Finite Group Databasebeta

← #19145326

Subgroups — #19145326

Order 5504.

370 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 117 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#14583434C212yesmaximal, complemented
2#14583283C211yesmaximal, characteristic, complemented
3#14583256C212yesmaximal, complemented
4#14583158C211yesmaximal, characteristic, complemented
5#14583153C211yesmaximal, characteristic
6#14583146C212yesmaximal, complemented
7#14583010C211yesmaximal, characteristic, complemented
8#14583005C211yesmaximal, characteristic, complemented
9#14582998C212yesmaximal, complemented
10C4×#10621872C211yesmaximal, characteristic, complemented
11C43×#499C211yesmaximal, characteristic, complemented
12C2×Dic172C2211yescharacteristic
13C2×#10621873C2212yes—
14C2×D344C2211yescharacteristic
15C2×#10621872C2211yescharacteristic
16C2×#10621872C2211yescharacteristic
17#13063320—22no—
18#13063313C2212yes—
19#13063310—22no—
20#13063305C2212yes—
21#13063300C2212yes—
22#13063290C2212yes—
23#13063287—22no—
24#13063287C2212yes—
25#13063283—22no—
26C42×D43C2211yescharacteristic
27#13063248C2212yes—
28#13063248C2212yes—
29#13063245C2212yes—
30#13063245C2212yes—
31#13063235C2211yescharacteristic
32#13063235C2211yescharacteristic
33C4×C43⋊C8C2211yescharacteristic
34#125×C43C2212yes—
35#107×C43C2212yes—
36#106×C43C2211yescharacteristic
37#106×C43C2211yescharacteristic
38C4×C8×C43C2211yescharacteristic
39C2×D172—22no—
40C2×D172C2312yes—
41C2×C4×D43—22no—
42C2×C4×D43D412yes—
43C2×C4×D43C2311yescharacteristic
44C2×Dic86C2312yes—
45C2×C8×C43C2311yescharacteristic
46C2×C8×C43C2311yescharacteristic
47C4⋊C4×C43—22no—
48C4⋊C4×C43—22no—
49C4⋊C4×C43C2312yes—
50C4⋊C4×C43C2312yes—
51C42×C43C2311yescharacteristic
52(C2×D43)⋊C4—22no—
53(C2×D43)⋊C4—22no—
54(C2×D43)⋊C4—22no—
55(C2×D43)⋊C4—22no—
56(C2×D43)⋊C4—22no—
57C4⋊Dic43—22no—
58Dic43⋊C4—22no—
59C4×Dic43—22no—
60C4×Dic43D412yes—
61C4×Dic43C2311yescharacteristic
62C2×C43⋊C8C2311yescharacteristic
63C2×C43⋊C8C2311yescharacteristic
64Dic172—22no—
65D344—22no—
66#10621873—24no—
67#10621872—22no—
68#10621872—22no—
69C22×D43—22no—
70C22×D43C2×D411yescharacteristic
71C2×C4×C43—22no—
72C2×C4×C43—22no—
73C2×C4×C43C2×D412yes—
74C2×C4×C43C2411yescharacteristic
75C2×Dic43—22no—
76C2×Dic43C2×D412yes—
77C2×Dic43C2×D411yescharacteristic
78D172—22no—
79D172—22no—
80D172—44no—
81C4×D43—21no—
82C4×D43—21no—
83C4×D43—42no—
84C4×D43—44no—
85Dic86—22no—
86Dic86—22no—
87C8×C43#4112yes—
88C8×C43#4112yes—
89C43⋊C8—21no—
90C43⋊C8—21no—
91C22×C43C22×D411yescharacteristic
92C2×D43—21no—
93C2×D43—22no—
94C2×D43—42no—
95C2×D43—42no—
96C2×D43—42no—
97C4×C43—22no—
98C4×C43—42no—
99C4×C43—42no—
100C4×C43C2×#4111yescharacteristic
101C4×C43C2×#4111yescharacteristic
102Dic43—21no—
103Dic43—22no—
104Dic43—42no—
105#3183—431nomaximal, Sylow
106C2×C43#53211yescharacteristic
107C2×C43#57512yes—
108D43—41no—
109D43—82no—
110#529—432no—
111#499D4311yescharacteristic, complemented
112#495—431no—
113#488—432no—
114#470—431no—
115#469—431no—
116#468—432no—
117#442—431no—
118#441—431no—
119#440—432no—
120C4×M16—431no—
121C43#318311yescharacteristic, complemented, Sylow
122C2×Q16—431no—
123C2×SD16—432no—
124C2×D8—431no—
125C2×M16—431no—
126C2×M16—431no—
127#126—862no—
128#125C2×D4312yes—
129#124—432no—
130#123—862no—
131C22⋊Q8—432no—
132#121—432no—
133C4×Q8—432no—
134C4×D4—432no—
135C4×D4—862no—
136#117—862no—
137C2×C42—431no—
138#107C2×D4312yes—
139#106C2×D4311yescharacteristic
140#106C2×D4311yescharacteristic
141#103—432no—
142#103—432no—
143#102—432no—
144#102—432no—
145#97—431no—
146#97—431no—
147C4×C8—431no—
148C4×C8C2×D4311yescharacteristic
149C2×Q8—432no—
150C2×D4—432no—
151C2×D4—862no—
152C22×C4—431no—
153C22×C4—432no—
154C22×C4—862no—
155Q16—862no—
156SD16—864no—
157D8—862no—
158M16—862no—
159M16—862no—
160C2×C8—431no—
161C2×C8—431no—
162C2×C8C22×D4311yescharacteristic
163C2×C8C22×D4311yescharacteristic
164C4⋊C4—22no—
165C4⋊C4—22no—
166C4⋊C4—862no—
167C4⋊C4—862no—
168C4⋊C4C22×D4312yes—
169C4⋊C4C22×D4312yes—
170C22⋊C4—862no—
171C22⋊C4—862no—
172C22⋊C4—862no—
173C22⋊C4—862no—
174C22⋊C4—862no—
175C42—432no—
176C42—431no—
177C42—862no—
178C42C22×D4311yescharacteristic
179C23—431no—
180C23—862no—
181Q8—862no—
182Q8—862no—
183D4—862no—
184D4—862no—
185D4—1724no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—432no—
189C2×C4—431no—
190C2×C4—861no—
191C2×C4—861no—
192C2×C4—862no—
193C2×C4—1722no—
194C2×C4—1724no—
195C2×C4D4×D4312yes—
196C2×C4C23×D4311yescharacteristic
197C8—861no—
198C8—861no—
199C8#1062190212yes—
200C8#1062190212yes—
201C22—862no—
202C22—861no—
203C22—1722no—
204C22—1722no—
205C22—1722no—
206C22C2×D4×D4311yescharacteristic
207C4—22no—
208C4—42no—
209C4—42no—
210C4—862no—
211C4—861no—
212C4—1722no—
213C4C2×#1062190211yescharacteristic
214C4C2×#1062190211yescharacteristic
215C2—3442no—
216C2—1721no—
217C2#1458345011yescharacteristic
218C2#1458369612yes—
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#499C2
socleC22×C43C22×D4
hypercenter#499D43
hypocenterC43#3183
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #499

Complements

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

NH ≅ G/Ntype
1. #14583434C2semidirect
2. #14583283C2semidirect
3. #14583256C2semidirect
4. #14583158C2semidirect
6. #14583146C2semidirect
7. #14583010C2semidirect
8. #14583005C2semidirect
9. #14582998C2semidirect
10. C4×#10621872C2semidirect
11. C43×#499C2semidirect
111. #499D43semidirect
121. C43#3183semidirect