Finite Group Databasebeta

← C22×SD16×D19 #14578352

Subgroups — C22×SD16×D19 #14578352

Order 2432.

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×Q8×D19C211yesmaximal, characteristic, complemented
2C22×D4×D19C211yesmaximal, characteristic
3C22×#64516C211yesmaximal, characteristic, complemented
4C22×#64526C211yesmaximal, characteristic, complemented
5C22×#64527C211yesmaximal, characteristic, complemented
6C2×SD16×D19C2124yesmaximal, direct product factor
7C22×C8×D19C211yesmaximal, characteristic, complemented
8C22×SD16×C19C211yesmaximal, characteristic, complemented
9C24×D19—21no—
10C22×Q8×C19C2211yescharacteristic, complemented
11C22×D4×C19C2211yescharacteristic
12C22×C22⋊D19—21no—
13C2×Q8×D19—26no—
14C2×Q8×D19C22112yescomplemented
15C2×D4×D19—26no—
16C2×D4×D19C22112yes—
17C22×D76C2211yescharacteristic
18C22×C4×D19—21no—
19C22×C4×D19C2211yescharacteristic
20C22×Dic38—21no—
21C22×Dic38C2211yescharacteristic, complemented
22C2×SD16×C19C22112yescomplemented
23C22×C8×C19C2211yescharacteristic, complemented
24C2×#64527C22112yescomplemented
25C2×#64526C22112yescomplemented
26C22×C19⋊C8C2211yescharacteristic, complemented
27SD16×D19C22164yesdirect product factor
28C2×#64516C22112yescomplemented
29C2×C8×D19C22112yescomplemented
30C24×C19—21no—
31C23×D19—21no—
32C23×D19—212no—
33C23×D19—48no—
34C23×D19D411yescharacteristic
35C2×Q8×C19—23no—
36C2×Q8×C19C2316yescomplemented
37C2×D4×C19—23no—
38C2×D4×C19C2316yes—
39C22×C4×C19—21no—
40C22×C4×C19C2311yescharacteristic
41C2×C22⋊D19—212no—
42C22×Dic19—21no—
43C22×Dic19D411yescharacteristic
44Q8×D19—224no—
45Q8×D19C23116yescomplemented
46D4×D19—224no—
47D4×D19C23116yes—
48C2×D76—23no—
49C2×D76C2316yes—
50C2×C4×D19—212no—
51C2×C4×D19D416yes—
52C2×C4×D19C2316yes—
53C2×Dic38—23no—
54C2×Dic38—212no—
55C2×Dic38C2316yescomplemented
56SD16×C19C23116yescomplemented
57C2×C8×C19C2316yescomplemented
58#64527C23116yescomplemented
59#64526C23116yescomplemented
60C2×C19⋊C8C2316yescomplemented
61#64516C23116yescomplemented
62C8×D19C23116yescomplemented
63C23×C19—26no—
64C23×C19—44no—
65C23×C19C2×D411yescharacteristic
66C22×D19—26no—
67C22×D19—216no—
68C22×D19—44no—
69C22×D19—448no—
70C22×D19SD1618yesdirect product factor
71C22×D19C2×D416yes—
72Q8×C19—26no—
73Q8×C19C2414yescomplemented
74D4×C19—26no—
75D4×C19C2414yes—
76C2×C4×C19—26no—
77C2×C4×C19C2×D413yes—
78C2×C4×C19C2413yes—
79C22⋊D19—216no—
80C2×Dic19—26no—
81C2×Dic19C2×D416yes—
82D76—26no—
83D76C2414yes—
84C4×D19—216no—
85C4×D19C2×D4112yes—
86C4×D19C2414yes—
87Dic38—26no—
88Dic38—216no—
89Dic38C2414yescomplemented
90C8×C19C2414yescomplemented
91C19⋊C8C2414yescomplemented
92C23×SD16—191nomaximal, Sylow
93C22×C19—24no—
94C22×C19—412no—
95C22×C19C2×SD1614yescomplemented
96C22×C19C22×D413yes—
97C2×D19—24no—
98C2×D19—412no—
99C2×D19—432no—
100C2×D19C2×SD16124yesdirect product factor
101C2×D19C22×D414yes—
102C4×C19—24no—
103C4×C19C22×D413yes—
104C4×C19C2511yescharacteristic
105Dic19—24no—
106Dic19C22×D414yes—
107C23×Q8—191no—
108C23×D4—191no—
109C22×SD16—191no—
110C22×SD16—191no—
111C22×SD16—1924no—
112C22×SD16—191no—
113C22×SD16D1911yescharacteristic, direct product factor
114C23×C8—191no—
115C2×C19—44no—
116C2×C19C22×SD1616yescomplemented
117C2×C19C23×D411yescharacteristic
118D19—44no—
119D19C22×SD1618yesdirect product factor
120C25—381no—
121C22×Q8—1912no—
122C22×Q8—191no—
123C22×Q8—381no—
124C22×Q8—386no—
125C22×Q8C2×D1911yescharacteristic, complemented
126C22×D4—1912no—
127C22×D4—191no—
128C22×D4—386no—
129C22×D4—381no—
130C22×D4C2×D1911yescharacteristic
131C23×C4—191no—
132C23×C4—381no—
133C2×SD16—1912no—
134C2×SD16—1912no—
135C2×SD16—1964no—
136C2×SD16—1912no—
137C2×SD16C2×D19112yesdirect product factor
138C22×C8—191no—
139C22×C8—1912no—
140C22×C8C2×D1911yescharacteristic, complemented
141C19C23×SD1611yescharacteristic, complemented, Sylow
142C24—21no—
143C24—191no—
144C24—3812no—
145C24—381no—
146C24—768no—
147C2×Q8—23no—
148C2×Q8—1916no—
149C2×Q8—196no—
150C2×Q8—3812no—
151C2×Q8—3824no—
152C2×Q8—383no—
153C2×Q8C22×D1916yescomplemented
154C2×D4—23no—
155C2×D4—1916no—
156C2×D4—196no—
157C2×D4—3824no—
158C2×D4—3812no—
159C2×D4—383no—
160C2×D4C22×D1916yes—
161C22×C4—21no—
162C22×C4—191no—
163C22×C4—196no—
164C22×C4—196no—
165C22×C4—3812no—
166C22×C4—381no—
167C22×C4C22×D1911yescharacteristic
168SD16—1916no—
169SD16—1916no—
170SD16—1916no—
171SD16C22×D19116yesdirect product factor
172C2×C8—196no—
173C2×C8—1916no—
174C2×C8C22×D1916yescomplemented
175C23—26no—
176C23—44no—
177C23—196no—
178C23—198no—
179C23—3816no—
180C23—386no—
181C23—7648no—
182C23—764no—
183C23D4×D1911yescharacteristic
184Q8—26no—
185Q8—194no—
186Q8—3816no—
187Q8—386no—
188Q8C23×D1914yescomplemented
189D4—26no—
190D4—194no—
191D4—3816no—
192D4—386no—
193D4C23×D1914yes—
194C2×C4—26no—
195C2×C4—196no—
196C2×C4—1912no—
197C2×C4—194no—
198C2×C4—3816no—
199C2×C4—386no—
200C2×C4D4×D1913yes—
201C2×C4C23×D1913yes—
202C8—194no—
203C8C23×D1914yescomplemented
204C22—24no—
205C22—412no—
206C22—1924no—
207C22—194no—
208C22—384no—
209C22—7632no—
210C22—7612no—
211C22SD16×D1914yesdirect product factor
212C22C2×D4×D1913yes—
213C4—24no—
214C4—194no—
215C4—384no—
216C4C2×D4×D1913yes—
217C4C24×D1911yescharacteristic
218C2—44no—
219C2—198no—
220C2—764no—
221C2C2×SD16×D1916yesdirect product factor
222C2C22×D4×D1911yescharacteristic
subgroupG/H
centerC23D4×D19
commutator, cosocleC4×C19C25
FrattiniC4C24×D19
FittingC22×SD16×C19C2
socleC23×C19C2×D4
prime radicalC22×D4×D19C2
hypercenterC22×SD16D19
hypocenterC19C23×SD16
LCSG ▷ C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×SD16

