Finite Group Databasebeta

← #18085407

Subgroups — #18085407

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#14574392C211yesmaximal, characteristic, complemented
2#14571922C211yesmaximal, characteristic, complemented
3#14563545C211yesmaximal, characteristic, complemented
4#14562206C211yesmaximal, characteristic, complemented
5#14562203C211yesmaximal, characteristic, complemented
6#14561502C211yesmaximal, characteristic, complemented
7C19×#2847C211yesmaximal, characteristic
8C2×#10597370—21no—
9C2×#10597370C2211yescharacteristic
10#11926874—21no—
11#11926860—21no—
12#11926771—22no—
13#11926695—21no—
14#11926682—21no—
15C2×C22⋊(C19⋊C8)—22no—
16C2×C22⋊(C19⋊C8)C2211yescharacteristic
17C2×C22⋊(C19⋊C8)C2211yescharacteristic
18#11926417—22no—
19#11926417—21no—
20#11926404—21no—
21#11926404C2211yescharacteristic
22#11926400—21no—
23#11926280—22no—
24#11926278—22no—
25C24×C4×C19C2211yescharacteristic
26C2×C19×#121—21no—
27C2×C19×#121C2211yescharacteristic
28C2×C19×#120—21no—
29C19×#386—22no—
30C19×#386—21no—
31C19×#380—21no—
32C19×#380C2211yescharacteristic
33C25×C19D411yescharacteristic
34C22×D4×C19—22no—
35C22×D4×C19—21no—
36C22×D4×C19D411yescharacteristic
37C23×C4×C19—21no—
38C23×C4×C19—21no—
39C23×C4×C19—21no—
40C23×C4×C19—21no—
41C23×C4×C19—21no—
42C23×C4×C19—21no—
43C23×C4×C19—44no—
44C23×C4×C19D411yescharacteristic
45C23×C4×C19C2311yescharacteristic
46C22×Dic38D411yescharacteristic, complemented
47C19×#121—21no—
48C19×#121—21no—
49C19×#121—21no—
50C19×#121—21no—
51C19×#121—44no—
52C19×#120—42no—
53C19×#120—42no—
54C2×C4⋊C4×C19—21no—
55C2×C4⋊C4×C19D411yescharacteristic
56C2×C22⋊C4×C19—22no—
57C2×C22⋊C4×C19—22no—
58C2×C22⋊C4×C19—21no—
59C2×C22⋊C4×C19—21no—
60C2×C22⋊Dic19—22no—
61C2×C22⋊Dic19—22no—
62C2×C22⋊Dic19—21no—
63C2×C22⋊Dic19—21no—
64C2×#64526—22no—
65C2×C4⋊Dic19—21no—
66C2×C4⋊Dic19D411yescharacteristic, complemented
67#10597370—21no—
68#10597370—21no—
69#10597370—21no—
70#10597370—21no—
71#10597370—44no—
72C2×Dic19⋊C4—22no—
73C2×Dic19⋊C4—21no—
74C22×C19⋊C8—21no—
75C22×C19⋊C8D412yescomplemented
76C19×#95—22no—
77C19×#95D412yes—
78#10597289—22no—
79C19⋊#95—22no—
80C19⋊#95D412yescomplemented
81C22⋊(C19⋊C8)—21no—
82C22⋊(C19⋊C8)—21no—
83C22⋊(C19⋊C8)—21no—
84C22⋊(C19⋊C8)—21no—
85C22⋊(C19⋊C8)—44no—
86#10597267—22no—
87#10597265—22no—
88C24×C19—21no—
89C24×C19—21no—
90C24×C19—21no—
91C24×C19—21no—
92C24×C19—21no—
93C24×C19—21no—
94C24×C19—21no—
95C24×C19—42no—
96C24×C19—42no—
97C24×C19SD1612yescomplemented
98C24×C19C2×D411yescharacteristic
99C2×D4×C19—21no—
100C2×D4×C19—21no—
101C2×D4×C19—42no—
102C2×D4×C19—44no—
103C2×D4×C19—44no—
104C2×D4×C19—44no—
105C2×D4×C19—41no—
106C2×D4×C19—41no—
107C2×D4×C19—41no—
108C2×D4×C19—41no—
109C2×D4×C19—41no—
110C2×D4×C19—41no—
111C22×C4×C19—24no—
112C22×C4×C19—24no—
113C22×C4×C19—24no—
114C22×C4×C19—21no—
115C22×C4×C19—21no—
116C22×C4×C19—21no—
117C22×C4×C19—22no—
118C22×C4×C19—21no—
119C22×C4×C19—42no—
120C22×C4×C19—42no—
121C22×C4×C19—42no—
122C22×C4×C19—42no—
123C22×C4×C19—42no—
124C22×C4×C19—42no—
125C22×C4×C19—42no—
126C22×C4×C19—42no—
127C22×C4×C19—42no—
128C22×C4×C19—42no—
129C22×C4×C19—42no—
130C22×C4×C19—41no—
131C22×C4×C19—41no—
132C22×C4×C19—41no—
133C22×C4×C19—41no—
134C22×C4×C19C2×D411yescharacteristic
135C22×C4×C19C2×D411yescharacteristic
136C22×C4×C19C2×D411yescharacteristic
137C22×C4×C19C2×D411yescharacteristic
