Finite Group Databasebeta

← #14574724

Subgroups — #14574724

Order 2432.

408 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11927163C211yesmaximal, characteristic, complemented
2#11927107C211yesmaximal, characteristic, complemented
3#11926926C211yesmaximal, characteristic, complemented
4#11926904C211yesmaximal, characteristic, complemented
5#11926890C211yesmaximal, characteristic, complemented
6#11926764C211yesmaximal, characteristic, complemented
7#11926757C211yesmaximal, characteristic, complemented
8#11926742C211yesmaximal, characteristic, complemented
9#11926737C211yesmaximal, characteristic, complemented
10#11926703C211yesmaximal, characteristic, complemented
11#11926693C211yesmaximal, characteristic, complemented
12#11926686C211yesmaximal, characteristic, complemented
13#11926676C211yesmaximal, characteristic, complemented
14#11926606C211yesmaximal, characteristic, complemented
15C19×#496C211yesmaximal, characteristic, complemented
16C2×#64543C2211yescharacteristic
17C2×D4×D19C2211yescharacteristic
18C2×SD16×C19C2211yescharacteristic
19C2×SD16×C19C2211yescharacteristic, complemented
20C2×D8×C19C2211yescharacteristic
21C2×D8×C19C2211yescharacteristic, complemented
22C19×#127C2211yescharacteristic
23C19×#124C2211yescharacteristic, complemented
24#10597392C2211yescharacteristic
25Q8×Dic19C2211yescharacteristic, complemented
26C2×#64528C2211yescharacteristic, complemented
27C2×#64527C2211yescharacteristic
28#10597386C2211yescharacteristic
29#10597385—21no—
30#10597385—21no—
31#10597384C2211yescharacteristic
32#10597383—21no—
33#10597383—21no—
34#10597382C2211yescharacteristic
35D4×Dic19C2211yescharacteristic, complemented
36C2×#64526C2211yescharacteristic, complemented
37C2×#64525C2211yescharacteristic
38#10597332—21no—
39#10597331—21no—
40#10597325—21no—
41#10597324—21no—
42#10597321C2211yescharacteristic
43#10597318C2211yescharacteristic
44#10597315C2211yescharacteristic, complemented
45C19×#97C2211yescharacteristic, complemented
46#10597289C2211yescharacteristic
47#10597289C2211yescharacteristic
48#10597289C2211yescharacteristic, complemented
49#10597289C2211yescharacteristic, complemented
50#10597278C2211yescharacteristic
51#10597278C2211yescharacteristic
52(C2×D19)⋊C8C2211yescharacteristic
53(C2×D19)⋊C8C2211yescharacteristic
54#10597273C2211yescharacteristic, complemented
55#10597273C2211yescharacteristic, complemented
56Dic19⋊C8C2211yescharacteristic, complemented
57Dic19⋊C8C2211yescharacteristic, complemented
58C4×C19⋊C8C2211yescharacteristic, complemented
59C23×D19—21no—
60C2×Q8×C19C2311yescharacteristic
61C2×D4×C19—21no—
62C2×D4×C19—21no—
63C2×D4×C19C2311yescharacteristic
64C2×D4×C19C2311yescharacteristic
65C2×D4×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×Dic19—21no—
73#64543—41no—
74#64543—41no—
75D4×D19—41no—
76D4×D19—41no—
77C2×D76C2311yescharacteristic
78C2×C4×D19C2311yescharacteristic
79C2×Dic38—21no—
80C2×Dic38C2311yescharacteristic
81SD16×C19—41no—
82SD16×C19—41no—
83D8×C19—41no—
84D8×C19—41no—
85C2×C8×C19C2311yescharacteristic
86C2×C8×C19C2311yescharacteristic
87C22⋊C4×C19—21no—
88C22⋊C4×C19—21no—
89C42×C19C2311yescharacteristic
90C22⋊Dic19—21no—
91C22⋊Dic19—21no—
92C22⋊Dic19—21no—
93C22⋊Dic19—21no—
94#64528—41no—
95#64527—41no—
96#64526—41no—
97#64525—41no—
98(C2×D19)⋊C4—21no—
99(C2×D19)⋊C4—21no—
100(C2×D19)⋊C4—21no—
101(C2×D19)⋊C4D411yescharacteristic
102(C2×D19)⋊C4D411yescharacteristic
103C4⋊Dic19—21no—
104C4⋊Dic19—21no—
105C4⋊Dic19C2311yescharacteristic
106C4⋊Dic19C2311yescharacteristic
107Dic19⋊C4—21no—
108Dic19⋊C4D411yescharacteristic
109Dic19⋊C4D411yescharacteristic
110C4×Dic19—21no—
111C4×Dic19C2311yescharacteristic
112C2×C19⋊C8C2311yescharacteristic
113C2×C19⋊C8C2311yescharacteristic
114C23×C19—21no—
115C23×C19—21no—
116C23×C19—21no—
117C22×D19—21no—
118C22×D19—42no—
119C22×D19—81no—
120C22×D19—81no—
121C22×D19C2×D411yescharacteristic
122Q8×C19—21no—
123Q8×C19—21no—
124D4×C19—21no—
125D4×C19—21no—
126D4×C19—21no—
127D4×C19—21no—
128D4×C19—21no—
129D4×C19—21no—
130D4×C19—81no—
131D4×C19—81no—
132C2×C4×C19—21no—
133C2×C4×C19C2×D411yescharacteristic
134C2×C4×C19C2×D411yescharacteristic
135C2×C4×C19C2411yescharacteristic
136C22⋊D19—42no—
137C22⋊D19—42no—
138C22⋊D19—81no—
139C22⋊D19—81no—
140C22⋊D19—81no—
141C2×Dic19—21no—
142C2×Dic19—21no—
143C2×Dic19—21no—
144C2×Dic19—42no—
145C2×Dic19—81no—
146C2×Dic19C2×D411yescharacteristic
