Finite Group Databasebeta

← #18077665

Subgroups — #18077665

Order 4864.

834 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11926683C211yesmaximal, characteristic
2#14566338C211yesmaximal, characteristic
3#14563570C211yesmaximal, characteristic, complemented
4C2×#11926277C211yesmaximal, characteristic
5#14561514C211yesmaximal, characteristic, complemented
6#14561478C211yesmaximal, characteristic, complemented
7C19×#1446C211yesmaximal, characteristic, complemented
8C22×#64527—21no—
9C2×#10597376C2211yescharacteristic
10C2×C4×C22⋊D19—21no—
11#11926683—22no—
12#11926683C414yescomplemented
13C2×#10597292—21no—
14C2×#10597292—21no—
15C2×#10597292—21no—
16C2×C22⋊(C19⋊C8)C2211yescharacteristic
17C2×C22⋊(C19⋊C8)C2211yescharacteristic
18#11926436—21no—
19#11926429—21no—
20#11926423—21no—
21#11926422—21no—
22#11926418—21no—
23#11926404C2211yescharacteristic
24#11926277—22no—
25C23×Q8×C19C2211yescharacteristic
26C2×C19×#95—21no—
27C2×C19×#95—21no—
28C2×C19×#95C2211yescharacteristic
29C2×C19×#95C2211yescharacteristic
30C22×Q8×C19—21no—
31C22×Q8×C19—21no—
32C22×Q8×C19—21no—
33C22×Q8×C19—21no—
34C22×Q8×C19—21no—
35C22×Q8×C19—42no—
36C22×Q8×C19—42no—
37C22×Q8×C19C2×C412yescomplemented
38C23×C4×C19—21no—
39C23×C4×C19—21no—
40C23×C4×C19D411yescharacteristic
41C23×C4×C19D411yescharacteristic
42C23×C4×C19C2311yescharacteristic
43C22×C22⋊D19—21no—
44C22×D76D411yescharacteristic
45C22×C4×D19—21no—
46C2×C22⋊Dic19—21no—
47C2×#64527—24no—
48C2×#64527—42no—
49C2×#64527—42no—
50#10597376—21no—
51#10597376—21no—
52#10597376C2×C412yes—
53#10597376D412yes—
54C4×C22⋊D19—42no—
55C4×C22⋊D19—42no—
56C2×(C2×D19)⋊C4—21no—
57C2×(C2×D19)⋊C4—21no—
58C2×(C2×D19)⋊C4—21no—
59C2×(C2×D19)⋊C4—21no—
60C2×C4⋊Dic19D411yescharacteristic
61C2×C4⋊Dic19D411yescharacteristic
62C2×C4⋊Dic19D411yescharacteristic
63C2×Dic19⋊C4—21no—
64C2×C4×Dic19—21no—
65C22×C19⋊C8—21no—
66C22×C19⋊C8—21no—
67C19×#95—21no—
68C19×#95—21no—
69C19×#95—21no—
70C19×#95—21no—
71C19×#95—42no—
72C19×#95—42no—
73#10597292—24no—
74#10597292—42no—
75#10597292—42no—
76C19⋊#95—21no—
77C19⋊#95—21no—
78C19⋊#95—21no—
79C22⋊(C19⋊C8)—21no—
80C22⋊(C19⋊C8)—21no—
81C22⋊(C19⋊C8)—21no—
82C22⋊(C19⋊C8)C2×C412yescomplemented
83C24×C19C2×D411yescharacteristic
84C23×D19—21no—
85C2×Q8×C19—22no—
86C2×Q8×C19—22no—
87C2×Q8×C19—22no—
88C2×Q8×C19—22no—
89C2×Q8×C19—22no—
90C2×Q8×C19—22no—
91C2×Q8×C19—44no—
92C2×Q8×C19—41no—
93C2×Q8×C19—41no—
94C2×Q8×C19—41no—
95C2×Q8×C19—41no—
96C2×Q8×C19—44no—
97C2×Q8×C19—44no—
98C2×Q8×C19—44no—
99C2×Q8×C19—41no—
100C2×Q8×C19—41no—
101C22×C4×C19—22no—
102C22×C4×C19—22no—
103C22×C4×C19—22no—
104C22×C4×C19—21no—
