Finite Group Databasebeta

← #18074817

Subgroups — #18074817

Order 4864.

828 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14564621C211yesmaximal, characteristic, complemented
2#14564104C211yesmaximal, characteristic, complemented
3#14564074C211yesmaximal, characteristic, complemented
4#14563938C211yesmaximal, characteristic, complemented
5#14562178C211yesmaximal, characteristic, complemented
6#14562151C211yesmaximal, characteristic, complemented
7C19×#3536C211yesmaximal, characteristic
8C22×#64520C2211yescharacteristic
9C2×#10597294—21no—
10C2×#10597289—21no—
11C2×#10597293—21no—
12#11926508C2211yescharacteristic
13#11926404C2211yescharacteristic
14C4×C22⋊Dic19C2211yescharacteristic
15#11926313—21no—
16#11926311—22no—
17#11926306—21no—
18#11926303—21no—
19#11926281—21no—
20#11926278—22no—
21#11926278—21no—
22C19×#562—22no—
23C19×#554—21no—
24C19×#548—21no—
25C19×#547—21no—
26C19×#546—21no—
27C19×#546—22no—
28C19×#543—21no—
29C19×#542—21no—
30C19×#539C412yescomplemented
31C19×#538—21no—
32C19×#537—21no—
33C19×#537C412yescomplemented
34C19×#525C2211yescharacteristic
35C2×C19×C22⋊Q8C2211yescharacteristic
36C2×C19×#121C2211yescharacteristic
37C2×#41×C19—21no—
38C2×#41×C19—22no—
39C2×#41×C19D411yescharacteristic
40C22×Q8×C19D411yescharacteristic
41C22×D4×C19—21no—
42C22×D4×C19D411yescharacteristic
43C23×C4×C19C2311yescharacteristic
44C19×C4⋊Q8—21no—
45C19×#126—22no—
46C19×#125—22no—
47C19×#124—22no—
48C19×#124—21no—
49C19×#124—22no—
50C19×#123—22no—
51C19×#123—22no—
52C19×#123—22no—
53C19×#123—22no—
54C19×#123—21no—
55C19×C22⋊Q8—21no—
56C19×C22⋊Q8—22no—
57C19×C22⋊Q8—22no—
58C19×C22⋊Q8—22no—
59C19×C22⋊Q8—22no—
60C19×C22⋊Q8—21no—
61C19×C22⋊Q8—21no—
62C19×C22⋊Q8—21no—
63C19×C22⋊Q8—21no—
64C19×C22⋊Q8—22no—
65C19×C22⋊Q8—22no—
66C19×C22⋊Q8C2×C411yescharacteristic
67C19×C22⋊Q8D411yescharacteristic
68C19×#121—21no—
69C19×#121—22no—
70C19×#121—22no—
71C19×#121—22no—
72C19×#121—22no—
73C19×#121—22no—
74C19×#121—21no—
75C19×#121—21no—
76C19×#121C2×C412yes—
77C19×#121C2×C411yescharacteristic
78C19×#121D412yes—
79C19×#121D411yescharacteristic
80C19×#120—22no—
81C19×#120—21no—
82C4×Q8×C19—21no—
83C4×D4×C19—22no—
84C4×D4×C19—21no—
85C4×D4×C19—22no—
86C4×D4×C19—21no—
87C4×D4×C19—21no—
88C19×#117D411yescharacteristic
89C2×C4⋊C4×C19—21no—
90C2×C4⋊C4×C19C2×C412yes—
91C2×C4⋊C4×C19D411yescharacteristic
92C2×C4⋊C4×C19D411yescharacteristic
93C2×C22⋊C4×C19—22no—
94C2×C22⋊C4×C19—21no—
95C2×C22⋊C4×C19D412yes—
96C2×C22⋊Dic19—21no—
97C2×C22⋊Dic19—21no—
98C2×C4⋊Dic19—21no—
99C2×C4×Dic19—21no—
100C2×#64520—21no—
101C2×#64520—21no—
102C2×#64520—21no—
103C2×#64520—42no—
