Finite Group Databasebeta

← #25245400

Subgroups — #25245400

Order 11008.

1576 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×Q8×D43C211yesmaximal, characteristic, complemented
2C2×#14583100C211yesmaximal, characteristic, complemented
3C2×#14583099C211yesmaximal, characteristic, complemented
4C2×#14583039C212yesmaximal, complemented
5#19142941C211yesmaximal, characteristic
6#19134951C212yesmaximal, complemented
7#19134948C212yesmaximal, complemented
8#19134911C212yesmaximal, complemented
9#19134597C211yesmaximal, characteristic, complemented
10#19134572C211yesmaximal, characteristic, complemented
11C43×#1803C211yesmaximal, characteristic, complemented
12C22×Q8×D43C2211yescharacteristic
13C22×#10621873C2212yes—
14C22×#10621884C2212yes—
15C2×#13063322C2211yescharacteristic
16C2×#13063300—21no—
17C2×#13063300—21no—
18C2×#13063300C2212yes—
19C2×Q8×Dic43C2211yescharacteristic
20C2×C4×Dic86—21no—
21C2×C4×Dic86C2211yescharacteristic
22C2×#13063290—21no—
23C2×#13063290C2211yescharacteristic
24C4×Q8×D43—24no—
25C4×Q8×D43—24no—
26C2×C4⋊C4×D43—21no—
27C2×C4⋊C4×D43C2211yescharacteristic
28C2×C42×D43—21no—
29C2×C42×D43C2211yescharacteristic
30#14583100—24no—
31#14583099—24no—
32#14583039—28no—
33C2×C4⋊(C43⋊C8)C2211yescharacteristic
34C2×#13063248C2212yes—
35C2×#13063247C2212yes—
36C2×#13063245C2212yes—
37C2×(C2×D43)⋊C8C2212yes—
38#14582800—21no—
39#14582800—21no—
40#14582800C2212yes—
41#14582661C2212yes—
42#14582653C2212yes—
43C2×C4×Q8×C43C2211yescharacteristic
44C2×C4⋊C8×C43C2211yescharacteristic
45C2×#103×C43C2212yes—
46C43×#384C2211yescharacteristic
47C43×#340C2212yes—
48C22×Dic86—21no—
49C22×Dic86C2311yescharacteristic
50C2×Q8×D43—22no—
51C2×Q8×D43—22no—
52C2×Q8×D43—22no—
53C2×Q8×D43—22no—
54C2×Q8×D43—22no—
55C2×Q8×D43D414yescomplemented
56C22×D172—22no—
57C22×D172—21no—
58C22×D172—21no—
59C22×D172C2312yes—
60C22×C4×D43—21no—
61C22×C4×D43—21no—
62C22×C4×D43D411yescharacteristic
63C22×C4×D43D411yescharacteristic
64C22×C4×D43C2311yescharacteristic
65C2×#10621873—24no—
66C2×#10621873—24no—
67C2×#10621873—24no—
68C2×#10621884—24no—
69C2×#10621884—24no—
70C2×#10621884—24no—
71C22×C43⋊C8C2312yes—
72#13063322—22no—
73#13063322—22no—
74#13063300—24no—
75#13063300—24no—
76#13063300—44no—
77#13063300—44no—
78Q8×Dic43—22no—
79Q8×Dic43—22no—
80C4×Dic86—28no—
81C4×Dic86—22no—
82C4×Dic86D414yescomplemented
83#13063290—28no—
84#13063290—22no—
85#13063290—22no—
86C2×C4⋊Dic43—21no—
87C2×C4⋊Dic43C2311yescharacteristic
88C2×Dic43⋊C4—21no—
89C2×Dic43⋊C4—21no—
90C2×Dic43⋊C4—21no—
91C4⋊C4×D43—28no—
92C4⋊C4×D43—22no—
93C4⋊C4×D43—22no—
94C2×(C2×D43)⋊C4—22no—
