Finite Group Databasebeta

← #77337⋊C3 #11921189

Subgroups — #77337⋊C3 #11921189

Order 1152.

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

normal subgroups only

This group has 222 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×#396⋊C3C211yesmaximal, characteristic, complemented
2C3⋊(#396⋊C3)C211yesmaximal, characteristic, complemented
3C3⋊(#376⋊C3)C211yesmaximal, characteristic, complemented
4#77337C311yesmaximal, characteristic, complemented
5#2644⋊C3—31nomaximal
6A4×#67—41nomaximal
7C3×#95⋊C3C2211yescharacteristic
8C3×#396C2×C311yescharacteristic, complemented
9#4992—31no—
10#4976—31no—
11#4957—31no—
12#4952—31no—
13#4676C2×C311yescharacteristic, complemented
14#4648C2×C311yescharacteristic, complemented
15#396⋊C3—21no—
16#396⋊C3—31no—
17#396⋊C3D311yescharacteristic, complemented
18#376⋊C3—31no—
19C22×C3×A4—41no—
20C2×D3×A4—41no—
21Dic3×A4—41no—
22#2644—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×Dic3⋊C4—31no—
31C2×Dic3⋊C4—31no—
32C2×C4×Dic3—31no—
33C3×#95C22×C311yescharacteristic
34C3⋊#95—32no—
35C3⋊#95—31no—
36#95⋊C3—21no—
37#95⋊C3C2×D311yescharacteristic
38C2×C3×A4—41no—
39C2×C3×A4—81no—
40D3×A4—81no—
41C3×#67—161no—
42#397—91no—
43#397—91no—
44#396—31no—
45#396C3×D311yescharacteristic, complemented
46#390—91no—
47#389—91no—
48#376—31no—
49C24×C3C2×A411yescharacteristic
50C23×D3C2×A411yescharacteristic
51C22×A4—41no—
52C22×A4—81no—
53C22×A4—121no—
54C22×C3×C4—31no—
55C22×C3×C4—31no—
56C2×#67—61no—
57C2×#67—61no—
58C22×Dic3—31no—
59C22×Dic3—31no—
60C22×Dic3C2×A411yescharacteristic
61C4×A4—121no—
62C3×C4⋊C4—121no—
63C3×C22⋊C4—121no—
64#217—121no—
65(C2×D3)⋊C4—121no—
66(C2×D3)⋊C4—121no—
67Dic3⋊C4—61no—
68Dic3⋊C4—61no—
69Dic3⋊C4—121no—
70C4×Dic3—61no—
71C4×Dic3—61no—
72C22×C32—161no—
73C2×C3×D3—161no—
74C3×A4—41no—
75C3×Dic3—161no—
76C22×D4—31no—
77C2×C4⋊C4—31no—
78C2×C4⋊C4—91no—
79C2×C4⋊C4—91no—
80C2×C22⋊C4—31no—
81C2×C22⋊C4—91no—
82C2×C22⋊C4—91no—
83C2×C22⋊C4—91no—
84C2×C42—91no—
85#95—91no—
86#95—92no—
87#95C2×C3×D311yescharacteristic
88C23×C3—21no—
89C23×C3—61no—
90C23×C3—61no—
91C23×C3C22×A411yescharacteristic
92C22×D3—21no—
93C22×D3—61no—
94C22×D3—61no—
95C2×A4—41no—
96C2×A4—81no—
97C2×A4—82no—
98C2×A4—81no—
99C2×A4—241no—
100C3×D4—481no—
101C2×C3×C4—61no—
102C2×C3×C4—61no—
103C2×C3×C4—61no—
104C2×C3×C4—61no—
105C2×C3×C4—61no—
106C2×C3×C4—61no—
107#67—41no—
108#67—121no—
109C2×Dic3—31no—
110C2×Dic3—31no—
111C2×Dic3—61no—
112C2×Dic3—61no—
113C2×Dic3—61no—
114C2×Dic3—61no—
115C2×Dic3—61no—
116C2×Dic3—61no—
117C2×C32—161no—
118C2×C32—321no—
119C3×D3—321no—
120C24—31no—
121C24D3×A411yescharacteristic
122C2×D4—181no—
123C2×D4—181no—
124C22×C4—31no—
125C22×C4—31no—
126C22×C4—31no—
127C22×C4—91no—
128C22×C4—91no—
129C4⋊C4—121no—
130C4⋊C4—181no—
131C4⋊C4—181no—
132C4⋊C4—361no—
133C22⋊C4—121no—
134C22⋊C4—361no—
135C22⋊C4—361no—
136C22⋊C4—361no—
137C42—181no—
138C42—181no—
139C22×C3—31no—
140C22×C3—31no—
141C22×C3—41no—
142C22×C3—121no—
143C22×C3—121no—
144C22×C3—161no—
145C22×C3—321no—
146C22×C3—481no—
147C22×C32−1+4⋊C311yescharacteristic
148C2×D3—41no—
149C2×D3—121no—
150C2×D3—121no—
151A4—41no—
152A4—81no—
153C3×C4—121no—
154C3×C4—121no—
155C3×C4—481no—
156Dic3—31no—
157Dic3—121no—
158Dic3—121no—
159Dic3#126⋊C311yescharacteristic
160C32—161noSylow
161C23—21no—
162C23—61no—
163C23—61no—
164C23—61no—
165C23—181no—
166C23—181no—
167C23C2×D3×A411yescharacteristic
168D4—121no—
169D4—361no—
170C2×C4—61no—
171C2×C4—61no—
172C2×C4—61no—
173C2×C4—61no—
174C2×C4—61no—
175C2×C4—61no—
176C2×C4—91no—
177C2×C4—91no—
178C2×C4—181no—
179C2×C4—181no—
180C2×C4—181no—
181C2×C4—181no—
182C2×C4—181no—
183C2×C4—181no—
184C2×C3—31no—
185C2×C3—31no—
186C2×C3—81no—
187C2×C3—161no—
188C2×C3—321no—
189C2×C3—322no—
190C2×C3—321no—
191C2×C3—961no—
192C2×C3C2×#126⋊C311yescharacteristic
193D3—81no—
194C22—31no—
195C22—31no—
196C22—41no—
197C22—121no—
198C22—121no—
199C22—121no—
200C22—361no—
201C22—361no—
202C22#1007⋊C311yescharacteristic
203C4—31no—
204C4—91no—
205C4—121no—
206C4—121no—
207C4—361no—
208C4—361no—
209C3—161no—
210C3—321no—
211C3#2644⋊C311yescharacteristic, complemented
212C2—31no—
213C2—31no—
214C2—81no—
215C2—241no—
216C2D3×#126⋊C311yescharacteristic
subgroupG/H
center, hypercenterC2D3×#126⋊C3
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⋊(#396⋊C3)C2semidirect
3. C3⋊(#376⋊C3)C2semidirect
4. #77337C3semidirect
8. C3×#396C2×C3semidirect
13. #4676C2×C3semidirect
14. #4648C2×C3semidirect
17. #396⋊C3D3semidirect
45. #396C3×D3semidirect
211. C3#2644⋊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⋊(#396⋊C3)2
C3⋊(#376⋊C3)2
#773373
#2644⋊C33
A4×#674