Finite Group Databasebeta

← #19140415

Subgroups — #19140415

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×#13063323C211yesmaximal, characteristic, complemented
2C2×#13063281C211yesmaximal, characteristic
3#14582840C212yesmaximal, complemented
4#14582835C212yesmaximal
5#14582820C211yesmaximal, characteristic, complemented
6#14582818C211yesmaximal, characteristic, complemented
7#14582811C211yesmaximal, characteristic
8#14582796C212yesmaximal, complemented
9#14582763C211yesmaximal, characteristic, complemented
10#14582757C212yesmaximal
11C43×#393C211yesmaximal, characteristic
12C22×Dic86C2211yescharacteristic
13C23×Dic43C2211yescharacteristic
14#13063323—24no—
15#13063281—24no—
16C2×C4⋊Dic43C2212yes—
17C2×Dic43⋊C4C2212yes—
18C2×Dic43⋊C4C2212yes—
19C2×Dic43⋊C4C2211yescharacteristic
20C2×Dic43⋊C4C2212yes—
21C2×Dic43⋊C4C2211yescharacteristic
22C2×Dic43⋊C4C2212yes—
23C2×C22⋊Dic43C2211yescharacteristic
24C2×C22⋊Dic43C2212yes—
25C2×C4×Dic43C2211yescharacteristic
26C2×C4×Dic43C2211yescharacteristic
27C43⋊#95C2212yes—
28C43⋊#95C2211yescharacteristic
29C43⋊#95C2212yes—
30C43⋊#95C2212yes—
31C43⋊#95C2212yes—
32C22×Q8×C43C2211yescharacteristic
33C2×C22⋊C4×C43C2211yescharacteristic
34C2×C22⋊C4×C43C2212yes—
35#95×C43C2212yes—
36#95×C43C2211yescharacteristic
37C24×C43C2311yescharacteristic
38C2×Q8×C43—22no—
39C2×Q8×C43—42no—
40C22×C4×C43C2311yescharacteristic
41C22×C4×C43C2312yes—
42C22×C4×C43C2312yes—
43C22×C4×C43C2311yescharacteristic
44C22×Dic43—22no—
45C22×Dic43—22no—
46C22×Dic43Q814yescomplemented
47C22×Dic43C2312yes—
48C22×Dic43C2312yes—
49C22×Dic43C2311yescharacteristic
50C22×Dic43C2311yescharacteristic
51C22×Dic43C2311yescharacteristic
52C22×Dic43C2311yescharacteristic
53C2×Dic86—22no—
54C2×Dic86—42no—
55C22⋊C4×C43—22no—
56C22⋊C4×C43—42no—
57C22⋊Dic43—22no—
58C22⋊Dic43—42no—
59C4⋊Dic43—42no—
60Dic43⋊C4—22no—
61Dic43⋊C4—22no—
62Dic43⋊C4—24no—
63Dic43⋊C4—24no—
64Dic43⋊C4—24no—
65Dic43⋊C4—42no—
66C4×Dic43—22no—
67C4×Dic43D414yes—
68C23×C43—21no—
69C23×C43—21no—
70C23×C43—22no—
71C23×C43—22no—
72C23×C43C2×Q812yes—
73C23×C43C2411yescharacteristic
74Q8×C43—44no—
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×C43—22no—
84C2×C4×C43C2×D412yes—
85C2×Dic43—21no—
86C2×Dic43—21no—
87C2×Dic43—22no—
88C2×Dic43—28no—
89C2×Dic43—21no—
90C2×Dic43—22no—
91C2×Dic43—22no—
92C2×Dic43—22no—
93C2×Dic43—22no—
94C2×Dic43—22no—
95C2×Dic43—22no—
96C2×Dic43—22no—
97C2×Dic43C2×D412yes—
98C2×Dic43C2×D412yes—
99C2×Dic43C2×Q812yes—
100C2×Dic43C2×Q812yes—
101C2×Dic43#4112yes—
102Dic86—44no—
103C22×C43—22no—
104C22×C43—24no—
105C22×C43—41no—
106C22×C43—41no—
107C22×C43—42no—
108C22×C43C22×D411yescharacteristic
109C22×C43C22×Q811yescharacteristic
110C22×C43C2×#4111yescharacteristic
111C22×C43H(5,𝔽2)12yes—
112C22×C432−1+412yes—
113C4×C43—22no—
114C4×C43—42no—
115C4×C43—41no—
116C4×C43—42no—
117Dic43—22no—
118Dic43—22no—
119Dic43—42no—
120Dic43—41no—
