Finite Group Databasebeta

← #14574487

Subgroups — #14574487

Order 2432.

422 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11927122C211yesmaximal, characteristic, complemented
2#11926885C211yesmaximal, characteristic, complemented
3#11926868C211yesmaximal, characteristic, complemented
4#11926860C211yesmaximal, characteristic, complemented
5#11926855C211yesmaximal, characteristic, complemented
6#11926795C211yesmaximal, characteristic, complemented
7#11926788C211yesmaximal, characteristic, complemented
8#11926778C211yesmaximal, characteristic, complemented
9#11926771C211yesmaximal, characteristic, complemented
10#11926695C211yesmaximal, characteristic, complemented
11#11926687C211yesmaximal, characteristic, complemented
12#11926687C211yesmaximal, characteristic, complemented
13#11926678C211yesmaximal, characteristic, complemented
14#11926511C211yesmaximal, characteristic, complemented
15C19×#535C211yesmaximal, characteristic, complemented
16C2×#41×C19C2211yescharacteristic
17C22×D4×C19C2211yescharacteristic
18C2×#64541C2211yescharacteristic, complemented
19C19×#127—21no—
20C19×#124—21no—
21C19×#121C2211yescharacteristic
22C19×#121C2211yescharacteristic
23C19×#121C2211yescharacteristic
24C19×#121C2211yescharacteristic
25C19×#120—21no—
26C19×#120—21no—
27C19×#117C2211yescharacteristic
28#10597392—21no—
29#10597385—21no—
30#10597385—21no—
31#10597384—21no—
32C2×#64526C2211yescharacteristic
33C2×#64526C2211yescharacteristic
34C2×#64525C2211yescharacteristic
35C2×#64525C2211yescharacteristic
36#10597376C2211yescharacteristic
37#10597376C2211yescharacteristic, complemented
38C2×C4⋊Dic19C2211yescharacteristic, complemented
39#10597370C2211yescharacteristic
40#10597370C2211yescharacteristic, complemented
41C2×#64520C2211yescharacteristic, complemented
42C22×C19⋊C8C2211yescharacteristic, complemented
43#10597289C2211yescharacteristic
44#10597289C2211yescharacteristic
45#10597289C2211yescharacteristic
46#10597289C2211yescharacteristic
47C22⋊(C19⋊C8)C2211yescharacteristic
48C22⋊(C19⋊C8)C2211yescharacteristic
49C22⋊(C19⋊C8)C2211yescharacteristic, complemented
50C22⋊(C19⋊C8)C2211yescharacteristic, complemented
51#10597267C2211yescharacteristic, complemented
52#10597267C2211yescharacteristic, complemented
53#10597266C2211yescharacteristic, complemented
54#10597266C2211yescharacteristic, complemented
55#10597265C2211yescharacteristic, complemented
56#10597265C2211yescharacteristic, complemented
57#10597264C2211yescharacteristic, complemented
58#10597264C2211yescharacteristic, complemented
59C24×C19—21no—
60#41×C19—41no—
61#41×C19—41no—
62C2×Q8×C19D411yescharacteristic
63C2×D4×C19—21no—
64C2×D4×C19—21no—
65C2×D4×C19—21no—
66C2×D4×C19—21no—
67C2×D4×C19—21no—
68C2×D4×C19—41no—
69C2×D4×C19—41no—
70C2×D4×C19D411yescharacteristic
71C2×D4×C19D411yescharacteristic
72C2×D4×C19D411yescharacteristic
73C2×D4×C19C2311yescharacteristic
74C2×D4×C19C2311yescharacteristic
75C22×C4×C19C2311yescharacteristic
76C22×C4×C19C2311yescharacteristic
77C22×C4×C19C2311yescharacteristic
78C2×C22⋊D19—21no—
79C2×C22⋊D19—21no—
80C2×C22⋊D19—21no—
81C22×Dic19—21no—
82#64541—41no—
83#64541—41no—
84C2×D76C2311yescharacteristic
85C2×C4×D19—21no—
86C2×Dic38C2311yescharacteristic
87C4⋊C4×C19C2311yescharacteristic
88C4⋊C4×C19C2311yescharacteristic
89C22⋊C4×C19—21no—
90C22⋊C4×C19—21no—
91C22⋊C4×C19—21no—
92C22⋊C4×C19—21no—
93C22⋊C4×C19—21no—
94C42×C19—21no—
95C22⋊Dic19—21no—
96C22⋊Dic19—21no—
97#64526—41no—
98#64526—41no—
99#64525—41no—
100#64525—41no—
101(C2×D19)⋊C4—21no—
102(C2×D19)⋊C4—21no—
103C4⋊Dic19—21no—
104C4⋊Dic19C2311yescharacteristic
105C4⋊Dic19C2311yescharacteristic
106Dic19⋊C4—21no—
107Dic19⋊C4—21no—
108#64520—41no—
109C2×C19⋊C8—41no—
110C2×C19⋊C8C2311yescharacteristic
111C2×C19⋊C8C2311yescharacteristic
112C2×C19⋊C8C2311yescharacteristic
113C2×C19⋊C8C2311yescharacteristic
114C23×C19—21no—
115C23×C19—21no—
116C23×C19—42no—
117C23×C19—81no—
118C23×C19—81no—
119C23×C19C2×D411yescharacteristic
120C23×C19C2×D411yescharacteristic
121C23×C19C2×D411yescharacteristic
122C22×D19—21no—
123Q8×C19—41no—
124D4×C19—21no—
125D4×C19—21no—
126D4×C19—21no—
127D4×C19—21no—
128D4×C19—41no—
129D4×C19—41no—
130D4×C19—41no—
131D4×C19—42no—
132D4×C19—81no—
133D4×C19—81no—
134D4×C19—81no—
135D4×C19—81no—
136C2×C4×C19—21no—
137C2×C4×C19—21no—
138C2×C4×C19—21no—
139C2×C4×C19—21no—
140C2×C4×C19—21no—
141C2×C4×C19—21no—
142C2×C4×C19—21no—
143C2×C4×C19—21no—
144C2×C4×C19C2×D411yescharacteristic
145C2×C4×C19C2×D411yescharacteristic
146C2×C4×C19C2×D411yescharacteristic
147C2×C4×C19C2411yescharacteristic
148C22⋊D19—42no—
149C22⋊D19—81no—
150C22⋊D19—81no—
151C2×Dic19—21no—
152C2×Dic19—21no—
