Finite Group Databasebeta

← #14574411

Subgroups — #14574411

Order 2432.

420 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11927054C211yesmaximal, characteristic
2C22⋊Q8×D19C211yesmaximal, characteristic, complemented
3#11926888C211yesmaximal, characteristic, complemented
4#11926884C211yesmaximal, characteristic, complemented
5#11926876C211yesmaximal, characteristic, complemented
6#11926856C211yesmaximal, characteristic, complemented
7#11926785C211yesmaximal, characteristic, complemented
8#11926783C211yesmaximal, characteristic, complemented
9#11926771C211yesmaximal, characteristic, complemented
10#11926707C211yesmaximal, characteristic, complemented
11#11926703C211yesmaximal, characteristic, complemented
12#11926701C211yesmaximal, characteristic, complemented
13#11926681C211yesmaximal, characteristic, complemented
14C2×(C2×D19)⋊C8C211yesmaximal, characteristic, complemented
15C19×#465C211yesmaximal, characteristic, complemented
16C2×Q8×D19C2211yescharacteristic
17C2×#64543C2211yescharacteristic
18C22×C4×D19C2211yescharacteristic
19C2×SD16×C19C2211yescharacteristic, complemented
20C22×C8×C19C2211yescharacteristic
21C19×C22⋊Q8C2211yescharacteristic
22C19×#121C2211yescharacteristic
23#10597392C2211yescharacteristic
24C2×#64528C2211yescharacteristic, complemented
25#10597384C2211yescharacteristic
26#10597383—21no—
27D4×Dic19—21no—
28C2×#64526C2211yescharacteristic, complemented
29#10597370C2211yescharacteristic
30#10597370C2211yescharacteristic
31C22×C19⋊C8C2211yescharacteristic
32C2×Dic76C2211yescharacteristic, complemented
33#10597343C2211yescharacteristic
34#10597343C2211yescharacteristic
35#10597342—21no—
36#10597338C2211yescharacteristic
37C4⋊C4×D19—21no—
38C4⋊C4×D19C2211yescharacteristic
39#10597329—21no—
40(C22⋊D19)⋊C4—21no—
41C22⋊C4×D19—21no—
42#10597324—21no—
43C19×#106C2211yescharacteristic, complemented
44C19×#103C2211yescharacteristic, complemented
45C19×#102C2211yescharacteristic, complemented
46#10597292C2211yescharacteristic, complemented
47#10597289C2211yescharacteristic, complemented
48(C2×D19)⋊C8C2211yescharacteristic
49(C2×D19)⋊C8C2211yescharacteristic
50(C2×D19)⋊C8C2211yescharacteristic
51(C2×D19)⋊C8C2211yescharacteristic
52#10597275C2211yescharacteristic, complemented
53#10597273C2211yescharacteristic, complemented
54#10597273C2211yescharacteristic, complemented
55#10597267C2211yescharacteristic, complemented
56#10597267C2211yescharacteristic, complemented
57#10597265C2211yescharacteristic, complemented
58#10597264C2211yescharacteristic, complemented
59C23×D19D411yescharacteristic
60C2×Q8×C19C2311yescharacteristic
61C2×D4×C19—21no—
62C2×D4×C19C2311yescharacteristic
63C22×C4×C19C2311yescharacteristic
64C2×C22⋊D19—21no—
65C2×C22⋊D19—21no—
66C22×Dic19—21no—
67C22×Dic19D411yescharacteristic
68Q8×D19—41no—
69Q8×D19—41no—
70#64543—41no—
71#64543—41no—
72C2×C4×D19—21no—
73C2×C4×D19—21no—
74C2×C4×D19—41no—
75C2×C4×D19—41no—
76C2×C4×D19D411yescharacteristic
77C2×C4×D19D411yescharacteristic
78C2×C4×D19C2311yescharacteristic
79C2×C4×D19C2311yescharacteristic
80C2×Dic38—21no—
81C2×Dic38C2311yescharacteristic
82C2×Dic38C2311yescharacteristic
83SD16×C19—41no—
84C2×C8×C19—41no—
85C2×C8×C19C2311yescharacteristic
86C2×C8×C19C2311yescharacteristic
87C4⋊C4×C19—21no—
88C4⋊C4×C19C2311yescharacteristic
89C4⋊C4×C19C2311yescharacteristic
90C22⋊C4×C19—21no—
91C22⋊C4×C19—21no—
92C22⋊Dic19—21no—
93C22⋊Dic19—21no—
94C22⋊Dic19—21no—
95#64528—41no—
