Finite Group Databasebeta

← #3028⋊C3 #73262

Subgroups — #3028⋊C3 #73262

Order 384.

156 conjugacy classes of subgroups; only the 18 normal subgroups are shown.

normal subgroups only

This group has 156 conjugacy classes of subgroups — too many to draw. Only its 18 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#5950C211yesmaximal, characteristic
2#458⋊C3C212yesmaximal, complemented
3#3028C311yesmaximal, characteristic, complemented, Sylow
4#997C2211yescharacteristic
5Q8×A4—41nomaximal
6#585C2×C311yescharacteristic
7#536—31no—
8#458—32no—
9#458C2×C312yes—
10#410—31no—
11#41⋊C3—81no—
12C4×A4—42no—
13C4×A4—41no—
14C4×A4—81no—
152−1+4—61no—
16H(5,𝔽2)—31no—
17H(5,𝔽2)—61no—
18H(5,𝔽2)C22×C311yescharacteristic
19C2×#41—31no—
20C2×#41—61no—
21C2×#41—61no—
22C22×Q8A411yescharacteristic, complemented
23C4⋊Q8—61no—
24#124—61no—
25#123—32no—
26#123—32no—
27C22⋊Q8—61no—
28C22⋊Q8—61no—
29#117—31no—
30#99—32no—
31#99—32no—
32C2×A4—41no—
33C2×A4—81no—
34C3×Q8—161no—
35SL(2,𝔽3)—81no—
36#41—21no—
37#41—62no—
38#41—62no—
39#41—61no—
40#41—62no—
41#41—61no—
42#41—62no—
43#41—62no—
44#41—61no—
45C2×Q8—31no—
46C2×Q8—61no—
47C2×Q8—61no—
48C2×Q8—61no—
49C2×Q8—61no—
50C2×D4—31no—
51C2×D4—31no—
52C2×D4—31no—
53C2×D4—61no—
54C2×D4—62no—
55C2×D4—61no—
56C2×D4—61no—
57C2×D4—61no—
58C22×C4—21no—
59C22×C4—31no—
60C22×C4—31no—
61C22×C4—61no—
62C22×C4C2×A411yescharacteristic
63C22×C4C2×A412yes—
64C4⋊C4—61no—
65C4⋊C4—62no—
66C4⋊C4—62no—
67C22⋊C4—32no—
68C22⋊C4—62no—
69C22⋊C4—62no—
70C42—61no—
71A4—41no—
72A4—81no—
73C3×C4—162no—
74C3×C4—161no—
75C23—21no—
76C23—31no—
77C23—31no—
78C23—61no—
79C23C22×A411yescharacteristic
80Q8—21no—
81Q8—41no—
82Q8—62no—
83Q8—61no—
84Q8—121no—
85D4—62no—
86D4—62no—
87D4—62no—
88D4—61no—
89D4—61no—
90D4—62no—
91C2×C4—31no—
92C2×C4—31no—
93C2×C4—31no—
94C2×C4—31no—
95C2×C4—61no—
96C2×C4—61no—
97C2×C4—62no—
98C2×C4—62no—
99C2×C4—61no—
100C2×C4—61no—
101C2×C4—61no—
102C2×C4—61no—
103C2×C4—62no—
104C2×C3—161no—
105C22—31no—
106C22—41no—
107C22—61no—
108C22—61no—
109C22—81no—
110C22—121no—
111C22—121no—
112C22—241no—
113C4—31no—
114C4—42no—
115C4—61no—
116C4—61no—
117C4—122no—
118C4#120⋊C311yescharacteristic
119C3—161noSylow
120C2—61no—
121C2—121no—
122C2—121no—
123C2C2×#120⋊C311yescharacteristic
subgroupG/H
center, socleC2C2×#120⋊C3
commutator, cosocle, hypocenterH(5,𝔽2)C22×C3
FrattiniC23C22×A4
Fitting#3028C3
prime radical#5950C2
hypercenterC4#120⋊C3
LCSG ▷ H(5,𝔽2)
UCSC1 ◁ C2 ◁ C4

Complements

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

NH ≅ G/Ntype
2. #458⋊C3C2semidirect
3. #3028C3semidirect
22. C22×Q8A4semidirect

Maximal subgroups

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

subgroupindex
#59502
#458⋊C32
#30283
Q8×A44