Finite Group Databasebeta

← #19145416

Subgroups — #19145416

Order 5504.

410 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 125 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
2#14583229C212yesmaximal, complemented
3#14583227C212yesmaximal, complemented
4#14583155C214yesmaximal, complemented
5#14583055C212yesmaximal, complemented
6#14583054C212yesmaximal, complemented
7#14582863C211yesmaximal, characteristic
8C2×C22⋊Q8×C43C211yesmaximal, characteristic
9C22×Dic86C2211yescharacteristic
10C2×#10621885C2214yescomplemented
11C2×#10621877C2212yes—
12#13063304—21no—
13#13063304—21no—
14#13063304C2212yes—
15#13063304C2212yes—
16C2×C4⋊Dic43C2211yescharacteristic
17C2×Dic43⋊C4—21no—
18C2×C22⋊Dic43—21no—
19#13063256C2214yescomplemented
20#13063249C2214yescomplemented
21#13063248C2214yescomplemented
22C22⋊(C43⋊C8)C2212yes—
23C22⋊(C43⋊C8)C2212yes—
24C22×Q8×C43C2211yescharacteristic
25C23×C4×C43C2211yescharacteristic
26C22⋊Q8×C43—21no—
27C22⋊Q8×C43—21no—
28C22⋊Q8×C43C2212yes—
29C22⋊Q8×C43C2212yes—
30C2×C4⋊C4×C43—21no—
31C2×C4⋊C4×C43C2211yescharacteristic
32C2×C22⋊C4×C43—21no—
33C24×C43D411yescharacteristic
34C2×Q8×C43—21no—
35C2×Q8×C43—42no—
36C2×Q8×C43C2312yes—
37C22×C4×C43—21no—
38C22×C4×C43—21no—
39C22×C4×C43—42no—
40C22×C4×C43D411yescharacteristic
41C22×C4×C43D411yescharacteristic
42C22×C4×C43D411yescharacteristic
43C22×C4×C43C2311yescharacteristic
44C22×C4×C43C2311yescharacteristic
45C22×C4×C43C2311yescharacteristic
46C22×Dic43—21no—
47C22×Dic43—21no—
48C2×Dic86—21no—
49C2×Dic86—42no—
50C2×Dic86C2312yes—
51C4⋊C4×C43—22no—
52C4⋊C4×C43—22no—
53C4⋊C4×C43—21no—
54C4⋊C4×C43C2312yes—
55C22⋊C4×C43—22no—
56C22⋊C4×C43—22no—
57C22⋊Dic43—22no—
58C22⋊Dic43—22no—
59#10621885—44no—
60C4⋊Dic43—21no—
61C4⋊Dic43C2312yes—
62Dic43⋊C4—22no—
63Dic43⋊C4—22no—
64#10621877—42no—
65C2×C43⋊C8C2314yes—
66C23×C43—22no—
67C23×C43—22no—
68C23×C43—41no—
69C23×C43C2×D411yescharacteristic
70C23×C43C2×D411yescharacteristic
71C23×C43C2×D411yescharacteristic
72Q8×C43—24no—
73Q8×C43—42no—
74C2×C4×C43—22no—
75C2×C4×C43—22no—
76C2×C4×C43—22no—
77C2×C4×C43—22no—
78C2×C4×C43—22no—
79C2×C4×C43—41no—
80C2×C4×C43—41no—
81C2×C4×C43—41no—
82C2×C4×C43—42no—
83C2×C4×C43—42no—
84C2×C4×C43C2×D411yescharacteristic
85C2×C4×C43C2×D411yescharacteristic
86C2×C4×C43C2×D411yescharacteristic
87C2×C4×C43C2411yescharacteristic
88C2×Dic43—22no—
89C2×Dic43—22no—
90C2×Dic43—42no—
91C2×Dic43—42no—
92Dic86—24no—
93Dic86—42no—
94C43⋊C8—24no—
95C22×C43—21no—
96C22×C43—21no—
97C22×C43—21no—
98C22×C43—21no—
99C22×C43—21no—
100C22×C43—21no—
101C22×C43—21no—
102C22×C43—44no—
103C22×C43#13712yes—
104C22×C43#13712yes—
105C22×C43C22×D411yescharacteristic
106C4×C43—21no—
107C4×C43—21no—
108C4×C43—21no—
109C4×C43—42no—
110C4×C43—42no—
111C4×C43H(5,𝔽2)12yes—
112Dic43—42no—
113Dic43—42no—
114#3195—431nomaximal, Sylow
115C2×C43—22no—
116C2×C43—22no—
117C2×C43—41no—
