Finite Group Databasebeta

← #18085866

Subgroups — #18085866

Order 4864.

716 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14569739C211yesmaximal, characteristic
2#14563952C211yesmaximal, characteristic, complemented
3C2×#11926279C211yesmaximal, characteristic, complemented
4C2×#11926278C211yesmaximal, characteristic, complemented
5#14561894C211yesmaximal, characteristic, complemented
6#14561477C211yesmaximal, characteristic, complemented
7C19×#1874C211yesmaximal, characteristic, complemented
8C2×#10597376C2211yescharacteristic
9C2×#10597385—21no—
10C2×#10597385—21no—
11C2×#10597266—21no—
12C2×C22⋊(C19⋊C8)C2211yescharacteristic
13#11926480—21no—
14#11926479—21no—
15#11926453—21no—
16#11926452—21no—
17C2×C19⋊#95—21no—
18C2×C19⋊#95—21no—
19C2×C19⋊#95C2211yescharacteristic
20C2×C19⋊#95C2211yescharacteristic
21#11926306—21no—
22#11926279—22no—
23#11926278—22no—
24C2×C19×#121C2211yescharacteristic
25C22×C4⋊C4×C19C2211yescharacteristic
26C2×C19×#102—21no—
27C2×C19×C22⋊C8C2211yescharacteristic
28C19×#340—21no—
29C22×D4×C19—21no—
30C22×D4×C19D411yescharacteristic
31C23×C4×C19—21no—
32C23×C4×C19C2311yescharacteristic
33C22×C22⋊D19—21no—
34C22×C22⋊D19—21no—
35C22×C22⋊D19—21no—
36C23×Dic19—21no—
37C23×Dic19D411yescharacteristic
38C23×Dic19D411yescharacteristic
39C22×D76D411yescharacteristic
40C22×C8×C19—21no—
41C19×#121—21no—
42C19×#121—21no—
43C19×#121—21no—
44C19×#121—21no—
45C2×C4⋊C4×C19—21no—
46C2×C4⋊C4×C19—21no—
47C2×C4⋊C4×C19—42no—
48C2×C4⋊C4×C19D411yescharacteristic
49C2×C22⋊C4×C19—21no—
50C2×C22⋊Dic19—21no—
51C2×C22⋊Dic19—21no—
52#10597385—42no—
53#10597385—42no—
54#10597385—42no—
55#10597385—42no—
56#10597376—21no—
57#10597376—21no—
58#10597376—21no—
59#10597376—21no—
60C2×(C2×D19)⋊C4—21no—
61C2×(C2×D19)⋊C4—21no—
62C2×(C2×D19)⋊C4—21no—
63C2×C4⋊Dic19D411yescharacteristic
64C2×Dic19⋊C4—21no—
65C2×Dic19⋊C4—21no—
66C22×C19⋊C8—21no—
67C19×#102—42no—
68C19×C22⋊C8—21no—
69C19×C22⋊C8—21no—
70C19⋊#95—21no—
71C19⋊#95—21no—
72C19⋊#95—21no—
73C19⋊#95—42no—
74C19⋊#95—42no—
75C19⋊#95D412yescomplemented
76C22⋊(C19⋊C8)—21no—
77C22⋊(C19⋊C8)—21no—
78#10597266—42no—
79C24×C19—21no—
80C24×C19C2×D411yescharacteristic
81C23×D19—21no—
82C2×D4×C19—21no—
83C2×D4×C19—21no—
84C2×D4×C19—41no—
85C2×D4×C19—41no—
86C2×D4×C19—41no—
87C2×D4×C19—41no—
88C2×D4×C19—41no—
89C2×D4×C19—41no—
90C2×D4×C19—41no—
91C2×D4×C19—41no—
92C22×C4×C19—22no—
93C22×C4×C19—21no—
94C22×C4×C19—41no—
95C22×C4×C19—41no—
96C22×C4×C19—41no—
97C22×C4×C19—41no—
98C22×C4×C19—41no—
99C22×C4×C19—41no—
100C22×C4×C19—41no—
101C22×C4×C19—41no—
102C22×C4×C19C2×D411yescharacteristic
