Finite Group Databasebeta

← #11797881

Subgroups — #11797881

Order 1152.

228 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 46 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#10593787C212yesmaximal, complemented
2#10592618C211yesmaximal, characteristic
3#10590198C212yesmaximal, complemented
4#10590141C211yesmaximal, characteristic, complemented
5#10590135C211yesmaximal, characteristic, complemented
6#64289—22no—
7#64128C2212yes—
8#63785—22no—
9#63771C2212yes—
10C8×#157C2211yescharacteristic
11#63764C2211yescharacteristic
12C32×Q32C411yescharacteristic, complemented
13#63655C412yescomplemented
14#63626C411yescharacteristic, complemented
15C16×C3⋊D3C2211yescharacteristic
16#4919—62no—
17#3832—22no—
18C4×#157D411yescharacteristic
19#3788—22no—
20#3788—42no—
21#3787—42no—
22#3787D411yescharacteristic
23C32×Q16C2×C412yes—
24#3755—22no—
25#3745C2×C412yes—
26C8×C3⋊D3C2311yescharacteristic
27#3708—21no—
28C32×C16C2×C411yescharacteristic
29C3⋊(C3⋊C16)C2×C411yescharacteristic
30#2179—91nomaximal, Sylow
31#919—64no—
32C3×Q32—22no—
33#828—64no—
34D48—62no—
35D3×C16—62no—
36C2×#157—21no—
37C32×Q8—22no—
38C4⋊(C3⋊D3)—22no—
39C4⋊(C3⋊D3)—42no—
40C4×C3⋊D3—42no—
41C4×C3⋊D3C2×D411yescharacteristic
42#622—42no—
43#622D812yes—
44C32×C8C22×C411yescharacteristic
45C3⋊(C3⋊C8)#4111yescharacteristic
46#508—91no—
47#443—92no—
48#368—91no—
49#359—92no—
50#346—91no—
51#239—124no—
52C3×Q16—24no—
53#215—124no—
54D24—64no—
55D3×C8—62no—
56C3×C16—22no—
57C3⋊C16—62no—
58C2×C3⋊D3—42no—
59C2×C3⋊D3#13511yescharacteristic
60#157—41no—
61C32×C4—42no—
62C32×C4C4×D411yescharacteristic
63C3⋊Dic3C2×D811yescharacteristic
64#135—92no—
65#131—182no—
66Q32#15711yescharacteristic, complemented
67SD32—92no—
68D16—91no—
69C2×C16—91no—
70C2×C16—91no—
71#108—92no—
72#104—182no—
73C4×C8—91no—
74C3×Q8—44no—
75D12—124no—
76D12—244no—
77C4×D3—62no—
78C4×D3—244no—
79C3×C8—22no—
80C3⋊C8—62no—
81C2×C32C4×D811yescharacteristic
82C3⋊D3—21no—
83C3⋊D3—82no—
84#41—182no—
85Q16C2×#15712yes—
86SD16—182no—
87D8—92no—
88M16—182no—
89M16—362no—
90C2×C8—91no—
91C2×C8—91no—
92C2×C8—362no—
93C42—91no—
94C16—91no—
95C16—181no—
96C16C2×#15711yescharacteristic
97C2×D3—62no—
98C2×D3—244no—
99C3×C4—22no—
100C3×C4—84no—
101Dic3—62no—
102C32#217911yescharacteristic, complemented, Sylow
103Q8—22no—
104D4—182no—
105D4—362no—
106C2×C4—91no—
107C2×C4—181no—
108C2×C4—362no—
109C8—92no—
110C8—91no—
111C8—362no—
112C8C22×#15711yescharacteristic
113C2×C3—22no—
114D3—122no—
115D3—484no—
116C22—91no—
117C22—362no—
118C4—42no—
119C4—91no—
120C4—361no—
121C4D4×#15711yescharacteristic
122C3—22no—
123C2—181no—
124C2—722no—
125C2D8×#15711yescharacteristic
subgroupG/H
centerC2D8×#157
commutatorC32×C8C22×C4
FrattiniC8C22×#157
FittingC32×Q32C4
socleC2×C32C4×D8
prime radical#10592618C2
cosocleC8×C3⋊D3C23
hypercenterQ32#157
hypocenterC32#2179
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ Q32

Complements

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

NH ≅ G/Ntype
1. #10593787C2semidirect
3. #10590198C2semidirect
4. #10590141C2semidirect
5. #10590135C2semidirect
12. C32×Q32C4semidirect
13. #63655C4semidirect
14. #63626C4semidirect
66. Q32#157semidirect
102. C32#2179semidirect

Maximal subgroups

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

subgroupindex
#105937872
#105926182
#105901982
#105901412
#105901352
#21799