Finite Group Databasebeta

← #19142888

Subgroups — #19142888

Order 5504.

1102 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 1102 conjugacy classes of subgroups — too many to draw. Only its 181 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
1C23×C4×D43C211yesmaximal, characteristic, complemented
2C2×#13063309C211yesmaximal, characteristic, complemented
3C2×#13063308C211yesmaximal, characteristic, complemented
4C2×#13063295C211yesmaximal, characteristic
5#14582777C214yesmaximal, complemented
6#14582773C214yesmaximal, complemented
7#14582760C211yesmaximal, characteristic, complemented
8#14582754C211yesmaximal, characteristic, complemented
9C43×#381C211yesmaximal, characteristic, complemented
10C24×D43C2211yescharacteristic
11C22×D172C2212yes—
12C22×C22⋊D43C2211yescharacteristic
13C23×Dic43C2211yescharacteristic
14C22×C4×D43—24no—
15C22×C4×D43—24no—
16C22×C4×D43—24no—
17C22×C4×D43C2214yes—
18#13063309—24no—
19#13063308—24no—
20#13063295—24no—
21C2×C4⋊Dic43C2212yescomplemented
22C2×Dic43⋊C4C2212yescomplemented
23C2×C22⋊Dic43C2211yescharacteristic
24C2×(C2×D43)⋊C4C2212yes—
25C2×(C2×D43)⋊C4C2214yes—
26C2×(C2×D43)⋊C4C2212yescomplemented
27C2×(C2×D43)⋊C4C2212yescomplemented
28C43⋊#95C2214yescomplemented
29C23×C4×C43C2211yescharacteristic
30C2×C22⋊C4×C43C2211yescharacteristic
31C2×C22⋊C4×C43C2211yescharacteristic
32#95×C43C2214yescomplemented
33C24×C43C2311yescharacteristic
34C23×D43—22no—
35C23×D43—22no—
36C23×D43—28no—
37C23×D43D414yes—
38C23×D43C2311yescharacteristic
39C23×D43C2312yes—
40C22×C4×C43—22no—
41C22×C4×C43—22no—
42C22×C4×C43D414yescomplemented
43C22×C4×C43C2312yes—
44C22×C4×C43C2312yes—
45C22×C4×C43C2312yes—
46C2×C22⋊D43—22no—
47C2×C22⋊D43—22no—
48C2×C22⋊D43—22no—
49C22×Dic43—22no—
50C22×Dic43—22no—
51C22×Dic43D414yescomplemented
52C22×Dic43C2312yes—
53C22×Dic43C2311yescharacteristic
54C22×Dic43C2312yes—
55C2×D172—24no—
56C2×D172—28no—
57C2×C4×D43—232no—
58C2×C4×D43—28no—
59C2×C4×D43—28no—
60C2×C4×D43—28no—
61C22⋊C4×C43—22no—
62C22⋊C4×C43—22no—
63C22⋊Dic43—22no—
64(C2×D43)⋊C4—24no—
65(C2×D43)⋊C4—24no—
66(C2×D43)⋊C4—24no—
67(C2×D43)⋊C4—28no—
68C4⋊Dic43—24no—
69Dic43⋊C4—24no—
70C23×C43—24no—
71C23×C43C2×D412yes—
72C23×C43C2×D412yes—
73C23×C43C2×D412yes—
74C23×C43C2411yescharacteristic
75C22×D43—216no—
76C22×D43—216no—
77C22×D43—28no—
78C22×D43—22no—
79C22×D43—22no—
80C22×D43—24no—
81C22×D43—216no—
82C22×D43—21no—
83C22×D43—21no—
84C22×D43—21no—
85C22×D43—24no—
86C22×D43C2×D414yes—
87C22×D43#4118yes—
88C2×C4×C43—28no—
89C2×C4×C43—22no—
90C2×C4×C43—22no—
91C2×C4×C43—22no—
92C2×C4×C43—22no—
93C2×C4×C43—24no—
94C2×C4×C43—24no—
95C2×C4×C43C2×D414yes—
96C22⋊D43—44no—
97C2×Dic43—28no—
98C2×Dic43—22no—
99C2×Dic43—22no—
100C2×Dic43—21no—
101C2×Dic43—22no—
102C2×Dic43—21no—
103C2×Dic43—21no—
104C2×Dic43—24no—
105C2×Dic43C2×D414yes—
106D172—48no—
107C4×D43—232no—
108C22×C43—24no—
109C22×C43—24no—
110C22×C43—24no—
111C22×C43#12014yes—
112C22×C43C22×D411yescharacteristic
113C22×C43C22×D411yescharacteristic
114C22×C43C22×D411yescharacteristic
115C22×C43C2×#4114yes—
116C2×D43—232no—
117C2×D43—24no—
118C2×D43—24no—
119C2×D43—28no—
120C2×D43—28no—
121C2×D43—41no—
122C2×D43—42no—
123C2×D43—42no—
124C2×D43—42no—
125C2×D43#12318yescomplemented
126C4×C43—24no—
127C4×C43—42no—
128C4×C43—42no—
129Dic43—24no—
130Dic43—41no—
131Dic43—42no—
132#2849—431nomaximal, Sylow
