Finite Group Databasebeta

← #18077934

Subgroups — #18077934

Order 4864.

712 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11926598C211yesmaximal, characteristic, complemented
2C2×#11926436C211yesmaximal, characteristic
3#14563701C211yesmaximal, characteristic, complemented
4C2×#11926267C211yesmaximal, characteristic
5C2×#11926267C211yesmaximal, characteristic
6#14561478C211yesmaximal, characteristic, complemented
7C19×#1280C211yesmaximal, characteristic, complemented
8C22×C4⋊Dic19C411yescharacteristic
9C22×(C2×D19)⋊C4C411yescharacteristic
10C22×(C2×D19)⋊C4C411yescharacteristic
11C22×(C2×D19)⋊C4C2211yescharacteristic
12C22×C4×Dic19C2211yescharacteristic
13#11926598—22no—
14#11926598—22no—
15C2×Dic19⋊C8—21no—
16C2×C22⋊(C19⋊C8)C2211yescharacteristic
17C2×C22⋊(C19⋊C8)C2211yescharacteristic
18C2×#10597272—21no—
19#11926436—21no—
20#11926436—21no—
21#11926436—21no—
22#11926436—21no—
23C2×C19⋊#95C411yescharacteristic
24#11926298—21no—
25#11926298—21no—
26#11926267—22no—
27#11926267—22no—
28C2×C19×C22⋊C8C2211yescharacteristic
29C2×C19×C22⋊C8C2211yescharacteristic
30C2×C19×#95C2211yescharacteristic
31C24×D19C2×C411yescharacteristic
32C23×C4×C19C2×C411yescharacteristic
33C23×C4×C19C2×C411yescharacteristic
34C23×C4×C19C2311yescharacteristic
35C23×Dic19C2×C411yescharacteristic
36C23×Dic19C2×C411yescharacteristic
37C23×Dic19C2×C411yescharacteristic
38C22×C8×C19—21no—
39C22×C8×C19—21no—
40C2×(C2×D19)⋊C4—22no—
41C2×(C2×D19)⋊C4—22no—
42C2×(C2×D19)⋊C4—21no—
43C2×(C2×D19)⋊C4—21no—
44C2×(C2×D19)⋊C4—21no—
45C2×(C2×D19)⋊C4—21no—
46C2×(C2×D19)⋊C4—21no—
47C2×(C2×D19)⋊C4—21no—
48C2×(C2×D19)⋊C4—21no—
49C2×(C2×D19)⋊C4—21no—
50C2×(C2×D19)⋊C4—21no—
51C2×(C2×D19)⋊C4—21no—
52C2×(C2×D19)⋊C4—42no—
53C2×C4⋊Dic19—21no—
54C2×C4⋊Dic19—21no—
55C2×C4⋊Dic19—42no—
56C2×C4×Dic19—21no—
57C2×C4×Dic19—21no—
58C2×C4×Dic19—21no—
59C2×C4×Dic19—21no—
60C2×C4×Dic19D411yescharacteristic
61C2×C4×Dic19D411yescharacteristic
62C2×C4×Dic19D411yescharacteristic
63C2×C4×Dic19D411yescharacteristic
64C22×C19⋊C8—21no—
65C22×C19⋊C8—21no—
66C19×C22⋊C8—21no—
67C19×C22⋊C8—21no—
68C19×C22⋊C8—21no—
69C19×C22⋊C8D412yes—
70C19×#95—21no—
71C19×#95—21no—
72C19⋊#95—21no—
73C19⋊#95—21no—
74C22⋊(C19⋊C8)—21no—
75C22⋊(C19⋊C8)—21no—
76C22⋊(C19⋊C8)—21no—
77C22⋊(C19⋊C8)D412yes—
78#10597272—24no—
79Dic19⋊C8—24no—
80C24×C19C22×C411yescharacteristic
81C23×D19—21no—
82C23×D19—21no—
83C23×D19—21no—
84C23×D19—21no—
85C23×D19—21no—
86C23×D19—21no—
87C23×D19—41no—
88C23×D19—41no—
89C23×D19—41no—
90C23×D19—41no—
91C23×D19M1612yes—
92C22×C4×C19—21no—
93C22×C4×C19—21no—
94C22×C4×C19—21no—
