Finite Group Databasebeta

← #71874

Subgroups — #71874

Order 384.

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

normal subgroups only

This group has 254 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×#537C211yesmaximal, characteristic
2#5033C212yesmaximal, complemented
3#4981C211yesmaximal, characteristic, complemented
4#4537C212yesmaximal, complemented
5#4528C211yesmaximal, characteristic, complemented
6#1610—31nomaximal, Sylow
7C2×C3×#41—21no—
8C3×C22⋊Q8—22no—
9C3×#121—22no—
10C3×#121—21no—
11C3×#121C2212yes—
12C2×C3×C4⋊C4C2211yescharacteristic
13C2×C4⋊Dic3C2211yescharacteristic
14C2×Dic3⋊C4—21no—
15#832—22no—
16C3⋊#95—21no—
17C3⋊#95C2211yescharacteristic
18#830C2212yes—
19#807—22no—
20#537D311yescharacteristic
21#480—32no—
22#398—31no—
23#327—32no—
24#324—31no—
25C3×#41—42no—
26C3×#41—42no—
27C2×C3×Q8—21no—
28C2×C3×D4—21no—
29C2×C3×D4—22no—
30C2×C3×D4—21no—
31C2×C3×D4D412yes—
32C22×C3×C4—22no—
33C22×C3×C4D411yescharacteristic
34C22×C3×C4D411yescharacteristic
35C22×C3×C4C2311yescharacteristic
36C22×Dic3—21no—
37C22×Dic3—21no—
38C3×C4⋊C4—21no—
39C3×C4⋊C4—22no—
40C3×C4⋊C4D412yes—
41C3×C22⋊C4—22no—
42C3×C22⋊C4—22no—
43C4⋊Dic3—22no—
44Dic3⋊C4—42no—
45C2×C3⋊C8—22no—
46C2×#41—21no—
47C22⋊Q8—22no—
48#121—22no—
49#121—21no—
50#121C2×D312yes—
51C2×C4⋊C4—31no—
52C2×C4⋊C4—61no—
53C2×C4⋊C4C2×D311yescharacteristic
54#107—62no—
55#102—62no—
56C22⋊C8—32no—
57#95—31no—
58#95—61no—
59C23×C3—22no—
60C23×C3C2×D411yescharacteristic
61C3×Q8—42no—
62C3×D4—42no—
63C3×D4—42no—
64C3×D4—42no—
65C3×D4—42no—
66C3×D4—81no—
67C2×C3×C4—21no—
68C2×C3×C4—21no—
69C2×C3×C4—21no—
70C2×C3×C4—22no—
71C2×C3×C4—41no—
72C2×C3×C4—44no—
73C2×C3×C4—41no—
74C2×C3×C4D812yes—
75C2×C3×C4C2×D412yes—
76C2×Dic3—22no—
77C2×Dic3—41no—
78C2×Dic3—41no—
79C2×Dic3—41no—
80C2×Dic3—41no—
81C2×Dic3—41no—
82C3⋊C8—42no—
83#41—42no—
84#41—42no—
85C2×Q8—21no—
86C2×D4—21no—
87C2×D4—22no—
88C2×D4—21no—
89C2×D4#6712yes—
90C22×C4—22no—
91C22×C4—61no—
92C22×C4—61no—
93C22×C4#6711yescharacteristic
94C22×C4#6711yescharacteristic
95C22×C4C22×D311yescharacteristic
96C2×C8—62no—
97C4⋊C4—21no—
98C4⋊C4—22no—
99C4⋊C4—62no—
100C4⋊C4—122no—
101C4⋊C4#6712yes—
102C22⋊C4—22no—
103C22⋊C4—22no—
104C22×C3—21no—
105C22×C3—21no—
106C22×C3—42no—
107C22×C3—42no—
108C22×C3—42no—
109C22×C3#12011yescharacteristic
110C22×C3C2×D811yescharacteristic
111C22×C3AGL(1,ℤ/8)11yescharacteristic
112C3×C4—22no—
113C3×C4—22no—
114C3×C4—42no—
115C3×C4—41no—
116Dic3—42no—
117Dic3—81no—
118C23—22no—
119C23C2×#6711yescharacteristic
120Q8—42no—
121D4—42no—
122D4—42no—
123D4—42no—
124D4—42no—
125D4—81no—
126C2×C4—21no—
127C2×C4—21no—
128C2×C4—21no—
129C2×C4—22no—
130C2×C4—41no—
131C2×C4—44no—
132C2×C4—41no—
133C2×C4—62no—
134C2×C4—121no—
135C2×C4—121no—
136C2×C4—121no—
137C2×C4—121no—
138C2×C4—121no—
139C2×C4#21312yes—
140C2×C4C2×#6712yes—
141C8—122no—
142C2×C3—21no—
143C2×C3—21no—
144C2×C3—82no—
145C2×C3#44711yescharacteristic
146C2×C3#45611yescharacteristic
147C2×C3#45811yescharacteristic
148C22—21no—
149C22—21no—
150C22—42no—
151C22—42no—
152C22—42no—
153C22C2×#21311yescharacteristic
154C22#93211yescharacteristic
155C22#95311yescharacteristic
156C4—22no—
157C4—22no—
158C4—42no—
159C4—41no—
160C4—122no—
161C4—241no—
162C3#161011yescharacteristic, complemented, Sylow
163C2—21no—
164C2—21no—
165C2—82no—
166C2#521711yescharacteristic
167C2#524311yescharacteristic
168C2#524611yescharacteristic
subgroupG/H
centerC22#953
commutator, cosocleC22×C3×C4C23
FrattiniC22×C4C22×D3
Fitting, prime radicalC3×#537C2
socleC22×C3#120
hypercenter#537D3
hypocenterC3#1610
LCSG ▷ C22×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22 ◁ C22×C4 ◁ #537

Complements

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

NH ≅ G/Ntype
2. #5033C2semidirect
3. #4981C2semidirect
4. #4537C2semidirect
5. #4528C2semidirect
162. C3#1610semidirect

Maximal subgroups

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

subgroupindex
C3×#5372
#50332
#49812
#45372
#45282
#16103