Finite Group Databasebeta

← #14574681

Subgroups — #14574681

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#11927147C211yesmaximal, characteristic, complemented
2#11927111C211yesmaximal, characteristic, complemented
3#11926932C211yesmaximal, characteristic, complemented
4#11926919C211yesmaximal, characteristic, complemented
5#11926907C211yesmaximal, characteristic, complemented
6#11926897C211yesmaximal, characteristic, complemented
7#11926758C211yesmaximal, characteristic, complemented
8#11926757C211yesmaximal, characteristic, complemented
9#11926738C211yesmaximal, characteristic, complemented
10#11926737C211yesmaximal, characteristic, complemented
11#11926691C211yesmaximal, characteristic, complemented
12#11926687C211yesmaximal, characteristic, complemented
13#11926678C211yesmaximal, characteristic, complemented
14#11926602C211yesmaximal, characteristic, complemented
15C19×#447C211yesmaximal, characteristic, complemented
16C22×D4×C19C2211yescharacteristic
17C2×#64541C2211yescharacteristic
18C2×D8×C19C2211yescharacteristic
19C2×D8×C19C2211yescharacteristic
20C19×#121C2211yescharacteristic
21#10597399—21no—
22#10597399—21no—
23#10597386C2211yescharacteristic
24#10597386C2211yescharacteristic
25#10597386C2211yescharacteristic, complemented
26#10597385—21no—
27#10597384—21no—
28#10597384—21no—
29#10597384—21no—
30#10597382C2211yescharacteristic
31#10597382C2211yescharacteristic
32D4×Dic19C2211yescharacteristic, complemented
33C2×#64526C2211yescharacteristic, complemented
34C2×#64525C2211yescharacteristic
35C2×#64525C2211yescharacteristic
36C2×#64525C2211yescharacteristic, complemented
37#10597376C2211yescharacteristic
38#10597372C2211yescharacteristic
39C2×D152C2211yescharacteristic, complemented
40C2×#64516C2211yescharacteristic, complemented
41#10597339C2211yescharacteristic, complemented
42#10597336C2211yescharacteristic, complemented
43#10597332—21no—
44#10597329—21no—
45C19×#102C2211yescharacteristic
46C19×#102C2211yescharacteristic
47C19×C22⋊C8C2211yescharacteristic
48#10597289C2211yescharacteristic
49#10597289C2211yescharacteristic
50C22⋊(C19⋊C8)C2211yescharacteristic
51#10597278C2211yescharacteristic, complemented
52#10597273C2211yescharacteristic, complemented
53#10597272C2211yescharacteristic, complemented
54Dic19⋊C8C2211yescharacteristic, complemented
55Dic19⋊C8C2211yescharacteristic, complemented
56C8×Dic19C2211yescharacteristic, complemented
57#10597267C2211yescharacteristic, complemented
58#10597266C2211yescharacteristic, complemented
59C24×C19—21no—
60C2×D4×C19—21no—
61C2×D4×C19—21no—
62C2×D4×C19—41no—
63C2×D4×C19—41no—
64C2×D4×C19C2311yescharacteristic
65C2×D4×C19C2311yescharacteristic
66C2×D4×C19C2311yescharacteristic
67C22×C4×C19C2311yescharacteristic
68C2×C22⋊D19—21no—
69C2×C22⋊D19—21no—
70C2×C22⋊D19—21no—
71C2×C22⋊D19—21no—
72C2×C22⋊D19—21no—
73C2×C22⋊D19—21no—
74C2×C22⋊D19—21no—
75C2×C22⋊D19—21no—
76C22×Dic19—21no—
77#64541—41no—
78#64541—41no—
79C2×D76C2311yescharacteristic
80C2×D76C2311yescharacteristic
81C2×C4×D19—21no—
82C2×C4×D19—21no—
83C2×Dic38C2311yescharacteristic
84D8×C19—41no—
85D8×C19—41no—
86C2×C8×C19C2311yescharacteristic
87C2×C8×C19C2311yescharacteristic
88C4⋊C4×C19C2311yescharacteristic
89C22⋊C4×C19—21no—
90C22⋊Dic19—21no—
91C22⋊Dic19—21no—
92C22⋊Dic19—21no—
93C22⋊Dic19—21no—
94C22⋊Dic19—21no—