95C2×(C2×D43)⋊C4—22no—
96C2×(C2×D43)⋊C4—22no—
97C2×C4×Dic43—21no—
98C2×C4×Dic43—21no—
99C2×C4×Dic43—21no—
100C2×C4×Dic43D411yescharacteristic
101C2×C4×Dic43D411yescharacteristic
102C2×C4×Dic43C2311yescharacteristic
103C42×D43—28no—
104C42×D43—22no—
105C42×D43—22no—
106C4⋊(C43⋊C8)—22no—
107#13063248—24no—
108#13063247—24no—
109#13063245—24no—
110(C2×D43)⋊C8—24no—
111C22×Q8×C43C2311yescharacteristic
112C22×C8×C43C2312yes—
113C4×Q8×C43—22no—
114C4×Q8×C43D414yescomplemented
115C2×C4⋊C4×C43—21no—
116C2×C4⋊C4×C43—21no—
117C2×C4⋊C4×C43—21no—
118C2×C4⋊C4×C43C2312yes—
119C2×C4⋊C4×C43C2311yescharacteristic
120C2×C42×C43—21no—
121C2×C42×C43C2311yescharacteristic
122C4⋊C8×C43—22no—
123#103×C43—24no—
124C23×D43—22no—
125C23×D43C2×D411yescharacteristic
126C2×Q8×C43—21no—
127C2×Q8×C43—21no—
128C2×Q8×C43—21no—
129C2×Q8×C43C2×D412yes—
130C2×Q8×C43C2×D412yes—
131C2×Q8×C43#4112yes—
132C22×C4×C43—21no—
133C22×C4×C43—21no—
134C22×C4×C43—22no—
135C22×C4×C43C2×D411yescharacteristic
136C22×C4×C43C2×D411yescharacteristic
137C22×C4×C43C2411yescharacteristic
138C22×Dic43—21no—
139C22×Dic43—21no—
140C22×Dic43C2×D411yescharacteristic
141C22×Dic43C2×D411yescharacteristic
142C22×Dic43C2×D411yescharacteristic
143Q8×D43—28no—
144Q8×D43—28no—
145Q8×D43—28no—
146Q8×D43—28no—
147C2×D172—22no—
148C2×D172—22no—
149C2×D172—22no—
150C2×D172—22no—
151C2×D172—22no—
152C2×D172—22no—
153C2×D172—42no—
154C2×D172—42no—
155C2×D172—42no—
156C2×D172—42no—
157C2×D172—42no—
158C2×D172—42no—
159C2×D172—44no—
160C2×D172—44no—
161C2×D172—44no—
162C2×C4×D43—24no—
163C2×C4×D43—24no—
164C2×C4×D43—22no—
165C2×C4×D43—22no—
166C2×C4×D43—21no—
167C2×C4×D43—21no—
168C2×C4×D43—21no—
169C2×C4×D43—21no—
170C2×C4×D43—24no—
171C2×C4×D43—22no—
172C2×C4×D43—24no—
173C2×C4×D43—22no—
174C2×C4×D43—41no—
175C2×C4×D43—42no—
176C2×C4×D43—42no—
177C2×C4×D43SD1614yescomplemented
178C2×C4×D43C2×D412yes—
179C2×C4×D43#4112yes—
180C2×Dic86—24no—
181C2×Dic86—24no—
182C2×Dic86—21no—
183C2×Dic86—21no—
184C2×Dic86—21no—
185C2×Dic86—24no—
186C2×Dic86C2×D412yes—
187C2×Dic86C2×D412yes—
188C2×Dic86#4112yes—
189C2×C8×C43—22no—
190C2×C8×C43—22no—
191C2×C8×C43—22no—
192C4⋊C4×C43—24no—
193C4⋊C4×C43—21no—
194C4⋊C4×C43—22no—
195C4⋊C4×C43—22no—
196C4⋊C4×C43—42no—
197C4⋊C4×C43—42no—
198C4⋊C4×C43C2×D412yes—
199C42×C43—24no—
200C42×C43C2×D412yes—
201C42×C43C2×D412yes—
202#10621884—48no—
203(C2×D43)⋊C4—44no—
204(C2×D43)⋊C4—44no—
205(C2×D43)⋊C4—44no—
206C4⋊Dic43—24no—
207C4⋊Dic43—21no—
208C4⋊Dic43C2×D412yes—
209Dic43⋊C4—24no—
210Dic43⋊C4—24no—
211Dic43⋊C4—24no—
212C4×Dic43—24no—
213C4×Dic43—24no—
214C4×Dic43—24no—
