Finite Group Databasebeta

← #18077231

Subgroups — #18077231

Order 4864.

908 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14572661C211yesmaximal, characteristic, complemented
2C4×#10597399C211yesmaximal, characteristic
3#14563545C211yesmaximal, characteristic, complemented
4#14561951C211yesmaximal, characteristic, complemented
5#14561482C211yesmaximal, characteristic, complemented
6#14561481C211yesmaximal, characteristic, complemented
7C19×#1779C211yesmaximal, characteristic, complemented
8C2×#10597399C411yescharacteristic
9C2×C4×C22⋊D19—21no—
10C2×C4×C22⋊D19C2211yescharacteristic
11#11926615—22no—
12#11926612—22no—
13#11926598—21no—
14#11926506—21no—
15C2×C22⋊(C19⋊C8)—22no—
16C2×C22⋊(C19⋊C8)C2211yescharacteristic
17C2×C22⋊(C19⋊C8)C2211yescharacteristic
18#11926423—21no—
19#11926423C411yescharacteristic
20#11926417—21no—
21#11926417C411yescharacteristic
22#11926400C411yescharacteristic
23C4×C22⋊Dic19—21no—
24C4×C22⋊Dic19C2211yescharacteristic
25#11926269—21no—
26#11926267—21no—
27C24×C4×C19C2211yescharacteristic
28C2×C19×C22⋊C8—22no—
29C2×C19×C22⋊C8C2211yescharacteristic
30C2×C19×C22⋊C8C2211yescharacteristic
31C25×C19C2×C411yescharacteristic
32C23×C4×C19—21no—
33C23×C4×C19—21no—
34C23×C4×C19—21no—
35C23×C4×C19—21no—
36C23×C4×C19—21no—
37C23×C4×C19—21no—
38C23×C4×C19—44no—
39C23×C4×C19C2×C411yescharacteristic
40C23×C4×C19C2311yescharacteristic
41C22×C22⋊D19—21no—
42C22×C22⋊D19C2×C411yescharacteristic
43C22×C4×D19D411yescharacteristic
44C22×C8×C19—21no—
45C22×C8×C19D412yescomplemented
46#10597399—22no—
47#10597399—22no—
48C2×C22⋊Dic19—21no—
49C2×C22⋊Dic19—21no—
50C2×C22⋊Dic19—21no—
51C2×C22⋊Dic19C2×C411yescharacteristic
52C2×C22⋊Dic19C2×C411yescharacteristic
53C2×C22⋊Dic19C2×C411yescharacteristic
54C4×C22⋊D19—21no—
55C4×C22⋊D19—21no—
56C4×C22⋊D19—21no—
57C4×C22⋊D19—21no—
58C4×C22⋊D19—44no—
59C2×(C2×D19)⋊C4—21no—
60C2×(C2×D19)⋊C4D411yescharacteristic
61C2×Dic19⋊C4—21no—
62C2×Dic19⋊C4D411yescharacteristic
63C2×C4×Dic19—21no—
64C2×C4×Dic19D411yescharacteristic
65C22×C19⋊C8—21no—
66C22×C19⋊C8D412yescomplemented
67C2×#64515—22no—
68C19×C22⋊C8—21no—
69C19×C22⋊C8—21no—
70C19×C22⋊C8—21no—
71C19×C22⋊C8—21no—
72C19×C22⋊C8—44no—
73C19⋊#95—21no—
74C19⋊#95—21no—
75C19⋊#95—21no—
76C22⋊(C19⋊C8)—21no—
77C22⋊(C19⋊C8)—21no—
78C22⋊(C19⋊C8)—21no—
79C22⋊(C19⋊C8)—21no—
80C22⋊(C19⋊C8)—44no—
81(C2×D19)⋊C8—22no—
82#10597272—22no—
83Dic19⋊C8—22no—
84C24×C19—21no—
85C24×C19—21no—
86C24×C19—21no—
87C24×C19—21no—
88C24×C19—21no—
89C24×C19—21no—
90C24×C19—42no—
91C24×C19—42no—
92C24×C19M1612yescomplemented
93C24×C19C22×C411yescharacteristic
94C23×D19C22⋊C411yescharacteristic
95C22×C4×C19—24no—
96C22×C4×C19—24no—
