Finite Group Databasebeta

← C22×#10597330 #14576856

Subgroups — C22×#10597330 #14576856

Order 2432.

2528 conjugacy classes of subgroups; only the 645 normal subgroups are shown.

normal subgroups only

This group has 2528 conjugacy classes of subgroups — too many to draw. Only its 645 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
1C23×D76C211yesmaximal, characteristic, complemented
2C23×C22⋊D19C211yesmaximal, characteristic, complemented
3C23×C22⋊D19C211yesmaximal, characteristic, complemented
4C23×C4×D19C211yesmaximal, characteristic, complemented
5C2×#10597330C2124yesmaximal, direct product factor
6C22×Dic19⋊C4C211yesmaximal, characteristic, complemented
7C22×(C2×D19)⋊C4C211yesmaximal, characteristic, complemented
8C22×C22⋊C4×C19C211yesmaximal, characteristic, complemented
9C25×C19C2211yescharacteristic
10C24×D19C2211yescharacteristic
11C24×D19C2211yescharacteristic
12C23×C4×C19C2211yescharacteristic
13C23×C4×C19C2211yescharacteristic
14C22×C22⋊D19—28no—
15C22×C22⋊D19—28no—
16C22×C22⋊D19C22112yescomplemented
17C22×C22⋊D19C22112yescomplemented
18C23×Dic19C2211yescharacteristic
19C23×Dic19C2211yescharacteristic
20C22×D76—28no—
21C22×D76C22112yescomplemented
22C22×C4×D19—28no—
23C22×C4×D19C22112yescomplemented
24C2×C22⋊C4×C19C22112yescomplemented
25C2×(C2×D19)⋊C4C22112yescomplemented
26C2×Dic19⋊C4C22112yescomplemented
27#10597330C22164yesdirect product factor
28C24×C19—24no—
29C24×C19—24no—
30C24×C19—24no—
31C24×C19C2316yes—
32C24×C19C2311yescharacteristic
33C23×D19—24no—
34C23×D19—24no—
35C23×D19—24no—
36C23×D19—24no—
37C23×D19—24no—
38C23×D19D418yescomplemented
39C23×D19C2316yes—
40C23×D19C2316yes—
41C22×C4×C19—24no—
42C22×C4×C19—24no—
43C22×C4×C19C2316yes—
44C22×C4×C19C2316yes—
45C2×C22⋊D19—248no—
46C2×C22⋊D19—248no—
47C2×C22⋊D19C23116yescomplemented
48C2×C22⋊D19C23116yescomplemented
49C22×Dic19—24no—
50C22×Dic19D418yescomplemented
51C22×Dic19C2316yes—
52C22×Dic19C2316yes—
53C2×D76—248no—
54C2×D76C23116yescomplemented
55C2×C4×D19—248no—
56C2×C4×D19C23116yescomplemented
57C22⋊C4×C19C23116yescomplemented
58(C2×D19)⋊C4C23116yescomplemented
59Dic19⋊C4C23116yescomplemented
60C23×C19—212no—
61C23×C19—212no—
62C23×C19—212no—
63C23×C19—416no—
64C23×C19C2×D414yes—
65C23×C19C2×D414yes—
66C23×C19#4114yes—
67C23×C19C2414yes—
68C23×C19C2413yes—
69C22×D19—232no—
70C22×D19—212no—
71C22×D19—212no—
72C22×D19—212no—
73C22×D19—212no—
74C22×D19—212no—
75C22×D19—416no—
76C22×D19C2×D4124yescomplemented
77C22×D19C2414yes—
78C22×D19C2414yes—
79C2×C4×C19—212no—
80C2×C4×C19—212no—
81C2×C4×C19C2414yes—
82C2×C4×C19C2414yes—
83C22⋊D19—232no—
84C22⋊D19—232no—
85C2×Dic19—212no—
86C2×Dic19C2×D4124yescomplemented
87C2×Dic19C2414yes—
88C2×Dic19C2414yes—
89D76—232no—
90C4×D19—232no—
91C22×#121—191nomaximal, Sylow
92C22×C19—24no—
93C22×C19—24no—
94C22×C19—24no—
95C22×C19—424no—
96C22×C19#121116yescomplemented
97C22×C19C22×D416yes—
98C22×C19C22×D416yes—
99C22×C19C2×#4116yes—
100C22×C19C2511yescharacteristic
101C2×D19—248no—
102C2×D19—24no—
103C2×D19—24no—
104C2×D19—24no—
105C2×D19—24no—
106C2×D19—24no—
107C2×D19—424no—
108C2×D19C22×D418yescomplemented
109C4×C19—24no—
110C4×C19—24no—
111Dic19—24no—
112Dic19C22×D418yescomplemented
113C23×D4—191no—
114C23×D4—191no—
115C23×D4—191no—
116C24×C4—191no—
117C2×#121—1924no—
118C22×C4⋊C4—191no—
119C22×C22⋊C4—191no—
120C22×C22⋊C4D1911yescharacteristic, complemented
121C2×C19—44no—
122C2×C19C2×#121112yescomplemented
123C2×C19C23×D411yescharacteristic
124C2×C19C23×D411yescharacteristic
125C2×C19C22×#4111yescharacteristic
126D19—28no—
127D19—44no—
128C25—191no—
