Finite Group Databasebeta

← #68376

Subgroups — #68376

Order 384.

172 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 172 conjugacy classes of subgroups — too many to draw. Only its 45 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⋊#564C211yesmaximal, characteristic
2#5064C211yesmaximal, characteristic
3#4703C211yesmaximal, characteristic
4#4702C211yesmaximal, characteristic
5C3×#330C211yesmaximal, characteristic
6#4465C211yesmaximal, characteristic
7#4465C211yesmaximal, characteristic
8#1663—31nomaximal, Sylow
9C3×#125C2211yescharacteristic
10#890—21no—
11#890—21no—
12#889—21no—
13#889—21no—
14#889—21no—
15#889—21no—
16#870C2211yescharacteristic
17#870C2211yescharacteristic
18#869C2211yescharacteristic
19C3×#97C2211yescharacteristic
20C3×#97C2211yescharacteristic
21#818—21no—
22#817—21no—
23#816—21no—
24#816—21no—
25#808—21no—
26#807—21no—
27#803C2211yescharacteristic
28#564—31no—
29#501—31no—
30#501—31no—
31#491—31no—
32#330—31no—
33#330—31no—
34#330D311yescharacteristic
35C2×Dic6—21no—
36C2×C3×C8—21no—
37C2×C3×C8—21no—
38C3×C4⋊C4—21no—
39C3×C4⋊C4—21no—
40C3×C4⋊C4D411yescharacteristic
41C3×C4⋊C4D411yescharacteristic
42C3×C42C2311yescharacteristic
43C4⋊Dic3—21no—
44C4⋊Dic3—21no—
45C4⋊Dic3—21no—
46C4⋊Dic3—21no—
47C4⋊Dic3D411yescharacteristic
48C4⋊Dic3D411yescharacteristic
49C4⋊Dic3D411yescharacteristic
50C4⋊Dic3D411yescharacteristic
51Dic3⋊C4—21no—
52Dic3⋊C4—21no—
53Dic3⋊C4—21no—
54Dic3⋊C4—21no—
55Dic3⋊C4—21no—
56Dic3⋊C4—21no—
57Dic3⋊C4—21no—
58Dic3⋊C4—21no—
59C4×Dic3—21no—
60C4×Dic3—21no—
61C2×C3⋊C8—21no—
62C4⋊Q8—31no—
63#125—31no—
64#125—31no—
65#125—61no—
66#125—61no—
67#125—61no—
68#125—61no—
69#125—61no—
70#125—61no—
71#125C2×D311yescharacteristic
72#107—61no—
73#107—61no—
74#106—61no—
75#106—61no—
76#103—61no—
77#103—61no—
78#97—31no—
79#97C2×D311yescharacteristic
80#97C2×D311yescharacteristic
81C2×C3×C4—21no—
82C2×C3×C4—21no—
83C2×C3×C4C2×D411yescharacteristic
84C2×C3×C4C2×D411yescharacteristic
85C2×C3×C4C2×D411yescharacteristic
86C2×Dic3—21no—
87C2×Dic3—21no—
88C2×Dic3—21no—
89C2×Dic3—21no—
90C2×Dic3—41no—
91Dic6—42no—
92C3×C8—22no—
93C3×C8—41no—
94C3⋊C8—22no—
95C2×Q8—61no—
96C2×C8—21no—
97C2×C8—21no—
98C2×C8—61no—
99C4⋊C4—21no—
100C4⋊C4—21no—
101C4⋊C4—31no—
102C4⋊C4—31no—
103C4⋊C4—31no—
104C4⋊C4—31no—
105C4⋊C4—61no—
106C4⋊C4—61no—
107C4⋊C4—61no—
108C4⋊C4—61no—
109C4⋊C4—61no—
110C4⋊C4—61no—
111C4⋊C4—61no—
112C4⋊C4—61no—
113C4⋊C4—61no—
114C4⋊C4—61no—
115C4⋊C4—61no—
116C4⋊C4—61no—
117C4⋊C4D1211yescharacteristic
118C4⋊C4D1211yescharacteristic
119C42—61no—
120C42—61no—
121C42C22×D311yescharacteristic
122C22×C3#12011yescharacteristic
123C3×C4—21no—
124C3×C4—21no—
125C3×C4—21no—
126C3×C4—41no—
127C3×C4—41no—
128Dic3—41no—
129Dic3—41no—
130Dic3—41no—
131Dic3—41no—
132Dic3—81no—
133Q8—122no—
134C2×C4—21no—
135C2×C4—21no—
136C2×C4—61no—
137C2×C4—61no—
138C2×C4—61no—
139C2×C4—61no—
140C2×C4—121no—
141C2×C4C2×D1211yescharacteristic
142C2×C4D3×D411yescharacteristic
143C2×C4D3×D411yescharacteristic
144C8—22no—
145C8—41no—
146C8—62no—
147C2×C3#45411yescharacteristic
148C2×C3#45611yescharacteristic
149C2×C3#45611yescharacteristic
150C22#88211yescharacteristic
151C4—21no—
152C4—21no—
153C4—21no—
154C4—41no—
155C4—41no—
156C4—121no—
157C4—121no—
158C4—121no—
159C4—121no—
160C4—241no—
161C3#166311yescharacteristic, complemented, Sylow
162C2#475211yescharacteristic
163C2#482611yescharacteristic
164C2#482711yescharacteristic
subgroupG/H
centerC22#882
commutator, cosocleC3×C42C23
FrattiniC42C22×D3
FittingC3×#330C2
socle, prime radicalC22×C3#120
hypercenter#330D3
hypocenterC3#1663
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
161. C3#1663semidirect

Maximal subgroups

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

subgroupindex
C3⋊#5642
#50642
#47032
#47022
C3×#3302
#44652
#16633