Finite Group Databasebeta

← #14574729

Subgroups — #14574729

Order 2432.

408 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11927165C211yesmaximal, characteristic, complemented
2#11926931C211yesmaximal, characteristic, complemented
3#11926926C211yesmaximal, characteristic, complemented
4#11926903C211yesmaximal, characteristic, complemented
5#11926890C211yesmaximal, characteristic, complemented
6#11926763C211yesmaximal, characteristic, complemented
7#11926756C211yesmaximal, characteristic, complemented
8#11926741C211yesmaximal, characteristic, complemented
9#11926736C211yesmaximal, characteristic, complemented
10#11926706C211yesmaximal, characteristic, complemented
11#11926695C211yesmaximal, characteristic, complemented
12#11926689C211yesmaximal, characteristic, complemented
13#11926678C211yesmaximal, characteristic, complemented
14#11926605C211yesmaximal, characteristic, complemented
15C19×#535C211yesmaximal, characteristic, complemented
16C2×#41×C19C2211yescharacteristic
17C22×D4×C19C2211yescharacteristic
18C19×#127C2211yescharacteristic
19C19×#127C2211yescharacteristic
20C19×#124C2211yescharacteristic
21C19×#124C2211yescharacteristic
22C19×#121—21no—
23C19×#121—21no—
24C19×#120—21no—
25C19×#120—21no—
26C19×#117C2211yescharacteristic
27C2×#64528C2211yescharacteristic, complemented
28C2×#64527C2211yescharacteristic, complemented
29C2×#64526C2211yescharacteristic
30C2×#64526C2211yescharacteristic
31C2×#64526C2211yescharacteristic, complemented
32C2×#64525C2211yescharacteristic
33C2×#64525C2211yescharacteristic
34C2×#64525C2211yescharacteristic, complemented
35#10597376C2211yescharacteristic
36#10597370C2211yescharacteristic
37#10597344—21no—
38#10597342—21no—
39#10597331—21no—
40#10597329—21no—
41#10597321C2211yescharacteristic, complemented
42C4×D76C2211yescharacteristic, complemented
43#10597315C2211yescharacteristic, complemented
44C4×Dic38C2211yescharacteristic, complemented
45#10597292C2211yescharacteristic, complemented
46#10597292C2211yescharacteristic, complemented
47#10597289C2211yescharacteristic
48#10597289C2211yescharacteristic
49#10597289C2211yescharacteristic
50#10597289C2211yescharacteristic
51#10597289C2211yescharacteristic, complemented
52#10597289C2211yescharacteristic, complemented
53C22⋊(C19⋊C8)C2211yescharacteristic
54C22⋊(C19⋊C8)C2211yescharacteristic
55C4⋊(C19⋊C8)C2211yescharacteristic, complemented
56C4⋊(C19⋊C8)C2211yescharacteristic, complemented
57#10597260C2211yescharacteristic, complemented
58C4×C19⋊C8C2211yescharacteristic, complemented
59C24×C19—21no—
60#41×C19—41no—
61#41×C19—41no—
62C2×Q8×C19C2311yescharacteristic
63C2×D4×C19—21no—
64C2×D4×C19—21no—
65C2×D4×C19—21no—
66C2×D4×C19—21no—
67C2×D4×C19—21no—
68C2×D4×C19—21no—
69C2×D4×C19—41no—
70C2×D4×C19—41no—
71C2×D4×C19C2311yescharacteristic
72C2×D4×C19C2311yescharacteristic
73C2×D4×C19C2311yescharacteristic
74C22×C4×C19—21no—
75C22×C4×C19C2311yescharacteristic
76C2×C22⋊D19—21no—
77C2×D76C2311yescharacteristic
78C2×C4×D19—21no—
79C2×Dic38—21no—
80C2×Dic38C2311yescharacteristic
81C4⋊C4×C19D411yescharacteristic
82C4⋊C4×C19D411yescharacteristic
83C22⋊C4×C19—21no—
84C22⋊C4×C19—21no—
85C22⋊C4×C19—21no—
86C22⋊C4×C19—21no—
87C22⋊C4×C19D411yescharacteristic
88C22⋊C4×C19D411yescharacteristic
89C42×C19C2311yescharacteristic
90C42×C19C2311yescharacteristic
91C22⋊Dic19—21no—
92#64528—41no—
93#64527—41no—
94#64526—41no—
95#64526—41no—
96#64526—41no—
97#64525—41no—
98#64525—41no—
99#64525—41no—
100(C2×D19)⋊C4—21no—
101(C2×D19)⋊C4—21no—
102(C2×D19)⋊C4—21no—
103(C2×D19)⋊C4—21no—
104C4⋊Dic19—21no—
105C4⋊Dic19C2311yescharacteristic
106C4⋊Dic19C2311yescharacteristic
107Dic19⋊C4—21no—
108Dic19⋊C4—21no—
109C4×Dic19—21no—
110C2×C19⋊C8C2311yescharacteristic
111C2×C19⋊C8C2311yescharacteristic
112C2×C19⋊C8C2311yescharacteristic
113C2×C19⋊C8C2311yescharacteristic
114C23×C19—21no—
115C23×C19—21no—
116C23×C19—21no—
117C23×C19—42no—
118C23×C19—81no—
119C23×C19—81no—
120C23×C19C2×D411yescharacteristic
121C22×D19—21no—
122Q8×C19—21no—
123Q8×C19—21no—
124D4×C19—21no—
125D4×C19—21no—
126D4×C19—21no—
127D4×C19—21no—
128D4×C19—21no—
129D4×C19—21no—
130D4×C19—42no—
131D4×C19—42no—
132D4×C19—81no—
133D4×C19—81no—
134D4×C19—81no—
135D4×C19—81no—
136C2×C4×C19—21no—
137C2×C4×C19—21no—
138C2×C4×C19—21no—
139C2×C4×C19—42no—
140C2×C4×C19C2×D411yescharacteristic
141C2×C4×C19C2×D411yescharacteristic
142C2×C4×C19C2×D411yescharacteristic
143C2×C4×C19C2×D411yescharacteristic
144C2×C4×C19C2×D411yescharacteristic
145C2×C4×C19C2411yescharacteristic
146C22⋊D19—81no—
147C2×Dic19—21no—
148C2×Dic19—21no—
