Finite Group Databasebeta

← #11797784

Subgroups — #11797784

Order 1152.

230 conjugacy classes of subgroups; only the 48 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 48 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
1Q16×#157C212yesmaximal
2C3⋊D3×Q32C211yesmaximal, characteristic
3#10590197C212yesmaximal
4#10590139C211yesmaximal, characteristic
5#10590135C211yesmaximal, characteristic
6Q8×#157—22no—
7Q16×C3⋊D3C2212yes—
8#63784—22no—
9#63769C2212yes—
10C8×#157C2211yescharacteristic
11#63764C2211yescharacteristic
12C32×Q32C411yescharacteristic, complemented
13#63656C412yescomplemented
14#63628C411yescharacteristic, complemented
15C16×C3⋊D3C2211yescharacteristic
16D3×Q32—62no—
17Q8×C3⋊D3—22no—
18C4⋊#157—22no—
19C4⋊#157—42no—
20C4×#157—42no—
21C4×#157D411yescharacteristic
22#3787D411yescharacteristic
23C32×Q16C2×C412yes—
24#3756—22no—
25#3746C2×C412yes—
26C8×C3⋊D3C2311yescharacteristic
27#3708—21no—
28C32×C16C2×C411yescharacteristic
29C3⋊(C3⋊C16)C2×C411yescharacteristic
30#2176—91nomaximal, Sylow
31D3×Q16—64no—
32C3×Q32—22no—
33#829—64no—
34Dic24—62no—
35D3×C16—62no—
36C2×#157—42no—
37C2×#157D812yes—
38C32×Q8—22no—
39C4×C3⋊D3—42no—
40C4×C3⋊D3C2×D411yescharacteristic
41#634—22no—
42#634—42no—
43#622—21no—
44C32×C8C22×C411yescharacteristic
45C3⋊(C3⋊C8)#4111yescharacteristic
46C2×Q32—91no—
47C4×Q16—92no—
48#367—91no—
49#358—92no—
50#346—91no—
51D3×Q8—124no—
52C3×Q16—24no—
53#216—124no—
54Dic12—64no—
55D3×C8—62no—
56C3×C16—22no—
57C3⋊C16—62no—
58C2×C3⋊D3C2×D811yescharacteristic
59#157—22no—
60#157—82no—
61C32×C4—42no—
62C32×C4C4×D411yescharacteristic
63C3⋊Dic3—42no—
64C3⋊Dic3#13511yescharacteristic
65C2×Q16—92no—
66C4×Q8—182no—
67Q32—92no—
68Q32—91no—
69Q32#15711yescharacteristic, complemented
70C2×C16—91no—
71C2×C16—91no—
72#107—92no—
73#103—182no—
74C4×C8—91no—
75C3×Q8—44no—
76C4×D3—62no—
77C4×D3—244no—
78Dic6—124no—
79Dic6—244no—
80C3×C8—22no—
81C3⋊C8—62no—
82C2×C32C4×D811yescharacteristic
83C3⋊D3#51012yes—
84C2×Q8—182no—
85Q16—92no—
86Q16—182no—
87Q16C2×#15712yes—
88C2×C8—91no—
89C2×C8—91no—
90C4⋊C4—182no—
91C4⋊C4—362no—
92C42—91no—
93C42—362no—
94C16—91no—
95C16—181no—
96C16C2×#15711yescharacteristic
97C2×D3—62no—
98C3×C4—22no—
99C3×C4—84no—
100Dic3—62no—
101Dic3—244no—
102C32#217611yescharacteristic, complemented, Sylow
103Q8—22no—
104Q8—182no—
105Q8—362no—
106C2×C4—91no—
107C2×C4—92no—
108C2×C4—362no—
109C2×C4—362no—
110C8—91no—
111C8—181no—
112C8C22×#15711yescharacteristic
113C2×C3—22no—
114D3—64no—
115C22—91no—
116C4—42no—
117C4—91no—
118C4—182no—
119C4—362no—
120C4—722no—
121C4D4×#15711yescharacteristic
122C3—22no—
123C2—92no—
124C2D8×#15711yescharacteristic
subgroupG/H
centerC2D8×#157
commutatorC32×C8C22×C4
FrattiniC8C22×#157
FittingC32×Q32C4
socleC2×C32C4×D8
prime radicalC2×C3⋊D3C2×D8
cosocleC8×C3⋊D3C23
hypercenterQ32#157
hypocenterC32#2176
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
12. C32×Q32C4semidirect
13. #63656C4semidirect
14. #63628C4semidirect
69. Q32#157semidirect
102. C32#2176semidirect

Maximal subgroups

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

subgroupindex
Q16×#1572
C3⋊D3×Q322
#105901972
#105901392
#105901352
#21769