Finite Group Databasebeta

← #14572882

Subgroups — #14572882

Order 2432.

806 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 806 conjugacy classes of subgroups — too many to draw. Only its 141 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×#64543C211yesmaximal, characteristic, complemented
2C2×#10597357C212yesmaximal, complemented
3#121×D19C211yesmaximal, characteristic, complemented
4#11926690C212yesmaximal, complemented
5#11926686C212yesmaximal, complemented
6#11926685C211yesmaximal, characteristic, complemented
7#11926682C211yesmaximal, characteristic, complemented
8#11926678C211yesmaximal, characteristic, complemented
9#11926542C212yesmaximal, complemented
10#11926506C211yesmaximal, characteristic, complemented
11C19×#447C211yesmaximal, characteristic, complemented
12C22×D4×C19C2211yescharacteristic, complemented
13C22×C22⋊D19—21no—
14C23×Dic19—21no—
15C2×#64543—28no—
16C2×#64543—21no—
17C2×#64543—21no—
18C2×#64543C2212yes—
19C2×#64543C2212yescomplemented
20C2×D4×D19—21no—
21C2×D4×D19C2211yescharacteristic, complemented
22C22×C4×D19C2211yescharacteristic
23C22×Dic38C2211yescharacteristic, complemented
24C2×D8×C19C2212yescomplemented
25C19×#121C2211yescharacteristic
26#10597385—21no—
27#10597384C2211yescharacteristic, complemented
28C2×#64526C2212yescomplemented
29C2×#64525C2212yescomplemented
30#10597376C2211yescharacteristic
31#10597357—28no—
32C2×#64516C2212yescomplemented
33C2×#64515C2212yescomplemented
34#10597341C2211yescharacteristic, complemented
35C4⋊C4×D19C2211yescharacteristic, complemented
36#10597330—21no—
37C22⋊C4×D19—21no—
38C19×#102C2212yescomplemented
39C19×C22⋊C8C2211yescharacteristic, complemented
40#10597289C2212yescomplemented
41C22⋊(C19⋊C8)C2211yescharacteristic, complemented
42(C2×D19)⋊C8C2212yescomplemented
43#10597273C2212yescomplemented
44#10597267C2212yescomplemented
45C24×C19—21no—
46C23×D19—21no—
47C23×D19D411yescharacteristic
48C2×D4×C19—24no—
49C2×D4×C19—21no—
50C2×D4×C19—21no—
51C2×D4×C19C2311yescharacteristic
52C2×D4×C19C2312yes—
53C22×C4×C19C2311yescharacteristic
54C2×C22⋊D19—28no—
55C2×C22⋊D19—22no—
56C2×C22⋊D19—22no—
57C2×C22⋊D19—21no—
58C2×C22⋊D19—21no—
59C2×C22⋊D19—21no—
60C22×Dic19—28no—
61C22×Dic19—21no—
62C22×Dic19—22no—
63C22×Dic19—22no—
64C22×Dic19D411yescharacteristic
65#64543—28no—
66#64543—28no—
67#64543—24no—
68#64543—24no—
69#64543—24no—
70#64543D418yescomplemented
71D4×D19—24no—
72D4×D19—44no—
73C2×D76—21no—
74C2×D76C2311yescharacteristic
75C2×C4×D19—24no—
76C2×C4×D19—21no—
77C2×C4×D19D411yescharacteristic
78C2×C4×D19D411yescharacteristic
79C2×C4×D19C2311yescharacteristic
80C2×C4×D19C2311yescharacteristic
81C2×Dic38—21no—
82C2×Dic38—24no—
83C2×Dic38C2312yes—
84D8×C19—24no—
85C2×C8×C19C2312yes—
86C4⋊C4×C19C2311yescharacteristic
87C22⋊C4×C19—21no—
88C22⋊Dic19—21no—
89#64526—24no—
90#64525—24no—
91(C2×D19)⋊C4—21no—
92(C2×D19)⋊C4—21no—
93C4⋊Dic19C2311yescharacteristic
94Dic19⋊C4—21no—
95C2×C19⋊C8C2312yes—
96#64516—24no—
97#64515—24no—
98C23×C19—24no—
99C23×C19—22no—
100C23×C19—21no—
101C23×C19—42no—
102C23×C19—42no—
103C23×C19C2×D411yescharacteristic
104C22×D19—22no—
105C22×D19—22no—
106C22×D19—21no—
107C22×D19—41no—
