Finite Group Databasebeta

← #19140423

Subgroups — #19140423

Order 5504.

488 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 488 conjugacy classes of subgroups — too many to draw. Only its 143 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×#13063324C211yesmaximal, characteristic, complemented
2C2×#13063283C211yesmaximal, characteristic
3#14582838C211yesmaximal, characteristic, complemented
4#14582836C211yesmaximal, characteristic
5#14582834C211yesmaximal, characteristic
6#14582820C212yesmaximal, complemented
7#14582812C212yesmaximal
8#14582796C212yesmaximal, complemented
9#14582763C211yesmaximal, characteristic, complemented
10#14582758C212yesmaximal
11C43×#400C211yesmaximal, characteristic, complemented
12C22×Dic86C2212yes—
13C22×C4×D43C2211yescharacteristic
14#13063324—24no—
15#13063283—24no—
16C2×C4⋊Dic43C2211yescharacteristic
17C2×C4⋊Dic43C2211yescharacteristic
18C2×C4⋊Dic43C2212yes—
19C2×Dic43⋊C4C2212yes—
20C2×Dic43⋊C4C2212yes—
21C2×Dic43⋊C4C2212yes—
22C2×(C2×D43)⋊C4C2211yescharacteristic
23C2×(C2×D43)⋊C4C2211yescharacteristic
24C2×(C2×D43)⋊C4C2212yes—
25C2×(C2×D43)⋊C4C2212yes—
26C2×C4×Dic43C2211yescharacteristic
27C2×C4×Dic43C2211yescharacteristic
28C43⋊#95C2212yes—
29C43⋊#95C2212yes—
30C43⋊#95C2212yes—
31C43⋊#95C2211yescharacteristic
32C2×C4⋊C4×C43C2211yescharacteristic
33C2×C4⋊C4×C43C2211yescharacteristic
34#95×C43C2212yes—
35#95×C43C2212yes—
36#95×C43C2211yescharacteristic
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×D43Q814yescomplemented
51C2×Dic86—24no—
52C2×Dic86—42no—
53C2×Dic86—42no—
54C4⋊C4×C43—22no—
55C4⋊C4×C43—22no—
56(C2×D43)⋊C4—22no—
57(C2×D43)⋊C4—22no—
58(C2×D43)⋊C4—42no—
59(C2×D43)⋊C4—42no—
60C4⋊Dic43—22no—
61C4⋊Dic43—22no—
62C4⋊Dic43—42no—
63Dic43⋊C4—24no—
64Dic43⋊C4—24no—
65Dic43⋊C4—42no—
66C4×Dic43—22no—
67C4×Dic43D414yes—
68C23×C43C2411yescharacteristic
69C22×D43—21no—
70C22×D43—21no—
71C22×D43—22no—
72C22×D43—22no—
73C22×D43C2×Q812yes—
74C2×C4×C43—21no—
75C2×C4×C43—21no—
76C2×C4×C43—22no—
77C2×C4×C43—21no—
78C2×C4×C43—22no—
79C2×C4×C43—22no—
80C2×C4×C43—22no—
81C2×C4×C43—22no—
82C2×C4×C43—22no—
83C2×C4×C43—22no—
84C2×C4×C43—22no—
85C2×C4×C43C2×D412yes—
86C2×C4×C43C2×Q812yes—
87C2×Dic43—22no—
88C2×Dic43—21no—
89C2×Dic43—22no—
90C2×Dic43—22no—
91C2×Dic43—22no—
92C2×Dic43—22no—
93C2×Dic43—22no—
94C2×Dic43—22no—
95C2×Dic43—22no—
96C2×Dic43C2×D412yes—
97C2×Dic43C2×D412yes—
98C2×Dic43C2×Q812yes—
99C2×Dic43#4112yes—
100C4×D43—28no—
101Dic86—48no—
102C22×C43C22×D411yescharacteristic
103C22×C43C22×Q811yescharacteristic
104C22×C43C2×#4111yescharacteristic
105C22×C43H(5,𝔽2)12yes—
106C22×C432−1+412yes—
107C2×D43—22no—
108C2×D43—24no—
109C2×D43—41no—
110C2×D43—41no—
111C2×D43—42no—
112C4×C43—22no—
113C4×C43—22no—
114C4×C43—42no—
115C4×C43—41no—
116C4×C43—42no—
117Dic43—22no—
118Dic43—42no—
119Dic43—41no—
120Dic43—42no—
121Dic43C22⋊Q814yes—
122#2628—431nomaximal, Sylow
