Finite Group Databasebeta

← #77283⋊C3 #11921184

Subgroups — #77283⋊C3 #11921184

Order 1152.

226 conjugacy classes of subgroups; only the 32 normal subgroups are shown.

normal subgroups only

This group has 226 conjugacy classes of subgroups — too many to draw. Only its 32 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
2C3⋊(#376⋊C3)C211yesmaximal, characteristic, complemented
3C3⋊(#401⋊C3)C211yesmaximal, characteristic, complemented
4#77283C311yesmaximal, characteristic, complemented
5#2401⋊C3—31nomaximal
6C2×Dic3×A4—41nomaximal
7C3×#95⋊C3C2211yescharacteristic
8C3×#396C2×C311yescharacteristic
9#4986—31no—
10Dic3×C4⋊C4—31no—
11#4953—31no—
12Dic3×C22⋊C4—31no—
13C3⋊#401C2×C311yescharacteristic, complemented
14#4648C2×C311yescharacteristic, complemented
15#401⋊C3—31no—
16#396⋊C3—21no—
17#396⋊C3D311yescharacteristic
18#376⋊C3—31no—
19C22×C3×A4—41no—
20Dic3×A4—41no—
21Dic3×A4—41no—
22#2401—31noSylow
23C23×Dic3A411yescharacteristic
24C2×C4×A4—121no—
25C2×C3×C4⋊C4—31no—
26C2×C3×C22⋊C4—31no—
27C2×#217—31no—
28C2×C4⋊Dic3—31no—
29C2×C4×Dic3—31no—
30C2×C4×Dic3—31no—
31C3×#95C22×C311yescharacteristic
32C3⋊#95—31no—
33C3⋊#95—31no—
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#400—91no—
44#397—91no—
45#396C3×D311yescharacteristic
46C4×C4⋊C4—91no—
47C4×C22⋊C4—91no—
48#376—31no—
49C24×C3C2×A411yescharacteristic
50C22×A4—41no—
51C22×A4—81no—
52C22×C3×C4—31no—
53C22×C3×C4—31no—
54C22×Dic3—31no—
55C22×Dic3—31no—
56C22×Dic3—61no—
57C22×Dic3—61no—
58C22×Dic3C2×A411yescharacteristic
59C22×Dic3C2×A411yescharacteristic
60C4×A4—121no—
61C4×A4—121no—
62C3×C4⋊C4—62no—
63C3×C22⋊C4—62no—
64#217—62no—
65C4⋊Dic3—62no—
66C4×Dic3—61no—
67C4×Dic3—61no—
68C4×Dic3—61no—
69C4×Dic3—61no—
70C22×C32—161no—
71C3×A4—41no—
72C3×Dic3—161no—
73C3×Dic3—161no—
74C23×C4—31no—
75C2×C4⋊C4—31no—
76C2×C4⋊C4—91no—
77C2×C22⋊C4—31no—
78C2×C22⋊C4—91no—
79C2×C42—91no—
80C2×C42—91no—
81#95—91no—
82#95—91no—
83#95—91no—
84#95—91no—
85#95—91no—
86#95C2×C3×D311yescharacteristic
87C23×C3—61no—
88C23×C3—61no—
89C23×C3#41⋊C312yes—
90C23×C3C22×A411yescharacteristic
91C2×A4—41no—
92C2×A4—42no—
93C2×A4—81no—
94C2×A4—82no—
95C2×C3×C4—32no—
96C2×C3×C4—61no—
97C2×C3×C4—61no—
98C2×C3×C4—61no—
99C2×C3×C4—61no—
100C2×C3×C4—61no—
101C2×C3×C4—481no—
102C2×Dic3—31no—
103C2×Dic3—31no—
104C2×Dic3—41no—
105C2×Dic3—61no—
106C2×Dic3—61no—
107C2×Dic3—61no—
108C2×Dic3—61no—
109C2×Dic3—61no—
110C2×Dic3—61no—
111C2×Dic3—61no—
112C2×Dic3—121no—
113C2×C32—162no—
114C2×C32—161no—
115C24D3×A411yescharacteristic
116C22×C4—31no—
117C22×C4—31no—
118C22×C4—31no—
119C22×C4—31no—
120C22×C4—91no—
121C22×C4—91no—
122C22×C4—181no—
123C22×C4—181no—
124C4⋊C4—62no—
125C4⋊C4—182no—
126C22⋊C4—62no—
127C22⋊C4—182no—
128C42—181no—
129C42—181no—
130C42—181no—
131C42—181no—
132C22×C3—31no—
133C22×C3—31no—
134C22×C3—41no—
135C22×C3—62no—
136C22×C3—121no—
137C22×C3—161no—
138C22×C3—321no—
139C22×C3C2×#41⋊C311yescharacteristic
140A4—41no—
141A4—81no—
142C3×C4—62no—
143C3×C4—121no—
144C3×C4—481no—
145C3×C4—481no—
146Dic3—31no—
147Dic3—41no—
148Dic3—121no—
149Dic3—121no—
150Dic3#126⋊C311yescharacteristic
151C32—161noSylow
152C23—61no—
153C23—61no—
154C23C3⋊(#41⋊C3)12yes—
155C23C2×D3×A411yescharacteristic
156C2×C4—32no—
157C2×C4—61no—
158C2×C4—61no—
159C2×C4—61no—
160C2×C4—61no—
161C2×C4—61no—
162C2×C4—91no—
163C2×C4—91no—
164C2×C4—121no—
165C2×C4—181no—
166C2×C4—181no—
167C2×C4—181no—
168C2×C4—181no—
169C2×C4—181no—
170C2×C4—181no—
171C2×C4—181no—
172C2×C4—361no—
173C2×C3—31no—
174C2×C3—31no—
175C2×C3—42no—
176C2×C3—162no—
177C2×C3—161no—
178C2×C3—322no—
179C2×C3—321no—
180C2×C3C2×#126⋊C311yescharacteristic
181C22—31no—
182C22—31no—
183C22—41no—
184C22—62no—
185C22—121no—
186C22C2×C3⋊(#41⋊C3)11yescharacteristic
187C4—31no—
188C4—62no—
189C4—91no—
190C4—121no—
191C4—121no—
192C4—361no—
193C4—361no—
194C3—161no—
195C3—321no—
196C3#2401⋊C311yescharacteristic, complemented
197C2—31no—
198C2—31no—
199C2—42no—
200C2D3×#126⋊C311yescharacteristic
subgroupG/H
center, hypercenterC2D3×#126⋊C3
commutator, cosocle, hypocenterC3×#95C22×C3
FrattiniC23C2×D3×A4
FittingC3×#396C2×C3
socleC23×C3C22×A4
prime radicalC3×#396⋊C3C2
LCSG ▷ C3×#95
UCSC1 ◁ C2

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C3⋊(#376⋊C3)C2semidirect
3. C3⋊(#401⋊C3)C2semidirect
4. #77283C3semidirect
13. C3⋊#401C2×C3semidirect
14. #4648C2×C3semidirect
196. C3#2401⋊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⋊(#376⋊C3)2
C3⋊(#401⋊C3)2
#772833
#2401⋊C33
C2×Dic3×A44