Finite Group Databasebeta

← C3×#1890 #72605

Subgroups — C3×#1890 #72605

Order 384.

386 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 112 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×C3×#123C211yesmaximal, characteristic
2C3×#518C211yesmaximal, characteristic
3C2×C3×#99C211yesmaximal, characteristic
4C3×#381C212yesmaximal, complemented
5C3×#342C212yesmaximal, complemented
6#1890C311yesmaximal, characteristic, direct product factor, Sylow
7C22×C3×D4C2211yescharacteristic
8C23×C3×C4C2211yescharacteristic
9C3×#123—22no—
10C3×#123C414yescomplemented
11C3×C4×D4—24no—
12C3×#117—21no—
13C2×C3×C4⋊C4—21no—
14C2×C3×C22⋊C4—21no—
15C2×C3×C22⋊C4—21no—
16C2×C3×C22⋊C4C2212yes—
17C2×C3×C22⋊C4C2212yes—
18C2×C3×C22⋊C4C2211yescharacteristic
19C3×#99—22no—
20C3×#95—24no—
21C2×#123C2×C311yescharacteristic
22#518C2×C311yescharacteristic
23C2×#99C2×C311yescharacteristic
24#381C2×C312yescomplemented
25#342C2×C312yescomplemented
26C24×C3D411yescharacteristic
27C24×C3C2311yescharacteristic
28C2×C3×D4—22no—
29C2×C3×D4—22no—
30C2×C3×D4C2×C412yes—
31C2×C3×D4D412yes—
32C22×C3×C4—22no—
33C22×C3×C4—21no—
34C22×C3×C4—21no—
35C22×C3×C4—21no—
36C22×C3×C4—22no—
37C22×C3×C4—22no—
38C22×C3×C4—22no—
39C22×C3×C4C2×C412yescomplemented
40C22×C3×C4D411yescharacteristic
41C22×C3×C4D414yes—
42C3×C4⋊C4—22no—
43C3×C4⋊C4—24no—
44C3×C22⋊C4—22no—
45C3×C22⋊C4—24no—
46C3×C22⋊C4—22no—
47C3×C22⋊C4—22no—
48C3×C22⋊C4—21no—
49C3×C22⋊C4—22no—
50C3×C22⋊C4—22no—
51C3×C22⋊C4C2×C412yescomplemented
52C3×C42—22no—
53C22×D4C22×C311yescharacteristic
54C23×C4C22×C311yescharacteristic
55#123—22no—
56#123C3×C414yescomplemented
57C4×D4—24no—
58#117—21no—
59C2×C4⋊C4—21no—
60C2×C22⋊C4—21no—
61C2×C22⋊C4—21no—
62C2×C22⋊C4C22×C312yes—
63C2×C22⋊C4C22×C312yes—
64C2×C22⋊C4C22×C311yescharacteristic
65#99—22no—
66#95—24no—
67C23×C3—21no—
68C23×C3—21no—
69C23×C3—42no—
70C23×C3—42no—
71C23×C3C22⋊C412yes—
72C23×C3C22×C411yescharacteristic
73C23×C3C2×D411yescharacteristic
74C23×C3C2×D412yes—
75C23×C3C2×D411yescharacteristic
76C23×C3#4112yes—
77C3×D4—24no—
78C3×D4—24no—
79C2×C3×C4—21no—
80C2×C3×C4—21no—
81C2×C3×C4—22no—
82C2×C3×C4—22no—
83C2×C3×C4—24no—
84C2×C3×C4—24no—
85C2×C3×C4—42no—
86C2×C3×C4—41no—
87C2×C3×C4—42no—
88C2×C3×C4—41no—
89C2×C3×C4—44no—
90C2×C3×C4—44no—
91C2×C3×C4—42no—
92C2×C3×C4—82no—
93C2×C3×C4C22⋊C412yes—
94C24C3×D411yescharacteristic
95C24C23×C311yescharacteristic
96C2×D4—22no—
97C2×D4—22no—
98C2×D4C2×C3×C412yes—
99C2×D4C3×D412yes—
100C22×C4—22no—
101C22×C4—21no—
102C22×C4—21no—
