Finite Group Databasebeta

← C19×#61877 #18067836

Subgroups — C19×#61877 #18067836

Order 4864.

1600 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C19×#3556C211yesmaximal, characteristic, complemented
2C19×#3504C211yesmaximal, characteristic
3C19×#3390C214yesmaximal, complemented
4C19×#3388C214yesmaximal, complemented
5C19×#3374C214yesmaximal, complemented
6C19×#3372C214yesmaximal, complemented
7C19×#3242C214yesmaximal, complemented
8C19×#3236C212yesmaximal, complemented
9C19×#3120C214yesmaximal
10C19×#3116C212yesmaximal
11C19×#2987C211yesmaximal, characteristic, complemented
12C19×#564—21no—
13C19×#564—21no—
14C19×#557—22no—
15C19×#557C2214yes—
16C19×#557C2214yes—
17C19×#557C2214yes—
18C19×#554—24no—
19C19×#554C2214yes—
20C19×#544—22no—
21C19×#544C2212yes—
22C19×#541—24no—
23C19×#541C2214yes—
24C19×#533—21no—
25C19×#533C2212yes—
26C19×#533C2211yescharacteristic
27C2×C19×#125—21no—
28C2×C19×#125C2211yescharacteristic
29C19×#520C2212yes—
30C4×#41×C19C2211yescharacteristic
31C19×#501C2214yes—
32C19×#501C2214yes—
33C19×#499C2214yes—
34C19×#491C2214yes—
35C19×#491C2214yes—
36C19×#487C2214yes—
37C19×#485C2214yes—
38C19×#484C2214yes—
39C19×#483C2214yes—
40C19×#479C2214yes—
41C19×#479C2214yes—
42C19×#479C2214yes—
43C19×#479C2214yes—
44C19×#479C2214yes—
45C19×#478C2214yes—
46C19×#477C2214yes—
47C19×#477C2212yes—
48C19×#476C2212yes—
49C19×#475C2214yes—
50C19×#462C2212yes—
51C19×#462C2214yes—
52C19×#461C2212yes—
53C19×#461C2214yes—
54C19×#452C2214yes—
55C19×#446C2214yes—
56C19×#446C2214yes—
57C19×#441C2214yes—
58C19×#441C2214yes—
59C19×#440C2214yes—
60C19×#440C2214yes—
61C4×Q16×C19C2214yes—
62C4×SD16×C19C2214yes—
63C19×#433C2214yes—
64C19×#432C2212yes—
65C2×#41×C19C2311yescharacteristic
66C2×Q16×C19C2314yes—
67C2×SD16×C19C2314yes—
68C19×C4⋊Q8—24no—
69C19×C4⋊Q8—24no—
70C19×C4⋊Q8—22no—
71C19×C4⋊Q8D412yes—
72C19×C4⋊Q8C2314yes—
73C19×C4⋊Q8C2312yes—
74C19×C4⋊Q8C2314yes—
75C19×C4⋊Q8C2312yes—
76C19×#126—24no—
77C19×#126—24no—
78C19×#125—22no—
79C19×#125—24no—
80C19×#125—24no—
81C19×#125—24no—
82C19×#125—24no—
83C19×#125—24no—
84C19×#125—24no—
85C19×#125—24no—
86C19×#125—24no—
87C19×#125—24no—
88C19×#125—21no—
89C19×#125—21no—
90C19×#125—22no—
91C19×#125D411yescharacteristic
92C19×#125D411yescharacteristic
93C19×#125C2314yes—
94C19×#125C2314yes—
95C19×#125C2314yes—
96C19×C22⋊Q8—24no—
97C19×C22⋊Q8—22no—
98C19×C22⋊Q8—24no—
99C19×C22⋊Q8—24no—
100C19×C22⋊Q8—24no—
101C19×C22⋊Q8D414yes—
