Finite Group Databasebeta

← C22×#10597354 #14578370

Subgroups — C22×#10597354 #14578370

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×#64541C211yesmaximal, characteristic, complemented
2C23×D76C211yesmaximal, characteristic, complemented
3C2×#10597354C2124yesmaximal, direct product factor
4C22×#64516C212yesmaximal, complemented
5C22×D152C212yesmaximal, complemented
6C22×M16×C19C211yesmaximal, characteristic, complemented
7C24×D19—21no—
8C23×C4×C19C2211yescharacteristic
9C22×C22⋊D19—21no—
10C2×#64541—26no—
11C2×#64541C22112yescomplemented
12C22×D76—26no—
13C22×D76—21no—
14C22×D76C2212yes—
15C22×D76C22112yescomplemented
16C22×D76C2211yescharacteristic, complemented
17C22×C4×D19—21no—
18C22×Dic38C2211yescharacteristic, complemented
19C2×M16×C19C22112yescomplemented
20C22×C8×C19C2212yescomplemented
21#10597354C22164yesdirect product factor
22C2×D152C22124yescomplemented
23C2×#64516C22124yescomplemented
24C24×C19D411yescharacteristic
25C23×D19—21no—
26C23×D19—22no—
27C23×D19—212no—
28C23×D19—48no—
29C22×C4×C19D411yescharacteristic
30C22×C4×C19D416yes—
31C22×C4×C19C2311yescharacteristic
32C22×C4×C19C2316yes—
33C2×C22⋊D19—212no—
34C22×Dic19—21no—
35#64541—224no—
36#64541C23116yescomplemented
37C2×D76—26no—
38C2×D76—224no—
39C2×D76—212no—
40C2×D76—23no—
41C2×D76C23112yes—
42C2×D76C23116yescomplemented
43C2×D76C2316yescomplemented
44C2×C4×D19—212no—
45C2×Dic38—23no—
46C2×Dic38C2316yescomplemented
47M16×C19C23116yescomplemented
48C2×C8×C19C23112yescomplemented
49D152C23132yescomplemented
50#64516C23132yescomplemented
51C23×C19—24no—
52C23×C19C2×D416yes—
53C23×C19C2×D411yescharacteristic
54C22×D19—26no—
55C22×D19—212no—
56C22×D19—216no—
57C22×D19—448no—
58C22×D19—44no—
59C22×D19—48no—
60C2×C4×C19C2×D413yes—
61C2×C4×C19C2×D416yes—
62C2×C4×C19C2×D4112yes—
63C2×C4×C19C2413yes—
64C2×C4×C19C2414yes—
65C22⋊D19—216no—
66C2×Dic19—26no—
67D76—212no—
68D76—216no—
69D76—26no—
70D76C2418yes—
71D76C2414yescomplemented
72C4×D19—216no—
73Dic38—26no—
74Dic38C2414yescomplemented
75C8×C19C2418yescomplemented
76C22×AGL(1,ℤ/8)—191nomaximal, Sylow
77C22×C19—212no—
78C22×C19AGL(1,ℤ/8)14yescomplemented
79C22×C19C22×D414yes—
80C22×C19C22×D413yes—
81C2×D19—24no—
82C2×D19—28no—
83C2×D19—432no—
84C2×D19—412no—
85C2×D19—424no—
86C4×C19C22×D413yes—
87C4×C19C22×D414yes—
88C4×C19C2511yescharacteristic
89Dic19—24no—
90C22×#41—191no—
91C23×D4—191no—
92C2×AGL(1,ℤ/8)—1924no—
93C22×SD16—192no—
94C22×D8—192no—
95C22×M16D1911yescharacteristic, complemented
96C2×C19—24no—
97C2×C19C2×AGL(1,ℤ/8)16yescomplemented
98C2×C19C23×D411yescharacteristic
99D19—44no—
100D19—48no—
101C25—381no—
102C2×#41—1912no—
103C2×#41—386no—
104C22×Q8—191no—
105C22×D4—192no—
106C22×D4—191no—
107C22×D4—1912no—
108C22×D4—381no—
109C22×D4—386no—
110C22×D4—381no—
111C23×C4—381no—
112C23×C4C2×D1911yescharacteristic
113AGL(1,ℤ/8)—1964no—
114C2×SD16—1924no—
115C2×D8—1924no—
116C2×M16C2×D19112yescomplemented
117C22×C8C2×D1912yescomplemented
118C19C22×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
119C24—3812no—
120C24—381no—
121C24—382no—
122C24—768no—
123C24D7611yescharacteristic
124#41—1916no—
125#41—3824no—
126C2×Q8—196no—
127C2×Q8—383no—
128C2×D4—1912no—
129C2×D4—196no—
130C2×D4—1916no—
131C2×D4—3812no—
132C2×D4—3812no—
133C2×D4—386no—
134C2×D4—3824no—
135C2×D4—383no—
136C22×C4—381no—
137C22×C4—3812no—
138C22×C4D7616yes—
139C22×C4D7611yescharacteristic
140C22×C4C22×D1916yes—
141C22×C4C22×D1911yescharacteristic
142SD16—1932no—
143D8—1932no—
144M16C22×D19116yescomplemented
145C2×C8C22×D19112yescomplemented
146C23—24no—
147C23—386no—
148C23—3816no—
149C23—3812no—
150C23—7648no—
151C23—768no—
152C23—764no—
153C23C2×D7616yes—
154C23C2×D7611yescharacteristic
155Q8—194no—
156Q8—386no—
157D4—194no—
158D4—198no—
159D4—3816no—
160D4—3816no—
161D4—3812no—
162D4—386no—
163C2×C4—386no—
164C2×C4—3816no—
165C2×C4C2×D7616yes—
166C2×C4C2×D7613yes—
167C2×C4C2×D76112yes—
168C2×C4C23×D1913yes—
169C2×C4C23×D1914yes—
170C8C23×D1918yescomplemented
171C22—212no—
172C22—384no—
173C22—388no—
174C22—7632no—
175C22—7624no—
176C22—7612no—
177C22#1059735414yesdirect product factor
178C22C22×D7614yes—
179C22C22×D7613yes—
180C4—384no—
181C4C22×D7614yes—
182C4C22×D7613yes—
183C4C24×D1911yescharacteristic
184C2—24no—
185C2—768no—
186C2—764no—
187C2C2×#1059735416yesdirect product factor
188C2C23×D7611yescharacteristic
subgroupG/H
centerC23C2×D76
commutator, cosocleC4×C19C25
FrattiniC4C24×D19
FittingC22×M16×C19C2
socleC23×C19C2×D4
hypercenterC22×M16D19
hypocenterC19C22×AGL(1,ℤ/8)
LCSG ▷ C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×M16

