Finite Group Databasebeta

← #14575590

Subgroups — #14575590

Order 2432.

442 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11927190C211yesmaximal, characteristic, complemented
2#11926906C211yesmaximal, characteristic, complemented
3#11926874C211yesmaximal, characteristic, complemented
4#11926862C211yesmaximal, characteristic, complemented
5#11926831C211yesmaximal, characteristic, complemented
6#11926795C211yesmaximal, characteristic, complemented
7#11926771C211yesmaximal, characteristic, complemented
8#11926759C211yesmaximal, characteristic, complemented
9#11926687C211yesmaximal, characteristic, complemented
10#11926677C211yesmaximal, characteristic, complemented
11#11926654C211yesmaximal, characteristic, complemented
12#11926616C211yesmaximal, characteristic, complemented
13#11926543C211yesmaximal, characteristic, complemented
14C2×#10597266C211yesmaximal, characteristic, complemented
15C19×#547C211yesmaximal, characteristic, complemented
16C2×#41×C19—21no—
17C2×#64541C2211yescharacteristic
18C22×D76C2211yescharacteristic
19C19×C4⋊Q8C2211yescharacteristic, complemented
20C19×#123—21no—
21C19×#123—21no—
22C19×C22⋊Q8—21no—
23C19×#121C2211yescharacteristic
24C19×#121C2211yescharacteristic, complemented
25C4×D4×C19C2211yescharacteristic
26C4×D4×C19C2211yescharacteristic, complemented
27C2×C4⋊C4×C19C2211yescharacteristic
28C2×C4⋊C4×C19C2211yescharacteristic, complemented
29#10597383—21no—
30C2×#64526C2211yescharacteristic, complemented
31C2×#64525C2211yescharacteristic
32C2×#64525C2211yescharacteristic
33#10597376C2211yescharacteristic
34#10597370C2211yescharacteristic
35C2×#64520C2211yescharacteristic, complemented
36C22×C19⋊C8C2211yescharacteristic
37#10597340—21no—
38#10597330—21no—
39C22⋊C4×D19—21no—
40#10597321C2211yescharacteristic
41C4×D76C2211yescharacteristic
42#10597289C2211yescharacteristic, complemented
43C22⋊(C19⋊C8)C2211yescharacteristic
44C22⋊(C19⋊C8)C2211yescharacteristic, complemented
45#10597267C2211yescharacteristic, complemented
46#10597267C2211yescharacteristic, complemented
47#10597267C2211yescharacteristic, complemented
48#10597266C2211yescharacteristic
49#10597266C2211yescharacteristic
50#10597266C2211yescharacteristic
51#10597266C2211yescharacteristic
52#10597266C2211yescharacteristic
53#10597266C2211yescharacteristic
54#10597265C2211yescharacteristic, complemented
55#10597265C2211yescharacteristic, complemented
56#10597265C2211yescharacteristic, complemented
57C4⋊(C19⋊C8)C2211yescharacteristic, complemented
58#10597260C2211yescharacteristic, complemented
59C23×D19—21no—
60#41×C19—44no—
61C2×Q8×C19—21no—
62C2×D4×C19—21no—
63C2×D4×C19—21no—
64C2×D4×C19D411yescharacteristic
65C2×D4×C19C2311yescharacteristic
66C22×C4×C19—21no—
67C22×C4×C19—21no—
68C22×C4×C19—21no—
69C22×C4×C19C2311yescharacteristic
70C22×C4×C19C2311yescharacteristic
71C2×C22⋊D19—21no—
72C2×C22⋊D19—21no—
73#64541—22no—
74#64541—41no—
75C2×D76—22no—
76C2×D76—21no—
77C2×D76—41no—
78C2×D76C2311yescharacteristic
79C2×D76C2311yescharacteristic
80C2×C4×D19—21no—
81C2×C4×D19—21no—
82C2×Dic38C2311yescharacteristic
83C4⋊C4×C19—21no—
84C4⋊C4×C19—21no—
85C4⋊C4×C19—21no—
86C4⋊C4×C19D411yescharacteristic
87C4⋊C4×C19C2311yescharacteristic
88C4⋊C4×C19C2311yescharacteristic
89C4⋊C4×C19C2311yescharacteristic
90C22⋊C4×C19—21no—
91C22⋊C4×C19—21no—
92C22⋊C4×C19—21no—
93C22⋊C4×C19D411yescharacteristic
94C22⋊C4×C19D411yescharacteristic
95C42×C19C2311yescharacteristic
96C22⋊Dic19—21no—
97#64526—41no—
98#64525—22no—
99#64525—41no—
100(C2×D19)⋊C4—21no—
101(C2×D19)⋊C4—21no—
102(C2×D19)⋊C4—21no—
103(C2×D19)⋊C4—21no—
104C4⋊Dic19C2311yescharacteristic
105Dic19⋊C4—21no—
106#64520—41no—
107C2×C19⋊C8—41no—
108C2×C19⋊C8C2311yescharacteristic
109C2×C19⋊C8C2311yescharacteristic
110C2×C19⋊C8C2311yescharacteristic
111C2×C19⋊C8C2311yescharacteristic
112C23×C19—21no—
113C23×C19C2×D411yescharacteristic
114C23×C19C2×D411yescharacteristic
115C22×D19—21no—
116C22×D19—21no—
117C22×D19—42no—
118C22×D19—42no—
119C22×D19—81no—
120Q8×C19—42no—
121D4×C19—22no—
122D4×C19—21no—
123D4×C19—21no—
124D4×C19—42no—
125D4×C19—42no—
126C2×C4×C19—21no—
127C2×C4×C19—21no—
128C2×C4×C19—21no—
129C2×C4×C19—21no—
130C2×C4×C19—21no—
131C2×C4×C19—21no—
132C2×C4×C19—21no—
133C2×C4×C19—42no—
134C2×C4×C19—42no—
135C2×C4×C19—42no—
136C2×C4×C19C2×D411yescharacteristic
137C2×C4×C19C2×D411yescharacteristic
138C2×C4×C19C2×D411yescharacteristic
139C2×C4×C19C2×D411yescharacteristic
140C2×C4×C19C2411yescharacteristic
141C22⋊D19—42no—
142C22⋊D19—81no—
143C2×Dic19—21no—
144C2×Dic19—21no—
145D76—21no—
146D76—21no—
147D76—21no—