102C19×C22⋊Q8C2314yes—
103C4×Q8×C19—24no—
104C4×Q8×C19—24no—
105C4×Q8×C19—24no—
106C4×Q8×C19—22no—
107C4×Q8×C19C2314yes—
108C4×Q8×C19C2314yes—
109C4×Q8×C19C2314yes—
110C4×Q8×C19C2314yes—
111C4×Q8×C19C2312yes—
112C4×Q8×C19C2314yes—
113C4×D4×C19—22no—
114C4×D4×C19—24no—
115C4×D4×C19C2314yes—
116C4×D4×C19C2312yes—
117C19×#117—22no—
118C19×#117—22no—
119C19×#117—21no—
120C19×#117C2311yescharacteristic
121C19×#117C2312yes—
122C2×C4⋊C4×C19—22no—
123C2×C4⋊C4×C19—22no—
124C2×C4⋊C4×C19—24no—
125C2×C4⋊C4×C19C2312yes—
126C2×C42×C19—21no—
127C2×C42×C19C2311yescharacteristic
128C19×#107C2314yes—
129C19×#107C2314yes—
130C19×#107C2314yes—
131C19×#106C2314yes—
132C19×#106C2314yes—
133C19×#106C2314yes—
134C19×C4⋊C8C2312yes—
135C19×C4⋊C8C2312yes—
136C19×C4⋊C8C2314yes—
137C19×C4⋊C8C2314yes—
138C19×#103C2314yes—
139C19×#103C2314yes—
140C19×#103C2314yes—
141C19×#103C2314yes—
142C19×#103C2314yes—
143C19×#103C2314yes—
144C19×#103C2314yes—
145C19×#102C2314yes—
146C19×C22⋊C8C2314yes—
147C19×#97C2314yes—
148C19×#97C2314yes—
149C4×C8×C19C2314yes—
150#41×C19—22no—
151#41×C19—22no—
152C2×Q8×C19—22no—
153C2×Q8×C19—24no—
154C2×Q8×C19C2×D414yes—
155C2×Q8×C19C2414yes—
156C2×Q8×C19C2411yescharacteristic
157C2×D4×C19—21no—
158C2×D4×C19C2411yescharacteristic
159C22×C4×C19—21no—
160C22×C4×C19—22no—
161C22×C4×C19—22no—
162C22×C4×C19—24no—
163C22×C4×C19C2×D412yes—
164C22×C4×C19C2411yescharacteristic
165Q16×C19—28no—
166SD16×C19—28no—
167C2×C8×C19C2414yes—
168C2×C8×C19C2414yes—
169C4⋊C4×C19—24no—
170C4⋊C4×C19—22no—
171C4⋊C4×C19—24no—
172C4⋊C4×C19—24no—
173C4⋊C4×C19—24no—
174C4⋊C4×C19—24no—
175C4⋊C4×C19—22no—
176C4⋊C4×C19—22no—
177C4⋊C4×C19—22no—
178C4⋊C4×C19—22no—
179C4⋊C4×C19—24no—
180C4⋊C4×C19—24no—
181C4⋊C4×C19—24no—
182C4⋊C4×C19—24no—
183C4⋊C4×C19—24no—
184C4⋊C4×C19—24no—
185C4⋊C4×C19—24no—
186C4⋊C4×C19—24no—
187C4⋊C4×C19—24no—
188C4⋊C4×C19C2×D412yes—
189C4⋊C4×C19C2×D414yes—
190C4⋊C4×C19C2×D412yes—
191C4⋊C4×C19C2×D414yes—
192C4⋊C4×C19C2×D414yes—
193C4⋊C4×C19C2414yes—
194C4⋊C4×C19C2412yes—
195C4⋊C4×C19C2414yes—
196C22⋊C4×C19—24no—
197C22⋊C4×C19—21no—
198C22⋊C4×C19—22no—
199C22⋊C4×C19—24no—
200C22⋊C4×C19C2×D414yes—
201C42×C19—21no—
202C42×C19—22no—
203C42×C19—24no—
204C42×C19—24no—
205C42×C19—24no—
206C42×C19—24no—
207C42×C19C2×D411yescharacteristic
208C42×C19C2×D411yescharacteristic
209C42×C19C2412yes—
210C42×C19C2414yes—
211#61877C1911yesmaximal, characteristic, direct product factor, Sylow
212C23×C19—21no—
