Finite Group Databasebeta

← #18075129

Subgroups — #18075129

Order 4864.

820 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14564104C211yesmaximal, characteristic, complemented
2#14564099C211yesmaximal, characteristic, complemented
3#14563933C211yesmaximal, characteristic, complemented
4#14561999C211yesmaximal, characteristic, complemented
5#14561995C211yesmaximal, characteristic, complemented
6#14561973C211yesmaximal, characteristic, complemented
7C19×#3505C211yesmaximal, characteristic
8C22×#64520C2211yescharacteristic
9C2×#10597293—21no—
10C2×#10597290—21no—
11#11926508C2211yescharacteristic
12#11926508C2211yescharacteristic
13C2×C22⋊(C19⋊C8)—21no—
14C2×C22⋊(C19⋊C8)C2211yescharacteristic
15#11926313—21no—
16#11926313—21no—
17#11926299—21no—
18#11926270—21no—
19#11926270—22no—
20#11926268—21no—
21#11926268—22no—
22C19×#553—21no—
23C19×#553—22no—
24C19×#552—21no—
25C19×#551—22no—
26C19×#548—21no—
27C19×#546—21no—
28C19×#539—21no—
29C19×#538—21no—
30C19×#534C412yes—
31C19×#529—21no—
32C19×#525—21no—
33C2×C19×C22⋊Q8C2211yescharacteristic
34C2×C19×#121C2211yescharacteristic
35C19×#518C412yes—
36C2×C4×D4×C19C2211yescharacteristic
37C2×#41×C19—21no—
38C22×Q8×C19D411yescharacteristic
39C22×D4×C19C2×C411yescharacteristic
40C22×D4×C19C2×C412yes—
41C22×D4×C19D411yescharacteristic
42C23×C4×C19D411yescharacteristic
43C23×C4×C19C2311yescharacteristic
44C19×#126—22no—
45C19×#126—22no—
46C19×#126—22no—
47C19×#125—21no—
48C19×#125—22no—
49C19×#124—21no—
50C19×#124—22no—
51C19×#123—22no—
52C19×#123—22no—
53C19×#123—22no—
54C19×#123—22no—
55C19×#123—22no—
56C19×C22⋊Q8—21no—
57C19×C22⋊Q8—22no—
58C19×C22⋊Q8—21no—
59C19×C22⋊Q8—21no—
60C19×C22⋊Q8—21no—
61C19×C22⋊Q8—21no—
62C19×#121—21no—
63C19×#121—22no—
64C19×#121—22no—
65C19×#121—22no—
66C19×#121—21no—
67C19×#121—21no—
68C19×#121—21no—
69C19×#121—21no—
70C19×#120—22no—
71C19×#120—22no—
72C4×Q8×C19—21no—
73C4×D4×C19—22no—
74C4×D4×C19—21no—
75C4×D4×C19—22no—
76C4×D4×C19—22no—
77C4×D4×C19—22no—
78C4×D4×C19—22no—
79C4×D4×C19—21no—
80C4×D4×C19—21no—
81C4×D4×C19—21no—
82C4×D4×C19—21no—
83C19×#117—21no—
84C19×#117—22no—
85C19×#117—22no—
86C2×C4⋊C4×C19D411yescharacteristic
87C2×C4⋊C4×C19D411yescharacteristic
88C2×C4⋊C4×C19D411yescharacteristic
89C2×C4⋊C4×C19D412yes—
90C2×C22⋊C4×C19—22no—
91C2×C22⋊C4×C19C2×C411yescharacteristic
92C2×C22⋊C4×C19C2×C412yes—
93C2×C22⋊C4×C19D411yescharacteristic
94C2×C22⋊C4×C19D412yes—
95C2×C42×C19D411yescharacteristic
96C2×#64520—21no—
97C2×#64520—21no—
98C2×#64520—21no—
99C2×#64520—21no—
100C2×#64520—42no—
101C22×C19⋊C8—21no—
