Finite Group Databasebeta

← #19145812

Subgroups — #19145812

Order 5504.

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

normal subgroups only

This group has 362 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
1C4⋊Q8×D43C211yesmaximal, characteristic, complemented
2#14583428C211yesmaximal, characteristic
3#14583308C211yesmaximal, characteristic, complemented
4#14583305C211yesmaximal, characteristic, complemented
5#14583258C211yesmaximal, characteristic, complemented
6#14583228C212yesmaximal, complemented
7#14583211C212yesmaximal
8#14583192C212yesmaximal, complemented
9#14583187C212yesmaximal, complemented
10#14582954C211yesmaximal, characteristic, complemented
11C43×#489C211yesmaximal, characteristic, complemented
12C2×Q8×D43—21no—
13#13063325C2211yescharacteristic
14#13063324—21no—
15#13063324C2212yes—
16#13063323—21no—
17#13063318—21no—
18#13063317C2211yescharacteristic
19#13063307—21no—
20#13063301C2211yescharacteristic
21#13063296C2211yescharacteristic
22Q8×Dic43C2211yescharacteristic
23D4×Dic43C2211yescharacteristic
24(C22⋊D43)⋊C4—21no—
25#13063281—21no—
26C4⋊C4×D43—21no—
27C4⋊C4×D43C2212yes—
28C42×D43C2211yescharacteristic
29#13063259C2212yes—
30#13063258C2212yes—
31#13063257C2212yes—
32#13063256C2212yes—
33Dic43⋊C8C2212yes—
34#13063249C2212yes—
35#13063246C2212yes—
36(C2×D43)⋊C8C2212yes—
37#13063236C2211yescharacteristic
38C4⋊Q8×C43C2211yescharacteristic
39#124×C43C2211yescharacteristic
40#103×C43C2212yes—
41#102×C43C2212yes—
42#97×C43C2211yescharacteristic
43C2×Q8×C43—21no—
44C2×Q8×C43C2311yescharacteristic
45C2×D4×C43C2311yescharacteristic
46C2×C22⋊D43—21no—
47C22×Dic43—21no—
48Q8×D43—44no—
49C2×C4×D43—22no—
50C2×C4×D43D411yescharacteristic
51C2×C4×D43D411yescharacteristic
52C2×C4×D43C2311yescharacteristic
53C2×Dic86—21no—
54C2×Dic86—22no—
55C2×C8×C43C2312yes—
56C4⋊C4×C43—21no—
57C4⋊C4×C43C2312yes—
58C22⋊C4×C43—21no—
59C22⋊C4×C43—21no—
60C42×C43C2311yescharacteristic
61C22⋊Dic43—21no—
62C22⋊Dic43—21no—
63(C2×D43)⋊C4—21no—
64C4⋊Dic43—21no—
65C4⋊Dic43—21no—
66C4⋊Dic43C2312yes—
67C4⋊Dic43C2311yescharacteristic
68C4⋊Dic43C2311yescharacteristic
69Dic43⋊C4—21no—
70Dic43⋊C4—21no—
71Dic43⋊C4—22no—
72Dic43⋊C4—22no—
73Dic43⋊C4—21no—
74C4×Dic43—21no—
75C4×Dic43D411yescharacteristic
76C4×Dic43D411yescharacteristic
77C4×Dic43C2311yescharacteristic
78C2×C43⋊C8C2312yes—
79C23×C43—21no—
80C22×D43C2×D411yescharacteristic
81Q8×C43—22no—
82Q8×C43—42no—
83D4×C43—22no—
84C2×C4×C43—21no—
85C2×C4×C43—22no—
86C2×C4×C43C2×D411yescharacteristic
87C2×C4×C43C2×D411yescharacteristic
88C2×C4×C43C2411yescharacteristic
89C22⋊D43—42no—
90C2×Dic43—21no—
91C2×Dic43—21no—
92C2×Dic43—22no—
93C2×Dic43—42no—
94C2×Dic43C2×D411yescharacteristic
95C2×Dic43C2×D411yescharacteristic
96C2×Dic43C2×D411yescharacteristic
97C4×D43—22no—
98C4×D43—22no—
99C4×D43—22no—
100C4×D43—44no—
101Dic86—44no—
102Dic86—42no—
103C8×C43—22no—
104C43⋊C8—22no—
105C22×C43—41no—
106C22×C43—41no—
107C22×C43—41no—
108C22×C43C22×D411yescharacteristic
109C2×D43—21no—
110C2×D43—21no—
111C2×D43AGL(1,ℤ/8)12yes—
112C4×C43—21no—
