Finite Group Databasebeta

← C22×#10597378 #14578368

Subgroups — C22×#10597378 #14578368

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
2C2×#10597378C2124yesmaximal, direct product factor
3C22×#64526C212yesmaximal, complemented
4C22×#64525C212yesmaximal, complemented
5C22×#64520C211yesmaximal, characteristic, complemented
6C23×D4×C19C211yesmaximal, characteristic, complemented
7C25×C19—21no—
8C22×D4×C19—21no—
9C22×D4×C19—26no—
10C22×D4×C19C2212yes—
11C22×D4×C19C22112yescomplemented
12C23×C4×C19C2211yescharacteristic
13C22×C22⋊D19—21no—
14C2×#64541—26no—
15C2×#64541C22112yescomplemented
16C22×D76C2211yescharacteristic, complemented
17C22×C4×D19—21no—
18C22×Dic38C2211yescharacteristic, complemented
19C2×#64526C22124yescomplemented
20#10597378C22164yesdirect product factor
21C2×#64525C22124yescomplemented
22C2×#64520C22112yescomplemented
23C22×C19⋊C8C2212yescomplemented
24C24×C19—22no—
25C24×C19—212no—
26C24×C19—48no—
27C24×C19D411yescharacteristic
28C23×D19—21no—
29C2×D4×C19—26no—
30C2×D4×C19—212no—
31C2×D4×C19—224no—
32C2×D4×C19C23112yes—
33C2×D4×C19C23116yescomplemented
34C22×C4×C19D411yescharacteristic
35C22×C4×C19D416yes—
36C22×C4×C19C2311yescharacteristic
37C22×C4×C19C2316yes—
38C2×C22⋊D19—212no—
39C22×Dic19—21no—
40#64541—224no—
41#64541C23116yescomplemented
42C2×D76—23no—
43C2×D76C2316yescomplemented
44C2×C4×D19—212no—
45C2×Dic38—23no—
46C2×Dic38C2316yescomplemented
47#64526C23132yescomplemented
48#64525C23132yescomplemented
49#64520C23116yescomplemented
50C2×C19⋊C8C23112yescomplemented
51C23×C19—24no—
52C23×C19—212no—
53C23×C19—216no—
54C23×C19—448no—
55C23×C19—48no—
56C23×C19C2×D416yes—
57C23×C19C2×D411yescharacteristic
58C22×D19—26no—
59C22×D19—44no—
60D4×C19—212no—
61D4×C19—216no—
62D4×C19C2418yes—
63C2×C4×C19C2×D413yes—
64C2×C4×C19C2×D416yes—
65C2×C4×C19C2×D4112yes—
66C2×C4×C19C2413yes—
67C2×C4×C19C2414yes—
68C22⋊D19—216no—
69C2×Dic19—26no—
70D76—26no—
71D76C2414yescomplemented
72C4×D19—216no—
73Dic38—26no—
74Dic38C2414yescomplemented
75C19⋊C8C2418yescomplemented
76C22×AGL(1,ℤ/8)—191nomaximal, Sylow
77C22×C19—212no—
78C22×C19—28no—
79C22×C19—432no—
80C22×C19—424no—
81C22×C19AGL(1,ℤ/8)14yescomplemented
82C22×C19C22×D414yes—
83C22×C19C22×D413yes—
84C2×D19—24no—
85C2×D19—412no—
86C4×C19C22×D413yes—
87C4×C19C22×D414yes—
88C4×C19C2511yescharacteristic
89Dic19—24no—
90C22×#41—191no—
91C23×D4D1911yescharacteristic, complemented
92C2×AGL(1,ℤ/8)—1924no—
93C22×SD16—192no—
94C22×D8—192no—
95C22×M16—191no—
96C2×C19—24no—
97C2×C19—48no—
98C2×C19C2×AGL(1,ℤ/8)16yescomplemented
99C2×C19C23×D411yescharacteristic
100D19—44no—
101C25—21no—
102C2×#41—1912no—
103C2×#41—386no—
104C22×Q8—191no—
105C22×D4—26no—
106C22×D4—21no—
107C22×D4—191no—
108C22×D4—381no—
109C22×D4C2×D1912yes—
110C22×D4C2×D19112yescomplemented
111C23×C4—381no—
112C23×C4C2×D1911yescharacteristic
113AGL(1,ℤ/8)—1964no—
114C2×SD16—1924no—
115C2×D8—1924no—
116C2×M16—1912no—
117C22×C8—192no—
118C19C22×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
119C24—212no—
120C24—22no—
121C24—48no—
122C24—381no—
123C24C22⋊D1911yescharacteristic
124#41—1916no—
125#41—3824no—
126C2×Q8—196no—
127C2×Q8—383no—
128C2×D4—26no—
129C2×D4—212no—
130C2×D4—224no—
131C2×D4—196no—
132C2×D4—3812no—
133C2×D4—383no—
134C2×D4C22×D19112yes—
135C2×D4C22×D19116yescomplemented
136C22×C4—381no—
137C22×C4—3812no—
138C22×C4C22⋊D1916yes—
139C22×C4C22⋊D1911yescharacteristic
140C22×C4C22×D1916yes—
141C22×C4C22×D1911yescharacteristic
142SD16—1932no—
143D8—1932no—
144M16—1916no—
145C2×C8—1912no—
146C23—24no—
147C23—212no—
148C23—216no—
149C23—448no—
150C23—48no—
151C23—386no—
152C23—764no—
153C23C2×C22⋊D1916yes—
154C23C2×C22⋊D1911yescharacteristic
155Q8—194no—
156Q8—386no—
157D4—212no—
158D4—216no—
159D4—194no—
160D4—3816no—
161D4—386no—
162D4C23×D1918yes—
163C2×C4—386no—
164C2×C4—3816no—
165C2×C4C2×C22⋊D1916yes—
166C2×C4C2×C22⋊D1913yes—
167C2×C4C2×C22⋊D19112yes—
168C2×C4C23×D1913yes—
169C2×C4C23×D1914yes—
170C8—198no—
171C22—212no—
172C22—28no—
173C22—432no—
174C22—424no—
175C22—384no—
176C22—7612no—
177C22#1059737814yesdirect product factor
178C22C22×C22⋊D1914yes—
179C22C22×C22⋊D1913yes—
180C4—384no—
181C4C22×C22⋊D1914yes—
182C4C22×C22⋊D1913yes—
183C4C24×D1911yescharacteristic
184C2—24no—
185C2—48no—
186C2—764no—
187C2C2×#1059737816yesdirect product factor
188C2C23×C22⋊D1911yescharacteristic
subgroupG/H
centerC23C2×C22⋊D19
commutator, cosocleC4×C19C25
FrattiniC4C24×D19
FittingC23×D4×C19C2
socleC23×C19C2×D4
hypercenterC23×D4D19
hypocenterC19C22×AGL(1,ℤ/8)
LCSG ▷ C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×D4