Complements

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

NH ≅ G/Ntype
1. C22×#64541C2semidirect
2. C23×D76C2semidirect
3. C2×#10597354C2direct (N × H)
4. C22×#64516C2semidirect
5. C22×D152C2semidirect
6. C22×M16×C19C2semidirect
11. C2×#64541C22semidirect
15. C22×D76C22semidirect
16. C22×D76C22semidirect
18. C22×Dic38C22semidirect
19. C2×M16×C19C22semidirect
20. C22×C8×C19C22semidirect
21. #10597354C22direct (N × H)
22. C2×D152C22semidirect
23. C2×#64516C22semidirect
36. #64541C23semidirect
42. C2×D76C23semidirect
43. C2×D76C23semidirect
46. C2×Dic38C23semidirect
47. M16×C19C23semidirect
48. C2×C8×C19C23semidirect
49. D152C23semidirect
50. #64516C23semidirect
71. D76C24semidirect
74. Dic38C24semidirect
75. C8×C19C24semidirect
78. C22×C19AGL(1,ℤ/8)semidirect
95. C22×M16D19semidirect
97. C2×C19C2×AGL(1,ℤ/8)semidirect
116. C2×M16C2×D19semidirect
117. C22×C8C2×D19semidirect
118. C19C22×AGL(1,ℤ/8)semidirect
144. M16C22×D19semidirect
145. C2×C8C22×D19semidirect
170. C8C23×D19semidirect
177. C22#10597354direct (N × H)
187. C2C2×#10597354direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#645412
C23×D762
C2×#105973542
C22×#645162
C22×D1522
C22×M16×C192
C22×AGL(1,ℤ/8)19