Finite Group Databasebeta

← #18085862

Subgroups — #18085862

Order 4864.

760 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14569739C211yesmaximal, characteristic
2#14563953C211yesmaximal, characteristic, complemented
3#14563950C211yesmaximal, characteristic, complemented
4C2×#11926277C211yesmaximal, characteristic, complemented
5#14561900C211yesmaximal, characteristic, complemented
6#14561477C211yesmaximal, characteristic, complemented
7C2×C19×#327C211yesmaximal, characteristic, complemented
8C2×#10597376C2211yescharacteristic
9C2×#10597385—21no—
10C2×#10597385—21no—
11C22×C4⋊Dic19—21no—
12C22×C4⋊Dic19C2211yescharacteristic
13C2×#10597278—21no—
14C2×#10597289—21no—
15C2×C22⋊(C19⋊C8)C2211yescharacteristic
16#11926480—21no—
17#11926479—21no—
18#11926453—21no—
19#11926452—21no—
20C2×C19⋊#95—21no—
21C2×C19⋊#95C2211yescharacteristic
22#11926307—21no—
23#11926306—21no—
24#11926277—22no—
25C2×C19×#121C2211yescharacteristic
26C2×C19×C22⋊C8C2211yescharacteristic
27C2×C19×#95C2211yescharacteristic
28C19×#327—22no—
29C22×D4×C19—21no—
30C22×D4×C19D411yescharacteristic
31C23×C4×C19—21no—
32C23×C4×C19C2311yescharacteristic
33C22×C22⋊D19—21no—
34C22×C22⋊D19—21no—
35C22×C22⋊D19—21no—
36C23×Dic19—21no—
37C23×Dic19D411yescharacteristic
38C23×Dic19D411yescharacteristic
39C22×D76D411yescharacteristic
40C22×C8×C19—21no—
41C19×#121—21no—
42C19×#121—21no—
43C19×#121—21no—
44C19×#121—21no—
45C2×C4⋊C4×C19D411yescharacteristic
46C2×C22⋊C4×C19—21no—
47C2×C22⋊Dic19—21no—
48C2×C22⋊Dic19—21no—
49#10597385—42no—
50#10597385—42no—
51#10597385—42no—
52#10597385—42no—
53#10597376—21no—
54#10597376—21no—
55#10597376—21no—
56#10597376—21no—
57C2×(C2×D19)⋊C4—21no—
58C2×(C2×D19)⋊C4—21no—
59C2×(C2×D19)⋊C4—21no—
60C2×C4⋊Dic19—21no—
61C2×C4⋊Dic19—21no—
62C2×C4⋊Dic19—42no—
63C2×C4⋊Dic19—42no—
64C2×C4⋊Dic19—42no—
65C2×C4⋊Dic19—42no—
66C2×C4⋊Dic19D411yescharacteristic
67C2×Dic19⋊C4—21no—
68C2×Dic19⋊C4—21no—
69C22×C19⋊C8—21no—
70C19×C22⋊C8—21no—
71C19×C22⋊C8—21no—
72C19×#95—21no—
73C19×#95D412yescomplemented
74#10597289—42no—
75C19⋊#95—21no—
76C19⋊#95—21no—
77C19⋊#95—42no—
78C22⋊(C19⋊C8)—21no—
79C22⋊(C19⋊C8)—21no—
80#10597278—42no—
81C24×C19—21no—
82C24×C19C2×D411yescharacteristic
83C23×D19—21no—
84C2×D4×C19—21no—
85C2×D4×C19—21no—
86C2×D4×C19—41no—
87C2×D4×C19—41no—
88C2×D4×C19—41no—
89C2×D4×C19—41no—
90C2×D4×C19—41no—
91C2×D4×C19—41no—
92C2×D4×C19—41no—
93C2×D4×C19—41no—
94C22×C4×C19—22no—
95C22×C4×C19—22no—
96C22×C4×C19—22no—
97C22×C4×C19—21no—
98C22×C4×C19—41no—
99C22×C4×C19—41no—
100C22×C4×C19—41no—
101C22×C4×C19—41no—
102C22×C4×C19—41no—
103C22×C4×C19—41no—
104C22×C4×C19C2×D411yescharacteristic
105C22×C4×C19C2×D411yescharacteristic
