Finite Group Databasebeta

← #14573574

Subgroups — #14573574

Order 2432.

462 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#121×D19C211yesmaximal, characteristic
2#117×D19C211yesmaximal, characteristic, complemented
3#11926869C211yesmaximal, characteristic, complemented
4#11926868C211yesmaximal, characteristic, complemented
5#11926865C211yesmaximal, characteristic, complemented
6#11926864C211yesmaximal, characteristic, complemented
7#11926861C211yesmaximal, characteristic, complemented
8#11926859C211yesmaximal, characteristic, complemented
9#11926856C211yesmaximal, characteristic, complemented
10#11926585C211yesmaximal, characteristic, complemented
11#11926583C211yesmaximal, characteristic, complemented
12#11926547C211yesmaximal, characteristic, complemented
13#11926547C211yesmaximal, characteristic, complemented
14#11926506C211yesmaximal, characteristic, complemented
15C19×#482C211yesmaximal, characteristic, complemented
16C2×D4×D19—21no—
17C2×D4×D19C2211yescharacteristic
18C22×C4×D19C2211yescharacteristic
19C19×#121C2211yescharacteristic
20C19×#117C2211yescharacteristic, complemented
21#10597385—21no—
22#10597384C2211yescharacteristic
23#10597376C2211yescharacteristic
24#10597372C2211yescharacteristic, complemented
25C2×#64515C2211yescharacteristic
26C2×#64515C2211yescharacteristic
27#10597341C2211yescharacteristic
28#10597338C2211yescharacteristic
29#10597338C2211yescharacteristic
30C4⋊C4×D19C2211yescharacteristic
31C4⋊C4×D19C2211yescharacteristic, complemented
32C4⋊C4×D19C2211yescharacteristic, complemented
33#10597330—21no—
34C22⋊C4×D19—21no—
35C22⋊C4×D19—21no—
36#10597323—21no—
37#10597318—21no—
38C42×D19—21no—
39C19×#107C2211yescharacteristic, complemented
40C19×#106C2211yescharacteristic, complemented
41C19×#102C2211yescharacteristic, complemented
42C19×#102C2211yescharacteristic, complemented
43C19×C22⋊C8C2211yescharacteristic, complemented
44#10597289C2211yescharacteristic, complemented
45#10597289C2211yescharacteristic, complemented
46C22⋊(C19⋊C8)C2211yescharacteristic, complemented
47#10597278C2211yescharacteristic, complemented
48#10597278C2211yescharacteristic, complemented
49(C2×D19)⋊C8C2211yescharacteristic, complemented
50(C2×D19)⋊C8C2211yescharacteristic, complemented
51#10597275C2211yescharacteristic, complemented
52#10597274C2211yescharacteristic, complemented
53#10597266C2211yescharacteristic, complemented
54#10597266C2211yescharacteristic, complemented
55#10597265C2211yescharacteristic, complemented
56#10597265C2211yescharacteristic, complemented
57#10597264C2211yescharacteristic, complemented
58#10597264C2211yescharacteristic, complemented
59C23×D19—21no—
60C23×D19D411yescharacteristic
61C2×D4×C19—21no—
62C2×D4×C19C2311yescharacteristic
63C22×C4×C19C2311yescharacteristic
64C2×C22⋊D19—21no—
65C2×C22⋊D19—21no—
66C2×C22⋊D19—21no—
67C22×Dic19D411yescharacteristic
68D4×D19—22no—
69D4×D19—22no—
70D4×D19—44no—
71C2×D76—21no—
72C2×D76C2311yescharacteristic
73C2×C4×D19—22no—
74C2×C4×D19—22no—
75C2×C4×D19—21no—
76C2×C4×D19—21no—
77C2×C4×D19—21no—
78C2×C4×D19D411yescharacteristic
79C2×C4×D19D411yescharacteristic
80C2×C4×D19C2311yescharacteristic
81C2×C4×D19C2311yescharacteristic
82C2×C8×C19C2311yescharacteristic
83C2×C8×C19C2311yescharacteristic
84C4⋊C4×C19C2311yescharacteristic
85C4⋊C4×C19C2311yescharacteristic
86C4⋊C4×C19C2311yescharacteristic
87C22⋊C4×C19—21no—
88C22⋊C4×C19—21no—
89C42×C19—21no—
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—
96C4⋊Dic19C2311yescharacteristic
97C4⋊Dic19C2311yescharacteristic
