Finite Group Databasebeta

← #11797879

Subgroups — #11797879

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#10593779C212yesmaximal, complemented
2#10592611C211yesmaximal, characteristic
3#10590194C212yesmaximal, complemented
4#10590141C211yesmaximal, characteristic, complemented
5#10590135C211yesmaximal, characteristic, complemented
6#64287—22no—
7#64121C2212yes—
8#63783—22no—
9#63771C2212yes—
10C8×#157C2211yescharacteristic
11#63764C2211yescharacteristic
12C32×D16C411yescharacteristic, complemented
13#63654C412yescomplemented
14#63628C411yescharacteristic, complemented
15C16×C3⋊D3C2211yescharacteristic
16#4912—62no—
17#3830—22no—
18#3792—42no—
19C2×#622—42no—
20C4×#157D411yescharacteristic
21#3788—22no—
22#3787D411yescharacteristic
23C32×D8C2×C412yes—
24#3754—22no—
25#3746C2×C412yes—
26C8×C3⋊D3C2311yescharacteristic
27#3708—21no—
28C32×C16C2×C411yescharacteristic
29C3⋊(C3⋊C16)C2×C411yescharacteristic
30#2179—91nomaximal, Sylow
31#912—64no—
32C3×D16—22no—
33#827—64no—
34Dic24—62no—
35D3×C16—62no—
36C2×#157—21no—
37C32×D4—22no—
38#638—42no—
39C2×C3⋊Dic3—42no—
40C4×C3⋊D3C2×D411yescharacteristic
41#634—22no—
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#237—124no—
52C3×D8—24no—
53#214—124no—
54Dic12—64no—
55D3×C8—62no—
56C3×C16—22no—
57C3⋊C16—62no—
58C22×C32—42no—
59C2×C3⋊D3#13511yescharacteristic
60#157—41no—
61C32×C4C4×D411yescharacteristic
62C3⋊Dic3—42no—
63C3⋊Dic3C2×D811yescharacteristic
64#135—92no—
65#131—182no—
66Q32—91no—
67SD32—92no—
68D16#15711yescharacteristic, complemented
69C2×C16—91no—
70C2×C16—91no—
71#108—92no—
72#104—182no—
73C4×C8—91no—
74C3×D4—44no—
75#67—244no—
76C2×Dic3—244no—
77C4×D3—62no—
78Dic6—124no—
79C3×C8—22no—
80C3⋊C8—62no—
81C2×C32—82no—
82C2×C32C4×D811yescharacteristic
83C3⋊D3—21no—
84#41—182no—
85Q16—92no—
86SD16—182no—
87D8C2×#15712yes—
88M16—182no—
89M16—362no—
90C2×C8—91no—
91C2×C8—91no—
92C2×C8—362no—
93C42—91no—
94C16—91no—
95C16—181no—
96C16C2×#15711yescharacteristic
97C22×C3—84no—
98C2×D3—62no—
99C3×C4—22no—
100Dic3—62no—
101Dic3—244no—
102C32#217911yescharacteristic, complemented, Sylow
103Q8—182no—
104D4—22no—
105D4—362no—
106C2×C4—91no—
107C2×C4—181no—
108C2×C4—362no—
109C8—92no—
110C8—91no—
111C8—362no—
112C8C22×#15711yescharacteristic
113C2×C3—22no—
114C2×C3—164no—
115D3—122no—
116C22—42no—
117C22—91no—
118C4—91no—
119C4—361no—
120C4—362no—
121C4D4×#15711yescharacteristic
122C3—22no—
123C2—82no—
124C2—181no—
125C2D8×#15711yescharacteristic
subgroupG/H
centerC2D8×#157
commutatorC32×C8C22×C4
FrattiniC8C22×#157
FittingC32×D16C4
socleC2×C32C4×D8
prime radical#10592611C2
cosocleC8×C3⋊D3C23
hypercenterD16#157
hypocenterC32#2179
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ D16

Complements

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

NH ≅ G/Ntype
1. #10593779C2semidirect
3. #10590194C2semidirect
4. #10590141C2semidirect
5. #10590135C2semidirect
12. C32×D16C4semidirect
13. #63654C4semidirect
14. #63628C4semidirect
68. D16#157semidirect
102. C32#2179semidirect

Maximal subgroups

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

subgroupindex
#105937792
#105926112
#105901942
#105901412
#105901352
#21799