Finite Group Databasebeta

← #25245394

Subgroups — #25245394

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×#14583096C211yesmaximal, characteristic, complemented
3C2×#14583036C212yesmaximal, complemented
4#19142937C211yesmaximal, characteristic
5#19134952C212yesmaximal, complemented
6#19134947C212yesmaximal, complemented
7#19134909C212yesmaximal, complemented
8#19134601C211yesmaximal, characteristic, complemented
9#19134600C211yesmaximal, characteristic, complemented
10#19134572C211yesmaximal, characteristic, complemented
11C2×C43×#460C211yesmaximal, characteristic, complemented
12C22×Q8×D43C2211yescharacteristic
13C22×#10621883C2212yes—
14C2×#13063296—21no—
15C2×#13063296—21no—
16C2×#13063296C2212yes—
17C2×Q8×Dic43C2211yescharacteristic
18C2×C4×Dic86—21no—
19C2×C4×Dic86C2211yescharacteristic
20C2×#13063290—21no—
21C2×#13063290C2211yescharacteristic
22C4×Q8×D43—24no—
23C4×Q8×D43—24no—
24C2×C4⋊C4×D43—21no—
25C2×C4⋊C4×D43C2211yescharacteristic
26C2×C42×D43—21no—
27C2×C42×D43C2211yescharacteristic
28#14583096—24no—
29#14583036—28no—
30C2×C4⋊(C43⋊C8)C2211yescharacteristic
31C2×#13063250C2212yes—
32C2×#13063249C2212yes—
33C2×#13063246C2212yes—
34C2×(C2×D43)⋊C8C2212yes—
35#14582802—21no—
36#14582802—21no—
37#14582802C2212yes—
38#14582769C2211yescharacteristic
39#14582662C2212yes—
40#14582661C2212yes—
41#14582653C2212yes—
42C22×SD16×C43C2212yes—
43C2×#127×C43C2211yescharacteristic
44C2×C4×Q8×C43C2211yescharacteristic
45C43×#460—24no—
46C2×C4⋊C8×C43C2211yescharacteristic
47C2×#102×C43C2212yes—
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×C22⋊D43—22no—
57C22×C4×D43—21no—
58C22×C4×D43—21no—
59C22×C4×D43D411yescharacteristic
60C22×C4×D43D411yescharacteristic
61C22×C4×D43C2311yescharacteristic
62C2×#10621883—24no—
63C2×#10621883—24no—
64C2×#10621883—24no—
65C22×C43⋊C8C2312yes—
66#13063296—24no—
67#13063296—24no—
68#13063296—44no—
69#13063296—44no—
70Q8×Dic43—22no—
71Q8×Dic43—22no—
72C4×Dic86—28no—
73C4×Dic86—22no—
74C4×Dic86D414yescomplemented
75#13063290—28no—
76#13063290—22no—
77#13063290—22no—
78C2×C4⋊Dic43—21no—
79C2×C4⋊Dic43—21no—
80C2×C4⋊Dic43—21no—
81C2×C4⋊Dic43C2312yes—
82C2×C4⋊Dic43C2311yescharacteristic
83C2×Dic43⋊C4—21no—
84C2×Dic43⋊C4—21no—
85C2×Dic43⋊C4—21no—
86C4⋊C4×D43—28no—
87C4⋊C4×D43—22no—
88C4⋊C4×D43—22no—
89C2×C22⋊Dic43—22no—
90C2×C22⋊Dic43—22no—
91C2×C22⋊Dic43—22no—
92C2×C4×Dic43—21no—
93C2×C4×Dic43—21no—
94C2×C4×Dic43—21no—
95C2×C4×Dic43D411yescharacteristic
96C2×C4×Dic43D411yescharacteristic
97C2×C4×Dic43C2311yescharacteristic
98C42×D43—28no—
99C42×D43—22no—
100C42×D43—22no—
101C4⋊(C43⋊C8)—22no—
102#13063250—24no—
