Finite Group Databasebeta

← #18085845

Subgroups — #18085845

Order 4864.

694 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14569443C211yesmaximal, characteristic
2#14563940C211yesmaximal, characteristic, complemented
3#14563822C211yesmaximal, characteristic, complemented
4C2×#11926280C211yesmaximal, characteristic, complemented
5C2×#11926267C211yesmaximal, characteristic
6#14561881C211yesmaximal, characteristic
7C19×#1294C211yesmaximal, characteristic, complemented
8C2×#10597370C2211yescharacteristic
9C22×C4⋊Dic19C2211yescharacteristic
10C22×(C2×D19)⋊C4—21no—
11C22×(C2×D19)⋊C4C2211yescharacteristic
12C2×#10597264—21no—
13C2×#10597273—21no—
14C2×C22⋊(C19⋊C8)C2211yescharacteristic
15#11926481—21no—
16#11926466—21no—
17#11926466—21no—
18#11926457—21no—
19#11926419—21no—
20#11926399—21no—
21C2×C19⋊#95—21no—
22#11926307—21no—
23#11926306—21no—
24#11926280—22no—
25#11926267—22no—
26C2×C19×C22⋊C8C2211yescharacteristic
27C19×#380C2211yescharacteristic
28C2×C19×#95C2211yescharacteristic
29C24×D19D411yescharacteristic
30C23×C4×C19—21no—
31C23×C4×C19C2311yescharacteristic
32C23×Dic19—21no—
33C23×Dic19D411yescharacteristic
34C22×Dic38D411yescharacteristic
35C22×C8×C19—21no—
36C2×C4⋊C4×C19D411yescharacteristic
37C2×C4⋊C4×C19D411yescharacteristic
38C2×C22⋊C4×C19—21no—
39C2×C22⋊Dic19—21no—
40C2×(C2×D19)⋊C4—21no—
41C2×(C2×D19)⋊C4—21no—
42C2×(C2×D19)⋊C4—21no—
43C2×(C2×D19)⋊C4—21no—
44C2×(C2×D19)⋊C4—21no—
45C2×(C2×D19)⋊C4—21no—
46C2×(C2×D19)⋊C4—21no—
47C2×(C2×D19)⋊C4—21no—
48C2×(C2×D19)⋊C4—21no—
49C2×(C2×D19)⋊C4—21no—
50C2×(C2×D19)⋊C4—42no—
51C2×(C2×D19)⋊C4—42no—
52C2×(C2×D19)⋊C4—42no—
53C2×C4⋊Dic19—21no—
54C2×C4⋊Dic19—21no—
55C2×C4⋊Dic19—21no—
56C2×C4⋊Dic19—21no—
57C2×C4⋊Dic19—42no—
58C2×C4⋊Dic19D411yescharacteristic
59#10597370—21no—
60#10597370—21no—
61#10597370—21no—
62#10597370—21no—
63C2×Dic19⋊C4—21no—
64C22×C19⋊C8—21no—
65C19×C22⋊C8—21no—
66C19×C22⋊C8—21no—
67C19×#95—21no—
68C19×#95—21no—
69C19×#95—21no—
70C19⋊#95—21no—
71C19⋊#95—21no—
72C19⋊#95—42no—
73C22⋊(C19⋊C8)—21no—
74C22⋊(C19⋊C8)D412yes—
75#10597273—42no—
76#10597264—42no—
77C24×C19C2×D411yescharacteristic
78C23×D19—21no—
79C23×D19—21no—
80C23×D19—21no—
81C23×D19—21no—
82C23×D19—21no—
83C23×D19—21no—
84C23×D19—41no—
85C23×D19—41no—
86C23×D19—41no—
87C23×D19—41no—
88C23×D19Q1612yes—
89C22×C4×C19—22no—
90C22×C4×C19—21no—
91C22×C4×C19—21no—
92C22×C4×C19—41no—
93C22×C4×C19—41no—
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×C19C2×D411yescharacteristic
101C22×C4×C19C2×D411yescharacteristic
