Finite Group Databasebeta

← C19×#9938 #18015897

Subgroups — C19×#9938 #18015897

Order 4864.

1008 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 1008 conjugacy classes of subgroups — too many to draw. Only its 102 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
1C19×#3006C211yesmaximal, characteristic, complemented
2C19×#2539C211yesmaximal, characteristic, complemented
3C19×#2404C211yesmaximal, characteristic, complemented
4C19×#1789C211yesmaximal, characteristic, complemented
5C19×#1510C211yesmaximal, characteristic, complemented
6C19×#1462C211yesmaximal, characteristic, complemented
7C19×#1284C211yesmaximal, characteristic, complemented
8C22×#41×C19C2211yescharacteristic
9C2×C19×AGL(1,ℤ/8)—21no—
10C2×C19×#123—21no—
11C2×C19×#121C2211yescharacteristic
12C2×C19×#120—21no—
13C2×C19×#120—21no—
14C22×C22⋊C4×C19C2211yescharacteristic
15C19×#449—22no—
16C19×#448—21no—
17C19×#447—21no—
18C2×C19×#104—22no—
19C19×#417—21no—
20C19×#407C2211yescharacteristic
21C19×#407C2211yescharacteristic
22C19×#399—21no—
23C19×#393—21no—
24C19×#392—21no—
25C19×#392—21no—
26C19×#390—22no—
27C19×#386—22no—
28C19×#386—21no—
29C19×#381C2211yescharacteristic
30C4×C22⋊C4×C19C2211yescharacteristic
31C19×#327—22no—
32C19×#323—22no—
33C25×C19D411yescharacteristic
34C2×#41×C19—21no—
35C2×#41×C19—21no—
36C2×#41×C19—21no—
37C2×#41×C19—21no—
38C2×#41×C19—44no—
39C22×Q8×C19D411yescharacteristic, complemented
40C22×D4×C19—21no—
41C22×D4×C19—21no—
42C22×D4×C19—22no—
43C22×D4×C19—22no—
44C22×D4×C19D411yescharacteristic, complemented
45C22×D4×C19D411yescharacteristic, complemented
46C23×C4×C19—21no—
47C23×C4×C19D411yescharacteristic
48C23×C4×C19C2311yescharacteristic
49C19×AGL(1,ℤ/8)—44no—
50C2×SD16×C19—22no—
51C2×D8×C19—22no—
52C2×M16×C19—21no—
53C2×M16×C19—21no—
54C19×#123—44no—
55C19×#121—21no—
56C19×#121—21no—
57C19×#121—21no—
58C19×#121—21no—
59C19×#120—44no—
60C19×#120—44no—
61C2×C4⋊C4×C19—22no—
62C2×C4⋊C4×C19D411yescharacteristic, complemented
63C2×C22⋊C4×C19—21no—
64C2×C22⋊C4×C19—22no—
65C2×C22⋊C4×C19—22no—
66C2×C22⋊C4×C19—22no—
67C2×C22⋊C4×C19—21no—
68C2×C22⋊C4×C19—21no—
69C2×C22⋊C4×C19—21no—
70C2×C22⋊C4×C19—21no—
71C2×C22⋊C4×C19—21no—
72C2×C22⋊C4×C19—21no—
73C2×C22⋊C4×C19—21no—
74C2×C22⋊C4×C19—21no—
75C2×C22⋊C4×C19—22no—
76C2×C42×C19D412yescomplemented
77C19×#104—44no—
78C19×#103—22no—
79C19×#102—22no—
80C19×C22⋊C8—21no—
81C19×C22⋊C8—21no—
82C19×C22⋊C8—21no—
83C19×C22⋊C8D412yescomplemented
84C19×#95—22no—
85C19×#95—21no—
86C19×#95—21no—
87C19×#95D412yescomplemented
88C24×C19—21no—
89C24×C19—21no—
90C24×C19—21no—
91C24×C19—21no—
92C24×C19—21no—
93C24×C19—42no—
94C24×C19—42no—
95C24×C19—42no—
96C24×C19C2×D411yescharacteristic
97#41×C19—24no—
98#41×C19—24no—
99#41×C19—42no—
100#41×C19—42no—
101#41×C19—42no—
102#41×C19—42no—
103#41×C19—42no—
104#41×C19—42no—
105C2×Q8×C19—21no—
106C2×Q8×C19—21no—
107C2×Q8×C19—42no—
108C2×D4×C19—24no—
109C2×D4×C19—21no—
110C2×D4×C19—21no—
111C2×D4×C19—21no—
112C2×D4×C19—21no—
113C2×D4×C19—42no—
114C2×D4×C19—44no—
115C2×D4×C19—42no—
