Finite Group Databasebeta

← C3×#3027⋊C3 #11919592

Subgroups — C3×#3027⋊C3 #11919592

Order 1152.

396 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 46 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×#5950C211yesmaximal, characteristic, complemented
2C3×B(4,𝔽2)⋊C3C212yesmaximal, complemented
3C3×#3027C311yesmaximal, characteristic, complemented
4#3027⋊C3C313yesmaximal, direct product factor
5C3×#997C2211yescharacteristic
6C3×D4×A4—41nomaximal
7C3×#585C2×C311yescharacteristic, complemented
8#5950C2×C313yescomplemented
9C3×#535—31no—
10C3×B(4,𝔽2)—32no—
11C3×B(4,𝔽2)C2×C312yescomplemented
12C3×#410—31no—
13B(4,𝔽2)⋊C3C2×C316yescomplemented
14C22×C3×A4—42no—
15C3×#41⋊C3—81no—
16C3×C4×A4—41no—
17C3×C4×A4—81no—
18#3027C3211yescharacteristic, complemented, Sylow
19C3×2−1+4—61no—
20C3×H(5,𝔽2)—31no—
21C3×H(5,𝔽2)—61no—
22C3×H(5,𝔽2)C22×C311yescharacteristic
23C2×C3×#41—31no—
24C2×C3×#41—61no—
25C2×C3×#41—61no—
26C22×C3×D4A411yescharacteristic, complemented
27#997C22×C313yes—
28D4×A4—43no—
29C3×#127—61no—
30C3×#124—61no—
31C3×#121—61no—
32C3×#121—61no—
33C3×#120—32no—
34C3×#120—32no—
35C3×#117—31no—
36C3×#99—32no—
37C3×#99—32no—
38C2×C3×A4—41no—
39C2×C3×A4—81no—
40C2×C3×A4—82no—
41C32×D4—161no—
42C3×SL(2,𝔽3)—81no—
43#585C2×C3211yescharacteristic, complemented
44#535—31no—
45B(4,𝔽2)—32no—
46B(4,𝔽2)C2×C3212yescomplemented
47#410—31no—
48C24×C3C2×A412yes—
49C22×A4—46no—
50C3×#41—21no—
51C3×#41—62no—
52C3×#41—62no—
53C3×#41—61no—
54C3×#41—62no—
55C3×#41—61no—
56C3×#41—62no—
57C3×#41—62no—
58C3×#41—61no—
59C2×C3×Q8—31no—
60C2×C3×Q8—61no—
61C2×C3×Q8—61no—
62C2×C3×D4—31no—
63C2×C3×D4—31no—
64C2×C3×D4—31no—
65C2×C3×D4—61no—
66C2×C3×D4—61no—
67C2×C3×D4—61no—
68C2×C3×D4—62no—
69C2×C3×D4—61no—
70C2×C3×D4—61no—
71C2×C3×D4—61no—
72C2×C3×D4—62no—
73C2×C3×D4—62no—
74C22×C3×C4—21no—
75C22×C3×C4—31no—
76C22×C3×C4—31no—
77C22×C3×C4—61no—
78C22×C3×C4C2×A411yescharacteristic
79#41⋊C3—83no—
80C4×A4—43no—
81C4×A4—83no—
82C3×C4⋊C4—61no—
83C3×C22⋊C4—32no—
84C3×C22⋊C4—62no—
85C3×C22⋊C4—62no—
86C3×C42—61no—
87C22×C32—162no—
88C3×A4—41no—
89C3×A4—81no—
90C32×C4—161no—
912−1+4—61no—
92H(5,𝔽2)—31no—
93H(5,𝔽2)—61no—
94H(5,𝔽2)C22×C3211yescharacteristic
95C2×#41—31no—
96C2×#41—61no—
97C2×#41—61no—
98C22×D4C3×A411yescharacteristic, complemented
99#127—61no—
100#124—61no—
101#121—61no—
102#121—61no—
103#120—32no—
104#120—32no—
105#117—31no—
106#99—32no—
107#99—32no—
108C23×C3—21no—
109C23×C3—31no—
110C23×C3—31no—
111C23×C3—62no—
112C23×C3—61no—
113C23×C3—82no—
114C23×C3C22×A411yescharacteristic
115C2×A4—43no—
116C2×A4—83no—
117C2×A4—86no—
118C3×Q8—21no—
119C3×Q8—62no—
120C3×Q8—61no—
121C3×D4—41no—
122C3×D4—62no—
123C3×D4—62no—
124C3×D4—62no—
125C3×D4—61no—
126C3×D4—61no—
127C3×D4—62no—
128C3×D4—121no—
129C3×D4—163no—
130C3×D4—242no—
131C3×D4—242no—
132C2×C3×C4—31no—
133C2×C3×C4—31no—
134C2×C3×C4—31no—
