Finite Group Databasebeta

← C19×#8399 #18014358

Subgroups — C19×#8399 #18014358

Order 4864.

868 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C19×#3459C211yesmaximal, characteristic
2C19×#1871C212yesmaximal, complemented
3C19×#1870C211yesmaximal, characteristic, complemented
4C4×C19×#99C211yesmaximal, characteristic, complemented
5C19×#1501C212yesmaximal, complemented
6C22×M16×C19C2211yescharacteristic, complemented
7C19×#543C411yescharacteristic, complemented
8C19×#539—22no—
9C19×#539C412yescomplemented
10C19×#538—22no—
11C19×#538—21no—
12C19×#534—21no—
13C19×#534C411yescharacteristic, complemented
14C19×#529—22no—
15C19×#529—21no—
16C19×#525—22no—
17C19×#525C2212yes—
18C2×C4×D4×C19—21no—
19C2×C4×D4×C19C2211yescharacteristic
20C2×C19×#104—22no—
21C2×C19×#99—21no—
22C2×C19×C22⋊C8—21no—
23C2×C19×C22⋊C8C2211yescharacteristic, complemented
24C4×C22⋊C4×C19C2212yescomplemented
25C19×#342—21no—
26C19×#339—22no—
27C19×#336—21no—
28C19×#328—22no—
29C19×#327—22no—
30C2×#41×C19D412yes—
31C22×D4×C19—21no—
32C22×D4×C19D411yescharacteristic
33C23×C4×C19—21no—
34C23×C4×C19D411yescharacteristic
35C23×C4×C19C2311yescharacteristic
36C2×M16×C19—22no—
37C2×M16×C19—42no—
38C22×C8×C19—21no—
39C22×C8×C19—21no—
40C19×#126—22no—
41C19×#126—22no—
42C19×#126—22no—
43C19×#125—21no—
44C19×#125—22no—
45C19×#124—22no—
46C19×#124—21no—
47C19×#123—22no—
48C19×#123—22no—
49C19×#123—22no—
50C19×#123—22no—
51C19×#123—22no—
52C19×#123—22no—
53C19×C22⋊Q8—22no—
54C19×C22⋊Q8—22no—
55C19×C22⋊Q8—21no—
56C19×C22⋊Q8—22no—
57C19×C22⋊Q8C2×C412yes—
58C19×C22⋊Q8D412yes—
59C19×#121—22no—
60C19×#121—22no—
61C19×#121—22no—
62C19×#121—21no—
63C19×#121C2×C412yes—
64C19×#121D412yes—
65C19×#120—22no—
66C19×#120—22no—
67C19×#120—22no—
68C4×Q8×C19—21no—
69C4×D4×C19—22no—
70C4×D4×C19—22no—
71C4×D4×C19—21no—
72C4×D4×C19—22no—
73C4×D4×C19—22no—
74C4×D4×C19—22no—
75C4×D4×C19—22no—
76C4×D4×C19—22no—
77C19×#117—22no—
78C19×#117D412yes—
79C2×C4⋊C4×C19—21no—
80C2×C4⋊C4×C19C2×C411yescharacteristic
81C2×C22⋊C4×C19—21no—
82C2×C22⋊C4×C19—21no—
83C2×C22⋊C4×C19—22no—
84C2×C22⋊C4×C19C2×C411yescharacteristic
85C2×C22⋊C4×C19D411yescharacteristic
86C2×C42×C19—21no—
87C2×C42×C19—22no—
88C2×C42×C19D411yescharacteristic
89C19×#104—44no—
90C19×#99—24no—
91C19×C22⋊C8—22no—
92C19×C22⋊C8—42no—
93C19×#95—22no—
94C24×C19—21no—
95C24×C19C22⋊C411yescharacteristic
96C24×C19C2×D411yescharacteristic
97#41×C19—42no—
98#41×C19—42no—
99C2×Q8×C19—21no—
100C2×Q8×C19C22⋊C412yes—
101C2×D4×C19—22no—
102C2×D4×C19—22no—
103C2×D4×C19—22no—
104C2×D4×C19—22no—
105C2×D4×C19—21no—
106C2×D4×C19—22no—
107C2×D4×C19—22no—
108C2×D4×C19—41no—
109C2×D4×C19—42no—
110C2×D4×C19—42no—
111C2×D4×C19C22⋊C412yes—
112C22×C4×C19—21no—
113C22×C4×C19—21no—
114C22×C4×C19—21no—
115C22×C4×C19—22no—
116C22×C4×C19—21no—
117C22×C4×C19—22no—
118C22×C4×C19—21no—
119C22×C4×C19—41no—
120C22×C4×C19—41no—
121C22×C4×C19—41no—
122C22×C4×C19—41no—
123C22×C4×C19—42no—
124C22×C4×C19—81no—
125C22×C4×C19—81no—
126C22×C4×C19C22⋊C411yescharacteristic
