Finite Group Databasebeta

← #14572887

Subgroups — #14572887

Order 2432.

806 conjugacy classes of subgroups; only the 169 normal subgroups are shown.

normal subgroups only

This group has 806 conjugacy classes of subgroups — too many to draw. Only its 169 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
1C2×#10597395C212yesmaximal, complemented
2C2×#10597376C211yesmaximal, characteristic, complemented
3#11926689C214yesmaximal, complemented
4#11926683C212yesmaximal, complemented
5#11926678C212yesmaximal, complemented
6#11926545C212yesmaximal, complemented
7#11926508C211yesmaximal, characteristic, complemented
8C22×#41×C19C211yesmaximal, characteristic, complemented
9C2×#41×C19—28no—
10C2×#41×C19—21no—
11C2×#41×C19—21no—
12C2×#41×C19C2212yes—
13C2×#41×C19C2212yescomplemented
14C22×Q8×C19C2211yescharacteristic, complemented
15C22×D4×C19—21no—
16C22×D4×C19C2211yescharacteristic, complemented
17C23×C4×C19—21no—
18C23×C4×C19C2211yescharacteristic
19C22×C22⋊D19—21no—
20C22×D76C2211yescharacteristic, complemented
21#10597395—28no—
22C2×#64527C2214yescomplemented
23C2×#64525C2214yescomplemented
24#10597376—21no—
25#10597376—21no—
26#10597376C2212yes—
27#10597376C2212yescomplemented
28C2×(C2×D19)⋊C4—21no—
29C2×C4⋊Dic19C2211yescharacteristic, complemented
30C2×#64520C2212yescomplemented
31#10597292C2214yescomplemented
32#10597289C2214yescomplemented
33C22⋊(C19⋊C8)C2212yescomplemented
34C22⋊(C19⋊C8)C2212yescomplemented
35C24×C19—21no—
36C24×C19D411yescharacteristic
37C23×D19—21no—
38#41×C19—28no—
39#41×C19—28no—
40#41×C19—24no—
41#41×C19—24no—
42#41×C19—24no—
43#41×C19D418yescomplemented
44C2×Q8×C19—24no—
45C2×Q8×C19—21no—
46C2×Q8×C19C2312yes—
47C2×D4×C19—28no—
48C2×D4×C19—22no—
49C2×D4×C19—22no—
50C2×D4×C19—24no—
51C2×D4×C19—21no—
52C2×D4×C19C2312yes—
53C22×C4×C19—28no—
54C22×C4×C19—21no—
55C22×C4×C19—22no—
56C22×C4×C19—22no—
57C22×C4×C19—24no—
58C22×C4×C19D411yescharacteristic
59C22×C4×C19D411yescharacteristic
60C22×C4×C19D411yescharacteristic
61C22×C4×C19C2311yescharacteristic
62C22×C4×C19C2311yescharacteristic
63C22×C4×C19C2311yescharacteristic
64C2×C22⋊D19—22no—
65C2×C22⋊D19—22no—
66C2×C22⋊D19—44no—
67C22×Dic19—21no—
68C2×D76—24no—
69C2×D76—21no—
70C2×D76C2312yes—
71#64527—28no—
72#64525—28no—
73(C2×D19)⋊C4—22no—
74(C2×D19)⋊C4—22no—
75C4⋊Dic19—21no—
76C4⋊Dic19C2312yes—
77#64520—24no—
78C2×C19⋊C8C2314yes—
79C23×C19—24no—
80C23×C19—22no—
81C23×C19—22no—
82C23×C19—22no—
83C23×C19—41no—
84C23×C19—42no—
85C23×C19—42no—
86C23×C19C2×D411yescharacteristic
87C23×C19C2×D411yescharacteristic
88C23×C19C2×D411yescharacteristic
89C22×D19—22no—
90C22×D19—42no—
91C22×D19—42no—
92C22×D19—42no—
93Q8×C19—24no—
94Q8×C19—22no—
95Q8×C19C2×D414yescomplemented
96D4×C19—28no—
97D4×C19—24no—
98D4×C19—28no—
99D4×C19—22no—
100D4×C19C2×D414yescomplemented
101C2×C4×C19—24no—
102C2×C4×C19—28no—
103C2×C4×C19—22no—
104C2×C4×C19—22no—
105C2×C4×C19—22no—
106C2×C4×C19—28no—
107C2×C4×C19—22no—
108C2×C4×C19—22no—
109C2×C4×C19—22no—
110C2×C4×C19C2×D411yescharacteristic
111C2×C4×C19C2×D411yescharacteristic
112C2×C4×C19C2×D411yescharacteristic
113C2×C4×C19C2×D414yes—
114C2×C4×C19C2411yescharacteristic
115C22⋊D19—44no—
116C22⋊D19—44no—
117C2×Dic19—22no—
118C2×Dic19—42no—
119D76—24no—
120D76—42no—
121C19⋊C8—24no—
122#3006—191nomaximal, Sylow
123C22×C19—21no—
124C22×C19—21no—
125C22×C19—21no—
126C22×C19—21no—
127C22×C19—21no—
128C22×C19—24no—
129C22×C19—21no—
130C22×C19—21no—
131C22×C19—44no—
132C22×C19—48no—
133C22×C19—42no—
134C22×C19—42no—
135C22×C19#12012yes—
136C22×C19AGL(1,ℤ/8)12yescomplemented
