Finite Group Databasebeta

← #18085405

Subgroups — #18085405

Order 4864.

988 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 988 conjugacy classes of subgroups — too many to draw. Only its 105 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
1#14574388C211yesmaximal, characteristic, complemented
2#14571917C211yesmaximal, characteristic
3#14563545C211yesmaximal, characteristic, complemented
4#14562207C211yesmaximal, characteristic, complemented
5#14562202C211yesmaximal, characteristic, complemented
6#14561502C211yesmaximal, characteristic, complemented
7C19×#2848C211yesmaximal, characteristic, complemented
8C2×#10597376—21no—
9C2×#10597376C2211yescharacteristic
10C2×#10597399—21no—
11#11926872—21no—
12#11926862—21no—
13#11926775—22no—
14#11926694—21no—
15#11926683—21no—
16C2×C22⋊(C19⋊C8)—22no—
17C2×C22⋊(C19⋊C8)C2211yescharacteristic
18C2×C22⋊(C19⋊C8)C2211yescharacteristic
19#11926423—22no—
20#11926423—21no—
21#11926404—21no—
22#11926404C2211yescharacteristic
23#11926281—22no—
24#11926277—22no—
25C24×C4×C19C2211yescharacteristic
26C2×C19×C22⋊Q8—21no—
27C2×C19×C22⋊Q8C2211yescharacteristic
28C19×#385—22no—
29C19×#385—21no—
30C19×#380—21no—
31C19×#380C2211yescharacteristic
32C19×#379—21no—
33C25×C19D411yescharacteristic
34C22×Q8×C19D411yescharacteristic, complemented
35C23×C4×C19—21no—
36C23×C4×C19—21no—
37C23×C4×C19—21no—
38C23×C4×C19—21no—
39C23×C4×C19—21no—
40C23×C4×C19—21no—
41C23×C4×C19—44no—
42C23×C4×C19D411yescharacteristic
43C23×C4×C19C2311yescharacteristic
44C22×C22⋊D19—22no—
45C22×C22⋊D19—21no—
46C22×D76D411yescharacteristic
47C19×C22⋊Q8—21no—
48C19×C22⋊Q8—21no—
49C19×C22⋊Q8—21no—
50C19×C22⋊Q8—21no—
51C19×C22⋊Q8—44no—
52C2×C4⋊C4×C19—22no—
53C2×C4⋊C4×C19—21no—
54C2×C4⋊C4×C19—21no—
55C2×C4⋊C4×C19D411yescharacteristic, complemented
56C2×C22⋊C4×C19—22no—
57C2×C22⋊C4×C19—22no—
58C2×C22⋊C4×C19—21no—
59C2×C22⋊C4×C19—21no—
60#10597399—42no—
61#10597399—42no—
62C2×C22⋊Dic19—22no—
63C2×C22⋊Dic19—21no—
64C2×#64527—22no—
65#10597376—21no—
66#10597376—21no—
67#10597376—21no—
68#10597376—21no—
69#10597376—44no—
70C2×(C2×D19)⋊C4—22no—
71C2×(C2×D19)⋊C4—21no—
72C2×C4⋊Dic19—21no—
73C2×C4⋊Dic19D411yescharacteristic
74C22×C19⋊C8—21no—
75C22×C19⋊C8D412yescomplemented
76C19×#95—22no—
77C19×#95D412yescomplemented
78#10597292—22no—
79C19⋊#95—22no—
80C19⋊#95D412yes—
81C22⋊(C19⋊C8)—21no—
82C22⋊(C19⋊C8)—21no—
83C22⋊(C19⋊C8)—21no—
84C22⋊(C19⋊C8)—21no—
85C22⋊(C19⋊C8)—44no—
86#10597266—22no—
87#10597265—22no—
88C24×C19—21no—
89C24×C19—21no—
90C24×C19—21no—
91C24×C19—21no—
92C24×C19—21no—
93C24×C19—21no—
94C24×C19—42no—
95C24×C19—42no—
96C24×C19SD1612yescomplemented
97C24×C19C2×D411yescharacteristic
98C23×D19—21no—
