Finite Group Databasebeta

← #18085814

Subgroups — #18085814

Order 4864.

772 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14569369C211yesmaximal, characteristic
2#14563952C211yesmaximal, characteristic, complemented
3#14563828C211yesmaximal, characteristic, complemented
4C2×#11926277C211yesmaximal, characteristic, complemented
5C2×#11926268C211yesmaximal, characteristic, complemented
6#14561514C211yesmaximal, characteristic, complemented
7C19×#1439C211yesmaximal, characteristic, complemented
8C2×#10597376C2211yescharacteristic
9C2×#10597399—21no—
10C2×#10597265—21no—
11C2×#10597266—21no—
12C2×C22⋊(C19⋊C8)C2211yescharacteristic
13C2×C22⋊(C19⋊C8)C2211yescharacteristic
14#11926469—21no—
15#11926460—21no—
16#11926460—21no—
17#11926453—21no—
18#11926423—21no—
19#11926404C2211yescharacteristic
20#11926306—21no—
21#11926306—21no—
22#11926277—22no—
23#11926268—22no—
24C22×C4⋊C4×C19C2211yescharacteristic
25C22×C22⋊C4×C19—21no—
26C22×C22⋊C4×C19C2211yescharacteristic
27C2×C19×#95—21no—
28C2×C19×#95C2211yescharacteristic
29C25×C19D411yescharacteristic
30C23×C4×C19—21no—
31C23×C4×C19—21no—
32C23×C4×C19D411yescharacteristic
33C23×C4×C19C2311yescharacteristic
34C22×C22⋊D19—21no—
35C22×C22⋊D19—21no—
36C22×C22⋊D19—21no—
37C22×D76D411yescharacteristic
38C2×C4⋊C4×C19—21no—
39C2×C4⋊C4×C19—21no—
40C2×C4⋊C4×C19—42no—
41C2×C22⋊C4×C19—21no—
42C2×C22⋊C4×C19—21no—
43C2×C22⋊C4×C19—21no—
44C2×C22⋊C4×C19—21no—
45C2×C22⋊C4×C19—21no—
46C2×C22⋊C4×C19—21no—
47C2×C22⋊C4×C19—42no—
48C2×C22⋊C4×C19—42no—
49C2×C22⋊C4×C19—42no—
50#10597399—42no—
51#10597399—42no—
52C2×C22⋊Dic19—21no—
53C2×C22⋊Dic19—21no—
54C2×C22⋊Dic19—21no—
55#10597376—21no—
56#10597376—21no—
57#10597376—21no—
58#10597376—21no—
59C2×(C2×D19)⋊C4—21no—
60C2×(C2×D19)⋊C4—21no—
61C2×(C2×D19)⋊C4—21no—
62C2×C4⋊Dic19D411yescharacteristic
63C2×C4⋊Dic19D411yescharacteristic
64C2×C4⋊Dic19D411yescharacteristic
65C22×C19⋊C8—21no—
66C22×C19⋊C8—21no—
67C19×#95—21no—
68C19×#95—21no—
69C19×#95—42no—
70C19⋊#95—21no—
71C19⋊#95—21no—
72C19⋊#95—21no—
73C22⋊(C19⋊C8)—21no—
74C22⋊(C19⋊C8)—21no—
75C22⋊(C19⋊C8)—21no—
76C22⋊(C19⋊C8)D412yescomplemented
77#10597266—42no—
78#10597265—42no—
79C24×C19—21no—
80C24×C19—21no—
81C24×C19—21no—
82C24×C19—21no—
83C24×C19—21no—
84C24×C19—21no—
85C24×C19—41no—
86C24×C19—41no—
87C24×C19—41no—
88C24×C19—41no—
89C24×C19SD1612yes—
90C24×C19C2×D411yescharacteristic
91C23×D19—21no—
92C22×C4×C19—22no—
93C22×C4×C19—22no—
94C22×C4×C19—21no—
95C22×C4×C19—21no—
96C22×C4×C19—21no—
97C22×C4×C19—41no—
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×C19—41no—
105C22×C4×C19—41no—
106C22×C4×C19—41no—
107C22×C4×C19—41no—
108C22×C4×C19—41no—
109C22×C4×C19—41no—
