Finite Group Databasebeta

← C3×#2856⋊C3 #11919506

Subgroups — C3×#2856⋊C3 #11919506

Order 1152.

436 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 54 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×#127⋊C3C211yesmaximal, characteristic, complemented
2C22×C3×C42⋊C3C211yesmaximal, characteristic, complemented
3C3×#384⋊C3C211yesmaximal, characteristic, complemented
4C3×#2856C311yesmaximal, characteristic, complemented
5#2856⋊C3C313yesmaximal, direct product factor
6C3×D4×A4—41nomaximal
7C3×#127⋊C3—21no—
8C2×C3×C42⋊C3—21no—
9C2×C3×C42⋊C3C2211yescharacteristic
10C2×C3×#127C2×C311yescharacteristic, complemented
11C2×C3×#121—31no—
12C2×C3×#121—31no—
13C22×C3×C42C2×C311yescharacteristic, complemented
14C2×#127⋊C3C2×C313yescomplemented
15C22×C42⋊C3C2×C313yescomplemented
16C3×#390—31no—
17C3×#390—31no—
18C3×#384C2×C311yescharacteristic, complemented
19#384⋊C3C2×C313yescomplemented
20C22×C3×A4—41no—
21C22×C3×A4—41no—
22C3×C4×A4—41no—
23C3×C42⋊C3D411yescharacteristic, complemented
24#2856C3211yescharacteristic, complemented, Sylow
25C22×C3×D4—31no—
26C22×C3×D4—31no—
27C22×C3×D4—31no—
28C22×C3×D4A411yescharacteristic
29C23×C3×C4—31no—
30D4×A4—43no—
31C3×#127—21no—
32C3×#127—61no—
33C3×#121—62no—
34C3×#121—62no—
35C3×#121—62no—
36C3×#121—62no—
37C2×C3×C4⋊C4—31no—
38C2×C3×C4⋊C4—31no—
39C2×C3×C22⋊C4—32no—
40C2×C3×C22⋊C4—31no—
41C2×C3×C22⋊C4—31no—
42C2×C3×C42—21no—
43C2×C3×C42—31no—
44C2×C3×C42—61no—
45C2×C3×C42C22×C311yescharacteristic
46#127⋊C3—23no—
47C2×C42⋊C3—23no—
48C2×C42⋊C3C22×C313yes—
49C2×C3×A4—41no—
50C2×C3×A4—81no—
51C2×C3×A4—81no—
52C32×D4—161no—
53C2×#127C2×C3211yescharacteristic, complemented
54C2×#121—31no—
55C2×#121—31no—
56C22×C42C2×C3211yescharacteristic, complemented
57#390—31no—
58#390—31no—
59#384C2×C3211yescharacteristic, complemented
60C24×C3—31no—
61C24×C3C2×A411yescharacteristic
62C24×C3C2×A411yescharacteristic
63C22×A4—43no—
64C22×A4—43no—
65C2×C3×D4—61no—
66C2×C3×D4—61no—
67C2×C3×D4—61no—
68C2×C3×D4—61no—
69C2×C3×D4—62no—
70C2×C3×D4—62no—
71C2×C3×D4—62no—
72C2×C3×D4—62no—
73C2×C3×D4—61no—
74C2×C3×D4—62no—
75C2×C3×D4—61no—
76C2×C3×D4—61no—
77C2×C3×D4—62no—
78C2×C3×D4—61no—
79C22×C3×C4—31no—
80C22×C3×C4—32no—
81C22×C3×C4—32no—
82C22×C3×C4—31no—
83C22×C3×C4—31no—
84C22×C3×C4—61no—
85C22×C3×C4—61no—
86C22×C3×C4—62no—
87C22×C3×C4C2×A411yescharacteristic
88C4×A4—43no—
89C3×C4⋊C4—62no—
90C3×C4⋊C4—62no—
91C3×C22⋊C4—62no—
92C3×C22⋊C4—62no—
93C3×C22⋊C4—64no—
94C3×C42—31no—
95C3×C42—61no—
96C3×C42—61no—
97C3×C42C3×D411yescharacteristic, complemented
98C42⋊C3C3×D413yescomplemented
99C22×C32—161no—
100C22×C32—161no—
101C3×A4—41no—
102C32×C4—161no—
103C22×D4—31no—
104C22×D4—31no—
105C22×D4—31no—
106C22×D4C3×A411yescharacteristic
107C23×C4—31no—
108#127—21no—
109#127—61no—
110#121—62no—
111#121—62no—
112#121—62no—
113#121—62no—
114C2×C4⋊C4—31no—
115C2×C4⋊C4—31no—
116C2×C22⋊C4—32no—
117C2×C22⋊C4—31no—
118C2×C22⋊C4—31no—
119C2×C42—21no—
120C2×C42—31no—
121C2×C42—61no—
122C2×C42C22×C3211yescharacteristic
123C23×C3—21no—
124C23×C3—21no—
125C23×C3—31no—
126C23×C3—31no—
127C23×C3—61no—
128C23×C3—61no—
129C23×C3—61no—
130C23×C3—61no—
131C23×C3—62no—
132C23×C3—61no—
133C23×C3—62no—
134C23×C3—61no—
135C23×C3C22×A411yescharacteristic
136C2×A4—43no—
137C2×A4—83no—
138C2×A4—83no—
139C3×D4—41no—
140C3×D4—122no—
141C3×D4—122no—
142C3×D4—122no—
143C3×D4—122no—
144C3×D4—121no—
145C3×D4—121no—
146C3×D4—122no—
147C3×D4—121no—
148C3×D4—163no—
149C2×C3×C4—32no—
150C2×C3×C4—32no—
151C2×C3×C4—31no—
152C2×C3×C4—31no—
153C2×C3×C4—32no—
154C2×C3×C4—62no—
155C2×C3×C4—62no—
