Finite Group Databasebeta

← #25062855

Subgroups — #25062855

Order 11008.

938 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583621C211yesmaximal, characteristic
2#19143254C212yesmaximal, complemented
3#19132965C212yesmaximal, complemented
4#19132963C212yesmaximal, complemented
5#19132957C212yesmaximal, complemented
6#19132937C211yesmaximal, characteristic, complemented
7#19132932C211yesmaximal, characteristic
8#19132919C211yesmaximal, characteristic, complemented
9#19132917C211yesmaximal, characteristic, complemented
10#19132912C211yesmaximal, characteristic
11C43×#1467C211yesmaximal, characteristic, complemented
12#14583621—22no—
13#14583621—22no—
14#14583621—22no—
15#14583621—22no—
16C2×#13063323C411yescharacteristic
17C2×#13063320C411yescharacteristic
18C2×#13063320C2211yescharacteristic
19C2×#13063319C411yescharacteristic
20C2×#13063319C2211yescharacteristic
21C2×#13063314C411yescharacteristic
22C2×#13063313C411yescharacteristic
23C2×#13063303C411yescharacteristic
24C2×#13063303C2211yescharacteristic
25C2×C4×Dic86C411yescharacteristic
26C2×#13063290C2211yescharacteristic
27C2×#13063287C2211yescharacteristic
28C2×#13063282C411yescharacteristic
29C2×#13063282C2211yescharacteristic
30#14582961—22no—
31#14582959—22no—
32#14582953C2212yes—
33#14582952C2212yes—
34#14582949C2212yes—
35#14582924—22no—
36#14582861C2212yes—
37C22⋊C8×D43C2212yes—
38#14582856—22no—
39#14582625C2211yescharacteristic
40#14582625C2212yes—
41#14582625C2211yescharacteristic
42#14582624C2212yes—
43#14582624C2212yes—
44#14582622C2212yes—
45#14582622C2212yes—
46C2×C4×Q8×C43C2211yescharacteristic
47C43×#432C2212yes—
48C43×#324C2211yescharacteristic
49C43×#324C2211yescharacteristic
50C43×#324C2212yes—
51C22×Dic86C2×C411yescharacteristic
52C22×Dic86C2×C411yescharacteristic
53C22×D172C2×C411yescharacteristic
54C22×C4×D43C2×C411yescharacteristic
55C22×C4×D43C2311yescharacteristic
56C2×#10621872—22no—
57C2×C8×D43—22no—
58#13063323—22no—
59#13063323—22no—
60#13063320—22no—
61#13063320—22no—
62#13063320—22no—
63#13063320—22no—
64#13063319—22no—
65#13063319—22no—
66#13063319—22no—
67#13063319—22no—
68#13063314—22no—
69#13063314—22no—
70#13063313—22no—
71#13063313—22no—
72#13063303—22no—
73#13063303—22no—
74#13063303—22no—
75#13063303—22no—
76C4×Dic86—21no—
77C4×Dic86—21no—
78C4×Dic86—21no—
79C4×Dic86—21no—
80#13063290—22no—
81#13063290—22no—
82#13063287—22no—
83#13063287—22no—
84#13063282—21no—
85#13063282—21no—
86#13063282—21no—
87#13063282—21no—
88#13063282D412yes—
89#13063282D412yes—
90#13063282D412yes—
91#13063282D412yes—
92C2×C4⋊Dic43C2×C411yescharacteristic
93C2×Dic43⋊C4C2×C411yescharacteristic
94C2×Dic43⋊C4C2×C411yescharacteristic
95C2×Dic43⋊C4C2×C411yescharacteristic
96C2×Dic43⋊C4C2×C411yescharacteristic
