Finite Group Databasebeta

← #18084853

Subgroups — #18084853

Order 4864.

728 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11926821C211yesmaximal, characteristic, complemented
2C2×#11926746C211yesmaximal, characteristic, complemented
3#14568551C211yesmaximal, characteristic
4C2×#11926273C211yesmaximal, characteristic, complemented
5C2×#11926273C211yesmaximal, characteristic, complemented
6#14561518C211yesmaximal, characteristic, complemented
7C19×#1990C211yesmaximal, characteristic, complemented
8C22×#64527—21no—
9C2×#10597341—21no—
10C2×#10597341—21no—
11C2×C4×D76C2211yescharacteristic
12C2×C4×D76C2211yescharacteristic
13#11926821—22no—
14#11926821—22no—
15#11926746—22no—
16#11926746—22no—
17C2×#10597264—21no—
18C2×C4⋊(C19⋊C8)C2211yescharacteristic
19C2×C4⋊(C19⋊C8)C2211yescharacteristic
20C2×#10597292—21no—
21C2×#10597266—21no—
22#11926461—22no—
23#11926401—21no—
24#11926401—21no—
25#11926273—22no—
26#11926273—22no—
27C2×C19×C4⋊Q8C2211yescharacteristic
28C2×C4×C8×C19C2211yescharacteristic
29C19×#384C2211yescharacteristic
30C19×#340—22no—
31C22×Q8×C19—21no—
32C22×D76—22no—
33C22×D76D411yescharacteristic
34C22×D76D411yescharacteristic
35C22×C4×D19—21no—
36C22×C4×D19—21no—
37C22×C8×C19—21no—
38C19×C4⋊Q8—21no—
39C19×C4⋊Q8—21no—
40C19×C4⋊Q8—21no—
41C19×C4⋊Q8D412yescomplemented
42C2×C4⋊C4×C19—21no—
43C2×C4⋊C4×C19—21no—
44C2×C4⋊C4×C19—21no—
45C2×C4⋊C4×C19—21no—
46C2×C4⋊C4×C19D412yes—
47C2×C42×C19C2311yescharacteristic
48C2×#64527—24no—
49C2×#64527—42no—
50C2×#64527—42no—
51C2×(C2×D19)⋊C4—22no—
52C2×(C2×D19)⋊C4—22no—
53C2×(C2×D19)⋊C4—21no—
54C2×(C2×D19)⋊C4—21no—
55C2×C4⋊Dic19D411yescharacteristic
56C2×C4⋊Dic19D411yescharacteristic
57C22×C19⋊C8—21no—
58C22×C19⋊C8—21no—
59#10597341—42no—
60#10597341—42no—
61#10597341—42no—
62#10597341—42no—
63C4×D76—21no—
64C4×D76—21no—
65C4×D76—21no—
66C4×D76—21no—
67C4×D76—21no—
68C4×D76—21no—
69C4×D76—21no—
70C4×D76—21no—
71C4×C8×C19—21no—
72C4×C8×C19—21no—
73#10597292—24no—
74C19⋊#95—22no—
75#10597266—24no—
76#10597264—24no—
77C4⋊(C19⋊C8)—21no—
78C4⋊(C19⋊C8)—21no—
79C4⋊(C19⋊C8)D412yescomplemented
80C4⋊(C19⋊C8)D412yescomplemented
81C23×D19—21no—
82C23×D19—21no—
83C2×Q8×C19—22no—
84C2×Q8×C19—41no—
85C2×Q8×C19—41no—
86C2×Q8×C19—41no—
87C2×Q8×C19—41no—
88C2×Q8×C19—41no—
89C22×C4×C19—22no—
90C22×C4×C19—41no—
91C22×C4×C19C2×D411yescharacteristic
92C22×C4×C19C2×D411yescharacteristic
93C22×C4×C19C2×D411yescharacteristic
94C22×Dic19—21no—
95C22×Dic19—21no—
96C2×D76—21no—
97C2×D76—21no—
98C2×D76—21no—
99C2×D76—21no—
100C2×D76—21no—
101C2×D76—21no—
102C2×D76—21no—
103C2×D76—21no—
104C2×D76—21no—
105C2×D76—21no—
106C2×D76—44no—
107C2×D76—44no—
108C2×D76—82no—
109C2×D76D812yes—
110C2×D76SD1612yescomplemented
111C2×C4×D19—41no—
112C2×C4×D19—41no—
113C2×C4×D19—41no—
114C2×C4×D19—41no—
115C2×C4×D19—41no—
116C2×C4×D19—41no—
117C2×C4×D19—41no—
118C2×C4×D19—41no—
119C2×C4×D19—41no—
120C2×C4×D19—41no—
121C2×C4×D19—41no—
122C2×C4×D19—41no—
123C2×C8×C19—22no—
124C2×C8×C19—41no—
125C2×C8×C19—41no—
126C4⋊C4×C19—22no—
127C4⋊C4×C19—22no—
128C4⋊C4×C19—42no—
129C4⋊C4×C19—41no—
130C4⋊C4×C19—41no—
