Finite Group Databasebeta

← #14574730

Subgroups — #14574730

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#11927168C211yesmaximal, characteristic, complemented
2#11927112C211yesmaximal, characteristic, complemented
3#11926933C211yesmaximal, characteristic, complemented
4#11926926C211yesmaximal, characteristic, complemented
5#11926892C211yesmaximal, characteristic, complemented
6#11926769C211yesmaximal, characteristic, complemented
7#11926762C211yesmaximal, characteristic, complemented
8#11926743C211yesmaximal, characteristic, complemented
9#11926738C211yesmaximal, characteristic, complemented
10#11926709C211yesmaximal, characteristic, complemented
11#11926696C211yesmaximal, characteristic, complemented
12#11926692C211yesmaximal, characteristic, complemented
13#11926679C211yesmaximal, characteristic, complemented
14#11926606C211yesmaximal, characteristic, complemented
15C19×#489C211yesmaximal, characteristic, complemented
16C2×#64545C2211yescharacteristic
17C2×D4×D19C2211yescharacteristic
18C19×C4⋊Q8C2211yescharacteristic, complemented
19C19×#124C2211yescharacteristic
20#10597393—21no—
21#10597393C2211yescharacteristic
22#10597392—21no—
23C2×#64528C2211yescharacteristic, complemented
24C2×#64527C2211yescharacteristic, complemented
25#10597386C2211yescharacteristic
26C2×#64526C2211yescharacteristic
27C2×#64525C2211yescharacteristic
28C2×D152C2211yescharacteristic
29C2×D152C2211yescharacteristic, complemented
30C2×#64516C2211yescharacteristic
31C2×#64516C2211yescharacteristic, complemented
32#10597344—21no—
33#10597343C2211yescharacteristic
34#10597341C2211yescharacteristic
35#10597340—21no—
36#10597339C2211yescharacteristic, complemented
37#10597333C2211yescharacteristic, complemented
38#10597330—21no—
39#10597330—21no—
40#10597328—21no—
41#10597328—21no—
42#10597321C2211yescharacteristic, complemented
43#10597320C2211yescharacteristic
44#10597318C2211yescharacteristic
45C19×#103C2211yescharacteristic, complemented
46C19×#103C2211yescharacteristic, complemented
47C19×#102C2211yescharacteristic
48C19×#102C2211yescharacteristic
49C19×#97C2211yescharacteristic, complemented
50(C2×D19)⋊C8C2211yescharacteristic
51(C2×D19)⋊C8C2211yescharacteristic
52Dic19⋊C8C2211yescharacteristic, complemented
53Dic19⋊C8C2211yescharacteristic, complemented
54#10597266C2211yescharacteristic
55#10597266C2211yescharacteristic
56#10597266C2211yescharacteristic, complemented
57#10597266C2211yescharacteristic, complemented
58C4×C19⋊C8C2211yescharacteristic, complemented
59C23×D19—21no—
60C2×Q8×C19—21no—
61C2×Q8×C19C2311yescharacteristic
62C2×D4×C19C2311yescharacteristic
63C2×C22⋊D19—21no—
64C2×C22⋊D19—21no—
65C2×C22⋊D19—21no—
66#64545—41no—
67#64545—41no—
68D4×D19—41no—
69D4×D19—41no—
70C2×D76—21no—
71C2×D76—21no—
72C2×D76—21no—
73C2×D76—21no—
74C2×D76C2311yescharacteristic
75C2×D76C2311yescharacteristic
76C2×D76C2311yescharacteristic
77C2×C4×D19—21no—
78C2×C4×D19—21no—
79C2×C4×D19C2311yescharacteristic
80C2×Dic38C2311yescharacteristic
81C2×C8×C19C2311yescharacteristic
82C2×C8×C19C2311yescharacteristic
83C4⋊C4×C19—21no—
