Finite Group Databasebeta

← #72996

Subgroups — #72996

Order 384.

130 conjugacy classes of subgroups; only the 12 normal subgroups are shown.

normal subgroups only

This group has 130 conjugacy classes of subgroups — too many to draw. Only its 12 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#392⋊C3C211yesmaximal, characteristic, complemented
2#4622C211yesmaximal, characteristic, complemented
3#4621C211yesmaximal, characteristic, complemented
4#1600—31nomaximal, Sylow
5C4×S4—41nomaximal
6#95⋊C3C2211yescharacteristic
7#538—31no—
8#450—31no—
9#447—31no—
10#392D311yescharacteristic, complemented
11#328—31no—
12#327—31no—
13#323—31no—
14C2×S4—41no—
15C4×A4—41no—
16SL(2,ℤ/4)—41no—
17C22×D4—31no—
18C2×SD16—61no—
19C2×D8—61no—
20#126—61no—
21#124—61no—
22#123—61no—
23C22⋊Q8—31no—
24#121—31no—
25#121—61no—
26#120—61no—
27C4×D4—61no—
28C2×C22⋊C4—31no—
29#102—61no—
30#102—61no—
31C22⋊C8—31no—
32C22⋊C8—31no—
33#95C2×D311yescharacteristic
34C2×A4—41no—
35S4—42no—
36C4×D3—161no—
37C24—31no—
38C2×Q8—31no—
39C2×D4—31no—
40C2×D4—61no—
41C2×D4—61no—
42C2×D4—61no—
43C2×D4—61no—
44C2×D4—61no—
45C2×D4—122no—
46C22×C4—31no—
47C22×C4—61no—
48C22×C4S411yescharacteristic
49SD16—122no—
50D8—122no—
51C2×C8—61no—
52C2×C8—61no—
53C4⋊C4—31no—
54C4⋊C4—31no—
55C4⋊C4—61no—
56C4⋊C4—61no—
57C22⋊C4—61no—
58C22⋊C4—61no—
59C22⋊C4—61no—
60C22⋊C4—61no—
61C22⋊C4—61no—
62C22⋊C4—61no—
63C22⋊C4—61no—
64C42—61no—
65C2×D3—161no—
66A4—41no—
67C3×C4—161no—
68Dic3—161no—
69C23—61no—
70C23—61no—
71C23—61no—
72C23—61no—
73C23—121no—
74C23—121no—
75C23C2×S411yescharacteristic
76Q8—121no—
77D4—62no—
78D4—62no—
79D4—121no—
80D4—121no—
81D4—121no—
82D4—121no—
83D4—121no—
84D4—241no—
85D4—241no—
86C2×C4—31no—
87C2×C4—31no—
88C2×C4—61no—
89C2×C4—61no—
90C2×C4—61no—
91C2×C4—61no—
92C2×C4—121no—
93C2×C4—241no—
94C8—121no—
95C8—121no—
96C2×C3—161no—
97D3—162no—
98C22—31no—
99C22—31no—
100C22—122no—
101C22—121no—
102C22—121no—
103C22—121no—
104C22—121no—
105C22—121no—
106C22—121no—
107C22—241no—
108C22#98511yescharacteristic
109C4—41no—
110C4—61no—
111C4—61no—
112C4—121no—
113C4—121no—
114C4—121no—
115C3—161noSylow
116C2—31no—
117C2—31no—
118C2—241no—
119C2—241no—
120C2#857⋊C211yescharacteristic
subgroupG/H
center, hypercenterC2#857⋊C2
commutator, cosocle, hypocenter#95⋊C3C22
Frattini, socleC23C2×S4
Fitting#392D3
LCSG ▷ #95⋊C3
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. #392⋊C3C2semidirect
2. #4622C2semidirect
3. #4621C2semidirect
10. #392D3semidirect

Maximal subgroups

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

subgroupindex
#392⋊C32
#46222
#46212
#16003
C4×S44