Finite Group Databasebeta

← #19138877

Subgroups — #19138877

Order 5504.

512 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 139 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×#13063283C211yesmaximal, characteristic
2C2×C4⋊C4×D43C211yesmaximal, characteristic
3#14582839C211yesmaximal, characteristic, complemented
4#14582838C211yesmaximal, characteristic, complemented
5#14582830C211yesmaximal, characteristic, complemented
6#14582785C212yesmaximal, complemented
7#14582781C212yesmaximal, complemented
8#14582770C212yesmaximal
9#14582761C211yesmaximal, characteristic
10#14582761C212yesmaximal
11C43×#398C211yesmaximal, characteristic, complemented
12C22×C4×D43C2211yescharacteristic
13C22×C4×D43C2211yescharacteristic
14C22×C4×D43C2211yescharacteristic
15#13063283—24no—
16C2×C4⋊Dic43C2211yescharacteristic
17C2×C4⋊Dic43C2211yescharacteristic
18C2×Dic43⋊C4C2211yescharacteristic
19C2×Dic43⋊C4C2212yes—
20C2×Dic43⋊C4C2211yescharacteristic
21C4⋊C4×D43—24no—
22C2×(C2×D43)⋊C4C2212yes—
23C2×(C2×D43)⋊C4C2212yes—
24C2×C4×Dic43C2212yes—
25C43⋊#95C2212yes—
26C43⋊#95C2212yes—
27C43⋊#95C2212yes—
28C43⋊#95C2212yes—
29C43⋊#95C2211yescharacteristic
30C43⋊#95C2212yes—
31C43⋊#95C2212yes—
32C2×C4⋊C4×C43C2212yes—
33C2×C4⋊C4×C43C2211yescharacteristic
34C2×C4⋊C4×C43C2211yescharacteristic
35#95×C43C2211yescharacteristic
36#95×C43C2212yes—
37C23×D43C2311yescharacteristic
38C22×C4×C43C2312yes—
39C22×C4×C43C2311yescharacteristic
40C22×C4×C43C2312yes—
41C22×C4×C43C2311yescharacteristic
42C22×C4×C43C2311yescharacteristic
43C22×Dic43C2312yes—
44C22×Dic43C2312yes—
45C22×Dic43C2311yescharacteristic
46C22×Dic43C2311yescharacteristic
47C22×Dic43C2311yescharacteristic
48C2×C4×D43—22no—
49C2×C4×D43—22no—
50C2×C4×D43—22no—
51C2×C4×D43—22no—
52C2×C4×D43—24no—
53C2×C4×D43—24no—
54C2×C4×D43D414yes—
55C4⋊C4×C43—22no—
56C4⋊C4×C43—22no—
57C4⋊C4×C43—24no—
58(C2×D43)⋊C4—24no—
59(C2×D43)⋊C4—24no—
60C4⋊Dic43—22no—
61C4⋊Dic43—22no—
62Dic43⋊C4—22no—
63Dic43⋊C4—22no—
64Dic43⋊C4—24no—
65C4×Dic43—24no—
66C23×C43C2411yescharacteristic
67C22×D43—21no—
68C22×D43—21no—
69C22×D43—22no—
70C22×D43C2×D412yes—
71C22×D43#4114yes—
72C2×C4×C43—21no—
73C2×C4×C43—22no—
74C2×C4×C43—21no—
75C2×C4×C43—22no—
76C2×C4×C43—21no—
77C2×C4×C43—22no—
78C2×C4×C43—22no—
79C2×C4×C43—22no—
80C2×C4×C43—22no—
81C2×C4×C43—22no—
82C2×C4×C43—22no—
83C2×C4×C43C2×D412yes—
84C2×C4×C43#4112yes—
85C2×Dic43—21no—
86C2×Dic43—22no—
87C2×Dic43—21no—
88C2×Dic43—22no—
89C2×Dic43—21no—
90C2×Dic43—22no—
91C2×Dic43—22no—
92C2×Dic43—22no—
93C2×Dic43—24no—
94C2×Dic43—22no—
95C2×Dic43C2×D412yes—
96C2×Dic43#4112yes—
97C4×D43—28no—
98C4×D43—28no—
99C4×D43—44no—
100C22×C43C22×D411yescharacteristic
101C22×C43C2×#4112yes—
102C22×C43C2×#4111yescharacteristic
103C22×C43C2×#4111yescharacteristic
104C22×C432−1+412yes—
105C2×D43—22no—
106C2×D43—22no—
107C2×D43—24no—
108C2×D43—24no—
109C2×D43#12314yes—
110C4×C43—22no—
111C4×C43—22no—
112C4×C43—41no—
113C4×C43—42no—
