Finite Group Databasebeta

← C3×C4⋊#857 #11920760

Subgroups — C3×C4⋊#857 #11920760

Order 1152.

337 conjugacy classes of subgroups; only the 30 normal subgroups are shown.

normal subgroups only

This group has 337 conjugacy classes of subgroups — too many to draw. Only its 30 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×#857C212yesmaximal, complemented
2C3×C4×C42⋊C3C211yesmaximal, characteristic, complemented
3C4⋊#857C311yesmaximal, characteristic, direct product factor
4C3×#1962—31nomaximal
5C3×C4⋊S4—41nomaximal
6C2×C3×C42⋊C3C2211yescharacteristic
7C3×#857—22no—
8C3×#532—31no—
9C2×#857C2×C312yescomplemented
10C3×#423—31no—
11C2×C3×#104—32no—
12C2×C3×#104—32no—
13C3×C43D311yescharacteristic, complemented
14C4×C42⋊C3—21no—
15C4×C42⋊C3C2×C311yescharacteristic, complemented
16C2×C3×S4—42no—
17C3×C4×A4—41no—
18C3×C42⋊C3D411yescharacteristic, complemented
19#1962—31noSylow
20C2×C3×#41—32no—
21C4⋊S4—41no—
22C2×C3×M16—32no—
23C3×C4⋊Q8—31no—
24C3×#127—31no—
25C3×#124—32no—
26C3×#121—61no—
27C3×#121—61no—
28C3×C4×D4—61no—
29C3×C4×D4—61no—
30C2×C3×C42—31no—
31C2×C3×C42—31no—
32C2×C3×C42C2×D311yescharacteristic
33C2×C42⋊C3—21no—
34C2×C42⋊C3C22×C311yescharacteristic
35#857—22no—
36C3×C4⋊C8—61no—
37C3×C4⋊C8—61no—
38C3×#104—62no—
39C3×#104—64no—
40C3×#104—62no—
41C2×C3×A4—41no—
42C3×S4—82no—
43C3×D12—161no—
44#532—31no—
45#423—31no—
46C2×#104—32no—
47C2×#104—32no—
48C43C3×D311yescharacteristic, complemented
49C2×S4—42no—
50C3×#41—62no—
51C3×#41—62no—
52C3×#41—62no—
53C3×#41—62no—
54C2×C3×Q8—32no—
55C2×C3×D4—32no—
56C2×C3×D4—61no—
57C2×C3×D4—61no—
58C2×C3×D4—62no—
59C22×C3×C4—31no—
60C22×C3×C4—31no—
61C22×C3×C4—62no—
62C22×C3×C4S411yescharacteristic
63C4×A4—41no—
64C4×A4—81no—
65C3×M16—62no—
66C3×M16—62no—
67C2×C3×C8—62no—
68C3×C4⋊C4—61no—
69C3×C4⋊C4—61no—
70C3×C22⋊C4—62no—
71C3×C22⋊C4—62no—
72C3×C42—31no—
73C3×C42—31no—
74C3×C42—31no—
75C3×C42—31no—
76C3×C42—31no—
77C3×C42—32no—
78C3×C42—61no—
79C3×C42D1211yescharacteristic, complemented
80C42⋊C3—21no—
81C42⋊C3C3×D411yescharacteristic, complemented
82C2×C3×D3—162no—
83C3×A4—41no—
84C32×C4—161no—
85C2×#41—32no—
86C2×M16—32no—
87C4⋊Q8—31no—
88#127—31no—
89#124—32no—
90#121—61no—
91#121—61no—
92C4×D4—61no—
93C4×D4—61no—
94C2×C42—31no—
95C2×C42—31no—
96C2×C42C2×C3×D311yescharacteristic
97C4⋊C8—61no—
98C4⋊C8—61no—
99#104—62no—
100#104—64no—
101#104—62no—
102C23×C3—62no—
103C23×C3C2×S411yescharacteristic
104C2×A4—41no—
105C2×A4—81no—
106S4—82no—
107C3×Q8—62no—
108C3×Q8—62no—
109C3×D4—62no—
110C3×D4—62no—
111C3×D4—122no—
112C3×D4—121no—
113C3×D4—122no—
114C3×D4—122no—
115C3×D4—121no—
116C2×C3×C4—31no—
117C2×C3×C4—31no—
118C2×C3×C4—31no—
119C2×C3×C4—31no—
120C2×C3×C4—31no—
