Finite Group Databasebeta

← C22×#10597396 #14578361

Subgroups — C22×#10597396 #14578361

Order 2432.

1504 conjugacy classes of subgroups; only the 565 normal subgroups are shown.

normal subgroups only

This group has 1504 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×#10597396C2124yesmaximal, direct product factor
3C22×#64528C211yesmaximal, characteristic, complemented
4C22×#64526C211yesmaximal, characteristic, complemented
5C22×#64527C211yesmaximal, characteristic, complemented
6C22×#64525C211yesmaximal, characteristic, complemented
7C23×C19⋊C8C211yesmaximal, characteristic, complemented
8C22×#41×C19C211yesmaximal, characteristic, complemented
9C2×#41×C19—26no—
10C2×#41×C19C22112yescomplemented
11C22×Q8×C19C2211yescharacteristic
12C22×D4×C19—21no—
13C22×D4×C19C2211yescharacteristic
14C23×C4×C19—21no—
15C23×C4×C19C2211yescharacteristic
16C22×C22⋊D19—21no—
17C2×#64541—26no—
18C2×#64541C22112yescomplemented
19C22×D76C2211yescharacteristic
20C22×C4×D19—21no—
21C22×Dic38C2211yescharacteristic
22#10597396C22164yesdirect product factor
23C2×#64528C22112yescomplemented
24C2×#64527C22112yescomplemented
25C2×#64526C22112yescomplemented
26C2×#64525C22112yescomplemented
27C22×C19⋊C8C2211yescharacteristic
28C22×C19⋊C8C2211yescharacteristic
29C22×C19⋊C8C22112yescomplemented
30C24×C19—21no—
31C24×C19D411yescharacteristic
32C23×D19—21no—
33#41×C19—224no—
34#41×C19C23116yescomplemented
35C2×Q8×C19—23no—
36C2×Q8×C19C2316yes—
37C2×D4×C19—212no—
38C2×D4×C19—23no—
39C2×D4×C19C2316yes—
40C22×C4×C19—21no—
41C22×C4×C19—212no—
42C22×C4×C19D416yes—
43C22×C4×C19D411yescharacteristic
44C22×C4×C19C2311yescharacteristic
45C22×C4×C19C2316yes—
46C2×C22⋊D19—212no—
47C22×Dic19—21no—
48#64541—224no—
49#64541C23116yescomplemented
50C2×D76—23no—
51C2×D76C2316yes—
52C2×C4×D19—212no—
53C2×Dic38—23no—
54C2×Dic38C2316yes—
55#64528C23116yescomplemented
56#64527C23116yescomplemented
57#64526C23116yescomplemented
58#64525C23116yescomplemented
59C2×C19⋊C8C2316yes—
60C2×C19⋊C8C2316yes—
61C2×C19⋊C8C23116yescomplemented
62C23×C19—24no—
63C23×C19—26no—
64C23×C19—44no—
65C23×C19C2×D416yes—
66C23×C19C2×D411yescharacteristic
67C22×D19—26no—
68C22×D19—44no—
69Q8×C19—26no—
70Q8×C19C2414yes—
71D4×C19—216no—
72D4×C19—26no—
73D4×C19C2414yes—
74C2×C4×C19—26no—
75C2×C4×C19—216no—
76C2×C4×C19C2×D413yes—
77C2×C4×C19C2×D416yes—
78C2×C4×C19C2×D4112yes—
79C2×C4×C19C2413yes—
80C2×C4×C19C2414yes—
81C22⋊D19—216no—
82C2×Dic19—26no—
83D76—26no—
84D76C2414yes—
85C4×D19—216no—
86Dic38—26no—
87Dic38C2414yes—
88C19⋊C8C2414yes—
89C19⋊C8C2414yes—
90C22×#135—191nomaximal, Sylow
91C22×C19—212no—
92C22×C19—24no—
93C22×C19—412no—
94C22×C19#13514yescomplemented
95C22×C19C22×D414yes—
96C22×C19C22×D413yes—
97C2×D19—24no—
98C2×D19—412no—
99C4×C19—24no—
100C4×C19C22×D413yes—
101C4×C19C22×D414yes—
102C4×C19C2511yescharacteristic
103Dic19—24no—
104C22×#41—191no—
105C22×#41D1911yescharacteristic, complemented
106C2×#135—1924no—
107C22×Q16—191no—
108C22×SD16—191no—
109C22×SD16—191no—
110C22×D8—191no—
111C23×C8—191no—
112C2×C19—24no—
113C2×C19—44no—
114C2×C19C2×#13516yescomplemented
115C2×C19C23×D411yescharacteristic
116D19—44no—
117C2×#41—26no—
118C2×#41—1912no—
119C2×#41—386no—
120C2×#41C2×D19112yescomplemented
121C22×Q8—191no—
122C22×Q8C2×D1911yescharacteristic
123C22×D4—21no—
124C22×D4—191no—
125C22×D4—381no—
126C22×D4C2×D1911yescharacteristic
127C23×C4—21no—
128C23×C4—381no—
129C23×C4C2×D1911yescharacteristic
130#135—1964no—
131C2×Q16—1912no—
132C2×SD16—1912no—
133C2×SD16—1912no—
134C2×D8—1912no—
135C22×C8—191no—
136C22×C8—191no—
137C22×C8—1912no—
138C19C22×#13511yescharacteristic, complemented, Sylow
139C24—21no—
140C24—381no—
141C24C22⋊D1911yescharacteristic
142#41—224no—
143#41—1916no—
144#41—3824no—
145#41C22×D19116yescomplemented
146C2×Q8—23no—
147C2×Q8—196no—
148C2×Q8—383no—
149C2×Q8C22×D1916yes—
150C2×D4—212no—
151C2×D4—23no—
152C2×D4—196no—
153C2×D4—3812no—
154C2×D4—383no—
155C2×D4C22×D1916yes—
156C22×C4—21no—
157C22×C4—212no—
158C22×C4—381no—
159C22×C4—3812no—
160C22×C4C22⋊D1916yes—
161C22×C4C22⋊D1911yescharacteristic
162C22×C4C22×D1911yescharacteristic
163C22×C4C22×D1916yes—
164Q16—1916no—
165SD16—1916no—
166SD16—1916no—
167D8—1916no—
168C2×C8—196no—
169C2×C8—196no—
170C2×C8—1916no—
171C23—24no—
172C23—26no—
173C23—44no—
174C23—386no—
175C23—764no—
176C23C2×C22⋊D1916yes—
177C23C2×C22⋊D1911yescharacteristic
178Q8—26no—
179Q8—194no—
180Q8—386no—
181Q8C23×D1914yes—
182D4—216no—
183D4—26no—
184D4—194no—
185D4—3816no—
186D4—386no—
187D4C23×D1914yes—
188C2×C4—26no—
189C2×C4—216no—
190C2×C4—386no—
191C2×C4—3816no—
192C2×C4C2×C22⋊D1916yes—
193C2×C4C2×C22⋊D1913yes—
194C2×C4C2×C22⋊D19112yes—
195C2×C4C23×D1913yes—
196C2×C4C23×D1914yes—
197C8—194no—
198C8—194no—
199C22—212no—
200C22—24no—
201C22—412no—
202C22—384no—
203C22—7612no—
204C22#1059739614yesdirect product factor
205C22C22×C22⋊D1914yes—
206C22C22×C22⋊D1913yes—
207C4—24no—
208C4—384no—
209C4C22×C22⋊D1914yes—
210C4C22×C22⋊D1913yes—
211C4C24×D1911yescharacteristic
212C2—24no—
213C2—44no—
214C2—764no—
215C2C2×#1059739616yesdirect product factor
216C2C23×C22⋊D1911yescharacteristic
subgroupG/H
centerC22×C4C22⋊D19
commutator, cosocleC4×C19C25
FrattiniC4C24×D19
FittingC22×#41×C19C2
socleC23×C19C2×D4
hypercenterC22×#41D19
hypocenterC19C22×#135
LCSG ▷ C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C22×#41