131C4⋊C4×C19—41no—
132C4⋊C4×C19—41no—
133C4⋊C4×C19—41no—
134C4⋊C4×C19—41no—
135C42×C19C2×D411yescharacteristic
136C42×C19C2×D411yescharacteristic
137C42×C19C2×D411yescharacteristic
138C42×C19#4111yescharacteristic
139#64527—48no—
140(C2×D19)⋊C4—44no—
141(C2×D19)⋊C4—44no—
142(C2×D19)⋊C4—41no—
143(C2×D19)⋊C4—41no—
144(C2×D19)⋊C4—41no—
145(C2×D19)⋊C4—41no—
146C4⋊Dic19—21no—
147C4⋊Dic19—21no—
148C4⋊Dic19—21no—
149C4⋊Dic19—21no—
150C2×C19⋊C8—22no—
151C2×C19⋊C8—22no—
152C2×C19⋊C8—41no—
153C2×C19⋊C8—41no—
154C2×C19⋊C8—41no—
155C2×C19⋊C8—41no—
156#10231—191nomaximal, Sylow
157C23×C19#12011yescharacteristic
158C22×D19—22no—
159C22×D19—22no—
160C22×D19—41no—
161C22×D19—41no—
162C22×D19—41no—
163C22×D19—41no—
164C22×D19—41no—
165C22×D19—41no—
166C22×D19—41no—
167C22×D19—41no—
168C22×D19—41no—
169C22×D19—41no—
170C22×D19—41no—
171C22×D19—41no—
172Q8×C19—42no—
173Q8×C19—42no—
174Q8×C19—81no—
175Q8×C19—81no—
176C2×C4×C19—21no—
177C2×C4×C19—21no—
178C2×C4×C19—42no—
179C2×C4×C19—42no—
180C2×C4×C19—42no—
181C2×C4×C19—42no—
182C2×C4×C19—81no—
183C2×C4×C19—81no—
184C2×C4×C19#12011yescharacteristic
185C2×C4×C19#12011yescharacteristic
186C2×C4×C19#12111yescharacteristic
187C2×C4×C19#12111yescharacteristic
188C2×C4×C19#12111yescharacteristic
189C2×C4×C19#12711yescharacteristic
190C2×C4×C19C2×D811yescharacteristic
191C2×C4×C19C2×SD1611yescharacteristic
192C2×C4×C19#13511yescharacteristic
193C2×C4×C19#13511yescharacteristic
194C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
195C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
196C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
197C2×C4×C19#13711yescharacteristic
198C2×Dic19—41no—
199C2×Dic19—41no—
200C2×Dic19—41no—
201C2×Dic19—41no—
202C2×Dic19—41no—
203C2×Dic19—41no—
204D76—22no—
205D76—22no—
206D76—22no—
207D76—22no—
208D76—41no—
209D76—41no—
210D76—41no—
211D76—41no—
212D76—88no—
213C4×D19—81no—
214C4×D19—81no—
215C4×D19—81no—
216C4×D19—81no—
217C4×D19—81no—
218C4×D19—81no—
219C4×D19—81no—
220C4×D19—81no—
221C8×C19—42no—
222C19⋊C8—42no—
223C19⋊C8—42no—
224C2×#474—191no—
225C2×#461—191no—
226#2537—191no—
227#1990D1911yescharacteristic, complemented
228C2×D4⋊C8—191no—
229C2×D4⋊C8—191no—
230#1296—191no—
231C22×C19#39211yescharacteristic
232C22×C19#44711yescharacteristic
233C22×C19#44911yescharacteristic
234C22×C19#45011yescharacteristic
235C22×C19#45211yescharacteristic
236C22×C19#45511yescharacteristic
237C22×C19#45611yescharacteristic
238C2×D19—42no—
239C2×D19—42no—
240C2×D19—42no—
241C2×D19—42no—
242C2×D19—42no—
243C2×D19—42no—
244C2×D19—81no—
245C2×D19—81no—
246C2×D19—81no—
247C2×D19—81no—
248C2×D19—81no—
249C2×D19—81no—
250C2×D19—81no—
251C2×D19—81no—
252C4×C19—21no—
253C4×C19—21no—
254C4×C19—82no—
255C4×C19—82no—
256C4×C19#44711yescharacteristic
257C4×C19#44811yescharacteristic
258C4×C19#44911yescharacteristic
259C4×C19#44911yescharacteristic
260C4×C19#46511yescharacteristic
261C4×C19#46611yescharacteristic
262C4×C19#46811yescharacteristic
263C4×C19#46911yescharacteristic
264Dic19—81no—
265Dic19—81no—
266C22×SD16—381no—
267C2×C4⋊Q8C2×D1911yescharacteristic
268C2×#121—381no—