215C4×Dic43—22no—
216C4×Dic43—22no—
217C4×Dic43—21no—
218C4×Dic43—21no—
219C2×C43⋊C8—22no—
220C2×C43⋊C8—22no—
221C2×C43⋊C8—22no—
222#10621873—48no—
223C23×C43C22×D411yescharacteristic
224C22×D43—21no—
225C22×D43—21no—
226C22×D43—21no—
227C22×D43—21no—
228C22×D43—42no—
229C22×D43—42no—
230C22×D43—42no—
231C22×D43—42no—
232C22×D43—42no—
233C22×D43—42no—
234C22×D43—42no—
235C22×D43#12112yes—
236C22×D43C2×SD1612yes—
237C22×D43AGL(1,ℤ/8)12yes—
238Q8×C43—22no—
239Q8×C43—22no—
240Q8×C43—22no—
241Q8×C43#12114yescomplemented
242C2×C4×C43—22no—
243C2×C4×C43—22no—
244C2×C4×C43—22no—
245C2×C4×C43—21no—
246C2×C4×C43—21no—
247C2×C4×C43—22no—
248C2×C4×C43—41no—
249C2×C4×C43—41no—
250C2×C4×C43—42no—
251C2×C4×C43—42no—
252C2×C4×C43—42no—
253C2×C4×C43#12012yes—
254C2×C4×C43#12012yes—
255C2×C4×C43C2×SD1612yes—
256C2×C4×C43#13712yes—
257C2×C4×C43C22×D411yescharacteristic
258C2×C4×C43C22×D411yescharacteristic
259C2×C4×C43C22×D411yescharacteristic
260C2×C4×C43C2×#4111yescharacteristic
261C2×C4×C43C2×#4111yescharacteristic
262C2×C4×C43C2×#4111yescharacteristic
263C2×Dic43—21no—
264C2×Dic43—21no—
265C2×Dic43—22no—
266C2×Dic43—22no—
267C2×Dic43—21no—
268C2×Dic43—22no—
269C2×Dic43—21no—
270C2×Dic43—21no—
271C2×Dic43—22no—
272C2×Dic43—21no—
273C2×Dic43—21no—
274C2×Dic43—41no—
275C2×Dic43—41no—
276C2×Dic43#12112yes—
277C2×Dic43C2×SD1612yes—
278D172—42no—
279D172—42no—
280D172—42no—
281D172—42no—
282D172—84no—
283D172—88no—
284D172—84no—
285C4×D43—216no—
286C4×D43—22no—
287C4×D43—22no—
288C4×D43—22no—
289C4×D43—22no—
290C4×D43—28no—
291C4×D43—44no—
292C4×D43—48no—
293Dic86—216no—
294Dic86—22no—
295Dic86—22no—
296Dic86—22no—
297Dic86#12114yescomplemented
298C8×C43—42no—
299C43⋊C8—42no—
300#32903—431nomaximal, Sylow
301C22×C43C2×#12011yescharacteristic
302C22×C43C2×#12111yescharacteristic
303C22×C43#52511yescharacteristic
304C22×C43C22×SD1611yescharacteristic
305C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
306C22×C43C2×#13711yescharacteristic
307C22×C43#57511yescharacteristic
308C2×D43—22no—
309C2×D43—22no—
310C2×D43—22no—
311C2×D43—22no—
312C2×D43—22no—
313C2×D43—22no—
314C2×D43—82no—
315C2×D43—82no—
316C2×D43—82no—
317C2×D43—82no—
318C2×D43—82no—
319C2×D43—82no—
320C2×D43—82no—
321C2×D43#46014yescomplemented
322C4×C43—24no—
323C4×C43—22no—
324C4×C43—42no—
325C4×C43—82no—
326C4×C43#44814yescomplemented
327C4×C43C2×#12111yescharacteristic
328C4×C43C2×#12111yescharacteristic
329C4×C43#52511yescharacteristic
330C4×C43#52511yescharacteristic
331Dic43—22no—
332Dic43—24no—
333Dic43—22no—
334Dic43—41no—
335Dic43—42no—
336C22×C4×Q8—431no—
337C2×#460—431no—