95C22×C4×C19—21no—
96C22×C4×C19—21no—
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×C19M1612yes—
104C22×C4×C19C2×D411yescharacteristic
105C22×C4×C19C2×D411yescharacteristic
106C22×C4×C19C2×D411yescharacteristic
107C22×C4×C19C2×D411yescharacteristic
108C22×C4×C19#4111yescharacteristic
109C22×C4×C19#4111yescharacteristic
110C22×Dic19—21no—
111C22×Dic19—21no—
112C22×Dic19—21no—
113C22×Dic19—21no—
114C22×Dic19—21no—
115C22×Dic19—21no—
116C22×Dic19—21no—
117C22×Dic19—21no—
118C22×Dic19—22no—
119C22×Dic19—21no—
120C22×Dic19—21no—
121C22×Dic19—21no—
122C22×Dic19—41no—
123C22×Dic19—41no—
124C22×Dic19—41no—
125C22×Dic19C22⋊C411yescharacteristic
126C22×Dic19C22⋊C411yescharacteristic
127C22×Dic19C22⋊C411yescharacteristic
128C22×Dic19C22⋊C411yescharacteristic
129C2×C8×C19—22no—
130C2×C8×C19—41no—
131C2×C8×C19—41no—
132C2×C8×C19—41no—
133C2×C8×C19—41no—
134C2×C8×C19—41no—
135(C2×D19)⋊C4—24no—
136(C2×D19)⋊C4—24no—
137(C2×D19)⋊C4—42no—
138(C2×D19)⋊C4—41no—
139(C2×D19)⋊C4—41no—
140(C2×D19)⋊C4—41no—
141(C2×D19)⋊C4—41no—
142(C2×D19)⋊C4—42no—
143C4⋊Dic19—42no—
144C4⋊Dic19—42no—
145C4×Dic19—21no—
146C4×Dic19—21no—
147C4×Dic19—21no—
148C4×Dic19—21no—
149C4×Dic19—21no—
150C4×Dic19—21no—
151C4×Dic19—21no—
152C4×Dic19—21no—
153C2×C19⋊C8—22no—
154C2×C19⋊C8—41no—
155C2×C19⋊C8—41no—
156C2×C19⋊C8—41no—
157C2×C19⋊C8—41no—
158C2×C19⋊C8—41no—
159#9084—191nomaximal, Sylow
160C23×C19—21no—
161C23×C19—21no—
162C23×C19—21no—
163C23×C19—21no—
164C23×C19C2×C22⋊C411yescharacteristic
165C23×C19C4×D411yescharacteristic
166C23×C19C4×D411yescharacteristic
167C23×C19C2×M1611yescharacteristic
168C23×C19C2×M1611yescharacteristic
169C23×C19#13111yescharacteristic
170C23×C19#13111yescharacteristic
171C22×D19—22no—
172C22×D19—22no—
173C22×D19—22no—
174C22×D19—42no—
175C22×D19—42no—
176C22×D19—41no—
177C22×D19—41no—
178C22×D19—41no—
179C22×D19—41no—
180C22×D19—41no—
181C22×D19—41no—
182C22×D19—41no—
183C22×D19—41no—
184C22×D19—42no—
185C22×D19—42no—
186C22×D19—81no—
187C22×D19—81no—
188C22×D19—81no—
189C22×D19—81no—
190C22×D19—81no—
191C22×D19—81no—
192C22×D19—81no—
193C22×D19—81no—
194C2×C4×C19—21no—
195C2×C4×C19—21no—
196C2×C4×C19—21no—
197C2×C4×C19—21no—
198C2×C4×C19—22no—
199C2×C4×C19—41no—
200C2×C4×C19—41no—
201C2×C4×C19—41no—
202C2×C4×C19—41no—
203C2×C4×C19—42no—
204C2×C4×C19—41no—
205C2×C4×C19—41no—
206C2×C4×C19—42no—
207C2×C4×C19—41no—
208C2×C4×C19—41no—
209C2×C4×C19—41no—
210C2×C4×C19—81no—
211C2×C4×C19—81no—
212C2×C4×C19#12011yescharacteristic
213C2×C4×C19#12111yescharacteristic
214C2×C4×C19#12111yescharacteristic
215C2×C4×C19#12311yescharacteristic
