Finite Group Databasebeta

← #19137964

Subgroups — #19137964

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×#13063300C211yesmaximal, characteristic, complemented
3C2×#13063298C211yesmaximal, characteristic, complemented
4C2×#13063295C211yesmaximal, characteristic, complemented
5C2×#13063295C211yesmaximal, characteristic, complemented
6C2×C22⋊C4×D43C211yesmaximal, characteristic, complemented
7#14582814C211yesmaximal, characteristic, complemented
8#14582808C211yesmaximal, characteristic, complemented
9#14582807C211yesmaximal, characteristic, complemented
10#14582777C211yesmaximal, characteristic, complemented
11#14582777C211yesmaximal, characteristic, complemented
12#14582775C211yesmaximal, characteristic, complemented
13#14582770C211yesmaximal, characteristic, complemented
14#14582754C211yesmaximal, characteristic, complemented
15C43×#394C211yesmaximal, characteristic, complemented
16C24×D43C2211yescharacteristic
17C24×D43C2211yescharacteristic
18C22×D172C2211yescharacteristic
19C22×D172C2211yescharacteristic
20C22×D172C2211yescharacteristic, complemented
21C22×D172C2211yescharacteristic, complemented
22C22×C22⋊D43C2211yescharacteristic
23C22×C22⋊D43C2211yescharacteristic
24C22×C22⋊D43C2211yescharacteristic, complemented
25C22×C22⋊D43C2211yescharacteristic, complemented
26C2×D4×D43—24no—
27C2×D4×D43—24no—
28C2×D4×D43—24no—
29C22×C4×D43C2211yescharacteristic
30C22×C4×D43C2211yescharacteristic, complemented
31C22×C4×D43C2211yescharacteristic, complemented
32#13063300—24no—
33#13063298—24no—
34#13063295—24no—
35#13063295—24no—
36C2×Dic43⋊C4C2211yescharacteristic, complemented
37C2×C22⋊Dic43C2211yescharacteristic, complemented
38C2×C22⋊Dic43C2211yescharacteristic, complemented
39C2×(C2×D43)⋊C4C2211yescharacteristic
40C2×(C2×D43)⋊C4C2211yescharacteristic
41C2×(C2×D43)⋊C4C2211yescharacteristic
42C2×(C2×D43)⋊C4C2211yescharacteristic, complemented
43C2×(C2×D43)⋊C4C2211yescharacteristic, complemented
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
53C2×C4⋊C4×C43C2211yescharacteristic, complemented
54C2×C22⋊C4×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
61C23×D43—22no—
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—41no—
71C23×D43—41no—
72C23×D43—41no—
73C23×D43—41no—
74C23×D43D414yescomplemented
75C23×D43C2311yescharacteristic
76C23×D43C2311yescharacteristic
77C23×D43C2311yescharacteristic
78C23×D43C2311yescharacteristic
79C2×D4×C43—22no—
80C2×D4×C43—22no—
81C2×D4×C43—22no—
82C22×C4×C43C2311yescharacteristic
83C22×C4×C43C2311yescharacteristic
84C22×C4×C43C2311yescharacteristic
85C22×C4×C43C2311yescharacteristic
86C22×C4×C43C2311yescharacteristic
87C2×C22⋊D43—22no—
88C2×C22⋊D43—22no—
89C2×C22⋊D43—22no—
90C2×C22⋊D43—22no—
91C2×C22⋊D43—22no—
92C2×C22⋊D43—22no—
93C2×C22⋊D43—22no—
94C2×C22⋊D43—22no—
95C2×C22⋊D43—41no—
96C2×C22⋊D43—41no—
97C2×C22⋊D43—41no—
98C2×C22⋊D43D414yescomplemented
99C22×Dic43C2311yescharacteristic
100C22×Dic43C2311yescharacteristic
101C22×Dic43C2311yescharacteristic
102C22×Dic43C2311yescharacteristic
103D4×D43—232no—
104C2×D172—22no—
105C2×D172—22no—
106C2×D172—22no—
107C2×D172—22no—
108C2×D172—22no—
109C2×D172—22no—
110C2×D172—22no—
111C2×D172—22no—
112C2×D172—22no—
113C2×D172—22no—
114C2×D172—41no—
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—
125C4⋊C4×C43—22no—
126C22⋊C4×C43—22no—
127C22⋊C4×C43—22no—
128C22⋊C4×C43—22no—
129C22⋊C4×C43—22no—
130C22⋊Dic43—22no—
131C22⋊Dic43—41no—
132(C2×D43)⋊C4—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—22no—
139(C2×D43)⋊C4—41no—
140(C2×D43)⋊C4D414yescomplemented
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×C43C2×D412yes—
