Finite Group Databasebeta

← #76776⋊C3 #11921167

Subgroups — #76776⋊C3 #11921167

Order 1152.

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

normal subgroups only

This group has 252 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×#392⋊C3C211yesmaximal, characteristic, complemented
2C3⋊(#396⋊C3)C211yesmaximal, characteristic, complemented
3C3⋊(#401⋊C3)C211yesmaximal, characteristic, complemented
4#76776C311yesmaximal, characteristic, complemented
5#2825⋊C3—31nomaximal
6C4×D3×A4—41nomaximal
7C3×#95⋊C3C2211yescharacteristic
8C3×#392C2×C311yescharacteristic, complemented
9#5223—31no—
10#5222—31no—
11#4956—31no—
12#4952—31no—
13#4676C2×C311yescharacteristic
14C3⋊#401C2×C311yescharacteristic, complemented
15#401⋊C3—31no—
16#396⋊C3—31no—
17#392⋊C3—21no—
18#392⋊C3D311yescharacteristic, complemented
19C2×D3×A4—41no—
20C3×C4×A4—41no—
21Dic3×A4—41no—
22#2825—31noSylow
23C22×C3×D4—31no—
24C22×#67—31no—
25C22×C4×D3A411yescharacteristic
26C2×C4×A4—121no—
27C2×C3×C22⋊C4—31no—
28C2×#217—31no—
29C2×#217—31no—
30C2×#217—31no—
31C2×(C2×D3)⋊C4—31no—
32C2×Dic3⋊C4—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#397—91no—
44#396—31no—
45#394—91no—
46#392—91no—
47#392C3×D311yescharacteristic, complemented
48#386—91no—
49C24×C3—31no—
50C23×D3C2×A411yescharacteristic
51C22×A4—121no—
52C2×C3×D4—121no—
53C2×C3×D4—121no—
54C2×C3×D4—121no—
55C22×C3×C4—31no—
56C22×C3×C4C2×A411yescharacteristic
57C2×#67—62no—
58C2×#67—121no—
59C2×#67—121no—
60C22×Dic3—31no—
61C22×Dic3—31no—
62C22×Dic3C2×A411yescharacteristic
63C2×C4×D3—121no—
64C4×A4—41no—
65C4×A4—81no—
66C4×A4—121no—
67C3×C22⋊C4—121no—
68#217—121no—
69#217—121no—
70#217—121no—
71(C2×D3)⋊C4—121no—
72Dic3⋊C4—121no—
73C2×C3×D3—161no—
74C3×A4—41no—
75C32×C4—161no—
76C3×Dic3—161no—
77C22×D4—31no—
78C22×D4—91no—
79C23×C4—31no—
80C2×C4⋊C4—91no—
81C2×C22⋊C4—31no—
82C2×C22⋊C4—91no—
83C2×C22⋊C4—91no—
84C2×C22⋊C4—91no—
85C2×C22⋊C4—91no—
86#95—91no—
87#95—91no—
88#95—91no—
89#95C2×C3×D311yescharacteristic
90C23×C3—61no—
91C23×C3—61no—
92C23×C3—61no—
93C23×C3—61no—
94C23×C3—61no—
95C23×C3—61no—
96C23×C3—61no—
97C23×C3C22×A411yescharacteristic
98C22×D3—61no—
99C22×D3—61no—
100C22×D3#41⋊C312yes—
101C2×A4—41no—
102C2×A4—81no—
103C2×A4—122no—
104C3×D4—124no—
105C2×C3×C4—61no—
106C2×C3×C4—61no—
107C2×C3×C4—61no—
108C2×C3×C4—61no—
109C2×C3×C4—481no—
110#67—124no—
111C2×Dic3—61no—
112C2×Dic3—61no—
113C2×Dic3—61no—
114C2×Dic3—61no—
115C2×Dic3—61no—
116C2×Dic3—61no—
117C2×Dic3—61no—
118C4×D3—41no—
119C4×D3—121no—
120C2×C32—161no—
121C3×D3—162no—
122C24—31no—
123C24—31no—
124C2×D4—121no—
125C2×D4—121no—
126C2×D4—121no—
127C2×D4—182no—
128C2×D4—361no—
129C2×D4—361no—
130C22×C4—31no—
131C22×C4—31no—
132C22×C4—91no—
133C22×C4—91no—
134C22×C4—361no—
135C22×C4D3×A411yescharacteristic
136C4⋊C4—361no—
137C22⋊C4—121no—
138C22⋊C4—361no—
139C22⋊C4—361no—
140C22⋊C4—361no—
141C22⋊C4—361no—
142C22×C3—31no—
143C22×C3—31no—
144C22×C3—121no—
145C22×C3—121no—
146C22×C3—121no—
147C22×C3—121no—
148C22×C3—121no—
149C22×C3—121no—
150C22×C3—121no—
151C22×C3—481no—
152C22×C3C2×#41⋊C311yescharacteristic
153C2×D3—41no—
154C2×D3—62no—
155C2×D3—121no—
156A4—41no—
157A4—81no—
158C3×C4—41no—
159C3×C4—121no—
160C3×C4—161no—
161C3×C4—321no—
162C3×C4—481no—
163Dic3—41no—
164Dic3—121no—
165Dic3—121no—
166C32—161noSylow
167C23—32no—
168C23—61no—
169C23—61no—
170C23—61no—
171C23—61no—
172C23—61no—
173C23—61no—
174C23—61no—
175C23—181no—
176C23—181no—
177C23C2×D3×A411yescharacteristic
178D4—124no—
179D4—364no—
180C2×C4—61no—
181C2×C4—61no—
182C2×C4—61no—
183C2×C4—61no—
184C2×C4—121no—
185C2×C4—181no—
186C2×C4—181no—
187C2×C4—181no—
188C2×C4—181no—
189C2×C4—181no—
190C2×C4—181no—
191C2×C4—181no—
192C2×C4—361no—
193C2×C3—31no—
194C2×C3—31no—
195C2×C3—161no—
196C2×C3—241no—
197C2×C3—321no—
198C2×C3—482no—
199C2×C3#560⋊C311yescharacteristic
200D3—42no—
201C22—31no—
202C22—31no—
203C22—121no—
204C22—121no—
205C22—121no—
206C22—121no—
207C22—121no—
208C22—121no—
209C22—121no—
210C22—121no—
211C22—182no—
212C22—361no—
213C22D3×#41⋊C311yescharacteristic
214C4—41no—
215C4—121no—
216C4—121no—
217C4—361no—
218C4—361no—
219C3—161no—
220C3—321no—
221C3#2825⋊C311yescharacteristic, complemented
222C2—31no—
223C2—31no—
224C2—122no—
225C2—241no—
226C2#5720⋊C311yescharacteristic
subgroupG/H
center, hypercenterC2#5720⋊C3
commutator, cosocle, hypocenterC3×#95C22×C3
FrattiniC23C2×D3×A4
FittingC3×#392C2×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×#392⋊C3C2semidirect
2. C3⋊(#396⋊C3)C2semidirect
3. C3⋊(#401⋊C3)C2semidirect
4. #76776C3semidirect
8. C3×#392C2×C3semidirect
14. C3⋊#401C2×C3semidirect
18. #392⋊C3D3semidirect
47. #392C3×D3semidirect
221. C3#2825⋊C3semidirect

Maximal subgroups

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

subgroupindex
C3×#392⋊C32
C3⋊(#396⋊C3)2
C3⋊(#401⋊C3)2
#767763
#2825⋊C33
C4×D3×A44