269C2×#121—381no—
270C2×C4×D4—191no—
271C2×C4×D4—191no—
272#474—382no—
273#474—382no—
274#461—382no—
275#461—382no—
276C2×#107—381no—
277C2×C4⋊C8—191no—
278C2×C4⋊C8—191no—
279C2×#103—381no—
280C2×#102—381no—
281C2×C4×C8C2×D1911yescharacteristic
282#394—382no—
283#384C2×D1911yescharacteristic
284#380—381no—
285#380—381no—
286#340—22no—
287D4⋊C8—382no—
288D4⋊C8—382no—
289C2×C19#163911yescharacteristic
290C2×C19#164611yescharacteristic
291C2×C19#164711yescharacteristic
292C2×C19#165411yescharacteristic
293C2×C19#199911yescharacteristic
294C2×C19#200011yescharacteristic
295C2×C19#200711yescharacteristic
296D19—82no—
297D19—82no—
298C22×Q8—21no—
299C22×D4—191no—
300C22×D4—191no—
301C22×D4—382no—
302C23×C4—381no—
303C23×C4—381no—
304C2×SD16—384no—
305C2×SD16—762no—
306C2×SD16—762no—
307C22×C8—21no—
308C22×C8—381no—
309C22×C8—381no—
310C4⋊Q8—21no—
311C4⋊Q8—21no—
312C4⋊Q8—21no—
313C4⋊Q8D7612yescomplemented
314#121—762no—
315#121—762no—
316#121—762no—
317#121—762no—
318C4×D4—381no—
319C4×D4—381no—
320C4×D4—381no—
321C4×D4—381no—
322C4×D4—381no—
323C4×D4—381no—
324C4×D4—381no—
325C4×D4—381no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—21no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—191no—
331C2×C4⋊C4—191no—
332C2×C4⋊C4C22⋊D1912yes—
333C2×C22⋊C4—382no—
334C2×C22⋊C4—382no—
335C2×C22⋊C4—381no—
336C2×C22⋊C4—381no—
337C2×C42C22×D1911yescharacteristic
338#107—384no—
339C4⋊C8—192no—
340C4⋊C8—192no—
341C4⋊C8—381no—
342C4⋊C8—381no—
343#103—384no—
344#102—384no—
345C4×C8—21no—
346C4×C8—21no—
347#95—382no—
348C19#1023111yescharacteristic, complemented, Sylow
349C24—381no—
350C24—381no—
351C2×Q8—22no—
352C2×Q8—41no—
353C2×Q8—41no—
354C2×Q8—41no—
355C2×Q8—41no—
356C2×Q8—41no—
357C2×D4—192no—
358C2×D4—192no—
359C2×D4—381no—
360C2×D4—381no—
361C2×D4—381no—
362C2×D4—381no—
363C2×D4—381no—
364C2×D4—381no—
365C2×D4—381no—
366C2×D4—381no—
367C2×D4—381no—
368C2×D4—381no—
369C2×D4—764no—
370C2×D4—764no—
371C2×D4—1522no—
372C22×C4—22no—
373C22×C4—41no—
374C22×C4—381no—
375C22×C4—381no—
376C22×C4—761no—
377C22×C4—761no—
378C22×C4—761no—
379C22×C4—761no—
380C22×C4—761no—
381C22×C4—761no—
382C22×C4—761no—
383C22×C4—761no—
384C22×C4—761no—
385C22×C4—761no—
386C22×C4—761no—
387C22×C4—761no—
388C22×C4D4×D1911yescharacteristic
389C22×C4D4×D1911yescharacteristic
390C22×C4C2×C22⋊D1911yescharacteristic
391SD16—768no—
392C2×C8—22no—
393C2×C8—41no—
394C2×C8—41no—
395C2×C8—382no—
396C2×C8—382no—
397C2×C8—761no—
398C2×C8—761no—
399C2×C8—761no—
400C2×C8—761no—
401C4⋊C4—22no—
402C4⋊C4—22no—
403C4⋊C4—42no—
404C4⋊C4—41no—
405C4⋊C4—41no—
406C4⋊C4—41no—
407C4⋊C4—41no—
408C4⋊C4—41no—
409C4⋊C4—41no—
410C4⋊C4—381no—
411C4⋊C4—381no—
412C4⋊C4—381no—
413C4⋊C4—381no—
414C22⋊C4—764no—
415C22⋊C4—764no—
416C22⋊C4—761no—
417C22⋊C4—761no—
418C22⋊C4—761no—
419C22⋊C4—761no—
420C42C2×D7611yescharacteristic
421C42#6454111yescharacteristic
422C42D4×D1911yescharacteristic
423C42D4×D1911yescharacteristic
424C23—382no—
425C23—382no—
426C23—761no—
427C23—761no—
428C23—761no—
429C23—761no—
430C23—761no—
431C23—761no—
432C23—761no—
433C23—761no—
434C23—761no—
