Finite Group Databasebeta

← #18080335

Subgroups — #18080335

Order 4864.

958 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 958 conjugacy classes of subgroups — too many to draw. Only its 97 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14566950C211yesmaximal, characteristic
2#14565987C211yesmaximal, characteristic, complemented
3#14563579C211yesmaximal, characteristic, complemented
4#14561961C211yesmaximal, characteristic, complemented
5#14561489C211yesmaximal, characteristic, complemented
6#14561488C211yesmaximal, characteristic, complemented
7C19×#1789C211yesmaximal, characteristic, complemented
8C2×#10597383—21no—
9C22×(C2×D19)⋊C4C2211yescharacteristic
10C2×C22⋊C4×D19—21no—
11C2×#10597294—22no—
12#11926508C2211yescharacteristic
13#11926455C412yescomplemented
14#11926452C412yescomplemented
15#11926424—21no—
16#11926423—22no—
17#11926407C2211yescharacteristic
18C22⋊C4×Dic19—21no—
19C4×(C2×D19)⋊C4—22no—
20C4×C22⋊Dic19C2211yescharacteristic
21#11926391—22no—
22#11926267—22no—
23C22×#41×C19C2211yescharacteristic
24C2×C19×#104—22no—
25C19×#407C2211yescharacteristic
26C4×C22⋊C4×C19C2211yescharacteristic
27C24×D19D411yescharacteristic
28C2×#41×C19—21no—
29C2×#41×C19—21no—
30C2×#41×C19—21no—
31C2×#41×C19—21no—
32C2×#41×C19—44no—
33C22×Q8×C19C2×C411yescharacteristic, complemented
34C22×D4×C19—21no—
35C22×D4×C19C2×C411yescharacteristic, complemented
36C23×C4×C19—21no—
37C23×C4×C19C2311yescharacteristic
38C22×C22⋊D19—22no—
39C23×Dic19D411yescharacteristic
40C22×C4×D19—22no—
41C2×M16×C19—21no—
42C2×C22⋊C4×C19—21no—
43C2×C42×C19D412yescomplemented
44C2×C22⋊Dic19—21no—
45C2×C22⋊Dic19—21no—
46C2×C22⋊Dic19—22no—
47#10597383—44no—
48C2×(C2×D19)⋊C4—22no—
49C2×(C2×D19)⋊C4—21no—
50C2×(C2×D19)⋊C4—21no—
51C2×(C2×D19)⋊C4—21no—
52C2×(C2×D19)⋊C4—21no—
53C2×(C2×D19)⋊C4—22no—
54C2×(C2×D19)⋊C4C2×C412yes—
55C2×(C2×D19)⋊C4D412yes—
56C2×C4×Dic19—22no—
57C2×C4×Dic19D412yescomplemented
58C2×#64520—21no—
59C22⋊C4×D19—28no—
60C19×#104—44no—
61C19×C22⋊C8—21no—
62C19×C22⋊C8—21no—
63C19×#95—21no—
64#10597294—44no—
65C19⋊#95—22no—
66C19⋊#95—21no—
67C19⋊#95—21no—
68C19⋊#95—22no—
69C19⋊#95C2×C412yescomplemented
70C22⋊(C19⋊C8)—21no—
71C22⋊(C19⋊C8)—21no—
72C24×C19—21no—
73C24×C19C2×D411yescharacteristic
74C23×D19—21no—
75C23×D19—21no—
76C23×D19—24no—
77C23×D19—42no—
78C23×D19—81no—
79C23×D19C22⋊C412yes—
80#41×C19—24no—
81#41×C19—24no—
82#41×C19—42no—
83#41×C19—42no—
84#41×C19—42no—
85#41×C19—42no—
86#41×C19—42no—
87#41×C19—42no—
88C2×Q8×C19—21no—
89C2×Q8×C19—21no—
90C2×Q8×C19—42no—
91C2×D4×C19—24no—
92C2×D4×C19—21no—
93C2×D4×C19—21no—
94C2×D4×C19—42no—
95C2×D4×C19—42no—
96C2×D4×C19—41no—
97C2×D4×C19—41no—
98C22×C4×C19—21no—
99C22×C4×C19—22no—
100C22×C4×C19—42no—
101C22×C4×C19—42no—
102C22×C4×C19—42no—
103C22×C4×C19—41no—
