Finite Group Databasebeta

← C32×#1821 #11768870

Subgroups — C32×#1821 #11768870

Order 1152.

948 conjugacy classes of subgroups; only the 336 normal subgroups are shown.

normal subgroups only

This group has 948 conjugacy classes of subgroups — too many to draw. Only its 336 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
1C22×C32×C4⋊C4C211yesmaximal, characteristic
2C32×#407C212yesmaximal
3C32×#343C214yesmaximal, complemented
4C3×#1821C314yesmaximal, direct product factor
5C23×C32×C4C412yes—
6C23×C32×C4C2211yescharacteristic
7C2×C32×M16C2214yes—
8C2×C32×C4⋊C4—22no—
9C2×C32×C4⋊C4—22no—
10C2×C32×C4⋊C4C412yes—
11C2×C32×C4⋊C4C2212yes—
12C32×C22⋊C8—22no—
13C32×C22⋊C8—22no—
14C22×C3×C4⋊C4C2×C314yes—
15C3×#407C2×C318yes—
16C3×#343C2×C3116yescomplemented
17C24×C32C2×C411yescharacteristic
18C22×C32×C4—24no—
19C22×C32×C4—22no—
20C22×C32×C4—22no—
21C22×C32×C4—44no—
22C22×C32×C4C2×C411yescharacteristic
23C22×C32×C4C2×C414yes—
24C22×C32×C4D412yes—
25C22×C32×C4D412yes—
26C22×C32×C4C2311yescharacteristic
27C32×M16—28no—
28C2×C32×C8—24no—
29C32×C4⋊C4—24no—
30C32×C4⋊C4—24no—
31#1821C3211yescharacteristic, direct product factor, Sylow
32C23×C3×C4C3×C418yes—
33C23×C3×C4C22×C314yes—
34C2×C3×M16C22×C3116yes—
35C2×C3×C4⋊C4—28no—
36C2×C3×C4⋊C4—28no—
37C2×C3×C4⋊C4C3×C418yes—
38C2×C3×C4⋊C4C22×C318yes—
39C3×C22⋊C8—28no—
40C3×C22⋊C8—28no—
41C23×C32—22no—
42C23×C32—22no—
43C23×C32—22no—
44C23×C32C22⋊C411yescharacteristic
45C23×C32C22⋊C411yescharacteristic
46C23×C32C22×C411yescharacteristic
47C2×C32×C4—22no—
48C2×C32×C4—24no—
49C2×C32×C4—24no—
50C2×C32×C4—24no—
51C2×C32×C4—44no—
52C2×C32×C4—44no—
53C2×C32×C4—44no—
54C2×C32×C4C22⋊C412yes—
55C2×C32×C4C2×D412yes—
56C2×C32×C4#4114yes—
57C32×C8—44no—
58C22×C4⋊C4C2×C3211yescharacteristic
59#407C2×C3212yes—
60#343C2×C3214yescomplemented
61C24×C3C2×C3×C414yes—
62C22×C3×C4—216no—
63C22×C3×C4—28no—
64C22×C3×C4—28no—
65C22×C3×C4—416no—
66C22×C3×C4C2×C3×C414yes—
67C22×C3×C4C2×C3×C4116yes—
68C22×C3×C4C3×D418yes—
69C22×C3×C4C3×D418yes—
70C22×C3×C4C23×C314yes—
71C3×M16—232no—
72C2×C3×C8—216no—
73C3×C4⋊C4—216no—
74C3×C4⋊C4—216no—
75C22×C32—28no—
76C22×C32—21no—
77C22×C32—21no—
78C22×C32—21no—
79C22×C32—21no—
80C22×C32—21no—
81C22×C32—21no—
82C22×C32#10012yes—
83C22×C32#10112yes—
84C22×C32C2×C22⋊C411yescharacteristic
85C22×C32#11712yes—
86C32×C4—22no—
87C32×C4—44no—
88C32×C4#12314yes—
89C23×C4C32×C412yes—
90C23×C4C22×C3211yescharacteristic
91C2×M16C22×C3214yes—
92C2×C4⋊C4—22no—
93C2×C4⋊C4—22no—
94C2×C4⋊C4C32×C412yes—
95C2×C4⋊C4C22×C3212yes—
96C22⋊C8—22no—
97C22⋊C8—22no—