213C23×C19C22×D411yescharacteristic
214Q8×C19—21no—
215Q8×C19—24no—
216Q8×C19—24no—
217Q8×C19—44no—
218Q8×C19—44no—
219Q8×C19—84no—
220Q8×C192−1+412yes—
221D4×C19—24no—
222D4×C19—21no—
223D4×C192−1+412yes—
224C2×C4×C19—24no—
225C2×C4×C19—21no—
226C2×C4×C19—21no—
227C2×C4×C19—21no—
228C2×C4×C19—24no—
229C2×C4×C19—24no—
230C2×C4×C19—22no—
231C2×C4×C19—24no—
232C2×C4×C19—42no—
233C2×C4×C19—82no—
234C2×C4×C19—84no—
235C2×C4×C19—82no—
236C2×C4×C19C22×D412yes—
237C2×C4×C19C22×D414yes—
238C2×C4×C19C22×D411yescharacteristic
239C2×C4×C19C22×D412yes—
240C2×C4×C19C22×D414yes—
241C2×C4×C19C2511yescharacteristic
242C8×C19—24no—
243C8×C19—24no—
244#3556C2×C1911yescharacteristic, complemented
245#3504C2×C1911yescharacteristic
246#3390C2×C1914yescomplemented
247#3388C2×C1914yescomplemented
248#3374C2×C1914yescomplemented
249#3372C2×C1914yescomplemented
250#3242C2×C1914yescomplemented
251#3236C2×C1912yescomplemented
252#3120C2×C1914yes—
253#3116C2×C1912yes—
254#2987C2×C1911yescharacteristic, complemented
255C22×C19—22no—
256C22×C19—21no—
257C22×C19—22no—
258C22×C19—42no—
259C22×C19C23×D411yescharacteristic
260C4×C19—22no—
261C4×C19—22no—
262C4×C19—24no—
263C4×C19—24no—
264C4×C19—21no—
265C4×C19—22no—
266C4×C19—44no—
267C4×C19—42no—
268C4×C19—44no—
269C4×C19—44no—
270C4×C19C2×2−1+411yescharacteristic
271C4×C19C2×2−1+411yescharacteristic
272#564—21no—
273#564—21no—
274#557—22no—
275#557C22×C1914yes—
276#557C22×C1914yes—
277#557C22×C1914yes—
278#554—24no—
279#554C22×C1914yes—
280#544—22no—
281#544C22×C1912yes—
282#541—24no—
283#541C22×C1914yes—
284#533—21no—
285#533C22×C1912yes—
286#533C22×C1911yescharacteristic
287C2×#125—21no—
288C2×#125C22×C1911yescharacteristic
289#520C22×C1912yes—
290C4×#41C22×C1911yescharacteristic
291#501C22×C1914yes—
292#501C22×C1914yes—
293#499C22×C1914yes—
294#491C22×C1914yes—
295#491C22×C1914yes—
296#487C22×C1914yes—
297#485C22×C1914yes—
298#484C22×C1914yes—
299#483C22×C1914yes—
300#479C22×C1914yes—
301#479C22×C1914yes—
302#479C22×C1914yes—
303#479C22×C1914yes—
304#479C22×C1914yes—
305#478C22×C1914yes—
306#477C22×C1912yes—
307#477C22×C1914yes—
308#476C22×C1912yes—
309#475C22×C1914yes—
310#462C22×C1912yes—
311#462C22×C1914yes—
312#461C22×C1912yes—
313#461C22×C1914yes—
314#452C22×C1914yes—
315#446C22×C1914yes—
316#446C22×C1914yes—
317#441C22×C1914yes—
318#441C22×C1914yes—
319#440C22×C1914yes—
320#440C22×C1914yes—
321C4×Q16C22×C1914yes—
322C4×SD16C22×C1914yes—
323#433C22×C1914yes—