105C22×C4×C19—21no—
106C22×C4×C19—22no—
107C22×C4×C19—21no—
108C22×C4×C19—21no—
109C22×C4×C19—21no—
110C22×C4×C19—41no—
111C22×C4×C19—41no—
112C22×C4×C19—41no—
113C22×C4×C19—41no—
114C22×C4×C19—41no—
115C22×C4×C19—41no—
116C22×C4×C19—41no—
117C22×C4×C19—41no—
118C22×C4×C19—41no—
119C22×C4×C19—41no—
120C22×C4×C19—41no—
121C22×C4×C19—41no—
122C22×C4×C19—41no—
123C22×C4×C19—41no—
124C22×C4×C19—41no—
125C22×C4×C19—41no—
126C22×C4×C19SD1612yescomplemented
127C22×C4×C19C22×C411yescharacteristic
128C22×C4×C19C2×D411yescharacteristic
129C22×C4×C19C2×D411yescharacteristic
130C22×C4×C19C2×D411yescharacteristic
131C22×C4×C19#4111yescharacteristic
132C22×C4×C19#4111yescharacteristic
133C2×C22⋊D19—22no—
134C2×C22⋊D19—22no—
135C2×C22⋊D19—41no—
136C2×C22⋊D19—41no—
137C2×C22⋊D19—41no—
138C2×C22⋊D19—41no—
139C22×Dic19—21no—
140C22×Dic19—21no—
141C22×Dic19—21no—
142C2×D76—21no—
143C2×D76—41no—
144C2×D76—41no—
145C2×D76C22⋊C412yes—
146C2×C4×D19—42no—
147C2×C4×D19—81no—
148C2×C4×D19—81no—
149C22⋊Dic19—41no—
150C22⋊Dic19—41no—
151#64527—48no—
152(C2×D19)⋊C4—22no—
153(C2×D19)⋊C4—22no—
154(C2×D19)⋊C4—42no—
155(C2×D19)⋊C4—81no—
156(C2×D19)⋊C4—81no—
157C4⋊Dic19—21no—
158C4⋊Dic19—41no—
159C4⋊Dic19—41no—
160C4⋊Dic19C22⋊C412yes—
161Dic19⋊C4—42no—
162C4×Dic19—42no—
163C2×C19⋊C8—22no—
164C2×C19⋊C8—41no—
165C2×C19⋊C8—41no—
166C2×C19⋊C8—41no—
167C2×C19⋊C8—41no—
168C2×C19⋊C8—41no—
169#9039—191nomaximal, Sylow
170C23×C19—21no—
171C23×C19—21no—
172C23×C19—21no—
173C23×C19—21no—
174C23×C19C4×D411yescharacteristic
175C23×C19#12011yescharacteristic
176C23×C19#12111yescharacteristic
177C23×C19C2×SD1611yescharacteristic
178C23×C19#13511yescharacteristic
179C23×C19AGL(1,ℤ/8)11yescharacteristic
180C23×C19#13711yescharacteristic
181C22×D19—22no—
182C22×D19—41no—
183C22×D19—41no—
184C22×D19—41no—
185C22×D19—41no—
186C22×D19—41no—
187C22×D19—41no—
188Q8×C19—24no—
189Q8×C19—24no—
190Q8×C19—42no—
191Q8×C19—42no—
192Q8×C19—42no—
193Q8×C19—42no—
194Q8×C19—42no—
195Q8×C19—42no—
196C2×C4×C19—21no—
197C2×C4×C19—21no—
198C2×C4×C19—21no—
199C2×C4×C19—21no—
200C2×C4×C19—24no—
201C2×C4×C19—22no—
202C2×C4×C19—41no—
203C2×C4×C19—41no—
204C2×C4×C19—41no—
205C2×C4×C19—41no—
206C2×C4×C19—42no—
207C2×C4×C19—42no—
208C2×C4×C19—42no—
209C2×C4×C19—42no—
210C2×C4×C19—41no—
211C2×C4×C19—41no—
212C2×C4×C19—42no—
213C2×C4×C19—42no—
214C2×C4×C19—42no—
215C2×C4×C19—42no—
216C2×C4×C19—42no—
217C2×C4×C19—42no—
218C2×C4×C19—42no—
219C2×C4×C19—41no—
220C2×C4×C19—41no—
221C2×C4×C19—41no—
222C2×C4×C19—81no—
223C2×C4×C19—81no—
224C2×C4×C19—81no—
225C2×C4×C19—81no—
226C2×C4×C19—81no—
227C2×C4×C19—81no—