338C2×#460—431no—
339C2×#448—432no—
340#2856—431no—
341#1880—432no—
342#1880—432no—
343#1874—432no—
344#1803—431no—
345#1803D4311yescharacteristic, complemented
346#1797—431no—
347C2×C43#284711yescharacteristic
348C2×C43C2×#44811yescharacteristic
349C2×C43#300611yescharacteristic
350C2×C43C2×#46011yescharacteristic
351C2×C43#303711yescharacteristic
352C2×C43#310311yescharacteristic
353C2×C43#311211yescharacteristic
354D43—24no—
355D43—162no—
356C23×Q8—431no—
357C22×SD16—432no—
358C22×SD16—432no—
359C2×#127—431no—
360C2×#121—432no—
361C2×#121—861no—
362C2×#121—861no—
363C2×C4×Q8—431no—
364C2×C4×Q8—431no—
365C2×C4×Q8—431no—
366C2×C4×Q8—861no—
367C2×C4×Q8—861no—
368C2×C4×Q8—864no—
369C2×C4×Q8—864no—
370C2×C4×Q8C2×D4311yescharacteristic
371C22×C4⋊C4—431no—
372C22×C4⋊C4—861no—
373C22×C42—431no—
374C22×C42—861no—
375#460—864no—
376#460—864no—
377#448—868no—
378C2×C4⋊C8—431no—
379C2×C4⋊C8C2×D4311yescharacteristic
380C2×#103—432no—
381C2×#103C2×D4312yes—
382C2×#102—432no—
383C2×#102—432no—
384C2×C22⋊C8—432no—
385#390—432no—
386#390—861no—
387#390—861no—
388#384C2×D4311yescharacteristic
389#340—432no—
390#340C2×D4312yes—
391#336—432no—
392C43#3290311yescharacteristic, complemented, Sylow
393C22×Q8—434no—
394C22×Q8—431no—
395C22×Q8—861no—
396C22×Q8—862no—
397C22×Q8—862no—
398C22×Q8—862no—
399C22×Q8—862no—
400C22×Q8—862no—
401C22×Q8C22×D4311yescharacteristic
402C22×D4—432no—
403C22×D4—862no—
404C22×D4—861no—
405C22×D4—861no—
406C23×C4—431no—
407C23×C4—431no—
408C23×C4—431no—
409C23×C4—861no—
410C23×C4—861no—
411C2×SD16—864no—
412C2×SD16—864no—
413C2×SD16—864no—
414C2×SD16—864no—
415C2×SD16—864no—
416C2×SD16—864no—
417C22×C8—432no—
418C22×C8C22×D4312yes—
419#127—862no—
420#127—862no—
421#121—864no—
422#121—864no—
423#121—1724no—
424#121—1724no—
425C4×Q8—22no—
426C4×Q8—434no—
427C4×Q8—868no—
428C4×Q8—862no—
429C4×Q8—868no—
430C4×Q8—862no—
431C4×Q8—862no—
432C4×Q8—862no—
433C4×Q8—862no—
434C4×Q8D17214yescomplemented
435C2×C4⋊C4—21no—
436C2×C4⋊C4—21no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4—431no—
439C2×C4⋊C4—862no—
440C2×C4⋊C4—868no—
441C2×C4⋊C4—861no—
442C2×C4⋊C4—861no—
443C2×C4⋊C4—861no—
444C2×C4⋊C4—861no—
445C2×C4⋊C4—862no—
446C2×C4⋊C4C22×D4312yes—
447C2×C4⋊C4C22×D4311yescharacteristic
448C2×C22⋊C4—862no—
449C2×C22⋊C4—862no—
450C2×C22⋊C4—862no—
451C2×C42—21no—
452C2×C42—431no—
453C2×C42—431no—
454C2×C42—431no—
455C2×C42—868no—
456C2×C42—861no—
457C2×C42—861no—
458C2×C42—861no—
459C2×C42—862no—
460C2×C42—862no—
461C2×C42C22×D4311yescharacteristic
462C4⋊C8—22no—
463C4⋊C8—862no—
464#103—24no—
465#103—864no—
466#102—864no—
467#102—864no—