216C2×Dic19—21no—
217C2×Dic19—21no—
218C2×Dic19—21no—
219C2×Dic19—21no—
220C2×Dic19—21no—
221C2×Dic19—21no—
222C2×Dic19—21no—
223C2×Dic19—21no—
224C2×Dic19—21no—
225C2×Dic19—21no—
226C2×Dic19—21no—
227C2×Dic19—42no—
228C2×Dic19—42no—
229C2×Dic19—41no—
230C2×Dic19—41no—
231C2×Dic19—41no—
232C2×Dic19—41no—
233C2×Dic19—41no—
234C2×Dic19—41no—
235C2×Dic19—41no—
236C2×Dic19—81no—
237C2×Dic19—81no—
238C2×Dic19#10012yes—
239C8×C19—42no—
240C8×C19—81no—
241C19⋊C8—42no—
242C19⋊C8—81no—
243C2×#432—191no—
244C2×#388—191no—
245#1817—191no—
246C2×#323—191no—
247C2×#323—191no—
248#1280—191no—
249#1280D1911yescharacteristic, complemented
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—21no—
259C22×C19—21no—
260C22×C19—21no—
261C22×C19—21no—
262C22×C19#38611yescharacteristic
263C22×C19#40711yescharacteristic
264C22×C19#40811yescharacteristic
265C22×C19#41011yescharacteristic
266C22×C19#41011yescharacteristic
267C22×C19C2×#10011yescharacteristic
268C22×C19#41311yescharacteristic
269C22×C19#43511yescharacteristic
270C22×C19#43511yescharacteristic
271C22×C19#43611yescharacteristic
272C22×C19#43611yescharacteristic
273C2×D19—42no—
274C2×D19—42no—
275C2×D19—42no—
276C2×D19—82no—
277C2×D19—82no—
278C2×D19—81no—
279C2×D19—81no—
280C2×D19—81no—
281C2×D19—81no—
282C2×D19—82no—
283C2×D19—82no—
284C4×C19—21no—
285C4×C19—21no—
286C4×C19—21no—
287C4×C19—21no—
288C4×C19—42no—
289C4×C19—81no—
290Dic19—22no—
291Dic19—41no—
292Dic19—41no—
293Dic19—41no—
294Dic19—81no—
295C22×C4⋊C4—191no—
296C22×C22⋊C4—191no—
297C22×C22⋊C4—191no—
298C22×C22⋊C4—191no—
299C22×C42—191no—
300#432—382no—
301#432—382no—
302C2×C4⋊C8—381no—
303C2×C22⋊C8—191no—
304C2×C22⋊C8—191no—
305C2×C22⋊C8C2×D1911yescharacteristic
306C2×C22⋊C8C2×D1911yescharacteristic
307C2×#97—381no—
308#388—381no—
309#388—381no—
310#388—381no—
311#388—381no—
312C2×#95—191no—
313C2×#95C2×D1911yescharacteristic
314#336—381no—
315#336—381no—
316#323—382no—
317#323—382no—
318C2×C19—21no—
319C2×C19—21no—
320C2×C19—21no—
321C2×C19—21no—
322C2×C19#146411yescharacteristic
323C2×C19#146611yescharacteristic
324C2×C19#146911yescharacteristic
325C2×C19#147311yescharacteristic
326C2×C19#187011yescharacteristic
327C2×C19#189911yescharacteristic
328C2×C19#190011yescharacteristic
329D19—82no—
330C25—191no—
331C23×C4—191no—
332C23×C4—191no—
333C23×C4—191no—
334C23×C4C4×D1911yescharacteristic
335C23×C4C4×D1911yescharacteristic
336C23×C4C22×D1911yescharacteristic
337C22×C8—21no—
338C22×C8—21no—
339C22×C8—381no—
340C22×C8—381no—
341C2×C4⋊C4—381no—
342C2×C4⋊C4—381no—
343C2×C4⋊C4—762no—
344C2×C22⋊C4—381no—
345C2×C22⋊C4—381no—