104C22×C19⋊C8—21no—
105#10597294—42no—
106#10597293—42no—
107#10597289—42no—
108C19⋊#95—21no—
109C19⋊#95—21no—
110C22⋊(C19⋊C8)—21no—
111C22⋊(C19⋊C8)—21no—
112C24×C19—21no—
113C24×C19C2×D411yescharacteristic
114#41×C19—41no—
115#41×C19—41no—
116#41×C19—84no—
117#41×C19—81no—
118#41×C19—81no—
119C2×Q8×C19—22no—
120C2×Q8×C19—21no—
121C2×Q8×C19—21no—
122C2×Q8×C19—41no—
123C2×Q8×C19—41no—
124C2×Q8×C19C22⋊C411yescharacteristic
125C2×D4×C19—21no—
126C2×D4×C19—22no—
127C2×D4×C19—21no—
128C2×D4×C19—22no—
129C2×D4×C19—22no—
130C2×D4×C19—21no—
131C2×D4×C19—22no—
132C2×D4×C19—21no—
133C2×D4×C19—41no—
134C2×D4×C19—41no—
135C2×D4×C19—82no—
136C2×D4×C19C22⋊C411yescharacteristic
137C2×D4×C19C22⋊C412yes—
138C22×C4×C19—22no—
139C22×C4×C19—22no—
140C22×C4×C19—22no—
141C22×C4×C19—21no—
142C22×C4×C19—21no—
143C22×C4×C19—41no—
144C22×C4×C19—41no—
145C22×C4×C19C22⋊C412yes—
146C22×C4×C19C22⋊C412yes—
147C22×C4×C19C22×C411yescharacteristic
148C22×C4×C19C2×D411yescharacteristic
149C22×C4×C19C2×D411yescharacteristic
150C22×C4×C19C2×D411yescharacteristic
151C22×C4×C19C2×D411yescharacteristic
152C22×C4×C19C2×D411yescharacteristic
153C22×Dic19—41no—
154C22×Dic19—41no—
155C4⋊C4×C19—22no—
156C4⋊C4×C19—22no—
157C4⋊C4×C19—22no—
158C4⋊C4×C19—22no—
159C4⋊C4×C19—22no—
160C4⋊C4×C19—22no—
161C4⋊C4×C19—21no—
162C4⋊C4×C19—21no—
163C4⋊C4×C19—21no—
164C4⋊C4×C19—21no—
165C4⋊C4×C19—21no—
166C4⋊C4×C19C22⋊C412yes—
167C4⋊C4×C19C22⋊C411yescharacteristic
168C4⋊C4×C19C22⋊C411yescharacteristic
169C22⋊C4×C19—22no—
170C22⋊C4×C19—22no—
171C22⋊C4×C19—22no—
172C22⋊C4×C19—22no—
173C22⋊C4×C19—22no—
174C22⋊C4×C19—21no—
175C22⋊C4×C19—21no—
176C22⋊C4×C19—22no—
177C22⋊C4×C19—22no—
178C22⋊C4×C19—21no—
179C22⋊C4×C19—22no—
180C22⋊C4×C19—21no—
181C22⋊C4×C19—22no—
182C22⋊C4×C19—21no—
183C42×C19—22no—
184C42×C19—21no—
185C22⋊Dic19—22no—
186C22⋊Dic19—41no—
187C22⋊Dic19—42no—
188C4⋊Dic19—41no—
189C4⋊Dic19—41no—
190C4×Dic19—41no—
191C4×Dic19—41no—
192#64520—22no—
193#64520—22no—
194#64520—41no—
195#64520—41no—
196#64520—41no—
197#64520—41no—
198C2×C19⋊C8—22no—
199C2×C19⋊C8—41no—
200C2×C19⋊C8—41no—
201C2×C19⋊C8—41no—
202#8480—191nomaximal, Sylow
203C23×C19—21no—
204C23×C19—21no—
205C23×C19—22no—
206C23×C19—21no—
207C23×C19—41no—
208C23×C19—41no—
209C23×C19—41no—
210C23×C19—41no—
211C23×C19—81no—
212C23×C19—81no—
213C23×C19C2×C22⋊C411yescharacteristic
214C23×C19#12011yescharacteristic
215C23×C19#12011yescharacteristic
216Q8×C19—41no—
217Q8×C19—41no—
218Q8×C19—41no—
219Q8×C19—81no—
220Q8×C19—82no—
221D4×C19—42no—
222D4×C19—41no—
223D4×C19—44no—
224D4×C19—42no—
225D4×C19—41no—
226D4×C19—41no—
227D4×C19—41no—
