Finite Group Databasebeta

← #78432⋊C3 #11921205

Subgroups — #78432⋊C3 #11921205

Order 1152.

232 conjugacy classes of subgroups; only the 28 normal subgroups are shown.

normal subgroups only

This group has 232 conjugacy classes of subgroups — too many to draw. Only its 28 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
2D3×#95⋊C3C211yesmaximal, characteristic, complemented
3C3⋊(#396⋊C3)C211yesmaximal, characteristic, complemented
4#78432C311yesmaximal, characteristic, complemented
5#2643⋊C3—31nomaximal
6A4×D12—41nomaximal
7C3×#95⋊C3C2211yescharacteristic
8C3×#401C2×C311yescharacteristic, complemented
9#4676C2×C311yescharacteristic, complemented
10#4674—31no—
11#4668—31no—
12#4665—31no—
13D3×#95C2×C311yescharacteristic, complemented
14#4660—31no—
15#401⋊C3—21no—
16#401⋊C3D311yescharacteristic, complemented
17#396⋊C3—31no—
18C2×#95⋊C3—31no—
19C2×D3×A4—41no—
20C2×D3×A4—41no—
21C3×C4×A4—41no—
22#2643—31noSylow
23C22×D12A411yescharacteristic
24C22×C4×D3—31no—
25D4×A4—121no—
26C2×(C2×D3)⋊C4—31no—
27C2×(C2×D3)⋊C4—31no—
28C2×(C2×D3)⋊C4—31no—
29C2×C4⋊Dic3—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—81no—
41D3×A4—81no—
42C3×D12—161no—
43#401C3×D311yescharacteristic, complemented
44#400—91no—
45#397—91no—
46#396—31no—
47#386—91no—
48#385—91no—
49C2×#95—31no—
50C23×D3C2×A411yescharacteristic
51C23×D3C2×A411yescharacteristic
52C22×A4—121no—
53C22×A4—121no—
54C22×C3×C4—31no—
55C22×C3×C4—31no—
56C22×C3×C4C2×A411yescharacteristic
57C22×Dic3—31no—
58C22×Dic3—31no—
59C2×D12—61no—
60C2×D12—61no—
61C2×C4×D3—61no—
62C2×C4×D3—61no—
63C2×C4×D3—121no—
64C2×C4×D3—121no—
65C4×A4—41no—
66C4×A4—81no—
67(C2×D3)⋊C4—61no—
68(C2×D3)⋊C4—61no—
69(C2×D3)⋊C4—121no—
70(C2×D3)⋊C4—121no—
71C4⋊Dic3—121no—
72Dic3⋊C4—121no—
73C2×C3×D3—161no—
74C2×C3×D3—161no—
75C3×A4—41no—
76C32×C4—161no—
77C22×D4—31no—
78C23×C4—91no—
79C2×C4⋊C4—91no—
80C2×C4⋊C4—91no—
81C2×C22⋊C4—91no—
82C2×C22⋊C4—91no—
83C2×C22⋊C4—91no—
84#95—31no—
85#95—31no—
86#95—91no—
87#95—91no—
88#95—91no—
89#95C2×C3×D311yescharacteristic
90C23×C3C22×A411yescharacteristic
91C22×D3—21no—
92C22×D3—21no—
93C22×D3—31no—
94C22×D3—31no—
95C22×D3—61no—
96C22×D3—61no—
97C22×D3—61no—
98C2×A4—41no—
99C2×A4—81no—
100C2×A4—241no—
101C2×A4—241no—
102C3×D4—481no—
103C2×C3×C4—61no—
104C2×C3×C4—61no—
105C2×C3×C4—61no—
106C2×C3×C4—61no—
107C2×C3×C4—61no—
108C2×C3×C4—61no—
109C2×C3×C4—61no—
110C2×Dic3—61no—
111C2×Dic3—61no—
112C2×Dic3—61no—
113C2×Dic3—61no—
114C2×Dic3—61no—