129C25—191no—
130C25C2×D1911yescharacteristic
131C22×D4—1912no—
132C22×D4—1912no—
133C22×D4—1912no—
134C22×D4—388no—
135C22×D4—388no—
136C22×D4—388no—
137C23×C4—191no—
138C23×C4—191no—
139C23×C4—1912no—
140C23×C4—388no—
141C23×C4C2×D1911yescharacteristic
142C23×C4C2×D1911yescharacteristic
143#121—1964no—
144C2×C4⋊C4—1912no—
145C2×C22⋊C4—1912no—
146C2×C22⋊C4C2×D19112yescomplemented
147C19C22×#12111yescharacteristic, complemented, Sylow
148C24—24no—
149C24—24no—
150C24—24no—
151C24—198no—
152C24—196no—
153C24—196no—
154C24—384no—
155C24—384no—
156C24—384no—
157C24—384no—
158C24—384no—
159C24C22×D1916yes—
160C24C22×D1911yescharacteristic
161C2×D4—1916no—
162C2×D4—1916no—
163C2×D4—1916no—
164C2×D4—3848no—
165C2×D4—3848no—
166C2×D4—3848no—
167C22×C4—24no—
168C22×C4—24no—
169C22×C4—198no—
170C22×C4—196no—
171C22×C4—196no—
172C22×C4—1916no—
173C22×C4—3848no—
174C22×C4—384no—
175C22×C4C22×D1916yes—
176C22×C4C22×D1916yes—
177C4⋊C4—1916no—
178C22⋊C4—1916no—
179C22⋊C4C22×D19116yescomplemented
180C23—212no—
181C23—212no—
182C23—212no—
183C23—416no—
184C23—1924no—
185C23—194no—
186C23—194no—
187C23—3812no—
188C23—3812no—
189C23—3832no—
190C23—3812no—
191C23—3812no—
192C23—3812no—
193C23—7616no—
194C23#6454114yes—
195C23D4×D1914yes—
196C23D4×D1914yes—
197C23C23×D1914yes—
198C23C23×D1913yes—
199D4—3832no—
200D4—3832no—
201D4—3832no—
202C2×C4—212no—
203C2×C4—212no—
204C2×C4—1924no—
205C2×C4—194no—
206C2×C4—194no—
207C2×C4—3832no—
208C2×C4—3812no—
209C2×C4C23×D1914yes—
210C2×C4C23×D1914yes—
211C22—24no—
212C22—24no—
213C22—24no—
214C22—424no—
215C22—198no—
216C22—384no—
217C22—384no—
218C22—3848no—
219C22—384no—
220C22—384no—
221C22—384no—
222C22—7624no—
223C22#10597330116yesdirect product factor
224C22C2×#6454116yes—
225C22C2×D4×D1916yes—
226C22C2×D4×D1916yes—
227C22C24×D1911yescharacteristic
228C4—24no—
229C4—24no—
230C4—198no—
231C4—384no—
232C2—44no—
233C2—388no—
234C2—764no—
235C2C2×#10597330112yesdirect product factor
236C2C22×D4×D1911yescharacteristic
237C2C22×D4×D1911yescharacteristic
238C2C22×#6454111yescharacteristic
subgroupG/H
centerC24C22×D19
commutator, cosocleC22×C19C25
FrattiniC22C24×D19
FittingC22×C22⋊C4×C19C2
socleC24×C19C23
hypercenterC22×C22⋊C4D19
hypocenterC19C22×#121
LCSG ▷ C22×C19 ▷ C19
UCSC1 ◁ C24 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C23×D76C2semidirect
2. C23×C22⋊D19C2semidirect
3. C23×C22⋊D19C2semidirect
4. C23×C4×D19C2semidirect
5. C2×#10597330C2direct (N × H)
6. C22×Dic19⋊C4C2semidirect
7. C22×(C2×D19)⋊C4C2semidirect
8. C22×C22⋊C4×C19C2semidirect
16. C22×C22⋊D19C22semidirect
17. C22×C22⋊D19C22semidirect
21. C22×D76C22semidirect
23. C22×C4×D19C22semidirect
24. C2×C22⋊C4×C19C22semidirect
25. C2×(C2×D19)⋊C4C22semidirect
26. C2×Dic19⋊C4C22semidirect
27. #10597330C22direct (N × H)
38. C23×D19D4semidirect
47. C2×C22⋊D19C23semidirect
48. C2×C22⋊D19C23semidirect
50. C22×Dic19D4semidirect
54. C2×D76C23semidirect
56. C2×C4×D19C23semidirect
57. C22⋊C4×C19C23semidirect
58. (C2×D19)⋊C4C23semidirect
59. Dic19⋊C4C23semidirect
76. C22×D19C2×D4semidirect
86. C2×Dic19C2×D4semidirect
96. C22×C19#121semidirect
108. C2×D19C22×D4semidirect
112. Dic19C22×D4semidirect
120. C22×C22⋊C4D19semidirect
122. C2×C19C2×#121semidirect
146. C2×C22⋊C4C2×D19semidirect
147. C19C22×#121semidirect
179. C22⋊C4C22×D19semidirect
223. C22#10597330direct (N × H)
235. C2C2×#10597330direct (N × H)

Maximal subgroups

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

subgroupindex
C23×D762
C23×C22⋊D192
C23×C4×D192
C2×#105973302
C22×Dic19⋊C42
C22×(C2×D19)⋊C42
C22×C22⋊C4×C192
C22×#12119