135C2×C3×C4—31no—
136C2×C3×C4—61no—
137C2×C3×C4—61no—
138C2×C3×C4—62no—
139C2×C3×C4—61no—
140C2×C3×C4—61no—
141C2×C3×C4—61no—
142C2×C3×C4—61no—
143C2×C3×C4—62no—
144SL(2,𝔽3)—83no—
145C2×C32—161no—
146C2×C32—322no—
147C24C2×C3×A412yes—
148#41—21no—
149#41—62no—
150#41—62no—
151#41—61no—
152#41—62no—
153#41—61no—
154#41—62no—
155#41—62no—
156#41—61no—
157C2×Q8—31no—
158C2×Q8—61no—
159C2×Q8—61no—
160C2×D4—31no—
161C2×D4—31no—
162C2×D4—31no—
163C2×D4—61no—
164C2×D4—61no—
165C2×D4—61no—
166C2×D4—62no—
167C2×D4—61no—
168C2×D4—61no—
169C2×D4—61no—
170C2×D4—62no—
171C2×D4—62no—
172C22×C4—21no—
173C22×C4—31no—
174C22×C4—31no—
175C22×C4—61no—
176C22×C4C2×C3×A411yescharacteristic
177C4⋊C4—61no—
178C22⋊C4—32no—
179C22⋊C4—62no—
180C22⋊C4—62no—
181C42—61no—
182C22×C3—31no—
183C22×C3—41no—
184C22×C3—42no—
185C22×C3—61no—
186C22×C3—61no—
187C22×C3—81no—
188C22×C3—122no—
189C22×C3—122no—
190C22×C3—121no—
191C22×C3—121no—
192C22×C3—166no—
193C22×C3—241no—
194A4—43no—
195A4—83no—
196C3×C4—31no—
197C3×C4—61no—
198C3×C4—61no—
199C3×C4—122no—
200C3×C4—163no—
201C3×C4#120⋊C311yescharacteristic
202C32—161noSylow
203C23—21no—
204C23—31no—
205C23—31no—
206C23—62no—
207C23—61no—
208C23—82no—
209C23C22×C3×A411yescharacteristic
210Q8—21no—
211Q8—62no—
212Q8—61no—
213D4—41no—
214D4—62no—
215D4—62no—
216D4—62no—
217D4—61no—
218D4—61no—
219D4—62no—
220D4—121no—
221D4—242no—
222D4—242no—
223C2×C4—31no—
224C2×C4—31no—
225C2×C4—31no—
226C2×C4—31no—
227C2×C4—61no—
228C2×C4—61no—
229C2×C4—62no—
230C2×C4—61no—
231C2×C4—61no—
232C2×C4—61no—
233C2×C4—61no—
234C2×C4—62no—
235C2×C3—61no—
236C2×C3—82no—
237C2×C3—121no—
238C2×C3—121no—
239C2×C3—163no—
240C2×C3—326no—
241C2×C3C2×#120⋊C311yescharacteristic
242C22—31no—
243C22—41no—
244C22—42no—
245C22—61no—
246C22—61no—
247C22—81no—
248C22—122no—
249C22—122no—
250C22—121no—
251C22—121no—
252C22—241no—
253C4—31no—
254C4—61no—
255C4—61no—
256C4—122no—
257C4C3×#120⋊C311yescharacteristic
258C3—163no—
259C3#3027⋊C311yescharacteristic, direct product factor
260C2—61no—
261C2—82no—
262C2—121no—
263C2—121no—
264C2C2×C3×#120⋊C311yescharacteristic
subgroupG/H
center, socleC2×C3C2×#120⋊C3
commutator, cosocle, hypocenterH(5,𝔽2)C22×C32
FrattiniC23C22×C3×A4
FittingC3×#3027C3
hypercenterC3×C4#120⋊C3
LCSG ▷ H(5,𝔽2)
UCSC1 ◁ C2×C3 ◁ C3×C4

Complements

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

NH ≅ G/Ntype
1. C3×#5950C2semidirect
2. C3×B(4,𝔽2)⋊C3C2semidirect
3. C3×#3027C3semidirect
4. #3027⋊C3C3direct (N × H)
7. C3×#585C2×C3semidirect
8. #5950C2×C3semidirect
11. C3×B(4,𝔽2)C2×C3semidirect
13. B(4,𝔽2)⋊C3C2×C3semidirect
18. #3027C32semidirect
26. C22×C3×D4A4semidirect
43. #585C2×C32semidirect
46. B(4,𝔽2)C2×C32semidirect
98. C22×D4C3×A4semidirect
259. C3#3027⋊C3direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#59502
C3×B(4,𝔽2)⋊C32
C3×#30273
#3027⋊C33
C3×D4×A44