110C22×C4×C19—41no—
111C22×C4×C19—41no—
112C22×C4×C19—41no—
113C22×C4×C19C2×D411yescharacteristic
114C22×C4×C19C2×D411yescharacteristic
115C22×C4×C19C2×D411yescharacteristic
116C22×C4×C19#4111yescharacteristic
117C22×C4×C19#4111yescharacteristic
118C22×C4×C19#4111yescharacteristic
119C2×C22⋊D19—42no—
120C2×C22⋊D19—42no—
121C2×C22⋊D19—41no—
122C2×C22⋊D19—41no—
123C2×C22⋊D19—41no—
124C2×C22⋊D19—41no—
125C2×C22⋊D19—41no—
126C2×C22⋊D19—41no—
127C2×C22⋊D19—81no—
128C2×C22⋊D19—81no—
129C2×C22⋊D19—81no—
130C2×C22⋊D19—81no—
131C22×Dic19—21no—
132C22×Dic19—21no—
133C22×Dic19—21no—
134C2×D76—21no—
135C2×D76—21no—
136C2×D76—41no—
137C2×D76—41no—
138C4⋊C4×C19—22no—
139C4⋊C4×C19—22no—
140C4⋊C4×C19—41no—
141C4⋊C4×C19—41no—
142C22⋊C4×C19—48no—
143C22⋊C4×C19—41no—
144C22⋊C4×C19—41no—
145C22⋊C4×C19—41no—
146C22⋊C4×C19—41no—
147C22⋊Dic19—42no—
148C22⋊Dic19—42no—
149C22⋊Dic19—41no—
150C22⋊Dic19—41no—
151(C2×D19)⋊C4—41no—
152(C2×D19)⋊C4—41no—
153(C2×D19)⋊C4—81no—
154(C2×D19)⋊C4—81no—
155C4⋊Dic19—21no—
156C4⋊Dic19—21no—
157C4⋊Dic19—41no—
158C4⋊Dic19—41no—
159C2×C19⋊C8—22no—
160C2×C19⋊C8—41no—
161C2×C19⋊C8—41no—
162C2×C19⋊C8—41no—
163C2×C19⋊C8—41no—
164C2×C19⋊C8—41no—
165#10395—191nomaximal, Sylow
166C23×C19—21no—
167C23×C19—21no—
168C23×C19—21no—
169C23×C19—21no—
170C23×C19—22no—
171C23×C19—22no—
172C23×C19—22no—
173C23×C19—42no—
174C23×C19—42no—
175C23×C19—42no—
176C23×C19—42no—
177C23×C19—42no—
178C23×C19—42no—
179C23×C19—41no—
180C23×C19—41no—
181C23×C19—41no—
182C23×C19—41no—
183C23×C19—41no—
184C23×C19—41no—
185C23×C19—41no—
186C23×C19—41no—
187C23×C19—81no—
188C23×C19—81no—
189C23×C19—81no—
190C23×C19—81no—
191C23×C19—81no—
192C23×C19—81no—
193C23×C19#12011yescharacteristic
194C23×C19#12111yescharacteristic
195C23×C19#12311yescharacteristic
196C23×C19C2×SD1611yescharacteristic
197C23×C19#13511yescharacteristic
198C23×C19AGL(1,ℤ/8)11yescharacteristic
199C23×C19AGL(1,ℤ/8)11yescharacteristic
200C22×D19—41no—
201C22×D19—41no—
202C22×D19—41no—
203C22×D19—41no—
204C22×D19—41no—
205C22×D19—41no—
206C22×D19—41no—
207C2×C4×C19—21no—
208C2×C4×C19—21no—
209C2×C4×C19—21no—
210C2×C4×C19—21no—
211C2×C4×C19—41no—
212C2×C4×C19—41no—
213C2×C4×C19—41no—
214C2×C4×C19—41no—
215C2×C4×C19—42no—
216C2×C4×C19—42no—
217C2×C4×C19—42no—
218C2×C4×C19—42no—
219C2×C4×C19—42no—
220C2×C4×C19—42no—
221C2×C4×C19—41no—
222C2×C4×C19—41no—
223C2×C4×C19—41no—
224C2×C4×C19—42no—
225C2×C4×C19—81no—
226C2×C4×C19—81no—
227C2×C4×C19—81no—
228C2×C4×C19—81no—
229C2×C4×C19—81no—
230C2×C4×C19—81no—
231C2×C4×C19—81no—
232C2×C4×C19—81no—
233C2×C4×C19—81no—
234C2×C4×C19#12111yescharacteristic
235C2×C4×C19#12111yescharacteristic
236C2×C4×C19#12311yescharacteristic
