Finite Group Databasebeta

← C3⋊(#1446⋊C3) #11920177

Subgroups — C3⋊(#1446⋊C3) #11920177

Order 1152.

342 conjugacy classes of subgroups; only the 33 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 33 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
1C2×C3×C22⋊SL(2,𝔽3)C211yesmaximal, characteristic
2#72134C311yesmaximal, characteristic, complemented
3#1446⋊C3—31nomaximal
4C3×C22⋊SL(2,𝔽3)C411yescharacteristic, complemented
5C2×Dic3×A4—41nomaximal
6C23×C3×Q8C2×C311yescharacteristic
7C2×C22⋊SL(2,𝔽3)—21no—
8C2×C22⋊SL(2,𝔽3)D311yescharacteristic
9C2×C3⋊#95—31no—
10C2×C3⋊#95—31no—
11C22×C3×A4—41no—
12C2×C3×SL(2,𝔽3)—82no—
13Dic3×A4—42no—
14#1446—31noSylow
15C22×C3×Q8—31no—
16C22×C3×Q8—62no—
17C22×C3×Q8—62no—
18C22×C3×Q8C3×C411yescharacteristic, complemented
19C23×C3×C4—31no—
20C23×Dic3—31no—
21C23×Dic3A411yescharacteristic
22C22⋊SL(2,𝔽3)—21no—
23C22⋊SL(2,𝔽3)Dic311yescharacteristic, complemented
24C2×C4×A4—121no—
25C3⋊#95—62no—
26C3⋊#95—62no—
27C2×C3×A4—41no—
28C2×C3×A4—41no—
29C2×C3×A4—41no—
30C2×C3×Dic3—161no—
31C3×SL(2,𝔽3)—82no—
32C23×Q8C3×D311yescharacteristic
33C2×#95—91no—
34C2×#95—91no—
35C24×C3C2×A411yescharacteristic
36C22×A4—41no—
37C22×A4—81no—
38C2×C3×Q8—22no—
39C2×C3×Q8—62no—
40C2×C3×Q8—62no—
41C2×C3×Q8—64no—
42C2×C3×Q8—62no—
43C2×C3×Q8—62no—
44C2×C3×Q8—64no—
45C2×C3×Q8—62no—
46C22×C3×C4—32no—
47C22×C3×C4—32no—
48C22×C3×C4—31no—
49C22×C3×C4—31no—
50C22×C3×C4—62no—
51C22×C3×C4—62no—
52C22×Dic3—32no—
53C22×Dic3—61no—
54C22×Dic3—62no—
55C22×Dic3—61no—
56C22×Dic3—62no—
57C22×Dic3—61no—
58C22×Dic3—61no—
59C22×Dic3SL(2,𝔽3)12yescomplemented
60C2×SL(2,𝔽3)—82no—
61C2×SL(2,𝔽3)—84no—
62C4×A4—122no—
63C22×C32—161no—
64C3×A4—41no—
65C3×Dic3—162no—
66C22×Q8—31no—
67C22×Q8—62no—
68C22×Q8—62no—
69C22×Q8C3×Dic311yescharacteristic, complemented
70C23×C4—31no—
71C23×C4—31no—
72C23×C4—91no—
73#95—182no—
74#95—182no—
75C23×C3—31no—
76C23×C3—31no—
77C23×C3—31no—
78C23×C3—31no—
79C23×C3C4×A411yescharacteristic
80C23×C3C2×SL(2,𝔽3)11yescharacteristic
81C23×C3#41⋊C311yescharacteristic
82C2×A4—41no—
83C2×A4—41no—
84C2×A4—41no—
85C2×A4—81no—
86C2×A4—81no—
87C2×A4—81no—
88C3×Q8—22no—
89C3×Q8—62no—
90C3×Q8—62no—
91C3×Q8—62no—
92C3×Q8—64no—
93C2×C3×C4—32no—
94C2×C3×C4—32no—
95C2×C3×C4—62no—
96C2×C3×C4—64no—
97C2×C3×C4—62no—
98C2×C3×C4—62no—
99C2×C3×C4—62no—
100C2×C3×C4—481no—
101C2×Dic3—41no—
102C2×Dic3—62no—
103C2×Dic3—64no—
104C2×Dic3—62no—
105C2×Dic3—121no—
106C2×Dic3—122no—
107C2×Dic3—121no—
108C2×Dic3—121no—
109SL(2,𝔽3)—82no—
110SL(2,𝔽3)—84no—
111C2×C32—161no—
112C2×C32—161no—
113C2×C32—161no—