138C22×C4×C19C2×D411yescharacteristic
139C22×C4×C19#4111yescharacteristic
140C22×Dic19—21no—
141C22×Dic19—21no—
142C22×Dic19—22no—
143C2×Dic38—21no—
144C2×Dic38—21no—
145C2×Dic38—42no—
146C4⋊C4×C19—21no—
147C4⋊C4×C19—21no—
148C4⋊C4×C19—42no—
149C22⋊C4×C19—44no—
150C22⋊C4×C19—44no—
151C22⋊C4×C19—41no—
152C22⋊C4×C19—41no—
153C22⋊C4×C19—41no—
154C22⋊C4×C19—41no—
155C22⋊Dic19—44no—
156C22⋊Dic19—44no—
157C22⋊Dic19—41no—
158C22⋊Dic19—41no—
159C22⋊Dic19—41no—
160C22⋊Dic19—41no—
161#64526—82no—
162C4⋊Dic19—21no—
163C4⋊Dic19—21no—
164C4⋊Dic19—42no—
165Dic19⋊C4—44no—
166Dic19⋊C4—41no—
167Dic19⋊C4—41no—
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—42no—
195C23×C19—42no—
196C23×C19—41no—
197C23×C19—41no—
198C23×C19—41no—
199C23×C19—41no—
200C23×C19—41no—
201C23×C19—41no—
202C23×C19—41no—
203C23×C19#12011yescharacteristic
204C23×C19#12011yescharacteristic
205C23×C19#12111yescharacteristic
206C23×C19C2×SD1611yescharacteristic
207C23×C19#13511yescharacteristic
208C23×C19AGL(1,ℤ/8)11yescharacteristic
209C23×C19#13711yescharacteristic
210D4×C19—42no—
211D4×C19—81no—
212D4×C19—88no—
213D4×C19—81no—
214D4×C19—81no—
215D4×C19—81no—
216D4×C19—81no—
217C2×C4×C19—22no—
218C2×C4×C19—22no—
219C2×C4×C19—22no—
220C2×C4×C19—22no—
221C2×C4×C19—22no—
222C2×C4×C19—22no—
223C2×C4×C19—41no—
224C2×C4×C19—41no—
225C2×C4×C19—41no—
226C2×C4×C19—44no—
227C2×C4×C19—44no—
228C2×C4×C19—44no—
229C2×C4×C19—41no—
230C2×C4×C19—41no—
231C2×C4×C19—41no—
232C2×C4×C19—41no—
233C2×C4×C19—44no—
234C2×C4×C19—42no—
235C2×C4×C19—42no—
236C2×C4×C19—41no—
237C2×C4×C19—42no—
238C2×C4×C19—41no—
239C2×C4×C19—41no—
240C2×C4×C19#12011yescharacteristic
241C2×C4×C19#12111yescharacteristic
242C2×C4×C19#12111yescharacteristic
243C2×C4×C19#12711yescharacteristic
244C2×Dic19—42no—
245C2×Dic19—42no—
246C2×Dic19—42no—
247C2×Dic19—42no—
248C2×Dic19—41no—
249C2×Dic19—41no—
250C2×Dic19—42no—
251Dic38—42no—
252Dic38—81no—
253C19⋊C8—42no—
254C19⋊C8—81no—
255#3187—191no—
256#2848—191no—
257#2847D1911yescharacteristic
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—82no—
288C22×C19—82no—
289C22×C19—81no—
290C22×C19—81no—
291C22×C19—81no—
292C22×C19#39211yescharacteristic
293C22×C19#44811yescharacteristic
294C22×C19#44911yescharacteristic
295C22×C19#45011yescharacteristic
296C22×C19#45211yescharacteristic
297C22×C19#46511yescharacteristic
298C22×C19#46811yescharacteristic
299C4×C19—21no—
300C4×C19—21no—
301C4×C19—21no—
302C4×C19—42no—
303C4×C19—82no—
304C4×C19—81no—
305C4×C19B(4,𝔽2)12yes—
306Dic19—82no—
307Dic19—81no—
308Dic19—81no—
309C24×C4C2×D1911yescharacteristic
310C2×C22⋊Q8—191no—
311C2×C22⋊Q8—381no—
312C2×#121—21no—
313C2×#121C2×D1911yescharacteristic
314C2×#120—21no—
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—21no—
324#386—22no—
325#385—382no—
326#385—381no—
327#380—21no—
328#380—191no—
329#380—381no—
330#380C2×D1911yescharacteristic
331#379—381no—
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—161no—
342C2×C19#200011yescharacteristic
343C2×C19#201011yescharacteristic
344C2×C19#202111yescharacteristic
345C25C22⋊D1911yescharacteristic
346C22×Q8—191no—
347C22×D4—22no—
348C22×D4—21no—
349C22×D4C22⋊D1911yescharacteristic
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—381no—
363C22⋊Q8—381no—
364C22⋊Q8—381no—
365C22⋊Q8—381no—
366C22⋊Q8—764no—
367#121—21no—
368#121—21no—