103C22×C4×C19C2×D411yescharacteristic
104C22×C4×C19C2×D411yescharacteristic
105C22×C4×C19#4111yescharacteristic
106C22×C4×C19#4111yescharacteristic
107C22×C4×C19#4111yescharacteristic
108C2×C22⋊D19—42no—
109C2×C22⋊D19—42no—
110C2×C22⋊D19—41no—
111C2×C22⋊D19—41no—
112C2×C22⋊D19—41no—
113C2×C22⋊D19—41no—
114C2×C22⋊D19—41no—
115C2×C22⋊D19—41no—
116C2×C22⋊D19—81no—
117C2×C22⋊D19—81no—
118C2×C22⋊D19—81no—
119C2×C22⋊D19—81no—
120C22×Dic19—21no—
121C22×Dic19—21no—
122C22×Dic19—21no—
123C22×Dic19—21no—
124C22×Dic19—21no—
125C22×Dic19—22no—
126C22×Dic19—41no—
127C22×Dic19—41no—
128C22×Dic19—41no—
129C22×Dic19—41no—
130C22×Dic19—41no—
131C22×Dic19—41no—
132C22×Dic19—41no—
133C22×Dic19—41no—
134C22×Dic19—41no—
135C22×Dic19—41no—
136C22×Dic19D812yes—
137C22×Dic19SD1612yes—
138C2×D76—21no—
139C2×D76—21no—
140C2×D76—41no—
141C2×D76—41no—
142C2×C8×C19—41no—
143C2×C8×C19—41no—
144C2×C8×C19—41no—
145C4⋊C4×C19—22no—
146C4⋊C4×C19—22no—
147C4⋊C4×C19—21no—
148C4⋊C4×C19—21no—
149C4⋊C4×C19—41no—
150C4⋊C4×C19—41no—
151C22⋊C4×C19—41no—
152C22⋊C4×C19—41no—
153C22⋊Dic19—42no—
154C22⋊Dic19—42no—
155(C2×D19)⋊C4—42no—
156(C2×D19)⋊C4—42no—
157(C2×D19)⋊C4—41no—
158(C2×D19)⋊C4—41no—
159C4⋊Dic19—21no—
160C4⋊Dic19—21no—
161Dic19⋊C4—42no—
162Dic19⋊C4—42no—
163C2×C19⋊C8—41no—
164C2×C19⋊C8—41no—
165C2×C19⋊C8—41no—
166#10403—191nomaximal, Sylow
167C23×C19—21no—
168C23×C19—21no—
169C23×C19—21no—
170C23×C19—21no—
171C23×C19—41no—
172C23×C19—41no—
173C23×C19—41no—
174C23×C19—41no—
175C23×C19—41no—
176C23×C19—41no—
177C23×C19—41no—
178C23×C19#12011yescharacteristic
179C23×C19#12111yescharacteristic
180C23×C19#12411yescharacteristic
181C23×C19C2×D811yescharacteristic
182C23×C19C2×SD1611yescharacteristic
183C23×C19AGL(1,ℤ/8)11yescharacteristic
184C23×C19AGL(1,ℤ/8)11yescharacteristic
185C22×D19—41no—
186C22×D19—41no—
187C22×D19—41no—
188C22×D19—41no—
189C22×D19—41no—
190C22×D19—41no—
191C22×D19—41no—
192D4×C19—42no—
193D4×C19—81no—
194D4×C19—81no—
195D4×C19—81no—
196D4×C19—81no—
197D4×C19—81no—
198C2×C4×C19—21no—
199C2×C4×C19—21no—
200C2×C4×C19—21no—
201C2×C4×C19—21no—
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—41no—
209C2×C4×C19—41no—
210C2×C4×C19—41no—
211C2×C4×C19—42no—
212C2×C4×C19—81no—
213C2×C4×C19—81no—
214C2×C4×C19—81no—
215C2×C4×C19—81no—
216C2×C4×C19#12111yescharacteristic
217C2×C4×C19#12111yescharacteristic
218C2×C4×C19#12311yescharacteristic
219C2×C4×C19#12311yescharacteristic
220C22⋊D19—84no—
221C22⋊D19—84no—
222C22⋊D19—81no—
223C22⋊D19—81no—
224C22⋊D19—81no—
225C22⋊D19—81no—
226C2×Dic19—22no—
227C2×Dic19—22no—
228C2×Dic19—41no—
229C2×Dic19—41no—
