Finite Group Databasebeta

← #73006

Subgroups — #73006

Order 384.

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

normal subgroups only

This group has 114 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#399⋊C3C211yesmaximal, characteristic, complemented
2#4622C211yesmaximal, characteristic, complemented
3#4621C211yesmaximal, characteristic, complemented
4#1618—31nomaximal, Sylow
5GL(2,ℤ/4)—41nomaximal
6#95⋊C3C2211yescharacteristic
7#538—31no—
8#484—31no—
9#481—31no—
10#399D311yescharacteristic, complemented
11#328—31no—
12#327—31no—
13#323—31no—
14C22×A4—41no—
15C2×S4—41no—
16SL(2,ℤ/4)—41no—
17#126—61no—
18#124—61no—
19#123—61no—
20C22⋊Q8—31no—
21#121—31no—
22#121—61no—
23#120—61no—
24C4×D4—61no—
25C2×C4⋊C4—31no—
26C2×C22⋊C4—31no—
27#107—61no—
28#106—61no—
29#103—61no—
30#102—61no—
31C22⋊C8—31no—
32C22⋊C8—31no—
33#95C2×D311yescharacteristic
34C2×A4—41no—
35C2×A4—81no—
36S4—81no—
37#67—161no—
38C24S411yescharacteristic
39C2×Q8—31no—
40C2×D4—31no—
41C2×D4—61no—
42C2×D4—61no—
43C2×D4—61no—
44C22×C4—31no—
45C22×C4—31no—
46C22×C4—61no—
47C2×C8—61no—
48C2×C8—61no—
49C4⋊C4—31no—
50C4⋊C4—31no—
51C4⋊C4—61no—
52C4⋊C4—61no—
53C4⋊C4—61no—
54C4⋊C4—61no—
55C22⋊C4—61no—
56C22⋊C4—61no—
57C22⋊C4—61no—
58C22⋊C4—61no—
59C22⋊C4—61no—
60C22⋊C4—61no—
61C22⋊C4—61no—
62C42—61no—
63C22×C3—161no—
64C2×D3—161no—
65A4—41no—
66Dic3—161no—
67C23—21no—
68C23—61no—
69C23—61no—
70C23—61no—
71C23C2×S411yescharacteristic
72Q8—121no—
73D4—121no—
74D4—121no—
75D4—121no—
76D4—241no—
77D4—241no—
78C2×C4—31no—
79C2×C4—31no—
80C2×C4—61no—
81C2×C4—61no—
82C2×C4—61no—
83C2×C4—61no—
84C2×C4—121no—
85C2×C4—121no—
86C2×C4—241no—
87C8—121no—
88C8—121no—
89C2×C3—161no—
90C2×C3—321no—
91D3—321no—
92C22—31no—
93C22—31no—
94C22—41no—
95C22—121no—
96C22—121no—
97C22—121no—
98C22—121no—
99C22—121no—
100C22#98311yescharacteristic
101C4—61no—
102C4—61no—
103C4—121no—
104C4—121no—
105C4—121no—
106C4—121no—
107C3—161noSylow
108C2—31no—
109C2—31no—
110C2—81no—
111C2—241no—
112C2#857⋊C211yescharacteristic
subgroupG/H
center, hypercenterC2#857⋊C2
commutator, cosocle, hypocenter#95⋊C3C22
Frattini, socleC23C2×S4
Fitting#399D3
LCSG ▷ #95⋊C3
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. #399⋊C3C2semidirect
2. #4622C2semidirect
3. #4621C2semidirect
10. #399D3semidirect

Maximal subgroups

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

subgroupindex
#399⋊C32
#46222
#46212
#16183
GL(2,ℤ/4)4