Finite Group Databasebeta

← #25062730

Subgroups — #25062730

Order 11008.

960 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583453C211yesmaximal, characteristic
2#19143225C211yesmaximal, characteristic
3#432×D43C211yesmaximal, characteristic
4#19132957C214yesmaximal
5#19132949C214yesmaximal, complemented
6#19132939C211yesmaximal, characteristic, complemented
7#19132938C211yesmaximal, characteristic, complemented
8#19132938C211yesmaximal, characteristic, complemented
9C43×#1467C211yesmaximal, characteristic, complemented
10#14583453—21no—
11#14583453—21no—
12#14583453—21no—
13#14583453—21no—
14#14583453—21no—
15#14583453—21no—
16#14583453—21no—
17#14583453—21no—
18C2×#13063324C411yescharacteristic
19C2×#13063323C411yescharacteristic
20C2×#13063315C2212yes—
21C2×#13063305C411yescharacteristic
22C2×#13063303C2212yes—
23C2×#13063301C411yescharacteristic
24C2×C4×Dic86C412yes—
25C2×C4×Dic86C2211yescharacteristic
26C2×#13063282C412yes—
27C2×C42×D43C2211yescharacteristic
28#14582956C2211yescharacteristic
29#14582956C2211yescharacteristic
30#14582955—21no—
31#14582954—21no—
32#14582954—21no—
33#14582953C2212yes—
34#14582951—21no—
35#14582949C2212yes—
36#14582921—21no—
37C4⋊C8×D43—21no—
38#14582861C2212yes—
39C22⋊C8×D43C2212yes—
40#14582851—21no—
41#97×D43—21no—
42#14582625C2214yes—
43#14582624C2214yes—
44#14582624C2214yes—
45C2×C4×Q8×C43C2211yescharacteristic
46C43×#432C2211yescharacteristic
47C43×#432C2211yescharacteristic
48C43×#324C2214yes—
49C22×Dic86C2×C412yes—
50C22×Dic86C2×C411yescharacteristic
51C22×C4×D43C2×C411yescharacteristic
52C22×C4×D43C2×C411yescharacteristic
53C22×C4×D43C2311yescharacteristic
54C2×#10621872—22no—
55C2×C8×D43—22no—
56#13063324—21no—
57#13063324—21no—
58#13063324—21no—
59#13063324—21no—
60#13063323—21no—
61#13063323—21no—
62#13063323—21no—
63#13063323—21no—
64#13063315—22no—
65#13063315—22no—
66#13063315—22no—
67#13063315—22no—
68#13063305—21no—
69#13063305—21no—
70#13063305—21no—
71#13063305—21no—
72#13063303—22no—
73#13063303—22no—
74#13063303—22no—
75#13063303—22no—
76#13063301—21no—
77#13063301—21no—
78#13063301—21no—
79#13063301—21no—
80C4×Dic86—21no—
81C4×Dic86—21no—
82C4×Dic86—21no—
83C4×Dic86—21no—
84C4×Dic86—22no—
85C4×Dic86—22no—
86C4×Dic86—22no—
87C4×Dic86—22no—
88#13063282—22no—
89#13063282—22no—
90#13063282—22no—
91#13063282—22no—
92C2×C4⋊Dic43C2×C412yes—
93C2×C4⋊Dic43C2×C411yescharacteristic
94C2×Dic43⋊C4C2×C412yes—
95C2×Dic43⋊C4C2×C412yes—
96C2×Dic43⋊C4C2×C412yes—
97C2×Dic43⋊C4C2×C412yes—
98C2×Dic43⋊C4C2312yes—
99C2×(C2×D43)⋊C4C2×C412yes—
100C2×(C2×D43)⋊C4C2×C412yes—
101C2×C4×Dic43C2×C412yes—
102C2×C4×Dic43C2×C411yescharacteristic
103C2×C4×Dic43C2×C411yescharacteristic
104C2×C4×Dic43C2311yescharacteristic
105C42×D43D411yescharacteristic
106C42×D43D411yescharacteristic
