Finite Group Databasebeta

← #19140227

Subgroups — #19140227

Order 5504.

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

normal subgroups only

This group has 470 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×#13063319C211yesmaximal, characteristic
2#14582837C211yesmaximal, characteristic, complemented
3#14582834C211yesmaximal, characteristic
4#14582818C211yesmaximal, characteristic, complemented
5#14582810C211yesmaximal, characteristic
6#14582794C212yesmaximal, complemented
7#14582790C212yesmaximal
8#14582789C212yesmaximal
9#14582783C212yesmaximal, complemented
10#14582745C211yesmaximal, characteristic, complemented
11C2×C4×Q8×C43C211yesmaximal, characteristic, complemented
12#13063319—24no—
13C2×Dic43⋊C4C2212yes—
14C2×Dic43⋊C4C2211yescharacteristic
15C2×Dic43⋊C4C2212yes—
16C2×Dic43⋊C4C2211yescharacteristic
17C2×Dic43⋊C4C2211yescharacteristic
18C2×(C2×D43)⋊C4C2211yescharacteristic
19C2×(C2×D43)⋊C4C2212yes—
20C2×(C2×D43)⋊C4C2212yes—
21C2×(C2×D43)⋊C4C2211yescharacteristic
22C2×(C2×D43)⋊C4C2211yescharacteristic
23C2×C4×Dic43C2212yes—
24C43⋊#95C2212yes—
25C43⋊#95C2212yes—
26C43⋊#95C2212yes—
27C43⋊#95C2212yes—
28C43⋊#95C2212yes—
29C43⋊#95C2211yescharacteristic
30C43⋊#95C2211yescharacteristic
31C22×Q8×C43C2211yescharacteristic
32C4×Q8×C43—24no—
33C2×C4⋊C4×C43C2212yes—
34C2×C4⋊C4×C43C2211yescharacteristic
35C2×C42×C43C2212yes—
36C2×C42×C43C2211yescharacteristic
37C23×D43C2311yescharacteristic
38C2×Q8×C43—22no—
39C2×Q8×C43—24no—
40C22×C4×C43C2312yes—
41C22×C4×C43C2311yescharacteristic
42C22×C4×C43C2311yescharacteristic
43C22×C4×C43C2311yescharacteristic
44C22×C4×C43C2312yes—
45C22×Dic43C2312yes—
46C22×Dic43C2311yescharacteristic
47C22×Dic43C2311yescharacteristic
48C22×Dic43C2311yescharacteristic
49C22×Dic43C2312yes—
50C4⋊C4×C43—24no—
51C4⋊C4×C43—22no—
52C42×C43—24no—
53C42×C43D414yes—
54(C2×D43)⋊C4—22no—
55(C2×D43)⋊C4—22no—
56(C2×D43)⋊C4—22no—
57(C2×D43)⋊C4—24no—
58(C2×D43)⋊C4—24no—
59Dic43⋊C4—22no—
60Dic43⋊C4—22no—
61Dic43⋊C4—22no—
62Dic43⋊C4—24no—
63Dic43⋊C4—24no—
64C4×Dic43—24no—
65C23×C43C2411yescharacteristic
66C22×D43—21no—
67C22×D43—22no—
68C22×D43—22no—
69C22×D43—21no—
70C22×D43—21no—
71Q8×C43—28no—
72C2×C4×C43—22no—
73C2×C4×C43—22no—
74C2×C4×C43—22no—
75C2×C4×C43—22no—
76C2×C4×C43—21no—
77C2×C4×C43—21no—
78C2×C4×C43—22no—
79C2×C4×C43—22no—
80C2×C4×C43—22no—
81C2×C4×C43C2×D412yes—
82C2×C4×C43C2×D412yes—
83C2×C4×C43C2×D412yes—
84C2×C4×C43#4114yes—
85C2×Dic43—22no—
86C2×Dic43—22no—
87C2×Dic43—21no—
88C2×Dic43—21no—
89C2×Dic43—21no—
90C2×Dic43—22no—
91C2×Dic43—22no—
92C2×Dic43—22no—
93C2×Dic43—22no—
94C2×Dic43—21no—
95C2×Dic43—21no—
96C2×Dic43—22no—
97C2×Dic43#4114yes—
98C22×C43C22×D411yescharacteristic
99C22×C43C2×#4112yes—
100C22×C43C2×#4112yes—
101C22×C432−1+411yescharacteristic
102C22×C432−1+411yescharacteristic
103C2×D43—41no—
104C2×D43—41no—
105C2×D43—41no—
106C2×D43—42no—
107C2×D43—42no—
108C4×C43—22no—
109C4×C43—24no—
110C4×C43—22no—