96#64526—41no—
97(C2×D19)⋊C4—21no—
98(C2×D19)⋊C4—21no—
99(C2×D19)⋊C4—21no—
100(C2×D19)⋊C4—21no—
101C4⋊Dic19—21no—
102C4⋊Dic19—21no—
103C4⋊Dic19C2311yescharacteristic
104C4⋊Dic19C2311yescharacteristic
105Dic19⋊C4—21no—
106Dic19⋊C4—21no—
107Dic19⋊C4—21no—
108Dic19⋊C4—21no—
109C4×Dic19—21no—
110C2×C19⋊C8—41no—
111C2×C19⋊C8C2311yescharacteristic
112C2×C19⋊C8C2311yescharacteristic
113Dic76—41no—
114C23×C19—21no—
115C23×C19C2×D411yescharacteristic
116C22×D19—22no—
117C22×D19—22no—
118C22×D19—41no—
119C22×D19C2×D411yescharacteristic
120C22×D19C2×D411yescharacteristic
121Q8×C19—21no—
122Q8×C19—21no—
123D4×C19—21no—
124D4×C19—21no—
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×C19C2×D411yescharacteristic
132C2×C4×C19C2411yescharacteristic
133C22⋊D19—42no—
134C22⋊D19—42no—
135C2×Dic19—21no—
136C2×Dic19—21no—
137C2×Dic19—21no—
138C2×Dic19—21no—
139C2×Dic19—41no—
140C2×Dic19—42no—
141C2×Dic19C2×D411yescharacteristic
142C2×Dic19C2×D411yescharacteristic
143C4×D19—21no—
144C4×D19—21no—
145C4×D19—21no—
146C4×D19—21no—
147C4×D19—41no—
148C4×D19—41no—
149C4×D19—42no—
150C4×D19—42no—
151Dic38—21no—
152Dic38—21no—
153Dic38—21no—
154Dic38—21no—
155Dic38—42no—
156C8×C19—21no—
157C8×C19—21no—
158C19⋊C8—21no—
159C19⋊C8—21no—
160#3190—191nomaximal, Sylow
161C22×C19—21no—
162C22×C19—21no—
163C22×C19—41no—
164C22×C19—41no—
165C22×C19—41no—
166C22×C19#13712yes—
167C22×C19C22×D411yescharacteristic
168C2×D19—21no—
169C2×D19—21no—
170C2×D19—21no—
171C2×D19—21no—
172C2×D19—21no—
173C2×D19—44no—
174C2×D19#13512yes—
175C4×C19—21no—
176C4×C19—41no—
177C4×C19—41no—
178C4×C19—41no—
179C4×C19H(5,𝔽2)11yescharacteristic
180C4×C19H(5,𝔽2)11yescharacteristic
181Dic19—21no—
182Dic19—21no—
183Dic19—41no—
184Dic19—41no—
185Dic19—41no—
186Dic19—41no—
187#525—191no—
188C2×C22⋊Q8—191no—
189#485—191no—
190#485—191no—
191#483—191no—
192#480—191no—
193#467—191no—
194#467—191no—
195#465—191no—
196#465D1911yescharacteristic, complemented
197#452—191no—
198#452—191no—
199#451—191no—
200#448—191no—
201C2×C22⋊C8—191no—
202C2×C19—22no—
203C2×C19—81no—
204C2×C19#53411yescharacteristic
205C2×C19C2×#13511yescharacteristic
206C2×C19C2×#13711yescharacteristic
207D19—22no—
208D19—41no—
209C2×#41—191no—
210C22×Q8—191no—
211C23×C4—191no—
212C2×Q16—191no—
213C2×Q16—191no—
214C2×SD16—191no—
215C2×SD16C2×D1911yescharacteristic, complemented
216C22×C8—191no—
217C22×C8C2×D1911yescharacteristic
218#123—381no—
219C22⋊Q8—191no—
220C22⋊Q8—191no—
221C22⋊Q8—191no—
222C22⋊Q8—191no—
223C22⋊Q8—191no—
224C22⋊Q8—381no—
225C22⋊Q8—381no—
226C22⋊Q8C2×D1911yescharacteristic
227#121—191no—
228#121C2×D1911yescharacteristic
229#120—381no—
230C4×D4—381no—
231C4×D4—381no—
232#117—191no—
233C2×C4⋊C4—191no—
234C2×C4⋊C4—381no—
235C2×C22⋊C4—381no—
236#107—191no—
237#107—191no—
238#106—191no—
239#106C2×D1911yescharacteristic, complemented
240#103—191no—
241#103—191no—
242#103—191no—
243#103—191no—
244#103—191no—
245#103C2×D1911yescharacteristic, complemented
246#102—191no—
247#102C2×D1911yescharacteristic, complemented
248C22⋊C8—191no—
249C22⋊C8—191no—
250C22⋊C8—191no—
251C22⋊C8—191no—
252C19#319011yescharacteristic, complemented, Sylow
253C24—191no—
254#41—761no—
255#41—761no—
256C2×Q8—191no—
257C2×Q8—191no—
258C2×Q8—381no—
259C2×Q8—761no—
260C2×Q8—761no—
261C2×Q8C22×D1911yescharacteristic
262C2×D4—21no—
263C2×D4—381no—
264C2×D4—381no—
265C2×D4C22×D1911yescharacteristic
266C22×C4—191no—
267C22×C4—191no—
268C22×C4—191no—
269C22×C4—191no—
