Finite Group Databasebeta

← #14573877

Subgroups — #14573877

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#11927145C211yesmaximal, characteristic, complemented
2#11927016C211yesmaximal, characteristic, complemented
3#11926870C211yesmaximal, characteristic, complemented
4#11926867C211yesmaximal, characteristic, complemented
5#11926846C211yesmaximal, characteristic, complemented
6#11926843C211yesmaximal, characteristic, complemented
7#11926738C211yesmaximal, characteristic, complemented
8#11926737C211yesmaximal, characteristic, complemented
9#11926679C211yesmaximal, characteristic, complemented
10#11926676C211yesmaximal, characteristic, complemented
11#11926657C211yesmaximal, characteristic, complemented
12C4×#64525C211yesmaximal, characteristic, complemented
13C4×#64525C211yesmaximal, characteristic, complemented
14#11926606C211yesmaximal, characteristic, complemented
15C19×#442C211yesmaximal, characteristic, complemented
16C2×D4×D19C2211yescharacteristic
17C2×D8×C19C2211yescharacteristic
18C4×D4×C19C2211yescharacteristic
19C4×D4×C19C2211yescharacteristic, complemented
20#10597386C2211yescharacteristic, complemented
21#10597384C2211yescharacteristic
22D4×Dic19C2211yescharacteristic
23C2×#64525C2211yescharacteristic
24C2×#64525C2211yescharacteristic
25#10597376—21no—
26#10597375—21no—
27C4×C22⋊D19—21no—
28C2×(C2×D19)⋊C4—21no—
29C2×D152C2211yescharacteristic
30#10597341C2211yescharacteristic
31#10597339C2211yescharacteristic
32#10597338C2211yescharacteristic
33#10597336C2211yescharacteristic, complemented
34#10597330—21no—
35#10597329—21no—
36(C22⋊D19)⋊C4—21no—
37C22⋊C4×D19—21no—
38C4×D76C2211yescharacteristic
39C4×D76C2211yescharacteristic, complemented
40#10597318C2211yescharacteristic
41C19×#106C2211yescharacteristic, complemented
42C19×#102C2211yescharacteristic
43C19×#102C2211yescharacteristic, complemented
44C19×#97C2211yescharacteristic, complemented
45#10597289C2211yescharacteristic
46#10597289C2211yescharacteristic, complemented
47#10597278C2211yescharacteristic
48#10597278C2211yescharacteristic, complemented
49(C2×D19)⋊C8C2211yescharacteristic
50(C2×D19)⋊C8C2211yescharacteristic
51#10597274C2211yescharacteristic, complemented
52Dic19⋊C8C2211yescharacteristic, complemented
53Dic19⋊C8C2211yescharacteristic, complemented
54#10597266C2211yescharacteristic
55#10597266C2211yescharacteristic, complemented
56#10597264C2211yescharacteristic, complemented
57#10597264C2211yescharacteristic, complemented
58C4×C19⋊C8C2211yescharacteristic, complemented
59C23×D19—21no—
60C2×D4×C19C2311yescharacteristic
61C2×D4×C19C2311yescharacteristic
62C22×C4×C19—21no—
63C22×C4×C19—21no—
64C2×C22⋊D19—21no—
65C2×C22⋊D19—21no—
66C2×C22⋊D19—21no—
67C2×C22⋊D19—21no—
68C22×Dic19—21no—
69D4×D19—22no—
70D4×D19—22no—
71C2×D76—21no—
72C2×D76C2311yescharacteristic
73C2×D76C2311yescharacteristic
74C2×C4×D19—21no—
75C2×C4×D19—21no—
76C2×C4×D19—21no—
77C2×C4×D19C2311yescharacteristic
78D8×C19—22no—
79C2×C8×C19C2311yescharacteristic
80C2×C8×C19C2311yescharacteristic
81C4⋊C4×C19C2311yescharacteristic
82C4⋊C4×C19C2311yescharacteristic
