Finite Group Databasebeta

← #78438⋊C3 #11921202

Subgroups — #78438⋊C3 #11921202

Order 1152.

202 conjugacy classes of subgroups; only the 29 normal subgroups are shown.

normal subgroups only

This group has 202 conjugacy classes of subgroups — too many to draw. Only its 29 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×#401⋊C3C211yesmaximal, characteristic, complemented
2C3⋊(#399⋊C3)C211yesmaximal, characteristic
3C3⋊(#401⋊C3)C211yesmaximal, characteristic, complemented
4#78438C311yesmaximal, characteristic, complemented
5#2834⋊C3—31nomaximal
6C4×D3×A4—41nomaximal
7C3×#95⋊C3C2211yescharacteristic
8C3×#401C2×C311yescharacteristic, complemented
9#4677C2×C311yescharacteristic
10#4675—31no—
11#4668—31no—
12C3⋊#401C2×C311yescharacteristic, complemented
13#4661—31no—
14#4657—31no—
15#401⋊C3—21no—
16#401⋊C3—31no—
17#401⋊C3D311yescharacteristic, complemented
18#399⋊C3—31no—
19C2×D3×A4—41no—
20C3×C4×A4—41no—
21Dic3×A4—41no—
22#2834—31noSylow
23C22×C4×D3A411yescharacteristic
24C2×C4×A4—121no—
25C2×(C2×D3)⋊C4—31no—
26C2×(C2×D3)⋊C4—31no—
27C2×C4⋊Dic3—31no—
28C2×C4⋊Dic3—31no—
29C2×Dic3⋊C4—31no—
30C2×Dic3⋊C4—31no—
31C3×#95—31no—
32C3×#95—31no—
33C3×#95C22×C311yescharacteristic
34C3⋊#95—31no—
35C3⋊#95—31no—
36C3⋊#95—31no—
37#95⋊C3—21no—
38#95⋊C3C2×D311yescharacteristic
39C2×C3×A4—41no—
40D3×A4—42no—
41C3×C4×D3—161no—
42#401—31no—
43#401C3×D311yescharacteristic, complemented
44#399—31no—
45#398—91no—
46#398—91no—
47#397—91no—
48#385—91no—
49C23×D3C2×A411yescharacteristic
50C22×A4—121no—
51C22×C3×C4—31no—
52C22×C3×C4—31no—
53C22×C3×C4C2×A411yescharacteristic
54C22×Dic3—31no—
55C22×Dic3—31no—
56C22×Dic3C2×A411yescharacteristic
57C2×C4×D3—121no—
58C4×A4—41no—
59C4×A4—81no—
60C4×A4—121no—
61(C2×D3)⋊C4—62no—
62(C2×D3)⋊C4—121no—
63C4⋊Dic3—121no—
64C4⋊Dic3—121no—
65Dic3⋊C4—121no—
66Dic3⋊C4—121no—
67C2×C3×D3—161no—
68C3×A4—41no—
69C32×C4—161no—
70C3×Dic3—161no—
71C23×C4—31no—
72C2×C4⋊C4—91no—
73C2×C4⋊C4—91no—
74C2×C4⋊C4—91no—
75C2×C4⋊C4—91no—
76C2×C22⋊C4—91no—
77C2×C22⋊C4—91no—
78#95—31no—
79#95—31no—
80#95—91no—
81#95—91no—
82#95—91no—
83#95C2×C3×D311yescharacteristic
84C23×C3C22×A411yescharacteristic
85C22×D3—61no—
86C22×D3—61no—
87C22×D3#41⋊C312yes—
88C2×A4—41no—
89C2×A4—81no—
90C2×A4—122no—
91C2×C3×C4—61no—
92C2×C3×C4—61no—
93C2×C3×C4—61no—
94C2×C3×C4—62no—
95C2×C3×C4—61no—
96C2×C3×C4—61no—
97C2×C3×C4—481no—
98C2×Dic3—61no—
99C2×Dic3—61no—
100C2×Dic3—61no—
101C2×Dic3—61no—
102C2×Dic3—61no—
103C2×Dic3—61no—
104C2×Dic3—61no—
105C4×D3—41no—
106C4×D3—121no—
107C2×C32—161no—
108C3×D3—162no—
109C24—31no—
110C22×C4—31no—
111C22×C4—31no—
112C22×C4—31no—
113C22×C4—91no—
114C22×C4—91no—
115C22×C4—361no—
116C22×C4D3×A411yescharacteristic
117C4⋊C4—361no—
118C4⋊C4—361no—
119C4⋊C4—361no—
120C4⋊C4—361no—
121C22⋊C4—182no—
122C22⋊C4—361no—
123C22×C3—31no—
124C22×C3—31no—
125C22×C3—481no—
126C22×C3C2×#41⋊C311yescharacteristic
127C2×D3—41no—
128C2×D3—62no—
129C2×D3—121no—
130A4—41no—
131A4—81no—
132C3×C4—41no—
133C3×C4—121no—
134C3×C4—121no—
135C3×C4—161no—
136C3×C4—321no—
137C3×C4—481no—
138Dic3—41no—
139Dic3—121no—
140Dic3—121no—
141C32—161noSylow
142C23—32no—
143C23—181no—
144C23—181no—
145C23C2×D3×A411yescharacteristic
146C2×C4—61no—
147C2×C4—61no—
148C2×C4—61no—
149C2×C4—62no—
150C2×C4—61no—
151C2×C4—61no—
152C2×C4—121no—
153C2×C4—181no—
154C2×C4—181no—
155C2×C4—181no—
156C2×C4—181no—
157C2×C4—181no—
158C2×C4—181no—
159C2×C4—181no—
160C2×C4—361no—
161C2×C3—31no—
162C2×C3—31no—
163C2×C3—161no—
164C2×C3—321no—
165C2×C3—482no—
166C2×C3#560⋊C311yescharacteristic
167D3—42no—
168C22—31no—
169C22—31no—
170C22—121no—
171C22—182no—
172C22—361no—
173C22D3×#41⋊C311yescharacteristic
174C4—41no—
175C4—121no—
176C4—121no—
177C4—121no—
178C4—361no—
179C4—361no—
180C3—161no—
181C3—321no—
182C3#2834⋊C311yescharacteristic, complemented
183C2—31no—
184C2—31no—
185C2—122no—
186C2(#126⋊C3)⋊D311yescharacteristic
subgroupG/H
center, hypercenterC2(#126⋊C3)⋊D3
commutator, cosocle, hypocenterC3×#95C22×C3
FrattiniC23C2×D3×A4
FittingC3×#401C2×C3
socleC23×C3C22×A4
prime radicalC3⋊(#399⋊C3)C2
LCSG ▷ C3×#95
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C3×#401⋊C3C2semidirect
3. C3⋊(#401⋊C3)C2semidirect
4. #78438C3semidirect
8. C3×#401C2×C3semidirect
12. C3⋊#401C2×C3semidirect
17. #401⋊C3D3semidirect
43. #401C3×D3semidirect
182. C3#2834⋊C3semidirect

Maximal subgroups

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

subgroupindex
C3×#401⋊C32
C3⋊(#399⋊C3)2
C3⋊(#401⋊C3)2
#784383
#2834⋊C33
C4×D3×A44