237C2×C4×C19#12411yescharacteristic
238C22⋊D19—84no—
239C22⋊D19—84no—
240C22⋊D19—81no—
241C22⋊D19—81no—
242C22⋊D19—81no—
243C22⋊D19—81no—
244C2×Dic19—41no—
245C2×Dic19—41no—
246C2×Dic19—41no—
247C2×Dic19—41no—
248C2×Dic19—41no—
249C2×Dic19—41no—
250C2×Dic19—41no—
251C2×Dic19—41no—
252C2×Dic19—41no—
253D76—42no—
254D76—81no—
255C19⋊C8—42no—
256C19⋊C8—81no—
257#2617—191no—
258#1874—191no—
259#1853—191no—
260C2×#327—191no—
261C2×#323—191no—
262#1439D1911yescharacteristic, complemented
263#1294—191no—
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—21no—
273C22×C19—21no—
274C22×C19—21no—
275C22×C19—21no—
276C22×C19—44no—
277C22×C19—42no—
278C22×C19—42no—
279C22×C19—42no—
280C22×C19—82no—
281C22×C19—82no—
282C22×C19—82no—
283C22×C19—81no—
284C22×C19—81no—
285C22×C19—81no—
286C22×C19—81no—
287C22×C19#39411yescharacteristic
288C22×C19#44911yescharacteristic
289C22×C19#45011yescharacteristic
290C22×C19#45311yescharacteristic
291C22×C19#45511yescharacteristic
292C22×C19B(4,𝔽2)11yescharacteristic
293C22×C19#45811yescharacteristic
294C22×C19#46511yescharacteristic
295C22×C19#46911yescharacteristic
296C22×C19#48111yescharacteristic
297C22×C19#48211yescharacteristic
298C2×D19—81no—
299C2×D19—81no—
300C2×D19—81no—
301C2×D19—81no—
302C2×D19—81no—
303C2×D19—81no—
304C2×D19—81no—
305C4×C19—21no—
306C4×C19—21no—
307C4×C19—21no—
308C4×C19—21no—
309C4×C19—82no—
310C4×C19—82no—
311C4×C19—81no—
312Dic19—81no—
313Dic19—81no—
314Dic19—81no—
315C2×#121—191no—
316C2×#120—381no—
317C22×C4⋊C4C2×D1911yescharacteristic
318C22×C22⋊C4—21no—
319C22×C22⋊C4C2×D1911yescharacteristic
320C2×#106—381no—
321C2×#102—381no—
322C2×C22⋊C8—191no—
323C2×C22⋊C8—191no—
324#397—381no—
325#394—381no—
326#394—381no—
327#392—381no—
328#386—381no—
329#380—191no—
330C2×#95—21no—
331C2×#95C2×D1911yescharacteristic
332#340—381no—
333#340—381no—
334#327—382no—
335#323—382no—
336C2×C19—21no—
337C2×C19—21no—
338C2×C19—21no—
339C2×C19—21no—
340C2×C19—82no—
341C2×C19#160011yescharacteristic
342C2×C19#160111yescharacteristic
343C2×C19#161211yescharacteristic
344C2×C19#161311yescharacteristic
345C2×C19#203411yescharacteristic
346C2×C19#203711yescharacteristic
347C2×C19#204411yescharacteristic
348D19—161no—
349C25C22⋊D1911yescharacteristic
350C22×D4—191no—
351C22×D4—381no—
352C22×D4—381no—
353C22×D4—381no—
354C23×C4—21no—
355C23×C4—21no—
356C23×C4C22⋊D1911yescharacteristic
357C23×C4C22×D1911yescharacteristic
358C22×C8—381no—
359C22×C8—381no—
360#121—381no—
361#121—381no—
362#121—381no—
363#121—381no—
364#120—762no—
365#120—762no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—42no—
369C2×C4⋊C4—191no—
370C2×C4⋊C4—191no—
371C2×C4⋊C4—191no—
