Finite Group Databasebeta

← C3×#11724029 #72220511

Subgroups — C3×#11724029 #72220511

Order 2592.

634 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 634 conjugacy classes of subgroups — too many to draw. Only its 40 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×(C3×A4)⋊A4C211yesmaximal, characteristic, complemented
2C32×#1020—32nomaximal
3C32×GL(2,ℤ/4)—32nomaximal
4#11724029C311yesmaximal, characteristic, direct product factor
5C3×#6258—42nomaximal
6C32×C22⋊A4D312yescomplemented
7C22×C32×A4D312yescomplemented
8C2×C32×S4—32no—
9C32×SL(2,ℤ/4)—32no—
10(C3×A4)⋊A4—22no—
11(C3×A4)⋊A4—22no—
12(C3×A4)⋊A4C2×C311yescharacteristic, complemented
13C3×C22⋊H(3,𝔽3)—42no—
14C3×#1020—36no—
15C3×#1020—32no—
16C3×GL(2,ℤ/4)—36no—
17C3×GL(2,ℤ/4)—32no—
18C32×#120—91no—
19C2×C32×A4—32no—
20C32×S4—62no—
21C32×S4—124no—
22C32×S4—122no—
23C32×#67—122no—
24#6258—42no—
25C3×#272—161no—
26C24×C32C3⋊D311yescharacteristic
27C3×C22⋊A4—22no—
28C3×C22⋊A4—36no—
29C3×C22⋊A4C3×D312yescomplemented
30C22×C3×A4—22no—
31C22×C3×A4—36no—
32C22×C3×A4C3×D312yescomplemented
33C2×C3×S4—36no—
34C2×C3×S4—32no—
35C2×C32×D4—92no—
36C2×C32×D4—91no—
37C3×SL(2,ℤ/4)—36no—
38C3×SL(2,ℤ/4)—32no—
39C32×C22⋊C4—92no—
40C32×C22⋊C4—91no—
41C22×C33—42no—
42C2×C32×D3—122no—
43C32×A4—44no—
44C32×A4—122no—
45C32×A4S412yescomplemented
46C32×Dic3—122no—
47C22⋊H(3,𝔽3)—42no—
48C22⋊H(3,𝔽3)—84no—
49C22⋊H(3,𝔽3)—82no—
50C22⋊H(3,𝔽3)—82no—
51#1020—32no—
52GL(2,ℤ/4)—32no—
53C3×#120—93no—
54C3×#120—91no—
55C3×H(3,𝔽3)—161noSylow
56C23×C32—32no—
57C23×C32—91no—
58C23×C32—91no—
59C2×C3×A4—36no—
60C2×C3×A4—32no—
61C2×C3×A4—62no—
62C2×C3×A4—66no—
63C3×S4—66no—
64C3×S4—62no—
65C3×S4—124no—
66C3×S4—122no—
67C3×S4—126no—
68C3×S4—1212no—
69C32×D4—182no—
70C32×D4—182no—
71C32×D4—182no—
72C2×C32×C4—92no—
73C2×C32×C4—91no—
74C3×#67—122no—
75C3×#67—126no—
76C2×C33—122no—
77C32×D3—242no—
78C32×D3—482no—
79#272—161no—
80C24×C3#27213yescomplemented
81C24×C3C3×C3⋊D311yescharacteristic
82C22⋊A4—32no—
83C22⋊A4—62no—
84C22×A4—32no—
85C22×A4—62no—
86C2×S4—32no—
87C2×C3×D4—96no—
88C2×C3×D4—92no—
89C2×C3×D4—93no—
90C2×C3×D4—91no—
91SL(2,ℤ/4)—32no—
92C3×C22⋊C4—96no—
93C3×C22⋊C4—92no—
94C3×C22⋊C4—93no—
95C3×C22⋊C4—91no—
96C22×C32—32no—
97C22×C32—42no—
98C22×C32—82no—
99C22×C32—91no—
100C22×C32—92no—
101C22×C32—126no—
102C22×C32—182no—
103C22×C32—181no—
104C22×C32C3⋊S412yes—
105C2×C3×D3—122no—
106C2×C3×D3—126no—
107C3×A4—22no—
108C3×A4—36no—
109C3×A4—44no—
110C3×A4—84no—
111C3×A4—122no—
112C3×A4—126no—
113C3×A4—1212no—
114C3×A4—242no—
115C3×A4—246no—
116C3×A4C3×S412yescomplemented
117C32×C4—182no—
118C32×C4—181no—
119C3×Dic3—122no—
120C3×Dic3—126no—
121#120—91noSylow
