Finite Group Databasebeta

← #19142931

Subgroups — #19142931

Order 5504.

564 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 564 conjugacy classes of subgroups — too many to draw. Only its 165 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×#13063302C211yesmaximal, characteristic
2C22×C4×Dic43C211yesmaximal, characteristic
3#14582803C212yesmaximal, complemented
4#14582794C212yesmaximal, complemented
5#14582785C212yesmaximal, complemented
6#14582781C212yesmaximal, complemented
7#14582772C211yesmaximal, characteristic
8#14582760C211yesmaximal, characteristic
9#14582760C211yesmaximal, characteristic
10#14582757C211yesmaximal, characteristic
11C43×#385C211yesmaximal, characteristic
12C22×Dic86C2211yescharacteristic
13C23×Dic43C2211yescharacteristic
14C23×Dic43C2211yescharacteristic
15#13063302—24no—
16C2×C4⋊Dic43C2211yescharacteristic
17C2×Dic43⋊C4C2211yescharacteristic
18C2×Dic43⋊C4C2212yes—
19C2×Dic43⋊C4C2212yes—
20C2×Dic43⋊C4C2211yescharacteristic
21C2×C22⋊Dic43C2211yescharacteristic
22C2×C22⋊Dic43C2211yescharacteristic
23C2×C4×Dic43—24no—
24C2×C4×Dic43C2212yes—
25C2×C4×Dic43C2212yes—
26C43⋊#95C2212yes—
27C43⋊#95C2212yes—
28C43⋊#95C2212yes—
29C43⋊#95C2212yes—
30C43⋊#95C2212yes—
31C43⋊#95C2212yes—
32C23×C4×C43C2211yescharacteristic
33C2×C4⋊C4×C43C2212yes—
34C2×C22⋊C4×C43C2211yescharacteristic
35C2×C22⋊C4×C43C2211yescharacteristic
36#95×C43C2212yes—
37C24×C43C2311yescharacteristic
38C22×C4×C43—24no—
39C22×C4×C43—22no—
40C22×C4×C43C2311yescharacteristic
41C22×C4×C43C2312yes—
42C22×C4×C43C2311yescharacteristic
43C22×C4×C43C2312yes—
44C22×Dic43—24no—
45C22×Dic43—22no—
46C22×Dic43—22no—
47C22×Dic43D414yes—
48C22×Dic43Q814yescomplemented
49C22×Dic43C2312yes—
50C22×Dic43C2311yescharacteristic
51C22×Dic43C2311yescharacteristic
52C22×Dic43C2311yescharacteristic
53C22×Dic43C2312yes—
54C22×Dic43C2311yescharacteristic
55C2×Dic86—22no—
56C2×Dic86—24no—
57C4⋊C4×C43—24no—
58C22⋊C4×C43—22no—
59C22⋊C4×C43—22no—
60C22⋊Dic43—22no—
61C22⋊Dic43—22no—
62C4⋊Dic43—22no—
63Dic43⋊C4—24no—
64Dic43⋊C4—22no—
65Dic43⋊C4—22no—
66Dic43⋊C4—24no—
67C4×Dic43—24no—
68C4×Dic43—24no—
69C23×C43—22no—
70C23×C43—22no—
71C23×C43C2×D412yes—
72C23×C43C2×Q812yes—
73C23×C43#4112yes—
74C23×C43C2411yescharacteristic
75C2×C4×C43—28no—
76C2×C4×C43—22no—
77C2×C4×C43—22no—
78C2×C4×C43—21no—
79C2×C4×C43—21no—
80C2×C4×C43—22no—
81C2×C4×C43—22no—
82C2×C4×C43—22no—
83C2×C4×C43—22no—
84C2×C4×C43—22no—
85C2×C4×C43#4114yes—
86C2×Dic43—28no—
87C2×Dic43—22no—
88C2×Dic43—22no—
89C2×Dic43—22no—
90C2×Dic43—28no—
91C2×Dic43—21no—
92C2×Dic43—21no—
93C2×Dic43—22no—
94C2×Dic43—22no—
95C2×Dic43—22no—
96C2×Dic43—22no—
97C2×Dic43—22no—
98C2×Dic43C2×D412yes—
99C2×Dic43C2×D412yes—
100C2×Dic43C2×Q814yes—
101C2×Dic43#4114yes—
102Dic86—44no—
103C22×C43—22no—
104C22×C43—22no—
105C22×C43—24no—
106C22×C43—24no—
107C22×C43C22⋊Q814yes—
108C22×C43C22×D411yescharacteristic
109C22×C43C22×Q811yescharacteristic
110C22×C43C2×#4112yes—
111C22×C43C2×#4112yes—
112C22×C43C2×#4111yescharacteristic