84C4⋊C4×C19C2311yescharacteristic
85C4⋊C4×C19C2311yescharacteristic
86C22⋊C4×C19—21no—
87C22⋊C4×C19—21no—
88C42×C19C2311yescharacteristic
89#64528—41no—
90#64527—41no—
91#64526—41no—
92#64525—41no—
93(C2×D19)⋊C4—21no—
94(C2×D19)⋊C4—21no—
95(C2×D19)⋊C4—21no—
96(C2×D19)⋊C4—21no—
97(C2×D19)⋊C4—21no—
98(C2×D19)⋊C4—21no—
99(C2×D19)⋊C4—21no—
100(C2×D19)⋊C4D411yescharacteristic
101(C2×D19)⋊C4D411yescharacteristic
102C4⋊Dic19—21no—
103Dic19⋊C4—21no—
104Dic19⋊C4D411yescharacteristic
105Dic19⋊C4D411yescharacteristic
106C4×Dic19—21no—
107C4×Dic19C2311yescharacteristic
108C2×C19⋊C8C2311yescharacteristic
109C2×C19⋊C8C2311yescharacteristic
110D152—41no—
111D152—41no—
112#64516—41no—
113#64516—41no—
114C23×C19—21no—
115C22×D19—21no—
116C22×D19—21no—
117C22×D19—21no—
118C22×D19—42no—
119C22×D19—81no—
120C22×D19—81no—
121C22×D19C2×D411yescharacteristic
122Q8×C19—21no—
123Q8×C19—21no—
124Q8×C19—81no—
125D4×C19—21no—
126D4×C19—21no—
127C2×C4×C19—21no—
128C2×C4×C19—21no—
129C2×C4×C19—21no—
130C2×C4×C19C2×D411yescharacteristic
131C2×C4×C19C2×D411yescharacteristic
132C2×C4×C19C2411yescharacteristic
133C22⋊D19—42no—
134C22⋊D19—81no—
135C22⋊D19—81no—
136C2×Dic19—21no—
137C2×Dic19C2×D411yescharacteristic
138C2×Dic19C2×D411yescharacteristic
139C2×Dic19C2×D411yescharacteristic
140D76—21no—
141D76—21no—
142D76—21no—
143D76—21no—
144D76—21no—
145D76—21no—
146D76—42no—
147D76—81no—
148D76—81no—
149D76—81no—
150C4×D19—21no—
151C4×D19—21no—
152C4×D19—42no—
153C4×D19—81no—
154Dic38—21no—
155Dic38—21no—
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×C19C22×D411yescharacteristic
165C2×D19—21no—
166C2×D19—21no—
167C2×D19—21no—
168C2×D19—41no—
169C2×D19—41no—
170C2×D19—41no—
171C2×D19—41no—
172C2×D19—41no—
173C2×D19—41no—
174C2×D19—41no—
175C2×D19—41no—
176C2×D19—41no—
177C2×D19—84no—
178C4×C19—21no—
179C4×C19—21no—
180C4×C19—41no—
181C4×C19—41no—
182C4×C19—41no—
183C4×C19H(5,𝔽2)11yescharacteristic
184C4×C19H(5,𝔽2)11yescharacteristic
185Dic19—21no—
186Dic19—21no—
187Dic19—21no—
188Dic19—41no—
189#542—191no—
190#535—191no—
191#496—191no—
192#495—191no—
193#489D1911yescharacteristic, complemented
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#53511yescharacteristic
206C2×C19#57611yescharacteristic
207C2×C19#57711yescharacteristic
208D19—41no—
209D19—81no—
210D19—81no—
211D19—81no—
212C2×#41—191no—
213C22×D4—191no—
214C2×Q16—191no—
215C2×SD16—191no—
216C2×SD16—191no—
217C2×SD16—191no—
218C2×SD16—191no—
219C2×D8—191no—
220C2×D8—191no—
221C2×D8—191no—
222C4⋊Q8C2×D1911yescharacteristic, complemented
223#127—191no—
224#127—191no—
225#126—381no—
226#124—191no—
227#124—191no—
228#124—381no—
229#124C2×D1911yescharacteristic
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#103C2×D1911yescharacteristic, complemented
244#103C2×D1911yescharacteristic, complemented
245#102—191no—
246#102—191no—
247#102—191no—
248#102—191no—
249#102C2×D1911yescharacteristic
250#102C2×D1911yescharacteristic
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—21no—
260C2×Q8—191no—
261C2×Q8C22×D1911yescharacteristic
262C2×D4—191no—
