Finite Group Databasebeta

← #19137962

Subgroups — #19137962

Order 5504.

1246 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D4×D43C211yesmaximal, characteristic, complemented
2C2×#13063298C211yesmaximal, characteristic, complemented
3C2×#13063296C211yesmaximal, characteristic, complemented
4C2×#13063293C211yesmaximal, characteristic, complemented
5C2×#13063293C211yesmaximal, characteristic, complemented
6C2×C22⋊C4×D43C211yesmaximal, characteristic, complemented
7#14582815C211yesmaximal, characteristic, complemented
8#14582813C211yesmaximal, characteristic, complemented
9#14582807C211yesmaximal, characteristic, complemented
10#14582777C211yesmaximal, characteristic, complemented
11#14582775C211yesmaximal, characteristic, complemented
12#14582775C211yesmaximal, characteristic, complemented
13#14582773C211yesmaximal, characteristic, complemented
14#14582754C211yesmaximal, characteristic, complemented
15C43×#392C211yesmaximal, characteristic, complemented
16C24×D43C2211yescharacteristic
17C24×D43C2211yescharacteristic
18C22×D172C2211yescharacteristic
19C22×C22⋊D43C2211yescharacteristic
20C22×C22⋊D43C2211yescharacteristic
21C22×C22⋊D43C2211yescharacteristic
22C22×C22⋊D43C2211yescharacteristic, complemented
23C22×C22⋊D43C2211yescharacteristic, complemented
24C2×D4×D43—24no—
25C2×D4×D43—24no—
26C2×D4×D43—24no—
27C22×C4×D43C2211yescharacteristic
28C22×C4×D43C2211yescharacteristic, complemented
29C22×C4×D43C2211yescharacteristic, complemented
30#13063298—24no—
31#13063296—24no—
32#13063293—24no—
33#13063293—24no—
34C2×C4⋊Dic43C2211yescharacteristic, complemented
35C2×Dic43⋊C4C2211yescharacteristic, complemented
36C2×C22⋊Dic43C2211yescharacteristic, complemented
37C2×C22⋊Dic43C2211yescharacteristic, complemented
38C2×C22⋊Dic43C2211yescharacteristic, complemented
39C2×C22⋊Dic43C2211yescharacteristic, complemented
40C2×C22⋊Dic43C2211yescharacteristic, complemented
41C2×(C2×D43)⋊C4C2211yescharacteristic
42C2×(C2×D43)⋊C4C2211yescharacteristic
43C2×(C2×D43)⋊C4C2211yescharacteristic
44C2×(C2×D43)⋊C4C2211yescharacteristic, complemented
45C2×(C2×D43)⋊C4C2211yescharacteristic, complemented
46C2×(C2×D43)⋊C4C2211yescharacteristic, complemented
47C2×(C2×D43)⋊C4C2211yescharacteristic, complemented
48C22⋊C4×D43—24no—
49C43⋊#95C2211yescharacteristic, complemented
50C43⋊#95C2211yescharacteristic, complemented
51C43⋊#95C2211yescharacteristic, complemented
52C22×D4×C43C2211yescharacteristic
53C22×D4×C43C2211yescharacteristic, complemented
54C22×D4×C43C2211yescharacteristic, complemented
55C2×C22⋊C4×C43C2211yescharacteristic, complemented
56C2×C22⋊C4×C43C2211yescharacteristic, complemented
57C2×C22⋊C4×C43C2211yescharacteristic, complemented
58#95×C43C2211yescharacteristic, complemented
59C24×C43C2311yescharacteristic
60C24×C43C2311yescharacteristic
61C24×C43C2311yescharacteristic
62C23×D43—22no—
63C23×D43—22no—
64C23×D43—22no—
65C23×D43—22no—
66C23×D43—22no—
67C23×D43—22no—
68C23×D43—22no—
69C23×D43—22no—
70C23×D43—22no—
71C23×D43—41no—