97C22×C4×C19—24no—
98C22×C4×C19—21no—
99C22×C4×C19—21no—
100C22×C4×C19—21no—
101C22×C4×C19—42no—
102C22×C4×C19—42no—
103C22×C4×C19—42no—
104C22×C4×C19—42no—
105C22×C4×C19—42no—
106C22×C4×C19—42no—
107C22×C4×C19—42no—
108C22×C4×C19—42no—
109C22×C4×C19—42no—
110C22×C4×C19—42no—
111C22×C4×C19—42no—
112C22×C4×C19—41no—
113C22×C4×C19—41no—
114C22×C4×C19—41no—
115C22×C4×C19—41no—
116C22×C4×C19C2×D411yescharacteristic
117C22×C4×C19C2×D411yescharacteristic
118C22×C4×C19C2×D411yescharacteristic
119C22×C4×C19C2×D411yescharacteristic
120C22×C4×C19#4111yescharacteristic
121C22×C4×C19#4111yescharacteristic
122C2×C22⋊D19—24no—
123C2×C22⋊D19—21no—
124C2×C22⋊D19—21no—
125C2×C22⋊D19—21no—
126C2×C22⋊D19—21no—
127C2×C22⋊D19—21no—
128C2×C22⋊D19—21no—
129C2×C22⋊D19—42no—
130C2×C22⋊D19—42no—
131C22×Dic19—21no—
132C22×Dic19—21no—
133C22×Dic19C22⋊C411yescharacteristic
134C22×Dic19C22⋊C411yescharacteristic
135C22×Dic19C22⋊C411yescharacteristic
136C2×C4×D19—21no—
137C2×C4×D19—21no—
138C2×C4×D19—42no—
139C2×C8×C19—22no—
140C2×C8×C19—42no—
141C2×C8×C19—42no—
142C2×C8×C19—41no—
143C22⋊Dic19—24no—
144C22⋊Dic19—21no—
145C22⋊Dic19—21no—
146C22⋊Dic19—21no—
147C22⋊Dic19—21no—
148C22⋊Dic19—21no—
149C22⋊Dic19—42no—
150C22⋊Dic19—42no—
151C22⋊Dic19M1612yescomplemented
152(C2×D19)⋊C4—21no—
153(C2×D19)⋊C4—21no—
154(C2×D19)⋊C4—42no—
155Dic19⋊C4—21no—
156Dic19⋊C4—21no—
157Dic19⋊C4—42no—
158C4×Dic19—21no—
159C4×Dic19—21no—
160C4×Dic19—42no—
161C2×C19⋊C8—22no—
162C2×C19⋊C8—42no—
163C2×C19⋊C8—42no—
164C2×C19⋊C8—41no—
165#64515—82no—
166#8967—191nomaximal, Sylow
167C23×C19—22no—
168C23×C19—22no—
169C23×C19—22no—
170C23×C19—22no—
171C23×C19—22no—
172C23×C19—22no—
173C23×C19—22no—
174C23×C19—22no—
175C23×C19—22no—
176C23×C19—41no—
177C23×C19—44no—
178C23×C19—41no—
179C23×C19—41no—
180C23×C19—41no—
181C23×C19—41no—
182C23×C19—41no—
183C23×C19—41no—
184C23×C19—41no—
185C23×C19—44no—
186C23×C19—44no—
187C23×C19—44no—
188C23×C19—41no—
189C23×C19—41no—
190C23×C19—41no—
191C23×C19—41no—
192C23×C19C2×C22⋊C411yescharacteristic
193C23×C19C4×D411yescharacteristic
194C23×C19C4×D411yescharacteristic
195C23×C19C2×M1611yescharacteristic
196C23×C19C2×M1611yescharacteristic
197C23×C19#13111yescharacteristic
198C23×C19#13111yescharacteristic
199C22×D19—21no—
200C22×D19—21no—
201C22×D19—21no—
202C22×D19—41no—
203C22×D19—41no—
204C2×C4×C19—22no—
205C2×C4×C19—22no—
206C2×C4×C19—22no—
207C2×C4×C19—22no—
208C2×C4×C19—22no—
209C2×C4×C19—22no—
210C2×C4×C19—41no—
211C2×C4×C19—41no—
212C2×C4×C19—41no—
213C2×C4×C19—44no—
214C2×C4×C19—44no—
215C2×C4×C19—44no—
216C2×C4×C19—41no—
217C2×C4×C19—41no—
218C2×C4×C19—41no—
219C2×C4×C19—41no—
220C2×C4×C19—44no—