97C2×Dic43⋊C4C2×C411yescharacteristic
98C2×Dic43⋊C4C2×C411yescharacteristic
99C2×Dic43⋊C4C2×C411yescharacteristic
100C2×Dic43⋊C4C2311yescharacteristic
101C2×(C2×D43)⋊C4C2×C411yescharacteristic
102C2×(C2×D43)⋊C4C2×C411yescharacteristic
103C2×(C2×D43)⋊C4C2×C411yescharacteristic
104C2×(C2×D43)⋊C4C2×C411yescharacteristic
105C2×(C2×D43)⋊C4C2×C411yescharacteristic
106C2×(C2×D43)⋊C4C2×C411yescharacteristic
107C2×(C2×D43)⋊C4C2×C411yescharacteristic
108C2×(C2×D43)⋊C4C2×C411yescharacteristic
109C2×(C2×D43)⋊C4C2×C411yescharacteristic
110C2×(C2×D43)⋊C4C2311yescharacteristic
111C2×C4×Dic43C2×C411yescharacteristic
112C2×C4×Dic43C2×C411yescharacteristic
113C2×C4×Dic43C2×C411yescharacteristic
114C2×C4×Dic43C2311yescharacteristic
115C4⋊(C43⋊C8)—22no—
116Dic43⋊C8—22no—
117Dic43⋊C8—22no—
118C22⋊(C43⋊C8)C2312yes—
119C22⋊(C43⋊C8)C2312yes—
120(C2×D43)⋊C8—22no—
121(C2×D43)⋊C8—22no—
122#13063235—22no—
123C4×C43⋊C8—22no—
124C8×Dic43—22no—
125C22×Q8×C43C2×C411yescharacteristic
126C4×Q8×C43—22no—
127C4×Q8×C43—22no—
128C2×C4⋊C4×C43C2×C411yescharacteristic
129C2×C4⋊C4×C43C2311yescharacteristic
130C2×C4⋊C4×C43C2311yescharacteristic
131C2×C42×C43C2×C411yescharacteristic
132C2×C42×C43C2×C411yescharacteristic
133C2×C42×C43C2311yescharacteristic
134C4⋊C8×C43—22no—
135C22⋊C8×C43C2312yes—
136C22⋊C8×C43C2312yes—
137#97×C43—22no—
138C23×D43C22×C411yescharacteristic
139C23×D43C22×C411yescharacteristic
140C2×Q8×C43—22no—
141C2×Q8×C43—22no—
142C2×Q8×C43—41no—
143C22×C4×C43C22×C411yescharacteristic
144C22×C4×C43C22×C411yescharacteristic
145C22×C4×C43C22×C411yescharacteristic
146C22×C4×C43C22×C411yescharacteristic
147C22×C4×C43C22×C411yescharacteristic
148C22×C4×C43C22×C411yescharacteristic
149C22×C4×C43C2411yescharacteristic
150C22×Dic43C22×C411yescharacteristic
151C22×Dic43C22×C411yescharacteristic
152C22×Dic43C22×C411yescharacteristic
153C22×Dic43C22×C411yescharacteristic
154C22×Dic43C22×C411yescharacteristic
155C22×Dic43C22×C411yescharacteristic
156C2×D172—22no—
157C2×D172—22no—
158C2×D172—41no—
159C2×C4×D43—21no—
160C2×C4×D43—21no—
161C2×C4×D43—42no—
162C2×C4×D43—42no—
163C2×C4×D43C2×D412yes—
164C2×C4×D43C2×D412yes—
165C2×Dic86—22no—
166C2×Dic86—22no—
167C2×Dic86—21no—
168C2×Dic86—21no—
169C2×Dic86—41no—
170C2×Dic86—42no—
171C2×C8×C43—22no—
172C2×C8×C43—22no—
173C4⋊C4×C43—22no—
174C4⋊C4×C43—22no—
175C4⋊C4×C43—22no—
176C42×C43—21no—
177C42×C43—21no—
178C42×C43—21no—
179C42×C43—21no—
180C42×C43C2×D412yes—
181C42×C43C2×D412yes—
182(C2×D43)⋊C4—21no—
183(C2×D43)⋊C4—21no—
184(C2×D43)⋊C4—22no—
185(C2×D43)⋊C4—22no—
186(C2×D43)⋊C4—21no—
187(C2×D43)⋊C4—21no—
188(C2×D43)⋊C4—22no—
189(C2×D43)⋊C4—22no—
190(C2×D43)⋊C4—22no—
191(C2×D43)⋊C4—22no—
192(C2×D43)⋊C4C22⋊C412yes—
193(C2×D43)⋊C4C22⋊C412yes—