102C22×C19⋊C8—21no—
103#10597293—42no—
104#10597290—42no—
105C22⋊(C19⋊C8)—21no—
106C22⋊(C19⋊C8)—21no—
107C22⋊(C19⋊C8)—21no—
108C22⋊(C19⋊C8)—21no—
109C22⋊(C19⋊C8)—21no—
110C22⋊(C19⋊C8)—21no—
111C22⋊(C19⋊C8)—42no—
112C24×C19C22⋊C411yescharacteristic
113C24×C19C22⋊C412yes—
114C24×C19C22×C411yescharacteristic
115#41×C19—81no—
116#41×C19—81no—
117C2×Q8×C19—21no—
118C2×Q8×C19—21no—
119C2×Q8×C19—41no—
120C2×Q8×C19—41no—
121C2×D4×C19—21no—
122C2×D4×C19—22no—
123C2×D4×C19—22no—
124C2×D4×C19—21no—
125C2×D4×C19—22no—
126C2×D4×C19—22no—
127C2×D4×C19—21no—
128C2×D4×C19—21no—
129C2×D4×C19—41no—
130C2×D4×C19—41no—
131C2×D4×C19—41no—
132C2×D4×C19—41no—
133C2×D4×C19—42no—
134C2×D4×C19—42no—
135C22×C4×C19—22no—
136C22×C4×C19—22no—
137C22×C4×C19—21no—
138C22×C4×C19—21no—
139C22×C4×C19—41no—
140C22×C4×C19—41no—
141C22×C4×C19—41no—
142C22×C4×C19—41no—
143C22×C4×C19C22⋊C411yescharacteristic
144C22×C4×C19C22⋊C411yescharacteristic
145C22×C4×C19C22⋊C412yes—
146C22×C4×C19C22⋊C411yescharacteristic
147C22×C4×C19C22⋊C412yes—
148C22×C4×C19C22⋊C412yes—
149C22×C4×C19C2×D411yescharacteristic
150C22×C4×C19C2×D411yescharacteristic
151C22×C4×C19C2×D411yescharacteristic
152C22×C4×C19C2×D411yescharacteristic
153C22×C4×C19C2×D411yescharacteristic
154C22×C4×C19C2×D411yescharacteristic
155C4⋊C4×C19—22no—
156C4⋊C4×C19—22no—
157C4⋊C4×C19—22no—
158C4⋊C4×C19—22no—
159C4⋊C4×C19—21no—
160C4⋊C4×C19—22no—
161C4⋊C4×C19—21no—
162C4⋊C4×C19—21no—
163C4⋊C4×C19—21no—
164C4⋊C4×C19—21no—
165C4⋊C4×C19—22no—
166C4⋊C4×C19—21no—
167C22⋊C4×C19—22no—
168C22⋊C4×C19—22no—
169C22⋊C4×C19—22no—
170C22⋊C4×C19—22no—
171C22⋊C4×C19—22no—
172C22⋊C4×C19—22no—
173C22⋊C4×C19—21no—
174C22⋊C4×C19—22no—
175C22⋊C4×C19—21no—
176C22⋊C4×C19—22no—
177C22⋊C4×C19—22no—
178C22⋊C4×C19—21no—
179C22⋊C4×C19—21no—
180C22⋊C4×C19—22no—
181C42×C19—22no—
182C42×C19—22no—
183C42×C19—21no—
184C42×C19—21no—
185#64520—22no—
186#64520—22no—
187#64520—41no—
188#64520—41no—
189#64520—41no—
190#64520—41no—
191#64520—41no—
192#64520—41no—
193C2×C19⋊C8—22no—
194C2×C19⋊C8—41no—
195C2×C19⋊C8—41no—
196C2×C19⋊C8—41no—
197C2×C19⋊C8—41no—
198C2×C19⋊C8—41no—
199C2×C19⋊C8—41no—
200C2×C19⋊C8—41no—
201#8538—191nomaximal, Sylow
202C23×C19—21no—
203C23×C19—21no—
204C23×C19—21no—
205C23×C19—22no—
206C23×C19—21no—
207C23×C19—21no—
208C23×C19—41no—
209C23×C19—41no—
210C23×C19—41no—
211C23×C19—41no—
212C23×C19—42no—
213C23×C19—42no—
214C23×C19—42no—
215C23×C19C2×C22⋊C411yescharacteristic
216C23×C19C2×C22⋊C411yescharacteristic
217C23×C19C2×C22⋊C411yescharacteristic
218Q8×C19—41no—
219Q8×C19—41no—
220Q8×C19—81no—
