Finite Group Databasebeta

← #14573880

Subgroups — #14573880

Order 2432.

418 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11927150C211yesmaximal, characteristic, complemented
2#11927016C211yesmaximal, characteristic, complemented
3#11926871C211yesmaximal, characteristic, complemented
4#11926870C211yesmaximal, characteristic, complemented
5#11926841C211yesmaximal, characteristic, complemented
6#11926740C211yesmaximal, characteristic, complemented
7#11926739C211yesmaximal, characteristic, complemented
8#11926679C211yesmaximal, characteristic, complemented
9#11926679C211yesmaximal, characteristic, complemented
10#11926655C211yesmaximal, characteristic, complemented
11#11926653C211yesmaximal, characteristic, complemented
12#11926626C211yesmaximal, characteristic, complemented
13#11926624C211yesmaximal, characteristic, complemented
14#11926604C211yesmaximal, characteristic, complemented
15C19×#478C211yesmaximal, characteristic, complemented
16C2×D4×D19C2211yescharacteristic
17C19×#125C2211yescharacteristic, complemented
18C4×D4×C19C2211yescharacteristic
19D4×Dic19C2211yescharacteristic
20C2×#64525C2211yescharacteristic
21C2×#64525C2211yescharacteristic
22C4×C22⋊D19—21no—
23C2×(C2×D19)⋊C4—21no—
24C2×D152C2211yescharacteristic
25C2×D152C2211yescharacteristic
26#10597341—21no—
27#10597341—21no—
28#10597341C2211yescharacteristic
29#10597341C2211yescharacteristic
30#10597340—21no—
31#10597340—21no—
32#10597339C2211yescharacteristic
33#10597339C2211yescharacteristic, complemented
34#10597339C2211yescharacteristic, complemented
35#10597338C2211yescharacteristic
36(C22⋊D19)⋊C4—21no—
37C22⋊C4×D19—21no—
38#10597320C2211yescharacteristic, complemented
39C4×D76C2211yescharacteristic
40#10597318C2211yescharacteristic
41C19×#107C2211yescharacteristic, complemented
42C19×#106C2211yescharacteristic, complemented
43C19×C4⋊C8C2211yescharacteristic, complemented
44C19×#102C2211yescharacteristic
45C19×#102C2211yescharacteristic
46#10597278C2211yescharacteristic, complemented
47#10597278C2211yescharacteristic, complemented
48(C2×D19)⋊C8C2211yescharacteristic
49(C2×D19)⋊C8C2211yescharacteristic
50#10597272C2211yescharacteristic, complemented
51C8×Dic19C2211yescharacteristic, complemented
52#10597266C2211yescharacteristic
53#10597266C2211yescharacteristic
54#10597266C2211yescharacteristic, complemented
55#10597266C2211yescharacteristic, complemented
56#10597265C2211yescharacteristic, complemented
57#10597264C2211yescharacteristic, complemented
58C4⋊(C19⋊C8)C2211yescharacteristic, complemented
59C23×D19—21no—
60C2×D4×C19C2311yescharacteristic
61C22×C4×C19—21no—
62C2×C22⋊D19—21no—
63C22×Dic19—21no—
64D4×D19—22no—
65D4×D19—22no—
66C2×D76—21no—
67C2×D76—21no—
68C2×D76—21no—
69C2×D76—21no—
70C2×D76C2311yescharacteristic
71C2×D76C2311yescharacteristic
72C2×D76C2311yescharacteristic
73C2×C4×D19—21no—
74C2×C4×D19—21no—
75C2×C4×D19—21no—
76C2×C4×D19—21no—
77C2×C4×D19C2311yescharacteristic
78C2×C8×C19C2311yescharacteristic
79C2×C8×C19C2311yescharacteristic
80C4⋊C4×C19—21no—
81C4⋊C4×C19—21no—
82C4⋊C4×C19C2311yescharacteristic
83C4⋊C4×C19C2311yescharacteristic
84C4⋊C4×C19C2311yescharacteristic
85C22⋊C4×C19—21no—
86C42×C19C2311yescharacteristic
87C22⋊Dic19—21no—
88#64525—22no—
89#64525—22no—
90(C2×D19)⋊C4—21no—
91(C2×D19)⋊C4—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)⋊C4D411yescharacteristic
