Finite Group Databasebeta

← C2×#11926687 #14572834

Subgroups — C2×#11926687 #14572834

Order 2432.

812 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 812 conjugacy classes of subgroups — too many to draw. Only its 165 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
2C22×#64526C211yesmaximal, characteristic, complemented
3C22×#64525C211yesmaximal, characteristic, complemented
4#11926687C218yesmaximal, direct product factor
5C2×#10597267C211yesmaximal, characteristic, complemented
6C2×#10597266C211yesmaximal, characteristic, complemented
7C2×C22⋊(C19⋊C8)C211yesmaximal, characteristic, complemented
8C2×C19×#121C211yesmaximal, characteristic, complemented
9C22×D4×C19—21no—
10C22×D4×C19C2211yescharacteristic
11C23×C4×C19C2211yescharacteristic
12C22×C22⋊D19—21no—
13C2×#64541—22no—
14C2×#64541—24no—
15C2×#64541—24no—
16C2×#64541C2214yescomplemented
17C22×D76C2211yescharacteristic
18C22×C4×D19—21no—
19C22×Dic38C2211yescharacteristic
20C19×#121—22no—
21C19×#121C2214yescomplemented
22C2×C4⋊C4×C19C2211yescharacteristic
23C2×C22⋊C4×C19—21no—
24C2×#64526—24no—
25C2×#64526C2214yescomplemented
26C2×#64525—24no—
27C2×#64525C2214yescomplemented
28C22×C19⋊C8C2211yescharacteristic
29C22×C19⋊C8C2211yescharacteristic
30C22⋊(C19⋊C8)C2214yescomplemented
31#10597267C2214yescomplemented
32#10597266C2214yescomplemented
33C24×C19—21no—
34C24×C19D411yescharacteristic
35C23×D19—21no—
36C2×D4×C19—24no—
37C2×D4×C19—22no—
38C2×D4×C19—22no—
39C2×D4×C19—21no—
40C2×D4×C19—44no—
41C2×D4×C19C2312yes—
42C22×C4×C19—22no—
43C22×C4×C19—22no—
44C22×C4×C19—21no—
45C22×C4×C19D411yescharacteristic
46C22×C4×C19D412yes—
47C22×C4×C19C2312yes—
48C22×C4×C19C2311yescharacteristic
49C2×C22⋊D19—28no—
50C2×C22⋊D19—24no—
51C22×Dic19—21no—
52#64541—216no—
53#64541—28no—
54#64541—28no—
55C2×D76—22no—
56C2×D76—21no—
57C2×D76D414yescomplemented
58C2×D76C2312yes—
59C2×C4×D19—28no—
60C2×C4×D19—24no—
61C2×Dic38—22no—
62C2×Dic38—21no—
63C2×Dic38D414yescomplemented
64C2×Dic38C2312yes—
65C4⋊C4×C19—21no—
66C4⋊C4×C19C2312yes—
67C22⋊C4×C19—24no—
68#64526—28no—
69#64525—28no—
70C2×C19⋊C8—22no—
71C2×C19⋊C8—22no—
72C2×C19⋊C8C2312yes—
73C2×C19⋊C8C2312yes—
74C23×C19—22no—
75C23×C19—22no—
76C23×C19—22no—
77C23×C19—22no—
78C23×C19—42no—
79C23×C19—42no—
80C23×C19—42no—
81C23×C19C2×D412yes—
82C23×C19C2×D411yescharacteristic
83C22×D19—24no—
84C22×D19—22no—
85C22×D19—42no—
86C22×D19—42no—
87D4×C19—22no—
88D4×C19—22no—
89D4×C19—48no—
90D4×C19—42no—
91C2×C4×C19—22no—
92C2×C4×C19—24no—
93C2×C4×C19—22no—
94C2×C4×C19—22no—
95C2×C4×C19—22no—
96C2×C4×C19—42no—
97C2×C4×C19C2×D412yes—
98C2×C4×C19C2×D412yes—
99C2×C4×C19C2×D412yes—
100C2×C4×C19C2×D411yescharacteristic
101C2×C4×C19C2411yescharacteristic
102C22⋊D19—216no—
103C2×Dic19—24no—
104C2×Dic19—22no—
105D76—24no—
106D76—22no—
107D76C2×D414yescomplemented
108C4×D19—216no—
109Dic38—24no—
110Dic38—22no—
111Dic38C2×D414yescomplemented
112C19⋊C8—22no—
113C19⋊C8—22no—
114C2×#449—191nomaximal, Sylow
115C22×C19—22no—
116C22×C19—22no—
117C22×C19—22no—
118C22×C19—44no—
119C22×C19—42no—
120C22×C19—42no—
121C22×C19—42no—
122C22×C19—84no—
123C22×C19#12012yes—
124C22×C19#13512yes—
125C22×C19AGL(1,ℤ/8)12yes—
126C22×C19C22×D411yescharacteristic
127C2×D19—24no—
128C2×D19—42no—
129C2×D19—42no—
130C2×D19—48no—
131C4×C19—22no—
132C4×C19—42no—
133C4×C19#12012yes—
134C4×C19C22×D411yescharacteristic
135C4×C19C22×D411yescharacteristic
136Dic19—24no—
137C22×#41—191no—
138C22×SD16—191no—
139C22×D8—191no—
140C2×#121D1911yescharacteristic, complemented
141#449—198no—
142C2×#103—191no—
143C2×#102—191no—
144C2×C22⋊C8—191no—
145C2×C19—42no—
146C2×C19—82no—
147C2×C19#44914yescomplemented