155C23×C43C2×D412yes—
156C23×C43C2411yescharacteristic
157C22×D43—21no—
158C22×D43—21no—
159C22×D43—21no—
160C22×D43—21no—
161C22×D43—21no—
162C22×D43—21no—
163C22×D43—21no—
164C22×D43—21no—
165C22×D43—28no—
166C22×D43—21no—
167C22×D43—21no—
168C22×D43—21no—
169C22×D43—21no—
170C22×D43—21no—
171C22×D43—21no—
172C22×D43—28no—
173C22×D43—28no—
174C22×D43—21no—
175C22×D43—21no—
176C22×D43—21no—
177C22×D43—21no—
178C22×D43—21no—
179C22×D43—21no—
180C22×D43—21no—
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—
200C2×C4×C43—21no—
201C2×C4×C43—21no—
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×C43—21no—
213C2×C4×C43C2×D412yes—
214C2×C4×C43C2×D412yescomplemented
215C22⋊D43—28no—
216C22⋊D43—28no—
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×Dic43C2×D412yes—
230C2×Dic43C2×D412yescomplemented
231D172—28no—
232D172—44no—
233D172—44no—
234D172—44no—
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×C43C22×D411yescharacteristic
253C22×C43C22×D411yescharacteristic
254C22×C43C22×D411yescharacteristic
255C22×C43C22×D411yescharacteristic
256C22×C43C2×#4111yescharacteristic
257C22×C43H(5,𝔽2)11yescharacteristic
258C22×C43H(5,𝔽2)11yescharacteristic
259C2×D43—22no—
260C2×D43—22no—
261C2×D43—22no—
262C2×D43—22no—
263C2×D43—22no—
264C2×D43—22no—
265C2×D43—22no—
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—416no—
275C2×D43—416no—
276C2×D43—41no—
277C2×D43—41no—
278C2×D43—41no—
279C2×D43—41no—
280C2×D43—41no—
281C2×D43—41no—
282C2×D43—41no—
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—
293C4×C43—41no—
294Dic43—22no—
295Dic43—22no—
296Dic43—41no—
297Dic43—41no—
298#2410—431nomaximal, Sylow
299C2×C43—42no—
300C2×C43—42no—
301C2×C43C2×#12011yescharacteristic
302C2×C43C2×#12111yescharacteristic
303C2×C43#53411yescharacteristic
304C2×C43D4211yescharacteristic
305C2×C43D4211yescharacteristic
306C2×C43#54611yescharacteristic
307C2×C43#54611yescharacteristic
308D43—24no—
309D43—24no—
310D43—42no—
311D43—81no—
312C23×D4—431no—
313C2×#121—431no—
314C2×#121—431no—
315C2×#120—431no—
316C2×#120—431no—
317C22×C22⋊C4—431no—
318#394—431no—
319#394D4311yescharacteristic, complemented
320#392—431no—
321#392—431no—
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—431no—
337C22×D4—431no—
338C22×D4—864no—
339C22×D4—864no—
340C22×D4—864no—
341C22×D4C2×D4311yescharacteristic
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⋊C4C2×D4311yescharacteristic, complemented
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—864no—
363C2×C22⋊C4C2×D4311yescharacteristic, complemented
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—431no—
376C24—862no—
377C24—862no—
378C24—862no—
379C24—862no—
380C24—862no—
381C24—862no—
382C24—862no—
383C24—862no—
384C24—862no—
385C24—1721no—
386C24—1721no—
387C24—1721no—
388C24—1721no—
389C24C22×D4311yescharacteristic
390C24C22×D4311yescharacteristic
391C2×D4—22no—
392C2×D4—22no—
393C2×D4—22no—
394C2×D4—434no—
395C2×D4—434no—
396C2×D4—862no—
397C2×D4—862no—
398C2×D4—862no—
399C2×D4—862no—
400C2×D4—862no—
401C2×D4—862no—
402C2×D4—862no—
403C2×D4—862no—
404C2×D4—862no—
405C2×D4—862no—
406C2×D4—862no—
407C2×D4—8632no—
408C2×D4—862no—
409C2×D4—862no—
410C2×D4—862no—
411C2×D4—862no—
412C2×D4—862no—
413C2×D4—862no—
414C2×D4—862no—
415C2×D4—1721no—
416C2×D4—1721no—
417C2×D4—1721no—
418C2×D4—1721no—
419C22×C4—431no—
420C22×C4—431no—
421C22×C4—431no—
422C22×C4—431no—
423C22×C4—862no—
424C22×C4—862no—
425C22×C4—862no—
426C22×C4—862no—
427C22×C4—862no—
428C22×C4—862no—
429C22×C4—862no—
430C22×C4—1721no—
431C22×C4—1721no—
432C22×C4C22×D4311yescharacteristic