99C2×Q8×C19—21no—
100C2×Q8×C19—21no—
101C2×Q8×C19—42no—
102C22×C4×C19—24no—
103C22×C4×C19—24no—
104C22×C4×C19—24no—
105C22×C4×C19—21no—
106C22×C4×C19—21no—
107C22×C4×C19—21no—
108C22×C4×C19—21no—
109C22×C4×C19—22no—
110C22×C4×C19—21no—
111C22×C4×C19—42no—
112C22×C4×C19—42no—
113C22×C4×C19—42no—
114C22×C4×C19—42no—
115C22×C4×C19—42no—
116C22×C4×C19—42no—
117C22×C4×C19—42no—
118C22×C4×C19—42no—
119C22×C4×C19—42no—
120C22×C4×C19—42no—
121C22×C4×C19—42no—
122C22×C4×C19—41no—
123C22×C4×C19—41no—
124C22×C4×C19—41no—
125C22×C4×C19—41no—
126C22×C4×C19C2×D411yescharacteristic
127C22×C4×C19C2×D411yescharacteristic
128C22×C4×C19C2×D411yescharacteristic
129C22×C4×C19C2×D411yescharacteristic
130C22×C4×C19C2×D411yescharacteristic
131C22×C4×C19#4111yescharacteristic
132C2×C22⋊D19—44no—
133C2×C22⋊D19—44no—
134C2×C22⋊D19—44no—
135C2×C22⋊D19—41no—
136C2×C22⋊D19—41no—
137C2×C22⋊D19—41no—
138C2×C22⋊D19—41no—
139C2×C22⋊D19—41no—
140C2×C22⋊D19—41no—
141C22×Dic19—21no—
142C22×Dic19—22no—
143C2×D76—21no—
144C2×D76—21no—
145C2×D76—42no—
146C4⋊C4×C19—21no—
147C4⋊C4×C19—21no—
148C4⋊C4×C19—42no—
149C4⋊C4×C19—44no—
150C4⋊C4×C19—41no—
151C4⋊C4×C19—41no—
152C22⋊C4×C19—44no—
153C22⋊C4×C19—44no—
154C22⋊C4×C19—41no—
155C22⋊C4×C19—41no—
156C22⋊C4×C19—41no—
157C22⋊C4×C19—41no—
158C22⋊Dic19—44no—
159C22⋊Dic19—41no—
160C22⋊Dic19—41no—
161#64527—82no—
162(C2×D19)⋊C4—44no—
163(C2×D19)⋊C4—41no—
164(C2×D19)⋊C4—41no—
165C4⋊Dic19—21no—
166C4⋊Dic19—21no—
167C4⋊Dic19—42no—
168C2×C19⋊C8—22no—
169C2×C19⋊C8—42no—
170C2×C19⋊C8—42no—
171C2×C19⋊C8—41no—
172#10322—191nomaximal, Sylow
173C23×C19—22no—
174C23×C19—22no—
175C23×C19—22no—
176C23×C19—22no—
177C23×C19—22no—
178C23×C19—22no—
179C23×C19—22no—
180C23×C19—22no—
181C23×C19—22no—
182C23×C19—41no—
183C23×C19—44no—
184C23×C19—41no—
185C23×C19—41no—
186C23×C19—41no—
187C23×C19—41no—
188C23×C19—41no—
189C23×C19—41no—
190C23×C19—41no—
191C23×C19—44no—
192C23×C19—44no—
193C23×C19—44no—
194C23×C19—41no—
195C23×C19—41no—
196C23×C19—41no—
197C23×C19—41no—
198C23×C19#12011yescharacteristic
199C23×C19#12011yescharacteristic
200C23×C19#12111yescharacteristic
201C23×C19C2×SD1611yescharacteristic
202C23×C19#13511yescharacteristic
203C23×C19AGL(1,ℤ/8)11yescharacteristic
204C23×C19#13711yescharacteristic
205C22×D19—42no—
206C22×D19—42no—
207C22×D19—41no—
208C22×D19—41no—
209C22×D19—41no—
210Q8×C19—42no—
211Q8×C19—81no—
212C2×C4×C19—22no—
213C2×C4×C19—22no—
214C2×C4×C19—22no—
215C2×C4×C19—22no—
216C2×C4×C19—22no—
217C2×C4×C19—22no—
218C2×C4×C19—41no—
219C2×C4×C19—41no—
220C2×C4×C19—41no—
221C2×C4×C19—44no—
222C2×C4×C19—44no—
223C2×C4×C19—44no—
224C2×C4×C19—41no—
225C2×C4×C19—41no—
226C2×C4×C19—41no—
227C2×C4×C19—41no—
228C2×C4×C19—44no—