Complements

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

NH ≅ G/Ntype
1. C22×#64541C2semidirect
2. C2×#10597378C2direct (N × H)
3. C22×#64526C2semidirect
4. C22×#64525C2semidirect
5. C22×#64520C2semidirect
6. C23×D4×C19C2semidirect
11. C22×D4×C19C22semidirect
15. C2×#64541C22semidirect
16. C22×D76C22semidirect
18. C22×Dic38C22semidirect
19. C2×#64526C22semidirect
20. #10597378C22direct (N × H)
21. C2×#64525C22semidirect
22. C2×#64520C22semidirect
23. C22×C19⋊C8C22semidirect
33. C2×D4×C19C23semidirect
41. #64541C23semidirect
43. C2×D76C23semidirect
46. C2×Dic38C23semidirect
47. #64526C23semidirect
48. #64525C23semidirect
49. #64520C23semidirect
50. C2×C19⋊C8C23semidirect
71. D76C24semidirect
74. Dic38C24semidirect
75. C19⋊C8C24semidirect
81. C22×C19AGL(1,ℤ/8)semidirect
91. C23×D4D19semidirect
98. C2×C19C2×AGL(1,ℤ/8)semidirect
110. C22×D4C2×D19semidirect
118. C19C22×AGL(1,ℤ/8)semidirect
135. C2×D4C22×D19semidirect
177. C22#10597378direct (N × H)
187. C2C2×#10597378direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#645412
C2×#105973782
C22×#645262
C22×#645252
C22×#645202
C23×D4×C192
C22×AGL(1,ℤ/8)19