Finite Group Databasebeta

← #18081663

Subgroups — #18081663

Order 4864.

856 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14571978C211yesmaximal, characteristic
2#14563613C211yesmaximal, characteristic, complemented
3C2×#11926279C211yesmaximal, characteristic, complemented
4C2×#11926278C211yesmaximal, characteristic, complemented
5C2×#11926277C211yesmaximal, characteristic, complemented
6#95×Dic19C211yesmaximal, characteristic, complemented
7C2×C19×#327C211yesmaximal, characteristic, complemented
8C2×#10597386C411yescharacteristic, complemented
9C2×#10597376C2211yescharacteristic
10C2×#10597385—21no—
11C2×#10597385—21no—
12C22×C4×Dic19—21no—
13C22×C4×Dic19C2211yescharacteristic
14C2×Dic19⋊C8—21no—
15C2×C22⋊(C19⋊C8)C2211yescharacteristic
16#11926447C411yescharacteristic, complemented
17#11926445C411yescharacteristic, complemented
18#11926444—21no—
19#11926444—21no—
20#11926413C411yescharacteristic, complemented
21C2×C19⋊#95—21no—
22C2×C19⋊#95C2211yescharacteristic
23#11926298—21no—
24#11926279—22no—
25#11926278—22no—
26#11926277—22no—
27C2×C19×#121C2211yescharacteristic
28C2×C19×C22⋊C8C2211yescharacteristic
29C2×C19×#95C2211yescharacteristic
30C19×#327—22no—
31C22×D4×C19—21no—
32C22×D4×C19C2×C411yescharacteristic
33C23×C4×C19—21no—
34C23×C4×C19C2311yescharacteristic
35C22×C22⋊D19—21no—
36C22×C22⋊D19—21no—
37C22×C22⋊D19—21no—
38C23×Dic19—21no—
39C23×Dic19D411yescharacteristic
40C23×Dic19D411yescharacteristic
41C22×D76C2×C411yescharacteristic
42C22×C8×C19—21no—
43C19×#121—21no—
44C19×#121—21no—
45C19×#121—21no—
46C19×#121—21no—
47C2×C4⋊C4×C19C2×C411yescharacteristic
48C2×C22⋊C4×C19—21no—
49C2×C22⋊Dic19—21no—
50C2×C22⋊Dic19—21no—
51#10597386—42no—
52#10597385—42no—
53#10597385—42no—
54#10597385—42no—
55#10597385—42no—
56#10597376—21no—
57#10597376—21no—
58#10597376—21no—
59#10597376—21no—
60C2×(C2×D19)⋊C4—21no—
61C2×(C2×D19)⋊C4—21no—
62C2×(C2×D19)⋊C4—21no—
63C2×C4⋊Dic19C2×C411yescharacteristic
64C2×Dic19⋊C4—21no—
65C2×Dic19⋊C4—21no—
66C2×C4×Dic19—24no—
67C2×C4×Dic19—42no—
68C2×C4×Dic19—42no—
69C2×C4×Dic19—42no—
70C2×C4×Dic19C2×C411yescharacteristic
71C2×C4×Dic19C2×C411yescharacteristic
72C2×C4×Dic19D411yescharacteristic
73C2×C4×Dic19D411yescharacteristic
74C22×C19⋊C8—21no—
75C19×C22⋊C8—21no—
76C19×C22⋊C8—21no—
77C19×#95—21no—
78C19×#95D412yescomplemented
79C19⋊#95—24no—
80C19⋊#95—21no—
81C19⋊#95D412yescomplemented
82C22⋊(C19⋊C8)—21no—
83C22⋊(C19⋊C8)—21no—
84Dic19⋊C8—42no—
85C24×C19—21no—
86C24×C19C2×D411yescharacteristic
87C23×D19—21no—
88C2×D4×C19—21no—
89C2×D4×C19—21no—
90C2×D4×C19—41no—
91C2×D4×C19—41no—
92C2×D4×C19—41no—
93C2×D4×C19—41no—
94C2×D4×C19—41no—
95C2×D4×C19—41no—
96C2×D4×C19—41no—
97C2×D4×C19—41no—
98C22×C4×C19—22no—
99C22×C4×C19—22no—
100C22×C4×C19—22no—
101C22×C4×C19—21no—
102C22×C4×C19—41no—
103C22×C4×C19—41no—
104C22×C4×C19—41no—
105C22×C4×C19—41no—