433C22×C4C22×D4311yescharacteristic
434C22×C4C22×D4311yescharacteristic
435C22×C4C22×D4311yescharacteristic
436C22×C4C22×D4311yescharacteristic
437C4⋊C4—22no—
438C4⋊C4—862no—
439C22⋊C4—22no—
440C22⋊C4—22no—
441C22⋊C4—22no—
442C22⋊C4—22no—
443C22⋊C4—434no—
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—1721no—
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—432no—
467C23—432no—
468C23—432no—
469C23—432no—
470C23—432no—
471C23—432no—
472C23—432no—
473C23—868no—
474C23—868no—
475C23—868no—
476C23—861no—
477C23—861no—
478C23—861no—
479C23—861no—
480C23—861no—
481C23—861no—
482C23—861no—
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—868no—
513D4—868no—
514D4—868no—
515D4—1724no—
516D4—1724no—
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—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—432no—
534C2×C4—432no—
535C2×C4—868no—
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—434no—
565C22—434no—
566C22—862no—
567C22—862no—
568C22—862no—
569C22—862no—
570C22—862no—
571C22—862no—
572C22—862no—
573C22—862no—
574C22—862no—
575C22—862no—
576C22—862no—
577C22—862no—
578C22—862no—
579C22—862no—
580C22—862no—
581C22—17216no—
582C22—17216no—
583C22—1721no—
584C22—1721no—
585C22—1721no—
586C22—1721no—
587C22—1721no—
588C22—1721no—
589C22—1721no—
590C22—1721no—
591C22—1721no—
592C22—1721no—
593C22—1721no—
594C22C2×D4×D4311yescharacteristic
595C22C2×D4×D4311yescharacteristic
596C22C2×D4×D4311yescharacteristic
597C22C2×D4×D4311yescharacteristic
598C22#41×D4311yescharacteristic
599C22#1306337111yescharacteristic
600C22#1306337111yescharacteristic
601C4—22no—
602C4—22no—
603C4—41no—
604C4—41no—
605C4—41no—
606C4—862no—
607C4—862no—
608C4—1721no—
609C4—1721no—
610C2—42no—
611C2—42no—
612C2—864no—
613C2—864no—
614C2—3441no—
615C2—1722no—
616C2#120×D4311yescharacteristic
617C2#121×D4311yescharacteristic
618C2#1458346011yescharacteristic
619C2#1458353311yescharacteristic
620C2#1458353311yescharacteristic
621C2#1458354111yescharacteristic
622C2#1458354211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#394C2
hypercenter#394D43
hypocenterC43#2410
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. C22×D4×D43C2semidirect
2. C2×#13063300C2semidirect
3. C2×#13063298C2semidirect
4. C2×#13063295C2semidirect
5. C2×#13063295C2semidirect
6. C2×C22⋊C4×D43C2semidirect
7. #14582814C2semidirect
8. #14582808C2semidirect
9. #14582807C2semidirect
10. #14582777C2semidirect
11. #14582777C2semidirect
12. #14582775C2semidirect
13. #14582770C2semidirect
14. #14582754C2semidirect
15. C43×#394C2semidirect
20. C22×D172C22semidirect
21. C22×D172C22semidirect
24. C22×C22⋊D43C22semidirect
25. C22×C22⋊D43C22semidirect
30. C22×C4×D43C22semidirect
31. C22×C4×D43C22semidirect
36. C2×Dic43⋊C4C22semidirect
37. C2×C22⋊Dic43C22semidirect
38. C2×C22⋊Dic43C22semidirect
42. C2×(C2×D43)⋊C4C22semidirect
43. C2×(C2×D43)⋊C4C22semidirect
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. C2×C4⋊C4×C43C22semidirect
54. C2×C22⋊C4×C43C22semidirect
55. C2×C22⋊C4×C43C22semidirect
56. C2×C22⋊C4×C43C22semidirect
57. C2×C22⋊C4×C43C22semidirect
58. #95×C43C22semidirect
74. C23×D43D4semidirect
98. C2×C22⋊D43D4semidirect
115. C2×D172D4semidirect
140. (C2×D43)⋊C4D4semidirect
214. C2×C4×C43C2×D4semidirect
230. C2×Dic43C2×D4semidirect
287. C2×D43#120semidirect
288. C2×D43#121semidirect
319. #394D43semidirect
327. C43#2410semidirect
350. C2×C4⋊C4C2×D43semidirect
363. C2×C22⋊C4C2×D43semidirect
364. C2×C22⋊C4C2×D43semidirect
365. C2×C22⋊C4C2×D43semidirect
366. C2×C22⋊C4C2×D43semidirect
370. #95C2×D43semidirect
549. C2×C4D4×D43semidirect