83C22⋊C4×C19—21no—
84C22⋊C4×C19—21no—
85C42×C19C2311yescharacteristic
86C22⋊Dic19—21no—
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)⋊C4D411yescharacteristic
96(C2×D19)⋊C4D411yescharacteristic
97C4⋊Dic19—21no—
98C4⋊Dic19C2311yescharacteristic
99C4⋊Dic19C2311yescharacteristic
100Dic19⋊C4—21no—
101Dic19⋊C4D411yescharacteristic
102Dic19⋊C4D411yescharacteristic
103C4×Dic19—21no—
104C4×Dic19C2311yescharacteristic
105C2×C19⋊C8C2311yescharacteristic
106C2×C19⋊C8C2311yescharacteristic
107D152—22no—
108C23×C19—21no—
109C23×C19—21no—
110C22×D19—21no—
111C22×D19—24no—
112C22×D19—21no—
113C22×D19—81no—
114C22×D19—81no—
115C22×D19C2×D411yescharacteristic
116D4×C19—21no—
117D4×C19—21no—
118D4×C19—21no—
119D4×C19#4112yes—
120C2×C4×C19—21no—
121C2×C4×C19—21no—
122C2×C4×C19—81no—
123C2×C4×C19—81no—
124C2×C4×C19C2×D411yescharacteristic
125C2×C4×C19C2×D411yescharacteristic
126C2×C4×C19C2411yescharacteristic
127C22⋊D19—24no—
128C22⋊D19—81no—
129C22⋊D19—81no—
130C22⋊D19—81no—
131C2×Dic19—21no—
132C2×Dic19—21no—
133C2×Dic19—81no—
134C2×Dic19C2×D411yescharacteristic
135C2×Dic19C2×D411yescharacteristic
136C2×Dic19C2×D411yescharacteristic
137D76—21no—
138D76—21no—
139D76—21no—
140D76—81no—
141D76#4112yes—
142C4×D19—21no—
143C4×D19—21no—
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×C19—41no—
156C22×C19—41no—
157C22×C19—41no—
158C22×C19C22×D411yescharacteristic
159C2×D19—21no—
160C2×D19—22no—
161C2×D19—21no—
162C2×D19—21no—
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×C19C2×#4111yescharacteristic
174C4×C19C2×#4111yescharacteristic
175Dic19—21no—
176Dic19—21no—
177Dic19—21no—
178Dic19—41no—
179Dic19—41no—
180#540—191no—
181#518—191no—
182#482—191no—
183#482—191no—
184#478—191no—
185#478—191no—
186#459—191no—
187#459—191no—
188#447—191no—
189#447—191no—
190#442—191no—
191#442D1911yescharacteristic, complemented
192C4×D8—191no—
193C4×D8—191no—
194#433—191no—
195C2×C19—42no—
196C2×C19—81no—
197C2×C19#52511yescharacteristic
198C2×C19#57611yescharacteristic
199C2×C19#57611yescharacteristic
200D19—41no—
201D19—42no—
202D19—81no—
203C22×D4—191no—
204C2×D8—191no—
205C2×D8—191no—
206C2×D8—191no—
207C2×D8C2×D1911yescharacteristic
208#127—191no—
209#125—191no—
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—381no—
221C4×D4—381no—
222C4×D4C2×D1911yescharacteristic
223C4×D4C2×D1911yescharacteristic, complemented
224#117—191no—
225#117—191no—
226C2×C22⋊C4—381no—
227C2×C22⋊C4—381no—
228#107—191no—
229#107—191no—
230#106—191no—
231#106C2×D1911yescharacteristic, complemented
232C4⋊C8—191no—
233C4⋊C8—191no—
234#102—191no—
235#102—191no—
236#102—191no—
237#102—191no—
238#102—191no—
239#102—191no—
240#102C2×D1911yescharacteristic
241#102C2×D1911yescharacteristic, complemented
242C22⋊C8—191no—
243C22⋊C8—191no—
244#97C2×D1911yescharacteristic, complemented
245C4×C8—191no—
246C19#312211yescharacteristic, complemented, Sylow
247C24—381no—
248C2×D4—191no—
249C2×D4—191no—
250C2×D4—381no—
251C2×D4—381no—
252C2×D4—381no—
253C2×D4—381no—
254C2×D4—382no—
255C2×D4—382no—
256C2×D4—381no—
257C2×D4C22×D1911yescharacteristic