106C22×C4×C19—41no—
107C22×C4×C19—41no—
108C22×C4×C19C22×C411yescharacteristic
109C22×C4×C19C2×D411yescharacteristic
110C22×C4×C19C2×D411yescharacteristic
111C22×C4×C19C2×D411yescharacteristic
112C22×C4×C19#4111yescharacteristic
113C22×C4×C19#4111yescharacteristic
114C2×C22⋊D19—42no—
115C2×C22⋊D19—42no—
116C2×C22⋊D19—41no—
117C2×C22⋊D19—41no—
118C2×C22⋊D19—41no—
119C2×C22⋊D19—41no—
120C2×C22⋊D19—41no—
121C2×C22⋊D19—41no—
122C2×C22⋊D19—42no—
123C2×C22⋊D19—42no—
124C2×C22⋊D19—42no—
125C2×C22⋊D19—42no—
126C22×Dic19—22no—
127C22×Dic19—22no—
128C22×Dic19—22no—
129C22×Dic19—22no—
130C22×Dic19—22no—
131C22×Dic19—21no—
132C22×Dic19—21no—
133C22×Dic19—22no—
134C22×Dic19—21no—
135C22×Dic19—41no—
136C22×Dic19—41no—
137C22×Dic19—41no—
138C22×Dic19—41no—
139C22×Dic19—41no—
140C22×Dic19C22⋊C411yescharacteristic
141C22×Dic19C22⋊C411yescharacteristic
142C22×Dic19C22⋊C411yescharacteristic
143C22×Dic19C22⋊C411yescharacteristic
144C22×Dic19D812yes—
145C22×Dic19SD1612yes—
146C2×D76—21no—
147C2×D76—21no—
148C2×D76—41no—
149C2×D76—41no—
150C2×C8×C19—41no—
151C2×C8×C19—41no—
152C2×C8×C19—41no—
153C4⋊C4×C19—21no—
154C4⋊C4×C19—21no—
155C22⋊C4×C19—41no—
156C22⋊C4×C19—41no—
157C22⋊Dic19—42no—
158C22⋊Dic19—42no—
159(C2×D19)⋊C4—42no—
160(C2×D19)⋊C4—41no—
161(C2×D19)⋊C4—41no—
162(C2×D19)⋊C4—42no—
163C4⋊Dic19—21no—
164C4⋊Dic19—21no—
165Dic19⋊C4—42no—
166Dic19⋊C4—42no—
167C4×Dic19—22no—
168C4×Dic19—22no—
169C4×Dic19—41no—
170C4×Dic19—41no—
171C4×Dic19—48no—
172C2×C19⋊C8—41no—
173C2×C19⋊C8—41no—
174C2×C19⋊C8—41no—
175#9712—191nomaximal, Sylow
176C23×C19—21no—
177C23×C19—21no—
178C23×C19—21no—
179C23×C19—21no—
180C23×C19—41no—
181C23×C19—41no—
182C23×C19—41no—
183C23×C19—41no—
184C23×C19—41no—
185C23×C19—41no—
186C23×C19—41no—
187C23×C19C2×C22⋊C411yescharacteristic
188C23×C19#12111yescharacteristic
189C23×C19#12111yescharacteristic
190C23×C19C2×D811yescharacteristic
191C23×C19C2×SD1611yescharacteristic
192C23×C19AGL(1,ℤ/8)11yescharacteristic
193C23×C19AGL(1,ℤ/8)11yescharacteristic
194C22×D19—41no—
195C22×D19—41no—
196C22×D19—41no—
197C22×D19—41no—
198C22×D19—41no—
199C22×D19—41no—
200C22×D19—41no—
201D4×C19—81no—
202D4×C19—81no—
203D4×C19—81no—
204D4×C19—81no—
205D4×C19—81no—
206D4×C19—81no—
207C2×C4×C19—21no—
208C2×C4×C19—21no—
209C2×C4×C19—21no—
210C2×C4×C19—21no—
211C2×C4×C19—24no—
212C2×C4×C19—41no—
213C2×C4×C19—41no—
214C2×C4×C19—41no—
215C2×C4×C19—41no—
216C2×C4×C19—42no—
217C2×C4×C19—42no—
218C2×C4×C19—42no—
219C2×C4×C19—42no—
220C2×C4×C19—42no—
221C2×C4×C19—42no—
222C2×C4×C19—41no—
223C2×C4×C19—41no—
224C2×C4×C19—41no—
225C2×C4×C19C4×D411yescharacteristic
226C2×C4×C19C4×D411yescharacteristic
227C2×C4×C19#12411yescharacteristic
228C2×C4×C19#12711yescharacteristic
229C22⋊D19—84no—
230C22⋊D19—81no—
231C22⋊D19—81no—
232C22⋊D19—81no—
233C22⋊D19—81no—
234C22⋊D19—84no—
235C2×Dic19—21no—
236C2×Dic19—21no—