108C22×D19—42no—
109C22×D19—42no—
110C22×D19—42no—
111C22×D19C2×D411yescharacteristic
112C22×D19C2×D411yescharacteristic
113D4×C19—24no—
114D4×C19—22no—
115D4×C19—22no—
116D4×C19—42no—
117D4×C19C2×D414yescomplemented
118C2×C4×C19—22no—
119C2×C4×C19—21no—
120C2×C4×C19C2×D411yescharacteristic
121C2×C4×C19C2411yescharacteristic
122C22⋊D19—28no—
123C22⋊D19—28no—
124C22⋊D19—42no—
125C22⋊D19—42no—
126C22⋊D19—42no—
127C2×Dic19—24no—
128C2×Dic19—28no—
129C2×Dic19—22no—
130C2×Dic19—22no—
131C2×Dic19—28no—
132C2×Dic19—21no—
133C2×Dic19C2×D411yescharacteristic
134C2×Dic19C2×D411yescharacteristic
135D76—22no—
136D76—42no—
137C4×D19—22no—
138C4×D19—22no—
139C4×D19—22no—
140C4×D19—42no—
141C4×D19C2×D414yes—
142Dic38—24no—
143Dic38—22no—
144Dic38C2×D414yescomplemented
145C8×C19—22no—
146C19⋊C8—22no—
147#3006—191nomaximal, Sylow
148C22×C19—21no—
149C22×C19—21no—
150C22×C19—24no—
151C22×C19—48no—
152C22×C19—42no—
153C22×C19—42no—
154C22×C19—41no—
155C22×C19—41no—
156C22×C19—41no—
157C22×C19AGL(1,ℤ/8)12yescomplemented
158C22×C19C22×D411yescharacteristic
159C2×D19—21no—
160C2×D19—21no—
161C2×D19—21no—
162C2×D19—21no—
163C2×D19—21no—
164C2×D19—44no—
165C2×D19—41no—
166C2×D19—41no—
167C2×D19—41no—
168C2×D19—84no—
169C2×D19#12012yes—
170C4×C19—21no—
171C4×C19—41no—
172C4×C19C22×D412yes—
173Dic19—24no—
174Dic19—21no—
175Dic19—41no—
176Dic19#12012yes—
177C22×#41—191no—
178C2×AGL(1,ℤ/8)—192no—
179C2×#121—191no—
180#449—192no—
181#449—192no—
182#448—191no—
183#448—191no—
184#447—191no—
185#447D1911yescharacteristic, complemented
186#417—192no—
187#407—191no—
188C2×C19—22no—
189C2×C19—44no—
190C2×C19—81no—
191C2×C19C2×#12011yescharacteristic
192C2×C19C2×AGL(1,ℤ/8)11yescharacteristic
193C2×C19#57511yescharacteristic
194D19—22no—
195D19—41no—
196D19—81no—
197C2×#41—192no—
198C2×#41—192no—
199C2×#41—381no—
200C2×#41—381no—
201C2×#41—388no—
202C22×Q8—191no—
203C22×D4—191no—
204C22×D4—381no—
205C22×D4—381no—
206C22×D4C2×D1911yescharacteristic, complemented
207C23×C4—191no—
208C23×C4—381no—
209AGL(1,ℤ/8)—388no—
210C2×SD16—192no—
211C2×SD16—192no—
212C2×D8—192no—
213C2×D8C2×D1912yescomplemented
214C2×M16—192no—
215#121—191no—
216#121—191no—
217#121—191no—
218#121—381no—
219#121—381no—
220#121C2×D1911yescharacteristic
221C2×C4⋊C4—191no—
222C2×C22⋊C4—381no—
223#103—192no—
224#103—192no—
225#102—192no—
226#102C2×D1912yescomplemented
227C22⋊C8—191no—
228C22⋊C8—192no—
229C22⋊C8C2×D1911yescharacteristic, complemented
230C19#300611yescharacteristic, complemented, Sylow
231C24—21no—
232C24—191no—
233C24—381no—
234#41—198no—
235#41—384no—
236#41—384no—
237#41—388no—
238#41—388no—
239#41—384no—
240C2×Q8—192no—
241C2×Q8—384no—
242C2×Q8—381no—
243C2×D4—24no—
244C2×D4—21no—
245C2×D4—21no—
246C2×D4—191no—
247C2×D4—381no—
248C2×D4—384no—
249C2×D4—381no—
250C2×D4—382no—
251C2×D4—382no—
252C2×D4—388no—
253C2×D4—381no—
254C2×D4—381no—
255C2×D4—764no—
256C2×D4C22×D1911yescharacteristic
257C2×D4C22×D1912yes—
258C22×C4—191no—
259C22×C4—191no—
260C22×C4—191no—
261C22×C4—191no—
262C22×C4—191no—
263C22×C4—384no—
264C22×C4—381no—
265C22×C4—382no—
266C22×C4—382no—
267C22×C4—388no—
268C22×C4—381no—
269C22×C4C22×D1911yescharacteristic
270SD16—384no—
