Finite Group Databasebeta

← #74292⋊C3 #11921149

Subgroups — #74292⋊C3 #11921149

Order 1152.

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

normal subgroups only

This group has 185 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×#383⋊C3C211yesmaximal, characteristic
2C3⋊(#383⋊C3)C211yesmaximal, characteristic
3C3⋊(#384⋊C3)C211yesmaximal, characteristic
4#74292C311yesmaximal, characteristic, complemented
5#2843⋊C3—31nomaximal
6A4×Dic6—41nomaximal
7C2×C3×C42⋊C3C2211yescharacteristic
8C3×#383C2×C311yescharacteristic
9#4937C2×C311yescharacteristic
10#4935C2×C311yescharacteristic
11#4661—31no—
12#4660—31no—
13#4657—31no—
14#4656—31no—
15#384⋊C3—31no—
16#383⋊C3—21no—
17#383⋊C3—31no—
18#383⋊C3D311yescharacteristic
19C3×C4×A4—41no—
20Dic3×A4—41no—
21Dic3×A4—41no—
22C3×C42⋊C3Q811yescharacteristic, complemented
23#2843—31noSylow
24C22×Dic6A411yescharacteristic
25Q8×A4—121no—
26C2×C3×C42C22×C311yescharacteristic
27C2×C4⋊Dic3—31no—
28C2×C4⋊Dic3—31no—
29C2×C4⋊Dic3—31no—
30C2×Dic3⋊C4—31no—
31C2×Dic3⋊C4—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#400—91no—
43#398—91no—
44#398—91no—
45#395—91no—
46#384—31no—
47#383—31no—
48#383C3×D311yescharacteristic
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—121no—
57C4×A4—41no—
58C4×A4—81no—
59C4×A4—121no—
60C4×A4—121no—
61C3×C42—31no—
62C3×C42C3×Q811yescharacteristic, complemented
63C4⋊Dic3—121no—
64C4⋊Dic3—121no—
65C4⋊Dic3—121no—
66Dic3⋊C4—121no—
67Dic3⋊C4—121no—
68C42⋊C3—21no—
69C42⋊C3Dic611yescharacteristic, complemented
70C3×A4—41no—
71C32×C4—161no—
72C3×Dic3—161no—
73C3×Dic3—161no—
74C22×Q8—31no—
75C2×C4⋊C4—91no—
76C2×C4⋊C4—91no—
77C2×C4⋊C4—91no—
78C2×C4⋊C4—91no—
79C2×C4⋊C4—91no—
80C2×C42C2×C3×D311yescharacteristic
81#95—31no—
82#95—31no—
83#95—91no—
84#95—91no—
85#95—91no—
86#95—91no—
87C23×C3C22×A411yescharacteristic
88C2×A4—41no—
89C2×A4—81no—
90C3×Q8—481no—
91C2×C3×C4—31no—
92C2×C3×C4—31no—
93C2×C3×C4—61no—
94C2×C3×C4—61no—
95C2×C3×C4—61no—
96C2×C3×C4—61no—
97C2×C3×C4—62no—
98C2×Dic3—61no—
99C2×Dic3—61no—
100C2×Dic3—61no—
101C2×Dic3—61no—
102C2×Dic3—61no—
103C2×Dic3—61no—
104C2×Dic3—62no—
105Dic6—41no—
106Dic6—121no—
107C2×C32—161no—
108C2×Q8—361no—
109C22×C4—31no—
110C22×C4—31no—
111C22×C4—31no—
112C22×C4—31no—
113C22×C4—91no—
114C22×C4—91no—
115C22×C4D3×A411yescharacteristic
116C4⋊C4—361no—
117C4⋊C4—361no—
118C4⋊C4—361no—
119C4⋊C4—361no—
120C4⋊C4—361no—
121C42—31no—
122C42C3×Dic611yescharacteristic, complemented
123C22×C3—31no—
124C22×C3—31no—
125C22×C3Q8×A411yescharacteristic
126A4—41no—
127A4—81no—
128C3×C4—41no—
129C3×C4—61no—
130C3×C4—61no—
131C3×C4—121no—
132C3×C4—161no—
133C3×C4—321no—
134C3×C4—481no—
135C3×C4—481no—
136Dic3—41no—
137Dic3—41no—
138Dic3—121no—
139Dic3—121no—
140C32—161noSylow
141C23C2×D3×A411yescharacteristic
142Q8—121no—
143Q8—361no—
144C2×C4—31no—
145C2×C4—31no—
146C2×C4—61no—
147C2×C4—61no—
148C2×C4—61no—
149C2×C4—61no—
150C2×C4—62no—
151C2×C4—181no—
152C2×C4—181no—
153C2×C4—181no—
154C2×C4—181no—
155C2×C4—181no—
156C2×C4—181no—
157C2×C4—182no—
158C2×C3—31no—
159C2×C3—31no—
160C2×C3—161no—
161C2×C3—321no—
162C2×C3#560⋊C311yescharacteristic
163C22—31no—
164C22—31no—
165C22A4×Dic611yescharacteristic
166C4—41no—
167C4—61no—
168C4—61no—
169C4—121no—
170C4—121no—
171C4—121no—
172C4—361no—
173C4—361no—
174C3—161no—
175C3—321no—
176C3#2843⋊C311yescharacteristic, complemented
177C2—31no—
178C2—31no—
179C2(#126⋊C3)⋊D311yescharacteristic
subgroupG/H
center, hypercenterC2(#126⋊C3)⋊D3
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. #74292C3semidirect
22. C3×C42⋊C3Q8semidirect
62. C3×C42C3×Q8semidirect
69. C42⋊C3Dic6semidirect
122. C42C3×Dic6semidirect
176. C3#2843⋊C3semidirect

Maximal subgroups

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

subgroupindex
C3×#383⋊C32
C3⋊(#383⋊C3)2
C3⋊(#384⋊C3)2
#742923
#2843⋊C33
A4×Dic64