Finite Group Databasebeta

← #14574427

Subgroups — #14574427

Order 2432.

424 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#11927057C211yesmaximal, characteristic, complemented
2#11927051C211yesmaximal, characteristic, complemented
3#11926883C211yesmaximal, characteristic, complemented
4#11926882C211yesmaximal, characteristic, complemented
5#11926869C211yesmaximal, characteristic, complemented
6#11926866C211yesmaximal, characteristic, complemented
7#11926782C211yesmaximal, characteristic, complemented
8#11926779C211yesmaximal, characteristic, complemented
9#11926776C211yesmaximal, characteristic, complemented
10#11926770C211yesmaximal, characteristic, complemented
11#11926705C211yesmaximal, characteristic, complemented
12#11926689C211yesmaximal, characteristic, complemented
13#11926688C211yesmaximal, characteristic, complemented
14C22⋊C8×D19C211yesmaximal, characteristic, complemented
15C19×#452C211yesmaximal, characteristic, complemented
16C2×#41×C19C2211yescharacteristic
17C2×#64545C2211yescharacteristic
18C22×C4×D19C2211yescharacteristic
19C2×Q16×C19C2211yescharacteristic, complemented
20C2×SD16×C19C2211yescharacteristic, complemented
21C19×C22⋊Q8C2211yescharacteristic
22#10597392C2211yescharacteristic
23#10597392C2211yescharacteristic
24#10597392C2211yescharacteristic
25C2×#64527C2211yescharacteristic, complemented
26#10597384C2211yescharacteristic
27#10597384C2211yescharacteristic
28#10597383—21no—
29#10597381—21no—
30C2×#64525C2211yescharacteristic, complemented
31#10597376C2211yescharacteristic
32C4×C22⋊D19—21no—
33C4×C22⋊D19—21no—
34#10597372C2211yescharacteristic
35C2×C8×D19C2211yescharacteristic
36C2×C8×D19C2211yescharacteristic
37#10597341C2211yescharacteristic
38#10597340—21no—
39#10597339—21no—
40#10597338C2211yescharacteristic
41#10597328—21no—
42(C22⋊D19)⋊C4—21no—
43C19×#103C2211yescharacteristic, complemented
44C19×#102C2211yescharacteristic, complemented
45C19×C22⋊C8C2211yescharacteristic
46#10597292C2211yescharacteristic, complemented
47#10597292C2211yescharacteristic, complemented
48#10597292C2211yescharacteristic, complemented
49#10597289C2211yescharacteristic, complemented
50C22⋊(C19⋊C8)C2211yescharacteristic
51#10597278C2211yescharacteristic, complemented
52#10597278C2211yescharacteristic, complemented
53(C2×D19)⋊C8C2211yescharacteristic
54(C2×D19)⋊C8C2211yescharacteristic
55#10597275C2211yescharacteristic, complemented
56#10597274C2211yescharacteristic, complemented
57#10597265C2211yescharacteristic, complemented
58#10597264C2211yescharacteristic, complemented
59C23×D19D411yescharacteristic
60#41×C19—41no—
61#41×C19—41no—
62C2×Q8×C19C2311yescharacteristic
63C2×Q8×C19C2311yescharacteristic
64C2×D4×C19—21no—
65C2×D4×C19C2311yescharacteristic
66C22×C4×C19—21no—
67C22×C4×C19C2311yescharacteristic
68C2×C22⋊D19—21no—
69C2×C22⋊D19—21no—
70C2×C22⋊D19—21no—
71C22×Dic19D411yescharacteristic
72#64545—41no—
73#64545—41no—
74C2×D76—21no—
75C2×D76—21no—
76C2×D76C2311yescharacteristic
77C2×C4×D19—21no—
78C2×C4×D19—41no—
79C2×C4×D19—41no—
80C2×C4×D19D411yescharacteristic
81C2×C4×D19D411yescharacteristic
82C2×C4×D19C2311yescharacteristic
83C2×C4×D19C2311yescharacteristic