113C4×C43—21no—
114C4×C43—41no—
115C4×C43—42no—
116C4×C432−1+412yes—
117Dic43—21no—
118Dic43—21no—
119Dic43—42no—
120Dic43—41no—
121Dic43—41no—
122Dic43#13712yes—
123#3238—431nomaximal, Sylow
124C2×C43—81no—
125C2×C43#53611yescharacteristic
126C2×C43C2×AGL(1,ℤ/8)11yescharacteristic
127C2×C43C2×#13711yescharacteristic
128D43—22no—
129C2×C4⋊Q8—431no—
130#529—431no—
131#501—431no—
132#501—431no—
133#489—431no—
134#489D4311yescharacteristic, complemented
135#483—432no—
136#480—432no—
137#477—432no—
138#476—432no—
139#432—431no—
140C43#323811yescharacteristic, complemented, Sylow
141C22×Q8—861no—
142C4⋊Q8—432no—
143C4⋊Q8—431no—
144C4⋊Q8—861no—
145C4⋊Q8—861no—
146C4⋊Q8C2×D4311yescharacteristic
147#126—861no—
148#125—431no—
149#124C2×D4311yescharacteristic
150#123—861no—
151C22⋊Q8—431no—
152#121—431no—
153C4×Q8—431no—
154C4×D4—431no—
155C4×D4—861no—
156#117—861no—
157C2×C4⋊C4—432no—
158C2×C4⋊C4—861no—
159C2×C42—431no—
160#107—432no—
161#107—432no—
162#106—432no—
163#106—432no—
164C4⋊C8—432no—
165#103—432no—
166#103C2×D4312yes—
167#102—432no—
168#102C2×D4312yes—
169C22⋊C8—432no—
170#97—431no—
171#97C2×D4311yescharacteristic
172C2×Q8—21no—
173C2×Q8—862no—
174C2×Q8—861no—
175C2×Q8—1724no—
176C2×Q8C22×D4311yescharacteristic
177C2×D4—861no—
178C2×D4C22×D4311yescharacteristic
179C22×C4—431no—
180C22×C4—431no—
181C22×C4—431no—
182C22×C4—862no—
183C22×C4—861no—
184C2×C8—432no—
185C2×C8C22×D4312yes—
186C4⋊C4—21no—
187C4⋊C4—432no—
188C4⋊C4—431no—
189C4⋊C4—431no—
190C4⋊C4—862no—
191C4⋊C4—862no—
192C4⋊C4—861no—
193C4⋊C4—861no—
194C4⋊C4—861no—
195C4⋊C4—861no—
196C4⋊C4—861no—
197C4⋊C4C22×D4312yes—
198C22⋊C4—21no—
199C22⋊C4—21no—
200C22⋊C4—861no—
201C22⋊C4—861no—
202C22⋊C4—861no—
203C42—431no—
204C42—431no—
205C42—431no—
206C42—861no—
207C42C22×D4311yescharacteristic
208C23—21no—
209C23—431no—
210Q8—22no—
211Q8—42no—
212Q8—1722no—
213Q8—1724no—
214D4—22no—
215D4—1722no—
216C2×C4—21no—
217C2×C4—22no—
218C2×C4—431no—
219C2×C4—431no—
220C2×C4—431no—
221C2×C4—862no—
222C2×C4—862no—
223C2×C4—862no—
224C2×C4—861no—
225C2×C4—861no—
226C2×C4—862no—
227C2×C4—1724no—
228C2×C4—1722no—
229C2×C4D4×D4311yescharacteristic
230C2×C4D4×D4311yescharacteristic
231C2×C4C23×D4311yescharacteristic
232C8—22no—
233C8—862no—
234C22—41no—
235C22—41no—
236C22—41no—
237C22—432no—
238C22—861no—
239C22—861no—
240C22C2×D4×D4311yescharacteristic
241C4—21no—
242C4—21no—
243C4—42no—
244C4—41no—
245C4—432no—
246C4—861no—
247C4—861no—
248C4—1722no—
249C4—1721no—
250C4—1721no—
251C4#1306337212yes—
252C2—81no—
253C2—862no—
254C2#1458346911yescharacteristic
255C2AGL(1,ℤ/8)×D4311yescharacteristic
256C2#137×D4311yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#489C2
socleC22×C43C22×D4
hypercenter#489D43
hypocenterC43#3238
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
1. C4⋊Q8×D43C2semidirect
3. #14583308C2semidirect
4. #14583305C2semidirect
5. #14583258C2semidirect
6. #14583228C2semidirect
8. #14583192C2semidirect
9. #14583187C2semidirect
10. #14582954C2semidirect
11. C43×#489C2semidirect
134. #489D43semidirect
140. C43#3238semidirect