Finite Group Databasebeta

← #14574414

Subgroups — #14574414

Order 2432.

420 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11927051C211yesmaximal, characteristic
2C22⋊Q8×D19C211yesmaximal, characteristic, complemented
3#11926886C211yesmaximal, characteristic, complemented
4#11926882C211yesmaximal, characteristic, complemented
5#11926873C211yesmaximal, characteristic, complemented
6#11926856C211yesmaximal, characteristic, complemented
7#11926784C211yesmaximal, characteristic, complemented
8#11926782C211yesmaximal, characteristic, complemented
9#11926772C211yesmaximal, characteristic, complemented
10#11926770C211yesmaximal, characteristic, complemented
11#11926706C211yesmaximal, characteristic, complemented
12#11926698C211yesmaximal, characteristic, complemented
13#11926681C211yesmaximal, characteristic, complemented
14C22⋊C8×D19C211yesmaximal, characteristic, complemented
15C19×#452C211yesmaximal, characteristic, complemented
16C2×#41×C19C2211yescharacteristic
17C2×Q8×D19C2211yescharacteristic
18C22×C4×D19C2211yescharacteristic
19C2×Q16×C19C2211yescharacteristic, complemented
20C2×SD16×C19C2211yescharacteristic, complemented
21C19×C22⋊Q8C2211yescharacteristic
22#10597392C2211yescharacteristic
23#10597392C2211yescharacteristic
24#10597392C2211yescharacteristic
25C2×#64528C2211yescharacteristic, complemented
26#10597384C2211yescharacteristic
27#10597384C2211yescharacteristic
28#10597383—21no—
29#10597381—21no—
30C2×#64526C2211yescharacteristic, complemented
31C4×C22⋊D19—21no—
32C4×C22⋊D19—21no—
33#10597372C2211yescharacteristic
34#10597370C2211yescharacteristic
35C2×C8×D19C2211yescharacteristic
36C2×C8×D19C2211yescharacteristic
37#10597343C2211yescharacteristic
38#10597342—21no—
39C4⋊C4×D19—21no—
40C4⋊C4×D19C2211yescharacteristic
41C22⋊C4×D19—21no—
42#10597324—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(C2×D19)⋊C8C2211yescharacteristic
52(C2×D19)⋊C8C2211yescharacteristic
53#10597275C2211yescharacteristic, complemented
54#10597274C2211yescharacteristic, complemented
55#10597273C2211yescharacteristic, complemented
56#10597273C2211yescharacteristic, 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—
70C22×Dic19D411yescharacteristic
71Q8×D19—41no—
72Q8×D19—41no—
73C2×C4×D19—21no—
74C2×C4×D19—21no—
75C2×C4×D19—41no—
76C2×C4×D19—41no—
77C2×C4×D19D411yescharacteristic
78C2×C4×D19D411yescharacteristic
79C2×C4×D19C2311yescharacteristic
80C2×C4×D19C2311yescharacteristic
81C2×Dic38—21no—
82C2×Dic38C2311yescharacteristic
83Q16×C19—41no—
84SD16×C19—41no—
85C2×C8×C19C2311yescharacteristic
86C2×C8×C19C2311yescharacteristic
87C4⋊C4×C19—21no—
88C4⋊C4×C19C2311yescharacteristic
89C22⋊C4×C19—21no—
90C22⋊Dic19—21no—
91C22⋊Dic19—21no—
92C22⋊Dic19—21no—
93C22⋊Dic19—21no—
94#64528—41no—
95#64526—41no—
96(C2×D19)⋊C4—21no—
97(C2×D19)⋊C4—21no—
98(C2×D19)⋊C4—21no—
99(C2×D19)⋊C4—21no—
100C4⋊Dic19—21no—
101C4⋊Dic19C2311yescharacteristic
102C4⋊Dic19C2311yescharacteristic
103C4⋊Dic19C2311yescharacteristic
104Dic19⋊C4—21no—
105Dic19⋊C4—21no—
106Dic19⋊C4—21no—
107Dic19⋊C4—21no—
108Dic19⋊C4—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—22no—
118C22×D19—41no—
119C22×D19C2×D411yescharacteristic
