Finite Group Databasebeta

← #19145322

Subgroups — #19145322

Order 5504.

370 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 115 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#14583431C212yesmaximal, complemented
2#14583299C211yesmaximal, characteristic, complemented
3#14583282C211yesmaximal, characteristic, complemented
4#14583252C212yesmaximal, complemented
5#14583158C211yesmaximal, characteristic, complemented
6#14583149C211yesmaximal, characteristic
7#14583144C212yesmaximal, complemented
8#14583007C211yesmaximal, characteristic, complemented
9#14582999C212yesmaximal, complemented
10#14582851C211yesmaximal, characteristic, complemented
11C43×#442C211yesmaximal, characteristic, complemented
12C2×Dic172C2211yescharacteristic
13C2×#10621883C2212yes—
14C2×#10621872C2211yescharacteristic
15C2×#10621872C2211yescharacteristic
16#13063318—22no—
17#13063316C2212yes—
18#13063312C2212yes—
19#13063307—22no—
20#13063305C2212yes—
21#13063296C2212yes—
22C4×Dic86C2212yes—
23C4×C22⋊D43—22no—
24#13063284—22no—
25C42×D43C2211yescharacteristic
26#13063258C2212yes—
27#13063257C2211yescharacteristic
28#13063250C2212yes—
29#13063248C2212yes—
30#13063246C2212yes—
31#13063236C2211yescharacteristic
32C8×Dic43C2211yescharacteristic
33C8×Dic43C2211yescharacteristic
34C2×D8×C43C2211yescharacteristic
35C4×D4×C43C2212yes—
36#106×C43C2211yescharacteristic
37#102×C43C2212yes—
38#97×C43C2211yescharacteristic
39C2×D4×C43C2312yes—
40C22×C4×C43—22no—
41C2×C22⋊D43—22no—
42C2×C4×D43D412yes—
43C2×C4×D43C2311yescharacteristic
44C2×Dic86C2312yes—
45D8×C43—22no—
46C2×C8×C43C2311yescharacteristic
47C2×C8×C43C2311yescharacteristic
48C4⋊C4×C43C2312yes—
49C22⋊C4×C43—22no—
50C42×C43C2311yescharacteristic
51C22⋊Dic43—22no—
52C22⋊Dic43—22no—
53C22⋊Dic43—22no—
54#10621883—24no—
55(C2×D43)⋊C4—22no—
56C4⋊Dic43—22no—
57C4⋊Dic43—22no—
58C4⋊Dic43C2312yes—
59Dic43⋊C4—22no—
60Dic43⋊C4—22no—
61C4×Dic43—22no—
62C4×Dic43D412yes—
63C4×Dic43C2311yescharacteristic
64C2×C43⋊C8C2311yescharacteristic
65C2×C43⋊C8C2311yescharacteristic
66Dic172—22no—
67#10621872—22no—
68#10621872—22no—
69C23×C43—22no—
70C22×D43C2×D411yescharacteristic
71D4×C43—22no—
72D4×C43—22no—
73C2×C4×C43—22no—
74C2×C4×C43—44no—
75C2×C4×C43C2×D412yes—
76C2×C4×C43C2411yescharacteristic
77C22⋊D43—44no—
78C2×Dic43—22no—
79C2×Dic43—22no—
80C2×Dic43C2×D411yescharacteristic
81C2×Dic43C2×D412yes—
82C4×D43—21no—
83C4×D43—21no—
84C4×D43—42no—
85Dic86—22no—
86Dic86—22no—
87C8×C43—21no—
88C8×C43#4112yes—
89C43⋊C8—21no—
90C43⋊C8#4112yes—
91C22×C43—42no—
92C22×C43—42no—
93C22×C43—42no—
94C22×C43C22×D411yescharacteristic
95C2×D43—21no—
96C2×D43—22no—
97C4×C43—22no—
98C4×C43—42no—
