Finite Group Databasebeta

← #14574723

Subgroups — #14574723

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#11927113C211yesmaximal, characteristic, complemented
2#11926934C211yesmaximal, characteristic, complemented
3#11926926C211yesmaximal, characteristic, complemented
4#11926906C211yesmaximal, characteristic, complemented
5#11926892C211yesmaximal, characteristic, complemented
6#11926766C211yesmaximal, characteristic, complemented
7#11926759C211yesmaximal, characteristic, complemented
8#11926744C211yesmaximal, characteristic, complemented
9#11926739C211yesmaximal, characteristic, complemented
10#11926704C211yesmaximal, characteristic, complemented
11#11926694C211yesmaximal, characteristic, complemented
12#11926687C211yesmaximal, characteristic, complemented
13#11926677C211yesmaximal, characteristic, complemented
14#11926605C211yesmaximal, characteristic, complemented
15C19×#542C211yesmaximal, characteristic, complemented
16C2×#64541C2211yescharacteristic
17C22×D76C2211yescharacteristic
18C19×C4⋊Q8C2211yescharacteristic, complemented
19C19×#126—21no—
20C19×#124—21no—
21C19×#124C2211yescharacteristic, complemented
22C19×#123—21no—
23C19×C22⋊Q8—21no—
24C19×C22⋊Q8C2211yescharacteristic
25C19×#121C2211yescharacteristic
26C4×Q8×C19C2211yescharacteristic, complemented
27C4×D4×C19C2211yescharacteristic, complemented
28C19×#117C2211yescharacteristic
29C2×#64528C2211yescharacteristic, complemented
30C2×#64527C2211yescharacteristic
31C2×#64527C2211yescharacteristic
32C2×#64527C2211yescharacteristic, complemented
33C2×#64526C2211yescharacteristic, complemented
34C2×#64525C2211yescharacteristic
35C2×#64525C2211yescharacteristic
36C2×#64525C2211yescharacteristic, complemented
37#10597341—21no—
38#10597341—21no—
39#10597328—21no—
40#10597328—21no—
41#10597321C2211yescharacteristic
42#10597321C2211yescharacteristic
43#10597320C2211yescharacteristic
44#10597320C2211yescharacteristic
45C22⋊(C19⋊C8)C2211yescharacteristic
46C22⋊(C19⋊C8)C2211yescharacteristic
47#10597267C2211yescharacteristic, complemented
48#10597267C2211yescharacteristic, complemented
49#10597266C2211yescharacteristic
50#10597266C2211yescharacteristic
51#10597266C2211yescharacteristic
52#10597266C2211yescharacteristic
53#10597266C2211yescharacteristic, complemented
54#10597266C2211yescharacteristic, complemented
55C4⋊(C19⋊C8)C2211yescharacteristic, complemented
56C4⋊(C19⋊C8)C2211yescharacteristic, complemented
57#10597260C2211yescharacteristic, complemented
58C4×C19⋊C8C2211yescharacteristic, complemented
59C23×D19—21no—
60C2×Q8×C19—21no—
61C2×Q8×C19C2311yescharacteristic
62C2×D4×C19—21no—
63C2×D4×C19C2311yescharacteristic
64C22×C4×C19—21no—
65C22×C4×C19C2311yescharacteristic
66C2×C22⋊D19—21no—
67#64541—41no—
68#64541—41no—
69C2×D76—21no—
70C2×D76—21no—
71C2×D76—21no—
72C2×D76—21no—
73C2×D76—21no—
74C2×D76—41no—
75C2×D76—41no—
76C2×D76C2311yescharacteristic
77C2×D76C2311yescharacteristic
78C2×D76C2311yescharacteristic
79C2×C4×D19—21no—
80C2×Dic38C2311yescharacteristic
81C4⋊C4×C19—21no—
82C4⋊C4×C19—21no—
83C4⋊C4×C19—21no—
84C4⋊C4×C19D411yescharacteristic
85C4⋊C4×C19D411yescharacteristic
86C4⋊C4×C19C2311yescharacteristic
87C4⋊C4×C19C2311yescharacteristic
88C22⋊C4×C19—21no—
89C22⋊C4×C19—21no—
90C22⋊C4×C19—21no—
91C22⋊C4×C19—21no—
92C22⋊C4×C19—21no—
93C22⋊C4×C19D411yescharacteristic
94C22⋊C4×C19D411yescharacteristic
95C42×C19—21no—
96C42×C19C2311yescharacteristic
97C42×C19C2311yescharacteristic
98#64528—41no—
99#64527—41no—
100#64527—41no—
101#64527—41no—
102#64526—41no—
103#64525—41no—
104#64525—41no—
105#64525—41no—
106(C2×D19)⋊C4—21no—
107(C2×D19)⋊C4—21no—
108(C2×D19)⋊C4—21no—
109(C2×D19)⋊C4—21no—
110C2×C19⋊C8C2311yescharacteristic
111C2×C19⋊C8C2311yescharacteristic
112C2×C19⋊C8C2311yescharacteristic
113C2×C19⋊C8C2311yescharacteristic
114C23×C19—21no—
115C23×C19C2×D411yescharacteristic
116C22×D19—21no—
117C22×D19—21no—
118C22×D19—21no—
119C22×D19—42no—
120C22×D19—81no—
121C22×D19—81no—
122Q8×C19—21no—
123Q8×C19—21no—
124Q8×C19—81no—
125D4×C19—21no—
126D4×C19—21no—
127D4×C19—81no—
