Finite Group Databasebeta

← #18081676

Subgroups — #18081676

Order 4864.

764 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14571978C211yesmaximal, characteristic
2#14563613C211yesmaximal, characteristic, complemented
3C2×#11926279C211yesmaximal, characteristic, complemented
4C2×#11926278C211yesmaximal, characteristic, complemented
5C2×#11926277C211yesmaximal, characteristic, complemented
6#14561860C211yesmaximal, characteristic, complemented
7C2×C19×#327C211yesmaximal, characteristic, complemented
8C2×#10597386C411yescharacteristic, complemented
9C2×#10597376C2211yescharacteristic
10C2×#10597385—21no—
11C2×#10597385—21no—
12C22×C4×Dic19C2211yescharacteristic
13C2×Dic19⋊C8—21no—
14C2×C22⋊(C19⋊C8)C2211yescharacteristic
15#11926447C411yescharacteristic, complemented
16#11926445C411yescharacteristic, complemented
17#11926444—21no—
18#11926444—21no—
19#11926413C411yescharacteristic, complemented
20C2×C19⋊#95—21no—
21C2×C19⋊#95—21no—
22C2×C19⋊#95C2211yescharacteristic
23#11926298—21no—
24#11926279—22no—
25#11926278—22no—
26#11926277—22no—
27C2×C19×#121C2211yescharacteristic
28C2×C19×C22⋊C8C2211yescharacteristic
29C2×C19×#95C2211yescharacteristic
30C19×#327—22no—
31C22×D4×C19—21no—
32C22×D4×C19C2×C411yescharacteristic
33C23×C4×C19—21no—
34C23×C4×C19C2311yescharacteristic
35C22×C22⋊D19—21no—
36C22×C22⋊D19—21no—
37C22×C22⋊D19—21no—
38C23×Dic19—21no—
39C23×Dic19D411yescharacteristic
40C23×Dic19D411yescharacteristic
41C22×D76C2×C411yescharacteristic
42C22×C8×C19—21no—
43C19×#121—21no—
44C19×#121—21no—
45C19×#121—21no—
46C19×#121—21no—
47C2×C4⋊C4×C19C2×C411yescharacteristic
48C2×C22⋊C4×C19—21no—
49C2×C22⋊Dic19—21no—
50C2×C22⋊Dic19—21no—
51#10597386—42no—
52#10597385—42no—
53#10597385—42no—
54#10597385—42no—
55#10597385—42no—
56#10597376—21no—
57#10597376—21no—
58#10597376—21no—
59#10597376—21no—
60C2×(C2×D19)⋊C4—21no—
61C2×(C2×D19)⋊C4—21no—
62C2×(C2×D19)⋊C4—21no—
63C2×C4⋊Dic19C2×C411yescharacteristic
64C2×Dic19⋊C4—21no—
65C2×Dic19⋊C4—21no—
66C2×C4×Dic19—42no—
67C2×C4×Dic19C2×C411yescharacteristic
68C2×C4×Dic19C2×C411yescharacteristic
69C2×C4×Dic19D411yescharacteristic
70C2×C4×Dic19D411yescharacteristic
71C22×C19⋊C8—21no—
72C19×C22⋊C8—21no—
73C19×C22⋊C8—21no—
74C19×#95—21no—
75C19×#95D412yescomplemented
76C19⋊#95—21no—
77C19⋊#95—42no—
78C19⋊#95—42no—
79C19⋊#95D412yescomplemented
80C22⋊(C19⋊C8)—21no—
81C22⋊(C19⋊C8)—21no—
82Dic19⋊C8—42no—
83C24×C19—21no—
84C24×C19C2×D411yescharacteristic
85C23×D19—21no—
86C2×D4×C19—21no—
87C2×D4×C19—21no—
88C2×D4×C19—41no—
89C2×D4×C19—41no—
90C2×D4×C19—41no—
91C2×D4×C19—41no—
92C2×D4×C19—41no—
93C2×D4×C19—41no—
94C2×D4×C19—41no—
95C2×D4×C19—41no—
96C22×C4×C19—21no—
97C22×C4×C19—22no—
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×C19C22×C411yescharacteristic
107C22×C4×C19C2×D411yescharacteristic