230C2×Dic19—41no—
231C2×Dic19—41no—
232C2×Dic19—42no—
233C2×Dic19—42no—
234C2×Dic19—42no—
235C2×Dic19—42no—
236C2×Dic19—41no—
237C2×Dic19—41no—
238C2×Dic19—41no—
239C2×Dic19—42no—
240C2×Dic19—81no—
241C2×Dic19—81no—
242C2×Dic19—81no—
243C2×Dic19—81no—
244C2×Dic19—81no—
245C2×Dic19—81no—
246D76—42no—
247D76—81no—
248C8×C19—81no—
249C19⋊C8—81no—
250#2656—191no—
251#1874—191no—
252#1874D1911yescharacteristic, complemented
253C2×#327—191no—
254C2×#327—191no—
255#1442—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—81no—
270C22×C19—81no—
271C22×C19—81no—
272C22×C19—81no—
273C22×C19—81no—
274C22×C19—81no—
275C22×C19—81no—
276C22×C19#39411yescharacteristic
277C22×C19#44711yescharacteristic
278C22×C19#45011yescharacteristic
279C22×C19#45411yescharacteristic
280C22×C19#45511yescharacteristic
281C22×C19B(4,𝔽2)11yescharacteristic
282C22×C19#45811yescharacteristic
283C22×C19#45911yescharacteristic
284C22×C19#46011yescharacteristic
285C22×C19#48611yescharacteristic
286C22×C19#49011yescharacteristic
287C2×D19—81no—
288C2×D19—81no—
289C2×D19—81no—
290C2×D19—81no—
291C2×D19—81no—
292C2×D19—81no—
293C2×D19—81no—
294C4×C19—21no—
295C4×C19—21no—
296C4×C19—21no—
297C4×C19—21no—
298C4×C19—82no—
299C4×C19—81no—
300Dic19—42no—
301Dic19—42no—
302Dic19—82no—
303Dic19—81no—
304C2×#121—191no—
305C2×#121—381no—
306C2×#121—381no—
307C2×#121C2×D1911yescharacteristic
308C22×C4⋊C4C2×D1911yescharacteristic
309C2×#102—21no—
310C2×#102—381no—
311C2×C22⋊C8—191no—
312C2×C22⋊C8C2×D1911yescharacteristic
313#399—381no—
314#399—381no—
315#392—381no—
316#392—381no—
317C2×#95—191no—
318C2×#95—191no—
319C2×#95—381no—
320C2×#95—381no—
321#340—21no—
322#340—381no—
323#327—382no—
324#327—382no—
325C2×C19—21no—
326C2×C19—21no—
327C2×C19—21no—
328C2×C19—21no—
329C2×C19—161no—
330C2×C19#159811yescharacteristic
331C2×C19#160111yescharacteristic
332C2×C19#160711yescharacteristic
333C2×C19#161611yescharacteristic
334C2×C19#204011yescharacteristic
335C2×C19#204111yescharacteristic
336C2×C19#204411yescharacteristic
337D19—161no—
338C22×D4—21no—
339C22×D4—191no—
340C22×D4—381no—
341C22×D4—381no—
342C22×D4—381no—
343C22×D4C22⋊D1911yescharacteristic
344C23×C4—21no—
345C23×C4—191no—
346C23×C4—191no—
347C23×C4—381no—
348C23×C4C22×D1911yescharacteristic
349C22×C8—21no—
350C22×C8—381no—
351#121—21no—
352#121—21no—
353#121—21no—
354#121—21no—
355#121—381no—
356#121—381no—
357#121—381no—
358#121—381no—
359#121—762no—
360#121—762no—
361#121—762no—
362#121—762no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—42no—
366C2×C4⋊C4—191no—
367C2×C4⋊C4—381no—
368C2×C4⋊C4—381no—
