Finite Group Databasebeta

← #14574504

Subgroups — #14574504

Order 2432.

410 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11927117C211yesmaximal, characteristic, complemented
2#11927111C211yesmaximal, characteristic
3#11926886C211yesmaximal, characteristic, complemented
4#11926882C211yesmaximal, characteristic, complemented
5#11926867C211yesmaximal, characteristic, complemented
6#11926866C211yesmaximal, characteristic, complemented
7#11926789C211yesmaximal, characteristic, complemented
8#11926787C211yesmaximal, characteristic, complemented
9#11926772C211yesmaximal, characteristic, complemented
10#11926770C211yesmaximal, characteristic, complemented
11#11926695C211yesmaximal, characteristic, complemented
12#11926681C211yesmaximal, characteristic, complemented
13#11926681C211yesmaximal, characteristic, complemented
14#11926509C211yesmaximal, characteristic, complemented
15C19×#450C211yesmaximal, characteristic, complemented
16C22×D4×C19C2211yescharacteristic
17C2×Q8×D19C2211yescharacteristic, complemented
18C2×#64541C2211yescharacteristic
19C2×SD16×C19C2211yescharacteristic
20C2×SD16×C19C2211yescharacteristic
21C19×C22⋊Q8C2211yescharacteristic
22#10597399—21no—
23#10597399—21no—
24#10597392C2211yescharacteristic, complemented
25#10597386—21no—
26#10597384C2211yescharacteristic
27#10597384C2211yescharacteristic
28#10597384C2211yescharacteristic
29#10597384C2211yescharacteristic
30#10597382—21no—
31C2×#64526C2211yescharacteristic
32C2×#64526C2211yescharacteristic
33#10597372C2211yescharacteristic
34#10597370C2211yescharacteristic
35C2×#64515C2211yescharacteristic, complemented
36C2×C8×D19C2211yescharacteristic, complemented
37#10597343C2211yescharacteristic, complemented
38#10597340—21no—
39#10597338C2211yescharacteristic, complemented
40#10597334—21no—
41#10597331—21no—
42#10597329—21no—
43C19×#102C2211yescharacteristic
44C19×#102C2211yescharacteristic
45C19×C22⋊C8C2211yescharacteristic
46#10597292C2211yescharacteristic, complemented
47#10597292C2211yescharacteristic, complemented
48#10597289C2211yescharacteristic
49#10597289C2211yescharacteristic
50C22⋊(C19⋊C8)C2211yescharacteristic
51(C2×D19)⋊C8C2211yescharacteristic, complemented
52(C2×D19)⋊C8C2211yescharacteristic, complemented
53#10597275C2211yescharacteristic, complemented
54#10597274C2211yescharacteristic, complemented
55#10597273C2211yescharacteristic, complemented
56#10597273C2211yescharacteristic, complemented
57#10597265C2211yescharacteristic, complemented
58#10597264C2211yescharacteristic, complemented
59C24×C19—21no—
60C2×Q8×C19C2311yescharacteristic
61C2×D4×C19—21no—
62C2×D4×C19—41no—
63C2×D4×C19—41no—
64C2×D4×C19C2311yescharacteristic
65C2×D4×C19C2311yescharacteristic
66C22×C4×C19C2311yescharacteristic
67C2×C22⋊D19—21no—
68C2×C22⋊D19—21no—
69C2×C22⋊D19—21no—
70C2×C22⋊D19—21no—
71C2×C22⋊D19D411yescharacteristic
72C2×C22⋊D19D411yescharacteristic
73Q8×D19—41no—
74Q8×D19—41no—
75#64541—41no—
76#64541—41no—
77C2×D76D411yescharacteristic
78C2×C4×D19—21no—
79C2×C4×D19C2311yescharacteristic
80C2×C4×D19C2311yescharacteristic
81C2×Dic38—21no—
82C2×Dic38D411yescharacteristic
83C2×Dic38C2311yescharacteristic
84SD16×C19—41no—
85SD16×C19—41no—
86C2×C8×C19C2311yescharacteristic
87C2×C8×C19C2311yescharacteristic
88C4⋊C4×C19—21no—
89C4⋊C4×C19C2311yescharacteristic
90C22⋊C4×C19—21no—
91C22⋊Dic19—21no—
92C22⋊Dic19—21no—
93C22⋊Dic19—21no—
