Finite Group Databasebeta

← #67453

Subgroups — #67453

Order 384.

134 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 134 conjugacy classes of subgroups — too many to draw. Only its 37 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#4975C211yesmaximal, characteristic
2C3×#324C211yesmaximal, characteristic
3#4528C211yesmaximal, characteristic
4#1325—31nomaximal, Sylow
5C2×C3×C4⋊C4C2211yescharacteristic
6C2×C4⋊Dic3C411yescharacteristic
7C2×Dic3⋊C4—21no—
8C2×Dic3⋊C4—21no—
9C2×C4×Dic3C411yescharacteristic
10C3×C22⋊C8—21no—
11#830—21no—
12#384—31no—
13#324—31no—
14#324D311yescharacteristic
15C22×C3×C4C2×C411yescharacteristic
16C22×C3×C4D411yescharacteristic
17C22×C3×C4D411yescharacteristic
18C22×Dic3—21no—
19C22×Dic3—21no—
20C2×C3×C8—41no—
21C3×C4⋊C4—41no—
22C4⋊Dic3—41no—
23Dic3⋊C4—42no—
24Dic3⋊C4—42no—
25C4×Dic3—21no—
26C4×Dic3C812yescomplemented
27C2×C3⋊C8—41no—
28C2×C4⋊C4—31no—
29C2×C4⋊C4—61no—
30C2×C4⋊C4—61no—
31C2×C4⋊C4C2×D311yescharacteristic
32C2×C42—31no—
33C22⋊C8—21no—
34C22⋊C8—61no—
35C23×C3C22⋊C411yescharacteristic
36C2×C3×C4—21no—
37C2×C3×C4—21no—
38C2×C3×C4—21no—
39C2×C3×C4—21no—
40C2×C3×C4—41no—
41C2×C3×C4—41no—
42C2×C3×C4C2×C811yescharacteristic
43C2×C3×C4M1611yescharacteristic
44C2×Dic3—22no—
45C2×Dic3—22no—
46C2×Dic3—22no—
47C2×Dic3—41no—
48C2×Dic3—41no—
49C2×Dic3—41no—
50C3×C8—81no—
51C3⋊C8—81no—
52C22×C4—61no—
53C22×C4—61no—
54C22×C4C4×D311yescharacteristic
55C22×C4D1211yescharacteristic
56C22×C4#6711yescharacteristic
57C2×C8—41no—
58C2×C8—121no—
59C4⋊C4—41no—
60C4⋊C4—121no—
61C4⋊C4—122no—
62C4⋊C4—122no—
63C42—32no—
64C42—61no—
65C22×C3—21no—
66C22×C3—21no—
67C22×C3C22⋊C811yescharacteristic
68C22×C3#9911yescharacteristic
69C22×C3#10111yescharacteristic
70C3×C4—21no—
71C3×C4—21no—
72C3×C4—41no—
73C3×C4—41no—
74Dic3—24no—
75Dic3—81no—
76C23(C2×D3)⋊C411yescharacteristic
77C2×C4—21no—
78C2×C4—21no—
79C2×C4—21no—
80C2×C4—21no—
81C2×C4—41no—
82C2×C4—41no—
83C2×C4—62no—
84C2×C4—62no—
85C2×C4—62no—
86C2×C4—121no—
87C2×C4—121no—
88C2×C4—121no—
89C2×C4D3×C811yescharacteristic
90C2×C4ΓL(1,𝔽25)11yescharacteristic
91C8—81no—
92C8—241no—
93C2×C3—21no—
94C2×C3—21no—
95C2×C3#32411yescharacteristic
96C2×C3#35311yescharacteristic
97C2×C3#35611yescharacteristic
98C22—21no—
99C22—21no—
100C22#80611yescharacteristic
101C22(C2×D3)⋊C811yescharacteristic
102C22#82411yescharacteristic
103C4—21no—
104C4—21no—
105C4—41no—
106C4—41no—
107C4—64no—
108C4—241no—
109C3#132511yescharacteristic, complemented, Sylow
110C2—21no—
111C2—21no—
112C2#446911yescharacteristic
113C2#447411yescharacteristic
114C2#447811yescharacteristic
subgroupG/H
centerC22#806
commutatorC2×C3×C4C2×C8
FrattiniC2×C4⋊C4C2×D3
FittingC3×#324C2
socleC22×C3#99
prime radicalC23×C3C22⋊C4
cosocleC2×C3×C4⋊C4C22
hypercenter#324D3
hypocenterC3#1325
LCSG ▷ C2×C3×C4 ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #324

Complements

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

NH ≅ G/Ntype
26. C4×Dic3C8semidirect
109. C3#1325semidirect

Maximal subgroups

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

subgroupindex
#49752
C3×#3242
#45282
#13253