Finite Group Databasebeta

← #25062800

Subgroups — #25062800

Order 11008.

944 conjugacy classes of subgroups.

The subgroup lattice has 634 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583583C211yesmaximal, characteristic
2#19143255C211yesmaximal, characteristic, complemented
3#19143249C211yesmaximal, characteristic, complemented
4#19132959C211yesmaximal, characteristic, complemented
5#19132949C212yesmaximal, complemented
6#19132949C212yesmaximal, complemented
7#19132931C211yesmaximal, characteristic
8#19132928C212yesmaximal, complemented
9#19132911C211yesmaximal, characteristic
10#19132908C212yesmaximal, complemented
11C43×#1472C211yesmaximal, characteristic, complemented
12#14583583—21no—
13#14583583—21no—
14#14583583—21no—
15#14583583—21no—
16#14583583—22no—
17#14583583—22no—
18C2×#13063318C412yes—
19C2×#13063316C411yescharacteristic
20C2×#13063315C2212yes—
21C2×#13063307C412yes—
22C2×#13063301C411yescharacteristic
23C2×Q8×Dic43C411yescharacteristic
24C2×C4×C22⋊D43C2211yescharacteristic
25C2×#13063284C2211yescharacteristic
26C2×#13063283C2212yes—
27C2×C4⋊C4×D43C411yescharacteristic
28#14582957—22no—
29#14582957—22no—
30#14582953C2212yes—
31#14582953C2212yes—
32#14582949C2212yes—
33#14582949C2212yes—
34#14582927—21no—
35#14582925—21no—
36#14582863C2211yescharacteristic
37C2×C22⋊(C43⋊C8)C2211yescharacteristic
38#14582857—21no—
39#14582854—21no—
40#14582625C2212yes—
41#14582625C2212yes—
42#14582624C2212yes—
43#14582624C2211yescharacteristic
44#14582624C2211yescharacteristic
45#14582622C2211yescharacteristic
46#14582622C2212yes—
47#14582622C2211yescharacteristic
48C2×C22⋊Q8×C43C2211yescharacteristic
49C43×#407C2211yescharacteristic
50C2×C22⋊C8×C43C2211yescharacteristic
51C43×#324C2212yes—
52C43×#324C2212yes—
53C22×C22⋊D43C2×C411yescharacteristic
54C22×C4×D43C2×C412yes—
55C22×C4×D43C2×C411yescharacteristic
56C2×#10621877—21no—
57C22×C43⋊C8—21no—
58#13063318—22no—
59#13063318—22no—
60#13063318—22no—
61#13063318—22no—
62#13063316—22no—
63#13063316—21no—
64#13063316—21no—
65#13063315—22no—
66#13063315—22no—
67#13063315—22no—
68#13063315—22no—
69#13063307—22no—
70#13063307—22no—
71#13063307—22no—
72#13063307—22no—
73#13063301—22no—
74#13063301—21no—
75#13063301—21no—
76Q8×Dic43—22no—
77Q8×Dic43—21no—
78Q8×Dic43—21no—
79C4×C22⋊D43—21no—
80C4×C22⋊D43—21no—
81C4×C22⋊D43—21no—
82C4×C22⋊D43—21no—
83#13063284D411yescharacteristic
84#13063284D411yescharacteristic
85#13063284D411yescharacteristic
86#13063284D411yescharacteristic
87#13063284D412yes—
88#13063284D412yes—
89#13063283—22no—
90#13063283—22no—
91#13063283—22no—
92#13063283—22no—
93C2×C4⋊Dic43C2×C412yes—
94C2×C4⋊Dic43C2×C412yes—
95C2×C4⋊Dic43C2×C411yescharacteristic
96C2×C4⋊Dic43C2×C411yescharacteristic
97C2×Dic43⋊C4C2×C412yes—
98C2×Dic43⋊C4C2×C412yes—
99C2×Dic43⋊C4C2×C412yes—