229C2×C4×C19—42no—
230C2×C4×C19—42no—
231C2×C4×C19—42no—
232C2×C4×C19—42no—
233C2×C4×C19—41no—
234C2×C4×C19—41no—
235C2×C4×C19—42no—
236C2×C4×C19#12011yescharacteristic
237C2×C4×C19#12111yescharacteristic
238C2×C4×C19#12111yescharacteristic
239C2×C4×C19#12711yescharacteristic
240C22⋊D19—88no—
241C22⋊D19—81no—
242C22⋊D19—81no—
243C22⋊D19—81no—
244C22⋊D19—81no—
245C2×Dic19—42no—
246C2×Dic19—42no—
247C2×Dic19—41no—
248C2×Dic19—42no—
249C2×Dic19—41no—
250C2×Dic19—41no—
251D76—42no—
252D76—81no—
253C19⋊C8—42no—
254C19⋊C8—81no—
255#3187—191no—
256#2848D1911yescharacteristic, complemented
257#2847—191no—
258#1779—191no—
259#1520—191no—
260#1519—191no—
261#1289—191no—
262C22×C19—21no—
263C22×C19—21no—
264C22×C19—21no—
265C22×C19—21no—
266C22×C19—21no—
267C22×C19—21no—
268C22×C19—24no—
269C22×C19—24no—
270C22×C19—24no—
271C22×C19—41no—
272C22×C19—41no—
273C22×C19—41no—
274C22×C19—41no—
275C22×C19—42no—
276C22×C19—42no—
277C22×C19—42no—
278C22×C19—42no—
279C22×C19—42no—
280C22×C19—42no—
281C22×C19—42no—
282C22×C19—42no—
283C22×C19—42no—
284C22×C19—42no—
285C22×C19—42no—
286C22×C19—42no—
287C22×C19#39211yescharacteristic
288C22×C19#44811yescharacteristic
289C22×C19#44911yescharacteristic
290C22×C19#45011yescharacteristic
291C22×C19#45211yescharacteristic
292C22×C19#46511yescharacteristic
293C22×C19#46811yescharacteristic
294C2×D19—82no—
295C2×D19—82no—
296C2×D19—81no—
297C2×D19—81no—
298C2×D19—81no—
299C4×C19—21no—
300C4×C19—21no—
301C4×C19—21no—
302C4×C19—42no—
303C4×C19—82no—
304C4×C19—81no—
305C4×C19—81no—
306C4×C19B(4,𝔽2)12yes—
307Dic19—82no—
308Dic19—81no—
309C24×C4C2×D1911yescharacteristic
310C2×C22⋊Q8—21no—
311C2×C22⋊Q8C2×D1911yescharacteristic
312C2×#121—191no—
313C2×#121—381no—
314C2×#120—381no—
315#483—381no—
316#481—381no—
317#465—382no—
318#450—381no—
319#448—381no—
320C2×C22⋊C8—191no—
321C2×C22⋊C8—191no—
322C2×C22⋊C8—382no—
323#386—382no—
324#386—381no—
325#385—21no—
326#385—22no—
327#380—21no—
328#380—191no—
329#380—381no—
330#380C2×D1911yescharacteristic
331#379—21no—
332#328—382no—
333#327—382no—
334C2×C19—21no—
335C2×C19—21no—
336C2×C19—21no—
337C2×C19—21no—
338C2×C19—21no—
339C2×C19—21no—
340C2×C19—44no—
341C2×C19#200011yescharacteristic
342C2×C19#201011yescharacteristic
343C2×C19#202111yescharacteristic
344D19—161no—
345C25C22⋊D1911yescharacteristic
346C22×Q8C22⋊D1911yescharacteristic, complemented
347C22×D4—191no—
348C22×D4—382no—
349C22×D4—381no—
350C23×C4—21no—
351C23×C4—21no—
352C23×C4—21no—
353C23×C4—21no—
354C23×C4—21no—
355C23×C4—21no—
356C23×C4—44no—
357C23×C4C22⋊D1911yescharacteristic
358C23×C4C22×D1911yescharacteristic
359C2×SD16—382no—
360C22×C8—192no—
361C22×C8—381no—
362C22⋊Q8—21no—