116C2×D4×C19—42no—
117C2×D4×C19—41no—
118C2×D4×C19—41no—
119C2×D4×C19—42no—
120C2×D4×C19—44no—
121C2×D4×C19—42no—
122C2×D4×C19—44no—
123C2×D4×C19—44no—
124C2×D4×C19—41no—
125C2×D4×C19—41no—
126C2×D4×C19—82no—
127C2×D4×C19—82no—
128C22×C4×C19—22no—
129C22×C4×C19—21no—
130C22×C4×C19—21no—
131C22×C4×C19—21no—
132C22×C4×C19—21no—
133C22×C4×C19—22no—
134C22×C4×C19—21no—
135C22×C4×C19—42no—
136C22×C4×C19—42no—
137C22×C4×C19—42no—
138C22×C4×C19—41no—
139C22×C4×C19—41no—
140C22×C4×C19—42no—
141C22×C4×C19C2×D411yescharacteristic
142C22×C4×C19C2×D411yescharacteristic
143C22×C4×C19C2×D411yescharacteristic
144C22×C4×C19C2×D411yescharacteristic
145C22×C4×C19C2×D411yescharacteristic
146C22×C4×C19#4111yescharacteristic
147SD16×C19—44no—
148D8×C19—44no—
149M16×C19—42no—
150M16×C19—42no—
151C2×C8×C19—22no—
152C2×C8×C19—41no—
153C4⋊C4×C19—21no—
154C4⋊C4×C19—21no—
155C4⋊C4×C19—44no—
156C22⋊C4×C19—24no—
157C22⋊C4×C19—44no—
158C22⋊C4×C19—44no—
159C22⋊C4×C19—44no—
160C22⋊C4×C19—42no—
161C22⋊C4×C19—41no—
162C22⋊C4×C19—41no—
163C22⋊C4×C19—41no—
164C22⋊C4×C19—41no—
165C22⋊C4×C19—41no—
166C22⋊C4×C19—41no—
167C22⋊C4×C19—82no—
168C42×C19—42no—
169#9938C1911yesmaximal, characteristic, direct product factor, Sylow
170C23×C19—22no—
171C23×C19—22no—
172C23×C19—22no—
173C23×C19—22no—
174C23×C19—22no—
175C23×C19—22no—
176C23×C19—41no—
177C23×C19—42no—
178C23×C19—42no—
179C23×C19—41no—
180C23×C19—42no—
181C23×C19—41no—
182C23×C19—41no—
183C23×C19—41no—
184C23×C19—41no—
185C23×C19—41no—
186C23×C19—42no—
187C23×C19—41no—
188C23×C19—41no—
189C23×C19—42no—
190C23×C19—42no—
191C23×C19—42no—
192C23×C19—41no—
193C23×C19—42no—
194C23×C19—81no—
195C23×C19—81no—
196C23×C19—88no—
197C23×C19#12011yescharacteristic
198C23×C19#12011yescharacteristic
199C23×C19#12111yescharacteristic
200Q8×C19—22no—
201Q8×C19—22no—
202Q8×C19—41no—
203Q8×C19—41no—
204D4×C19—22no—
205D4×C19—22no—
206D4×C19—41no—
207D4×C19—41no—
208D4×C19—42no—
209D4×C19—44no—
210D4×C19—44no—
211D4×C19—81no—
212D4×C19—88no—
213D4×C19—82no—
214D4×C19—88no—
215D4×C19—82no—
216C2×C4×C19—22no—
217C2×C4×C19—22no—
218C2×C4×C19—24no—
219C2×C4×C19—22no—
220C2×C4×C19—41no—
221C2×C4×C19—41no—
222C2×C4×C19—41no—
223C2×C4×C19—41no—
224C2×C4×C19—44no—
225C2×C4×C19—44no—
226C2×C4×C19—41no—
227C2×C4×C19—42no—
228C2×C4×C19—41no—
229C2×C4×C19—42no—
230C2×C4×C19—42no—
231C2×C4×C19—41no—
232C2×C4×C19—42no—
233C2×C4×C19—41no—
234C2×C4×C19—42no—
235C2×C4×C19—41no—
236C2×C4×C19—41no—
237C2×C4×C19—42no—
238C2×C4×C19—42no—
239C2×C4×C19—81no—
240C2×C4×C19#12011yescharacteristic
241C2×C4×C19#12111yescharacteristic
242C2×C4×C19#12111yescharacteristic
243C2×C4×C19#12711yescharacteristic
244C8×C19—42no—
245C8×C19—81no—
246#3006C2×C1911yescharacteristic, complemented
247#2539C2×C1911yescharacteristic, complemented
248#2404C2×C1911yescharacteristic, complemented
249#1789C2×C1911yescharacteristic, complemented
250#1510C2×C1911yescharacteristic, complemented
251#1462C2×C1911yescharacteristic, complemented
252#1284C2×C1911yescharacteristic, complemented