100C2×Dic43⋊C4C2311yescharacteristic
101C4⋊C4×D43—22no—
102C4⋊C4×D43—21no—
103C4⋊C4×D43—21no—
104C2×C22⋊Dic43C2×C411yescharacteristic
105C2×C22⋊Dic43C2×C412yes—
106C2×(C2×D43)⋊C4C2×C412yes—
107C2×(C2×D43)⋊C4C2311yescharacteristic
108C2×C4×Dic43C2×C412yes—
109C2×C4×Dic43C2×C411yescharacteristic
110C2×C4×Dic43C2312yes—
111Dic43⋊C8—22no—
112Dic43⋊C8—22no—
113Dic43⋊C8—22no—
114Dic43⋊C8—22no—
115C22⋊(C43⋊C8)—21no—
116C22⋊(C43⋊C8)—21no—
117C22⋊(C43⋊C8)C2311yescharacteristic
118C22⋊(C43⋊C8)C2311yescharacteristic
119C22⋊(C43⋊C8)C2312yes—
120#13063235—22no—
121#13063235—22no—
122C8×Dic43—22no—
123C8×Dic43—22no—
124C22×Q8×C43C2×C411yescharacteristic
125C23×C4×C43C2311yescharacteristic
126C2×M16×C43—21no—
127C22×C8×C43—21no—
128C22⋊Q8×C43—21no—
129C22⋊Q8×C43—21no—
130C22⋊Q8×C43—21no—
131C22⋊Q8×C43—21no—
132C2×C4⋊C4×C43C2×C411yescharacteristic
133C2×C4⋊C4×C43C2312yes—
134C2×C22⋊C4×C43C2×C412yes—
135C22⋊C8×C43—21no—
136C22⋊C8×C43—21no—
137C22⋊C8×C43C2311yescharacteristic
138C22⋊C8×C43C2311yescharacteristic
139C22⋊C8×C43C2312yes—
140C24×C43C22×C411yescharacteristic
141C23×D43C22×C411yescharacteristic
142C2×Q8×C43—21no—
143C2×Q8×C43—21no—
144C2×Q8×C43—42no—
145C22×C4×C43—42no—
146C22×C4×C43C22×C412yes—
147C22×C4×C43C22×C411yescharacteristic
148C22×C4×C43C22×C412yes—
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43C2411yescharacteristic
154C2×C22⋊D43—21no—
155C2×C22⋊D43—21no—
156C2×C22⋊D43—22no—
157C2×C22⋊D43—41no—
158C22×Dic43C22×C411yescharacteristic
159C22×Dic43C22×C412yes—
160C22×Dic43C22×C411yescharacteristic
161C22×Dic43C22×C411yescharacteristic
162C22×Dic43C22×C412yes—
163C2×C4×D43—21no—
164C2×C4×D43—21no—
165C2×C4×D43—22no—
166C2×C4×D43—22no—
167C2×C4×D43—24no—
168C2×C4×D43—42no—
169C2×C4×D43—42no—
170M16×C43—42no—
171C2×C8×C43—21no—
172C2×C8×C43—21no—
173C2×C8×C43—22no—
174C2×C8×C43—42no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—22no—
178C4⋊C4×C43—22no—
179C22⋊C4×C43—22no—
180C22⋊C4×C43—22no—
181C22⋊Dic43—21no—
182C22⋊Dic43—21no—
183C22⋊Dic43C22⋊C412yes—
184C22⋊Dic43C22⋊C412yes—
185C22⋊Dic43C22⋊C412yes—
186C22⋊Dic43C22⋊C412yes—
187(C2×D43)⋊C4—21no—
188(C2×D43)⋊C4—21no—
189(C2×D43)⋊C4—22no—
190(C2×D43)⋊C4—22no—
191C4⋊Dic43—22no—
192C4⋊Dic43—22no—
193C4⋊Dic43—22no—
194C4⋊Dic43—22no—
195C4⋊Dic43C22⋊C412yes—
196C4⋊Dic43C22⋊C411yescharacteristic
197C4⋊Dic43C22⋊C411yescharacteristic
198C4⋊Dic43C22⋊C412yes—
199C4⋊Dic43C22⋊C411yescharacteristic
200C4⋊Dic43C22⋊C411yescharacteristic
201Dic43⋊C4—21no—
202Dic43⋊C4—21no—
203Dic43⋊C4—22no—
204Dic43⋊C4—22no—
205Dic43⋊C4—22no—
206Dic43⋊C4—22no—
207Dic43⋊C4—22no—
208Dic43⋊C4—22no—
209C4×Dic43—21no—
210C4×Dic43—21no—
211C4×Dic43—22no—
212C4×Dic43—22no—
213C4×Dic43C2×D412yes—
214C4×Dic43C2×D412yes—
215C4×Dic43C2×D412yes—
216C4×Dic43C2×D412yes—
217#10621877—42no—
218C2×C43⋊C8—21no—
