Finite Group Databasebeta

← #18074343

Subgroups — #18074343

Order 4864.

1364 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11927106C211yesmaximal, characteristic
2#14563952C212yesmaximal, complemented
3C2×#11926277C212yesmaximal, complemented
4C2×#11926268C211yesmaximal, characteristic, complemented
5C19×#1439C211yesmaximal, characteristic, complemented
6C23×C22⋊D19—21no—
7#11927106—22no—
8#11927106—24no—
9#11927106C414yescomplemented
10C2×#10597332—22no—
11C2×#10597376—21no—
12C2×#10597376C2212yes—
13C2×#10597328—22no—
14C2×#10597266—22no—
15C2×C22⋊(C19⋊C8)C2212yescomplemented
16#11926306—22no—
17#11926277—24no—
18#11926268—22no—
19C22×C4⋊C4×C19C2211yescharacteristic, complemented
20C22×C22⋊C4×C19—21no—
21C22×C22⋊C4×C19C2211yescharacteristic
22C2×C19×#95—21no—
23C2×C19×#95C2211yescharacteristic, complemented
24C25×C19D411yescharacteristic
25C24×D19—21no—
26C23×C4×C19—21no—
27C23×C4×C19—21no—
28C23×C4×C19D411yescharacteristic
29C23×C4×C19C2311yescharacteristic
30C22×C22⋊D19—22no—
31C22×C22⋊D19—24no—
32C22×C22⋊D19—24no—
33C22×C22⋊D19—22no—
34C22×C22⋊D19—42no—
35C22×C22⋊D19—42no—
36C22×C22⋊D19—42no—
37C22×C22⋊D19—42no—
38C23×Dic19—21no—
39C22×D76—21no—
40C22×D76D412yes—
41C2×C4⋊C4×C19—22no—
42C2×C4⋊C4×C19—42no—
43C2×C22⋊C4×C19—22no—
44C2×C22⋊C4×C19—22no—
45C2×C22⋊C4×C19—42no—
46C2×C22⋊C4×C19—42no—
47C2×C22⋊C4×C19—42no—
48C2×C22⋊C4×C19C2×C412yes—
49C2×C22⋊C4×C19D412yes—
50#10597376—24no—
51#10597376—24no—
52#10597376—22no—
53#10597376—22no—
54#10597376C2×C414yes—
55#10597376D414yes—
56C2×(C2×D19)⋊C4—22no—
57C2×(C2×D19)⋊C4—22no—
58C2×C4⋊Dic19—21no—
59C2×C4⋊Dic19D412yes—
60C22×C19⋊C8—22no—
61#10597332—28no—
62#10597332—28no—
63#10597328—28no—
64#10597328—28no—
65C19×#95—22no—
66C19×#95—42no—
67C22⋊(C19⋊C8)—22no—
68C22⋊(C19⋊C8)—22no—
69#10597266—44no—
70C24×C19—21no—
71C24×C19—21no—
72C24×C19—21no—
73C24×C19—21no—
74C24×C19—41no—
75C24×C19—41no—
76C24×C19—41no—
77C24×C19—41no—
78C24×C19C22⋊C412yes—
79C24×C19D812yes—
80C24×C19SD1612yes—
81C24×C19C2×D411yescharacteristic
82C23×D19—22no—
83C23×D19—24no—
84C23×D19—42no—
85C23×D19—42no—
86C23×D19—81no—
87C23×D19—81no—
88C23×D19—81no—
89C23×D19—81no—
90C22×C4×C19—21no—
91C22×C4×C19—21no—
92C22×C4×C19—22no—
93C22×C4×C19—22no—
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×C19—41no—
101C22×C4×C19—41no—
102C22×C4×C19—41no—
103C22×C4×C19—41no—
104C22×C4×C19—41no—
105C22×C4×C19—41no—
106C22×C4×C19—41no—
107C22×C4×C19—41no—
108C22×C4×C19—41no—
109C22×C4×C19—41no—
110C22×C4×C19C22⋊C412yes—
111C22×C4×C19C22×C411yescharacteristic
112C22×C4×C19C2×D411yescharacteristic
113C22×C4×C19C2×D412yes—
114C22×C4×C19C2×D412yes—
115C2×C22⋊D19—28no—
116C2×C22⋊D19—24no—
117C2×C22⋊D19—24no—
118C2×C22⋊D19—48no—
119C2×C22⋊D19—48no—
120C2×C22⋊D19—48no—
121C2×C22⋊D19—44no—
122C2×C22⋊D19—44no—
123C2×C22⋊D19—48no—
124C2×C22⋊D19—42no—
125C2×C22⋊D19—42no—
126C2×C22⋊D19—42no—
127C2×C22⋊D19—42no—
128C22×Dic19—24no—
129C22×Dic19—22no—
130C22×Dic19—42no—
131C22×Dic19—42no—
132C2×D76—24no—
133C2×D76—22no—
134C2×D76—42no—
135C2×D76—42no—
136C2×D76—81no—
137C2×D76—81no—
138C2×D76C22⋊C414yescomplemented
139C4⋊C4×C19—24no—
140C4⋊C4×C19—42no—
141C22⋊C4×C19—24no—