228C2×C4×C19C2×C22⋊C411yescharacteristic
229C2×C4×C19C4×D411yescharacteristic
230C2×C4×C19#12111yescharacteristic
231C2×C4×C19#12311yescharacteristic
232C22⋊D19—42no—
233C22⋊D19—42no—
234C22⋊D19—42no—
235C22⋊D19—42no—
236C2×Dic19—22no—
237C2×Dic19—41no—
238C2×Dic19—41no—
239C2×Dic19—41no—
240C2×Dic19—41no—
241C2×Dic19—41no—
242C2×Dic19—41no—
243C2×Dic19—41no—
244C2×Dic19—41no—
245D76—42no—
246D76—81no—
247C4×D19—84no—
248C19⋊C8—42no—
249C19⋊C8—81no—
250C2×#448—191no—
251#2325—191no—
252#1787—191no—
253C2×#327—191no—
254#1446D1911yescharacteristic, complemented
255#1294—191no—
256#1280—191no—
257C22×C19—21no—
258C22×C19—21no—
259C22×C19—21no—
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#38611yescharacteristic
270C22×C19C4×SD1611yescharacteristic
271C22×C19#44011yescharacteristic
272C22×C19#45011yescharacteristic
273C22×C19#45211yescharacteristic
274C22×C19#45511yescharacteristic
275C22×C19#45611yescharacteristic
276C22×C19B(4,𝔽2)11yescharacteristic
277C22×C19B(4,𝔽2)11yescharacteristic
278C22×C19#46111yescharacteristic
279C22×C19#46311yescharacteristic
280C2×D19—42no—
281C2×D19—42no—
282C2×D19—42no—
283C2×D19—81no—
284C2×D19—81no—
285C2×D19—81no—
286C2×D19—81no—
287C4×C19—21no—
288C4×C19—21no—
289C4×C19—21no—
290C4×C19—21no—
291C4×C19—42no—
292C4×C19—44no—
293C4×C19—82no—
294C4×C19—81no—
295Dic19—42no—
296Dic19—81no—
297Dic19—81no—
298C23×Q8C2×D1911yescharacteristic
299C22×SD16—381no—
300C2×#121—191no—
301C2×C4×D4—381no—
302#448—194no—
303#448—382no—
304C2×#103—381no—
305C2×#103—381no—
306C2×#103—381no—
307C2×C22⋊C8—191no—
308C2×C22⋊C8—191no—
309#388—381no—
310#387—381no—
311#386—381no—
312#386—381no—
313#385—381no—
314#380—191no—
315C2×#95—21no—
316C2×#95—21no—
317C2×#95C2×D1911yescharacteristic
318C2×#95C2×D1911yescharacteristic
319#327—382no—
320C2×C19—21no—
321C2×C19—21no—
322C2×C19—21no—
323C2×C19—21no—
324C2×C19#160111yescharacteristic
325C2×C19#160311yescharacteristic
326C2×C19#160411yescharacteristic
327C2×C19#160611yescharacteristic
328C2×C19#187711yescharacteristic
329C2×C19#188211yescharacteristic
330C2×C19#188911yescharacteristic
331D19—82no—
332C22×Q8—21no—
333C22×Q8—21no—
334C22×Q8—21no—
335C22×Q8—21no—
336C22×Q8—21no—
337C22×Q8—42no—
338C22×Q8—42no—
339C22×Q8C4×D1912yescomplemented
340C22×D4—191no—
341C22×D4—381no—
342C23×C4—21no—
343C23×C4—21no—
344C23×C4—381no—
345C23×C4C22⋊D1911yescharacteristic
346C23×C4C22⋊D1911yescharacteristic
347C23×C4C22×D1911yescharacteristic
348C2×SD16—384no—
349C2×SD16—762no—
350C2×SD16—762no—
351C22×C8—381no—
352C22×C8—381no—
353#121—192no—
354#121—192no—
355#121—381no—
356#121—381no—
357C4×D4—762no—