121Dic43—42no—
122Dic43C22⋊Q814yes—
123#2628—431nomaximal, Sylow
124C2×C43—42no—
125C2×C43C2×C22⋊Q811yescharacteristic
126C2×C43#53511yescharacteristic
127C2×C43#53611yescharacteristic
128C2×C43#54212yes—
129C2×C43#54412yes—
130C2×C4⋊Q8—431no—
131C2×#117—431no—
132#400—432no—
133#399—432no—
134#395—431no—
135#395—431no—
136#393—431no—
137#393D4311yescharacteristic
138#389—432no—
139#382—431no—
140#380—432no—
141C43#262811yescharacteristic, complemented, Sylow
142C22×Q8—431no—
143C22×Q8C2×D4311yescharacteristic
144C23×C4—431no—
145C4⋊Q8—864no—
146#117—864no—
147C2×C4⋊C4—431no—
148C2×C4⋊C4—431no—
149C2×C4⋊C4—432no—
150C2×C4⋊C4—432no—
151C2×C4⋊C4—432no—
152C2×C4⋊C4—432no—
153C2×C4⋊C4—432no—
154C2×C22⋊C4—431no—
155C2×C22⋊C4—432no—
156C2×C22⋊C4C2×D4311yescharacteristic
157C2×C22⋊C4C2×D4312yes—
158C2×C42—431no—
159C2×C42—431no—
160#95—432no—
161#95—432no—
162#95—431no—
163#95—432no—
164#95—432no—
165#95C2×D4311yescharacteristic
166#95C2×D4312yes—
167C24C22×D4311yescharacteristic
168C2×Q8—22no—
169C2×Q8—42no—
170C2×Q8—862no—
171C2×Q8—1722no—
172C22×C4—431no—
173C22×C4—434no—
174C22×C4—431no—
175C22×C4—431no—
176C22×C4—432no—
177C22×C4—432no—
178C22×C4—431no—
179C22×C4—862no—
180C22×C4—862no—
181C22×C4C22×D4311yescharacteristic
182C22×C4C22×D4312yes—
183C22×C4C22×D4312yes—
184C22×C4C22×D4311yescharacteristic
185C4⋊C4—862no—
186C4⋊C4—864no—
187C4⋊C4—864no—
188C4⋊C4—864no—
189C4⋊C4—862no—
190C4⋊C4—1722no—
191C4⋊C4—1722no—
192C22⋊C4—22no—
193C22⋊C4—42no—
194C22⋊C4—862no—
195C22⋊C4—1722no—
196C42—434no—
197C42—862no—
198C23—21no—
199C23—21no—
200C23—22no—
201C23—22no—
202C23Q8×D4312yes—
203C23C23×D4311yescharacteristic
204Q8—44no—
205Q8—1724no—
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—432no—
220C2×C4—868no—
221C2×C4—861no—
222C2×C4—861no—
223C2×C4—862no—
224C2×C4—861no—
225C2×C4—862no—
226C2×C4—862no—
227C2×C4—862no—
228C2×C4—862no—
229C2×C4—862no—
230C2×C4—862no—
231C2×C4—862no—
232C2×C4D4×D4312yes—
233C22—22no—
234C22—24no—
235C22—41no—
236C22—41no—
237C22—42no—
238C22C2×D4×D4311yescharacteristic
239C22C2×Q8×D4311yescharacteristic
240C22#41×D4311yescharacteristic
241C22#1306337012yes—
242C22#1306337212yes—
243C4—22no—
244C4—42no—
245C4—41no—
246C4—42no—
247C4—434no—
248C4—862no—
249C4—862no—
250C4—1722no—
251C4—1721no—
252C4—1722no—
253C2—42no—
254C2C22⋊Q8×D4311yescharacteristic
255C2#1458346411yescharacteristic
256C2#1458346911yescharacteristic
257C2#1458351312yes—
258C2#1458352812yes—
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#393C2
hypercenter#393D43
hypocenterC43#2628
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #393

Complements

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

NH ≅ G/Ntype
1. C2×#13063323C2semidirect
3. #14582840C2semidirect
5. #14582820C2semidirect
6. #14582818C2semidirect
8. #14582796C2semidirect
9. #14582763C2semidirect
46. C22×Dic43Q8semidirect
141. C43#2628semidirect