Finite Group Databasebeta

← #14575481

Subgroups — #14575481

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#11927242C211yesmaximal, characteristic, complemented
2#11927188C211yesmaximal, characteristic, complemented
3#11926897C211yesmaximal, characteristic, complemented
4#11926879C211yesmaximal, characteristic, complemented
5#11926867C211yesmaximal, characteristic, complemented
6#11926846C211yesmaximal, characteristic, complemented
7#11926779C211yesmaximal, characteristic, complemented
8#11926773C211yesmaximal, characteristic, complemented
9#11926758C211yesmaximal, characteristic, complemented
10#11926690C211yesmaximal, characteristic, complemented
11#11926678C211yesmaximal, characteristic, complemented
12#11926624C211yesmaximal, characteristic, complemented
13C8×C22⋊D19C211yesmaximal, characteristic, complemented
14#11926537C211yesmaximal, characteristic, complemented
15C2×C19×#102C211yesmaximal, characteristic, complemented
16C22×D4×C19C2211yescharacteristic
17C2×#64543C2211yescharacteristic
18C22×C8×C19C2211yescharacteristic
19C2×C4⋊C4×C19C2211yescharacteristic
20#10597399—21no—
21C2×C22⋊Dic19—21no—
22#10597385—21no—
23#10597384C2211yescharacteristic
24#10597382C2211yescharacteristic
25#10597381—21no—
26D4×Dic19C2211yescharacteristic
27C2×#64525C2211yescharacteristic
28C2×#64525C2211yescharacteristic
29#10597376—21no—
30#10597376C2211yescharacteristic
31C4×C22⋊D19—21no—
32C4×C22⋊D19C2211yescharacteristic
33#10597370C2211yescharacteristic
34C2×#64516C2211yescharacteristic, complemented
35C2×C8×D19C2211yescharacteristic, complemented
36#10597344—21no—
37#10597341C2211yescharacteristic, complemented
38#10597340—21no—
39#10597339C2211yescharacteristic, complemented
40#10597338C2211yescharacteristic, complemented
41#10597336C2211yescharacteristic, complemented
42C19×#102C2211yescharacteristic
43C19×#102C2211yescharacteristic
44C19×#102C2211yescharacteristic
45C19×#102C2211yescharacteristic
46#10597289C2211yescharacteristic
47#10597289C2211yescharacteristic
48C22⋊(C19⋊C8)C2211yescharacteristic
49#10597278C2211yescharacteristic, complemented
50(C2×D19)⋊C8C2211yescharacteristic, complemented
51#10597274C2211yescharacteristic, complemented
52#10597273C2211yescharacteristic, complemented
53Dic19⋊C8C2211yescharacteristic, complemented
54C8×Dic19C2211yescharacteristic, complemented
55#10597267C2211yescharacteristic, complemented
56#10597267C2211yescharacteristic, complemented
57#10597264C2211yescharacteristic, complemented
58#10597264C2211yescharacteristic, complemented
59C24×C19—21no—
60C2×D4×C19—22no—
61C2×D4×C19—21no—
62C2×D4×C19—41no—
63C2×D4×C19C2311yescharacteristic
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—
72C22×Dic19—21no—
73#64543—22no—
74#64543—41no—
75C2×D76—21no—
76C2×D76C2311yescharacteristic
77C2×C4×D19—21no—
78C2×C4×D19C2311yescharacteristic
79C2×Dic38C2311yescharacteristic
80C2×C8×C19—41no—
81C2×C8×C19C2311yescharacteristic
82C2×C8×C19C2311yescharacteristic
83C4⋊C4×C19—21no—
84C4⋊C4×C19C2311yescharacteristic
85C4⋊C4×C19C2311yescharacteristic
86C22⋊Dic19—21no—
87C22⋊Dic19—21no—
88C22⋊Dic19—21no—
89C22⋊Dic19—21no—
90C22⋊Dic19—21no—
91C22⋊Dic19D411yescharacteristic
92#64525—22no—
93#64525—41no—
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⋊C4D411yescharacteristic
105C4×Dic19—21no—
106C4×Dic19C2311yescharacteristic
107C2×C19⋊C8C2311yescharacteristic
108C2×C19⋊C8C2311yescharacteristic
109#64516—41no—
110C8×D19—41no—
111C23×C19—21no—
112C23×C19—21no—
113C23×C19—42no—
114C23×C19—42no—
115C23×C19—81no—
116C23×C19C2×D411yescharacteristic
117C22×D19—21no—
118C22×D19C2×D411yescharacteristic
119D4×C19—21no—
120D4×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—81no—
129C2×C4×C19C2×D411yescharacteristic
130C2×C4×C19C2411yescharacteristic
131C22⋊D19—22no—
132C22⋊D19—42no—
133C22⋊D19—42no—
134C22⋊D19—81no—
135C2×Dic19—21no—
136C2×Dic19—21no—
137C2×Dic19—21no—
138C2×Dic19—42no—
139C2×Dic19—81no—
140C2×Dic19C2×D411yescharacteristic
141C2×Dic19C2×D411yescharacteristic
142C2×Dic19C2×D411yescharacteristic
143D76—21no—
144D76—21no—
145D76—81no—
146C4×D19—21no—
147C4×D19—21no—
148C4×D19—81no—
149Dic38—21no—
150Dic38—21no—
151C8×C19—21no—
152C8×C19—21no—
153C19⋊C8—21no—
154C19⋊C8—21no—
155#3297—191nomaximal, Sylow
156C22×C19—21no—
157C22×C19—21no—
158C22×C19—22no—
159C22×C19—41no—
160C22×C19—41no—