156C2×C3×C4—62no—
157C2×C3×C4—62no—
158C2×C3×C4—61no—
159C2×C3×C4—61no—
160C2×C3×C4—61no—
161C2×C3×C4—61no—
162C2×C3×C4—62no—
163C2×C32—161no—
164C2×C32—321no—
165C2×C32—321no—
166C24—31no—
167C24C2×C3×A411yescharacteristic
168C24C2×C3×A411yescharacteristic
169C2×D4—61no—
170C2×D4—61no—
171C2×D4—61no—
172C2×D4—61no—
173C2×D4—62no—
174C2×D4—62no—
175C2×D4—62no—
176C2×D4—62no—
177C2×D4—61no—
178C2×D4—62no—
179C2×D4—61no—
180C2×D4—61no—
181C2×D4—62no—
182C2×D4—61no—
183C22×C4—31no—
184C22×C4—32no—
185C22×C4—32no—
186C22×C4—31no—
187C22×C4—31no—
188C22×C4—61no—
189C22×C4—61no—
190C22×C4—62no—
191C22×C4C2×C3×A411yescharacteristic
192C4⋊C4—62no—
193C4⋊C4—62no—
194C22⋊C4—62no—
195C22⋊C4—62no—
196C22⋊C4—64no—
197C42—31no—
198C42—61no—
199C42—61no—
200C42C32×D411yescharacteristic, complemented
201C22×C3—31no—
202C22×C3—31no—
203C22×C3—31no—
204C22×C3—41no—
205C22×C3—61no—
206C22×C3—61no—
207C22×C3—61no—
208C22×C3—61no—
209C22×C3—121no—
210C22×C3—121no—
211C22×C3—121no—
212C22×C3—122no—
213C22×C3—121no—
214C22×C3—122no—
215C22×C3—121no—
216C22×C3—163no—
217C22×C3—163no—
218C22×C3#127⋊C311yescharacteristic, complemented
219C22×C3D4×A411yescharacteristic
220A4—43no—
221C3×C4—32no—
222C3×C4—32no—
223C3×C4—41no—
224C3×C4—62no—
225C3×C4—121no—
226C3×C4—163no—
227C32—161noSylow
228C23—21no—
229C23—21no—
230C23—31no—
231C23—31no—
232C23—61no—
233C23—61no—
234C23—61no—
235C23—61no—
236C23—62no—
237C23—61no—
238C23—62no—
239C23—61no—
240C23C22×C3×A411yescharacteristic
241D4—41no—
242D4—122no—
243D4—122no—
244D4—122no—
245D4—122no—
246D4—121no—
247D4—121no—
248D4—122no—
249D4—121no—
250C2×C4—32no—
251C2×C4—32no—
252C2×C4—31no—
253C2×C4—31no—
254C2×C4—32no—
255C2×C4—62no—
256C2×C4—62no—
257C2×C4—62no—
258C2×C4—62no—
259C2×C4—61no—
260C2×C4—61no—
261C2×C4—61no—
262C2×C4—61no—
263C2×C4—62no—
264C2×C3—21no—
265C2×C3—31no—
266C2×C3—31no—
267C2×C3—61no—
268C2×C3—81no—
269C2×C3—163no—
270C2×C3—241no—
271C2×C3—323no—
272C2×C3—323no—
273C2×C3C2×#127⋊C311yescharacteristic
274C22—31no—
275C22—31no—
276C22—31no—
277C22—41no—
278C22—61no—
279C22—61no—
280C22—61no—
281C22—61no—
282C22—121no—
283C22—121no—
284C22—121no—
285C22—122no—
286C22—121no—
287C22—122no—
288C22—121no—
289C22C3×#127⋊C311yescharacteristic, complemented
290C22C3×D4×A411yescharacteristic
291C4—32no—
292C4—32no—
293C4—41no—
294C4—62no—
295C4—121no—
296C3—163no—
297C3#2856⋊C311yescharacteristic, direct product factor
298C2—21no—
299C2—31no—
300C2—31no—
301C2—61no—
302C2—81no—
303C2—241no—
304C2C2×C3×#127⋊C311yescharacteristic
subgroupG/H
centerC2×C3C2×#127⋊C3
commutator, cosocleC2×C42C22×C32
FrattiniC23C22×C3×A4
FittingC3×#2856C3
socleC23×C3C22×A4
hypercenterC22×C3#127⋊C3
hypocenterC42C32×D4
LCSG ▷ C2×C42 ▷ C42
UCSC1 ◁ C2×C3 ◁ C22×C3

Complements

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

NH ≅ G/Ntype
1. C2×C3×#127⋊C3C2semidirect
2. C22×C3×C42⋊C3C2semidirect
3. C3×#384⋊C3C2semidirect
4. C3×#2856C3semidirect
5. #2856⋊C3C3direct (N × H)
10. C2×C3×#127C2×C3semidirect
13. C22×C3×C42C2×C3semidirect
14. C2×#127⋊C3C2×C3semidirect
15. C22×C42⋊C3C2×C3semidirect
18. C3×#384C2×C3semidirect
19. #384⋊C3C2×C3semidirect
23. C3×C42⋊C3D4semidirect
24. #2856C32semidirect
53. C2×#127C2×C32semidirect
56. C22×C42C2×C32semidirect
59. #384C2×C32semidirect
97. C3×C42C3×D4semidirect
98. C42⋊C3C3×D4semidirect
200. C42C32×D4semidirect
218. C22×C3#127⋊C3semidirect
289. C22C3×#127⋊C3semidirect
297. C3#2856⋊C3direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#127⋊C32
C22×C3×C42⋊C32
C3×#384⋊C32
C3×#28563
#2856⋊C33
C3×D4×A44