Finite Group Databasebeta

← #19145779

Subgroups — #19145779

Order 5504.

332 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 113 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
1#14583454C211yesmaximal, characteristic, complemented
2#14583436C211yesmaximal, characteristic
3#14583300C212yesmaximal, complemented
4#14583255C212yesmaximal, complemented
5#14583239C212yesmaximal, complemented
6#14583226C212yesmaximal
7#14583186C211yesmaximal, characteristic, complemented
8#14583184C211yesmaximal, characteristic, complemented
9#14583180C211yesmaximal, characteristic, complemented
10#14582951C211yesmaximal, characteristic, complemented
11C43×#477C211yesmaximal, characteristic, complemented
12#13063325C2211yescharacteristic
13#13063320—21no—
14#13063316C2211yescharacteristic
15#13063316C2212yes—
16#13063314C2211yescharacteristic
17#13063310—21no—
18#13063305—21no—
19#13063301—21no—
20#13063301C2211yescharacteristic
21#13063300C2211yescharacteristic
22Q8×Dic43—21no—
23#13063290—21no—
24C4×D172—21no—
25C4×D172C2211yescharacteristic
26#13063283C2212yes—
27#13063282—21no—
28C42×D43C2211yescharacteristic
29#13063259C2212yes—
30#13063256C2212yes—
31#13063256C2212yes—
32C4⋊(C43⋊C8)C2211yescharacteristic
33#13063249C2212yes—
34#13063247C2212yes—
35#13063245C2212yes—
36(C2×D43)⋊C8C2212yes—
37C8×Dic43C2212yes—
38C4⋊Q8×C43C2211yescharacteristic
39C4×Q8×C43C2211yescharacteristic
40#107×C43C2212yes—
41C4⋊C8×C43C2211yescharacteristic
42#103×C43C2212yes—
43C2×Q8×C43—21no—
44C2×Q8×C43C2311yescharacteristic
45C2×D172—21no—
46C2×D172C2311yescharacteristic
47C2×C4×D43—21no—
48C2×C4×D43D411yescharacteristic
49C2×C4×D43D411yescharacteristic
50C2×C4×D43C2311yescharacteristic
51C2×Dic86—21no—
52C2×C8×C43C2312yes—
53C4⋊C4×C43—21no—
54C4⋊C4×C43—21no—
55C4⋊C4×C43C2312yes—
56C4⋊C4×C43C2311yescharacteristic
57C42×C43—21no—
58C42×C43C2311yescharacteristic
59(C2×D43)⋊C4—21no—
60(C2×D43)⋊C4—21no—
61(C2×D43)⋊C4—21no—
62(C2×D43)⋊C4—21no—
63(C2×D43)⋊C4—22no—
64(C2×D43)⋊C4—21no—
65C4⋊Dic43—21no—
66C4⋊Dic43—21no—
67C4⋊Dic43—22no—
68C4⋊Dic43C2312yes—
69C4⋊Dic43C2311yescharacteristic
70Dic43⋊C4—21no—
71Dic43⋊C4—21no—
72Dic43⋊C4—22no—
73C4×Dic43—22no—
74C4×Dic43D411yescharacteristic
75C4×Dic43D411yescharacteristic
76C4×Dic43C2311yescharacteristic
77C2×C43⋊C8C2312yes—
78C22×D43—21no—
79C22×D43C2×D411yescharacteristic
80Q8×C43—21no—
81Q8×C43—21no—
82Q8×C43—42no—
83C2×C4×C43—22no—
84C2×C4×C43—21no—
85C2×C4×C43—21no—
86C2×C4×C43C2×D411yescharacteristic
87C2×C4×C43C2×D411yescharacteristic
88C2×C4×C43C2411yescharacteristic
89C2×Dic43—22no—
90C2×Dic43—21no—
91C2×Dic43C2×D411yescharacteristic
92C2×Dic43C2×D411yescharacteristic
93C2×Dic43C2×D411yescharacteristic
94D172—21no—
95D172—21no—
96D172—42no—
97C4×D43—22no—
98C4×D43—21no—
99C4×D43—21no—
100C4×D43—41no—
101C4×D43—42no—
102Dic86—42no—
103C8×C43—22no—
104C43⋊C8—22no—
105C22×C43C22×D411yescharacteristic
106C2×D43—21no—
107C2×D43—21no—
108C2×D43—21no—
109C2×D43—41no—
110C2×D43—41no—
111C2×D43—41no—
112C4×C43—21no—
113C4×C43—41no—
114C4×C43—41no—
115C4×C43—42no—
116C4×C43#13512yes—
117C4×C432−1+411yescharacteristic