219C2×C43⋊C8—22no—
220C2×C43⋊C8—21no—
221C2×C43⋊C8—42no—
222C23×C43—21no—
223C23×C43—21no—
224C23×C43—41no—
225C23×C43—41no—
226C23×C43C2×C22⋊C411yescharacteristic
227C23×C43C2×C22⋊C411yescharacteristic
228C23×C43C23×C411yescharacteristic
229C22×D43—21no—
230C22×D43—21no—
231C22×D43—41no—
232C22×D43—41no—
233C22×D43#13112yes—
234Q8×C43—42no—
235Q8×C43—42no—
236C2×C4×C43—22no—
237C2×C4×C43—22no—
238C2×C4×C43—22no—
239C2×C4×C43—22no—
240C2×C4×C43—22no—
241C2×C4×C43—22no—
242C2×C4×C43—22no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43—42no—
247C2×C4×C43C2×C22⋊C411yescharacteristic
248C2×C4×C43C2×C22⋊C411yescharacteristic
249C2×C4×C43C22×D411yescharacteristic
250C2×C4×C43C22×D411yescharacteristic
251C22⋊D43—42no—
252C22⋊D43—42no—
253C2×Dic43—22no—
254C2×Dic43—22no—
255C2×Dic43—21no—
256C2×Dic43—21no—
257C2×Dic43—21no—
258C2×Dic43—21no—
259C2×Dic43—21no—
260C2×Dic43—42no—
261C2×Dic43—41no—
262C2×Dic43—41no—
263C2×Dic43C2×C22⋊C412yes—
264C2×Dic43C2×C22⋊C412yes—
265C2×Dic43C2×C22⋊C412yes—
266C2×Dic43C2×C22⋊C412yes—
267C4×D43—44no—
268C4×D43—44no—
269C4×D43—42no—
270C4×D43—42no—
271C8×C43—41no—
272C8×C43—41no—
273C8×C43—42no—
274C43⋊C8—41no—
275C43⋊C8—41no—
276C43⋊C8—42no—
277#17413—431nomaximal, Sylow
278C22×C43—21no—
279C22×C43—21no—
280C22×C43—21no—
281C22×C43—21no—
282C22×C43—21no—
283C22×C43—21no—
284C22×C43—21no—
285C22×C43—21no—
286C22×C43—81no—
287C22×C43—81no—
288C22×C43C22×C22⋊C411yescharacteristic
289C22×C43C2×#13111yescharacteristic
290C22×C43#56811yescharacteristic
291C2×D43—22no—
292C2×D43—42no—
293C2×D43—41no—
294C2×D43—41no—
295C2×D43—42no—
296C4×C43—21no—
297C4×C43—21no—
298C4×C43—21no—
299C4×C43—42no—
300C4×C43—42no—
301C4×C43#41012yes—
302Dic43—22no—
303Dic43—22no—
304Dic43—22no—
305Dic43—22no—
306Dic43—41no—
307Dic43—41no—
308Dic43—41no—
309C2×#552—431no—
310#2924—431no—
311#2924—431no—
312#1472—431no—
313#1472D4311yescharacteristic, complemented
314#1470—432no—
315#1470—432no—
316#1465—431no—
317#1464—432no—
318#1459—431no—
319#1458—432no—
320C2×C43—21no—
321C2×C43—21no—
322C2×C43—41no—
323C2×C43—41no—
324C2×C43#288011yescharacteristic
325C2×C43C2×#41011yescharacteristic
326C2×C43#288911yescharacteristic
327D43—42no—
328#552—861no—
329#552—861no—
330#552—861no—
331#552—861no—
332#552—862no—
333#552—862no—
334C2×#126—432no—
335C2×#125—432no—
336C2×#125—431no—
337C2×#123—432no—
338C2×C22⋊Q8—431no—
339C2×C22⋊Q8C2×D4311yescharacteristic
340C2×C4×Q8—431no—
341C2×C4×D4—431no—
342C2×#117—431no—
343C2×#117—432no—
344C22×C4⋊C4—431no—
345#433—862no—
346#433—862no—
347#432—432no—
348#432—432no—
349#431—432no—
350#431—432no—
351#424—861no—
352#424—861no—
353#407—431no—
354#407C2×D4311yescharacteristic
355C2×C22⋊C8—431no—
356C2×C22⋊C8C2×D4311yescharacteristic
357#405—861no—
358#405—861no—
359#324—432no—
360#324—432no—
