Finite Group Databasebeta

← #74293⋊C3 #11921148

Subgroups — #74293⋊C3 #11921148

Order 1152.

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

normal subgroups only

This group has 205 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×#383⋊C3C211yesmaximal, characteristic
2Dic3×C42⋊C3C211yesmaximal, characteristic
3C3⋊(#383⋊C3)C211yesmaximal, characteristic
4#74293C311yesmaximal, characteristic, complemented
5#2863⋊C3—31nomaximal
6A4×Dic6—41nomaximal
7C2×C3×C42⋊C3C2211yescharacteristic
8C3×#383C2×C311yescharacteristic
9#4937C2×C311yescharacteristic
10C42×Dic3C2×C311yescharacteristic
11#4655—31no—
12#4654—31no—
13#4647—31no—
14#4646—31no—
15#383⋊C3—21no—
16#383⋊C3—31no—
17#383⋊C3D311yescharacteristic
18C4×C42⋊C3—31no—
19C3×C4×A4—41no—
20Dic3×A4—41no—
21Dic3×A4—41no—
22C3×C42⋊C3Q811yescharacteristic, complemented
23#2863—31noSylow
24C22×Dic6A411yescharacteristic
25Q8×A4—121no—
26C2×C3×C42C22×C311yescharacteristic
27C2×C4⋊Dic3—31no—
28C2×Dic3⋊C4—31no—
29C2×Dic3⋊C4—31no—
30C2×C4×Dic3—31no—
31C2×C4×Dic3—31no—
32C2×C42⋊C3—21no—
33C2×C42⋊C3C2×D311yescharacteristic
34C3×#95—31no—
35C3×#95—31no—
36C3⋊#95—31no—
37C3⋊#95—31no—
38C3⋊#95—31no—
39C3⋊#95—31no—
40C2×C3×A4—41no—
41C3×Dic6—161no—
42#391—91no—
43#389—91no—
44#387—91no—
45#387—91no—
46#383—31no—
47#383C3×D311yescharacteristic
48C43—31no—
49C22×C3×C4—31no—
50C22×C3×C4—31no—
51C22×C3×C4C2×A411yescharacteristic
52C22×Dic3—31no—
53C22×Dic3—31no—
54C22×Dic3C2×A411yescharacteristic
55C22×Dic3C2×A411yescharacteristic
56C2×Dic6—61no—
57C2×Dic6—61no—
58C4×A4—41no—
59C4×A4—81no—
60C4×A4—121no—
61C4×A4—121no—
62C3×C42—31no—
63C3×C42C3×Q811yescharacteristic, complemented
64C4⋊Dic3—62no—
65Dic3⋊C4—61no—
66Dic3⋊C4—61no—
67Dic3⋊C4—62no—
68C4×Dic3—61no—
69C4×Dic3—61no—
70C4×Dic3—62no—
71C42⋊C3—21no—
72C42⋊C3Dic611yescharacteristic, complemented
73C3×A4—41no—
74C32×C4—161no—
75C3×Dic3—161no—
76C3×Dic3—161no—
77C22×Q8—31no—
78C2×C4⋊C4—91no—
79C2×C4⋊C4—91no—
80C2×C4⋊C4—91no—
81C2×C42—91no—
82C2×C42—91no—
83C2×C42C2×C3×D311yescharacteristic
84#95—31no—
85#95—31no—
86#95—91no—
87#95—91no—
88#95—91no—
89#95—91no—
90C23×C3C22×A411yescharacteristic
91C2×A4—41no—
92C2×A4—81no—
93C3×Q8—481no—
94C2×C3×C4—31no—
95C2×C3×C4—31no—
96C2×C3×C4—61no—
97C2×C3×C4—61no—
98C2×C3×C4—61no—
99C2×C3×C4—61no—
100C2×C3×C4—61no—
101C2×C3×C4—61no—
102C2×Dic3—31no—
103C2×Dic3—31no—
104C2×Dic3—32no—
105C2×Dic3—61no—
106C2×Dic3—61no—
107C2×Dic3—61no—
108C2×Dic3—61no—
109C2×Dic3—61no—
110C2×Dic3—61no—
111Dic6—41no—
112Dic6—121no—
113C2×C32—161no—
114C2×Q8—181no—
115C2×Q8—181no—
116C22×C4—31no—
117C22×C4—31no—
118C22×C4—31no—
119C22×C4—31no—
120C22×C4—91no—
121C22×C4—91no—
122C22×C4D3×A411yescharacteristic
123C4⋊C4—181no—
124C4⋊C4—181no—
125C4⋊C4—182no—
126C4⋊C4—182no—
127C42—31no—
128C42—181no—
129C42—181no—
130C42—182no—
131C42C3×Dic611yescharacteristic, complemented
132C22×C3—31no—
133C22×C3—31no—
134C22×C3Q8×A411yescharacteristic
135A4—41no—
136A4—81no—
137C3×C4—41no—
138C3×C4—61no—
139C3×C4—61no—
140C3×C4—121no—
141C3×C4—161no—
142C3×C4—321no—
143C3×C4—481no—
144C3×C4—481no—
145Dic3—31no—
146Dic3—41no—
147Dic3—62no—
148Dic3—121no—
149Dic3#126⋊C311yescharacteristic
150C32—161noSylow
151C23C2×D3×A411yescharacteristic
152Q8—121no—
153Q8—361no—
154C2×C4—31no—
155C2×C4—31no—
156C2×C4—61no—
157C2×C4—61no—
158C2×C4—61no—
159C2×C4—61no—
160C2×C4—61no—
161C2×C4—61no—
162C2×C4—91no—
163C2×C4—91no—
164C2×C4—92no—
165C2×C4—181no—
166C2×C4—181no—
167C2×C4—181no—
168C2×C4—181no—
169C2×C4—181no—
170C2×C4—181no—
171C2×C3—31no—
172C2×C3—31no—
173C2×C3—161no—
174C2×C3—321no—
175C2×C3C2×#126⋊C311yescharacteristic
176C22—31no—
177C22—31no—
178C22A4×Dic611yescharacteristic
179C4—31no—
180C4—41no—
181C4—61no—
182C4—61no—
183C4—91no—
184C4—121no—
185C4—121no—
186C4—182no—
187C4—361no—
188C3—161no—
189C3—321no—
190C3#2863⋊C311yescharacteristic, complemented
191C2—31no—
192C2—31no—
193C2D3×#126⋊C311yescharacteristic
subgroupG/H
center, hypercenterC2D3×#126⋊C3
commutator, cosocleC2×C3×C42C22×C3
FrattiniC23C2×D3×A4
FittingC3×#383C2×C3
socleC23×C3C22×A4
prime radicalC2×C3×C42⋊C3C22
hypocenterC3×C42C3×Q8
LCSG ▷ C2×C3×C42 ▷ C3×C42
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
4. #74293C3semidirect
22. C3×C42⋊C3Q8semidirect
63. C3×C42C3×Q8semidirect
72. C42⋊C3Dic6semidirect
131. C42C3×Dic6semidirect
190. C3#2863⋊C3semidirect

Maximal subgroups

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

subgroupindex
C3×#383⋊C32
Dic3×C42⋊C32
C3⋊(#383⋊C3)2
#742933
#2863⋊C33
A4×Dic64