102C22×C4×C19C2×D411yescharacteristic
103C22×C4×C19#4111yescharacteristic
104C22×C4×C19#4111yescharacteristic
105C22×C4×C19#4111yescharacteristic
106C22×Dic19—22no—
107C22×Dic19—21no—
108C22×Dic19—21no—
109C22×Dic19—21no—
110C22×Dic19—21no—
111C22×Dic19—21no—
112C22×Dic19—41no—
113C22×Dic19—41no—
114C22×Dic19—41no—
115C22×Dic19—41no—
116C22×Dic19—41no—
117C22×Dic19—41no—
118C22×Dic19—41no—
119C22×Dic19—41no—
120C2×Dic38—21no—
121C2×Dic38—21no—
122C2×Dic38—41no—
123C2×Dic38—41no—
124C2×C8×C19—41no—
125C2×C8×C19—41no—
126C2×C8×C19—41no—
127C4⋊C4×C19—41no—
128C4⋊C4×C19—41no—
129C22⋊C4×C19—41no—
130C22⋊C4×C19—41no—
131C22⋊Dic19—41no—
132C22⋊Dic19—41no—
133(C2×D19)⋊C4—48no—
134(C2×D19)⋊C4—41no—
135(C2×D19)⋊C4—41no—
136(C2×D19)⋊C4—41no—
137(C2×D19)⋊C4—41no—
138(C2×D19)⋊C4—81no—
139(C2×D19)⋊C4—81no—
140(C2×D19)⋊C4—81no—
141(C2×D19)⋊C4—81no—
142C4⋊Dic19—22no—
143C4⋊Dic19—22no—
144C4⋊Dic19—21no—
145C4⋊Dic19—21no—
146C4⋊Dic19—41no—
147C4⋊Dic19—41no—
148C4⋊Dic19—81no—
149C4⋊Dic19—81no—
150Dic19⋊C4—41no—
151Dic19⋊C4—41no—
152C2×C19⋊C8—22no—
153C2×C19⋊C8—41no—
154C2×C19⋊C8—41no—
155#10399—191nomaximal, Sylow
156C23×C19—21no—
157C23×C19—21no—
158C23×C19—21no—
159C23×C19—21no—
160C23×C19#12011yescharacteristic
161C23×C19#12111yescharacteristic
162C23×C19#12311yescharacteristic
163C23×C19C2×Q1611yescharacteristic
164C23×C19#13511yescharacteristic
165C23×C19AGL(1,ℤ/8)11yescharacteristic
166C23×C19#13711yescharacteristic
167C22×D19—22no—
168C22×D19—22no—
169C22×D19—22no—
170C22×D19—42no—
171C22×D19—42no—
172C22×D19—42no—
173C22×D19—42no—
174C22×D19—42no—
175C22×D19—42no—
176C22×D19—41no—
177C22×D19—41no—
178C22×D19—41no—
179C22×D19—41no—
180C22×D19—41no—
181C22×D19—41no—
182C22×D19—41no—
183C22×D19—41no—
184C22×D19—81no—
185C22×D19—81no—
186C22×D19—81no—
187C22×D19—81no—
188C22×D19—81no—
189C22×D19—81no—
190C2×C4×C19—21no—
191C2×C4×C19—21no—
192C2×C4×C19—21no—
193C2×C4×C19—21no—
194C2×C4×C19—41no—
195C2×C4×C19—41no—
196C2×C4×C19—41no—
197C2×C4×C19—41no—
198C2×C4×C19—42no—
199C2×C4×C19—42no—
200C2×C4×C19—42no—
201C2×C4×C19—41no—
202C2×C4×C19—41no—
203C2×C4×C19—41no—
204C2×C4×C19—41no—
205C2×C4×C19—41no—
206C2×C4×C19—41no—
207C2×C4×C19—81no—
208C2×C4×C19—81no—
209C2×C4×C19—81no—
210C2×C4×C19—81no—
211C2×C4×C19#12111yescharacteristic
212C2×C4×C19#12111yescharacteristic
213C2×C4×C19#12311yescharacteristic
214C2×C4×C19#12411yescharacteristic
215C2×Dic19—42no—
216C2×Dic19—42no—
217C2×Dic19—42no—
218C2×Dic19—41no—
219C2×Dic19—41no—
220C2×Dic19—41no—
