Finite Group Databasebeta

← #18075110

Subgroups — #18075110

Order 4864.

1408 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 1408 conjugacy classes of subgroups — too many to draw. Only its 147 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14564089C214yesmaximal, complemented
2#14563550C211yesmaximal, characteristic, complemented
3#14561876C211yesmaximal, characteristic, complemented
4C19×#3484C211yesmaximal, characteristic
5C22×C22⋊Dic19—21no—
6C22×C22⋊Dic19C2212yescomplemented
7C2×#10597291—21no—
8C2×#10597291—21no—
9C2×#10597291—24no—
10#11926400C2212yescomplemented
11C2×C19⋊#95—21no—
12#11926311—24no—
13C2×C19×H(5,𝔽2)C411yescharacteristic, complemented
14C23×D4×C19C2211yescharacteristic
15C19×#546—24no—
16D42×C19—24no—
17C19×#535—21no—
18C19×#534—21no—
19C19×#534C412yescomplemented
20C19×#525—21no—
21C2×C19×#120—21no—
22C2×C19×#120C2212yes—
23C19×#518C411yescharacteristic, complemented
24C25×C19D411yescharacteristic
25C25×C19C2311yescharacteristic
26C19×H(5,𝔽2)—42no—
27C19×H(5,𝔽2)—42no—
28C2×#41×C19—21no—
29C2×#41×C19—22no—
30C22×D4×C19—21no—
31C22×D4×C19—22no—
32C22×D4×C19—24no—
33C22×D4×C19—22no—
34C22×D4×C19—42no—
35C22×D4×C19—42no—
36C22×D4×C19C2×C411yescharacteristic
37C22×D4×C19C2×C411yescharacteristic
38C22×D4×C19C2×C412yes—
39C22×D4×C19D411yescharacteristic
40C22×D4×C19D411yescharacteristic
41C22×D4×C19D414yes—
42C23×C4×C19D411yescharacteristic
43C23×Dic19—22no—
44C19×#127—22no—
45C19×#124—22no—
46C19×#123—22no—
47C19×#123—22no—
48C19×#123—22no—
49C19×C22⋊Q8—22no—
50C19×#121—22no—
51C19×#121—24no—
52C19×#121—24no—
53C19×#121—24no—
54C19×#120—24no—
55C19×#120—22no—
56C19×#120—22no—
57C19×#120—22no—
58C19×#120—22no—
59C19×#120—22no—
60C19×#120—24no—
61C4×D4×C19—24no—
62C4×D4×C19—24no—
63C19×#117—21no—
64C2×C22⋊C4×C19—22no—
65C2×C22⋊C4×C19—21no—
66C2×C22⋊C4×C19C2×C412yes—
67C2×C22⋊C4×C19D414yes—
68C2×C22⋊Dic19—24no—
69C2×C22⋊Dic19—24no—
70C2×C22⋊Dic19—22no—
71C2×C22⋊Dic19—44no—
72C2×C22⋊Dic19—44no—
73C2×C22⋊Dic19—42no—
74#10597291—48no—
75#10597291—42no—
76#10597291—42no—
77C19⋊#95—42no—
78C24×C19—21no—
79C24×C19—22no—
80C24×C19—22no—
81C24×C19—42no—
82C24×C19—41no—
83C24×C19—41no—
84C24×C19—41no—
85C24×C19—42no—
86C24×C19—42no—
87C24×C19—42no—
88C24×C19C22⋊C411yescharacteristic
89C24×C19C22⋊C411yescharacteristic
90C24×C19C22⋊C412yescomplemented
91C24×C19C22×C411yescharacteristic
92C24×C19C2×D411yescharacteristic
93C24×C19C2×D414yes—
94C24×C19C2×D411yescharacteristic
95#41×C19—42no—
96#41×C19—48no—
97#41×C19—42no—
98C2×Q8×C19—21no—
99C2×D4×C19—22no—
