Finite Group Databasebeta

← #29504956

Subgroups — #29504956

Order 15296.

142 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 142 conjugacy classes of subgroups — too many to draw. Only its 39 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#21440007C211yesmaximal, characteristic
2#21439993C211yesmaximal, characteristic, complemented
3#21439990C211yesmaximal, characteristic, complemented
4#21439960C211yesmaximal, characteristic, complemented
5#21439888C211yesmaximal, characteristic, complemented
6#21439878C211yesmaximal, characteristic, complemented
7#104×C239C211yesmaximal, characteristic, complemented
8#16838548—21no—
9#16838548C2211yescharacteristic
10#16838547—22no—
11#16838547—21no—
12C2×Dic478—21no—
13C2×Dic478C2211yescharacteristic
14C2×Dic478C2211yescharacteristic
15Q8×D239—21no—
16Dic956—21no—
17#16838538—21no—
18#16838537—21no—
19#16838536—21no—
20#16838532C2211yescharacteristic
21C4⋊Dic239—22no—
22#41×C239C2211yescharacteristic
23M16×C239C2211yescharacteristic
24C42×C239C2211yescharacteristic
25Dic478—22no—
26Dic478—21no—
27Dic478—21no—
28Dic478—21no—
29Dic478—21no—
30Dic478D411yescharacteristic
31D956D411yescharacteristic
32C22⋊D239—22no—
33C22⋊D239—21no—
34C2×Dic239—22no—
35C2×Dic239—21no—
36C2×Dic239D412yes—
37C4×D239—22no—
38C4×D239—21no—
39C239⋊C8—21no—
40Q8×C239D411yescharacteristic
41D4×C239—21no—
42D4×C239D411yescharacteristic
43C2×C4×C239—21no—
44C2×C4×C239—21no—
45C2×C4×C239C2311yescharacteristic
46C8×C239—21no—
47C22×C239—21no—
48C22×C239C2×D411yescharacteristic
49C2×D239—21no—
50C4×C239—22no—
51C4×C239—21no—
52C4×C239C2×D411yescharacteristic
53C4×C239C2×D411yescharacteristic
54Dic239—21no—
55Dic239—22no—
56Dic239—41no—
57C2×C239—21no—
58C2×C239—41no—
59C2×C239#12011yescharacteristic
60D239—41no—
61C239#45611yescharacteristic, complemented, Sylow
62#456—2391nomaximal, Sylow
632−1+4—2391no—
64#137—2391no—
65#137—2391no—
66C4⋊Q8—2391no—
67#104—2391no—
68#104D23911yescharacteristic, complemented
69#101—2391no—
70#41—4781no—
71#41—4781no—
72#41—4782no—
73#41—2391no—
74#41C2×D23911yescharacteristic
75C2×Q8—4781no—
76C2×Q8—4781no—
77C2×Q8—2391no—
78C2×Q8—2391no—
79Q16—4781no—
80Q16—4781no—
81SD16—4781no—
82SD16—4781no—
83M16—2391no—
84M16C2×D23911yescharacteristic
85C4⋊C4—4782no—
86C42C2×D23911yescharacteristic
87Q8—4782no—
88Q8—4781no—
89Q8—4781no—
90Q8—4781no—
91Q8—4781no—
92Q8—2391no—
93Q8D95611yescharacteristic
94D4—21no—
95D4—4782no—
96D4—4781no—
97D4—2391no—
98D4D95611yescharacteristic
99C2×C4—21no—
100C2×C4—21no—
101C2×C4—4782no—
102C2×C4—4781no—
103C2×C4—4782no—
104C2×C4—4781no—
105C2×C4—2392no—
106C2×C4C22×D23911yescharacteristic
107C8—21no—
108C8—4781no—
109C22—21no—
110C22—4781no—
111C22D4×D23911yescharacteristic
112C4—22no—
113C4—21no—
114C4—9561no—
115C4—4781no—
116C4—4782no—
117C4D4×D23911yescharacteristic
118C4C2×D95611yescharacteristic
119C2—21no—
120C2—41no—
121C2—9561no—
122C2#2143993011yescharacteristic
subgroupG/H
centerC2#21439930
commutator, cosocleC2×C4×C239C23
FrattiniC2×C4C22×D239
Fitting#104×C239C2
socleC2×C239#120
prime radical#21440007C2
hypercenter#104D239
hypocenterC239#456
LCSG ▷ C2×C4×C239 ▷ C2×C239 ▷ C239
UCSC1 ◁ C2 ◁ C2×C4 ◁ #104

Complements

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

NH ≅ G/Ntype
2. #21439993C2semidirect
3. #21439990C2semidirect
4. #21439960C2semidirect
5. #21439888C2semidirect
6. #21439878C2semidirect
7. #104×C239C2semidirect
61. C239#456semidirect
68. #104D239semidirect

Maximal subgroups

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

subgroupindex
#214400072
#214399932
#214399902
#214399602
#214398882
#214398782
#104×C2392
#456239