372C2×C22⋊C4—21no—
373C2×C22⋊C4—21no—
374C2×C22⋊C4—21no—
375C2×C22⋊C4—21no—
376C2×C22⋊C4—21no—
377C2×C22⋊C4—21no—
378C2×C22⋊C4—42no—
379C2×C22⋊C4—42no—
380C2×C22⋊C4—42no—
381C2×C22⋊C4—381no—
382C2×C22⋊C4—381no—
383C2×C22⋊C4—381no—
384C2×C22⋊C4—381no—
385C2×C22⋊C4—381no—
386C2×C22⋊C4—381no—
387#106—762no—
388#102—762no—
389C22⋊C8—192no—
390C22⋊C8—381no—
391C22⋊C8—381no—
392C22⋊C8—381no—
393#95—21no—
394#95—21no—
395#95—42no—
396#95—381no—
397#95—381no—
398#95—381no—
399C19#1039511yescharacteristic, complemented, Sylow
400C24—21no—
401C24—21no—
402C24—21no—
403C24—21no—
404C24—21no—
405C24—21no—
406C24—41no—
407C24—41no—
408C24—41no—
409C24—41no—
410C24—381no—
411C24#6452712yes—
412C24C2×C22⋊D1911yescharacteristic
413C2×D4—381no—
414C2×D4—381no—
415C2×D4—761no—
416C2×D4—761no—
417C2×D4—762no—
418C2×D4—762no—
419C2×D4—761no—
420C2×D4—761no—
421C2×D4—761no—
422C2×D4—761no—
423C2×D4—761no—
424C2×D4—761no—
425C2×D4—1521no—
426C2×D4—1521no—
427C2×D4—1521no—
428C2×D4—1521no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—41no—
435C22×C4—41no—
436C22×C4—41no—
437C22×C4—41no—
438C22×C4—41no—
439C22×C4—41no—
440C22×C4—41no—
441C22×C4—41no—
442C22×C4—41no—
443C22×C4—41no—
444C22×C4—41no—
445C22×C4—41no—
446C22×C4—41no—
447C22×C4—41no—
448C22×C4—41no—
449C22×C4—41no—
450C22×C4—381no—
451C22×C4—381no—
452C22×C4—381no—
453C22×C4#6454111yescharacteristic
454C22×C4#6454111yescharacteristic
455C22×C4D4×D1911yescharacteristic
456C22×C4D4×D1911yescharacteristic
457C22×C4D4×D1911yescharacteristic
458C22×C4#6454311yescharacteristic
459C2×C8—382no—
460C2×C8—761no—
461C2×C8—761no—
462C2×C8—761no—
463C2×C8—761no—
464C2×C8—761no—
465C4⋊C4—22no—
466C4⋊C4—22no—
467C4⋊C4—41no—
468C4⋊C4—41no—
469C4⋊C4—381no—
470C4⋊C4—381no—
471C4⋊C4—761no—
472C4⋊C4—761no—
473C22⋊C4—48no—
474C22⋊C4—41no—
475C22⋊C4—41no—
476C22⋊C4—41no—
477C22⋊C4—41no—
478C22⋊C4—762no—
479C22⋊C4—762no—
480C22⋊C4—761no—
481C22⋊C4—761no—
482C22⋊C4—761no—
483C22⋊C4—761no—
484C22⋊C4—1521no—
485C22⋊C4—1521no—
486C23—21no—
487C23—21no—
488C23—21no—
489C23—21no—
490C23—22no—
491C23—22no—
492C23—22no—
493C23—42no—
494C23—42no—
495C23—42no—
496C23—42no—
497C23—42no—
498C23—42no—
499C23—41no—
500C23—41no—
501C23—41no—
502C23—41no—
503C23—41no—
504C23—41no—
505C23—41no—
506C23—41no—
507C23—81no—
508C23—81no—
509C23—81no—
510C23—81no—
511C23—81no—
512C23—81no—
513C23—761no—
514C23—761no—
515C23—761no—
516C23—761no—
517C23—761no—
518C23—761no—
519C23—761no—
520C23#1059737511yescharacteristic
521C23#1059737811yescharacteristic
522C23#1059738311yescharacteristic
523C23#1059738511yescharacteristic
524C23C2×#6452711yescharacteristic
525C23#1059739511yescharacteristic
