Finite Group Databasebeta

← #19144544

Subgroups — #19144544

Order 5504.

410 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 137 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×#13063304C211yesmaximal, characteristic
2C2×#13063284C211yesmaximal, characteristic
3#14583241C214yesmaximal, complemented
4#14583235C212yesmaximal, complemented
5#14583230C212yesmaximal, complemented
6#14582941C212yesmaximal, complemented
7#14582909C212yesmaximal, complemented
8C43×#407C211yesmaximal, characteristic
9C22×Dic86C2211yescharacteristic
10#13063304—21no—
11#13063304—21no—
12#13063304C2212yes—
13#13063304C2212yes—
14#13063284—21no—
15#13063284—21no—
16#13063284C2212yes—
17#13063284C2212yes—
18C2×C4⋊Dic43C2211yescharacteristic
19C2×C4⋊Dic43C2211yescharacteristic
20C2×C4⋊Dic43C2211yescharacteristic
21C2×Dic43⋊C4—21no—
22C2×C22⋊Dic43—21no—
23C2×C22⋊Dic43—21no—
24C2×C4×Dic43—21no—
25#13063259C2214yescomplemented
26#13063257C2214yescomplemented
27#13063250C2214yescomplemented
28#13063250C2214yescomplemented
29C23×C4×C43C2211yescharacteristic
30C2×M16×C43C2212yes—
31C22⋊C8×C43C2212yes—
32C22⋊C8×C43C2212yes—
33C24×C43D411yescharacteristic
34C22×C4×C43—24no—
35C22×C4×C43D411yescharacteristic
36C22×C4×C43D411yescharacteristic
37C22×C4×C43D411yescharacteristic
38C22×C4×C43C2311yescharacteristic
39C22×C4×C43C2311yescharacteristic
40C22×C4×C43C2311yescharacteristic
41C22×Dic43—21no—
42C22×Dic43—21no—
43C22×Dic43—21no—
44C22×Dic43—21no—
45C2×Dic86—24no—
46C2×Dic86—21no—
47C2×Dic86C2312yes—
48M16×C43—24no—
49C2×C8×C43C2314yes—
50C22⋊Dic43—22no—
51C22⋊Dic43—22no—
52C22⋊Dic43—22no—
53C22⋊Dic43—22no—
54C4⋊Dic43—21no—
55C4⋊Dic43—21no—
56C4⋊Dic43—21no—
57C4⋊Dic43C2312yes—
58C4⋊Dic43C2312yes—
59C4⋊Dic43C2312yes—
60Dic43⋊C4—22no—
61Dic43⋊C4—22no—
62C4×Dic43—22no—
63C4×Dic43—22no—
64C23×C43—22no—
65C23×C43—22no—
66C23×C43—41no—
67C23×C43C2×D411yescharacteristic
68C23×C43C2×D411yescharacteristic
69C23×C43C2×D411yescharacteristic
70C2×C4×C43—22no—
71C2×C4×C43—22no—
72C2×C4×C43—22no—
73C2×C4×C43—22no—
74C2×C4×C43—22no—
75C2×C4×C43C2×D411yescharacteristic
76C2×C4×C43C2×D411yescharacteristic
77C2×C4×C43C2×D411yescharacteristic
78C2×C4×C43#4114yes—
79C2×C4×C43C2411yescharacteristic
80C2×Dic43—22no—
81C2×Dic43—22no—
82C2×Dic43—22no—
83C2×Dic43—22no—
84C2×Dic43—42no—
85C2×Dic43—42no—
86C2×Dic43—42no—
87C2×Dic43—42no—
88Dic86—24no—
89Dic86—42no—
90C8×C43—24no—
91C22×C43—21no—
92C22×C43—21no—
93C22×C43—21no—
94C22×C43—21no—
95C22×C43—21no—
96C22×C43—21no—
97C22×C43—21no—
98C22×C43—44no—
99C22×C43#12312yes—
100C22×C43#13712yes—
101C22×C43C22×D411yescharacteristic
102C4×C43—21no—
103C4×C43—21no—
104C4×C43#12312yes—
105C4×C43C2×#4112yes—
106Dic43—42no—
107Dic43—42no—
108Dic43—42no—
109Dic43—42no—
110#3095—431nomaximal, Sylow
111C2×C43—22no—
112C2×C43—22no—
113C2×C43—41no—