100C2×D4×C19—22no—
101C2×D4×C19—22no—
102C2×D4×C19—21no—
103C2×D4×C19—22no—
104C2×D4×C19—22no—
105C2×D4×C19—22no—
106C2×D4×C19—22no—
107C2×D4×C19—24no—
108C2×D4×C19—22no—
109C2×D4×C19—22no—
110C2×D4×C19—24no—
111C2×D4×C19—24no—
112C2×D4×C19—22no—
113C2×D4×C19—22no—
114C2×D4×C19—41no—
115C2×D4×C19—41no—
116C2×D4×C19—41no—
117C2×D4×C19—41no—
118C2×D4×C19—416no—
119C2×D4×C19—48no—
120C2×D4×C19—42no—
121C2×D4×C19—42no—
122C2×D4×C19—42no—
123C2×D4×C19—42no—
124C2×D4×C19—44no—
125C2×D4×C19—44no—
126C2×D4×C19—82no—
127C2×D4×C19—82no—
128C22×C4×C19—21no—
129C22×C4×C19—22no—
130C22×C4×C19—22no—
131C22×C4×C19—22no—
132C22×C4×C19—22no—
133C22×C4×C19—41no—
134C22×C4×C19C22⋊C411yescharacteristic
135C22×C4×C19C22⋊C411yescharacteristic
136C22×C4×C19C22⋊C414yescomplemented
137C22×C4×C19C22⋊C412yescomplemented
138C22×Dic19—24no—
139C22×Dic19—42no—
140C22×Dic19—42no—
141C22×Dic19—42no—
142C22×Dic19—42no—
143C22×Dic19—42no—
144C22×Dic19—42no—
145C22×Dic19—42no—
146C4⋊C4×C19—22no—
147C4⋊C4×C19—24no—
148C22⋊C4×C19—22no—
149C22⋊C4×C19—24no—
150C22⋊C4×C19—24no—
151C22⋊C4×C19—22no—
152C22⋊C4×C19—22no—
153C22⋊C4×C19—24no—
154C22⋊C4×C19—24no—
155C42×C19—22no—
156C22⋊Dic19—28no—
157C22⋊Dic19—44no—
158C22⋊Dic19—48no—
159C22⋊Dic19—44no—
160C22⋊Dic19—42no—
161C22⋊Dic19—42no—
162C22⋊Dic19—44no—
163#8534—191nomaximal, Sylow
164C23×C19—21no—
165C23×C19—21no—
166C23×C19—22no—
167C23×C19—22no—
168C23×C19—21no—
169C23×C19—21no—
170C23×C19—21no—
171C23×C19—21no—
172C23×C19—21no—
173C23×C19—21no—
174C23×C19—24no—
175C23×C19—24no—
176C23×C19—21no—
177C23×C19—22no—
178C23×C19—21no—
179C23×C19—21no—
180C23×C19—44no—
181C23×C19—42no—
182C23×C19—44no—
183C23×C19—42no—
184C23×C19—44no—
185C23×C19—42no—
186C23×C19—42no—
187C23×C19—42no—
188C23×C19—44no—
189C23×C19—42no—
190C23×C19—42no—
191C23×C19—42no—
192C23×C19—44no—
193C23×C19—42no—
194C23×C19—42no—
195C23×C19—82no—
196C23×C19—81no—
197C23×C19—82no—
198C23×C19—82no—
199C23×C19—81no—
200C23×C19—81no—
201C23×C19—82no—
202C23×C19—81no—
203C23×C19—81no—
204C23×C19—81no—
205C23×C19—82no—
206C23×C19#9912yescomplemented
207C23×C19C2×C22⋊C412yes—
208C23×C19C2×C22⋊C411yescharacteristic
209C23×C19#12012yes—
210C23×C19#12012yes—
211Q8×C19—42no—
212D4×C19—28no—
213D4×C19—44no—
214D4×C19—42no—
215D4×C19—44no—
216D4×C19—44no—
217D4×C19—44no—
218D4×C19—44no—
219D4×C19—42no—
220D4×C19—42no—
221D4×C19—44no—
222D4×C19—44no—
223D4×C19—84no—
224D4×C19—84no—
225C2×C4×C19—21no—
226C2×C4×C19—21no—
227C2×C4×C19—24no—
228C2×C4×C19—22no—
229C2×C4×C19—21no—
230C2×C4×C19—21no—
231C2×C4×C19—21no—