435C23—761no—
436C23—761no—
437C23—761no—
438C23#1059738311yescharacteristic
439Q8—42no—
440Q8—42no—
441Q8—81no—
442Q8—81no—
443D4—382no—
444D4—382no—
445D4—382no—
446D4—382no—
447D4—761no—
448D4—761no—
449D4—761no—
450D4—761no—
451D4—1528no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—42no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—42no—
458C2×C4—81no—
459C2×C4—81no—
460C2×C4—761no—
461C2×C4—761no—
462C2×C4—761no—
463C2×C4—761no—
464C2×C4—761no—
465C2×C4—761no—
466C2×C4—1521no—
467C2×C4—1521no—
468C2×C4—1521no—
469C2×C4—1521no—
470C2×C4—1521no—
471C2×C4—1521no—
472C2×C4—1521no—
473C2×C4—1521no—
474C2×C4#1059732811yescharacteristic
475C2×C4#1059732811yescharacteristic
476C2×C4#1059733011yescharacteristic
477C2×C4#1059733011yescharacteristic
478C2×C4D8×D1911yescharacteristic
479C2×C4#1059735711yescharacteristic
480C2×C4SD16×D1911yescharacteristic
481C2×C4#1059736011yescharacteristic
482C2×C4#1059736011yescharacteristic
483C2×C4#1059736211yescharacteristic
484C2×C4#1059736411yescharacteristic
485C2×C4#1059736511yescharacteristic
486C2×C4#1059737611yescharacteristic
487C2×C4#1059738611yescharacteristic
488C8—42no—
489C8—762no—
490C8—762no—
491C22—762no—
492C22—762no—
493C22—762no—
494C22—762no—
495C22—762no—
496C22—762no—
497C22—1521no—
498C22—1521no—
499C22—1521no—
500C22—1521no—
501C22—1521no—
502C22—1521no—
503C22—1521no—
504C22—1521no—
505C22#1192645311yescharacteristic
506C22#1192667611yescharacteristic
507C22#1192668811yescharacteristic
508C22#1192669311yescharacteristic
509C22#1192670511yescharacteristic
510C22#1192672111yescharacteristic
511C22#1192672611yescharacteristic
512C4—21no—
513C4—21no—
514C4—82no—
515C4—82no—
516C4—1521no—
517C4—1521no—
518C4#1192667911yescharacteristic
519C4#1192668411yescharacteristic
520C4#1192669011yescharacteristic
521C4#1192669211yescharacteristic
522C4#1192677611yescharacteristic
523C4#1192677911yescharacteristic
524C4#1192679311yescharacteristic
525C4#1192679611yescharacteristic
526C2—1522no—
527C2—1522no—
528C2#1456281111yescharacteristic
529C2#1456286011yescharacteristic
530C2#1456286711yescharacteristic
531C2#1456291611yescharacteristic
532C2#1456463211yescharacteristic
533C2#1456463711yescharacteristic
534C2#1456468111yescharacteristic
subgroupG/H
centerC23#10597383
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#1990C2
socleC23×C19#120
prime radical#14568551C2
hypercenter#1990D19
hypocenterC19#10231
LCSG ▷ C2×C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1990

Complements

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

NH ≅ G/Ntype
1. C2×#11926821C2semidirect
2. C2×#11926746C2semidirect
4. C2×#11926273C2semidirect
5. C2×#11926273C2semidirect
6. #14561518C2semidirect
7. C19×#1990C2semidirect
41. C19×C4⋊Q8D4semidirect
79. C4⋊(C19⋊C8)D4semidirect
80. C4⋊(C19⋊C8)D4semidirect
110. C2×D76SD16semidirect
227. #1990D19semidirect
313. C4⋊Q8D76semidirect
348. C19#10231semidirect

Maximal subgroups

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

subgroupindex
C2×#119268212
C2×#119267462
#145685512
C2×#119262732
#145615182
C19×#19902
#1023119