194(C2×D43)⋊C4C22⋊C412yes—
195(C2×D43)⋊C4C22⋊C412yes—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198Dic43⋊C4—21no—
199Dic43⋊C4—21no—
200Dic43⋊C4—22no—
201Dic43⋊C4—22no—
202Dic43⋊C4—21no—
203Dic43⋊C4—21no—
204Dic43⋊C4—22no—
205Dic43⋊C4—22no—
206Dic43⋊C4C22⋊C411yescharacteristic
207Dic43⋊C4C22⋊C411yescharacteristic
208Dic43⋊C4C22⋊C411yescharacteristic
209Dic43⋊C4C22⋊C411yescharacteristic
210Dic43⋊C4C22⋊C412yes—
211Dic43⋊C4C22⋊C412yes—
212C4×Dic43—21no—
213C4×Dic43—21no—
214C4×Dic43—21no—
215C4×Dic43—21no—
216C4×Dic43—21no—
217C4×Dic43—21no—
218C4×Dic43C2×D412yes—
219C4×Dic43C2×D412yes—
220C2×C43⋊C8—22no—
221C2×C43⋊C8—22no—
222#10621872—44no—
223C8×D43—44no—
224C23×C43C23×C411yescharacteristic
225C22×D43—21no—
226C22×D43—21no—
227C22×D43—21no—
228C22×D43—21no—
229C22×D43—21no—
230C22×D43—41no—
231C22×D43—41no—
232C22×D43—41no—
233C22×D43—41no—
234C22×D43C2×C22⋊C412yes—
235Q8×C43—44no—
236C2×C4×C43—21no—
237C2×C4×C43—21no—
238C2×C4×C43—21no—
239C2×C4×C43—21no—
240C2×C4×C43—21no—
241C2×C4×C43—21no—
242C2×C4×C43—21no—
243C2×C4×C43—21no—
244C2×C4×C43—21no—
245C2×C4×C43—41no—
246C2×C4×C43—41no—
247C2×C4×C43—41no—
248C2×C4×C43—41no—
249C2×C4×C43C2×C22⋊C411yescharacteristic
250C2×C4×C43C2×C22⋊C411yescharacteristic
251C2×C4×C43C2×C22⋊C412yes—
252C2×C4×C43#13112yes—
253C2×C4×C43C22×D412yes—
254C2×Dic43—21no—
255C2×Dic43—21no—
256C2×Dic43—22no—
257C2×Dic43—21no—
258C2×Dic43—21no—
259C2×Dic43—21no—
260C2×Dic43—21no—
261C2×Dic43—21no—
262C2×Dic43—41no—
263C2×Dic43—41no—
264C2×Dic43—41no—
265C2×Dic43C2×C22⋊C411yescharacteristic
266C2×Dic43C2×C22⋊C411yescharacteristic
267C2×Dic43C2×C22⋊C411yescharacteristic
268C2×Dic43C2×C22⋊C412yes—
269C2×Dic43C2×C22⋊C411yescharacteristic
270D172—44no—
271C4×D43—24no—
272C4×D43—42no—
273C4×D43—42no—
274C4×D43—42no—
275Dic86—44no—
276Dic86—42no—
277Dic86—42no—
278C8×C43—42no—
279C8×C43—42no—
280C43⋊C8—42no—
281C43⋊C8—42no—
282#17420—431nomaximal, Sylow
283C22×C43—21no—
284C22×C43—21no—
285C22×C43C22×C22⋊C411yescharacteristic
286C22×C43C2×#13111yescharacteristic
287C22×C43#56811yescharacteristic
288C2×D43—22no—
289C2×D43—22no—
290C2×D43—22no—
291C2×D43—41no—
292C2×D43—41no—
293C2×D43—41no—
294C2×D43—81no—
295C2×D43—81no—
296C2×D43—81no—
297C2×D43—81no—
298C4×C43—22no—
299C4×C43—22no—
300C4×C43—22no—
301C4×C43—21no—
302C4×C43—21no—
303C4×C43—41no—
304C4×C43—41no—
305C4×C43—41no—
306Dic43—22no—
307Dic43—21no—
308Dic43—21no—
309Dic43—21no—
310Dic43—41no—
311Dic43—41no—
312Dic43—41no—
313Dic43#41012yes—
314C2×#556—431no—
315#2924—432no—
316#1473—432no—
317#1473—432no—
318#1472—432no—
319#1467—431no—
320#1467D4311yescharacteristic, complemented
321#1465—431no—
322#1461—431no—
323#1461—431no—
324#1459—431no—
325C2×C43—21no—
326C2×C43—21no—
