Finite Group Databasebeta

← #19143958

Subgroups — #19143958

Order 5504.

698 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 698 conjugacy classes of subgroups — too many to draw. Only its 145 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
1C2×#13063373C211yesmaximal, characteristic, complemented
2#14583697C212yesmaximal, complemented
3#14583081C214yesmaximal, complemented
4#14583071C214yesmaximal, complemented
5#14582917C212yesmaximal, complemented
6C2×#13063244C211yesmaximal, characteristic, complemented
7C43×#536C211yesmaximal, characteristic, complemented
8#13063373—22no—
9#13063373—24no—
10#13063373C2214yes—
11C2×#10621902—22no—
12C2×#10621898—22no—
13C2×#10621898C2212yes—
14C2×Q8×D43—22no—
15#13063356C2214yescomplemented
16#13063355—22no—
17#13063351C2214yescomplemented
18#13063350—22no—
19#13063345—24no—
20C2×#10621877C2212yes—
21#13063253C2218yescomplemented
22#13063244C2214yescomplemented
23C2×#41×C43C2211yescharacteristic
24C22×Q8×C43C2211yescharacteristic
25C4⋊Q8×C43C2212yescomplemented
26#124×C43C2212yescomplemented
27#123×C43—22no—
28C22⋊Q8×C43—22no—
29#117×C43C2211yescharacteristic
30#41×C43—22no—
31#41×C43—22no—
32C2×Q8×C43—22no—
33C2×Q8×C43—22no—
34C2×Q8×C43D412yes—
35C2×Q8×C43C2311yescharacteristic
36C2×Q8×C43C2312yes—
37C2×D4×C43—21no—
38C2×D4×C43C2311yescharacteristic
39C22×C4×C43—21no—
40C22×C4×C43D412yes—
41C22×C4×C43C2311yescharacteristic
42C2×C22⋊D43—22no—
43#10621902—28no—
44#10621902—28no—
45Q8×D43—28no—
46Q8×D43—28no—
47#10621898—28no—
48#10621898—28no—
49#10621898—22no—
50#10621898—22no—
51#10621898D414yes—
52#10621898C2314yes—
53C2×D172—22no—
54C2×D172D412yes—
55C2×C4×D43—24no—
56C2×C4×D43—22no—
57C2×Dic86—22no—
58C2×Dic86D412yes—
59C4⋊C4×C43—21no—
60C4⋊C4×C43—24no—
61C22⋊C4×C43—24no—
62C22⋊C4×C43—21no—
63C42×C43C2312yes—
64#10621885—24no—
65#10621884—24no—
66#10621883—24no—
67#10621882—24no—
68#10621877—22no—
69#10621877C2314yes—
70C2×C43⋊C8—22no—
71C23×C43—21no—
72C23×C43C2×D411yescharacteristic
73C22×D43—22no—
74Q8×C43—24no—
75Q8×C43—24no—
76Q8×C43—22no—
77D4×C43—22no—
78D4×C43—41no—
79D4×C43—41no—
80C2×C4×C43—22no—
81C2×C4×C43—22no—
82C2×C4×C43—22no—
83C2×C4×C43—21no—
84C2×C4×C43—42no—
85C2×C4×C43C2×D412yes—
86C2×C4×C43C2×D412yes—
87C2×C4×C43C2×D414yes—
88C2×C4×C43C2×D411yescharacteristic
89C2×C4×C43C2411yescharacteristic
90C22⋊D43—24no—
91C22⋊D43—24no—
92C2×Dic43—22no—
93D172—28no—
94D172—22no—
95D172C2×D414yes—
96C4×D43—216no—
97C4×D43—24no—
98C4×D43—24no—
99Dic86—28no—
100Dic86—22no—
101Dic86C2×D414yes—
102C43⋊C8—24no—
103C22×C43—41no—
104C22×C43—42no—
105C22×C43—41no—
106C22×C43#12011yescharacteristic
107C22×C43#12011yescharacteristic
108C22×C43C22×D411yescharacteristic
109C2×D43—24no—
110C2×D43—44no—
111C4×C43—24no—
112C4×C43—42no—
113C4×C43—41no—
114C4×C43#12012yes—
115C4×C43C22×D412yes—
116Dic43—24no—
117#3020—431nomaximal, Sylow
118C2×C43—21no—
119C2×C43—21no—
120C2×C43—21no—
121C2×C43—81no—
122C2×C43C2×#12011yescharacteristic
123D43—44no—
124C2×2−1+4—431no—