108C22×C4×C19C2×D411yescharacteristic
109C22×C4×C19C2×D411yescharacteristic
110C22×C4×C19#4111yescharacteristic
111C22×C4×C19#4111yescharacteristic
112C2×C22⋊D19—42no—
113C2×C22⋊D19—42no—
114C2×C22⋊D19—42no—
115C2×C22⋊D19—42no—
116C2×C22⋊D19—41no—
117C2×C22⋊D19—41no—
118C2×C22⋊D19—41no—
119C2×C22⋊D19—41no—
120C2×C22⋊D19—41no—
121C2×C22⋊D19—41no—
122C2×C22⋊D19—42no—
123C2×C22⋊D19—42no—
124C22×Dic19—21no—
125C22×Dic19—21no—
126C22×Dic19—22no—
127C22×Dic19—21no—
128C22×Dic19—22no—
129C22×Dic19—41no—
130C22×Dic19—41no—
131C22×Dic19—41no—
132C22×Dic19—41no—
133C22×Dic19—41no—
134C22×Dic19—41no—
135C22×Dic19—41no—
136C22×Dic19—41no—
137C22×Dic19—41no—
138C22×Dic19C22⋊C411yescharacteristic
139C22×Dic19C22⋊C411yescharacteristic
140C22×Dic19C22⋊C411yescharacteristic
141C22×Dic19C22⋊C411yescharacteristic
142C22×Dic19D812yes—
143C22×Dic19SD1612yes—
144C2×D76—21no—
145C2×D76—21no—
146C2×D76—41no—
147C2×D76—41no—
148C2×C8×C19—41no—
149C2×C8×C19—41no—
150C2×C8×C19—41no—
151C4⋊C4×C19—21no—
152C4⋊C4×C19—21no—
153C22⋊C4×C19—41no—
154C22⋊C4×C19—41no—
155C22⋊Dic19—42no—
156C22⋊Dic19—42no—
157(C2×D19)⋊C4—42no—
158(C2×D19)⋊C4—41no—
159(C2×D19)⋊C4—41no—
160(C2×D19)⋊C4—42no—
161C4⋊Dic19—21no—
162C4⋊Dic19—21no—
163Dic19⋊C4—42no—
164Dic19⋊C4—42no—
165C4×Dic19—22no—
166C4×Dic19—22no—
167C4×Dic19—41no—
168C4×Dic19—41no—
169C2×C19⋊C8—41no—
170C2×C19⋊C8—41no—
171C2×C19⋊C8—41no—
172#9715—191nomaximal, Sylow
173C23×C19—21no—
174C23×C19—21no—
175C23×C19—21no—
176C23×C19—21no—
177C23×C19—41no—
178C23×C19—41no—
179C23×C19—41no—
180C23×C19—41no—
181C23×C19—41no—
182C23×C19—41no—
183C23×C19—41no—
184C23×C19C2×C22⋊C411yescharacteristic
185C23×C19#12111yescharacteristic
186C23×C19#12111yescharacteristic
187C23×C19C2×D811yescharacteristic
188C23×C19C2×SD1611yescharacteristic
189C23×C19AGL(1,ℤ/8)11yescharacteristic
190C23×C19AGL(1,ℤ/8)11yescharacteristic
191C22×D19—41no—
192C22×D19—41no—
193C22×D19—41no—
194C22×D19—41no—
195C22×D19—41no—
196C22×D19—41no—
197C22×D19—41no—
198D4×C19—81no—
199D4×C19—81no—
200D4×C19—81no—
201D4×C19—81no—
202D4×C19—81no—
203D4×C19—81no—
204C2×C4×C19—21no—
205C2×C4×C19—21no—
206C2×C4×C19—21no—
207C2×C4×C19—21no—
208C2×C4×C19—41no—
209C2×C4×C19—41no—
210C2×C4×C19—41no—
211C2×C4×C19—41no—
212C2×C4×C19—42no—
213C2×C4×C19—42no—
214C2×C4×C19—41no—
215C2×C4×C19—41no—
216C2×C4×C19—41no—
217C2×C4×C19—42no—
218C2×C4×C19—81no—
219C2×C4×C19—81no—
220C2×C4×C19—81no—
221C2×C4×C19—81no—
222C2×C4×C19C4×D411yescharacteristic
223C2×C4×C19C4×D411yescharacteristic
224C2×C4×C19#12411yescharacteristic
225C2×C4×C19#12711yescharacteristic
226C22⋊D19—84no—
227C22⋊D19—84no—
228C22⋊D19—81no—
229C22⋊D19—81no—
230C22⋊D19—81no—
231C22⋊D19—81no—
232C2×Dic19—21no—
233C2×Dic19—21no—
234C2×Dic19—21no—
235C2×Dic19—21no—
236C2×Dic19—21no—
237C2×Dic19—21no—
238C2×Dic19—21no—
239C2×Dic19—21no—
