Finite Group Databasebeta

← #25063008

Subgroups — #25063008

Order 11008.

1268 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#10621902C211yesmaximal, characteristic
2#19143227C211yesmaximal, characteristic, complemented
3#431×D43C211yesmaximal, characteristic, complemented
4#19133028C214yesmaximal, complemented
5#19133024C211yesmaximal, characteristic, complemented
6#19133021C211yesmaximal, characteristic, complemented
7#19133019C211yesmaximal, characteristic, complemented
8#19132976C214yesmaximal, complemented
9C43×#1487C211yesmaximal, characteristic, complemented
10C22×#10621902C411yescharacteristic
11C4×#10621902—21no—
12C4×#10621902—21no—
13C4×#10621902—21no—
14C4×#10621902—21no—
15C4×#10621902C412yes—
16C4×#10621902C412yes—
17C4×#10621902C2212yes—
18C4×#10621902C2212yes—
19C2×Q8×Dic43C411yescharacteristic
20C2×C4×D172—21no—
21C2×C4×D172C2211yescharacteristic
22C2×#13063287—21no—
23C2×#13063287C411yescharacteristic
24C2×#13063283—21no—
25C2×#13063283C411yescharacteristic
26C2×C42×D43—21no—
27C2×C42×D43C2211yescharacteristic
28#14582955—21no—
29#14582955C2212yescomplemented
30#14582952C2211yescharacteristic
31#14582951—21no—
32#14582951—21no—
33#14582951C2212yescomplemented
34#14582950C2212yescomplemented
35#14582949—21no—
36#14582923C2211yescharacteristic
37C4⋊C8×D43—21no—
38#14582862—21no—
39C22⋊C8×D43—21no—
40M16×Dic43—21no—
41C4×C8×D43C2212yescomplemented
42Q8⋊(C43⋊C8)C2214yescomplemented
43#14582628C2214yescomplemented
44#14582626C2214yescomplemented
45C2×C4×Q8×C43C2211yescharacteristic
46C43×#431C2211yescharacteristic
47C43×#423C2211yescharacteristic
48C43×Q8⋊C8C2214yescomplemented
49C2×#10621902—28no—
50C2×#10621902—21no—
51C2×#10621902—21no—
52C2×#10621902C2×C412yes—
53C2×#10621902C2×C412yes—
54C22×D172—21no—
55C22×D172C2×C411yescharacteristic
56C22×C4×D43—21no—
57C22×C4×D43—21no—
58C22×C4×D43—21no—
59C22×C4×D43C2×C411yescharacteristic
60C22×C4×D43D411yescharacteristic
61C22×C4×D43D411yescharacteristic
62C2×#10621877—21no—
63C2×C8×D43—22no—
64Q8×Dic43—21no—
65Q8×Dic43—21no—
66Q8×Dic43C2×C412yes—
67Q8×Dic43C2×C412yes—
68C4×D172—22no—
69C4×D172—22no—
70C4×D172—22no—
71C4×D172—22no—
72C4×D172—21no—
73C4×D172—21no—
74C4×D172C2×C412yes—
75C4×D172C2312yes—
76#13063287—22no—
77#13063287—22no—
78#13063287—22no—
79#13063287—22no—
80#13063287—21no—
81#13063287—21no—
82#13063287C2×C412yes—
83#13063287C2×C412yes—
84#13063283—21no—
85#13063283—21no—
86#13063283—22no—
87#13063283—22no—
88#13063283—22no—
89#13063283—22no—
90#13063283C2×C412yes—
91#13063283C2×C412yes—
92C2×C4⋊Dic43—21no—
93C2×C4⋊Dic43C2×C411yescharacteristic
