Finite Group Databasebeta

← #78435⋊C3 #11921200

Subgroups — #78435⋊C3 #11921200

Order 1152.

238 conjugacy classes of subgroups; only the 27 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 27 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⋊(#401⋊C3)C211yesmaximal, characteristic, complemented
3C3⋊(#392⋊C3)C211yesmaximal, characteristic
4#78435C311yesmaximal, characteristic, complemented
5#2760⋊C3—31nomaximal
6A4×Dic6—41nomaximal
7C3×#95⋊C3C2211yescharacteristic
8C3×#401C2×C311yescharacteristic
9#4673—31no—
10#4671C2×C311yescharacteristic
11#4665—31no—
12#4665—31no—
13#4664—31no—
14C3⋊#401C2×C311yescharacteristic
15#401⋊C3—21no—
16#401⋊C3—31no—
17#401⋊C3D311yescharacteristic, complemented
18#392⋊C3—31no—
19C3×C4×A4—41no—
20Dic3×A4—41no—
21Dic3×A4—41no—
22#2760—31noSylow
23C22×D12—31no—
24C22×C4×D3—31no—
25C22×Dic6A411yescharacteristic
26Q8×A4—121no—
27C2×(C2×D3)⋊C4—31no—
28C2×(C2×D3)⋊C4—31no—
29C2×(C2×D3)⋊C4—31no—
30C2×(C2×D3)⋊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—
40C3×Dic6—161no—
41#401—31no—
42#401C3×D311yescharacteristic
43#393—91no—
44#392—31no—
45#386—91no—
46#386—91no—
47#381—91no—
48C23×D3—31no—
49C22×C3×C4—31no—
50C22×C3×C4—31no—
51C22×C3×C4C2×A411yescharacteristic
52C22×Dic3—31no—
53C22×Dic3C2×A411yescharacteristic
54C22×Dic3C2×A411yescharacteristic
55C2×D12—62no—
56C2×D12—62no—
57C2×D12—121no—
58C2×C4×D3—62no—
59C2×C4×D3—121no—
60C2×C4×D3—121no—
61C2×Dic6—121no—
62C4×A4—41no—
63C4×A4—81no—
64C4×A4—121no—
65C4×A4—121no—
66(C2×D3)⋊C4—121no—
67(C2×D3)⋊C4—121no—
68(C2×D3)⋊C4—121no—
69(C2×D3)⋊C4—121no—
70C3×A4—41no—
71C32×C4—161no—
72C3×Dic3—161no—
73C3×Dic3—161no—
74C22×Q8—31no—
75C22×D4—91no—
76C23×C4—91no—
77C2×C22⋊C4—91no—
78C2×C22⋊C4—91no—
79C2×C22⋊C4—91no—
80C2×C22⋊C4—91no—
81#95—31no—
82#95—31no—
83#95—91no—
84#95—91no—
85#95—91no—
86#95C2×C3×D311yescharacteristic
87C23×C3C22×A411yescharacteristic
88C22×D3—32no—
89C22×D3—61no—
90C22×D3—61no—
91C22×D3—61no—
92C22×D3—61no—
93C22×D3—61no—
94C22×D3—61no—
95C2×A4—41no—
96C2×A4—81no—
97C3×Q8—481no—
98C2×C3×C4—61no—
99C2×C3×C4—61no—
100C2×C3×C4—61no—
101C2×C3×C4—61no—
102C2×C3×C4—61no—
103C2×C3×C4—61no—
104C2×C3×C4—61no—
105C2×Dic3—61no—
106C2×Dic3—61no—
107C2×Dic3—61no—
108C2×Dic3—61no—
109C2×Dic3—61no—
110D12—124no—
111C4×D3—124no—
112Dic6—41no—
113Dic6—121no—
114C2×C32—161no—
115C24—91no—
116C2×Q8—361no—
117C2×D4—182no—
118C2×D4—182no—
119C2×D4—361no—
120C22×C4—31no—
121C22×C4—31no—
122C22×C4—31no—
123C22×C4—31no—
124C22×C4—91no—
125C22×C4—182no—
126C22×C4—361no—
127C22×C4—361no—
128C22×C4D3×A411yescharacteristic
129C22⋊C4—361no—
130C22⋊C4—361no—
131C22⋊C4—361no—
132C22⋊C4—361no—
133C22×C3—31no—
134C22×C3—31no—
135C22×C3#99411yescharacteristic
136C2×D3—62no—
137C2×D3—62no—
138C2×D3—62no—
139C2×D3—121no—
140C2×D3—121no—
141C2×D3—121no—
142C2×D3—121no—
143A4—41no—
144A4—81no—
145C3×C4—41no—
146C3×C4—121no—
147C3×C4—121no—
148C3×C4—161no—
149C3×C4—321no—
150C3×C4—481no—
151C3×C4—481no—
152Dic3—41no—
153Dic3—41no—
154Dic3—121no—
155C32—161noSylow
156C23—92no—
157C23—181no—
158C23—181no—
159C23—181no—
160C23—181no—
161C23—181no—
162C23—181no—
163C23C2×D3×A411yescharacteristic
164Q8—121no—
165Q8—361no—
166D4—364no—
167C2×C4—61no—
168C2×C4—61no—
169C2×C4—61no—
170C2×C4—61no—
171C2×C4—61no—
172C2×C4—61no—
173C2×C4—61no—
174C2×C4—181no—
175C2×C4—181no—
176C2×C4—181no—
177C2×C4—181no—
178C2×C4—181no—
179C2×C4—364no—
180C2×C3—31no—
181C2×C3—31no—
182C2×C3—161no—
183C2×C3—321no—
184C2×C3#560⋊C311yescharacteristic
185D3—122no—
186C22—31no—
187C22—31no—
188C22—182no—
189C22—182no—
190C22—182no—
191C22—361no—
192C22—361no—
193C22—361no—
194C22—361no—
195C22C3⋊#99411yescharacteristic
196C4—41no—
197C4—121no—
198C4—121no—
199C4—121no—
200C4—121no—
201C4—361no—
202C3—161no—
203C3—321no—
204C3#2760⋊C311yescharacteristic, complemented
205C2—31no—
206C2—31no—
207C2—362no—
208C2(#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⋊(#392⋊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
2. C3⋊(#401⋊C3)C2semidirect
4. #78435C3semidirect
17. #401⋊C3D3semidirect
204. C3#2760⋊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⋊(#401⋊C3)2
C3⋊(#392⋊C3)2
#784353
#2760⋊C33
A4×Dic64