99C4×C43C2×#4111yescharacteristic
100C4×C43C2×#4111yescharacteristic
101Dic43—21no—
102Dic43—22no—
103Dic43—42no—
104Dic43—42no—
105#3183—431nomaximal, Sylow
106C2×C43—82no—
107C2×C43#53211yescharacteristic
108C2×C43#57512yes—
109D43—41no—
110#529—432no—
111#499—431no—
112#495—431no—
113#488—432no—
114#470—431no—
115#469—431no—
116#468—432no—
117#442D4311yescharacteristic, complemented
118#441—431no—
119#440—432no—
120C4×M16—431no—
121C43#318311yescharacteristic, complemented, Sylow
122C2×Q16—431no—
123C2×SD16—432no—
124C2×D8C2×D4311yescharacteristic
125C2×M16—431no—
126C2×M16—431no—
127#126—862no—
128#125—432no—
129#124—432no—
130#123—862no—
131C22⋊Q8—432no—
132#121—432no—
133C4×Q8—432no—
134C4×D4—862no—
135C4×D4C2×D4312yes—
136#117—862no—
137C2×C42—431no—
138#107—432no—
139#106—431no—
140#106C2×D4311yescharacteristic
141#103—432no—
142#103—432no—
143#102—432no—
144#102C2×D4312yes—
145#97—431no—
146#97C2×D4311yescharacteristic
147C4×C8—431no—
148C4×C8—431no—
149C2×Q8—432no—
150C2×D4—862no—
151C2×D4C22×D4312yes—
152C22×C4—22no—
153C22×C4—431no—
154C22×C4—432no—
155Q16—862no—
156SD16—864no—
157D8—22no—
158M16—862no—
159M16—862no—
160C2×C8—431no—
161C2×C8—431no—
162C2×C8C22×D4311yescharacteristic
163C2×C8C22×D4311yescharacteristic
164C4⋊C4—432no—
165C4⋊C4—862no—
166C4⋊C4—862no—
167C4⋊C4—862no—
168C4⋊C4—862no—
169C4⋊C4C22×D4312yes—
170C22⋊C4—22no—
171C22⋊C4—862no—
172C22⋊C4—862no—
173C22⋊C4—862no—
174C22⋊C4—862no—
175C42—432no—
176C42—431no—
177C42—862no—
178C42C22×D4311yescharacteristic
179C23—22no—
180C23—431no—
181Q8—862no—
182Q8—862no—
183D4—22no—
184D4—22no—
185D4—1724no—
186C2×C4—22no—
187C2×C4—44no—
188C2×C4—432no—
189C2×C4—431no—
190C2×C4—861no—
191C2×C4—861no—
192C2×C4—862no—
193C2×C4—862no—
194C2×C4—1722no—
195C2×C4D4×D4312yes—
196C2×C4C23×D4311yescharacteristic
197C8—21no—
198C8—432no—
199C8—861no—
200C8#1062189812yes—
201C22—42no—
202C22—42no—
203C22—42no—
204C22—862no—
205C22—861no—
206C22C2×D4×D4311yescharacteristic
207C4—22no—
208C4—42no—
209C4—862no—
210C4—861no—
211C4—1722no—
212C4—1722no—
213C4#41×D4311yescharacteristic
214C4C2×#1062189811yescharacteristic
215C2—82no—
216C2—1721no—
217C2#1458344611yescharacteristic
218C2#1458369512yes—
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#442C2
socleC22×C43C22×D4
hypercenter#442D43
hypocenterC43#3183
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
1. #14583431C2semidirect
2. #14583299C2semidirect
3. #14583282C2semidirect
4. #14583252C2semidirect
5. #14583158C2semidirect
7. #14583144C2semidirect
8. #14583007C2semidirect
9. #14582999C2semidirect
10. #14582851C2semidirect
11. C43×#442C2semidirect
117. #442D43semidirect
121. C43#3183semidirect