Finite Group Databasebeta

← #19140381

Subgroups — #19140381

Order 5504.

526 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 141 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×#13063309C211yesmaximal, characteristic
2C22×Dic43⋊C4C211yesmaximal, characteristic, complemented
3#14582841C212yesmaximal, complemented
4#14582834C212yesmaximal, complemented
5#14582832C212yesmaximal, complemented
6#14582828C212yesmaximal, complemented
7#14582778C211yesmaximal, characteristic
8#14582776C211yesmaximal, characteristic
9#14582771C211yesmaximal, characteristic, complemented
10#14582760C211yesmaximal, characteristic, complemented
11C43×#385C211yesmaximal, characteristic, complemented
12C22×C22⋊D43C2211yescharacteristic
13C23×Dic43C2211yescharacteristic
14C23×Dic43C2211yescharacteristic
15#13063309—24no—
16C2×C4⋊Dic43C2211yescharacteristic
17C2×C4⋊Dic43C2211yescharacteristic
18C2×Dic43⋊C4—24no—
19C2×Dic43⋊C4C2212yes—
20C2×Dic43⋊C4C2212yes—
21C2×Dic43⋊C4C2212yes—
22C2×C22⋊Dic43C2211yescharacteristic
23C2×(C2×D43)⋊C4C2211yescharacteristic
24C2×(C2×D43)⋊C4C2211yescharacteristic
25C2×(C2×D43)⋊C4C2212yes—
26C2×(C2×D43)⋊C4C2212yes—
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
38C23×D43C2311yescharacteristic
39C22×C4×C43—22no—
40C22×C4×C43—42no—
41C22×C4×C43C2311yescharacteristic
42C22×C4×C43C2312yes—
43C22×C4×C43C2312yes—
44C22×C4×C43C2311yescharacteristic
45C2×C22⋊D43—22no—
46C2×C22⋊D43—22no—
47C2×C22⋊D43—22no—
48C22×Dic43—22no—
49C22×Dic43—22no—
50C22×Dic43—22no—
51C22×Dic43—42no—
52C22×Dic43D414yes—
53C22×Dic43C2312yes—
54C22×Dic43C2311yescharacteristic
55C22×Dic43C2312yes—
56C22×Dic43C2311yescharacteristic
57C22×Dic43C2311yescharacteristic
58C4⋊C4×C43—42no—
59C22⋊C4×C43—22no—
60C22⋊C4×C43—22no—
61C22⋊Dic43—22no—
62(C2×D43)⋊C4—22no—
63(C2×D43)⋊C4—22no—
64(C2×D43)⋊C4—42no—
65(C2×D43)⋊C4—42no—
66C4⋊Dic43—22no—
67C4⋊Dic43—22no—
68Dic43⋊C4—24no—
69Dic43⋊C4—24no—
70Dic43⋊C4—42no—
71C23×C43—22no—
72C23×C43—22no—
73C23×C43C2×D412yes—
74C23×C43#4112yes—
75C23×C43#4112yes—
76C23×C43C2411yescharacteristic
77C22×D43—21no—
78C22×D43—21no—
79C22×D43—21no—
80C22×D43—22no—
81C22×D43—22no—
82C2×C4×C43—22no—
83C2×C4×C43—21no—
84C2×C4×C43—21no—
85C2×C4×C43—22no—
86C2×C4×C43—22no—
87C2×C4×C43—22no—
88C2×C4×C43—22no—
89C2×C4×C43—22no—
90C2×C4×C43—22no—
91C2×C4×C43—22no—
92C2×C4×C43—44no—
93C22⋊D43—44no—
94C2×Dic43—28no—
95C2×Dic43—21no—
96C2×Dic43—21no—
97C2×Dic43—21no—
98C2×Dic43—21no—
99C2×Dic43—22no—
100C2×Dic43—21no—
101C2×Dic43—22no—
102C2×Dic43—21no—
103C2×Dic43—21no—
104C2×Dic43—22no—
105C2×Dic43—22no—
106C2×Dic43—22no—
107C2×Dic43—22no—
108C2×Dic43—44no—
109C2×Dic43C2×D412yes—
110C2×Dic43C2×D412yes—
111C22×C43—22no—
112C22×C43—22no—
113C22×C43—24no—
114C22×C43—24no—
115C22×C43#12314yes—
116C22×C43C22×D411yescharacteristic
117C22×C43C2×#4111yescharacteristic
118C22×C43C2×#4111yescharacteristic
119C22×C43H(5,𝔽2)12yes—
120C22×C432−1+412yes—
121C2×D43—41no—
122C2×D43—41no—
123C2×D43—41no—
124C2×D43—42no—
125C2×D43—42no—
126C4×C43—41no—
127C4×C43—42no—
128C4×C43—41no—
129C4×C43—42no—
130Dic43—22no—
131Dic43—22no—
132Dic43—41no—
133Dic43—42no—
134Dic43—42no—
135#2623—431nomaximal, Sylow