72C23×D43—41no—
73C23×D43—41no—
74C23×D43—41no—
75C23×D43D414yescomplemented
76C23×D43C2311yescharacteristic
77C23×D43C2311yescharacteristic
78C23×D43C2311yescharacteristic
79C2×D4×C43—22no—
80C2×D4×C43—22no—
81C2×D4×C43—22no—
82C2×D4×C43—22no—
83C2×D4×C43—22no—
84C2×D4×C43—22no—
85C2×D4×C43—41no—
86C2×D4×C43—41no—
87C2×D4×C43—41no—
88C22×C4×C43C2311yescharacteristic
89C22×C4×C43C2311yescharacteristic
90C22×C4×C43C2311yescharacteristic
91C22×C4×C43C2311yescharacteristic
92C2×C22⋊D43—22no—
93C2×C22⋊D43—22no—
94C2×C22⋊D43—22no—
95C2×C22⋊D43—22no—
96C2×C22⋊D43—22no—
97C2×C22⋊D43—22no—
98C2×C22⋊D43—22no—
99C2×C22⋊D43—22no—
100C2×C22⋊D43—22no—
101C2×C22⋊D43—22no—
102C2×C22⋊D43—22no—
103C2×C22⋊D43—22no—
104C2×C22⋊D43—22no—
105C2×C22⋊D43—41no—
106C2×C22⋊D43D414yescomplemented
107C22×Dic43C2311yescharacteristic
108C22×Dic43C2311yescharacteristic
109C22×Dic43C2311yescharacteristic
110C22×Dic43C2311yescharacteristic
111C22×Dic43C2311yescharacteristic
112D4×D43—232no—
113C2×D172—22no—
114C2×D172—22no—
115C2×D172D414yescomplemented
116C2×C4×D43—22no—
117C2×C4×D43—22no—
118C2×C4×D43—22no—
119C2×C4×D43—22no—
120C2×C4×D43—22no—
121C2×C4×D43—22no—
122C2×C4×D43—22no—
123C2×C4×D43—41no—
124C2×C4×D43—41no—
125C22⋊C4×C43—22no—
126C22⋊C4×C43—22no—
127C22⋊C4×C43—41no—
128C22⋊Dic43—22no—
129C22⋊Dic43—22no—
130C22⋊Dic43—22no—
131C22⋊Dic43—22no—
132C22⋊Dic43—22no—
133(C2×D43)⋊C4—22no—
134(C2×D43)⋊C4—22no—
135(C2×D43)⋊C4—22no—
136(C2×D43)⋊C4—22no—
137(C2×D43)⋊C4—22no—
138(C2×D43)⋊C4—41no—
139(C2×D43)⋊C4D414yescomplemented
140C4⋊Dic43—22no—
141Dic43⋊C4—22no—
142C23×C43—21no—
143C23×C43—21no—
144C23×C43—21no—
145C23×C43—21no—
146C23×C43—21no—
147C23×C43—21no—
148C23×C43—21no—
149C23×C43—21no—
150C23×C43—21no—
151C23×C43—21no—
152C23×C43—21no—
153C23×C43—21no—
154C23×C43—21no—
155C23×C43—21no—
156C23×C43—21no—
157C23×C43—21no—
158C23×C43—21no—
159C23×C43—21no—
160C23×C43—21no—
161C23×C43C2×D412yes—
162C23×C43C2×D412yes—
163C23×C43C2411yescharacteristic
164C22×D43—21no—
165C22×D43—21no—
166C22×D43—21no—
167C22×D43—21no—
168C22×D43—21no—
169C22×D43—21no—
170C22×D43—21no—
171C22×D43—21no—
172C22×D43—28no—
173C22×D43—21no—
174C22×D43—21no—
175C22×D43—21no—
176C22×D43—21no—
177C22×D43—21no—
178C22×D43—21no—
179C22×D43—28no—
180C22×D43—28no—
181C22×D43—44no—
182C22×D43—44no—
183C22×D43—44no—
184C22×D43—44no—
185C22×D43—44no—
186C22×D43—44no—
187C22×D43—44no—
188C22×D43—44no—
189C22×D43—44no—
190C22×D43—44no—
191C22×D43—44no—
192C22×D43C2×D412yes—
193C22×D43C2×D412yes—
194C22×D43C2×D412yes—
195C22×D43C2×D412yes—
196C22×D43C2×D412yes—
197C22×D43C2×D412yes—
198C22×D43#4112yes—
199D4×C43—28no—
200D4×C43—44no—
201D4×C43—44no—
202C2×C4×C43—21no—
203C2×C4×C43—21no—
204C2×C4×C43—21no—
205C2×C4×C43—21no—
206C2×C4×C43—21no—
207C2×C4×C43—21no—
208C2×C4×C43—21no—
209C2×C4×C43—21no—
210C2×C4×C43—21no—
211C2×C4×C43—21no—
212C2×C4×C43C2×D412yes—
213C2×C4×C43C2×D412yescomplemented
214C22⋊D43—28no—
215C22⋊D43—28no—
216C22⋊D43—44no—
217C22⋊D43—44no—
218C22⋊D43—44no—