118C2×C43#53411yescharacteristic
119C2×C43C2×#13711yescharacteristic
120C2×C43C2×#13711yescharacteristic
121C2×C22⋊Q8—431no—
122C2×C22⋊Q8D4311yescharacteristic
123#483—432no—
124#483—432no—
125#470—434no—
126#451—432no—
127#451—432no—
128#407—431no—
129C43#319511yescharacteristic, complemented, Sylow
130C22×Q8—431no—
131C22×Q8C2×D4311yescharacteristic
132C23×C4C2×D4311yescharacteristic
133C2×Q16—434no—
134C2×M16—432no—
135C22⋊Q8—21no—
136C22⋊Q8—21no—
137C22⋊Q8—432no—
138C22⋊Q8—432no—
139C22⋊Q8—861no—
140C22⋊Q8—861no—
141C22⋊Q8C2×D4312yes—
142C22⋊Q8C2×D4312yes—
143C2×C4⋊C4—21no—
144C2×C4⋊C4—431no—
145C2×C4⋊C4—861no—
146C2×C4⋊C4C2×D4311yescharacteristic
147C2×C22⋊C4—21no—
148C2×C22⋊C4—861no—
149#106—434no—
150#103—434no—
151#103—434no—
152C22⋊C8—432no—
153C22⋊C8—432no—
154C24C22⋊D4311yescharacteristic
155C2×Q8—21no—
156C2×Q8—42no—
157C2×Q8—432no—
158C2×Q8—861no—
159C2×Q8—1722no—
160C2×Q8C22×D4312yes—
161C22×C4—21no—
162C22×C4—21no—
163C22×C4—42no—
164C22×C4—861no—
165C22×C4—861no—
166C22×C4C22⋊D4311yescharacteristic
167C22×C4C22⋊D4311yescharacteristic
168C22×C4C22⋊D4311yescharacteristic
169C22×C4C22×D4311yescharacteristic
170C22×C4C22×D4311yescharacteristic
171C22×C4C22×D4311yescharacteristic
172Q16—1724no—
173M16—1722no—
174C2×C8—434no—
175C4⋊C4—22no—
176C4⋊C4—22no—
177C4⋊C4—21no—
178C4⋊C4—432no—
179C4⋊C4—861no—
180C4⋊C4—862no—
181C4⋊C4—862no—
182C4⋊C4C22×D4312yes—
183C22⋊C4—22no—
184C22⋊C4—22no—
185C22⋊C4—862no—
186C22⋊C4—862no—
187C23—22no—
188C23—22no—
189C23—41no—
190C23C2×C22⋊D4311yescharacteristic
191C23C2×C22⋊D4311yescharacteristic
192C23C2×C22⋊D4311yescharacteristic
193Q8—24no—
194Q8—42no—
195Q8—864no—
196Q8—1722no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—41no—
203C2×C4—41no—
204C2×C4—41no—
205C2×C4—42no—
206C2×C4—42no—
207C2×C4—862no—
208C2×C4—862no—
209C2×C4—1722no—
210C2×C4—1722no—
211C2×C4C2×C22⋊D4311yescharacteristic
212C2×C4C2×C22⋊D4311yescharacteristic
213C2×C4C2×C22⋊D4311yescharacteristic
214C2×C4C23×D4311yescharacteristic
215C8—864no—
216C22—21no—
217C22—21no—
218C22—21no—
219C22—21no—
220C22—21no—
221C22—21no—
222C22—21no—
223C22—44no—
224C22#1306335512yes—
225C22#1306335612yes—
226C22C22×C22⋊D4311yescharacteristic
227C4—21no—
228C4—21no—
229C4—21no—
230C4—42no—
231C4—42no—
232C4—1722no—
233C4—1722no—
234C4#1306337012yes—
235C2—22no—
236C2—22no—
237C2—41no—
238C2#1458345811yescharacteristic
239C2C2×#1306335511yescharacteristic
240C2C2×#1306335611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC2×C22⋊Q8×C43C2
socleC22×C43C22×D4
hypercenterC2×C22⋊Q8D43
hypocenterC43#3195
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. #14583229C2semidirect
3. #14583227C2semidirect
4. #14583155C2semidirect
5. #14583055C2semidirect
6. #14583054C2semidirect
10. C2×#10621885C22semidirect
19. #13063256C22semidirect
20. #13063249C22semidirect
21. #13063248C22semidirect
129. C43#3195semidirect