228D4×C19—41no—
229D4×C19—82no—
230D4×C19—81no—
231D4×C19—82no—
232D4×C19—82no—
233C2×C4×C19—21no—
234C2×C4×C19—21no—
235C2×C4×C19—21no—
236C2×C4×C19—21no—
237C2×C4×C19—21no—
238C2×C4×C19—21no—
239C2×C4×C19—21no—
240C2×C4×C19—22no—
241C2×C4×C19—21no—
242C2×C4×C19—22no—
243C2×C4×C19—21no—
244C2×C4×C19—22no—
245C2×C4×C19—41no—
246C2×C4×C19—41no—
247C2×C4×C19—41no—
248C2×C4×C19—41no—
249C2×C4×C19—41no—
250C2×C4×C19—42no—
251C2×C4×C19—42no—
252C2×C4×C19—81no—
253C2×C4×C19—82no—
254C2×C4×C19—82no—
255C2×C4×C19—82no—
256C2×C4×C19C2×C22⋊C411yescharacteristic
257C2×C4×C19C2×C22⋊C411yescharacteristic
258C2×C4×C19#12011yescharacteristic
259C2×C4×C19#12011yescharacteristic
260C2×Dic19—42no—
261C2×Dic19—81no—
262C2×Dic19—81no—
263C2×Dic19—81no—
264C2×Dic19—81no—
265C2×Dic19—81no—
266C19⋊C8—42no—
267C19⋊C8—81no—
268#3536D1911yescharacteristic
269#1996—191no—
270#1901—191no—
271#1895—191no—
272#1871—191no—
273#1513—191no—
274#1507—191no—
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—41no—
284C22×C19—42no—
285C22×C19—41no—
286C22×C19—42no—
287C22×C19—41no—
288C22×C19—42no—
289C22×C19—81no—
290C22×C19—81no—
291C22×C19—161no—
292C22×C19—161no—
293C22×C19#37911yescharacteristic
294C22×C19#45411yescharacteristic
295C22×C19#45611yescharacteristic
296C4×C19—21no—
297C4×C19—21no—
298C4×C19—21no—
299C4×C19—41no—
300C4×C19—42no—
301C4×C19—42no—
302C4×C19—41no—
303C4×C19—41no—
304C4×C19—42no—
305C4×C19B(4,𝔽2)11yescharacteristic
306C4×C19#45811yescharacteristic
307Dic19—82no—
308Dic19—161no—
309C22×M16—191no—
310#562—22no—
311#554—21no—
312#548—21no—
313#547—21no—
314#546—21no—
315#546—22no—
316#543—21no—
317#542—21no—
318#539Dic1912yescomplemented
319#538—21no—
320#537—21no—
321#537Dic1912yescomplemented
322#525C2×D1911yescharacteristic
323C2×C22⋊Q8C2×D1911yescharacteristic
324C2×#121C2×D1911yescharacteristic
325C2×#104—381no—
326C2×#102—381no—
327C2×#101—381no—
328#407—191no—
329#380—191no—
330C4×C22⋊C4—191no—
331#343—381no—
332#342—382no—
333#340—381no—
334#339—381no—
335#328—381no—
336#327—382no—
337#327—381no—
338C2×C19—21no—
339C2×C19—21no—
340C2×C19—41no—
341C2×C19—41no—
342C2×C19—81no—
343C2×C19—82no—
344C2×C19#179011yescharacteristic
345C2×C19#179311yescharacteristic
346C2×C19#179511yescharacteristic
347C2×#41—21no—
348C2×#41—22no—
349C2×#41C22⋊D1911yescharacteristic
350C22×Q8C22⋊D1911yescharacteristic
351C22×D4—21no—
352C22×D4C22⋊D1911yescharacteristic
353C23×C4C22×D1911yescharacteristic
354C2×M16—381no—
355C2×M16—381no—
356C2×M16—381no—
357C2×M16—762no—
358C22×C8—381no—
359C4⋊Q8—21no—
360#126—22no—
361#125—22no—
362#124—22no—
363#124—21no—
