Finite Group Databasebeta

← C3×#3529⋊C3 #11919840

Subgroups — C3×#3529⋊C3 #11919840

Order 1152.

550 conjugacy classes of subgroups; only the 48 normal subgroups are shown.

normal subgroups only

This group has 550 conjugacy classes of subgroups — too many to draw. Only its 48 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×#5465C211yesmaximal, characteristic, complemented
2C3×#3529C311yesmaximal, characteristic, complemented
3#3529⋊C3C313yesmaximal, direct product factor
4C2×C3×#41⋊C3—41nomaximal
5C2×C3×C4×A4—42nomaximal
6C3×C4×SL(2,𝔽3)—42nomaximal
7C3×#563—31no—
8C3×#562—32no—
9C3×H(3,𝔽4)C2×C311yescharacteristic
10C3×#560—32no—
11C3×#532—31no—
12C3×#529—32no—
13C3×#525—32no—
14#5465C2×C313yescomplemented
15C22×C3×A4—42no—
16C3×#41⋊C3—42no—
17C2×C3×SL(2,𝔽3)—41no—
18C2×C3×SL(2,𝔽3)—42no—
19C3×C4×A4—44no—
20#3529C3211yescharacteristic, complemented, Sylow
21C2×C3×#41—31no—
22C2×C3×#41A411yescharacteristic, complemented
23C23×C3×C4A412yescomplemented
24C2×#41⋊C3—43no—
25C2×C4×A4—46no—
26C3×C4⋊Q8—31no—
27C3×#127—31no—
28C3×#126—34no—
29C3×#125—32no—
30C3×#124—31no—
31C3×#124—32no—
32C3×#124—31no—
33C3×#123—34no—
34C3×#123—32no—
35C3×#123—32no—
36C3×C22⋊Q8—34no—
37C3×C22⋊Q8—32no—
38C3×#121—32no—
39C3×#121—34no—
40C3×#121—34no—
41C3×#120—32no—
42C3×#120—32no—
43C3×C4×Q8A412yescomplemented
44C3×C4×D4—32no—
45C3×C4×D4—34no—
46C3×#117—32no—
47C2×C3×C42—31no—
48C4×SL(2,𝔽3)—46no—
49C2×C3×A4—44no—
50C2×C3×A4—42no—
51C2×C32×C4—161no—
52C3×SL(2,𝔽3)—42no—
53C3×SL(2,𝔽3)—41no—
54#563—31no—
55#562—32no—
56H(3,𝔽4)C2×C3211yescharacteristic
57#560—32no—
58#532—31no—
59#529—32no—
60#525—32no—
61C24×C3C2×A412yes—
62C22×A4—46no—
63C3×#41—42no—
64C3×#41—122no—
65C2×C3×Q8—31no—
66C2×C3×Q8C2×A412yes—
67C2×C3×Q8C2×A411yescharacteristic
68C2×C3×D4—31no—
69C2×C3×D4—32no—
70C2×C3×D4—34no—
71C2×C3×D4—31no—
72C2×C3×D4—32no—
73C22×C3×C4—32no—
74C22×C3×C4—31no—
75C22×C3×C4—32no—
76C22×C3×C4—32no—
77C22×C3×C4—44no—
78#41⋊C3—46no—
79C2×SL(2,𝔽3)—46no—
80C2×SL(2,𝔽3)—43no—
81C4×A4—412no—
82C3×C4⋊C4—32no—
83C3×C4⋊C4—34no—
84C3×C4⋊C4—34no—
85C3×C4⋊C4—32no—
86C3×C22⋊C4—32no—
87C3×C22⋊C4—32no—
88C3×C22⋊C4—34no—
89C3×C22⋊C4—34no—
90C3×C22⋊C4—34no—
91C3×C42—31no—
92C3×C42—31no—
93C3×C42—32no—
94C22×C32—161no—
95C3×A4—42no—
96C32×C4—162no—
97C2×#41—31no—
98C2×#41C3×A411yescharacteristic, complemented
99C23×C4C3×A412yescomplemented
100C4⋊Q8—31no—
101#127—31no—
102#126—34no—
103#125—32no—
104#124—31no—
105#124—32no—
106#124—31no—
107#123—32no—
108#123—32no—
109#123—34no—
110C22⋊Q8—34no—
111C22⋊Q8—32no—
112#121—34no—
113#121—32no—
114#121—34no—
115#120—32no—
116#120—32no—
117C4×Q8C3×A412yescomplemented
118C4×D4—32no—
119C4×D4—34no—
120#117—32no—
121C2×C42—31no—
