Finite Group Databasebeta

← C3⋊D3×#379 #11800953

Subgroups — C3⋊D3×#379 #11800953

Order 1152.

10392 conjugacy classes of subgroups; only the 625 normal subgroups are shown.

normal subgroups only

This group has 10392 conjugacy classes of subgroups — too many to draw. Only its 625 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
1C25×C3⋊D3C211yesmaximal, characteristic
2C2×C22⋊C4×C3⋊D3C216yesmaximal, complemented
3C32×#379C211yesmaximal, characteristic, complemented
4#10592946C211yesmaximal, characteristic, complemented
5#10592654C216yesmaximal, complemented
6D3×#379—34nomaximal
7C25×C32C2211yescharacteristic
8C24×C3⋊D3—224no—
9C24×C3⋊D3C418yescomplemented
10C24×C3⋊D3C2213yes—
11C24×C3⋊D3C2213yes—
12C22×C4×C3⋊D3C2214yescomplemented
13C2×C32×C22⋊C4C2216yescomplemented
14C2×#3757C2216yescomplemented
15C2×#3752C22112yescomplemented
16C22⋊C4×C3⋊D3—224no—
17C25×D3—34no—
18C2×D3×C22⋊C4—324no—
19C3×#379D314yescomplemented
20#5247—34no—
21#4955—324no—
22C24×C32—212no—
23C24×C32C2×C414yescomplemented
24C24×C32C2313yes—
25C23×C3⋊D3—2128no—
26C23×C3⋊D3—212no—
27C23×C3⋊D3—296no—
28C23×C3⋊D3—224no—
29C23×C3⋊D3—224no—
30C23×C3⋊D3C2×C4112yes—
31C23×C3⋊D3C2×C4112yescomplemented
32C23×C3⋊D3D4124yes—
33C23×C3⋊D3C2313yes—
34C23×C3⋊D3C2311yescharacteristic
35C22×C32×C4C2314yescomplemented
36C22×C3⋊Dic3C2314yescomplemented
37C2×C4×C3⋊D3—224no—
38C32×C22⋊C4—212no—
39#3757—212no—
40#3752—224no—
41C2×#379—91noSylow
42C25×C3C2×D314yes—
43C24×D3—312no—
44C24×D3—332no—
45C24×D3—312no—
46C24×D3—696no—
47C22×C4×D3—316no—
48C2×C3×C22⋊C4C2×D3124yescomplemented
49C2×#217—324no—
50C2×(C2×D3)⋊C4—348no—
51D3×C22⋊C4—696no—
52C23×C32—232no—
53C23×C32—224no—
54C23×C32—212no—
55C23×C32C22×C416yes—
56C23×C32C2×D4112yes—
57C23×C32C2411yescharacteristic
58C22×C3⋊D3—296no—
59C22×C3⋊D3—2256no—
60C22×C3⋊D3—224no—
61C22×C3⋊D3—212no—
62C22×C3⋊D3—248no—
63C22×C3⋊D3—248no—
64C22×C3⋊D3—296no—
65C22×C3⋊D3C22⋊C4148yescomplemented
66C22×C3⋊D3C22×C416yes—
67C22×C3⋊D3C22×C412yes—
68C22×C3⋊D3C2×D4112yes—
69C22×C3⋊D3C2×D4112yes—
70C2×C32×C4—212no—
71C2×C3⋊Dic3—212no—
72C4×C3⋊D3—416no—
73C26—91no—
74C22×C22⋊C4—96no—
75#379—91no—
76#379—96no—
77#379C3⋊D311yescharacteristic, direct product factor
78C24×C3—248no—
79C24×C3C4×D3116yescomplemented
80C24×C3C22×D3112yes—
81C23×D3—34no—
82C23×D3—348no—
83C23×D3—396no—
84C23×D3—312no—
85C23×D3—348no—
86C23×D3—696no—
87C23×D3—6384no—
88C23×D3—696no—
89C23×D3—6512no—
90C23×D3—648no—
91C22×C3×C4C22×D3116yescomplemented
92C22×Dic3—316no—
93C2×C4×D3—696no—
94C3×C22⋊C4—248no—
95#217—648no—
96(C2×D3)⋊C4—696no—
97C22×C32—232no—
98C22×C32—212no—
99C22×C32—224no—
100C22×C32C2×C22⋊C4112yescomplemented
101C22×C32C23×C411yescharacteristic
102C22×C32C22×D416yes—
103C2×C3⋊D3—296no—
104C2×C3⋊D3—212no—
105C2×C3⋊D3—224no—
106C2×C3⋊D3—296no—
107C2×C3⋊D3C2×C22⋊C4112yes—
108C2×C3⋊D3C2×C22⋊C4112yescomplemented
109C2×C3⋊D3#120116yes—
110C32×C4—44no—
111C3⋊Dic3—44no—
112C25—93no—
113C25—98no—
114C25—93no—
115C25—1824no—
116C25C2×C3⋊D311yescharacteristic
117C23×C4—94no—
118C2×C22⋊C4—96no—
119C2×C22⋊C4—912no—
120C2×C22⋊C4—1824no—
121C2×C22⋊C4C2×C3⋊D316yescomplemented
122C23×C3—2128no—
123C23×C3—296no—
124C23×C3—248no—
125C23×C3C2×C4×D3124yes—
126C23×C3D3×D4148yes—
127C23×C3C23×D314yes—
128C22×D3—38no—
129C22×D3—348no—
130C22×D3—3192no—
131C22×D3—324no—
132C22×D3—348no—
133C22×D3—6192no—
134C22×D3—6384no—
135C22×D3—6192no—
136C22×D3—61024no—
137C22×D3—6384no—
138C22×D3—696no—
139C22×D3—648no—
140C2×C3×C4—248no—
141C2×Dic3—648no—
142C4×D3—1264no—
143C2×C32—212no—
144C2×C32C22×C22⋊C413yes—
145C2×C32C2×#12014yes—
146C3⋊D3—212no—
147C3⋊D3#37918yesdirect product factor
148C24—212no—
149C24—91no—
150C24—93no—
151C24—912no—
152C24—924no—
153C24—912no—
154C24—1896no—
155C24—1824no—
156C24—1824no—
157C24—18128no—
158C24—1812no—
159C24C4×C3⋊D314yescomplemented
160C24C22×C3⋊D313yes—
161C22×C4—94no—
162C22×C4—1824no—
163C22×C4C22×C3⋊D314yescomplemented
164C22⋊C4—212no—
165C22⋊C4—1824no—
166C22⋊C4—1812no—
167C22×C3—2128no—
168C22×C3—248no—
169C22×C3—296no—
170C22×C3D3×C22⋊C4148yescomplemented
171C22×C3C22×C4×D314yes—
172C22×C3C2×D3×D4124yes—
173C2×D3—348no—
174C2×D3—364no—
175C2×D3—348no—
176C2×D3—6384no—
177C2×D3—6384no—
178C2×D3—648no—
179C2×D3—696no—
180C3×C4—416no—
181Dic3—1216no—
182C32C2×#37911yescharacteristic, complemented, Sylow
183C23—232no—
184C23—224no—
185C23—212no—
186C23—92no—
187C23—912no—
188C23—948no—
189C23—96no—
190C23—912no—
191C23—1848no—
192C23—1848no—
193C23—1896no—
194C23—18256no—
195C23—1896no—
196C23—1824no—
197C23—1812no—
198C23C2×C4×C3⋊D316yes—
199C23D4×C3⋊D3112yes—
200C23C23×C3⋊D311yescharacteristic
201C2×C4—212no—
202C2×C4—1812no—
203C2×C4—3616no—
204C2×C3—248no—
205C2×C3C2×D3×C22⋊C4112yes—
206C2×C3D3×#120116yes—
207D3—332no—
208D3—648no—
209C22—232no—
210C22—212no—
211C22—224no—
212C22—912no—
213C22—916no—
214C22—912no—
215C22—1896no—
216C22—1896no—
217C22—1812no—
218C22—1824no—
219C22C22⋊C4×C3⋊D3112yescomplemented
220C22C22×C4×C3⋊D311yescharacteristic
221C22C2×D4×C3⋊D316yes—
222C4—44no—
223C4—364no—
224C3D3×#37914yescomplemented
225C2—212no—
226C2—98no—
227C2—1812no—
228C2C2×C22⋊C4×C3⋊D313yes—
229C2C3⋊D3×#12014yes—
subgroupG/H
center, FrattiniC23C23×C3⋊D3
commutatorC22×C32C23×C4
FittingC32×#379C2
socle, cosocleC23×C32C24
prime radicalC25×C3⋊D3C2
hypercenter#379C3⋊D3
hypocenterC32C2×#379
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #379