237C2×Dic19—21no—
238C2×Dic19—21no—
239C2×Dic19—24no—
240C2×Dic19—24no—
241C2×Dic19—24no—
242C2×Dic19—21no—
243C2×Dic19—21no—
244C2×Dic19—21no—
245C2×Dic19—42no—
246C2×Dic19—42no—
247C2×Dic19—42no—
248C2×Dic19—42no—
249C2×Dic19—42no—
250C2×Dic19—42no—
251C2×Dic19—42no—
252C2×Dic19—42no—
253C2×Dic19—41no—
254C2×Dic19—41no—
255C2×Dic19—41no—
256C2×Dic19#9912yes—
257C2×Dic19#10212yes—
258C2×Dic19#10212yes—
259C2×Dic19#10412yes—
260C2×Dic19#10412yes—
261D76—81no—
262D76—81no—
263C8×C19—81no—
264C19⋊C8—81no—
265#2856—191no—
266#1797—191no—
267C2×#327—191no—
268C2×#327—191no—
269C2×#327—191no—
270C2×#327D1911yescharacteristic, complemented
271C4×#95—191no—
272C22×C19—21no—
273C22×C19—21no—
274C22×C19—21no—
275C22×C19—21no—
276C22×C19—21no—
277C22×C19—21no—
278C22×C19—21no—
279C22×C19—21no—
280C22×C19—21no—
281C22×C19—21no—
282C22×C19—21no—
283C22×C19—21no—
284C22×C19—81no—
285C22×C19—81no—
286C22×C19—81no—
287C22×C19—81no—
288C22×C19—81no—
289C22×C19—81no—
290C22×C19—81no—
291C22×C19#39011yescharacteristic
292C22×C19C2×#9911yescharacteristic
293C22×C19#41011yescharacteristic
294C22×C19C2×#10211yescharacteristic
295C22×C19#41811yescharacteristic
296C22×C19C2×#10411yescharacteristic
297C22×C19C2×#10411yescharacteristic
298C22×C19#45911yescharacteristic
299C22×C19#45911yescharacteristic
300C22×C19#46011yescharacteristic
301C22×C19#46011yescharacteristic
302C2×D19—81no—
303C2×D19—81no—
304C2×D19—81no—
305C2×D19—81no—
306C2×D19—81no—
307C2×D19—81no—
308C2×D19—81no—
309C4×C19—21no—
310C4×C19—21no—
311C4×C19—21no—
312C4×C19—21no—
313C4×C19—44no—
314C4×C19—81no—
315Dic19—22no—
316Dic19—22no—
317Dic19—44no—
318Dic19—41no—
319Dic19—81no—
320Dic19#32714yescomplemented
321C2×#127—191no—
322C2×#121—191no—
323C2×#121—381no—
324C2×#121—381no—
325C2×#121C2×D1911yescharacteristic
326C22×C42—191no—
327C22×C42—381no—
328C2×C4⋊C8—381no—
329C2×C22⋊C8—191no—
330C2×C22⋊C8C2×D1911yescharacteristic
331#390—191no—
332#390—191no—
333#390—381no—
334#390—381no—
335#384—191no—
336C2×#95—191no—
337C2×#95—381no—
338C2×#95C2×D1911yescharacteristic
339#336—381no—
340#327—22no—
341#327—382no—
342#327—382no—
343#327—382no—
344C2×C19—21no—
345C2×C19—21no—
346C2×C19—21no—
347C2×C19—21no—
348C2×C19—161no—
349C2×C19C2×#32711yescharacteristic
350C2×C19#150211yescharacteristic
351C2×C19#150511yescharacteristic
352C2×C19#150711yescharacteristic
353C2×C19#196211yescharacteristic
354C2×C19#196411yescharacteristic
355C2×C19#198211yescharacteristic
356D19—161no—
357C22×D4—21no—
358C22×D4—191no—
359C22×D4—381no—
360C22×D4—381no—
361C22×D4—381no—
362C22×D4C4×D1911yescharacteristic
363C23×C4—21no—
364C23×C4—191no—
365C23×C4—191no—
366C23×C4—381no—
367C23×C4C22×D1911yescharacteristic
368C22×C8—21no—
369C22×C8—381no—
370#127—762no—
371#121—21no—
372#121—21no—
373#121—21no—
374#121—21no—
375#121—381no—
376#121—381no—
377#121—381no—