127C22×C4×C19C22⋊C411yescharacteristic
128C22×C4×C19C22⋊C411yescharacteristic
129C22×C4×C19C22×C411yescharacteristic
130C22×C4×C19C2×D412yes—
131C22×C4×C19C2×D411yescharacteristic
132C22×C4×C19C2×D412yes—
133M16×C19—24no—
134M16×C19—42no—
135C2×C8×C19—22no—
136C2×C8×C19—41no—
137C2×C8×C19—41no—
138C2×C8×C19—41no—
139C2×C8×C19—41no—
140C2×C8×C19—41no—
141C4⋊C4×C19—22no—
142C4⋊C4×C19—22no—
143C4⋊C4×C19—22no—
144C4⋊C4×C19—21no—
145C4⋊C4×C19—21no—
146C4⋊C4×C19—22no—
147C4⋊C4×C19—22no—
148C4⋊C4×C19—22no—
149C4⋊C4×C19—22no—
150C4⋊C4×C19C22⋊C412yes—
151C4⋊C4×C19C22⋊C412yes—
152C22⋊C4×C19—22no—
153C22⋊C4×C19—22no—
154C22⋊C4×C19—22no—
155C22⋊C4×C19—22no—
156C22⋊C4×C19—22no—
157C22⋊C4×C19—22no—
158C22⋊C4×C19—22no—
159C22⋊C4×C19—22no—
160C22⋊C4×C19—22no—
161C22⋊C4×C19—22no—
162C22⋊C4×C19—22no—
163C22⋊C4×C19—22no—
164C22⋊C4×C19—24no—
165C22⋊C4×C19—42no—
166C42×C19—22no—
167C42×C19—21no—
168C42×C19—22no—
169C42×C19—21no—
170C42×C19—42no—
171C42×C19—42no—
172#8399C1911yesmaximal, characteristic, direct product factor, Sylow
173C23×C19—21no—
174C23×C19—21no—
175C23×C19—21no—
176C23×C19—21no—
177C23×C19—22no—
178C23×C19—41no—
179C23×C19—41no—
180C23×C19—41no—
181C23×C19—41no—
182C23×C19—42no—
183C23×C19—81no—
184C23×C19—81no—
185C23×C19#10412yescomplemented
186C23×C19C2×C22⋊C411yescharacteristic
187C23×C19#12012yes—
188Q8×C19—42no—
189Q8×C19—81no—
190D4×C19—42no—
191D4×C19—44no—
192D4×C19—44no—
193D4×C19—42no—
194D4×C19—42no—
195D4×C19—82no—
196D4×C19—82no—
197D4×C19—81no—
198C2×C4×C19—22no—
199C2×C4×C19—21no—
200C2×C4×C19—22no—
201C2×C4×C19—21no—
202C2×C4×C19—21no—
203C2×C4×C19—22no—
204C2×C4×C19—21no—
205C2×C4×C19—22no—
206C2×C4×C19—21no—
207C2×C4×C19—22no—
208C2×C4×C19—21no—
209C2×C4×C19—21no—
210C2×C4×C19—41no—
211C2×C4×C19—42no—
212C2×C4×C19—42no—
213C2×C4×C19—41no—
214C2×C4×C19—42no—
215C2×C4×C19—41no—
216C2×C4×C19—42no—
217C2×C4×C19—41no—
218C2×C4×C19—41no—
219C2×C4×C19—44no—
220C2×C4×C19—81no—
221C2×C4×C19—81no—
222C2×C4×C19—82no—
223C2×C4×C19—81no—
224C2×C4×C19—82no—
225C2×C4×C19—82no—
226C2×C4×C19C2×C22⋊C412yes—
227C2×C4×C19#12011yescharacteristic
228C2×C4×C19#12011yescharacteristic
229C8×C19—42no—
230C8×C19—81no—
231#3459C2×C1911yescharacteristic
232#1871C2×C1912yescomplemented
233#1870C2×C1911yescharacteristic, complemented
234C4×#99C2×C1911yescharacteristic, complemented
235#1501C2×C1912yescomplemented
236C22×C19—21no—
237C22×C19—21no—
238C22×C19—22no—
239C22×C19—22no—
240C22×C19—22no—
241C22×C19—22no—
242C22×C19—42no—
243C22×C19—41no—
244C22×C19—41no—
245C22×C19—42no—
246C22×C19—42no—
247C22×C19—42no—
248C22×C19—81no—
249C22×C19—81no—
250C22×C19—81no—
251C22×C19—84no—
252C22×C19#37911yescharacteristic
253C22×C19C2×#10411yescharacteristic
254C22×C19#42111yescharacteristic
255C4×C19—21no—
256C4×C19—22no—
257C4×C19—41no—
258C4×C19—42no—
259C4×C19—41no—
260C4×C19—42no—
261C4×C19—41no—
262C4×C19—42no—
263C4×C19—84no—
264C4×C19B(4,𝔽2)11yescharacteristic
265C4×C19#45811yescharacteristic
266C22×M16C22×C1911yescharacteristic, complemented
267#543C4×C1911yescharacteristic, complemented