149C2×Dic19—21no—
150D76—21no—
151D76—21no—
152C4×D19—81no—
153Dic38—21no—
154Dic38—21no—
155Dic38—81no—
156C19⋊C8—21no—
157C19⋊C8—21no—
158C19⋊C8—21no—
159C19⋊C8—21no—
160#3224—191nomaximal, Sylow
161C22×C19—21no—
162C22×C19—21no—
163C22×C19—21no—
164C22×C19—41no—
165C22×C19—41no—
166C22×C19—41no—
167C22×C19—41no—
168C22×C19—41no—
169C22×C19—41no—
170C22×C19—41no—
171C22×C19—41no—
172C22×C19—41no—
173C22×C19—84no—
174C22×C19C22×D411yescharacteristic
175C2×D19—41no—
176C2×D19—41no—
177C2×D19—41no—
178C4×C19—21no—
179C4×C19—21no—
180C4×C19—21no—
181C4×C19—21no—
182C4×C19—21no—
183C4×C19—41no—
184C4×C19H(5,𝔽2)11yescharacteristic
185C4×C19H(5,𝔽2)11yescharacteristic
186Dic19—41no—
187Dic19—41no—
188Dic19—41no—
189#542—191no—
190#535D1911yescharacteristic, complemented
191#496—191no—
192#495—191no—
193#489—191no—
194#486—191no—
195#464—191no—
196#463—191no—
197#460—191no—
198#459—191no—
199#452—191no—
200#450—191no—
201#449—191no—
202#447—191no—
203#433—191no—
204C2×C19—41no—
205C2×C19—81no—
206C2×C19—81no—
207C2×C19—81no—
208C2×C19#53511yescharacteristic
209C2×C19#57611yescharacteristic
210C2×C19#57711yescharacteristic
211D19—81no—
212C2×#41C2×D1911yescharacteristic
213C22×D4C2×D1911yescharacteristic
214C2×Q16—191no—
215C2×SD16—191no—
216C2×SD16—191no—
217C2×SD16—191no—
218C2×SD16—191no—
219C2×D8—191no—
220C2×D8—191no—
221C2×D8—191no—
222C4⋊Q8—191no—
223#127C2×D1911yescharacteristic
224#127C2×D1911yescharacteristic
225#126—381no—
226#124—191no—
227#124—381no—
228#124C2×D1911yescharacteristic
229#124C2×D1911yescharacteristic
230#123—381no—
231C22⋊Q8—191no—
232C22⋊Q8—381no—
233#121—21no—
234#121—21no—
235#121—191no—
236#120—21no—
237#120—21no—
238C4×Q8—191no—
239C4×D4—191no—
240#117C2×D1911yescharacteristic
241C4⋊C8—191no—
242C4⋊C8—191no—
243#103—191no—
244#103—191no—
245#102—191no—
246#102—191no—
247#102—191no—
248#102—191no—
249#102—191no—
250#102—191no—
251C22⋊C8—191no—
252C22⋊C8—191no—
253#97—191no—
254C4×C8—191no—
255C19#322411yescharacteristic, complemented, Sylow
256C24—21no—
257#41—41no—
258#41—41no—
259C2×Q8—191no—
260C2×Q8—381no—
261C2×Q8C22×D1911yescharacteristic
262C2×D4—21no—
263C2×D4—21no—
264C2×D4—21no—
265C2×D4—21no—
266C2×D4—21no—
267C2×D4—21no—
268C2×D4—41no—
269C2×D4—41no—
270C2×D4—191no—
271C2×D4—381no—
272C2×D4C22×D1911yescharacteristic
273C2×D4C22×D1911yescharacteristic
274C2×D4C22×D1911yescharacteristic
275C22×C4—21no—
276C22×C4—381no—
277C22×C4C22×D1911yescharacteristic
278Q16—761no—
279SD16—761no—
280SD16—761no—
281SD16—761no—
282SD16—761no—
283D8—761no—
284D8—761no—
285D8—761no—
286C2×C8—191no—
287C2×C8—191no—
288C2×C8—191no—
289C2×C8—191no—
290C4⋊C4—191no—
291C4⋊C4—191no—
292C4⋊C4—381no—
293C4⋊C4—381no—
294C4⋊C4—381no—
295C4⋊C4C22⋊D1911yescharacteristic
296C4⋊C4C22⋊D1911yescharacteristic
297C22⋊C4—21no—
298C22⋊C4—21no—
299C22⋊C4—21no—
300C22⋊C4—21no—
301C22⋊C4—381no—
302C22⋊C4—381no—
303C22⋊C4—381no—
304C22⋊C4—381no—
305C22⋊C4—381no—
306C22⋊C4C22⋊D1911yescharacteristic
307C22⋊C4C22⋊D1911yescharacteristic
308C42—381no—
309C42C22×D1911yescharacteristic
310C42C22×D1911yescharacteristic
311C23—21no—
312C23—21no—
313C23—21no—
314C23—42no—
315C23—81no—
316C23—81no—
317C23—381no—
318C23C2×C22⋊D1911yescharacteristic
319Q8—21no—
320Q8—21no—
321Q8—381no—
322Q8—381no—
323Q8—1521no—
324D4—21no—
325D4—21no—
326D4—21no—
327D4—21no—
328D4—21no—
329D4—21no—
330D4—42no—
331D4—42no—
332D4—81no—
333D4—81no—
334D4—81no—
335D4—81no—
336D4—381no—
337D4—381no—
338D4—1521no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—42no—
343C2×C4—381no—
344C2×C4—381no—
345C2×C4—381no—
346C2×C4—1521no—
347C2×C4C2×C22⋊D1911yescharacteristic
348C2×C4C2×C22⋊D1911yescharacteristic
349C2×C4C2×C22⋊D1911yescharacteristic
350C2×C4C2×C22⋊D1911yescharacteristic
351C2×C4C2×C22⋊D1911yescharacteristic
352C2×C4C23×D1911yescharacteristic
353C8—381no—
354C8—381no—
355C8—381no—
356C8—381no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—84no—
370C22—761no—
371C22—761no—
372C22—761no—
373C22C22×C22⋊D1911yescharacteristic
374C4—21no—
375C4—21no—
376C4—21no—
377C4—21no—
378C4—21no—
379C4—41no—
380C4—761no—
381C4—761no—
382C4—761no—
383C4#1059743011yescharacteristic
384C4#1059743011yescharacteristic
385C2—41no—
386C2—81no—
387C2—81no—
388C2—81no—
389C2—1521no—
390C2#1192711111yescharacteristic
391C2#1192734711yescharacteristic
392C2#1192735511yescharacteristic
subgroupG/H
centerC22C22×C22⋊D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#535C2
socleC22×C19C22×D4
hypercenter#535D19
hypocenterC19#3224
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ #117 ◁ #535