123C2×C43C2×C22⋊Q811yescharacteristic
124C2×C43#53511yescharacteristic
125C2×C43#53611yescharacteristic
126C2×C43#54212yes—
127C2×C43#54412yes—
128D43—42no—
129C2×C4⋊Q8—431no—
130C2×#117—431no—
131#400—431no—
132#400D4311yescharacteristic, complemented
133#399—431no—
134#399—431no—
135#395—432no—
136#393—432no—
137#389—432no—
138#382—431no—
139#380—432no—
140C43#262811yescharacteristic, complemented, Sylow
141C22×Q8—432no—
142C23×C4—431no—
143C4⋊Q8—864no—
144#117—864no—
145C2×C4⋊C4—431no—
146C2×C4⋊C4—432no—
147C2×C4⋊C4—431no—
148C2×C4⋊C4—432no—
149C2×C4⋊C4—432no—
150C2×C4⋊C4—432no—
151C2×C4⋊C4C2×D4311yescharacteristic
152C2×C4⋊C4C2×D4311yescharacteristic
153C2×C22⋊C4—431no—
154C2×C22⋊C4—431no—
155C2×C22⋊C4—432no—
156C2×C22⋊C4—432no—
157C2×C42—431no—
158C2×C42—431no—
159#95—432no—
160#95—432no—
161#95—431no—
162#95—432no—
163#95C2×D4312yes—
164#95C2×D4311yescharacteristic
165#95C2×D4312yes—
166C24—431no—
167C2×Q8—864no—
168C2×Q8—1722no—
169C2×Q8—1722no—
170C22×C4—431no—
171C22×C4—431no—
172C22×C4—434no—
173C22×C4—432no—
174C22×C4—432no—
175C22×C4—431no—
176C22×C4—862no—
177C22×C4—862no—
178C22×C4C22×D4311yescharacteristic
179C22×C4C22×D4312yes—
180C22×C4C22×D4312yes—
181C22×C4C22×D4311yescharacteristic
182C22×C4C22×D4311yescharacteristic
183C4⋊C4—22no—
184C4⋊C4—22no—
185C4⋊C4—862no—
186C4⋊C4—864no—
187C4⋊C4—864no—
188C4⋊C4—862no—
189C4⋊C4—1722no—
190C4⋊C4—1722no—
191C22⋊C4—862no—
192C22⋊C4—862no—
193C22⋊C4—1722no—
194C22⋊C4—1722no—
195C42—434no—
196C42—862no—
197C23—432no—
198C23—861no—
199C23—861no—
200C23—862no—
201C23—862no—
202C23C23×D4311yescharacteristic
203Q8—1728no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—22no—
207C2×C4—21no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—432no—
216C2×C4—432no—
217C2×C4—432no—
218C2×C4—432no—
219C2×C4—868no—
220C2×C4—862no—
221C2×C4—861no—
222C2×C4—862no—
223C2×C4—862no—
224C2×C4—862no—
225C2×C4—862no—
226C2×C4—862no—
227C2×C4—862no—
228C2×C4—862no—
229C2×C4D4×D4312yes—
230C2×C4Q8×D4312yes—
231C22—862no—
232C22—864no—
233C22—1721no—
234C22—1721no—
235C22—1722no—
236C22C2×D4×D4311yescharacteristic
237C22C2×Q8×D4311yescharacteristic
238C22#41×D4311yescharacteristic
239C22#1306337112yes—
240C22#1306337212yes—
241C4—22no—
242C4—22no—
243C4—42no—
244C4—41no—
245C4—42no—
246C4—434no—
247C4—862no—
248C4—1722no—
249C4—1721no—
250C4—1722no—
251C2—1722no—
252C2C22⋊Q8×D4311yescharacteristic
253C2#1458346711yescharacteristic
254C2#1458347111yescharacteristic
255C2#1458351512yes—
256C2#1458352912yes—
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#400C2
hypercenter#400D43
hypocenterC43#2628
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
1. C2×#13063324C2semidirect
3. #14582838C2semidirect
6. #14582820C2semidirect
8. #14582796C2semidirect
9. #14582763C2semidirect
11. C43×#400C2semidirect
50. C2×C4×D43Q8semidirect
132. #400D43semidirect
140. C43#2628semidirect