364#124—22no—
365#123—22no—
366#123—22no—
367#123—22no—
368#123—22no—
369#123—21no—
370C22⋊Q8—21no—
371C22⋊Q8—22no—
372C22⋊Q8—22no—
373C22⋊Q8—22no—
374C22⋊Q8—22no—
375C22⋊Q8—21no—
376C22⋊Q8—21no—
377C22⋊Q8—21no—
378C22⋊Q8—21no—
379C22⋊Q8—22no—
380C22⋊Q8—22no—
381C22⋊Q8C2×Dic1911yescharacteristic
382C22⋊Q8C22⋊D1911yescharacteristic
383#121—21no—
384#121—22no—
385#121—22no—
386#121—22no—
387#121—22no—
388#121—22no—
389#121—21no—
390#121—21no—
391#121C2×Dic1912yes—
392#121C2×Dic1911yescharacteristic
393#121C22⋊D1912yes—
394#121C22⋊D1911yescharacteristic
395#120—22no—
396#120—21no—
397C4×Q8—21no—
398C4×D4—22no—
399C4×D4—21no—
400C4×D4—22no—
401C4×D4—21no—
402C4×D4—21no—
403#117C22⋊D1911yescharacteristic
404C2×C4⋊C4—21no—
405C2×C4⋊C4—381no—
406C2×C4⋊C4C2×Dic1912yes—
407C2×C4⋊C4C22⋊D1911yescharacteristic
408C2×C4⋊C4C22⋊D1911yescharacteristic
409C2×C22⋊C4—22no—
410C2×C22⋊C4—21no—
411C2×C22⋊C4—381no—
412C2×C22⋊C4—381no—
413C2×C22⋊C4C22⋊D1912yes—
414C2×C42—381no—
415#104—762no—
416#102—762no—
417#101—762no—
418C22⋊C8—381no—
419C22⋊C8—381no—
420#95—381no—
421#95—381no—
422C19#848011yescharacteristic, complemented, Sylow
423C24—21no—
424C24C2×C22⋊D1911yescharacteristic
425#41—41no—
426#41—41no—
427#41—84no—
428#41—81no—
429#41—81no—
430C2×Q8—22no—
431C2×Q8—21no—
432C2×Q8—21no—
433C2×Q8—41no—
434C2×Q8—41no—
435C2×Q8C22⋊Dic1911yescharacteristic
436C2×D4—21no—
437C2×D4—22no—
438C2×D4—21no—
439C2×D4—22no—
440C2×D4—22no—
441C2×D4—21no—
442C2×D4—22no—
443C2×D4—21no—
444C2×D4—41no—
445C2×D4—41no—
446C2×D4—82no—
447C2×D4C22⋊Dic1911yescharacteristic
448C2×D4C22⋊Dic1912yes—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—41no—
455C22×C4—41no—
456C22×C4—761no—
457C22×C4—761no—
458C22×C4C22⋊Dic1912yes—
459C22×C4C22⋊Dic1912yes—
460C22×C4C22×Dic1911yescharacteristic
461C22×C4C2×C22⋊D1911yescharacteristic
462C22×C4C2×C22⋊D1911yescharacteristic
463C22×C4C2×C22⋊D1911yescharacteristic
464C22×C4C2×C22⋊D1911yescharacteristic
465C22×C4C2×C22⋊D1911yescharacteristic
466M16—382no—
467M16—382no—
468M16—761no—
469M16—761no—
470M16—761no—
471M16—761no—
472C2×C8—382no—
473C2×C8—761no—
474C2×C8—761no—
475C2×C8—761no—
476C4⋊C4—22no—
477C4⋊C4—22no—
478C4⋊C4—22no—
479C4⋊C4—22no—
480C4⋊C4—22no—
481C4⋊C4—22no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—761no—
488C4⋊C4—761no—
489C4⋊C4C22⋊Dic1912yes—
490C4⋊C4C22⋊Dic1911yescharacteristic
491C4⋊C4C22⋊Dic1911yescharacteristic
492C22⋊C4—22no—
493C22⋊C4—22no—
494C22⋊C4—22no—
495C22⋊C4—22no—
496C22⋊C4—22no—
497C22⋊C4—21no—
498C22⋊C4—21no—
499C22⋊C4—22no—
500C22⋊C4—22no—
501C22⋊C4—21no—
502C22⋊C4—22no—
503C22⋊C4—21no—