94C2×(C2×D43)⋊C4—21no—
95C2×(C2×D43)⋊C4—21no—
96C2×(C2×D43)⋊C4—21no—
97C2×C4×Dic43—21no—
98C2×C4×Dic43—21no—
99C2×C4×Dic43C2×C411yescharacteristic
100C2×C4×Dic43D411yescharacteristic
101C2×C4×Dic43D411yescharacteristic
102C42×D43—22no—
103C42×D43—22no—
104C42×D43—22no—
105C42×D43—22no—
106C42×D43C2×C411yescharacteristic
107C42×D43C2×C411yescharacteristic
108C42×D43D411yescharacteristic
109C42×D43D411yescharacteristic
110C42×D43D411yescharacteristic
111C42×D43D411yescharacteristic
112C42×D43C2311yescharacteristic
113C42×D43C2311yescharacteristic
114C4⋊(C43⋊C8)—21no—
115C4⋊(C43⋊C8)—21no—
116C4⋊(C43⋊C8)C2312yes—
117Dic43⋊C8—22no—
118C22⋊(C43⋊C8)—21no—
119(C2×D43)⋊C8—22no—
120(C2×D43)⋊C8—22no—
121(C2×D43)⋊C8—22no—
122#13063235—22no—
123C4×C43⋊C8C2312yes—
124C8×Dic43—22no—
125C8×Dic43—22no—
126C22×Q8×C43C2×C411yescharacteristic
127C2×M16×C43—21no—
128C4×Q8×C43—21no—
129C4×Q8×C43—21no—
130C4×Q8×C43C2×C412yes—
131C4×Q8×C43C2312yes—
132C2×C4⋊C4×C43—21no—
133C2×C4⋊C4×C43C2×C411yescharacteristic
134C2×C42×C43—21no—
135C2×C42×C43C2311yescharacteristic
136C4⋊C8×C43—21no—
137C4⋊C8×C43—21no—
138C4⋊C8×C43C2312yes—
139C22⋊C8×C43—21no—
140C4×C8×C43C2312yes—
141C23×D43—21no—
142C23×D43C22⋊C411yescharacteristic
143C2×Q8×C43—24no—
144C2×Q8×C43—21no—
145C2×Q8×C43C22×C412yes—
146C22×C4×C43—21no—
147C22×C4×C43—21no—
148C22×C4×C43C22×C411yescharacteristic
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2×D411yescharacteristic
151C22×Dic43—21no—
152C22×Dic43C22⋊C411yescharacteristic
153C22×Dic43C22⋊C411yescharacteristic
154C22×Dic43C22⋊C411yescharacteristic
155#10621902—28no—
156#10621902—28no—
157#10621902—24no—
158#10621902—24no—
159#10621902—24no—
160#10621902M1618yescomplemented
161C2×D172—28no—
162C2×D172—21no—
163C2×D172—24no—
164C2×D172—22no—
165C2×D172—22no—
166C2×D172C22×C412yes—
167C2×C4×D43—28no—
168C2×C4×D43—22no—
169C2×C4×D43—22no—
170C2×C4×D43—22no—
171C2×C4×D43—22no—
172C2×C4×D43—24no—
173C2×C4×D43—22no—
174C2×C4×D43—22no—
175C2×C4×D43—22no—
176C2×C4×D43—22no—
177C2×C4×D43—42no—
178C2×C4×D43—44no—
179C2×C4×D43—42no—
180C2×C4×D43—42no—
181C2×C4×D43C22⋊C411yescharacteristic
182C2×C4×D43C22⋊C411yescharacteristic
183C2×C4×D43C22⋊C411yescharacteristic
184C2×C4×D43C22⋊C411yescharacteristic
185C2×C4×D43C22⋊C411yescharacteristic
186C2×C4×D43C22⋊C411yescharacteristic
187C2×C4×D43C22×C411yescharacteristic
188C2×C4×D43C22×C411yescharacteristic
189C2×C4×D43C2×D411yescharacteristic
190C2×C4×D43C2×D411yescharacteristic
191C2×C4×D43C2×D411yescharacteristic
192C2×C4×D43C2×D411yescharacteristic
193M16×C43—42no—
194C2×C8×C43—22no—
195C2×C8×C43—22no—
196C4⋊C4×C43—22no—