98C23×C3—28no—
99C23×C3—28no—
100C23×C3—28no—
101C23×C3C3×C22⋊C414yes—
102C23×C3C3×C22⋊C414yes—
103C23×C3C22×C3×C414yes—
104C2×C3×C4—28no—
105C2×C3×C4—216no—
106C2×C3×C4—216no—
107C2×C3×C4—216no—
108C2×C3×C4—416no—
109C2×C3×C4—416no—
110C2×C3×C4—416no—
111C2×C3×C4C3×C22⋊C418yes—
112C2×C3×C4C2×C3×D418yes—
113C2×C3×C4C3×#41116yes—
114C3×C8—416no—
115C2×C32—22no—
116C2×C32—22no—
117C2×C32—22no—
118C2×C32#38111yescharacteristic
119C2×C32C2×#10011yescharacteristic
120C2×C32C2×#10111yescharacteristic
121C24C2×C32×C411yescharacteristic
122C22×C4—24no—
123C22×C4—22no—
124C22×C4—22no—
125C22×C4—44no—
126C22×C4C2×C32×C411yescharacteristic
127C22×C4C2×C32×C414yes—
128C22×C4C32×D412yes—
129C22×C4C32×D412yes—
130C22×C4C23×C3211yescharacteristic
131M16—28no—
132C2×C8—24no—
133C4⋊C4—24no—
134C4⋊C4—24no—
135C22×C3—232no—
136C22×C3—24no—
137C22×C3—24no—
138C22×C3—24no—
139C22×C3—24no—
140C22×C3—24no—
141C22×C3—24no—
142C22×C3C3×#10018yes—
143C22×C3C3×#10118yes—
144C22×C3C2×C3×C22⋊C414yes—
145C22×C3C3×#11718yes—
146C3×C4—28no—
147C3×C4—416no—
148C3×C4C3×#123116yes—
149C32#182111yescharacteristic, direct product factor, Sylow
150C23—22no—
151C23—22no—
152C23—22no—
153C23C32×C22⋊C411yescharacteristic
154C23C32×C22⋊C411yescharacteristic
155C23C22×C32×C411yescharacteristic
156C2×C4—22no—
157C2×C4—24no—
158C2×C4—24no—
159C2×C4—24no—
160C2×C4—44no—
161C2×C4—44no—
162C2×C4—44no—
163C2×C4C32×C22⋊C412yes—
164C2×C4C2×C32×D412yes—
165C2×C4C32×#4114yes—
166C8—44no—
167C2×C3—28no—
168C2×C3—28no—
169C2×C3—28no—
170C2×C3C3×#38114yes—
171C2×C3C2×C3×#10014yes—
172C2×C3C2×C3×#10114yes—
173C22—28no—
174C22—21no—
175C22—21no—
176C22—21no—
177C22—21no—
178C22—21no—
179C22—21no—
180C22C32×#10012yes—
181C22C32×#10112yes—
182C22C2×C32×C22⋊C411yescharacteristic
183C22C32×#11712yes—
184C4—22no—
185C4—44no—
186C4C32×#12314yes—
187C3C3×#182114yesdirect product factor
188C2—22no—
189C2—22no—
190C2—22no—
191C2C32×#38111yescharacteristic
192C2C2×C32×#10011yescharacteristic
193C2C2×C32×#10111yescharacteristic
subgroupG/H
center, socleC22×C32C2×C22⋊C4
commutatorC23C22×C32×C4
Frattini, cosocleC22×C4C23×C32
prime radicalC24×C32C2×C4
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C32 ◁ C23×C32×C4 ◁ G

Complements

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

NH ≅ G/Ntype
3. C32×#343C2semidirect
4. C3×#1821C3direct (N × H)
16. C3×#343C2×C3semidirect
31. #1821C32direct (N × H)
60. #343C2×C32semidirect
149. C32#1821direct (N × H)
187. C3C3×#1821direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C32×C4⋊C42
C32×#4072
C32×#3432
C3×#18213