324#432C22×C1912yes—
325C2×C19—41no—
326C2×C19—42no—
327C2×C19#348611yescharacteristic
328C2×C19#358612yes—
329C2×#41C23×C1911yescharacteristic
330C2×Q16C23×C1914yes—
331C2×SD16C23×C1914yes—
332C4⋊Q8—24no—
333C4⋊Q8—24no—
334C4⋊Q8—22no—
335C4⋊Q8D4×C1912yes—
336C4⋊Q8C23×C1912yes—
337C4⋊Q8C23×C1914yes—
338C4⋊Q8C23×C1912yes—
339C4⋊Q8C23×C1914yes—
340#126—24no—
341#126—24no—
342#125—22no—
343#125—24no—
344#125—24no—
345#125—24no—
346#125—24no—
347#125—24no—
348#125—24no—
349#125—24no—
350#125—24no—
351#125—24no—
352#125—21no—
353#125—21no—
354#125—22no—
355#125D4×C1911yescharacteristic
356#125D4×C1911yescharacteristic
357#125C23×C1914yes—
358#125C23×C1914yes—
359#125C23×C1914yes—
360C22⋊Q8—24no—
361C22⋊Q8—22no—
362C22⋊Q8—24no—
363C22⋊Q8—24no—
364C22⋊Q8—24no—
365C22⋊Q8D4×C1914yes—
366C22⋊Q8C23×C1914yes—
367C4×Q8—24no—
368C4×Q8—24no—
369C4×Q8—24no—
370C4×Q8—22no—
371C4×Q8C23×C1912yes—
372C4×Q8C23×C1914yes—
373C4×Q8C23×C1914yes—
374C4×Q8C23×C1914yes—
375C4×Q8C23×C1914yes—
376C4×Q8C23×C1914yes—
377C4×D4—22no—
378C4×D4—24no—
379C4×D4C23×C1912yes—
380C4×D4C23×C1914yes—
381#117—22no—
382#117—22no—
383#117—21no—
384#117C23×C1911yescharacteristic
385#117C23×C1912yes—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—24no—
389C2×C4⋊C4C23×C1912yes—
390C2×C42—21no—
391C2×C42C23×C1911yescharacteristic
392#107C23×C1914yes—
393#107C23×C1914yes—
394#107C23×C1914yes—
395#106C23×C1914yes—
396#106C23×C1914yes—
397#106C23×C1914yes—
398C4⋊C8C23×C1912yes—
399C4⋊C8C23×C1912yes—
400C4⋊C8C23×C1914yes—
401C4⋊C8C23×C1914yes—
402#103C23×C1914yes—
403#103C23×C1914yes—
404#103C23×C1914yes—
405#103C23×C1914yes—
406#103C23×C1914yes—
407#103C23×C1914yes—
408#103C23×C1914yes—
409#102C23×C1914yes—
410C22⋊C8C23×C1914yes—
411#97C23×C1914yes—
412#97C23×C1914yes—
413C4×C8C23×C1914yes—
414C19#6187711yescharacteristic, direct product factor, Sylow
415#41—22no—
416#41—22no—
417C2×Q8—22no—
418C2×Q8—24no—
419C2×Q8C2×D4×C1914yes—
420C2×Q8C24×C1914yes—
421C2×Q8C24×C1911yescharacteristic
422C2×D4—21no—
423C2×D4C24×C1911yescharacteristic
424C22×C4—21no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—24no—
428C22×C4C2×D4×C1912yes—
429C22×C4C24×C1911yescharacteristic
430Q16—28no—
431SD16—28no—
432C2×C8C24×C1914yes—
433C2×C8C24×C1914yes—
434C4⋊C4—24no—
435C4⋊C4—22no—
436C4⋊C4—24no—
437C4⋊C4—24no—
438C4⋊C4—24no—
439C4⋊C4—24no—
440C4⋊C4—22no—
441C4⋊C4—22no—
442C4⋊C4—22no—
443C4⋊C4—22no—
444C4⋊C4—24no—
445C4⋊C4—24no—
446C4⋊C4—24no—
447C4⋊C4—24no—
