Finite Group Databasebeta

← C22×#10597360 #14578369

Subgroups — C22×#10597360 #14578369

Order 2432.

1720 conjugacy classes of subgroups; only the 525 normal subgroups are shown.

normal subgroups only

This group has 1720 conjugacy classes of subgroups — too many to draw. Only its 525 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×#64545C211yesmaximal, characteristic, complemented
2C22×D4×D19C211yesmaximal, characteristic, complemented
3C2×#10597360C2124yesmaximal, direct product factor
4C22×#64527C211yesmaximal, characteristic, complemented
5C22×D152C211yesmaximal, characteristic, complemented
6C22×#64525C211yesmaximal, characteristic, complemented
7C22×#64515C211yesmaximal, characteristic, complemented
8C22×SD16×C19C211yesmaximal, characteristic, complemented
9C24×D19—21no—
10C22×Q8×C19C2211yescharacteristic, complemented
11C22×D4×C19C2211yescharacteristic
12C22×C22⋊D19—21no—
13C2×#64545—26no—
14C2×#64545C22112yescomplemented
15C2×D4×D19—26no—
16C2×D4×D19C22112yescomplemented
17C22×D76—21no—
18C22×D76C2211yescharacteristic
19C22×D76C2211yescharacteristic, complemented
20C22×C4×D19—21no—
21C22×C4×D19C2211yescharacteristic
22C2×SD16×C19C22112yescomplemented
23C22×C8×C19C2211yescharacteristic, complemented
24C2×#64527C22112yescomplemented
25C2×#64525C22112yescomplemented
26C22×C19⋊C8C2211yescharacteristic, complemented
27#10597360C22164yesdirect product factor
28C2×D152C22112yescomplemented
29C2×#64515C22112yescomplemented
30C24×C19—21no—
31C23×D19—21no—
32C23×D19—21no—
33C23×D19—212no—
34C23×D19—48no—
35C23×D19D411yescharacteristic
36C2×Q8×C19—23no—
37C2×Q8×C19C2316yescomplemented
38C2×D4×C19—23no—
39C2×D4×C19C2316yes—
40C22×C4×C19—21no—
41C22×C4×C19C2311yescharacteristic
42C2×C22⋊D19—212no—
43C22×Dic19D411yescharacteristic
44#64545—224no—
45#64545C23116yescomplemented
46D4×D19—224no—
47D4×D19C23116yescomplemented
48C2×D76—212no—
49C2×D76—23no—
50C2×D76—23no—
51C2×D76C2316yes—
52C2×D76C2316yescomplemented
53C2×C4×D19—212no—
54C2×C4×D19D416yes—
55C2×C4×D19C2316yes—
56SD16×C19C23116yescomplemented
57C2×C8×C19C2316yescomplemented
58#64527C23116yescomplemented
59#64525C23116yescomplemented
60C2×C19⋊C8C2316yescomplemented
61D152C23116yescomplemented
62#64515C23116yescomplemented
63C23×C19—26no—
64C23×C19—44no—
65C23×C19C2×D411yescharacteristic
66C22×D19—24no—
67C22×D19—26no—
68C22×D19—26no—
69C22×D19—216no—
70C22×D19—448no—
71C22×D19—44no—
72C22×D19—44no—
73C22×D19C2×D416yes—
74Q8×C19—26no—
75Q8×C19C2414yescomplemented
76D4×C19—26no—
77D4×C19C2414yes—
78C2×C4×C19—26no—
79C2×C4×C19C2×D413yes—
80C2×C4×C19C2413yes—
81C22⋊D19—216no—
82C2×Dic19C2×D416yes—
83D76—216no—
84D76—26no—
85D76—26no—
86D76C2414yes—
87D76C2414yescomplemented
88C4×D19—216no—
89C4×D19C2×D4112yes—
90C4×D19C2414yes—
91C8×C19C2414yescomplemented
92C19⋊C8C2414yescomplemented
93C22×AGL(1,ℤ/8)—191nomaximal, Sylow
94C22×C19—24no—
95C22×C19—412no—
96C22×C19AGL(1,ℤ/8)14yescomplemented
97C22×C19C22×D413yes—
98C2×D19—212no—
99C2×D19—24no—
100C2×D19—24no—
101C2×D19—432no—
102C2×D19—412no—
103C2×D19—412no—
104C2×D19C22×D414yes—
105C4×C19—24no—
106C4×C19C22×D413yes—
107C4×C19C2511yescharacteristic
108Dic19C22×D414yes—
109C22×#41—191no—
110C23×D4—191no—
111C2×AGL(1,ℤ/8)—1924no—
112C22×SD16—191no—
113C22×SD16D1911yescharacteristic, complemented
114C22×D8—191no—
115C22×D8—191no—
116C22×M16—191no—
117C2×C19—44no—
118C2×C19C2×AGL(1,ℤ/8)16yescomplemented
119C2×C19C23×D411yescharacteristic
120D19—24no—
121D19—44no—
122D19—44no—
123C25—381no—
124C2×#41—1912no—
125C2×#41—386no—
126C22×Q8C2×D1911yescharacteristic, complemented
127C22×D4—1912no—
128C22×D4—191no—