268#539—22no—
269#539C4×C1912yescomplemented
270#538—22no—
271#538—21no—
272#534—21no—
273#534C4×C1911yescharacteristic, complemented
274#529—22no—
275#529—21no—
276#525—22no—
277#525C22×C1912yes—
278C2×C4×D4—21no—
279C2×C4×D4C22×C1911yescharacteristic
280C2×#104—22no—
281C2×#99—21no—
282C2×C22⋊C8—21no—
283C2×C22⋊C8C22×C1911yescharacteristic, complemented
284C4×C22⋊C4C22×C1912yescomplemented
285#342—21no—
286#339—22no—
287#336—21no—
288#328—22no—
289#327—22no—
290C2×C19—21no—
291C2×C19—21no—
292C2×C19—42no—
293C2×C19—42no—
294C2×C19—82no—
295C2×C19#178911yescharacteristic
296C2×C19#179011yescharacteristic
297C2×C19#179411yescharacteristic
298C2×#41D4×C1912yes—
299C22×D4—21no—
300C22×D4D4×C1911yescharacteristic
301C23×C4—21no—
302C23×C4D4×C1911yescharacteristic
303C23×C4C23×C1911yescharacteristic
304C2×M16—22no—
305C2×M16—42no—
306C22×C8—21no—
307C22×C8—21no—
308#126—22no—
309#126—22no—
310#126—22no—
311#125—21no—
312#125—22no—
313#124—22no—
314#124—21no—
315#123—22no—
316#123—22no—
317#123—22no—
318#123—22no—
319#123—22no—
320#123—22no—
321C22⋊Q8—22no—
322C22⋊Q8—22no—
323C22⋊Q8—21no—
324C22⋊Q8—22no—
325C22⋊Q8C2×C4×C1912yes—
326C22⋊Q8D4×C1912yes—
327#121—22no—
328#121—22no—
329#121—22no—
330#121—21no—
331#121C2×C4×C1912yes—
332#121D4×C1912yes—
333#120—22no—
334#120—22no—
335#120—22no—
336C4×Q8—21no—
337C4×D4—22no—
338C4×D4—22no—
339C4×D4—21no—
340C4×D4—22no—
341C4×D4—22no—
342C4×D4—22no—
343C4×D4—22no—
344C4×D4—22no—
345#117—22no—
346#117D4×C1912yes—
347C2×C4⋊C4—21no—
348C2×C4⋊C4C2×C4×C1911yescharacteristic
349C2×C22⋊C4—21no—
350C2×C22⋊C4—21no—
351C2×C22⋊C4—22no—
352C2×C22⋊C4C2×C4×C1911yescharacteristic
353C2×C22⋊C4D4×C1911yescharacteristic
354C2×C42—21no—
355C2×C42—22no—
356C2×C42D4×C1911yescharacteristic
357#104—44no—
358#99—24no—
359C22⋊C8—22no—
360C22⋊C8—42no—
361#95—22no—
362C19#839911yescharacteristic, direct product factor, Sylow
363C24—21no—
364C24C22⋊C4×C1911yescharacteristic
365C24C2×D4×C1911yescharacteristic
366#41—42no—
367#41—42no—
368C2×Q8—21no—
369C2×Q8C22⋊C4×C1912yes—
370C2×D4—22no—
371C2×D4—22no—
372C2×D4—22no—
373C2×D4—22no—
374C2×D4—21no—
375C2×D4—22no—
376C2×D4—22no—
377C2×D4—41no—
378C2×D4—42no—
379C2×D4—42no—
380C2×D4C22⋊C4×C1912yes—
381C22×C4—21no—
382C22×C4—21no—
383C22×C4—21no—
384C22×C4—22no—
385C22×C4—21no—
386C22×C4—22no—
387C22×C4—21no—
388C22×C4—41no—
389C22×C4—41no—
390C22×C4—41no—
391C22×C4—41no—
392C22×C4—42no—
393C22×C4—81no—
394C22×C4—81no—
395C22×C4C22⋊C4×C1911yescharacteristic
396C22×C4C22⋊C4×C1911yescharacteristic
397C22×C4C22⋊C4×C1911yescharacteristic
398C22×C4C22×C4×C1911yescharacteristic
399C22×C4C2×D4×C1912yes—
400C22×C4C2×D4×C1911yescharacteristic
401C22×C4C2×D4×C1912yes—
402M16—24no—
403M16—42no—
404C2×C8—22no—
405C2×C8—41no—
406C2×C8—41no—
407C2×C8—41no—
408C2×C8—41no—
409C2×C8—41no—
410C4⋊C4—22no—
411C4⋊C4—22no—
412C4⋊C4—22no—
413C4⋊C4—21no—
414C4⋊C4—21no—
415C4⋊C4—22no—
416C4⋊C4—22no—
417C4⋊C4—22no—
418C4⋊C4—22no—
419C4⋊C4C22⋊C4×C1912yes—
420C4⋊C4C22⋊C4×C1912yes—