468C22⋊C8—864no—
469C24—431no—
470C24—862no—
471C2×Q8—21no—
472C2×Q8—21no—
473C2×Q8—21no—
474C2×Q8—432no—
475C2×Q8—432no—
476C2×Q8—432no—
477C2×Q8—864no—
478C2×Q8—864no—
479C2×Q8—864no—
480C2×Q8—868no—
481C2×Q8—868no—
482C2×Q8—868no—
483C2×Q8—868no—
484C2×Q8—861no—
485C2×Q8—861no—
486C2×Q8—861no—
487C2×Q8C2×D17212yes—
488C2×Q8D4×D4312yes—
489C2×Q8#1062190212yes—
490C2×D4—862no—
491C2×D4—862no—
492C2×D4—862no—
493C2×D4—862no—
494C2×D4—862no—
495C2×D4—862no—
496C2×D4—1722no—
497C2×D4—1722no—
498C2×D4—1724no—
499C2×D4—1724no—
500C2×D4—1724no—
501C2×D4—1722no—
502C2×D4—1722no—
503C2×D4—1722no—
504C2×D4—1722no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—22no—
508C22×C4—431no—
509C22×C4—431no—
510C22×C4—434no—
511C22×C4—432no—
512C22×C4—432no—
513C22×C4—431no—
514C22×C4—864no—
515C22×C4—864no—
516C22×C4—864no—
517C22×C4—862no—
518C22×C4—864no—
519C22×C4—861no—
520C22×C4—862no—
521C22×C4—862no—
522C22×C4—861no—
523C22×C4—861no—
524C22×C4—861no—
525C22×C4—861no—
526C22×C4—861no—
527C22×C4—862no—
528C22×C4—1721no—
529C22×C4—1722no—
530C22×C4—1722no—
531C22×C4D4×D4311yescharacteristic
532C22×C4D4×D4311yescharacteristic
533C22×C4C23×D4311yescharacteristic
534SD16—1728no—
535SD16—1728no—
536C2×C8—22no—
537C2×C8—22no—
538C2×C8—22no—
539C2×C8—862no—
540C2×C8—862no—
541C2×C8—862no—
542C4⋊C4—24no—
543C4⋊C4—21no—
544C4⋊C4—22no—
545C4⋊C4—22no—
546C4⋊C4—42no—
547C4⋊C4—42no—
548C4⋊C4—432no—
549C4⋊C4—864no—
550C4⋊C4—864no—
551C4⋊C4—864no—
552C4⋊C4—864no—
553C4⋊C4—861no—
554C4⋊C4C2×D17212yes—
555C22⋊C4—1724no—
556C22⋊C4—1724no—
557C22⋊C4—1724no—
558C42—24no—
559C42—864no—
560C42—864no—
561C42—862no—
562C42—862no—
563C42—864no—
564C42—861no—
565C42—861no—
566C42C2×D17212yes—
567C42D4×D4312yes—
568C23—432no—
569C23—432no—
570C23—432no—
571C23—861no—
572C23—861no—
573C23—861no—
574C23—861no—
575C23—1722no—
576C23—1722no—
577C23—1722no—
578C23—1722no—
579C23—1722no—
580C23—1722no—
581C23—1722no—
582C23C2×D4×D4311yescharacteristic
583Q8—22no—
584Q8—22no—
585Q8—22no—
586Q8—434no—
587Q8—8616no—
588Q8—862no—
589Q8—862no—
590Q8—862no—
591Q8#1306330014yescomplemented
592D4—3444no—
593D4—3448no—
594D4—3444no—
595D4—1722no—
596D4—1722no—
597D4—1722no—
598D4—1722no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—22no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—42no—
608C2×C4—42no—
609C2×C4—42no—
610C2×C4—432no—
611C2×C4—432no—
612C2×C4—8616no—
613C2×C4—861no—
614C2×C4—861no—
615C2×C4—862no—
616C2×C4—862no—
617C2×C4—861no—
618C2×C4—862no—
619C2×C4—861no—
620C2×C4—862no—
621C2×C4—862no—
622C2×C4—862no—
623C2×C4—862no—
624C2×C4—868no—
625C2×C4—862no—