111C4×C43—22no—
112C4×C43—42no—
113Dic43—24no—
114Dic43—41no—
115Dic43—41no—
116Dic43—41no—
117Dic43—42no—
118#2604—431nomaximal, Sylow
119C2×C43#52511yescharacteristic
120C2×C43#53211yescharacteristic
121C2×C43#53611yescharacteristic
122C2×C43#55212yes—
123C2×C43#55612yes—
124D43—81no—
125C2×#126—431no—
126C2×C4×Q8D4311yescharacteristic, complemented
127#400—431no—
128#399—431no—
129#395—431no—
130#393—431no—
131#389—432no—
132#388—432no—
133#388—432no—
134#387—432no—
135#376—431no—
136C43#260411yescharacteristic, complemented, Sylow
137C22×Q8C2×D4311yescharacteristic
138#126—864no—
139C4×Q8—24no—
140C2×C4⋊C4—431no—
141C2×C4⋊C4—431no—
142C2×C4⋊C4—431no—
143C2×C4⋊C4—432no—
144C2×C4⋊C4—432no—
145C2×C4⋊C4C2×D4312yes—
146C2×C4⋊C4C2×D4311yescharacteristic
147C2×C22⋊C4—431no—
148C2×C22⋊C4—431no—
149C2×C22⋊C4—431no—
150C2×C22⋊C4—432no—
151C2×C22⋊C4—432no—
152C2×C42—432no—
153C2×C42C2×D4312yes—
154C2×C42C2×D4311yescharacteristic
155#95—432no—
156#95—431no—
157#95—431no—
158#95—432no—
159#95—432no—
160#95—432no—
161#95—432no—
162C24—431no—
163C2×Q8—24no—
164C2×Q8—22no—
165C22×C4—432no—
166C22×C4—432no—
167C22×C4—431no—
168C22×C4—431no—
169C22×C4—431no—
170C22×C4C22×D4312yes—
171C22×C4C22×D4312yes—
172C22×C4C22×D4311yescharacteristic
173C22×C4C22×D4311yescharacteristic
174C22×C4C22×D4311yescharacteristic
175C4⋊C4—24no—
176C4⋊C4—22no—
177C4⋊C4—864no—
178C4⋊C4—864no—
179C4⋊C4—862no—
180C4⋊C4—862no—
181C4⋊C4—862no—
182C22⋊C4—864no—
183C22⋊C4—864no—
184C22⋊C4—862no—
185C22⋊C4—862no—
186C22⋊C4—862no—
187C42—24no—
188C42—864no—
189C42C22⋊D4314yes—
190C23—861no—
191C23—862no—
192C23—862no—
193C23—861no—
194C23—861no—
195C23C23×D4311yescharacteristic
196Q8—28no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—434no—
207C2×C4—862no—
208C2×C4—862no—
209C2×C4—861no—
210C2×C4—861no—
211C2×C4—861no—
212C2×C4—862no—
213C2×C4—862no—
214C2×C4—862no—
215C2×C4—862no—
216C2×C4—862no—
217C2×C4—861no—
218C2×C4—861no—
219C2×C4#1062189814yes—
220C2×C4C2×C22⋊D4312yes—
221C2×C4C2×C22⋊D4312yes—
222C2×C4C2×C22⋊D4312yes—
223C22—1722no—
224C22—1722no—
225C22—1721no—
226C22—1721no—
227C22—1721no—
228C22C22×C22⋊D4311yescharacteristic
229C22#41×D4312yes—
230C22C2×#1062189812yes—
231C22#1306337311yescharacteristic
232C22#1306337311yescharacteristic
233C4—24no—
234C4—22no—
235C4—22no—
236C4—22no—
237C4—42no—
238C4—864no—
239C4—1722no—
240C4—1721no—
241C4—1721no—
242C4—1721no—
243C2—3441no—
244C2#1458341011yescharacteristic
245C2#1458344511yescharacteristic
246C2#1458347311yescharacteristic
247C2#1458359012yes—
248C2#1458362112yes—
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC2×C4×Q8×C43C2
hypercenterC2×C4×Q8D43
hypocenterC43#2604
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
2. #14582837C2semidirect
4. #14582818C2semidirect
6. #14582794C2semidirect
9. #14582783C2semidirect
10. #14582745C2semidirect
11. C2×C4×Q8×C43C2semidirect
126. C2×C4×Q8D43semidirect
136. C43#2604semidirect