Finite Group Databasebeta

← #14575487

Subgroups — #14575487

Order 2432.

420 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11927240C211yesmaximal, characteristic, complemented
2#11927190C211yesmaximal, characteristic, complemented
3#11926899C211yesmaximal, characteristic, complemented
4#11926880C211yesmaximal, characteristic, complemented
5#11926869C211yesmaximal, characteristic, complemented
6#11926845C211yesmaximal, characteristic, complemented
7#11926780C211yesmaximal, characteristic, complemented
8#11926773C211yesmaximal, characteristic, complemented
9#11926760C211yesmaximal, characteristic, complemented
10#11926691C211yesmaximal, characteristic, complemented
11#11926680C211yesmaximal, characteristic, complemented
12C4×D152C211yesmaximal, characteristic, complemented
13#11926541C211yesmaximal, characteristic, complemented
14C2×#10597278C211yesmaximal, characteristic, complemented
15C8×D4×C19C211yesmaximal, characteristic, complemented
16C2×#64541C2211yescharacteristic
17C22×D76C2211yescharacteristic
18C22×C8×C19C2211yescharacteristic
19C22×C8×C19C2211yescharacteristic, complemented
20C4×D4×C19C2211yescharacteristic
21#10597385—21no—
22#10597383—21no—
23#10597376C2211yescharacteristic
24#10597376C2211yescharacteristic
25#10597376C2211yescharacteristic, complemented
26#10597372C2211yescharacteristic, complemented
27C2×C4⋊Dic19C2211yescharacteristic
28#10597370C2211yescharacteristic
29C2×D152C2211yescharacteristic
30C2×D152C2211yescharacteristic
31C2×#64516C2211yescharacteristic, complemented
32#10597344—21no—
33#10597340—21no—
34#10597330—21no—
35#10597329—21no—
36(C22⋊D19)⋊C4—21no—
37C22⋊C4×D19—21no—
38#10597321C2211yescharacteristic
39C4×D76C2211yescharacteristic
40C4×D76C2211yescharacteristic, complemented
41#10597316C2211yescharacteristic, complemented
42C19×C4⋊C8C2211yescharacteristic, complemented
43C19×C22⋊C8C2211yescharacteristic
44C19×C22⋊C8C2211yescharacteristic, complemented
45C4×C8×C19C2211yescharacteristic, complemented
46#10597278C2211yescharacteristic
47#10597278C2211yescharacteristic
48#10597278C2211yescharacteristic
49#10597278C2211yescharacteristic
50#10597278C2211yescharacteristic
51#10597278C2211yescharacteristic
52#10597278C2211yescharacteristic, complemented
53#10597275C2211yescharacteristic, complemented
54#10597275C2211yescharacteristic, complemented
55#10597274C2211yescharacteristic, complemented
56#10597273C2211yescharacteristic, complemented
57#10597273C2211yescharacteristic, complemented
58#10597273C2211yescharacteristic, complemented
59C23×D19—21no—
60C2×D4×C19D411yescharacteristic
61C22×C4×C19C2311yescharacteristic
62C22×C4×C19C2311yescharacteristic
63C2×C22⋊D19—21no—
64C2×C22⋊D19—21no—
65C2×C22⋊D19—21no—
66C2×C22⋊D19—21no—
67C22×Dic19—21no—
68#64541—22no—
69#64541—41no—
70C2×D76—22no—
71C2×D76—21no—
72C2×D76—41no—
73C2×D76C2311yescharacteristic
74C2×D76C2311yescharacteristic
75C2×D76C2311yescharacteristic
76C2×C4×D19—21no—
77C2×C4×D19—21no—
78C2×C4×D19—21no—
79C2×Dic38C2311yescharacteristic
80C2×C8×C19—41no—
81C2×C8×C19—41no—
82C2×C8×C19C2311yescharacteristic
83C2×C8×C19C2311yescharacteristic
84C2×C8×C19C2311yescharacteristic
85C2×C8×C19C2311yescharacteristic
86C4⋊C4×C19D411yescharacteristic
87C22⋊C4×C19D411yescharacteristic
88C22⋊C4×C19D411yescharacteristic
89C42×C19C2311yescharacteristic
90C22⋊Dic19—21no—
91C22⋊Dic19—21no—
92(C2×D19)⋊C4—21no—
93(C2×D19)⋊C4—21no—
94(C2×D19)⋊C4—21no—
95(C2×D19)⋊C4—21no—
96(C2×D19)⋊C4—21no—
97(C2×D19)⋊C4—21no—
98(C2×D19)⋊C4—21no—
99C4⋊Dic19—21no—
100C4⋊Dic19C2311yescharacteristic
101C4⋊Dic19C2311yescharacteristic
102C4⋊Dic19C2311yescharacteristic
103C4⋊Dic19C2311yescharacteristic
104Dic19⋊C4—21no—
105Dic19⋊C4—21no—
106Dic19⋊C4—21no—
107C4×Dic19—21no—
108D152—22no—
109D152—41no—
110#64516—41no—
111C23×C19C2×D411yescharacteristic
112C23×C19C2×D411yescharacteristic
113C22×D19—21no—
114C22×D19—21no—
115C22×D19—21no—
116C22×D19—42no—
117C22×D19—42no—
118C22×D19—81no—
119D4×C19—22no—
120C2×C4×C19—21no—
121C2×C4×C19—21no—
122C2×C4×C19—21no—
123C2×C4×C19—21no—
124C2×C4×C19C2×D411yescharacteristic
125C2×C4×C19C2×D411yescharacteristic
126C2×C4×C19C2×D411yescharacteristic
127C2×C4×C19C2×D411yescharacteristic
128C2×C4×C19C2411yescharacteristic
129C22⋊D19—42no—
130C22⋊D19—42no—
131C22⋊D19—81no—
132C22⋊D19—81no—
133C2×Dic19—21no—
134C2×Dic19—21no—
135C2×Dic19—21no—
136C2×Dic19—21no—
137C2×Dic19—21no—
138C2×Dic19—81no—
139D76—21no—
140D76—21no—
141D76—21no—
142D76—21no—
143D76—21no—
144D76—42no—
145D76#4112yes—
146C4×D19—42no—
