Finite Group Databasebeta

← #19140457

Subgroups — #19140457

Order 5504.

500 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 129 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×#13063311C211yesmaximal, characteristic
2C2×#13063290C211yesmaximal, characteristic, complemented
3#14582834C211yesmaximal, characteristic, complemented
4#14582819C212yesmaximal, complemented
5#14582814C212yesmaximal
6#14582812C211yesmaximal, characteristic, complemented
7#14582811C211yesmaximal, characteristic, complemented
8#14582793C212yesmaximal, complemented
9#14582789C212yesmaximal, complemented
10#14582766C211yesmaximal, characteristic, complemented
11C43×#399C211yesmaximal, characteristic, complemented
12C22×Dic86C2211yescharacteristic
13C22×Dic86C2211yescharacteristic
14C22×C22⋊D43C2211yescharacteristic
15#13063311—24no—
16#13063290—24no—
17C2×Dic43⋊C4C2212yes—
18C2×Dic43⋊C4C2212yes—
19C2×C22⋊Dic43C2211yescharacteristic
20C2×C22⋊Dic43C2212yes—
21C2×(C2×D43)⋊C4C2211yescharacteristic
22C2×(C2×D43)⋊C4C2212yes—
23C2×(C2×D43)⋊C4C2211yescharacteristic
24C2×(C2×D43)⋊C4C2212yes—
25C2×C4×Dic43C2212yes—
26C2×C4×Dic43C2211yescharacteristic
27C43⋊#95C2212yes—
28C43⋊#95C2212yes—
29C43⋊#95C2212yes—
30C43⋊#95C2211yescharacteristic
31C43⋊#95C2212yes—
32C2×C4⋊C4×C43C2211yescharacteristic
33C2×C4⋊C4×C43C2212yes—
34C2×C22⋊C4×C43C2211yescharacteristic
35C2×C22⋊C4×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—42no—
45C22×Dic43C2312yes—
46C22×Dic43C2311yescharacteristic
47C22×Dic43C2311yescharacteristic
48C22×Dic43C2311yescharacteristic
49C22×Dic43C2312yes—
50C2×Dic86—22no—
51C2×Dic86—24no—
52C2×Dic86—22no—
53C2×Dic86—42no—
54C4⋊C4×C43—22no—
55C4⋊C4×C43—42no—
56C22⋊C4×C43—22no—
57C22⋊C4×C43—42no—
58C22⋊Dic43—22no—
59C22⋊Dic43—24no—
60(C2×D43)⋊C4—22no—
61(C2×D43)⋊C4—22no—
62(C2×D43)⋊C4—24no—
63(C2×D43)⋊C4—42no—
64Dic43⋊C4—24no—
65Dic43⋊C4—42no—
66C4×Dic43—24no—
67C4×Dic43D414yes—
68C23×C43—21no—
69C23×C43—22no—
70C23×C43—22no—
71C23×C43—21no—
72C23×C43—21no—
73C23×C43C2411yescharacteristic
74C22×D43—21no—
75C22×D43—22no—
76C22×D43—22no—
77C22×D43—21no—
78C22×D43—21no—
79C2×C4×C43—22no—
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×C43C2×D412yes—
89C22⋊D43—44no—
90C2×Dic43—22no—
91C2×Dic43—22no—
92C2×Dic43—22no—
93C2×Dic43—21no—
94C2×Dic43—21no—
95C2×Dic43—21no—
96C2×Dic43—22no—
97C2×Dic43—22no—
98C2×Dic43—22no—
99C2×Dic43—22no—
100C2×Dic43C2×D412yes—
101C2×Dic43C2×D412yes—
102C2×Dic43#4114yes—
103Dic86—28no—
104Dic86—44no—
105C22×C43—41no—
106C22×C43—41no—
107C22×C43—41no—
108C22×C43—42no—
109C22×C43—42no—
110C22×C43C22×D411yescharacteristic
111C22×C43C2×#4112yes—
112C22×C43H(5,𝔽2)12yes—
113C22×C432−1+411yescharacteristic
114C22×C432−1+411yescharacteristic
115C2×D43—41no—
116C2×D43—41no—
117C2×D43—41no—
118C2×D43—42no—
119C2×D43—42no—
120C4×C43—22no—
121C4×C43—41no—
122C4×C43—42no—
123C4×C43—42no—
124Dic43—24no—
125Dic43—22no—
126Dic43—22no—
127Dic43—41no—
128Dic43—42no—
129#2632—431nomaximal, Sylow
130C2×C43—81no—
131C2×C43#52511yescharacteristic
132C2×C43#53511yescharacteristic
