Finite Group Databasebeta

← C3×C4×#857 #11920759

Subgroups — C3×C4×#857 #11920759

Order 1152.

337 conjugacy classes of subgroups; only the 34 normal subgroups are shown.

normal subgroups only

This group has 337 conjugacy classes of subgroups — too many to draw. Only its 34 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×#857C211yesmaximal, characteristic
2C3×C4×C42⋊C3C211yesmaximal, characteristic, complemented
3C3×#4623C211yesmaximal, characteristic, complemented
4C4×#857C311yesmaximal, characteristic, direct product factor
5C3×C4×#104—31nomaximal
6C3×C4×S4—41nomaximal
7C2×C3×C42⋊C3C2211yescharacteristic
8C3×#857C412yesdirect product factor
9C3×C4×#41—31no—
10C2×#857C2×C311yescharacteristic
11C2×C3×#104—31no—
12C2×C3×#104—31no—
13C3×C4×M16—31no—
14C3×C43D311yescharacteristic, complemented
15C4×C42⋊C3—21no—
16C4×C42⋊C3C2×C311yescharacteristic, complemented
17#4623C2×C311yescharacteristic, complemented
18C3×#339—31no—
19C3×#339—31no—
20C2×C3×S4—41no—
21C3×C4×A4—41no—
22C3×SL(2,ℤ/4)—41no—
23C3×C42⋊C3C2×C411yescharacteristic, complemented
24C4×#104—31noSylow
25C2×C3×#41—31no—
26C4×S4—41no—
27C2×C3×M16—31no—
28C2×C3×M16—31no—
29C3×C4×Q8—31no—
30C3×C4×Q8—31no—
31C3×C4×D4—31no—
32C3×C4×D4—31no—
33C3×C4×D4—61no—
34C3×C4×D4—61no—
35C3×#117—31no—
36C3×#117—61no—
37C2×C3×C42—31no—
38C2×C3×C42—31no—
39C2×C3×C42—61no—
40C2×C3×C42C2×D311yescharacteristic
41C2×C42⋊C3—21no—
42C2×C42⋊C3C22×C311yescharacteristic
43#857C3×C412yesdirect product factor
44C3×#104—32no—
45C3×#104—34no—
46C3×#104—32no—
47C3×#97—61no—
48C3×C4×C8—61no—
49C2×C3×A4—41no—
50C3×S4—42no—
51C3×C4×D3—161no—
52C4×#41—31no—
53C2×#104—31no—
54C2×#104—31no—
55C4×M16—31no—
56C43C3×D311yescharacteristic, complemented
57#339—31no—
58#339—31no—
59C2×S4—41no—
60C3×#41—32no—
61C3×#41—32no—
62C3×#41—61no—
63C3×#41—61no—
64C2×C3×Q8—31no—
65C2×C3×D4—31no—
66C2×C3×D4—61no—
67C22×C3×C4—31no—
68C22×C3×C4—31no—
69C22×C3×C4—61no—
70C22×C3×C4—61no—
71C22×C3×C4—61no—
72C22×C3×C4S411yescharacteristic
73C4×A4—41no—
74C4×A4—81no—
75SL(2,ℤ/4)—41no—
76C3×M16—32no—
77C3×M16—32no—
78C3×M16—61no—
79C3×M16—61no—
80C2×C3×C8—61no—
81C2×C3×C8—61no—
82C3×C4⋊C4—31no—
83C3×C4⋊C4—31no—
84C3×C4⋊C4—61no—
85C3×C4⋊C4—61no—
86C3×C22⋊C4—61no—
87C3×C22⋊C4—61no—
88C3×C22⋊C4—61no—
89C3×C42—31no—
90C3×C42—31no—
91C3×C42—31no—
92C3×C42—31no—
93C3×C42—31no—
94C3×C42—32no—
95C3×C42—61no—
96C3×C42—61no—
97C3×C42—61no—
98C3×C42—61no—
99C3×C42C4×D311yescharacteristic, complemented
100C42⋊C3—21no—
101C42⋊C3C2×C3×C411yescharacteristic, complemented
102C2×C3×D3—161no—
103C3×A4—41no—
104C32×C4—161no—
105C3×Dic3—161no—
106C2×#41—31no—
107C2×M16—31no—
108C2×M16—31no—
109C4×Q8—31no—
110C4×Q8—31no—
111C4×D4—31no—
112C4×D4—31no—
113C4×D4—61no—
114C4×D4—61no—
115#117—31no—
116#117—61no—
117C2×C42—31no—
118C2×C42—31no—
119C2×C42—61no—
120C2×C42C2×C3×D311yescharacteristic
121#104—32no—
122#104—34no—
123#104—32no—
124#97—61no—
125C4×C8—61no—
126C23×C3—61no—
127C23×C3C2×S411yescharacteristic
128C2×A4—41no—
129C2×A4—81no—
130S4—42no—
131C3×Q8—32no—
132C3×Q8—61no—
133C3×D4—32no—
134C3×D4—61no—
135C3×D4—62no—
136C3×D4—62no—
137C2×C3×C4—31no—
138C2×C3×C4—31no—
139C2×C3×C4—31no—
140C2×C3×C4—31no—
