Finite Group Databasebeta

← #11797847

Subgroups — #11797847

Order 1152.

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

normal subgroups only

This group has 230 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#10590140C211yesmaximal, characteristic, complemented
5C16×#157C211yesmaximal, 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#2178—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#622D811yescharacteristic
44#622D811yescharacteristic
45C32×C8C22×C411yescharacteristic
46C3⋊(C3⋊C8)#4111yescharacteristic
47#508—91no—
48#443—92no—
49#368—91no—
50#359—92no—
51C4×C16—91no—
52#237—124no—
53C3×D8—24no—
54#214—124no—
55Dic12—64no—
56D3×C8—62no—
57C3×C16—22no—
58C3⋊C16—62no—
59C22×C32—42no—
60C2×C3⋊D3#13511yescharacteristic
61#157—22no—
62C32×C4C4×D411yescharacteristic
63C3⋊Dic3—42no—
64C3⋊Dic3C2×D811yescharacteristic
65#135—92no—
66#131—182no—
67Q32—91no—
68SD32—92no—
69D16#15711yescharacteristic, complemented
70C2×C16—91no—
71C2×C16—91no—
72#108—92no—
73#104—182no—
74C4×C8—91no—
75C3×D4—44no—
76#67—244no—
77C2×Dic3—244no—
78C4×D3—62no—
79Dic6—124no—
80C3×C8—22no—
81C3⋊C8—62no—
82C2×C32—82no—
83C2×C32C4×D811yescharacteristic
84C3⋊D3—21no—
85#41—182no—
86Q16—92no—
87SD16—182no—
88D8C2×#15712yes—
89M16—182no—
90M16—362no—
91C2×C8—91no—
92C2×C8—91no—
93C2×C8—362no—
94C42—91no—
95C16—91no—
96C16—181no—
97C16C2×#15711yescharacteristic
98C22×C3—84no—
99C2×D3—62no—
100C3×C4—22no—
101Dic3—62no—
102Dic3—244no—
103C32#217811yescharacteristic, complemented, Sylow
104Q8—182no—
105D4—22no—
106D4—362no—
107C2×C4—91no—
108C2×C4—181no—
109C2×C4—362no—
110C8—91no—
111C8—91no—
112C8—91no—
113C8—362no—
114C8C22×#15711yescharacteristic
115C2×C3—22no—
116C2×C3—164no—
117D3—122no—
118C22—42no—
119C22—91no—
120C4—91no—
121C4—182no—
122C4—362no—
123C4D4×#15711yescharacteristic
124C3—22no—
125C2—82no—
126C2—181no—
127C2D8×#15711yescharacteristic
subgroupG/H
centerC2D8×#157
commutatorC32×C8C22×C4
FrattiniC8C22×#157
FittingC32×D16C4
socleC2×C32C4×D8
prime radical#10592611C2
cosocleC8×C3⋊D3C23
hypercenterD16#157
hypocenterC32#2178
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. #10590140C2semidirect
5. C16×#157C2semidirect
12. C32×D16C4semidirect
13. #63654C4semidirect
14. #63628C4semidirect
69. D16#157semidirect
103. C32#2178semidirect

Maximal subgroups

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

subgroupindex
#105937792
#105926112
#105901942
#105901402
C16×#1572
#21789