103#13063249—24no—
104#13063246—24no—
105(C2×D43)⋊C8—24no—
106C22×Q8×C43C2311yescharacteristic
107C22×D4×C43—21no—
108C22×D4×C43—21no—
109C22×D4×C43C2312yes—
110C2×SD16×C43—24no—
111C2×SD16×C43—24no—
112C2×SD16×C43—24no—
113C22×C8×C43C2312yes—
114#127×C43—22no—
115#127×C43—22no—
116C4×Q8×C43—22no—
117C4×Q8×C43D414yescomplemented
118C2×C4⋊C4×C43—21no—
119C2×C4⋊C4×C43C2311yescharacteristic
120C2×C42×C43—21no—
121C2×C42×C43C2311yescharacteristic
122C4⋊C8×C43—22no—
123#102×C43—24no—
124C24×C43—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—
132C2×D4×C43—22no—
133C2×D4×C43—22no—
134C2×D4×C43—22no—
135C2×D4×C43—22no—
136C2×D4×C43—22no—
137C2×D4×C43—22no—
138C2×D4×C43—42no—
139C2×D4×C43—42no—
140C2×D4×C43—42no—
141C2×D4×C43—42no—
142C2×D4×C43—42no—
143C2×D4×C43—42no—
144C22×C4×C43—21no—
145C22×C4×C43—21no—
146C22×C4×C43C2×D411yescharacteristic
147C22×C4×C43C2×D411yescharacteristic
148C22×C4×C43C2411yescharacteristic
149C2×C22⋊D43—44no—
150C2×C22⋊D43—44no—
151C2×C22⋊D43—44no—
152C22×Dic43—21no—
153C22×Dic43—21no—
154C22×Dic43—22no—
155C22×Dic43C2×D411yescharacteristic
156C22×Dic43C2×D411yescharacteristic
157C22×Dic43C2×D411yescharacteristic
158Q8×D43—28no—
159Q8×D43—28no—
160Q8×D43—28no—
161Q8×D43—28no—
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—
189SD16×C43—48no—
190C2×C8×C43—22no—
191C2×C8×C43—22no—
192C2×C8×C43—22no—
193C4⋊C4×C43—24no—
194C4⋊C4×C43—21no—
195C4⋊C4×C43C2×D412yes—
196C42×C43—24no—
197C42×C43C2×D412yes—
198C42×C43C2×D412yes—
199C22⋊Dic43—44no—
200C22⋊Dic43—44no—
201C22⋊Dic43—44no—
202#10621883—48no—
203C4⋊Dic43—24no—
204C4⋊Dic43—21no—
205C4⋊Dic43—22no—
206C4⋊Dic43—22no—
207C4⋊Dic43—42no—
208C4⋊Dic43—42no—
209C4⋊Dic43C2×D412yes—
210Dic43⋊C4—24no—
211Dic43⋊C4—24no—
212Dic43⋊C4—24no—
213C4×Dic43—24no—
214C4×Dic43—24no—
215C4×Dic43—24no—
216C4×Dic43—22no—
217C4×Dic43—22no—
218C4×Dic43—21no—
219C4×Dic43—21no—
220C2×C43⋊C8—22no—
221C2×C43⋊C8—22no—
222C2×C43⋊C8—22no—
223C23×C43—42no—
224C23×C43—42no—
225C23×C43—42no—
226C23×C43—42no—
227C23×C43—42no—
228C23×C43—42no—
229C23×C43—42no—
230C23×C43C22×D411yescharacteristic
231C22×D43—21no—
232C22×D43—21no—
233C22×D43—21no—
234C22×D43—21no—
235C22×D43#12112yes—
236C22×D43C2×SD1612yes—
237C22×D43AGL(1,ℤ/8)12yes—
238Q8×C43—22no—
239Q8×C43—22no—
240Q8×C43—22no—
241Q8×C43#12114yescomplemented
242D4×C43—42no—
243D4×C43—42no—
244D4×C43—42no—
245D4×C43—42no—
246D4×C43—84no—
247D4×C43—84no—
248C2×C4×C43—22no—
249C2×C4×C43—22no—
250C2×C4×C43—22no—
251C2×C4×C43—21no—
252C2×C4×C43—21no—
253C2×C4×C43—22no—
254C2×C4×C43—41no—
255C2×C4×C43—41no—
256C2×C4×C43#12012yes—
257C2×C4×C43#12012yes—
258C2×C4×C43C2×SD1612yes—
