Finite Group Databasebeta

← #83042

Subgroups — #83042

Order 384.

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

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 137 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×C4×Dic6C211yesmaximal, characteristic
3#4986C212yesmaximal
4#4985C212yesmaximal
5#4983C212yesmaximal
6#4979C212yesmaximal
7#4978C214yesmaximal
8#4937C211yesmaximal, characteristic
9#2634—31nomaximal, Sylow
10C22×Dic6C2211yescharacteristic
11C3×#125—24no—
12C2×C3×C4⋊C4C2212yes—
13C2×C3×C4⋊C4C2212yes—
14C2×C3×C4⋊C4C2211yescharacteristic
15C2×C3×C4⋊C4C2211yescharacteristic
16C2×C3×C42C2211yescharacteristic
17C2×C4⋊Dic3C2211yescharacteristic
18C2×Dic3⋊C4C2212yes—
19C2×Dic3⋊C4C2214yes—
20C2×C4×Dic3C2212yes—
21C4×Dic6—24no—
22C3⋊#95C2212yes—
23C3⋊#95C2212yes—
24C3⋊#95C2212yes—
25C3⋊#95C2214yes—
26C3⋊#95C2214yes—
27C3⋊#95C2214yes—
28C2×#125D311yescharacteristic
29C2×C4×Q8—31no—
30#400—32no—
31#400—32no—
32#398—32no—
33#395—32no—
34#387—34no—
35#383—31no—
36C22×C3×C4C2312yes—
37C22×C3×C4C2312yes—
38C22×C3×C4C2311yescharacteristic
39C22×C3×C4C2311yescharacteristic
40C22×C3×C4C2311yescharacteristic
41C22×Dic3C2314yes—
42C22×Dic3C2312yes—
43C22×Dic3C2312yes—
44C2×Dic6—22no—
45C2×Dic6—24no—
46C3×C4⋊C4—24no—
47C3×C4⋊C4—22no—
48C3×C4⋊C4—22no—
49C3×C4⋊C4—24no—
50C3×C42D414yes—
51C4⋊Dic3—22no—
52Dic3⋊C4—24no—
53Dic3⋊C4—28no—
54C4×Dic3—24no—
55C22×Q8—31no—
56#125—24no—
57C4×Q8—64no—
58C2×C4⋊C4—32no—
59C2×C4⋊C4—31no—
60C2×C4⋊C4—34no—
61C2×C4⋊C4C2×D312yes—
62C2×C4⋊C4C2×D312yes—
63C2×C4⋊C4C2×D311yescharacteristic
64C2×C4⋊C4C2×D311yescharacteristic
65C2×C42—32no—
66C2×C42C2×D311yescharacteristic
67#95—32no—
68#95—32no—
69#95—32no—
70#95—34no—
71#95—34no—
72#95—34no—
73C23×C3C2411yescharacteristic
74C2×C3×C4—22no—
75C2×C3×C4—22no—
76C2×C3×C4—22no—
77C2×C3×C4—22no—
78C2×C3×C4—22no—
79C2×C3×C4—24no—
80C2×C3×C4—24no—
81C2×C3×C4C2×D412yes—
82C2×C3×C4C2×D412yes—
83C2×C3×C4C2×D412yes—
84C2×Dic3—22no—
85C2×Dic3—22no—
86C2×Dic3—22no—
87C2×Dic3—24no—
88C2×Dic3—24no—
89C2×Dic3—24no—
90C2×Dic3—24no—
91C2×Dic3#4114yes—
92Dic6—28no—
93C2×Q8—64no—
94C2×Q8—62no—
95C22×C4—32no—
96C22×C4—34no—
97C22×C4—32no—
98C22×C4C22×D312yes—
99C22×C4C22×D312yes—
100C22×C4C22×D311yescharacteristic
101C22×C4C22×D311yescharacteristic
102C22×C4C22×D311yescharacteristic
103C4⋊C4—24no—
104C4⋊C4—22no—
105C4⋊C4—22no—
106C4⋊C4—24no—
107C4⋊C4—68no—
108C4⋊C4—64no—
109C4⋊C4—62no—
110C42—64no—
111C42#6714yes—
112C22×C3C22×D411yescharacteristic
113C22×C3C2×#4112yes—
114C22×C32−1+412yes—
115C22×C32−1+412yes—
116C3×C4—22no—
117C3×C4—22no—
118C3×C4—22no—
119C3×C4—42no—
120C3×C4—42no—
121Dic3—24no—
122Dic3—42no—
123Dic3—44no—
124C23C23×D311yescharacteristic
125Q8—68no—
126C2×C4—22no—
127C2×C4—22no—
128C2×C4—22no—
129C2×C4—24no—
130C2×C4—24no—
131C2×C4—22no—
132C2×C4—22no—
133C2×C4—34no—
134C2×C4—62no—
135C2×C4—62no—
136C2×C4—64no—
137C2×C4—64no—
138C2×C4—64no—
139C2×C4—64no—
140C2×C4—62no—
141C2×C4C2×#6712yes—
142C2×C4C2×#6712yes—
143C2×C4C2×#6712yes—
144C2×C3#52511yescharacteristic
145C2×C3#53611yescharacteristic
146C2×C3#53611yescharacteristic
147C2×C3#54114yes—
148C22#100712yes—
149C22D3×#4112yes—
150C22#101012yes—
151C22C22×#6711yescharacteristic
152C4—22no—
153C4—22no—
154C4—22no—
155C4—42no—
156C4—42no—
157C4—64no—
158C4—124no—
159C4—122no—
160C3#263411yescharacteristic, complemented, Sylow
161C2#569614yes—
162C2#581611yescharacteristic
163C2#582511yescharacteristic
164C2#582811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D3
commutator, socle, prime radical, cosocleC23×C3C24
FittingC2×C3×#125C2
hypercenterC2×#125D3
hypocenterC3#2634
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
160. C3#2634semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#1252
C2×C4×Dic62
#49862
#49852
#49832
#49792
#49782
#49372
#26343