121C2×C3×C4—31no—
122C2×C3×C4—31no—
123C2×C3×C4—31no—
124C2×C3×C4—31no—
125C2×C3×C4—31no—
126C2×C3×C4—62no—
127C2×C3×C4—62no—
128C2×C3×C4—122no—
129C2×C3×C4—122no—
130D12—161no—
131C3×C8—122no—
132C2×C32—161no—
133C3×D3—322no—
134#41—62no—
135#41—62no—
136#41—62no—
137#41—62no—
138C2×Q8—32no—
139C2×D4—32no—
140C2×D4—61no—
141C2×D4—61no—
142C2×D4—62no—
143C22×C4—31no—
144C22×C4—31no—
145C22×C4—62no—
146C22×C4C3×S411yescharacteristic
147M16—62no—
148M16—62no—
149C2×C8—62no—
150C4⋊C4—61no—
151C4⋊C4—61no—
152C22⋊C4—62no—
153C22⋊C4—62no—
154C42—31no—
155C42—31no—
156C42—31no—
157C42—31no—
158C42—31no—
159C42—32no—
160C42—61no—
161C42C3×D1211yescharacteristic, complemented
162C22×C3—31no—
163C22×C3—31no—
164C22×C3—122no—
165C22×C3—122no—
166C22×C3—122no—
167C22×C3C4⋊S411yescharacteristic
168C2×D3—162no—
169A4—41no—
170A4—81no—
171C3×C4—31no—
172C3×C4—31no—
173C3×C4—31no—
174C3×C4—31no—
175C3×C4—32no—
176C3×C4—31no—
177C3×C4—61no—
178C3×C4—122no—
179C3×C4—161no—
180C3×C4—321no—
181C3×C4#85711yescharacteristic, complemented
182C32—161noSylow
183C23—62no—
184C23C2×C3×S411yescharacteristic
185Q8—62no—
186Q8—62no—
187D4—62no—
188D4—62no—
189D4—122no—
190D4—121no—
191D4—122no—
192D4—122no—
193D4—121no—
194C2×C4—31no—
195C2×C4—31no—
196C2×C4—31no—
197C2×C4—31no—
198C2×C4—31no—
199C2×C4—31no—
200C2×C4—31no—
201C2×C4—31no—
202C2×C4—31no—
203C2×C4—31no—
204C2×C4—62no—
205C2×C4—62no—
206C2×C4—122no—
207C2×C4—122no—
208C8—122no—
209C2×C3—31no—
210C2×C3—31no—
211C2×C3—161no—
212C2×C3—242no—
213C2×C3—321no—
214C2×C3C2×#85711yescharacteristic
215D3—322no—
216C22—31no—
217C22—31no—
218C22—122no—
219C22—122no—
220C22—122no—
221C22C3×C4⋊S411yescharacteristic
222C4—31no—
223C4—31no—
224C4—31no—
225C4—31no—
226C4—32no—
227C4—31no—
228C4—61no—
229C4—122no—
230C4C3×#85711yescharacteristic, complemented
231C3—161no—
232C3—321no—
233C3C4⋊#85711yescharacteristic, direct product factor
234C2—31no—
235C2—31no—
236C2—242no—
237C2C2×C3×#85711yescharacteristic
subgroupG/H
centerC2×C3C2×#857
commutator, cosocleC2×C42⋊C3C22×C3
FrattiniC23C2×C3×S4
FittingC3×C43D3
socleC23×C3C2×S4
hypercenterC3×C4#857
hypocenterC42⋊C3C3×D4
LCSG ▷ C2×C42⋊C3 ▷ C42⋊C3
UCSC1 ◁ C2×C3 ◁ C3×C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#857C2semidirect
2. C3×C4×C42⋊C3C2semidirect
3. C4⋊#857C3direct (N × H)
9. C2×#857C2×C3semidirect
13. C3×C43D3semidirect
15. C4×C42⋊C3C2×C3semidirect
18. C3×C42⋊C3D4semidirect
48. C43C3×D3semidirect
79. C3×C42D12semidirect
81. C42⋊C3C3×D4semidirect
161. C42C3×D12semidirect
181. C3×C4#857semidirect
230. C4C3×#857semidirect
233. C3C4⋊#857direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#8572
C3×C4×C42⋊C32
C4⋊#8573
C3×#19623
C3×C4⋊S44