147C4×D19—81no—
148C4×D19—81no—
149Dic38—21no—
150Dic38—21no—
151C8×C19—21no—
152C8×C19—21no—
153C8×C19—21no—
154C8×C19—21no—
155#3297—191nomaximal, Sylow
156C22×C19—21no—
157C22×C19—21no—
158C22×C19—21no—
159C22×C19—21no—
160C22×C19—21no—
161C22×C19#13512yes—
162C22×C19C22×D411yescharacteristic
163C2×D19—22no—
164C2×D19—41no—
165C2×D19—41no—
166C2×D19—41no—
167C2×D19—41no—
168C2×D19—41no—
169C2×D19—41no—
170C2×D19—41no—
171C2×D19—41no—
172C2×D19—84no—
173C4×C19—21no—
174C4×C19—21no—
175C4×C19—21no—
176C4×C19—21no—
177C4×C19C2×#4111yescharacteristic
178C4×C19H(5,𝔽2)11yescharacteristic
179Dic19—41no—
180Dic19—41no—
181Dic19—41no—
182Dic19—41no—
183Dic19—41no—
184#553—191no—
185#546—191no—
186#488—191no—
187#484—191no—
188#482—191no—
189#478—191no—
190#466—191no—
191#465—191no—
192#463—191no—
193#449—191no—
194#447—191no—
195C4×D8—191no—
196C8×D4D1911yescharacteristic, complemented
197#416—191no—
198C2×#102—191no—
199C2×C19—22no—
200C2×C19—41no—
201C2×C19#54611yescharacteristic
202C2×C19C2×#13511yescharacteristic
203C2×C19#57611yescharacteristic
204D19—42no—
205D19—81no—
206D19—81no—
207C2×#41—191no—
208C22×D4—191no—
209C2×SD16—191no—
210C2×D8—191no—
211C2×D8—191no—
212C22×C8C2×D1911yescharacteristic
213C22×C8C2×D1911yescharacteristic, complemented
214#126—381no—
215#125—191no—
216#124—191no—
217#123—381no—
218#123—381no—
219C22⋊Q8—191no—
220#121—191no—
221#121—191no—
222#121—191no—
223#121—381no—
224#121—381no—
225#120—381no—
226C4×D4—191no—
227C4×D4—191no—
228C4×D4—381no—
229C4×D4C2×D1911yescharacteristic
230#117—191no—
231C2×C4⋊C4—191no—
232C2×C22⋊C4—381no—
233#107—191no—
234#107—191no—
235#106—191no—
236C4⋊C8C2×D1911yescharacteristic, complemented
237#103—191no—
238#103—191no—
239#103—191no—
240#102—191no—
241#102—191no—
242#102—191no—
243#102—191no—
244#102—191no—
245#102—191no—
246#102—191no—
247C22⋊C8C2×D1911yescharacteristic
248C22⋊C8C2×D1911yescharacteristic, complemented
249C4×C8C2×D1911yescharacteristic, complemented
250C19#329711yescharacteristic, complemented, Sylow
251C24—381no—
252#41—382no—
253#41—761no—
254C2×Q8—191no—
255C2×D4—191no—
256C2×D4—191no—
257C2×D4—191no—
258C2×D4—382no—
259C2×D4—381no—
260C2×D4—381no—
261C2×D4—381no—
262C2×D4—381no—
263C2×D4—381no—
264C2×D4—761no—
265C2×D4D7611yescharacteristic
266C22×C4—381no—
267C22×C4—381no—
268C22×C4—381no—
269C22×C4—381no—
270C22×C4C22×D1911yescharacteristic
271C22×C4C22×D1911yescharacteristic
272SD16—761no—
273D8—382no—
274D8—761no—
275C2×C8—41no—
276C2×C8—41no—
277C2×C8C22×D1911yescharacteristic
278C2×C8C22×D1911yescharacteristic
279C2×C8C22×D1911yescharacteristic
280C2×C8C22×D1911yescharacteristic
281C4⋊C4—191no—
282C4⋊C4—191no—
283C4⋊C4—191no—
284C4⋊C4—191no—
285C4⋊C4—381no—
286C4⋊C4—381no—
287C4⋊C4—381no—
288C4⋊C4—381no—
289C4⋊C4D7611yescharacteristic
290C22⋊C4—381no—
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⋊C4D7611yescharacteristic
300C22⋊C4D7611yescharacteristic
301C42—381no—
302C42C22×D1911yescharacteristic
303C23—381no—
304C23—381no—
305C23—381no—
306C23—762no—
307C23—762no—
308C23—1521no—
309C23C2×D7611yescharacteristic
310C23C2×D7611yescharacteristic
311Q8—381no—
312Q8—381no—
313D4—22no—
314D4—192no—
315D4—381no—
316D4—381no—
317D4—381no—
318D4—381no—
319D4—381no—
320D4—762no—
321D4—762no—
322D4—762no—
323D4—1521no—
324D4—1521no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—381no—
330C2×C4—381no—
331C2×C4—381no—
332C2×C4—381no—
333C2×C4—381no—
334C2×C4—762no—
335C2×C4—1521no—
336C2×C4—1521no—
337C2×C4—1521no—
338C2×C4C2×D7611yescharacteristic
339C2×C4C2×D7611yescharacteristic
340C2×C4C2×D7611yescharacteristic
341C2×C4C2×D7611yescharacteristic
342C2×C4C23×D1911yescharacteristic
343C8—21no—
344C8—21no—
345C8—21no—
346C8—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—382no—
353C22—761no—
354C22—761no—
355C22—761no—
356C22—761no—
357C22—761no—
358C22—761no—
359C22—761no—
360C22—761no—
361C22—1524no—
362C22#1059735012yes—
363C22C22×D7611yescharacteristic
364C4—21no—
365C4—21no—
366C4—21no—
367C4—21no—
368C4—761no—
369C4—761no—
370C4—761no—
371C4—761no—
372C4—761no—
373C4#1059743011yescharacteristic
374C4#41×D1911yescharacteristic
375C2—22no—
376C2—41no—
377C2—762no—
378C2—1521no—
379C2—1521no—
380C2#1192718911yescharacteristic
381C2C2×#1059735011yescharacteristic
382C2#1192734911yescharacteristic
subgroupG/H
centerC22C22×D76
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC8×D4×C19C2
socleC22×C19C22×D4
hypercenterC8×D4D19
hypocenterC19#3297
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4

