Finite Group Databasebeta

← C22×#10597362 #14578362

Subgroups — C22×#10597362 #14578362

Order 2432.

1504 conjugacy classes of subgroups; only the 525 normal subgroups are shown.

normal subgroups only

This group has 1504 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×#64543C211yesmaximal, characteristic, complemented
3C2×#10597362C2124yesmaximal, direct product factor
4C22×#64528C211yesmaximal, characteristic, complemented
5C22×#64516C211yesmaximal, characteristic, complemented
6C22×#64525C211yesmaximal, characteristic, complemented
7C22×C8×D19C211yesmaximal, characteristic, complemented
8C22×SD16×C19C211yesmaximal, characteristic, complemented
9C22×Q8×C19C2211yescharacteristic
10C22×D4×C19C2211yescharacteristic
11C22×C22⋊D19—21no—
12C23×Dic19—21no—
13C2×#64545—26no—
14C2×#64545C22112yescomplemented
15C2×#64543—26no—
16C2×#64543C22112yescomplemented
17C22×D76—21no—
18C22×D76C2211yescharacteristic
19C22×C4×D19—21no—
20C22×C4×D19C2211yescharacteristic
21C22×Dic38C2211yescharacteristic
22C2×SD16×C19C22112yescomplemented
23C22×C8×C19C2211yescharacteristic
24C2×#64528C22112yescomplemented
25C2×#64525C22112yescomplemented
26C22×C19⋊C8C2211yescharacteristic
27#10597362C22164yesdirect product factor
28C2×#64516C22112yescomplemented
29C2×C8×D19C22112yescomplemented
30C24×C19—21no—
31C23×D19—21no—
32C23×D19D411yescharacteristic
33C2×Q8×C19—23no—
34C2×Q8×C19C2316yes—
35C2×D4×C19—23no—
36C2×D4×C19C2316yes—
37C22×C4×C19—21no—
38C22×C4×C19C2311yescharacteristic
39C2×C22⋊D19—212no—
40C22×Dic19—21no—
41C22×Dic19—212no—
42C22×Dic19D411yescharacteristic
43#64545—224no—
44#64545C23116yescomplemented
45#64543—224no—
46#64543C23116yescomplemented
47C2×D76—212no—
48C2×D76—23no—
49C2×D76C2316yes—
50C2×C4×D19—212no—
51C2×C4×D19D416yes—
52C2×C4×D19C2316yes—
53C2×Dic38—23no—
54C2×Dic38C2316yes—
55SD16×C19C23116yescomplemented
56C2×C8×C19C2316yes—
57#64528C23116yescomplemented
58#64525C23116yescomplemented
59C2×C19⋊C8C2316yes—
60#64516C23116yescomplemented
61C8×D19C23116yescomplemented
62C23×C19—26no—
63C23×C19—44no—
64C23×C19C2×D411yescharacteristic
65C22×D19—24no—
66C22×D19—26no—
67C22×D19—44no—
68C22×D19C2×D416yes—
69Q8×C19—26no—
70Q8×C19C2414yes—
71D4×C19—26no—
72D4×C19C2414yes—
73C2×C4×C19—26no—
74C2×C4×C19C2×D413yes—
75C2×C4×C19C2413yes—
76C22⋊D19—216no—
77C2×Dic19—26no—
78C2×Dic19—216no—
79C2×Dic19C2×D416yes—
80D76—216no—
81D76—26no—
82D76C2414yes—
83C4×D19—216no—
84C4×D19C2×D4112yes—
85C4×D19C2414yes—
86Dic38—26no—
87Dic38C2414yes—
88C8×C19C2414yes—
89C19⋊C8C2414yes—
90C22×#135—191nomaximal, Sylow
91C22×C19—24no—
92C22×C19—412no—
93C22×C19#13514yescomplemented
94C22×C19C22×D413yes—
95C2×D19—212no—
96C2×D19—24no—
97C2×D19—412no—
98C2×D19C22×D414yes—
99C4×C19—24no—
100C4×C19C22×D413yes—
101C4×C19C2511yescharacteristic
102Dic19—24no—
103Dic19C22×D414yes—
104C22×#41—191no—
105C22×#41—191no—
106C2×#135—1924no—
107C22×Q16—191no—
108C22×SD16—191no—
109C22×SD16D1911yescharacteristic, complemented
110C22×D8—191no—
111C23×C8—191no—
112C2×C19—44no—
113C2×C19C2×#13516yescomplemented
114C2×C19C23×D411yescharacteristic