378#121—381no—
379#121—762no—
380#121—762no—
381#121—762no—
382#121—762no—
383C2×C4⋊C4—191no—
384C2×C4⋊C4—381no—
385C2×C4⋊C4—381no—
386C2×C4⋊C4C4×D1911yescharacteristic
387C2×C22⋊C4—21no—
388C2×C22⋊C4—381no—
389C2×C22⋊C4—381no—
390C2×C22⋊C4—381no—
391C2×C22⋊C4—381no—
392C2×C22⋊C4—381no—
393C2×C42—191no—
394C2×C42—191no—
395C2×C42—191no—
396C2×C42—191no—
397C2×C42—384no—
398C2×C42—762no—
399C2×C42—762no—
400C2×C42—762no—
401C4⋊C8—762no—
402C22⋊C8—21no—
403C22⋊C8—21no—
404C22⋊C8—381no—
405C22⋊C8—381no—
406#95—21no—
407#95—192no—
408#95—384no—
409#95—381no—
410#95C22⋊D1912yescomplemented
411C19#971211yescharacteristic, complemented, Sylow
412C24—21no—
413C24—381no—
414C24D4×D1911yescharacteristic
415C2×D4—21no—
416C2×D4—21no—
417C2×D4—41no—
418C2×D4—41no—
419C2×D4—41no—
420C2×D4—41no—
421C2×D4—41no—
422C2×D4—41no—
423C2×D4—41no—
424C2×D4—41no—
425C2×D4—381no—
426C2×D4—381no—
427C2×D4—761no—
428C2×D4—761no—
429C2×D4—762no—
430C2×D4—762no—
431C2×D4—762no—
432C2×D4—762no—
433C2×D4—762no—
434C2×D4—762no—
435C2×D4—761no—
436C2×D4—761no—
437C2×D4—761no—
438C2×D4—761no—
439C2×D4—761no—
440C2×D4—761no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—21no—
445C22×C4—41no—
446C22×C4—41no—
447C22×C4—41no—
448C22×C4—41no—
449C22×C4—41no—
450C22×C4—41no—
451C22×C4—191no—
452C22×C4—191no—
453C22×C4—191no—
454C22×C4—192no—
455C22×C4—192no—
456C22×C4—191no—
457C22×C4—382no—
458C22×C4—382no—
459C22×C4—382no—
460C22×C4—382no—
461C22×C4—382no—
462C22×C4—382no—
463C22×C4—381no—
464C22×C4—381no—
465C22×C4—381no—
466C22×C4—761no—
467C22×C4—761no—
468C22×C4—761no—
469C22×C4—761no—
470C22×C4—761no—
471C22×C4C2×C4×D1911yescharacteristic
472C22×C4#6454111yescharacteristic
473C22×C4D4×D1911yescharacteristic
474C22×C4D4×D1911yescharacteristic
475C22×C4#6454311yescharacteristic
476C22×C4C2×C22⋊D1911yescharacteristic
477C2×C8—41no—
478C2×C8—41no—
479C2×C8—41no—
480C2×C8—761no—
481C2×C8—761no—
482C2×C8—761no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—381no—
486C4⋊C4—381no—
487C4⋊C4—762no—
488C4⋊C4—762no—
489C22⋊C4—41no—
490C22⋊C4—41no—
491C22⋊C4—762no—
492C22⋊C4—762no—
493C22⋊C4—762no—
494C22⋊C4—762no—
495C22⋊C4—761no—
496C22⋊C4—761no—
497C42—382no—
498C42—382no—
499C42—761no—
500C42—761no—
501C42—768no—
502C23—21no—
503C23—21no—
504C23—21no—
505C23—21no—
506C23—41no—
507C23—41no—
508C23—41no—
509C23—41no—
510C23—41no—
511C23—41no—
512C23—41no—
513C23—761no—
514C23—761no—
515C23—761no—
516C23—761no—
517C23—761no—
518C23—761no—
519C23—761no—
520C23C22⋊C4×D1911yescharacteristic
521C23#1059733011yescharacteristic
522C23D8×D1911yescharacteristic
523C23#1059735711yescharacteristic
524C23SD16×D1911yescharacteristic
525C23#1059736011yescharacteristic
526C23#1059738511yescharacteristic
527D4—81no—
528D4—81no—
529D4—81no—
530D4—81no—
531D4—81no—
532D4—81no—
533D4—1521no—
534D4—1521no—
535D4—1524no—
