Finite Group Databasebeta

← #19144002

Subgroups — #19144002

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#14583475C212yesmaximal, complemented
3#14583470C211yesmaximal, characteristic, complemented
4#14583090C218yesmaximal, complemented
5#14582872C212yesmaximal, complemented
6C43×#410C211yesmaximal, 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—
15C22×Dic86C2211yescharacteristic, complemented
16#13063325—22no—
17#13063323—21no—
18#13063313—22no—
19#13063312—21no—
20#13063309C2218yescomplemented
21#13063306C2214yescomplemented
22#13063305—24no—
23#13063304—22no—
24#13063284C2211yescharacteristic, complemented
25#13063239C2218yescomplemented
26C2×#41×C43C2211yescharacteristic
27#117×C43C2212yescomplemented
28#99×C43C2214yescomplemented
29#41×C43—22no—
30#41×C43—22no—
31C2×Q8×C43D411yescharacteristic
32C2×D4×C43D411yescharacteristic
33C2×D4×C43C2312yes—
34C22×C4×C43D412yes—
35C22×C4×C43C2311yescharacteristic
36C2×C22⋊D43—24no—
37C2×C22⋊D43C2314yes—
38C22×Dic43C2312yes—
39#10621902—24no—
40Q8×D43—24no—
41#10621900—24no—
42#10621900—28no—
43D4×D43—24no—
44D4×D43—28no—
45#10621898—24no—
46#10621898—24no—
47#10621898—22no—
48#10621898—22no—
49#10621898—24no—
50#10621898—22no—
51#10621898—22no—
52C2×D172—22no—
53C2×D172D412yes—
54C2×C4×D43—24no—
55C2×C4×D43D414yes—
56C2×Dic86—22no—
57C2×Dic86—21no—
58C2×Dic86—22no—
59C2×Dic86—21no—
60C2×Dic86—22no—
61C2×Dic86D412yes—
62C4⋊C4×C43—22no—
63C22⋊C4×C43C2314yes—
64C42×C43—22no—
65C22⋊Dic43—24no—
66C22⋊Dic43C2312yes—
67(C2×D43)⋊C4—28no—
68C4⋊Dic43—21no—
69C4⋊Dic43—28no—
70Dic43⋊C4—24no—
71C4×Dic43—21no—
72C23×C43C2×D412yes—
73C23×C43C2411yescharacteristic
74C22×D43—24no—
75C22×D43C2×D414yes—
76Q8×C43—22no—
77D4×C43—24no—
78D4×C43—22no—
79C2×C4×C43—22no—
80C2×C4×C43—22no—
81C2×C4×C43—24no—
82C2×C4×C43C2×D412yes—
83C2×C4×C43C2×D411yescharacteristic
84C2×C4×C43C2×D411yescharacteristic
85C2×C4×C43C2×D412yes—
86C2×C4×C43C2×D412yes—
87C22⋊D43—28no—
88C22⋊D43—24no—
89C22⋊D43—24no—
90C2×Dic43—24no—
91C2×Dic43—22no—
92C2×Dic43—22no—
93C2×Dic43—24no—
94C2×Dic43C2×D414yes—
95D172—24no—
96D172—22no—
97D172—22no—
98C4×D43—28no—
99C4×D43—24no—
100C4×D43—24no—
101Dic86—24no—
102Dic86—22no—
103Dic86—22no—
104Dic86—41no—
105Dic86—42no—
106Dic86—41no—
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—44no—
117C4×C43#12011yescharacteristic
118C4×C43#12012yes—
119C4×C43#12011yescharacteristic
120Dic43—24no—
121Dic43—42no—
122Dic43—42no—
123#3028—431nomaximal, Sylow
124C2×C43—21no—
125C2×C43—22no—
126C2×C43—42no—
127C2×C43C2×#12011yescharacteristic
128D43—44no—
129#585—431no—
130#536—431no—
131#536—432no—
132#458—438no—
133#410—432no—
134#410D4311yescharacteristic, complemented
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×Q8—431no—
146C4⋊Q8—862no—
147C4⋊Q8—861no—
148#124—862no—
149#124—861no—
150#123—434no—
151#123—438no—
152C22⋊Q8—864no—
153C22⋊Q8—862no—
154#117—431no—
155#117C2×D4312yescomplemented
156#99—438no—
157#99C2×D4314yescomplemented
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—864no—
168#41—862no—
169#41—862no—
170C2×Q8—432no—
171C2×Q8—862no—
172C2×Q8—864no—
173C2×Q8—861no—
174C2×Q8—861no—
175C2×Q8—862no—
176C2×Q8—862no—
177C2×Q8D17211yescharacteristic
178C2×D4—434no—
179C2×D4—432no—
180C2×D4—862no—
181C2×D4—868no—
182C2×D4—864no—
183C2×D4—864no—
184C2×D4D17211yescharacteristic
185C2×D4C22×D4312yes—
186C22×C4—434no—
187C22×C4—432no—
188C22×C4—864no—
189C22×C4D17212yes—
190C22×C4C22×D4311yescharacteristic
191C4⋊C4—22no—
192C4⋊C4—868no—
193C4⋊C4—861no—
194C4⋊C4—864no—
195C22⋊C4—432no—
196C22⋊C4—868no—
197C22⋊C4—864no—
198C22⋊C4C22×D4314yes—
199C42—22no—
200C42—861no—
201C23—434no—
202C23—864no—
203C23C2×D17212yes—
204C23C23×D4311yescharacteristic
205Q8—22no—
206Q8—864no—
207Q8—862no—
208Q8—862no—
209Q8—1721no—
210Q8—1721no—
211Q8—1722no—
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—434no—
224C2×C4—868no—
225C2×C4—864no—
226C2×C4—864no—
227C2×C4—864no—
228C2×C4—864no—
229C2×C4—862no—
230C2×C4—862no—
231C2×C4C2×D17212yes—
232C2×C4C2×D17211yescharacteristic
233C2×C4C2×D17211yescharacteristic
234C2×C4D4×D4312yes—
235C2×C4D4×D4312yes—
236C22—22no—
237C22—41no—
238C22—42no—
239C22—864no—
240C22—3444no—
241C22—1724no—
242C22C2×D4×D4312yes—
243C22C22×D17211yescharacteristic
244C4—22no—
245C4—44no—
246C4—864no—
247C4—1722no—
248C4—1722no—
249C4#1306329511yescharacteristic
250C4#1306329511yescharacteristic
251C4#1306329512yes—
252C2—22no—
253C2—21no—
254C2—42no—
255C2—1724no—
256C2C2×#1306329511yescharacteristic
subgroupG/H
centerC2C2×#13063295
commutatorC23×C43C24
FrattiniC23C23×D43
FittingC43×#410C2
socleC2×C43C2×#120
hypercenter#410D43
hypocenterC43#3028
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C22×C4 ◁ #410

Complements

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

NH ≅ G/Ntype
2. #14583475C2semidirect
3. #14583470C2semidirect
4. #14583090C2semidirect
5. #14582872C2semidirect
6. C43×#410C2semidirect
15. C22×Dic86C22semidirect
20. #13063309C22semidirect
21. #13063306C22semidirect
24. #13063284C22semidirect
25. #13063239C22semidirect
27. #117×C43C22semidirect
28. #99×C43C22semidirect
134. #410D43semidirect
135. C43#3028semidirect
155. #117C2×D43semidirect
157. #99C2×D43semidirect