312yes—
221C22C2×D4×D4311yescharacteristic
222C4—21no—
223C4—42no—
224C4—42no—
225C4—862no—
226C4—1722no—
227C4—1722no—
228C4#1306337011yescharacteristic
229C4#1306337111yescharacteristic
230C2—22no—
231C2—864no—
232C2#1458345711yescharacteristic
233C2C2×Q16×D4311yescharacteristic
234C2#1458369611yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#467C2
socleC22×C43C22×D4
hypercenter#467D43
hypocenterC43#3189
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #467

Complements

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

NH ≅ G/Ntype
2. #14583236C2semidirect
3. #14583233C2semidirect
4. #14583140C2semidirect
5. #14583138C2semidirect
6. #14583056C2semidirect
7. #14583053C2semidirect
9. C43×#467C2semidirect
12. C2×Dic172C22semidirect
13. C2×#10621885C22semidirect
23. #13063259C22semidirect
24. #13063258C22semidirect
25. #13063250C22semidirect
26. #13063249C22semidirect
27. #13063248C22semidirect
30. C2×Q16×C43C22semidirect
33. #107×C43C22semidirect
34. #103×C43C22semidirect
71. C22×D43Q16semidirect
123. #467D43semidirect
127. C43#3189semidirect
132. C2×Q16C2×D43semidirect
146. #107C2×D43semidirect
150. #103C2×D43semidirect