Finite Group Databasebeta

← #14574444

Subgroups — #14574444

Order 2432.

466 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11927054C211yesmaximal, characteristic, complemented
2#121×D19C211yesmaximal, characteristic, complemented
3#11926876C211yesmaximal, characteristic, complemented
4#11926870C211yesmaximal, characteristic, complemented
5#11926866C211yesmaximal, characteristic, complemented
6#11926856C211yesmaximal, characteristic, complemented
7#11926795C211yesmaximal, characteristic, complemented
8#11926790C211yesmaximal, characteristic, complemented
9#11926788C211yesmaximal, characteristic, complemented
10#11926696C211yesmaximal, characteristic, complemented
11#11926690C211yesmaximal, characteristic, complemented
12#11926686C211yesmaximal, characteristic, complemented
13#11926676C211yesmaximal, characteristic, complemented
14#11926507C211yesmaximal, characteristic, complemented
15C19×#469C211yesmaximal, characteristic, complemented
16C2×#64543C2211yescharacteristic, complemented
17C2×D4×D19—21no—
18C2×D4×D19C2211yescharacteristic
19C22×C4×D19C2211yescharacteristic
20C2×D8×C19C2211yescharacteristic, complemented
21C2×M16×C19C2211yescharacteristic, complemented
22C19×#121C2211yescharacteristic
23C19×#121C2211yescharacteristic, complemented
24#10597385—21no—
25#10597384C2211yescharacteristic
26#10597384C2211yescharacteristic
27#10597383—21no—
28D4×Dic19—21no—
29C2×#64526C2211yescharacteristic, complemented
30C2×#64525C2211yescharacteristic, complemented
31#10597376C2211yescharacteristic
32#10597370C2211yescharacteristic, complemented
33C2×#64520C2211yescharacteristic, complemented
34C2×#64516C2211yescharacteristic, complemented
35#10597343C2211yescharacteristic
36#10597341C2211yescharacteristic
37#10597338C2211yescharacteristic, complemented
38C4⋊C4×D19C2211yescharacteristic
39#10597330—21no—
40#10597329—21no—
41(C22⋊D19)⋊C4—21no—
42C22⋊C4×D19—21no—
43C19×#106C2211yescharacteristic, complemented
44C19×#102C2211yescharacteristic, complemented
45C19×#102C2211yescharacteristic, complemented
46#10597289C2211yescharacteristic, complemented
47#10597289C2211yescharacteristic, complemented
48#10597278C2211yescharacteristic, complemented
49(C2×D19)⋊C8C2211yescharacteristic
50(C2×D19)⋊C8C2211yescharacteristic
51(C2×D19)⋊C8C2211yescharacteristic, complemented
52(C2×D19)⋊C8C2211yescharacteristic, complemented
53#10597275C2211yescharacteristic, complemented
54#10597273C2211yescharacteristic, complemented
55#10597267C2211yescharacteristic, complemented
56#10597266C2211yescharacteristic, complemented
57#10597265C2211yescharacteristic, complemented
58#10597264C2211yescharacteristic, complemented
59C23×D19—21no—
60C23×D19D411yescharacteristic
61C2×D4×C19—21no—
62C2×D4×C19—21no—
63C2×D4×C19C2311yescharacteristic
