Finite Group Databasebeta

← #78416⋊C3 #11921199

Subgroups — #78416⋊C3 #11921199

Order 1152.

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

normal subgroups only

This group has 182 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×#401⋊C3C211yesmaximal, characteristic
2C3⋊(#376⋊C3)C211yesmaximal, characteristic
3C3⋊(#401⋊C3)C211yesmaximal, characteristic
4#78416C311yesmaximal, characteristic, complemented
5#2645⋊C3—31nomaximal
6A4×Dic6—41nomaximal
7C3×#95⋊C3C2211yescharacteristic
8C3×#401C2×C311yescharacteristic
9C3⋊#401C2×C311yescharacteristic
10#4660—31no—
11#4659—31no—
12#4648C2×C311yescharacteristic
13#4647—31no—
14#4646—31no—
15#401⋊C3—21no—
16#401⋊C3—31no—
17#401⋊C3D311yescharacteristic
18#376⋊C3—31no—
19C3×C4×A4—41no—
20Dic3×A4—41no—
21Dic3×A4—41no—
22#2645—31noSylow
23C22×Dic6A411yescharacteristic
24Q8×A4—121no—
25C2×C4⋊Dic3—31no—
26C2×Dic3⋊C4—31no—
27C2×Dic3⋊C4—31no—
28C2×C4×Dic3—31no—
29C3×#95—31no—
30C3×#95—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—41no—
40C3×Dic6—161no—
41#401—31no—
42#401C3×D311yescharacteristic
43#400—91no—
44#400—91no—
45#391—91no—
46#389—91no—
47#376—31no—
48C22×C3×C4—31no—
49C22×C3×C4—31no—
50C22×C3×C4C2×A411yescharacteristic
51C22×Dic3—31no—
52C22×Dic3—31no—
53C22×Dic3C2×A411yescharacteristic
54C22×Dic3C2×A411yescharacteristic
55C2×Dic6—61no—
56C2×Dic6—61no—
57C4×A4—41no—
58C4×A4—81no—
59C4×A4—121no—
60C4×A4—121no—
61C4⋊Dic3—121no—
62Dic3⋊C4—61no—
63Dic3⋊C4—61no—
64Dic3⋊C4—121no—
65C4×Dic3—61no—
66C4×Dic3—61no—
67C3×A4—41no—
68C32×C4—161no—
69C3×Dic3—161no—
70C3×Dic3—161no—
71C22×Q8—31no—
72C2×C4⋊C4—91no—
73C2×C4⋊C4—91no—
74C2×C4⋊C4—91no—
75C2×C42—91no—
76#95—31no—
77#95—31no—
78#95—91no—
79#95—91no—
80#95—91no—
81#95—91no—
82#95—91no—
83#95C2×C3×D311yescharacteristic
84C23×C3C22×A411yescharacteristic
85C2×A4—41no—
86C2×A4—81no—
87C3×Q8—481no—
88C2×C3×C4—61no—
89C2×C3×C4—61no—
90C2×C3×C4—61no—
91C2×C3×C4—62no—
92C2×C3×C4—61no—
93C2×C3×C4—61no—
94C2×Dic3—31no—
95C2×Dic3—31no—
96C2×Dic3—61no—
97C2×Dic3—61no—
98C2×Dic3—61no—
99C2×Dic3—61no—
100C2×Dic3—61no—
101C2×Dic3—61no—
102C2×Dic3—61no—
103Dic6—41no—
104Dic6—121no—
105C2×C32—161no—
106C2×Q8—181no—
107C2×Q8—181no—
108C22×C4—31no—
109C22×C4—31no—
110C22×C4—31no—
111C22×C4—31no—
112C22×C4—91no—
113C22×C4—91no—
114C22×C4D3×A411yescharacteristic
115C4⋊C4—181no—
116C4⋊C4—181no—
117C4⋊C4—361no—
118C4⋊C4—361no—
119C42—181no—
120C42—181no—
121C22×C3—31no—
122C22×C3—31no—
123C22×C3#99411yescharacteristic
124A4—41no—
125A4—81no—
126C3×C4—41no—
127C3×C4—121no—
128C3×C4—121no—
129C3×C4—161no—
130C3×C4—321no—
131C3×C4—481no—
132C3×C4—481no—
133Dic3—31no—
134Dic3—41no—
135Dic3—121no—
136Dic3—121no—
137Dic3#126⋊C311yescharacteristic
138C32—161noSylow
139C23C2×D3×A411yescharacteristic
140Q8—121no—
141Q8—361no—
142C2×C4—61no—
143C2×C4—61no—
144C2×C4—61no—
145C2×C4—62no—
146C2×C4—61no—
147C2×C4—61no—
148C2×C4—91no—
149C2×C4—91no—
150C2×C4—181no—
151C2×C4—181no—
152C2×C4—181no—
153C2×C4—181no—
154C2×C4—181no—
155C2×C4—181no—
156C2×C4—181no—
157C2×C3—31no—
158C2×C3—31no—
159C2×C3—161no—
160C2×C3—321no—
161C2×C3C2×#126⋊C311yescharacteristic
162C22—31no—
163C22—31no—
164C22C3⋊#99411yescharacteristic
165C4—31no—
166C4—41no—
167C4—91no—
168C4—121no—
169C4—121no—
170C4—121no—
171C4—361no—
172C4—361no—
173C3—161no—
174C3—321no—
175C3#2645⋊C311yescharacteristic, complemented
176C2—31no—
177C2—31no—
178C2D3×#126⋊C311yescharacteristic
subgroupG/H
center, hypercenterC2D3×#126⋊C3
commutator, cosocle, hypocenterC3×#95C22×C3
FrattiniC23C2×D3×A4
FittingC3×#401C2×C3
socleC23×C3C22×A4
prime radicalC3×#95⋊C3C22
LCSG ▷ C3×#95
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
4. #78416C3semidirect
175. C3#2645⋊C3semidirect

Maximal subgroups

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

subgroupindex
C3×#401⋊C32
C3⋊(#376⋊C3)2
C3⋊(#401⋊C3)2
#784163
#2645⋊C33
A4×Dic64