Finite Group Databasebeta

← #19140167

Subgroups — #19140167

Order 5504.

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

normal subgroups only

This group has 492 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×Q8×Dic43C211yesmaximal, characteristic, complemented
2C2×#13063283C211yesmaximal, characteristic
3#14582829C211yesmaximal, characteristic, complemented
4#14582826C211yesmaximal, characteristic
5#14582810C211yesmaximal, characteristic
6#14582789C212yesmaximal
7#14582786C212yesmaximal, complemented
8#14582785C212yesmaximal, complemented
9#14582773C212yesmaximal
10#14582766C211yesmaximal, characteristic, complemented
11C43×#395C211yesmaximal, characteristic, complemented
12C22×C4×D43C2211yescharacteristic
13Q8×Dic43—24no—
14#13063283—24no—
15C2×C4⋊Dic43C2212yes—
16C2×C4⋊Dic43C2211yescharacteristic
17C2×C4⋊Dic43C2211yescharacteristic
18C2×Dic43⋊C4C2212yes—
19C2×(C2×D43)⋊C4C2211yescharacteristic
20C2×(C2×D43)⋊C4C2212yes—
21C2×(C2×D43)⋊C4C2212yes—
22C2×(C2×D43)⋊C4C2211yescharacteristic
23C2×C4×Dic43C2211yescharacteristic
24C2×C4×Dic43C2212yes—
25C2×C4×Dic43C2211yescharacteristic
26C43⋊#95C2212yes—
27C43⋊#95C2212yes—
28C43⋊#95C2212yes—
29C43⋊#95C2212yes—
30C43⋊#95C2212yes—
31C43⋊#95C2211yescharacteristic
32C22×Q8×C43C2211yescharacteristic
33C2×C4⋊C4×C43C2212yes—
34C2×C4⋊C4×C43C2211yescharacteristic
35#95×C43C2212yes—
36#95×C43C2211yescharacteristic
37C23×D43C2311yescharacteristic
38C2×Q8×C43—22no—
39C2×Q8×C43—24no—
40C22×C4×C43C2312yes—
41C22×C4×C43C2311yescharacteristic
42C22×C4×C43C2311yescharacteristic
43C22×C4×C43C2311yescharacteristic
44C22×C4×C43C2312yes—
45C22×Dic43C2312yes—
46C22×Dic43C2311yescharacteristic
47C22×Dic43C2312yes—
48C22×Dic43C2311yescharacteristic
49C22×Dic43C2311yescharacteristic
50C2×C4×D43—22no—
51C2×C4×D43—22no—
52C2×C4×D43—22no—
53C4⋊C4×C43—22no—
54C4⋊C4×C43—24no—
55(C2×D43)⋊C4—22no—
56(C2×D43)⋊C4—24no—
57(C2×D43)⋊C4—22no—
58(C2×D43)⋊C4—24no—
59C4⋊Dic43—22no—
60C4⋊Dic43—22no—
61C4⋊Dic43—24no—
62Dic43⋊C4—24no—
63C4×Dic43—22no—
64C4×Dic43—24no—
65C4×Dic43D414yes—
66C23×C43C2411yescharacteristic
67C22×D43—21no—
68C22×D43—22no—
69C22×D43—21no—
70C22×D43—22no—
71C22×D43#4112yes—
72Q8×C43—28no—
73C2×C4×C43—22no—
74C2×C4×C43—21no—
75C2×C4×C43—21no—
76C2×C4×C43—22no—
77C2×C4×C43—22no—
78C2×C4×C43—21no—
79C2×C4×C43—22no—
80C2×C4×C43—22no—
81C2×C4×C43—22no—
82C2×C4×C43—22no—
83C2×C4×C43C2×D412yes—
84C2×C4×C43#4114yes—
85C2×C4×C43#4112yes—
86C2×Dic43—21no—
87C2×Dic43—21no—
88C2×Dic43—22no—
89C2×Dic43—22no—
90C2×Dic43—21no—
91C2×Dic43—22no—
92C2×Dic43—22no—
93C2×Dic43—22no—
94C2×Dic43—22no—
95C2×Dic43—22no—
96C2×Dic43—22no—
97C2×Dic43C2×D412yes—
98C2×Dic43C2×D412yes—
99C4×D43—28no—
100C22×C43C22×D411yescharacteristic
101C22×C43C2×#4111yescharacteristic
102C22×C43C2×#4112yes—
103C22×C43C2×#4111yescharacteristic
104C22×C432−1+412yes—
105C2×D43—22no—
106C2×D43—24no—
107C2×D43—41no—
108C2×D43—41no—
109C2×D43—42no—
110C4×C43—22no—
111C4×C43—22no—
112C4×C43—24no—