114C24D3×A411yescharacteristic
115C2×Q8—22no—
116C2×Q8—62no—
117C2×Q8—62no—
118C2×Q8—64no—
119C2×Q8—62no—
120C2×Q8—62no—
121C2×Q8—64no—
122C2×Q8—62no—
123C22×C4—32no—
124C22×C4—32no—
125C22×C4—31no—
126C22×C4—31no—
127C22×C4—32no—
128C22×C4—62no—
129C22×C4—62no—
130C22×C4—92no—
131C22×C4—181no—
132C22×C4—182no—
133C22×C4—181no—
134C22×C4—182no—
135C22×C4—181no—
136C22×C4—181no—
137C22×C3—31no—
138C22×C3—31no—
139C22×C3—31no—
140C22×C3—32no—
141C22×C3—31no—
142C22×C3—31no—
143C22×C3—31no—
144C22×C3—31no—
145C22×C3—31no—
146C22×C3—31no—
147C22×C3—161no—
148C22×C3—321no—
149C22×C3C4×SL(2,𝔽3)11yescharacteristic
150C22×C3#120⋊C311yescharacteristic
151A4—41no—
152A4—81no—
153C3×C4—62no—
154C3×C4—62no—
155C3×C4—482no—
156Dic3—42no—
157Dic3—122no—
158C32—161noSylow
159C23—31no—
160C23—31no—
161C23—31no—
162C23—31no—
163C23C3⋊(#41⋊C3)11yescharacteristic
164C23D3×SL(2,𝔽3)11yescharacteristic
165C23Dic3×A411yescharacteristic
166Q8—22no—
167Q8—62no—
168Q8—62no—
169Q8—62no—
170Q8—64no—
171C2×C4—32no—
172C2×C4—32no—
173C2×C4—62no—
174C2×C4—64no—
175C2×C4—62no—
176C2×C4—62no—
177C2×C4—62no—
178C2×C4—121no—
179C2×C4—182no—
180C2×C4—184no—
181C2×C4—182no—
182C2×C4—361no—
183C2×C4—362no—
184C2×C4—361no—
185C2×C4—361no—
186C2×C3—31no—
187C2×C3—31no—
188C2×C3—31no—
189C2×C3—31no—
190C2×C3—161no—
191C2×C3—161no—
192C2×C3—161no—
193C2×C3—321no—
194C2×C3—321no—
195C2×C3—321no—
196C2×C3#379⋊C311yescharacteristic
197C2×C3#393⋊C311yescharacteristic
198C2×C3#395⋊C311yescharacteristic
199C22—31no—
200C22—31no—
201C22—31no—
202C22—32no—
203C22—31no—
204C22—31no—
205C22—31no—
206C22—31no—
207C22—31no—
208C22—31no—
209C22Dic3×SL(2,𝔽3)11yescharacteristic
210C22C3⋊(#120⋊C3)11yescharacteristic
211C4—62no—
212C4—62no—
213C4—122no—
214C4—362no—
215C3—161no—
216C3—321no—
217C3#1446⋊C311yescharacteristic, complemented
218C2—31no—
219C2—31no—
220C2—31no—
221C2—31no—
222C2C3⋊(#395⋊C3)11yescharacteristic
223C2C3⋊(#393⋊C3)11yescharacteristic
224C2C3⋊(#379⋊C3)11yescharacteristic
subgroupG/H
center, hypercenterC22C3⋊(#120⋊C3)
commutator, hypocenterC22×C3×Q8C3×C4
FrattiniC24D3×A4
Fitting, cosocleC23×C3×Q8C2×C3
socleC24×C3C2×A4
prime radicalC2×C3×C22⋊SL(2,𝔽3)C2
LCSG ▷ C22×C3×Q8
UCSC1 ◁ C22

Complements

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

NH ≅ G/Ntype
2. #72134C3semidirect
4. C3×C22⋊SL(2,𝔽3)C4semidirect
18. C22×C3×Q8C3×C4semidirect
23. C22⋊SL(2,𝔽3)Dic3semidirect
59. C22×Dic3SL(2,𝔽3)semidirect
69. C22×Q8C3×Dic3semidirect
217. C3#1446⋊C3semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C22⋊SL(2,𝔽3)2
#721343
#1446⋊C33
C2×Dic3×A44