129C22×D4—191no—
130C22×D4—381no—
131C22×D4—386no—
132C22×D4—381no—
133C22×D4C2×D1911yescharacteristic
134C23×C4—191no—
135C23×C4—381no—
136AGL(1,ℤ/8)—1964no—
137C2×SD16—1912no—
138C2×SD16C2×D19112yescomplemented
139C2×D8—1912no—
140C2×D8—1912no—
141C2×M16—1912no—
142C22×C8—191no—
143C22×C8C2×D1911yescharacteristic, complemented
144C19C22×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
145C24—21no—
146C24—191no—
147C24—3812no—
148C24—381no—
149C24—381no—
150C24—768no—
151#41—1916no—
152#41—3824no—
153C2×Q8—23no—
154C2×Q8C22×D1916yescomplemented
155C2×D4—23no—
156C2×D4—1916no—
157C2×D4—196no—
158C2×D4—196no—
159C2×D4—3812no—
160C2×D4—3824no—
161C2×D4—3812no—
162C2×D4—383no—
163C2×D4—383no—
164C2×D4C22×D1916yes—
165C22×C4—21no—
166C22×C4—191no—
167C22×C4—196no—
168C22×C4—196no—
169C22×C4—3812no—
170C22×C4C22×D1911yescharacteristic
171SD16—1916no—
172SD16C22×D19116yescomplemented
173D8—1916no—
174D8—1916no—
175M16—1916no—
176C2×C8—196no—
177C2×C8C22×D1916yescomplemented
178C23—26no—
179C23—44no—
180C23—196no—
181C23—3816no—
182C23—384no—
183C23—386no—
184C23—386no—
185C23—7648no—
186C23—764no—
187C23—764no—
188C23D4×D1911yescharacteristic
189Q8—26no—
190Q8C23×D1914yescomplemented
191D4—26no—
192D4—194no—
193D4—194no—
194D4—3816no—
195D4—3816no—
196D4—386no—
197D4—386no—
198D4C23×D1914yes—
199C2×C4—26no—
200C2×C4—196no—
201C2×C4—1912no—
202C2×C4—194no—
203C2×C4—3816no—
204C2×C4D4×D1913yes—
205C2×C4C23×D1913yes—
206C8—194no—
207C8C23×D1914yescomplemented
208C22—24no—
209C22—412no—
210C22—194no—
211C22—3812no—
212C22—384no—
213C22—384no—
214C22—7632no—
215C22—7612no—
216C22—7612no—
217C22#1059736014yesdirect product factor
218C22C2×D4×D1913yes—
219C4—24no—
220C4—194no—
221C4C2×D4×D1913yes—
222C4C24×D1911yescharacteristic
223C2—44no—
224C2—384no—
225C2—764no—
226C2—764no—
227C2C2×#1059736016yesdirect product factor
228C2C22×D4×D1911yescharacteristic
subgroupG/H
centerC23D4×D19
commutator, cosocleC4×C19C25
FrattiniC4C24×D19
FittingC22×SD16×C19C2
socleC23×C19C2×D4
hypercenterC22×SD16D19
hypocenterC19C22×AGL(1,ℤ/8)
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×#64545C2semidirect
2. C22×D4×D19C2semidirect
3. C2×#10597360C2direct (N × H)
4. C22×#64527C2semidirect
5. C22×D152C2semidirect
6. C22×#64525C2semidirect
7. C22×#64515C2semidirect
8. C22×SD16×C19C2semidirect
10. C22×Q8×C19C22semidirect
14. C2×#64545C22semidirect
16. C2×D4×D19C22semidirect
19. C22×D76C22semidirect
22. C2×SD16×C19C22semidirect
23. C22×C8×C19C22semidirect
24. C2×#64527C22semidirect
25. C2×#64525C22semidirect
26. C22×C19⋊C8C22semidirect
27. #10597360C22direct (N × H)
28. C2×D152C22semidirect
29. C2×#64515C22semidirect
37. C2×Q8×C19C23semidirect
45. #64545C23semidirect
47. D4×D19C23semidirect
52. C2×D76C23semidirect
56. SD16×C19C23semidirect
57. C2×C8×C19C23semidirect
58. #64527C23semidirect
59. #64525C23semidirect
60. C2×C19⋊C8C23semidirect
61. D152C23semidirect
62. #64515C23semidirect
75. Q8×C19C24semidirect
87. D76C24semidirect
91. C8×C19C24semidirect
92. C19⋊C8C24semidirect
96. C22×C19AGL(1,ℤ/8)semidirect
113. C22×SD16D19semidirect
118. C2×C19C2×AGL(1,ℤ/8)semidirect
126. C22×Q8C2×D19semidirect
138. C2×SD16C2×D19semidirect
143. C22×C8C2×D19semidirect
144. C19C22×AGL(1,ℤ/8)semidirect
154. C2×Q8C22×D19semidirect
172. SD16C22×D19semidirect
177. C2×C8C22×D19semidirect
190. Q8C23×D19semidirect
207. C8C23×D19semidirect
217. C22#10597360direct (N × H)
227. C2C2×#10597360direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#645452
C22×D4×D192
C2×#105973602
C22×#645272
C22×D1522
C22×#645252
C22×#645152
C22×SD16×C192
C22×AGL(1,ℤ/8)19