197C4⋊C4×C43—21no—
198C4⋊C4×C43—22no—
199C4⋊C4×C43C22×C412yes—
200C42×C43—22no—
201C42×C43—22no—
202C42×C43C22×C411yescharacteristic
203C42×C43C2×D411yescharacteristic
204C42×C43C2×D411yescharacteristic
205C42×C43C2411yescharacteristic
206(C2×D43)⋊C4—22no—
207(C2×D43)⋊C4—22no—
208(C2×D43)⋊C4—22no—
209(C2×D43)⋊C4—22no—
210(C2×D43)⋊C4—22no—
211(C2×D43)⋊C4—22no—
212C4⋊Dic43—21no—
213C4⋊Dic43—22no—
214C4⋊Dic43—22no—
215C4⋊Dic43C22×C412yes—
216C4×Dic43—22no—
217C4×Dic43—22no—
218C4×Dic43—22no—
219C4×Dic43—22no—
220C4×Dic43C22⋊C411yescharacteristic
221C4×Dic43C22⋊C411yescharacteristic
222C4×Dic43C22⋊C411yescharacteristic
223C4×Dic43C22⋊C411yescharacteristic
224C4×Dic43C22⋊C411yescharacteristic
225C4×Dic43C22⋊C411yescharacteristic
226C4×Dic43C22×C411yescharacteristic
227C4×Dic43C22×C411yescharacteristic
228C4×Dic43C2×D411yescharacteristic
229C4×Dic43C2×D411yescharacteristic
230C4×Dic43C2×D411yescharacteristic
231C4×Dic43C2×D411yescharacteristic
232#10621877—42no—
233C2×C43⋊C8—22no—
234C2×C43⋊C8—22no—
235C8×D43—44no—
236C23×C43C2×C22⋊C411yescharacteristic
237C22×D43—24no—
238C22×D43—22no—
239C22×D43—22no—
240C22×D43—22no—
241C22×D43—41no—
242C22×D43—42no—
243C22×D43—42no—
244C22×D43C2×C22⋊C411yescharacteristic
245C22×D43C2×C22⋊C411yescharacteristic
246Q8×C43—24no—
247Q8×C43—22no—
248Q8×C43C2×M1614yes—
249C2×C4×C43—24no—
250C2×C4×C43—22no—
251C2×C4×C43—22no—
252C2×C4×C43—22no—
253C2×C4×C43—41no—
254C2×C4×C43—42no—
255C2×C4×C43C2×C22⋊C411yescharacteristic
256C2×C4×C43C2×C22⋊C411yescharacteristic
257C2×C4×C43C2×C22⋊C411yescharacteristic
258C2×C4×C43#13512yes—
259C2×C4×C43#13512yes—
260C2×C4×C43C23×C411yescharacteristic
261C2×C4×C43C22×D411yescharacteristic
262C2×C4×C43C22×D411yescharacteristic
263C2×Dic43—22no—
264C2×Dic43—22no—
265C2×Dic43—22no—
266C2×Dic43—22no—
267C2×Dic43—42no—
268C2×Dic43C2×C22⋊C411yescharacteristic
269C2×Dic43C2×C22⋊C411yescharacteristic
270C2×Dic43C2×C22⋊C411yescharacteristic
271C2×Dic43C2×C22⋊C411yescharacteristic
272C2×Dic43C2×C22⋊C411yescharacteristic
273C2×Dic43C2×C22⋊C411yescharacteristic
274D172—28no—
275D172—24no—
276D172—28no—
277D172—22no—
278D172C2×M1614yes—
279C4×D43—28no—
280C4×D43—22no—
281C4×D43—22no—
282C4×D43—21no—
283C4×D43—21no—
284C4×D43—21no—
285C4×D43—21no—
286C4×D43—22no—
287C4×D43—22no—
288C4×D43—28no—
289C4×D43—22no—
290C4×D43—22no—
291C4×D43—22no—
292C4×D43—41no—
293C4×D43—41no—
294C4×D43—44no—
295C4×D43—42no—
296C4×D43—42no—
297C4×D43—44no—
298C4×D43—44no—
299C4×D43C2×M1614yes—
300C8×C43—42no—
301C8×C43—42no—
302C43⋊C8—42no—
303C43⋊C8—42no—
304#17443—431nomaximal, Sylow
305C22×C43—21no—
306C22×C43—21no—