147C2×Dic19C2×D411yescharacteristic
148C2×Dic19C2×D411yescharacteristic
149D76—21no—
150D76—21no—
151C4×D19—21no—
152C4×D19—21no—
153Dic38—21no—
154Dic38—21no—
155Dic38—81no—
156C8×C19—21no—
157C8×C19—21no—
158C19⋊C8—21no—
159C19⋊C8—21no—
160#3224—191nomaximal, Sylow
161C22×C19—41no—
162C22×C19—41no—
163C22×C19—41no—
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—84no—
178C4×C19—21no—
179C4×C19—21no—
180C4×C19—41no—
181C4×C19H(5,𝔽2)11yescharacteristic
182C4×C19H(5,𝔽2)11yescharacteristic
183Dic19—21no—
184Dic19—21no—
185Dic19—21no—
186Dic19—41no—
187Dic19—41no—
188Dic19—41no—
189#542—191no—
190#535—191no—
191#496D1911yescharacteristic, complemented
192#495—191no—
193#489—191no—
194#486—191no—
195#464—191no—
196#463—191no—
197#460—191no—
198#459—191no—
199#452—191no—
200#450—191no—
201#449—191no—
202#447—191no—
203#433—191no—
204C2×C19—81no—
205C2×C19—81no—
206C2×C19—81no—
207C2×C19#53511yescharacteristic
208C2×C19#57611yescharacteristic
209C2×C19#57711yescharacteristic
210D19—41no—
211D19—81no—
212C2×#41—191no—
213C22×D4—191no—
214C2×Q16—191no—
215C2×SD16—191no—
216C2×SD16—191no—
217C2×SD16C2×D1911yescharacteristic
218C2×SD16C2×D1911yescharacteristic, complemented
219C2×D8—191no—
220C2×D8C2×D1911yescharacteristic
221C2×D8C2×D1911yescharacteristic, complemented
222C4⋊Q8—191no—
223#127—191no—
224#127C2×D1911yescharacteristic
225#126—381no—
226#124—191no—
227#124—191no—
228#124—381no—
229#124C2×D1911yescharacteristic, complemented
230#123—381no—
231C22⋊Q8—191no—
232C22⋊Q8—381no—
233#121—191no—
234#121—381no—
235#121—381no—
236#120—381no—
237#120—381no—
238C4×Q8—191no—
239C4×D4—191no—
240#117—191no—
241C4⋊C8—191no—
242C4⋊C8—191no—
243#103—191no—
244#103—191no—
245#102—191no—
246#102—191no—
247#102—191no—
248#102—191no—
249#102—191no—
250#102—191no—
251C22⋊C8—191no—
252C22⋊C8—191no—
253#97C2×D1911yescharacteristic, complemented
254C4×C8—191no—
255C19#322411yescharacteristic, complemented, Sylow
256C24—381no—
257#41—761no—
258#41—761no—
259C2×Q8—191no—
260C2×Q8—381no—
261C2×Q8C22×D1911yescharacteristic
262C2×D4—21no—
263C2×D4—21no—
264C2×D4—191no—
265C2×D4—381no—
266C2×D4—381no—
267C2×D4—381no—
268C2×D4—381no—
269C2×D4—381no—
270C2×D4—761no—
271C2×D4—761no—
272C2×D4C22×D1911yescharacteristic
273C2×D4C22×D1911yescharacteristic
274C2×D4C22×D1911yescharacteristic
275C22×C4—191no—
276C22×C4—381no—
277C22×C4—381no—
278Q16—761no—
279SD16—41no—
280SD16—41no—
281SD16—761no—
282SD16—761no—
283D8—41no—
284D8—41no—
285D8—761no—
286C2×C8—191no—
287C2×C8—191no—
288C2×C8C22×D1911yescharacteristic
289C2×C8C22×D1911yescharacteristic
290C4⋊C4—191no—
291C4⋊C4—191no—
292C4⋊C4—191no—
293C4⋊C4—191no—
294C4⋊C4—381no—
295C4⋊C4—381no—
296C4⋊C4—381no—
297C22⋊C4—21no—
298C22⋊C4—21no—
299C22⋊C4—191no—
300C22⋊C4—191no—
301C22⋊C4—381no—
302C22⋊C4—381no—
303C22⋊C4—381no—
304C22⋊C4—381no—
305C22⋊C4—381no—
306C22⋊C4—381no—
307C22⋊C4—381no—
308C42—191no—
309C42—381no—
310C42C22×D1911yescharacteristic
311C23—21no—
312C23—21no—
313C23—21no—
314C23—191no—
315C23—381no—
316C23—762no—
317C23—1521no—
318C23—1521no—
319Q8—21no—
320Q8—21no—
321Q8—381no—
322Q8—381no—
323Q8—1521no—
324D4—21no—
325D4—21no—
326D4—21no—
327D4—21no—
328D4—21no—
329D4—21no—
330D4—81no—
331D4—81no—
332D4—381no—
333D4—381no—
334D4—762no—
335D4—762no—
336D4—1521no—
337D4—1521no—
338D4—1521no—
339C2×C4—21no—
340C2×C4—191no—
341C2×C4—191no—
342C2×C4—191no—
343C2×C4—381no—
344C2×C4—381no—
345C2×C4—381no—
346C2×C4—381no—
347C2×C4—381no—
348C2×C4—762no—
349C2×C4—1521no—
350C2×C4D4×D1911yescharacteristic
351C2×C4D4×D1911yescharacteristic
352C2×C4C23×D1911yescharacteristic
353C8—21no—
354C8—21no—
355C8—381no—
356C8—381no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—381no—
367C22—381no—
368C22—381no—
369C22—761no—
370C22—761no—
371C22—761no—
372C22—1524no—
373C22C2×D4×D1911yescharacteristic
374C4—21no—
375C4—21no—
376C4—41no—
377C4—381no—
378C4—381no—
379C4—381no—
380C4—761no—
381C4—761no—
382C4—761no—
383C4#1059743011yescharacteristic
384C4#1059743011yescharacteristic
385C2—81no—
386C2—81no—
387C2—81no—
388C2—761no—
389C2—1521no—
390C2#1192710711yescharacteristic
391C2#1192734811yescharacteristic
392C2#1192735411yescharacteristic
subgroupG/H
centerC22C2×D4×D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#496C2
socleC22×C19C22×D4
hypercenter#496D19
hypocenterC19#3224
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C42 ◁ #496