Complements

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

NH ≅ G/Ntype
2. C2×C22⋊C4×C3⋊D3C2semidirect
3. C32×#379C2semidirect
4. #10592946C2semidirect
5. #10592654C2semidirect
9. C24×C3⋊D3C4semidirect
12. C22×C4×C3⋊D3C22semidirect
13. C2×C32×C22⋊C4C22semidirect
14. C2×#3757C22semidirect
15. C2×#3752C22semidirect
19. C3×#379D3semidirect
23. C24×C32C2×C4semidirect
31. C23×C3⋊D3C2×C4semidirect
35. C22×C32×C4C23semidirect
36. C22×C3⋊Dic3C23semidirect
48. C2×C3×C22⋊C4C2×D3semidirect
65. C22×C3⋊D3C22⋊C4semidirect
77. #379C3⋊D3direct (N × H)
79. C24×C3C4×D3semidirect
91. C22×C3×C4C22×D3semidirect
100. C22×C32C2×C22⋊C4semidirect
108. C2×C3⋊D3C2×C22⋊C4semidirect
121. C2×C22⋊C4C2×C3⋊D3semidirect
147. C3⋊D3#379direct (N × H)
159. C24C4×C3⋊D3semidirect
163. C22×C4C22×C3⋊D3semidirect
170. C22×C3D3×C22⋊C4semidirect
182. C32C2×#379semidirect
219. C22C22⋊C4×C3⋊D3semidirect
224. C3D3×#379semidirect

Maximal subgroups

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

subgroupindex
C25×C3⋊D32
C2×C22⋊C4×C3⋊D32
C32×#3792
#105929462
#105926542
D3×#3793