Finite Group Databasebeta

← #19140500

Subgroups — #19140500

Order 5504.

450 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 450 conjugacy classes of subgroups — too many to draw. Only its 133 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×#13063318C211yesmaximal, characteristic
2C2×Q8×Dic43C211yesmaximal, characteristic, complemented
3#14582831C211yesmaximal, characteristic, complemented
4#14582831C212yesmaximal, complemented
5#14582824C211yesmaximal, characteristic
6#14582822C212yesmaximal
7#14582818C211yesmaximal, characteristic, complemented
8#14582792C212yesmaximal
9#14582781C212yesmaximal, complemented
10#14582763C211yesmaximal, characteristic, complemented
11C43×#393C211yesmaximal, characteristic
12#13063318—24no—
13Q8×Dic43—24no—
14C2×C4⋊Dic43C2212yes—
15C2×C4⋊Dic43C2211yescharacteristic
16C2×C4⋊Dic43C2211yescharacteristic
17C2×C4⋊Dic43C2212yes—
18C2×Dic43⋊C4C2212yes—
19C2×Dic43⋊C4C2211yescharacteristic
20C2×Dic43⋊C4C2211yescharacteristic
21C2×Dic43⋊C4C2212yes—
22C2×C22⋊Dic43C2211yescharacteristic
23C2×C22⋊Dic43C2211yescharacteristic
24C2×C22⋊Dic43C2212yes—
25C2×C4×Dic43C2212yes—
26C2×C4×Dic43C2211yescharacteristic
27C43⋊#95C2212yes—
28C43⋊#95C2212yes—
29C43⋊#95C2211yescharacteristic
30C43⋊#95C2212yes—
31C43⋊#95C2212yes—
32C22×Q8×C43C2211yescharacteristic
33C2×C22⋊C4×C43C2212yes—
34C2×C22⋊C4×C43C2211yescharacteristic
35#95×C43C2211yescharacteristic
36#95×C43C2212yes—
37C24×C43C2311yescharacteristic
38C2×Q8×C43—22no—
39C2×Q8×C43—24no—
40C22×C4×C43C2311yescharacteristic
41C22×C4×C43C2312yes—
42C22×C4×C43C2311yescharacteristic
43C22×C4×C43C2312yes—
44C22×Dic43C2312yes—
45C22×Dic43C2312yes—
46C22×Dic43C2311yescharacteristic
47C22×Dic43C2311yescharacteristic
48C22×Dic43C2311yescharacteristic
49C22×Dic43C2311yescharacteristic
50C22⋊C4×C43—22no—
51C22⋊C4×C43—24no—
52C22⋊Dic43—22no—
53C22⋊Dic43—22no—
54C22⋊Dic43—42no—
55C4⋊Dic43—22no—
56C4⋊Dic43—24no—
57C4⋊Dic43—22no—
58C4⋊Dic43—42no—
59Dic43⋊C4—22no—
60Dic43⋊C4—24no—
61Dic43⋊C4—22no—
62Dic43⋊C4—42no—
63C4×Dic43—24no—
64C4×Dic43D414yes—
65C23×C43—21no—
66C23×C43—22no—
67C23×C43—21no—
68C23×C43—22no—
69C23×C43—21no—
70C23×C43C2411yescharacteristic
71Q8×C43—28no—
72C2×C4×C43—22no—
73C2×C4×C43—22no—
74C2×C4×C43—22no—
75C2×C4×C43—21no—
76C2×C4×C43—22no—
77C2×C4×C43—22no—
78C2×C4×C43—22no—
79C2×C4×C43—22no—
80C2×C4×C43C2×D412yes—
81C2×C4×C43#4114yes—
82C2×Dic43—21no—
83C2×Dic43—22no—
84C2×Dic43—21no—
85C2×Dic43—22no—
86C2×Dic43—21no—
87C2×Dic43—21no—
88C2×Dic43—22no—
89C2×Dic43—22no—
90C2×Dic43—22no—
91C2×Dic43—21no—
92C2×Dic43—22no—
93C2×Dic43—22no—
94C2×Dic43—22no—
95C2×Dic43—21no—
96C2×Dic43C2×D412yes—
97C2×Dic43C2×D412yes—
98C22×C43—41no—
99C22×C43—41no—
100C22×C43—41no—
101C22×C43—42no—
102C22×C43—42no—
103C22×C43C22×D411yescharacteristic
104C22×C43C2×#4112yes—
105C22×C43H(5,𝔽2)11yescharacteristic
106C22×C432−1+412yes—
107C22×C432−1+411yescharacteristic
108C4×C43—22no—
109C4×C43—24no—
110C4×C43—41no—
111C4×C43—42no—
112Dic43—22no—