421C22⋊C4—22no—
422C22⋊C4—22no—
423C22⋊C4—22no—
424C22⋊C4—22no—
425C22⋊C4—22no—
426C22⋊C4—22no—
427C22⋊C4—22no—
428C22⋊C4—22no—
429C22⋊C4—22no—
430C22⋊C4—22no—
431C22⋊C4—22no—
432C22⋊C4—22no—
433C22⋊C4—24no—
434C22⋊C4—42no—
435C42—22no—
436C42—22no—
437C42—21no—
438C42—21no—
439C42—42no—
440C42—42no—
441C23—21no—
442C23—21no—
443C23—21no—
444C23—21no—
445C23—22no—
446C23—41no—
447C23—41no—
448C23—41no—
449C23—41no—
450C23—42no—
451C23—81no—
452C23—81no—
453C23C19×#10412yescomplemented
454C23C2×C22⋊C4×C1911yescharacteristic
455C23C19×#12012yes—
456Q8—42no—
457Q8—81no—
458D4—42no—
459D4—44no—
460D4—44no—
461D4—42no—
462D4—42no—
463D4—82no—
464D4—82no—
465D4—81no—
466C2×C4—22no—
467C2×C4—21no—
468C2×C4—22no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—22no—
472C2×C4—21no—
473C2×C4—22no—
474C2×C4—21no—
475C2×C4—22no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—41no—
479C2×C4—42no—
480C2×C4—42no—
481C2×C4—41no—
482C2×C4—42no—
483C2×C4—41no—
484C2×C4—42no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—44no—
488C2×C4—81no—
489C2×C4—82no—
490C2×C4—81no—
491C2×C4—81no—
492C2×C4—82no—
493C2×C4—82no—
494C2×C4C2×C22⋊C4×C1912yes—
495C2×C4C19×#12011yescharacteristic
496C2×C4C19×#12011yescharacteristic
497C8—42no—
498C8—81no—
499C22—21no—
500C22—21no—
501C22—22no—
502C22—22no—
503C22—22no—
504C22—22no—
505C22—42no—
506C22—41no—
507C22—41no—
508C22—42no—
509C22—42no—
510C22—42no—
511C22—81no—
512C22—81no—
513C22—81no—
514C22—84no—
515C22C19×#37911yescharacteristic
516C22C2×C19×#10411yescharacteristic
517C22C19×#42111yescharacteristic
518C4—21no—
519C4—22no—
520C4—41no—
521C4—42no—
522C4—41no—
523C4—42no—
524C4—41no—
525C4—42no—
526C4—84no—
527C4C19×B(4,𝔽2)11yescharacteristic
528C4C19×#45811yescharacteristic
529C2—21no—
530C2—21no—
531C2—42no—
532C2—42no—
533C2—82no—
534C2C19×#178911yescharacteristic
535C2C19×#179011yescharacteristic
536C2C19×#179411yescharacteristic
subgroupG/H
centerC2×C4×C19#120
commutatorC22×C4C22×C4×C19
Frattini, cosocleC23×C4C23×C19
socleC22×C19#379
prime radicalC19×#3459C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C19 ◁ C23×C4×C19 ◁ G

Complements

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

NH ≅ G/Ntype
2. C19×#1871C2semidirect
3. C19×#1870C2semidirect
4. C4×C19×#99C2semidirect
5. C19×#1501C2semidirect
6. C22×M16×C19C22semidirect
7. C19×#543C4semidirect
9. C19×#539C4semidirect
13. C19×#534C4semidirect
23. C2×C19×C22⋊C8C22semidirect
24. C4×C22⋊C4×C19C22semidirect
172. #8399C19direct (N × H)
185. C23×C19#104semidirect
232. #1871C2×C19semidirect
233. #1870C2×C19semidirect
234. C4×#99C2×C19semidirect
235. #1501C2×C19semidirect
266. C22×M16C22×C19semidirect
267. #543C4×C19semidirect
269. #539C4×C19semidirect
273. #534C4×C19semidirect
283. C2×C22⋊C8C22×C19semidirect
284. C4×C22⋊C4C22×C19semidirect
362. C19#8399direct (N × H)
453. C23C19×#104semidirect

Maximal subgroups

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

subgroupindex
C19×#34592
C19×#18712
C19×#18702
C4×C19×#992
C19×#15012
#839919