133C2×C43#53611yescharacteristic
134C2×C43#54212yes—
135C2×C43#54212yes—
136D43—81no—
137C2×#124—431no—
138C2×C4×Q8—431no—
139#399—431no—
140#399D4311yescharacteristic, complemented
141#395—432no—
142#394—432no—
143#393—431no—
144#393—431no—
145#388—432no—
146#388—432no—
147#383—431no—
148C43#263211yescharacteristic, complemented, Sylow
149C22×Q8—431no—
150C22×Q8—431no—
151C22×D4—431no—
152#124—864no—
153C4×Q8—864no—
154C2×C4⋊C4—432no—
155C2×C4⋊C4—432no—
156C2×C4⋊C4C2×D4311yescharacteristic
157C2×C4⋊C4C2×D4312yes—
158C2×C22⋊C4—431no—
159C2×C22⋊C4—432no—
160C2×C22⋊C4—431no—
161C2×C22⋊C4—431no—
162C2×C22⋊C4—432no—
163C2×C22⋊C4—432no—
164C2×C22⋊C4C2×D4311yescharacteristic
165C2×C22⋊C4C2×D4312yes—
166C2×C42—431no—
167C2×C42—432no—
168#95—432no—
169#95—431no—
170#95—432no—
171#95—432no—
172#95—432no—
173#95C2×D4311yescharacteristic
174C24—431no—
175C24C22×D4311yescharacteristic
176C2×Q8—864no—
177C2×Q8—862no—
178C2×Q8—862no—
179C2×Q8—1722no—
180C2×D4—862no—
181C2×D4—1722no—
182C22×C4—431no—
183C22×C4—432no—
184C22×C4—431no—
185C22×C4—432no—
186C22×C4—431no—
187C22×C4C22×D4312yes—
188C22×C4C22×D4311yescharacteristic
189C22×C4C22×D4312yes—
190C22×C4C22×D4311yescharacteristic
191C4⋊C4—22no—
192C4⋊C4—42no—
193C4⋊C4—864no—
194C4⋊C4—1722no—
195C22⋊C4—22no—
196C22⋊C4—42no—
197C22⋊C4—862no—
198C22⋊C4—864no—
199C22⋊C4—862no—
200C22⋊C4—864no—
201C22⋊C4—862no—
202C22⋊C4—1722no—
203C42—434no—
204C42—864no—
205C23—21no—
206C23—22no—
207C23—22no—
208C23—21no—
209C23—21no—
210C23—861no—
211C23—862no—
212C23—862no—
213C23—861no—
214C23—861no—
215C23C23×D4311yescharacteristic
216Q8—868no—
217Q8—1724no—
218D4—1724no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—21no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—432no—
229C2×C4—432no—
230C2×C4—434no—
231C2×C4—862no—
232C2×C4—862no—
233C2×C4—862no—
234C2×C4—861no—
235C2×C4—861no—
236C2×C4—861no—
237C2×C4—862no—
238C2×C4—862no—
239C2×C4—862no—
240C2×C4—862no—
241C2×C4D4×D4312yes—
242C22—41no—
243C22—41no—
244C22—41no—
245C22—42no—
246C22—42no—
247C22—1721no—
248C22—1721no—
249C22—1721no—
250C22—1722no—
251C22—1722no—
252C22C2×D4×D4311yescharacteristic
253C22#41×D4312yes—
254C22#1306337012yes—
255C22#1306337211yescharacteristic
256C22#1306337311yescharacteristic
257C4—22no—
258C4—41no—
259C4—42no—
260C4—42no—
261C4—864no—
262C4—862no—
263C4—862no—
264C4—1721no—
265C4—1722no—
266C2—81no—
267C2—3441no—
268C2#1458340711yescharacteristic
269C2#1458346211yescharacteristic
270C2#1458347211yescharacteristic
271C2#1458351712yes—
272C2#1458351912yes—
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#399C2
hypercenter#399D43
hypocenterC43#2632
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #399

Complements

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

NH ≅ G/Ntype
2. C2×#13063290C2semidirect
3. #14582834C2semidirect
4. #14582819C2semidirect
6. #14582812C2semidirect
7. #14582811C2semidirect
8. #14582793C2semidirect
9. #14582789C2semidirect
10. #14582766C2semidirect
11. C43×#399C2semidirect
140. #399D43semidirect
148. C43#2632semidirect