Finite Group Databasebeta

← #72985

Subgroups — #72985

Order 384.

137 conjugacy classes of subgroups; only the 13 normal subgroups are shown.

normal subgroups only

This group has 137 conjugacy classes of subgroups — too many to draw. Only its 13 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
1C2×#95⋊C3C211yesmaximal, characteristic, complemented
2#4622C211yesmaximal, characteristic, complemented
3#4621C211yesmaximal, characteristic, complemented
4#1504—31nomaximal, Sylow
5GL(2,ℤ/4)—41nomaximal
6#95⋊C3C2211yescharacteristic
7#525—31no—
8#407—31no—
9C2×#95D311yescharacteristic, complemented
10#328—31no—
11#328—31no—
12#327—31no—
13#327—31no—
14C22×A4—41no—
15C2×S4—41no—
16SL(2,ℤ/4)—41no—
17C2×#41—31no—
18C23×C4—31no—
19C2×M16—61no—
20#123—61no—
21C22⋊Q8—31no—
22C22⋊Q8—31no—
23#121—31no—
24#121—31no—
25#120—61no—
26C4×D4—61no—
27C4×D4—61no—
28#117—31no—
29C22⋊C8—31no—
30C22⋊C8—31no—
31C22⋊C8—61no—
32#95—31no—
33#95C2×D311yescharacteristic
34C2×A4—41no—
35C2×A4—81no—
36S4—81no—
37#67—161no—
38C24S411yescharacteristic
39#41—122no—
40C2×Q8—31no—
41C2×D4—31no—
42C2×D4—61no—
43C2×D4—61no—
44C2×D4—61no—
45C22×C4—31no—
46C22×C4—31no—
47C22×C4—31no—
48C22×C4—31no—
49C22×C4—31no—
50C22×C4—31no—
51C22×C4—61no—
52C22×C4—122no—
53M16—122no—
54C2×C8—61no—
55C2×C8—61no—
56C4⋊C4—31no—
57C4⋊C4—31no—
58C4⋊C4—61no—
59C4⋊C4—61no—
60C22⋊C4—61no—
61C22⋊C4—61no—
62C22⋊C4—61no—
63C22⋊C4—61no—
64C22⋊C4—61no—
65C42—61no—
66C22×C3—161no—
67C2×D3—161no—
68A4—41no—
69Dic3—161no—
70C23—21no—
71C23—31no—
72C23—31no—
73C23—61no—
74C23—61no—
75C23C2×S411yescharacteristic
76Q8—121no—
77D4—121no—
78D4—121no—
79D4—121no—
80D4—122no—
81D4—121no—
82D4—121no—
83C2×C4—31no—
84C2×C4—31no—
85C2×C4—31no—
86C2×C4—31no—
87C2×C4—62no—
88C2×C4—62no—
89C2×C4—61no—
90C2×C4—61no—
91C2×C4—61no—
92C2×C4—121no—
93C2×C4—121no—
94C2×C4—121no—
95C2×C4—121no—
96C2×C4—122no—
97C8—121no—
98C8—121no—
99C2×C3—161no—
100C2×C3—321no—
101D3—321no—
102C22—31no—
103C22—31no—
104C22—32no—
105C22—31no—
106C22—61no—
107C22—61no—
108C22—61no—
109C22—121no—
110C22—121no—
111C22—121no—
112C22#85711yescharacteristic
113C22#98311yescharacteristic
114C4—61no—
115C4—61no—
116C4—61no—
117C4—61no—
118C4—121no—
119C4—121no—
120C4—121no—
121C3—161noSylow
122C2—21no—
123C2—31no—
124C2—31no—
125C2—61no—
126C2—241no—
127C2C2×#85711yescharacteristic
subgroupG/H
centerC2C2×#857
commutator, cosocle, hypocenter#95⋊C3C22
Frattini, socleC23C2×S4
FittingC2×#95D3
hypercenterC22#857
LCSG ▷ #95⋊C3
UCSC1 ◁ C2 ◁ C22

Complements

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

NH ≅ G/Ntype
1. C2×#95⋊C3C2semidirect
2. #4622C2semidirect
3. #4621C2semidirect
9. C2×#95D3semidirect

Maximal subgroups

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

subgroupindex
C2×#95⋊C32
#46222
#46212
#15043
GL(2,ℤ/4)4