115D19—24no—
116D19—44no—
117C2×#41—1912no—
118C2×#41—1912no—
119C2×#41—386no—
120C2×#41—386no—
121C22×Q8—191no—
122C22×Q8C2×D1911yescharacteristic
123C22×D4—191no—
124C22×D4—381no—
125C22×D4—381no—
126C22×D4C2×D1911yescharacteristic
127C23×C4—191no—
128C23×C4—381no—
129C23×C4—381no—
130#135—1964no—
131C2×Q16—1912no—
132C2×SD16—1912no—
133C2×SD16C2×D19112yescomplemented
134C2×D8—1912no—
135C22×C8—191no—
136C22×C8—1912no—
137C22×C8C2×D1911yescharacteristic
138C19C22×#13511yescharacteristic, complemented, Sylow
139C24—21no—
140C24—191no—
141C24—381no—
142#41—1916no—
143#41—1916no—
144#41—3824no—
145#41—3824no—
146C2×Q8—23no—
147C2×Q8—196no—
148C2×Q8—383no—
149C2×Q8C22×D1916yes—
150C2×D4—23no—
151C2×D4—196no—
152C2×D4—3812no—
153C2×D4—3812no—
154C2×D4—383no—
155C2×D4C22×D1916yes—
156C22×C4—21no—
157C22×C4—191no—
158C22×C4—196no—
159C22×C4—196no—
160C22×C4—3812no—
161C22×C4—3812no—
162C22×C4—381no—
163C22×C4C22×D1911yescharacteristic
164Q16—1916no—
165SD16—1916no—
166SD16C22×D19116yescomplemented
167D8—1916no—
168C2×C8—196no—
169C2×C8—1916no—
170C2×C8C22×D1916yes—
171C23—26no—
172C23—44no—
173C23—196no—
174C23—384no—
175C23—386no—
176C23—764no—
177C23D4×D1911yescharacteristic
178Q8—26no—
179Q8—194no—
180Q8—386no—
181Q8C23×D1914yes—
182D4—26no—
183D4—194no—
184D4—3816no—
185D4—3816no—
186D4—386no—
187D4C23×D1914yes—
188C2×C4—26no—
189C2×C4—196no—
190C2×C4—1912no—
191C2×C4—194no—
192C2×C4—3816no—
193C2×C4—3816no—
194C2×C4—386no—
195C2×C4D4×D1913yes—
196C2×C4C23×D1913yes—
197C8—194no—
198C8C23×D1914yes—
199C22—24no—
200C22—412no—
201C22—194no—
202C22—3812no—
203C22—384no—
204C22—7612no—
205C22#1059736214yesdirect product factor
206C22C2×D4×D1913yes—
207C4—24no—
208C4—194no—
209C4—384no—
210C4C2×D4×D1913yes—
211C4C24×D1911yescharacteristic
212C2—44no—
213C2—384no—
214C2—764no—
215C2C2×#1059736216yesdirect product factor
216C2C22×D4×D1911yescharacteristic
subgroupG/H
centerC23D4×D19
commutator, cosocleC4×C19C25
FrattiniC4C24×D19
FittingC22×SD16×C19C2
socleC23×C19C2×D4
hypercenterC22×SD16D19
hypocenterC19C22×#135
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×#64543C2semidirect
3. C2×#10597362C2direct (N × H)
4. C22×#64528C2semidirect
5. C22×#64516C2semidirect
6. C22×#64525C2semidirect
7. C22×C8×D19C2semidirect
8. C22×SD16×C19C2semidirect
14. C2×#64545C22semidirect
16. C2×#64543C22semidirect
22. C2×SD16×C19C22semidirect
24. C2×#64528C22semidirect
25. C2×#64525C22semidirect
27. #10597362C22direct (N × H)
28. C2×#64516C22semidirect
29. C2×C8×D19C22semidirect
44. #64545C23semidirect
46. #64543C23semidirect
55. SD16×C19C23semidirect
57. #64528C23semidirect
58. #64525C23semidirect
60. #64516C23semidirect
61. C8×D19C23semidirect
93. C22×C19#135semidirect
109. C22×SD16D19semidirect
113. C2×C19C2×#135semidirect
133. C2×SD16C2×D19semidirect
138. C19C22×#135semidirect
166. SD16C22×D19semidirect
205. C22#10597362direct (N × H)
215. C2C2×#10597362direct (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×#645432
C2×#105973622
C22×#645282
C22×#645162
C22×#645252
C22×C8×D192
C22×SD16×C192
C22×#13519