526C23#1059739611yescharacteristic
527D4—762no—
528D4—1521no—
529D4—1524no—
530D4—1524no—
531D4—1521no—
532D4—1521no—
533D4—1521no—
534D4—1521no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—42no—
553C2×C4—81no—
554C2×C4—81no—
555C2×C4—81no—
556C2×C4—81no—
557C2×C4—81no—
558C2×C4—81no—
559C2×C4—81no—
560C2×C4—81no—
561C2×C4—81no—
562C2×C4—761no—
563C2×C4—761no—
564C2×C4—761no—
565C2×C4—761no—
566C2×C4—761no—
567C2×C4—761no—
568C2×C4—761no—
569C2×C4—761no—
570C2×C4—761no—
571C2×C4#1059732911yescharacteristic
572C2×C4#1059733011yescharacteristic
573C2×C4#1059733011yescharacteristic
574C2×C4#1059733111yescharacteristic
575C8—762no—
576C8—1521no—
577C22—21no—
578C22—21no—
579C22—21no—
580C22—21no—
581C22—21no—
582C22—21no—
583C22—21no—
584C22—21no—
585C22—21no—
586C22—21no—
587C22—21no—
588C22—21no—
589C22—44no—
590C22—42no—
591C22—42no—
592C22—42no—
593C22—82no—
594C22—82no—
595C22—82no—
596C22—81no—
597C22—81no—
598C22—81no—
599C22—81no—
600C22—1521no—
601C22—1521no—
602C22—1521no—
603C22—1521no—
604C22—1521no—
605C22—1521no—
606C22—1521no—
607C22#1192645911yescharacteristic
608C22#1192668711yescharacteristic
609C22#1192669411yescharacteristic
610C22#1192671111yescharacteristic
611C22#1192672111yescharacteristic
612C22#1192673011yescharacteristic
613C22#1192673311yescharacteristic
614C22#1192677511yescharacteristic
615C22#1192679511yescharacteristic
616C22#1192686211yescharacteristic
617C22#1192686811yescharacteristic
618C4—21no—
619C4—21no—
620C4—21no—
621C4—21no—
622C4—82no—
623C4—82no—
624C4—81no—
625C4—1521no—
626C4—1521no—
627C4—1521no—
628C2—21no—
629C2—21no—
630C2—21no—
631C2—21no—
632C2—82no—
633C2—3041no—
634C2#1456257911yescharacteristic
635C2#1456258611yescharacteristic
636C2#1456264711yescharacteristic
637C2#1456265411yescharacteristic
638C2#1456482411yescharacteristic
639C2#1456484511yescharacteristic
640C2#1456488411yescharacteristic
subgroupG/H
centerC23#10597383
commutator, cosocleC23×C4×C19C23
FrattiniC23×C4C22×D19
FittingC19×#1439C2
socleC23×C19#120
prime radical#14569369C2
hypercenter#1439D19
hypocenterC19#10395
LCSG ▷ C23×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1439

Complements

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

NH ≅ G/Ntype
2. #14563952C2semidirect
3. #14563828C2semidirect
4. C2×#11926277C2semidirect
5. C2×#11926268C2semidirect
6. #14561514C2semidirect
7. C19×#1439C2semidirect
76. C22⋊(C19⋊C8)D4semidirect
262. #1439D19semidirect
399. C19#10395semidirect

Maximal subgroups

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

subgroupindex
#145693692
#145639522
#145638282
C2×#119262772
C2×#119262682
#145615142
C19×#14392
#1039519