259C2×C4×C43#13712yes—
260C2×C4×C43C22×D411yescharacteristic
261C2×C4×C43C22×D411yescharacteristic
262C2×C4×C43C22×D411yescharacteristic
263C2×C4×C43C2×#4111yescharacteristic
264C2×C4×C43C2×#4111yescharacteristic
265C2×C4×C43C2×#4111yescharacteristic
266C22⋊D43—88no—
267C2×Dic43—21no—
268C2×Dic43—21no—
269C2×Dic43—22no—
270C2×Dic43—22no—
271C2×Dic43—21no—
272C2×Dic43—22no—
273C2×Dic43—21no—
274C2×Dic43—21no—
275C2×Dic43—22no—
276C2×Dic43—21no—
277C2×Dic43—21no—
278C2×Dic43—41no—
279C2×Dic43—41no—
280C2×Dic43—42no—
281C2×Dic43—42no—
282C2×Dic43—42no—
283C2×Dic43#12112yes—
284C2×Dic43C2×SD1612yes—
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×C43—82no—
302C22×C43—82no—
303C22×C43—82no—
304C22×C43—82no—
305C22×C43—82no—
306C22×C43—82no—
307C22×C43—82no—
308C22×C43C2×#12011yescharacteristic
309C22×C43C2×#12111yescharacteristic
310C22×C43#52511yescharacteristic
311C22×C43C22×SD1611yescharacteristic
312C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
313C22×C43C2×#13711yescharacteristic
314C22×C43#57511yescharacteristic
315C2×D43—22no—
316C2×D43—22no—
317C2×D43—22no—
318C2×D43—22no—
319C2×D43—22no—
320C2×D43—22no—
321C2×D43#46014yescomplemented
322C4×C43—24no—
323C4×C43—22no—
324C4×C43—42no—
325C4×C43#44814yescomplemented
326C4×C43C2×#12111yescharacteristic
327C4×C43C2×#12111yescharacteristic
328C4×C43#52511yescharacteristic
329C4×C43#52511yescharacteristic
330Dic43—22no—
331Dic43—24no—
332Dic43—22no—
333Dic43—41no—
334Dic43—42no—
335Dic43—82no—
336C22×C4×Q8—431no—
337C2×#460—431no—
338C2×#460D4311yescharacteristic, complemented
339C2×#448—432no—
340#2856—431no—
341#1880—432no—
342#1880—432no—
343#1874—432no—
344#1803—431no—
345#1803—431no—
346#1797—431no—
347C2×C43—162no—
348C2×C43#284711yescharacteristic
349C2×C43C2×#44811yescharacteristic
350C2×C43#300611yescharacteristic
351C2×C43C2×#46011yescharacteristic
352C2×C43#303711yescharacteristic
353C2×C43#310311yescharacteristic
354C2×C43#311211yescharacteristic
355D43—24no—
356C23×Q8—431no—
357C22×SD16—432no—
358C22×SD16C2×D4312yes—
359C2×#127C2×D4311yescharacteristic
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—24no—
376#460—864no—
377#448—868no—
378C2×C4⋊C8—431no—
379C2×C4⋊C8C2×D4311yescharacteristic
380C2×#103—432no—
381C2×#103—432no—
382C2×#102—432no—
383C2×#102C2×D4312yes—
384C2×C22⋊C8—432no—
385#390—432no—
386#390—861no—
387#390—861no—
388#384—431no—
389#340—432no—
390#340—432no—
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—21no—
403C22×D4—21no—
404C22×D4—862no—
405C22×D4C22×D4312yes—
406C23×C4—431no—
407C23×C4—431no—
408C23×C4—431no—
409C23×C4—861no—
410C23×C4—861no—
