Finite Group Databasebeta

← #14575486

Subgroups — #14575486

Order 2432.

420 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11927238C211yesmaximal, characteristic, complemented
2#11927182C211yesmaximal, characteristic, complemented
3#11926900C211yesmaximal, characteristic, complemented
4#11926878C211yesmaximal, characteristic, complemented
5#11926868C211yesmaximal, characteristic, complemented
6#11926842C211yesmaximal, characteristic, complemented
7#11926780C211yesmaximal, characteristic, complemented
8#11926776C211yesmaximal, characteristic, complemented
9#11926762C211yesmaximal, characteristic, complemented
10#11926689C211yesmaximal, characteristic, complemented
11#11926679C211yesmaximal, characteristic, complemented
12#11926624C211yesmaximal, characteristic, complemented
13C8×C22⋊D19C211yesmaximal, characteristic, complemented
14#102×D19C211yesmaximal, characteristic, complemented
15C19×#416C211yesmaximal, characteristic, complemented
16C2×#41×C19C2211yescharacteristic
17C2×D4×D19C2211yescharacteristic
18C22×C8×C19C2211yescharacteristic, complemented
19C19×#117C2211yescharacteristic, complemented
20#10597393C2211yescharacteristic
21#10597392C2211yescharacteristic
22C2×#64527C2211yescharacteristic, complemented
23#10597385—21no—
24#10597383—21no—
25D4×Dic19C2211yescharacteristic
26C2×#64525C2211yescharacteristic
27#10597376C2211yescharacteristic
28#10597376C2211yescharacteristic, complemented
29#10597375—21no—
30C4×C22⋊D19C2211yescharacteristic
31C2×(C2×D19)⋊C4—21no—
32C2×D152C2211yescharacteristic
33C2×C8×D19C2211yescharacteristic
34#10597341C2211yescharacteristic
35#10597339C2211yescharacteristic, complemented
36C4⋊C4×D19C2211yescharacteristic
37#10597336C2211yescharacteristic, complemented
38#10597330—21no—
39#10597329—21no—
40#10597322—21no—
41C4×D76—21no—
42C19×#103C2211yescharacteristic, complemented
43C19×#103C2211yescharacteristic, complemented
44C19×#102C2211yescharacteristic
45C19×#102C2211yescharacteristic
46#10597292C2211yescharacteristic, complemented
47#10597289C2211yescharacteristic
48C22⋊(C19⋊C8)C2211yescharacteristic, complemented
49#10597278C2211yescharacteristic
50#10597278C2211yescharacteristic, complemented
51(C2×D19)⋊C8C2211yescharacteristic
52#10597275C2211yescharacteristic, complemented
53Dic19⋊C8C2211yescharacteristic, complemented
54C8×Dic19C2211yescharacteristic, complemented
55#10597266C2211yescharacteristic
56#10597266C2211yescharacteristic
57#10597265C2211yescharacteristic, complemented
58#10597264C2211yescharacteristic, complemented
59C23×D19—21no—
60#41×C19—22no—
61#41×C19—41no—
62C2×Q8×C19C2311yescharacteristic
63C2×D4×C19—21no—
64C2×D4×C19C2311yescharacteristic
65C22×C4×C19—21no—
66C22×C4×C19C2311yescharacteristic
67C2×C22⋊D19—21no—
68C2×C22⋊D19—21no—
69C2×C22⋊D19—21no—
70C2×C22⋊D19D411yescharacteristic
71C22×Dic19—21no—
72D4×D19—22no—
73D4×D19—41no—
74C2×D76—21no—
75C2×D76C2311yescharacteristic
76C2×D76C2311yescharacteristic
77C2×C4×D19—21no—
78C2×C4×D19—21no—
79C2×C4×D19C2311yescharacteristic
80C2×C8×C19—41no—
81C2×C8×C19C2311yescharacteristic
82C2×C8×C19C2311yescharacteristic
83C4⋊C4×C19C2311yescharacteristic
84C4⋊C4×C19C2311yescharacteristic
85C22⋊C4×C19—21no—
86C42×C19—21no—
87C22⋊Dic19—21no—
88C22⋊Dic19D411yescharacteristic
89#64527—41no—
90#64525—22no—
91(C2×D19)⋊C4—21no—
92(C2×D19)⋊C4—21no—
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)⋊C4D411yescharacteristic