128C2×C4×C19—21no—
129C2×C4×C19—21no—
130C2×C4×C19—21no—
131C2×C4×C19—21no—
132C2×C4×C19—21no—
133C2×C4×C19—81no—
134C2×C4×C19C2×D411yescharacteristic
135C2×C4×C19C2×D411yescharacteristic
136C2×C4×C19C2×D411yescharacteristic
137C2×C4×C19C2×D411yescharacteristic
138C2×C4×C19C2×D411yescharacteristic
139C2×C4×C19C2411yescharacteristic
140C22⋊D19—42no—
141C2×Dic19—21no—
142D76—21no—
143D76—21no—
144D76—21no—
145D76—21no—
146D76—21no—
147D76—21no—
148D76—42no—
149D76—81no—
150D76—81no—
151D76—81no—
152D76—81no—
153C4×D19—42no—
154Dic38—21no—
155Dic38—21no—
156C19⋊C8—21no—
157C19⋊C8—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×C19C22×D411yescharacteristic
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—21no—
181C4×C19—21no—
182C4×C19—21no—
183C4×C19—41no—
184C4×C19—41no—
185C4×C19—41no—
186C4×C19H(5,𝔽2)11yescharacteristic
187C4×C19H(5,𝔽2)11yescharacteristic
188Dic19—41no—
189#542D1911yescharacteristic, complemented
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#447—191no—
203#433—191no—
204C2×C19—41no—
205C2×C19—81no—
206C2×C19#53511yescharacteristic
207C2×C19#57611yescharacteristic
208C2×C19#57711yescharacteristic
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—21no—
226#124—21no—
227#124—191no—
228#124—191no—
229#124C2×D1911yescharacteristic, complemented
230#123—21no—
231C22⋊Q8—21no—
232C22⋊Q8C2×D1911yescharacteristic
233#121—381no—
234#121—381no—
235#121C2×D1911yescharacteristic
236#120—381no—
237#120—381no—
238C4×Q8C2×D1911yescharacteristic, complemented
239C4×D4C2×D1911yescharacteristic, complemented
240#117C2×D1911yescharacteristic
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#97—191no—
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—21no—
263C2×D4—191no—
264C2×D4—191no—
265C2×D4—191no—
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—21no—
276C22×C4—381no—
277C22×C4C22×D1911yescharacteristic
278Q16—761no—
279SD16—761no—
280SD16—761no—
281SD16—761no—
282SD16—761no—
283D8—761no—
284D8—761no—
285D8—761no—
286C2×C8—191no—
287C2×C8—191no—
288C2×C8—191no—
289C2×C8—191no—
290C4⋊C4—21no—
291C4⋊C4—21no—
292C4⋊C4—21no—
293C4⋊C4C22⋊D1911yescharacteristic
294C4⋊C4C22⋊D1911yescharacteristic
295C4⋊C4C22×D1911yescharacteristic
296C4⋊C4C22×D1911yescharacteristic
297C22⋊C4—21no—
298C22⋊C4—21no—
299C22⋊C4—21no—
300C22⋊C4—21no—
301C22⋊C4—21no—
302C22⋊C4—381no—
303C22⋊C4—381no—
304C22⋊C4—381no—
305C22⋊C4—381no—
306C22⋊C4C22⋊D1911yescharacteristic
307C22⋊C4C22⋊D1911yescharacteristic
308C42—21no—
309C42C22×D1911yescharacteristic
310C42C22×D1911yescharacteristic
311C23—21no—
312C23—381no—
313C23—381no—
314C23—381no—
315C23—762no—
316C23—1521no—
317C23—1521no—
318C23C2×C22⋊D1911yescharacteristic
319Q8—21no—
320Q8—21no—
321Q8—81no—
322Q8—381no—
323Q8—381no—
324D4—21no—
325D4—21no—
326D4—81no—
327D4—381no—
328D4—381no—
329D4—381no—
330D4—381no—
331D4—381no—
332D4—381no—
333D4—762no—
334D4—762no—
335D4—1521no—
336D4—1521no—
337D4—1521no—
338D4—1521no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—81no—
345C2×C4—381no—
346C2×C4—762no—
347C2×C4C2×C22⋊D1911yescharacteristic
348C2×C4C2×C22⋊D1911yescharacteristic
349C2×C4C2×C22⋊D1911yescharacteristic
350C2×C4C2×C22⋊D1911yescharacteristic
351C2×C4C2×C22⋊D1911yescharacteristic
352C2×C4C23×D1911yescharacteristic
353C8—381no—
354C8—381no—
355C8—381no—
356C8—381no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—761no—
364C22—761no—
365C22—761no—
366C22—761no—
367C22—761no—
368C22—761no—
369C22—761no—
370C22—761no—
371C22—761no—
372C22—1524no—
373C22C22×C22⋊D1911yescharacteristic
374C4—21no—
375C4—21no—
376C4—21no—
377C4—21no—
378C4—21no—
379C4—41no—
380C4—41no—
381C4—41no—
382C4—761no—
383C4#1059743511yescharacteristic
384C4#1059743511yescharacteristic
385C2—41no—
386C2—81no—
387C2—1521no—
388C2—1521no—
389C2—1521no—
390C2#1192710811yescharacteristic
391C2#1192734711yescharacteristic
392C2#1192735211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#542C2
socleC22×C19C22×D4
hypercenter#542D19
hypocenterC19#3224
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ #117 ◁ #542