270C22×C4—191no—
271C22×C4—381no—
272C22×C4—381no—
273C22×C4—381no—
274C22×C4—761no—
275C22×C4—761no—
276C22×C4C22×D1911yescharacteristic
277Q16—761no—
278Q16—761no—
279SD16—41no—
280SD16—761no—
281C2×C8—41no—
282C2×C8—191no—
283C2×C8—191no—
284C2×C8—761no—
285C2×C8C22×D1911yescharacteristic
286C2×C8C22×D1911yescharacteristic
287C4⋊C4—21no—
288C4⋊C4—191no—
289C4⋊C4—191no—
290C4⋊C4—381no—
291C4⋊C4—381no—
292C4⋊C4—381no—
293C4⋊C4—381no—
294C4⋊C4—381no—
295C4⋊C4—381no—
296C4⋊C4C22×D1911yescharacteristic
297C4⋊C4C22×D1911yescharacteristic
298C22⋊C4—21no—
299C22⋊C4—21no—
300C22⋊C4—381no—
301C22⋊C4—381no—
302C22⋊C4—381no—
303C22⋊C4—381no—
304C22⋊C4—381no—
305C22⋊C4—381no—
306C22⋊C4—381no—
307C42—381no—
308C23—21no—
309C23—191no—
310C23—191no—
311C23—382no—
312C23—382no—
313C23—761no—
314C23D4×D1911yescharacteristic
315Q8—21no—
316Q8—21no—
317Q8—381no—
318Q8—381no—
319Q8—381no—
320Q8—381no—
321Q8—762no—
322D4—21no—
323D4—21no—
324D4—42no—
325D4—762no—
326D4—762no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—191no—
333C2×C4—191no—
334C2×C4—381no—
335C2×C4—381no—
336C2×C4—381no—
337C2×C4—381no—
338C2×C4—381no—
339C2×C4—381no—
340C2×C4—381no—
341C2×C4—381no—
342C2×C4—761no—
343C2×C4—761no—
344C2×C4—762no—
345C2×C4—762no—
346C2×C4—761no—
347C2×C4—762no—
348C2×C4D4×D1911yescharacteristic
349C2×C4C23×D1911yescharacteristic
350C8—21no—
351C8—21no—
352C8—381no—
353C8—381no—
354C22—21no—
355C22—21no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22—192no—
360C22—381no—
361C22—381no—
362C22—381no—
363C22—381no—
364C22—381no—
365C22—764no—
366C22#1059736112yes—
367C22C2×D4×D1911yescharacteristic
368C4—21no—
369C4—41no—
370C4—41no—
371C4—41no—
372C4—381no—
373C4—381no—
374C4—761no—
375C4—761no—
376C4—761no—
377C4—761no—
378C4#1059743011yescharacteristic
379C4#1059743511yescharacteristic
380C2—22no—
381C2—81no—
382C2—382no—
383C2—761no—
384C2#1192710211yescharacteristic
385C2#135×D1911yescharacteristic
386C2C2×#1059736111yescharacteristic
subgroupG/H
centerC22C2×D4×D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#465C2
socleC22×C19C22×D4
prime radical#11927054C2
hypercenter#465D19
hypocenterC19#3190
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
2. C22⋊Q8×D19C2semidirect
3. #11926888C2semidirect
4. #11926884C2semidirect
5. #11926876C2semidirect
6. #11926856C2semidirect
7. #11926785C2semidirect
8. #11926783C2semidirect
9. #11926771C2semidirect
10. #11926707C2semidirect
11. #11926703C2semidirect
12. #11926701C2semidirect
13. #11926681C2semidirect
14. C2×(C2×D19)⋊C8C2semidirect
15. C19×#465C2semidirect
19. C2×SD16×C19C22semidirect
24. C2×#64528C22semidirect
28. C2×#64526C22semidirect
32. C2×Dic76C22semidirect
43. C19×#106C22semidirect
44. C19×#103C22semidirect
45. C19×#102C22semidirect
46. #10597292C22semidirect
47. #10597289C22semidirect
52. #10597275C22semidirect
53. #10597273C22semidirect
54. #10597273C22semidirect
55. #10597267C22semidirect
56. #10597267C22semidirect
57. #10597265C22semidirect
58. #10597264C22semidirect
196. #465D19semidirect
215. C2×SD16C2×D19semidirect
239. #106C2×D19semidirect
245. #103C2×D19semidirect
247. #102C2×D19semidirect
252. C19#3190semidirect

Maximal subgroups

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

subgroupindex
#119270542
C22⋊Q8×D192
#119268882
#119268842
#119268762
#119268562
#119267852
#119267832
#119267712
#119267072
#119267032
#119267012
#119266812
C2×(C2×D19)⋊C82
C19×#4652
#319019