64C2×D4×C19C2311yescharacteristic
65C22×C4×C19C2311yescharacteristic
66C2×C22⋊D19—21no—
67C2×C22⋊D19—21no—
68C2×C22⋊D19—21no—
69C2×C22⋊D19—21no—
70C2×C22⋊D19—21no—
71C22×Dic19—21no—
72C22×Dic19D411yescharacteristic
73#64543—41no—
74#64543—41no—
75D4×D19—41no—
76D4×D19—41no—
77D4×D19—44no—
78C2×D76—21no—
79C2×D76C2311yescharacteristic
80C2×C4×D19—21no—
81C2×C4×D19—41no—
82C2×C4×D19—41no—
83C2×C4×D19D411yescharacteristic
84C2×C4×D19D411yescharacteristic
85C2×C4×D19C2311yescharacteristic
86C2×C4×D19C2311yescharacteristic
87C2×Dic38C2311yescharacteristic
88D8×C19—41no—
89M16×C19—41no—
90C2×C8×C19C2311yescharacteristic
91C2×C8×C19C2311yescharacteristic
92C4⋊C4×C19C2311yescharacteristic
93C4⋊C4×C19C2311yescharacteristic
94C22⋊C4×C19—21no—
95C22⋊C4×C19—21no—
96C22⋊Dic19—21no—
97C22⋊Dic19—21no—
98C22⋊Dic19—21no—
99#64526—41no—
100#64525—41no—
101(C2×D19)⋊C4—21no—
102(C2×D19)⋊C4—21no—
103(C2×D19)⋊C4—21no—
104(C2×D19)⋊C4—21no—
105C4⋊Dic19—21no—
106C4⋊Dic19C2311yescharacteristic
107C4⋊Dic19C2311yescharacteristic
108Dic19⋊C4—21no—
109Dic19⋊C4—21no—
110C4×Dic19—21no—
111#64520—41no—
112C2×C19⋊C8C2311yescharacteristic
113C2×C19⋊C8C2311yescharacteristic
114#64516—41no—
115C23×C19—21no—
116C23×C19—21no—
117C23×C19C2×D411yescharacteristic
118C22×D19—22no—
119C22×D19—21no—
120C22×D19—41no—
121C22×D19—41no—
122C22×D19—42no—
123C22×D19—42no—
124C22×D19—42no—
125C22×D19C2×D411yescharacteristic
126C22×D19C2×D411yescharacteristic
127D4×C19—21no—
128D4×C19—21no—
129D4×C19—21no—
130D4×C19—21no—
131D4×C19—42no—
132D4×C19—42no—
133C2×C4×C19—21no—
134C2×C4×C19—21no—
135C2×C4×C19—21no—
136C2×C4×C19—21no—
137C2×C4×C19C2×D411yescharacteristic
138C2×C4×C19C2411yescharacteristic
139C22⋊D19—42no—
140C22⋊D19—42no—
141C22⋊D19—42no—
142C22⋊D19—42no—
143C22⋊D19—42no—
144C2×Dic19—21no—
145C2×Dic19—21no—
146C2×Dic19—21no—
147C2×Dic19—41no—
148C2×Dic19—42no—
149C2×Dic19C2×D411yescharacteristic
150C2×Dic19C2×D411yescharacteristic
151D76—21no—
152D76—21no—
153D76—42no—
154C4×D19—21no—
155C4×D19—21no—
156C4×D19—21no—
157C4×D19—21no—
158C4×D19—41no—
159C4×D19—41no—
160C4×D19—42no—
161Dic38—21no—
162Dic38—21no—
163C8×C19—21no—
164C8×C19—21no—
165C19⋊C8—21no—
166C19⋊C8—21no—
167#3194—191nomaximal, Sylow
168C22×C19—21no—
169C22×C19—21no—
170C22×C19—21no—
171C22×C19—41no—
172C22×C19—41no—
173C22×C19—41no—
174C22×C19—41no—
175C22×C19—41no—
176C22×C19—41no—
177C22×C19C22×D411yescharacteristic
178C2×D19—21no—
179C2×D19—21no—
180C2×D19—21no—
181C2×D19—21no—
182C2×D19—21no—
183C2×D19—44no—
184C2×D19—41no—
185C2×D19—41no—
186C2×D19—41no—
187C2×D19—84no—
188C2×D19AGL(1,ℤ/8)12yes—
189C4×C19—21no—
190C4×C19—41no—
191C4×C19—41no—
192C4×C19H(5,𝔽2)11yescharacteristic
193C4×C19H(5,𝔽2)11yescharacteristic
194Dic19—21no—
195Dic19—21no—
196Dic19—41no—
197Dic19—41no—
198Dic19—41no—
199#525—191no—