107C42×D43D411yescharacteristic
108C42×D43D411yescharacteristic
109C42×D43D411yescharacteristic
110C42×D43D411yescharacteristic
111C42×D43D411yescharacteristic
112C42×D43D411yescharacteristic
113C4⋊(C43⋊C8)—21no—
114C4⋊(C43⋊C8)—21no—
115Dic43⋊C8—22no—
116Dic43⋊C8—22no—
117C22⋊(C43⋊C8)C2312yes—
118C22⋊(C43⋊C8)C2312yes—
119(C2×D43)⋊C8—22no—
120(C2×D43)⋊C8—22no—
121#13063236—21no—
122#13063236—21no—
123#13063235—22no—
124C8×Dic43—22no—
125C22×Q8×C43C2×C411yescharacteristic
126C4×Q8×C43—21no—
127C4×Q8×C43—21no—
128C4×Q8×C43—21no—
129C4×Q8×C43—21no—
130C2×C4⋊C4×C43C2×C411yescharacteristic
131C2×C4⋊C4×C43C2312yes—
132C2×C42×C43C2×C412yes—
133C2×C42×C43C2311yescharacteristic
134C4⋊C8×C43—21no—
135C4⋊C8×C43—21no—
136C22⋊C8×C43C2312yes—
137C22⋊C8×C43C2312yes—
138#97×C43—21no—
139#97×C43—21no—
140C23×D43C22×C411yescharacteristic
141C2×Q8×C43—21no—
142C2×Q8×C43—21no—
143C2×Q8×C43—42no—
144C22×C4×C43C22×C412yes—
145C22×C4×C43C22×C411yescharacteristic
146C22×C4×C43C22×C411yescharacteristic
147C22×C4×C43C22×C412yes—
148C22×C4×C43C2411yescharacteristic
149C22×Dic43C22×C412yes—
150C22×Dic43C22×C411yescharacteristic
151C22×Dic43C22×C411yescharacteristic
152C22×Dic43C22×C411yescharacteristic
153C22×Dic43C22×C412yes—
154C2×C4×D43—24no—
155C2×C4×D43—42no—
156C2×C4×D43—42no—
157C2×C4×D43C22⋊C411yescharacteristic
158C2×C4×D43C22⋊C411yescharacteristic
159C2×C4×D43C22⋊C411yescharacteristic
160C2×C4×D43C22⋊C411yescharacteristic
161C2×C4×D43C22⋊C411yescharacteristic
162C2×C4×D43C22⋊C411yescharacteristic
163C2×C4×D43C22⋊C411yescharacteristic
164C2×C4×D43C22⋊C411yescharacteristic
165C2×C4×D43C2×D411yescharacteristic
166C2×C4×D43C2×D411yescharacteristic
167C2×C4×D43C2×D411yescharacteristic
168C2×C4×D43C2×D411yescharacteristic
169C2×Dic86—21no—
170C2×Dic86—21no—
171C2×Dic86—22no—
172C2×Dic86—22no—
173C2×Dic86—42no—
174C2×Dic86—44no—
175C2×C8×C43—22no—
176C2×C8×C43—22no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—22no—
180C4⋊C4×C43—22no—
181C42×C43—22no—
182C42×C43—22no—
183C42×C43C2×D411yescharacteristic
184C42×C43C2×D411yescharacteristic
185C42×C43C2×D411yescharacteristic
186C42×C43C2×D411yescharacteristic
187(C2×D43)⋊C4—22no—
188(C2×D43)⋊C4—22no—
189(C2×D43)⋊C4—22no—
190(C2×D43)⋊C4—22no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—22no—
194C4⋊Dic43—22no—
195Dic43⋊C4—22no—
196Dic43⋊C4—22no—
197Dic43⋊C4—22no—
198Dic43⋊C4—22no—
199Dic43⋊C4—22no—
200Dic43⋊C4—22no—
201Dic43⋊C4—22no—
202Dic43⋊C4—22no—
203Dic43⋊C4—22no—
204Dic43⋊C4—22no—
205C4×Dic43—22no—
206C4×Dic43—22no—
207C4×Dic43C22⋊C411yescharacteristic
208C4×Dic43C22⋊C411yescharacteristic
209C4×Dic43C22⋊C411yescharacteristic
210C4×Dic43C22⋊C411yescharacteristic
211C4×Dic43C22⋊C411yescharacteristic
212C4×Dic43C22⋊C411yescharacteristic
213C4×Dic43C22⋊C411yescharacteristic
214C4×Dic43C22⋊C411yescharacteristic