98C4⋊Dic19C2311yescharacteristic
99Dic19⋊C4—21no—
100Dic19⋊C4—21no—
101Dic19⋊C4—21no—
102C4×Dic19—21no—
103C4×Dic19—21no—
104C4×Dic19—21no—
105C2×C19⋊C8C2311yescharacteristic
106C2×C19⋊C8C2311yescharacteristic
107#64515—22no—
108#64515—22no—
109C23×C19—21no—
110C23×C19C2×D411yescharacteristic
111C22×D19—22no—
112C22×D19—22no—
113C22×D19—21no—
114C22×D19—41no—
115C22×D19—42no—
116C22×D19—42no—
117C22×D19—42no—
118C22×D19C2×D411yescharacteristic
119C22×D19C2×D411yescharacteristic
120D4×C19—21no—
121D4×C19—21no—
122D4×C19—42no—
123C2×C4×C19—21no—
124C2×C4×C19—21no—
125C2×C4×C19—21no—
126C2×C4×C19—21no—
127C2×C4×C19—21no—
128C2×C4×C19C2×D411yescharacteristic
129C2×C4×C19C2411yescharacteristic
130C22⋊D19—42no—
131C22⋊D19—42no—
132C22⋊D19—42no—
133C2×Dic19—22no—
134C2×Dic19—21no—
135C2×Dic19—21no—
136C2×Dic19—21no—
137C2×Dic19C2×D411yescharacteristic
138C2×Dic19C2×D411yescharacteristic
139D76—21no—
140D76—21no—
141D76—42no—
142C4×D19—22no—
143C4×D19—21no—
144C4×D19—21no—
145C4×D19—22no—
146C4×D19—42no—
147C4×D19—42no—
148C4×D19—42no—
149C4×D19#4112yes—
150C4×D19#4112yes—
151C8×C19—21no—
152C8×C19—21no—
153C19⋊C8—21no—
154C19⋊C8—21no—
155#3094—191nomaximal, Sylow
156C22×C19—21no—
157C22×C19—21no—
158C22×C19—21no—
159C22×C19—41no—
160C22×C19—41no—
161C22×C19—41no—
162C22×C19C22×D411yescharacteristic
163C2×D19—21no—
164C2×D19—21no—
165C2×D19—21no—
166C2×D19—21no—
167C2×D19—44no—
168C2×D19—41no—
169C2×D19—41no—
170C2×D19—41no—
171C2×D19—84no—
172C2×D19#12312yes—
173C2×D19AGL(1,ℤ/8)12yes—
174C4×C19—21no—
175C4×C19—41no—
176C4×C19—41no—
177C4×C19—41no—
178C4×C19C2×#4111yescharacteristic
179C4×C19C2×#4111yescharacteristic
180Dic19—21no—
181Dic19—41no—
182Dic19—41no—
183Dic19—41no—
184Dic19#12312yes—
185C2×#121—191no—
186C2×#117—191no—
187#482—191no—
188#482—191no—
189#482—191no—
190#482D1911yescharacteristic, complemented
191#481—191no—
192#481—191no—
193#480—191no—
194#480—191no—
195#428—191no—
196#428—191no—
197#418—191no—
198#418—191no—
199#407—191no—
200C2×C19—41no—
201C2×C19—81no—
202C2×C19C2×#12311yescharacteristic
203C2×C19C2×AGL(1,ℤ/8)11yescharacteristic
204C2×C19#57511yescharacteristic
205D19—22no—
206D19—22no—
207D19—81no—
208C22×D4—191no—
209C22×D4—381no—
210C23×C4—191no—
211C2×M16—191no—
212C2×M16—191no—
213#121—191no—
214#121—191no—
215#121—191no—
216#121—381no—
217#121—381no—
218#121C2×D1911yescharacteristic
219#117—191no—
220#117—191no—
221#117—191no—
222#117—381no—
223#117—381no—
224#117C2×D1911yescharacteristic, complemented
225C2×C4⋊C4—191no—
226C2×C4⋊C4—191no—
227C2×C4⋊C4—191no—
228C2×C22⋊C4—381no—
229C2×C22⋊C4—381no—
230C2×C42—381no—
231#107—191no—
232#107—191no—
233#107—191no—
234#107C2×D1911yescharacteristic, complemented
235#106—191no—
236#106—191no—
237#106—191no—
238#106C2×D1911yescharacteristic, complemented
239#102—191no—
240#102—191no—
241#102—191no—
242#102—191no—
243#102—191no—
244#102—191no—
245#102C2×D1911yescharacteristic, complemented
246#102C2×D1911yescharacteristic, complemented
247C22⋊C8—191no—
248C22⋊C8—191no—
249C22⋊C8—191no—
250C22⋊C8C2×D1911yescharacteristic, complemented
251C19#309411yescharacteristic, complemented, Sylow
252C24—191no—
253C24—381no—
254C2×D4—21no—
255C2×D4—191no—
256C2×D4—381no—
257C2×D4—382no—
258C2×D4—382no—
259C2×D4—381no—
260C2×D4—381no—
261C2×D4—381no—
262C2×D4—764no—
263C2×D4C22×D1911yescharacteristic
264C22×C4—191no—
265C22×C4—191no—
266C22×C4—191no—
267C22×C4—191no—
268C22×C4—191no—
269C22×C4—382no—
270C22×C4—382no—
271C22×C4—381no—
272C22×C4—381no—
273C22×C4—381no—