104C22×C4×C19—41no—
105C22×C4×C19C22×C411yescharacteristic
106C22×C4×C19C2×D411yescharacteristic
107C22×C4×C19C2×D411yescharacteristic
108C22×C4×C19C2×D411yescharacteristic
109C22×C4×C19#4111yescharacteristic
110C22×C4×C19#4111yescharacteristic
111C2×C22⋊D19—44no—
112C2×C22⋊D19—44no—
113C2×C22⋊D19—82no—
114C22×Dic19—22no—
115C22×Dic19—21no—
116C22×Dic19—21no—
117C22×Dic19—22no—
118C22×Dic19—81no—
119C22×Dic19C22⋊C412yes—
120C2×C4×D19—28no—
121C2×C4×D19—82no—
122C2×C4×D19—82no—
123M16×C19—42no—
124C2×C8×C19—41no—
125C22⋊C4×C19—24no—
126C42×C19—42no—
127C22⋊Dic19—24no—
128C22⋊Dic19—42no—
129C22⋊Dic19—82no—
130(C2×D19)⋊C4—28no—
131(C2×D19)⋊C4—22no—
132(C2×D19)⋊C4—22no—
133(C2×D19)⋊C4—22no—
134(C2×D19)⋊C4—22no—
135(C2×D19)⋊C4—44no—
136C4×Dic19—42no—
137C4×Dic19—82no—
138#64520—42no—
139C2×C19⋊C8—41no—
140#9475—191nomaximal, Sylow
141C23×C19—22no—
142C23×C19—22no—
143C23×C19—22no—
144C23×C19—41no—
145C23×C19—42no—
146C23×C19—41no—
147C23×C19—41no—
148C23×C19—42no—
149C23×C19C2×C22⋊C411yescharacteristic
150C23×C19#12011yescharacteristic
151C23×C19#12311yescharacteristic
152C22×D19—22no—
153C22×D19—22no—
154C22×D19—22no—
155C22×D19—24no—
156C22×D19—22no—
157C22×D19—42no—
158C22×D19—42no—
159C22×D19—42no—
160C22×D19—42no—
161C22×D19—88no—
162C22×D19—81no—
163C22×D19—81no—
164C22×D19#10414yescomplemented
165Q8×C19—22no—
166Q8×C19—22no—
167Q8×C19—41no—
168Q8×C19—41no—
169D4×C19—22no—
170D4×C19—22no—
171D4×C19—41no—
172D4×C19—41no—
173D4×C19—44no—
174D4×C19—44no—
175C2×C4×C19—22no—
176C2×C4×C19—22no—
177C2×C4×C19—24no—
178C2×C4×C19—22no—
179C2×C4×C19—41no—
180C2×C4×C19—41no—
181C2×C4×C19—41no—
182C2×C4×C19—41no—
183C2×C4×C19—44no—
184C2×C4×C19—44no—
185C2×C4×C19—42no—
186C2×C4×C19—41no—
187C2×C4×C19—41no—
188C2×C4×C19—42no—
189C2×C4×C19C4×D411yescharacteristic
190C2×C4×C19C4×D411yescharacteristic
191C2×C4×C19#12111yescharacteristic
192C2×C4×C19#12111yescharacteristic
193C22⋊D19—88no—
194C2×Dic19—24no—
195C2×Dic19—22no—
196C2×Dic19—42no—
197C2×Dic19—42no—
198C2×Dic19—42no—
199C2×Dic19—42no—
200C2×Dic19—42no—
201C2×Dic19—42no—
202C2×Dic19—42no—
203C2×Dic19—81no—
204C4×D19—88no—
205C8×C19—81no—
206C19⋊C8—81no—
207#2404—191no—
208#2273—191no—
209#1789—191no—
210#1789D1911yescharacteristic, complemented
211#1462—191no—
212#1284—191no—
213#1284—191no—
214C22×C19—21no—
215C22×C19—21no—
216C22×C19—21no—
217C22×C19—21no—
218C22×C19—21no—
219C22×C19—21no—
220C22×C19—21no—
221C22×C19—44no—
222C22×C19—44no—
223C22×C19—42no—
224C22×C19—82no—
225C22×C19—81no—
226C22×C19—81no—
227C22×C19#38611yescharacteristic
228C22×C19C2×#10412yes—
229C22×C19B(4,𝔽2)12yes—
230C2×D19—24no—
231C2×D19—44no—
232C2×D19—44no—
233C2×D19—42no—
234C2×D19—42no—
235C2×D19—44no—
236C2×D19—82no—
237C2×D19—84no—
238C4×C19—21no—
239C4×C19—21no—
240C4×C19—21no—
