Finite Group Databasebeta

← #11786120

Subgroups — #11786120

Order 1152.

306 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 63 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#10593723C211yesmaximal, characteristic
2#10590340C212yesmaximal
3#10590051C214yesmaximal
4C2×#3787C2212yes—
5C42×C3⋊D3C2211yescharacteristic
6C2×#3712C2214yes—
7#63777C414yes—
8C3×C4⋊(C3⋊C8)—22no—
9#63572—22no—
10#4837—62no—
11C2×C4×C3⋊D3Q812yes—
12C2×C4×C3⋊D3C2311yescharacteristic
13C2×#622C2×C414yes—
14#3787—24no—
15C32×C42D411yescharacteristic
16C4×C3⋊Dic3C2×C412yes—
17C4×C3⋊Dic3D411yescharacteristic
18C2×C3×C3⋊C8—24no—
19#3712—28no—
20#1838—91nomaximal, Sylow
21C2×ΓL(1,𝔽25)—64no—
22C42×D3—62no—
23C3×C4⋊C8—62no—
24Dic3⋊C8—64no—
25C4⋊(C3⋊C8)—22no—
26C22×C3⋊D3C2×Q811yescharacteristic
27C2×C32×C4C4⋊C412yes—
28C2×C32×C4C2×D411yescharacteristic
29C2×C3⋊Dic3C4⋊C412yes—
30C2×C3⋊Dic3C22×C411yescharacteristic
31C4×C3⋊D3—42no—
32C4×C3⋊D3#4114yes—
33#622—24no—
34C3×C3⋊C8—44no—
35#423—92no—
36C2×#97—91no—
37#341—94no—
38C2×C4×D3—62no—
39C2×C4×D3—62no—
40C2×C4×D3—62no—
41C2×C3×C8—64no—
42C3×C42—22no—
43C4×Dic3—62no—
44C4×Dic3—62no—
45C4×Dic3—62no—
46C2×C3⋊C8—24no—
47ΓL(1,𝔽25)—128no—
48C22×C32C2×C4⋊C411yescharacteristic
49C2×C3⋊D3—22no—
50C2×C3⋊D3#12512yes—
51C32×C4—22no—
52C32×C4#12412yes—
53C3⋊Dic3—22no—
54C3⋊Dic3#11712yes—
55C2×M16—94no—
56C22×C8—92no—
57C2×C42—91no—
58C4⋊C8—62no—
59C4⋊C8—182no—
60#97—94no—
61C22×D3—62no—
62C2×C3×C4—22no—
63C2×C3×C4—22no—
64C2×C3×C4—22no—
65C2×Dic3—62no—
66C2×Dic3—62no—
67C2×Dic3—62no—
68C4×D3—64no—
69C4×D3—64no—
70C4×D3—124no—
71C4×D3—124no—
72C3×C8—124no—
73C3⋊C8—44no—
74C2×C32#38211yescharacteristic
75C2×C32#43012yes—
76C3⋊D3—22no—
77C22×C4—91no—
78C22×C4—92no—
79M16—188no—
80C2×C8—64no—
81C2×C8—94no—
82C2×C8—184no—
83C42—91no—
84C42—92no—
85C42GO+(4,𝔽2)11yescharacteristic
86C22×C3—22no—
87C2×D3—64no—
88C2×D3—122no—
89C2×D3—122no—
90C3×C4—24no—
91C3×C4—22no—
92C3×C4—22no—
93C3×C4—42no—
94Dic3—64no—
95Dic3—64no—
96Dic3—122no—
97C32#183811yescharacteristic, complemented, Sylow
98C23—91no—
99C2×C4—91no—
100C2×C4—94no—
101C2×C4—92no—
102C2×C4—362no—
103C2×C4#377312yes—
104C2×C4C2×GO+(4,𝔽2)11yescharacteristic
105C8—124no—
106C8—184no—
107C2×C3—22no—
108C2×C3—22no—
109C2×C3—22no—
110D3—124no—
111C22—92no—
112C22—182no—
113C22C2×#377311yescharacteristic
114C4—22no—
115C4—92no—
116C4—182no—
117C4#6422112yes—
118C3—22no—
119C2—182no—
120C2#1059333012yes—
121C2#1059334411yescharacteristic
subgroupG/H
center, FrattiniC2×C4C2×GO+(4,𝔽2)
commutatorC2×C3⋊Dic3C22×C4
FittingC32×C42D4
socleC22×C32C2×C4⋊C4
prime radicalC22×C3⋊D3C2×Q8
cosocleC2×C4×C3⋊D3C23
hypercenterC42GO+(4,𝔽2)
hypocenterC32#1838
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
97. C32#1838semidirect

Maximal subgroups

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

subgroupindex
#105937232
#105903402
#105900512
#18389