98(C2×D19)⋊C4D411yescharacteristic
99C4⋊Dic19C2311yescharacteristic
100Dic19⋊C4D411yescharacteristic
101Dic19⋊C4D411yescharacteristic
102C4×Dic19—21no—
103C4×Dic19C2311yescharacteristic
104C2×C19⋊C8C2311yescharacteristic
105C2×C19⋊C8C2311yescharacteristic
106D152—22no—
107D152—22no—
108C23×C19—21no—
109C22×D19—21no—
110C22×D19—24no—
111C22×D19—21no—
112C22×D19—21no—
113C22×D19—81no—
114C22×D19—81no—
115C22×D19C2×D411yescharacteristic
116D4×C19—21no—
117D4×C19#4112yes—
118C2×C4×C19—21no—
119C2×C4×C19—21no—
120C2×C4×C19—21no—
121C2×C4×C19—81no—
122C2×C4×C19C2×D411yescharacteristic
123C2×C4×C19C2×D411yescharacteristic
124C2×C4×C19C2411yescharacteristic
125C22⋊D19—24no—
126C2×Dic19—21no—
127C2×Dic19—81no—
128C2×Dic19C2×D411yescharacteristic
129C2×Dic19C2×D411yescharacteristic
130C2×Dic19C2×D411yescharacteristic
131D76—21no—
132D76—21no—
133D76—21no—
134D76—21no—
135D76—21no—
136D76—81no—
137D76—81no—
138D76—81no—
139D76—81no—
140D76#4112yes—
141C4×D19—21no—
142C4×D19—21no—
143C4×D19—81no—
144C4×D19—81no—
145C4×D19—81no—
146C4×D19—81no—
147C8×C19—21no—
148C8×C19—21no—
149C19⋊C8—21no—
150C19⋊C8—21no—
151#3122—191nomaximal, Sylow
152C22×C19—22no—
153C22×C19—41no—
154C22×C19—41no—
155C22×C19C22×D411yescharacteristic
156C2×D19—21no—
157C2×D19—22no—
158C2×D19—21no—
159C2×D19—21no—
160C2×D19—41no—
161C2×D19—41no—
162C2×D19—41no—
163C2×D19—41no—
164C2×D19—41no—
165C2×D19—41no—
166C2×D19—41no—
167C2×D19—41no—
168C2×D19—84no—
169C4×C19—21no—
170C4×C19—21no—
171C4×C19—41no—
172C4×C19—41no—
173C4×C19—41no—
174C4×C19C2×#4111yescharacteristic
175C4×C19C2×#4111yescharacteristic
176Dic19—21no—
177Dic19—21no—
178Dic19—21no—
179Dic19—41no—
180#540—191no—
181#518—191no—
182#482—191no—
183#482—191no—
184#478—191no—
185#478D1911yescharacteristic, complemented
186#459—191no—
187#459—191no—
188#447—191no—
189#447—191no—
190#442—191no—
191#442—191no—
192C4×D8—191no—
193C4×D8—191no—
194#433—191no—
195C2×C19—42no—
196C2×C19#52511yescharacteristic
197C2×C19#57611yescharacteristic
198C2×C19#57611yescharacteristic
199D19—41no—
200D19—42no—
201D19—81no—
202D19—81no—
203C22×D4—191no—
204C2×D8—191no—
205C2×D8—191no—
206C2×D8—191no—
207C2×D8—191no—
208#127—191no—
209#125C2×D1911yescharacteristic, complemented
210#123—381no—
211#123—381no—
212#121—191no—
213#121—191no—
214#121—381no—
215#121—381no—
216C4×D4—191no—
217C4×D4—191no—
218C4×D4—191no—
219C4×D4—191no—
220C4×D4—191no—
221C4×D4—381no—
222C4×D4—381no—
223C4×D4C2×D1911yescharacteristic
224#117—191no—
225#117—191no—
226C2×C22⋊C4—381no—
227C2×C22⋊C4—381no—
228#107—191no—
229#107C2×D1911yescharacteristic, complemented
230#106—191no—
231#106C2×D1911yescharacteristic, complemented
232C4⋊C8—191no—
233C4⋊C8C2×D1911yescharacteristic, complemented
234#102—191no—
235#102—191no—
236#102—191no—
237#102—191no—
238#102—191no—
239#102—191no—
240#102C2×D1911yescharacteristic
241#102C2×D1911yescharacteristic
242C22⋊C8—191no—
243C22⋊C8—191no—
244#97—191no—
245C4×C8—191no—
246C19#312211yescharacteristic, complemented, Sylow
247C24—381no—
248C2×D4—191no—
249C2×D4—191no—
250C2×D4—191no—
251C2×D4—381no—
252C2×D4—381no—
253C2×D4—381no—
254C2×D4—382no—
255C2×D4—382no—
256C2×D4—381no—
257C2×D4—381no—
258C2×D4C22×D1911yescharacteristic
259C22×C4—21no—
260C22×C4—191no—
261C22×C4—381no—
262C22×C4—381no—
263C22×C4—381no—
264C22×C4—381no—