411C2×SD16—24no—
412C2×SD16—24no—
413C2×SD16—24no—
414C2×SD16—864no—
415C2×SD16—864no—
416C2×SD16—864no—
417C22×C8—432no—
418C22×C8C22×D4312yes—
419#127—22no—
420#127—22no—
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×Q8C22⋊D4314yescomplemented
435C2×C4⋊C4—21no—
436C2×C4⋊C4—431no—
437C2×C4⋊C4—432no—
438C2×C4⋊C4—862no—
439C2×C4⋊C4—868no—
440C2×C4⋊C4—861no—
441C2×C4⋊C4—861no—
442C2×C4⋊C4—861no—
443C2×C4⋊C4—861no—
444C2×C4⋊C4—862no—
445C2×C4⋊C4—861no—
446C2×C4⋊C4—861no—
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—864no—
465#103—864no—
466#102—24no—
467#102—864no—
468C22⋊C8—864no—
469C24—22no—
470C24—431no—
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×Q8D4×D4312yes—
488C2×Q8#1062190012yes—
489C2×Q8C2×C22⋊D4312yes—
490C2×D4—22no—
491C2×D4—22no—
492C2×D4—22no—
493C2×D4—22no—
494C2×D4—22no—
495C2×D4—22no—
496C2×D4—42no—
497C2×D4—42no—
498C2×D4—42no—
499C2×D4—42no—
500C2×D4—42no—
501C2×D4—42no—
502C2×D4—1724no—
503C2×D4—1724no—
504C2×D4—1724no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—431no—
508C22×C4—431no—
509C22×C4—434no—
510C22×C4—432no—
511C22×C4—432no—
512C22×C4—431no—
513C22×C4—864no—
514C22×C4—864no—
515C22×C4—864no—
516C22×C4—862no—
517C22×C4—864no—
518C22×C4—861no—
519C22×C4—862no—
520C22×C4—862no—
521C22×C4—861no—
522C22×C4—861no—
523C22×C4—861no—
524C22×C4—861no—
525C22×C4—861no—
526C22×C4—862no—
527C22×C4—862no—
528C22×C4—1721no—
529C22×C4—1722no—
530C22×C4—1722no—
531C22×C4D4×D4311yescharacteristic
532C22×C4D4×D4311yescharacteristic
533C22×C4C23×D4311yescharacteristic
534SD16—48no—
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—432no—
545C4⋊C4—864no—
546C4⋊C4—864no—
547C4⋊C4—864no—
548C4⋊C4—864no—
549C4⋊C4—861no—
550C4⋊C4—862no—
551C4⋊C4—862no—
552C4⋊C4—1722no—
553C4⋊C4—1722no—
554C4⋊C4C2×C22⋊D4312yes—
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—
566C42D4×D4312yes—
567C42C2×C22⋊D4312yes—
568C23—42no—
569C23—42no—
570C23—42no—
571C23—42no—
572C23—42no—
573C23—42no—
574C23—42no—
575C23—432no—
576C23—432no—
577C23—432no—
578C23—861no—
579C23—861no—
580C23—861no—
581C23—861no—
582C23C2×D4×D4311yescharacteristic
583Q8—22no—
584Q8—22no—
585Q8—22no—
586Q8—434no—
587Q8—8616no—
588Q8—862no—
589Q8—862no—
590Q8—862no—
591Q8#1306329614yescomplemented
592D4—42no—
593D4—42no—
594D4—42no—
595D4—42no—
596D4—84no—
597D4—84no—
598D4—3448no—
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—432no—
608C2×C4—432no—
609C2×C4—8616no—
610C2×C4—861no—
611C2×C4—861no—
612C2×C4—862no—
613C2×C4—862no—
614C2×C4—861no—
615C2×C4—862no—
616C2×C4—861no—
617C2×C4—862no—
618C2×C4—862no—
619C2×C4—862no—
620C2×C4—862no—