241C4×C19—21no—
242C4×C19—44no—
243C4×C19—42no—
244Dic19—44no—
245Dic19—42no—
246Dic19—82no—
247C22×#41C2×D1911yescharacteristic
248C2×#120—381no—
249C22×C22⋊C4—191no—
250C22×C22⋊C4—381no—
251C2×#104—22no—
252C2×#104—382no—
253#407—191no—
254#407C2×D1911yescharacteristic
255#393—192no—
256#392—192no—
257#386—382no—
258#386—381no—
259#381—191no—
260C4×C22⋊C4—191no—
261C4×C22⋊C4—382no—
262C4×C22⋊C4—381no—
263C4×C22⋊C4—382no—
264C4×C22⋊C4C2×D1911yescharacteristic
265#323—382no—
266C2×C19—22no—
267C2×C19—22no—
268C2×C19—41no—
269C2×C19—82no—
270C2×C19#188911yescharacteristic
271C2×C19#189611yescharacteristic
272C2×C19#191111yescharacteristic
273D19—44no—
274C25—191no—
275C2×#41—21no—
276C2×#41—21no—
277C2×#41—21no—
278C2×#41—21no—
279C2×#41—44no—
280C22×Q8C4×D1911yescharacteristic, complemented
281C22×D4—21no—
282C22×D4—382no—
283C22×D4C4×D1911yescharacteristic, complemented
284C23×C4—21no—
285C23×C4—191no—
286C23×C4—382no—
287C23×C4C22×D1911yescharacteristic
288C2×M16—21no—
289C2×M16—381no—
290#120—764no—
291C2×C22⋊C4—21no—
292C2×C22⋊C4—192no—
293C2×C22⋊C4—192no—
294C2×C22⋊C4—388no—
295C2×C22⋊C4—382no—
296C2×C22⋊C4—381no—
297C2×C22⋊C4—381no—
298C2×C22⋊C4—381no—
299C2×C22⋊C4—381no—
300C2×C22⋊C4—381no—
301C2×C22⋊C4—382no—
302C2×C22⋊C4—381no—
303C2×C22⋊C4—382no—
304C2×C42—192no—
305C2×C42—382no—
306C2×C42C22⋊D1912yescomplemented
307#104—44no—
308#104—764no—
309C22⋊C8—21no—
310C22⋊C8—21no—
311C22⋊C8—381no—
312C22⋊C8—381no—
313#95—21no—
314#95—192no—
315#95—382no—
316#95—382no—
317#95—381no—
318#95—381no—
319C19#947511yescharacteristic, complemented, Sylow
320C24—21no—
321C24—192no—
322C24—384no—
323C24—381no—
324C24—381no—
325C24—762no—
326C24—1521no—
327C24D4×D1911yescharacteristic
328#41—24no—
329#41—24no—
330#41—42no—
331#41—42no—
332#41—42no—
333#41—42no—
334#41—42no—
335#41—42no—
336C2×Q8—21no—
337C2×Q8—21no—
338C2×Q8—42no—
339C2×D4—24no—
340C2×D4—21no—
341C2×D4—21no—
342C2×D4—42no—
343C2×D4—42no—
344C2×D4—41no—
345C2×D4—41no—
346C2×D4—764no—
347C2×D4—764no—
348C2×D4—1522no—
349C22×C4—22no—
350C22×C4—21no—
351C22×C4—42no—
352C22×C4—42no—
353C22×C4—42no—
354C22×C4—41no—
355C22×C4—41no—
356C22×C4—192no—
357C22×C4—388no—
358C22×C4—382no—
359C22×C4—381no—
360C22×C4—381no—
361C22×C4—382no—
362C22×C4—1522no—
363C22×C4—1522no—
364C22×C4—1521no—
365C22×C4C2×C4×D1911yescharacteristic
366C22×C4#6454111yescharacteristic
367C22×C4D4×D1911yescharacteristic
368C22×C4D4×D1911yescharacteristic
369C22×C4#6454311yescharacteristic
370C22×C4C2×C22⋊D1911yescharacteristic
371M16—42no—
372M16—762no—
373C2×C8—41no—
374C2×C8—761no—
375C22⋊C4—24no—
376C22⋊C4—388no—
377C22⋊C4—384no—
378C22⋊C4—382no—
379C22⋊C4—382no—
380C22⋊C4—382no—
381C22⋊C4—382no—
382C22⋊C4—764no—
383C22⋊C4—762no—
384C22⋊C4—1522no—
385C42—42no—
386C42—762no—
387C42—1522no—
