Finite Group Databasebeta

← #78426⋊C3 #11921206

Subgroups — #78426⋊C3 #11921206

Order 1152.

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

normal subgroups only

This group has 218 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⋊(#399⋊C3)C211yesmaximal, characteristic, complemented
3C3⋊(#396⋊C3)C211yesmaximal, characteristic, complemented
4#78426C311yesmaximal, characteristic, complemented
5#2801⋊C3—31nomaximal
6A4×D12—41nomaximal
7C3×#95⋊C3C2211yescharacteristic
8C3×#401C2×C311yescharacteristic, complemented
9#4677C2×C311yescharacteristic, complemented
10#4676C2×C311yescharacteristic, complemented
11#4672—31no—
12#4670—31no—
13#4669—31no—
14#4647—31no—
15#401⋊C3—21no—
16#401⋊C3D311yescharacteristic, complemented
17#399⋊C3—31no—
18#396⋊C3—31no—
19C2×D3×A4—41no—
20C2×D3×A4—41no—
21C3×C4×A4—41no—
22#2801—31noSylow
23C22×D12A411yescharacteristic
24D4×A4—121no—
25C2×(C2×D3)⋊C4—31no—
26C2×(C2×D3)⋊C4—31no—
27C2×(C2×D3)⋊C4—31no—
28C2×(C2×D3)⋊C4—31no—
29C2×C4⋊Dic3—31no—
30C2×Dic3⋊C4—31no—
31C2×Dic3⋊C4—31no—
32C2×C4×Dic3—31no—
33C3×#95—31no—
34C3×#95—31no—
35C3×#95C22×C311yescharacteristic
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#399—31no—
45#396—31no—
46#394—91no—
47#389—91no—
48#388—91no—
49#388—91no—
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—121no—
60C4×A4—41no—
61C4×A4—81no—
62(C2×D3)⋊C4—62no—
63(C2×D3)⋊C4—62no—
64(C2×D3)⋊C4—121no—
65(C2×D3)⋊C4—121no—
66C4⋊Dic3—121no—
67Dic3⋊C4—62no—
68Dic3⋊C4—121no—
69C4×Dic3—121no—
70C2×C3×D3—161no—
71C2×C3×D3—161no—
72C3×A4—41no—
73C32×C4—161no—
74C22×D4—31no—
75C2×C4⋊C4—91no—
76C2×C4⋊C4—91no—
77C2×C4⋊C4—91no—
78C2×C22⋊C4—91no—
79C2×C22⋊C4—91no—
80C2×C22⋊C4—91no—
81C2×C22⋊C4—91no—
82C2×C42—91no—
83#95—31no—
84#95—31no—
85#95—91no—
86#95C2×C3×D311yescharacteristic
87C23×C3C22×A411yescharacteristic
88C22×D3—21no—
89C22×D3—21no—
90C22×D3—61no—
91C22×D3—61no—
92C22×D3—61no—
93C22×D3—61no—
94C2×A4—41no—
95C2×A4—81no—
96C2×A4—241no—
97C2×A4—241no—
98C3×D4—481no—
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×C3×C4—61no—
106C2×Dic3—32no—
107C2×Dic3—61no—
108C2×Dic3—61no—
109C2×Dic3—61no—
110C2×Dic3—61no—
111C2×Dic3—61no—
112D12—41no—
113D12—121no—
114C2×C32—161no—
115C3×D3—321no—
116C3×D3—321no—
117C24—31no—
118C24—31no—
119C2×D4—361no—
120C22×C4—31no—
121C22×C4—31no—
122C22×C4—91no—
123C22×C4—91no—
124C22×C4D3×A411yescharacteristic
125C4⋊C4—182no—
126C4⋊C4—361no—
127C4⋊C4—361no—
128C22⋊C4—182no—
129C22⋊C4—182no—
130C22⋊C4—361no—
131C22⋊C4—361no—
132C42—361no—
133C22×C3—31no—
134C22×C3—31no—
135C22×C3—481no—
136C22×C3—481no—
137C22×C32−1+4⋊C311yescharacteristic
138C2×D3—41no—
139C2×D3—41no—
140C2×D3—121no—
141C2×D3—121no—
142C2×D3—121no—
143C2×D3—121no—
144A4—41no—
145A4—81no—
146C3×C4—41no—
147C3×C4—121no—
148C3×C4—121no—
149C3×C4—161no—
150C3×C4—321no—
151Dic3—62no—
152Dic3—121no—
153C32—161noSylow
154C23—61no—
155C23—61no—
156C23—181no—
157C23—181no—
158C23—181no—
159C23—181no—
160C23C2×D3×A411yescharacteristic
161D4—121no—
162D4—361no—
163C2×C4—61no—
164C2×C4—61no—
165C2×C4—61no—
166C2×C4—61no—
167C2×C4—61no—
168C2×C4—61no—
169C2×C4—61no—
170C2×C4—92no—
171C2×C4—181no—
172C2×C4—181no—
173C2×C4—181no—
174C2×C4—181no—
175C2×C4—181no—
176C2×C3—31no—
177C2×C3—31no—
178C2×C3—161no—
179C2×C3—321no—
180C2×C3—961no—
181C2×C3—961no—
182C2×C3#560⋊C311yescharacteristic
183D3—81no—
184D3—81no—
185C22—31no—
186C22—31no—
187C22—121no—
188C22—121no—
189C22—361no—
190C22—361no—
191C22—361no—
192C22—361no—
193C22#1010⋊C311yescharacteristic
194C4—41no—
195C4—121no—
196C4—121no—
197C4—182no—
198C4—361no—
199C3—161no—
200C3—321no—
201C3#2801⋊C311yescharacteristic, complemented
202C2—31no—
203C2—31no—
204C2—241no—
205C2—241no—
206C2(#126⋊C3)⋊D311yescharacteristic
subgroupG/H
center, hypercenterC2(#126⋊C3)⋊D3
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. C3⋊(#399⋊C3)C2semidirect
3. C3⋊(#396⋊C3)C2semidirect
4. #78426C3semidirect
8. C3×#401C2×C3semidirect
9. #4677C2×C3semidirect
10. #4676C2×C3semidirect
16. #401⋊C3D3semidirect
43. #401C3×D3semidirect
201. C3#2801⋊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⋊(#396⋊C3)2
#784263
#2801⋊C33
A4×D124