Finite Group Databasebeta

← #14574725

Subgroups — #14574725

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#11927161C211yesmaximal, characteristic, complemented
2#11927111C211yesmaximal, characteristic, complemented
3#11926932C211yesmaximal, characteristic, complemented
4#11926927C211yesmaximal, characteristic, complemented
5#11926902C211yesmaximal, characteristic, complemented
6#11926889C211yesmaximal, characteristic, complemented
7#11926765C211yesmaximal, characteristic, complemented
8#11926757C211yesmaximal, characteristic, complemented
9#11926743C211yesmaximal, characteristic, complemented
10#11926737C211yesmaximal, characteristic, complemented
11#11926708C211yesmaximal, characteristic, complemented
12#11926695C211yesmaximal, characteristic, complemented
13#11926687C211yesmaximal, 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#10597384—21no—
26#10597384—21no—
27#10597382—21no—
28#10597382C2211yescharacteristic
29#10597382C2211yescharacteristic
30#10597382C2211yescharacteristic, complemented
31#10597381—21no—
32D4×Dic19C2211yescharacteristic, complemented
33C2×#64526C2211yescharacteristic
34C2×#64526C2211yescharacteristic
35C2×#64526C2211yescharacteristic, complemented
36C2×#64525C2211yescharacteristic, complemented
37#10597372C2211yescharacteristic
38#10597370C2211yescharacteristic
39C2×Dic76C2211yescharacteristic, complemented
40C2×#64516C2211yescharacteristic, complemented
41#10597334C2211yescharacteristic, complemented
42#10597333C2211yescharacteristic, complemented
43#10597325—21no—
44#10597324—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—
73C22×Dic19—21no—
74#64541—41no—
75#64541—41no—
76C2×D76C2311yescharacteristic
77C2×C4×D19—21no—
78C2×Dic38—21no—
79C2×Dic38C2311yescharacteristic
80C2×Dic38C2311yescharacteristic
81D8×C19—41no—
82D8×C19—41no—
83C2×C8×C19C2311yescharacteristic
84C2×C8×C19C2311yescharacteristic
85C4⋊C4×C19C2311yescharacteristic
86C22⋊C4×C19—21no—
87C22⋊Dic19—21no—
88C22⋊Dic19—21no—
89C22⋊Dic19—21no—
90C22⋊Dic19—21no—
91C22⋊Dic19—21no—
92C22⋊Dic19—21no—
93C22⋊Dic19—21no—
94C22⋊Dic19—21no—
95C22⋊Dic19D411yescharacteristic
96C22⋊Dic19D411yescharacteristic
97#64526—41no—
98#64526—41no—
99#64526—41no—
100#64525—41no—
101C4⋊Dic19D411yescharacteristic
102C4⋊Dic19D411yescharacteristic
103C4⋊Dic19C2311yescharacteristic
104Dic19⋊C4—21no—
105Dic19⋊C4—21no—
106Dic19⋊C4—21no—
107C4×Dic19—21no—
108C4×Dic19C2311yescharacteristic
109C4×Dic19C2311yescharacteristic
110C2×C19⋊C8C2311yescharacteristic
111C2×C19⋊C8C2311yescharacteristic
112Dic76—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—
122D4×C19—21no—
123D4×C19—21no—
124D4×C19—21no—
125D4×C19—21no—
126D4×C19—21no—
127D4×C19—21no—
128D4×C19—42no—
129D4×C19—81no—
130C2×C4×C19—21no—
131C2×C4×C19—21no—
132C2×C4×C19—21no—
133C2×C4×C19C2×D411yescharacteristic
134C2×C4×C19C2411yescharacteristic
135C22⋊D19—42no—
136C22⋊D19—81no—
137C22⋊D19—81no—
138C22⋊D19—81no—
139C22⋊D19—81no—
140C2×Dic19—21no—
141C2×Dic19—21no—
142C2×Dic19—21no—
143C2×Dic19—81no—
144C2×Dic19C2×D411yescharacteristic
145C2×Dic19C2×D411yescharacteristic
146C2×Dic19C2×D411yescharacteristic
147C2×Dic19C2×D411yescharacteristic
148D76—21no—
149D76—21no—
150C4×D19—42no—
151Dic38—21no—
152Dic38—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—21no—
162C22×C19—21no—
163C22×C19—21no—
164C22×C19—41no—
165C22×C19—41no—
166C22×C19—41no—
167C22×C19—41no—
168C22×C19—41no—
169C22×C19—41no—
170C22×C19—41no—
171C22×C19—41no—
172C22×C19—41no—
173C22×C19—84no—
174C22×C19C22×D411yescharacteristic
175C2×D19—41no—
176C2×D19—41no—
177C2×D19—41no—
178C4×C19—21no—
179C4×C19—41no—
180C4×C19H(5,𝔽2)11yescharacteristic
181C4×C19H(5,𝔽2)11yescharacteristic
182Dic19—21no—
183Dic19—21no—
184Dic19—21no—
185Dic19—21no—
186Dic19—41no—
187Dic19—41no—
188Dic19—41no—
189#542—191no—
190#535—191no—
191#496—191no—
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#447D1911yescharacteristic, complemented
203#433—191no—
204C2×C19—41no—
205C2×C19—81no—
206C2×C19—81no—
207C2×C19—81no—
208C2×C19#53511yescharacteristic