148D76—42no—
149D76#4112yescomplemented
150C4×D19—42no—
151C4×D19—81no—
152Dic38—21no—
153Dic38—21no—
154C19⋊C8—21no—
155C19⋊C8—21no—
156C19⋊C8—21no—
157C19⋊C8—21no—
158#3306—191nomaximal, Sylow
159C22×C19—21no—
160C22×C19—21no—
161C22×C19—21no—
162C22×C19—21no—
163C22×C19—21no—
164C22×C19—41no—
165C22×C19—41no—
166C22×C19—41no—
167C22×C19AGL(1,ℤ/8)12yes—
168C22×C19C22×D411yescharacteristic
169C2×D19—22no—
170C2×D19—41no—
171C2×D19—41no—
172C2×D19—41no—
173C2×D19—41no—
174C2×D19—41no—
175C2×D19—84no—
176C4×C19—21no—
177C4×C19—21no—
178C4×C19—21no—
179C4×C19—21no—
180C4×C19—41no—
181C4×C19—41no—
182C4×C19—41no—
183C4×C19C2×#4111yescharacteristic
184C4×C19H(5,𝔽2)11yescharacteristic
185Dic19—41no—
186Dic19—41no—
187#547D1911yescharacteristic, complemented
188#546—191no—
189#489—191no—
190#483—191no—
191#481—191no—
192#476—191no—
193#469—191no—
194#465—191no—
195#463—191no—
196#449—191no—
197#447—191no—
198#442—191no—
199#435—191no—
200#417—191no—
201C2×#102—191no—
202C2×C19—22no—
203C2×C19—41no—
204C2×C19—81no—
205C2×C19#54611yescharacteristic
206C2×C19C2×AGL(1,ℤ/8)11yescharacteristic
207C2×C19#57711yescharacteristic
208D19—42no—
209D19—81no—
210C2×#41—21no—
211C2×#41—191no—
212C22×D4—191no—
213C2×SD16—191no—
214C2×D8—191no—
215C2×D8—191no—
216C2×M16—191no—
217C22×C8—191no—
218C4⋊Q8C2×D1911yescharacteristic, complemented
219#124—191no—
220#123—21no—
221#123—21no—
222#123—381no—
223C22⋊Q8—21no—
224C22⋊Q8—191no—
225#121—191no—
226#121—381no—
227#121C2×D1911yescharacteristic
228#121C2×D1911yescharacteristic, complemented
229#120—381no—
230C4×D4—191no—
231C4×D4C2×D1911yescharacteristic
232C4×D4C2×D1911yescharacteristic, complemented
233C2×C4⋊C4C2×D1911yescharacteristic
234C2×C4⋊C4C2×D1911yescharacteristic, complemented
235C2×C22⋊C4—381no—
236#106—191no—
237#106—191no—
238#106—191no—
239C4⋊C8—191no—
240#103—191no—
241#103—191no—
242#103—191no—
243#102—191no—
244#102—191no—
245#102—191no—
246#102—191no—
247#102—191no—
248#102—191no—
249#102—191no—
250C22⋊C8—191no—
251C22⋊C8—191no—
252#97—191no—
253C19#330611yescharacteristic, complemented, Sylow
254C24—381no—
255#41—44no—
256#41—382no—
257#41—761no—
258C2×Q8—21no—
259C2×Q8—191no—
260C2×D4—21no—
261C2×D4—21no—
262C2×D4—191no—
263C2×D4—191no—
264C2×D4—382no—
265C2×D4—381no—
266C2×D4—381no—
267C2×D4—381no—
268C2×D4—761no—
269C2×D4C22⋊D1911yescharacteristic
270C2×D4C22×D1911yescharacteristic
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—381no—
275C22×C4—381no—
276C22×C4C22×D1911yescharacteristic
277C22×C4C22×D1911yescharacteristic
278SD16—761no—
279D8—382no—
280D8—761no—
281M16—761no—
282C2×C8—191no—
283C2×C8—191no—
284C2×C8—191no—
285C2×C8—191no—
286C2×C8—761no—
287C4⋊C4—21no—
288C4⋊C4—21no—
289C4⋊C4—21no—
290C4⋊C4—191no—
291C4⋊C4—381no—
292C4⋊C4C22⋊D1911yescharacteristic
293C4⋊C4C22×D1911yescharacteristic
294C4⋊C4C22×D1911yescharacteristic
295C4⋊C4C22×D1911yescharacteristic
296C22⋊C4—21no—
297C22⋊C4—21no—
298C22⋊C4—21no—
299C22⋊C4—381no—
300C22⋊C4—381no—
301C22⋊C4—381no—
302C22⋊C4—381no—
303C22⋊C4—381no—
304C22⋊C4C22⋊D1911yescharacteristic
305C22⋊C4C22⋊D1911yescharacteristic
306C42C22×D1911yescharacteristic
307C23—21no—
308C23—381no—
309C23—381no—
310C23—762no—
311C23—762no—
312C23—1521no—
313C23C2×C22⋊D1911yescharacteristic
314C23C2×C22⋊D1911yescharacteristic
315Q8—42no—
316Q8—381no—
317Q8—381no—
318D4—22no—
319D4—21no—
320D4—21no—
321D4—42no—
322D4—42no—
323D4—192no—
324D4—381no—
325D4—381no—
326D4—381no—
327D4—762no—
328D4—762no—
329D4—1521no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—381no—
341C2×C4—381no—
342C2×C4—762no—
343C2×C4—1521no—
344C2×C4C2×C22⋊D1911yescharacteristic
345C2×C4C2×C22⋊D1911yescharacteristic
346C2×C4C2×C22⋊D1911yescharacteristic
347C2×C4C2×C22⋊D1911yescharacteristic
348C2×C4C23×D1911yescharacteristic
349C8—381no—
350C8—381no—
351C8—381no—
352C8—381no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—382no—
362C22—761no—
363C22—761no—
364C22—761no—
365C22—761no—
366C22—761no—
367C22—1524no—
368C22#1059737812yes—
369C22C22×C22⋊D1911yescharacteristic
370C4—21no—
371C4—21no—
372C4—21no—
373C4—21no—
374C4—41no—
375C4—41no—
376C4—41no—
377C4—761no—
378C4—761no—
379C4#41×D1911yescharacteristic
380C4#1059743511yescharacteristic
381C2—22no—
382C2—41no—
383C2—81no—
384C2—762no—
385C2—1521no—
386C2#1192718211yescharacteristic
387C2C2×#1059737811yescharacteristic
388C2#1192735211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#547C2
socleC22×C19C22×D4
hypercenter#547D19
hypocenterC19#3306
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C4×D4 ◁ #547

