Finite Group Databasebeta

← #14574595

Subgroups — #14574595

Order 2432.

410 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11927073C211yesmaximal, characteristic, complemented
2#124×D19C211yesmaximal, characteristic, complemented
3#11926926C211yesmaximal, characteristic, complemented
4#11926899C211yesmaximal, characteristic, complemented
5#11926898C211yesmaximal, characteristic, complemented
6#11926768C211yesmaximal, characteristic, complemented
7#11926764C211yesmaximal, characteristic, complemented
8#11926761C211yesmaximal, characteristic, complemented
9#11926757C211yesmaximal, characteristic, complemented
10#11926698C211yesmaximal, characteristic, complemented
11#11926693C211yesmaximal, characteristic, complemented
12#11926681C211yesmaximal, characteristic, complemented
13#11926676C211yesmaximal, characteristic
14#11926595C211yesmaximal, characteristic, complemented
15C19×#495C211yesmaximal, characteristic, complemented
16C2×Q8×D19C2211yescharacteristic
17C2×D4×D19C2211yescharacteristic
18C2×Q16×C19C2211yescharacteristic, complemented
19C2×SD16×C19C2211yescharacteristic
20C2×SD16×C19C2211yescharacteristic, complemented
21C2×D8×C19C2211yescharacteristic
22C19×#124C2211yescharacteristic
23C19×#124C2211yescharacteristic, complemented
24#10597393C2211yescharacteristic
25#10597392C2211yescharacteristic
26Q8×Dic19C2211yescharacteristic, complemented
27C2×#64528C2211yescharacteristic, complemented
28C2×#64527C2211yescharacteristic
29#10597384C2211yescharacteristic
30#10597382C2211yescharacteristic
31D4×Dic19C2211yescharacteristic, complemented
32C2×#64526C2211yescharacteristic, complemented
33C2×#64525C2211yescharacteristic
34#10597331—21no—
35#10597331—21no—
36#10597329—21no—
37(C22⋊D19)⋊C4—21no—
38C22⋊C4×D19—21no—
39C22⋊C4×D19—21no—
40#10597325—21no—
41#10597323—21no—
42#10597321C2211yescharacteristic
43C42×D19C2211yescharacteristic
44#10597316C2211yescharacteristic, complemented
45C4×C8×C19C2211yescharacteristic, complemented
46#10597292C2211yescharacteristic, complemented
47#10597292C2211yescharacteristic, complemented
48#10597289C2211yescharacteristic
49#10597289C2211yescharacteristic
50#10597278C2211yescharacteristic
51#10597278C2211yescharacteristic
52(C2×D19)⋊C8C2211yescharacteristic
53(C2×D19)⋊C8C2211yescharacteristic
54#10597273C2211yescharacteristic, complemented
55#10597273C2211yescharacteristic, complemented
56Dic19⋊C8C2211yescharacteristic, complemented
57Dic19⋊C8C2211yescharacteristic, complemented
58C4×C19⋊C8C2211yescharacteristic, complemented
59C23×D19—21no—
60C2×Q8×C19C2311yescharacteristic
61C2×Q8×C19C2311yescharacteristic
62C2×D4×C19C2311yescharacteristic
63C2×D4×C19C2311yescharacteristic
64C2×C22⋊D19—21no—
65C2×C22⋊D19—21no—
66C22×Dic19—21no—
67Q8×D19—41no—
68Q8×D19—41no—
69D4×D19—41no—
70D4×D19—41no—
71C2×D76C2311yescharacteristic
72C2×C4×D19—21no—
73C2×C4×D19D411yescharacteristic
74C2×C4×D19D411yescharacteristic
75C2×C4×D19C2311yescharacteristic
76C2×Dic38—21no—
77C2×Dic38C2311yescharacteristic
78Q16×C19—41no—
79SD16×C19—41no—
80SD16×C19—41no—
81D8×C19—41no—
82C2×C8×C19C2311yescharacteristic
83C2×C8×C19C2311yescharacteristic
84C22⋊C4×C19—21no—
85C22⋊C4×C19—21no—
86C22⋊C4×C19—21no—
87C22⋊C4×C19—21no—
88C42×C19C2311yescharacteristic
89C22⋊Dic19—21no—
90C22⋊Dic19—21no—
91C22⋊Dic19—21no—
92C22⋊Dic19—21no—
93#64528—41no—
94#64527—41no—
95#64526—41no—
96#64525—41no—
97(C2×D19)⋊C4—21no—
98(C2×D19)⋊C4—21no—
99(C2×D19)⋊C4—21no—
100(C2×D19)⋊C4—21no—
101(C2×D19)⋊C4—21no—
102C4⋊Dic19—21no—
103C4⋊Dic19C2311yescharacteristic
104C4⋊Dic19C2311yescharacteristic
105Dic19⋊C4—21no—
106Dic19⋊C4—21no—
107Dic19⋊C4—21no—
108C4×Dic19—21no—
109C4×Dic19D411yescharacteristic
110C4×Dic19D411yescharacteristic
111C4×Dic19C2311yescharacteristic
112C2×C19⋊C8C2311yescharacteristic
113C2×C19⋊C8C2311yescharacteristic
114C23×C19—21no—
115C23×C19—21no—
116C22×D19—21no—
117C22×D19—42no—
118C22×D19—42no—
119C22×D19—42no—
120C22×D19C2×D411yescharacteristic
121Q8×C19—21no—
122Q8×C19—21no—
123Q8×C19—21no—
124Q8×C19—21no—
125D4×C19—21no—
126D4×C19—21no—
127D4×C19—21no—
128D4×C19—21no—
129C2×C4×C19—21no—
130C2×C4×C19—21no—
131C2×C4×C19C2×D411yescharacteristic
132C2×C4×C19C2×D411yescharacteristic
133C2×C4×C19C2411yescharacteristic
134C22⋊D19—42no—
135C22⋊D19—42no—
136C2×Dic19—21no—
137C2×Dic19—21no—
138C2×Dic19—21no—
139C2×Dic19—42no—
140C2×Dic19C2×D411yescharacteristic
141C2×Dic19C2×D411yescharacteristic
142C2×Dic19C2×D411yescharacteristic
143D76—21no—
144D76—21no—
145C4×D19—22no—