219C2×Dic43—21no—
220C2×Dic43—21no—
221C2×Dic43—21no—
222C2×Dic43—21no—
223C2×Dic43—21no—
224C2×Dic43—21no—
225C2×Dic43—21no—
226C2×Dic43—21no—
227C2×Dic43—21no—
228C2×Dic43—21no—
229C2×Dic43—21no—
230C2×Dic43—21no—
231C2×Dic43—21no—
232C2×Dic43C2×D412yes—
233C2×Dic43C2×D412yescomplemented
234D172—28no—
235C4×D43—28no—
236C4×D43—44no—
237C4×D43—44no—
238C22×C43—22no—
239C22×C43—22no—
240C22×C43—22no—
241C22×C43—22no—
242C22×C43—22no—
243C22×C43—22no—
244C22×C43—41no—
245C22×C43—41no—
246C22×C43—41no—
247C22×C43—41no—
248C22×C43—41no—
249C22×C43—41no—
250C22×C43—41no—
251C22×C43—41no—
252C22×C43—41no—
253C22×C43—41no—
254C22×C43—41no—
255C22×C43—41no—
256C22×C43—41no—
257C22×C43—41no—
258C22×C43—41no—
259C22×C43C22×D411yescharacteristic
260C22×C43C22×D411yescharacteristic
261C22×C43C22×D411yescharacteristic
262C22×C43C22×D411yescharacteristic
263C22×C43C2×#4111yescharacteristic
264C22×C43H(5,𝔽2)11yescharacteristic
265C22×C43H(5,𝔽2)11yescharacteristic
266C2×D43—22no—
267C2×D43—22no—
268C2×D43—22no—
269C2×D43—22no—
270C2×D43—22no—
271C2×D43—22no—
272C2×D43—22no—
273C2×D43—22no—
274C2×D43—22no—
275C2×D43—22no—
276C2×D43—22no—
277C2×D43—22no—
278C2×D43—22no—
279C2×D43—22no—
280C2×D43—22no—
281C2×D43—416no—
282C2×D43—416no—
283C2×D43—41no—
284C2×D43—41no—
285C2×D43—41no—
286C2×D43—41no—
287C2×D43#12014yescomplemented
288C2×D43#12114yescomplemented
289C4×C43—22no—
290C4×C43—22no—
291C4×C43—41no—
292C4×C43—41no—
293Dic43—22no—
294Dic43—22no—
295Dic43—41no—
296Dic43—41no—
297Dic43—41no—
298#2410—431nomaximal, Sylow
299C2×C43—42no—
300C2×C43—42no—
301C2×C43—81no—
302C2×C43C2×#12011yescharacteristic
303C2×C43C2×#12111yescharacteristic
304C2×C43#53411yescharacteristic
305C2×C43D4211yescharacteristic
306C2×C43D4211yescharacteristic
307C2×C43#54611yescharacteristic
308C2×C43#54611yescharacteristic
309D43—24no—
310D43—24no—
311D43—42no—
312C23×D4—431no—
313C2×#121—431no—
314C2×#121—431no—
315C2×#120—431no—
316C2×#120—431no—
317C22×C22⋊C4—431no—
318#394—431no—
319#394—431no—
320#392—431no—
321#392D4311yescharacteristic, complemented
322#386—431no—
323#386—431no—
324#386—431no—
325#385—431no—
326#379—431no—
327C43#241011yescharacteristic, complemented, Sylow
328C25—431no—
329C25—431no—
330C22×D4—431no—
331C22×D4—431no—
332C22×D4—431no—
333C22×D4—431no—
334C22×D4—431no—
335C22×D4—431no—
336C22×D4—864no—
337C22×D4—864no—
338C22×D4—864no—
339C22×D4C2×D4311yescharacteristic
340C22×D4C2×D4311yescharacteristic, complemented
341C22×D4C2×D4311yescharacteristic, complemented
342C23×C4—431no—
343C23×C4—431no—
344C23×C4—431no—
345#121—864no—
346#121—864no—
347#120—864no—
348#120—864no—
349C2×C4⋊C4—431no—
350C2×C4⋊C4—431no—
351C2×C22⋊C4—431no—
352C2×C22⋊C4—431no—
353C2×C22⋊C4—431no—
354C2×C22⋊C4—431no—
355C2×C22⋊C4—431no—
356C2×C22⋊C4—431no—
357C2×C22⋊C4—431no—
358C2×C22⋊C4—431no—
359C2×C22⋊C4—431no—
360C2×C22⋊C4—431no—
361C2×C22⋊C4—431no—
362C2×C22⋊C4—431no—
363C2×C22⋊C4—864no—
364C2×C22⋊C4C2×D4311yescharacteristic, complemented