327C2×C43#288011yescharacteristic
328C2×C43C2×#41011yescharacteristic
329C2×C43#288911yescharacteristic
330D43—42no—
331D43—81no—
332#556—862no—
333#556—862no—
334#556—862no—
335#556—862no—
336C2×C4⋊Q8—431no—
337C2×#126—431no—
338C2×#126—431no—
339C2×#126—431no—
340C2×#126—431no—
341C2×#124—431no—
342C2×#124—431no—
343C2×C22⋊Q8—431no—
344C2×C22⋊Q8—431no—
345C2×C4×Q8—431no—
346C2×C4×Q8—431no—
347C2×C4×Q8C2×D4311yescharacteristic
348C2×C4×D4—431no—
349C2×#117—431no—
350C2×#117—431no—
351#433—862no—
352#433—862no—
353#432—432no—
354#432C2×D4312yes—
355#431—432no—
356#431—432no—
357#424—862no—
358#407—432no—
359C2×C22⋊C8—432no—
360#405—862no—
361#324—431no—
362#324—431no—
363#324—432no—
364#324—432no—
365#324—432no—
366#324C2×D4311yescharacteristic
367#324C2×D4311yescharacteristic
368#324C2×D4312yes—
369#323—432no—
370#323—432no—
371C43#1742011yescharacteristic, complemented, Sylow
372C22×Q8—431no—
373C22×Q8—431no—
374C22×Q8C4×D4311yescharacteristic
375C22×D4—431no—
376C23×C4—431no—
377C23×C4—431no—
378C2×M16—862no—
379C22×C8—862no—
380C4⋊Q8—862no—
381C4⋊Q8—862no—
382#126—862no—
383#126—862no—
384#126—862no—
385#126—862no—
386#126—862no—
387#126—862no—
388#126—862no—
389#126—862no—
390#124—862no—
391#124—862no—
392#124—862no—
393#124—862no—
394C22⋊Q8—862no—
395C22⋊Q8—862no—
396C22⋊Q8—862no—
397C22⋊Q8—862no—
398C4×Q8—22no—
399C4×Q8—22no—
400C4×Q8—861no—
401C4×Q8—861no—
402C4×Q8—861no—
403C4×Q8—861no—
404C4×Q8—862no—
405C4×Q8—862no—
406C4×D4—862no—
407C4×D4—862no—
408#117—432no—
409#117—432no—
410#117—432no—
411#117—432no—
412#117—861no—
413#117—861no—
414#117—861no—
415#117—861no—
416C2×C4⋊C4—431no—
417C2×C4⋊C4—431no—
418C2×C4⋊C4—431no—
419C2×C4⋊C4—431no—
420C2×C4⋊C4—431no—
421C2×C4⋊C4—431no—
422C2×C4⋊C4—431no—
423C2×C4⋊C4—431no—
424C2×C4⋊C4—431no—
425C2×C4⋊C4C4×D4311yescharacteristic
426C2×C4⋊C4C22×D4311yescharacteristic
427C2×C4⋊C4C22×D4311yescharacteristic
428C2×C22⋊C4—431no—
429C2×C22⋊C4—431no—
430C2×C22⋊C4—431no—
431C2×C22⋊C4—431no—
432C2×C22⋊C4—431no—
433C2×C22⋊C4—431no—
434C2×C22⋊C4—431no—
435C2×C22⋊C4—431no—
436C2×C22⋊C4—431no—
437C2×C22⋊C4—431no—
438C2×C42—431no—
439C2×C42—431no—
440C2×C42—431no—
441C2×C42—431no—
442C2×C42C4×D4311yescharacteristic
443C2×C42C4×D4311yescharacteristic
444C2×C42C22×D4311yescharacteristic
445C4⋊C8—22no—
446C4⋊C8—862no—
447C4⋊C8—862no—
448C4⋊C8—862no—
449C22⋊C8—432no—
450C22⋊C8—432no—
451C22⋊C8—862no—
452C22⋊C8—862no—
453C22⋊C8C22×D4312yes—
454C22⋊C8C22×D4312yes—
455#97—22no—
456#97—862no—
457C4×C8—862no—
458C4×C8—862no—
459C24—431no—
460C24—431no—
461C2×Q8—22no—
462C2×Q8—22no—
463C2×Q8—41no—
464C2×Q8—861no—
465C2×Q8—861no—
466C2×Q8—862no—
467C2×Q8—862no—
468C2×Q8—1721no—
469C2×Q8—1722no—
470C2×D4—862no—
471C2×D4—862no—
472C2×D4—1721no—