215C4×Dic43C2×D411yescharacteristic
216C4×Dic43C2×D411yescharacteristic
217C4×Dic43C2×D411yescharacteristic
218C4×Dic43C2×D411yescharacteristic
219C2×C43⋊C8—22no—
220C2×C43⋊C8—22no—
221#10621872—44no—
222C8×D43—44no—
223C23×C43C23×C411yescharacteristic
224C22×D43—22no—
225C22×D43—22no—
226C22×D43—41no—
227C22×D43C2×C22⋊C411yescharacteristic
228C22×D43C2×C22⋊C411yescharacteristic
229Q8×C43—42no—
230Q8×C43—42no—
231C2×C4×C43—22no—
232C2×C4×C43—22no—
233C2×C4×C43—22no—
234C2×C4×C43—22no—
235C2×C4×C43—24no—
236C2×C4×C43—41no—
237C2×C4×C43—42no—
238C2×C4×C43C2×C22⋊C411yescharacteristic
239C2×C4×C43C2×C22⋊C411yescharacteristic
240C2×C4×C43C2×C22⋊C411yescharacteristic
241C2×C4×C43C2×C22⋊C411yescharacteristic
242C2×C4×C43C22×D411yescharacteristic
243C2×C4×C43C22×D411yescharacteristic
244C2×Dic43—22no—
245C2×Dic43—22no—
246C2×Dic43—22no—
247C2×Dic43—22no—
248C2×Dic43—22no—
249C2×Dic43—24no—
250C2×Dic43—42no—
251C2×Dic43C2×C22⋊C411yescharacteristic
252C2×Dic43C2×C22⋊C411yescharacteristic
253C2×Dic43C2×C22⋊C411yescharacteristic
254C2×Dic43C2×C22⋊C411yescharacteristic
255C2×Dic43C2×C22⋊C411yescharacteristic
256C2×Dic43C2×C22⋊C411yescharacteristic
257C4×D43—22no—
258C4×D43—22no—
259C4×D43—22no—
260C4×D43—22no—
261C4×D43—22no—
262C4×D43—41no—
263C4×D43—41no—
264C4×D43—41no—
265C4×D43—41no—
266C4×D43—41no—
267C4×D43—41no—
268C4×D43#10114yes—
269Dic86—44no—
270Dic86—42no—
271Dic86—42no—
272Dic86—44no—
273C8×C43—42no—
274C8×C43—42no—
275C43⋊C8—42no—
276C43⋊C8—42no—
277#17404—431nomaximal, Sylow
278C22×C43—21no—
279C22×C43—21no—
280C22×C43C22×C22⋊C411yescharacteristic
281C22×C43#56812yes—
282C2×D43—21no—
283C2×D43—21no—
284C2×D43—21no—
285C2×D43—21no—
286C2×D43—21no—
287C2×D43—44no—
288C2×D43C2×#10112yes—
289C4×C43—21no—
290C4×C43—21no—
291C4×C43—21no—
292C4×C43—21no—
293C4×C43—21no—
294C4×C43—42no—
295C4×C43—42no—
296C4×C43C2×#10112yes—
297Dic43—21no—
298Dic43—21no—
299Dic43—21no—
300Dic43—21no—
301Dic43—42no—
302Dic43—42no—
303Dic43#41012yes—
304Dic43C2×#10112yes—
305C2×#533—431no—
306#2920—431no—
307C2×#432—431no—
308#1472—434no—
309#1470—434no—
310#1467—431no—
311#1467—431no—
312#1467—431no—
313#1467D4311yescharacteristic, complemented
314C2×C43—22no—
315C2×C43#287911yescharacteristic
316C2×C43C2×#41011yescharacteristic
317C2×C43C22×#10111yescharacteristic
318D43—22no—
319D43—41no—
320#533—861no—
321#533—861no—
322#533—861no—
323#533—861no—
324#533—861no—
325#533—861no—
326#533—861no—
327#533—861no—
328C2×C4⋊Q8—431no—
329C2×C4⋊Q8—431no—
330C2×#125—432no—
331C2×C22⋊Q8—431no—
332C2×C22⋊Q8—432no—
333C2×C22⋊Q8—431no—
334C2×C4×Q8—431no—
335C2×C4×Q8—432no—
336C2×C4×Q8C2×D4311yescharacteristic
337C2×#117—432no—
338C22×C42—431no—
339#432—431no—
340#432—431no—
341#432—432no—
342#432—861no—
343#432—861no—
344#432—861no—
345#432C2×D4311yescharacteristic
