Finite Group Databasebeta

← #1791⋊C3 #68027

Subgroups — #1791⋊C3 #68027

Order 384.

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

normal subgroups only

This group has 118 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#5950C211yesmaximal, characteristic
2#1791C311yesmaximal, characteristic, complemented, Sylow
3#997C411yescharacteristic
4C8×A4—41nomaximal
5#585C2×C311yescharacteristic
6#413—31no—
7#408—31no—
8#41⋊C3—81no—
9C4×A4—41no—
10C4×A4—81no—
112−1+4—61no—
12H(5,𝔽2)—31no—
13H(5,𝔽2)—61no—
14H(5,𝔽2)C3×C411yescharacteristic
15C2×#41—31no—
16C2×#41—61no—
17C2×#41—61no—
18C2×M16—31no—
19C22×C8A411yescharacteristic, complemented
20#101—61no—
21#100—61no—
22C22⋊C8—61no—
23C22⋊C8—61no—
24C2×A4—41no—
25C2×A4—81no—
26SL(2,𝔽3)—81no—
27C3×C8—161no—
28#41—21no—
29#41—62no—
30#41—62no—
31#41—61no—
32#41—62no—
33#41—61no—
34#41—62no—
35#41—62no—
36#41—61no—
37C2×Q8—31no—
38C2×Q8—61no—
39C2×Q8—61no—
40C2×D4—31no—
41C2×D4—31no—
42C2×D4—31no—
43C2×D4—61no—
44C2×D4—62no—
45C2×D4—61no—
46C2×D4—61no—
47C2×D4—61no—
48C22×C4—21no—
49C22×C4—31no—
50C22×C4—31no—
51C22×C4—61no—
52C22×C4C2×A411yescharacteristic
53M16—62no—
54C2×C8—61no—
55C2×C8—61no—
56A4—41no—
57A4—81no—
58C3×C4—161no—
59C23—21no—
60C23—31no—
61C23—31no—
62C23—61no—
63C23C4×A411yescharacteristic
64Q8—21no—
65Q8—62no—
66Q8—61no—
67D4—62no—
68D4—62no—
69D4—62no—
70D4—61no—
71D4—61no—
72D4—62no—
73C2×C4—31no—
74C2×C4—31no—
75C2×C4—31no—
76C2×C4—31no—
77C2×C4—61no—
78C2×C4—61no—
79C2×C4—62no—
80C2×C4—61no—
81C2×C4—61no—
82C2×C4—61no—
83C2×C4—61no—
84C8—41no—
85C8—121no—
86C2×C3—161no—
87C22—31no—
88C22—41no—
89C22—61no—
90C22—61no—
91C22—81no—
92C22—121no—
93C22—121no—
94C22—241no—
95C4—31no—
96C4—61no—
97C4—61no—
98C4#120⋊C311yescharacteristic
99C3—161noSylow
100C2—61no—
101C2—121no—
102C2—121no—
103C2#379⋊C311yescharacteristic
subgroupG/H
center, hypercenterC4#120⋊C3
commutator, hypocenterH(5,𝔽2)C3×C4
FrattiniC22×C4C2×A4
Fitting#1791C3
socleC2#379⋊C3
prime radical#5950C2
cosocle#585C2×C3
LCSG ▷ H(5,𝔽2)
UCSC1 ◁ C4

Complements

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

NH ≅ G/Ntype
2. #1791C3semidirect
19. C22×C8A4semidirect

Maximal subgroups

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

subgroupindex
#59502
#17913
C8×A44