106C22×C4×C19C2×D411yescharacteristic
107C22×C4×C19#4111yescharacteristic
108C22×C4×C19#4111yescharacteristic
109C22×C4×C19#4111yescharacteristic
110C2×C22⋊D19—42no—
111C2×C22⋊D19—42no—
112C2×C22⋊D19—41no—
113C2×C22⋊D19—41no—
114C2×C22⋊D19—41no—
115C2×C22⋊D19—41no—
116C2×C22⋊D19—41no—
117C2×C22⋊D19—41no—
118C2×C22⋊D19—81no—
119C2×C22⋊D19—81no—
120C2×C22⋊D19—81no—
121C2×C22⋊D19—81no—
122C22×Dic19—21no—
123C22×Dic19—21no—
124C22×Dic19—21no—
125C22×Dic19—21no—
126C22×Dic19—22no—
127C22×Dic19—21no—
128C22×Dic19—41no—
129C22×Dic19—41no—
130C22×Dic19—41no—
131C22×Dic19—41no—
132C22×Dic19—41no—
133C22×Dic19—41no—
134C22×Dic19—41no—
135C22×Dic19—41no—
136C22×Dic19—41no—
137C22×Dic19—41no—
138C22×Dic19D812yes—
139C22×Dic19SD1612yes—
140C2×D76—21no—
141C2×D76—21no—
142C2×D76—41no—
143C2×D76—41no—
144C2×C8×C19—41no—
145C2×C8×C19—41no—
146C2×C8×C19—41no—
147C4⋊C4×C19—21no—
148C4⋊C4×C19—21no—
149C22⋊C4×C19—41no—
150C22⋊C4×C19—41no—
151C22⋊Dic19—42no—
152C22⋊Dic19—42no—
153(C2×D19)⋊C4—42no—
154(C2×D19)⋊C4—42no—
155(C2×D19)⋊C4—41no—
156(C2×D19)⋊C4—41no—
157C4⋊Dic19—22no—
158C4⋊Dic19—22no—
159C4⋊Dic19—21no—
160C4⋊Dic19—21no—
161C4⋊Dic19—41no—
162C4⋊Dic19—41no—
163C4⋊Dic19—48no—
164Dic19⋊C4—42no—
165Dic19⋊C4—42no—
166C2×C19⋊C8—41no—
167C2×C19⋊C8—41no—
168C2×C19⋊C8—41no—
169#10402—191nomaximal, Sylow
170C23×C19—21no—
171C23×C19—21no—
172C23×C19—21no—
173C23×C19—21no—
174C23×C19—41no—
175C23×C19—41no—
176C23×C19—41no—
177C23×C19—41no—
178C23×C19—41no—
179C23×C19—41no—
180C23×C19—41no—
181C23×C19#12011yescharacteristic
182C23×C19#12111yescharacteristic
183C23×C19#12411yescharacteristic
184C23×C19C2×D811yescharacteristic
185C23×C19C2×SD1611yescharacteristic
186C23×C19AGL(1,ℤ/8)11yescharacteristic
187C23×C19AGL(1,ℤ/8)11yescharacteristic
188C22×D19—41no—
189C22×D19—41no—
190C22×D19—41no—
191C22×D19—41no—
192C22×D19—41no—
193C22×D19—41no—
194C22×D19—41no—
195D4×C19—42no—
196D4×C19—81no—
197D4×C19—81no—
198D4×C19—81no—
199D4×C19—81no—
200D4×C19—81no—
201C2×C4×C19—21no—
202C2×C4×C19—21no—
203C2×C4×C19—21no—
204C2×C4×C19—21no—
205C2×C4×C19—24no—
206C2×C4×C19—41no—
207C2×C4×C19—41no—
208C2×C4×C19—41no—
209C2×C4×C19—41no—
210C2×C4×C19—42no—
211C2×C4×C19—42no—
212C2×C4×C19—42no—
213C2×C4×C19—42no—
214C2×C4×C19—42no—
215C2×C4×C19—42no—
216C2×C4×C19—41no—
217C2×C4×C19—41no—
218C2×C4×C19—41no—
219C2×C4×C19#12111yescharacteristic
220C2×C4×C19#12111yescharacteristic
221C2×C4×C19#12311yescharacteristic
222C2×C4×C19#12311yescharacteristic
223C22⋊D19—84no—
224C22⋊D19—84no—
225C22⋊D19—81no—
226C22⋊D19—81no—
227C22⋊D19—81no—
228C22⋊D19—81no—
229C2×Dic19—22no—
230C2×Dic19—22no—
231C2×Dic19—41no—
232C2×Dic19—41no—
233C2×Dic19—41no—
