Finite Group Databasebeta

← #18079866

Subgroups — #18079866

Order 4864.

618 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14572661C211yesmaximal, characteristic, complemented
2#14568597C211yesmaximal, characteristic
3#14563620C211yesmaximal, characteristic, complemented
4#14562203C211yesmaximal, characteristic, complemented
5#14561515C211yesmaximal, characteristic, complemented
6#14561513C211yesmaximal, characteristic, complemented
7C19×#1519C211yesmaximal, characteristic, complemented
8C2×#10597385—21no—
9C2×C4×C22⋊D19C2211yescharacteristic
10#11926615—22no—
11#11926612—22no—
12#11926598—21no—
13C2×#10597263—21no—
14#11926506—21no—
15C2×C22⋊(C19⋊C8)C2211yescharacteristic
16#11926475C411yescharacteristic, complemented
17#11926470C411yescharacteristic, complemented
18#11926458C411yescharacteristic, complemented
19#11926452C411yescharacteristic, complemented
20#11926432—21no—
21#11926424—21no—
22#11926420—21no—
23#11926404C2211yescharacteristic
24C2×C19⋊#95C2211yescharacteristic
25#11926310—21no—
26#11926278—22no—
27C2×C19×#121C2211yescharacteristic
28C2×C19×C22⋊C8C2211yescharacteristic
29C19×#380C2211yescharacteristic
30C19×#327—22no—
31C22×D4×C19—21no—
32C22×D4×C19C2×C411yescharacteristic
33C23×C4×C19C2311yescharacteristic
34C22×C22⋊D19—21no—
35C22×C22⋊D19D411yescharacteristic
36C23×Dic19—21no—
37C22×C4×D19D411yescharacteristic
38C22×C8×C19—21no—
39C19×#121—21no—
40C19×#121—21no—
41C19×#121—21no—
42C19×#121—21no—
43C2×C4⋊C4×C19—21no—
44C2×C4⋊C4×C19C2×C411yescharacteristic
45C2×C22⋊C4×C19—21no—
46C2×C22⋊C4×C19—21no—
47C2×C22⋊Dic19—21no—
48C2×C22⋊Dic19—21no—
49C2×C22⋊Dic19—21no—
50C2×C22⋊Dic19—21no—
51C2×C22⋊Dic19D411yescharacteristic
52#10597385—42no—
53#10597385—42no—
54C4×C22⋊D19—21no—
55C4×C22⋊D19—21no—
56C4×C22⋊D19—21no—
57C4×C22⋊D19—21no—
58C2×(C2×D19)⋊C4—21no—
59C2×(C2×D19)⋊C4C2×C411yescharacteristic
60C2×C4⋊Dic19—21no—
61C2×Dic19⋊C4—21no—
62C2×Dic19⋊C4C2×C411yescharacteristic
63C2×C4×Dic19D411yescharacteristic
64C22×C19⋊C8—21no—
65C2×#64515—22no—
66C19×C22⋊C8—21no—
67C19×C22⋊C8D412yescomplemented
68C19×#95—21no—
69C19⋊#95—21no—
70C19⋊#95—21no—
71C19⋊#95—21no—
72C19⋊#95—21no—
73C19⋊#95C2×C411yescharacteristic
74C19⋊#95C2×C411yescharacteristic
75C22⋊(C19⋊C8)—21no—
76C22⋊(C19⋊C8)D412yescomplemented
77(C2×D19)⋊C8—22no—
78#10597272—22no—
79Dic19⋊C8—22no—
80#10597263—42no—
81C24×C19—21no—
82C24×C19C2×D411yescharacteristic
83C23×D19C22⋊C411yescharacteristic
84C2×D4×C19—21no—
85C2×D4×C19—21no—
86C2×D4×C19—41no—
87C2×D4×C19—41no—
88C2×D4×C19—41no—
89C2×D4×C19—41no—
90C2×D4×C19—41no—
91C2×D4×C19—41no—
92C2×D4×C19—81no—
93C22×C4×C19—21no—
94C22×C4×C19—41no—
95C22×C4×C19—81no—
96C22×C4×C19C22×C411yescharacteristic
97C22×C4×C19C2×D411yescharacteristic
98C22×C4×C19C2×D411yescharacteristic
99C22×C4×C19C2×D411yescharacteristic
100C22×C4×C19#4111yescharacteristic
101C22×C4×C19#4111yescharacteristic
102C2×C22⋊D19—21no—
103C2×C22⋊D19—21no—
104C2×C22⋊D19—21no—
105C2×C22⋊D19—21no—
106C2×C22⋊D19—21no—
107C2×C22⋊D19—21no—
108C2×C22⋊D19—42no—
109C2×C22⋊D19—42no—
110C2×C22⋊D19—81no—
