Finite Group Databasebeta

← C3×#11709313 #72276685

Subgroups — C3×#11709313 #72276685

Order 2304.

2406 conjugacy classes of subgroups; only the 36 normal subgroups are shown.

normal subgroups only

This group has 2406 conjugacy classes of subgroups — too many to draw. Only its 36 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
1#11709313C313yesmaximal, direct product factor
2C3×#15947C311yesmaximal, characteristic, complemented
3C22×C3×C22⋊A4—42nomaximal
4C2×C3×#95⋊C3—43nomaximal
5C22×C3×#120—32no—
6C3×#1438—33no—
7C2×C3×C22⋊A4—46no—
8C3×#95⋊C3—43no—
9#15947C3211yescharacteristic, complemented, Sylow
10C26×C3A412yescomplemented
11C22×C22⋊A4—46no—
12C23×C3×D4—33no—
13C2×C3×#120—624no—
14C22×C3×C22⋊C4—36no—
15C2×C3×#95—31no—
16C2×C3×#95A413yescomplemented
17C2×#95⋊C3—49no—
18C3×C22⋊A4—42no—
19C22×C3×A4—168no—
20C22×C3×A4—161no—
21C22×#120—32no—
22#1438—33no—
23C25×C3—32no—
24C25×C3—46no—
25C25×C3—612no—
26C25×C3—122no—
27C2×C22⋊A4—418no—
28C22×C3×D4—312no—
29C22×C3×D4—624no—
30C22×C3×D4—123no—
31C22×C3×D4—123no—
32C23×C3×C4—33no—
33C3×#120—632no—
34C3×#120—632no—
35C2×C3×C22⋊C4—624no—
36C2×C3×C22⋊C4—612no—
37C3×#95—43no—
38C3×#95—121no—
39#95⋊C3—49no—
40C2×C3×A4—1624no—
41C2×C3×A4—163no—
42C26C3×A412yescomplemented
43C23×D4—33no—
44C2×#120—624no—
45C22×C22⋊C4—36no—
46C2×#95—31no—
47C2×#95C3×A413yescomplemented
48C24×C3—312no—
49C24×C3—48no—
50C24×C3—42no—
51C24×C3—612no—
52C24×C3—66no—
53C24×C3—66no—
54C24×C3—68no—
55C24×C3—68no—
56C24×C3—128no—
57C24×C3—1212no—
58C24×C3—1224no—
59C24×C3—1224no—
60C24×C3—1212no—
61C24×C3—122no—
62C24×C3C22⋊A411yescharacteristic
63C22⋊A4—46no—
64C22×A4—1624no—
65C22×A4—163no—
66C2×C3×D4—648no—
67C2×C3×D4—1212no—
68C2×C3×D4—1224no—
69C2×C3×D4—1224no—
70C22×C3×C4—36no—
71C22×C3×C4—63no—
72C22×C3×C4—612no—
73C22×C3×C4—63no—
74C3×C22⋊C4—648no—
75C22×C32—641no—
76C3×A4—168no—
77C3×A4—161no—
78C25—32no—
79C25—46no—
80C25—612no—
81C25—122no—
82C22×D4—312no—
83C22×D4—624no—
84C22×D4—123no—
85C22×D4—123no—
86C23×C4—33no—
87#120—632no—
88#120—632no—
89C2×C22⋊C4—624no—
90C2×C22⋊C4—612no—
91#95—43no—
92#95—121no—
93C23×C3—33no—
94C23×C3—31no—
95C23×C3—38no—
96C23×C3—424no—
97C23×C3—612no—
98C23×C3—624no—
99C23×C3—612no—
100C23×C3—624no—
101C23×C3—126no—
102C23×C3—124no—
103C23×C3—1212no—
104C23×C3—126no—
105C23×C3—1224no—
106C23×C3—128no—
107C23×C3—1248no—
108C23×C3—1224no—
109C23×C3—1224no—
110C23×C3—1224no—
111C23×C3—122no—
112C23×C3—122no—
113C23×C3#99713yes—
114C2×A4—1672no—
115C2×A4—169no—
116C3×D4—1248no—
117C2×C3×C4—612no—
118C2×C3×C4—66no—
119C2×C3×C4—126no—
120C2×C3×C4—126no—
121C2×C32—643no—
122C24—312no—
123C24—48no—
124C24—42no—
125C24—612no—
126C24—66no—
127C24—66no—
128C24—68no—
129C24—68no—
130C24—128no—
131C24—1212no—
132C24—1224no—
133C24—1224no—
134C24—1212no—
135C24—122no—
136C24C3×C22⋊A411yescharacteristic
137C2×D4—648no—
138C2×D4—1212no—
139C2×D4—1224no—
140C2×D4—1224no—
141C22×C4—36no—
142C22×C4—63no—
143C22×C4—612no—
144C22×C4—63no—
145C22⋊C4—648no—
146C22×C3—33no—
147C22×C3—32no—
148C22×C3—33no—
149C22×C3—33no—
150C22×C3—48no—
151C22×C3—624no—
152C22×C3—1224no—
153C22×C3—1212no—
154C22×C3—1224no—
155C22×C3—128no—
156C22×C3—128no—
157C22×C3—1212no—
158C22×C3—643no—
159C22×C3#546411yescharacteristic
160C22×C3#546511yescharacteristic
161A4—1624no—
162A4—163no—
163C3×C4—126no—
164C32—641noSylow
165C23—33no—
166C23—31no—
167C23—38no—
168C23—424no—
169C23—612no—
170C23—624no—
171C23—612no—
172C23—624no—
173C23—126no—
174C23—124no—
175C23—1212no—
176C23—126no—
177C23—1224no—
178C23—128no—
179C23—1248no—
180C23—1224no—
181C23—1224no—
182C23—1224no—
183C23—122no—
184C23—122no—
185C23C3×#99713yes—
186D4—1248no—
187C2×C4—612no—
188C2×C4—66no—
189C2×C4—126no—
190C2×C4—126no—
191C2×C3—33no—
192C2×C3—31no—
193C2×C3—128no—
194C2×C3—649no—
195C2×C3#2679⋊C313yes—
196C22—33no—
197C22—32no—
198C22—33no—
199C22—33no—
200C22—48no—
201C22—624no—
202C22—1224no—
203C22—1212no—
204C22—1224no—
205C22—128no—
206C22—128no—
207C22—1212no—
208C22C3×#546411yescharacteristic
209C22C3×#546511yescharacteristic
210C4—126no—
211C3—643no—
212C3#1170931311yescharacteristic, direct product factor
213C2—33no—
214C2—31no—
215C2—128no—
216C2C3×#2679⋊C313yes—
subgroupG/H
center, hypercenterC22×C3#5464
commutator, cosocle, hypocenter#15947C32
FrattiniC24C3×C22⋊A4
FittingC3×#15947C3
socleC24×C3C22⋊A4
LCSG ▷ #15947
UCSC1 ◁ C22×C3

Complements

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

NH ≅ G/Ntype
1. #11709313C3direct (N × H)
2. C3×#15947C3semidirect
9. #15947C32semidirect
10. C26×C3A4semidirect
16. C2×C3×#95A4semidirect
42. C26C3×A4semidirect
47. C2×#95C3×A4semidirect
212. C3#11709313direct (N × H)

Maximal subgroups

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

subgroupindex
#117093133
C3×#159473
C22×C3×C22⋊A44
C2×C3×#95⋊C34