346C2×C22⋊C4—382no—
347C2×C22⋊C4—382no—
348C2×C22⋊C4—381no—
349C2×C22⋊C4—381no—
350C2×C22⋊C4—381no—
351C2×C22⋊C4—381no—
352C2×C22⋊C4—381no—
353C2×C22⋊C4—381no—
354C2×C22⋊C4—381no—
355C2×C22⋊C4—381no—
356C2×C22⋊C4—762no—
357C2×C42—191no—
358C2×C42—191no—
359C2×C42—191no—
360C2×C42—191no—
361C2×C42—381no—
362C2×C42—381no—
363C2×C42—381no—
364C2×C42—381no—
365C4⋊C8—384no—
366C22⋊C8—21no—
367C22⋊C8—21no—
368C22⋊C8—21no—
369C22⋊C8—192no—
370C22⋊C8—381no—
371C22⋊C8—381no—
372C22⋊C8—381no—
373C22⋊C8D7612yes—
374#97—384no—
375#95—21no—
376#95—21no—
377#95—381no—
378#95—381no—
379C19#908411yescharacteristic, complemented, Sylow
380C24—192no—
381C24—381no—
382C24—381no—
383C24—381no—
384C24—381no—
385C24—381no—
386C24—381no—
387C24—761no—
388C24—761no—
389C24—761no—
390C24—761no—
391C24C2×C4×D1911yescharacteristic
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—41no—
398C22×C4—41no—
399C22×C4—41no—
400C22×C4—41no—
401C22×C4—41no—
402C22×C4—41no—
403C22×C4—191no—
404C22×C4—191no—
405C22×C4—191no—
406C22×C4—191no—
407C22×C4—382no—
408C22×C4—381no—
409C22×C4—381no—
410C22×C4—381no—
411C22×C4—381no—
412C22×C4—381no—
413C22×C4—381no—
414C22×C4—381no—
415C22×C4—381no—
416C22×C4—381no—
417C22×C4—381no—
418C22×C4—381no—
419C22×C4—761no—
420C22×C4—761no—
421C22×C4—761no—
422C22×C4#6451512yes—
423C22×C4C2×D7611yescharacteristic
424C22×C4#6454111yescharacteristic
425C22×C4D4×D1911yescharacteristic
426C22×C4D4×D1911yescharacteristic
427C22×C4D4×D1911yescharacteristic
428C22×C4#6454511yescharacteristic
429C2×C8—22no—
430C2×C8—41no—
431C2×C8—41no—
432C2×C8—41no—
433C2×C8—41no—
434C2×C8—41no—
435C2×C8—382no—
436C2×C8—761no—
437C2×C8—761no—
438C2×C8—761no—
439C2×C8—761no—
440C2×C8—761no—
441C4⋊C4—762no—
442C4⋊C4—762no—
443C22⋊C4—384no—
444C22⋊C4—384no—
445C22⋊C4—762no—
446C22⋊C4—762no—
447C22⋊C4—761no—
448C22⋊C4—761no—
449C22⋊C4—761no—
450C22⋊C4—761no—
451C42—381no—
452C42—381no—
453C42—381no—
454C42—381no—
455C42—381no—
456C42—381no—
457C42—381no—
458C42—381no—
459C23—21no—
460C23—21no—
461C23—21no—
462C23—21no—
463C23—382no—
464C23—382no—
465C23—382no—
466C23—762no—
467C23—762no—
468C23—762no—
469C23—762no—
470C23—761no—
471C23—761no—
472C23—761no—
473C23—761no—
474C23—761no—
475C23—761no—
476C23—761no—
477C23—761no—
478C23—1521no—
479C23—1521no—
480C23—1521no—
481C23—1521no—
482C23—1521no—
483C23—1521no—
484C23—1521no—
485C23—1521no—
486C23C4×D7611yescharacteristic
487C23C22⋊C4×D1911yescharacteristic
488C23#1059733911yescharacteristic
489C23C2×#6451511yescharacteristic
490C23#1059734711yescharacteristic
491C23M16×D1911yescharacteristic
