Finite Group Databasebeta

← #18078122

Subgroups — #18078122

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
1C2×#11926508C211yesmaximal, characteristic, complemented
2#14571917C211yesmaximal, characteristic
3C2×#11926277C212yesmaximal, complemented
4#14561514C212yesmaximal, complemented
5C19×C22⋊#95C211yesmaximal, characteristic, complemented
6C22×#64520—21no—
7C2×#10597376C411yescharacteristic, complemented
8C2×#10597376C411yescharacteristic, complemented
9C2×#10597376C2211yescharacteristic
10C2×#10597399—21no—
11#11926508—24no—
12C2×C22⋊(C19⋊C8)—21no—
13C2×C22⋊(C19⋊C8)C2212yes—
14#11926423—21no—
15#11926423—21no—
16#11926423—21no—
17#11926404C411yescharacteristic, complemented
18#11926404C411yescharacteristic, complemented
19#11926404C2211yescharacteristic
20#11926277—24no—
21C24×C4×C19C2211yescharacteristic
22C22×C22⋊C4×C19—21no—
23C2×C19×#95—21no—
24C2×C19×#95C2212yes—
25C25×C19D411yescharacteristic
26C23×C4×C19—22no—
27C23×C4×C19—22no—
28C23×C4×C19—22no—
29C23×C4×C19—42no—
30C23×C4×C19—42no—
31C23×C4×C19C2×C411yescharacteristic
32C23×C4×C19C2×C411yescharacteristic
33C23×C4×C19D411yescharacteristic
34C23×C4×C19D411yescharacteristic
35C23×C4×C19D411yescharacteristic
36C23×C4×C19C2311yescharacteristic
37C22×C22⋊D19—21no—
38C22×C22⋊D19—21no—
39C22×C22⋊D19—21no—
40C22×D76C2×C411yescharacteristic
41C2×C22⋊C4×C19—24no—
42C2×C22⋊C4×C19—42no—
43C2×C22⋊C4×C19—42no—
44#10597399—44no—
45C2×C22⋊Dic19—21no—
46C2×C22⋊Dic19—21no—
47C2×C22⋊Dic19—21no—
48#10597376—22no—
49#10597376—22no—
50#10597376—42no—
51#10597376—42no—
52C2×(C2×D19)⋊C4—21no—
53C2×(C2×D19)⋊C4—21no—
54C2×(C2×D19)⋊C4—21no—
55C2×C4⋊Dic19C2×C411yescharacteristic
56C2×C4⋊Dic19C2×C411yescharacteristic
57C2×C4⋊Dic19C2×C411yescharacteristic
58C2×#64520—24no—
59C2×#64520—42no—
60C2×#64520—42no—
61C22×C19⋊C8—22no—
62C19×#95—22no—
63C19×#95—22no—
64C19×#95—42no—
65C19⋊#95—21no—
66C19⋊#95—21no—
67C19⋊#95—21no—
68C22⋊(C19⋊C8)—24no—
69C22⋊(C19⋊C8)—22no—
70C22⋊(C19⋊C8)D414yescomplemented
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—24no—
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—41no—
103C22×C4×C19—48no—
104C22×C4×C19—48no—
105C22×C4×C19—42no—
106C22×C4×C19—42no—
107C22×C4×C19—42no—
108C22×C4×C19—42no—
109C22×C4×C19—42no—
110C22×C4×C19—42no—
111C22×C4×C19C22⋊C411yescharacteristic
112C22×C4×C19C22⋊C411yescharacteristic
113C22×C4×C19C22×C411yescharacteristic
114C22×C4×C19C2×D411yescharacteristic
115C22×C4×C19C2×D412yes—
116C22×C4×C19#4112yes—
117C2×C22⋊D19—42no—
118C2×C22⋊D19—42no—
119C2×C22⋊D19—42no—
120C2×C22⋊D19—42no—
121C2×C22⋊D19—42no—
122C2×C22⋊D19—42no—
123C2×C22⋊D19—42no—
124C2×C22⋊D19—42no—
125C2×C22⋊D19—41no—
126C2×C22⋊D19—41no—
127C22×Dic19—21no—
128C22×Dic19—21no—
129C22×Dic19—21no—
130C2×D76—22no—
131C2×D76—41no—
132C2×D76—41no—
133C22⋊C4×C19—48no—
134C22⋊Dic19—42no—
135C22⋊Dic19—42no—
