Finite Group Databasebeta

← #19145306

Subgroups — #19145306

Order 5504.

366 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 366 conjugacy classes of subgroups — too many to draw. Only its 119 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#14583434C211yesmaximal, characteristic
3#14583293C211yesmaximal, characteristic, complemented
4#14583269C211yesmaximal, characteristic, complemented
5#14583261C211yesmaximal, characteristic, complemented
6#14583141C212yesmaximal, complemented
7#14583129C212yesmaximal
8#14583005C212yesmaximal, complemented
9#14582998C212yesmaximal, complemented
10#97×D43C211yesmaximal, characteristic, complemented
11C43×#501C211yesmaximal, characteristic, complemented
12C2×Dic172C2212yes—
13C2×#10621873C2212yes—
14C2×C8×D43C2212yes—
15#13063325C2211yescharacteristic
16#13063320—21no—
17#13063316—21no—
18#13063313C2211yescharacteristic
19#13063310—21no—
20#13063305C2212yes—
21#13063305C2211yescharacteristic
22#13063301—21no—
23#13063300C2211yescharacteristic
24Q8×Dic43—21no—
25#13063290C2211yescharacteristic
26#13063290C2212yes—
27#13063287—21no—
28#13063287C2211yescharacteristic
29#13063283—21no—
30#13063283—21no—
31C42×D43C2211yescharacteristic
32#13063248C2212yes—
33#13063248C2212yes—
34#13063248C2212yes—
35#13063245C2212yes—
36#13063236C2211yescharacteristic
37#13063235C2212yes—
38C4⋊Q8×C43C2211yescharacteristic
39#125×C43C2211yescharacteristic
40#107×C43C2212yes—
41#106×C43C2212yes—
42#97×C43C2211yescharacteristic
43C2×Q8×C43—21no—
44C2×D172—21no—
45C2×D172C2311yescharacteristic
46C2×C4×D43—21no—
47C2×C4×D43D411yescharacteristic
48C2×C4×D43D411yescharacteristic
49C2×C4×D43C2311yescharacteristic
50C2×Dic86C2311yescharacteristic
51C2×Dic86C2312yes—
52C2×C8×C43C2312yes—
53C4⋊C4×C43—21no—
54C4⋊C4×C43—21no—
55C4⋊C4×C43—21no—
56C4⋊C4×C43C2311yescharacteristic
57C4⋊C4×C43C2312yes—
58C4⋊C4×C43C2311yescharacteristic
59C42×C43C2311yescharacteristic
60(C2×D43)⋊C4—21no—
61(C2×D43)⋊C4—21no—
62(C2×D43)⋊C4—21no—
63(C2×D43)⋊C4—21no—
64(C2×D43)⋊C4—22no—
65(C2×D43)⋊C4—21no—
66C4⋊Dic43—21no—
67C4⋊Dic43—21no—
68C4⋊Dic43—21no—
69C4⋊Dic43—22no—
70Dic43⋊C4—22no—
71Dic43⋊C4—21no—
72C4×Dic43—21no—
73C4×Dic43—22no—
74C4×Dic43D411yescharacteristic
75C4×Dic43D411yescharacteristic
76C4×Dic43C2311yescharacteristic
77C2×C43⋊C8C2312yes—
78Dic172—24no—
79#10621873—24no—
80C8×D43—24no—
81C22×D43—21no—
82C22×D43C2×D411yescharacteristic
83Q8×C43—42no—
84C2×C4×C43—22no—
85C2×C4×C43—21no—
86C2×C4×C43—21no—
87C2×C4×C43C2×D411yescharacteristic
88C2×C4×C43C2×D411yescharacteristic
89C2×C4×C43C2411yescharacteristic
90C2×Dic43—22no—
91C2×Dic43—21no—
92C2×Dic43C2×D411yescharacteristic
93C2×Dic43C2×D411yescharacteristic
94C2×Dic43C2×D411yescharacteristic
95D172—22no—
96D172—42no—
97C4×D43—22no—
98C4×D43—22no—
99C4×D43—41no—
100C4×D43—42no—
101Dic86—22no—
102Dic86—22no—
103Dic86—22no—
104C8×C43#4114yes—
105C43⋊C8—22no—
106C22×C43C22×D411yescharacteristic
107C2×D43—21no—
108C2×D43—21no—
109C2×D43—41no—
110C2×D43—41no—
111C2×D43—41no—
112C2×D43#13712yes—
113C4×C43—21no—
114C4×C43—21no—