253C22×C19—21no—
254C22×C19—21no—
255C22×C19—21no—
256C22×C19—21no—
257C22×C19—21no—
258C22×C19—21no—
259C22×C19—21no—
260C22×C19—44no—
261C22×C19—44no—
262C22×C19—44no—
263C22×C19—44no—
264C22×C19—42no—
265C22×C19—42no—
266C22×C19—82no—
267C22×C19—82no—
268C22×C19—82no—
269C22×C19—82no—
270C22×C19—82no—
271C22×C19—82no—
272C22×C19—82no—
273C22×C19—81no—
274C22×C19—81no—
275C22×C19—81no—
276C22×C19—81no—
277C22×C19—81no—
278C22×C19—81no—
279C22×C19—81no—
280C22×C19#39211yescharacteristic
281C22×C19#45312yes—
282C22×C19B(4,𝔽2)12yes—
283C4×C19—21no—
284C4×C19—21no—
285C4×C19—21no—
286C4×C19—21no—
287C4×C19—44no—
288C4×C19—42no—
289C4×C19—82no—
290C4×C19—81no—
291C4×C19—81no—
292C22×#41C22×C1911yescharacteristic
293C2×AGL(1,ℤ/8)—21no—
294C2×#123—21no—
295C2×#121C22×C1911yescharacteristic
296C2×#120—21no—
297C2×#120—21no—
298C22×C22⋊C4C22×C1911yescharacteristic
299#449—22no—
300#448—21no—
301#447—21no—
302C2×#104—22no—
303#417—21no—
304#407C22×C1911yescharacteristic
305#407C22×C1911yescharacteristic
306#399—21no—
307#393—21no—
308#392—21no—
309#392—21no—
310#390—22no—
311#386—21no—
312#386—22no—
313#381C22×C1911yescharacteristic
314C4×C22⋊C4C22×C1911yescharacteristic
315#327—22no—
316#323—22no—
317C2×C19—22no—
318C2×C19—22no—
319C2×C19—41no—
320C2×C19—82no—
321C2×C19—82no—
322C2×C19—161no—
323C2×C19#200211yescharacteristic
324C2×C19#201011yescharacteristic
325C2×C19#202111yescharacteristic
326C25D4×C1911yescharacteristic
327C2×#41—21no—
328C2×#41—21no—
329C2×#41—21no—
330C2×#41—21no—
331C2×#41—44no—
332C22×Q8D4×C1911yescharacteristic, complemented
333C22×D4—21no—
334C22×D4—21no—
335C22×D4—22no—
336C22×D4—22no—
337C22×D4D4×C1911yescharacteristic, complemented
338C22×D4D4×C1911yescharacteristic, complemented
339C23×C4—21no—
340C23×C4D4×C1911yescharacteristic
341C23×C4C23×C1911yescharacteristic
342AGL(1,ℤ/8)—44no—
343C2×SD16—22no—
344C2×D8—22no—
345C2×M16—21no—
346C2×M16—21no—
347#123—44no—
348#121—21no—
349#121—21no—
350#121—21no—
351#121—21no—
352#120—44no—
353#120—44no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4D4×C1911yescharacteristic, complemented
356C2×C22⋊C4—21no—
357C2×C22⋊C4—22no—
358C2×C22⋊C4—22no—
359C2×C22⋊C4—22no—
360C2×C22⋊C4—21no—
361C2×C22⋊C4—21no—
362C2×C22⋊C4—21no—
363C2×C22⋊C4—21no—
364C2×C22⋊C4—21no—
365C2×C22⋊C4—21no—
366C2×C22⋊C4—21no—
367C2×C22⋊C4—21no—
368C2×C22⋊C4—22no—
369C2×C42D4×C1912yescomplemented
370#104—44no—
371#103—22no—
372#102—22no—
373C22⋊C8—21no—
374C22⋊C8—21no—
375C22⋊C8—21no—
376C22⋊C8D4×C1912yescomplemented
377#95—22no—
378#95—21no—
379#95—21no—
380#95D4×C1912yescomplemented
381C19#993811yescharacteristic, direct product factor, Sylow
382C24—21no—
383C24—21no—
384C24—21no—
385C24—21no—
386C24—21no—
387C24—42no—
388C24—42no—
389C24—42no—
390C24C2×D4×C1911yescharacteristic
391#41—24no—
392#41—24no—
393#41—42no—
394#41—42no—
395#41—42no—
396#41—42no—
397#41—42no—
398#41—42no—
399C2×Q8—21no—
400C2×Q8—21no—
401C2×Q8—42no—
402C2×D4—24no—
403C2×D4—21no—
404C2×D4—21no—
405C2×D4—21no—
406C2×D4—21no—