346#432C2×D4311yescharacteristic
347#431—432no—
348#431—861no—
349#423—861no—
350C2×C4⋊C8—861no—
351#407—432no—
352C2×C22⋊C8—432no—
353C4×M16—861no—
354C2×#97—861no—
355#324—434no—
356#324—434no—
357#324—434no—
358#324C2×D4314yes—
359C43#1740411yescharacteristic, complemented, Sylow
360C22×Q8—432no—
361C22×Q8—431no—
362C22×Q8C4×D4311yescharacteristic
363C23×C4—431no—
364C23×C4—431no—
365C23×C4—431no—
366C2×M16—862no—
367C22×C8—862no—
368C4⋊Q8—861no—
369C4⋊Q8—861no—
370C4⋊Q8—861no—
371C4⋊Q8—861no—
372C4⋊Q8—861no—
373C4⋊Q8—861no—
374C4⋊Q8—861no—
375C4⋊Q8—861no—
376#125—862no—
377#125—862no—
378#125—862no—
379#125—862no—
380C22⋊Q8—862no—
381C22⋊Q8—862no—
382C22⋊Q8—862no—
383C22⋊Q8—862no—
384C22⋊Q8—861no—
385C22⋊Q8—861no—
386C22⋊Q8—861no—
387C22⋊Q8—861no—
388C22⋊Q8—861no—
389C22⋊Q8—861no—
390C22⋊Q8—861no—
391C22⋊Q8—861no—
392C4×Q8—21no—
393C4×Q8—21no—
394C4×Q8—21no—
395C4×Q8—21no—
396C4×Q8—862no—
397C4×Q8—862no—
398C4×Q8—862no—
399C4×Q8—862no—
400C4×Q8—861no—
401C4×Q8—861no—
402C4×Q8—861no—
403C4×Q8—861no—
404#117—862no—
405#117—862no—
406#117—862no—
407#117—862no—
408C2×C4⋊C4—432no—
409C2×C4⋊C4—432no—
410C2×C4⋊C4—432no—
411C2×C4⋊C4—432no—
412C2×C4⋊C4—432no—
413C2×C4⋊C4—431no—
414C2×C4⋊C4—432no—
415C2×C4⋊C4C4×D4311yescharacteristic
416C2×C4⋊C4C22×D4312yes—
417C2×C22⋊C4—432no—
418C2×C22⋊C4—432no—
419C2×C42—431no—
420C2×C42—431no—
421C2×C42—431no—
422C2×C42—431no—
423C2×C42—431no—
424C2×C42—431no—
425C2×C42—431no—
426C2×C42—431no—
427C2×C42—431no—
428C2×C42—431no—
429C2×C42—431no—
430C2×C42—432no—
431C2×C42C4×D4312yes—
432C2×C42C22×D4311yescharacteristic
433C4⋊C8—21no—
434C4⋊C8—21no—
435C4⋊C8—862no—
436C4⋊C8—862no—
437C4⋊C8—861no—
438C4⋊C8—861no—
439C22⋊C8—432no—
440C22⋊C8—432no—
441C22⋊C8—862no—
442C22⋊C8—862no—
443C22⋊C8C22×D4312yes—
444C22⋊C8C22×D4312yes—
445#97—21no—
446#97—21no—
447#97—862no—
448#97—861no—
449#97—861no—
450C4×C8—862no—
451C24—431no—
452C2×Q8—21no—
453C2×Q8—21no—
454C2×Q8—42no—
455C2×Q8—862no—
456C2×Q8—862no—
457C2×Q8—861no—
458C2×Q8—861no—
459C2×Q8—1722no—
460C2×Q8—1724no—
461C22×C4—431no—
462C22×C4—431no—
463C22×C4—431no—
464C22×C4—431no—
465C22×C4—431no—
466C22×C4—431no—
467C22×C4—431no—
468C22×C4—431no—
469C22×C4—431no—
470C22×C4—431no—
471C22×C4—431no—
472C22×C4—431no—
473C22×C4—431no—
474C22×C4—431no—
475C22×C4—431no—
476C22×C4—432no—
477C22×C4—432no—
478C22×C4—864no—
479C22×C4—1722no—
480C22×C4—1722no—
481C22×C4C2×C4×D4312yes—
482C22×C4C2×C4×D4311yescharacteristic
483C22×C4C2×C4×D4311yescharacteristic
484C22×C4C2×C4×D4312yes—
485C22×C4C23×D4311yescharacteristic
486M16—1724no—
487C2×C8—22no—
488C2×C8—22no—
489C2×C8—862no—
490C2×C8—862no—
491C2×C8—1724no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—22no—
495C4⋊C4—22no—
496C4⋊C4—862no—
497C4⋊C4—862no—
498C4⋊C4—862no—
499C4⋊C4—862no—
500C4⋊C4—862no—
