Finite Group Databasebeta

← #19146389

Subgroups — #19146389

Order 5504.

460 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 125 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#14583711C212yesmaximal, complemented
2#14583706C212yesmaximal, complemented
3#14583272C211yesmaximal, characteristic, complemented
4#14583163C212yesmaximal, complemented
5#14583162C212yesmaximal, complemented
6#14583083C212yesmaximal, complemented
7#14583068C212yesmaximal, complemented
8#14583017C211yesmaximal, characteristic, complemented
9C43×#443C211yesmaximal, characteristic, complemented
10#13063372C2212yes—
11#13063371C2212yescomplemented
12#13063358—22no—
13#13063358C2212yescomplemented
14#13063357—22no—
15#13063355C2212yescomplemented
16#13063353—22no—
17#13063353C2212yes—
18#13063350C2212yes—
19#13063349—22no—
20#13063347—22no—
21#13063347C2211yescharacteristic
22#13063346—22no—
23C2×#10621873—22no—
24C2×#10621873C2212yescomplemented
25C2×#10621873C2212yescomplemented
26SD16×D43—22no—
27#13063331C2212yescomplemented
28#13063325C2211yescharacteristic, complemented
29#13063322C2211yescharacteristic
30#13063261C2211yescharacteristic, complemented
31#13063253C2212yescomplemented
32#13063243C2212yescomplemented
33#13063241C2212yescomplemented
34#135×C43C2211yescharacteristic
35#131×C43C2212yescomplemented
36#108×C43C2211yescharacteristic, complemented
37#104×C43C2212yescomplemented
38C4×C8×C43C2211yescharacteristic, complemented
39#41×C43C2312yes—
40#10621902—22no—
41Q8×D43—22no—
42#10621900—22no—
43#10621900—42no—
44D4×D43—22no—
45D4×D43—42no—
46#10621898—22no—
47#10621898—22no—
48#10621898C2312yes—
49C2×D172—22no—
50C2×D172—41no—
51C2×D172C2312yes—
52C2×Dic86—22no—
53C2×Dic86C2312yes—
54Q16×C43D411yescharacteristic, complemented
55SD16×C43D412yescomplemented
56D8×C43D411yescharacteristic, complemented
57M16×C43—22no—
58M16×C43C2312yes—
59C2×C8×C43—22no—
60C2×C8×C43C2311yescharacteristic
61C2×C8×C43C2311yescharacteristic
62C42×C43C2311yescharacteristic
63#10621885—22no—
64#10621884—22no—
65#10621883—22no—
66#10621882—22no—
67C4⋊Dic43—41no—
68#10621877C2312yes—
69Dic172—22no—
70Dic172D411yescharacteristic, complemented
71D344—22no—
72D344D411yescharacteristic, complemented
73#10621873—22no—
74#10621873—22no—
75#10621873—22no—
76#10621873—22no—
77#10621873—22no—
78#10621873—22no—
79#10621873D412yescomplemented
80#10621872—22no—
81C8×D43—22no—
82C22×D43—22no—
83C22×D43—42no—
84Q8×C43C2×D412yes—
85D4×C43—22no—
86D4×C43C2×D412yes—
87C2×C4×C43—21no—
88C2×C4×C43—22no—
89C2×C4×C43C2411yescharacteristic
90C22⋊D43—22no—
91C22⋊D43—42no—
92C22⋊D43—42no—
93C2×Dic43—22no—
94C2×Dic43—42no—
95D172—22no—
96D172—22no—
97D172—42no—
98D172—82no—
99D172C2×D412yes—
100C4×D43—22no—
101C4×D43—42no—
102C4×D43—42no—
103Dic86—22no—
104Dic86—22no—
105Dic86—42no—
106Dic86C2×D412yes—
107C8×C43—22no—
108C8×C43C2×D411yescharacteristic
109C8×C43C2×D411yescharacteristic
110C8×C43C2×D411yescharacteristic
111C8×C43C2×D411yescharacteristic
112C43⋊C8—22no—
113C22×C43—22no—
114C22×C43H(5,𝔽2)11yescharacteristic
115C2×D43—22no—
116C2×D43—42no—
117C2×D43—82no—
118C2×D43—162no—
119C4×C43—22no—
120C4×C43—22no—
121C4×C43C22×D411yescharacteristic
122C4×C43C22×D411yescharacteristic
123Dic43—22no—
124Dic43—42no—
125#3291—431nomaximal, Sylow
126C2×C43—21no—
127C2×C43—42no—
128C2×C43D4211yescharacteristic
129D43—42no—
130D43—82no—
131#577—432no—
132#577—432no—
133#492—431no—
134#471—432no—
135#471—432no—
136#456—432no—
137#453—432no—
138#443—431no—
139#443D4311yescharacteristic, complemented
140C43#329111yescharacteristic, complemented, Sylow
1412−1+4—432no—
142H(5,𝔽2)—432no—
143#137—432no—
144#137—432no—
145#137—862no—
146#137—862no—
147AGL(1,ℤ/8)—432no—
148AGL(1,ℤ/8)—432no—
149AGL(1,ℤ/8)—862no—
150AGL(1,ℤ/8)—862no—
151#135—431no—
152#135—862no—
153#135—862no—
154#135C2×D4311yescharacteristic
155C2×SD16—432no—
156C2×SD16—432no—
157C2×SD16—862no—
158C2×SD16—862no—
159#131—432no—
160#131C2×D4312yescomplemented
161C4⋊Q8—431no—
162#127—431no—
163#108—431no—
164#108C2×D4311yescharacteristic, complemented
165#104—432no—
166#104C2×D4312yescomplemented
167#101—432no—
168#100—432no—
169C4×C8C2×D4311yescharacteristic, complemented
170#41—432no—
171#41—862no—
172#41—862no—
173#41—862no—
174#41—862no—
175#41—1722no—
176#41C22×D4312yes—
177C2×Q8—432no—
178C2×Q8—862no—
179C2×Q8—862no—
180C2×D4—432no—
181C2×D4—862no—
182C2×D4—862no—
183C2×D4—1721no—
184C2×D4—1722no—
185Q16—431no—
186Q16—862no—
187Q16—862no—
188Q16D17211yescharacteristic, complemented
189SD16—432no—
190SD16—862no—
191SD16—862no—
192SD16—862no—
193SD16—862no—
194SD16—862no—
195SD16—862no—
196SD16—862no—
197SD16—862no—
198SD16D17212yescomplemented
199D8—431no—
200D8—862no—
201D8—862no—
202D8D17211yescharacteristic, complemented
203M16—22no—
204M16—432no—
205M16—862no—
206M16C22×D4312yes—
207C2×C8—22no—
208C2×C8—862no—
209C2×C8C22×D4311yescharacteristic
210C2×C8C22×D4311yescharacteristic
211C4⋊C4—1721no—
212C42C22×D4311yescharacteristic
213C23—862no—
214C23—1722no—
215Q8—432no—
216Q8—862no—
217Q8—862no—
218Q8—1722no—
219Q8C2×D17212yes—
220D4—22no—
221D4—432no—
222D4—862no—
223D4—862no—
224D4—862no—
225D4—3442no—
226D4—1722no—
227D4—1722no—
228D4—1722no—
229D4C2×D17212yes—
230C2×C4—21no—
231C2×C4—22no—
232C2×C4—862no—
233C2×C4—862no—
234C2×C4—1722no—
235C2×C4—1722no—
236C2×C4—1722no—
237C2×C4C23×D4311yescharacteristic
238C8—22no—
239C8—862no—
240C8C2×D17211yescharacteristic
241C8C2×D17211yescharacteristic
242C8D4×D4311yescharacteristic
243C8D4×D4311yescharacteristic
244C22—22no—
245C22—862no—
246C22—3442no—
247C22—1722no—
248C22—6882no—
249C22#1306337111yescharacteristic
250C4—22no—
251C4—22no—
252C4—862no—
253C4—1722no—
254C4C2×D4×D4311yescharacteristic
255C4C22×D17211yescharacteristic
256C2—21no—
257C2—42no—
258C2—3442no—
259C2—1722no—
260C2D4×D17211yescharacteristic
subgroupG/H
centerC2D4×D172
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#443C2
socleC2×C43D42
hypercenter#443D43
hypocenterC43#3291
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ #443

