Finite Group Databasebeta

← C3×#85645 #11919816

Subgroups — C3×#85645 #11919816

Order 1152.

1728 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 1728 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×C22⋊(C22⋊A4)C211yesmaximal, characteristic, complemented
2C22×C3×#120C311yesmaximal, characteristic, complemented
3#85645C313yesmaximal, direct product factor
4C2×C3×C22⋊A4—41nomaximal
5C3×#120⋊C3—44nomaximal
6C26×C3C2×C311yescharacteristic, complemented
7C22⋊(C22⋊A4)C2×C313yescomplemented
8C23×C3×D4—31no—
9C2×C3×#120—34no—
10C2×C3×#120—34no—
11C22×C3×C22⋊C4—31no—
12C3×C22⋊A4—41no—
13C3×C22⋊A4—44no—
14C3×C22⋊A4—88no—
15C22×#120C3211yescharacteristic, complemented, Sylow
16C25×C3—31no—
17C25×C3—34no—
18C25×C3—68no—
19C25×C3A411yescharacteristic, complemented
20C2×C22⋊A4—43no—
21C22×C3×D4—36no—
22C22×C3×D4—36no—
23C22×C3×D4—68no—
24C23×C3×C4—31no—
25C3×#120—34no—
26C3×#120—312no—
27C3×#120—34no—
28C3×#120A414yescomplemented
29C2×C3×C22⋊C4—312no—
30#120⋊C3—412no—
31C2×C3×A4—164no—
32C2×C3×A4—161no—
33C26C2×C3211yescharacteristic, complemented
34C23×D4—31no—
35C2×#120—34no—
36C2×#120—34no—
37C22×C22⋊C4—31no—
38C24×C3—28no—
39C24×C3—36no—
40C24×C3—38no—
41C24×C3—34no—
42C24×C3—31no—
43C24×C3—31no—
44C24×C3—64no—
45C24×C3—68no—
46C24×C3—648no—
47C24×C3—68no—
48C24×C3—632no—
49C24×C3C2×A411yescharacteristic
50C24×C3C2×A414yescomplemented
51C22⋊A4—43no—
52C22⋊A4—412no—
53C22⋊A4—824no—
54C2×C3×D4—312no—
55C2×C3×D4—34no—
56C2×C3×D4—624no—
57C2×C3×D4—624no—
58C22×C3×C4—36no—
59C22×C3×C4—64no—
60C3×C22⋊C4—312no—
61C3×C22⋊C4—34no—
62C3×A4—164no—
63C3×A4—161no—
64C3×A4—328no—
65C25—31no—
66C25—34no—
67C25—68no—
68C25C3×A411yescharacteristic, complemented
69C22×D4—36no—
70C22×D4—36no—
71C22×D4—68no—
72C23×C4—31no—
73#120—34no—
74#120—312no—
75#120—34no—
76#120C3×A414yescomplemented
77C2×C22⋊C4—312no—
78C23×C3—34no—
79C23×C3—31no—
80C23×C3—324no—
81C23×C3—34no—
82C23×C3—31no—
83C23×C3—44no—
84C23×C3—68no—
85C23×C3—632no—
86C23×C3—624no—
87C23×C3—624no—
88C23×C3—624no—
89C23×C3—66no—
90C23×C3—66no—
91C23×C3—696no—
92C23×C3—68no—
93C23×C3—124no—
94C23×C3C22⋊A411yescharacteristic, complemented
95C2×A4—1612no—
96C2×A4—163no—
97C3×D4—68no—
98C3×D4—624no—
99C2×C3×C4—34no—
100C2×C3×C4—612no—
101C2×C32—641no—
102C24—28no—
103C24—36no—
104C24—38no—
105C24—34no—
106C24—31no—
107C24—31no—
108C24—64no—
109C24—68no—
110C24—648no—
111C24—68no—
112C24—632no—
113C24C2×C3×A411yescharacteristic
114C24C2×C3×A414yescomplemented
115C2×D4—312no—
116C2×D4—34no—
117C2×D4—624no—
118C2×D4—624no—
119C22×C4—36no—
120C22×C4—64no—
121C22⋊C4—312no—
122C22⋊C4—34no—
123C22×C3—28no—
124C22×C3—36no—
125C22×C3—34no—
126C22×C3—38no—
127C22×C3—61no—
128C22×C3—68no—
129C22×C3—648no—
130C22×C3—63no—
131C22×C3—68no—
132C22×C3—632no—
133C22×C3—124no—
134C22×C3—124no—
135C22×C3#120⋊C314yescomplemented
136C22×C3C2×C22⋊A411yescharacteristic
137A4—163no—
138A4—1612no—
139A4—3224no—
140C3×C4—64no—
141C32—641noSylow
142C23—31no—
143C23—34no—
144C23—324no—
145C23—34no—
146C23—31no—
147C23—44no—
148C23—68no—
149C23—632no—
150C23—624no—
151C23—624no—
152C23—624no—
153C23—66no—
154C23—66no—
155C23—696no—
156C23—68no—
157C23—124no—
158C23C3×C22⋊A411yescharacteristic, complemented
159D4—68no—
160D4—624no—
161C2×C4—34no—
162C2×C4—612no—
163C2×C3—31no—
164C2×C3—34no—
165C2×C3—41no—
166C2×C3—68no—
167C2×C3—121no—
168C2×C3—643no—
169C22—28no—
170C22—36no—
171C22—34no—
172C22—38no—
173C22—61no—
174C22—68no—
175C22—648no—
176C22—63no—
177C22—68no—
178C22—632no—
179C22—124no—
180C22—124no—
181C22C3×#120⋊C314yescomplemented
182C22C2×C3×C22⋊A411yescharacteristic
183C4—64no—
184C3—643no—
185C3#8564511yescharacteristic, direct product factor
186C2—31no—
187C2—34no—
188C2—41no—
189C2—68no—
190C2—121no—
subgroupG/H
center, hypercenterC3#85645
commutator, cosocle, hypocenterC26C2×C32
FrattiniC22C2×C3×C22⋊A4
FittingC22×C3×#120C3
socleC24×C3C2×A4
LCSG ▷ C26
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C3×C22⋊(C22⋊A4)C2semidirect
2. C22×C3×#120C3semidirect
3. #85645C3direct (N × H)
6. C26×C3C2×C3semidirect
7. C22⋊(C22⋊A4)C2×C3semidirect
15. C22×#120C32semidirect
19. C25×C3A4semidirect
28. C3×#120A4semidirect
33. C26C2×C32semidirect
50. C24×C3C2×A4semidirect
68. C25C3×A4semidirect
76. #120C3×A4semidirect
94. C23×C3C22⋊A4semidirect
114. C24C2×C3×A4semidirect
135. C22×C3#120⋊C3semidirect
158. C23C3×C22⋊A4semidirect
181. C22C3×#120⋊C3semidirect
185. C3#85645direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C22⋊(C22⋊A4)2
C22×C3×#1203
#856453
C2×C3×C22⋊A44
C3×#120⋊C34