307C22×C43#41612yes—
308C22×C43C22×C22⋊C411yescharacteristic
309C2×D43—21no—
310C2×D43—21no—
311C2×D43—24no—
312C2×D43—21no—
313C2×D43—21no—
314C2×D43—21no—
315C2×D43—44no—
316C2×D43—48no—
317C2×D43—42no—
318C2×D43—42no—
319C2×D43#40712yes—
320C4×C43—24no—
321C4×C43—21no—
322C4×C43—21no—
323C4×C43—21no—
324C4×C43—42no—
325C4×C43#41612yes—
326C4×C43C22×M1612yes—
327C4×C43C2×#13511yescharacteristic
328C4×C43C2×#13511yescharacteristic
329Dic43—21no—
330Dic43—21no—
331Dic43—21no—
332Dic43—21no—
333Dic43—42no—
334Dic43#40712yes—
335Dic43#42112yes—
336C2×C4×#41—431no—
337#2920—431no—
338C2×#431—431no—
339#1488—434no—
340#1487—431no—
341#1487D4311yescharacteristic, complemented
342#1486—431no—
343#1486—431no—
344#1476—434no—
345C2×C43—22no—
346C2×C43C2×#40711yescharacteristic
347C2×C43C2×#41611yescharacteristic
348C2×C43C2×#42111yescharacteristic
349D43—22no—
350D43—41no—
351D43—44no—
352C22×#41—431no—
353C4×#41—432no—
354C4×#41—432no—
355C4×#41—432no—
356C4×#41—432no—
357C4×#41—861no—
358C4×#41—861no—
359C4×#41—861no—
360C4×#41—861no—
361C2×C4×Q8—431no—
362C2×C4×Q8C2×D4311yescharacteristic
363C2×C4×D4—431no—
364C2×C4×D4—431no—
365C2×C4×D4—861no—
366C2×C4×D4—861no—
367C2×#117—431no—
368C2×#117—861no—
369C22×C42—431no—
370C22×C42—861no—
371#432—432no—
372#432—861no—
373#431—431no—
374#431—432no—
375#431—432no—
376#431—861no—
377#431—861no—
378#431—861no—
379#431C2×D4311yescharacteristic
380#423—431no—
381#423C2×D4311yescharacteristic
382C2×C4⋊C8—861no—
383#407—861no—
384C2×C22⋊C8—861no—
385C4×M16—861no—
386C2×C4×C8—432no—
387Q8⋊C8—434no—
388Q8⋊C8C2×D4314yescomplemented
389D4⋊C8—434no—
390D4⋊C8—434no—
391C43#1744311yescharacteristic, complemented, Sylow
392C2×#41—432no—
393C2×#41—432no—
394C2×#41—861no—
395C2×#41—861no—
396C2×#41—868no—
397C22×Q8C4×D4311yescharacteristic
398C22×D4—431no—
399C22×D4—861no—
400C23×C4—431no—
401C23×C4—431no—
402C23×C4—431no—
403C23×C4—861no—
404C23×C4—861no—
405C23×C4—861no—
406C2×M16—21no—
407C2×M16—861no—
408C22×C8—862no—
409C4×Q8—21no—
410C4×Q8—21no—
411C4×Q8—432no—
412C4×Q8—432no—
413C4×Q8—861no—
414C4×Q8—861no—
415C4×Q8C4×D4312yes—
416C4×Q8C22×D4312yes—
417C4×D4—432no—
418C4×D4—432no—
419C4×D4—432no—
420C4×D4—432no—
421C4×D4—862no—
422C4×D4—862no—
423C4×D4—862no—
424C4×D4—862no—
425C4×D4—861no—
426C4×D4—861no—
427C4×D4—862no—
428C4×D4—862no—
429C4×D4—862no—
430C4×D4—862no—
431C4×D4—861no—
432C4×D4—861no—
433#117—432no—
434#117—432no—
435#117—862no—
436#117—862no—
437#117—862no—
438#117—862no—
439#117—861no—
440#117—861no—
441C2×C4⋊C4—21no—
442C2×C4⋊C4—431no—
443C2×C4⋊C4—861no—
444C2×C4⋊C4C4×D4311yescharacteristic
