Finite Group Databasebeta

← C3×D4×C22⋊A4 #11919888

Subgroups — C3×D4×C22⋊A4 #11919888

Order 1152.

3816 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 3816 conjugacy classes of subgroups — too many to draw. Only its 108 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×C3×C22⋊A4C212yesmaximal, complemented
2C3×C4×C22⋊A4C211yesmaximal, characteristic, complemented
3C24×C3×D4C311yesmaximal, characteristic, complemented
4D4×C22⋊A4C313yesmaximal, direct product factor
5C2×C3×C22⋊A4—22no—
6C2×C3×C22⋊A4C2211yescharacteristic
7C3×D4×A4—45nomaximal
8C26×C3C2×C312yescomplemented
9C22×C22⋊A4C2×C316yescomplemented
10C23×C3×D4—35no—
11C23×C3×D4—310no—
12C23×C3×D4—35no—
13C24×C3×C4C2×C311yescharacteristic, complemented
14C4×C22⋊A4C2×C313yescomplemented
15C3×C22⋊A4D411yescharacteristic, direct product factor
16C22×C3×A4—410no—
17C3×C4×A4—45no—
18C24×D4C3211yescharacteristic, complemented, Sylow
19C25×C3—22no—
20C25×C3—310no—
21C25×C3—310no—
22C25×C3—610no—
23C25×C3C22×C311yescharacteristic
24C2×C22⋊A4—26no—
25C2×C22⋊A4C22×C313yes—
26C22×C3×D4—360no—
27C22×C3×D4—360no—
28C22×C3×D4—330no—
29C22×C3×D4—310no—
30C22×C3×D4—310no—
31C22×C3×D4—310no—
32C22×C3×D4—35no—
33C22×C3×D4A415yescomplemented
34C23×C3×C4—35no—
35C23×C3×C4—35no—
36D4×A4—415no—
37C2×C3×A4—45no—
38C2×C3×A4—810no—
39C32×D4—161no—
40C26C2×C3212yescomplemented
41C23×D4—35no—
42C23×D4—35no—
43C23×D4—310no—
44C24×C4C2×C3211yescharacteristic, complemented
45C24×C3—35no—
46C24×C3—35no—
47C24×C3—360no—
48C24×C3—320no—
49C24×C3—310no—
50C24×C3—610no—
51C24×C3—610no—
52C24×C3—610no—
53C24×C3—610no—
54C24×C3—660no—
55C24×C3—660no—
56C24×C3C3×D411yescharacteristic, complemented
57C24×C3C2×A4110yescomplemented
58C22⋊A4C3×D413yesdirect product factor
59C22×A4—430no—
60C2×C3×D4—3120no—
61C2×C3×D4—360no—
62C2×C3×D4—360no—
63C2×C3×D4—330no—
64C2×C3×D4—330no—
65C2×C3×D4—35no—
66C2×C3×D4—35no—
67C2×C3×D4—310no—
68C22×C3×C4—330no—
69C22×C3×C4—310no—
70C22×C3×C4—35no—
71C22×C3×C4C2×A415yescomplemented
72C4×A4—415no—
73C22×C32—162no—
74C3×A4—45no—
75C32×C4—161no—
76C25—22no—
77C25—310no—
78C25—310no—
79C25—610no—
80C25C22×C3211yescharacteristic
81C22×D4—360no—
82C22×D4—360no—
83C22×D4—330no—
84C22×D4—310no—
85C22×D4—310no—
86C22×D4—310no—
87C22×D4—35no—
88C22×D4C3×A415yescomplemented
89C23×C4—35no—
90C23×C4—35no—
91C23×C3—210no—
92C23×C3—310no—
93C23×C3—330no—
94C23×C3—35no—
95C23×C3—35no—
96C23×C3—360no—
97C23×C3—310no—
98C23×C3—310no—
99C23×C3—610no—
100C23×C3—630no—
101C23×C3—620no—
102C23×C3—660no—
103C23×C3—660no—
104C23×C3—660no—
105C23×C3—6120no—
106C23×C3—610no—
107C23×C3C22×A415yes—
108C2×A4—415no—
109C2×A4—830no—
110C3×D4—360no—
111C3×D4—310no—
112C3×D4—310no—
113C3×D4—35no—
114C3×D4—163no—
115C3×D4C22⋊A411yescharacteristic, direct product factor
116C2×C3×C4—330no—
117C2×C3×C4—35no—
118C2×C3×C4—35no—
119C2×C32—161no—
120C2×C32—322no—
121C24—35no—
122C24—35no—
123C24—360no—
124C24—320no—
125C24—310no—
126C24—610no—
127C24—610no—
128C24—610no—
129C24—610no—
130C24—660no—
131C24—660no—
132C24C32×D411yescharacteristic, complemented
133C24C2×C3×A4110yescomplemented
134C2×D4—3120no—
135C2×D4—360no—
136C2×D4—360no—
137C2×D4—330no—
138C2×D4—330no—
139C2×D4—35no—
140C2×D4—35no—
141C2×D4—310no—
142C22×C4—330no—
143C22×C4—310no—
144C22×C4—35no—
145C22×C4C2×C3×A415yescomplemented
146C22×C3—35no—
147C22×C3—330no—
148C22×C3—310no—
149C22×C3—35no—
150C22×C3—310no—
151C22×C3—610no—
152C22×C3—610no—
153C22×C3—610no—
154C22×C3—610no—
155C22×C3—660no—
156C22×C3—660no—
157C22×C3—166no—
158C22×C3D4×A415yescomplemented
159C22×C3C2×C22⋊A412yescomplemented
160A4—415no—
161C3×C4—35no—
162C3×C4—163no—
163C3×C4C2×C22⋊A411yescharacteristic, complemented
164C32—161noSylow
165C23—210no—
166C23—310no—
167C23—330no—
168C23—35no—
169C23—35no—
170C23—360no—
171C23—310no—
172C23—310no—
173C23—610no—
174C23—630no—
175C23—620no—
176C23—660no—
177C23—660no—
178C23—660no—
179C23—6120no—
180C23—610no—
181C23C22×C3×A415yes—
182D4—360no—
183D4—310no—
184D4—310no—
185D4—35no—
186D4C3×C22⋊A411yescharacteristic, direct product factor
187C2×C4—330no—
188C2×C4—35no—
189C2×C4—35no—
190C2×C3—22no—
191C2×C3—35no—
192C2×C3—35no—
193C2×C3—610no—
194C2×C3—163no—
195C2×C3—326no—
196C2×C3C22×C22⋊A411yescharacteristic
197C22—35no—
198C22—310no—
199C22—330no—
200C22—35no—
201C22—310no—
202C22—610no—
203C22—610no—
204C22—610no—
205C22—610no—
206C22—660no—
207C22—660no—
208C22C3×D4×A415yescomplemented
209C22C2×C3×C22⋊A412yescomplemented
210C4—35no—
211C4C2×C3×C22⋊A411yescharacteristic, complemented
212C3—163no—
213C3D4×C22⋊A411yescharacteristic, direct product factor
214C2—22no—
215C2—35no—
216C2—35no—
217C2—610no—
218C2C22×C3×C22⋊A411yescharacteristic
subgroupG/H
centerC2×C3C22×C22⋊A4
commutator, cosocleC25C22×C32
FrattiniC2C22×C3×C22⋊A4
FittingC24×C3×D4C3
socleC25×C3C22×C3
hypercenterC3×D4C22⋊A4
hypocenterC24C32×D4
LCSG ▷ C25 ▷ C24
UCSC1 ◁ C2×C3 ◁ C3×D4