111C22×Dic19—21no—
112C22×Dic19—21no—
113C22×Dic19—42no—
114C22×Dic19—41no—
115C22×Dic19—41no—
116C22×Dic19—41no—
117C22×Dic19—81no—
118C22×Dic19C22⋊C411yescharacteristic
119C22×Dic19C22⋊C411yescharacteristic
120C22×Dic19C22⋊C411yescharacteristic
121C2×C4×D19—21no—
122C2×C4×D19—21no—
123C2×C4×D19—81no—
124C2×C8×C19—22no—
125C2×C8×C19—81no—
126C4⋊C4×C19—21no—
127C4⋊C4×C19—21no—
128C4⋊C4×C19—81no—
129C22⋊C4×C19—41no—
130C22⋊C4×C19—41no—
131C22⋊C4×C19—41no—
132C22⋊C4×C19—41no—
133C22⋊Dic19—21no—
134C22⋊Dic19—21no—
135C22⋊Dic19—42no—
136C22⋊Dic19—42no—
137C22⋊Dic19—41no—
138C22⋊Dic19—41no—
139C22⋊Dic19—81no—
140(C2×D19)⋊C4—21no—
141(C2×D19)⋊C4—21no—
142(C2×D19)⋊C4—42no—
143C4⋊Dic19—81no—
144Dic19⋊C4—21no—
145Dic19⋊C4—21no—
146Dic19⋊C4—42no—
147C4×Dic19—21no—
148C4×Dic19—21no—
149C2×C19⋊C8—22no—
150C2×C19⋊C8—81no—
151#64515—82no—
152#9386—191nomaximal, Sylow
153C23×C19—41no—
154C23×C19—41no—
155C23×C19—41no—
156C23×C19—41no—
157C23×C19—41no—
158C23×C19—41no—
159C23×C19—41no—
160C23×C19—41no—
161C23×C19—41no—
162C23×C19C2×C22⋊C411yescharacteristic
163C23×C19#12111yescharacteristic
164C23×C19#12111yescharacteristic
165C23×C19AGL(1,ℤ/8)11yescharacteristic
166C23×C19AGL(1,ℤ/8)11yescharacteristic
167C23×C19AGL(1,ℤ/8)11yescharacteristic
168C23×C19#13711yescharacteristic
169C22×D19—21no—
170C22×D19—21no—
171C22×D19—21no—
172C22×D19—41no—
173C22×D19—41no—
174D4×C19—81no—
175D4×C19—81no—
176D4×C19—81no—
177D4×C19—81no—
178D4×C19—81no—
179D4×C19—81no—
180C2×C4×C19—41no—
181C2×C4×C19—41no—
182C2×C4×C19—41no—
183C2×C4×C19—41no—
184C2×C4×C19—41no—
185C2×C4×C19—41no—
186C2×C4×C19—41no—
187C2×C4×C19—41no—
188C2×C4×C19—41no—
189C2×C4×C19—81no—
190C2×C4×C19—81no—
191C2×C4×C19—81no—
192C2×C4×C19C4×D411yescharacteristic
193C2×C4×C19C4×D411yescharacteristic
194C2×C4×C19#12011yescharacteristic
195C2×C4×C19#12311yescharacteristic
196C22⋊D19—41no—
197C22⋊D19—41no—
198C22⋊D19—41no—
199C22⋊D19—41no—
200C22⋊D19—84no—
201C2×Dic19—22no—
202C2×Dic19—21no—
203C2×Dic19—21no—
204C2×Dic19—21no—
205C2×Dic19—21no—
206C2×Dic19—21no—
207C2×Dic19—41no—
208C2×Dic19—41no—
209C2×Dic19—41no—
210C2×Dic19—41no—
211C2×Dic19—41no—
212C2×Dic19—41no—
213C2×Dic19—41no—
214C2×Dic19—82no—
215C2×Dic19—82no—
216C2×Dic19—81no—
217C2×Dic19—81no—
218C2×Dic19—81no—
219C4×D19—42no—
220C4×D19—81no—
221C8×C19—42no—
222C19⋊C8—42no—
223#2973—191no—
224#2543—191no—
225#1799—191no—
226#1519—191no—
227#1519D1911yescharacteristic, complemented
228#1294—191no—
229#1294—191no—
230C22×C19—21no—
231C22×C19—21no—
232C22×C19—21no—
233C22×C19—21no—
234C22×C19—21no—
235C22×C19—21no—
236C22×C19—41no—
237C22×C19—41no—
238C22×C19—41no—
239C22×C19—41no—
240C22×C19—81no—
241C22×C19—81no—
242C22×C19—81no—
243C22×C19—81no—
244C22×C19—81no—
245C22×C19—81no—
246C22×C19—81no—
247C22×C19#38611yescharacteristic
248C22×C19#41711yescharacteristic
249C22×C19#41811yescharacteristic
250C22×C19#46811yescharacteristic
251C22×C19#46811yescharacteristic
252C22×C19#46911yescharacteristic
253C22×C19#46911yescharacteristic
254C2×D19—42no—
255C2×D19—41no—
256C2×D19—41no—
257C2×D19—41no—