142C22⋊C4×C19—24no—
143C22⋊C4×C19—48no—
144(C2×D19)⋊C4—28no—
145(C2×D19)⋊C4—24no—
146(C2×D19)⋊C4—24no—
147C4⋊Dic19—24no—
148C4⋊Dic19—22no—
149C4⋊Dic19C22⋊C414yescomplemented
150C2×C19⋊C8—42no—
151C2×C19⋊C8—42no—
152C2×C19⋊C8—42no—
153#8403—191nomaximal, Sylow
154C23×C19—21no—
155C23×C19—21no—
156C23×C19—21no—
157C23×C19—21no—
158C23×C19—22no—
159C23×C19—22no—
160C23×C19—22no—
161C23×C19—22no—
162C23×C19—22no—
163C23×C19—22no—
164C23×C19—42no—
165C23×C19—42no—
166C23×C19—42no—
167C23×C19—42no—
168C23×C19—42no—
169C23×C19—42no—
170C23×C19—41no—
171C23×C19—41no—
172C23×C19—41no—
173C23×C19—41no—
174C23×C19—81no—
175C23×C19—81no—
176C23×C19—81no—
177C23×C19—81no—
178C23×C19—81no—
179C23×C19—81no—
180C23×C19#10214yescomplemented
181C23×C19C2×C22⋊C411yescharacteristic
182C23×C19#12011yescharacteristic
183C23×C19#12011yescharacteristic
184C23×C19C2×D811yescharacteristic
185C23×C19C2×SD1611yescharacteristic
186C23×C19AGL(1,ℤ/8)11yescharacteristic
187C23×C19AGL(1,ℤ/8)11yescharacteristic
188C22×D19—24no—
189C22×D19—48no—
190C22×D19—42no—
191C22×D19—42no—
192C22×D19—42no—
193C22×D19—42no—
194C22×D19—42no—
195C22×D19—42no—
196C22×D19—84no—
197C22×D19—84no—
198C22×D19—84no—
199C22×D19—84no—
200C22×D19—84no—
201C22×D19—84no—
202C2×C4×C19—22no—
203C2×C4×C19—22no—
204C2×C4×C19—22no—
205C2×C4×C19—41no—
206C2×C4×C19—41no—
207C2×C4×C19—42no—
208C2×C4×C19—41no—
209C2×C4×C19—41no—
210C2×C4×C19—42no—
211C2×C4×C19—42no—
212C2×C4×C19—42no—
213C2×C4×C19—42no—
214C2×C4×C19—42no—
215C2×C4×C19—42no—
216C2×C4×C19—42no—
217C2×C4×C19—81no—
218C2×C4×C19—81no—
219C2×C4×C19—81no—
220C2×C4×C19—81no—
221C2×C4×C19—81no—
222C2×C4×C19—81no—
223C2×C4×C19—81no—
224C2×C4×C19—81no—
225C2×C4×C19—81no—
226C2×C4×C19C2×C22⋊C412yes—
227C2×C4×C19#12012yes—
228C22⋊D19—416no—
229C22⋊D19—44no—
230C22⋊D19—44no—
231C22⋊D19—44no—
232C22⋊D19—44no—
233C2×Dic19—24no—
234C2×Dic19—48no—
235C2×Dic19—42no—
236C2×Dic19—42no—
237D76—44no—
238D76—82no—
239D76—84no—
240C19⋊C8—82no—
241C2×#534—191no—
242#1874—192no—
243C2×#327—192no—
244C2×#323—191no—
245#1439D1911yescharacteristic, complemented
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—21no—
257C22×C19—21no—
258C22×C19—24no—
259C22×C19—44no—
260C22×C19—42no—
261C22×C19—42no—
262C22×C19—42no—
263C22×C19—42no—
264C22×C19—42no—
265C22×C19—42no—
266C22×C19—82no—
267C22×C19—82no—
268C22×C19—82no—
269C22×C19#37911yescharacteristic
270C22×C19C2×#10211yescharacteristic
271C22×C19#41811yescharacteristic
272C22×C19#44711yescharacteristic
273C22×C19#44711yescharacteristic
274C22×C19#45011yescharacteristic
275C22×C19#45011yescharacteristic
276C22×C19#45311yescharacteristic
277C22×C19#45511yescharacteristic
278C22×C19B(4,𝔽2)11yescharacteristic
279C22×C19#45811yescharacteristic
280C2×D19—44no—
281C2×D19—44no—
282C2×D19—44no—
283C2×D19—816no—
284C2×D19—82no—
285C2×D19—82no—
286C2×D19—82no—
287C2×D19—82no—
288C4×C19—22no—
289C4×C19—22no—
290C4×C19—42no—
291C4×C19—82no—
292C4×C19—82no—
293Dic19—44no—
294C23×D4—381no—
295#534—194no—
296#534—384no—
297#534—382no—
298C2×#123—382no—
299C2×#121—192no—
300C2×#121—381no—
301C2×#120—382no—
302C22×C4⋊C4C2×D1911yescharacteristic, complemented