265C22×C4—381no—
266D8—382no—
267D8—382no—
268D8—382no—
269D8—382no—
270C2×C8—191no—
271C2×C8—191no—
272C2×C8C22×D1911yescharacteristic
273C2×C8C22×D1911yescharacteristic
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—191no—
277C4⋊C4—191no—
278C4⋊C4—191no—
279C4⋊C4C22×D1911yescharacteristic
280C4⋊C4C22×D1911yescharacteristic
281C4⋊C4C22×D1911yescharacteristic
282C22⋊C4—21no—
283C22⋊C4—191no—
284C22⋊C4—191no—
285C22⋊C4—381no—
286C22⋊C4—381no—
287C22⋊C4—381no—
288C22⋊C4—381no—
289C22⋊C4—381no—
290C22⋊C4—381no—
291C22⋊C4—381no—
292C22⋊C4—381no—
293C42—191no—
294C42—381no—
295C42C22×D1911yescharacteristic
296C23—21no—
297C23—191no—
298C23—384no—
299C23—381no—
300C23—381no—
301C23—381no—
302C23—1521no—
303C23—1521no—
304D4—21no—
305D4—192no—
306D4—384no—
307D4—381no—
308D4—381no—
309D4—381no—
310D4—381no—
311D4—381no—
312D4—1521no—
313D4—1521no—
314D4—1521no—
315D4—1521no—
316D4#6454512yes—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—81no—
321C2×C4—191no—
322C2×C4—191no—
323C2×C4—191no—
324C2×C4—381no—
325C2×C4—381no—
326C2×C4—381no—
327C2×C4—1521no—
328C2×C4—1521no—
329C2×C4—1521no—
330C2×C4—1521no—
331C2×C4—1521no—
332C2×C4D4×D1911yescharacteristic
333C2×C4D4×D1911yescharacteristic
334C2×C4C23×D1911yescharacteristic
335C8—21no—
336C8—21no—
337C8—381no—
338C8—381no—
339C22—22no—
340C22—41no—
341C22—41no—
342C22—381no—
343C22—382no—
344C22—381no—
345C22—381no—
346C22—761no—
347C22—761no—
348C22—761no—
349C22—761no—
350C22—761no—
351C22—761no—
352C22—761no—
353C22—761no—
354C22—1524no—
355C22C2×D4×D1911yescharacteristic
356C4—21no—
357C4—21no—
358C4—41no—
359C4—41no—
360C4—41no—
361C4—381no—
362C4—381no—
363C4—381no—
364C4—761no—
365C4C2×#6454511yescharacteristic
366C4#41×D1911yescharacteristic
367C2—42no—
368C2—761no—
369C2—762no—
370C2—1521no—
371C2—1521no—
372C2#1192705711yescharacteristic
373C2#1192734611yescharacteristic
374C2#1192734811yescharacteristic
subgroupG/H
centerC22C2×D4×D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#478C2
socleC22×C19C22×D4
hypercenter#478D19
hypocenterC19#3122
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #11927150C2semidirect
2. #11927016C2semidirect
3. #11926871C2semidirect
4. #11926870C2semidirect
5. #11926841C2semidirect
6. #11926740C2semidirect
7. #11926739C2semidirect
8. #11926679C2semidirect
9. #11926679C2semidirect
10. #11926655C2semidirect
11. #11926653C2semidirect
12. #11926626C2semidirect
13. #11926624C2semidirect
14. #11926604C2semidirect
15. C19×#478C2semidirect
17. C19×#125C22semidirect
33. #10597339C22semidirect
34. #10597339C22semidirect
38. #10597320C22semidirect
41. C19×#107C22semidirect
42. C19×#106C22semidirect
43. C19×C4⋊C8C22semidirect
46. #10597278C22semidirect
47. #10597278C22semidirect
50. #10597272C22semidirect
51. C8×Dic19C22semidirect
54. #10597266C22semidirect
55. #10597266C22semidirect
56. #10597265C22semidirect
57. #10597264C22semidirect
58. C4⋊(C19⋊C8)C22semidirect
185. #478D19semidirect
209. #125C2×D19semidirect
229. #107C2×D19semidirect
231. #106C2×D19semidirect
233. C4⋊C8C2×D19semidirect
246. C19#3122semidirect

Maximal subgroups

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

subgroupindex
#119271502
#119270162
#119268712
#119268702
#119268412
#119267402
#119267392
#119266792
#119266552
#119266532
#119266262
#119266242
#119266042
C19×#4782
#312219