258C2×D19—81no—
259C4×C19—21no—
260C4×C19—21no—
261C4×C19—21no—
262C4×C19—21no—
263C4×C19—81no—
264C4×C19—161no—
265Dic19—42no—
266Dic19—41no—
267Dic19—41no—
268Dic19—41no—
269Dic19—81no—
270Dic19—161no—
271C2×#121—381no—
272C2×#121C2×D1911yescharacteristic
273C2×C4×D4—191no—
274#435—382no—
275#435—382no—
276#432—381no—
277C2×#99—381no—
278#407—381no—
279C2×C22⋊C8—191no—
280C2×C22⋊C8C2×D1911yescharacteristic
281#398—191no—
282#397—191no—
283#394—191no—
284#392—191no—
285#388—381no—
286#386—381no—
287#386—381no—
288#380—191no—
289#380C2×D1911yescharacteristic
290C2×#95—191no—
291#342—381no—
292#327—22no—
293#327—382no—
294C2×C19—21no—
295C2×C19—21no—
296C2×C19—21no—
297C2×C19—21no—
298C2×C19—21no—
299C2×C19—21no—
300C2×C19—161no—
301C2×C19#188411yescharacteristic
302C2×C19#189511yescharacteristic
303C2×C19#191311yescharacteristic
304D19—81no—
305C22×D4—21no—
306C22×D4—191no—
307C22×D4—381no—
308C22×D4C4×D1911yescharacteristic
309C23×C4—191no—
310C23×C4—381no—
311C23×C4C22×D1911yescharacteristic
312C2×M16—382no—
313C22×C8—21no—
314C22×C8—381no—
315#121—21no—
316#121—21no—
317#121—21no—
318#121—21no—
319#121—762no—
320#121—762no—
321C4×D4—381no—
322C4×D4—381no—
323C4×D4—381no—
324C4×D4—381no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—191no—
327C2×C4⋊C4—381no—
328C2×C4⋊C4—381no—
329C2×C4⋊C4C4×D1911yescharacteristic
330C2×C22⋊C4—21no—
331C2×C22⋊C4—21no—
332C2×C22⋊C4—191no—
333C2×C22⋊C4—191no—
334C2×C22⋊C4—381no—
335C2×C22⋊C4—381no—
336C2×C22⋊C4—381no—
337C2×C22⋊C4—381no—
338C2×C22⋊C4—381no—
339C2×C42—191no—
340C4⋊C8—382no—
341#99—762no—
342C22⋊C8—21no—
343C22⋊C8—192no—
344C22⋊C8—382no—
345C22⋊C8—381no—
346C22⋊C8C22⋊D1912yescomplemented
347#97—382no—
348#95—21no—
349#95—191no—
350#95—191no—
351#95—381no—
352#95—381no—
353#95—381no—
354#95—381no—
355C19#938611yescharacteristic, complemented, Sylow
356C24—21no—
357C24—191no—
358C24D4×D1911yescharacteristic
359C2×D4—21no—
360C2×D4—21no—
361C2×D4—41no—
362C2×D4—41no—
363C2×D4—41no—
364C2×D4—41no—
365C2×D4—41no—
366C2×D4—41no—
367C2×D4—81no—
368C2×D4—381no—
369C2×D4—381no—
370C2×D4—381no—
371C2×D4—381no—
372C2×D4—381no—
373C2×D4—381no—
374C2×D4—762no—
375C2×D4—762no—
376C2×D4—1521no—
377C22×C4—21no—
378C22×C4—41no—
379C22×C4—81no—
380C22×C4—191no—
381C22×C4—191no—
382C22×C4—191no—
383C22×C4—381no—
384C22×C4—381no—
385C22×C4—381no—
386C22×C4—381no—
387C22×C4—762no—
388C22×C4—761no—
389C22×C4—761no—
390C22×C4—761no—
391C22×C4—1521no—
392C22×C4—1521no—
393C22×C4C2×C4×D1911yescharacteristic
394C22×C4#6454111yescharacteristic
395C22×C4D4×D1911yescharacteristic
396C22×C4D4×D1911yescharacteristic
397C22×C4#6454311yescharacteristic
398C22×C4C2×C22⋊D1911yescharacteristic
399M16—1522no—
400C2×C8—22no—
401C2×C8—81no—
402C2×C8—382no—
403C2×C8—1521no—
404C4⋊C4—21no—
405C4⋊C4—21no—
406C4⋊C4—81no—
407C4⋊C4—381no—
408C4⋊C4—381no—
409C4⋊C4—762no—
410C4⋊C4—1521no—
411C22⋊C4—41no—
412C22⋊C4—41no—
413C22⋊C4—41no—
414C22⋊C4—41no—
415C22⋊C4—381no—
416C22⋊C4—381no—
417C22⋊C4—381no—
418C22⋊C4—381no—
419C22⋊C4—762no—
420C22⋊C4—762no—
421C22⋊C4—762no—