Complements

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

NH ≅ G/Ntype
1. #14583711C2semidirect
2. #14583706C2semidirect
3. #14583272C2semidirect
4. #14583163C2semidirect
5. #14583162C2semidirect
6. #14583083C2semidirect
7. #14583068C2semidirect
8. #14583017C2semidirect
9. C43×#443C2semidirect
11. #13063371C22semidirect
13. #13063358C22semidirect
15. #13063355C22semidirect
24. C2×#10621873C22semidirect
25. C2×#10621873C22semidirect
27. #13063331C22semidirect
28. #13063325C22semidirect
30. #13063261C22semidirect
31. #13063253C22semidirect
32. #13063243C22semidirect
33. #13063241C22semidirect
35. #131×C43C22semidirect
36. #108×C43C22semidirect
37. #104×C43C22semidirect
38. C4×C8×C43C22semidirect
54. Q16×C43D4semidirect
55. SD16×C43D4semidirect
56. D8×C43D4semidirect
70. Dic172D4semidirect
72. D344D4semidirect
79. #10621873D4semidirect
139. #443D43semidirect
140. C43#3291semidirect
160. #131C2×D43semidirect
164. #108C2×D43semidirect
166. #104C2×D43semidirect
169. C4×C8C2×D43semidirect
188. Q16D172semidirect
198. SD16D172semidirect
202. D8D172semidirect