303C22×C22⋊C4—21no—
304C22×C22⋊C4C2×D1911yescharacteristic
305C2×#102—382no—
306C2×C22⋊C8—192no—
307C2×#95—21no—
308C2×#95C2×D1911yescharacteristic, complemented
309#340—382no—
310#327—384no—
311#323—382no—
312C2×C19—21no—
313C2×C19—21no—
314C2×C19—21no—
315C2×C19—21no—
316C2×C19—44no—
317C2×C19#159511yescharacteristic
318C2×C19#160111yescharacteristic
319C2×C19#160711yescharacteristic
320C2×C19#161311yescharacteristic
321C2×C19#178611yescharacteristic
322C2×C19#179011yescharacteristic
323C2×C19#179211yescharacteristic
324D19—84no—
325C25—381no—
326C25C22⋊D1911yescharacteristic
327C22×D4—192no—
328C22×D4—381no—
329C22×D4—382no—
330C22×D4—384no—
331C22×D4—384no—
332C22×D4—382no—
333C22×D4—762no—
334C22×D4—762no—
335C22×D4—762no—
336C22×D4—762no—
337C23×C4—21no—
338C23×C4—21no—
339C23×C4—381no—
340C23×C4C22⋊D1911yescharacteristic
341C23×C4C22×D1911yescharacteristic
342C22×C8—382no—
343#123—388no—
344#123—388no—
345#121—194no—
346#121—194no—
347#121—384no—
348#121—384no—
349#121—382no—
350#121—382no—
351#120—388no—
352#120—388no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—42no—
355C2×C4⋊C4—192no—
356C2×C4⋊C4—381no—
357C2×C22⋊C4—22no—
358C2×C22⋊C4—22no—
359C2×C22⋊C4—42no—
360C2×C22⋊C4—42no—
361C2×C22⋊C4—42no—
362C2×C22⋊C4—382no—
363C2×C22⋊C4—382no—
364C2×C22⋊C4C4×D1912yes—
365C2×C22⋊C4D7612yes—
366#102—764no—
367C22⋊C8—382no—
368C22⋊C8—382no—
369#95—22no—
370#95—42no—
371C19#840311yescharacteristic, complemented, Sylow
372C24—21no—
373C24—21no—
374C24—21no—
375C24—21no—
376C24—41no—
377C24—41no—
378C24—41no—
379C24—41no—
380C24—384no—
381C24—382no—
382C24—762no—
383C24—762no—
384C24—1521no—
385C24—1521no—
386C24—1521no—
387C24—1521no—
388C24(C2×D19)⋊C412yes—
389C24#6452512yes—
390C24#6452712yes—
391C24C2×C22⋊D1911yescharacteristic
392C2×D4—194no—
393C2×D4—384no—
394C2×D4—388no—
395C2×D4—384no—
396C2×D4—384no—
397C2×D4—382no—
398C2×D4—762no—
399C2×D4—762no—
400C2×D4—768no—
401C2×D4—768no—
402C2×D4—768no—
403C2×D4—764no—
404C2×D4—764no—
405C2×D4—762no—
406C2×D4—762no—
407C2×D4—762no—
408C2×D4—762no—
409C2×D4—768no—
410C2×D4—1521no—
411C2×D4—1521no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—41no—
417C22×C4—41no—
418C22×C4—41no—
419C22×C4—41no—
420C22×C4—41no—
421C22×C4—41no—
422C22×C4—41no—
423C22×C4—41no—
424C22×C4—41no—
425C22×C4—41no—
426C22×C4—41no—
427C22×C4—41no—
428C22×C4—41no—
429C22×C4—41no—
430C22×C4—41no—
431C22×C4—41no—
432C22×C4—384no—
433C22×C4—382no—
434C22×C4—762no—
435C22×C4—762no—
436C22×C4(C2×D19)⋊C412yes—
437C22×C4C2×C4×D1911yescharacteristic
438C22×C4C2×D7611yescharacteristic
439C22×C4D4×D1912yes—
440C22×C4D4×D1912yes—
441C2×C8—762no—
442C2×C8—762no—
443C2×C8—762no—
444C4⋊C4—24no—
445C4⋊C4—42no—
446C4⋊C4—194no—
447C4⋊C4—384no—
448C4⋊C4—382no—
449C22⋊C4—24no—
450C22⋊C4—24no—
451C22⋊C4—48no—
452C22⋊C4—388no—
453C22⋊C4—384no—
454C22⋊C4—384no—
455C23—21no—
456C23—21no—
457C23—21no—
458C23—21no—
459C23—22no—
460C23—22no—
461C23—22no—
462C23—22no—
463C23—22no—
464C23—22no—
465C23—42no—
466C23—42no—
467C23—42no—
468C23—42no—
469C23—42no—
470C23—42no—
471C23—41no—
472C23—41no—
473C23—41no—
474C23—41no—
475C23—81no—
476C23—81no—
477C23—81no—