146C4×D19—21no—
147C4×D19—21no—
148C4×D19—41no—
149C4×D19—42no—
150Dic38—21no—
151Dic38—21no—
152Dic38—42no—
153C8×C19—21no—
154C8×C19—21no—
155C19⋊C8—21no—
156C19⋊C8—21no—
157#3211—191nomaximal, Sylow
158C22×C19—41no—
159C22×C19—41no—
160C22×C19—41no—
161C22×C19—41no—
162C22×C19—41no—
163C22×C19—41no—
164C22×C19C22×D411yescharacteristic
165C2×D19—21no—
166C2×D19—21no—
167C2×D19—41no—
168C2×D19—41no—
169C2×D19—41no—
170C2×D19—84no—
171C2×D19#13512yes—
172C4×C19—21no—
173C4×C19—21no—
174C4×C19—41no—
175C4×C19—41no—
176C4×C19H(5,𝔽2)11yescharacteristic
177C4×C19H(5,𝔽2)11yescharacteristic
178Dic19—21no—
179Dic19—21no—
180Dic19—21no—
181Dic19—41no—
182Dic19—41no—
183Dic19—41no—
184#529—191no—
185C2×#124—191no—
186#495—191no—
187#495D1911yescharacteristic, complemented
188#488—191no—
189#488—191no—
190#464—191no—
191#464—191no—
192#463—191no—
193#463—191no—
194#451—191no—
195#450—191no—
196#448—191no—
197#447—191no—
198#431—191no—
199C2×C19—81no—
200C2×C19—81no—
201C2×C19#53511yescharacteristic
202C2×C19C2×#13511yescharacteristic
203C2×C19#57511yescharacteristic
204D19—22no—
205D19—81no—
206C22×Q8—191no—
207C22×D4—191no—
208C2×Q16—191no—
209C2×Q16C2×D1911yescharacteristic, complemented
210C2×SD16—191no—
211C2×SD16—191no—
212C2×SD16C2×D1911yescharacteristic
213C2×SD16C2×D1911yescharacteristic, complemented
214C2×D8—191no—
215C2×D8C2×D1911yescharacteristic
216#126—381no—
217#125—191no—
218#124—191no—
219#124—191no—
220#124—191no—
221#124—381no—
222#124—381no—
223#124C2×D1911yescharacteristic
224#124C2×D1911yescharacteristic, complemented
225#123—381no—
226C22⋊Q8—191no—
227#121—191no—
228C4×Q8—191no—
229C4×D4—191no—
230C4×D4—381no—
231#117—381no—
232C2×C22⋊C4—381no—
233C2×C22⋊C4—381no—
234C2×C42—191no—
235C4⋊C8—191no—
236C4⋊C8—191no—
237#103—191no—
238#103—191no—
239#103—191no—
240#103—191no—
241#102—191no—
242#102—191no—
243#102—191no—
244#102—191no—
245C22⋊C8—191no—
246C22⋊C8—191no—
247C4×C8—191no—
248C4×C8C2×D1911yescharacteristic, complemented
249C19#321111yescharacteristic, complemented, Sylow
250C24—381no—
251C2×Q8—191no—
252C2×Q8—381no—
253C2×Q8—761no—
254C2×Q8—761no—
255C2×Q8C22×D1911yescharacteristic
256C2×Q8C22×D1911yescharacteristic
257C2×D4—191no—
258C2×D4—381no—
259C2×D4—381no—
260C2×D4—761no—
261C2×D4—761no—
262C2×D4C22×D1911yescharacteristic
263C2×D4C22×D1911yescharacteristic
264C22×C4—191no—
265C22×C4—191no—
266C22×C4—191no—
267C22×C4—381no—
268C22×C4—381no—
269Q16—41no—
270Q16—761no—
271SD16—41no—
272SD16—41no—
273SD16—761no—
274SD16—761no—
275D8—41no—
276D8—761no—
277C2×C8—191no—
278C2×C8—191no—
279C2×C8C22×D1911yescharacteristic
280C2×C8C22×D1911yescharacteristic
281C4⋊C4—191no—
282C4⋊C4—191no—
283C4⋊C4—381no—
284C4⋊C4—381no—
285C4⋊C4—381no—
286C4⋊C4—381no—
287C22⋊C4—21no—
288C22⋊C4—21no—
289C22⋊C4—21no—
290C22⋊C4—21no—
291C22⋊C4—381no—
292C22⋊C4—381no—
293C22⋊C4—381no—
294C22⋊C4—381no—
295C22⋊C4—381no—
296C22⋊C4—381no—
297C22⋊C4—381no—
298C22⋊C4—381no—
299C22⋊C4—381no—
300C42—191no—
301C42—191no—
302C42—191no—
303C42—381no—
304C42C22×D1911yescharacteristic
305C23—21no—
306C23—21no—
307C23—191no—
308C23—381no—
309C23—762no—
310C23—762no—
311C23—762no—
312Q8—21no—
313Q8—21no—
314Q8—21no—
315Q8—21no—
316Q8—381no—
317Q8—381no—
318Q8—762no—
319D4—21no—
320D4—21no—
321D4—21no—
322D4—21no—
323D4—381no—
324D4—381no—
325D4—762no—
326D4—762no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—191no—
330C2×C4—191no—
331C2×C4—191no—
332C2×C4—382no—
333C2×C4—381no—
334C2×C4—381no—
335C2×C4—381no—
336C2×C4—381no—
337C2×C4—381no—
338C2×C4—761no—
339C2×C4—762no—
340C2×C4—762no—
341C2×C4D4×D1911yescharacteristic
342C2×C4D4×D1911yescharacteristic
343C2×C4C23×D1911yescharacteristic
344C8—21no—
345C8—21no—
346C8—381no—
347C8—381no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—192no—
355C22—381no—
356C22—381no—
357C22—761no—
358C22—761no—
359C22—761no—
360C22—1524no—
361C22C2×D4×D1911yescharacteristic
362C4—21no—
363C4—21no—
364C4—41no—
365C4—41no—
366C4—381no—
367C4—381no—
368C4—381no—
369C4—761no—
370C4—761no—
371C4—761no—
372C4#1059743011yescharacteristic
373C4#1059743011yescharacteristic
374C2—81no—
375C2—81no—
376C2—382no—
377C2—1521no—
378C2#1192710711yescharacteristic
379C2#135×D1911yescharacteristic
380C2#1192734111yescharacteristic
subgroupG/H
centerC22C2×D4×D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#495C2
socleC22×C19C22×D4
prime radical#11926676C2
hypercenter#495D19
hypocenterC19#3211
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C42 ◁ #495

