Finite Group Databasebeta

← #71891

Subgroups — #71891

Order 384.

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

normal subgroups only

This group has 236 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×#543C211yesmaximal, characteristic
2#5044C212yesmaximal, complemented
3#4949C211yesmaximal, characteristic
4#4538C212yesmaximal, complemented
5#4525C211yesmaximal, characteristic
6#1614—31nomaximal, Sylow
7C3×C22⋊Q8—22no—
8C3×C22⋊Q8—21no—
9C3×C22⋊Q8—22no—
10C3×C22⋊Q8C2212yes—
11C2×C3×C22⋊C4—21no—
12C2×C3×C22⋊C4C2211yescharacteristic
13C2×#217—21no—
14C2×C4⋊Dic3C2211yescharacteristic
15C2×Dic3⋊C4—21no—
16#835—22no—
17C3⋊#95C2211yescharacteristic
18#830C2212yes—
19#807—22no—
20#543D311yescharacteristic
21#484—32no—
22#399—31no—
23#328—32no—
24#323—31no—
25C24×C3D411yescharacteristic
26C2×C3×Q8—21no—
27C2×C3×Q8D412yes—
28C22×C3×C4—21no—
29C22×C3×C4—21no—
30C22×C3×C4D411yescharacteristic
31C22×C3×C4C2311yescharacteristic
32C22×Dic3—21no—
33C22×Dic3—21no—
34C3×C4⋊C4—21no—
35C3×C4⋊C4—22no—
36C3×C4⋊C4—22no—
37C3×C4⋊C4D412yes—
38C3×C22⋊C4—22no—
39C3×C22⋊C4—22no—
40C3×C22⋊C4—22no—
41#217—42no—
42C4⋊Dic3—22no—
43Dic3⋊C4—42no—
44C2×C3⋊C8—22no—
45C22⋊Q8—22no—
46C22⋊Q8—21no—
47C22⋊Q8—22no—
48C22⋊Q8C2×D312yes—
49C2×C4⋊C4—31no—
50C2×C4⋊C4—61no—
51C2×C22⋊C4—21no—
52C2×C22⋊C4—61no—
53C2×C22⋊C4C2×D311yescharacteristic
54#107—62no—
55#103—62no—
56C22⋊C8—32no—
57#95—31no—
58C23×C3—21no—
59C23×C3—21no—
60C23×C3—41no—
61C23×C3—41no—
62C23×C3Q1612yes—
63C23×C3C2×D411yescharacteristic
64C3×Q8—42no—
65C3×Q8—81no—
66C2×C3×C4—22no—
67C2×C3×C4—21no—
68C2×C3×C4—22no—
69C2×C3×C4—41no—
70C2×C3×C4—41no—
71C2×C3×C4—81no—
72C2×C3×C4—81no—
73C2×C3×C4C2×D412yes—
74C2×Dic3—22no—
75C2×Dic3—41no—
76C2×Dic3—41no—
77C2×Dic3—41no—
78C2×Dic3—41no—
79C2×Dic3—41no—
80C3⋊C8—42no—
81C24#6711yescharacteristic
82C2×Q8—21no—
83C2×Q8#6712yes—
84C22×C4—21no—
85C22×C4—21no—
86C22×C4—61no—
87C22×C4—61no—
88C22×C4#6711yescharacteristic
89C22×C4C22×D311yescharacteristic
90C2×C8—62no—
91C4⋊C4—21no—
92C4⋊C4—22no—
93C4⋊C4—22no—
94C4⋊C4—62no—
95C4⋊C4—122no—
96C4⋊C4#6712yes—
97C22⋊C4—22no—
98C22⋊C4—22no—
99C22⋊C4—22no—
100C22⋊C4—122no—
101C22×C3—21no—
102C22×C3—21no—
103C22×C3—22no—
104C22×C3—42no—
105C22×C3—41no—
106C22×C3—41no—
107C22×C3—81no—
108C22×C3#12011yescharacteristic
109C22×C3C2×Q1611yescharacteristic
110C22×C3#13711yescharacteristic
111C3×C4—22no—
112C3×C4—41no—
113C3×C4—42no—
114C3×C4—42no—
115Dic3—42no—
116Dic3—81no—
117C23—21no—
118C23—21no—
119C23—41no—
120C23—41no—
121C23#21612yes—
122C23C2×#6711yescharacteristic
123Q8—42no—
124Q8—81no—
125C2×C4—22no—
126C2×C4—21no—
127C2×C4—22no—
128C2×C4—41no—
129C2×C4—41no—
130C2×C4—62no—
131C2×C4—81no—
132C2×C4—81no—
133C2×C4—121no—
134C2×C4—121no—
135C2×C4—121no—
136C2×C4—121no—
137C2×C4—121no—
138C2×C4C2×#6712yes—
139C8—122no—
140C2×C3—21no—
141C2×C3—21no—
142C2×C3—42no—
143C2×C3#45111yescharacteristic
144C2×C3#45311yescharacteristic
145C2×C3#45811yescharacteristic
146C22—21no—
147C22—21no—
148C22—22no—
149C22—42no—
150C22—41no—
151C22—41no—
152C22—81no—
153C22#94211yescharacteristic
154C22C2×#21611yescharacteristic
155C22#95311yescharacteristic
156C4—22no—
157C4—41no—
158C4—42no—
159C4—42no—
160C4—122no—
161C4—241no—
162C3#161411yescharacteristic, complemented, Sylow
163C2—21no—
164C2—21no—
165C2—42no—
166C2#522811yescharacteristic
167C2#524111yescharacteristic
168C2#524311yescharacteristic
subgroupG/H
centerC22#953
commutator, cosocleC22×C3×C4C23
FrattiniC22×C4C22×D3
FittingC3×#543C2
socleC22×C3#120
prime radicalC24×C3D4
hypercenter#543D3
hypocenterC3#1614
LCSG ▷ C22×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22 ◁ C22×C4 ◁ #543

Complements

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

NH ≅ G/Ntype
2. #5044C2semidirect
4. #4538C2semidirect
162. C3#1614semidirect

Maximal subgroups

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

subgroupindex
C3×#5432
#50442
#49492
#45382
#45252
#16143