Finite Group Databasebeta

← #18078124

Subgroups — #18078124

Order 4864.

1030 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#14571917C211yesmaximal, characteristic
2C2×#11926279C212yesmaximal, complemented
3#14561858C211yesmaximal, characteristic, complemented
4#14561515C212yesmaximal, complemented
5C2×C19×#407C211yesmaximal, characteristic, complemented
6C2×#10597376C411yescharacteristic, complemented
7C2×#10597376C411yescharacteristic, complemented
8C2×#10597376C2211yescharacteristic
9C2×#10597399—21no—
10C22×C22⋊Dic19—21no—
11#11926423—21no—
12#11926423—21no—
13#11926423—21no—
14#11926404C411yescharacteristic, complemented
15#11926404C411yescharacteristic, complemented
16#11926404C2211yescharacteristic
17C2×C19⋊#95—21no—
18C2×C19⋊#95C2212yes—
19#11926279—24no—
20C24×C4×C19C2211yescharacteristic
21C22×M16×C19—21no—
22C19×#407—24no—
23C2×C19×C22⋊C8—21no—
24C2×C19×C22⋊C8C2212yes—
25C25×C19D411yescharacteristic
26C23×C4×C19—22no—
27C23×C4×C19—22no—
28C23×C4×C19—42no—
29C23×C4×C19—42no—
30C23×C4×C19C2×C411yescharacteristic
31C23×C4×C19C2×C411yescharacteristic
32C23×C4×C19D411yescharacteristic
33C23×C4×C19D411yescharacteristic
34C23×C4×C19D411yescharacteristic
35C23×C4×C19C2311yescharacteristic
36C22×C22⋊D19—21no—
37C22×C22⋊D19—21no—
38C22×C22⋊D19—21no—
39C23×Dic19—22no—
40C22×D76C2×C411yescharacteristic
41C2×M16×C19—24no—
42C2×M16×C19—42no—
43C2×M16×C19—42no—
44C22×C8×C19—22no—
45#10597399—44no—
46C2×C22⋊Dic19—24no—
47C2×C22⋊Dic19—21no—
48C2×C22⋊Dic19—21no—
49C2×C22⋊Dic19—21no—
50C2×C22⋊Dic19—42no—
51C2×C22⋊Dic19—42no—
52#10597376—22no—
53#10597376—22no—
54#10597376—42no—
55#10597376—42no—
56C2×(C2×D19)⋊C4—21no—
57C2×(C2×D19)⋊C4—21no—
58C2×(C2×D19)⋊C4—21no—
59C2×C4⋊Dic19C2×C411yescharacteristic
60C2×C4⋊Dic19C2×C411yescharacteristic
61C2×C4⋊Dic19C2×C411yescharacteristic
62C19×C22⋊C8—24no—
63C19×C22⋊C8—22no—
64C19×C22⋊C8D414yescomplemented
65C19⋊#95—21no—
66C19⋊#95—21no—
67C19⋊#95—21no—
68C19⋊#95—22no—
69C19⋊#95—22no—
70C19⋊#95—42no—
71C24×C19—22no—
72C24×C19—22no—
73C24×C19—21no—
74C24×C19—21no—
75C24×C19—22no—
76C24×C19—22no—
77C24×C19—41no—
78C24×C19—41no—
79C24×C19C22⋊C411yescharacteristic
80C24×C19C22⋊C411yescharacteristic
81C24×C19C2×D411yescharacteristic
82C23×D19—21no—
83C22×C4×C19—22no—
84C22×C4×C19—22no—
85C22×C4×C19—21no—
86C22×C4×C19—21no—
87C22×C4×C19—22no—
88C22×C4×C19—22no—
89C22×C4×C19—22no—
90C22×C4×C19—22no—
91C22×C4×C19—22no—
92C22×C4×C19—22no—
93C22×C4×C19—21no—
94C22×C4×C19—21no—
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×C19—48no—
103C22×C4×C19—48no—
104C22×C4×C19C22⋊C411yescharacteristic
105C22×C4×C19C22⋊C411yescharacteristic
106C22×C4×C19C22×C411yescharacteristic
107C22×C4×C19C2×D411yescharacteristic
108C22×C4×C19C2×D412yes—
109C22×C4×C19#4112yes—
110C2×C22⋊D19—42no—
111C2×C22⋊D19—42no—
112C2×C22⋊D19—42no—
113C2×C22⋊D19—42no—
114C2×C22⋊D19—42no—
115C2×C22⋊D19—42no—
116C2×C22⋊D19—42no—
117C2×C22⋊D19—42no—
118C2×C22⋊D19—41no—
119C2×C22⋊D19—41no—
120C22×Dic19—24no—
121C22×Dic19—21no—
122C22×Dic19—21no—
123C22×Dic19—21no—
124C22×Dic19—42no—
125C22×Dic19—42no—