263C2×D4—191no—
264C2×D4—191no—
265C2×D4—381no—
266C2×D4—381no—
267C2×D4—381no—
268C2×D4—381no—
269C2×D4—381no—
270C2×D4—381no—
271C2×D4—381no—
272C2×D4—761no—
273C2×D4—761no—
274C2×D4C22×D1911yescharacteristic
275C22×C4—191no—
276C22×C4—381no—
277C22×C4—381no—
278Q16—761no—
279SD16—761no—
280SD16—761no—
281SD16—761no—
282SD16—761no—
283D8—761no—
284D8—761no—
285D8—761no—
286C2×C8—191no—
287C2×C8—191no—
288C2×C8C22×D1911yescharacteristic
289C2×C8C22×D1911yescharacteristic
290C4⋊C4—21no—
291C4⋊C4—191no—
292C4⋊C4—191no—
293C4⋊C4—381no—
294C4⋊C4—381no—
295C4⋊C4C22×D1911yescharacteristic
296C4⋊C4C22×D1911yescharacteristic
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—191no—
313C23—381no—
314C23—381no—
315C23—381no—
316C23—762no—
317C23—1521no—
318C23—1521no—
319Q8—21no—
320Q8—21no—
321Q8—81no—
322Q8—381no—
323Q8—381no—
324D4—21no—
325D4—21no—
326D4—381no—
327D4—381no—
328D4—381no—
329D4—381no—
330D4—381no—
331D4—381no—
332D4—762no—
333D4—762no—
334D4—1521no—
335D4—1521no—
336D4—1521no—
337D4—1521no—
338D4—1521no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—191no—
343C2×C4—191no—
344C2×C4—191no—
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—381no—
361C22—381no—
362C22—381no—
363C22—761no—
364C22—761no—
365C22—761no—
366C22—761no—
367C22—761no—
368C22—761no—
369C22—761no—
370C22—761no—
371C22—761no—
372C22—1524no—
373C22C2×D4×D1911yescharacteristic
374C4—21no—
375C4—21no—
376C4—41no—
377C4—41no—
378C4—41no—
379C4—381no—
380C4—381no—
381C4—381no—
382C4—761no—
383C4#1059743511yescharacteristic
384C4#1059743511yescharacteristic
385C2—81no—
386C2—761no—
387C2—1521no—
388C2—1521no—
389C2—1521no—
390C2#1192711211yescharacteristic
391C2#1192734811yescharacteristic
392C2#1192735311yescharacteristic
subgroupG/H
centerC22C2×D4×D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#489C2
socleC22×C19C22×D4
hypercenter#489D19
hypocenterC19#3224
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
1. #11927168C2semidirect
2. #11927112C2semidirect
3. #11926933C2semidirect
4. #11926926C2semidirect
5. #11926892C2semidirect
6. #11926769C2semidirect
7. #11926762C2semidirect
8. #11926743C2semidirect
9. #11926738C2semidirect
10. #11926709C2semidirect
11. #11926696C2semidirect
12. #11926692C2semidirect
13. #11926679C2semidirect
14. #11926606C2semidirect
15. C19×#489C2semidirect
18. C19×C4⋊Q8C22semidirect
23. C2×#64528C22semidirect
24. C2×#64527C22semidirect
29. C2×D152C22semidirect
31. C2×#64516C22semidirect
36. #10597339C22semidirect
37. #10597333C22semidirect
42. #10597321C22semidirect
45. C19×#103C22semidirect
46. C19×#103C22semidirect
49. C19×#97C22semidirect
52. Dic19⋊C8C22semidirect
53. Dic19⋊C8C22semidirect
56. #10597266C22semidirect
57. #10597266C22semidirect
58. C4×C19⋊C8C22semidirect
193. #489D19semidirect
222. C4⋊Q8C2×D19semidirect
243. #103C2×D19semidirect
244. #103C2×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
#119271682
#119271122
#119269332
#119269262
#119268922
#119267692
#119267622
#119267432
#119267382
#119267092
#119266962
#119266922
#119266792
#119266062
C19×#4892
#322419