113Dic43—22no—
114Dic43—41no—
115Dic43—42no—
116Dic43—41no—
117Dic43—42no—
118#2637—431nomaximal, Sylow
119C2×C43—81no—
120C2×C43#52511yescharacteristic
121C2×C43#53611yescharacteristic
122C2×C43#53711yescharacteristic
123C2×C43#54112yes—
124C2×C43#54212yes—
125C2×#126—431no—
126C2×C4×Q8—431no—
127#398—431no—
128#398—432no—
129#397—431no—
130#396—432no—
131#395—431no—
132#393D4311yescharacteristic
133#388—432no—
134#387—432no—
135#382—431no—
136C43#263711yescharacteristic, complemented, Sylow
137C22×Q8C2×D4311yescharacteristic
138#126—864no—
139C4×Q8—864no—
140C2×C4⋊C4—432no—
141C2×C4⋊C4—431no—
142C2×C4⋊C4—431no—
143C2×C4⋊C4—431no—
144C2×C4⋊C4—431no—
145C2×C4⋊C4—432no—
146C2×C4⋊C4—432no—
147C2×C4⋊C4—432no—
148C2×C22⋊C4—431no—
149C2×C22⋊C4—431no—
150C2×C22⋊C4—432no—
151C2×C22⋊C4C2×D4311yescharacteristic
152C2×C22⋊C4C2×D4312yes—
153C2×C42—431no—
154C2×C42—432no—
155#95—432no—
156#95—431no—
157#95—432no—
158#95—432no—
159#95—432no—
160#95C2×D4311yescharacteristic
161#95C2×D4312yes—
162C24C22×D4311yescharacteristic
163C2×Q8—22no—
164C2×Q8—24no—
165C22×C4—431no—
166C22×C4—431no—
167C22×C4—432no—
168C22×C4—432no—
169C22×C4—431no—
170C22×C4—431no—
171C22×C4C22×D4311yescharacteristic
172C22×C4C22×D4312yes—
173C22×C4C22×D4311yescharacteristic
174C22×C4C22×D4312yes—
175C4⋊C4—864no—
176C4⋊C4—862no—
177C4⋊C4—862no—
178C4⋊C4—862no—
179C4⋊C4—862no—
180C4⋊C4—864no—
181C4⋊C4—1722no—
182C4⋊C4—1722no—
183C22⋊C4—22no—
184C22⋊C4—24no—
185C22⋊C4—862no—
186C22⋊C4—862no—
187C22⋊C4—1722no—
188C42—434no—
189C42—864no—
190C23—21no—
191C23—22no—
192C23—21no—
193C23—22no—
194C23—21no—
195C23C23×D4311yescharacteristic
196Q8—28no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—21no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—432no—
206C2×C4—432no—
207C2×C4—861no—
208C2×C4—862no—
209C2×C4—861no—
210C2×C4—862no—
211C2×C4—861no—
212C2×C4—861no—
213C2×C4—862no—
214C2×C4—862no—
215C2×C4—862no—
216C2×C4—862no—
217C2×C4—861no—
218C2×C4—862no—
219C2×C4—862no—
220C2×C4—861no—
221C2×C4D4×D4312yes—
222C2×C4#1062190014yes—
223C22—41no—
224C22—41no—
225C22—41no—
226C22—42no—
227C22—42no—
228C22C2×D4×D4311yescharacteristic
229C22C2×#1062190012yes—
230C22#1306337111yescharacteristic
231C22#1306337212yes—
232C22#1306337311yescharacteristic
233C4—22no—
234C4—24no—
235C4—41no—
236C4—42no—
237C4—862no—
238C4—862no—
239C4—1721no—
240C4—1722no—
241C4—1721no—
242C4—1722no—
243C2—81no—
244C2#1458340511yescharacteristic
245C2#1458346911yescharacteristic
246C2#1458347911yescharacteristic
247C2#1458350912yes—
248C2#1458351812yes—
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#393C2
hypercenter#393D43
hypocenterC43#2637
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #393

Complements

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

NH ≅ G/Ntype
2. C2×Q8×Dic43C2semidirect
3. #14582831C2semidirect
4. #14582831C2semidirect
7. #14582818C2semidirect
9. #14582781C2semidirect
10. #14582763C2semidirect
136. C43#2637semidirect