115C4×C43—41no—
116C4×C43—41no—
117C4×C43—42no—
118C4×C43C2×#4112yes—
119Dic43—21no—
120Dic43—21no—
121Dic43—21no—
122Dic43—42no—
123Dic43—41no—
124#3181—431nomaximal, Sylow
125C2×C43#53211yescharacteristic
126C2×C43C2×#13711yescharacteristic
127C2×C43#57511yescharacteristic
128D43—22no—
129D43—81no—
130#533—431no—
131#529—431no—
132#501D4311yescharacteristic, complemented
133#497—431no—
134#491—431no—
135#489—431no—
136#467—432no—
137#465—432no—
138#441—432no—
139#440—432no—
140C2×#97—431no—
141C43#318111yescharacteristic, complemented, Sylow
142C2×Q16—432no—
143C2×SD16—432no—
144C22×C8—432no—
145C4⋊Q8—431no—
146C4⋊Q8C2×D4311yescharacteristic
147#126—861no—
148#125—861no—
149#125C2×D4311yescharacteristic
150#124—431no—
151#123—861no—
152C22⋊Q8—431no—
153C22⋊Q8—432no—
154C22⋊Q8—861no—
155#121—431no—
156C4×Q8—431no—
157C4×Q8—432no—
158C4×Q8—861no—
159C4×D4—431no—
160C4×D4—861no—
161#117—861no—
162#117—861no—
163C2×C42—431no—
164#107C2×D4312yes—
165#106C2×D4312yes—
166#103—432no—
167#103—432no—
168#103—432no—
169#102—432no—
170#97—432no—
171#97—431no—
172#97C2×D4311yescharacteristic
173C2×Q8—21no—
174C2×Q8—431no—
175C2×Q8—432no—
176C2×D4—431no—
177C2×D4—861no—
178C22×C4—431no—
179C22×C4—431no—
180C22×C4—431no—
181C22×C4—861no—
182Q16—864no—
183SD16—864no—
184C2×C8—432no—
185C2×C8—864no—
186C2×C8C22×D4312yes—
187C4⋊C4—21no—
188C4⋊C4—21no—
189C4⋊C4—21no—
190C4⋊C4—861no—
191C4⋊C4—862no—
192C4⋊C4—861no—
193C4⋊C4—862no—
194C4⋊C4—861no—
195C4⋊C4—861no—
196C4⋊C4C22×D4312yes—
197C4⋊C4C22×D4311yescharacteristic
198C4⋊C4C22×D4311yescharacteristic
199C22⋊C4—861no—
200C22⋊C4—861no—
201C22⋊C4—862no—
202C22⋊C4—861no—
203C22⋊C4—861no—
204C22⋊C4—861no—
205C42—431no—
206C42—431no—
207C42—431no—
208C42—861no—
209C42—862no—
210C42C22×D4311yescharacteristic
211C23—431no—
212C23—861no—
213Q8—42no—
214Q8—862no—
215Q8—862no—
216Q8—862no—
217D4—862no—
218D4—1722no—
219C2×C4—21no—
220C2×C4—22no—
221C2×C4—21no—
222C2×C4—431no—
223C2×C4—431no—
224C2×C4—431no—
225C2×C4—862no—
226C2×C4—862no—
227C2×C4—861no—
228C2×C4—862no—
229C2×C4—1721no—
230C2×C4—1722no—
231C2×C4D4×D4311yescharacteristic
232C2×C4D4×D4311yescharacteristic
233C2×C4C23×D4311yescharacteristic
234C8—862no—
235C8#1062190214yes—
236C22—432no—
237C22—861no—
238C22—861no—
239C22—1721no—
240C22—1721no—
241C22—1721no—
242C22C2×D4×D4311yescharacteristic
243C4—21no—
244C4—21no—
245C4—41no—
246C4—41no—
247C4—42no—
248C4—861no—
249C4—861no—
250C4—861no—
251C4—1721no—
252C4—1722no—
253C4C2×#1062190212yes—
254C2—862no—
255C2—3441no—
256C2#1458345011yescharacteristic
257C2#137×D4311yescharacteristic
258C2#1458369511yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#501C2
socleC22×C43C22×D4
hypercenter#501D43
hypocenterC43#3181
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
1. #14583454C2semidirect
3. #14583293C2semidirect
4. #14583269C2semidirect
5. #14583261C2semidirect
6. #14583141C2semidirect
8. #14583005C2semidirect
9. #14582998C2semidirect
10. #97×D43C2semidirect
11. C43×#501C2semidirect
132. #501D43semidirect
141. C43#3181semidirect