126C22×Dic19—42no—
127C22×Dic19—42no—
128C22×Dic19—42no—
129C22×Dic19—42no—
130C2×D76—22no—
131C2×D76—41no—
132C2×D76—41no—
133M16×C19—48no—
134C2×C8×C19—24no—
135C2×C8×C19—42no—
136C2×C8×C19—42no—
137C22⋊Dic19—48no—
138C22⋊Dic19—42no—
139C22⋊Dic19—42no—
140C22⋊Dic19—42no—
141(C2×D19)⋊C4—42no—
142(C2×D19)⋊C4—42no—
143(C2×D19)⋊C4—41no—
144(C2×D19)⋊C4—41no—
145C4⋊Dic19—22no—
146C4⋊Dic19—41no—
147C4⋊Dic19—41no—
148#9117—191nomaximal, Sylow
149C23×C19—21no—
150C23×C19—21no—
151C23×C19—21no—
152C23×C19—21no—
153C23×C19—24no—
154C23×C19—24no—
155C23×C19—21no—
156C23×C19—21no—
157C23×C19—21no—
158C23×C19—21no—
159C23×C19—21no—
160C23×C19—21no—
161C23×C19—21no—
162C23×C19—21no—
163C23×C19—21no—
164C23×C19—21no—
165C23×C19—21no—
166C23×C19—21no—
167C23×C19—44no—
168C23×C19—44no—
169C23×C19—44no—
170C23×C19—44no—
171C23×C19—42no—
172C23×C19—42no—
173C23×C19—42no—
174C23×C19—42no—
175C23×C19#9912yes—
176C23×C19#10412yes—
177C23×C19C2×C22⋊C411yescharacteristic
178C23×C19#12112yes—
179C23×C19AGL(1,ℤ/8)11yescharacteristic
180C23×C19AGL(1,ℤ/8)12yes—
181C23×C19#13711yescharacteristic
182C22×D19—41no—
183C22×D19—41no—
184C22×D19—41no—
185C22×D19—41no—
186C22×D19—41no—
187C22×D19—41no—
188C22×D19—41no—
189C2×C4×C19—24no—
190C2×C4×C19—24no—
191C2×C4×C19—21no—
192C2×C4×C19—21no—
193C2×C4×C19—21no—
194C2×C4×C19—21no—
195C2×C4×C19—21no—
196C2×C4×C19—21no—
197C2×C4×C19—21no—
198C2×C4×C19—21no—
199C2×C4×C19—21no—
200C2×C4×C19—42no—
201C2×C4×C19—42no—
202C2×C4×C19—44no—
203C2×C4×C19—44no—
204C2×C4×C19—44no—
205C2×C4×C19—42no—
206C2×C4×C19—42no—
207C2×C4×C19#9912yes—
208C2×C4×C19C4×D412yes—
209C2×C4×C19#12011yescharacteristic
210C2×C4×C19#12311yescharacteristic
211C22⋊D19—84no—
212C22⋊D19—84no—
213C22⋊D19—82no—
214C22⋊D19—82no—
215C2×Dic19—44no—
216C2×Dic19—44no—
217C2×Dic19—44no—
218C2×Dic19—41no—
219C2×Dic19—41no—
220C2×Dic19—41no—
221C2×Dic19—41no—
222C2×Dic19—41no—
223C2×Dic19—41no—
224C2×Dic19—41no—
225C2×Dic19—41no—
226C2×Dic19—41no—
227C2×Dic19—82no—
228C2×Dic19—82no—
229C2×Dic19—82no—
230C2×Dic19—82no—
231D76—82no—
232C8×C19—44no—
233C2×#407D1911yescharacteristic, complemented
234#2847—191no—
235C2×#327—192no—
236C22⋊#95—191no—
237#1294—192no—
238C22×C19—22no—
239C22×C19—22no—
240C22×C19—21no—
241C22×C19—21no—
242C22×C19—22no—
243C22×C19—22no—
244C22×C19—21no—
245C22×C19—21no—
246C22×C19—22no—
247C22×C19—22no—
248C22×C19—22no—
249C22×C19—22no—
250C22×C19—22no—
251C22×C19—22no—
252C22×C19—48no—
253C22×C19—48no—
254C22×C19—41no—
255C22×C19—41no—
256C22×C19—41no—
257C22×C19—41no—
258C22×C19—41no—
259C22×C19—41no—
260C22×C19—41no—
261C22×C19—41no—
262C22×C19#38611yescharacteristic
263C22×C19C2×#9911yescharacteristic
264C22×C19C2×#9911yescharacteristic
265C22×C19#41711yescharacteristic
266C22×C19#41811yescharacteristic
267C22×C19C2×#10411yescharacteristic
268C22×C19#42111yescharacteristic
269C22×C19#46812yes—
270C22×C19#46912yes—
271C2×D19—81no—
272C2×D19—81no—
273C2×D19—81no—
274C2×D19—81no—
275C2×D19—81no—
276C2×D19—81no—
277C2×D19—81no—
278C4×C19—21no—
279C4×C19—22no—
280C4×C19—22no—
281C4×C19—21no—
282C4×C19—41no—
