Finite Group Databasebeta

← #77401⋊C3 #11921188

Subgroups — #77401⋊C3 #11921188

Order 1152.

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

normal subgroups only

This group has 222 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×#396⋊C3C211yesmaximal, characteristic, complemented
2C3⋊(#399⋊C3)C211yesmaximal, characteristic, complemented
3C3⋊(#401⋊C3)C211yesmaximal, characteristic, complemented
4#77401C311yesmaximal, characteristic, complemented
5#2801⋊C3—31nomaximal
6A4×#67—41nomaximal
7C3×#95⋊C3C2211yescharacteristic
8C3×#396C2×C311yescharacteristic, complemented
9#4990—31no—
10#4984—31no—
11#4961—31no—
12#4951—31no—
13#4677C2×C311yescharacteristic, complemented
14C3⋊#401C2×C311yescharacteristic, complemented
15#401⋊C3—31no—
16#399⋊C3—31no—
17#396⋊C3—21no—
18#396⋊C3D311yescharacteristic, complemented
19C22×C3×A4—41no—
20C2×D3×A4—41no—
21Dic3×A4—41no—
22#2801—31noSylow
23C22×#67A411yescharacteristic
24D4×A4—121no—
25C2×C3×C4⋊C4—31no—
26C2×C3×C22⋊C4—31no—
27C2×#217—31no—
28C2×(C2×D3)⋊C4—31no—
29C2×(C2×D3)⋊C4—31no—
30C2×C4⋊Dic3—31no—
31C2×C4⋊Dic3—31no—
32C2×C4×Dic3—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—
40C2×C3×A4—81no—
41D3×A4—81no—
42C3×#67—161no—
43#401—31no—
44#399—31no—
45#396C3×D311yescharacteristic, complemented
46#394—91no—
47#389—91no—
48#388—91no—
49#388—91no—
50C24×C3C2×A411yescharacteristic
51C23×D3C2×A411yescharacteristic
52C22×A4—41no—
53C22×A4—81no—
54C22×A4—121no—
55C22×C3×C4—31no—
56C22×C3×C4—31no—
57C2×#67—121no—
58C22×Dic3—31no—
59C22×Dic3—31no—
60C22×Dic3C2×A411yescharacteristic
61C4×A4—121no—
62C3×C4⋊C4—62no—
63C3×C22⋊C4—62no—
64#217—121no—
65(C2×D3)⋊C4—62no—
66(C2×D3)⋊C4—121no—
67C4⋊Dic3—121no—
68C4⋊Dic3—121no—
69C4×Dic3—121no—
70C22×C32—161no—
71C2×C3×D3—161no—
72C3×A4—41no—
73C3×Dic3—161no—
74C22×D4—31no—
75C2×C4⋊C4—31no—
76C2×C4⋊C4—91no—
77C2×C4⋊C4—91no—
78C2×C22⋊C4—31no—
79C2×C22⋊C4—91no—
80C2×C22⋊C4—91no—
81C2×C22⋊C4—91no—
82C2×C42—91no—
83#95—91no—
84#95—91no—
85#95—91no—
86#95C2×C3×D311yescharacteristic
87C23×C3—21no—
88C23×C3—61no—
89C23×C3—61no—
90C23×C3C22×A411yescharacteristic
91C22×D3—21no—
92C22×D3—61no—
93C22×D3—61no—
94C2×A4—41no—
95C2×A4—81no—
96C2×A4—82no—
97C2×A4—81no—
98C2×A4—241no—
99C3×D4—481no—
100C2×C3×C4—32no—
101C2×C3×C4—61no—
102C2×C3×C4—61no—
103C2×C3×C4—61no—
104C2×C3×C4—61no—
105C2×C3×C4—61no—
106#67—41no—
107#67—121no—
108C2×Dic3—61no—
109C2×Dic3—61no—
110C2×Dic3—61no—
111C2×Dic3—61no—
112C2×Dic3—61no—
113C2×Dic3—61no—
114C2×Dic3—61no—
115C2×C32—161no—
116C2×C32—321no—
117C3×D3—321no—
118C24—31no—
119C24D3×A411yescharacteristic
120C2×D4—361no—
121C22×C4—31no—
122C22×C4—31no—
123C22×C4—31no—
124C22×C4—91no—
125C22×C4—91no—
126C4⋊C4—62no—
127C4⋊C4—361no—
128C4⋊C4—361no—
129C22⋊C4—62no—
130C22⋊C4—182no—
131C22⋊C4—361no—
132C22⋊C4—361no—
133C42—361no—
134C22×C3—31no—
135C22×C3—31no—
136C22×C3—41no—
137C22×C3—121no—
138C22×C3—121no—
139C22×C3—161no—
140C22×C3—321no—
141C22×C3—481no—
142C22×C32−1+4⋊C311yescharacteristic
143C2×D3—41no—
144C2×D3—121no—
145C2×D3—121no—
146A4—41no—
147A4—81no—
148C3×C4—62no—
149C3×C4—121no—
150C3×C4—481no—
151Dic3—41no—
152Dic3—121no—
153Dic3—121no—
154C32—161noSylow
155C23—21no—
156C23—61no—
157C23—61no—
158C23—61no—
159C23—181no—
160C23—181no—
161C23C2×D3×A411yescharacteristic
162D4—121no—
163D4—361no—
164C2×C4—32no—
165C2×C4—61no—
166C2×C4—61no—
167C2×C4—61no—
168C2×C4—61no—
169C2×C4—61no—
170C2×C4—181no—
171C2×C4—181no—
172C2×C4—181no—
173C2×C4—181no—
174C2×C4—181no—
175C2×C4—181no—
176C2×C4—181no—
177C2×C3—31no—
178C2×C3—31no—
179C2×C3—81no—
180C2×C3—161no—
181C2×C3—321no—
182C2×C3—322no—
183C2×C3—321no—
184C2×C3—961no—
185C2×C3#560⋊C311yescharacteristic
186D3—81no—
187C22—31no—
188C22—31no—
189C22—41no—
190C22—121no—
191C22—121no—
192C22—121no—
193C22—361no—
194C22—361no—
195C22#1007⋊C311yescharacteristic
196C4—62no—
197C4—121no—
198C4—121no—
199C4—361no—
200C4—361no—
201C3—161no—
202C3—321no—
203C3#2801⋊C311yescharacteristic, complemented
204C2—31no—
205C2—31no—
206C2—81no—
207C2—241no—
208C2(#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⋊(#399⋊C3)C2semidirect
3. C3⋊(#401⋊C3)C2semidirect
4. #77401C3semidirect
8. C3×#396C2×C3semidirect
13. #4677C2×C3semidirect
14. C3⋊#401C2×C3semidirect
18. #396⋊C3D3semidirect
45. #396C3×D3semidirect
203. C3#2801⋊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⋊(#399⋊C3)2
C3⋊(#401⋊C3)2
#774013
#2801⋊C33
A4×#674