361#324—431no—
362#324—431no—
363#324—432no—
364#324C2×D4312yes—
365#324C2×D4312yes—
366#323—431no—
367#323—432no—
368#323—431no—
369C43#1741311yescharacteristic, complemented, Sylow
370C22×Q8C4×D4311yescharacteristic
371C22×D4—431no—
372C23×C4—432no—
373C23×C4—431no—
374C23×C4C22×D4311yescharacteristic
375C2×M16—21no—
376C2×M16—861no—
377C22×C8—21no—
378C22×C8—861no—
379#126—862no—
380#126—862no—
381#126—862no—
382#126—862no—
383#125—862no—
384#125—862no—
385#125—862no—
386#125—862no—
387#125—862no—
388#125—861no—
389#125—861no—
390#123—862no—
391#123—862no—
392#123—862no—
393#123—862no—
394C22⋊Q8—21no—
395C22⋊Q8—21no—
396C22⋊Q8—21no—
397C22⋊Q8—21no—
398C22⋊Q8—862no—
399C22⋊Q8—861no—
400C22⋊Q8—861no—
401C4×Q8—862no—
402C4×Q8—861no—
403C4×Q8—861no—
404C4×D4—861no—
405C4×D4—861no—
406C4×D4—861no—
407C4×D4—861no—
408#117—431no—
409#117—431no—
410#117—431no—
411#117—431no—
412#117—432no—
413#117—432no—
414#117—862no—
415#117—862no—
416#117—862no—
417#117—862no—
418C2×C4⋊C4—431no—
419C2×C4⋊C4—431no—
420C2×C4⋊C4—432no—
421C2×C4⋊C4—432no—
422C2×C4⋊C4—432no—
423C2×C4⋊C4—432no—
424C2×C4⋊C4—432no—
425C2×C4⋊C4—431no—
426C2×C4⋊C4—862no—
427C2×C4⋊C4—861no—
428C2×C4⋊C4—861no—
429C2×C4⋊C4C4×D4311yescharacteristic
430C2×C4⋊C4C22×D4312yes—
431C2×C22⋊C4—432no—
432C2×C22⋊C4—431no—
433C2×C22⋊C4—432no—
434C2×C22⋊C4—431no—
435C2×C22⋊C4C4×D4312yes—
436C2×C42—432no—
437C2×C42—432no—
438C2×C42—431no—
439C4⋊C8—862no—
440C4⋊C8—862no—
441C4⋊C8—862no—
442C4⋊C8—862no—
443C22⋊C8—21no—
444C22⋊C8—21no—
445C22⋊C8—431no—
446C22⋊C8—431no—
447C22⋊C8—432no—
448C22⋊C8—861no—
449C22⋊C8—861no—
450C22⋊C8C22×D4311yescharacteristic
451C22⋊C8C22×D4311yescharacteristic
452C22⋊C8C22×D4312yes—
453#97—862no—
454#97—862no—
455C4×C8—862no—
456C4×C8—862no—
457C24—431no—
458C24C2×C4×D4311yescharacteristic
459C2×Q8—21no—
460C2×Q8—21no—
461C2×Q8—42no—
462C2×D4—862no—
463C2×D4—861no—
464C2×D4—861no—
465C2×D4—1721no—
466C22×C4—42no—
467C22×C4—432no—
468C22×C4—432no—
469C22×C4—431no—
470C22×C4—431no—
471C22×C4—431no—
472C22×C4—862no—
473C22×C4—862no—
474C22×C4—864no—
475C22×C4—861no—
476C22×C4—861no—
477C22×C4—1722no—
478C22×C4—1722no—
479C22×C4C2×C4×D4312yes—
480C22×C4C2×C4×D4311yescharacteristic
481C22×C4C2×C4×D4312yes—
482C22×C4D4×D4311yescharacteristic
483C22×C4D4×D4311yescharacteristic
484C22×C4D4×D4311yescharacteristic
485C22×C4D4×D4311yescharacteristic
486C22×C4C23×D4311yescharacteristic
487M16—42no—
488M16—1722no—
489C2×C8—21no—
490C2×C8—22no—
491C2×C8—21no—
492C2×C8—42no—
493C2×C8—861no—
494C2×C8—862no—
495C2×C8—861no—
496C2×C8—1722no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—22no—
500C4⋊C4—22no—
501C4⋊C4—432no—
502C4⋊C4—431no—
503C4⋊C4—431no—
504C4⋊C4—432no—
505C4⋊C4—431no—
506C4⋊C4—431no—
507C4⋊C4—862no—
508C4⋊C4—862no—
509C4⋊C4—862no—
510C4⋊C4—862no—