136C22⋊Dic19—42no—
137(C2×D19)⋊C4—42no—
138(C2×D19)⋊C4—42no—
139(C2×D19)⋊C4—41no—
140(C2×D19)⋊C4—41no—
141C4⋊Dic19—22no—
142C4⋊Dic19—41no—
143C4⋊Dic19—41no—
144#64520—48no—
145C2×C19⋊C8—24no—
146C2×C19⋊C8—42no—
147C2×C19⋊C8—42no—
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—44no—
208C2×C4×C19—44no—
209C2×C4×C19—44no—
210C2×C4×C19—82no—
211C2×C4×C19—82no—
212C2×C4×C19—82no—
213C2×C4×C19—82no—
214C2×C4×C19#9912yes—
215C2×C4×C19C4×D412yes—
216C2×C4×C19#12011yescharacteristic
217C2×C4×C19#12311yescharacteristic
218C22⋊D19—84no—
219C22⋊D19—84no—
220C22⋊D19—82no—
221C22⋊D19—82no—
222C2×Dic19—41no—
223C2×Dic19—41no—
224C2×Dic19—41no—
225C2×Dic19—41no—
226C2×Dic19—41no—
227C2×Dic19—41no—
228C2×Dic19—41no—
229C2×Dic19—41no—
230C2×Dic19—41no—
231D76—82no—
232C19⋊C8—44no—
233C2×#407—191no—
234#2847—191no—
235C2×#327—192no—
236C22⋊#95D1911yescharacteristic, complemented
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—
283C4×C19—84no—
284Dic19—81no—
285Dic19—81no—
286Dic19—81no—
287C24×C4C2×D1911yescharacteristic
288C22×M16—381no—
289C2×#121—191no—
290C2×#121—191no—
291C2×#121—191no—
292C2×#120—381no—
293C22×C22⋊C4—21no—
294#407—384no—
295C2×C22⋊C8—192no—
296C2×C22⋊C8—381no—
297#386—381no—
298#386—381no—
299#386—381no—
300#380—191no—
301#380—191no—
302#380—191no—
303C2×#95—21no—
304C2×#95C2×D1912yes—
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—
318C25C22⋊D1911yescharacteristic
319C22×D4—191no—
320C22×D4—381no—
321C22×D4—381no—
322C22×D4—381no—
323C23×C4—22no—
324C23×C4—22no—
325C23×C4—22no—
326C23×C4—42no—
327C23×C4—42no—
328C23×C4C4×D1911yescharacteristic
329C23×C4C4×D1911yescharacteristic
330C23×C4D7611yescharacteristic
331C23×C4D7611yescharacteristic
332C23×C4C22⋊D1911yescharacteristic
333C23×C4C22×D1911yescharacteristic
334C2×M16—384no—
335C2×M16—762no—
336C2×M16—762no—
337C22×C8—382no—
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—24no—
347C2×C22⋊C4—42no—
348C2×C22⋊C4—42no—
349C2×C22⋊C4—381no—
350C2×C22⋊C4—381no—
351C2×C22⋊C4—381no—
352C2×C22⋊C4—381no—
353C2×C22⋊C4—381no—
354C2×C22⋊C4—381no—
355C22⋊C8—194no—
356C22⋊C8—384no—
357C22⋊C8—382no—
358#95—22no—
359#95—22no—
360#95—42no—
361#95—381no—
362#95—381no—
363#95—381no—
364C19#911711yescharacteristic, complemented, Sylow
365C24—21no—
366C24—21no—
367C24—22no—
368C24—22no—
369C24—22no—
370C24—22no—
371C24—41no—
372C24—41no—
373C24—381no—
374C24(C2×D19)⋊C411yescharacteristic
375C24(C2×D19)⋊C411yescharacteristic
376C24C2×C22⋊D1911yescharacteristic
377C2×D4—382no—
378C2×D4—761no—
379C2×D4—761no—
380C2×D4—762no—
381C2×D4—762no—
382C2×D4—762no—
383C2×D4—762no—
384C2×D4—761no—
385C2×D4—762no—
386C2×D4—761no—
387C2×D4—762no—
388C2×D4—762no—
389C2×D4—762no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—24no—
403C22×C4—41no—
404C22×C4—41no—
405C22×C4—41no—
406C22×C4—41no—
407C22×C4—41no—
408C22×C4—41no—
