Finite Group Databasebeta

← #26205607

Subgroups — #26205607

Order 12032.

736 conjugacy classes of subgroups; only the 179 normal subgroups are shown.

normal subgroups only

This group has 736 conjugacy classes of subgroups — too many to draw. Only its 179 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#20254133C213yesmaximal, complemented
2#20253763C213yesmaximal
3#20243048C216yesmaximal, complemented
4#20243000C212yesmaximal, complemented
5C47×#1455C211yesmaximal, characteristic, complemented
6#15689680C2213yes—
7C2×#13094021C2211yescharacteristic
8#15689521C2213yescomplemented
9#15689503C2213yescomplemented
10#15689488—26no—
11#15689474C2216yescomplemented
12#15689470C2216yes—
13#15689470C2216yes—
14#15689381—26no—
15#15689231—26no—
16#15689129—26no—
17C4×M16×C47C2213yes—
18C47×#322C2213yescomplemented
19C82×C47C2211yescharacteristic, complemented
20C22×D188—23no—
21C2×Dic188—26no—
22#13094024C2316yes—
23#13094021—23no—
24#13094021C2312yes—
25#13094016—23no—
26#13094003—26no—
27C4×Dic94—26no—
28#13093983—23no—
29#13093956—26no—
30#13093949—212no—
31#13093946—212no—
32#13093946—212no—
33C2×M16×C47D416yes—
34C2×C42×C47C2311yescharacteristic
35#97×C47D416yes—
36C4×C8×C47C2313yes—
37C4×C8×C47C2313yes—
38C23×D47—41no—
39C22×C4×C47C2×D413yes—
40C2×D188—26no—
41C2×D188—412no—
42C2×D188—43no—
43C2×Dic94—26no—
44M16×C47—46no—
45C2×C8×C47C2×D416yes—
46C2×C8×C47C2×D416yes—
47C42×C47C2×D413yes—
48C42×C47C2411yescharacteristic
49C22⋊Dic47—43no—
50C4⋊Dic47—26no—
51C4⋊Dic47—26no—
52Dic47⋊C4—46no—
53C4×Dic47—43no—
54Dic188—412no—
55C23×C47#12711yescharacteristic
56C22×D47—42no—
57C22×D47—86no—
58C2×C4×C47—26no—
59C2×C4×C47#12713yes—
60C2×C4×C47C22×D413yes—
61C2×Dic47—46no—
62D188—412no—
63D188—86no—
64Dic94—412no—
65C8×C47—26no—
66C8×C47—26no—
67#19753—471nomaximal, Sylow
68C22×C47—23no—
69C22×C47C2×#12711yescharacteristic
70C2×D47—86no—
71C2×D47—164no—
72C4×C47—23no—
73C4×C47#57516yes—
74Dic47—86no—
75#3185—473no—
76#3138—473no—
77#1720—476no—
78#1711—472no—
79#1455D4711yescharacteristic, complemented
80C2×C47—41no—
81C2×C47#315313yes—
82D47—162no—
83#533—473no—
84C2×#127—471no—
85#498—473no—
86#494—473no—
87#490—946no—
88#487—476no—
89#486—476no—
90#486—476no—
91#470—946no—
92#441—946no—
93#418—946no—
94C4×M16C2×D4713yes—
95#322C2×D4713yescomplemented
96C82C2×D4711yescharacteristic, complemented
97C47#1975311yescharacteristic, complemented, Sylow
98C22×D4—943no—
99C2×Q16—946no—
100C2×M16D18816yes—
101C4⋊Q8—476no—
102#127—472no—
103#127—943no—
104#125—943no—
105C22⋊Q8—946no—
106C4×Q8—946no—
107#117—943no—
108C2×C42C22×D4711yescharacteristic
109#106—946no—
110#103—9412no—
111#102—9412no—
112#102—9412no—
113#97D18816yes—
114C4×C8C22×D4713yes—
115C4×C8C22×D4713yes—
116C24—1881no—
117C2×Q8—946no—
118C2×D4—946no—
119C2×D4—18812no—
120C2×D4—1883no—
121C22×C4C2×D18813yes—
122Q16—18812no—
123M16—46no—
124C2×C8C2×D18816yes—
125C2×C8C2×D18816yes—
126C4⋊C4—946no—
127C4⋊C4—946no—
128C4⋊C4—1886no—
129C22⋊C4—1883no—
130C42—1883no—
131C42C2×D18813yes—
132C42C23×D4711yescharacteristic
133C23—3766no—
134C23—1882no—
135C23#1309402111yescharacteristic
136Q8—18812no—
137D4—3766no—
138D4—18812no—
139C2×C4—26no—
140C2×C4—1886no—
141C2×C4#1309402113yes—
142C2×C4C22×D18813yes—
143C8—26no—
144C8—26no—
145C22—23no—
146C22—3766no—
147C22—7524no—
148C22C2×#1309402111yescharacteristic
149C4—23no—
150C4—3766no—
151C4#1568992316yes—
152C2—41no—
153C2—7522no—
154C2#2025385413yes—
subgroupG/H
centerC22C2×#13094021
commutator, cosocleC42×C47C24
FrattiniC42C23×D47
FittingC47×#1455C2
socleC22×C47C2×#127
prime radicalC2×#13094021C22
hypercenter#1455D47
hypocenterC47#19753
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1455

Complements

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

NH ≅ G/Ntype
1. #20254133C2semidirect
3. #20243048C2semidirect
4. #20243000C2semidirect
5. C47×#1455C2semidirect
8. #15689521C22semidirect
9. #15689503C22semidirect
11. #15689474C22semidirect
18. C47×#322C22semidirect
19. C82×C47C22semidirect
79. #1455D47semidirect
95. #322C2×D47semidirect
96. C82C2×D47semidirect
97. C47#19753semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#202541332
#202537632
#202430482
#202430002
C47×#14552
#1975347