99C4⋊Dic19—21no—
100C4⋊Dic19C2311yescharacteristic
101C4⋊Dic19C2311yescharacteristic
102Dic19⋊C4—21no—
103Dic19⋊C4—21no—
104Dic19⋊C4—21no—
105Dic19⋊C4D411yescharacteristic
106C4×Dic19C2311yescharacteristic
107C2×C19⋊C8C2311yescharacteristic
108C2×C19⋊C8C2311yescharacteristic
109D152—41no—
110C8×D19—41no—
111C23×C19—21no—
112C23×C19C2×D411yescharacteristic
113C22×D19—21no—
114C22×D19—21no—
115C22×D19—42no—
116C22×D19—42no—
117C22×D19—81no—
118C22×D19C2×D411yescharacteristic
119Q8×C19—21no—
120Q8×C19—21no—
121D4×C19—21no—
122D4×C19—42no—
123D4×C19#4112yes—
124C2×C4×C19—21no—
125C2×C4×C19—21no—
126C2×C4×C19—21no—
127C2×C4×C19—21no—
128C2×C4×C19—21no—
129C2×C4×C19—42no—
130C2×C4×C19C2×D411yescharacteristic
131C2×C4×C19C2411yescharacteristic
132C22⋊D19—22no—
133C22⋊D19—42no—
134C22⋊D19—81no—
135C22⋊D19—81no—
136C2×Dic19—21no—
137C2×Dic19—21no—
138C2×Dic19—81no—
139C2×Dic19C2×D411yescharacteristic
140C2×Dic19C2×D411yescharacteristic
141C2×Dic19C2×D411yescharacteristic
142D76—21no—
143D76—21no—
144D76—21no—
145D76—21no—
146D76—42no—
147C4×D19—21no—
148C4×D19—21no—
149C4×D19—81no—
150C4×D19—81no—
151C8×C19—21no—
152C8×C19—21no—
153C19⋊C8—21no—
154C19⋊C8—21no—
155#3297—191nomaximal, Sylow
156C22×C19—22no—
157C22×C19—21no—
158C22×C19—21no—
159C22×C19—21no—
160C22×C19—41no—
161C22×C19—41no—
162C22×C19C22×D411yescharacteristic
163C2×D19—21no—
164C2×D19—21no—
165C2×D19—41no—
166C2×D19—41no—
167C2×D19—41no—
168C2×D19—41no—
169C2×D19—41no—
170C2×D19—41no—
171C2×D19—84no—
172C2×D19#13512yes—
173C4×C19—21no—
174C4×C19—41no—
175C4×C19—41no—
176C4×C19—41no—
177C4×C19C2×#4111yescharacteristic
178C4×C19H(5,𝔽2)11yescharacteristic
179Dic19—21no—
180Dic19—21no—
181Dic19—21no—
182Dic19—41no—
183Dic19—41no—
184#553—191no—
185#546—191no—
186#488—191no—
187#484—191no—
188#482—191no—
189#478—191no—
190#466—191no—
191#465—191no—
192#463—191no—
193#449—191no—
194#447—191no—
195C4×D8—191no—
196C8×D4—191no—
197#416D1911yescharacteristic, complemented
198C2×#102—191no—
199C2×C19—42no—
200C2×C19—41no—
201C2×C19#54611yescharacteristic
202C2×C19C2×#13511yescharacteristic
203C2×C19#57611yescharacteristic
204D19—22no—
205D19—81no—
206D19—81no—
207C2×#41C2×D1911yescharacteristic
208C22×D4—191no—
209C2×SD16—191no—
210C2×D8—191no—
211C2×D8—191no—
212C22×C8—191no—
213C22×C8C2×D1911yescharacteristic, complemented
214#126—381no—
215#125—191no—
216#124—191no—
217#123—381no—
218#123—381no—
219C22⋊Q8—191no—
220#121—191no—
221#121—191no—
222#121—191no—
223#121—381no—
224#121—381no—
225#120—381no—
226C4×D4—191no—
227C4×D4—191no—
228C4×D4—191no—
229C4×D4—381no—
230#117C2×D1911yescharacteristic, complemented
231C2×C4⋊C4—191no—
232C2×C22⋊C4—381no—
233#107—191no—
234#107—191no—
235#106—191no—
236C4⋊C8—191no—
237#103—191no—
238#103C2×D1911yescharacteristic, complemented
239#103C2×D1911yescharacteristic, complemented
240#102—191no—
241#102—191no—
242#102—191no—
243#102—191no—
244#102—191no—
245#102C2×D1911yescharacteristic
246#102C2×D1911yescharacteristic
247C22⋊C8—191no—
248C22⋊C8—191no—
249C4×C8—191no—
250C19#329711yescharacteristic, complemented, Sylow
251C24—381no—
252#41—22no—
253#41—41no—
254C2×Q8C22×D1911yescharacteristic
255C2×D4—21no—
256C2×D4—191no—
257C2×D4—191no—
258C2×D4—191no—
259C2×D4—381no—
260C2×D4—381no—
261C2×D4—382no—
262C2×D4—381no—
263C2×D4—381no—
264C2×D4—761no—
265C2×D4C22×D1911yescharacteristic
266C22×C4—21no—