369C2×C4⋊C4C22⋊D1911yescharacteristic
370C2×C22⋊C4—21no—
371C2×C22⋊C4—381no—
372C2×C22⋊C4—381no—
373C2×C22⋊C4—381no—
374C2×C22⋊C4—381no—
375C2×C22⋊C4—381no—
376#102—42no—
377#102—762no—
378C22⋊C8—21no—
379C22⋊C8—21no—
380C22⋊C8—381no—
381C22⋊C8—381no—
382#95—192no—
383#95—381no—
384#95—381no—
385#95—381no—
386#95—762no—
387#95—762no—
388C19#1040311yescharacteristic, complemented, Sylow
389C24—21no—
390C24—381no—
391C24D4×D1911yescharacteristic
392C2×D4—21no—
393C2×D4—21no—
394C2×D4—41no—
395C2×D4—41no—
396C2×D4—41no—
397C2×D4—41no—
398C2×D4—41no—
399C2×D4—41no—
400C2×D4—41no—
401C2×D4—41no—
402C2×D4—381no—
403C2×D4—381no—
404C2×D4—761no—
405C2×D4—761no—
406C2×D4—762no—
407C2×D4—762no—
408C2×D4—761no—
409C2×D4—761no—
410C2×D4—761no—
411C2×D4—761no—
412C2×D4—761no—
413C2×D4—761no—
414C2×D4—1521no—
415C2×D4—1521no—
416C2×D4—1521no—
417C2×D4—1521no—
418C22×C4—22no—
419C22×C4—21no—
420C22×C4—41no—
421C22×C4—41no—
422C22×C4—41no—
423C22×C4—41no—
424C22×C4—41no—
425C22×C4—41no—
426C22×C4—41no—
427C22×C4—41no—
428C22×C4—192no—
429C22×C4—192no—
430C22×C4—381no—
431C22×C4—381no—
432C22×C4—381no—
433C22×C4—381no—
434C22×C4—381no—
435C22×C4—382no—
436C22×C4—761no—
437C22×C4—761no—
438C22×C4—761no—
439C22×C4—761no—
440C22×C4—761no—
441C22×C4—761no—
442C22×C4—761no—
443C22×C4—761no—
444C22×C4—761no—
445C22×C4—761no—
446C22×C4#6454111yescharacteristic
447C22×C4#6454111yescharacteristic
448C22×C4D4×D1911yescharacteristic
449C22×C4D4×D1911yescharacteristic
450C22×C4#6454311yescharacteristic
451C22×C4C2×C22⋊D1911yescharacteristic
452C2×C8—41no—
453C2×C8—41no—
454C2×C8—41no—
455C2×C8—761no—
456C2×C8—761no—
457C2×C8—761no—
458C4⋊C4—22no—
459C4⋊C4—22no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—41no—
463C4⋊C4—41no—
464C4⋊C4—381no—
465C4⋊C4—381no—
466C4⋊C4—762no—
467C4⋊C4—762no—
468C22⋊C4—41no—
469C22⋊C4—41no—
470C22⋊C4—762no—
471C22⋊C4—762no—
472C22⋊C4—762no—
473C22⋊C4—762no—
474C22⋊C4—761no—
475C22⋊C4—761no—
476C23—21no—
477C23—21no—
478C23—21no—
479C23—21no—
480C23—41no—
481C23—41no—
482C23—41no—
483C23—41no—
484C23—41no—
485C23—41no—
486C23—41no—
487C23—761no—
488C23—761no—
489C23—761no—
490C23—761no—
491C23—761no—
492C23—761no—
493C23—761no—
494C23#1059733011yescharacteristic
495C23#1059733111yescharacteristic
496C23D8×D1911yescharacteristic
497C23#1059735711yescharacteristic
498C23SD16×D1911yescharacteristic
499C23#1059736011yescharacteristic
500C23#1059738311yescharacteristic
501D4—42no—
502D4—81no—
503D4—81no—
504D4—81no—
505D4—81no—
506D4—81no—
507D4—762no—
508D4—1521no—
509D4—1524no—
510D4—1524no—
511D4—1521no—
512D4—1521no—