369#121—21no—
370#121—21no—
371#121—44no—
372#120—42no—
373#120—42no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—191no—
376C2×C4⋊C4—382no—
377C2×C4⋊C4—381no—
378C2×C4⋊C4—381no—
379C2×C4⋊C4C22⋊D1911yescharacteristic
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⋊D1912yes—
400C19#1032211yescharacteristic, complemented, Sylow
401C24—21no—
402C24—21no—
403C24—21no—
404C24—21no—
405C24—21no—
406C24—21no—
407C24—21no—
408C24—42no—
409C24—42no—
410C24#6452612yescomplemented
411C24C2×C22⋊D1911yescharacteristic
412C2×Q8—381no—
413C2×Q8—381no—
414C2×Q8—762no—
415C2×D4—21no—
416C2×D4—21no—
417C2×D4—42no—
418C2×D4—44no—
419C2×D4—44no—
420C2×D4—44no—
421C2×D4—41no—
422C2×D4—41no—
423C2×D4—41no—
424C2×D4—41no—
425C2×D4—41no—
426C2×D4—41no—
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—42no—
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—41no—
447C22×C4—41no—
448C22×C4—41no—
449C22×C4—41no—
450C22×C4—382no—
451C22×C4—381no—
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—381no—
468C4⋊C4—381no—
469C4⋊C4—764no—
470C4⋊C4—762no—
471C4⋊C4—761no—
472C4⋊C4—761no—
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—42no—
507C23—42no—
508C23—41no—
509C23—41no—
510C23—41no—
511C23—41no—
512C23—41no—
513C23—41no—
514C23—41no—
515C23#1059737811yescharacteristic
516C23C2×#6452611yescharacteristic
517C23#1059738311yescharacteristic
518C23#1059738511yescharacteristic
519C23#1059739611yescharacteristic
520C23#1059739711yescharacteristic
521C23#1059739911yescharacteristic
522Q8—762no—
523Q8—1521no—
524D4—42no—
525D4—81no—
526D4—88no—
527D4—81no—
528D4—81no—
529D4—81no—
530D4—81no—
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—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—762no—
555C2×C4—762no—
556C2×C4—762no—
557C2×C4—762no—
558C2×C4—762no—
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—82no—
593C22—82no—
594C22—81no—
595C22—81no—
596C22—81no—
597C22#1192645211yescharacteristic
598C22#1192668211yescharacteristic
599C22#1192668711yescharacteristic
600C22#1192669511yescharacteristic
601C22#1192670611yescharacteristic
602C22#1192677111yescharacteristic
603C22#1192678811yescharacteristic
604C4—21no—
605C4—21no—
606C4—21no—
607C4—42no—
608C4—82no—
609C4—81no—
610C4—1522no—
611C4—1521no—
612C4—1521no—
613C4#1192673012yes—
614C2—21no—
615C2—21no—
616C2—21no—
617C2—21no—
618C2—21no—
619C2—21no—
620C2—44no—
621C2—161no—
622C2#1456463811yescharacteristic
623C2#1456470011yescharacteristic
624C2#1456475811yescharacteristic
subgroupG/H
centerC22#11926452
commutator, cosocleC23×C4×C19C23
FrattiniC23×C4C22×D19
Fitting, prime radicalC19×#2847C2
socleC22×C19#392
hypercenter#2847D19
hypocenterC19#10322
LCSG ▷ C23×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2847

Complements

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

NH ≅ G/Ntype
1. #14574392C2semidirect
2. #14571922C2semidirect
3. #14563545C2semidirect
4. #14562206C2semidirect
5. #14562203C2semidirect
6. #14561502C2semidirect
46. C22×Dic38D4semidirect
66. C2×C4⋊Dic19D4semidirect
75. C22×C19⋊C8D4semidirect
80. C19⋊#95D4semidirect
97. C24×C19SD16semidirect
400. C19#10322semidirect
410. C24#64526semidirect

Maximal subgroups

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

subgroupindex
#145743922
#145719222
#145635452
#145622062
#145622032
#145615022
C19×#28472
#1032219