94C22⋊Dic19—21no—
95C22⋊Dic19—21no—
96C22⋊Dic19—21no—
97#64526—41no—
98#64526—41no—
99(C2×D19)⋊C4—21no—
100(C2×D19)⋊C4—21no—
101(C2×D19)⋊C4—21no—
102C4⋊Dic19—21no—
103C4⋊Dic19C2311yescharacteristic
104C4⋊Dic19C2311yescharacteristic
105C4⋊Dic19C2311yescharacteristic
106Dic19⋊C4—21no—
107Dic19⋊C4—21no—
108C4×Dic19—21no—
109C4×Dic19—21no—
110C2×C19⋊C8C2311yescharacteristic
111C2×C19⋊C8C2311yescharacteristic
112#64515—41no—
113C8×D19—41no—
114C23×C19—21no—
115C23×C19—21no—
116C23×C19—42no—
117C23×C19—81no—
118C23×C19—81no—
119C23×C19C2×D411yescharacteristic
120C22×D19C2×D411yescharacteristic
121C22×D19C2×D411yescharacteristic
122Q8×C19—21no—
123Q8×C19—21no—
124D4×C19—21no—
125D4×C19—21no—
126D4×C19—21no—
127D4×C19—21no—
128D4×C19—42no—
129C2×C4×C19—21no—
130C2×C4×C19—21no—
131C2×C4×C19—21no—
132C2×C4×C19—21no—
133C2×C4×C19C2×D411yescharacteristic
134C2×C4×C19C2411yescharacteristic
135C22⋊D19—41no—
136C22⋊D19—41no—
137C22⋊D19—81no—
138C22⋊D19—81no—
139C22⋊D19—81no—
140C22⋊D19—81no—
141C2×Dic19—21no—
142C2×Dic19—21no—
143C2×Dic19—21no—
144C2×Dic19—21no—
145C2×Dic19C2×D411yescharacteristic
146C2×Dic19C2×D411yescharacteristic
147D76—41no—
148C4×D19—21no—
149C4×D19—21no—
150C4×D19—21no—
151C4×D19—21no—
152C4×D19—42no—
153Dic38—21no—
154Dic38—21no—
155Dic38—41no—
156Dic38—42no—
157C8×C19—21no—
158C8×C19—21no—
159C19⋊C8—21no—
160C19⋊C8—21no—
161#3200—191nomaximal, Sylow
162C22×C19—21no—
163C22×C19—21no—
164C22×C19—21no—
165C22×C19—41no—
166C22×C19—41no—
167C22×C19—41no—
168C22×C19—41no—
169C22×C19—41no—
170C22×C19—41no—
171C22×C19—84no—
172C22×C19C22×D411yescharacteristic
173C2×D19—21no—
174C2×D19—21no—
175C2×D19—21no—
176C2×D19—21no—
177C2×D19—21no—
178C2×D19—21no—
179C4×C19—21no—
180C4×C19—41no—
181C4×C19—41no—
182C4×C19H(5,𝔽2)11yescharacteristic
183C4×C19H(5,𝔽2)11yescharacteristic
184Dic19—21no—
185Dic19—21no—
186Dic19—41no—
187Dic19—41no—
188Dic19—41no—
189Dic19—41no—
190#536—191no—
191#535—191no—
192#485—191no—
193#485—191no—
194#482—191no—
195#482—191no—
196#468—191no—
197#468—191no—
198#465—191no—
199#465—191no—
200#450—191no—
201#450D1911yescharacteristic, complemented
202#448—191no—
203#448—191no—
204#408—191no—
205C2×C19—41no—
206C2×C19—81no—
207C2×C19—81no—
208C2×C19#53411yescharacteristic
209C2×C19#57711yescharacteristic
210C2×C19#57711yescharacteristic
211D19—41no—
212D19—41no—
213C2×#41—191no—
214C22×Q8—191no—
215C22×D4C2×D1911yescharacteristic
216C2×SD16—191no—
217C2×SD16—191no—
218C2×SD16C2×D1911yescharacteristic
219C2×SD16C2×D1911yescharacteristic
220C2×M16—191no—
221C22×C8—191no—
222C4⋊Q8—381no—
223#127—381no—
224#124—381no—
225#124—381no—
226#123—381no—
227#123—381no—
228C22⋊Q8—191no—
229C22⋊Q8—191no—
230C22⋊Q8—191no—
231C22⋊Q8C2×D1911yescharacteristic
232#121—191no—
233#121—191no—
234#121—191no—
235#121—191no—
236#120—381no—
237#120—381no—
238#117—191no—
239#117—191no—
240#107—191no—
241#107—191no—
242#106—191no—
243#106—191no—
244#103—191no—
245#103—191no—
246#103—191no—
247#103—191no—
248#102—191no—
249#102—191no—
250#102C2×D1911yescharacteristic
251#102C2×D1911yescharacteristic
252C22⋊C8—191no—
253C22⋊C8—191no—
254C22⋊C8—191no—
255C22⋊C8C2×D1911yescharacteristic
256C19#320011yescharacteristic, complemented, Sylow
257C24—21no—
258#41—761no—
259#41—761no—
260C2×Q8—191no—
261C2×Q8—191no—
262C2×Q8—381no—
263C2×Q8—761no—
264C2×Q8—761no—
265C2×Q8C22×D1911yescharacteristic
266C2×D4—21no—