153C2×Dic19—21no—
154C2×Dic19—81no—
155D76—21no—
156D76—21no—
157C4×D19—42no—
158Dic38—21no—
159Dic38—21no—
160C19⋊C8—21no—
161C19⋊C8—21no—
162C19⋊C8—21no—
163C19⋊C8—21no—
164#3198—191nomaximal, Sylow
165C22×C19—21no—
166C22×C19—21no—
167C22×C19—21no—
168C22×C19—21no—
169C22×C19—21no—
170C22×C19—21no—
171C22×C19—21no—
172C22×C19—21no—
173C22×C19—21no—
174C22×C19—41no—
175C22×C19—41no—
176C22×C19—41no—
177C22×C19—41no—
178C22×C19—41no—
179C22×C19—41no—
180C22×C19—84no—
181C22×C19C22×D411yescharacteristic
182C2×D19—41no—
183C2×D19—41no—
184C2×D19—41no—
185C4×C19—21no—
186C4×C19—21no—
187C4×C19—21no—
188C4×C19—41no—
189C4×C19—41no—
190C4×C19H(5,𝔽2)11yescharacteristic
191C4×C19H(5,𝔽2)11yescharacteristic
192Dic19—41no—
193Dic19—41no—
194Dic19—41no—
195#537—191no—
196#535D1911yescharacteristic, complemented
197#485—191no—
198#482—191no—
199#481—191no—
200#480—191no—
201#469—191no—
202#468—191no—
203#466—191no—
204#465—191no—
205#450—191no—
206#449—191no—
207#449—191no—
208#447—191no—
209#408—191no—
210C2×C19—41no—
211C2×C19—41no—
212C2×C19—41no—
213C2×C19—81no—
214C2×C19—81no—
215C2×C19#53411yescharacteristic
216C2×C19#57611yescharacteristic
217C2×C19#57711yescharacteristic
218D19—81no—
219C2×#41—191no—
220C2×#41C2×D1911yescharacteristic
221C22×D4C2×D1911yescharacteristic
222C2×SD16—191no—
223C2×SD16—191no—
224C2×D8—191no—
225C2×D8—191no—
226C2×M16—191no—
227C22×C8—191no—
228#127—21no—
229#124—21no—
230C22⋊Q8—191no—
231C22⋊Q8—191no—
232C22⋊Q8—381no—
233#121—191no—
234#121—191no—
235#121—381no—
236#121—381no—
237#121—381no—
238#121C2×D1911yescharacteristic
239#121C2×D1911yescharacteristic
240#121C2×D1911yescharacteristic
241#121C2×D1911yescharacteristic
242#120—21no—
243#120—21no—
244#117C2×D1911yescharacteristic
245C2×C4⋊C4—191no—
246#107—191no—
247#107—191no—
248#106—191no—
249#106—191no—
250#103—191no—
251#103—191no—
252#102—191no—
253#102—191no—
254#102—191no—
255#102—191no—
256#102—191no—
257#102—191no—
258C22⋊C8—191no—
259C22⋊C8—191no—
260C22⋊C8—191no—
261C22⋊C8—191no—
262C19#319811yescharacteristic, complemented, Sylow
263C24—21no—
264#41—41no—
265#41—41no—
266#41—761no—
267#41—761no—
268C2×Q8—191no—
269C2×Q8C22⋊D1911yescharacteristic
270C2×D4—21no—
271C2×D4—21no—
272C2×D4—21no—
273C2×D4—21no—
274C2×D4—21no—
275C2×D4—41no—
276C2×D4—41no—
277C2×D4—191no—
278C2×D4—381no—
279C2×D4—381no—
280C2×D4—381no—
281C2×D4C22⋊D1911yescharacteristic
282C2×D4C22⋊D1911yescharacteristic
283C2×D4C22⋊D1911yescharacteristic
284C2×D4C22×D1911yescharacteristic
285C2×D4C22×D1911yescharacteristic
286C22×C4—381no—
287C22×C4—381no—
288C22×C4C22×D1911yescharacteristic
289C22×C4C22×D1911yescharacteristic
290C22×C4C22×D1911yescharacteristic
291SD16—761no—
292SD16—761no—
293D8—761no—
294D8—761no—
295M16—761no—
296C2×C8—191no—
297C2×C8—191no—
298C2×C8—191no—
299C2×C8—191no—
300C2×C8—761no—
301C4⋊C4—191no—
302C4⋊C4—191no—
303C4⋊C4—381no—
304C4⋊C4—381no—
305C4⋊C4—381no—
306C4⋊C4C22×D1911yescharacteristic
307C4⋊C4C22×D1911yescharacteristic
308C22⋊C4—21no—
309C22⋊C4—21no—
310C22⋊C4—21no—
311C22⋊C4—21no—
312C22⋊C4—21no—
313C22⋊C4—381no—
314C22⋊C4—381no—
315C22⋊C4—381no—
316C22⋊C4—381no—
317C42—21no—
318C23—21no—
319C23—21no—
320C23—42no—
321C23—81no—
322C23—81no—
323C23—381no—
324C23C2×C22⋊D1911yescharacteristic
325C23C2×C22⋊D1911yescharacteristic
326C23C2×C22⋊D1911yescharacteristic
327Q8—41no—
328Q8—381no—
329Q8—381no—
330D4—21no—
331D4—21no—
332D4—21no—
333D4—21no—
334D4—41no—
335D4—41no—
336D4—41no—
337D4—42no—
338D4—81no—
339D4—81no—
340D4—81no—
341D4—81no—
342D4—381no—
343D4—381no—
344D4—762no—
345D4—1521no—
346D4—1521no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—381no—
356C2×C4—381no—
357C2×C4—381no—
358C2×C4—762no—
359C2×C4—1521no—
360C2×C4C2×C22⋊D1911yescharacteristic
361C2×C4C2×C22⋊D1911yescharacteristic
362C2×C4C2×C22⋊D1911yescharacteristic
363C2×C4C23×D1911yescharacteristic
364C8—381no—
365C8—381no—
366C8—381no—
367C8—381no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—41no—
381C22—41no—
382C22—41no—
383C22—84no—
384C22—761no—
385C22—761no—
386C22—761no—
387C22C22×C22⋊D1911yescharacteristic
388C4—21no—
389C4—21no—
390C4—21no—
391C4—41no—
392C4—41no—
393C4—761no—
394C4—761no—
395C4—761no—
396C4#1059743011yescharacteristic
397C4#1059743011yescharacteristic
398C2—41no—
399C2—41no—
400C2—41no—
401C2—81no—
402C2—81no—
403C2—1521no—
404C2#1192710311yescharacteristic
405C2#1192734711yescharacteristic
406C2#1192735511yescharacteristic
subgroupG/H
centerC22C22×C22⋊D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#535C2
socleC22×C19C22×D4
hypercenter#535D19
hypocenterC19#3198
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×#41 ◁ #535