221C2×Dic19—41no—
222C2×Dic19—41no—
223C2×Dic19—41no—
224C2×Dic19—41no—
225C2×Dic19—42no—
226C2×Dic19—41no—
227C2×Dic19—41no—
228C2×Dic19—81no—
229C2×Dic19—81no—
230C2×Dic19—81no—
231C2×Dic19—81no—
232C2×Dic19—81no—
233Dic38—42no—
234Dic38—81no—
235C8×C19—81no—
236C19⋊C8—42no—
237#2626—191no—
238#1872—191no—
239#1852—191no—
240C2×#328—191no—
241C2×#323—191no—
242#1439—191no—
243#1294D1911yescharacteristic, complemented
244C22×C19—21no—
245C22×C19—21no—
246C22×C19—21no—
247C22×C19—21no—
248C22×C19—21no—
249C22×C19—21no—
250C22×C19—21no—
251C22×C19—21no—
252C22×C19—21no—
253C22×C19—21no—
254C22×C19—21no—
255C22×C19—21no—
256C22×C19#39411yescharacteristic
257C22×C19#44911yescharacteristic
258C22×C19#45111yescharacteristic
259C22×C19#45311yescharacteristic
260C22×C19#45511yescharacteristic
261C22×C19B(4,𝔽2)11yescharacteristic
262C22×C19#45811yescharacteristic
263C22×C19#46711yescharacteristic
264C22×C19#46811yescharacteristic
265C22×C19#48411yescharacteristic
266C22×C19#48511yescharacteristic
267C2×D19—44no—
268C2×D19—42no—
269C2×D19—42no—
270C2×D19—42no—
271C2×D19—82no—
272C2×D19—82no—
273C2×D19—81no—
274C2×D19—81no—
275C2×D19—81no—
276C2×D19—81no—
277C2×D19—82no—
278C4×C19—21no—
279C4×C19—21no—
280C4×C19—21no—
281C4×C19—21no—
282C4×C19—82no—
283C4×C19—81no—
284C4×C19—81no—
285Dic19—82no—
286Dic19—81no—
287Dic19—81no—
288Dic19—81no—
289C2×C22⋊Q8—191no—
290C22×C4⋊C4—191no—
291C22×C22⋊C4—191no—
292C22×C22⋊C4—381no—
293C2×#107—381no—
294C2×#103—381no—
295C2×C22⋊C8—191no—
296C2×C22⋊C8C2×D1911yescharacteristic
297#399—381no—
298#396—381no—
299#396—381no—
300#393—381no—
301#385—381no—
302#380C2×D1911yescharacteristic
303#379—381no—
304C2×#95—381no—
305C2×#95C2×D1911yescharacteristic
306#340—381no—
307#340—381no—
308#328—382no—
309#323—382no—
310C2×C19—21no—
311C2×C19—21no—
312C2×C19—21no—
313C2×C19—21no—
314C2×C19#160011yescharacteristic
315C2×C19#160211yescharacteristic
316C2×C19#161211yescharacteristic
317C2×C19#161411yescharacteristic
318C2×C19#203611yescharacteristic
319C2×C19#203711yescharacteristic
320C2×C19#204411yescharacteristic
321D19—82no—
322C25—191no—
323C22×Q8—191no—
324C23×C4—21no—
325C23×C4—191no—
326C23×C4—381no—
327C23×C4C22×D1911yescharacteristic
328C22×C8—21no—
329C22×C8—381no—
330C22⋊Q8—381no—
331C22⋊Q8—381no—
332C22⋊Q8—381no—
333C22⋊Q8—381no—
334C2×C4⋊C4—191no—
335C2×C4⋊C4—381no—
336C2×C4⋊C4—381no—
337C2×C4⋊C4—381no—
338C2×C4⋊C4—381no—
339C2×C4⋊C4—381no—
340C2×C4⋊C4—762no—
341C2×C4⋊C4D7611yescharacteristic