283Dic19—84no—
284Dic19—81no—
285Dic19—81no—
286Dic19—81no—
287C24×C4C2×D1911yescharacteristic
288C22×M16—21no—
289C2×#121—191no—
290C2×#121—191no—
291C2×#121—191no—
292C2×#120—381no—
293C22×C22⋊C4—381no—
294#407—24no—
295C2×C22⋊C8—21no—
296C2×C22⋊C8C2×D1912yes—
297#386—381no—
298#386—381no—
299#386—381no—
300#380—191no—
301#380—191no—
302#380—191no—
303C2×#95—192no—
304C2×#95—381no—
305#327—384no—
306C2×C19—22no—
307C2×C19—22no—
308C2×C19—42no—
309C2×C19—42no—
310C2×C19#150411yescharacteristic
311C2×C19#150711yescharacteristic
312C2×C19#151011yescharacteristic
313C2×C19#151311yescharacteristic
314C2×C19#187111yescharacteristic
315C2×C19#189511yescharacteristic
316C2×C19#189811yescharacteristic
317D19—161no—
318C25D7611yescharacteristic
319C22×D4—191no—
320C22×D4—381no—
321C22×D4—381no—
322C22×D4—381no—
323C23×C4—22no—
324C23×C4—22no—
325C23×C4—42no—
326C23×C4—42no—
327C23×C4—382no—
328C23×C4C4×D1911yescharacteristic
329C23×C4C4×D1911yescharacteristic
330C23×C4D7611yescharacteristic
331C23×C4C22⋊D1911yescharacteristic
332C23×C4C22⋊D1911yescharacteristic
333C23×C4C22×D1911yescharacteristic
334C2×M16—24no—
335C2×M16—42no—
336C2×M16—42no—
337C22×C8—22no—
338#121—382no—
339#121—382no—
340#121—762no—
341#121—762no—
342#120—764no—
343C2×C4⋊C4—191no—
344C2×C4⋊C4—191no—
345C2×C4⋊C4—191no—
346C2×C22⋊C4—384no—
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—762no—
354C2×C22⋊C4—762no—
355C22⋊C8—24no—
356C22⋊C8—22no—
357C22⋊C8C22⋊D1914yescomplemented
358#95—381no—
359#95—381no—
360#95—381no—
361#95—382no—
362#95—382no—
363#95—762no—
364C19#911711yescharacteristic, complemented, Sylow
365C24—22no—
366C24—22no—
367C24—21no—
368C24—21no—
369C24—22no—
370C24—22no—
371C24—41no—
372C24—41no—
373C24—381no—
374C24(C2×D19)⋊C411yescharacteristic
375C24(C2×D19)⋊C411yescharacteristic
376C24C2×D7611yescharacteristic
377C2×D4—382no—
378C2×D4—761no—
379C2×D4—761no—
380C2×D4—762no—
381C2×D4—762no—
382C2×D4—762no—
383C2×D4—762no—
384C2×D4—762no—
385C2×D4—762no—
386C2×D4—762no—
387C2×D4—762no—
388C2×D4—761no—
389C2×D4—761no—
390C22×C4—22no—
391C22×C4—21no—
392C22×C4—22no—
393C22×C4—21no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—21no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—21no—
402C22×C4—41no—
403C22×C4—41no—
404C22×C4—41no—
405C22×C4—41no—
406C22×C4—41no—
407C22×C4—41no—
408C22×C4—41no—
409C22×C4—48no—
410C22×C4—48no—
411C22×C4—384no—
412C22×C4—381no—
413C22×C4—381no—
414C22×C4—381no—
415C22×C4—762no—
416C22×C4—762no—
417C22×C4—762no—
418C22×C4—762no—
419C22×C4—762no—
420C22×C4—762no—
421C22×C4(C2×D19)⋊C411yescharacteristic
422C22×C4(C2×D19)⋊C411yescharacteristic
423C22×C4C2×C4×D1911yescharacteristic
424C22×C4#6454112yes—
425C22×C4C2×C22⋊D1911yescharacteristic
426C22×C4C2×C22⋊D1912yes—
427M16—48no—
428C2×C8—24no—
429C2×C8—42no—
430C2×C8—42no—
431C4⋊C4—382no—
432C4⋊C4—761no—
433C4⋊C4—761no—
434C22⋊C4—762no—
435C22⋊C4—768no—
436C22⋊C4—762no—
437C22⋊C4—762no—
438C22⋊C4—762no—
439C22⋊C4—761no—
440C22⋊C4—762no—
441C22⋊C4—761no—
442C23—21no—
443C23—21no—
444C23—21no—
445C23—21no—
446C23—24no—
447C23—24no—
