Finite Group Databasebeta

← #19145327

Subgroups — #19145327

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#14583436C212yesmaximal, complemented
2#14583299C211yesmaximal, characteristic, complemented
3#14583284C211yesmaximal, characteristic, complemented
4#14583255C212yesmaximal, complemented
5#14583154C211yesmaximal, characteristic, complemented
6#14583153C211yesmaximal, characteristic
7#14583148C212yesmaximal, complemented
8#14583012C211yesmaximal, characteristic, complemented
9#14582997C212yesmaximal, complemented
10#14582851C211yesmaximal, characteristic, complemented
11C43×#441C211yesmaximal, characteristic, complemented
12C2×#10621884C2212yes—
13C2×D344C2211yescharacteristic
14C2×#10621872C2211yescharacteristic
15C2×#10621872C2211yescharacteristic
16#13063320—22no—
17#13063316C2212yes—
18#13063314C2212yes—
19#13063310—22no—
20#13063301C2212yes—
21#13063300C2212yes—
22C4×D172—22no—
23C4×D172C2212yes—
24#13063282—22no—
25C42×D43C2211yescharacteristic
26#13063258C2212yes—
27#13063257C2211yescharacteristic
28#13063249C2212yes—
29#13063247C2212yes—
30#13063245C2212yes—
31#13063236C2211yescharacteristic
32C8×Dic43C2211yescharacteristic
33C8×Dic43C2211yescharacteristic
34C2×Q16×C43C2211yescharacteristic
35C4×Q8×C43C2212yes—
36#106×C43C2211yescharacteristic
37#103×C43C2212yes—
38#97×C43C2211yescharacteristic
39C2×Q8×C43C2312yes—
40C2×D172—22no—
41C2×D172C2312yes—
42C2×C4×D43—22no—
43C2×C4×D43D412yes—
44C2×C4×D43C2311yescharacteristic
45Q16×C43—22no—
46C2×C8×C43C2311yescharacteristic
47C2×C8×C43C2311yescharacteristic
48C4⋊C4×C43—22no—
49C4⋊C4×C43C2312yes—
50C42×C43—22no—
51C42×C43C2311yescharacteristic
52#10621884—24no—
53(C2×D43)⋊C4—22no—
54(C2×D43)⋊C4—22no—
55(C2×D43)⋊C4—22no—
56(C2×D43)⋊C4—22no—
57(C2×D43)⋊C4—22no—
58C4⋊Dic43—22no—
59C4⋊Dic43C2312yes—
60Dic43⋊C4—22no—
61Dic43⋊C4—22no—
62C4×Dic43D412yes—
63C4×Dic43C2311yescharacteristic
64C2×C43⋊C8C2311yescharacteristic
65C2×C43⋊C8C2311yescharacteristic
66D344—22no—
67#10621872—22no—
68#10621872—22no—
69C22×D43—22no—
70C22×D43C2×D411yescharacteristic
71Q8×C43—22no—
72Q8×C43—22no—
73C2×C4×C43—22no—
74C2×C4×C43—22no—
75C2×C4×C43C2×D412yes—
76C2×C4×C43C2411yescharacteristic
77C2×Dic43—22no—
78C2×Dic43C2×D411yescharacteristic
79C2×Dic43C2×D412yes—
80D172—22no—
81D172—22no—
82D172—44no—
83C4×D43—21no—
84C4×D43—21no—
85C4×D43—42no—
86C4×D43—44no—
87C8×C43—21no—
88C8×C43#4112yes—
89C43⋊C8—21no—
90C43⋊C8#4112yes—
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#499—431no—
112#495—431no—
113#488—432no—
114#470—431no—
115#469—431no—
116#468—432no—
117#442—431no—
118#441D4311yescharacteristic, complemented
119#440—432no—
120C4×M16—431no—
121C43#318311yescharacteristic, complemented, Sylow
122C2×Q16C2×D4311yescharacteristic
123C2×SD16—432no—
124C2×D8—431no—
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×Q8C2×D4312yes—
134C4×D4—432no—
135C4×D4—862no—
136#117—862no—
137C2×C42—431no—
138#107—432no—
139#106—431no—
140#106C2×D4311yescharacteristic
141#103—432no—
142#103C2×D4312yes—
143#102—432no—
144#102—432no—
145#97—431no—
146#97C2×D4311yescharacteristic
147C4×C8—431no—
148C4×C8—431no—
149C2×Q8C22×D4312yes—
150C2×D4—432no—
151C2×D4—862no—
152C22×C4—431no—
153C22×C4—432no—
154C22×C4—862no—
155Q16—22no—
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—432no—
166C4⋊C4—862no—
167C4⋊C4—862no—
168C4⋊C4—862no—
169C4⋊C4C22×D4312yes—
170C22⋊C4—862no—
171C22⋊C4—862no—
172C22⋊C4—862no—
173C22⋊C4—862no—
174C22⋊C4—862no—
175C42—22no—
176C42—432no—
177C42—431no—
178C42C22×D4311yescharacteristic
179C23—431no—
180C23—862no—
181Q8—22no—
182Q8—22no—
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—21no—
198C8—432no—
199C8—861no—
200C8#1062189812yes—
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—
213C4#41×D4311yescharacteristic
214C4C2×#1062189811yescharacteristic
215C2—3442no—
216C2—1721no—
217C2#1458344611yescharacteristic
218C2#1458369812yes—
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#441C2
socleC22×C43C22×D4
hypercenter#441D43
hypocenterC43#3183
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #441

Complements

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

NH ≅ G/Ntype
1. #14583436C2semidirect
2. #14583299C2semidirect
3. #14583284C2semidirect
4. #14583255C2semidirect
5. #14583154C2semidirect
7. #14583148C2semidirect
8. #14583012C2semidirect
9. #14582997C2semidirect
10. #14582851C2semidirect
11. C43×#441C2semidirect
118. #441D43semidirect
121. C43#3183semidirect