342C2×C4⋊C4D7611yescharacteristic
343C2×C22⋊C4—21no—
344C2×C22⋊C4—381no—
345C2×C22⋊C4—381no—
346C2×C22⋊C4—381no—
347C2×C22⋊C4—381no—
348C2×C22⋊C4—381no—
349C2×C22⋊C4—381no—
350C2×C22⋊C4—381no—
351C2×C22⋊C4—381no—
352C2×C22⋊C4—381no—
353C2×C22⋊C4—381no—
354C2×C22⋊C4—381no—
355C2×C22⋊C4—762no—
356C2×C22⋊C4—762no—
357C2×C22⋊C4—762no—
358#107—762no—
359#103—762no—
360C22⋊C8—21no—
361C22⋊C8—21no—
362C22⋊C8—192no—
363C22⋊C8—381no—
364#95—21no—
365#95—21no—
366#95—21no—
367#95—381no—
368#95—381no—
369#95—762no—
370C19#1039911yescharacteristic, complemented, Sylow
371C24—192no—
372C24—381no—
373C24—381no—
374C24—381no—
375C24—381no—
376C24—381no—
377C24—381no—
378C24—761no—
379C24—761no—
380C24—761no—
381C24—761no—
382C24D4×D1911yescharacteristic
383C2×Q8—381no—
384C2×Q8—381no—
385C2×Q8—761no—
386C2×Q8—761no—
387C22×C4—22no—
388C22×C4—21no—
389C22×C4—21no—
390C22×C4—41no—
391C22×C4—41no—
392C22×C4—41no—
393C22×C4—41no—
394C22×C4—41no—
395C22×C4—41no—
396C22×C4—41no—
397C22×C4—41no—
398C22×C4—382no—
399C22×C4—381no—
400C22×C4—381no—
401C22×C4—381no—
402C22×C4—381no—
403C22×C4—381no—
404C22×C4—761no—
405C22×C4—761no—
406C22×C4—761no—
407C22×C4—761no—
408C22×C4—761no—
409C22×C4—761no—
410C22×C4—761no—
411C22×C4—761no—
412C22×C4C2×D7611yescharacteristic
413C22×C4#6454111yescharacteristic
414C22×C4#6454111yescharacteristic
415C22×C4D4×D1911yescharacteristic
416C22×C4D4×D1911yescharacteristic
417C22×C4#6454511yescharacteristic
418C2×C8—41no—
419C2×C8—41no—
420C2×C8—41no—
421C2×C8—382no—
422C2×C8—761no—
423C2×C8—761no—
424C4⋊C4—41no—
425C4⋊C4—41no—
426C4⋊C4—382no—
427C4⋊C4—382no—
428C4⋊C4—381no—
429C4⋊C4—381no—
430C4⋊C4—761no—
431C4⋊C4—761no—
432C4⋊C4—761no—
433C4⋊C4—761no—
434C4⋊C4—1521no—
435C4⋊C4—1521no—
436C22⋊C4—41no—
437C22⋊C4—41no—
438C22⋊C4—768no—
439C22⋊C4—761no—
440C22⋊C4—761no—
441C22⋊C4—761no—
442C22⋊C4—761no—
443C22⋊C4—761no—
444C22⋊C4—761no—
445C22⋊C4—1521no—
446C22⋊C4—1521no—
447C22⋊C4—1521no—
448C22⋊C4—1521no—
449C23—21no—
450C23—21no—
451C23—21no—
452C23—21no—
453C23—382no—
454C23—382no—
455C23—382no—
456C23—762no—
457C23—762no—
458C23—762no—
459C23—762no—
460C23—762no—
461C23—762no—
462C23—761no—
463C23—761no—
464C23—761no—
465C23—761no—
466C23—761no—
467C23—761no—
468C23—761no—
469C23—761no—
470C23—1521no—
471C23—1521no—
472C23—1521no—
473C23—1521no—
474C23—1521no—
475C23—1521no—
476C23#1059732811yescharacteristic
477C23#1059733011yescharacteristic
478C23#1059734011yescharacteristic
479C23#1059735711yescharacteristic
480C23#1059736111yescharacteristic