221C2×C4×C19#12011yescharacteristic
222C2×C4×C19#12111yescharacteristic
223C2×C4×C19#12111yescharacteristic
224C2×C4×C19#12311yescharacteristic
225C22⋊D19—48no—
226C22⋊D19—41no—
227C22⋊D19—41no—
228C22⋊D19—41no—
229C22⋊D19—41no—
230C2×Dic19—21no—
231C2×Dic19—21no—
232C2×Dic19—21no—
233C2×Dic19—21no—
234C2×Dic19—22no—
235C2×Dic19—21no—
236C2×Dic19—41no—
237C2×Dic19—41no—
238C2×Dic19—41no—
239C2×Dic19—41no—
240C2×Dic19—41no—
241C2×Dic19—41no—
242C2×Dic19—41no—
243C4×D19—42no—
244C4×D19—81no—
245C8×C19—42no—
246C8×C19—81no—
247C19⋊C8—42no—
248C19⋊C8—81no—
249#2973—191no—
250C4×#120—191no—
251#1779—191no—
252#1779D1911yescharacteristic, complemented
253#1459—191no—
254#1282—191no—
255#1282—191no—
256C22×C19—21no—
257C22×C19—21no—
258C22×C19—21no—
259C22×C19—21no—
260C22×C19—21no—
261C22×C19—21no—
262C22×C19—24no—
263C22×C19—24no—
264C22×C19—24no—
265C22×C19—41no—
266C22×C19—41no—
267C22×C19—41no—
268C22×C19—41no—
269C22×C19—42no—
270C22×C19—42no—
271C22×C19—42no—
272C22×C19—42no—
273C22×C19—42no—
274C22×C19—42no—
275C22×C19—42no—
276C22×C19—42no—
277C22×C19—42no—
278C22×C19—42no—
279C22×C19—42no—
280C22×C19—42no—
281C22×C19#38611yescharacteristic
282C22×C19#40711yescharacteristic
283C22×C19#40811yescharacteristic
284C22×C19#43511yescharacteristic
285C22×C19#43511yescharacteristic
286C22×C19#43611yescharacteristic
287C22×C19#43611yescharacteristic
288C2×D19—42no—
289C2×D19—41no—
290C2×D19—41no—
291C2×D19—41no—
292C2×D19—81no—
293C4×C19—21no—
294C4×C19—21no—
295C4×C19—21no—
296C4×C19—42no—
297C4×C19B(4,𝔽2)12yes—
298Dic19—42no—
299Dic19—41no—
300Dic19—41no—
301Dic19—41no—
302Dic19—81no—
303C24×C4C2×D1911yescharacteristic
304C2×#120—191no—
305C2×C4×D4—191no—
306C2×C4×D4—381no—
307#435—382no—
308#435—382no—
309#432—381no—
310#407—381no—
311C2×C22⋊C8—22no—
312C2×C22⋊C8—191no—
313C2×C22⋊C8—191no—
314C2×C22⋊C8—382no—
315C2×C22⋊C8C2×D1911yescharacteristic
316C2×C22⋊C8C2×D1911yescharacteristic
317#386—191no—
318#386—381no—
319#385—191no—
320#385—381no—
321#379—191no—
322C4×C22⋊C4—191no—
323C4×C22⋊C4—381no—
324#324—381no—
325#323—381no—
326C2×C19—21no—
327C2×C19—21no—
328C2×C19—21no—
329C2×C19—21no—
330C2×C19—21no—
331C2×C19—21no—
332C2×C19—44no—
333C2×C19#187011yescharacteristic
334C2×C19#188911yescharacteristic
335C2×C19#189111yescharacteristic
336D19—81no—
337C25C4×D1911yescharacteristic
338C22×D4—191no—
339C22×D4—381no—
340C23×C4—21no—
341C23×C4—21no—
342C23×C4—21no—
343C23×C4—21no—
344C23×C4—21no—
345C23×C4—21no—
346C23×C4—44no—
347C23×C4—191no—
348C23×C4C4×D1911yescharacteristic
349C23×C4C22×D1911yescharacteristic
350C2×M16—382no—
351C22×C8—21no—
352C22×C8—192no—
353C22×C8—381no—
354C22×C8C22⋊D1912yescomplemented