Complements

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

NH ≅ G/Ntype
1. C22×#64541C2semidirect
2. C2×#10597396C2direct (N × H)
3. C22×#64528C2semidirect
4. C22×#64526C2semidirect
5. C22×#64527C2semidirect
6. C22×#64525C2semidirect
7. C23×C19⋊C8C2semidirect
8. C22×#41×C19C2semidirect
10. C2×#41×C19C22semidirect
18. C2×#64541C22semidirect
22. #10597396C22direct (N × H)
23. C2×#64528C22semidirect
24. C2×#64527C22semidirect
25. C2×#64526C22semidirect
26. C2×#64525C22semidirect
29. C22×C19⋊C8C22semidirect
34. #41×C19C23semidirect
49. #64541C23semidirect
55. #64528C23semidirect
56. #64527C23semidirect
57. #64526C23semidirect
58. #64525C23semidirect
61. C2×C19⋊C8C23semidirect
94. C22×C19#135semidirect
105. C22×#41D19semidirect
114. C2×C19C2×#135semidirect
120. C2×#41C2×D19semidirect
138. C19C22×#135semidirect
145. #41C22×D19semidirect
204. C22#10597396direct (N × H)
215. C2C2×#10597396direct (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×#105973962
C22×#645282
C22×#645262
C22×#645272
C22×#645252
C23×C19⋊C82
C22×#41×C192
C22×#13519