365C2×C22⋊C4C2×D4311yescharacteristic, complemented
366C2×C22⋊C4C2×D4311yescharacteristic, complemented
367#95—431no—
368#95—431no—
369#95—431no—
370#95C2×D4311yescharacteristic, complemented
371C24—431no—
372C24—431no—
373C24—431no—
374C24—434no—
375C24—862no—
376C24—862no—
377C24—862no—
378C24—862no—
379C24—862no—
380C24—862no—
381C24—862no—
382C24—862no—
383C24—862no—
384C24—1721no—
385C24—1721no—
386C24—1721no—
387C24—1721no—
388C24C22×D4311yescharacteristic
389C24C22×D4311yescharacteristic
390C24C22×D4311yescharacteristic
391C2×D4—22no—
392C2×D4—22no—
393C2×D4—22no—
394C2×D4—22no—
395C2×D4—22no—
396C2×D4—22no—
397C2×D4—41no—
398C2×D4—41no—
399C2×D4—41no—
400C2×D4—434no—
401C2×D4—434no—
402C2×D4—862no—
403C2×D4—862no—
404C2×D4—862no—
405C2×D4—862no—
406C2×D4—8632no—
407C2×D4—862no—
408C2×D4—862no—
409C2×D4—862no—
410C2×D4—862no—
411C2×D4—862no—
412C2×D4—862no—
413C2×D4—862no—
414C2×D4—862no—
415C2×D4—862no—
416C2×D4—862no—
417C2×D4—862no—
418C2×D4—1721no—
419C22×C4—431no—
420C22×C4—431no—
421C22×C4—431no—
422C22×C4—431no—
423C22×C4—431no—
424C22×C4—862no—
425C22×C4—862no—
426C22×C4—862no—
427C22×C4—862no—
428C22×C4—862no—
429C22×C4—862no—
430C22×C4—862no—
431C22×C4—1721no—
432C22×C4—1721no—
433C22×C4C22×D4311yescharacteristic
434C22×C4C22×D4311yescharacteristic
435C22×C4C22×D4311yescharacteristic
436C22×C4C22×D4311yescharacteristic
437C4⋊C4—862no—
438C4⋊C4—862no—
439C22⋊C4—22no—
440C22⋊C4—22no—
441C22⋊C4—41no—
442C22⋊C4—434no—
443C22⋊C4—862no—
444C22⋊C4—862no—
445C22⋊C4—862no—
446C22⋊C4—862no—
447C22⋊C4—862no—
448C22⋊C4—862no—
449C22⋊C4—862no—
450C22⋊C4—862no—
451C22⋊C4—862no—
452C22⋊C4—862no—
453C22⋊C4—1721no—
454C23—21no—
455C23—21no—
456C23—21no—
457C23—21no—
458C23—21no—
459C23—21no—
460C23—21no—
461C23—21no—
462C23—21no—
463C23—21no—
464C23—21no—
465C23—21no—
466C23—21no—
467C23—21no—
468C23—21no—
469C23—21no—
470C23—21no—
471C23—21no—
472C23—21no—
473C23—432no—
474C23—432no—
475C23—432no—
476C23—432no—
477C23—432no—
478C23—432no—
479C23—432no—
480C23—868no—
481C23—868no—
482C23—868no—
483C23—861no—
484C23—861no—
485C23—861no—
486C23—861no—
487C23—861no—
488C23—861no—
489C23—861no—
490C23—861no—
491C23—861no—
492C23—861no—
493C23—861no—
494C23—861no—
495C23—861no—
496C23—861no—
497C23—1724no—
498C23—1724no—
499C23—1724no—
500C23—1724no—
501C23—1724no—
502C23—1724no—
503C23—1724no—
504C23—1724no—
505C23—1724no—
506C23—1724no—
507C23—1724no—
508C23D4×D4312yes—
509C23D4×D4312yes—
510C23C23×D4311yescharacteristic
511D4—28no—
512D4—44no—
513D4—44no—
514D4—868no—
515D4—868no—
516D4—868no—
517D4—1724no—
518D4—1724no—
519D4—1724no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—432no—
531C2×C4—432no—
532C2×C4—868no—
533C2×C4—861no—
534C2×C4—861no—
535C2×C4—861no—
536C2×C4—861no—
537C2×C4—861no—
538C2×C4—861no—
539C2×C4—861no—
540C2×C4—861no—
541C2×C4—861no—
542C2×C4—861no—
543C2×C4—861no—
544C2×C4—861no—
545C2×C4—861no—
546C2×C4—1724no—
547C2×C4—1724no—
548C2×C4D4×D4312yes—
549C2×C4D4×D4312yescomplemented