221D4×C19—42no—
222D4×C19—42no—
223D4×C19—44no—
224D4×C19—42no—
225D4×C19—42no—
226D4×C19—41no—
227D4×C19—41no—
228D4×C19—81no—
229D4×C19—82no—
230D4×C19—82no—
231C2×C4×C19—21no—
232C2×C4×C19—21no—
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—22no—
240C2×C4×C19—21no—
241C2×C4×C19—22no—
242C2×C4×C19—22no—
243C2×C4×C19—21no—
244C2×C4×C19—21no—
245C2×C4×C19—41no—
246C2×C4×C19—41no—
247C2×C4×C19—41no—
248C2×C4×C19—41no—
249C2×C4×C19—41no—
250C2×C4×C19—41no—
251C2×C4×C19—41no—
252C2×C4×C19—42no—
253C2×C4×C19—42no—
254C2×C4×C19—42no—
255C2×C4×C19—81no—
256C2×C4×C19—82no—
257C2×C4×C19—82no—
258C2×C4×C19#12011yescharacteristic
259C2×C4×C19#12011yescharacteristic
260C2×C4×C19#12011yescharacteristic
261C2×C4×C19#12011yescharacteristic
262C19⋊C8—42no—
263C19⋊C8—81no—
264C19⋊C8—81no—
265C19⋊C8—81no—
266#3505D1911yescharacteristic
267#1901—191no—
268#1900—191no—
269#1870—191no—
270#1472—191no—
271#1471—191no—
272#1465—191no—
273C22×C19—21no—
274C22×C19—21no—
275C22×C19—21no—
276C22×C19—21no—
277C22×C19—21no—
278C22×C19—21no—
279C22×C19—21no—
280C22×C19—21no—
281C22×C19—42no—
282C22×C19—41no—
283C22×C19—42no—
284C22×C19—41no—
285C22×C19—42no—
286C22×C19—42no—
287C22×C19—41no—
288C22×C19—81no—
289C22×C19—81no—
290C22×C19—81no—
291C22×C19—162no—
292C22×C19#37911yescharacteristic
293C22×C19#41311yescharacteristic
294C22×C19#41311yescharacteristic
295C4×C19—21no—
296C4×C19—21no—
297C4×C19—21no—
298C4×C19—41no—
299C4×C19—42no—
300C4×C19—41no—
301C4×C19—42no—
302C4×C19—41no—
303C4×C19—42no—
304C4×C19B(4,𝔽2)11yescharacteristic
305C4×C19#45811yescharacteristic
306C22×M16—191no—
307#553—22no—
308#553—21no—
309#552—21no—
310#551—22no—
311#548—21no—
312#546—21no—
313#539—21no—
314#538—21no—
315#534Dic1912yes—
316#529—21no—
317#525—21no—
318C2×C22⋊Q8C2×D1911yescharacteristic
319C2×#121C2×D1911yescharacteristic
320#518Dic1912yes—
321C2×C4×D4C2×D1911yescharacteristic
322C2×#101—381no—
323C2×#100—381no—
324#407—191no—
325#407—191no—
326C2×C22⋊C8—191no—
327C2×C22⋊C8—381no—
328#343—381no—
329#343—381no—
330#336—381no—
331#324—381no—
332#324—382no—
333#323—381no—
334#323—382no—
335C2×C19—21no—
336C2×C19—21no—
337C2×C19—41no—
338C2×C19—41no—
339C2×C19—81no—
340C2×C19—82no—
341C2×C19#178511yescharacteristic
342C2×C19#179011yescharacteristic
343C2×C19#179111yescharacteristic
344C2×#41—21no—
345C22×Q8C22⋊D1911yescharacteristic
346C22×D4C2×Dic1911yescharacteristic
347C22×D4C2×Dic1912yes—
348C22×D4C22⋊D1911yescharacteristic
349C23×C4C22⋊D1911yescharacteristic
350C23×C4C22×D1911yescharacteristic
351C2×M16—381no—