136C2×C43—24no—
137C2×C43C2×#12311yescharacteristic
138C2×C43#53511yescharacteristic
139C2×C43#53611yescharacteristic
140C2×C43#53912yes—
141C2×C43#53912yes—
142D43—81no—
143C2×#123—431no—
144C22×C4⋊C4—431no—
145#400—432no—
146#399—432no—
147#398—432no—
148#397—432no—
149#386—431no—
150#386—431no—
151#385—431no—
152#385D4311yescharacteristic, complemented
153#381—431no—
154C43#262311yescharacteristic, complemented, Sylow
155C22×D4—431no—
156C23×C4—431no—
157C23×C4—431no—
158C23×C4C2×D4311yescharacteristic
159#123—864no—
160C2×C4⋊C4—432no—
161C2×C4⋊C4—432no—
162C2×C4⋊C4—431no—
163C2×C4⋊C4—431no—
164C2×C4⋊C4—432no—
165C2×C4⋊C4—864no—
166C2×C4⋊C4C2×D4312yes—
167C2×C22⋊C4—431no—
168C2×C22⋊C4—431no—
169C2×C22⋊C4—431no—
170C2×C22⋊C4—432no—
171C2×C22⋊C4—432no—
172C2×C22⋊C4C2×D4311yescharacteristic
173C2×C22⋊C4C2×D4311yescharacteristic
174#95—432no—
175#95—432no—
176#95—432no—
177#95—432no—
178#95—432no—
179#95C2×D4312yes—
180C24—431no—
181C24C22×D4311yescharacteristic
182C2×D4—862no—
183C2×D4—862no—
184C2×D4—862no—
185C22×C4—22no—
186C22×C4—42no—
187C22×C4—434no—
188C22×C4—431no—
189C22×C4—431no—
190C22×C4—432no—
191C22×C4—431no—
192C22×C4—432no—
193C22×C4—862no—
194C22×C4—862no—
195C22×C4—862no—
196C22×C4—1722no—
197C22×C4C22×D4312yes—
198C22×C4C22×D4311yescharacteristic
199C22×C4C22×D4312yes—
200C22×C4C22×D4311yescharacteristic
201C4⋊C4—42no—
202C4⋊C4—864no—
203C4⋊C4—864no—
204C4⋊C4—862no—
205C4⋊C4—862no—
206C4⋊C4—1722no—
207C22⋊C4—22no—
208C22⋊C4—22no—
209C22⋊C4—862no—
210C22⋊C4—862no—
211C22⋊C4—862no—
212C22⋊C4—1722no—
213C22⋊C4—1722no—
214C23—22no—
215C23—22no—
216C23—861no—
217C23—861no—
218C23—861no—
219C23—862no—
220C23—862no—
221C23#1062189812yes—
222C23D4×D4312yes—
223C23#1062190212yes—
224C23C23×D4311yescharacteristic
225D4—1724no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—22no—
236C2×C4—44no—
237C2×C4—432no—
238C2×C4—432no—
239C2×C4—868no—
240C2×C4—861no—
241C2×C4—861no—
242C2×C4—861no—
243C2×C4—861no—
244C2×C4—862no—
245C2×C4—861no—
246C2×C4—861no—
247C2×C4—862no—
248C2×C4—861no—
249C2×C4—862no—
250C2×C4—862no—
251C2×C4—862no—
252C2×C4—862no—
253C2×C4—1724no—
254C22—22no—
255C22—22no—
256C22—24no—
257C22—24no—
258C22—1721no—
259C22—1721no—
260C22—1721no—
261C22—1722no—
262C22—1722no—
263C22#1306331014yes—
264C22C2×D4×D4311yescharacteristic
265C22C2×#1062189811yescharacteristic
266C22C2×#1062190211yescharacteristic
267C22#1306337012yes—
268C22#1306337212yes—
269C4—42no—
270C4—41no—
271C4—41no—
272C4—42no—
273C4—862no—
274C4—862no—
275C4—1721no—
276C4—1722no—
277C4—1722no—
278C2—24no—
279C2—3441no—
280C2C2×#1306331011yescharacteristic
281C2#1458346411yescharacteristic
282C2#1458347111yescharacteristic
283C2#1458349112yes—
284C2#1458349812yes—
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#385C2
hypercenter#385D43
hypocenterC43#2623
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
2. C22×Dic43⋊C4C2semidirect
3. #14582841C2semidirect
4. #14582834C2semidirect
5. #14582832C2semidirect
6. #14582828C2semidirect
9. #14582771C2semidirect
10. #14582760C2semidirect
11. C43×#385C2semidirect
152. #385D43semidirect
154. C43#2623semidirect