445C2×C22⋊C4—861no—
446C2×C22⋊C4—861no—
447C2×C22⋊C4—861no—
448C2×C42—21no—
449C2×C42—431no—
450C2×C42—431no—
451C2×C42—431no—
452C2×C42—431no—
453C2×C42—431no—
454C2×C42—431no—
455C2×C42—431no—
456C2×C42—431no—
457C2×C42—431no—
458C2×C42—431no—
459C2×C42—431no—
460C2×C42—862no—
461C2×C42—862no—
462C2×C42—862no—
463C2×C42—862no—
464C2×C42—861no—
465C2×C42—861no—
466C2×C42C22×D4311yescharacteristic
467C4⋊C8—21no—
468C4⋊C8—21no—
469C4⋊C8—432no—
470C4⋊C8—862no—
471C4⋊C8—861no—
472C4⋊C8—861no—
473C4⋊C8C22×D4312yes—
474C22⋊C8—21no—
475C22⋊C8—862no—
476C22⋊C8—862no—
477C22⋊C8—862no—
478C22⋊C8—861no—
479#97—862no—
480C4×C8—432no—
481C4×C8—862no—
482C4×C8—862no—
483C4×C8C22×D4312yes—
484C24—431no—
485C24—861no—
486#41—438no—
487#41—864no—
488#41—864no—
489#41—868no—
490#41—868no—
491#41—864no—
492C2×Q8—24no—
493C2×Q8—21no—
494C2×Q8C2×C4×D4312yes—
495C2×D4—432no—
496C2×D4—864no—
497C2×D4—862no—
498C2×D4—862no—
499C2×D4—868no—
500C2×D4—861no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—431no—
504C22×C4—431no—
505C22×C4—431no—
506C22×C4—431no—
507C22×C4—431no—
508C22×C4—431no—
509C22×C4—431no—
510C22×C4—431no—
511C22×C4—431no—
512C22×C4—431no—
513C22×C4—431no—
514C22×C4—431no—
515C22×C4—431no—
516C22×C4—431no—
517C22×C4—431no—
518C22×C4—862no—
519C22×C4—862no—
520C22×C4—864no—
521C22×C4—862no—
522C22×C4—862no—
523C22×C4—868no—
524C22×C4—862no—
525C22×C4—862no—
526C22×C4—861no—
527C22×C4—862no—
528C22×C4—862no—
529C22×C4—1722no—
530C22×C4—1724no—
531C22×C4—1722no—
532C22×C4—1722no—
533C22×C4C2×C4×D4311yescharacteristic
534C22×C4D4×D4311yescharacteristic
535C22×C4D4×D4311yescharacteristic
536M16—42no—
537M16—1722no—
538C2×C8—22no—
539C2×C8—22no—
540C2×C8—862no—
541C2×C8—862no—
542C2×C8—1724no—
543C4⋊C4—22no—
544C4⋊C4—21no—
545C4⋊C4—22no—
546C4⋊C4—432no—
547C4⋊C4—862no—
548C4⋊C4—862no—
549C4⋊C4—861no—
550C4⋊C4C2×C4×D4312yes—
551C22⋊C4—862no—
552C22⋊C4—862no—
553C22⋊C4—862no—
554C22⋊C4—862no—
555C22⋊C4—862no—
556C22⋊C4—862no—
557C42—22no—
558C42—22no—
559C42—431no—
560C42—431no—
561C42—431no—
562C42—431no—
563C42—431no—
564C42—431no—
565C42—431no—
566C42—431no—
567C42—431no—
568C42—431no—
569C42—431no—
570C42—431no—
571C42—862no—
572C42—862no—
573C42—862no—
574C42—862no—
575C42C2×C4×D4311yescharacteristic
576C42D4×D4311yescharacteristic
577C42D4×D4311yescharacteristic
578C42C23×D4311yescharacteristic
579C23—431no—
580C23—431no—
581C23—862no—
582C23—864no—
583C23—862no—
584C23—862no—
585C23—1721no—
586C23—1722no—
587C23—1722no—
588C23C22⋊C4×D4311yescharacteristic
589Q8—24no—
590Q8—22no—
591Q8M16×D4314yes—
592D4—434no—
593D4—868no—
594D4—868no—
595D4—864no—