363C22⋊Q8—21no—
364C22⋊Q8—21no—
365C22⋊Q8—21no—
366C22⋊Q8—44no—
367#121—381no—
368#121—381no—
369#121—381no—
370#121—381no—
371#121—764no—
372#120—762no—
373#120—762no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—191no—
378C2×C4⋊C4—381no—
379C2×C4⋊C4C22⋊D1911yescharacteristic, complemented
380C2×C22⋊C4—22no—
381C2×C22⋊C4—22no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—382no—
385C2×C22⋊C4—382no—
386C2×C22⋊C4—381no—
387C2×C22⋊C4—381no—
388#106—382no—
389#103—382no—
390#102—382no—
391C22⋊C8—381no—
392C22⋊C8—381no—
393C22⋊C8—381no—
394C22⋊C8—381no—
395C22⋊C8—764no—
396#95—22no—
397#95—192no—
398#95—382no—
399#95C22⋊D1912yescomplemented
400C19#1032211yescharacteristic, complemented, Sylow
401C24—21no—
402C24—21no—
403C24—21no—
404C24—21no—
405C24—21no—
406C24—21no—
407C24—42no—
408C24—42no—
409C24—381no—
410C24#6452712yescomplemented
411C24C2×C22⋊D1911yescharacteristic
412C2×Q8—21no—
413C2×Q8—21no—
414C2×Q8—42no—
415C2×D4—381no—
416C2×D4—381no—
417C2×D4—762no—
418C2×D4—764no—
419C2×D4—764no—
420C2×D4—764no—
421C2×D4—761no—
422C2×D4—761no—
423C2×D4—761no—
424C2×D4—761no—
425C2×D4—761no—
426C2×D4—761no—
427C22×C4—24no—
428C22×C4—24no—
429C22×C4—24no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—22no—
435C22×C4—21no—
436C22×C4—42no—
437C22×C4—42no—
438C22×C4—42no—
439C22×C4—42no—
440C22×C4—42no—
441C22×C4—42no—
442C22×C4—42no—
443C22×C4—42no—
444C22×C4—42no—
445C22×C4—42no—
446C22×C4—42no—
447C22×C4—41no—
448C22×C4—41no—
449C22×C4—41no—
450C22×C4—41no—
451C22×C4—382no—
452C22×C4—381no—
453C22×C4D4×D1911yescharacteristic
454C22×C4D4×D1911yescharacteristic
455C22×C4D4×D1911yescharacteristic
456C22×C4#6454311yescharacteristic
457C22×C4C2×C22⋊D1911yescharacteristic
458C22×C4C2×C22⋊D1911yescharacteristic
459SD16—1522no—
460C2×C8—382no—
461C2×C8—762no—
462C2×C8—762no—
463C2×C8—761no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—42no—
467C4⋊C4—44no—
468C4⋊C4—41no—
469C4⋊C4—41no—
470C4⋊C4—381no—
471C4⋊C4—381no—
472C4⋊C4—762no—
473C22⋊C4—44no—
474C22⋊C4—44no—
475C22⋊C4—41no—
476C22⋊C4—41no—
477C22⋊C4—41no—
478C22⋊C4—41no—
479C22⋊C4—764no—
480C22⋊C4—764no—
481C22⋊C4—761no—
482C22⋊C4—761no—
483C22⋊C4—761no—
484C22⋊C4—761no—
485C23—22no—
486C23—22no—
487C23—22no—
488C23—22no—
489C23—22no—
490C23—22no—
491C23—22no—
492C23—22no—
493C23—22no—
494C23—41no—
495C23—44no—
496C23—41no—
497C23—41no—
498C23—41no—
499C23—41no—
500C23—41no—
501C23—41no—
502C23—41no—
503C23—44no—
504C23—44no—
505C23—44no—
506C23—41no—
507C23—41no—
508C23—41no—
509C23—41no—
510C23—762no—
511C23—762no—
512C23—761no—
513C23—761no—
514C23—761no—
515C23#1059738311yescharacteristic
516C23#1059738511yescharacteristic
517C23C2×#6452711yescharacteristic