Complements

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

NH ≅ G/Ntype
1. #11927240C2semidirect
2. #11927190C2semidirect
3. #11926899C2semidirect
4. #11926880C2semidirect
5. #11926869C2semidirect
6. #11926845C2semidirect
7. #11926780C2semidirect
8. #11926773C2semidirect
9. #11926760C2semidirect
10. #11926691C2semidirect
11. #11926680C2semidirect
12. C4×D152C2semidirect
13. #11926541C2semidirect
14. C2×#10597278C2semidirect
15. C8×D4×C19C2semidirect
19. C22×C8×C19C22semidirect
25. #10597376C22semidirect
26. #10597372C22semidirect
31. C2×#64516C22semidirect
40. C4×D76C22semidirect
41. #10597316C22semidirect
42. C19×C4⋊C8C22semidirect
44. C19×C22⋊C8C22semidirect
45. C4×C8×C19C22semidirect
52. #10597278C22semidirect
53. #10597275C22semidirect
54. #10597275C22semidirect
55. #10597274C22semidirect
56. #10597273C22semidirect
57. #10597273C22semidirect
58. #10597273C22semidirect
196. C8×D4D19semidirect
213. C22×C8C2×D19semidirect
236. C4⋊C8C2×D19semidirect
248. C22⋊C8C2×D19semidirect
249. C4×C8C2×D19semidirect
250. C19#3297semidirect

Maximal subgroups

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

subgroupindex
#119272402
#119271902
#119268992
#119268802
#119268692
#119268452
#119267802
#119267732
#119267602
#119266912
#119266802
C4×D1522
#119265412
C2×#105972782
C8×D4×C192
#329719