448C4⋊C4—24no—
449C4⋊C4—24no—
450C4⋊C4—24no—
451C4⋊C4—24no—
452C4⋊C4—24no—
453C4⋊C4C2×D4×C1912yes—
454C4⋊C4C2×D4×C1914yes—
455C4⋊C4C2×D4×C1912yes—
456C4⋊C4C2×D4×C1914yes—
457C4⋊C4C2×D4×C1914yes—
458C4⋊C4C24×C1914yes—
459C4⋊C4C24×C1914yes—
460C4⋊C4C24×C1912yes—
461C22⋊C4—24no—
462C22⋊C4—21no—
463C22⋊C4—22no—
464C22⋊C4—24no—
465C22⋊C4C2×D4×C1914yes—
466C42—21no—
467C42—22no—
468C42—24no—
469C42—24no—
470C42—24no—
471C42—24no—
472C42C2×D4×C1911yescharacteristic
473C42C2×D4×C1911yescharacteristic
474C42C24×C1914yes—
475C42C24×C1912yes—
476C23—21no—
477C23C22×D4×C1911yescharacteristic
478Q8—21no—
479Q8—24no—
480Q8—24no—
481Q8—44no—
482Q8—44no—
483Q8—84no—
484Q8C19×2−1+412yes—
485D4—24no—
486D4—21no—
487D4C19×2−1+412yes—
488C2×C4—24no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—24no—
493C2×C4—24no—
494C2×C4—22no—
495C2×C4—24no—
496C2×C4—42no—
497C2×C4—82no—
498C2×C4—84no—
499C2×C4—82no—
500C2×C4C22×D4×C1912yes—
501C2×C4C22×D4×C1914yes—
502C2×C4C22×D4×C1911yescharacteristic
503C2×C4C22×D4×C1912yes—
504C2×C4C22×D4×C1914yes—
505C2×C4C25×C1911yescharacteristic
506C8—24no—
507C8—24no—
508C22—21no—
509C22—22no—
510C22—22no—
511C22—42no—
512C22C23×D4×C1911yescharacteristic
513C4—21no—
514C4—22no—
515C4—22no—
516C4—22no—
517C4—24no—
518C4—24no—
519C4—44no—
520C4—44no—
521C4—42no—
522C4—44no—
523C4C2×C19×2−1+411yescharacteristic
524C4C2×C19×2−1+411yescharacteristic
525C2—41no—
526C2—42no—
527C2C19×#348611yescharacteristic
528C2C19×#358612yes—
subgroupG/H
center, socleC22×C19C23×D4
commutator, Frattini, cosocleC2×C4C25×C19
prime radicalC2×#41×C19C23
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C19 ◁ C19×#533 ◁ G

Complements

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

NH ≅ G/Ntype
1. C19×#3556C2semidirect
3. C19×#3390C2semidirect
4. C19×#3388C2semidirect
5. C19×#3374C2semidirect
6. C19×#3372C2semidirect
7. C19×#3242C2semidirect
8. C19×#3236C2semidirect
11. C19×#2987C2semidirect
211. #61877C19direct (N × H)
244. #3556C2×C19semidirect
246. #3390C2×C19semidirect
247. #3388C2×C19semidirect
248. #3374C2×C19semidirect
249. #3372C2×C19semidirect
250. #3242C2×C19semidirect
251. #3236C2×C19semidirect
254. #2987C2×C19semidirect
414. C19#61877direct (N × H)

Maximal subgroups

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

subgroupindex
C19×#35562
C19×#35042
C19×#33902
C19×#33882
C19×#33742
C19×#33722
C19×#32422
C19×#32362
C19×#31202
C19×#31162
C19×#29872
#6187719