120C22×D19C2×D411yescharacteristic
121Q8×C19—21no—
122Q8×C19—21no—
123Q8×C19—21no—
124Q8×C19—21no—
125D4×C19—21no—
126D4×C19—21no—
127D4×C19—42no—
128C2×C4×C19—21no—
129C2×C4×C19—21no—
130C2×C4×C19—21no—
131C2×C4×C19—21no—
132C2×C4×C19—21no—
133C2×C4×C19—42no—
134C2×C4×C19C2×D411yescharacteristic
135C2×C4×C19C2411yescharacteristic
136C22⋊D19—42no—
137C22⋊D19—42no—
138C2×Dic19—21no—
139C2×Dic19—21no—
140C2×Dic19—21no—
141C2×Dic19—21no—
142C2×Dic19—41no—
143C2×Dic19C2×D411yescharacteristic
144C2×Dic19C2×D411yescharacteristic
145C4×D19—21no—
146C4×D19—21no—
147C4×D19—21no—
148C4×D19—21no—
149C4×D19—41no—
150C4×D19—41no—
151C4×D19—42no—
152C4×D19—42no—
153Dic38—21no—
154Dic38—21no—
155Dic38—42no—
156C8×C19—21no—
157C8×C19—21no—
158C19⋊C8—21no—
159C19⋊C8—21no—
160#3190—191nomaximal, Sylow
161C22×C19—21no—
162C22×C19—21no—
163C22×C19—21no—
164C22×C19—41no—
165C22×C19—41no—
166C22×C19—41no—
167C22×C19C22×D411yescharacteristic
168C2×D19—21no—
169C2×D19—21no—
170C2×D19—21no—
171C2×D19—21no—
172C2×D19—44no—
173C2×D19#13512yes—
174C2×D19#13712yes—
175C4×C19—21no—
176C4×C19—41no—
177C4×C19—41no—
178C4×C19—41no—
179C4×C19H(5,𝔽2)11yescharacteristic
180C4×C19H(5,𝔽2)11yescharacteristic
181Dic19—21no—
182Dic19—21no—
183Dic19—41no—
184Dic19—41no—
185Dic19—41no—
186Dic19—41no—
187#525—191no—
188C2×C22⋊Q8—191no—
189#485—191no—
190#485—191no—
191#483—191no—
192#480—191no—
193#467—191no—
194#467—191no—
195#465—191no—
196#465—191no—
197#452—191no—
198#452D1911yescharacteristic, complemented
199#451—191no—
200#448—191no—
201C2×C22⋊C8—191no—
202C2×C19—41no—
203C2×C19—81no—
204C2×C19#53411yescharacteristic
205C2×C19C2×#13511yescharacteristic
206C2×C19C2×#13711yescharacteristic
207D19—22no—
208D19—22no—
209C2×#41C2×D1911yescharacteristic
210C22×Q8—191no—
211C23×C4—191no—
212C2×Q16—191no—
213C2×Q16C2×D1911yescharacteristic, complemented
214C2×SD16—191no—
215C2×SD16C2×D1911yescharacteristic, complemented
216C22×C8—191no—
217C22×C8—191no—
218#123—381no—
219C22⋊Q8—191no—
220C22⋊Q8—191no—
221C22⋊Q8—191no—
222C22⋊Q8—191no—
223C22⋊Q8—191no—
224C22⋊Q8—381no—
225C22⋊Q8—381no—
226C22⋊Q8C2×D1911yescharacteristic
227#121—191no—
228#121—191no—
229#120—381no—
230C4×D4—381no—
231C4×D4—381no—
232#117—191no—
233C2×C4⋊C4—191no—
234C2×C4⋊C4—381no—
235C2×C22⋊C4—381no—
236#107—191no—
237#107—191no—
238#106—191no—
239#106—191no—
240#103—191no—
241#103—191no—
242#103—191no—
243#103—191no—
244#103—191no—
245#103C2×D1911yescharacteristic, complemented
246#102—191no—
247#102C2×D1911yescharacteristic, complemented
248C22⋊C8—191no—
249C22⋊C8—191no—
250C22⋊C8—191no—
251C22⋊C8C2×D1911yescharacteristic
252C19#319011yescharacteristic, complemented, Sylow
253C24—191no—
254#41—41no—
255#41—41no—
256C2×Q8—191no—
257C2×Q8—381no—
258C2×Q8—761no—
259C2×Q8—761no—
260C2×Q8C22×D1911yescharacteristic
261C2×Q8C22×D1911yescharacteristic
262C2×D4—21no—
263C2×D4—381no—
264C2×D4—381no—
265C2×D4C22×D1911yescharacteristic
266C22×C4—21no—
267C22×C4—191no—
268C22×C4—191no—
269C22×C4—191no—
270C22×C4—191no—
271C22×C4—191no—
272C22×C4—381no—
273C22×C4—381no—
274C22×C4—761no—
275C22×C4—761no—
276C22×C4C22×D1911yescharacteristic
277Q16—41no—
278Q16—761no—
279SD16—41no—