200C2×#121—191no—
201#483—191no—
202#482—191no—
203#482—191no—
204#480—191no—
205#469—191no—
206#469D1911yescharacteristic, complemented
207#468—191no—
208#468—191no—
209#450—191no—
210#449—191no—
211#449—191no—
212#447—191no—
213#407—191no—
214C2×C19—41no—
215C2×C19—81no—
216C2×C19—81no—
217C2×C19#53411yescharacteristic
218C2×C19C2×AGL(1,ℤ/8)11yescharacteristic
219C2×C19#57511yescharacteristic
220D19—22no—
221D19—41no—
222D19—81no—
223C2×#41—191no—
224C22×D4—191no—
225C22×D4—381no—
226C23×C4—191no—
227C2×SD16—191no—
228C2×SD16—191no—
229C2×D8—191no—
230C2×D8C2×D1911yescharacteristic, complemented
231C2×M16—191no—
232C2×M16C2×D1911yescharacteristic, complemented
233#123—381no—
234C22⋊Q8—191no—
235C22⋊Q8—191no—
236#121—191no—
237#121—191no—
238#121—191no—
239#121—191no—
240#121—381no—
241#121—381no—
242#121C2×D1911yescharacteristic
243#121C2×D1911yescharacteristic, complemented
244#120—381no—
245C4×D4—381no—
246C4×D4—381no—
247#117—191no—
248C2×C4⋊C4—191no—
249C2×C22⋊C4—381no—
250#107—191no—
251#107—191no—
252#106—191no—
253#106C2×D1911yescharacteristic, complemented
254#103—191no—
255#103—191no—
256#102—191no—
257#102—191no—
258#102—191no—
259#102—191no—
260#102C2×D1911yescharacteristic, complemented
261#102C2×D1911yescharacteristic, complemented
262C22⋊C8—191no—
263C22⋊C8—191no—
264C22⋊C8—191no—
265C22⋊C8—191no—
266C19#319411yescharacteristic, complemented, Sylow
267C24—191no—
268C24—381no—
269#41—761no—
270#41—761no—
271C2×Q8—191no—
272C2×D4—21no—
273C2×D4—21no—
274C2×D4—191no—
275C2×D4—381no—
276C2×D4—381no—
277C2×D4—381no—
278C2×D4—381no—
279C2×D4—381no—
280C2×D4—381no—
281C2×D4—761no—
282C2×D4—761no—
283C2×D4—764no—
284C2×D4C22×D1911yescharacteristic
285C2×D4C22×D1911yescharacteristic
286C22×C4—191no—
287C22×C4—191no—
288C22×C4—191no—
289C22×C4—191no—
290C22×C4—191no—
291C22×C4—381no—
292C22×C4—381no—
293C22×C4—761no—
294C22×C4—761no—
295C22×C4C22×D1911yescharacteristic
296SD16—761no—
297SD16—761no—
298D8—41no—
299D8—761no—
300M16—41no—
301M16—761no—
302C2×C8—191no—
303C2×C8—191no—
304C2×C8C22×D1911yescharacteristic
305C2×C8C22×D1911yescharacteristic
306C4⋊C4—191no—
307C4⋊C4—191no—
308C4⋊C4—381no—
309C4⋊C4—381no—
310C4⋊C4—381no—
311C4⋊C4C22×D1911yescharacteristic
312C4⋊C4C22×D1911yescharacteristic
313C22⋊C4—21no—
314C22⋊C4—21no—
315C22⋊C4—381no—
316C22⋊C4—381no—
317C22⋊C4—381no—
318C22⋊C4—381no—
319C22⋊C4—381no—
320C22⋊C4—381no—
321C22⋊C4—381no—
322C42—381no—
323C23—21no—
324C23—21no—
325C23—191no—
326C23—191no—
327C23—382no—
328C23—381no—
329C23—761no—
330C23—761no—
331C23—762no—
332C23—762no—
333C23—762no—
334C23D4×D1911yescharacteristic
335Q8—381no—
336Q8—381no—
337D4—21no—
338D4—21no—
339D4—21no—
340D4—21no—
341D4—42no—
342D4—42no—
343D4—381no—
344D4—381no—
345D4—762no—
346D4—762no—
347D4—762no—
348D4—762no—
