Finite Group Databasebeta

← #19137857

Subgroups — #19137857

Order 5504.

560 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 560 conjugacy classes of subgroups — too many to draw. Only its 143 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×(C22⋊D43)⋊C4C211yesmaximal, characteristic
2C2×#13063283C211yesmaximal, characteristic, complemented
3#14582839C211yesmaximal, characteristic, complemented
4#14582835C211yesmaximal, characteristic, complemented
5#14582830C211yesmaximal, characteristic, complemented
6#14582828C212yesmaximal, complemented
7#14582814C212yesmaximal
8#14582750C212yesmaximal, complemented
9C22⋊C4×Dic43C212yesmaximal, complemented
10#14582746C211yesmaximal, characteristic, complemented
11C43×#397C211yesmaximal, characteristic, complemented
12C22×C22⋊D43C2211yescharacteristic
13C23×Dic43C2211yescharacteristic
14C22×C4×D43C2211yescharacteristic
15(C22⋊D43)⋊C4—24no—
16#13063283—24no—
17C2×C4⋊Dic43C2211yescharacteristic
18C2×Dic43⋊C4C2212yes—
19C2×Dic43⋊C4C2212yes—
20C2×Dic43⋊C4C2211yescharacteristic
21C2×C22⋊Dic43C2212yes—
22C2×(C2×D43)⋊C4C2212yes—
23C2×(C2×D43)⋊C4C2212yes—
24C2×(C2×D43)⋊C4C2211yescharacteristic
25C2×C4×Dic43C2212yes—
26C2×C4×Dic43C2211yescharacteristic
27C2×C4×Dic43C2212yes—
28C43⋊#95C2212yes—
29C43⋊#95C2212yes—
30C43⋊#95C2212yes—
31C43⋊#95C2211yescharacteristic
32C2×C4⋊C4×C43C2211yescharacteristic
33C2×C22⋊C4×C43C2212yes—
34C2×C22⋊C4×C43C2211yescharacteristic
35#95×C43C2212yes—
36#95×C43C2211yescharacteristic
37C24×C43C2311yescharacteristic
38C23×D43C2311yescharacteristic
39C22×C4×C43C2312yes—
40C22×C4×C43C2311yescharacteristic
41C22×C4×C43C2312yes—
42C22×C4×C43C2311yescharacteristic
43C2×C22⋊D43—22no—
44C2×C22⋊D43—22no—
45C2×C22⋊D43—22no—
46C22×Dic43—22no—
47C22×Dic43—24no—
48C22×Dic43C2311yescharacteristic
49C22×Dic43C2312yes—
50C22×Dic43C2312yes—
51C22×Dic43C2311yescharacteristic
52C22×Dic43C2311yescharacteristic
53C2×C4×D43—24no—
54C2×C4×D43D414yes—
55C4⋊C4×C43—22no—
56C22⋊C4×C43—22no—
57C22⋊C4×C43—24no—
58C22⋊Dic43—24no—
59(C2×D43)⋊C4—24no—
60(C2×D43)⋊C4—24no—
61(C2×D43)⋊C4—22no—
62C4⋊Dic43—22no—
63Dic43⋊C4—22no—
64Dic43⋊C4—24no—
65Dic43⋊C4—24no—
66C4×Dic43—24no—
67C4×Dic43—22no—
68C4×Dic43—24no—
69C23×C43—21no—
70C23×C43—22no—
71C23×C43—22no—
72C23×C43—21no—
73C23×C43#4112yes—
74C23×C43C2411yescharacteristic
75C22×D43—22no—
76C22×D43—22no—
77C22×D43—21no—
78C22×D43—21no—
79C22×D43C2×D412yes—
80C2×C4×C43—22no—
81C2×C4×C43—21no—
82C2×C4×C43—22no—
83C2×C4×C43—22no—
84C2×C4×C43—22no—
85C2×C4×C43—22no—
86C2×C4×C43—22no—
87C2×C4×C43—22no—
88C2×C4×C43—22no—
89C2×C4×C43C2×D412yes—
90C22⋊D43—28no—
91C2×Dic43—21no—
92C2×Dic43—22no—
93C2×Dic43—22no—
94C2×Dic43—21no—
95C2×Dic43—22no—
96C2×Dic43—21no—
97C2×Dic43—22no—
98C2×Dic43—22no—
99C2×Dic43—22no—
100C2×Dic43—44no—
101C2×Dic43C2×D412yes—
102C2×Dic43#4112yes—
103C2×Dic43#4114yes—
104C2×Dic43#4114yes—
105C4×D43—28no—
106C22×C43—22no—
107C22×C43—24no—
108C22×C43—41no—
109C22×C43—42no—
110C22×C43—41no—
111C22×C43C22×D411yescharacteristic
112C22×C43C2×#4112yes—
113C22×C43C2×#4111yescharacteristic
114C22×C43C2×#4112yes—
115C22×C43C2×#4111yescharacteristic
116C2×D43—22no—
117C2×D43—22no—
118C2×D43—22no—
119C2×D43—42no—
120C2×D43—42no—
121C4×C43—22no—