274C22×C4C22×D1911yescharacteristic
275M16—382no—
276M16—382no—
277C2×C8—191no—
278C2×C8—191no—
279C2×C8C22×D1911yescharacteristic
280C2×C8C22×D1911yescharacteristic
281C4⋊C4—191no—
282C4⋊C4—191no—
283C4⋊C4—191no—
284C4⋊C4—381no—
285C4⋊C4—381no—
286C4⋊C4—381no—
287C4⋊C4C22×D1911yescharacteristic
288C4⋊C4C22×D1911yescharacteristic
289C4⋊C4C22×D1911yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—381no—
293C22⋊C4—381no—
294C22⋊C4—381no—
295C22⋊C4—381no—
296C22⋊C4—381no—
297C22⋊C4—381no—
298C42—21no—
299C42—381no—
300C42—381no—
301C42—381no—
302C23—21no—
303C23—191no—
304C23—191no—
305C23—382no—
306C23—382no—
307C23—381no—
308C23—761no—
309C23—762no—
310C23—762no—
311C23—762no—
312C23D4×D1911yescharacteristic
313D4—21no—
314D4—21no—
315D4—42no—
316D4—381no—
317D4—381no—
318D4—762no—
319D4—762no—
320D4—762no—
321D4—762no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—191no—
328C2×C4—192no—
329C2×C4—192no—
330C2×C4—191no—
331C2×C4—382no—
332C2×C4—382no—
333C2×C4—382no—
334C2×C4—381no—
335C2×C4—381no—
336C2×C4—381no—
337C2×C4—381no—
338C2×C4—381no—
339C2×C4—762no—
340C2×C4—762no—
341C2×C4—762no—
342C2×C4D4×D1911yescharacteristic
343C2×C4C23×D1911yescharacteristic
344C8—21no—
345C8—21no—
346C8—381no—
347C8—381no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—192no—
355C22—192no—
356C22—381no—
357C22—381no—
358C22—381no—
359C22—381no—
360C22—764no—
361C22—761no—
362C22—761no—
363C22—761no—
364C22—1524no—
365C22C2×D4×D1911yescharacteristic
366C4—21no—
367C4—41no—
368C4—41no—
369C4—41no—
370C4—192no—
371C4—381no—
372C4—761no—
373C4—761no—
374C4—761no—
375C4#41×D1911yescharacteristic
376C4#41×D1911yescharacteristic
377C2—41no—
378C2—81no—
379C2—382no—
380C2—382no—
381C2—1521no—
382C2#123×D1911yescharacteristic
383C2AGL(1,ℤ/8)×D1911yescharacteristic
384C2#1192734111yescharacteristic
subgroupG/H
centerC22C2×D4×D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#482C2
socleC22×C19C22×D4
prime radical#121×D19C2
hypercenter#482D19
hypocenterC19#3094
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
2. #117×D19C2semidirect
3. #11926869C2semidirect
4. #11926868C2semidirect
5. #11926865C2semidirect
6. #11926864C2semidirect
7. #11926861C2semidirect
8. #11926859C2semidirect
9. #11926856C2semidirect
10. #11926585C2semidirect
11. #11926583C2semidirect
12. #11926547C2semidirect
13. #11926547C2semidirect
14. #11926506C2semidirect
15. C19×#482C2semidirect
20. C19×#117C22semidirect
24. #10597372C22semidirect
31. C4⋊C4×D19C22semidirect
32. C4⋊C4×D19C22semidirect
39. C19×#107C22semidirect
40. C19×#106C22semidirect
41. C19×#102C22semidirect
42. C19×#102C22semidirect
43. C19×C22⋊C8C22semidirect
44. #10597289C22semidirect
45. #10597289C22semidirect
46. C22⋊(C19⋊C8)C22semidirect
47. #10597278C22semidirect
48. #10597278C22semidirect
49. (C2×D19)⋊C8C22semidirect
50. (C2×D19)⋊C8C22semidirect
51. #10597275C22semidirect
52. #10597274C22semidirect
53. #10597266C22semidirect
54. #10597266C22semidirect
55. #10597265C22semidirect
56. #10597265C22semidirect
57. #10597264C22semidirect
58. #10597264C22semidirect
190. #482D19semidirect
224. #117C2×D19semidirect
234. #107C2×D19semidirect
238. #106C2×D19semidirect
245. #102C2×D19semidirect
246. #102C2×D19semidirect
250. C22⋊C8C2×D19semidirect
251. C19#3094semidirect

Maximal subgroups

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

subgroupindex
#121×D192
#117×D192
#119268692
#119268682
#119268652
#119268642
#119268612
#119268592
#119268562
#119265852
#119265832
#119265472
#119265062
C19×#4822
#309419