137C22×C19C22×D411yescharacteristic
138C2×D19—42no—
139C2×D19—42no—
140C2×D19—42no—
141C2×D19—84no—
142C4×C19—21no—
143C4×C19—24no—
144C4×C19—21no—
145C4×C19#12012yes—
146C4×C19C22×D412yes—
147Dic19—42no—
148C22×#41D1911yescharacteristic, complemented
149C2×AGL(1,ℤ/8)—192no—
150C2×#121—191no—
151#449—194no—
152#448—192no—
153#447—192no—
154#417—192no—
155#407—191no—
156C2×C19—22no—
157C2×C19—22no—
158C2×C19—41no—
159C2×C19—44no—
160C2×C19C2×#12011yescharacteristic
161C2×C19C2×AGL(1,ℤ/8)11yescharacteristic
162C2×C19#57511yescharacteristic
163D19—82no—
164C2×#41—28no—
165C2×#41—21no—
166C2×#41—21no—
167C2×#41C2×D1912yes—
168C2×#41C2×D1912yescomplemented
169C22×Q8C2×D1911yescharacteristic, complemented
170C22×D4—21no—
171C22×D4—191no—
172C22×D4—381no—
173C22×D4C2×D1911yescharacteristic, complemented
174C23×C4—21no—
175C23×C4C2×D1911yescharacteristic
176AGL(1,ℤ/8)—388no—
177C2×SD16—194no—
178C2×D8—194no—
179C2×M16—192no—
180#121—192no—
181#121—192no—
182#121—381no—
183#121—381no—
184C2×C4⋊C4—191no—
185C2×C22⋊C4—381no—
186#103—194no—
187#102—194no—
188C22⋊C8—192no—
189C22⋊C8—192no—
190C19#300611yescharacteristic, complemented, Sylow
191C24—21no—
192C24—381no—
193C24C22⋊D1911yescharacteristic
194#41—28no—
195#41—28no—
196#41—24no—
197#41—24no—
198#41—24no—
199#41C22⋊D1918yescomplemented
200C2×Q8—24no—
201C2×Q8—21no—
202C2×Q8C22×D1912yes—
203C2×D4—28no—
204C2×D4—22no—
205C2×D4—22no—
206C2×D4—24no—
207C2×D4—21no—
208C2×D4—192no—
209C2×D4—382no—
210C2×D4—382no—
211C2×D4—384no—
212C2×D4—381no—
213C2×D4—764no—
214C2×D4C22×D1912yes—
215C22×C4—28no—
216C22×C4—21no—
217C22×C4—22no—
218C22×C4—22no—
219C22×C4—24no—
220C22×C4—381no—
221C22×C4C22⋊D1911yescharacteristic
222C22×C4C22⋊D1911yescharacteristic
223C22×C4C22⋊D1911yescharacteristic
224C22×C4C22×D1911yescharacteristic
225C22×C4C22×D1911yescharacteristic
226C22×C4C22×D1911yescharacteristic
227SD16—388no—
228D8—388no—
229M16—384no—
230C2×C8—194no—
231C4⋊C4—192no—
232C4⋊C4—381no—
233C22⋊C4—382no—
234C22⋊C4—382no—
235C23—24no—
236C23—22no—
237C23—22no—
238C23—22no—
239C23—41no—
240C23—42no—
241C23—42no—
242C23—382no—
243C23—762no—
244C23—762no—
245C23—762no—
246C23C2×C22⋊D1911yescharacteristic
247C23C2×C22⋊D1911yescharacteristic
248C23C2×C22⋊D1911yescharacteristic
249Q8—24no—
250Q8—22no—
251Q8C2×C22⋊D1914yescomplemented
252D4—28no—
253D4—24no—
254D4—28no—
255D4—22no—
256D4—384no—
257D4—764no—
258D4—764no—
259D4—762no—
260D4C2×C22⋊D1914yescomplemented
261C2×C4—24no—
262C2×C4—28no—
263C2×C4—22no—
264C2×C4—22no—
265C2×C4—22no—
266C2×C4—28no—
267C2×C4—22no—
268C2×C4—22no—
269C2×C4—22no—
270C2×C4—382no—
271C2×C4—762no—
272C2×C4C2×C22⋊D1911yescharacteristic
273C2×C4C2×C22⋊D1911yescharacteristic
274C2×C4C2×C22⋊D1911yescharacteristic
275C2×C4C2×C22⋊D1914yes—
276C2×C4C23×D1911yescharacteristic
277C8—384no—
278C22—21no—
279C22—21no—
280C22—21no—
281C22—21no—
282C22—21no—
283C22—21no—
284C22—21no—
285C22—24no—
286C22—44no—
287C22—48no—
288C22—42no—
289C22—42no—
290C22—762no—
291C22—762no—
292C22—762no—
293C22—1524no—
294C22#1059739512yescomplemented
295C22#1059739912yes—
296C22C22×C22⋊D1911yescharacteristic
297C4—21no—
298C4—24no—
299C4—21no—
300C4—762no—
301C4#1059739912yes—
302C4C22×C22⋊D1912yes—
303C2—22no—
304C2—22no—
305C2—41no—
306C2—44no—
307C2—1522no—
308C2C2×#1059739911yescharacteristic
309C2C2×#1059739511yescharacteristic
310C2#1192734211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC22×#41×C19C2
socleC22×C19C22×D4
hypercenterC22×#41D19
hypocenterC19#3006
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×#41

