Finite Group Databasebeta

← (C3⋊#4622)⋊C3 #13136752

Subgroups — (C3⋊#4622)⋊C3 #13136752

Order 1728.

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

normal subgroups only

This group has 193 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, complemented
2C3⋊#4622C311yesmaximal, characteristic, complemented
3C3×#4451—31nomaximal
4C2×(C3⋊S4)⋊C3—41nomaximal
5C3×#930—31no—
6C32×#95D311yescharacteristic, complemented
7C3×#830—31no—
8C3×#95⋊C3—21no—
9C3×#95⋊C3C2×C311yescharacteristic, complemented
10C2×C22⋊H(3,𝔽3)—41no—
11(C3⋊S4)⋊C3—42no—
12#4622—91no—
13C3×#327—91no—
14#4451—31no—
15C2×C3⋊S4—41no—
16C22×C32×C4—31no—
17C2×C3×#67—61no—
18C2×C3×D12—31no—
19C3×(C2×D3)⋊C4—61no—
20C3×C4⋊Dic3—31no—
21C2×C3×C3⋊C8—61no—
22C2×(C3⋊D3)⋊C3—161no—
23C22⋊H(3,𝔽3)—41no—
24C3×#121—91no—
25#930—31no—
26C3×C22⋊C8—91no—
27C3×#95—31no—
28C3×#95C3×D311yescharacteristic
29#830—31no—
30#95⋊C3—31no—
31#95⋊C3—61no—
32C23×C32S411yescharacteristic
33C22×C3×D3—61no—
34C2×C3×A4—41no—
35C2×C3×A4—81no—
36C3⋊S4—42no—
37C2×C32×C4—31no—
38C2×C32×C4—31no—
39C2×C32×C4—121no—
40C3×#67—121no—
41C3×#67—121no—
42C2×C3×Dic3—61no—
43C3×D12—121no—
44C3×C3⋊C8—121no—
45#327—91noSylow
46C2×H(3,𝔽3)—161no—
47(C3⋊D3)⋊C3—162no—
48C2×S4—361no—
49C2×C3×D4—91no—
50C2×C3×D4—181no—
51C22×C3×C4—31no—
52C22×C3×C4—31no—
53C22×C3×C4—61no—
54C2×#67—61no—
55C2×D12—31no—
56C2×C3×C8—181no—
57C3×C4⋊C4—91no—
58C3×C22⋊C4—181no—
59(C2×D3)⋊C4—61no—
60C4⋊Dic3—31no—
61C2×C3⋊C8—61no—
62C22×C32—31no—
63C22×C32—31no—
64C22×C32GL(2,𝔽3)11yescharacteristic
65C2×C3⋊D3—161no—
66C2×C3×D3—121no—
67C2×C3×D3—121no—
68C2×C3×D3—121no—
69C3×A4—41no—
70C3×A4—81no—
71C32×C4—61no—
72C32×C4—61no—
73C3×Dic3—121no—
74#121—91no—
75C22⋊C8—91no—
76#95(C3⋊D3)⋊C311yescharacteristic, complemented
77H(3,𝔽3)—161noSylow
78C23×C3—31no—
79C23×C3—181no—
80C23×C3C3×S411yescharacteristic
81C22×D3—61no—
82C2×A4—121no—
83C2×A4—241no—
84S4—362no—
85C3×D4—361no—
86C3×D4—361no—
87C3×D4—361no—
88C2×C3×C4—31no—
89C2×C3×C4—31no—
90C2×C3×C4—31no—
91C2×C3×C4—31no—
92C2×C3×C4—61no—
93C2×C3×C4—61no—
94C2×C3×C4—121no—
95C2×C3×C4—121no—
96C2×C3×C4—121no—
97C2×C3×C4—121no—
98C2×C3×C4—181no—
99#67—121no—
100#67—121no—
101C2×Dic3—61no—
102D12—121no—
103C3×C8—361no—
104C3⋊C8—121no—
105C2×C32—31no—
106C2×C32—31no—
107C2×C32—161no—
108C2×C32—321no—
109C2×C32#85711yescharacteristic
110C3⋊D3—162no—
111C3×D3—241no—
112C2×D4—91no—
113C2×D4—181no—
114C22×C4—31no—
115C2×C8—181no—
116C4⋊C4—91no—
117C22⋊C4—181no—
118C22×C3—31no—
119C22×C3—31no—
120C22×C3—31no—
121C22×C3—31no—
122C22×C3—31no—
123C22×C3—61no—
124C22×C3—61no—
125C22×C3—361no—
126C22×C3—361no—
127C22×C3—361no—
128C22×C3C3×GL(2,𝔽3)11yescharacteristic
129C2×D3—121no—
130C2×D3—121no—
131C2×D3—121no—
132C2×D3—1441no—
133A4—121no—
134A4—241no—
135C3×C4—61no—
136C3×C4—61no—
137C3×C4—61no—
138C3×C4—61no—
139C3×C4—121no—
140C3×C4—121no—
141C3×C4—361no—
142Dic3—121no—
143C32—161no—
144C32—321no—
145C32#462211yescharacteristic, complemented
146C23—181no—
147C23(C3⋊S4)⋊C311yescharacteristic
148D4—361no—
149D4—361no—
150D4—361no—
151C2×C4—31no—
152C2×C4—31no—
153C2×C4—121no—
154C2×C4—181no—
155C8—361no—
156C2×C3—31no—
157C2×C3—31no—
158C2×C3—31no—
159C2×C3—31no—
160C2×C3—31no—
161C2×C3—61no—
162C2×C3—61no—
163C2×C3—481no—
164C2×C3—721no—
165C2×C3—961no—
166C2×C3C3×#85711yescharacteristic
167D3—241no—
168D3—1442no—
169C22—31no—
170C22—31no—
171C22—361no—
172C22—361no—
173C22—361no—
174C22(C3⋊GL(2,𝔽3))⋊C311yescharacteristic
175C4—61no—
176C4—61no—
177C4—361no—
178C3—31no—
179C3—481no—
180C3—961no—
181C3C3×#462211yescharacteristic
182C2—31no—
183C2—31no—
184C2—721no—
185C2(C3⋊#857)⋊C311yescharacteristic
subgroupG/H
center, hypercenterC2(C3⋊#857)⋊C3
commutator, cosocle, hypocenterC3×#95⋊C3C2×C3
Frattini, socleC23×C3C3×S4
FittingC32×#95D3
LCSG ▷ C3×#95⋊C3
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. #95⋊H(3,𝔽3)C2semidirect
2. C3⋊#4622C3semidirect
6. C32×#95D3semidirect
9. C3×#95⋊C3C2×C3semidirect
76. #95(C3⋊D3)⋊C3semidirect
145. C32#4622semidirect

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⋊#46223
C3×#44513
C2×(C3⋊S4)⋊C34