267C22×C4—191no—
268C22×C4—381no—
269C22×C4—381no—
270C22×C4—381no—
271C22×C4C22×D1911yescharacteristic
272SD16—761no—
273D8—382no—
274D8—761no—
275C2×C8—41no—
276C2×C8—191no—
277C2×C8—191no—
278C2×C8—761no—
279C2×C8C22×D1911yescharacteristic
280C2×C8C22×D1911yescharacteristic
281C4⋊C4—191no—
282C4⋊C4—191no—
283C4⋊C4—191no—
284C4⋊C4—381no—
285C4⋊C4—381no—
286C4⋊C4—381no—
287C4⋊C4—381no—
288C4⋊C4C22×D1911yescharacteristic
289C4⋊C4C22×D1911yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—191no—
292C22⋊C4—191no—
293C22⋊C4—381no—
294C22⋊C4—381no—
295C22⋊C4—381no—
296C22⋊C4—381no—
297C22⋊C4—381no—
298C22⋊C4—381no—
299C22⋊C4—381no—
300C22⋊C4—381no—
301C42—21no—
302C42—191no—
303C23—21no—
304C23—191no—
305C23—381no—
306C23—381no—
307C23—762no—
308C23—762no—
309C23—1521no—
310C23D4×D1911yescharacteristic
311Q8—21no—
312Q8—21no—
313D4—21no—
314D4—42no—
315D4—382no—
316D4—381no—
317D4—381no—
318D4—381no—
319D4—381no—
320D4—762no—
321D4—762no—
322D4—1521no—
323D4—1521no—
324D4#6454112yes—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—42no—
331C2×C4—191no—
332C2×C4—191no—
333C2×C4—191no—
334C2×C4—381no—
335C2×C4—381no—
336C2×C4—381no—
337C2×C4—381no—
338C2×C4—1521no—
339C2×C4—1521no—
340C2×C4—1521no—
341C2×C4D4×D1911yescharacteristic
342C2×C4C23×D1911yescharacteristic
343C8—21no—
344C8—21no—
345C8—381no—
346C8—381no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—22no—
351C22—41no—
352C22—41no—
353C22—192no—
354C22—381no—
355C22—381no—
356C22—761no—
357C22—761no—
358C22—761no—
359C22—761no—
360C22—761no—
361C22—761no—
362C22—1524no—
363C22C2×D4×D1911yescharacteristic
364C4—21no—
365C4—41no—
366C4—41no—
367C4—41no—
368C4—381no—
369C4—381no—
370C4—381no—
371C4—761no—
372C4—761no—
373C4C2×#6454111yescharacteristic
374C4#1059743011yescharacteristic
375C2—41no—
376C2—42no—
377C2—382no—
378C2—1521no—
379C2—1521no—
380C2#1192718411yescharacteristic
381C2#135×D1911yescharacteristic
382C2#1192734611yescharacteristic
subgroupG/H
centerC22C2×D4×D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#416C2
socleC22×C19C22×D4
hypercenter#416D19
hypocenterC19#3297
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
1. #11927238C2semidirect
2. #11927182C2semidirect
3. #11926900C2semidirect
4. #11926878C2semidirect
5. #11926868C2semidirect
6. #11926842C2semidirect
7. #11926780C2semidirect
8. #11926776C2semidirect
9. #11926762C2semidirect
10. #11926689C2semidirect
11. #11926679C2semidirect
12. #11926624C2semidirect
13. C8×C22⋊D19C2semidirect
14. #102×D19C2semidirect
15. C19×#416C2semidirect
18. C22×C8×C19C22semidirect
19. C19×#117C22semidirect
22. C2×#64527C22semidirect
28. #10597376C22semidirect
35. #10597339C22semidirect
37. #10597336C22semidirect
42. C19×#103C22semidirect
43. C19×#103C22semidirect
46. #10597292C22semidirect
48. C22⋊(C19⋊C8)C22semidirect
50. #10597278C22semidirect
52. #10597275C22semidirect
53. Dic19⋊C8C22semidirect
54. C8×Dic19C22semidirect
57. #10597265C22semidirect
58. #10597264C22semidirect
197. #416D19semidirect
213. C22×C8C2×D19semidirect
230. #117C2×D19semidirect
238. #103C2×D19semidirect
239. #103C2×D19semidirect
250. C19#3297semidirect

Maximal subgroups

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

subgroupindex
#119272382
#119271822
#119269002
#119268782
#119268682
#119268422
#119267802
#119267762
#119267622
#119266892
#119266792
#119266242
C8×C22⋊D192
#102×D192
C19×#4162
#329719