Complements

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

NH ≅ G/Ntype
1. C2×#10597395C2semidirect
2. C2×#10597376C2semidirect
3. #11926689C2semidirect
4. #11926683C2semidirect
5. #11926678C2semidirect
6. #11926545C2semidirect
7. #11926508C2semidirect
8. C22×#41×C19C2semidirect
13. C2×#41×C19C22semidirect
14. C22×Q8×C19C22semidirect
16. C22×D4×C19C22semidirect
20. C22×D76C22semidirect
22. C2×#64527C22semidirect
23. C2×#64525C22semidirect
27. #10597376C22semidirect
29. C2×C4⋊Dic19C22semidirect
30. C2×#64520C22semidirect
31. #10597292C22semidirect
32. #10597289C22semidirect
33. C22⋊(C19⋊C8)C22semidirect
34. C22⋊(C19⋊C8)C22semidirect
43. #41×C19D4semidirect
95. Q8×C19C2×D4semidirect
100. D4×C19C2×D4semidirect
136. C22×C19AGL(1,ℤ/8)semidirect
148. C22×#41D19semidirect
168. C2×#41C2×D19semidirect
169. C22×Q8C2×D19semidirect
173. C22×D4C2×D19semidirect
190. C19#3006semidirect
199. #41C22⋊D19semidirect
251. Q8C2×C22⋊D19semidirect
260. D4C2×C22⋊D19semidirect
294. C22#10597395semidirect

Maximal subgroups

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

subgroupindex
C2×#105973952
C2×#105973762
#119266892
#119266832
#119266782
#119265452
#119265082
C22×#41×C192
#300619