Complements

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

NH ≅ G/Ntype
1. C22×Q8×D19C2semidirect
3. C22×#64516C2semidirect
4. C22×#64526C2semidirect
5. C22×#64527C2semidirect
6. C2×SD16×D19C2direct (N × H)
7. C22×C8×D19C2semidirect
8. C22×SD16×C19C2semidirect
10. C22×Q8×C19C22semidirect
14. C2×Q8×D19C22semidirect
21. C22×Dic38C22semidirect
22. C2×SD16×C19C22semidirect
23. C22×C8×C19C22semidirect
24. C2×#64527C22semidirect
25. C2×#64526C22semidirect
26. C22×C19⋊C8C22semidirect
27. SD16×D19C22direct (N × H)
28. C2×#64516C22semidirect
29. C2×C8×D19C22semidirect
36. C2×Q8×C19C23semidirect
45. Q8×D19C23semidirect
55. C2×Dic38C23semidirect
56. SD16×C19C23semidirect
57. C2×C8×C19C23semidirect
58. #64527C23semidirect
59. #64526C23semidirect
60. C2×C19⋊C8C23semidirect
61. #64516C23semidirect
62. C8×D19C23semidirect
70. C22×D19SD16direct (N × H)
73. Q8×C19C24semidirect
89. Dic38C24semidirect
90. C8×C19C24semidirect
91. C19⋊C8C24semidirect
95. C22×C19C2×SD16semidirect
100. C2×D19C2×SD16direct (N × H)
113. C22×SD16D19direct (N × H)
116. C2×C19C22×SD16semidirect
119. D19C22×SD16direct (N × H)
125. C22×Q8C2×D19semidirect
137. C2×SD16C2×D19direct (N × H)
140. C22×C8C2×D19semidirect
141. C19C23×SD16semidirect
153. C2×Q8C22×D19semidirect
171. SD16C22×D19direct (N × H)
174. C2×C8C22×D19semidirect
188. Q8C23×D19semidirect
203. C8C23×D19semidirect
211. C22SD16×D19direct (N × H)
221. C2C2×SD16×D19direct (N × H)

Maximal subgroups

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

subgroupindex
C22×Q8×D192
C22×D4×D192
C22×#645162
C22×#645262
C22×#645272
C2×SD16×D192
C22×C8×D192
C22×SD16×C192
C23×SD1619