Complements

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

NH ≅ G/Ntype
1. #11927190C2semidirect
2. #11926906C2semidirect
3. #11926874C2semidirect
4. #11926862C2semidirect
5. #11926831C2semidirect
6. #11926795C2semidirect
7. #11926771C2semidirect
8. #11926759C2semidirect
9. #11926687C2semidirect
10. #11926677C2semidirect
11. #11926654C2semidirect
12. #11926616C2semidirect
13. #11926543C2semidirect
14. C2×#10597266C2semidirect
15. C19×#547C2semidirect
19. C19×C4⋊Q8C22semidirect
24. C19×#121C22semidirect
26. C4×D4×C19C22semidirect
28. C2×C4⋊C4×C19C22semidirect
30. C2×#64526C22semidirect
35. C2×#64520C22semidirect
42. #10597289C22semidirect
44. C22⋊(C19⋊C8)C22semidirect
45. #10597267C22semidirect
46. #10597267C22semidirect
47. #10597267C22semidirect
54. #10597265C22semidirect
55. #10597265C22semidirect
56. #10597265C22semidirect
57. C4⋊(C19⋊C8)C22semidirect
58. #10597260C22semidirect
149. D76#41semidirect
187. #547D19semidirect
218. C4⋊Q8C2×D19semidirect
228. #121C2×D19semidirect
232. C4×D4C2×D19semidirect
234. C2×C4⋊C4C2×D19semidirect
253. C19#3306semidirect

Maximal subgroups

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

subgroupindex
#119271902
#119269062
#119268742
#119268622
#119268312
#119267952
#119267712
#119267592
#119266872
#119266772
#119266542
#119266162
#119265432
C2×#105972662
C19×#5472
#330619