122C4×C43—42no—
123C4×C43—42no—
124C4×C43—41no—
125Dic43—22no—
126Dic43—24no—
127Dic43—41no—
128Dic43—42no—
129Dic43#12314yes—
130#2395—431nomaximal, Sylow
131C2×C43—42no—
132C2×C43C2×#12311yescharacteristic
133C2×C43#52511yescharacteristic
134C2×C43#52912yes—
135C2×C43#52912yes—
136C2×C43#53211yescharacteristic
137D43—42no—
138C2×C4×D4—431no—
139C2×#117—431no—
140#400—431no—
141#399—431no—
142#398—431no—
143#397—432no—
144#397D4311yescharacteristic, complemented
145#394—432no—
146C4×C4⋊C4—432no—
147C4×C22⋊C4—432no—
148C4×C22⋊C4—431no—
149C43#239511yescharacteristic, complemented, Sylow
150C22×D4—431no—
151C23×C4—431no—
152C23×C4—431no—
153C4×D4—864no—
154#117—864no—
155C2×C4⋊C4—431no—
156C2×C4⋊C4—431no—
157C2×C4⋊C4—432no—
158C2×C4⋊C4—432no—
159C2×C4⋊C4C2×D4311yescharacteristic
160C2×C22⋊C4—432no—
161C2×C22⋊C4—432no—
162C2×C22⋊C4—431no—
163C2×C22⋊C4—432no—
164C2×C22⋊C4C2×D4311yescharacteristic
165C2×C22⋊C4C2×D4312yes—
166C2×C42—432no—
167C2×C42—431no—
168C2×C42—432no—
169#95—432no—
170#95—432no—
171#95—431no—
172#95—432no—
173#95C2×D4311yescharacteristic
174#95C2×D4312yes—
175C24—431no—
176C24C22×D4311yescharacteristic
177C2×D4—862no—
178C2×D4—862no—
179C2×D4—862no—
180C22×C4—431no—
181C22×C4—432no—
182C22×C4—431no—
183C22×C4—434no—
184C22×C4—431no—
185C22×C4—432no—
186C22×C4—864no—
187C22×C4—862no—
188C22×C4—864no—
189C22×C4C22×D4312yes—
190C22×C4C22×D4312yes—
191C22×C4C22×D4311yescharacteristic
192C22×C4C22×D4311yescharacteristic
193C4⋊C4—22no—
194C4⋊C4—864no—
195C4⋊C4—864no—
196C4⋊C4—862no—
197C4⋊C4—862no—
198C22⋊C4—24no—
199C22⋊C4—22no—
200C22⋊C4—864no—
201C22⋊C4—864no—
202C22⋊C4—862no—
203C22⋊C4—864no—
204C42—864no—
205C42—862no—
206C42—864no—
207C23—21no—
208C23—22no—
209C23—22no—
210C23—21no—
211C23—432no—
212C23—862no—
213C23—862no—
214C23—861no—
215C23—861no—
216C23#1062190012yes—
217C23C23×D4311yescharacteristic
218D4—868no—
219C2×C4—22no—
220C2×C4—21no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—432no—
229C2×C4—434no—
230C2×C4—434no—
231C2×C4—432no—
232C2×C4—868no—
233C2×C4—861no—
234C2×C4—862no—
235C2×C4—862no—
236C2×C4—861no—
237C2×C4—862no—
238C2×C4—861no—
239C2×C4—862no—
240C2×C4—862no—
241C2×C4—862no—
242C2×C4—1724no—
243C2×C4D4×D4312yes—
244C22—22no—
245C22—24no—
246C22—41no—
247C22—42no—
248C22—41no—
249C22—862no—
250C22—862no—
251C22—862no—
252C22—1722no—
253C22—1722no—
254C22C2×D4×D4311yescharacteristic
255C22#41×D4312yes—
256C22#41×D4311yescharacteristic
257C22#41×D4312yes—
258C22C2×#1062190011yescharacteristic
259C4—22no—
260C4—42no—
261C4—42no—
262C4—41no—
263C4—434no—
264C4—862no—
265C4—864no—
266C4—1721no—
267C4—1722no—
268C2—42no—
269C2—1722no—
270C2#123×D4311yescharacteristic
271C2#1458340911yescharacteristic
272C2#1458342612yes—
273C2#1458343212yes—
274C2#1458344811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#397C2
hypercenter#397D43
hypocenterC43#2395
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
2. C2×#13063283C2semidirect
3. #14582839C2semidirect
4. #14582835C2semidirect
5. #14582830C2semidirect
6. #14582828C2semidirect
8. #14582750C2semidirect
9. C22⋊C4×Dic43C2semidirect
10. #14582746C2semidirect
11. C43×#397C2semidirect
144. #397D43semidirect
149. C43#2395semidirect