Finite Group Databasebeta

← #14574682

Subgroups — #14574682

Order 2432.

420 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11927145C211yesmaximal, characteristic, complemented
2#11927112C211yesmaximal, characteristic, complemented
3#11926930C211yesmaximal, characteristic, complemented
4#11926919C211yesmaximal, characteristic, complemented
5#11926907C211yesmaximal, characteristic, complemented
6#11926900C211yesmaximal, characteristic, complemented
7#11926756C211yesmaximal, characteristic, complemented
8#11926740C211yesmaximal, characteristic, complemented
9#11926739C211yesmaximal, characteristic, complemented
10#11926692C211yesmaximal, characteristic, complemented
11#11926688C211yesmaximal, characteristic, complemented
12#11926679C211yesmaximal, characteristic, complemented
13#11926676C211yesmaximal, characteristic, complemented
14#11926604C211yesmaximal, characteristic, complemented
15C19×#463C211yesmaximal, characteristic, complemented
16C2×#64545C2211yescharacteristic
17C2×D4×D19C2211yescharacteristic
18C2×SD16×C19C2211yescharacteristic, complemented
19C2×D8×C19C2211yescharacteristic
20C19×#124C2211yescharacteristic
21C4×D4×C19C2211yescharacteristic, complemented
22#10597393C2211yescharacteristic
23C2×#64527C2211yescharacteristic, complemented
24#10597386C2211yescharacteristic
25#10597386C2211yescharacteristic, complemented
26#10597384C2211yescharacteristic
27C2×#64525C2211yescharacteristic
28C2×#64525C2211yescharacteristic
29C2×#64525C2211yescharacteristic, complemented
30#10597376—21no—
31#10597375—21no—
32C2×D152C2211yescharacteristic
33C2×D152C2211yescharacteristic, complemented
34#10597341C2211yescharacteristic
35#10597336C2211yescharacteristic, complemented
36#10597330—21no—
37#10597330—21no—
38#10597330—21no—
39#10597329—21no—
40#10597328—21no—
41#10597328—21no—
42#10597320C2211yescharacteristic
43C4×D76C2211yescharacteristic, complemented
44#10597318C2211yescharacteristic
45C19×C4⋊C8C2211yescharacteristic, complemented
46C19×#103C2211yescharacteristic, complemented
47C19×#102C2211yescharacteristic
48#10597292C2211yescharacteristic, complemented
49#10597289C2211yescharacteristic
50#10597278C2211yescharacteristic
51#10597278C2211yescharacteristic, complemented
52(C2×D19)⋊C8C2211yescharacteristic
53(C2×D19)⋊C8C2211yescharacteristic
54#10597272C2211yescharacteristic, complemented
55C8×Dic19C2211yescharacteristic, complemented
56#10597266C2211yescharacteristic
57#10597266C2211yescharacteristic, complemented
58C4⋊(C19⋊C8)C2211yescharacteristic, complemented
59C23×D19—21no—
60C2×Q8×C19C2311yescharacteristic
61C2×D4×C19C2311yescharacteristic
62C2×D4×C19C2311yescharacteristic
63C22×C4×C19—21no—
64C2×C22⋊D19—21no—
65C2×C22⋊D19—21no—
66C2×C22⋊D19—21no—
67C2×C22⋊D19—21no—
68C2×C22⋊D19—21no—
69C2×C22⋊D19—21no—
70#64545—41no—
71#64545—41no—
72D4×D19—41no—
73D4×D19—41no—
74C2×D76—21no—
75C2×D76—21no—
76C2×D76—21no—
77C2×D76—21no—
78C2×D76C2311yescharacteristic
79C2×D76C2311yescharacteristic
80C2×D76C2311yescharacteristic
81C2×C4×D19—21no—
82C2×C4×D19—21no—
83C2×C4×D19C2311yescharacteristic
84SD16×C19—41no—
85D8×C19—41no—
86C2×C8×C19C2311yescharacteristic
87C2×C8×C19C2311yescharacteristic
88C4⋊C4×C19C2311yescharacteristic
89C22⋊C4×C19—21no—
90C22⋊C4×C19—21no—
91C22⋊C4×C19—21no—
92C42×C19C2311yescharacteristic
93C22⋊Dic19—21no—
94#64527—41no—
95#64525—41no—
96#64525—41no—
97#64525—41no—
98(C2×D19)⋊C4—21no—
99(C2×D19)⋊C4—21no—
100(C2×D19)⋊C4—21no—
101(C2×D19)⋊C4—21no—
102(C2×D19)⋊C4D411yescharacteristic