280SD16—761no—
281C2×C8—191no—
282C2×C8—191no—
283C2×C8—761no—
284C2×C8—761no—
285C2×C8C22×D1911yescharacteristic
286C2×C8C22×D1911yescharacteristic
287C4⋊C4—21no—
288C4⋊C4—191no—
289C4⋊C4—191no—
290C4⋊C4—191no—
291C4⋊C4—381no—
292C4⋊C4—381no—
293C4⋊C4—381no—
294C4⋊C4—381no—
295C4⋊C4—381no—
296C4⋊C4—381no—
297C4⋊C4C22×D1911yescharacteristic
298C22⋊C4—21no—
299C22⋊C4—381no—
300C22⋊C4—381no—
301C22⋊C4—381no—
302C22⋊C4—381no—
303C22⋊C4—381no—
304C22⋊C4—381no—
305C22⋊C4—381no—
306C22⋊C4—381no—
307C42—381no—
308C23—21no—
309C23—191no—
310C23—191no—
311C23—382no—
312C23—382no—
313C23—761no—
314C23D4×D1911yescharacteristic
315Q8—21no—
316Q8—21no—
317Q8—21no—
318Q8—21no—
319Q8—381no—
320Q8—381no—
321Q8—762no—
322D4—21no—
323D4—21no—
324D4—42no—
325D4—762no—
326D4—762no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—42no—
333C2×C4—191no—
334C2×C4—191no—
335C2×C4—381no—
336C2×C4—381no—
337C2×C4—381no—
338C2×C4—381no—
339C2×C4—381no—
340C2×C4—381no—
341C2×C4—381no—
342C2×C4—381no—
343C2×C4—761no—
344C2×C4—761no—
345C2×C4—762no—
346C2×C4—762no—
347C2×C4—761no—
348C2×C4D4×D1911yescharacteristic
349C2×C4C23×D1911yescharacteristic
350C8—21no—
351C8—21no—
352C8—381no—
353C8—381no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—192no—
361C22—192no—
362C22—381no—
363C22—381no—
364C22—381no—
365C22—381no—
366C22—764no—
367C22C2×D4×D1911yescharacteristic
368C4—21no—
369C4—41no—
370C4—41no—
371C4—41no—
372C4—381no—
373C4—381no—
374C4—761no—
375C4—761no—
376C4—761no—
377C4—761no—
378C4#1059743011yescharacteristic
379C4#1059743011yescharacteristic
380C2—41no—
381C2—81no—
382C2—382no—
383C2—382no—
384C2#1192710411yescharacteristic
385C2#135×D1911yescharacteristic
386C2#137×D1911yescharacteristic
subgroupG/H
centerC22C2×D4×D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#452C2
socleC22×C19C22×D4
prime radical#11927051C2
hypercenter#452D19
hypocenterC19#3190
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
2. C22⋊Q8×D19C2semidirect
3. #11926886C2semidirect
4. #11926882C2semidirect
5. #11926873C2semidirect
6. #11926856C2semidirect
7. #11926784C2semidirect
8. #11926782C2semidirect
9. #11926772C2semidirect
10. #11926770C2semidirect
11. #11926706C2semidirect
12. #11926698C2semidirect
13. #11926681C2semidirect
14. C22⋊C8×D19C2semidirect
15. C19×#452C2semidirect
19. C2×Q16×C19C22semidirect
20. C2×SD16×C19C22semidirect
25. C2×#64528C22semidirect
30. C2×#64526C22semidirect
43. C19×#103C22semidirect
44. C19×#102C22semidirect
46. #10597292C22semidirect
47. #10597292C22semidirect
48. #10597292C22semidirect
49. #10597289C22semidirect
53. #10597275C22semidirect
54. #10597274C22semidirect
55. #10597273C22semidirect
56. #10597273C22semidirect
57. #10597265C22semidirect
58. #10597264C22semidirect
198. #452D19semidirect
213. C2×Q16C2×D19semidirect
215. C2×SD16C2×D19semidirect
245. #103C2×D19semidirect
247. #102C2×D19semidirect
252. C19#3190semidirect

Maximal subgroups

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

subgroupindex
#119270512
C22⋊Q8×D192
#119268862
#119268822
#119268732
#119268562
#119267842
#119267822
#119267722
#119267702
#119267062
#119266982
#119266812
C22⋊C8×D192
C19×#4522
#319019