550C22—22no—
551C22—22no—
552C22—22no—
553C22—22no—
554C22—22no—
555C22—22no—
556C22—41no—
557C22—41no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22—41no—
562C22—41no—
563C22—41no—
564C22—41no—
565C22—41no—
566C22—41no—
567C22—41no—
568C22—41no—
569C22—41no—
570C22—41no—
571C22—434no—
572C22—434no—
573C22—862no—
574C22—862no—
575C22—862no—
576C22—862no—
577C22—862no—
578C22—862no—
579C22—862no—
580C22—862no—
581C22—862no—
582C22—862no—
583C22—862no—
584C22—862no—
585C22—862no—
586C22—862no—
587C22—862no—
588C22—17216no—
589C22—17216no—
590C22—1721no—
591C22—1721no—
592C22—1721no—
593C22—1721no—
594C22C2×D4×D4311yescharacteristic
595C22C2×D4×D4311yescharacteristic
596C22C2×D4×D4311yescharacteristic
597C22C2×D4×D4311yescharacteristic
598C22#41×D4311yescharacteristic
599C22#1306337011yescharacteristic
600C22#1306337011yescharacteristic
601C4—22no—
602C4—22no—
603C4—41no—
604C4—41no—
605C4—862no—
606C4—862no—
607C4—1721no—
608C4—1721no—
609C4—1721no—
610C2—42no—
611C2—42no—
612C2—81no—
613C2—864no—
614C2—864no—
615C2—1722no—
616C2#120×D4311yescharacteristic
617C2#121×D4311yescharacteristic
618C2#1458345911yescharacteristic
619C2#1458353111yescharacteristic
620C2#1458353411yescharacteristic
621C2#1458353811yescharacteristic
622C2#1458354611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#392C2
hypercenter#392D43
hypocenterC43#2410
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C22×D4×D43C2semidirect
2. C2×#13063298C2semidirect
3. C2×#13063296C2semidirect
4. C2×#13063293C2semidirect
5. C2×#13063293C2semidirect
6. C2×C22⋊C4×D43C2semidirect
7. #14582815C2semidirect
8. #14582813C2semidirect
9. #14582807C2semidirect
10. #14582777C2semidirect
11. #14582775C2semidirect
12. #14582775C2semidirect
13. #14582773C2semidirect
14. #14582754C2semidirect
15. C43×#392C2semidirect
22. C22×C22⋊D43C22semidirect
23. C22×C22⋊D43C22semidirect
28. C22×C4×D43C22semidirect
29. C22×C4×D43C22semidirect
34. C2×C4⋊Dic43C22semidirect
35. C2×Dic43⋊C4C22semidirect
36. C2×C22⋊Dic43C22semidirect
37. C2×C22⋊Dic43C22semidirect
38. C2×C22⋊Dic43C22semidirect
39. C2×C22⋊Dic43C22semidirect
40. C2×C22⋊Dic43C22semidirect
44. C2×(C2×D43)⋊C4C22semidirect
45. C2×(C2×D43)⋊C4C22semidirect
46. C2×(C2×D43)⋊C4C22semidirect
47. C2×(C2×D43)⋊C4C22semidirect
49. C43⋊#95C22semidirect
50. C43⋊#95C22semidirect
51. C43⋊#95C22semidirect
53. C22×D4×C43C22semidirect
54. C22×D4×C43C22semidirect
55. C2×C22⋊C4×C43C22semidirect
56. C2×C22⋊C4×C43C22semidirect
57. C2×C22⋊C4×C43C22semidirect
58. #95×C43C22semidirect
75. C23×D43D4semidirect
106. C2×C22⋊D43D4semidirect
115. C2×D172D4semidirect
139. (C2×D43)⋊C4D4semidirect
213. C2×C4×C43C2×D4semidirect
233. C2×Dic43C2×D4semidirect
287. C2×D43#120semidirect
288. C2×D43#121semidirect
321. #392D43semidirect
327. C43#2410semidirect
340. C22×D4C2×D43semidirect
341. C22×D4C2×D43semidirect
364. C2×C22⋊C4C2×D43semidirect
365. C2×C22⋊C4C2×D43semidirect
366. C2×C22⋊C4C2×D43semidirect
370. #95C2×D43semidirect
549. C2×C4D4×D43semidirect