Finite Group Databasebeta

← #83055

Subgroups — #83055

Order 384.

380 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 133 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×C3×#125C211yesmaximal, characteristic
2C2×#870C211yesmaximal, characteristic
3#4986C212yesmaximal
4#4985C212yesmaximal
5#4983C212yesmaximal
6#4982C214yesmaximal
7#4981C212yesmaximal
8#4936C211yesmaximal, characteristic
9#2822—31nomaximal, Sylow
10C3×#125—24no—
11C2×C3×C4⋊C4C2212yes—
12C2×C3×C4⋊C4C2212yes—
13C2×C3×C4⋊C4C2211yescharacteristic
14C2×C3×C4⋊C4C2211yescharacteristic
15C2×C3×C42C2211yescharacteristic
16C2×C4⋊Dic3C2211yescharacteristic
17C2×C4⋊Dic3C2211yescharacteristic
18C2×C4⋊Dic3C2212yes—
19C2×Dic3⋊C4C2212yes—
20C2×Dic3⋊C4C2212yes—
21C2×Dic3⋊C4C2214yes—
22#870—24no—
23C3⋊#95C2212yes—
24C3⋊#95C2212yes—
25C3⋊#95C2214yes—
26C3⋊#95C2214yes—
27C3⋊#95C2214yes—
28C2×#125—31no—
29C2×#125D311yescharacteristic
30#400—32no—
31#400—32no—
32#398—32no—
33#398—34no—
34#398—32no—
35#382—31no—
36C22×C3×C4C2312yes—
37C22×C3×C4C2312yes—
38C22×C3×C4C2311yescharacteristic
39C22×C3×C4C2311yescharacteristic
40C22×C3×C4C2311yescharacteristic
41C22×Dic3C2314yes—
42C22×Dic3C2312yes—
43C22×Dic3C2312yes—
44C3×C4⋊C4—24no—
45C3×C4⋊C4—22no—
46C3×C4⋊C4—22no—
47C3×C4⋊C4—24no—
48C3×C42D414yes—
49C4⋊Dic3—22no—
50C4⋊Dic3—22no—
51C4⋊Dic3—42no—
52Dic3⋊C4—24no—
53Dic3⋊C4—24no—
54Dic3⋊C4—44no—
55#125—24no—
56#125—64no—
57C2×C4⋊C4—32no—
58C2×C4⋊C4—31no—
59C2×C4⋊C4—32no—
60C2×C4⋊C4—31no—
61C2×C4⋊C4—32no—
62C2×C4⋊C4—34no—
63C2×C4⋊C4C2×D312yes—
64C2×C4⋊C4C2×D311yescharacteristic
65C2×C4⋊C4C2×D312yes—
66C2×C4⋊C4C2×D311yescharacteristic
67C2×C42C2×D311yescharacteristic
68#95—32no—
69#95—32no—
70#95—34no—
71#95—34no—
72#95—34no—
73C23×C3C2411yescharacteristic
74C2×C3×C4—21no—
75C2×C3×C4—22no—
76C2×C3×C4—22no—
77C2×C3×C4—21no—
78C2×C3×C4—22no—
79C2×C3×C4—22no—
80C2×C3×C4—22no—
81C2×C3×C4—24no—
82C2×C3×C4—22no—
83C2×C3×C4C2×D412yes—
84C2×C3×C4C2×D412yes—
85C2×C3×C4C2×D412yes—
86C2×Dic3—22no—
87C2×Dic3—22no—
88C2×Dic3—22no—
89C2×Dic3—24no—
90C2×Dic3—24no—
91C2×Dic3—24no—
92C2×Dic3—22no—
93C2×Dic3—24no—
94C22×C4—34no—
95C22×C4—32no—
96C22×C4—32no—
97C22×C4C22×D312yes—
98C22×C4C22×D312yes—
99C22×C4C22×D311yescharacteristic
100C22×C4C22×D311yescharacteristic
101C22×C4C22×D311yescharacteristic
102C4⋊C4—24no—
103C4⋊C4—22no—
104C4⋊C4—24no—
105C4⋊C4—22no—
106C4⋊C4—64no—
107C4⋊C4—64no—
108C4⋊C4—62no—
109C4⋊C4—62no—
110C4⋊C4—124no—
111C4⋊C4—122no—
112C42#6714yes—
113C22×C3C22×D411yescharacteristic
114C22×C3H(5,𝔽2)11yescharacteristic
115C22×C32−1+412yes—
116C22×C32−1+412yes—
117C22×C32−1+411yescharacteristic
118C3×C4—22no—
119C3×C4—22no—
120C3×C4—22no—
121C3×C4—42no—
122C3×C4—42no—
123Dic3—42no—
124Dic3—42no—
125Dic3—44no—
126C23C23×D311yescharacteristic
127C2×C4—22no—
128C2×C4—21no—
129C2×C4—22no—
130C2×C4—21no—
131C2×C4—22no—
132C2×C4—24no—
133C2×C4—22no—
134C2×C4—22no—
135C2×C4—22no—
136C2×C4—64no—
137C2×C4—64no—
138C2×C4—64no—
139C2×C4—62no—
140C2×C4—64no—
141C2×C4—62no—
142C2×C4—62no—
143C2×C4—62no—
144C2×C4C2×#6712yes—
145C2×C4C2×#6712yes—
146C2×C4C2×#6712yes—
147C2×C3#53611yescharacteristic
148C2×C3#53611yescharacteristic
149C2×C3#53711yescharacteristic
150C2×C3#56312yes—
151C2×C3#56412yes—
152C22#100712yes—
153C22#100911yescharacteristic
154C22#101011yescharacteristic
155C22#101012yes—
156C22C22×#6711yescharacteristic
157C4—22no—
158C4—22no—
159C4—22no—
160C4—42no—
161C4—42no—
162C4—124no—
163C4—122no—
164C4—122no—
165C3#282211yescharacteristic, complemented, Sylow
166C2C3⋊#56412yes—
167C2#569912yes—
168C2#581611yescharacteristic
169C2#582511yescharacteristic
170C2#583311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D3
commutator, socle, prime radical, cosocleC23×C3C24
FittingC2×C3×#125C2
hypercenterC2×#125D3
hypocenterC3#2822
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
165. C3#2822semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#1252
C2×#8702
#49862
#49852
#49832
#49822
#49812
#49362
#28223