Complements

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

NH ≅ G/Ntype
1. #11927165C2semidirect
2. #11926931C2semidirect
3. #11926926C2semidirect
4. #11926903C2semidirect
5. #11926890C2semidirect
6. #11926763C2semidirect
7. #11926756C2semidirect
8. #11926741C2semidirect
9. #11926736C2semidirect
10. #11926706C2semidirect
11. #11926695C2semidirect
12. #11926689C2semidirect
13. #11926678C2semidirect
14. #11926605C2semidirect
15. C19×#535C2semidirect
27. C2×#64528C22semidirect
28. C2×#64527C22semidirect
31. C2×#64526C22semidirect
34. C2×#64525C22semidirect
41. #10597321C22semidirect
42. C4×D76C22semidirect
43. #10597315C22semidirect
44. C4×Dic38C22semidirect
45. #10597292C22semidirect
46. #10597292C22semidirect
51. #10597289C22semidirect
52. #10597289C22semidirect
55. C4⋊(C19⋊C8)C22semidirect
56. C4⋊(C19⋊C8)C22semidirect
57. #10597260C22semidirect
58. C4×C19⋊C8C22semidirect
190. #535D19semidirect
255. C19#3224semidirect

Maximal subgroups

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

subgroupindex
#119271652
#119269312
#119269262
#119269032
#119268902
#119267632
#119267562
#119267412
#119267362
#119267062
#119266952
#119266892
#119266782
#119266052
C19×#5352
#322419