448C23—21no—
449C23—21no—
450C23—21no—
451C23—21no—
452C23—21no—
453C23—21no—
454C23—21no—
455C23—21no—
456C23—21no—
457C23—21no—
458C23—21no—
459C23—21no—
460C23—44no—
461C23—44no—
462C23—44no—
463C23—44no—
464C23—42no—
465C23—42no—
466C23—42no—
467C23—42no—
468C23—761no—
469C23—761no—
470C23—761no—
471C23—761no—
472C23—761no—
473C23—761no—
474C23—761no—
475C23#1059726312yes—
476C23#1059728212yes—
477C23#1059735412yes—
478C23#1059735411yescharacteristic
479C23#1059735511yescharacteristic
480C23C2×(C2×D19)⋊C411yescharacteristic
481C23#1059737612yes—
482D4—1522no—
483D4—1524no—
484D4—1524no—
485D4—1522no—
486D4—1522no—
487C2×C4—24no—
488C2×C4—24no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—44no—
501C2×C4—44no—
502C2×C4—44no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—764no—
506C2×C4—764no—
507C2×C4—764no—
508C2×C4—761no—
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—1522no—
518C2×C4—1522no—
519C2×C4—1522no—
520C2×C4—1522no—
521C2×C4#1059726312yes—
522C2×C4C4×C22⋊D1912yes—
523C2×C4#1059737511yescharacteristic
524C2×C4#1059739911yescharacteristic
525C8—44no—
526C22—21no—
527C22—21no—
528C22—22no—
529C22—22no—
530C22—22no—
531C22—21no—
532C22—21no—
533C22—22no—
534C22—22no—
535C22—22no—
536C22—22no—
537C22—22no—
538C22—22no—
539C22—22no—
540C22—48no—
541C22—48no—
542C22—41no—
543C22—41no—
544C22—41no—
545C22—41no—
546C22—41no—
547C22—41no—
548C22—41no—
549C22—41no—
550C22—1521no—
551C22—1521no—
552C22—1521no—
553C22—1521no—
554C22—1521no—
555C22—1521no—
556C22—1521no—
557C22#1192642311yescharacteristic
558C22C2×#1059726311yescharacteristic
559C22C2×#1059726311yescharacteristic
560C22#1192654611yescharacteristic
561C22#1192655011yescharacteristic
562C22C2×#1059728211yescharacteristic
563C22#1192656011yescharacteristic
564C22#1192679012yes—
565C22#1192679712yes—
566C4—21no—
567C4—22no—
568C4—21no—
569C4—22no—
570C4—41no—
571C4—1524no—
572C4—1521no—
573C4—1521no—
574C4—1521no—
575C2—22no—
576C2—22no—
577C2—42no—
578C2—42no—
579C2—3041no—
580C2#1456214011yescharacteristic
581C2#1456215211yescharacteristic
582C2#1456216511yescharacteristic
583C2#1456217911yescharacteristic
584C2#1456393711yescharacteristic
585C2#1456407311yescharacteristic
586C2#1456408811yescharacteristic
subgroupG/H
centerC23C2×(C2×D19)⋊C4
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC2×C19×#407C2
socleC23×C19C2×C22⋊C4
prime radical#14571917C2
cosocleC23×C4×C19C23
hypercenterC2×#407D19
hypocenterC19#9117
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×#407

Complements

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

NH ≅ G/Ntype
2. C2×#11926279C2semidirect
3. #14561858C2semidirect
4. #14561515C2semidirect
5. C2×C19×#407C2semidirect
6. C2×#10597376C4semidirect
7. C2×#10597376C4semidirect
14. #11926404C4semidirect
15. #11926404C4semidirect
64. C19×C22⋊C8D4semidirect
233. C2×#407D19semidirect
357. C22⋊C8C22⋊D19semidirect
364. C19#9117semidirect

Maximal subgroups

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

subgroupindex
#145719172
C2×#119262792
#145618582
#145615152
C2×C19×#4072
#911719