626C2×C4—861no—
627C2×C4—861no—
628C2×C4—861no—
629C2×C4—1724no—
630C2×C4—1728no—
631C2×C4—1721no—
632C2×C4—1721no—
633C2×C4#1306329512yes—
634C2×C4#1306329512yes—
635C2×C4SD16×D4312yes—
636C2×C4#1306335712yes—
637C2×C4C2×D4×D4311yescharacteristic
638C2×C4C2×D4×D4311yescharacteristic
639C2×C4C22×D17211yescharacteristic
640C2×C4#41×D4311yescharacteristic
641C2×C4#41×D4311yescharacteristic
642C2×C4C2×#1062190211yescharacteristic
643C8—42no—
644C8—1722no—
645C22—434no—
646C22—862no—
647C22—862no—
648C22—862no—
649C22—862no—
650C22—862no—
651C22—862no—
652C22—3442no—
653C22—3442no—
654C22—3442no—
655C22—3442no—
656C22—3442no—
657C22—3442no—
658C22—3442no—
659C22C2×#1306329511yescharacteristic
660C22#121×D4311yescharacteristic
661C22#1458341211yescharacteristic
662C22C2×SD16×D4311yescharacteristic
663C22AGL(1,ℤ/8)×D4311yescharacteristic
664C22C2×#1306335711yescharacteristic
665C22#1458369811yescharacteristic
666C4—22no—
667C4—24no—
668C4—42no—
669C4—82no—
670C4—862no—
671C4—862no—
672C4—864no—
673C4—1721no—
674C4—1722no—
675C4#1458303914yescomplemented
676C4#121×D4311yescharacteristic
677C4C2×#1306330011yescharacteristic
678C4#1458341111yescharacteristic
679C4#1458341211yescharacteristic
680C2—864no—
681C2—6882no—
682C2#1914287811yescharacteristic
683C2C2×#1458303911yescharacteristic
684C2#1914384811yescharacteristic
685C2#460×D4311yescharacteristic
686C2#1914406811yescharacteristic
687C2#1914462811yescharacteristic
688C2#1914471911yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1803C2
socleC23×C43C22×D4
prime radical#19142941C2
hypercenter#1803D43
hypocenterC43#32903
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1803

Complements

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

NH ≅ G/Ntype
1. C2×C4×Q8×D43C2semidirect
2. C2×#14583100C2semidirect
3. C2×#14583099C2semidirect
4. C2×#14583039C2semidirect
6. #19134951C2semidirect
7. #19134948C2semidirect
8. #19134911C2semidirect
9. #19134597C2semidirect
10. #19134572C2semidirect
11. C43×#1803C2semidirect
55. C2×Q8×D43D4semidirect
82. C4×Dic86D4semidirect
114. C4×Q8×C43D4semidirect
177. C2×C4×D43SD16semidirect
241. Q8×C43#121semidirect
297. Dic86#121semidirect
321. C2×D43#460semidirect
326. C4×C43#448semidirect
345. #1803D43semidirect
392. C43#32903semidirect
434. C4×Q8D172semidirect
591. Q8#13063300semidirect
675. C4#14583039semidirect

Maximal subgroups

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

subgroupindex
C2×C4×Q8×D432
C2×#145831002
C2×#145830992
C2×#145830392
#191429412
#191349512
#191349482
#191349112
#191345972
#191345722
C43×#18032
#3290343