349D4—762no—
350D4—762no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—191no—
356C2×C4—191no—
357C2×C4—381no—
358C2×C4—381no—
359C2×C4—381no—
360C2×C4—381no—
361C2×C4—381no—
362C2×C4—381no—
363C2×C4—381no—
364C2×C4—761no—
365C2×C4—761no—
366C2×C4—762no—
367C2×C4—761no—
368C2×C4—762no—
369C2×C4D4×D1911yescharacteristic
370C2×C4C23×D1911yescharacteristic
371C8—21no—
372C8—21no—
373C8—381no—
374C8—381no—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—41no—
379C22—41no—
380C22—41no—
381C22—41no—
382C22—41no—
383C22—41no—
384C22—192no—
385C22—381no—
386C22—381no—
387C22—381no—
388C22—381no—
389C22—381no—
390C22—764no—
391C22—761no—
392C22—761no—
393C22—761no—
394C22—1524no—
395C22C2×D4×D1911yescharacteristic
396C4—21no—
397C4—41no—
398C4—41no—
399C4—381no—
400C4—381no—
401C4—761no—
402C4—761no—
403C4—761no—
404C4#1059743011yescharacteristic
405C4#1059743511yescharacteristic
406C2—41no—
407C2—81no—
408C2—81no—
409C2—382no—
410C2—761no—
411C2—1521no—
412C2#1192710211yescharacteristic
413C2AGL(1,ℤ/8)×D1911yescharacteristic
414C2#1192734011yescharacteristic
subgroupG/H
centerC22C2×D4×D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#469C2
socleC22×C19C22×D4
hypercenter#469D19
hypocenterC19#3194
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. #11927054C2semidirect
2. #121×D19C2semidirect
3. #11926876C2semidirect
4. #11926870C2semidirect
5. #11926866C2semidirect
6. #11926856C2semidirect
7. #11926795C2semidirect
8. #11926790C2semidirect
9. #11926788C2semidirect
10. #11926696C2semidirect
11. #11926690C2semidirect
12. #11926686C2semidirect
13. #11926676C2semidirect
14. #11926507C2semidirect
15. C19×#469C2semidirect
16. C2×#64543C22semidirect
20. C2×D8×C19C22semidirect
21. C2×M16×C19C22semidirect
23. C19×#121C22semidirect
29. C2×#64526C22semidirect
30. C2×#64525C22semidirect
32. #10597370C22semidirect
33. C2×#64520C22semidirect
34. C2×#64516C22semidirect
37. #10597338C22semidirect
43. C19×#106C22semidirect
44. C19×#102C22semidirect
45. C19×#102C22semidirect
46. #10597289C22semidirect
47. #10597289C22semidirect
48. #10597278C22semidirect
51. (C2×D19)⋊C8C22semidirect
52. (C2×D19)⋊C8C22semidirect
53. #10597275C22semidirect
54. #10597273C22semidirect
55. #10597267C22semidirect
56. #10597266C22semidirect
57. #10597265C22semidirect
58. #10597264C22semidirect
206. #469D19semidirect
230. C2×D8C2×D19semidirect
232. C2×M16C2×D19semidirect
243. #121C2×D19semidirect
253. #106C2×D19semidirect
260. #102C2×D19semidirect
261. #102C2×D19semidirect
266. C19#3194semidirect

Maximal subgroups

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

subgroupindex
#119270542
#121×D192
#119268762
#119268702
#119268662
#119268562
#119267952
#119267902
#119267882
#119266962
#119266902
#119266862
#119266762
#119265072
C19×#4692
#319419