114C4×C43—42no—
115Dic43—22no—
116Dic43—22no—
117Dic43—41no—
118Dic43—42no—
119Dic43—42no—
120#2484—431nomaximal, Sylow
121C2×C43C2×#12311yescharacteristic
122C2×C43#52511yescharacteristic
123C2×C43#53611yescharacteristic
124C2×C43#55212yes—
125C2×C43#55212yes—
126D43—24no—
127C2×#117—431no—
128C22×C4⋊C4—431no—
129#400—431no—
130#400—431no—
131#398—431no—
132#398D4311yescharacteristic, complemented
133#387—432no—
134#387—432no—
135#385—432no—
136#381—431no—
137#381—432no—
138C43#248411yescharacteristic, complemented, Sylow
139C23×C4—431no—
140C23×C4—431no—
141C23×C4—431no—
142#117—864no—
143C2×C4⋊C4—431no—
144C2×C4⋊C4—431no—
145C2×C4⋊C4—431no—
146C2×C4⋊C4—431no—
147C2×C4⋊C4—432no—
148C2×C4⋊C4—864no—
149C2×C4⋊C4C2×D4311yescharacteristic
150C2×C4⋊C4C2×D4311yescharacteristic
151C2×C4⋊C4C2×D4312yes—
152C2×C22⋊C4—432no—
153C2×C22⋊C4—432no—
154C2×C42—432no—
155#95—432no—
156#95—432no—
157#95—432no—
158#95—432no—
159#95—431no—
160#95—432no—
161#95—432no—
162#95C2×D4312yes—
163#95C2×D4311yescharacteristic
164C24—431no—
165C22×C4—431no—
166C22×C4—431no—
167C22×C4—434no—
168C22×C4—432no—
169C22×C4—432no—
170C22×C4—431no—
171C22×C4—862no—
172C22×C4—862no—
173C22×C4—864no—
174C22×C4—862no—
175C22×C4—864no—
176C22×C4—862no—
177C22×C4C22×D4312yes—
178C22×C4C22×D4311yescharacteristic
179C22×C4C22×D4312yes—
180C22×C4C22×D4311yescharacteristic
181C22×C4C22×D4311yescharacteristic
182C4⋊C4—22no—
183C4⋊C4—22no—
184C4⋊C4—24no—
185C4⋊C4—862no—
186C4⋊C4—862no—
187C4⋊C4—864no—
188C4⋊C4—862no—
189C4⋊C4—862no—
190C22⋊C4—864no—
191C22⋊C4—864no—
192C42—864no—
193C23—432no—
194C23—434no—
195C23—861no—
196C23—861no—
197C23—862no—
198C23C23×D4311yescharacteristic
199C2×C4—21no—
200C2×C4—22no—
201C2×C4—21no—
202C2×C4—22no—
203C2×C4—21no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—432no—
211C2×C4—432no—
212C2×C4—868no—
213C2×C4—868no—
214C2×C4—861no—
215C2×C4—862no—
216C2×C4—861no—
217C2×C4—862no—
218C2×C4—861no—
219C2×C4—862no—
220C2×C4—862no—
221C2×C4—862no—
222C2×C4—862no—
223C2×C4—864no—
224C2×C4—1724no—
225C2×C4D4×D4312yes—
226C2×C4#1062190012yes—
227C22—434no—
228C22—864no—
229C22—864no—
230C22—862no—
231C22—862no—
232C22C2×D4×D4311yescharacteristic
233C22#41×D4311yescharacteristic
234C22#41×D4312yes—
235C22C2×#1062190011yescharacteristic
236C22#1306337312yes—
237C4—22no—
238C4—22no—
239C4—42no—
240C4—41no—
241C4—42no—
242C4—862no—
243C4—862no—
244C4—1722no—
245C4—1721no—
246C4—1722no—
247C2—864no—
248C2#123×D4311yescharacteristic
249C2#1458340911yescharacteristic
250C2#1458347411yescharacteristic
251C2#1458358112yes—
252C2#1458358312yes—
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#398C2
hypercenter#398D43
hypocenterC43#2484
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
3. #14582839C2semidirect
4. #14582838C2semidirect
5. #14582830C2semidirect
6. #14582785C2semidirect
7. #14582781C2semidirect
11. C43×#398C2semidirect
132. #398D43semidirect
138. C43#2484semidirect