271SD16—384no—
272D8—24no—
273D8—384no—
274M16—384no—
275C2×C8—192no—
276C2×C8C22×D1912yes—
277C4⋊C4—191no—
278C4⋊C4—381no—
279C4⋊C4C22×D1911yescharacteristic
280C22⋊C4—21no—
281C22⋊C4—381no—
282C22⋊C4—381no—
283C22⋊C4—381no—
284C23—24no—
285C23—22no—
286C23—21no—
287C23—42no—
288C23—42no—
289C23—191no—
290C23—191no—
291C23—382no—
292C23—382no—
293C23—381no—
294C23—761no—
295C23—762no—
296C23—762no—
297C23—762no—
298C23D4×D1911yescharacteristic
299Q8—194no—
300Q8—384no—
301Q8—382no—
302D4—24no—
303D4—22no—
304D4—22no—
305D4—42no—
306D4—388no—
307D4—388no—
308D4—382no—
309D4—762no—
310D4—762no—
311D4—762no—
312D4—762no—
313D4D4×D1914yescomplemented
314C2×C4—22no—
315C2×C4—21no—
316C2×C4—191no—
317C2×C4—194no—
318C2×C4—191no—
319C2×C4—382no—
320C2×C4—382no—
321C2×C4—382no—
322C2×C4—388no—
323C2×C4—384no—
324C2×C4—388no—
325C2×C4—382no—
326C2×C4—382no—
327C2×C4—381no—
328C2×C4—762no—
329C2×C4D4×D1911yescharacteristic
330C2×C4C23×D1911yescharacteristic
331C8—22no—
332C8—382no—
333C22—21no—
334C22—21no—
335C22—24no—
336C22—48no—
337C22—42no—
338C22—42no—
339C22—41no—
340C22—41no—
341C22—41no—
342C22—192no—
343C22—381no—
344C22—381no—
345C22—381no—
346C22—381no—
347C22—381no—
348C22—764no—
349C22—761no—
350C22—761no—
351C22—761no—
352C22—1524no—
353C22#1059735712yescomplemented
354C22C2×D4×D1911yescharacteristic
355C4—21no—
356C4—41no—
357C4—192no—
358C4—381no—
359C4—384no—
360C4—761no—
361C4C2×D4×D1912yes—
362C2—22no—
363C2—44no—
364C2—81no—
365C2—382no—
366C2—761no—
367C2—1521no—
368C2#120×D1911yescharacteristic
369C2C2×#1059735711yescharacteristic
370C2#1192734011yescharacteristic
subgroupG/H
centerC22C2×D4×D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#447C2
socleC22×C19C22×D4
hypercenter#447D19
hypocenterC19#3006
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. C22×#64543C2semidirect
2. C2×#10597357C2semidirect
3. #121×D19C2semidirect
4. #11926690C2semidirect
5. #11926686C2semidirect
6. #11926685C2semidirect
7. #11926682C2semidirect
8. #11926678C2semidirect
9. #11926542C2semidirect
10. #11926506C2semidirect
11. C19×#447C2semidirect
12. C22×D4×C19C22semidirect
19. C2×#64543C22semidirect
21. C2×D4×D19C22semidirect
23. C22×Dic38C22semidirect
24. C2×D8×C19C22semidirect
27. #10597384C22semidirect
28. C2×#64526C22semidirect
29. C2×#64525C22semidirect
32. C2×#64516C22semidirect
33. C2×#64515C22semidirect
34. #10597341C22semidirect
35. C4⋊C4×D19C22semidirect
38. C19×#102C22semidirect
39. C19×C22⋊C8C22semidirect
40. #10597289C22semidirect
41. C22⋊(C19⋊C8)C22semidirect
42. (C2×D19)⋊C8C22semidirect
43. #10597273C22semidirect
44. #10597267C22semidirect
70. #64543D4semidirect
117. D4×C19C2×D4semidirect
144. Dic38C2×D4semidirect
157. C22×C19AGL(1,ℤ/8)semidirect
185. #447D19semidirect
206. C22×D4C2×D19semidirect
213. C2×D8C2×D19semidirect
226. #102C2×D19semidirect
229. C22⋊C8C2×D19semidirect
230. C19#3006semidirect
313. D4D4×D19semidirect
353. C22#10597357semidirect

Maximal subgroups

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

subgroupindex
C22×#645432
C2×#105973572
#121×D192
#119266902
#119266862
#119266852
#119266822
#119266782
#119265422
#119265062
C19×#4472
#300619