240C2×Dic19—21no—
241C2×Dic19—42no—
242C2×Dic19—42no—
243C2×Dic19—42no—
244C2×Dic19—42no—
245C2×Dic19—42no—
246C2×Dic19—42no—
247C2×Dic19—41no—
248C2×Dic19—41no—
249C2×Dic19—41no—
250C2×Dic19—42no—
251C2×Dic19—81no—
252C2×Dic19—81no—
253C2×Dic19—81no—
254C2×Dic19—81no—
255C2×Dic19#9912yes—
256C2×Dic19#10212yes—
257C2×Dic19#10212yes—
258D76—81no—
259D76—81no—
260C8×C19—81no—
261C19⋊C8—81no—
262#2856—191no—
263#1797—191no—
264C2×#327—191no—
265C2×#327—191no—
266C2×#327—191no—
267C2×#327D1911yescharacteristic, complemented
268#1434—191no—
269C22×C19—21no—
270C22×C19—21no—
271C22×C19—21no—
272C22×C19—21no—
273C22×C19—21no—
274C22×C19—21no—
275C22×C19—21no—
276C22×C19—21no—
277C22×C19—21no—
278C22×C19—21no—
279C22×C19—21no—
280C22×C19—21no—
281C22×C19—81no—
282C22×C19—81no—
283C22×C19—81no—
284C22×C19—81no—
285C22×C19—81no—
286C22×C19—81no—
287C22×C19—81no—
288C22×C19#39011yescharacteristic
289C22×C19C2×#9911yescharacteristic
290C22×C19#41011yescharacteristic
291C22×C19C2×#10211yescharacteristic
292C22×C19#41811yescharacteristic
293C22×C19#42111yescharacteristic
294C22×C19#42111yescharacteristic
295C22×C19#45911yescharacteristic
296C22×C19#45911yescharacteristic
297C22×C19#46011yescharacteristic
298C22×C19#46011yescharacteristic
299C2×D19—81no—
300C2×D19—81no—
301C2×D19—81no—
302C2×D19—81no—
303C2×D19—81no—
304C2×D19—81no—
305C2×D19—81no—
306C4×C19—21no—
307C4×C19—21no—
308C4×C19—21no—
309C4×C19—21no—
310C4×C19—82no—
311C4×C19—81no—
312Dic19—22no—
313Dic19—22no—
314Dic19—22no—
315Dic19—41no—
316Dic19—82no—
317Dic19—81no—
318C2×#127—191no—
319C2×#121—191no—
320C2×#121—381no—
321C2×#121—381no—
322C2×#121C2×D1911yescharacteristic
323C22×C42—191no—
324C2×C4⋊C8—381no—
325C2×C22⋊C8—191no—
326C2×C22⋊C8C2×D1911yescharacteristic
327#390—191no—
328#390—191no—
329#390—381no—
330#390—381no—
331#384—191no—
332C2×#95—191no—
333C2×#95—381no—
334C2×#95—381no—
335C2×#95C2×D1911yescharacteristic
336#336—381no—
337#327—22no—
338#327—382no—
339#327—382no—
340#327—382no—
341C2×C19—21no—
342C2×C19—21no—
343C2×C19—21no—
344C2×C19—21no—
345C2×C19—161no—
346C2×C19#151011yescharacteristic
347C2×C19#151411yescharacteristic
348C2×C19#151711yescharacteristic
349C2×C19#151911yescharacteristic
350C2×C19#196311yescharacteristic
351C2×C19#196411yescharacteristic
352C2×C19#198211yescharacteristic
353D19—161no—
354C22×D4—21no—
355C22×D4—191no—
356C22×D4—381no—
357C22×D4—381no—
358C22×D4—381no—
359C22×D4C4×D1911yescharacteristic
360C23×C4—21no—
361C23×C4—191no—
362C23×C4—191no—
363C23×C4—381no—
364C23×C4C22×D1911yescharacteristic
365C22×C8—21no—
366C22×C8—381no—
367#127—762no—
368#121—21no—
369#121—21no—
370#121—21no—
371#121—21no—
372#121—381no—
373#121—381no—
374#121—381no—
375#121—381no—
376#121—762no—
377#121—762no—
378#121—762no—
379#121—762no—
380C2×C4⋊C4—191no—
381C2×C4⋊C4—381no—