118C4×C432−1+411yescharacteristic
119Dic43—21no—
120Dic43—21no—
121Dic43—21no—
122Dic43—42no—
123Dic43—41no—
124#3233—431nomaximal, Sylow
125C2×C43#53611yescharacteristic
126C2×C43C2×#13511yescharacteristic
127C2×C43#57511yescharacteristic
128D43—41no—
129D43—81no—
130#533—431no—
131#529—431no—
132#499—432no—
133#488—432no—
134#485—432no—
135#482—432no—
136#477D4311yescharacteristic, complemented
137#476—431no—
138#475—431no—
139#474—431no—
140#431—431no—
141C43#323311yescharacteristic, complemented, Sylow
142C4⋊Q8—431no—
143C4⋊Q8C2×D4311yescharacteristic
144#126—861no—
145#125—431no—
146#125—432no—
147#124—431no—
148#123—861no—
149C22⋊Q8—431no—
150C22⋊Q8—861no—
151C22⋊Q8—861no—
152#121—431no—
153C4×Q8—861no—
154C4×Q8—861no—
155C4×Q8C2×D4311yescharacteristic
156C4×D4—431no—
157C4×D4—861no—
158#117—432no—
159#117—861no—
160C2×C42—431no—
161#107—432no—
162#107C2×D4312yes—
163#106—432no—
164#106—432no—
165C4⋊C8—431no—
166C4⋊C8C2×D4311yescharacteristic
167#103—432no—
168#103C2×D4312yes—
169#102—432no—
170#102—432no—
171C22⋊C8—432no—
172C4×C8—432no—
173C2×Q8—21no—
174C2×Q8—861no—
175C2×Q8C22×D4311yescharacteristic
176C2×D4—431no—
177C2×D4—861no—
178C22×C4—431no—
179C22×C4—431no—
180C22×C4—431no—
181C22×C4—861no—
182C2×C8—432no—
183C2×C8C22×D4312yes—
184C4⋊C4—21no—
185C4⋊C4—21no—
186C4⋊C4—432no—
187C4⋊C4—431no—
188C4⋊C4—861no—
189C4⋊C4—861no—
190C4⋊C4—861no—
191C4⋊C4—862no—
192C4⋊C4—862no—
193C4⋊C4—861no—
194C4⋊C4C22×D4312yes—
195C4⋊C4C22×D4311yescharacteristic
196C22⋊C4—861no—
197C22⋊C4—861no—
198C22⋊C4—861no—
199C22⋊C4—862no—
200C22⋊C4—861no—
201C22⋊C4—861no—
202C42—21no—
203C42—431no—
204C42—431no—
205C42—431no—
206C42—862no—
207C42C22×D4311yescharacteristic
208C23—431no—
209C23—861no—
210Q8—21no—
211Q8—21no—
212Q8—42no—
213Q8—1722no—
214D4—861no—
215D4—861no—
216D4—1722no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—431no—
221C2×C4—431no—
222C2×C4—431no—
223C2×C4—862no—
224C2×C4—861no—
225C2×C4—861no—
226C2×C4—862no—
227C2×C4—861no—
228C2×C4—1721no—
229C2×C4—1722no—
230C2×C4D4×D4311yescharacteristic
231C2×C4D4×D4311yescharacteristic
232C2×C4C23×D4311yescharacteristic
233C8—22no—
234C8—862no—
235C22—861no—
236C22—861no—
237C22—861no—
238C22—1721no—
239C22—1721no—
240C22—1721no—
241C22C2×D4×D4311yescharacteristic
242C4—21no—
243C4—41no—
244C4—42no—
245C4—41no—
246C4—861no—
247C4—861no—
248C4—861no—
249C4—1721no—
250C4—1722no—
251C4#1306334812yes—
252C4#1306337211yescharacteristic
253C4#1306337311yescharacteristic
254C2—3441no—
255C2—1721no—
256C2#1458347211yescharacteristic
257C2C2×#1306334811yescharacteristic
258C2#1458369511yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#477C2
socleC22×C43C22×D4
hypercenter#477D43
hypocenterC43#3233
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #477

Complements

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

NH ≅ G/Ntype
1. #14583454C2semidirect
3. #14583300C2semidirect
4. #14583255C2semidirect
5. #14583239C2semidirect
7. #14583186C2semidirect
8. #14583184C2semidirect
9. #14583180C2semidirect
10. #14582951C2semidirect
11. C43×#477C2semidirect
136. #477D43semidirect
141. C43#3233semidirect