407C2×D4—42no—
408C2×D4—44no—
409C2×D4—42no—
410C2×D4—42no—
411C2×D4—41no—
412C2×D4—41no—
413C2×D4—42no—
414C2×D4—44no—
415C2×D4—42no—
416C2×D4—44no—
417C2×D4—44no—
418C2×D4—41no—
419C2×D4—41no—
420C2×D4—82no—
421C2×D4—82no—
422C22×C4—21no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—42no—
430C22×C4—42no—
431C22×C4—42no—
432C22×C4—41no—
433C22×C4—41no—
434C22×C4—42no—
435C22×C4C2×D4×C1911yescharacteristic
436C22×C4C2×D4×C1911yescharacteristic
437C22×C4C2×D4×C1911yescharacteristic
438C22×C4C2×D4×C1911yescharacteristic
439C22×C4C2×D4×C1911yescharacteristic
440C22×C4#41×C1911yescharacteristic
441SD16—44no—
442D8—44no—
443M16—42no—
444M16—42no—
445C2×C8—22no—
446C2×C8—41no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—44no—
450C22⋊C4—24no—
451C22⋊C4—44no—
452C22⋊C4—44no—
453C22⋊C4—44no—
454C22⋊C4—42no—
455C22⋊C4—41no—
456C22⋊C4—41no—
457C22⋊C4—41no—
458C22⋊C4—41no—
459C22⋊C4—41no—
460C22⋊C4—41no—
461C22⋊C4—82no—
462C42—42no—
463C23—22no—
464C23—22no—
465C23—22no—
466C23—22no—
467C23—22no—
468C23—22no—
469C23—41no—
470C23—42no—
471C23—42no—
472C23—41no—
473C23—42no—
474C23—41no—
475C23—41no—
476C23—41no—
477C23—41no—
478C23—41no—
479C23—42no—
480C23—41no—
481C23—41no—
482C23—42no—
483C23—42no—
484C23—42no—
485C23—41no—
486C23—42no—
487C23—81no—
488C23—81no—
489C23—88no—
490C23C19×#12011yescharacteristic
491C23C19×#12011yescharacteristic
492C23C19×#12111yescharacteristic
493Q8—22no—
494Q8—22no—
495Q8—41no—
496Q8—41no—
497D4—22no—
498D4—22no—
499D4—41no—
500D4—41no—
501D4—42no—
502D4—44no—
503D4—44no—
504D4—81no—
505D4—88no—
506D4—82no—
507D4—88no—
508D4—82no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—24no—
512C2×C4—22no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—44no—
518C2×C4—44no—
519C2×C4—41no—
520C2×C4—42no—
521C2×C4—41no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—41no—
525C2×C4—42no—
526C2×C4—41no—
527C2×C4—42no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—81no—
533C2×C4C19×#12011yescharacteristic
534C2×C4C19×#12111yescharacteristic
535C2×C4C19×#12111yescharacteristic
536C2×C4C19×#12711yescharacteristic
537C8—42no—
538C8—81no—
539C22—21no—
540C22—21no—
541C22—21no—
542C22—21no—
543C22—21no—
544C22—21no—
545C22—21no—
546C22—44no—
547C22—44no—
548C22—44no—
549C22—44no—
550C22—42no—
551C22—42no—
552C22—82no—
553C22—82no—
554C22—82no—
555C22—82no—
556C22—82no—
557C22—82no—
558C22—82no—
559C22—81no—
560C22—81no—
561C22—81no—
562C22—81no—
563C22—81no—
564C22—81no—
565C22—81no—
566C22C19×#39211yescharacteristic
567C22C19×#45312yes—
568C22C19×B(4,𝔽2)12yes—
569C4—21no—
570C4—21no—
571C4—21no—
572C4—21no—
573C4—44no—
574C4—42no—
575C4—82no—
576C4—81no—
577C4—81no—
578C2—22no—
579C2—22no—
580C2—41no—
581C2—82no—
582C2—82no—
583C2—161no—
584C2C19×#200211yescharacteristic
585C2C19×#201011yescharacteristic
586C2C19×#202111yescharacteristic
subgroupG/H
center, socleC22×C19#392
commutator, Frattini, cosocleC23×C4C23×C19
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C19 ◁ C23×C4×C19 ◁ G

