Finite Group Databasebeta

← #72987

Subgroups — #72987

Order 384.

113 conjugacy classes of subgroups; only the 13 normal subgroups are shown.

normal subgroups only

This group has 113 conjugacy classes of subgroups — too many to draw. Only its 13 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#376⋊C3C211yesmaximal, characteristic, complemented
2#4622C211yesmaximal, characteristic
3#4621C211yesmaximal, characteristic, complemented
4#1500—31nomaximal, Sylow
5C4×S4—41nomaximal
6#95⋊C3C2211yescharacteristic
7#529—31no—
8#431—31no—
9#376D311yescharacteristic, complemented
10#328—31no—
11#328—31no—
12#327—31no—
13#327—31no—
14C2×S4—41no—
15C4×A4—41no—
16SL(2,ℤ/4)—41no—
17#126—61no—
18#125—31no—
19#124—31no—
20#123—61no—
21C22⋊Q8—31no—
22#121—31no—
23C4×Q8—31no—
24C4×D4—31no—
25C4×D4—61no—
26#117—61no—
27C2×C42—31no—
28C4⋊C8—61no—
29C22⋊C8—31no—
30C22⋊C8—31no—
31C4×C8—61no—
32#95—31no—
33#95C2×D311yescharacteristic
34C2×A4—41no—
35S4—42no—
36C4×D3—161no—
37C2×Q8—31no—
38C2×D4—31no—
39C2×D4—61no—
40C22×C4—31no—
41C22×C4—31no—
42C22×C4—61no—
43C22×C4S411yescharacteristic
44C2×C8—61no—
45C2×C8—61no—
46C4⋊C4—31no—
47C4⋊C4—31no—
48C4⋊C4—61no—
49C4⋊C4—61no—
50C4⋊C4—61no—
51C4⋊C4—61no—
52C22⋊C4—61no—
53C22⋊C4—61no—
54C22⋊C4—61no—
55C22⋊C4—61no—
56C22⋊C4—61no—
57C42—31no—
58C42—31no—
59C42—31no—
60C42—31no—
61C42—61no—
62C2×D3—161no—
63A4—41no—
64C3×C4—161no—
65Dic3—161no—
66C23—61no—
67C23C2×S411yescharacteristic
68Q8—121no—
69D4—121no—
70D4—121no—
71D4—121no—
72C2×C4—31no—
73C2×C4—31no—
74C2×C4—31no—
75C2×C4—31no—
76C2×C4—31no—
77C2×C4—31no—
78C2×C4—61no—
79C2×C4—61no—
80C2×C4—61no—
81C2×C4—61no—
82C2×C4—61no—
83C2×C4—121no—
84C2×C4—121no—
85C2×C4—121no—
86C8—121no—
87C8—121no—
88C2×C3—161no—
89D3—162no—
90C22—31no—
91C22—31no—
92C22—121no—
93C22—121no—
94C22—121no—
95C22#98511yescharacteristic
96C4—31no—
97C4—61no—
98C4—61no—
99C4—61no—
100C4—61no—
101C4—121no—
102C4—121no—
103C4—121no—
104C4#85711yescharacteristic
105C3—161noSylow
106C2—31no—
107C2—31no—
108C2—241no—
109C2C2×#85711yescharacteristic
subgroupG/H
center, hypercenterC4#857
commutator, cosocle, hypocenter#95⋊C3C22
Frattini, socleC23C2×S4
Fitting#376D3
prime radical#4622C2
LCSG ▷ #95⋊C3
UCSC1 ◁ C4

Complements

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

NH ≅ G/Ntype
1. #376⋊C3C2semidirect
3. #4621C2semidirect
9. #376D3semidirect

Maximal subgroups

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

subgroupindex
#376⋊C32
#46222
#46212
#15003
C4×S44