Finite Group Databasebeta

← C22×D3×SD16 #87173

Subgroups — C22×D3×SD16 #87173

Order 384.

1720 conjugacy classes of subgroups; only the 565 normal subgroups are shown.

normal subgroups only

This group has 1720 conjugacy classes of subgroups — too many to draw. Only its 565 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×D3×Q8C211yesmaximal, characteristic, complemented
2C22×D3×D4C211yesmaximal, characteristic
3C22×C3×SD16C211yesmaximal, characteristic, complemented
4C22×#215C211yesmaximal, characteristic, complemented
5C22×#214C211yesmaximal, characteristic, complemented
6C2×D3×SD16C2124yesmaximal, direct product factor
7C22×#204C211yesmaximal, characteristic, complemented
8C22×D3×C8C211yesmaximal, characteristic, complemented
9C23×SD16—31nomaximal, Sylow
10C24×D3—21no—
11C22×C3×Q8C2211yescharacteristic, complemented
12C22×C3×D4C2211yescharacteristic
13C22×#67—21no—
14C2×D3×Q8—26no—
15C2×D3×Q8C22112yescomplemented
16C2×D3×D4—26no—
17C2×D3×D4C22112yes—
18C22×D12C2211yescharacteristic
19C22×C4×D3—21no—
20C22×C4×D3C2211yescharacteristic
21C22×Dic6—21no—
22C22×Dic6C2211yescharacteristic, complemented
23C2×C3×SD16C22112yescomplemented
24C22×C3×C8C2211yescharacteristic, complemented
25C2×#215C22112yescomplemented
26C2×#214C22112yescomplemented
27C22×C3⋊C8C2211yescharacteristic, complemented
28D3×SD16C22164yesdirect product factor
29C2×#204C22112yescomplemented
30C2×D3×C8C22112yescomplemented
31C23×Q8—31no—
32C23×D4—31no—
33C22×SD16—31no—
34C22×SD16—31no—
35C22×SD16—324no—
36C22×SD16—31no—
37C22×SD16D311yescharacteristic, direct product factor
38C23×C8—31no—
39C24×C3—21no—
40C23×D3—21no—
41C23×D3—212no—
42C23×D3—48no—
43C23×D3D411yescharacteristic
44C2×C3×Q8—23no—
45C2×C3×Q8C2316yescomplemented
46C2×C3×D4—23no—
47C2×C3×D4C2316yes—
48C22×C3×C4—21no—
49C22×C3×C4C2311yescharacteristic
50C2×#67—212no—
51C22×Dic3—21no—
52C22×Dic3D411yescharacteristic
53D3×Q8—224no—
54D3×Q8C23116yescomplemented
55D3×D4—224no—
56D3×D4C23116yes—
57C2×D12—23no—
58C2×D12C2316yes—
59C2×C4×D3—212no—
60C2×C4×D3D416yes—
61C2×C4×D3C2316yes—
62C2×Dic6—23no—
63C2×Dic6—212no—
64C2×Dic6C2316yescomplemented
65C3×SD16C23116yescomplemented
66C2×C3×C8C2316yescomplemented
67#215C23116yescomplemented
68#214C23116yescomplemented
69C2×C3⋊C8C2316yescomplemented
70#204C23116yescomplemented
71D3×C8C23116yescomplemented
72C25—61no—
73C22×Q8—312no—
74C22×Q8—31no—
75C22×Q8—61no—
76C22×Q8—66no—
77C22×Q8C2×D311yescharacteristic, complemented
78C22×D4—312no—
79C22×D4—31no—
80C22×D4—66no—
81C22×D4—61no—
82C22×D4C2×D311yescharacteristic
83C23×C4—31no—
84C23×C4—61no—
85C2×SD16—312no—
86C2×SD16—312no—
87C2×SD16—364no—
88C2×SD16—312no—
89C2×SD16C2×D3112yesdirect product factor
90C22×C8—31no—
91C22×C8—312no—
92C22×C8C2×D311yescharacteristic, complemented
93C23×C3—26no—
94C23×C3—44no—
95C23×C3C2×D411yescharacteristic
96C22×D3—26no—
97C22×D3—216no—
98C22×D3—44no—
99C22×D3—448no—
100C22×D3SD1618yesdirect product factor
101C22×D3C2×D416yes—
102C3×Q8—26no—
103C3×Q8C2414yescomplemented
104C3×D4—26no—
105C3×D4C2414yes—
106C2×C3×C4—26no—
107C2×C3×C4C2×D413yes—
108C2×C3×C4C2413yes—
109#67—216no—
110C2×Dic3—26no—
111C2×Dic3C2×D416yes—
112D12—26no—
113D12C2414yes—
114C4×D3—216no—
115C4×D3C2×D4112yes—
116C4×D3C2414yes—
117Dic6—26no—
118Dic6—216no—
119Dic6C2414yescomplemented
120C3×C8C2414yescomplemented
121C3⋊C8C2414yescomplemented
122C24—21no—
123C24—31no—
124C24—612no—
125C24—61no—
126C24—128no—
127C2×Q8—23no—
128C2×Q8—316no—
129C2×Q8—36no—
130C2×Q8—612no—
131C2×Q8—624no—
132C2×Q8—63no—
133C2×Q8C22×D316yescomplemented
134C2×D4—23no—
135C2×D4—316no—
136C2×D4—36no—
137C2×D4—624no—
138C2×D4—612no—
139C2×D4—63no—
140C2×D4C22×D316yes—
141C22×C4—21no—
142C22×C4—31no—
143C22×C4—36no—
144C22×C4—36no—
145C22×C4—612no—
146C22×C4—61no—
147C22×C4C22×D311yescharacteristic
148SD16—316no—
149SD16—316no—
150SD16—316no—
151SD16C22×D3116yesdirect product factor
152C2×C8—36no—
153C2×C8—316no—
154C2×C8C22×D316yescomplemented
155C22×C3—24no—
156C22×C3—412no—
157C22×C3C2×SD1614yescomplemented
158C22×C3C22×D413yes—
159C2×D3—24no—
160C2×D3—412no—
161C2×D3—432no—
162C2×D3C2×SD16124yesdirect product factor
163C2×D3C22×D414yes—
164C3×C4—24no—
165C3×C4C22×D413yes—
166C3×C4C2511yescharacteristic
167Dic3—24no—
168Dic3C22×D414yes—
169C23—26no—
170C23—38no—
171C23—36no—
172C23—44no—
173C23—616no—
174C23—66no—
175C23—1248no—
176C23—124no—
177C23D3×D411yescharacteristic
178Q8—26no—
179Q8—34no—
180Q8—616no—
181Q8—66no—
182Q8C23×D314yescomplemented
183D4—26no—
184D4—34no—
185D4—616no—
186D4—66no—
187D4C23×D314yes—
188C2×C4—26no—
189C2×C4—36no—
190C2×C4—312no—
191C2×C4—34no—
192C2×C4—616no—
193C2×C4—66no—
194C2×C4D3×D413yes—
195C2×C4C23×D313yes—
196C8—34no—
197C8C23×D314yescomplemented
198C2×C3—44no—
199C2×C3C22×SD1616yescomplemented
200C2×C3C23×D411yescharacteristic
201D3—44no—
202D3C22×SD1618yesdirect product factor
203C22—24no—
204C22—34no—
205C22—324no—
206C22—412no—
207C22—64no—
208C22—1232no—
209C22—1212no—
210C22D3×SD1614yesdirect product factor
211C22C2×D3×D413yes—
212C4—24no—
213C4—34no—
214C4—64no—
215C4C2×D3×D413yes—
216C4C24×D311yescharacteristic
217C3C23×SD1611yescharacteristic, complemented, Sylow
218C2—38no—
219C2—44no—
220C2—124no—
221C2C2×D3×SD1616yesdirect product factor
222C2C22×D3×D411yescharacteristic
subgroupG/H
centerC23D3×D4
commutator, cosocleC3×C4C25
FrattiniC4C24×D3
FittingC22×C3×SD16C2
socleC23×C3C2×D4
prime radicalC22×D3×D4C2
hypercenterC22×SD16D3
hypocenterC3C23×SD16
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×SD16

