Finite Group Databasebeta

← #18074824

Subgroups — #18074824

Order 4864.

844 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14564472C211yesmaximal, characteristic, complemented
2#14564099C211yesmaximal, characteristic, complemented
3#14564069C211yesmaximal, characteristic, complemented
4#14563938C211yesmaximal, characteristic, complemented
5#14562178C211yesmaximal, characteristic, complemented
6#14562155C211yesmaximal, characteristic, complemented
7C19×#3536C211yesmaximal, characteristic
8C22×#64520C2211yescharacteristic
9C2×#10597294—21no—
10C2×#10597292—21no—
11C2×#10597290—21no—
12C2×#10597291—22no—
13#11926508C2211yescharacteristic
14#11926404C2211yescharacteristic
15C4×C22⋊Dic19C2211yescharacteristic
16#11926313—21no—
17#11926306—21no—
18#11926303—21no—
19#11926281—22no—
20#11926281—21no—
21#11926278—21no—
22C19×#562—22no—
23C19×#554—21no—
24C19×#548—21no—
25C19×#547—21no—
26C19×#546—21no—
27C19×#546—22no—
28C19×#543C412yescomplemented
29C19×#542—21no—
30C19×#539—21no—
31C19×#538C412yescomplemented
32C19×#537—21no—
33C19×#537—21no—
34C19×#525C2211yescharacteristic
35C2×C19×C22⋊Q8C2211yescharacteristic
36C2×C19×#121C2211yescharacteristic
37C2×#41×C19—22no—
38C2×#41×C19—21no—
39C2×#41×C19D411yescharacteristic
40C22×Q8×C19D411yescharacteristic
41C22×D4×C19D412yes—
42C22×D4×C19D411yescharacteristic
43C23×C4×C19C2311yescharacteristic
44C19×C4⋊Q8—21no—
45C19×#126—22no—
46C19×#125—22no—
47C19×#124—21no—
48C19×#124—22no—
49C19×#124—22no—
50C19×#123—22no—
51C19×#123—22no—
52C19×#123—22no—
53C19×#123—21no—
54C19×#123—22no—
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—22no—
63C19×C22⋊Q8—22no—
64C19×C22⋊Q8C2×C412yes—
65C19×C22⋊Q8C2×C411yescharacteristic
66C19×C22⋊Q8D412yes—
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×#121—21no—
77C19×#121—21no—
78C19×#121C2×C411yescharacteristic
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×C19—21no—
91C2×C4⋊C4×C19D411yescharacteristic
92C2×C4⋊C4×C19D411yescharacteristic
93C2×C22⋊C4×C19—22no—
94C2×C22⋊C4×C19—21no—
95C2×C22⋊C4×C19C2×C412yes—
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#10597292—42no—
107#10597291—44no—
108#10597290—42no—
109C19⋊#95—21no—
110C19⋊#95—21no—
111C22⋊(C19⋊C8)—21no—
112C22⋊(C19⋊C8)—21no—
113C24×C19C22⋊C412yes—
114C24×C19C2×D411yescharacteristic
115#41×C19—41no—
116#41×C19—41no—
117#41×C19—82no—
118#41×C19—82no—
119#41×C19—81no—
120#41×C19—81no—
121C2×Q8×C19—22no—
122C2×Q8×C19—21no—
123C2×Q8×C19—41no—
124C2×Q8×C19—41no—
125C2×Q8×C19C22⋊C411yescharacteristic
126C2×Q8×C19C22⋊C412yes—
127C2×D4×C19—21no—
128C2×D4×C19—21no—
129C2×D4×C19—22no—
130C2×D4×C19—22no—
131C2×D4×C19—22no—
132C2×D4×C19—21no—
133C2×D4×C19—22no—
134C2×D4×C19—21no—
135C2×D4×C19—21no—
136C2×D4×C19—41no—
137C2×D4×C19—41no—
138C2×D4×C19—42no—
139C2×D4×C19—42no—
140C2×D4×C19C22⋊C411yescharacteristic
141C22×C4×C19—21no—
142C22×C4×C19—22no—
143C22×C4×C19—22no—
144C22×C4×C19—22no—
145C22×C4×C19—21no—
146C22×C4×C19—21no—
147C22×C4×C19—41no—
148C22×C4×C19—41no—
149C22×C4×C19C22⋊C412yes—
150C22×C4×C19C22×C411yescharacteristic
151C22×C4×C19C2×D411yescharacteristic
152C22×C4×C19C2×D411yescharacteristic
153C22×C4×C19C2×D411yescharacteristic