113C4×C43—41no—
114C4×C43—42no—
115Dic43—22no—
116Dic43—22no—
117Dic43—42no—
118Dic43—41no—
119Dic43—42no—
120#2599—431nomaximal, Sylow
121C2×C43#52511yescharacteristic
122C2×C43#52511yescharacteristic
123C2×C43#53611yescharacteristic
124C2×C43#55212yes—
125C2×C43#55612yes—
126D43—42no—
127C2×C4×Q8—431no—
128C2×#117—431no—
129#398—431no—
130#397—431no—
131#395D4311yescharacteristic, complemented
132#393—431no—
133#388—432no—
134#387—432no—
135#387—432no—
136#385—432no—
137#383—431no—
138C43#259911yescharacteristic, complemented, Sylow
139C22×Q8C2×D4311yescharacteristic
140C23×C4—431no—
141C4×Q8—864no—
142#117—864no—
143C2×C4⋊C4—431no—
144C2×C4⋊C4—432no—
145C2×C4⋊C4—431no—
146C2×C4⋊C4—432no—
147C2×C4⋊C4C2×D4311yescharacteristic
148C2×C4⋊C4C2×D4312yes—
149C2×C22⋊C4—431no—
150C2×C22⋊C4—431no—
151C2×C22⋊C4—432no—
152C2×C22⋊C4—432no—
153C2×C42—431no—
154C2×C42—431no—
155C2×C42—432no—
156#95—432no—
157#95—432no—
158#95—431no—
159#95—432no—
160#95—432no—
161#95—432no—
162#95C2×D4311yescharacteristic
163#95C2×D4312yes—
164C24—431no—
165C2×Q8—22no—
166C2×Q8—24no—
167C22×C4—431no—
168C22×C4—431no—
169C22×C4—432no—
170C22×C4—431no—
171C22×C4—432no—
172C22×C4—862no—
173C22×C4—862no—
174C22×C4—862no—
175C22×C4C22×D4312yes—
176C22×C4C22×D4311yescharacteristic
177C22×C4C22×D4311yescharacteristic
178C22×C4C22×D4312yes—
179C22×C4C22×D4311yescharacteristic
180C4⋊C4—22no—
181C4⋊C4—24no—
182C4⋊C4—862no—
183C4⋊C4—864no—
184C4⋊C4—862no—
185C4⋊C4—864no—
186C22⋊C4—862no—
187C22⋊C4—864no—
188C22⋊C4—862no—
189C22⋊C4—864no—
190C42—434no—
191C42—862no—
192C42—864no—
193C23—432no—
194C23—861no—
195C23—862no—
196C23—861no—
197C23—862no—
198C23C23×D4311yescharacteristic
199Q8—28no—
200C2×C4—22no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—21no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—432no—
211C2×C4—432no—
212C2×C4—868no—
213C2×C4—861no—
214C2×C4—861no—
215C2×C4—862no—
216C2×C4—861no—
217C2×C4—862no—
218C2×C4—862no—
219C2×C4—862no—
220C2×C4—862no—
221C2×C4—862no—
222C2×C4—862no—
223C2×C4—862no—
224C2×C4D4×D4312yes—
225C2×C4#1062190014yes—
226C2×C4#1062190212yes—
227C22—864no—
228C22—862no—
229C22—1722no—
230C22—1721no—
231C22—1721no—
232C22C2×D4×D4311yescharacteristic
233C22#41×D4311yescharacteristic
234C22C2×#1062190012yes—
235C22C2×#1062190211yescharacteristic
236C22#1306337312yes—
237C4—22no—
238C4—24no—
239C4—22no—
240C4—42no—
241C4—41no—
242C4—862no—
243C4—862no—
244C4—1722no—
245C4—1722no—
246C4—1721no—
247C2—1722no—
248C2#1458340511yescharacteristic
249C2#1458341211yescharacteristic
250C2#1458347411yescharacteristic
251C2#1458358312yes—
252C2#1458362312yes—
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#395C2
hypercenter#395D43
hypocenterC43#2599
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
1. C2×Q8×Dic43C2semidirect
3. #14582829C2semidirect
7. #14582786C2semidirect
8. #14582785C2semidirect
10. #14582766C2semidirect
11. C43×#395C2semidirect
131. #395D43semidirect
138. C43#2599semidirect