Complements

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

NH ≅ G/Ntype
1. #11927113C2semidirect
2. #11926934C2semidirect
3. #11926926C2semidirect
4. #11926906C2semidirect
5. #11926892C2semidirect
6. #11926766C2semidirect
7. #11926759C2semidirect
8. #11926744C2semidirect
9. #11926739C2semidirect
10. #11926704C2semidirect
11. #11926694C2semidirect
12. #11926687C2semidirect
13. #11926677C2semidirect
14. #11926605C2semidirect
15. C19×#542C2semidirect
18. C19×C4⋊Q8C22semidirect
21. C19×#124C22semidirect
26. C4×Q8×C19C22semidirect
27. C4×D4×C19C22semidirect
29. C2×#64528C22semidirect
32. C2×#64527C22semidirect
33. C2×#64526C22semidirect
36. C2×#64525C22semidirect
47. #10597267C22semidirect
48. #10597267C22semidirect
53. #10597266C22semidirect
54. #10597266C22semidirect
55. C4⋊(C19⋊C8)C22semidirect
56. C4⋊(C19⋊C8)C22semidirect
57. #10597260C22semidirect
58. C4×C19⋊C8C22semidirect
189. #542D19semidirect
222. C4⋊Q8C2×D19semidirect
229. #124C2×D19semidirect
238. C4×Q8C2×D19semidirect
239. C4×D4C2×D19semidirect
255. C19#3224semidirect

Maximal subgroups

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

subgroupindex
#119271132
#119269342
#119269262
#119269062
#119268922
#119267662
#119267592
#119267442
#119267392
#119267042
#119266942
#119266872
#119266772
#119266052
C19×#5422
#322419