154C22×C4×C19C2×D411yescharacteristic
155C22×C4×C19C2×D411yescharacteristic
156C22×Dic19—41no—
157C22×Dic19—41no—
158C4⋊C4×C19—22no—
159C4⋊C4×C19—22no—
160C4⋊C4×C19—22no—
161C4⋊C4×C19—22no—
162C4⋊C4×C19—22no—
163C4⋊C4×C19—21no—
164C4⋊C4×C19—21no—
165C4⋊C4×C19—21no—
166C4⋊C4×C19—22no—
167C4⋊C4×C19—21no—
168C4⋊C4×C19—21no—
169C4⋊C4×C19C22⋊C412yes—
170C4⋊C4×C19C22⋊C411yescharacteristic
171C4⋊C4×C19C22⋊C411yescharacteristic
172C22⋊C4×C19—22no—
173C22⋊C4×C19—22no—
174C22⋊C4×C19—22no—
175C22⋊C4×C19—22no—
176C22⋊C4×C19—22no—
177C22⋊C4×C19—22no—
178C22⋊C4×C19—21no—
179C22⋊C4×C19—22no—
180C22⋊C4×C19—21no—
181C22⋊C4×C19—21no—
182C22⋊C4×C19—22no—
183C22⋊C4×C19—22no—
184C22⋊C4×C19—21no—
185C22⋊C4×C19—21no—
186C42×C19—22no—
187C42×C19—21no—
188C22⋊Dic19—22no—
189C22⋊Dic19—41no—
190C22⋊Dic19—42no—
191C4⋊Dic19—41no—
192C4⋊Dic19—41no—
193C4×Dic19—41no—
194C4×Dic19—41no—
195#64520—22no—
196#64520—22no—
197#64520—41no—
198#64520—41no—
199#64520—41no—
200#64520—41no—
201C2×C19⋊C8—22no—
202C2×C19⋊C8—41no—
203C2×C19⋊C8—41no—
204C2×C19⋊C8—41no—
205#8481—191nomaximal, Sylow
206C23×C19—21no—
207C23×C19—21no—
208C23×C19—22no—
209C23×C19—21no—
210C23×C19—41no—
211C23×C19—41no—
212C23×C19—42no—
213C23×C19—42no—
214C23×C19—42no—
215C23×C19C2×C22⋊C411yescharacteristic
216C23×C19#12011yescharacteristic
217C23×C19#12011yescharacteristic
218Q8×C19—42no—
219Q8×C19—41no—
220Q8×C19—41no—
221Q8×C19—41no—
222Q8×C19—82no—
223D4×C19—41no—
224D4×C19—42no—
225D4×C19—42no—
226D4×C19—41no—
227D4×C19—42no—
228D4×C19—41no—
229D4×C19—41no—
230D4×C19—41no—
231D4×C19—81no—
232D4×C19—82no—
233D4×C19—81no—
234D4×C19—82no—
235D4×C19—82no—
236C2×C4×C19—21no—
237C2×C4×C19—21no—
238C2×C4×C19—21no—
239C2×C4×C19—21no—
240C2×C4×C19—21no—
241C2×C4×C19—21no—
242C2×C4×C19—21no—
243C2×C4×C19—22no—
244C2×C4×C19—21no—
245C2×C4×C19—22no—
246C2×C4×C19—21no—
247C2×C4×C19—22no—
248C2×C4×C19—41no—
249C2×C4×C19—41no—
250C2×C4×C19—41no—
251C2×C4×C19—41no—
252C2×C4×C19—41no—
253C2×C4×C19—41no—
254C2×C4×C19—41no—
255C2×C4×C19—42no—
256C2×C4×C19—81no—
257C2×C4×C19—82no—
258C2×C4×C19—82no—
259C2×C4×C19—82no—
260C2×C4×C19C2×C22⋊C411yescharacteristic
261C2×C4×C19C2×C22⋊C411yescharacteristic
262C2×C4×C19#12011yescharacteristic
263C2×C4×C19#12011yescharacteristic
264C2×Dic19—42no—
265C2×Dic19—81no—
266C2×Dic19—81no—
267C2×Dic19—81no—
268C2×Dic19—81no—
269C2×Dic19—81no—
270C19⋊C8—42no—
271C19⋊C8—81no—
272#3536D1911yescharacteristic
273#1964—191no—
274#1900—191no—
275#1894—191no—
276#1871—191no—
277#1513—191no—
278#1508—191no—
279C22×C19—21no—
280C22×C19—21no—
281C22×C19—21no—
282C22×C19—21no—
283C22×C19—21no—
284C22×C19—21no—
285C22×C19—21no—
286C22×C19—21no—
287C22×C19—41no—
288C22×C19—42no—
289C22×C19—41no—
290C22×C19—42no—
291C22×C19—41no—
292C22×C19—42no—
293C22×C19—81no—
294C22×C19—81no—
295C22×C19—162no—
296C22×C19#37911yescharacteristic
297C22×C19#45311yescharacteristic
298C22×C19#45511yescharacteristic
299C4×C19—21no—
300C4×C19—21no—
301C4×C19—21no—
302C4×C19—42no—
303C4×C19—42no—
304C4×C19—41no—
305C4×C19—41no—
306C4×C19—41no—
307C4×C19—42no—
308C4×C19B(4,𝔽2)11yescharacteristic
309C4×C19#45811yescharacteristic
310Dic19—82no—
311Dic19—161no—