352C2×M16—381no—
353C2×M16—381no—
354C2×M16—381no—
355C2×M16—762no—
356C22×C8—381no—
357C22×C8—381no—
358#126—22no—
359#126—22no—
360#126—22no—
361#125—21no—
362#125—22no—
363#124—21no—
364#124—22no—
365#123—22no—
366#123—22no—
367#123—22no—
368#123—22no—
369#123—22no—
370C22⋊Q8—21no—
371C22⋊Q8—22no—
372C22⋊Q8—21no—
373C22⋊Q8—21no—
374C22⋊Q8—21no—
375C22⋊Q8—21no—
376#121—21no—
377#121—22no—
378#121—22no—
379#121—22no—
380#121—21no—
381#121—21no—
382#121—21no—
383#121—21no—
384#120—22no—
385#120—22no—
386C4×Q8—21no—
387C4×D4—22no—
388C4×D4—21no—
389C4×D4—22no—
390C4×D4—22no—
391C4×D4—22no—
392C4×D4—22no—
393C4×D4—21no—
394C4×D4—21no—
395C4×D4—21no—
396C4×D4—21no—
397#117—21no—
398#117—22no—
399#117—22no—
400C2×C4⋊C4C22⋊D1911yescharacteristic
401C2×C4⋊C4C22⋊D1911yescharacteristic
402C2×C4⋊C4C22⋊D1912yes—
403C2×C4⋊C4C22⋊D1911yescharacteristic
404C2×C22⋊C4—22no—
405C2×C22⋊C4C2×Dic1911yescharacteristic
406C2×C22⋊C4C2×Dic1912yes—
407C2×C22⋊C4C22⋊D1911yescharacteristic
408C2×C22⋊C4C22⋊D1912yes—
409C2×C42C22⋊D1911yescharacteristic
410#101—762no—
411#100—762no—
412C22⋊C8—381no—
413C22⋊C8—381no—
414C22⋊C8—381no—
415C22⋊C8—381no—
416C22⋊C8—381no—
417C22⋊C8—381no—
418C22⋊C8—762no—
419C19#853811yescharacteristic, complemented, Sylow
420C24C22⋊Dic1911yescharacteristic
421C24C22⋊Dic1912yes—
422C24C22×Dic1911yescharacteristic
423#41—81no—
424#41—81no—
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8—41no—
428C2×Q8—41no—
429C2×D4—21no—
430C2×D4—22no—
431C2×D4—22no—
432C2×D4—21no—
433C2×D4—22no—
434C2×D4—22no—
435C2×D4—21no—
436C2×D4—21no—
437C2×D4—41no—
438C2×D4—41no—
439C2×D4—41no—
440C2×D4—41no—
441C2×D4—42no—
442C2×D4—42no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—41no—
448C22×C4—41no—
449C22×C4—41no—
450C22×C4—41no—
451C22×C4C22⋊Dic1911yescharacteristic
452C22×C4C22⋊Dic1911yescharacteristic
453C22×C4C22⋊Dic1912yes—
454C22×C4C22⋊Dic1911yescharacteristic
455C22×C4C22⋊Dic1912yes—
456C22×C4C22⋊Dic1912yes—
457C22×C4C2×C22⋊D1911yescharacteristic
458C22×C4C2×C22⋊D1911yescharacteristic
459C22×C4C2×C22⋊D1911yescharacteristic
460C22×C4C2×C22⋊D1911yescharacteristic
461C22×C4C2×C22⋊D1911yescharacteristic
462C22×C4C2×C22⋊D1911yescharacteristic
463M16—382no—
464M16—382no—
465M16—761no—
466M16—761no—
467M16—761no—
468M16—761no—
469M16—761no—
470M16—761no—
471C2×C8—382no—
472C2×C8—761no—
473C2×C8—761no—
474C2×C8—761no—
475C2×C8—761no—
476C2×C8—761no—
477C2×C8—761no—
478C2×C8—761no—
479C4⋊C4—22no—
480C4⋊C4—22no—
481C4⋊C4—22no—
482C4⋊C4—22no—
483C4⋊C4—21no—
484C4⋊C4—22no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—22no—