621C2×C4—868no—
622C2×C4—862no—
623C2×C4—861no—
624C2×C4—861no—
625C2×C4—861no—
626C2×C4—1724no—
627C2×C4—1728no—
628C2×C4—1722no—
629C2×C4—1722no—
630C2×C4—1722no—
631C2×C4—1721no—
632C2×C4—1721no—
633C2×C4#1306329312yes—
634C2×C4#1306329312yes—
635C2×C4SD16×D4312yes—
636C2×C4#1306335412yes—
637C2×C4C2×D4×D4311yescharacteristic
638C2×C4C2×D4×D4311yescharacteristic
639C2×C4C22×C22⋊D4311yescharacteristic
640C2×C4#41×D4311yescharacteristic
641C2×C4#41×D4311yescharacteristic
642C2×C4C2×#1062190011yescharacteristic
643C8—42no—
644C8—1722no—
645C22—82no—
646C22—82no—
647C22—82no—
648C22—82no—
649C22—82no—
650C22—82no—
651C22—82no—
652C22—434no—
653C22—862no—
654C22—862no—
655C22—862no—
656C22—862no—
657C22—862no—
658C22—862no—
659C22C2×#1306329311yescharacteristic
660C22#121×D4311yescharacteristic
661C22#1458340911yescharacteristic
662C22C2×SD16×D4311yescharacteristic
663C22AGL(1,ℤ/8)×D4311yescharacteristic
664C22C2×#1306335411yescharacteristic
665C22#1458369511yescharacteristic
666C4—22no—
667C4—24no—
668C4—42no—
669C4—862no—
670C4—862no—
671C4—864no—
672C4—3442no—
673C4—1721no—
674C4—1722no—
675C4#1458303614yescomplemented
676C4#121×D4311yescharacteristic
677C4C2×#1306329611yescharacteristic
678C4#1458340611yescharacteristic
679C4#1458340911yescharacteristic
680C2—162no—
681C2—864no—
682C2#1914287411yescharacteristic
683C2C2×#1458303611yescharacteristic
684C2#1914384311yescharacteristic
685C2#460×D4311yescharacteristic
686C2#1914406211yescharacteristic
687C2#1914462511yescharacteristic
688C2#1914471611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#460C2
socleC23×C43C22×D4
prime radical#19142937C2
hypercenterC2×#460D43
hypocenterC43#32903
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#460

Complements

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

NH ≅ G/Ntype
1. C2×C4×Q8×D43C2semidirect
2. C2×#14583096C2semidirect
3. C2×#14583036C2semidirect
5. #19134952C2semidirect
6. #19134947C2semidirect
7. #19134909C2semidirect
8. #19134601C2semidirect
9. #19134600C2semidirect
10. #19134572C2semidirect
11. C2×C43×#460C2semidirect
55. C2×Q8×D43D4semidirect
74. C4×Dic86D4semidirect
117. C4×Q8×C43D4semidirect
177. C2×C4×D43SD16semidirect
241. Q8×C43#121semidirect
297. Dic86#121semidirect
321. C2×D43#460semidirect
325. C4×C43#448semidirect
338. C2×#460D43semidirect
392. C43#32903semidirect
434. C4×Q8C22⋊D43semidirect
591. Q8#13063296semidirect
675. C4#14583036semidirect

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×#145830962
C2×#145830362
#191429372
#191349522
#191349472
#191349092
#191346012
#191346002
#191345722
C2×C43×#4602
#3290343