Finite Group Databasebeta

← C3×#64144 #11723890

Subgroups — C3×#64144 #11723890

Order 864.

684 conjugacy classes of subgroups; only the 154 normal subgroups are shown.

normal subgroups only

This group has 684 conjugacy classes of subgroups — too many to draw. Only its 154 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×C33×D4C211yesmaximal, characteristic
2C22×C3×C3⋊Dic3C211yesmaximal, characteristic, complemented
3C3×#3757C211yesmaximal, characteristic, complemented
4C3×#3757C212yesmaximal, complemented
5C3×#3750C212yesmaximal, complemented
6#64144C311yesmaximal, characteristic, direct product factor
7C3×#935—34nomaximal
8C23×C33C2211yescharacteristic
9C23×C33C2211yescharacteristic
10C33×D4—22no—
11C2×C33×C4C2211yescharacteristic
12C2×C3×C3⋊Dic3—22no—
13C2×C3×C3⋊Dic3C2212yes—
14C2×C3×C3⋊Dic3C2212yes—
15C2×C32×D4—24no—
16C2×C32×D4D314yes—
17C2×C32×D4C2×C311yescharacteristic
18C22×C3⋊Dic3C2×C311yescharacteristic, complemented
19C22×C3×Dic3—34no—
20#3757C2×C311yescharacteristic, complemented
21#3757C2×C312yescomplemented
22#3750C2×C312yescomplemented
23C3×#217—34no—
24C3×#217—38no—
25C3×Dic3⋊C4—38no—
26C22×C33—22no—
27C22×C33—21no—
28C22×C33—22no—
29C22×C33D412yes—
30C22×C33C2311yescharacteristic
31C33×C4—21no—
32C3×C3⋊Dic3—22no—
33C3×C3⋊Dic3—22no—
34C3×#123—91no—
35#935—34no—
36C23×C32—24no—
37C23×C32—24no—
38C23×C32C2×D314yes—
39C23×C32C2×D314yes—
40C23×C32C22×C311yescharacteristic
41C23×C32C22×C311yescharacteristic
42C32×D4—216no—
43C32×D4—28no—
44C32×D4—22no—
45C2×C32×C4—24no—
46C2×C32×C4C2×D314yes—
47C2×C32×C4C22×C311yescharacteristic
48C2×C3⋊Dic3—22no—
49C2×C3⋊Dic3C22×C312yes—
50C2×C3⋊Dic3C22×C312yes—
51C2×C3×Dic3—38no—
52C2×C3×Dic3—38no—
53C2×C3×Dic3—68no—
54C2×C33—22no—
55C2×C33—41no—
56C2×C33C2×D411yescharacteristic
57C2×C33#4112yes—
58C2×C3×D4—24no—
59C2×C3×D4C3×D314yes—
60C2×C3×D4C3⋊D311yescharacteristic
61C22×C3×C4—91no—
62C22×Dic3—34no—
63C3×C4⋊C4—92no—
64C3×C22⋊C4—91no—
65C3×C22⋊C4—92no—
66#217—34no—
67#217—38no—
68Dic3⋊C4—38no—
69C22×C32—22no—
70C22×C32—28no—
71C22×C32—24no—
72C22×C32—21no—
73C22×C32—22no—
74C22×C32—28no—
75C22×C32—24no—
76C22×C32—28no—
77C22×C32—28no—
78C22×C32—48no—
79C22×C32—48no—
80C22×C32#6718yes—
81C22×C32C3×D412yes—
82C22×C32C22×D314yes—
83C22×C32C23×C311yescharacteristic
84C32×C4—28no—
85C32×C4—24no—
86C32×C4—21no—
87C3⋊Dic3—22no—
88C3⋊Dic3—22no—
89C3×Dic3—68no—
90C3×Dic3—68no—
91#123—91noSylow
92C33#12311yescharacteristic, complemented, Sylow
93C23×C3—24no—
94C23×C3—24no—
95C23×C3C2×C3×D314yes—
96C23×C3C2×C3×D314yes—
97C23×C3C2×C3⋊D311yescharacteristic