258C2×D4C22×D1911yescharacteristic
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—191no—
262C22×C4—381no—
263C22×C4—381no—
264C22×C4—381no—
265C22×C4—381no—
266D8—22no—
267D8—382no—
268D8—382no—
269D8—382no—
270C2×C8—191no—
271C2×C8—191no—
272C2×C8C22×D1911yescharacteristic
273C2×C8C22×D1911yescharacteristic
274C4⋊C4—191no—
275C4⋊C4—191no—
276C4⋊C4—191no—
277C4⋊C4—191no—
278C4⋊C4—381no—
279C4⋊C4—381no—
280C4⋊C4C22×D1911yescharacteristic
281C4⋊C4C22×D1911yescharacteristic
282C22⋊C4—21no—
283C22⋊C4—21no—
284C22⋊C4—191no—
285C22⋊C4—191no—
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—21no—
298C23—191no—
299C23—384no—
300C23—381no—
301C23—381no—
302C23—1521no—
303C23—1521no—
304D4—21no—
305D4—21no—
306D4—21no—
307D4—192no—
308D4—384no—
309D4—381no—
310D4—381no—
311D4—381no—
312D4—1521no—
313D4—1521no—
314D4—1521no—
315D4—1521no—
316D4#6454112yes—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—81no—
320C2×C4—81no—
321C2×C4—191no—
322C2×C4—191no—
323C2×C4—191no—
324C2×C4—381no—
325C2×C4—381no—
326C2×C4—381no—
327C2×C4—381no—
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—41no—
343C22—41no—
344C22—41no—
345C22—381no—
346C22—382no—
347C22—381no—
348C22—381no—
349C22—761no—
350C22—761no—
351C22—761no—
352C22—761no—
353C22—761no—
354C22—1524no—
355C22C2×D4×D1911yescharacteristic
356C4—21no—
357C4—21no—
358C4—41no—
359C4—41no—
360C4—381no—
361C4—381no—
362C4—381no—
363C4—761no—
364C4—761no—
365C4C2×#6454111yescharacteristic
366C4#41×D1911yescharacteristic
367C2—42no—
368C2—81no—
369C2—761no—
370C2—762no—
371C2—1521no—
372C2#1192705311yescharacteristic
373C2#1192734811yescharacteristic
374C2#1192734811yescharacteristic
subgroupG/H
centerC22C2×D4×D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#442C2
socleC22×C19C22×D4
hypercenter#442D19
hypocenterC19#3122
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
1. #11927145C2semidirect
2. #11927016C2semidirect
3. #11926870C2semidirect
4. #11926867C2semidirect
5. #11926846C2semidirect
6. #11926843C2semidirect
7. #11926738C2semidirect
8. #11926737C2semidirect
9. #11926679C2semidirect
10. #11926676C2semidirect
11. #11926657C2semidirect
12. C4×#64525C2semidirect
13. C4×#64525C2semidirect
14. #11926606C2semidirect
15. C19×#442C2semidirect
19. C4×D4×C19C22semidirect
20. #10597386C22semidirect
33. #10597336C22semidirect
39. C4×D76C22semidirect
41. C19×#106C22semidirect
43. C19×#102C22semidirect
44. C19×#97C22semidirect
46. #10597289C22semidirect
48. #10597278C22semidirect
51. #10597274C22semidirect
52. Dic19⋊C8C22semidirect
53. Dic19⋊C8C22semidirect
55. #10597266C22semidirect
56. #10597264C22semidirect
57. #10597264C22semidirect
58. C4×C19⋊C8C22semidirect
191. #442D19semidirect
223. C4×D4C2×D19semidirect
231. #106C2×D19semidirect
241. #102C2×D19semidirect
244. #97C2×D19semidirect
246. C19#3122semidirect

Maximal subgroups

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

subgroupindex
#119271452
#119270162
#119268702
#119268672
#119268462
#119268432
#119267382
#119267372
#119266792
#119266762
#119266572
C4×#645252
#119266062
C19×#4422
#312219