Finite Group Databasebeta

← C3×#2852⋊C3 #11919504

Subgroups — C3×#2852⋊C3 #11919504

Order 1152.

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

normal subgroups only

This group has 322 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×#126⋊C3C211yesmaximal, characteristic, complemented
2C22×C3×C42⋊C3C211yesmaximal, characteristic, complemented
3C3×#383⋊C3C211yesmaximal, characteristic, complemented
4C3×#2852C311yesmaximal, characteristic, complemented
5#2852⋊C3C313yesmaximal, direct product factor
6C3×D4×A4—41nomaximal
7C3×#126⋊C3—21no—
8C2×C3×C42⋊C3—21no—
9C2×C3×C42⋊C3C2211yescharacteristic
10C2×C3×#126C2×C311yescharacteristic, complemented
11C22×C3×C42C2×C311yescharacteristic, complemented
12C2×#126⋊C3C2×C313yescomplemented
13C22×C42⋊C3C2×C313yescomplemented
14C3×#388—31no—
15C3×#387—31no—
16C3×#386—31no—
17C3×#385—31no—
18C3×#383C2×C311yescharacteristic, complemented
19#383⋊C3C2×C313yescomplemented
20C22×C3×A4—41no—
21C22×C3×A4—41no—
22C3×C4×A4—41no—
23C3×C42⋊C3D411yescharacteristic, complemented
24#2852C3211yescharacteristic, complemented, Sylow
25C22×C3×D4A411yescharacteristic
26C23×C3×C4—31no—
27D4×A4—43no—
28C3×#126—21no—
29C3×#126—61no—
30C2×C3×C4⋊C4—31no—
31C2×C3×C4⋊C4—31no—
32C2×C3×C22⋊C4—31no—
33C2×C3×C22⋊C4—31no—
34C2×C3×C22⋊C4—31no—
35C2×C3×C42—21no—
36C2×C3×C42—31no—
37C2×C3×C42—61no—
38C2×C3×C42C22×C311yescharacteristic
39#126⋊C3—23no—
40C2×C42⋊C3—23no—
41C2×C42⋊C3C22×C313yes—
42C3×#95—31no—
43C3×#95—31no—
44C3×#95—31no—
45C3×#95—31no—
46C2×C3×A4—41no—
47C2×C3×A4—81no—
48C2×C3×A4—81no—
49C32×D4—161no—
50C2×#126C2×C3211yescharacteristic, complemented
51C22×C42C2×C3211yescharacteristic, complemented
52#388—31no—
53#387—31no—
54#386—31no—
55#385—31no—
56#383C2×C3211yescharacteristic, complemented
57C24×C3C2×A411yescharacteristic
58C24×C3C2×A411yescharacteristic
59C22×A4—43no—
60C22×A4—43no—
61C2×C3×D4—61no—
62C2×C3×D4—61no—
63C22×C3×C4—31no—
64C22×C3×C4—31no—
65C22×C3×C4—31no—
66C22×C3×C4—31no—
67C22×C3×C4—61no—
68C22×C3×C4—61no—
69C22×C3×C4—62no—
70C22×C3×C4—61no—
71C22×C3×C4—61no—
72C22×C3×C4C2×A411yescharacteristic
73C4×A4—43no—
74C3×C4⋊C4—61no—
75C3×C4⋊C4—61no—
76C3×C4⋊C4—62no—
77C3×C22⋊C4—61no—
78C3×C22⋊C4—61no—
79C3×C22⋊C4—62no—
80C3×C22⋊C4—61no—
81C3×C22⋊C4—61no—
82C3×C42—31no—
83C3×C42—61no—
84C3×C42—61no—
85C3×C42C3×D411yescharacteristic, complemented
86C42⋊C3C3×D413yescomplemented
87C22×C32—161no—
88C22×C32—161no—
89C3×A4—41no—
90C32×C4—161no—
91C22×D4C3×A411yescharacteristic
92C23×C4—31no—
93#126—21no—
94#126—61no—
95C2×C4⋊C4—31no—
96C2×C4⋊C4—31no—
97C2×C22⋊C4—31no—
98C2×C22⋊C4—31no—
99C2×C22⋊C4—31no—
100C2×C42—21no—
101C2×C42—31no—
102C2×C42—61no—
103C2×C42C22×C3211yescharacteristic
104#95—31no—
105#95—31no—
106#95—31no—
107#95—31no—
108C23×C3—21no—
109C23×C3—21no—
110C23×C3—31no—
111C23×C3—31no—
112C23×C3—61no—
113C23×C3—61no—
114C23×C3—61no—
115C23×C3C22×A411yescharacteristic
116C2×A4—43no—
117C2×A4—83no—
118C2×A4—83no—
119C3×D4—41no—
120C3×D4—121no—
121C3×D4—163no—
122C2×C3×C4—32no—
123C2×C3×C4—31no—
124C2×C3×C4—31no—
125C2×C3×C4—61no—
126C2×C3×C4—61no—
127C2×C3×C4—61no—
128C2×C3×C4—61no—