536D4—1524no—
537D4—1521no—
538D4—1521no—
539D4—1521no—
540D4—1521no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—24no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—192no—
560C2×C4—192no—
561C2×C4—192no—
562C2×C4—192no—
563C2×C4—192no—
564C2×C4—384no—
565C2×C4—384no—
566C2×C4—381no—
567C2×C4—381no—
568C2×C4—381no—
569C2×C4—381no—
570C2×C4—384no—
571C2×C4—381no—
572C2×C4—381no—
573C2×C4—381no—
574C2×C4—762no—
575C2×C4—762no—
576C2×C4—762no—
577C2×C4—762no—
578C2×C4—762no—
579C2×C4—762no—
580C2×C4—762no—
581C2×C4—762no—
582C2×C4—761no—
583C2×C4—761no—
584C2×C4—761no—
585C2×C4(C22⋊D19)⋊C411yescharacteristic
586C2×C4#1059733111yescharacteristic
587C2×C4C4×C22⋊D1911yescharacteristic
588C2×C4#1059738611yescharacteristic
589C8—81no—
590C8—1521no—
591C22—21no—
592C22—21no—
593C22—21no—
594C22—21no—
595C22—21no—
596C22—21no—
597C22—21no—
598C22—21no—
599C22—21no—
600C22—21no—
601C22—21no—
602C22—21no—
603C22—81no—
604C22—81no—
605C22—81no—
606C22—81no—
607C22—81no—
608C22—81no—
609C22—81no—
610C22—1521no—
611C22—1521no—
612C22—1521no—
613C22—1521no—
614C22—1521no—
615C22—1521no—
616C22—1521no—
617C22#1192644411yescharacteristic
618C22#99×D1911yescharacteristic
619C22#1192651611yescharacteristic
620C22#102×D1911yescharacteristic
621C22#1192654711yescharacteristic
622C22#104×D1911yescharacteristic
623C22#104×D1911yescharacteristic
624C22#1192673711yescharacteristic
625C22#1192673811yescharacteristic
626C22#1192674211yescharacteristic
627C22#1192674311yescharacteristic
628C4—21no—
629C4—21no—
630C4—21no—
631C4—21no—
632C4—44no—
633C4—81no—
634C4—194no—
635C4—382no—
636C4—382no—
637C4—764no—
638C4—761no—
639C4—1521no—
640C2—21no—
641C2—21no—
642C2—21no—
643C2—21no—
644C2—161no—
645C2—3041no—
646C2D19×#32711yescharacteristic
647C2#1456212811yescharacteristic
648C2#1456214111yescharacteristic
649C2#1456214911yescharacteristic
650C2#1456446111yescharacteristic
651C2#1456446911yescharacteristic
652C2#1456456011yescharacteristic
subgroupG/H
centerC23C22⋊C4×D19
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC2×C19×#327C2
socleC23×C19C2×C22⋊C4
prime radical#14571978C2
cosocleC23×C4×C19C23
hypercenterC2×#327D19
hypocenterC19#9712
LCSG ▷ C22×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. #14563613C2semidirect
3. C2×#11926279C2semidirect
4. C2×#11926278C2semidirect
5. C2×#11926277C2semidirect
6. #95×Dic19C2semidirect
7. C2×C19×#327C2semidirect
8. C2×#10597386C4semidirect
16. #11926447C4semidirect
17. #11926445C4semidirect
20. #11926413C4semidirect
78. C19×#95D4semidirect
81. C19⋊#95D4semidirect
270. C2×#327D19semidirect
320. Dic19#327semidirect
410. #95C22⋊D19semidirect
411. C19#9712semidirect

Maximal subgroups

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

subgroupindex
#145719782
#145636132
C2×#119262792
C2×#119262782
C2×#119262772
#95×Dic192
C2×C19×#3272
#971219