Finite Group Databasebeta

← #2643⋊C3 #73193

Subgroups — #2643⋊C3 #73193

Order 384.

112 conjugacy classes of subgroups; only the 19 normal subgroups are shown.

normal subgroups only

This group has 112 conjugacy classes of subgroups — too many to draw. Only its 19 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#401⋊C3C211yesmaximal, characteristic, complemented
2#396⋊C3C211yesmaximal, characteristic, complemented
3C2×#95⋊C3C211yesmaximal, characteristic, complemented
4#2643C311yesmaximal, characteristic, complemented, Sylow
5D4×A4—41nomaximal
6#95⋊C3C2211yescharacteristic
7#401C2×C311yescharacteristic, complemented
8#400—31no—
9#397—31no—
10#396C2×C311yescharacteristic, complemented
11#386—31no—
12#385—31no—
13C2×#95C2×C311yescharacteristic, complemented
14C22×A4—41no—
15C22×A4—41no—
16C4×A4—41no—
17C22×D4A411yescharacteristic
18C23×C4—31no—
19C2×C4⋊C4—31no—
20C2×C4⋊C4—31no—
21C2×C22⋊C4—31no—
22C2×C22⋊C4—31no—
23C2×C22⋊C4—31no—
24#95—31no—
25#95—31no—
26#95—31no—
27#95—31no—
28#95—31no—
29#95C22×C311yescharacteristic
30C2×A4—41no—
31C2×A4—81no—
32C2×A4—81no—
33C3×D4—161no—
34C24C2×A411yescharacteristic
35C24C2×A411yescharacteristic
36C2×D4—61no—
37C2×D4—61no—
38C22×C4—31no—
39C22×C4—31no—
40C22×C4—31no—
41C22×C4—31no—
42C22×C4—61no—
43C22×C4—61no—
44C22×C4—121no—
45C22×C4—121no—
46C22×C4C2×A411yescharacteristic
47C4⋊C4—121no—
48C4⋊C4—121no—
49C22⋊C4—61no—
50C22⋊C4—61no—
51C22⋊C4—121no—
52C22⋊C4—121no—
53C22×C3—161no—
54C22×C3—161no—
55A4—41no—
56C3×C4—161no—
57C23—21no—
58C23—21no—
59C23—31no—
60C23—31no—
61C23—61no—
62C23—61no—
63C23—61no—
64C23C22×A411yescharacteristic
65D4—41no—
66D4—121no—
67C2×C4—61no—
68C2×C4—61no—
69C2×C4—61no—
70C2×C4—61no—
71C2×C4—61no—
72C2×C4—61no—
73C2×C4—61no—
74C2×C4—61no—
75C2×C4—61no—
76C2×C4—61no—
77C2×C4—61no—
78C2×C4—61no—
79C2×C4—61no—
80C2×C4—122no—
81C2×C4—122no—
82C2×C3—161no—
83C2×C3—321no—
84C2×C3—321no—
85C22—31no—
86C22—31no—
87C22—31no—
88C22—41no—
89C22—61no—
90C22—61no—
91C22—61no—
92C22—61no—
93C22—121no—
94C22—121no—
95C22#126⋊C311yescharacteristic
96C222−1+4⋊C311yescharacteristic
97C4—41no—
98C4—121no—
99C4—121no—
100C4—121no—
101C4—121no—
102C3—161noSylow
103C2—21no—
104C2—31no—
105C2—31no—
106C2—61no—
107C2—81no—
108C2C2×#126⋊C311yescharacteristic
subgroupG/H
centerC2C2×#126⋊C3
commutator, cosocle, hypocenter#95C22×C3
Frattini, socleC23C22×A4
Fitting#2643C3
hypercenterC22#126⋊C3
LCSG ▷ #95
UCSC1 ◁ C2 ◁ C22

Complements

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

NH ≅ G/Ntype
1. #401⋊C3C2semidirect
2. #396⋊C3C2semidirect
3. C2×#95⋊C3C2semidirect
4. #2643C3semidirect
7. #401C2×C3semidirect
10. #396C2×C3semidirect
13. C2×#95C2×C3semidirect

Maximal subgroups

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

subgroupindex
#401⋊C32
#396⋊C32
C2×#95⋊C32
#26433
D4×A44