Finite Group Databasebeta

← (C3⋊#4621)⋊C3 #13136751

Subgroups — (C3⋊#4621)⋊C3 #13136751

Order 1728.

161 conjugacy classes of subgroups; only the 19 normal subgroups are shown.

normal subgroups only

This group has 161 conjugacy classes of subgroups — too many to draw. Only its 19 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
1#95⋊H(3,𝔽3)C211yesmaximal, characteristic
2C3⋊#4621C311yesmaximal, characteristic, complemented
3C3×#4452—31nomaximal
4(C3⋊SL(2,ℤ/4))⋊C3—41nomaximal
5C3×#924—31no—
6C32×#95D311yescharacteristic
7C3×#830—31no—
8C3×#95⋊C3—21no—
9C3×#95⋊C3C2×C311yescharacteristic
10C2×C22⋊H(3,𝔽3)—41no—
11#4621—91no—
12C3×#328—91no—
13#4452—31no—
14C22×C32×C4—31no—
15C2×C3×Dic6—31no—
16C3⋊SL(2,ℤ/4)—41no—
17C3×#217—61no—
18C3×C4⋊Dic3—31no—
19C3×Dic3⋊C4—61no—
20C2×C3×C3⋊C8—61no—
21C22⋊H(3,𝔽3)—41no—
22(C3⋊Dic3)⋊C3—161no—
23C3×C22⋊Q8—91no—
24#924—31no—
25C3×C22⋊C8—91no—
26C3×#95—31no—
27C3×#95C3×D311yescharacteristic
28#830—31no—
29#95⋊C3—31no—
30#95⋊C3—61no—
31C23×C32S411yescharacteristic
32C2×C3×A4—41no—
33C2×C3×A4—81no—
34C2×C32×C4—31no—
35C2×C32×C4—31no—
36C2×C32×C4—121no—
37C2×C3×Dic3—61no—
38C2×C3×Dic3—61no—
39C3×Dic6—121no—
40C3×C3⋊C8—121no—
41#328—91noSylow
42C2×H(3,𝔽3)—161no—
43C2×C3×Q8—91no—
44C22×C3×C4—31no—
45C22×C3×C4—31no—
46C22×C3×C4—61no—
47C2×Dic6—31no—
48SL(2,ℤ/4)—361no—
49C2×C3×C8—181no—
50C3×C4⋊C4—91no—
51C3×C4⋊C4—181no—
52C3×C22⋊C4—181no—
53#217—61no—
54C4⋊Dic3—31no—
55Dic3⋊C4—61no—
56C2×C3⋊C8—61no—
57C22×C32—31no—
58C22×C32—31no—
59C22×C32#22611yescharacteristic
60C3×A4—41no—
61C3×A4—81no—
62C32×C4—61no—
63C32×C4—61no—
64C3⋊Dic3—161no—
65C3×Dic3—121no—
66C3×Dic3—121no—
67C22⋊Q8—91no—
68C22⋊C8—91no—
69#95(C3⋊D3)⋊C311yescharacteristic
70H(3,𝔽3)—161noSylow
71C23×C3—31no—
72C23×C3C3×S411yescharacteristic
73C2×A4—121no—
74C2×A4—241no—
75C3×Q8—361no—
76C2×C3×C4—31no—
77C2×C3×C4—31no—
78C2×C3×C4—31no—
79C2×C3×C4—31no—
80C2×C3×C4—61no—
81C2×C3×C4—61no—
82C2×C3×C4—121no—
83C2×C3×C4—121no—
84C2×C3×C4—121no—
85C2×C3×C4—121no—
86C2×C3×C4—181no—
87C2×C3×C4—181no—
88C2×Dic3—61no—
89C2×Dic3—61no—
90Dic6—121no—
91C3×C8—361no—
92C3⋊C8—121no—
93C2×C32—31no—
94C2×C32—31no—
95C2×C32—161no—
96C2×C32—321no—
97C2×C32#85711yescharacteristic
98C2×Q8—91no—
99C22×C4—31no—
100C2×C8—181no—
101C4⋊C4—91no—
102C4⋊C4—181no—
103C22⋊C4—181no—
104C22×C3—31no—
105C22×C3—31no—
106C22×C3—31no—
107C22×C3—31no—
108C22×C3—31no—
109C22×C3—61no—
110C22×C3—61no—
111C22×C3C3×#22611yescharacteristic
112A4—121no—
113A4—241no—
114C3×C4—61no—
115C3×C4—61no—
116C3×C4—61no—
117C3×C4—61no—
118C3×C4—121no—
119C3×C4—121no—
120C3×C4—361no—
121C3×C4—361no—
122Dic3—121no—
123Dic3—121no—
124Dic3—1441no—
125C32—161no—
126C32—321no—
127C32#462111yescharacteristic, complemented
128C23(C3⋊S4)⋊C311yescharacteristic
129Q8—361no—
130C2×C4—31no—
131C2×C4—31no—
132C2×C4—121no—
133C2×C4—181no—
134C2×C4—181no—
135C8—361no—
136C2×C3—31no—
137C2×C3—31no—
138C2×C3—31no—
139C2×C3—31no—
140C2×C3—31no—
141C2×C3—61no—
142C2×C3—61no—
143C2×C3—481no—
144C2×C3—961no—
145C2×C3C3×#85711yescharacteristic
146C22—31no—
147C22—31no—
148C22(C3⋊#226)⋊C311yescharacteristic
149C4—61no—
150C4—61no—
151C4—361no—
152C4—361no—
153C3—31no—
154C3—481no—
155C3—961no—
156C3C3×#462111yescharacteristic
157C2—31no—
158C2—31no—
159C2(C3⋊#857)⋊C311yescharacteristic
subgroupG/H
center, hypercenterC2(C3⋊#857)⋊C3
commutator, cosocle, hypocenterC3×#95⋊C3C2×C3
Frattini, socleC23×C3C3×S4
FittingC32×#95D3
prime radical#95⋊H(3,𝔽3)C2
LCSG ▷ C3×#95⋊C3
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
2. C3⋊#4621C3semidirect
127. C32#4621semidirect

Maximal subgroups

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

subgroupindex
#95⋊H(3,𝔽3)2
C3⋊#46213
C3×#44523
(C3⋊SL(2,ℤ/4))⋊C34