148C2×C19C2×#12011yescharacteristic
149C2×C19C2×#13511yescharacteristic
150C2×C19C2×AGL(1,ℤ/8)11yescharacteristic
151D19—44no—
152C2×#41—194no—
153C2×#41—384no—
154C2×#41—384no—
155C2×#41—382no—
156C22×Q8—191no—
157C22×D4—21no—
158C22×D4—191no—
159C22×D4—381no—
160C22×D4C2×D1911yescharacteristic
161C23×C4—381no—
162C23×C4C2×D1911yescharacteristic
163C2×SD16—194no—
164C2×SD16—384no—
165C2×D8—194no—
166C2×D8—384no—
167C22×C8—191no—
168C22×C8—191no—
169#121—22no—
170#121C2×D1914yescomplemented
171C2×C4⋊C4C2×D1911yescharacteristic
172C2×C22⋊C4—21no—
173#103—194no—
174#102—194no—
175C22⋊C8—194no—
176C19C2×#44911yescharacteristic, complemented, Sylow
177C24—21no—
178C24—381no—
179C24C22⋊D1911yescharacteristic
180#41—388no—
181#41—388no—
182#41—3816no—
183C2×Q8—194no—
184C2×Q8—192no—
185C2×Q8—382no—
186C2×Q8—381no—
187C2×D4—24no—
188C2×D4—22no—
189C2×D4—22no—
190C2×D4—21no—
191C2×D4—44no—
192C2×D4—194no—
193C2×D4—192no—
194C2×D4—388no—
195C2×D4—384no—
196C2×D4—382no—
197C2×D4—381no—
198C2×D4C22×D1912yes—
199C22×C4—22no—
200C22×C4—22no—
201C22×C4—21no—
202C22×C4—388no—
203C22×C4—381no—
204C22×C4—384no—
205C22×C4C22⋊D1912yes—
206C22×C4C22⋊D1911yescharacteristic
207C22×C4C22×D1912yes—
208C22×C4C22×D1911yescharacteristic
209SD16—388no—
210D8—388no—
211C2×C8—192no—
212C2×C8—192no—
213C2×C8—382no—
214C2×C8—382no—
215C4⋊C4—21no—
216C4⋊C4C22×D1912yes—
217C22⋊C4—24no—
218C23—22no—
219C23—22no—
220C23—22no—
221C23—22no—
222C23—42no—
223C23—42no—
224C23—42no—
225C23—384no—
226C23—382no—
227C23—762no—
228C23—762no—
229C23C2×C22⋊D1912yes—
230C23C2×C22⋊D1911yescharacteristic
231Q8—194no—
232Q8—384no—
233Q8—382no—
234D4—22no—
235D4—22no—
236D4—48no—
237D4—42no—
238D4—194no—
239D4—3816no—
240D4—384no—
241D4—382no—
242C2×C4—22no—
243C2×C4—24no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—22no—
247C2×C4—42no—
248C2×C4—3816no—
249C2×C4—384no—
250C2×C4—382no—
251C2×C4D4×D1912yes—
252C2×C4D4×D1912yes—
253C2×C4C2×C22⋊D1912yes—
254C2×C4C2×C22⋊D1911yescharacteristic
255C2×C4C23×D1911yescharacteristic
256C8—382no—
257C8—382no—
258C22—22no—
259C22—22no—
260C22—22no—
261C22—44no—
262C22—42no—
263C22—42no—
264C22—42no—
265C22—84no—
266C22—384no—
267C22—762no—
268C22—762no—
269C22—768no—
270C22#1059737812yes—
271C22#1059738312yes—
272C22#1059739612yes—
273C22C22×C22⋊D1911yescharacteristic
274C4—22no—
275C4—42no—
276C4—384no—
277C4#1059738312yes—
278C4C2×D4×D1911yescharacteristic
279C4C2×D4×D1911yescharacteristic
280C2—42no—
281C2—82no—
282C2—764no—
283C2#1192668714yesdirect product factor
284C2C2×#1059738311yescharacteristic
285C2C2×#1059739611yescharacteristic
286C2C2×#1059737811yescharacteristic
subgroupG/H
centerC23C2×C22⋊D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC2×C19×#121C2
socleC23×C19C2×D4
hypercenterC2×#121D19
hypocenterC19C2×#449
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C22×#64541C2semidirect
2. C22×#64526C2semidirect
3. C22×#64525C2semidirect
4. #11926687C2direct (N × H)
5. C2×#10597267C2semidirect
6. C2×#10597266C2semidirect
7. C2×C22⋊(C19⋊C8)C2semidirect
8. C2×C19×#121C2semidirect
16. C2×#64541C22semidirect
21. C19×#121C22semidirect
25. C2×#64526C22semidirect
27. C2×#64525C22semidirect
30. C22⋊(C19⋊C8)C22semidirect
31. #10597267C22semidirect
32. #10597266C22semidirect
57. C2×D76D4semidirect
63. C2×Dic38D4semidirect
107. D76C2×D4semidirect
111. Dic38C2×D4semidirect
140. C2×#121D19semidirect
147. C2×C19#449semidirect
170. #121C2×D19semidirect
176. C19C2×#449semidirect
283. C2#11926687direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#645412
C22×#645262
C22×#645252
#119266872
C2×#105972672
C2×#105972662
C2×C22⋊(C19⋊C8)2
C2×C19×#1212
C2×#44919