113C4×C43—24no—
114C4×C43—41no—
115C4×C43—41no—
116C4×C43—42no—
117Dic43—24no—
118Dic43—22no—
119Dic43—41no—
120Dic43—41no—
121Dic43—42no—
122Dic43#12314yes—
123#2855—431nomaximal, Sylow
124C2×C43—24no—
125C2×C43C2×C22⋊Q811yescharacteristic
126C2×C43C2×#12311yescharacteristic
127C2×C43#52511yescharacteristic
128C2×C43#52912yes—
129C2×C43#53312yes—
130C2×C22⋊Q8—431no—
131C22×C42—431no—
132#391—432no—
133#389—432no—
134#387—432no—
135#387—432no—
136#385—431no—
137#385D4311yescharacteristic
138#381—431no—
139#381—431no—
140#380—431no—
141C43#285511yescharacteristic, complemented, Sylow
142C22×Q8—431no—
143C23×C4—431no—
144C23×C4—431no—
145C23×C4C2×D4311yescharacteristic
146C22⋊Q8—864no—
147C2×C4⋊C4—431no—
148C2×C4⋊C4—431no—
149C2×C4⋊C4—431no—
150C2×C4⋊C4—432no—
151C2×C4⋊C4—432no—
152C2×C4⋊C4C2×D4312yes—
153C2×C22⋊C4—431no—
154C2×C22⋊C4—431no—
155C2×C22⋊C4C2×D4311yescharacteristic
156C2×C22⋊C4C2×D4311yescharacteristic
157C2×C42—432no—
158C2×C42—432no—
159C2×C42—864no—
160#95—432no—
161#95—432no—
162#95—432no—
163#95—432no—
164#95—432no—
165#95—432no—
166#95C2×D4312yes—
167C24C22×D4311yescharacteristic
168C2×Q8—862no—
169C2×Q8—864no—
170C22×C4—22no—
171C22×C4—24no—
172C22×C4—431no—
173C22×C4—434no—
174C22×C4—434no—
175C22×C4—432no—
176C22×C4—431no—
177C22×C4—432no—
178C22×C4—431no—
179C22×C4—431no—
180C22×C4—864no—
181C22×C4—862no—
182C22×C4—862no—
183C22×C4C22×D4312yes—
184C22×C4C22×D4311yescharacteristic
185C22×C4C22×D4311yescharacteristic
186C22×C4C22×D4312yes—
187C4⋊C4—24no—
188C4⋊C4—862no—
189C4⋊C4—862no—
190C4⋊C4—862no—
191C4⋊C4—864no—
192C4⋊C4—864no—
193C22⋊C4—22no—
194C22⋊C4—22no—
195C22⋊C4—862no—
196C22⋊C4—862no—
197C42—864no—
198C42—864no—
199C23—22no—
200C23—22no—
201C23#1062189812yes—
202C23D4×D4312yes—
203C23Q8×D4312yes—
204C23C23×D4311yescharacteristic
205Q8—1724no—
206C2×C4—28no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—432no—
217C2×C4—434no—
218C2×C4—432no—
219C2×C4—434no—
220C2×C4—868no—
221C2×C4—868no—
222C2×C4—862no—
223C2×C4—862no—
224C2×C4—862no—
225C2×C4—861no—
226C2×C4—861no—
227C2×C4—862no—
228C2×C4—862no—
229C2×C4—862no—
230C2×C4—862no—
231C2×C4—862no—
232C2×C4#1062190014yes—
233C22—22no—
234C22—22no—
235C22—24no—
236C22—24no—
237C22#1306330314yes—
238C22C2×D4×D4311yescharacteristic
239C22C2×Q8×D4311yescharacteristic
240C22#41×D4312yes—
241C22C2×#1062190012yes—
242C22C2×#1062189811yescharacteristic
243C4—24no—
244C4—41no—
245C4—41no—
246C4—42no—
247C4—434no—
248C4—864no—
249C4—862no—
250C4—1721no—
251C4—1721no—
252C4—1722no—
253C2—24no—
254C2C2×#1306330311yescharacteristic
255C2#123×D4311yescharacteristic
256C2#1458340511yescharacteristic
257C2#1458342912yes—
258C2#1458345112yes—
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#385C2
hypercenter#385D43
hypocenterC43#2855
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
3. #14582803C2semidirect
4. #14582794C2semidirect
5. #14582785C2semidirect
6. #14582781C2semidirect
48. C22×Dic43Q8semidirect
141. C43#2855semidirect