232C2×C4×C19—44no—
233C2×C4×C19—44no—
234C2×C4×C19—42no—
235C2×C4×C19—44no—
236C2×C4×C19—42no—
237C2×C4×C19—82no—
238C2×C4×C19#9912yescomplemented
239C2×Dic19—44no—
240C2×Dic19—44no—
241C2×Dic19—44no—
242C2×Dic19—82no—
243C2×Dic19—82no—
244C2×Dic19—82no—
245C2×Dic19—82no—
246C2×Dic19—82no—
247C2×Dic19—84no—
248#3484D1911yescharacteristic
249#1898—194no—
250#1781—191no—
251#1438—191no—
252C22×C19—21no—
253C22×C19—22no—
254C22×C19—21no—
255C22×C19—22no—
256C22×C19—21no—
257C22×C19—21no—
258C22×C19—22no—
259C22×C19—22no—
260C22×C19—22no—
261C22×C19—22no—
262C22×C19—22no—
263C22×C19—22no—
264C22×C19—24no—
265C22×C19—24no—
266C22×C19—42no—
267C22×C19—42no—
268C22×C19—42no—
269C22×C19—42no—
270C22×C19—41no—
271C22×C19—44no—
272C22×C19—42no—
273C22×C19—84no—
274C22×C19—81no—
275C22×C19—81no—
276C22×C19—81no—
277C22×C19—81no—
278C22×C19—81no—
279C22×C19—84no—
280C22×C19—84no—
281C22×C19—84no—
282C22×C19—81no—
283C22×C19—162no—
284C22×C19—162no—
285C22×C19#37911yescharacteristic
286C22×C19C2×#9911yescharacteristic
287C22×C19C2×#9911yescharacteristic
288C22×C19B(4,𝔽2)12yes—
289C22×C19#45812yes—
290C4×C19—22no—
291C4×C19—41no—
292C4×C19—42no—
293C4×C19—44no—
294Dic19—84no—
295Dic19—162no—
296C2×H(5,𝔽2)Dic1911yescharacteristic, complemented
297C23×D4C2×D1911yescharacteristic
298#546—24no—
299D42—24no—
300#535—21no—
301#534—21no—
302#534Dic1912yescomplemented
303#525—21no—
304C2×#120—21no—
305C2×#120C2×D1912yes—
306#518Dic1911yescharacteristic, complemented
307C22×C22⋊C4—192no—
308C22×C22⋊C4—381no—
309C2×#99—384no—
310C2×#99—381no—
311C2×#99—381no—
312#379—192no—
313C2×#95—381no—
314#342—384no—
315C2×C19—22no—
316C2×C19—21no—
317C2×C19—21no—
318C2×C19—22no—
319C2×C19—42no—
320C2×C19—42no—
321C2×C19—42no—
322C2×C19—81no—
323C2×C19—82no—
324C2×C19#178111yescharacteristic
325C2×C19#179012yes—
326C25C22⋊D1911yescharacteristic
327C25C22×D1911yescharacteristic
328H(5,𝔽2)—42no—
329H(5,𝔽2)—42no—
330C2×#41—21no—
331C2×#41—22no—
332C22×D4—21no—
333C22×D4—22no—
334C22×D4—24no—
335C22×D4—22no—
336C22×D4—42no—
337C22×D4—42no—
338C22×D4C2×Dic1911yescharacteristic
339C22×D4C2×Dic1911yescharacteristic
340C22×D4C2×Dic1912yes—
341C22×D4C22⋊D1911yescharacteristic
342C22×D4C22⋊D1911yescharacteristic
343C22×D4C22⋊D1914yes—
344C23×C4—382no—
345C23×C4C22⋊D1911yescharacteristic
346#127—22no—
347#124—22no—
348#123—22no—
349#123—22no—
350#123—22no—
351C22⋊Q8—22no—
352#121—22no—
353#121—24no—
354#121—24no—
355#121—24no—
356#120—24no—
357#120—22no—
358#120—22no—
359#120—22no—
360#120—22no—
361#120—22no—