133C2×C43—24no—
134C2×C43C2×#12011yescharacteristic
135C2×C43C2×#12312yes—
136C2×C43#52512yes—
137C2×C43#52512yes—
138D43—28no—
139D43—81no—
140C24×C4—431no—
141C2×#123—431no—
142C2×#123—431no—
143C2×#120—431no—
144#386—434no—
145#385—434no—
146#381—431no—
147#381D4311yescharacteristic, complemented
148#379—431no—
149C43#284911yescharacteristic, complemented, Sylow
150C25—431no—
151C22×D4—431no—
152C22×D4—432no—
153C23×C4—431no—
154C23×C4—434no—
155C23×C4—864no—
156C23×C4—864no—
157C23×C4—864no—
158C23×C4C2×D4311yescharacteristic
159#123—864no—
160#123—864no—
161#120—864no—
162C2×C4⋊C4—432no—
163C2×C4⋊C4—432no—
164C2×C22⋊C4—431no—
165C2×C22⋊C4—432no—
166C2×C22⋊C4—432no—
167C2×C22⋊C4—432no—
168C2×C22⋊C4—434no—
169C2×C22⋊C4C2×D4311yescharacteristic
170C2×C22⋊C4C2×D4311yescharacteristic
171#95—434no—
172#95C2×D4314yescomplemented
173C24—432no—
174C24—434no—
175C24—431no—
176C24—868no—
177C24—862no—
178C24—862no—
179C24C22×D4311yescharacteristic
180C2×D4—864no—
181C2×D4—868no—
182C2×D4—862no—
183C2×D4—862no—
184C2×D4—862no—
185C22×C4—22no—
186C22×C4—22no—
187C22×C4—434no—
188C22×C4—432no—
189C22×C4—432no—
190C22×C4—431no—
191C22×C4—868no—
192C22×C4—868no—
193C22×C4—8632no—
194C22×C4—862no—
195C22×C4—862no—
196C22×C4—868no—
197C22×C4D17214yescomplemented
198C22×C4C22×D4312yes—
199C22×C4C22×D4312yes—
200C22×C4C22×D4312yes—
201C4⋊C4—864no—
202C4⋊C4—864no—
203C22⋊C4—22no—
204C22⋊C4—22no—
205C22⋊C4—864no—
206C22⋊C4—864no—
207C22⋊C4—868no—
208C22⋊C4—862no—
209C22⋊C4—864no—
210C23—24no—
211C23—434no—
212C23—438no—
213C23—8616no—
214C23—8616no—
215C23—8616no—
216C23—868no—
217C23—862no—
218C23—862no—
219C23—864no—
220C23—861no—
221C23—861no—
222C23—861no—
223C23—864no—
224C23C2×D17212yes—
225C23D4×D4312yes—
226C23D4×D4312yes—
227C23C23×D4311yescharacteristic
228D4—1728no—
229D4—1724no—
230C2×C4—28no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—24no—
236C2×C4—24no—
237C2×C4—434no—
238C2×C4—8632no—
239C2×C4—868no—
240C2×C4—862no—
241C2×C4—862no—
242C2×C4—861no—
243C2×C4—861no—
244C2×C4—862no—
245C2×C4—861no—
246C2×C4—864no—
247C2×C4C2×D17214yes—
248C22—24no—
249C22—24no—
250C22—24no—
251C22—438no—
252C22—8632no—
253C22—864no—
254C22—864no—
255C22—868no—
256C22—868no—
257C22—1721no—
258C22—1722no—
259C22—1722no—
260C22—1722no—
261C22#1306329514yes—
262C22C2×D4×D4311yescharacteristic
263C22C2×D4×D4311yescharacteristic
264C22C22×D17211yescharacteristic
265C22#41×D4314yes—
266C4—24no—
267C4—42no—
268C4—42no—
269C4—864no—
270C4—1721no—
271C4—1722no—
272C2—24no—
273C2—868no—
274C2—3441no—
275C2C2×#1306329511yescharacteristic
276C2#123×D4312yes—
277C2#1458340712yes—
278C2#1458341112yes—
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#381C2
hypercenter#381D43
hypocenterC43#2849
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
1. C23×C4×D43C2semidirect
2. C2×#13063309C2semidirect
3. C2×#13063308C2semidirect
5. #14582777C2semidirect
6. #14582773C2semidirect
7. #14582760C2semidirect
8. #14582754C2semidirect
9. C43×#381C2semidirect
21. C2×C4⋊Dic43C22semidirect
22. C2×Dic43⋊C4C22semidirect
26. C2×(C2×D43)⋊C4C22semidirect
27. C2×(C2×D43)⋊C4C22semidirect
28. C43⋊#95C22semidirect
32. #95×C43C22semidirect
42. C22×C4×C43D4semidirect
51. C22×Dic43D4semidirect
125. C2×D43#123semidirect
147. #381D43semidirect
149. C43#2849semidirect
172. #95C2×D43semidirect
197. C22×C4D172semidirect