84Q16×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—
94#64527—41no—
95#64525—41no—
96(C2×D19)⋊C4—21no—
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⋊Dic19C2311yescharacteristic
103C4⋊Dic19C2311yescharacteristic
104C4⋊Dic19C2311yescharacteristic
105Dic19⋊C4—21no—
106Dic19⋊C4—21no—
107Dic19⋊C4—21no—
108C4×Dic19—21no—
109C4×Dic19—21no—
110C2×C19⋊C8C2311yescharacteristic
111C2×C19⋊C8C2311yescharacteristic
112C8×D19—41no—
113C8×D19—41no—
114C23×C19—21no—
115C23×C19C2×D411yescharacteristic
116C22×D19—22no—
117C22×D19—21no—
118C22×D19—41no—
119C22×D19—41no—
120C22×D19C2×D411yescharacteristic
121C22×D19C2×D411yescharacteristic
122Q8×C19—21no—
123Q8×C19—21no—
124Q8×C19—21no—
125Q8×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×C19—21no—
134C2×C4×C19—42no—
135C2×C4×C19C2×D411yescharacteristic
136C2×C4×C19C2411yescharacteristic
137C22⋊D19—42no—
138C22⋊D19—42no—
139C22⋊D19—42no—
140C2×Dic19—21no—
141C2×Dic19—21no—
142C2×Dic19—21no—
143C2×Dic19—41no—
144C2×Dic19C2×D411yescharacteristic
145C2×Dic19C2×D411yescharacteristic
146D76—21no—
147D76—21no—
148D76—42no—
149D76—42no—
150C4×D19—21no—
151C4×D19—21no—
152C4×D19—21no—
153C4×D19—21no—
154C4×D19—41no—
155C4×D19—41no—
156C4×D19—42no—
157C8×C19—21no—
158C8×C19—21no—
159C19⋊C8—21no—
160C19⋊C8—21no—
161#3191—191nomaximal, Sylow
162C22×C19—21no—
163C22×C19—21no—
164C22×C19—21no—
165C22×C19—41no—
166C22×C19—41no—
167C22×C19—41no—
168C22×C19C22×D411yescharacteristic
169C2×D19—21no—
170C2×D19—21no—
171C2×D19—21no—
172C2×D19—21no—
173C2×D19—21no—
174C2×D19—44no—
175C2×D19—41no—
176C2×D19—41no—
177C2×D19—41no—
178C2×D19#13512yes—
179C4×C19—21no—
180C4×C19—41no—
181C4×C19—41no—
182C4×C19—41no—
183C4×C19H(5,𝔽2)11yescharacteristic
184C4×C19H(5,𝔽2)11yescharacteristic
185Dic19—21no—
186Dic19—21no—
187Dic19—41no—
188Dic19—41no—
189Dic19—41no—
190#525—191no—
191#525—191no—
192#485—191no—
193#485—191no—
194#482—191no—
195#482—191no—
196#467—191no—
197#466—191no—
198#465—191no—
199#465—191no—
200#452—191no—
201#452D1911yescharacteristic, complemented
202#449—191no—
203#449—191no—
204C2×C22⋊C8—191no—
205C2×C19—41no—
206C2×C19—81no—
207C2×C19#53411yescharacteristic
208C2×C19C2×#13511yescharacteristic
209C2×C19#57511yescharacteristic
210D19—22no—
211D19—41no—
212D19—81no—
213C2×#41—191no—
214C2×#41C2×D1911yescharacteristic
215C23×C4—191no—
216C2×Q16C2×D1911yescharacteristic, complemented
217C2×SD16—191no—
218C2×SD16C2×D1911yescharacteristic, complemented
219C2×D8—191no—
220C22×C8—191no—
221C22×C8—191no—
222#123—381no—
223#123—381no—
224C22⋊Q8—191no—
225C22⋊Q8—191no—
226C22⋊Q8—191no—
227C22⋊Q8C2×D1911yescharacteristic
228#121—191no—
229#121—191no—
230#121—191no—
231#121—191no—
232#120—381no—
233#120—381no—
234C4×D4—381no—
235C4×D4—381no—
236C4×D4—381no—
237C4×D4—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#103C2×D1911yescharacteristic, complemented
248#102—191no—
249#102—191no—
250#102—191no—
251#102C2×D1911yescharacteristic, complemented
252C22⋊C8—191no—
253C22⋊C8—191no—
254C22⋊C8—191no—
255C22⋊C8C2×D1911yescharacteristic
256C19#319111yescharacteristic, complemented, Sylow
257C24—191no—
258#41—41no—
259#41—41no—