115C2×Dic3—61no—
116D12—41no—
117D12—121no—
118C4×D3—122no—
119C4×D3—122no—
120C2×C32—161no—
121C3×D3—321no—
122C3×D3—321no—
123C24—31no—
124C24—31no—
125C2×D4—181no—
126C2×D4—181no—
127C22×C4—31no—
128C22×C4—31no—
129C22×C4—91no—
130C22×C4—91no—
131C22×C4—181no—
132C22×C4—181no—
133C22×C4—361no—
134C22×C4—361no—
135C22×C4D3×A411yescharacteristic
136C4⋊C4—361no—
137C4⋊C4—361no—
138C22⋊C4—181no—
139C22⋊C4—181no—
140C22⋊C4—361no—
141C22⋊C4—361no—
142C22×C3—31no—
143C22×C3—31no—
144C22×C3—481no—
145C22×C3—481no—
146C22×C32−1+4⋊C311yescharacteristic
147C2×D3—31no—
148C2×D3—41no—
149C2×D3—61no—
150C2×D3—61no—
151C2×D3—61no—
152C2×D3—61no—
153C2×D3—121no—
154C2×D3—121no—
155C2×D3#126⋊C311yescharacteristic
156A4—41no—
157A4—81no—
158C3×C4—41no—
159C3×C4—121no—
160C3×C4—121no—
161C3×C4—161no—
162C3×C4—321no—
163Dic3—121no—
164Dic3—121no—
165C32—161noSylow
166C23—61no—
167C23—61no—
168C23—91no—
169C23—91no—
170C23—181no—
171C23—181no—
172C23—181no—
173C23C2×D3×A411yescharacteristic
174D4—121no—
175D4—361no—
176C2×C4—61no—
177C2×C4—61no—
178C2×C4—61no—
179C2×C4—61no—
180C2×C4—61no—
181C2×C4—61no—
182C2×C4—61no—
183C2×C4—181no—
184C2×C4—181no—
185C2×C4—181no—
186C2×C4—181no—
187C2×C4—181no—
188C2×C4—181no—
189C2×C4—362no—
190C2×C4—362no—
191C2×C3—31no—
192C2×C3—31no—
193C2×C3—161no—
194C2×C3—321no—
195C2×C3—961no—
196C2×C3—961no—
197C2×C3C2×#126⋊C311yescharacteristic
198D3—21no—
199D3—61no—
200D3—81no—
201C22—31no—
202C22—31no—
203C22—31no—
204C22—91no—
205C22—121no—
206C22—181no—
207C22—181no—
208C22—181no—
209C22—181no—
210C22—361no—
211C22—361no—
212C22#1010⋊C311yescharacteristic
213C4—41no—
214C4—121no—
215C4—121no—
216C4—361no—
217C4—361no—
218C3—161no—
219C3—321no—
220C3#2643⋊C311yescharacteristic, complemented
221C2—31no—
222C2—31no—
223C2—61no—
224C2—181no—
225C2—241no—
226C2D3×#126⋊C311yescharacteristic
subgroupG/H
center, hypercenterC2D3×#126⋊C3
commutator, cosocle, hypocenterC3×#95C22×C3
FrattiniC23C2×D3×A4
FittingC3×#401C2×C3
socleC23×C3C22×A4
LCSG ▷ C3×#95
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C3×#401⋊C3C2semidirect
2. D3×#95⋊C3C2semidirect
3. C3⋊(#396⋊C3)C2semidirect
4. #78432C3semidirect
8. C3×#401C2×C3semidirect
9. #4676C2×C3semidirect
13. D3×#95C2×C3semidirect
16. #401⋊C3D3semidirect
43. #401C3×D3semidirect
220. C3#2643⋊C3semidirect

Maximal subgroups

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

subgroupindex
C3×#401⋊C32
D3×#95⋊C32
C3⋊(#396⋊C3)2
#784323
#2643⋊C33
A4×D124