Complements

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

NH ≅ G/Ntype
1. #11927122C2semidirect
2. #11926885C2semidirect
3. #11926868C2semidirect
4. #11926860C2semidirect
5. #11926855C2semidirect
6. #11926795C2semidirect
7. #11926788C2semidirect
8. #11926778C2semidirect
9. #11926771C2semidirect
10. #11926695C2semidirect
11. #11926687C2semidirect
12. #11926687C2semidirect
13. #11926678C2semidirect
14. #11926511C2semidirect
15. C19×#535C2semidirect
18. C2×#64541C22semidirect
37. #10597376C22semidirect
38. C2×C4⋊Dic19C22semidirect
40. #10597370C22semidirect
41. C2×#64520C22semidirect
42. C22×C19⋊C8C22semidirect
49. C22⋊(C19⋊C8)C22semidirect
50. C22⋊(C19⋊C8)C22semidirect
51. #10597267C22semidirect
52. #10597267C22semidirect
53. #10597266C22semidirect
54. #10597266C22semidirect
55. #10597265C22semidirect
56. #10597265C22semidirect
57. #10597264C22semidirect
58. #10597264C22semidirect
196. #535D19semidirect
262. C19#3198semidirect

Maximal subgroups

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

subgroupindex
#119271222
#119268852
#119268682
#119268602
#119268552
#119267952
#119267882
#119267782
#119267712
#119266952
#119266872
#119266782
#119265112
C19×#5352
#319819