Complements

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

NH ≅ G/Ntype
1. #11927163C2semidirect
2. #11927107C2semidirect
3. #11926926C2semidirect
4. #11926904C2semidirect
5. #11926890C2semidirect
6. #11926764C2semidirect
7. #11926757C2semidirect
8. #11926742C2semidirect
9. #11926737C2semidirect
10. #11926703C2semidirect
11. #11926693C2semidirect
12. #11926686C2semidirect
13. #11926676C2semidirect
14. #11926606C2semidirect
15. C19×#496C2semidirect
19. C2×SD16×C19C22semidirect
21. C2×D8×C19C22semidirect
23. C19×#124C22semidirect
25. Q8×Dic19C22semidirect
26. C2×#64528C22semidirect
35. D4×Dic19C22semidirect
36. C2×#64526C22semidirect
44. #10597315C22semidirect
45. C19×#97C22semidirect
48. #10597289C22semidirect
49. #10597289C22semidirect
54. #10597273C22semidirect
55. #10597273C22semidirect
56. Dic19⋊C8C22semidirect
57. Dic19⋊C8C22semidirect
58. C4×C19⋊C8C22semidirect
191. #496D19semidirect
218. C2×SD16C2×D19semidirect
221. C2×D8C2×D19semidirect
229. #124C2×D19semidirect
253. #97C2×D19semidirect
255. C19#3224semidirect

Maximal subgroups

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

subgroupindex
#119271632
#119271072
#119269262
#119269042
#119268902
#119267642
#119267572
#119267422
#119267372
#119267032
#119266932
#119266862
#119266762
#119266062
C19×#4962
#322419