234C2×Dic19—41no—
235C2×Dic19—42no—
236C2×Dic19—42no—
237C2×Dic19—42no—
238C2×Dic19—42no—
239C2×Dic19—41no—
240C2×Dic19—41no—
241C2×Dic19—41no—
242C2×Dic19—42no—
243C2×Dic19—81no—
244C2×Dic19—81no—
245C2×Dic19—81no—
246C2×Dic19—81no—
247C2×Dic19—81no—
248C2×Dic19—81no—
249D76—42no—
250D76—81no—
251C8×C19—81no—
252C19⋊C8—81no—
253#2656—191no—
254#1874—191no—
255#1874—191no—
256C2×#327—191no—
257C2×#327D1911yescharacteristic, complemented
258#1444—191no—
259#1280—191no—
260C22×C19—21no—
261C22×C19—21no—
262C22×C19—21no—
263C22×C19—21no—
264C22×C19—21no—
265C22×C19—21no—
266C22×C19—21no—
267C22×C19—21no—
268C22×C19—21no—
269C22×C19—21no—
270C22×C19—21no—
271C22×C19—21no—
272C22×C19—81no—
273C22×C19—81no—
274C22×C19—81no—
275C22×C19—81no—
276C22×C19—81no—
277C22×C19—81no—
278C22×C19—81no—
279C22×C19#39411yescharacteristic
280C22×C19#44711yescharacteristic
281C22×C19#45011yescharacteristic
282C22×C19#45311yescharacteristic
283C22×C19#45611yescharacteristic
284C22×C19B(4,𝔽2)11yescharacteristic
285C22×C19#45811yescharacteristic
286C22×C19#45911yescharacteristic
287C22×C19#46011yescharacteristic
288C22×C19#48611yescharacteristic
289C22×C19#49011yescharacteristic
290C2×D19—81no—
291C2×D19—81no—
292C2×D19—81no—
293C2×D19—81no—
294C2×D19—81no—
295C2×D19—81no—
296C2×D19—81no—
297C4×C19—21no—
298C4×C19—21no—
299C4×C19—21no—
300C4×C19—21no—
301C4×C19—44no—
302C4×C19—81no—
303Dic19—42no—
304Dic19—42no—
305Dic19—82no—
306Dic19—81no—
307C2×#121—191no—
308C2×#121—381no—
309C2×#121—381no—
310C2×#121C2×D1911yescharacteristic
311C22×C4⋊C4—191no—
312C22×C4⋊C4—381no—
313C2×#102—381no—
314C2×#102—381no—
315C2×C22⋊C8—191no—
316C2×C22⋊C8C2×D1911yescharacteristic
317#399—381no—
318#399—381no—
319#392—381no—
320#392—381no—
321C2×#95—191no—
322C2×#95—381no—
323C2×#95C2×D1911yescharacteristic
324#340—381no—
325#340—381no—
326#327—22no—
327#327—382no—
328C2×C19—21no—
329C2×C19—21no—
330C2×C19—21no—
331C2×C19—21no—
332C2×C19—161no—
333C2×C19#159511yescharacteristic
334C2×C19#160411yescharacteristic
335C2×C19#161011yescharacteristic
336C2×C19#161311yescharacteristic
337C2×C19#203911yescharacteristic
338C2×C19#204111yescharacteristic
339C2×C19#204411yescharacteristic
340D19—161no—
341C22×D4—21no—
342C22×D4—191no—
343C22×D4—381no—
344C22×D4—381no—
345C22×D4—381no—
346C22×D4D7611yescharacteristic
347C23×C4—21no—
348C23×C4—191no—
349C23×C4—191no—
350C23×C4—381no—
351C23×C4C22×D1911yescharacteristic
352C22×C8—21no—
353C22×C8—381no—
354#121—21no—
355#121—21no—
356#121—21no—
357#121—21no—
358#121—381no—
359#121—381no—
360#121—381no—
361#121—381no—
362#121—762no—
363#121—762no—
364#121—762no—
365#121—762no—
366C2×C4⋊C4—191no—
367C2×C4⋊C4—381no—
