Finite Group Databasebeta

← #3567⋊C3 #85662

Subgroups — #3567⋊C3 #85662

Order 384.

185 conjugacy classes of subgroups; only the 17 normal subgroups are shown.

normal subgroups only

This group has 185 conjugacy classes of subgroups — too many to draw. Only its 17 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#564⋊C3C211yesmaximal, characteristic, complemented
2#3567C311yesmaximal, characteristic, complemented, Sylow
3#127⋊C3—42nomaximal
4#126⋊C3—42nomaximal
5C2×C42⋊C3—41nomaximal
6#564C2×C311yescharacteristic, complemented
7#562—31no—
8#553—32no—
9#552—32no—
10#540—32no—
11#539—32no—
12#529—31no—
13C42⋊C3—41no—
14C42⋊C3—42no—
15C42⋊C3—42no—
16#127A412yes—
17#126—32no—
18#126—32no—
19#126A412yes—
20#125—32no—
21#125—31no—
22#125—32no—
23#125—32no—
24#124—31no—
25#123—32no—
26#123—32no—
27#123—32no—
28#123—32no—
29#123—32no—
30C22⋊Q8—31no—
31C22⋊Q8—32no—
32C22⋊Q8—32no—
33#121—31no—
34#121—32no—
35#121—32no—
36#121—32no—
37#121—32no—
38C4×Q8—31no—
39C4×D4—32no—
40C4×D4—31no—
41C4×D4—32no—
42C4×D4—32no—
43#117—32no—
44#117—32no—
45C2×C4⋊C4—32no—
46C2×C42A411yescharacteristic
47C2×A4—161no—
48C2×Q8—31no—
49C2×D4—32no—
50C2×D4—32no—
51C2×D4—31no—
52C2×D4—32no—
53C22×C4—32no—
54C22×C4—32no—
55C22×C4—32no—
56C22×C4—31no—
57C4⋊C4—32no—
58C4⋊C4—32no—
59C4⋊C4—32no—
60C4⋊C4—32no—
61C4⋊C4—32no—
62C4⋊C4—32no—
63C4⋊C4—32no—
64C4⋊C4—32no—
65C4⋊C4—31no—
66C4⋊C4—31no—
67C22⋊C4—32no—
68C22⋊C4—32no—
69C22⋊C4—32no—
70C22⋊C4—32no—
71C22⋊C4—32no—
72C22⋊C4—32no—
73C22⋊C4—32no—
74C42—31no—
75C42—32no—
76C42C2×A411yescharacteristic
77C42C2×A412yes—
78C42C2×A412yes—
79A4—161no—
80C23—32no—
81C23C22⋊A411yescharacteristic
82Q8—121no—
83D4—122no—
84D4—122no—
85D4—122no—
86D4—121no—
87C2×C4—31no—
88C2×C4—31no—
89C2×C4—32no—
90C2×C4—32no—
91C2×C4—32no—
92C2×C4—122no—
93C2×C4—121no—
94C2×C4—122no—
95C2×C4—122no—
96C2×C3—641no—
97C22—61no—
98C22—62no—
99C22—62no—
100C22—62no—
101C22C2×C22⋊A411yescharacteristic
102C4—61no—
103C4—62no—
104C4—62no—
105C4—62no—
106C4—61no—
107C3—641noSylow
108C2—31no—
109C2—41no—
110C2—122no—
subgroupG/H
center, hypercenterC1G
commutator, cosocle, hypocenter#564C2×C3
Frattini, socleC22C2×C22⋊A4
Fitting#3567C3
LCSG ▷ #564
UCSC1

Complements

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

NH ≅ G/Ntype
1. #564⋊C3C2semidirect
2. #3567C3semidirect
6. #564C2×C3semidirect

Maximal subgroups

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

subgroupindex
#564⋊C32
#35673
#127⋊C34
#126⋊C34
C2×C42⋊C34