492C23#1059735311yescharacteristic
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—22no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—42no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—42no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—81no—
510C2×C4—81no—
511C2×C4—192no—
512C2×C4—381no—
513C2×C4—381no—
514C2×C4—381no—
515C2×C4—381no—
516C2×C4—381no—
517C2×C4—381no—
518C2×C4—381no—
519C2×C4—381no—
520C2×C4—381no—
521C2×C4—381no—
522C2×C4—381no—
523C2×C4—762no—
524C2×C4—762no—
525C2×C4—761no—
526C2×C4—761no—
527C2×C4—761no—
528C2×C4—761no—
529C2×C4—761no—
530C2×C4—761no—
531C2×C4—761no—
532C2×C4—1521no—
533C2×C4—1521no—
534C2×C4#1059732811yescharacteristic
535C2×C4#1059733011yescharacteristic
536C2×C4#1059734011yescharacteristic
537C2×C4#1059734111yescharacteristic
538C8—42no—
539C8—81no—
540C8—762no—
541C8—1521no—
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—762no—
555C22—762no—
556C22—762no—
557C22—1522no—
558C22—1522no—
559C22—1522no—
560C22—1522no—
561C22—1521no—
562C22—1521no—
563C22—1521no—
564C22—1521no—
565C22#1192642211yescharacteristic
566C22#1192650611yescharacteristic
567C22#1192650911yescharacteristic
568C22#1192651611yescharacteristic
569C22#1192651611yescharacteristic
570C22#100×D1911yescharacteristic
571C22#1192652711yescharacteristic
572C22#1192661411yescharacteristic
573C22#1192661711yescharacteristic
574C22#1192662111yescharacteristic
575C22#1192662311yescharacteristic
576C4—21no—
577C4—21no—
578C4—21no—
579C4—21no—
580C4—42no—
581C4—81no—
582C4—382no—
583C4—761no—
584C4—761no—
585C4—761no—
586C4—1521no—
587C2—21no—
588C2—21no—
589C2—21no—
590C2—21no—
591C2—1522no—
592C2#1456196811yescharacteristic
593C2#1456197411yescharacteristic
594C2#1456198511yescharacteristic
595C2#1456200311yescharacteristic
596C2#1456393111yescharacteristic
597C2#1456409211yescharacteristic
598C2#1456409711yescharacteristic
subgroupG/H
centerC23C22⋊C4×D19
commutatorC24×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#1280C2
socleC23×C19C2×C22⋊C4
prime radicalC24×D19C2×C4
cosocleC23×C4×C19C23
hypercenter#1280D19
hypocenterC19#9084
LCSG ▷ C24×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1280

Complements

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

NH ≅ G/Ntype
1. C2×#11926598C2semidirect
3. #14563701C2semidirect
6. #14561478C2semidirect
7. C19×#1280C2semidirect
249. #1280D19semidirect
379. C19#9084semidirect

Maximal subgroups

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

subgroupindex
C2×#119265982
C2×#119264362
#145637012
C2×#119262672
#145614782
C19×#12802
#908419