511C4⋊C4—862no—
512C4⋊C4—862no—
513C4⋊C4—862no—
514C4⋊C4—862no—
515C4⋊C4—862no—
516C4⋊C4—862no—
517C4⋊C4—861no—
518C4⋊C4—861no—
519C22⋊C4—22no—
520C22⋊C4—22no—
521C22⋊C4—432no—
522C22⋊C4—432no—
523C22⋊C4—432no—
524C22⋊C4—432no—
525C22⋊C4—862no—
526C22⋊C4—862no—
527C22⋊C4—861no—
528C22⋊C4—861no—
529C22⋊C4—861no—
530C22⋊C4—861no—
531C42—432no—
532C42—432no—
533C42—432no—
534C42—432no—
535C42—862no—
536C42—862no—
537C42—861no—
538C42—861no—
539C23—21no—
540C23—21no—
541C23—41no—
542C23—41no—
543C23—432no—
544C23—861no—
545C23—861no—
546C23—1721no—
547C23—1721no—
548C23C22⋊C4×D4311yescharacteristic
549C23C22⋊C4×D4311yescharacteristic
550C23C22×C4×D4311yescharacteristic
551Q8—42no—
552Q8—42no—
553D4—1722no—
554D4—1722no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—42no—
566C2×C4—432no—
567C2×C4—432no—
568C2×C4—432no—
569C2×C4—432no—
570C2×C4—862no—
571C2×C4—862no—
572C2×C4—861no—
573C2×C4—861no—
574C2×C4—861no—
575C2×C4—861no—
576C2×C4—861no—
577C2×C4—1722no—
578C2×C4—1724no—
579C2×C4—1724no—
580C2×C4—1722no—
581C2×C4—1722no—
582C2×C4—1721no—
583C2×C4—1721no—
584C2×C4C22⋊C4×D4311yescharacteristic
585C2×C4C22⋊C4×D4311yescharacteristic
586C2×C4C2×D4×D4311yescharacteristic
587C2×C4C2×D4×D4311yescharacteristic
588C8—41no—
589C8—41no—
590C8—42no—
591C8—1721no—
592C8—1721no—
593C8—1722no—
594C22—21no—
595C22—21no—
596C22—21no—
597C22—21no—
598C22—21no—
599C22—21no—
600C22—21no—
601C22—21no—
602C22—81no—
603C22—81no—
604C22—862no—
605C22—1722no—
606C22—1722no—
607C22—1721no—
608C22—1721no—
609C22C2×C22⋊C4×D4311yescharacteristic
610C22#131×D4311yescharacteristic
611C22#1458366411yescharacteristic
612C4—21no—
613C4—21no—
614C4—21no—
615C4—42no—
616C4—42no—
617C4—862no—
618C4—862no—
619C4—862no—
620C4—862no—
621C4—1721no—
622C4—1721no—
623C4—1721no—
624C4#1458287112yes—
625C2—21no—
626C2—21no—
627C2—41no—
628C2—41no—
629C2—1722no—
630C2#1914304311yescharacteristic
631C2C2×#1458287111yescharacteristic
632C2#1914307511yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC23×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1472C2
socleC22×C43C22×C22⋊C4
prime radicalC22×C22⋊D43C2×C4
cosocleC22×C4×C43C24
hypercenter#1472D43
hypocenterC43#17413
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1472

Complements

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

NH ≅ G/Ntype
2. #19143255C2semidirect
3. #19143249C2semidirect
4. #19132959C2semidirect
5. #19132949C2semidirect
6. #19132949C2semidirect
8. #19132928C2semidirect
10. #19132908C2semidirect
11. C43×#1472C2semidirect
313. #1472D43semidirect
369. C43#17413semidirect

Maximal subgroups

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

subgroupindex
C2×#145835832
#191432552
#191432492
#191329592
#191329492
#191329312
#191329282
#191329112
#191329082
C43×#14722
#1741343