368C2×C4⋊C4—381no—
369C2×C4⋊C4—381no—
370C2×C4⋊C4—381no—
371C2×C4⋊C4—762no—
372C2×C4⋊C4—762no—
373C2×C4⋊C4—762no—
374C2×C4⋊C4—762no—
375C2×C4⋊C4D7611yescharacteristic
376C2×C22⋊C4—21no—
377C2×C22⋊C4—381no—
378C2×C22⋊C4—381no—
379C2×C22⋊C4—381no—
380C2×C22⋊C4—381no—
381C2×C22⋊C4—381no—
382#102—762no—
383#102—762no—
384C22⋊C8—21no—
385C22⋊C8—21no—
386C22⋊C8—381no—
387C22⋊C8—381no—
388#95—21no—
389#95—381no—
390#95—381no—
391#95—762no—
392#95C22⋊D1912yescomplemented
393C19#1040211yescharacteristic, complemented, Sylow
394C24—21no—
395C24—381no—
396C24D4×D1911yescharacteristic
397C2×D4—21no—
398C2×D4—21no—
399C2×D4—41no—
400C2×D4—41no—
401C2×D4—41no—
402C2×D4—41no—
403C2×D4—41no—
404C2×D4—41no—
405C2×D4—41no—
406C2×D4—41no—
407C2×D4—381no—
408C2×D4—381no—
409C2×D4—761no—
410C2×D4—761no—
411C2×D4—762no—
412C2×D4—762no—
413C2×D4—761no—
414C2×D4—761no—
415C2×D4—761no—
416C2×D4—761no—
417C2×D4—761no—
418C2×D4—761no—
419C2×D4—1521no—
420C2×D4—1521no—
421C2×D4—1521no—
422C2×D4—1521no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—21no—
427C22×C4—41no—
428C22×C4—41no—
429C22×C4—41no—
430C22×C4—41no—
431C22×C4—41no—
432C22×C4—41no—
433C22×C4—192no—
434C22×C4—192no—
435C22×C4—381no—
436C22×C4—381no—
437C22×C4—381no—
438C22×C4—381no—
439C22×C4—382no—
440C22×C4—381no—
441C22×C4—761no—
442C22×C4—761no—
443C22×C4—761no—
444C22×C4—761no—
445C22×C4—761no—
446C22×C4—761no—
447C22×C4—761no—
448C22×C4—761no—
449C22×C4—761no—
450C22×C4—761no—
451C22×C4C2×D7611yescharacteristic
452C22×C4#6454111yescharacteristic
453C22×C4D4×D1911yescharacteristic
454C22×C4#6454311yescharacteristic
455C22×C4#6454311yescharacteristic
456C22×C4C2×C22⋊D1911yescharacteristic
457C2×C8—41no—
458C2×C8—41no—
459C2×C8—41no—
460C2×C8—761no—
461C2×C8—761no—
462C2×C8—761no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—382no—
466C4⋊C4—382no—
467C4⋊C4—381no—
468C4⋊C4—381no—
469C4⋊C4—761no—
470C4⋊C4—761no—
471C4⋊C4—762no—
472C4⋊C4—762no—
473C4⋊C4—768no—
474C22⋊C4—41no—
475C22⋊C4—41no—
476C22⋊C4—762no—
477C22⋊C4—762no—
478C22⋊C4—762no—
479C22⋊C4—762no—
480C22⋊C4—761no—
481C22⋊C4—761no—
482C23—21no—
483C23—21no—
484C23—21no—
485C23—21no—
486C23—41no—
487C23—41no—
488C23—41no—
489C23—41no—
490C23—41no—
491C23—41no—
492C23—41no—
493C23—761no—
494C23—761no—
495C23—761no—
496C23—761no—
497C23—761no—
498C23—761no—
499C23—761no—
500C23#1059732811yescharacteristic
501C23#1059733111yescharacteristic
502C23D8×D1911yescharacteristic
503C23#1059735711yescharacteristic
504C23SD16×D1911yescharacteristic
505C23#1059736011yescharacteristic
506C23#1059738511yescharacteristic
507D4—42no—
508D4—81no—
509D4—81no—
510D4—81no—
511D4—81no—
512D4—81no—
513D4—762no—
