Finite Group Databasebeta

← #19144000

Subgroups — #19144000

Order 5504.

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

normal subgroups only

This group has 716 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
1#14583735C211yesmaximal, characteristic
2#14583473C212yesmaximal, complemented
3#14583088C218yesmaximal, complemented
4#14582873C211yesmaximal, characteristic, complemented
5#14582872C212yesmaximal, complemented
6C43×#536C211yesmaximal, characteristic, complemented
7#13063373—21no—
8#13063372—22no—
9#13063371—22no—
10#13063370—21no—
11#13063370C2214yes—
12C2×#10621898—22no—
13C2×#10621898C2212yes—
14#41×D43—24no—
15#13063323—22no—
16#13063314—22no—
17#13063308C2218yescomplemented
18#13063301—24no—
19#13063284C2212yescomplemented
20#13063240C2214yescomplemented
21#13063239C2218yescomplemented
22C2×#41×C43C2211yescharacteristic
23C22×Q8×C43C2211yescharacteristic, complemented
24C4⋊Q8×C43—21no—
25#124×C43—21no—
26#123×C43C2214yescomplemented
27C22⋊Q8×C43—22no—
28#117×C43C2211yescharacteristic, complemented
29#41×C43—22no—
30#41×C43—22no—
31C2×Q8×C43—21no—
32C2×Q8×C43—21no—
33C2×Q8×C43—22no—
34C2×Q8×C43—22no—
35C2×Q8×C43D411yescharacteristic
36C2×D4×C43D411yescharacteristic
37C2×D4×C43C2312yes—
38C22×C4×C43D412yes—
39C22×C4×C43C2312yes—
40C22×C4×C43C2311yescharacteristic
41C2×C22⋊D43—24no—
42C2×C22⋊D43C2314yes—
43#10621902—24no—
44Q8×D43—24no—
45#10621900—24no—
46#10621900—28no—
47D4×D43—24no—
48D4×D43—28no—
49#10621898—24no—
50#10621898—24no—
51#10621898—22no—
52#10621898—22no—
53#10621898—24no—
54#10621898—22no—
55#10621898—22no—
56C2×D172—22no—
57C2×D172D412yes—
58C2×C4×D43—24no—
59C2×C4×D43D414yes—
60C2×Dic86—22no—
61C2×Dic86D412yes—
62C4⋊C4×C43—21no—
63C4⋊C4×C43—24no—
64C22⋊C4×C43—24no—
65C22⋊C4×C43C2312yes—
66C42×C43—21no—
67C22⋊Dic43C2314yes—
68(C2×D43)⋊C4—28no—
69C4⋊Dic43—22no—
70Dic43⋊C4—28no—
71C4×Dic43—22no—
72C23×C43C2×D412yes—
73C23×C43C2411yescharacteristic
74C22×D43—24no—
75C22×D43C2×D414yes—
76Q8×C43—22no—
77Q8×C43—41no—
78Q8×C43—42no—
79Q8×C43—41no—
80D4×C43—24no—
81D4×C43—22no—
82C2×C4×C43—22no—
83C2×C4×C43—22no—
84C2×C4×C43—24no—
85C2×C4×C43—22no—
86C2×C4×C43—22no—
87C2×C4×C43C2×D412yes—
88C2×C4×C43C2×D412yes—
89C2×C4×C43C2×D412yes—
90C2×C4×C43C2×D411yescharacteristic
91C2×C4×C43C2×D411yescharacteristic
92C22⋊D43—28no—
93C22⋊D43—24no—
94C22⋊D43—24no—
95C2×Dic43—24no—
96C2×Dic43—24no—
97C2×Dic43C2×D414yes—
98D172—24no—
99D172—22no—
100D172—22no—
101C4×D43—28no—
102C4×D43—24no—
103C4×D43—24no—
104Dic86—24no—
105Dic86—22no—
106Dic86—22no—
107C22×C43—22no—
108C22×C43—41no—
109C22×C43—42no—
110C22×C43C22×D412yes—
111C22×C43C22×D411yescharacteristic
112C2×D43—24no—
113C2×D43—44no—
114C2×D43—84no—
115C4×C43—22no—
116C4×C43—42no—
117C4×C43—42no—
118C4×C43#12011yescharacteristic
119C4×C43#12012yes—
120C4×C43#12011yescharacteristic
121Dic43—24no—
122Dic43—44no—
123#3028—431nomaximal, Sylow
124C2×C43—22no—
125C2×C43—21no—
126C2×C43—42no—
127C2×C43C2×#12011yescharacteristic
128D43—44no—
129#585—431no—
130#536—432no—
131#536D4311yescharacteristic, complemented