518C23#1059738811yescharacteristic
519C23#1059739511yescharacteristic
520C23#1059739611yescharacteristic
521C23#1059739911yescharacteristic
522Q8—42no—
523Q8—81no—
524D4—762no—
525D4—1521no—
526D4—1528no—
527D4—1521no—
528D4—1521no—
529D4—1521no—
530D4—1521no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—44no—
541C2×C4—44no—
542C2×C4—44no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—44no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—762no—
556C2×C4—762no—
557C2×C4—762no—
558C2×C4—761no—
559C2×C4—761no—
560C2×C4—761no—
561C2×C4#1059738311yescharacteristic
562C2×C4#1059738411yescharacteristic
563C2×C4#1059738511yescharacteristic
564C2×C4#1059738611yescharacteristic
565C8—762no—
566C8—1521no—
567C22—21no—
568C22—21no—
569C22—21no—
570C22—21no—
571C22—21no—
572C22—21no—
573C22—24no—
574C22—24no—
575C22—24no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—42no—
581C22—42no—
582C22—42no—
583C22—42no—
584C22—42no—
585C22—42no—
586C22—42no—
587C22—42no—
588C22—42no—
589C22—42no—
590C22—42no—
591C22—42no—
592C22—1522no—
593C22—1522no—
594C22—1521no—
595C22—1521no—
596C22—1521no—
597C22#1192645211yescharacteristic
598C22#1192668311yescharacteristic
599C22#1192668911yescharacteristic
600C22#1192669411yescharacteristic
601C22#1192670411yescharacteristic
602C22#1192677511yescharacteristic
603C22#1192679211yescharacteristic
604C4—21no—
605C4—21no—
606C4—21no—
607C4—42no—
608C4—82no—
609C4—81no—
610C4—81no—
611C4—1522no—
612C4—1521no—
613C4#1192673012yes—
614C2—21no—
615C2—21no—
616C2—21no—
617C2—21no—
618C2—21no—
619C2—21no—
620C2—44no—
621C2—3041no—
622C2#1456463611yescharacteristic
623C2#1456470011yescharacteristic
624C2#1456475811yescharacteristic
subgroupG/H
centerC22#11926452
commutator, cosocleC23×C4×C19C23
FrattiniC23×C4C22×D19
FittingC19×#2848C2
socleC22×C19#392
prime radical#14571917C2
hypercenter#2848D19
hypocenterC19#10322
LCSG ▷ C23×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2848

Complements

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

NH ≅ G/Ntype
1. #14574388C2semidirect
3. #14563545C2semidirect
4. #14562207C2semidirect
5. #14562202C2semidirect
6. #14561502C2semidirect
7. C19×#2848C2semidirect
34. C22×Q8×C19D4semidirect
55. C2×C4⋊C4×C19D4semidirect
75. C22×C19⋊C8D4semidirect
77. C19×#95D4semidirect
96. C24×C19SD16semidirect
256. #2848D19semidirect
346. C22×Q8C22⋊D19semidirect
379. C2×C4⋊C4C22⋊D19semidirect
399. #95C22⋊D19semidirect
400. C19#10322semidirect
410. C24#64527semidirect

Maximal subgroups

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

subgroupindex
#145743882
#145719172
#145635452
#145622072
#145622022
#145615022
C19×#28482
#1032219