422C22⋊C4—761no—
423C22⋊C4—761no—
424C22⋊C4—1521no—
425C42—381no—
426C42—381no—
427C23—41no—
428C23—41no—
429C23—41no—
430C23—41no—
431C23—41no—
432C23—41no—
433C23—41no—
434C23—41no—
435C23—41no—
436C23—381no—
437C23—381no—
438C23—381no—
439C23—761no—
440C23—761no—
441C23C22⋊C4×D1911yescharacteristic
442C23#1059733011yescharacteristic
443C23#1059735711yescharacteristic
444C23#1059735711yescharacteristic
445C23#1059736011yescharacteristic
446C23#1059736111yescharacteristic
447C23#1059738411yescharacteristic
448D4—81no—
449D4—81no—
450D4—81no—
451D4—81no—
452D4—81no—
453D4—81no—
454D4—761no—
455D4—761no—
456D4—761no—
457D4—761no—
458D4—1524no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—81no—
469C2×C4—81no—
470C2×C4—81no—
471C2×C4—382no—
472C2×C4—381no—
473C2×C4—381no—
474C2×C4—381no—
475C2×C4—381no—
476C2×C4—381no—
477C2×C4—762no—
478C2×C4—761no—
479C2×C4—761no—
480C2×C4—761no—
481C2×C4—761no—
482C2×C4—761no—
483C2×C4—761no—
484C2×C4—761no—
485C2×C4—1521no—
486C2×C4—1521no—
487C2×C4—1521no—
488C2×C4—1521no—
489C2×C4—1522no—
490C2×C4—1522no—
491C2×C4(C22⋊D19)⋊C411yescharacteristic
492C2×C4#1059732911yescharacteristic
493C2×C4C4×C22⋊D1911yescharacteristic
494C2×C4#1059738311yescharacteristic
495C8—42no—
496C8—762no—
497C22—21no—
498C22—21no—
499C22—21no—
500C22—21no—
501C22—21no—
502C22—21no—
503C22—41no—
504C22—41no—
505C22—41no—
506C22—41no—
507C22—81no—
508C22—81no—
509C22—81no—
510C22—81no—
511C22—81no—
512C22—81no—
513C22—81no—
514C22—762no—
515C22—761no—
516C22—761no—
517C22—761no—
518C22—1521no—
519C22#1192642011yescharacteristic
520C22#1192654211yescharacteristic
521C22#1192654711yescharacteristic
522C22#1192678711yescharacteristic
523C22#1192678911yescharacteristic
524C22#1192679411yescharacteristic
525C22#1192679611yescharacteristic
526C4—21no—
527C4—21no—
528C4—21no—
529C4—21no—
530C4—81no—
531C4—161no—
532C4—3041no—
533C4—762no—
534C4—761no—
535C4—761no—
536C4—761no—
537C4—1521no—
538C2—21no—
539C2—21no—
540C2—21no—
541C2—21no—
542C2—21no—
543C2—21no—
544C2—161no—
545C2—1521no—
546C2#1456401511yescharacteristic
547C2#1456407011yescharacteristic
548C2#1456417411yescharacteristic
subgroupG/H
centerC22#11926420
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#1519C2
socleC22×C19#386
prime radical#14568597C2
cosocleC23×C4×C19C23
hypercenter#1519D19
hypocenterC19#9386
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1519

Complements

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

NH ≅ G/Ntype
1. #14572661C2semidirect
3. #14563620C2semidirect
4. #14562203C2semidirect
5. #14561515C2semidirect
6. #14561513C2semidirect
7. C19×#1519C2semidirect
16. #11926475C4semidirect
17. #11926470C4semidirect
18. #11926458C4semidirect
19. #11926452C4semidirect
67. C19×C22⋊C8D4semidirect
76. C22⋊(C19⋊C8)D4semidirect
227. #1519D19semidirect
346. C22⋊C8C22⋊D19semidirect
355. C19#9386semidirect

Maximal subgroups

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

subgroupindex
#145726612
#145685972
#145636202
#145622032
#145615152
#145615132
C19×#15192
#938619