132#458—438no—
133#410—431no—
134#410—432no—
135C43#302811yescharacteristic, complemented, Sylow
1362−1+4—862no—
1372−1+4—861no—
138H(5,𝔽2)—434no—
139H(5,𝔽2)—862no—
140H(5,𝔽2)—861no—
141C2×#41—432no—
142C2×#41—864no—
143C2×#41—862no—
144C2×#41C2×D4311yescharacteristic
145C22×Q8C2×D4311yescharacteristic, complemented
146C4⋊Q8—21no—
147C4⋊Q8—862no—
148#124—21no—
149#124—862no—
150#123—438no—
151#123C2×D4314yescomplemented
152C22⋊Q8—22no—
153C22⋊Q8—864no—
154#117—432no—
155#117C2×D4311yescharacteristic, complemented
156#99—434no—
157#99—438no—
158#41—22no—
159#41—22no—
160#41—864no—
161#41—864no—
162#41—868no—
163#41—864no—
164#41—864no—
165#41—862no—
166#41—862no—
167#41—862no—
168#41—862no—
169#41—864no—
170C2×Q8—22no—
171C2×Q8—22no—
172C2×Q8—21no—
173C2×Q8—21no—
174C2×Q8—432no—
175C2×Q8—862no—
176C2×Q8—864no—
177C2×Q8C22⋊D4311yescharacteristic
178C2×D4—434no—
179C2×D4—432no—
180C2×D4—862no—
181C2×D4—868no—
182C2×D4—864no—
183C2×D4—864no—
184C2×D4C22⋊D4311yescharacteristic
185C2×D4C22×D4312yes—
186C22×C4—434no—
187C22×C4—864no—
188C22×C4C22⋊D4312yes—
189C22×C4C22×D4312yes—
190C22×C4C22×D4311yescharacteristic
191C4⋊C4—21no—
192C4⋊C4—24no—
193C4⋊C4—868no—
194C4⋊C4—862no—
195C22⋊C4—24no—
196C22⋊C4—434no—
197C22⋊C4—868no—
198C22⋊C4C22×D4312yes—
199C42—21no—
200C42—862no—
201C23—434no—
202C23—864no—
203C23C2×C22⋊D4312yes—
204C23C23×D4311yescharacteristic
205Q8—22no—
206Q8—41no—
207Q8—41no—
208Q8—42no—
209Q8—864no—
210Q8—862no—
211Q8—862no—
212D4—24no—
213D4—22no—
214D4—864no—
215D4—868no—
216D4—864no—
217D4—864no—
218D4—862no—
219D4—862no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—24no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—434no—
226C2×C4—868no—
227C2×C4—864no—
228C2×C4—864no—
229C2×C4—864no—
230C2×C4—864no—
231C2×C4D4×D4312yes—
232C2×C4D4×D4312yes—
233C2×C4C2×C22⋊D4312yes—
234C2×C4C2×C22⋊D4311yescharacteristic
235C2×C4C2×C22⋊D4311yescharacteristic
236C22—22no—
237C22—41no—
238C22—42no—
239C22—864no—
240C22—3444no—
241C22—1724no—
242C22C2×D4×D4312yes—
243C22C22×C22⋊D4311yescharacteristic
244C4—22no—
245C4—42no—
246C4—42no—
247C4—864no—
248C4—1724no—
249C4#1306329311yescharacteristic
250C4#1306329311yescharacteristic
251C4#1306329312yes—
252C2—21no—
253C2—22no—
254C2—42no—
255C2—1724no—
256C2C2×#1306329311yescharacteristic
subgroupG/H
centerC2C2×#13063293
commutatorC23×C43C24
FrattiniC23C23×D43
FittingC43×#536C2
socleC2×C43C2×#120
hypercenter#536D43
hypocenterC43#3028
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C22×C4 ◁ #536

Complements

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

NH ≅ G/Ntype
2. #14583473C2semidirect
3. #14583088C2semidirect
4. #14582873C2semidirect
5. #14582872C2semidirect
6. C43×#536C2semidirect
17. #13063308C22semidirect
19. #13063284C22semidirect
20. #13063240C22semidirect
21. #13063239C22semidirect
23. C22×Q8×C43C22semidirect
26. #123×C43C22semidirect
28. #117×C43C22semidirect
131. #536D43semidirect
135. C43#3028semidirect
145. C22×Q8C2×D43semidirect
151. #123C2×D43semidirect
155. #117C2×D43semidirect