355#120—382no—
356#120—382no—
357C4×D4—381no—
358C4×D4—381no—
359C4×D4—381no—
360C4×D4—381no—
361C4×D4—764no—
362C2×C4⋊C4—191no—
363C2×C4⋊C4—381no—
364C2×C22⋊C4—191no—
365C2×C22⋊C4—191no—
366C2×C22⋊C4—191no—
367C2×C22⋊C4—191no—
368C2×C22⋊C4—381no—
369C2×C22⋊C4—381no—
370C2×C22⋊C4—381no—
371C2×C22⋊C4—381no—
372C2×C42—191no—
373C2×C42—381no—
374C4⋊C8—382no—
375C22⋊C8—21no—
376C22⋊C8—21no—
377C22⋊C8—21no—
378C22⋊C8—21no—
379C22⋊C8—44no—
380C22⋊C8—382no—
381C22⋊C8—381no—
382C22⋊C8—381no—
383C22⋊C8—381no—
384C22⋊C8—381no—
385C22⋊C8—764no—
386#97—382no—
387#95—381no—
388#95—381no—
389#95—381no—
390C19#896711yescharacteristic, complemented, Sylow
391C24—21no—
392C24—21no—
393C24—21no—
394C24—21no—
395C24—21no—
396C24—21no—
397C24—42no—
398C24—42no—
399C24—191no—
400C24#6451512yescomplemented
401C24C2×C4×D1911yescharacteristic
402C2×D4—384no—
403C2×D4—381no—
404C2×D4—381no—
405C2×D4—381no—
406C2×D4—381no—
407C2×D4—381no—
408C2×D4—381no—
409C2×D4—762no—
410C2×D4—762no—
411C22×C4—24no—
412C22×C4—24no—
413C22×C4—24no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—42no—
418C22×C4—42no—
419C22×C4—42no—
420C22×C4—42no—
421C22×C4—42no—
422C22×C4—42no—
423C22×C4—42no—
424C22×C4—42no—
425C22×C4—42no—
426C22×C4—42no—
427C22×C4—42no—
428C22×C4—41no—
429C22×C4—41no—
430C22×C4—41no—
431C22×C4—41no—
432C22×C4—191no—
433C22×C4—191no—
434C22×C4—191no—
435C22×C4—381no—
436C22×C4—381no—
437C22×C4—381no—
438C22×C4—381no—
439C22×C4—762no—
440C22×C4#6454111yescharacteristic
441C22×C4D4×D1911yescharacteristic
442C22×C4D4×D1911yescharacteristic
443C22×C4D4×D1911yescharacteristic
444C22×C4#6454311yescharacteristic
445C22×C4C2×C22⋊D1911yescharacteristic
446M16—1522no—
447C2×C8—22no—
448C2×C8—42no—
449C2×C8—42no—
450C2×C8—41no—
451C2×C8—382no—
452C2×C8—762no—
453C2×C8—762no—
454C2×C8—761no—
455C4⋊C4—381no—
456C4⋊C4—381no—
457C4⋊C4—762no—
458C22⋊C4—192no—
459C22⋊C4—384no—
460C22⋊C4—381no—
461C22⋊C4—381no—
462C22⋊C4—381no—
463C22⋊C4—381no—
464C22⋊C4—381no—
465C22⋊C4—381no—
466C22⋊C4—381no—
467C22⋊C4—762no—
468C22⋊C4—762no—
469C22⋊C4—762no—
470C42—381no—
471C42—381no—
472C42—762no—
473C23—22no—
474C23—22no—
475C23—22no—
476C23—22no—
477C23—22no—
478C23—22no—
479C23—22no—
480C23—22no—
481C23—22no—
482C23—41no—
483C23—44no—
484C23—41no—
485C23—41no—
486C23—41no—
487C23—41no—
488C23—41no—
489C23—41no—
490C23—41no—
491C23—44no—
492C23—44no—
493C23—44no—
494C23—41no—
495C23—41no—
496C23—41no—
497C23—41no—
498C23—381no—
499C23—381no—
500C23—381no—
501C23—761no—
502C23—761no—
503C23C22⋊C4×D1911yescharacteristic
504C23(C22⋊D19)⋊C411yescharacteristic
505C23C2×#6451511yescharacteristic
506C23#1059734711yescharacteristic