122C23×C3—32no—
123C23×C3—31no—
124C23×C3—42no—
125C23×C3—44no—
126C2×A4—46no—
127C2×A4—412no—
128C3×Q8—42no—
129C3×Q8—41no—
130C3×Q8—121no—
131C3×D4—121no—
132C3×D4—124no—
133C3×D4—122no—
134C3×D4—122no—
135C3×D4—121no—
136C2×C3×C4—32no—
137C2×C3×C4—32no—
138C2×C3×C4—31no—
139C2×C3×C4—32no—
140C2×C3×C4—64no—
141C2×C3×C4—62no—
142C2×C3×C4—122no—
143C2×C3×C4—122no—
144C2×C3×C4—163no—
145C2×C3×C4C22⋊A411yescharacteristic
146SL(2,𝔽3)—46no—
147SL(2,𝔽3)—43no—
148C2×C32—161no—
149C2×C32—162no—
150C24C2×C3×A412yes—
151#41—42no—
152#41—122no—
153C2×Q8—31no—
154C2×Q8C2×C3×A412yes—
155C2×Q8C2×C3×A411yescharacteristic
156C2×D4—31no—
157C2×D4—32no—
158C2×D4—34no—
159C2×D4—31no—
160C2×D4—32no—
161C22×C4—32no—
162C22×C4—31no—
163C22×C4—32no—
164C22×C4—32no—
165C22×C4—44no—
166C4⋊C4—32no—
167C4⋊C4—34no—
168C4⋊C4—34no—
169C4⋊C4—32no—
170C22⋊C4—32no—
171C22⋊C4—32no—
172C22⋊C4—34no—
173C22⋊C4—34no—
174C22⋊C4—34no—
175C42—31no—
176C42—31no—
177C42—32no—
178C22×C3—42no—
179C22×C3—62no—
180C22×C3—61no—
181C22×C3—62no—
182C22×C3—64no—
183C22×C3—122no—
184C22×C3—163no—
185C22×C3C2×C22⋊A411yescharacteristic
186A4—46no—
187C3×C4—62no—
188C3×C4—61no—
189C3×C4—62no—
190C3×C4—62no—
191C3×C4—166no—
192C3×C4#99712yes—
193C32—161noSylow
194C23—32no—
195C23—31no—
196C23—42no—
197C23—44no—
198Q8—41no—
199Q8—42no—
200Q8—121no—
201D4—121no—
202D4—122no—
203D4—121no—
204D4—124no—
205D4—122no—
206C2×C4—32no—
207C2×C4—32no—
208C2×C4—31no—
209C2×C4—32no—
210C2×C4—64no—
211C2×C4—62no—
212C2×C4—122no—
213C2×C4—122no—
214C2×C4C3×C22⋊A411yescharacteristic
215C2×C3—122no—
216C2×C3—121no—
217C2×C3—163no—
218C2×C3—166no—
219C2×C3C2×#99711yescharacteristic
220C2×C3#595012yes—
221C22—42no—
222C22—62no—
223C22—61no—
224C22—62no—
225C22—64no—
226C22—122no—
227C22C2×C3×C22⋊A411yescharacteristic
228C4—62no—
229C4—61no—
230C4—62no—
231C4—62no—
232C4C3×#99712yes—
233C3—163no—
234C3#3529⋊C311yescharacteristic, direct product factor
235C2—122no—
236C2—121no—
237C2C2×C3×#99711yescharacteristic
238C2C3×#595012yes—
subgroupG/H
center, hypercenterC2×C3×C4C22⋊A4
commutator, cosocle, hypocenterH(3,𝔽4)C2×C32
FrattiniC22C2×C3×C22⋊A4
FittingC3×#3529C3
socleC22×C3C2×C22⋊A4
LCSG ▷ H(3,𝔽4)
UCSC1 ◁ C2×C3×C4

Complements

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

NH ≅ G/Ntype
1. C3×#5465C2semidirect
2. C3×#3529C3semidirect
3. #3529⋊C3C3direct (N × H)
14. #5465C2×C3semidirect
20. #3529C32semidirect
22. C2×C3×#41A4semidirect
23. C23×C3×C4A4semidirect
43. C3×C4×Q8A4semidirect
98. C2×#41C3×A4semidirect
99. C23×C4C3×A4semidirect
117. C4×Q8C3×A4semidirect
234. C3#3529⋊C3direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#54652
C3×#35293
#3529⋊C33
C2×C3×#41⋊C34
C2×C3×C4×A44
C3×C4×SL(2,𝔽3)4