Finite Group Databasebeta

← #2801⋊C3 #73202

Subgroups — #2801⋊C3 #73202

Order 384.

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

normal subgroups only

This group has 105 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#401⋊C3C211yesmaximal, characteristic, complemented
2#399⋊C3C211yesmaximal, characteristic, complemented
3#396⋊C3C211yesmaximal, characteristic, complemented
4#2801C311yesmaximal, characteristic, complemented, Sylow
5D4×A4—41nomaximal
6#95⋊C3C2211yescharacteristic
7#401C2×C311yescharacteristic, complemented
8#399C2×C311yescharacteristic, complemented
9#396C2×C311yescharacteristic, complemented
10#394—31no—
11#389—31no—
12#388—31no—
13#388—31no—
14C22×A4—41no—
15C22×A4—41no—
16C4×A4—41no—
17C22×D4A411yescharacteristic
18C2×C4⋊C4—31no—
19C2×C4⋊C4—31no—
20C2×C4⋊C4—31no—
21C2×C22⋊C4—31no—
22C2×C22⋊C4—31no—
23C2×C22⋊C4—31no—
24C2×C22⋊C4—31no—
25C2×C42—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—121no—
37C22×C4—31no—
38C22×C4—31no—
39C22×C4—31no—
40C22×C4—31no—
41C22×C4C2×A411yescharacteristic
42C4⋊C4—62no—
43C4⋊C4—121no—
44C4⋊C4—121no—
45C22⋊C4—62no—
46C22⋊C4—62no—
47C22⋊C4—121no—
48C22⋊C4—121no—
49C42—121no—
50C22×C3—161no—
51C22×C3—161no—
52A4—41no—
53C3×C4—161no—
54C23—21no—
55C23—21no—
56C23—61no—
57C23—61no—
58C23—61no—
59C23—61no—
60C23C22×A411yescharacteristic
61D4—41no—
62D4—121no—
63C2×C4—32no—
64C2×C4—61no—
65C2×C4—61no—
66C2×C4—61no—
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×C3—161no—
77C2×C3—321no—
78C2×C3—321no—
79C22—31no—
80C22—31no—
81C22—41no—
82C22—41no—
83C22—121no—
84C22—121no—
85C22—121no—
86C22—121no—
87C222−1+4⋊C311yescharacteristic
88C4—41no—
89C4—62no—
90C4—121no—
91C4—121no—
92C4—121no—
93C3—161noSylow
94C2—31no—
95C2—31no—
96C2—81no—
97C2—81no—
98C2#560⋊C311yescharacteristic
subgroupG/H
center, hypercenterC2#560⋊C3
commutator, cosocle, hypocenter#95C22×C3
Frattini, socleC23C22×A4
Fitting#2801C3
LCSG ▷ #95
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. #401⋊C3C2semidirect
2. #399⋊C3C2semidirect
3. #396⋊C3C2semidirect
4. #2801C3semidirect
7. #401C2×C3semidirect
8. #399C2×C3semidirect
9. #396C2×C3semidirect

Maximal subgroups

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

subgroupindex
#401⋊C32
#399⋊C32
#396⋊C32
#28013
D4×A44