129C2×C3×C4—62no—
130C2×C3×C4—62no—
131C2×C3×C4—62no—
132C2×C3×C4—62no—
133C2×C3×C4—61no—
134C2×C3×C4—61no—
135C2×C3×C4—61no—
136C2×C3×C4—61no—
137C2×C3×C4—61no—
138C2×C3×C4—61no—
139C2×C3×C4—61no—
140C2×C32—161no—
141C2×C32—321no—
142C2×C32—321no—
143C24C2×C3×A411yescharacteristic
144C24C2×C3×A411yescharacteristic
145C2×D4—61no—
146C2×D4—61no—
147C22×C4—31no—
148C22×C4—31no—
149C22×C4—31no—
150C22×C4—31no—
151C22×C4—61no—
152C22×C4—61no—
153C22×C4—62no—
154C22×C4—61no—
155C22×C4—61no—
156C22×C4C2×C3×A411yescharacteristic
157C4⋊C4—61no—
158C4⋊C4—61no—
159C4⋊C4—62no—
160C22⋊C4—61no—
161C22⋊C4—61no—
162C22⋊C4—62no—
163C22⋊C4—61no—
164C22⋊C4—61no—
165C42—31no—
166C42—61no—
167C42—61no—
168C42C32×D411yescharacteristic, complemented
169C22×C3—31no—
170C22×C3—31no—
171C22×C3—31no—
172C22×C3—41no—
173C22×C3—61no—
174C22×C3—61no—
175C22×C3—61no—
176C22×C3—61no—
177C22×C3—121no—
178C22×C3—121no—
179C22×C3—163no—
180C22×C3—163no—
181C22×C3#126⋊C311yescharacteristic, complemented
182C22×C3D4×A411yescharacteristic
183A4—43no—
184C3×C4—41no—
185C3×C4—62no—
186C3×C4—61no—
187C3×C4—61no—
188C3×C4—121no—
189C3×C4—121no—
190C3×C4—163no—
191C32—161noSylow
192C23—21no—
193C23—21no—
194C23—31no—
195C23—31no—
196C23—61no—
197C23—61no—
198C23—61no—
199C23C22×C3×A411yescharacteristic
200D4—41no—
201D4—121no—
202C2×C4—32no—
203C2×C4—31no—
204C2×C4—31no—
205C2×C4—61no—
206C2×C4—61no—
207C2×C4—61no—
208C2×C4—61no—
209C2×C4—62no—
210C2×C4—62no—
211C2×C4—62no—
212C2×C4—62no—
213C2×C4—61no—
214C2×C4—61no—
215C2×C4—61no—
216C2×C4—61no—
217C2×C4—61no—
218C2×C4—61no—
219C2×C4—61no—
220C2×C3—21no—
221C2×C3—31no—
222C2×C3—31no—
223C2×C3—61no—
224C2×C3—81no—
225C2×C3—163no—
226C2×C3—323no—
227C2×C3—323no—
228C2×C3C2×#126⋊C311yescharacteristic
229C22—31no—
230C22—31no—
231C22—31no—
232C22—41no—
233C22—61no—
234C22—61no—
235C22—61no—
236C22—61no—
237C22—121no—
238C22—121no—
239C22C3×#126⋊C311yescharacteristic, complemented
240C22C3×D4×A411yescharacteristic
241C4—41no—
242C4—62no—
243C4—61no—
244C4—61no—
245C4—121no—
246C4—121no—
247C3—163no—
248C3#2852⋊C311yescharacteristic, direct product factor
249C2—21no—
250C2—31no—
251C2—31no—
252C2—61no—
253C2—81no—
254C2C2×C3×#126⋊C311yescharacteristic
subgroupG/H
centerC2×C3C2×#126⋊C3
commutator, cosocleC2×C42C22×C32
FrattiniC23C22×C3×A4
FittingC3×#2852C3
socleC23×C3C22×A4
hypercenterC22×C3#126⋊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×#126⋊C3C2semidirect
2. C22×C3×C42⋊C3C2semidirect
3. C3×#383⋊C3C2semidirect
4. C3×#2852C3semidirect
5. #2852⋊C3C3direct (N × H)
10. C2×C3×#126C2×C3semidirect
11. C22×C3×C42C2×C3semidirect
12. C2×#126⋊C3C2×C3semidirect
13. C22×C42⋊C3C2×C3semidirect
18. C3×#383C2×C3semidirect
19. #383⋊C3C2×C3semidirect
23. C3×C42⋊C3D4semidirect
24. #2852C32semidirect
50. C2×#126C2×C32semidirect
51. C22×C42C2×C32semidirect
56. #383C2×C32semidirect
85. C3×C42C3×D4semidirect
86. C42⋊C3C3×D4semidirect
168. C42C32×D4semidirect
181. C22×C3#126⋊C3semidirect
239. C22C3×#126⋊C3semidirect
248. C3#2852⋊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×#126⋊C32
C22×C3×C42⋊C32
C3×#383⋊C32
C3×#28523
#2852⋊C33
C3×D4×A44