209C2×C19#57611yescharacteristic
210C2×C19#57711yescharacteristic
211D19—81no—
212C2×#41—191no—
213C22×D4C2×D1911yescharacteristic
214C2×Q16—191no—
215C2×SD16—191no—
216C2×SD16—191no—
217C2×SD16—191no—
218C2×SD16—191no—
219C2×D8—191no—
220C2×D8C2×D1911yescharacteristic
221C2×D8C2×D1911yescharacteristic
222C4⋊Q8—191no—
223#127—191no—
224#127—191no—
225#126—381no—
226#124—191no—
227#124—191no—
228#124—191no—
229#124—381no—
230#123—381no—
231C22⋊Q8—191no—
232C22⋊Q8—381no—
233#121—381no—
234#121—381no—
235#121C2×D1911yescharacteristic
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#102C2×D1911yescharacteristic
250#102C2×D1911yescharacteristic
251C22⋊C8—191no—
252C22⋊C8C2×D1911yescharacteristic
253#97—191no—
254C4×C8—191no—
255C19#322411yescharacteristic, complemented, Sylow
256C24—21no—
257#41—761no—
258#41—761no—
259C2×Q8—191no—
260C2×Q8—191no—
261C2×Q8—381no—
262C2×D4—21no—
263C2×D4—21no—
264C2×D4—41no—
265C2×D4—41no—
266C2×D4—191no—
267C2×D4—381no—
268C2×D4—381no—
269C2×D4—381no—
270C2×D4—381no—
271C2×D4—381no—
272C2×D4C22×D1911yescharacteristic
273C2×D4C22×D1911yescharacteristic
274C2×D4C22×D1911yescharacteristic
275C22×C4—381no—
276C22×C4—381no—
277C22×C4C22×D1911yescharacteristic
278Q16—761no—
279SD16—761no—
280SD16—761no—
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—381no—
294C4⋊C4—381no—
295C4⋊C4—381no—
296C4⋊C4C22×D1911yescharacteristic
297C22⋊C4—21no—
298C22⋊C4—191no—
299C22⋊C4—191no—
300C22⋊C4—381no—
301C22⋊C4—381no—
302C22⋊C4—381no—
303C22⋊C4—381no—
304C22⋊C4—381no—
305C22⋊C4—381no—
306C22⋊C4—381no—
307C22⋊C4—381no—
308C42—191no—
309C42—191no—
310C42—381no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—42no—
315C23—81no—
316C23—81no—
317C23—381no—
318C23D4×D1911yescharacteristic
319Q8—381no—
320Q8—381no—
321Q8—381no—
322Q8—381no—
323Q8—1521no—
324D4—21no—
325D4—21no—
326D4—21no—
327D4—21no—
328D4—21no—
329D4—21no—
330D4—42no—
331D4—81no—
332D4—381no—
333D4—381no—
334D4—762no—
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—191no—
346C2×C4—381no—
347C2×C4—381no—
348C2×C4—381no—
349C2×C4—762no—
350C2×C4—1521no—
351C2×C4D4×D1911yescharacteristic
352C2×C4C23×D1911yescharacteristic
353C8—21no—
354C8—21no—
355C8—381no—
356C8—381no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—84no—
370C22—761no—
371C22—761no—
372C22—761no—
373C22C2×D4×D1911yescharacteristic
374C4—21no—
375C4—41no—
376C4—381no—
377C4—381no—
378C4—381no—
379C4—381no—
380C4—761no—
381C4—761no—
382C4—761no—
383C4#1059743011yescharacteristic
384C4#1059743011yescharacteristic
385C2—41no—
386C2—81no—
387C2—81no—
388C2—81no—
389C2—1521no—
390C2#1192710911yescharacteristic
391C2#1192734511yescharacteristic
392C2#1192735411yescharacteristic
subgroupG/H
centerC22C2×D4×D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#447C2
socleC22×C19C22×D4
hypercenter#447D19
hypocenterC19#3224
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. #11927161C2semidirect
2. #11927111C2semidirect
3. #11926932C2semidirect
4. #11926927C2semidirect
5. #11926902C2semidirect
6. #11926889C2semidirect
7. #11926765C2semidirect
8. #11926757C2semidirect
9. #11926743C2semidirect
10. #11926737C2semidirect
11. #11926708C2semidirect
12. #11926695C2semidirect
13. #11926687C2semidirect
14. #11926602C2semidirect
15. C19×#447C2semidirect
30. #10597382C22semidirect
32. D4×Dic19C22semidirect
35. C2×#64526C22semidirect
36. C2×#64525C22semidirect
39. C2×Dic76C22semidirect
40. C2×#64516C22semidirect
41. #10597334C22semidirect
42. #10597333C22semidirect
51. #10597278C22semidirect
52. #10597273C22semidirect
53. #10597272C22semidirect
54. Dic19⋊C8C22semidirect
55. Dic19⋊C8C22semidirect
56. C8×Dic19C22semidirect
57. #10597267C22semidirect
58. #10597266C22semidirect
202. #447D19semidirect
255. C19#3224semidirect

Maximal subgroups

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

subgroupindex
#119271612
#119271112
#119269322
#119269272
#119269022
#119268892
#119267652
#119267572
#119267432
#119267372
#119267082
#119266952
#119266872
#119266022
C19×#4472
#322419