Complements

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

NH ≅ G/Ntype
1. C22×C3×C22⋊A4C2semidirect
2. C3×C4×C22⋊A4C2semidirect
3. C24×C3×D4C3semidirect
4. D4×C22⋊A4C3direct (N × H)
8. C26×C3C2×C3semidirect
9. C22×C22⋊A4C2×C3semidirect
13. C24×C3×C4C2×C3semidirect
14. C4×C22⋊A4C2×C3semidirect
15. C3×C22⋊A4D4direct (N × H)
18. C24×D4C32semidirect
33. C22×C3×D4A4semidirect
40. C26C2×C32semidirect
44. C24×C4C2×C32semidirect
56. C24×C3C3×D4semidirect
57. C24×C3C2×A4semidirect
58. C22⋊A4C3×D4direct (N × H)
71. C22×C3×C4C2×A4semidirect
88. C22×D4C3×A4semidirect
115. C3×D4C22⋊A4direct (N × H)
132. C24C32×D4semidirect
133. C24C2×C3×A4semidirect
145. C22×C4C2×C3×A4semidirect
158. C22×C3D4×A4semidirect
159. C22×C3C2×C22⋊A4semidirect
163. C3×C4C2×C22⋊A4semidirect
186. D4C3×C22⋊A4direct (N × H)
208. C22C3×D4×A4semidirect
209. C22C2×C3×C22⋊A4semidirect
211. C4C2×C3×C22⋊A4semidirect
213. C3D4×C22⋊A4direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×C22⋊A42
C3×C4×C22⋊A42
C24×C3×D43
D4×C22⋊A43
C3×D4×A44