161C22×C19—41no—
162C22×C19—41no—
163C22×C19—41no—
164C22×C19—84no—
165C22×C19#13512yes—
166C22×C19C22×D411yescharacteristic
167C2×D19—21no—
168C2×D19—21no—
169C2×D19—21no—
170C2×D19—41no—
171C2×D19—41no—
172C2×D19—41no—
173C4×C19—21no—
174C4×C19—41no—
175C4×C19—41no—
176C4×C19C2×#4111yescharacteristic
177C4×C19H(5,𝔽2)11yescharacteristic
178Dic19—21no—
179Dic19—21no—
180Dic19—21no—
181Dic19—41no—
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#416—191no—
198C2×#102D1911yescharacteristic, complemented
199C2×C19—22no—
200C2×C19—42no—
201C2×C19—81no—
202C2×C19#54611yescharacteristic
203C2×C19C2×#13511yescharacteristic
204C2×C19#57611yescharacteristic
205D19—41no—
206D19—81no—
207C2×#41—191no—
208C22×D4C2×D1911yescharacteristic
209C2×SD16—191no—
210C2×D8—191no—
211C2×D8—191no—
212C22×C8—191no—
213C22×C8C2×D1911yescharacteristic
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#117—191no—
231C2×C4⋊C4C2×D1911yescharacteristic
232C2×C22⋊C4—381no—
233#107—191no—
234#107—191no—
235#106—191no—
236C4⋊C8—191no—
237#103—191no—
238#103—191no—
239#103—191no—
240#102—191no—
241#102—191no—
242#102—191no—
243#102C2×D1911yescharacteristic
244#102C2×D1911yescharacteristic
245#102C2×D1911yescharacteristic
246#102C2×D1911yescharacteristic
247C22⋊C8—191no—
248C22⋊C8—191no—
249C4×C8—191no—
250C19#329711yescharacteristic, complemented, Sylow
251C24—21no—
252#41—382no—
253#41—761no—
254C2×Q8—191no—
255C2×D4—22no—
256C2×D4—21no—
257C2×D4—41no—
258C2×D4—191no—
259C2×D4—191no—
260C2×D4—381no—
261C2×D4—381no—
262C2×D4—381no—
263C2×D4—381no—
264C2×D4C22×D1911yescharacteristic
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—21no—
282C4⋊C4—191no—
283C4⋊C4—191no—
284C4⋊C4—191no—
285C4⋊C4—381no—
286C4⋊C4—381no—
287C4⋊C4—381no—
288C4⋊C4C22×D1911yescharacteristic
289C4⋊C4C22×D1911yescharacteristic
290C22⋊C4—191no—
291C22⋊C4—191no—
292C22⋊C4—381no—
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—191no—
302C42—381no—
303C23—21no—
304C23—21no—
305C23—42no—
306C23—42no—
307C23—81no—
308C23—191no—
309C23—381no—
310C23D4×D1911yescharacteristic
311Q8—381no—
312Q8—381no—
313D4—21no—
314D4—21no—
315D4—21no—
316D4—42no—
317D4—382no—
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—81no—
330C2×C4—191no—
331C2×C4—191no—
332C2×C4—191no—
333C2×C4—381no—
334C2×C4—381no—
335C2×C4—381no—
336C2×C4—381no—
337C2×C4—381no—
338C2×C4—762no—
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—22no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—84no—
356C22—381no—
357C22—381no—
358C22—381no—
359C22—761no—
360C22—761no—
361C22—761no—
362C22#1059736212yes—
363C22C2×D4×D1911yescharacteristic
364C4—21no—
365C4—41no—
366C4—41no—
367C4—381no—
368C4—381no—
369C4—381no—
370C4—761no—
371C4—761no—
372C4—761no—
373C4C2×#6454111yescharacteristic
374C4#1059743011yescharacteristic
375C2—22no—
376C2—42no—
377C2—81no—
378C2—761no—
379C2—1521no—
380C2#1192718411yescharacteristic
381C2C2×#1059736211yescharacteristic
382C2#1192734511yescharacteristic
subgroupG/H
centerC22C2×D4×D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC2×C19×#102C2
socleC22×C19C22×D4
hypercenterC2×#102D19
hypocenterC19#3297
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
1. #11927242C2semidirect
2. #11927188C2semidirect
3. #11926897C2semidirect
4. #11926879C2semidirect
5. #11926867C2semidirect
6. #11926846C2semidirect
7. #11926779C2semidirect
8. #11926773C2semidirect
9. #11926758C2semidirect
10. #11926690C2semidirect
11. #11926678C2semidirect
12. #11926624C2semidirect
13. C8×C22⋊D19C2semidirect
14. #11926537C2semidirect
15. C2×C19×#102C2semidirect
34. C2×#64516C22semidirect
35. C2×C8×D19C22semidirect
37. #10597341C22semidirect
39. #10597339C22semidirect
40. #10597338C22semidirect
41. #10597336C22semidirect
49. #10597278C22semidirect
50. (C2×D19)⋊C8C22semidirect
51. #10597274C22semidirect
52. #10597273C22semidirect
53. Dic19⋊C8C22semidirect
54. C8×Dic19C22semidirect
55. #10597267C22semidirect
56. #10597267C22semidirect
57. #10597264C22semidirect
58. #10597264C22semidirect
198. C2×#102D19semidirect
250. C19#3297semidirect

Maximal subgroups

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

subgroupindex
#119272422
#119271882
#119268972
#119268792
#119268672
#119268462
#119267792
#119267732
#119267582
#119266902
#119266782
#119266242
C8×C22⋊D192
#119265372
C2×C19×#1022
#329719