141C2×C3×C4—31no—
142C2×C3×C4—31no—
143C2×C3×C4—31no—
144C2×C3×C4—31no—
145C2×C3×C4—31no—
146C2×C3×C4—31no—
147C2×C3×C4—62no—
148C2×C3×C4—62no—
149C2×C3×C4—62no—
150C2×C3×C4—61no—
151C2×C3×C4—61no—
152C2×C3×C4—61no—
153C2×C3×C4—122no—
154C2×C3×C4—121no—
155C2×C3×C4—121no—
156C4×D3—161no—
157C3×C8—62no—
158C3×C8—62no—
159C2×C32—161no—
160C3×D3—162no—
161#41—32no—
162#41—32no—
163#41—61no—
164#41—61no—
165C2×Q8—31no—
166C2×D4—31no—
167C2×D4—61no—
168C22×C4—31no—
169C22×C4—31no—
170C22×C4—61no—
171C22×C4—61no—
172C22×C4—61no—
173C22×C4C3×S411yescharacteristic
174M16—32no—
175M16—32no—
176M16—61no—
177M16—61no—
178C2×C8—61no—
179C2×C8—61no—
180C4⋊C4—31no—
181C4⋊C4—31no—
182C4⋊C4—61no—
183C4⋊C4—61no—
184C22⋊C4—61no—
185C22⋊C4—61no—
186C22⋊C4—61no—
187C42—31no—
188C42—31no—
189C42—31no—
190C42—31no—
191C42—31no—
192C42—32no—
193C42—61no—
194C42—61no—
195C42—61no—
196C42—61no—
197C42C3×C4×D311yescharacteristic, complemented
198C22×C3—31no—
199C22×C3—31no—
200C22×C3—62no—
201C22×C3—121no—
202C22×C3—121no—
203C22×C3C4×S411yescharacteristic
204C2×D3—161no—
205A4—41no—
206A4—81no—
207C3×C4—31no—
208C3×C4—31no—
209C3×C4—31no—
210C3×C4—31no—
211C3×C4—32no—
212C3×C4—31no—
213C3×C4—61no—
214C3×C4—62no—
215C3×C4—121no—
216C3×C4—121no—
217C3×C4—161no—
218C3×C4—321no—
219C3×C4#85711yescharacteristic, direct product factor
220Dic3—161no—
221C32—161noSylow
222C23—61no—
223C23C2×C3×S411yescharacteristic
224Q8—32no—
225Q8—61no—
226D4—32no—
227D4—61no—
228D4—62no—
229D4—62no—
230C2×C4—31no—
231C2×C4—31no—
232C2×C4—31no—
233C2×C4—31no—
234C2×C4—31no—
235C2×C4—31no—
236C2×C4—31no—
237C2×C4—31no—
238C2×C4—31no—
239C2×C4—31no—
240C2×C4—62no—
241C2×C4—62no—
242C2×C4—62no—
243C2×C4—61no—
244C2×C4—61no—
245C2×C4—61no—
246C2×C4—122no—
247C2×C4—121no—
248C2×C4—121no—
249C8—62no—
250C8—62no—
251C2×C3—31no—
252C2×C3—31no—
253C2×C3—122no—
254C2×C3—161no—
255C2×C3—321no—
256C2×C3C2×#85711yescharacteristic
257D3—162no—
258C22—31no—
259C22—31no—
260C22—62no—
261C22—121no—
262C22—121no—
263C22C3×C4×S411yescharacteristic
264C4—31no—
265C4—31no—
266C4—31no—
267C4—31no—
268C4—32no—
269C4—31no—
270C4—61no—
271C4—62no—
272C4—121no—
273C4—121no—
274C4C3×#85711yescharacteristic, direct product factor
275C3—161no—
276C3—321no—
277C3C4×#85711yescharacteristic, direct product factor
278C2—31no—
279C2—31no—
280C2—122no—
281C2C2×C3×#85711yescharacteristic
subgroupG/H
center, hypercenterC3×C4#857
commutator, hypocenterC42⋊C3C2×C3×C4
FrattiniC23C2×C3×S4
FittingC3×C43D3
socleC23×C3C2×S4
prime radicalC2×C3×#857C2
cosocleC2×C42⋊C3C22×C3
LCSG ▷ C42⋊C3
UCSC1 ◁ C3×C4

Complements

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

NH ≅ G/Ntype
2. C3×C4×C42⋊C3C2semidirect
3. C3×#4623C2semidirect
4. C4×#857C3direct (N × H)
8. C3×#857C4direct (N × H)
14. C3×C43D3semidirect
16. C4×C42⋊C3C2×C3semidirect
17. #4623C2×C3semidirect
23. C3×C42⋊C3C2×C4semidirect
43. #857C3×C4direct (N × H)
56. C43C3×D3semidirect
99. C3×C42C4×D3semidirect
101. C42⋊C3C2×C3×C4semidirect
197. C42C3×C4×D3semidirect
219. C3×C4#857direct (N × H)
274. C4C3×#857direct (N × H)
277. 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
C3×#46232
C4×#8573
C3×C4×#1043
C3×C4×S44