98C23×C3C2×C3⋊D311yescharacteristic
99C3×D4—216no—
100C3×D4—28no—
101C3×D4—22no—
102C2×C3×C4—24no—
103C2×C3×C4—92no—
104C2×C3×C4—92no—
105C2×C3×C4—182no—
106C2×C3×C4C2×C3×D314yes—
107C2×C3×C4C2×C3⋊D311yescharacteristic
108C2×Dic3—38no—
109C2×Dic3—38no—
110C2×Dic3—68no—
111C2×C32—22no—
112C2×C32—28no—
113C2×C32—24no—
114C2×C32—28no—
115C2×C32—48no—
116C2×C32—48no—
117C2×C32—44no—
118C2×C32—41no—
119C2×C32#23718yes—
120C2×C32C2×#6714yes—
121C2×C32C2×C3×D411yescharacteristic
122C2×C32C3×#4112yes—
123C2×D4C3×C3⋊D311yescharacteristic
124C22×C4—91no—
125C4⋊C4—92no—
126C22⋊C4—91no—
127C22⋊C4—92no—
128C22×C3—28no—
129C22×C3—22no—
130C22×C3—28no—
131C22×C3—28no—
132C22×C3—24no—
133C22×C3—22no—
134C22×C3—21no—
135C22×C3—28no—
136C22×C3—24no—
137C22×C3—48no—
138C22×C3—48no—
139C22×C3C3×#6718yes—
140C22×C3#63812yes—
141C22×C3C22×C3×D314yes—
142C22×C3C22×C3⋊D311yescharacteristic
143C3×C4—28no—
144C3×C4—24no—
145C3×C4—21no—
146C3×C4—182no—
147C3×C4—182no—
148Dic3—68no—
149Dic3—68no—
150C32—24no—
151C32#93514yescomplemented
152C32C3×#12311yescharacteristic, complemented
153C23C2×C3×C3⋊D311yescharacteristic
154C23C2×C3×C3⋊D311yescharacteristic
155D4—22no—
156C2×C4—92no—
157C2×C4—92no—
158C2×C4—182no—
159C2×C4C2×C3×C3⋊D311yescharacteristic
160C2×C3—28no—
161C2×C3—22no—
162C2×C3—28no—
163C2×C3—24no—
164C2×C3—48no—
165C2×C3—48no—
166C2×C3—44no—
167C2×C3—41no—
168C2×C3C3×#23718yes—
169C2×C3C2×C3×#6714yes—
170C2×C3#383012yes—
171C2×C3C2×#63811yescharacteristic
172C22—22no—
173C22—22no—
174C22—21no—
175C22C3×#63812yes—
176C22C22×C3×C3⋊D311yescharacteristic
177C4—21no—
178C4—182no—
179C4—182no—
180C3—24no—
181C3C3×#93514yescomplemented
182C3#6414411yescharacteristic, direct product factor
183C2—22no—
184C2—41no—
185C2C3×#383012yes—
186C2C2×C3×#63811yescharacteristic
subgroupG/H
centerC22×C3C22×C3⋊D3
commutator, cosocleC22×C32C23×C3
FrattiniC22C22×C3×C3⋊D3
Fitting, prime radicalC2×C33×D4C2
socleC22×C33C23
hypercenterC2×C3×D4C3⋊D3
hypocenterC32C3×#123
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C2×C3×D4

Complements

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

NH ≅ G/Ntype
2. C22×C3×C3⋊Dic3C2semidirect
3. C3×#3757C2semidirect
4. C3×#3757C2semidirect
5. C3×#3750C2semidirect
6. #64144C3direct (N × H)
18. C22×C3⋊Dic3C2×C3semidirect
20. #3757C2×C3semidirect
21. #3757C2×C3semidirect
22. #3750C2×C3semidirect
92. C33#123semidirect
151. C32#935semidirect
152. C32C3×#123semidirect
181. C3C3×#935semidirect
182. C3#64144direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C33×D42
C22×C3×C3⋊Dic32
C3×#37572
C3×#37502
#641443
C3×#9353