95C22⋊Dic19D411yescharacteristic
96C22⋊Dic19D411yescharacteristic
97#64526—41no—
98#64525—41no—
99#64525—41no—
100#64525—41no—
101(C2×D19)⋊C4—21no—
102(C2×D19)⋊C4—21no—
103C4⋊Dic19—21no—
104C4⋊Dic19D411yescharacteristic
105C4⋊Dic19D411yescharacteristic
106C4⋊Dic19C2311yescharacteristic
107Dic19⋊C4—21no—
108C4×Dic19C2311yescharacteristic
109C4×Dic19C2311yescharacteristic
110C2×C19⋊C8C2311yescharacteristic
111C2×C19⋊C8C2311yescharacteristic
112D152—41no—
113#64516—41no—
114C23×C19—21no—
115C23×C19—21no—
116C23×C19—21no—
117C23×C19—42no—
118C23×C19—81no—
119C23×C19—81no—
120C23×C19C2×D411yescharacteristic
121C22×D19—21no—
122C22×D19—21no—
123D4×C19—21no—
124D4×C19—21no—
125D4×C19—21no—
126D4×C19—21no—
127D4×C19—21no—
128D4×C19—21no—
129D4×C19—42no—
130D4×C19—81no—
131C2×C4×C19—21no—
132C2×C4×C19—21no—
133C2×C4×C19—21no—
134C2×C4×C19C2×D411yescharacteristic
135C2×C4×C19C2411yescharacteristic
136C22⋊D19—42no—
137C22⋊D19—81no—
138C22⋊D19—81no—
139C22⋊D19—81no—
140C22⋊D19—81no—
141C22⋊D19—81no—
142C22⋊D19—81no—
143C22⋊D19—81no—
144C2×Dic19—21no—
145C2×Dic19—21no—
146C2×Dic19—81no—
147C2×Dic19C2×D411yescharacteristic
148C2×Dic19C2×D411yescharacteristic
149C2×Dic19C2×D411yescharacteristic
150C2×Dic19C2×D411yescharacteristic
151D76—21no—
152D76—21no—
153D76—21no—
154D76—21no—
155C4×D19—42no—
156C4×D19—81no—
157Dic38—21no—
158Dic38—21no—
159C8×C19—21no—
160C8×C19—21no—
161C19⋊C8—21no—
162C19⋊C8—21no—
163#3220—191nomaximal, Sylow
164C22×C19—21no—
165C22×C19—21no—
166C22×C19—21no—
167C22×C19—41no—
168C22×C19—41no—
169C22×C19—41no—
170C22×C19—41no—
171C22×C19—41no—
172C22×C19—41no—
173C22×C19—41no—
174C22×C19—41no—
175C22×C19—41no—
176C22×C19—84no—
177C22×C19C22×D411yescharacteristic
178C2×D19—41no—
179C2×D19—41no—
180C2×D19—41no—
181C2×D19—41no—
182C2×D19—41no—
183C2×D19—41no—
184C4×C19—21no—
185C4×C19—41no—
186C4×C19H(5,𝔽2)11yescharacteristic
187C4×C19H(5,𝔽2)11yescharacteristic
188Dic19—21no—
189Dic19—21no—
190Dic19—21no—
191Dic19—21no—
192Dic19—41no—
193Dic19—41no—
194#540—191no—
195#535—191no—
196#496—191no—
197#493—191no—
198#490—191no—
199#488—191no—
200#463—191no—
201#463—191no—
202#459—191no—
203#459—191no—
204#449—191no—
205#449—191no—
206#447—191no—
207#447D1911yescharacteristic, complemented
208#433—191no—
209C2×C19—41no—
210C2×C19—81no—
211C2×C19—81no—
212C2×C19—81no—
213C2×C19#53511yescharacteristic
214C2×C19#57611yescharacteristic
215C2×C19#57611yescharacteristic
216D19—81no—
217D19—81no—
218C2×#41—191no—
219C22×D4C2×D1911yescharacteristic
220C2×SD16—191no—
221C2×SD16—191no—
222C2×D8—191no—
223C2×D8—191no—
224C2×D8—191no—
225C2×D8—191no—
226C2×D8C2×D1911yescharacteristic
227C2×D8C2×D1911yescharacteristic
228#127—191no—
229#127—191no—
230#127—191no—
231#125—191no—
232#124—191no—
233#124—191no—
234#123—381no—
235#123—381no—
236#121—191no—
237#121—381no—
238#121—381no—
239#121—381no—
240#121—381no—
241#121C2×D1911yescharacteristic
242#120—381no—
243#120—381no—
244C4×D4—191no—
245C4×D4—191no—
246#117—191no—
247C4⋊C8—191no—
248C4⋊C8—191no—
249#103—191no—
250#103—191no—
251#102—191no—
252#102—191no—
253#102—191no—
254#102—191no—
255#102C2×D1911yescharacteristic
256#102C2×D1911yescharacteristic
257C22⋊C8—191no—
258C22⋊C8C2×D1911yescharacteristic
259#97—191no—
260C4×C8—191no—
261C19#322011yescharacteristic, complemented, Sylow
262C24—21no—