362#120—24no—
363C4×D4—24no—
364C4×D4—24no—
365#117—21no—
366C2×C22⋊C4—22no—
367C2×C22⋊C4—21no—
368C2×C22⋊C4—384no—
369C2×C22⋊C4—384no—
370C2×C22⋊C4—382no—
371C2×C22⋊C4—764no—
372C2×C22⋊C4—764no—
373C2×C22⋊C4—762no—
374C2×C22⋊C4C2×Dic1912yes—
375C2×C22⋊C4C22⋊D1914yes—
376#99—768no—
377#99—762no—
378#99—762no—
379#95—762no—
380C19#853411yescharacteristic, complemented, Sylow
381C24—21no—
382C24—22no—
383C24—22no—
384C24—42no—
385C24—41no—
386C24—41no—
387C24—41no—
388C24—42no—
389C24—42no—
390C24—42no—
391C24C22⋊Dic1911yescharacteristic
392C24C22⋊Dic1911yescharacteristic
393C24C22⋊Dic1912yescomplemented
394C24C22×Dic1911yescharacteristic
395C24C2×C22⋊D1911yescharacteristic
396C24C2×C22⋊D1914yes—
397C24C2×C22⋊D1911yescharacteristic
398#41—42no—
399#41—48no—
400#41—42no—
401C2×Q8—21no—
402C2×D4—22no—
403C2×D4—22no—
404C2×D4—22no—
405C2×D4—21no—
406C2×D4—22no—
407C2×D4—22no—
408C2×D4—22no—
409C2×D4—24no—
410C2×D4—22no—
411C2×D4—22no—
412C2×D4—22no—
413C2×D4—24no—
414C2×D4—24no—
415C2×D4—22no—
416C2×D4—22no—
417C2×D4—41no—
418C2×D4—41no—
419C2×D4—41no—
420C2×D4—41no—
421C2×D4—416no—
422C2×D4—48no—
423C2×D4—42no—
424C2×D4—42no—
425C2×D4—42no—
426C2×D4—42no—
427C2×D4—44no—
428C2×D4—44no—
429C2×D4—82no—
430C2×D4—82no—
431C22×C4—21no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—41no—
437C22×C4—384no—
438C22×C4—762no—
439C22×C4—762no—
440C22×C4—762no—
441C22×C4—762no—
442C22×C4—762no—
443C22×C4—762no—
444C22×C4—762no—
445C22×C4C22⋊Dic1911yescharacteristic
446C22×C4C22⋊Dic1911yescharacteristic
447C22×C4C22⋊Dic1914yescomplemented
448C22×C4C22⋊Dic1912yescomplemented
449C4⋊C4—22no—
450C4⋊C4—24no—
451C22⋊C4—22no—
452C22⋊C4—24no—
453C22⋊C4—24no—
454C22⋊C4—22no—
455C22⋊C4—22no—
456C22⋊C4—24no—
457C22⋊C4—24no—
458C22⋊C4—388no—
459C22⋊C4—764no—
460C22⋊C4—768no—
461C22⋊C4—764no—
462C22⋊C4—762no—
463C22⋊C4—762no—
464C22⋊C4—764no—
465C42—22no—
466C23—22no—
467C23—22no—
468C23—21no—
469C23—21no—
470C23—21no—
471C23—24no—
472C23—24no—
473C23—21no—
474C23—21no—
475C23—21no—
476C23—21no—
477C23—21no—
478C23—21no—
479C23—22no—
480C23—21no—
481C23—21no—
482C23—44no—
483C23—42no—
484C23—44no—
485C23—42no—
486C23—44no—
487C23—42no—
488C23—42no—
489C23—42no—
490C23—44no—
491C23—42no—
492C23—42no—
493C23—42no—
494C23—44no—
495C23—42no—
496C23—42no—
497C23—82no—
498C23—81no—
499C23—82no—
500C23—82no—
501C23—81no—
502C23—81no—
503C23—82no—
504C23—81no—
505C23—81no—
506C23—81no—
507C23—82no—
508C23#1059729112yescomplemented
509C23C2×C22⋊Dic1912yes—
510C23C2×C22⋊Dic1911yescharacteristic
511C23#1059739912yes—