382C2×C4⋊C4—381no—
383C2×C4⋊C4C4×D1911yescharacteristic
384C2×C22⋊C4—21no—
385C2×C22⋊C4—381no—
386C2×C22⋊C4—381no—
387C2×C22⋊C4—381no—
388C2×C22⋊C4—381no—
389C2×C22⋊C4—381no—
390C2×C42—191no—
391C2×C42—191no—
392C2×C42—191no—
393C2×C42—191no—
394C2×C42—762no—
395C4⋊C8—762no—
396C22⋊C8—21no—
397C22⋊C8—21no—
398C22⋊C8—381no—
399C22⋊C8—381no—
400#95—21no—
401#95—192no—
402#95—381no—
403#95—762no—
404#95—762no—
405#95C22⋊D1912yescomplemented
406C19#971511yescharacteristic, complemented, Sylow
407C24—21no—
408C24—381no—
409C24D4×D1911yescharacteristic
410C2×D4—21no—
411C2×D4—21no—
412C2×D4—41no—
413C2×D4—41no—
414C2×D4—41no—
415C2×D4—41no—
416C2×D4—41no—
417C2×D4—41no—
418C2×D4—41no—
419C2×D4—41no—
420C2×D4—381no—
421C2×D4—381no—
422C2×D4—761no—
423C2×D4—761no—
424C2×D4—762no—
425C2×D4—762no—
426C2×D4—762no—
427C2×D4—762no—
428C2×D4—762no—
429C2×D4—762no—
430C2×D4—761no—
431C2×D4—761no—
432C2×D4—761no—
433C2×D4—761no—
434C2×D4—761no—
435C2×D4—761no—
436C22×C4—22no—
437C22×C4—21no—
438C22×C4—41no—
439C22×C4—41no—
440C22×C4—41no—
441C22×C4—41no—
442C22×C4—41no—
443C22×C4—41no—
444C22×C4—41no—
445C22×C4—41no—
446C22×C4—191no—
447C22×C4—191no—
448C22×C4—191no—
449C22×C4—192no—
450C22×C4—192no—
451C22×C4—191no—
452C22×C4—382no—
453C22×C4—381no—
454C22×C4—381no—
455C22×C4—381no—
456C22×C4—382no—
457C22×C4—761no—
458C22×C4—761no—
459C22×C4—761no—
460C22×C4—761no—
461C22×C4—761no—
462C22×C4—761no—
463C22×C4—761no—
464C22×C4—761no—
465C22×C4—761no—
466C22×C4C2×C4×D1911yescharacteristic
467C22×C4#6454111yescharacteristic
468C22×C4D4×D1911yescharacteristic
469C22×C4D4×D1911yescharacteristic
470C22×C4#6454311yescharacteristic
471C22×C4C2×C22⋊D1911yescharacteristic
472C2×C8—41no—
473C2×C8—41no—
474C2×C8—41no—
475C2×C8—761no—
476C2×C8—761no—
477C2×C8—761no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—381no—
481C4⋊C4—381no—
482C4⋊C4—762no—
483C4⋊C4—762no—
484C22⋊C4—41no—
485C22⋊C4—41no—
486C22⋊C4—762no—
487C22⋊C4—762no—
488C22⋊C4—762no—
489C22⋊C4—762no—
490C22⋊C4—761no—
491C22⋊C4—761no—
492C42—382no—
493C42—382no—
494C42—761no—
495C42—761no—
496C23—21no—
497C23—21no—
498C23—21no—
499C23—21no—
500C23—41no—
501C23—41no—
502C23—41no—
503C23—41no—
504C23—41no—
505C23—41no—
506C23—41no—
507C23—761no—
508C23—761no—
509C23—761no—
510C23—761no—
511C23—761no—
512C23—761no—
513C23—761no—
514C23C22⋊C4×D1911yescharacteristic
515C23#1059733011yescharacteristic
516C23D8×D1911yescharacteristic
517C23#1059735711yescharacteristic
518C23SD16×D1911yescharacteristic
519C23#1059736011yescharacteristic
520C23#1059738511yescharacteristic
521D4—81no—
522D4—81no—
523D4—81no—
524D4—81no—
525D4—81no—
526D4—81no—
527D4—1521no—
528D4—1521no—
529D4—1524no—
530D4—1524no—
531D4—1521no—
532D4—1521no—
533D4—1521no—
534D4—1521no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—42no—