490C4⋊C4—21no—
491C22⋊C4—22no—
492C22⋊C4—22no—
493C22⋊C4—22no—
494C22⋊C4—22no—
495C22⋊C4—22no—
496C22⋊C4—22no—
497C22⋊C4—21no—
498C22⋊C4—22no—
499C22⋊C4—21no—
500C22⋊C4—22no—
501C22⋊C4—22no—
502C22⋊C4—21no—
503C22⋊C4—21no—
504C22⋊C4—22no—
505C42—22no—
506C42—22no—
507C42—21no—
508C42—21no—
509C23—21no—
510C23—21no—
511C23—21no—
512C23—22no—
513C23—21no—
514C23—21no—
515C23—41no—
516C23—41no—
517C23—41no—
518C23—41no—
519C23—42no—
520C23—42no—
521C23—42no—
522C23C2×C22⋊Dic1911yescharacteristic
523C23C2×C22⋊Dic1911yescharacteristic
524C23C2×C22⋊Dic1911yescharacteristic
525Q8—41no—
526Q8—41no—
527Q8—81no—
528D4—42no—
529D4—42no—
530D4—44no—
531D4—42no—
532D4—42no—
533D4—41no—
534D4—41no—
535D4—81no—
536D4—82no—
537D4—82no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—22no—
549C2×C4—21no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4—41no—
561C2×C4—42no—
562C2×C4—81no—
563C2×C4—82no—
564C2×C4—82no—
565C2×C4#1059739911yescharacteristic
566C2×C4#1059739911yescharacteristic
567C2×C4#1059739911yescharacteristic
568C2×C4#1059739911yescharacteristic
569C8—762no—
570C8—1521no—
571C8—1521no—
572C8—1521no—
573C22—21no—
574C22—21no—
575C22—21no—
576C22—21no—
577C22—21no—
578C22—21no—
579C22—21no—
580C22—21no—
581C22—42no—
582C22—42no—
583C22—41no—
584C22—41no—
585C22—42no—
586C22—41no—
587C22—42no—
588C22—81no—
589C22—81no—
590C22—81no—
591C22—162no—
592C22#1192640011yescharacteristic
593C22#1192652811yescharacteristic
594C22#1192652811yescharacteristic
595C4—21no—
596C4—21no—
597C4—21no—
598C4—41no—
599C4—42no—
600C4—41no—
601C4—42no—
602C4—41no—
603C4—42no—
604C4#1192673111yescharacteristic
605C4#1192673411yescharacteristic
606C2—21no—
607C2—21no—
608C2—41no—
609C2—41no—
610C2—81no—
611C2—82no—
612C2#1456356311yescharacteristic
613C2#1456358311yescharacteristic
614C2#1456358611yescharacteristic
subgroupG/H
centerC22#11926400
commutatorC24×C19C22×C4
FrattiniC23×C4C22×D19
Fitting, prime radicalC19×#3505C2
socleC22×C19#379
cosocleC23×C4×C19C23
hypercenter#3505D19
hypocenterC19#8538
LCSG ▷ C24×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3505

Complements

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

NH ≅ G/Ntype
1. #14564104C2semidirect
2. #14564099C2semidirect
3. #14563933C2semidirect
4. #14561999C2semidirect
5. #14561995C2semidirect
6. #14561973C2semidirect
419. C19#8538semidirect

Maximal subgroups

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

subgroupindex
#145641042
#145640992
#145639332
#145619992
#145619952
#145619732
C19×#35052
#853819