Finite Group Databasebeta

← #77451⋊C3 #11921185

Subgroups — #77451⋊C3 #11921185

Order 1152.

256 conjugacy classes of subgroups; only the 31 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 31 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×#396⋊C3C211yesmaximal, characteristic, complemented
2C3⋊(#401⋊C3)C211yesmaximal, characteristic, complemented
3C3⋊(#392⋊C3)C211yesmaximal, characteristic, complemented
4#77451C311yesmaximal, characteristic, complemented
5#2825⋊C3—31nomaximal
6C2×Dic3×A4—41nomaximal
7C3×#95⋊C3C2211yescharacteristic
8C3×#396C2×C311yescharacteristic
9#4992—31no—
10#4991—31no—
11#4960—31no—
12#4958—31no—
13#4671C2×C311yescharacteristic, complemented
14C3⋊#401C2×C311yescharacteristic, complemented
15#401⋊C3—31no—
16#396⋊C3—21no—
17#396⋊C3D311yescharacteristic, complemented
18#392⋊C3—31no—
19C22×C3×A4—41no—
20Dic3×A4—41no—
21Dic3×A4—41no—
22#2825—31noSylow
23C22×#67—31no—
24C23×Dic3A411yescharacteristic
25C22×D12—31no—
26C2×C4×A4—121no—
27C2×C3×C4⋊C4—31no—
28C2×C3×C22⋊C4—31no—
29C2×(C2×D3)⋊C4—31no—
30C2×(C2×D3)⋊C4—31no—
31C2×(C2×D3)⋊C4—31no—
32C2×(C2×D3)⋊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—42no—
40C2×C3×A4—41no—
41C2×C3×Dic3—161no—
42#401—31no—
43#397—91no—
44#396C3×D311yescharacteristic
45#394—91no—
46#392—31no—
47#392—91no—
48#386—91no—
49C24×C3C2×A411yescharacteristic
50C23×D3—31no—
51C22×A4—41no—
52C22×A4—81no—
53C22×C3×C4—31no—
54C22×C3×C4—31no—
55C2×#67—62no—
56C2×#67—121no—
57C2×#67—121no—
58C22×Dic3—31no—
59C22×Dic3—121no—
60C22×Dic3C2×A411yescharacteristic
61C22×Dic3C2×A411yescharacteristic
62C2×D12—121no—
63C2×D12—121no—
64C2×D12—121no—
65C4×A4—121no—
66C4×A4—121no—
67C3×C4⋊C4—121no—
68C3×C22⋊C4—121no—
69(C2×D3)⋊C4—121no—
70(C2×D3)⋊C4—121no—
71(C2×D3)⋊C4—121no—
72(C2×D3)⋊C4—121no—
73C22×C32—161no—
74C3×A4—41no—
75C3×Dic3—161no—
76C3×Dic3—161no—
77C22×D4—91no—
78C22×D4—91no—
79C23×C4—31no—
80C2×C4⋊C4—31no—
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#41⋊C312yes—
93C23×C3C22×A411yescharacteristic
94C22×D3—61no—
95C22×D3—61no—
96C22×D3—61no—
97C22×D3—61no—
98C22×D3—61no—
99C22×D3—61no—
100C22×D3—61no—
101C2×A4—41no—
102C2×A4—42no—
103C2×A4—81no—
104C2×A4—82no—
105C2×C3×C4—61no—
106C2×C3×C4—61no—
107C2×C3×C4—61no—
108C2×C3×C4—61no—
109C2×C3×C4—61no—
110C2×C3×C4—61no—
111C2×C3×C4—481no—
112#67—124no—
113C2×Dic3—41no—
114C2×Dic3—61no—
115C2×Dic3—61no—
116C2×Dic3—61no—
117C2×Dic3—61no—
118C2×Dic3—61no—
119C2×Dic3—121no—
120D12—124no—
121C2×C32—162no—
122C2×C32—161no—
123C24—91no—
124C24D3×A411yescharacteristic
125C2×D4—182no—
126C2×D4—361no—
127C2×D4—361no—
128C2×D4—361no—
129C2×D4—361no—
130C2×D4—361no—
131C22×C4—31no—
132C22×C4—31no—
133C22×C4—31no—
134C22×C4—31no—
135C22×C4—91no—
136C22×C4—361no—
137C4⋊C4—121no—
138C22⋊C4—121no—
139C22⋊C4—361no—
140C22⋊C4—361no—
141C22⋊C4—361no—
142C22⋊C4—361no—
143C22×C3—31no—
144C22×C3—31no—
145C22×C3—41no—
146C22×C3—62no—
147C22×C3—121no—
148C22×C3—161no—
149C22×C3—321no—
150C22×C3C2×#41⋊C311yescharacteristic
151C2×D3—121no—
152C2×D3—121no—
153C2×D3—121no—
154C2×D3—121no—
155C2×D3—121no—
156C2×D3—121no—
157C2×D3—121no—
158A4—41no—
159A4—81no—
160C3×C4—121no—
161C3×C4—121no—
162C3×C4—481no—
163C3×C4—481no—
164Dic3—41no—
165Dic3—41no—
166Dic3—121no—
167C32—161noSylow
168C23—61no—
169C23—61no—
170C23—181no—
171C23—181no—
172C23—181no—
173C23—181no—
174C23—181no—
175C23—181no—
176C23—181no—
177C23C3⋊(#41⋊C3)12yes—
178C23C2×D3×A411yescharacteristic
179D4—364no—
180D4—364no—
181C2×C4—61no—
182C2×C4—61no—
183C2×C4—61no—
184C2×C4—61no—
185C2×C4—61no—
186C2×C4—61no—
187C2×C4—121no—
188C2×C4—181no—
189C2×C4—181no—
190C2×C4—181no—
191C2×C4—181no—
192C2×C4—181no—
193C2×C4—361no—
194C2×C3—31no—
195C2×C3—31no—
196C2×C3—42no—
197C2×C3—162no—
198C2×C3—161no—
199C2×C3—322no—
200C2×C3—321no—
201C2×C3#560⋊C311yescharacteristic
202D3—241no—
203C22—31no—
204C22—31no—
205C22—41no—
206C22—62no—
207C22—121no—
208C22—361no—
209C22—361no—
210C22—361no—
211C22—361no—
212C22—361no—
213C22—361no—
214C22—361no—
215C22C2×C3⋊(#41⋊C3)11yescharacteristic
216C4—121no—
217C4—121no—
218C4—121no—
219C4—121no—
220C4—361no—
221C3—161no—
222C3—321no—
223C3#2825⋊C311yescharacteristic, complemented
224C2—31no—
225C2—31no—
226C2—42no—
227C2—721no—
228C2(#126⋊C3)⋊D311yescharacteristic
subgroupG/H
center, hypercenterC2(#126⋊C3)⋊D3
commutator, cosocle, hypocenterC3×#95C22×C3
FrattiniC23C2×D3×A4
FittingC3×#396C2×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×#396⋊C3C2semidirect
2. C3⋊(#401⋊C3)C2semidirect
3. C3⋊(#392⋊C3)C2semidirect
4. #77451C3semidirect
13. #4671C2×C3semidirect
14. C3⋊#401C2×C3semidirect
17. #396⋊C3D3semidirect
223. C3#2825⋊C3semidirect

Maximal subgroups

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

subgroupindex
C3×#396⋊C32
C3⋊(#401⋊C3)2
C3⋊(#392⋊C3)2
#774513
#2825⋊C33
C2×Dic3×A44