478C23—81no—
479C23—81no—
480C23—81no—
481C23—384no—
482C23—768no—
483C23—762no—
484C23—762no—
485C23—762no—
486C23—762no—
487C23—762no—
488C23—762no—
489C23—1524no—
490C23—1524no—
491C23—1524no—
492C23—1524no—
493C23—1524no—
494C23—1524no—
495C23#1059726614yescomplemented
496C23C2×(C2×D19)⋊C411yescharacteristic
497C23C2×#6452511yescharacteristic
498C23#1059738311yescharacteristic
499C23#1059738311yescharacteristic
500C23C2×#6452711yescharacteristic
501C23#1059739511yescharacteristic
502C23#1059739511yescharacteristic
503D4—764no—
504D4—7616no—
505D4—764no—
506D4—764no—
507D4—764no—
508D4—764no—
509D4—1522no—
510D4—1524no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—42no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—81no—
527C2×C4—81no—
528C2×C4—81no—
529C2×C4—81no—
530C2×C4—81no—
531C2×C4—81no—
532C2×C4—81no—
533C2×C4—81no—
534C2×C4—81no—
535C2×C4—384no—
536C2×C4—768no—
537C2×C4—762no—
538C2×C4—762no—
539C2×C4C22⋊C4×D1912yes—
540C2×C4#1059732812yes—
541C8—1522no—
542C22—21no—
543C22—21no—
544C22—21no—
545C22—21no—
546C22—21no—
547C22—21no—
548C22—21no—
549C22—21no—
550C22—21no—
551C22—21no—
552C22—21no—
553C22—21no—
554C22—24no—
555C22—44no—
556C22—42no—
557C22—42no—
558C22—42no—
559C22—42no—
560C22—42no—
561C22—42no—
562C22—82no—
563C22—82no—
564C22—82no—
565C22—764no—
566C22—764no—
567C22—764no—
568C22—15216no—
569C22—1522no—
570C22—1522no—
571C22—1522no—
572C22—1522no—
573C22#1192639911yescharacteristic
574C22C2×#1059726611yescharacteristic
575C22#1192654811yescharacteristic
576C22#1192667711yescharacteristic
577C22#1192667711yescharacteristic
578C22#1192669411yescharacteristic
579C22#1192669411yescharacteristic
580C22#1192671111yescharacteristic
581C22#1192672111yescharacteristic
582C22#1192673011yescharacteristic
583C22#1192673311yescharacteristic
584C4—22no—
585C4—22no—
586C4—42no—
587C4—82no—
588C4—82no—
589C4—764no—
590C2—21no—
591C2—21no—
592C2—21no—
593C2—21no—
594C2—44no—
595C2—1524no—
596C2#1456255211yescharacteristic
597C2#1456258611yescharacteristic
598C2#1456262011yescharacteristic
599C2#1456265411yescharacteristic
600C2#1456356511yescharacteristic
601C2#1456358211yescharacteristic
602C2#1456358811yescharacteristic
subgroupG/H
centerC23#10597383
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#1439C2
socleC23×C19#120
prime radicalC2×#11927106C2
cosocleC23×C4×C19C23
hypercenter#1439D19
hypocenterC19#8403
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1439

Complements

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

NH ≅ G/Ntype
2. #14563952C2semidirect
3. C2×#11926277C2semidirect
4. C2×#11926268C2semidirect
5. C19×#1439C2semidirect
9. #11927106C4semidirect
15. C2×C22⋊(C19⋊C8)C22semidirect
19. C22×C4⋊C4×C19C22semidirect
23. C2×C19×#95C22semidirect
138. C2×D76C22⋊C4semidirect
149. C4⋊Dic19C22⋊C4semidirect
180. C23×C19#102semidirect
245. #1439D19semidirect
302. C22×C4⋊C4C2×D19semidirect
308. C2×#95C2×D19semidirect
371. C19#8403semidirect
495. C23#10597266semidirect

Maximal subgroups

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

subgroupindex
C2×#119271062
#145639522
C2×#119262772
C2×#119262682
C19×#14392
#840319