312C22×M16—191no—
313#562—22no—
314#554—21no—
315#548—21no—
316#547—21no—
317#546—21no—
318#546—22no—
319#543Dic1912yescomplemented
320#542—21no—
321#539—21no—
322#538Dic1912yescomplemented
323#537—21no—
324#537—21no—
325#525C2×D1911yescharacteristic
326C2×C22⋊Q8C2×D1911yescharacteristic
327C2×#121C2×D1911yescharacteristic
328C2×#104—381no—
329C2×#103—381no—
330C2×#100—381no—
331C2×#99—382no—
332#407—191no—
333#380—191no—
334C4×C22⋊C4—191no—
335#343—381no—
336#340—381no—
337#339—381no—
338#328—382no—
339#328—381no—
340#327—381no—
341C2×C19—21no—
342C2×C19—21no—
343C2×C19—41no—
344C2×C19—41no—
345C2×C19—81no—
346C2×C19—82no—
347C2×C19#179011yescharacteristic
348C2×C19#179211yescharacteristic
349C2×C19#179611yescharacteristic
350C2×#41—22no—
351C2×#41—21no—
352C2×#41C22⋊D1911yescharacteristic
353C22×Q8C22⋊D1911yescharacteristic
354C22×D4C22⋊D1912yes—
355C22×D4C22⋊D1911yescharacteristic
356C23×C4C22×D1911yescharacteristic
357C2×M16—381no—
358C2×M16—381no—
359C2×M16—381no—
360C2×M16—762no—
361C22×C8—381no—
362C4⋊Q8—21no—
363#126—22no—
364#125—22no—
365#124—21no—
366#124—22no—
367#124—22no—
368#123—22no—
369#123—22no—
370#123—22no—
371#123—21no—
372#123—22no—
373C22⋊Q8—21no—
374C22⋊Q8—22no—
375C22⋊Q8—22no—
376C22⋊Q8—22no—
377C22⋊Q8—22no—
378C22⋊Q8—21no—
379C22⋊Q8—21no—
380C22⋊Q8—22no—
381C22⋊Q8—22no—
382C22⋊Q8C2×Dic1912yes—
383C22⋊Q8C2×Dic1911yescharacteristic
384C22⋊Q8C22⋊D1912yes—
385C22⋊Q8C22⋊D1911yescharacteristic
386#121—21no—
387#121—22no—
388#121—22no—
389#121—22no—
390#121—22no—
391#121—22no—
392#121—21no—
393#121—21no—
394#121—21no—
395#121—21no—
396#121C2×Dic1911yescharacteristic
397#121C22⋊D1911yescharacteristic
398#120—22no—
399#120—21no—
400C4×Q8—21no—
401C4×D4—22no—
402C4×D4—21no—
403C4×D4—22no—
404C4×D4—21no—
405C4×D4—21no—
406#117C22⋊D1911yescharacteristic
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—381no—
410C2×C4⋊C4C22⋊D1911yescharacteristic
411C2×C4⋊C4C22⋊D1911yescharacteristic
412C2×C22⋊C4—22no—
413C2×C22⋊C4—21no—
414C2×C22⋊C4—381no—
415C2×C22⋊C4—381no—
416C2×C22⋊C4C2×Dic1912yes—
417C2×C42—381no—
418#104—762no—
419#103—762no—
420#100—762no—
421#99—764no—
422C22⋊C8—381no—
423C22⋊C8—381no—
424#95—381no—
425#95—381no—
426C19#848111yescharacteristic, complemented, Sylow
427C24C22⋊Dic1912yes—
428C24C2×C22⋊D1911yescharacteristic
429#41—41no—
430#41—41no—
431#41—82no—
432#41—82no—
433#41—81no—
434#41—81no—
435C2×Q8—22no—
436C2×Q8—21no—
437C2×Q8—41no—
438C2×Q8—41no—
439C2×Q8C22⋊Dic1911yescharacteristic
440C2×Q8C22⋊Dic1912yes—
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—22no—
444C2×D4—22no—
445C2×D4—22no—
446C2×D4—21no—
447C2×D4—22no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—41no—
451C2×D4—41no—
452C2×D4—42no—
453C2×D4—42no—
454C2×D4C22⋊Dic1911yescharacteristic
455C22×C4—21no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—41no—
462C22×C4—41no—
463C22×C4—761no—
464C22×C4—761no—
465C22×C4C22⋊Dic1912yes—
466C22×C4C22×Dic1911yescharacteristic
467C22×C4C2×C22⋊D1911yescharacteristic
468C22×C4C2×C22⋊D1911yescharacteristic
469C22×C4C2×C22⋊D1911yescharacteristic
470C22×C4C2×C22⋊D1911yescharacteristic
471C22×C4C2×C22⋊D1911yescharacteristic