358C4×D4—762no—
359C2×C4⋊C4—191no—
360C2×C4⋊C4—191no—
361C2×C4⋊C4—191no—
362C2×C4⋊C4—381no—
363C2×C22⋊C4—381no—
364C2×C22⋊C4—381no—
365C2×C22⋊C4—381no—
366C2×C22⋊C4—381no—
367C2×C22⋊C4—381no—
368C2×C42—381no—
369#103—384no—
370#103—762no—
371#103—762no—
372C22⋊C8—192no—
373C22⋊C8—381no—
374C22⋊C8—381no—
375C22⋊C8—381no—
376#95—21no—
377#95—21no—
378#95—21no—
379#95—21no—
380#95—42no—
381#95—42no—
382#95—381no—
383#95—381no—
384#95—381no—
385C19#903911yescharacteristic, complemented, Sylow
386C24—381no—
387C24C2×C22⋊D1911yescharacteristic
388C2×Q8—22no—
389C2×Q8—22no—
390C2×Q8—22no—
391C2×Q8—22no—
392C2×Q8—22no—
393C2×Q8—22no—
394C2×Q8—44no—
395C2×Q8—41no—
396C2×Q8—41no—
397C2×Q8—41no—
398C2×Q8—41no—
399C2×Q8—44no—
400C2×Q8—44no—
401C2×Q8—44no—
402C2×Q8—41no—
403C2×Q8—41no—
404C2×D4—192no—
405C2×D4—382no—
406C2×D4—382no—
407C2×D4—381no—
408C2×D4—761no—
409C2×D4—761no—
410C2×D4—761no—
411C2×D4—761no—
412C2×D4—761no—
413C2×D4—761no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—21no—
417C22×C4—22no—
418C22×C4—21no—
419C22×C4—22no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—41no—
424C22×C4—41no—
425C22×C4—41no—
426C22×C4—41no—
427C22×C4—41no—
428C22×C4—41no—
429C22×C4—41no—
430C22×C4—41no—
431C22×C4—41no—
432C22×C4—41no—
433C22×C4—41no—
434C22×C4—41no—
435C22×C4—41no—
436C22×C4—41no—
437C22×C4—41no—
438C22×C4—41no—
439C22×C4—381no—
440C22×C4—381no—
441C22×C4—381no—
442C22×C4—762no—
443C22×C4—1521no—
444C22×C4—1521no—
445C22×C4#6452712yescomplemented
446C22×C4C2×C4×D1911yescharacteristic
447C22×C4#6454111yescharacteristic
448C22×C4D4×D1911yescharacteristic
449C22×C4D4×D1911yescharacteristic
450C22×C4D4×D1911yescharacteristic
451C22×C4#6454311yescharacteristic
452SD16—768no—
453C2×C8—382no—
454C2×C8—761no—
455C2×C8—761no—
456C2×C8—761no—
457C2×C8—761no—
458C2×C8—761no—
459C4⋊C4—192no—
460C4⋊C4—381no—
461C4⋊C4—761no—
462C4⋊C4—761no—
463C4⋊C4—762no—
464C22⋊C4—382no—
465C22⋊C4—382no—
466C22⋊C4—762no—
467C22⋊C4—761no—
468C22⋊C4—761no—
469C22⋊C4—1521no—
470C22⋊C4—1521no—
471C42—762no—
472C23—21no—
473C23—21no—
474C23—21no—
475C23—21no—
476C23—382no—
477C23—761no—
478C23—761no—
479C23—761no—
480C23—761no—
481C23—761no—
482C23—761no—
483C23C4×C22⋊D1911yescharacteristic
484C23#1059738311yescharacteristic
485C23#1059738411yescharacteristic
486C23C2×#6452711yescharacteristic
487C23#1059738811yescharacteristic
488C23#1059739511yescharacteristic
489C23#1059739611yescharacteristic
490Q8—24no—
491Q8—24no—
492Q8—42no—
493Q8—42no—
494Q8—42no—
495Q8—42no—
496Q8—42no—
497Q8—42no—
498D4—762no—
499D4—762no—
500D4—762no—
501D4—762no—
502D4—762no—