103(C2×D19)⋊C4D411yescharacteristic
104C4⋊Dic19—21no—
105C4⋊Dic19C2311yescharacteristic
106Dic19⋊C4—21no—
107Dic19⋊C4D411yescharacteristic
108Dic19⋊C4D411yescharacteristic
109C4×Dic19C2311yescharacteristic
110C2×C19⋊C8C2311yescharacteristic
111C2×C19⋊C8C2311yescharacteristic
112D152—41no—
113D152—41no—
114C23×C19—21no—
115C23×C19—21no—
116C22×D19—21no—
117C22×D19—21no—
118C22×D19—21no—
119C22×D19—42no—
120C22×D19—81no—
121C22×D19—81no—
122C22×D19C2×D411yescharacteristic
123Q8×C19—21no—
124Q8×C19—21no—
125D4×C19—21no—
126D4×C19—21no—
127D4×C19—21no—
128D4×C19—21no—
129C2×C4×C19—21no—
130C2×C4×C19—21no—
131C2×C4×C19—81no—
132C2×C4×C19C2×D411yescharacteristic
133C2×C4×C19C2×D411yescharacteristic
134C2×C4×C19C2411yescharacteristic
135C22⋊D19—42no—
136C22⋊D19—81no—
137C22⋊D19—81no—
138C22⋊D19—81no—
139C22⋊D19—81no—
140C22⋊D19—81no—
141C2×Dic19—21no—
142C2×Dic19C2×D411yescharacteristic
143C2×Dic19C2×D411yescharacteristic
144C2×Dic19C2×D411yescharacteristic
145D76—21no—
146D76—21no—
147D76—21no—
148D76—21no—
149D76—21no—
150D76—21no—
151D76—42no—
152D76—81no—
153D76—81no—
154D76—81no—
155C4×D19—21no—
156C4×D19—21no—
157C4×D19—42no—
158C4×D19—81no—
159C8×C19—21no—
160C8×C19—21no—
161C19⋊C8—21no—
162C19⋊C8—21no—
163#3220—191nomaximal, Sylow
164C22×C19—41no—
165C22×C19—41no—
166C22×C19—41no—
167C22×C19—41no—
168C22×C19—41no—
169C22×C19—41no—
170C22×C19C22×D411yescharacteristic
171C2×D19—21no—
172C2×D19—21no—
173C2×D19—21no—
174C2×D19—41no—
175C2×D19—41no—
176C2×D19—41no—
177C2×D19—41no—
178C2×D19—41no—
179C2×D19—41no—
180C2×D19—41no—
181C2×D19—41no—
182C2×D19—41no—
183C2×D19—84no—
184C4×C19—21no—
185C4×C19—21no—
186C4×C19—41no—
187C4×C19—41no—
188C4×C19H(5,𝔽2)11yescharacteristic
189C4×C19H(5,𝔽2)11yescharacteristic
190Dic19—21no—
191Dic19—21no—
192Dic19—21no—
193Dic19—41no—
194#540—191no—
195#535—191no—
196#496—191no—
197#493—191no—
198#490—191no—
199#488—191no—
200#463—191no—
201#463D1911yescharacteristic, complemented
202#459—191no—
203#459—191no—
204#449—191no—
205#449—191no—
206#447—191no—
207#447—191no—
208#433—191no—
209C2×C19—81no—
210C2×C19—81no—
211C2×C19#53511yescharacteristic
212C2×C19#57611yescharacteristic
213C2×C19#57611yescharacteristic
214D19—41no—
215D19—81no—
216D19—81no—
217D19—81no—
218C2×#41—191no—
219C22×D4—191no—
220C2×SD16—191no—
221C2×SD16C2×D1911yescharacteristic, complemented
222C2×D8—191no—
223C2×D8—191no—
224C2×D8—191no—
225C2×D8—191no—
226C2×D8—191no—
227C2×D8C2×D1911yescharacteristic
228#127—191no—
229#127—191no—
230#127—191no—
231#125—191no—
232#124—191no—
233#124C2×D1911yescharacteristic
234#123—381no—
235#123—381no—
236#121—191no—
237#121—191no—
238#121—381no—
239#121—381no—
240#121—381no—
241#121—381no—
242#120—381no—
243#120—381no—
244C4×D4—191no—
245C4×D4C2×D1911yescharacteristic, complemented
246#117—191no—
247C4⋊C8—191no—
248C4⋊C8C2×D1911yescharacteristic, complemented
249#103—191no—
250#103C2×D1911yescharacteristic, complemented
251#102—191no—
252#102—191no—
253#102—191no—
254#102—191no—
255#102—191no—
256#102C2×D1911yescharacteristic
257C22⋊C8—191no—
258C22⋊C8—191no—
259#97—191no—
260C4×C8—191no—
261C19#322011yescharacteristic, complemented, Sylow
262C24—381no—
263#41—761no—
264#41—761no—
265C2×Q8C22×D1911yescharacteristic
266C2×D4—191no—
267C2×D4—191no—
268C2×D4—191no—
269C2×D4—381no—
270C2×D4—381no—
271C2×D4—381no—
272C2×D4—381no—
273C2×D4—381no—
274C2×D4—381no—
275C2×D4—381no—
276C2×D4—381no—
277C2×D4—381no—
278C2×D4—381no—
279C2×D4—761no—
280C2×D4—761no—