267C2×D4—41no—
268C2×D4—41no—
269C2×D4—191no—
270C2×D4—191no—
271C2×D4—191no—
272C2×D4—381no—
273C2×D4—381no—
274C2×D4—381no—
275C2×D4—381no—
276C2×D4C22×D1911yescharacteristic
277C2×D4C22×D1911yescharacteristic
278C22×C4—191no—
279C22×C4—191no—
280C22×C4—381no—
281C22×C4C22×D1911yescharacteristic
282SD16—41no—
283SD16—41no—
284SD16—761no—
285SD16—761no—
286M16—761no—
287C2×C8—191no—
288C2×C8—191no—
289C2×C8—761no—
290C2×C8C22×D1911yescharacteristic
291C2×C8C22×D1911yescharacteristic
292C4⋊C4—21no—
293C4⋊C4—191no—
294C4⋊C4—191no—
295C4⋊C4—191no—
296C4⋊C4—381no—
297C4⋊C4—381no—
298C4⋊C4—381no—
299C4⋊C4C22×D1911yescharacteristic
300C22⋊C4—21no—
301C22⋊C4—381no—
302C22⋊C4—381no—
303C22⋊C4—381no—
304C22⋊C4—381no—
305C22⋊C4—381no—
306C22⋊C4—381no—
307C22⋊C4—381no—
308C22⋊C4—381no—
309C22⋊C4—381no—
310C42—381no—
311C42—381no—
312C23—21no—
313C23—21no—
314C23—42no—
315C23—81no—
316C23—81no—
317C23—191no—
318C23—191no—
319C23D4×D1911yescharacteristic
320Q8—21no—
321Q8—21no—
322Q8—381no—
323Q8—381no—
324Q8—761no—
325Q8—762no—
326D4—21no—
327D4—21no—
328D4—21no—
329D4—21no—
330D4—42no—
331D4—761no—
332D4—761no—
333D4—761no—
334D4—1521no—
335D4—1521no—
336D4—1521no—
337D4—1521no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—191no—
343C2×C4—191no—
344C2×C4—381no—
345C2×C4—381no—
346C2×C4—381no—
347C2×C4—381no—
348C2×C4—381no—
349C2×C4—381no—
350C2×C4—381no—
351C2×C4—381no—
352C2×C4—762no—
353C2×C4D4×D1911yescharacteristic
354C2×C4C23×D1911yescharacteristic
355C8—21no—
356C8—21no—
357C8—381no—
358C8—381no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—84no—
369C22—381no—
370C22—381no—
371C22—381no—
372C22—381no—
373C22—381no—
374C22—381no—
375C22C2×D4×D1911yescharacteristic
376C4—21no—
377C4—41no—
378C4—41no—
379C4—381no—
380C4—381no—
381C4—761no—
382C4—761no—
383C4—761no—
384C4—761no—
385C4#1059743011yescharacteristic
386C4#1059743011yescharacteristic
387C2—41no—
388C2—81no—
389C2—81no—
390C2—761no—
391C2—761no—
392C2#1192710411yescharacteristic
393C2#1192735011yescharacteristic
394C2#1192735411yescharacteristic
subgroupG/H
centerC22C2×D4×D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#450C2
socleC22×C19C22×D4
prime radical#11927111C2
hypercenter#450D19
hypocenterC19#3200
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. #11927117C2semidirect
3. #11926886C2semidirect
4. #11926882C2semidirect
5. #11926867C2semidirect
6. #11926866C2semidirect
7. #11926789C2semidirect
8. #11926787C2semidirect
9. #11926772C2semidirect
10. #11926770C2semidirect
11. #11926695C2semidirect
12. #11926681C2semidirect
13. #11926681C2semidirect
14. #11926509C2semidirect
15. C19×#450C2semidirect
17. C2×Q8×D19C22semidirect
24. #10597392C22semidirect
35. C2×#64515C22semidirect
36. C2×C8×D19C22semidirect
37. #10597343C22semidirect
39. #10597338C22semidirect
46. #10597292C22semidirect
47. #10597292C22semidirect
51. (C2×D19)⋊C8C22semidirect
52. (C2×D19)⋊C8C22semidirect
53. #10597275C22semidirect
54. #10597274C22semidirect
55. #10597273C22semidirect
56. #10597273C22semidirect
57. #10597265C22semidirect
58. #10597264C22semidirect
201. #450D19semidirect
256. C19#3200semidirect

Maximal subgroups

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

subgroupindex
#119271172
#119271112
#119268862
#119268822
#119268672
#119268662
#119267892
#119267872
#119267722
#119267702
#119266952
#119266812
#119265092
C19×#4502
#320019