507C23M16×D1911yescharacteristic
508C23#1059735311yescharacteristic
509C23C4×C22⋊D1911yescharacteristic
510D4—768no—
511D4—761no—
512D4—761no—
513D4—761no—
514D4—761no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—44no—
525C2×C4—44no—
526C2×C4—44no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—44no—
532C2×C4—381no—
533C2×C4—381no—
534C2×C4—381no—
535C2×C4—382no—
536C2×C4—381no—
537C2×C4—381no—
538C2×C4—761no—
539C2×C4—761no—
540C2×C4—762no—
541C2×C4—761no—
542C2×C4—761no—
543C2×C4—761no—
544C2×C4—761no—
545C2×C4—761no—
546C2×C4—1521no—
547C2×C4#1059732911yescharacteristic
548C2×C4#1059733011yescharacteristic
549C2×C4#1059738311yescharacteristic
550C2×C4#1059738411yescharacteristic
551C8—42no—
552C8—81no—
553C8—762no—
554C8—1521no—
555C22—21no—
556C22—21no—
557C22—21no—
558C22—21no—
559C22—21no—
560C22—21no—
561C22—24no—
562C22—24no—
563C22—24no—
564C22—41no—
565C22—41no—
566C22—41no—
567C22—41no—
568C22—42no—
569C22—42no—
570C22—42no—
571C22—42no—
572C22—42no—
573C22—42no—
574C22—42no—
575C22—42no—
576C22—42no—
577C22—42no—
578C22—42no—
579C22—42no—
580C22—762no—
581C22—761no—
582C22—761no—
583C22—761no—
584C22—1521no—
585C22#1192642011yescharacteristic
586C22#1192650611yescharacteristic
587C22#1192650911yescharacteristic
588C22#1192661211yescharacteristic
589C22#1192661511yescharacteristic
590C22#1192661911yescharacteristic
591C22#1192662011yescharacteristic
592C4—21no—
593C4—21no—
594C4—21no—
595C4—42no—
596C4—762no—
597C4—761no—
598C4—761no—
599C4—761no—
600C4—1521no—
601C4#1192673012yes—
602C2—21no—
603C2—21no—
604C2—21no—
605C2—21no—
606C2—21no—
607C2—21no—
608C2—44no—
609C2—1521no—
610C2#1456392911yescharacteristic
611C2#1456404011yescharacteristic
612C2#1456405011yescharacteristic
subgroupG/H
centerC2×C4#10597383
commutatorC24×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#1779C2
socleC22×C19#386
prime radicalC2×#10597399C4
cosocleC23×C4×C19C23
hypercenter#1779D19
hypocenterC19#8967
LCSG ▷ C24×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1779

Complements

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

NH ≅ G/Ntype
1. #14572661C2semidirect
3. #14563545C2semidirect
4. #14561951C2semidirect
5. #14561482C2semidirect
6. #14561481C2semidirect
7. C19×#1779C2semidirect
45. C22×C8×C19D4semidirect
66. C22×C19⋊C8D4semidirect
92. C24×C19M16semidirect
151. C22⋊Dic19M16semidirect
252. #1779D19semidirect
354. C22×C8C22⋊D19semidirect
390. C19#8967semidirect
400. C24#64515semidirect

Maximal subgroups

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

subgroupindex
#145726612
C4×#105973992
#145635452
#145619512
#145614822
#145614812
C19×#17792
#896719