103C22×C4—21no—
104C22×C4—22no—
105C22×C4—22no—
106C22×C4—22no—
107C22×C4C2×C3×C412yescomplemented
108C22×C4C3×D411yescharacteristic
109C22×C4C3×D414yes—
110C4⋊C4—22no—
111C4⋊C4—24no—
112C22⋊C4—22no—
113C22⋊C4—24no—
114C22⋊C4—22no—
115C22⋊C4—22no—
116C22⋊C4—21no—
117C22⋊C4—22no—
118C22⋊C4—22no—
119C22⋊C4C2×C3×C412yescomplemented
120C42—22no—
121C22×C3—24no—
122C22×C3—22no—
123C22×C3—22no—
124C22×C3—41no—
125C22×C3—41no—
126C22×C3—42no—
127C22×C3—42no—
128C22×C3—42no—
129C22×C3—81no—
130C22×C3C2×C22⋊C411yescharacteristic
131C22×C3C4×D412yes—
132C22×C3#12011yescharacteristic
133C22×C3#12112yes—
134C22×C3#12311yescharacteristic
135C3×C4—22no—
136C3×C4—42no—
137C3×C4—42no—
138C3×C4—44no—
139C3×C4—82no—
140C23—21no—
141C23—21no—
142C23—42no—
143C23—42no—
144C23C3×C22⋊C412yes—
145C23C22×C3×C411yescharacteristic
146C23C2×C3×D411yescharacteristic
147C23C2×C3×D412yes—
148C23C2×C3×D411yescharacteristic
149C23C3×#4112yes—
150D4—24no—
151D4—24no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—22no—
155C2×C4—22no—
156C2×C4—24no—
157C2×C4—24no—
158C2×C4—42no—
159C2×C4—41no—
160C2×C4—42no—
161C2×C4—41no—
162C2×C4—44no—
163C2×C4—44no—
164C2×C4—42no—
165C2×C4—82no—
166C2×C4C3×C22⋊C412yes—
167C2×C3—21no—
168C2×C3—22no—
169C2×C3—21no—
170C2×C3—22no—
171C2×C3—42no—
172C2×C3#38611yescharacteristic
173C2×C3#45812yes—
174C22—24no—
175C22—22no—
176C22—22no—
177C22—41no—
178C22—41no—
179C22—42no—
180C22—42no—
181C22—42no—
182C22—81no—
183C22C2×C3×C22⋊C411yescharacteristic
184C22C3×C4×D412yes—
185C22C3×#12011yescharacteristic
186C22C3×#12112yes—
187C22C3×#12311yescharacteristic
188C4—22no—
189C4—42no—
190C4—42no—
191C4—44no—
192C4—82no—
193C3#189011yescharacteristic, direct product factor, Sylow
194C2—21no—
195C2—22no—
196C2—21no—
197C2—22no—
198C2—42no—
199C2C3×#38611yescharacteristic
200C2C3×#45812yes—
subgroupG/H
center, socleC22×C3#120
commutatorC23C22×C3×C4
Frattini, cosocleC24C23×C3
prime radicalC22×C3×D4C22
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C3 ◁ C24×C3 ◁ G

Complements

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

NH ≅ G/Ntype
4. C3×#381C2semidirect
5. C3×#342C2semidirect
6. #1890C3direct (N × H)
10. C3×#123C4semidirect
24. #381C2×C3semidirect
25. #342C2×C3semidirect
39. C22×C3×C4C2×C4semidirect
51. C3×C22⋊C4C2×C4semidirect
56. #123C3×C4semidirect
107. C22×C4C2×C3×C4semidirect
119. C22⋊C4C2×C3×C4semidirect
193. C3#1890direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#1232
C3×#5182
C2×C3×#992
C3×#3812
C3×#3422
#18903