122C33—42no—
123C33—162no—
124H(3,𝔽3)—161no—
125H(3,𝔽3)—322no—
126H(3,𝔽3)—322no—
127C23×C3—36no—
128C23×C3—32no—
129C23×C3—93no—
130C23×C3—91no—
131C23×C3—91no—
132C23×C3—93no—
133C2×A4—32no—
134C2×A4—62no—
135C2×A4—66no—
136S4—62no—
137S4—122no—
138S4—124no—
139C3×D4—182no—
140C3×D4—186no—
141C3×D4—182no—
142C3×D4—186no—
143C3×D4—186no—
144C3×D4—182no—
145C2×C3×C4—92no—
146C2×C3×C4—96no—
147C2×C3×C4—91no—
148C2×C3×C4—93no—
149#67—122no—
150C2×C32—32no—
151C2×C32—91no—
152C2×C32—122no—
153C2×C32—126no—
154C2×C32—242no—
155C2×C32—246no—
156C2×C32—361no—
157C3×D3—242no—
158C3×D3—246no—
159C3×D3—482no—
160C3×D3—486no—
161C24C3×#27211yescharacteristic, complemented
162C2×D4—92no—
163C2×D4—91no—
164C22⋊C4—92no—
165C22⋊C4—91no—
166C22×C3—32no—
167C22×C3—36no—
168C22×C3—91no—
169C22×C3—93no—
170C22×C3—92no—
171C22×C3—96no—
172C22×C3—122no—
173C22×C3—182no—
174C22×C3—186no—
175C22×C3—181no—
176C22×C3—183no—
177C22×C3—242no—
178C22×C3#625816yescomplemented
179C22×C3C3×C3⋊S412yes—
180C2×D3—122no—
181A4—32no—
182A4—62no—
183A4—122no—
184A4—124no—
185A4—242no—
186A4—246no—
187A4—244no—
188C3×C4—182no—
189C3×C4—186no—
190C3×C4—181no—
191C3×C4—183no—
192Dic3—122no—
193C32—42no—
194C32—82no—
195C32—126no—
196C32—162no—
197C32—322no—
198C32—486no—
199C32A4⋊S411yescharacteristic
200C23—32no—
201C23—91no—
202C23—91no—
203D4—182no—
204D4—182no—
205D4—182no—
206C2×C4—92no—
207C2×C4—91no—
208C2×C3—32no—
209C2×C3—36no—
210C2×C3—91no—
211C2×C3—93no—
212C2×C3—122no—
213C2×C3—242no—
214C2×C3—246no—
215C2×C3—361no—
216C2×C3—363no—
217D3—242no—
218D3—482no—
219C22—32no—
220C22—91no—
221C22—92no—
222C22—182no—
223C22—181no—
224C22C3×#625812yescomplemented
225C4—182no—
226C4—181no—
227C3—122no—
228C3—242no—
229C3—482no—
230C3—962no—
231C3#1172402913yesdirect product factor
232C3C3×A4⋊S411yescharacteristic
233C2—32no—
234C2—91no—
235C2—361no—
subgroupG/H
center, hypercenterC32A4⋊S4
commutator, cosocle, hypocenter(C3×A4)⋊A4C2×C3
FrattiniC3C3×A4⋊S4
Fitting, socleC24×C32C3⋊D3
LCSG ▷ (C3×A4)⋊A4
UCSC1 ◁ C32

Complements

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

NH ≅ G/Ntype
1. C3×(C3×A4)⋊A4C2semidirect
4. #11724029C3direct (N × H)
6. C32×C22⋊A4D3semidirect
7. C22×C32×A4D3semidirect
12. (C3×A4)⋊A4C2×C3semidirect
29. C3×C22⋊A4C3×D3semidirect
32. C22×C3×A4C3×D3semidirect
45. C32×A4S4semidirect
80. C24×C3#272semidirect
116. C3×A4C3×S4semidirect
161. C24C3×#272semidirect
178. C22×C3#6258semidirect
224. C22C3×#6258semidirect
231. C3#11724029direct (N × H)

Maximal subgroups

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

subgroupindex
C3×(C3×A4)⋊A42
C32×#10203
C32×GL(2,ℤ/4)3
#117240293
C3×#62584