Complements

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

NH ≅ G/Ntype
1. #11927073C2semidirect
2. #124×D19C2semidirect
3. #11926926C2semidirect
4. #11926899C2semidirect
5. #11926898C2semidirect
6. #11926768C2semidirect
7. #11926764C2semidirect
8. #11926761C2semidirect
9. #11926757C2semidirect
10. #11926698C2semidirect
11. #11926693C2semidirect
12. #11926681C2semidirect
14. #11926595C2semidirect
15. C19×#495C2semidirect
18. C2×Q16×C19C22semidirect
20. C2×SD16×C19C22semidirect
23. C19×#124C22semidirect
26. Q8×Dic19C22semidirect
27. C2×#64528C22semidirect
31. D4×Dic19C22semidirect
32. C2×#64526C22semidirect
44. #10597316C22semidirect
45. C4×C8×C19C22semidirect
46. #10597292C22semidirect
47. #10597292C22semidirect
54. #10597273C22semidirect
55. #10597273C22semidirect
56. Dic19⋊C8C22semidirect
57. Dic19⋊C8C22semidirect
58. C4×C19⋊C8C22semidirect
187. #495D19semidirect
209. C2×Q16C2×D19semidirect
213. C2×SD16C2×D19semidirect
224. #124C2×D19semidirect
248. C4×C8C2×D19semidirect
249. C19#3211semidirect

Maximal subgroups

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

subgroupindex
#119270732
#124×D192
#119269262
#119268992
#119268982
#119267682
#119267642
#119267612
#119267572
#119266982
#119266932
#119266812
#119266762
#119265952
C19×#4952
#321119