512C23#1059739912yes—
513Q8—42no—
514D4—28no—
515D4—44no—
516D4—42no—
517D4—44no—
518D4—44no—
519D4—44no—
520D4—44no—
521D4—44no—
522D4—44no—
523D4—42no—
524D4—42no—
525D4—84no—
526D4—84no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—24no—
530C2×C4—22no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—44no—
535C2×C4—44no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—44no—
539C2×C4—82no—
540C2×C4—764no—
541C2×C4—764no—
542C2×C4—764no—
543C2×C4—1522no—
544C2×C4—1524no—
545C2×C4—1522no—
546C2×C4—1522no—
547C2×C4—1522no—
548C2×C4—1522no—
549C2×C4#1059729112yescomplemented
550C22—21no—
551C22—22no—
552C22—21no—
553C22—22no—
554C22—21no—
555C22—21no—
556C22—22no—
557C22—22no—
558C22—22no—
559C22—22no—
560C22—22no—
561C22—22no—
562C22—24no—
563C22—24no—
564C22—42no—
565C22—42no—
566C22—42no—
567C22—42no—
568C22—41no—
569C22—44no—
570C22—42no—
571C22—84no—
572C22—81no—
573C22—81no—
574C22—84no—
575C22—81no—
576C22—81no—
577C22—81no—
578C22—84no—
579C22—84no—
580C22—81no—
581C22—162no—
582C22—162no—
583C22#1192640011yescharacteristic
584C22C2×#1059729111yescharacteristic
585C22C2×#1059729111yescharacteristic
586C22#1192673112yes—
587C22#1192673412yes—
588C4—22no—
589C4—41no—
590C4—42no—
591C4—44no—
592C4—3042no—
593C4—1524no—
594C2—22no—
595C2—21no—
596C2—22no—
597C2—21no—
598C2—42no—
599C2—42no—
600C2—42no—
601C2—81no—
602C2—82no—
603C2#1456355011yescharacteristic
604C2#1456358312yes—
subgroupG/H
centerC22#11926400
commutatorC24×C19C22×C4
FrattiniC25C22×D19
Fitting, prime radicalC19×#3484C2
socleC22×C19#379
cosocleC25×C19C23
hypercenter#3484D19
hypocenterC19#8534
LCSG ▷ C24×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C25 ◁ #3484

Complements

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

NH ≅ G/Ntype
1. #14564089C2semidirect
2. #14563550C2semidirect
3. #14561876C2semidirect
6. C22×C22⋊Dic19C22semidirect
10. #11926400C22semidirect
13. C2×C19×H(5,𝔽2)C4semidirect
19. C19×#534C4semidirect
23. C19×#518C4semidirect
90. C24×C19C22⋊C4semidirect
136. C22×C4×C19C22⋊C4semidirect
137. C22×C4×C19C22⋊C4semidirect
206. C23×C19#99semidirect
238. C2×C4×C19#99semidirect
296. C2×H(5,𝔽2)Dic19semidirect
302. #534Dic19semidirect
306. #518Dic19semidirect
380. C19#8534semidirect
393. C24C22⋊Dic19semidirect
447. C22×C4C22⋊Dic19semidirect
448. C22×C4C22⋊Dic19semidirect
508. C23#10597291semidirect
549. C2×C4#10597291semidirect

Maximal subgroups

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

subgroupindex
#145640892
#145635502
#145618762
C19×#34842
#853419