501C4⋊C4—862no—
502C4⋊C4—862no—
503C4⋊C4—862no—
504C4⋊C4—862no—
505C4⋊C4—862no—
506C4⋊C4—861no—
507C4⋊C4—861no—
508C4⋊C4—862no—
509C4⋊C4—862no—
510C22⋊C4—862no—
511C22⋊C4—862no—
512C22⋊C4—862no—
513C22⋊C4—862no—
514C42—22no—
515C42—22no—
516C42—431no—
517C42—431no—
518C42—431no—
519C42—431no—
520C42—431no—
521C42—431no—
522C42—431no—
523C42—431no—
524C42—431no—
525C42—431no—
526C42—431no—
527C42—431no—
528C42—862no—
529C42—862no—
530C42D4×D4311yescharacteristic
531C42D4×D4311yescharacteristic
532C42D4×D4311yescharacteristic
533C42D4×D4311yescharacteristic
534C23—431no—
535C23—431no—
536C23—862no—
537C23—862no—
538C23—1721no—
539C23C22×C4×D4311yescharacteristic
540Q8—42no—
541Q8—42no—
542Q8—1722no—
543Q8—1722no—
544Q8—1724no—
545Q8—1724no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—24no—
551C2×C4—41no—
552C2×C4—42no—
553C2×C4—431no—
554C2×C4—431no—
555C2×C4—434no—
556C2×C4—431no—
557C2×C4—431no—
558C2×C4—431no—
559C2×C4—431no—
560C2×C4—862no—
561C2×C4—862no—
562C2×C4—862no—
563C2×C4—862no—
564C2×C4—862no—
565C2×C4—862no—
566C2×C4—862no—
567C2×C4—862no—
568C2×C4—862no—
569C2×C4—862no—
570C2×C4—864no—
571C2×C4—1721no—
572C2×C4—1721no—
573C2×C4—1721no—
574C2×C4—1721no—
575C2×C4—1721no—
576C2×C4—1721no—
577C2×C4—1722no—
578C2×C4C22⋊C4×D4311yescharacteristic
579C2×C4C22⋊C4×D4311yescharacteristic
580C2×C4C22⋊C4×D4311yescharacteristic
581C2×C4C22⋊C4×D4311yescharacteristic
582C2×C4C2×D4×D4311yescharacteristic
583C2×C4C2×D4×D4311yescharacteristic
584C8—42no—
585C8—42no—
586C8—1722no—
587C8—1722no—
588C22—21no—
589C22—21no—
590C22—432no—
591C22—861no—
592C22—861no—
593C22—861no—
594C22—861no—
595C22—861no—
596C22—1724no—
597C22C2×C22⋊C4×D4311yescharacteristic
598C22#1458366512yes—
599C4—21no—
600C4—21no—
601C4—21no—
602C4—21no—
603C4—21no—
604C4—42no—
605C4—42no—
606C4—432no—
607C4—432no—
608C4—861no—
609C4—861no—
610C4—861no—
611C4—861no—
612C4—1722no—
613C4—1722no—
614C4#101×D4312yes—
615C2—22no—
616C2—862no—
617C2—1721no—
618C2#1914303811yescharacteristic
619C2#410×D4311yescharacteristic
620C2C2×#101×D4311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC23×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1467C2
socleC22×C43C22×C22⋊C4
prime radicalC23×D43C22×C4
cosocleC22×C4×C43C24
hypercenter#1467D43
hypocenterC43#17404
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1467

Complements

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

NH ≅ G/Ntype
5. #19132949C2semidirect
6. #19132939C2semidirect
7. #19132938C2semidirect
8. #19132938C2semidirect
9. C43×#1467C2semidirect
313. #1467D43semidirect
359. C43#17404semidirect

Maximal subgroups

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

subgroupindex
C2×#145834532
#191432252
#432×D432
#191329572
#191329492
#191329392
#191329382
C43×#14672
#1740443