596D4—862no—
597C2×C4—24no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—41no—
602C2×C4—42no—
603C2×C4—431no—
604C2×C4—431no—
605C2×C4—434no—
606C2×C4—431no—
607C2×C4—431no—
608C2×C4—431no—
609C2×C4—431no—
610C2×C4—862no—
611C2×C4—862no—
612C2×C4—862no—
613C2×C4—868no—
614C2×C4—862no—
615C2×C4—868no—
616C2×C4—862no—
617C2×C4—862no—
618C2×C4—862no—
619C2×C4—862no—
620C2×C4—862no—
621C2×C4—862no—
622C2×C4—861no—
623C2×C4—861no—
624C2×C4—861no—
625C2×C4—861no—
626C2×C4—862no—
627C2×C4—1721no—
628C2×C4—1721no—
629C2×C4—1724no—
630C2×C4—1724no—
631C2×C4—1722no—
632C2×C4—1724no—
633C2×C4—1722no—
634C2×C4—1722no—
635C2×C4C22⋊C4×D4311yescharacteristic
636C2×C4C22⋊C4×D4311yescharacteristic
637C2×C4C22⋊C4×D4311yescharacteristic
638C2×C4#1306334612yes—
639C2×C4#1306334812yes—
640C2×C4C22×C4×D4311yescharacteristic
641C2×C4C2×D4×D4311yescharacteristic
642C2×C4C2×D4×D4311yescharacteristic
643C8—42no—
644C8—42no—
645C8—1722no—
646C8—1722no—
647C22—21no—
648C22—21no—
649C22—432no—
650C22—861no—
651C22—861no—
652C22—864no—
653C22—861no—
654C22—861no—
655C22—861no—
656C22—1724no—
657C22—1728no—
658C22—1722no—
659C22—1722no—
660C22#1458289412yes—
661C22C2×C22⋊C4×D4311yescharacteristic
662C4—24no—
663C4—21no—
664C4—21no—
665C4—21no—
666C4—42no—
667C4—432no—
668C4—432no—
669C4—861no—
670C4—861no—
671C4—861no—
672C4—861no—
673C4—1722no—
674C4#1458289412yes—
675C4C2×M16×D4312yes—
676C4C2×#1306334611yescharacteristic
677C4C2×#1306334811yescharacteristic
678C2—22no—
679C2—862no—
680C2—1721no—
681C2—1724no—
682C2#407×D4311yescharacteristic
683C2C2×#1458289411yescharacteristic
684C2#421×D4311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1487C2
socleC22×C43C22×C22⋊C4
prime radicalC22×#10621902C4
cosocleC42×C43C24
hypercenter#1487D43
hypocenterC43#17443
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1487

Complements

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

NH ≅ G/Ntype
2. #19143227C2semidirect
3. #431×D43C2semidirect
4. #19133028C2semidirect
5. #19133024C2semidirect
6. #19133021C2semidirect
7. #19133019C2semidirect
8. #19132976C2semidirect
9. C43×#1487C2semidirect
29. #14582955C22semidirect
33. #14582951C22semidirect
34. #14582950C22semidirect
41. C4×C8×D43C22semidirect
42. Q8⋊(C43⋊C8)C22semidirect
43. #14582628C22semidirect
44. #14582626C22semidirect
48. C43×Q8⋊C8C22semidirect
160. #10621902M16semidirect
341. #1487D43semidirect
388. Q8⋊C8C2×D43semidirect
391. C43#17443semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#106219022
#191432272
#431×D432
#191330282
#191330242
#191330212
#191330192
#191329762
C43×#14872
#1744343