472M16—382no—
473M16—382no—
474M16—761no—
475M16—761no—
476M16—761no—
477M16—761no—
478C2×C8—382no—
479C2×C8—761no—
480C2×C8—761no—
481C2×C8—761no—
482C4⋊C4—22no—
483C4⋊C4—22no—
484C4⋊C4—22no—
485C4⋊C4—22no—
486C4⋊C4—22no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—22no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—761no—
494C4⋊C4—761no—
495C4⋊C4C22⋊Dic1912yes—
496C4⋊C4C22⋊Dic1911yescharacteristic
497C4⋊C4C22⋊Dic1911yescharacteristic
498C22⋊C4—22no—
499C22⋊C4—22no—
500C22⋊C4—22no—
501C22⋊C4—22no—
502C22⋊C4—22no—
503C22⋊C4—22no—
504C22⋊C4—21no—
505C22⋊C4—22no—
506C22⋊C4—21no—
507C22⋊C4—21no—
508C22⋊C4—22no—
509C22⋊C4—22no—
510C22⋊C4—21no—
511C22⋊C4—21no—
512C22⋊C4—382no—
513C22⋊C4—761no—
514C22⋊C4—762no—
515C42—22no—
516C42—21no—
517C42—761no—
518C42—761no—
519C23—21no—
520C23—21no—
521C23—22no—
522C23—21no—
523C23—41no—
524C23—41no—
525C23—42no—
526C23—42no—
527C23—42no—
528C23C2×C22⋊Dic1911yescharacteristic
529C23#1059739911yescharacteristic
530C23#1059739911yescharacteristic
531Q8—42no—
532Q8—41no—
533Q8—41no—
534Q8—41no—
535Q8—82no—
536D4—41no—
537D4—42no—
538D4—42no—
539D4—41no—
540D4—42no—
541D4—41no—
542D4—41no—
543D4—41no—
544D4—81no—
545D4—82no—
546D4—81no—
547D4—82no—
548D4—82no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—22no—
557C2×C4—21no—
558C2×C4—22no—
559C2×C4—21no—
560C2×C4—22no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—42no—
569C2×C4—81no—
570C2×C4—82no—
571C2×C4—82no—
572C2×C4—82no—
573C2×C4—762no—
574C2×C4—1521no—
575C2×C4—1521no—
576C2×C4—1521no—
577C2×C4—1521no—
578C2×C4—1521no—
579C2×C4C2×C22⋊Dic1911yescharacteristic
580C2×C4C2×C22⋊Dic1911yescharacteristic
581C2×C4#1059739911yescharacteristic
582C2×C4#1059739911yescharacteristic
583C8—762no—
584C8—1521no—
585C22—21no—
586C22—21no—
587C22—21no—
588C22—21no—
589C22—21no—
590C22—21no—
591C22—21no—
592C22—21no—
593C22—41no—
594C22—42no—
595C22—41no—
596C22—42no—
597C22—41no—
598C22—42no—
599C22—81no—
600C22—81no—
601C22—162no—
602C22#1192640011yescharacteristic
603C22#1192671211yescharacteristic
604C22#1192672211yescharacteristic
605C4—21no—
606C4—21no—
607C4—21no—
608C4—42no—
609C4—42no—
610C4—41no—
611C4—41no—
612C4—41no—
613C4—42no—
614C4—3041no—
615C4—1522no—
616C4#1192673111yescharacteristic
617C4#1192673411yescharacteristic
618C2—21no—
619C2—21no—
620C2—41no—
621C2—41no—
622C2—82no—
623C2—81no—
624C2#1456358311yescharacteristic
625C2#1456358911yescharacteristic
626C2#1456361011yescharacteristic
subgroupG/H
centerC22#11926400
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
Fitting, prime radicalC19×#3536C2
socleC22×C19#379
cosocleC23×C4×C19C23
hypercenter#3536D19
hypocenterC19#8481
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. #14564472C2semidirect
2. #14564099C2semidirect
3. #14564069C2semidirect
4. #14563938C2semidirect
5. #14562178C2semidirect
6. #14562155C2semidirect
28. C19×#543C4semidirect
31. C19×#538C4semidirect
319. #543Dic19semidirect
322. #538Dic19semidirect
426. C19#8481semidirect

Maximal subgroups

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

subgroupindex
#145644722
#145640992
#145640692
#145639382
#145621782
#145621552
C19×#35362
#848119