263#41—761no—
264#41—761no—
265C2×Q8—191no—
266C2×D4—21no—
267C2×D4—21no—
268C2×D4—41no—
269C2×D4—41no—
270C2×D4—191no—
271C2×D4—191no—
272C2×D4—381no—
273C2×D4—381no—
274C2×D4—381no—
275C2×D4—381no—
276C2×D4—381no—
277C2×D4—381no—
278C2×D4—381no—
279C2×D4—381no—
280C2×D4C22×D1911yescharacteristic
281C2×D4C22×D1911yescharacteristic
282C2×D4C22×D1911yescharacteristic
283C22×C4—381no—
284C22×C4—381no—
285C22×C4—381no—
286C22×C4C22×D1911yescharacteristic
287SD16—761no—
288SD16—761no—
289D8—41no—
290D8—41no—
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—191no—
307C22⋊C4—191no—
308C22⋊C4—381no—
309C22⋊C4—381no—
310C22⋊C4—381no—
311C22⋊C4—381no—
312C22⋊C4—381no—
313C22⋊C4—381no—
314C22⋊C4—381no—
315C42—191no—
316C42—191no—
317C23—21no—
318C23—21no—
319C23—21no—
320C23—42no—
321C23—81no—
322C23—81no—
323C23—381no—
324C23—381no—
325C23D4×D1911yescharacteristic
326Q8—381no—
327Q8—381no—
328D4—21no—
329D4—21no—
330D4—21no—
331D4—21no—
332D4—21no—
333D4—21no—
334D4—42no—
335D4—81no—
336D4—381no—
337D4—381no—
338D4—381no—
339D4—381no—
340D4—762no—
341D4—1521no—
342D4—1521no—
343D4—1521no—
344D4—1521no—
345D4—1521no—
346D4—1521no—
347D4—1521no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—191no—
352C2×C4—191no—
353C2×C4—191no—
354C2×C4—191no—
355C2×C4—381no—
356C2×C4—381no—
357C2×C4—762no—
358C2×C4—1521no—
359C2×C4—1521no—
360C2×C4D4×D1911yescharacteristic
361C2×C4C23×D1911yescharacteristic
362C8—21no—
363C8—21no—
364C8—381no—
365C8—381no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22—84no—
379C22—761no—
380C22—761no—
381C22—761no—
382C22—761no—
383C22—761no—
384C22—761no—
385C22C2×D4×D1911yescharacteristic
386C4—21no—
387C4—41no—
388C4—381no—
389C4—381no—
390C4—381no—
391C4—381no—
392C4—761no—
393C4—761no—
394C4#1059743011yescharacteristic
395C4#1059743011yescharacteristic
396C2—41no—
397C2—81no—
398C2—81no—
399C2—81no—
400C2—1521no—
401C2—1521no—
402C2#1192710911yescharacteristic
403C2#1192734511yescharacteristic
404C2#1192734811yescharacteristic
subgroupG/H
centerC22C2×D4×D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#447C2
socleC22×C19C22×D4
hypercenter#447D19
hypocenterC19#3220
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. #11927147C2semidirect
2. #11927111C2semidirect
3. #11926932C2semidirect
4. #11926919C2semidirect
5. #11926907C2semidirect
6. #11926897C2semidirect
7. #11926758C2semidirect
8. #11926757C2semidirect
9. #11926738C2semidirect
10. #11926737C2semidirect
11. #11926691C2semidirect
12. #11926687C2semidirect
13. #11926678C2semidirect
14. #11926602C2semidirect
15. C19×#447C2semidirect
25. #10597386C22semidirect
32. D4×Dic19C22semidirect
33. C2×#64526C22semidirect
36. C2×#64525C22semidirect
39. C2×D152C22semidirect
40. C2×#64516C22semidirect
41. #10597339C22semidirect
42. #10597336C22semidirect
51. #10597278C22semidirect
52. #10597273C22semidirect
53. #10597272C22semidirect
54. Dic19⋊C8C22semidirect
55. Dic19⋊C8C22semidirect
56. C8×Dic19C22semidirect
57. #10597267C22semidirect
58. #10597266C22semidirect
207. #447D19semidirect
261. C19#3220semidirect

Maximal subgroups

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

subgroupindex
#119271472
#119271112
#119269322
#119269192
#119269072
#119268972
#119267582
#119267572
#119267382
#119267372
#119266912
#119266872
#119266782
#119266022
C19×#4472
#322019