513D4—1521no—
514D4—1521no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—42no—
529C2×C4—81no—
530C2×C4—81no—
531C2×C4—81no—
532C2×C4—81no—
533C2×C4—382no—
534C2×C4—382no—
535C2×C4—761no—
536C2×C4—761no—
537C2×C4—761no—
538C2×C4—761no—
539C2×C4—762no—
540C2×C4—762no—
541C2×C4—762no—
542C2×C4—762no—
543C2×C4—761no—
544C2×C4—761no—
545C2×C4—761no—
546C2×C4—762no—
547C2×C4—1521no—
548C2×C4—1521no—
549C2×C4—1521no—
550C2×C4—1521no—
551C2×C4—1521no—
552C2×C4—1521no—
553C2×C4#1059732911yescharacteristic
554C2×C4#1059733011yescharacteristic
555C2×C4#1059737511yescharacteristic
556C2×C4#1059738511yescharacteristic
557C8—81no—
558C8—1521no—
559C22—21no—
560C22—21no—
561C22—21no—
562C22—21no—
563C22—21no—
564C22—21no—
565C22—21no—
566C22—21no—
567C22—21no—
568C22—21no—
569C22—21no—
570C22—21no—
571C22—81no—
572C22—81no—
573C22—81no—
574C22—81no—
575C22—81no—
576C22—81no—
577C22—81no—
578C22—1521no—
579C22—1521no—
580C22—1521no—
581C22—1521no—
582C22—1521no—
583C22—1521no—
584C22—1521no—
585C22#1192645911yescharacteristic
586C22#1192667611yescharacteristic
587C22#1192669311yescharacteristic
588C22#1192671511yescharacteristic
589C22#1192672011yescharacteristic
590C22#1192673011yescharacteristic
591C22#1192673311yescharacteristic
592C22#1192673811yescharacteristic
593C22#1192674311yescharacteristic
594C22#1192688911yescharacteristic
595C22#1192690711yescharacteristic
596C4—21no—
597C4—21no—
598C4—21no—
599C4—21no—
600C4—81no—
601C4—82no—
602C4—762no—
603C4—762no—
604C4—1522no—
605C4—1521no—
606C2—21no—
607C2—21no—
608C2—21no—
609C2—21no—
610C2—161no—
611C2—3041no—
612C2#1456256811yescharacteristic
613C2#1456258511yescharacteristic
614C2#1456261911yescharacteristic
615C2#1456267011yescharacteristic
616C2#1456486211yescharacteristic
617C2#1456486711yescharacteristic
618C2#1456488411yescharacteristic
subgroupG/H
centerC23#10597383
commutator, cosocleC23×C4×C19C23
FrattiniC23×C4C22×D19
FittingC19×#1874C2
socleC23×C19#120
prime radical#14569739C2
hypercenter#1874D19
hypocenterC19#10403
LCSG ▷ C23×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1874

Complements

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

NH ≅ G/Ntype
2. #14563952C2semidirect
3. C2×#11926279C2semidirect
4. C2×#11926278C2semidirect
5. #14561894C2semidirect
6. #14561477C2semidirect
7. C19×#1874C2semidirect
75. C19⋊#95D4semidirect
252. #1874D19semidirect
388. C19#10403semidirect

Maximal subgroups

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

subgroupindex
#145697392
#145639522
C2×#119262792
C2×#119262782
#145618942
#145614772
C19×#18742
#1040319