114C2×C43C2×#12311yescharacteristic
115C2×C43C2×#13711yescharacteristic
116C2×C43#57511yescharacteristic
117C2×C22⋊Q8—431no—
118C2×#117—431no—
119#485—434no—
120#484—432no—
121#483—432no—
122#428—432no—
123#419—432no—
124#407D4311yescharacteristic
125C43#309511yescharacteristic, complemented, Sylow
126C22×Q8—431no—
127C23×C4C2×D4311yescharacteristic
128C2×M16C2×D4312yes—
129C22⋊Q8—432no—
130C22⋊Q8—432no—
131C22⋊Q8—861no—
132C22⋊Q8—861no—
133#117—432no—
134#117—432no—
135#117—861no—
136#117—861no—
137C2×C4⋊C4—431no—
138C2×C4⋊C4—431no—
139C2×C4⋊C4—431no—
140C2×C4⋊C4—861no—
141C2×C22⋊C4—861no—
142C2×C22⋊C4—861no—
143C2×C42—861no—
144#107—434no—
145#106—434no—
146#103—434no—
147#103—434no—
148C22⋊C8C2×D4312yes—
149C22⋊C8C2×D4312yes—
150C24D17211yescharacteristic
151C2×Q8—432no—
152C2×Q8—861no—
153C2×Q8—864no—
154C22×C4—24no—
155C22×C4—861no—
156C22×C4—861no—
157C22×C4—861no—
158C22×C4—861no—
159C22×C4D17211yescharacteristic
160C22×C4D17211yescharacteristic
161C22×C4D17211yescharacteristic
162C22×C4C22×D4311yescharacteristic
163C22×C4C22×D4311yescharacteristic
164C22×C4C22×D4311yescharacteristic
165M16—24no—
166C2×C8C22×D4314yes—
167C4⋊C4—432no—
168C4⋊C4—432no—
169C4⋊C4—432no—
170C4⋊C4—861no—
171C4⋊C4—861no—
172C4⋊C4—861no—
173C4⋊C4—862no—
174C4⋊C4—862no—
175C22⋊C4—862no—
176C22⋊C4—862no—
177C22⋊C4—862no—
178C22⋊C4—862no—
179C42—862no—
180C42—862no—
181C23—22no—
182C23—22no—
183C23—41no—
184C23C2×D17211yescharacteristic
185C23C2×D17211yescharacteristic
186C23C2×D17211yescharacteristic
187Q8—864no—
188Q8—1722no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—862no—
195C2×C4—862no—
196C2×C4—862no—
197C2×C4—862no—
198C2×C4—1722no—
199C2×C4—1722no—
200C2×C4—1722no—
201C2×C4—1722no—
202C2×C4C2×D17211yescharacteristic
203C2×C4C2×D17211yescharacteristic
204C2×C4C2×D17211yescharacteristic
205C2×C4#1062190014yes—
206C2×C4C23×D4311yescharacteristic
207C8—24no—
208C22—21no—
209C22—21no—
210C22—21no—
211C22—21no—
212C22—21no—
213C22—21no—
214C22—21no—
215C22—44no—
216C22#1306330912yes—
217C22#1306335812yes—
218C22C22×D17211yescharacteristic
219C4—21no—
220C4—21no—
221C4—1722no—
222C4—1722no—
223C4—1722no—
224C4—1722no—
225C4#1306330912yes—
226C4C2×#1062190012yes—
227C2—22no—
228C2—22no—
229C2—41no—
230C2C2×#1306330911yescharacteristic
231C2C2×#1306335811yescharacteristic
232C2#1458369911yescharacteristic
subgroupG/H
centerC22C22×D172
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#407C2
socleC22×C43C22×D4
hypercenter#407D43
hypocenterC43#3095
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
3. #14583241C2semidirect
4. #14583235C2semidirect
5. #14583230C2semidirect
6. #14582941C2semidirect
7. #14582909C2semidirect
25. #13063259C22semidirect
26. #13063257C22semidirect
27. #13063250C22semidirect
28. #13063250C22semidirect
125. C43#3095semidirect