281C2×D4C22×D1911yescharacteristic
282C2×D4C22×D1911yescharacteristic
283C22×C4—21no—
284C22×C4—191no—
285C22×C4—381no—
286C22×C4—381no—
287SD16—41no—
288SD16—761no—
289D8—41no—
290D8—761no—
291D8—761no—
292D8—761no—
293D8—761no—
294D8—761no—
295C2×C8—191no—
296C2×C8—191no—
297C2×C8C22×D1911yescharacteristic
298C2×C8C22×D1911yescharacteristic
299C4⋊C4—191no—
300C4⋊C4—191no—
301C4⋊C4—191no—
302C4⋊C4—381no—
303C4⋊C4—381no—
304C4⋊C4C22×D1911yescharacteristic
305C22⋊C4—21no—
306C22⋊C4—21no—
307C22⋊C4—21no—
308C22⋊C4—191no—
309C22⋊C4—191no—
310C22⋊C4—381no—
311C22⋊C4—381no—
312C22⋊C4—381no—
313C22⋊C4—381no—
314C22⋊C4—381no—
315C42—191no—
316C42C22×D1911yescharacteristic
317C23—21no—
318C23—21no—
319C23—191no—
320C23—381no—
321C23—381no—
322C23—381no—
323C23—762no—
324C23—1521no—
325C23—1521no—
326Q8—21no—
327Q8—21no—
328D4—21no—
329D4—21no—
330D4—21no—
331D4—21no—
332D4—381no—
333D4—381no—
334D4—381no—
335D4—381no—
336D4—381no—
337D4—381no—
338D4—762no—
339D4—762no—
340D4—1521no—
341D4—1521no—
342D4—1521no—
343D4—1521no—
344D4—1521no—
345D4—1521no—
346D4—1521no—
347D4—1521no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—81no—
351C2×C4—191no—
352C2×C4—191no—
353C2×C4—191no—
354C2×C4—381no—
355C2×C4—381no—
356C2×C4—381no—
357C2×C4—762no—
358C2×C4—1521no—
359C2×C4D4×D1911yescharacteristic
360C2×C4D4×D1911yescharacteristic
361C2×C4C23×D1911yescharacteristic
362C8—21no—
363C8—21no—
364C8—381no—
365C8—381no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22—381no—
373C22—381no—
374C22—381no—
375C22—761no—
376C22—761no—
377C22—761no—
378C22—761no—
379C22—761no—
380C22—761no—
381C22—761no—
382C22—761no—
383C22—761no—
384C22—1524no—
385C22C2×D4×D1911yescharacteristic
386C4—21no—
387C4—21no—
388C4—41no—
389C4—41no—
390C4—381no—
391C4—381no—
392C4—381no—
393C4—761no—
394C4#1059743011yescharacteristic
395C4#1059743511yescharacteristic
396C2—81no—
397C2—81no—
398C2—761no—
399C2—1521no—
400C2—1521no—
401C2—1521no—
402C2#1192711011yescharacteristic
403C2#1192734611yescharacteristic
404C2#1192734811yescharacteristic
subgroupG/H
centerC22C2×D4×D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#463C2
socleC22×C19C22×D4
hypercenter#463D19
hypocenterC19#3220
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. #11927145C2semidirect
2. #11927112C2semidirect
3. #11926930C2semidirect
4. #11926919C2semidirect
5. #11926907C2semidirect
6. #11926900C2semidirect
7. #11926756C2semidirect
8. #11926740C2semidirect
9. #11926739C2semidirect
10. #11926692C2semidirect
11. #11926688C2semidirect
12. #11926679C2semidirect
13. #11926676C2semidirect
14. #11926604C2semidirect
15. C19×#463C2semidirect
18. C2×SD16×C19C22semidirect
21. C4×D4×C19C22semidirect
23. C2×#64527C22semidirect
25. #10597386C22semidirect
29. C2×#64525C22semidirect
33. C2×D152C22semidirect
35. #10597336C22semidirect
43. C4×D76C22semidirect
45. C19×C4⋊C8C22semidirect
46. C19×#103C22semidirect
48. #10597292C22semidirect
51. #10597278C22semidirect
54. #10597272C22semidirect
55. C8×Dic19C22semidirect
57. #10597266C22semidirect
58. C4⋊(C19⋊C8)C22semidirect
201. #463D19semidirect
221. C2×SD16C2×D19semidirect
245. C4×D4C2×D19semidirect
248. C4⋊C8C2×D19semidirect
250. #103C2×D19semidirect
261. C19#3220semidirect

Maximal subgroups

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

subgroupindex
#119271452
#119271122
#119269302
#119269192
#119269072
#119269002
#119267562
#119267402
#119267392
#119266922
#119266882
#119266792
#119266762
#119266042
C19×#4632
#322019