Complements

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

NH ≅ G/Ntype
1. C22×D3×Q8C2semidirect
3. C22×C3×SD16C2semidirect
4. C22×#215C2semidirect
5. C22×#214C2semidirect
6. C2×D3×SD16C2direct (N × H)
7. C22×#204C2semidirect
8. C22×D3×C8C2semidirect
11. C22×C3×Q8C22semidirect
15. C2×D3×Q8C22semidirect
22. C22×Dic6C22semidirect
23. C2×C3×SD16C22semidirect
24. C22×C3×C8C22semidirect
25. C2×#215C22semidirect
26. C2×#214C22semidirect
27. C22×C3⋊C8C22semidirect
28. D3×SD16C22direct (N × H)
29. C2×#204C22semidirect
30. C2×D3×C8C22semidirect
37. C22×SD16D3direct (N × H)
45. C2×C3×Q8C23semidirect
54. D3×Q8C23semidirect
64. C2×Dic6C23semidirect
65. C3×SD16C23semidirect
66. C2×C3×C8C23semidirect
67. #215C23semidirect
68. #214C23semidirect
69. C2×C3⋊C8C23semidirect
70. #204C23semidirect
71. D3×C8C23semidirect
77. C22×Q8C2×D3semidirect
89. C2×SD16C2×D3direct (N × H)
92. C22×C8C2×D3semidirect
100. C22×D3SD16direct (N × H)
103. C3×Q8C24semidirect
119. Dic6C24semidirect
120. C3×C8C24semidirect
121. C3⋊C8C24semidirect
133. C2×Q8C22×D3semidirect
151. SD16C22×D3direct (N × H)
154. C2×C8C22×D3semidirect
157. C22×C3C2×SD16semidirect
162. C2×D3C2×SD16direct (N × H)
182. Q8C23×D3semidirect
197. C8C23×D3semidirect
199. C2×C3C22×SD16semidirect
202. D3C22×SD16direct (N × H)
210. C22D3×SD16direct (N × H)
217. C3C23×SD16semidirect
221. C2C2×D3×SD16direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D3×Q82
C22×D3×D42
C22×C3×SD162
C22×#2152
C22×#2142
C2×D3×SD162
C22×#2042
C22×D3×C82
C23×SD163