481C23#1059736211yescharacteristic
482C23Q16×D1911yescharacteristic
483Q8—762no—
484Q8—1521no—
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—81no—
503C2×C4—81no—
504C2×C4—81no—
505C2×C4—81no—
506C2×C4—762no—
507C2×C4—762no—
508C2×C4—762no—
509C2×C4—761no—
510C2×C4—761no—
511C2×C4—761no—
512C2×C4—761no—
513C2×C4—761no—
514C2×C4—761no—
515C2×C4—761no—
516C2×C4—761no—
517C2×C4—762no—
518C2×C4—761no—
519C2×C4—1521no—
520C2×C4—1521no—
521C2×C4—1521no—
522C2×C4—1521no—
523C2×C4—1521no—
524C2×C4#1059732111yescharacteristic
525C2×C4#1059733011yescharacteristic
526C2×C4#1059734011yescharacteristic
527C2×C4#1059734111yescharacteristic
528C8—81no—
529C8—762no—
530C22—21no—
531C22—21no—
532C22—21no—
533C22—21no—
534C22—21no—
535C22—21no—
536C22—21no—
537C22—21no—
538C22—21no—
539C22—21no—
540C22—21no—
541C22—21no—
542C22—764no—
543C22—762no—
544C22—762no—
545C22—762no—
546C22—1522no—
547C22—1522no—
548C22—1522no—
549C22—1521no—
550C22—1521no—
551C22—1521no—
552C22—1521no—
553C22#1192646211yescharacteristic
554C22#1192669011yescharacteristic
555C22#1192670111yescharacteristic
556C22#1192671311yescharacteristic
557C22#1192672311yescharacteristic
558C22#1192673211yescharacteristic
559C22#1192673511yescharacteristic
560C22#1192678411yescharacteristic
561C22#1192678911yescharacteristic
562C22#1192688111yescharacteristic
563C22#1192688811yescharacteristic
564C4—21no—
565C4—21no—
566C4—21no—
567C4—21no—
568C4—82no—
569C4—81no—
570C4—81no—
571C4—1522no—
572C4—1521no—
573C4—1521no—
574C4—1521no—
575C2—21no—
576C2—21no—
577C2—21no—
578C2—21no—
579C2—1522no—
580C2#1456258211yescharacteristic
581C2#1456259311yescharacteristic
582C2#1456265011yescharacteristic
583C2#1456266111yescharacteristic
584C2#1456484111yescharacteristic
585C2#1456484811yescharacteristic
586C2#1456488711yescharacteristic
subgroupG/H
centerC23#10597328
commutator, cosocleC23×C4×C19C23
FrattiniC23×C4C22×D19
FittingC19×#1294C2
socleC23×C19#120
prime radicalC24×D19D4
hypercenter#1294D19
hypocenterC19#10399
LCSG ▷ C23×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1294

Complements

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

NH ≅ G/Ntype
2. #14563940C2semidirect
3. #14563822C2semidirect
4. C2×#11926280C2semidirect
7. C19×#1294C2semidirect
243. #1294D19semidirect
370. C19#10399semidirect

Maximal subgroups

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

subgroupindex
#145694432
#145639402
#145638222
C2×#119262802
C2×#119262672
#145618812
C19×#12942
#1039919