549C2×C4—81no—
550C2×C4—81no—
551C2×C4—81no—
552C2×C4—81no—
553C2×C4—192no—
554C2×C4—192no—
555C2×C4—192no—
556C2×C4—381no—
557C2×C4—381no—
558C2×C4—381no—
559C2×C4—381no—
560C2×C4—381no—
561C2×C4—381no—
562C2×C4—381no—
563C2×C4—381no—
564C2×C4—381no—
565C2×C4—762no—
566C2×C4—762no—
567C2×C4—762no—
568C2×C4—762no—
569C2×C4—762no—
570C2×C4—762no—
571C2×C4—761no—
572C2×C4—761no—
573C2×C4—761no—
574C2×C4—762no—
575C2×C4—1521no—
576C2×C4—1521no—
577C2×C4—1521no—
578C2×C4—1521no—
579C2×C4(C22⋊D19)⋊C411yescharacteristic
580C2×C4#1059733111yescharacteristic
581C2×C4C4×C22⋊D1911yescharacteristic
582C2×C4#1059738611yescharacteristic
583C8—81no—
584C8—1521no—
585C22—21no—
586C22—21no—
587C22—21no—
588C22—21no—
589C22—21no—
590C22—21no—
591C22—21no—
592C22—21no—
593C22—21no—
594C22—21no—
595C22—21no—
596C22—21no—
597C22—81no—
598C22—81no—
599C22—81no—
600C22—81no—
601C22—81no—
602C22—81no—
603C22—81no—
604C22—1521no—
605C22—1521no—
606C22—1521no—
607C22—1521no—
608C22—1521no—
609C22—1521no—
610C22—1521no—
611C22#1192644411yescharacteristic
612C22#99×D1911yescharacteristic
613C22#1192651611yescharacteristic
614C22#102×D1911yescharacteristic
615C22#1192654711yescharacteristic
616C22#1192655911yescharacteristic
617C22#1192655911yescharacteristic
618C22#1192673711yescharacteristic
619C22#1192673811yescharacteristic
620C22#1192674211yescharacteristic
621C22#1192674311yescharacteristic
622C4—21no—
623C4—21no—
624C4—21no—
625C4—21no—
626C4—82no—
627C4—81no—
628C4—382no—
629C4—382no—
630C4—382no—
631C4—761no—
632C4—1522no—
633C4—1521no—
634C2—21no—
635C2—21no—
636C2—21no—
637C2—21no—
638C2—161no—
639C2—3041no—
640C2#1456216211yescharacteristic
641C2#1456218011yescharacteristic
642C2#1456219311yescharacteristic
643C2#1456220111yescharacteristic
644C2#1456446511yescharacteristic
645C2#1456446911yescharacteristic
646C2#1456456011yescharacteristic
subgroupG/H
centerC23C22⋊C4×D19
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC2×C19×#327C2
socleC23×C19C2×C22⋊C4
prime radical#14571978C2
cosocleC23×C4×C19C23
hypercenterC2×#327D19
hypocenterC19#9715
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#327

Complements

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

NH ≅ G/Ntype
2. #14563613C2semidirect
3. C2×#11926279C2semidirect
4. C2×#11926278C2semidirect
5. C2×#11926277C2semidirect
6. #14561860C2semidirect
7. C2×C19×#327C2semidirect
8. C2×#10597386C4semidirect
15. #11926447C4semidirect
16. #11926445C4semidirect
19. #11926413C4semidirect
75. C19×#95D4semidirect
79. C19⋊#95D4semidirect
267. C2×#327D19semidirect
405. #95C22⋊D19semidirect
406. C19#9715semidirect

Maximal subgroups

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

subgroupindex
#145719782
#145636132
C2×#119262792
C2×#119262782
C2×#119262772
#145618602
C2×C19×#3272
#971519