Finite Group Databasebeta

← #2825⋊C3 #73207

Subgroups — #2825⋊C3 #73207

Order 384.

122 conjugacy classes of subgroups; only the 20 normal subgroups are shown.

normal subgroups only

This group has 122 conjugacy classes of subgroups — too many to draw. Only its 20 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
3#392⋊C3C211yesmaximal, characteristic, complemented
4#2825C311yesmaximal, characteristic, complemented, Sylow
5C2×C4×A4—41nomaximal
6#95⋊C3C2211yescharacteristic
7#401C2×C311yescharacteristic, complemented
8#397—31no—
9#396C2×C311yescharacteristic
10#394—31no—
11#392—31no—
12#392C2×C311yescharacteristic, complemented
13#386—31no—
14C22×A4—41no—
15C4×A4—41no—
16C4×A4—41no—
17C22×D4—31no—
18C22×D4—31no—
19C23×C4A411yescharacteristic
20C2×C4⋊C4—31no—
21C2×C22⋊C4—31no—
22C2×C22⋊C4—31no—
23C2×C22⋊C4—31no—
24C2×C22⋊C4—31no—
25C2×C22⋊C4—31no—
26#95—31no—
27#95—31no—
28#95—31no—
29#95C22×C311yescharacteristic
30C2×A4—42no—
31C2×A4—41no—
32C2×C3×C4—161no—
33C24—31no—
34C24C2×A411yescharacteristic
35C2×D4—62no—
36C2×D4—121no—
37C2×D4—121no—
38C2×D4—121no—
39C2×D4—121no—
40C2×D4—121no—
41C22×C4—31no—
42C22×C4—31no—
43C22×C4—31no—
44C22×C4—121no—
45C22×C4C2×A411yescharacteristic
46C22×C4C2×A411yescharacteristic
47C4⋊C4—121no—
48C22⋊C4—121no—
49C22⋊C4—121no—
50C22⋊C4—121no—
51C22⋊C4—121no—
52C22⋊C4—121no—
53C22×C3—161no—
54A4—41no—
55C3×C4—161no—
56C3×C4—161no—
57C23—61no—
58C23—61no—
59C23—61no—
60C23—61no—
61C23—61no—
62C23—61no—
63C23—61no—
64C23—61no—
65C23—61no—
66C23#41⋊C312yes—
67C23C22×A411yescharacteristic
68D4—124no—
69D4—124no—
70C2×C4—41no—
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—61no—
81C2×C4—61no—
82C2×C4—121no—
83C2×C3—162no—
84C2×C3—161no—
85C22—31no—
86C22—31no—
87C22—41no—
88C22—62no—
89C22—121no—
90C22—121no—
91C22—121no—
92C22—121no—
93C22—121no—
94C22—121no—
95C22—121no—
96C22—121no—
97C22C2×#41⋊C311yescharacteristic
98C4—41no—
99C4—41no—
100C4—121no—
101C4—121no—
102C4—121no—
103C3—161noSylow
104C2—31no—
105C2—31no—
106C2—42no—
107C2—241no—
108C2#560⋊C311yescharacteristic
subgroupG/H
center, hypercenterC2#560⋊C3
commutator, cosocle, hypocenter#95C22×C3
Frattini, socleC23C22×A4
Fitting#2825C3
LCSG ▷ #95
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. #401⋊C3C2semidirect
2. #396⋊C3C2semidirect
3. #392⋊C3C2semidirect
4. #2825C3semidirect
7. #401C2×C3semidirect
12. #392C2×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
#392⋊C32
#28253
C2×C4×A44