Complements

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

NH ≅ G/Ntype
1. C19×#3006C2semidirect
2. C19×#2539C2semidirect
3. C19×#2404C2semidirect
4. C19×#1789C2semidirect
5. C19×#1510C2semidirect
6. C19×#1462C2semidirect
7. C19×#1284C2semidirect
39. C22×Q8×C19D4semidirect
44. C22×D4×C19D4semidirect
45. C22×D4×C19D4semidirect
62. C2×C4⋊C4×C19D4semidirect
76. C2×C42×C19D4semidirect
83. C19×C22⋊C8D4semidirect
87. C19×#95D4semidirect
169. #9938C19direct (N × H)
246. #3006C2×C19semidirect
247. #2539C2×C19semidirect
248. #2404C2×C19semidirect
249. #1789C2×C19semidirect
250. #1510C2×C19semidirect
251. #1462C2×C19semidirect
252. #1284C2×C19semidirect
332. C22×Q8D4×C19semidirect
337. C22×D4D4×C19semidirect
338. C22×D4D4×C19semidirect
355. C2×C4⋊C4D4×C19semidirect
369. C2×C42D4×C19semidirect
376. C22⋊C8D4×C19semidirect
380. #95D4×C19semidirect
381. C19#9938direct (N × H)

Maximal subgroups

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

subgroupindex
C19×#30062
C19×#25392
C19×#24042
C19×#17892
C19×#15102
C19×#14622
C19×#12842
#993819