409C22×C4—41no—
410C22×C4—48no—
411C22×C4—48no—
412C22×C4—42no—
413C22×C4—42no—
414C22×C4—42no—
415C22×C4—42no—
416C22×C4—42no—
417C22×C4—42no—
418C22×C4—381no—
419C22×C4—381no—
420C22×C4—381no—
421C22×C4(C2×D19)⋊C411yescharacteristic
422C22×C4(C2×D19)⋊C411yescharacteristic
423C22×C4C2×C4×D1911yescharacteristic
424C22×C4C2×D7611yescharacteristic
425C22×C4D4×D1912yes—
426C22×C4#6454312yes—
427M16—768no—
428C2×C8—384no—
429C2×C8—762no—
430C2×C8—762no—
431C4⋊C4—382no—
432C4⋊C4—761no—
433C4⋊C4—761no—
434C22⋊C4—48no—
435C22⋊C4—762no—
436C22⋊C4—762no—
437C22⋊C4—762no—
438C22⋊C4—762no—
439C22⋊C4—762no—
440C22⋊C4—761no—
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#1059726212yes—
476C23#1059726312yes—
477C23C2×(C2×D19)⋊C411yescharacteristic
478C23#1059737811yescharacteristic
479C23#1059738512yes—
480C23#1059738811yescharacteristic
481C23#1059739512yes—
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—44no—
506C2×C4—44no—
507C2×C4—44no—
508C2×C4—82no—
509C2×C4—82no—
510C2×C4—82no—
511C2×C4—82no—
512C2×C4—761no—
513C2×C4—761no—
514C2×C4—761no—
515C2×C4—761no—
516C2×C4—761no—
517C2×C4—761no—
518C2×C4—761no—
519C2×C4—761no—
520C2×C4—761no—
521C2×C4#1059726312yes—
522C2×C4(C22⋊D19)⋊C412yes—
523C2×C4#1059732811yescharacteristic
524C2×C4#1059733211yescharacteristic
525C8—764no—
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#1192642111yescharacteristic
558C22C2×#1059726311yescharacteristic
559C22C2×#1059726311yescharacteristic
560C22#1192654311yescharacteristic
561C22#1192654811yescharacteristic
562C22C2×#1059726211yescharacteristic
563C22#1192656211yescharacteristic
564C22#1192679212yes—
565C22#1192679512yes—
566C4—21no—
567C4—22no—
568C4—21no—
569C4—22no—
570C4—41no—
571C4—84no—
572C4—1521no—
573C4—1521no—
574C4—1521no—
575C2—22no—
576C2—22no—
577C2—42no—
578C2—42no—
579C2—3041no—
580C2#1456213711yescharacteristic
581C2#1456215011yescharacteristic
582C2#1456216311yescharacteristic
583C2#1456217611yescharacteristic
584C2#1456393511yescharacteristic
585C2#1456407111yescharacteristic
586C2#1456408611yescharacteristic
subgroupG/H
centerC23C2×(C2×D19)⋊C4
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×C22⋊#95C2
socleC23×C19C2×C22⋊C4
prime radical#14571917C2
cosocleC23×C4×C19C23
hypercenterC22⋊#95D19
hypocenterC19#9117
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C24×C4 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
1. C2×#11926508C2semidirect
3. C2×#11926277C2semidirect
4. #14561514C2semidirect
5. C19×C22⋊#95C2semidirect
7. C2×#10597376C4semidirect
8. C2×#10597376C4semidirect
17. #11926404C4semidirect
18. #11926404C4semidirect
70. C22⋊(C19⋊C8)D4semidirect
236. C22⋊#95D19semidirect
364. C19#9117semidirect

Maximal subgroups

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

subgroupindex
C2×#119265082
#145719172
C2×#119262772
#145615142
C19×C22⋊#952
#911719