125#575—432no—
126#536D4311yescharacteristic, complemented
127#456—434no—
128#454—434no—
129#421—432no—
130C2×#101—431no—
131C43#302011yescharacteristic, complemented, Sylow
1322−1+4—434no—
1332−1+4—864no—
1342−1+4—862no—
135C2×#41—432no—
136C2×#41—862no—
137C2×#41—862no—
138C2×#41C2×D4311yescharacteristic
139C22×Q8—862no—
140C22×Q8C2×D4311yescharacteristic
141#137—434no—
142#137—862no—
143AGL(1,ℤ/8)—434no—
144AGL(1,ℤ/8)—862no—
145#135—864no—
146C2×M16—432no—
147C4⋊Q8C2×D4312yescomplemented
148#124C2×D4312yescomplemented
149#123—22no—
150C22⋊Q8—22no—
151#117C2×D4311yescharacteristic
152#104—438no—
153#101—434no—
154#41—22no—
155#41—22no—
156#41—434no—
157#41—434no—
158#41—868no—
159#41—868no—
160#41—868no—
161#41—862no—
162#41—862no—
163#41—868no—
164C2×Q8—22no—
165C2×Q8—22no—
166C2×Q8—432no—
167C2×Q8—862no—
168C2×Q8—868no—
169C2×Q8—868no—
170C2×Q8C22⋊D4312yes—
171C2×Q8C22×D4311yescharacteristic
172C2×Q8C22×D4312yes—
173C2×D4—21no—
174C2×D4—432no—
175C2×D4—862no—
176C2×D4—862no—
177C2×D4C22×D4311yescharacteristic
178C22×C4—21no—
179C22×C4—864no—
180C22×C4—862no—
181C22×C4C22⋊D4312yes—
182C22×C4C22×D4311yescharacteristic
183Q16—864no—
184SD16—864no—
185SD16—864no—
186D8—864no—
187M16—434no—
188M16—862no—
189C2×C8—862no—
190C4⋊C4—21no—
191C4⋊C4—24no—
192C22⋊C4—21no—
193C22⋊C4—24no—
194C42C22×D4312yes—
195C23—21no—
196C23—862no—
197C23C2×C22⋊D4311yescharacteristic
198Q8—24no—
199Q8—24no—
200Q8—22no—
201Q8—434no—
202Q8—868no—
203Q8—862no—
204D4—22no—
205D4—41no—
206D4—41no—
207D4—434no—
208D4—868no—
209D4—864no—
210D4—864no—
211D4—862no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—21no—
216C2×C4—42no—
217C2×C4—8616no—
218C2×C4—862no—
219C2×C4—864no—
220C2×C4—864no—
221C2×C4D4×D4312yes—
222C2×C4D4×D4312yes—
223C2×C4C2×C22⋊D4314yes—
224C2×C4C2×C22⋊D4311yescharacteristic
225C2×C4C23×D4311yescharacteristic
226C8—864no—
227C22—41no—
228C22—42no—
229C22—41no—
230C22—864no—
231C22—1724no—
232C22#1306329311yescharacteristic
233C22#1306329311yescharacteristic
234C22C22×C22⋊D4311yescharacteristic
235C4—24no—
236C4—42no—
237C4—41no—
238C4—864no—
239C4#1306329312yes—
240C4C2×D4×D4312yes—
241C2—21no—
242C2—21no—
243C2—21no—
244C2—81no—
245C2—1724no—
246C2C2×#1306329311yescharacteristic
subgroupG/H
centerC2C2×#13063293
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#536C2
socleC2×C43C2×#120
hypercenter#536D43
hypocenterC43#3020
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C22×C4 ◁ #536

Complements

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

NH ≅ G/Ntype
1. C2×#13063373C2semidirect
2. #14583697C2semidirect
3. #14583081C2semidirect
4. #14583071C2semidirect
5. #14582917C2semidirect
6. C2×#13063244C2semidirect
7. C43×#536C2semidirect
15. #13063356C22semidirect
17. #13063351C22semidirect
21. #13063253C22semidirect
22. #13063244C22semidirect
25. C4⋊Q8×C43C22semidirect
26. #124×C43C22semidirect
126. #536D43semidirect
131. C43#3020semidirect
147. C4⋊Q8C2×D43semidirect
148. #124C2×D43semidirect