504C22⋊C4—22no—
505C22⋊C4—21no—
506C22⋊C4—382no—
507C22⋊C4—761no—
508C22⋊C4—762no—
509C42—22no—
510C42—21no—
511C42—761no—
512C42—761no—
513C23—21no—
514C23—21no—
515C23—22no—
516C23—21no—
517C23—41no—
518C23—41no—
519C23—41no—
520C23—41no—
521C23—81no—
522C23—81no—
523C23C2×C22⋊Dic1911yescharacteristic
524C23#1059739911yescharacteristic
525C23#1059739911yescharacteristic
526Q8—41no—
527Q8—41no—
528Q8—41no—
529Q8—81no—
530Q8—82no—
531D4—42no—
532D4—41no—
533D4—44no—
534D4—42no—
535D4—41no—
536D4—41no—
537D4—41no—
538D4—41no—
539D4—82no—
540D4—81no—
541D4—82no—
542D4—82no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—22no—
551C2×C4—21no—
552C2×C4—22no—
553C2×C4—21no—
554C2×C4—22no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—81no—
563C2×C4—82no—
564C2×C4—82no—
565C2×C4—82no—
566C2×C4—762no—
567C2×C4—1521no—
568C2×C4—1521no—
569C2×C4—1521no—
570C2×C4—1521no—
571C2×C4—1521no—
572C2×C4C2×C22⋊Dic1911yescharacteristic
573C2×C4C2×C22⋊Dic1911yescharacteristic
574C2×C4#1059739911yescharacteristic
575C2×C4#1059739911yescharacteristic
576C8—762no—
577C8—1521no—
578C22—21no—
579C22—21no—
580C22—21no—
581C22—21no—
582C22—21no—
583C22—21no—
584C22—21no—
585C22—21no—
586C22—41no—
587C22—42no—
588C22—41no—
589C22—42no—
590C22—41no—
591C22—42no—
592C22—81no—
593C22—81no—
594C22—161no—
595C22—161no—
596C22#1192640011yescharacteristic
597C22#1192671711yescharacteristic
598C22#1192672711yescharacteristic
599C4—21no—
600C4—21no—
601C4—21no—
602C4—41no—
603C4—42no—
604C4—42no—
605C4—41no—
606C4—41no—
607C4—42no—
608C4—3041no—
609C4—1522no—
610C4#1192673111yescharacteristic
611C4#1192673411yescharacteristic
612C2—21no—
613C2—21no—
614C2—41no—
615C2—41no—
616C2—82no—
617C2—81no—
618C2#1456358311yescharacteristic
619C2#1456359411yescharacteristic
620C2#1456360511yescharacteristic
subgroupG/H
centerC22#11926400
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
Fitting, prime radicalC19×#3536C2
socleC22×C19#379
cosocleC23×C4×C19C23
hypercenter#3536D19
hypocenterC19#8480
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3536

Complements

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

NH ≅ G/Ntype
1. #14564621C2semidirect
2. #14564104C2semidirect
3. #14564074C2semidirect
4. #14563938C2semidirect
5. #14562178C2semidirect
6. #14562151C2semidirect
30. C19×#539C4semidirect
33. C19×#537C4semidirect
318. #539Dic19semidirect
321. #537Dic19semidirect
422. C19#8480semidirect

Maximal subgroups

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

subgroupindex
#145646212
#145641042
#145640742
#145639382
#145621782
#145621512
C19×#35362
#848019