Finite Group Databasebeta

← #71899

Subgroups — #71899

Order 384.

202 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 202 conjugacy classes of subgroups — too many to draw. Only its 57 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
1C3×#544C211yesmaximal, characteristic
2#5044C212yesmaximal
3#4986C211yesmaximal, characteristic
4#4538C212yesmaximal
5#4528C211yesmaximal, characteristic
6#1617—31nomaximal, Sylow
7C3×C4⋊Q8—22no—
8C3×#125—22no—
9C3×C22⋊Q8—21no—
10C3×C22⋊Q8C2212yes—
11C3×#117—21no—
12C2×C3×C4⋊C4C2211yescharacteristic
13C2×C4⋊Dic3C2211yescharacteristic
14#835—22no—
15C3⋊#95—21no—
16C3⋊#95—21no—
17C3⋊#95C2211yescharacteristic
18#830C2212yes—
19#807—22no—
20#544D311yescharacteristic
21#484—32no—
22#400—31no—
23#328—32no—
24#324—31no—
25C2×C3×Q8—21no—
26C2×C3×Q8D412yes—
27C22×C3×C4D411yescharacteristic
28C22×C3×C4D411yescharacteristic
29C22×C3×C4C2311yescharacteristic
30C22×Dic3—21no—
31C22×Dic3—21no—
32C3×C4⋊C4—21no—
33C3×C4⋊C4—21no—
34C3×C4⋊C4—21no—
35C3×C4⋊C4—22no—
36C3×C4⋊C4—22no—
37C3×C4⋊C4—22no—
38C3×C4⋊C4D412yes—
39C3×C22⋊C4—22no—
40C3×C42—22no—
41C4⋊Dic3—22no—
42C2×C3⋊C8—22no—
43C4⋊Q8—22no—
44#125—22no—
45C22⋊Q8—21no—
46C22⋊Q8C2×D312yes—
47#117—21no—
48C2×C4⋊C4—31no—
49C2×C4⋊C4C2×D311yescharacteristic
50#107—62no—
51#103—62no—
52C22⋊C8—32no—
53#95—31no—
54#95—61no—
55#95—61no—
56C23×C3C2×D411yescharacteristic
57C3×Q8—42no—
58C3×Q8—81no—
59C2×C3×C4—21no—
60C2×C3×C4—21no—
61C2×C3×C4—22no—
62C2×C3×C4—22no—
63C2×C3×C4—21no—
64C2×C3×C4—41no—
65C2×C3×C4—41no—
66C2×C3×C4Q1612yes—
67C2×C3×C4C2×D412yes—
68C2×Dic3—41no—
69C2×Dic3—41no—
70C2×Dic3—42no—
71C2×Dic3—41no—
72C2×Dic3—41no—
73C3⋊C8—42no—
74C2×Q8—21no—
75C2×Q8#6712yes—
76C22×C4—61no—
77C22×C4—61no—
78C22×C4#6711yescharacteristic
79C22×C4#6711yescharacteristic
80C22×C4C22×D311yescharacteristic
81C2×C8—62no—
82C4⋊C4—21no—
83C4⋊C4—21no—
84C4⋊C4—21no—
85C4⋊C4—22no—
86C4⋊C4—22no—
87C4⋊C4—22no—
88C4⋊C4—62no—
89C4⋊C4#6712yes—
90C22⋊C4—22no—
91C42—22no—
92C22×C3—21no—
93C22×C3—21no—
94C22×C3#12011yescharacteristic
95C22×C3C2×Q1611yescharacteristic
96C22×C3#13711yescharacteristic
97C3×C4—22no—
98C3×C4—22no—
99C3×C4—42no—
100C3×C4—41no—
101C3×C4—42no—
102Dic3—81no—
103Dic3—81no—
104C23C2×#6711yescharacteristic
105Q8—42no—
106Q8—81no—
107C2×C4—21no—
108C2×C4—21no—
109C2×C4—22no—
110C2×C4—22no—
111C2×C4—21no—
112C2×C4—41no—
113C2×C4—41no—
114C2×C4—121no—
115C2×C4—121no—
116C2×C4—122no—
117C2×C4—121no—
118C2×C4—121no—
119C2×C4#21612yes—
120C2×C4C2×#6712yes—
121C8—122no—
122C2×C3—21no—
123C2×C3—21no—
124C2×C3#45111yescharacteristic
125C2×C3#45411yescharacteristic
126C2×C3#45811yescharacteristic
127C22—21no—
128C22—21no—
129C22#94211yescharacteristic
130C22C2×#21611yescharacteristic
131C22#95311yescharacteristic
132C4—22no—
133C4—22no—
134C4—41no—
135C4—42no—
136C4—42no—
137C4—241no—
138C4—241no—
139C3#161711yescharacteristic, complemented, Sylow
140C2—21no—
141C2—21no—
142C2#522811yescharacteristic
143C2#524311yescharacteristic
144C2#524511yescharacteristic
subgroupG/H
centerC22#953
commutator, cosocleC22×C3×C4C23
FrattiniC22×C4C22×D3
FittingC3×#544C2
socleC22×C3#120
prime radicalC23×C3C2×D4
hypercenter#544D3
hypocenterC3#1617
LCSG ▷ C22×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22 ◁ C22×C4 ◁ #544

Complements

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

NH ≅ G/Ntype
139. C3#1617semidirect

Maximal subgroups

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

subgroupindex
C3×#5442
#50442
#49862
#45382
#45282
#16173