514D4—1521no—
515D4—1524no—
516D4—1524no—
517D4—1521no—
518D4—1521no—
519D4—1521no—
520D4—1521no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—24no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—382no—
540C2×C4—382no—
541C2×C4—761no—
542C2×C4—761no—
543C2×C4—761no—
544C2×C4—761no—
545C2×C4—762no—
546C2×C4—762no—
547C2×C4—762no—
548C2×C4—762no—
549C2×C4—761no—
550C2×C4—761no—
551C2×C4—761no—
552C2×C4—762no—
553C2×C4—1521no—
554C2×C4—1521no—
555C2×C4—1521no—
556C2×C4—1521no—
557C2×C4—1521no—
558C2×C4—1521no—
559C2×C4#1059732911yescharacteristic
560C2×C4#1059733211yescharacteristic
561C2×C4#1059737611yescharacteristic
562C2×C4#1059738411yescharacteristic
563C8—81no—
564C8—1521no—
565C22—21no—
566C22—21no—
567C22—21no—
568C22—21no—
569C22—21no—
570C22—21no—
571C22—21no—
572C22—21no—
573C22—21no—
574C22—21no—
575C22—21no—
576C22—21no—
577C22—81no—
578C22—81no—
579C22—81no—
580C22—81no—
581C22—81no—
582C22—81no—
583C22—81no—
584C22—1521no—
585C22—1521no—
586C22—1521no—
587C22—1521no—
588C22—1521no—
589C22—1521no—
590C22—1521no—
591C22#1192646011yescharacteristic
592C22#1192667911yescharacteristic
593C22#1192669611yescharacteristic
594C22#1192671311yescharacteristic
595C22#1192672811yescharacteristic
596C22#1192673211yescharacteristic
597C22#1192673511yescharacteristic
598C22#1192673711yescharacteristic
599C22#1192674211yescharacteristic
600C22#1192688911yescharacteristic
601C22#1192690711yescharacteristic
602C4—21no—
603C4—21no—
604C4—21no—
605C4—21no—
606C4—44no—
607C4—81no—
608C4—762no—
609C4—762no—
610C4—1521no—
611C4—1522no—
612C2—21no—
613C2—21no—
614C2—21no—
615C2—21no—
616C2—161no—
617C2—3041no—
618C2#1456255411yescharacteristic
619C2#1456260511yescharacteristic
620C2#1456263911yescharacteristic
621C2#1456265611yescharacteristic
622C2#1456485811yescharacteristic
623C2#1456486811yescharacteristic
624C2#1456488511yescharacteristic
subgroupG/H
centerC23#10597328
commutator, cosocleC23×C4×C19C23
FrattiniC23×C4C22×D19
FittingC2×C19×#327C2
socleC23×C19#120
prime radical#14569739C2
hypercenterC2×#327D19
hypocenterC19#10402
LCSG ▷ C23×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#327

Complements

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

NH ≅ G/Ntype
2. #14563953C2semidirect
3. #14563950C2semidirect
4. C2×#11926277C2semidirect
5. #14561900C2semidirect
6. #14561477C2semidirect
7. C2×C19×#327C2semidirect
73. C19×#95D4semidirect
257. C2×#327D19semidirect
392. #95C22⋊D19semidirect
393. C19#10402semidirect

Maximal subgroups

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

subgroupindex
#145697392
#145639532
#145639502
C2×#119262772
#145619002
#145614772
C2×C19×#3272
#1040219