260#41—761no—
261#41—761no—
262C2×Q8C22×D1911yescharacteristic
263C2×Q8C22×D1911yescharacteristic
264C2×D4—21no—
265C2×D4—191no—
266C2×D4—381no—
267C2×D4—381no—
268C2×D4—381no—
269C2×D4—381no—
270C2×D4—381no—
271C2×D4C22×D1911yescharacteristic
272C22×C4—21no—
273C22×C4—191no—
274C22×C4—191no—
275C22×C4—191no—
276C22×C4—191no—
277C22×C4—191no—
278C22×C4—381no—
279C22×C4—761no—
280C22×C4—761no—
281C22×C4C22×D1911yescharacteristic
282Q16—41no—
283SD16—41no—
284SD16—761no—
285D8—761no—
286C2×C8—191no—
287C2×C8—191no—
288C2×C8—761no—
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—191no—
314C23—191no—
315C23—382no—
316C23—381no—
317C23—761no—
318C23—761no—
319C23D4×D1911yescharacteristic
320Q8—21no—
321Q8—21no—
322Q8—21no—
323Q8—21no—
324D4—21no—
325D4—21no—
326D4—42no—
327D4—381no—
328D4—381no—
329D4—762no—
330D4—762no—
331D4—762no—
332D4—762no—
333D4—762no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—42no—
340C2×C4—191no—
341C2×C4—191no—
342C2×C4—381no—
343C2×C4—381no—
344C2×C4—381no—
345C2×C4—381no—
346C2×C4—381no—
347C2×C4—381no—
348C2×C4—381no—
349C2×C4—761no—
350C2×C4—761no—
351C2×C4—762no—
352C2×C4—761no—
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—192no—
366C22—381no—
367C22—381no—
368C22—381no—
369C22—381no—
370C22—381no—
371C22—764no—
372C22—761no—
373C22—761no—
374C22—761no—
375C22C2×D4×D1911yescharacteristic
376C4—21no—
377C4—41no—
378C4—41no—
379C4—41no—
380C4—381no—
381C4—381no—
382C4—761no—
383C4—761no—
384C4—761no—
385C4#1059743011yescharacteristic
386C4#1059743011yescharacteristic
387C2—41no—
388C2—81no—
389C2—382no—
390C2—761no—
391C2—1521no—
392C2#1192710411yescharacteristic
393C2#135×D1911yescharacteristic
394C2#1192734311yescharacteristic
subgroupG/H
centerC22C2×D4×D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#452C2
socleC22×C19C22×D4
hypercenter#452D19
hypocenterC19#3191
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
1. #11927057C2semidirect
2. #11927051C2semidirect
3. #11926883C2semidirect
4. #11926882C2semidirect
5. #11926869C2semidirect
6. #11926866C2semidirect
7. #11926782C2semidirect
8. #11926779C2semidirect
9. #11926776C2semidirect
10. #11926770C2semidirect
11. #11926705C2semidirect
12. #11926689C2semidirect
13. #11926688C2semidirect
14. C22⋊C8×D19C2semidirect
15. C19×#452C2semidirect
19. C2×Q16×C19C22semidirect
20. C2×SD16×C19C22semidirect
25. C2×#64527C22semidirect
30. C2×#64525C22semidirect
43. C19×#103C22semidirect
44. C19×#102C22semidirect
46. #10597292C22semidirect
47. #10597292C22semidirect
48. #10597292C22semidirect
49. #10597289C22semidirect
51. #10597278C22semidirect
52. #10597278C22semidirect
55. #10597275C22semidirect
56. #10597274C22semidirect
57. #10597265C22semidirect
58. #10597264C22semidirect
201. #452D19semidirect
216. C2×Q16C2×D19semidirect
218. C2×SD16C2×D19semidirect
247. #103C2×D19semidirect
251. #102C2×D19semidirect
256. C19#3191semidirect

Maximal subgroups

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

subgroupindex
#119270572
#119270512
#119268832
#119268822
#119268692
#119268662
#119267822
#119267792
#119267762
#119267702
#119267052
#119266892
#119266882
C22⋊C8×D192
C19×#4522
#319119