388C23—22no—
389C23—22no—
390C23—22no—
391C23—41no—
392C23—42no—
393C23—41no—
394C23—42no—
395C23—41no—
396C23—194no—
397C23—382no—
398C23—382no—
399C23—384no—
400C23—382no—
401C23—382no—
402C23—762no—
403C23—762no—
404C23—762no—
405C23—762no—
406C23—1521no—
407C23—1521no—
408C23—1528no—
409C23C22⋊C4×D1911yescharacteristic
410C23#1059732911yescharacteristic
411C23#1059738311yescharacteristic
412Q8—22no—
413Q8—22no—
414Q8—41no—
415Q8—41no—
416D4—22no—
417D4—22no—
418D4—41no—
419D4—41no—
420D4—44no—
421D4—44no—
422D4—1528no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—24no—
426C2×C4—22no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—44no—
432C2×C4—44no—
433C2×C4—42no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—42no—
437C2×C4—384no—
438C2×C4—382no—
439C2×C4—762no—
440C2×C4—762no—
441C2×C4—762no—
442C2×C4—762no—
443C2×C4—762no—
444C2×C4—762no—
445C2×C4—762no—
446C2×C4—1528no—
447C2×C4—1521no—
448C2×C4(C22⋊D19)⋊C411yescharacteristic
449C2×C4#1059733011yescharacteristic
450C2×C4C4×C22⋊D1911yescharacteristic
451C2×C4#1059738411yescharacteristic
452C8—81no—
453C8—1521no—
454C22—21no—
455C22—21no—
456C22—21no—
457C22—21no—
458C22—21no—
459C22—21no—
460C22—21no—
461C22—44no—
462C22—44no—
463C22—42no—
464C22—82no—
465C22—81no—
466C22—81no—
467C22—384no—
468C22—764no—
469C22—764no—
470C22—764no—
471C22—762no—
472C22—762no—
473C22—1522no—
474C22—1524no—
475C22#1192642011yescharacteristic
476C22#104×D1912yes—
477C22#1192673012yes—
478C4—21no—
479C4—21no—
480C4—21no—
481C4—21no—
482C4—44no—
483C4—42no—
484C4—764no—
485C4—762no—
486C4—1522no—
487C2—22no—
488C2—22no—
489C2—41no—
490C2—82no—
491C2—764no—
492C2#1456404011yescharacteristic
493C2#1456407511yescharacteristic
494C2#1456416411yescharacteristic
subgroupG/H
centerC22#11926420
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#1789C2
socleC22×C19#386
prime radical#14566950C2
cosocleC23×C4×C19C23
hypercenter#1789D19
hypocenterC19#9475
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1789

Complements

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

NH ≅ G/Ntype
2. #14565987C2semidirect
3. #14563579C2semidirect
4. #14561961C2semidirect
5. #14561489C2semidirect
6. #14561488C2semidirect
7. C19×#1789C2semidirect
13. #11926455C4semidirect
14. #11926452C4semidirect
33. C22×Q8×C19C2×C4semidirect
35. C22×D4×C19C2×C4semidirect
43. C2×C42×C19D4semidirect
57. C2×C4×Dic19D4semidirect
69. C19⋊#95C2×C4semidirect
164. C22×D19#104semidirect
210. #1789D19semidirect
280. C22×Q8C4×D19semidirect
283. C22×D4C4×D19semidirect
306. C2×C42C22⋊D19semidirect
319. C19#9475semidirect

Maximal subgroups

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

subgroupindex
#145669502
#145659872
#145635792
#145619612
#145614892
#145614882
C19×#17892
#947519