503D4—1521no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—24no—
509C2×C4—22no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—41no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—41no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—81no—
531C2×C4—81no—
532C2×C4—81no—
533C2×C4—81no—
534C2×C4—81no—
535C2×C4—81no—
536C2×C4—382no—
537C2×C4—761no—
538C2×C4—761no—
539C2×C4—761no—
540C2×C4—761no—
541C2×C4—761no—
542C2×C4—761no—
543C2×C4—761no—
544C2×C4—761no—
545C2×C4—1524no—
546C2×C4C22⋊C4×D1911yescharacteristic
547C2×C4(C22⋊D19)⋊C411yescharacteristic
548C2×C4#1059732911yescharacteristic
549C2×C4#1059733011yescharacteristic
550C8—762no—
551C8—1521no—
552C22—21no—
553C22—21no—
554C22—21no—
555C22—21no—
556C22—21no—
557C22—21no—
558C22—21no—
559C22—21no—
560C22—21no—
561C22—21no—
562C22—21no—
563C22—21no—
564C22—762no—
565C22—762no—
566C22—762no—
567C22—1521no—
568C22—1521no—
569C22—1521no—
570C22—1521no—
571C22#1192642011yescharacteristic
572C22C4×#6452711yescharacteristic
573C22#1192664211yescharacteristic
574C22#1192669411yescharacteristic
575C22#1192670411yescharacteristic
576C22#1192672111yescharacteristic
577C22#1192672611yescharacteristic
578C22#1192673011yescharacteristic
579C22#1192673011yescharacteristic
580C22#1192674611yescharacteristic
581C22#1192675611yescharacteristic
582C4—21no—
583C4—21no—
584C4—21no—
585C4—21no—
586C4—42no—
587C4—44no—
588C4—82no—
589C4—81no—
590C4—762no—
591C4—1521no—
592C4—1521no—
593C2—21no—
594C2—21no—
595C2—21no—
596C2—21no—
597C2—1522no—
598C2#1456258611yescharacteristic
599C2#1456259611yescharacteristic
600C2#1456260311yescharacteristic
601C2#1456261311yescharacteristic
602C2#1456397211yescharacteristic
603C2#1456400711yescharacteristic
604C2#1456404011yescharacteristic
subgroupG/H
centerC23#10597383
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#1446C2
socleC23×C19#120
prime radicalC2×#10597376C22
cosocleC23×C4×C19C23
hypercenter#1446D19
hypocenterC19#9039
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1446

Complements

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

NH ≅ G/Ntype
3. #14563570C2semidirect
5. #14561514C2semidirect
6. #14561478C2semidirect
7. C19×#1446C2semidirect
12. #11926683C4semidirect
37. C22×Q8×C19C2×C4semidirect
82. C22⋊(C19⋊C8)C2×C4semidirect
126. C22×C4×C19SD16semidirect
254. #1446D19semidirect
339. C22×Q8C4×D19semidirect
385. C19#9039semidirect
445. C22×C4#64527semidirect

Maximal subgroups

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

subgroupindex
C2×#119266832
#145663382
#145635702
C2×#119262772
#145615142
#145614782
C19×#14462
#903919