473C22×C4—431no—
474C22×C4—431no—
475C22×C4—431no—
476C22×C4—432no—
477C22×C4—432no—
478C22×C4—431no—
479C22×C4—431no—
480C22×C4—431no—
481C22×C4—861no—
482C22×C4—861no—
483C22×C4—1722no—
484C22×C4—1722no—
485C22×C4C2×C4×D4311yescharacteristic
486C22×C4C2×C4×D4311yescharacteristic
487C22×C4C2×C4×D4311yescharacteristic
488C22×C4C2×C4×D4311yescharacteristic
489C22×C4C2×C4×D4311yescharacteristic
490C22×C4C2×C4×D4311yescharacteristic
491C22×C4C23×D4311yescharacteristic
492M16—1724no—
493C2×C8—22no—
494C2×C8—22no—
495C2×C8—862no—
496C2×C8—862no—
497C2×C8—1724no—
498C4⋊C4—22no—
499C4⋊C4—22no—
500C4⋊C4—22no—
501C4⋊C4—431no—
502C4⋊C4—431no—
503C4⋊C4—431no—
504C4⋊C4—431no—
505C4⋊C4—432no—
506C4⋊C4—432no—
507C4⋊C4—861no—
508C4⋊C4—861no—
509C4⋊C4—862no—
510C4⋊C4—861no—
511C4⋊C4—861no—
512C4⋊C4—862no—
513C4⋊C4—861no—
514C4⋊C4—861no—
515C4⋊C4—862no—
516C4⋊C4—862no—
517C22⋊C4—432no—
518C22⋊C4—432no—
519C22⋊C4—432no—
520C22⋊C4—432no—
521C22⋊C4—861no—
522C22⋊C4—861no—
523C22⋊C4—862no—
524C22⋊C4—862no—
525C22⋊C4—862no—
526C22⋊C4—862no—
527C22⋊C4—861no—
528C22⋊C4—861no—
529C22⋊C4—862no—
530C22⋊C4—862no—
531C42—21no—
532C42—21no—
533C42—21no—
534C42—21no—
535C42—432no—
536C42—432no—
537C42—861no—
538C42—861no—
539C42—861no—
540C42—861no—
541C42—861no—
542C42—861no—
543C42D4×D4312yes—
544C42D4×D4312yes—
545C23—432no—
546C23—861no—
547C23—861no—
548C23—861no—
549C23—861no—
550C23—861no—
551C23—1721no—
552C23—1721no—
553C23—1721no—
554C23—1721no—
555C23C22×C4×D4311yescharacteristic
556Q8—44no—
557Q8—1724no—
558Q8—1722no—
559Q8—1722no—
560D4—1724no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—431no—
575C2×C4—431no—
576C2×C4—431no—
577C2×C4—432no—
578C2×C4—431no—
579C2×C4—864no—
580C2×C4—862no—
581C2×C4—861no—
582C2×C4—861no—
583C2×C4—861no—
584C2×C4—861no—
585C2×C4—861no—
586C2×C4—861no—
587C2×C4—861no—
588C2×C4—1722no—
589C2×C4—1722no—
590C2×C4—1722no—
591C2×C4—1721no—
592C2×C4—1721no—
593C2×C4—1721no—
594C2×C4C22⋊C4×D4311yescharacteristic
595C2×C4C22⋊C4×D4311yescharacteristic
596C2×C4C22⋊C4×D4312yes—
597C2×C4#1306333312yes—
598C2×C4C2×D4×D4312yes—
599C8—42no—
600C8—42no—
601C8—1722no—
602C8—1722no—
603C22—21no—
604C22—21no—
605C22—862no—
606C22—862no—
607C22—862no—
608C22—3441no—
609C22—3441no—
610C22—3441no—
611C22—3441no—
612C22—1721no—
613C22—1721no—
614C22—1721no—
615C22C2×C22⋊C4×D4311yescharacteristic
616C22C2×#1306333311yescharacteristic
617C22#1458366511yescharacteristic
618C4—22no—
619C4—22no—
620C4—22no—
621C4—21no—
622C4—21no—
623C4—41no—
624C4—41no—
625C4—41no—
626C4—432no—
627C4—862no—
628C4—861no—
629C4—861no—
630C4—861no—
631C4—1721no—
632C4—1721no—
633C4—1721no—
634C2—21no—
635C2—21no—
636C2—3441no—
637C2—1722no—
638C2#1914304511yescharacteristic
639C2#410×D4311yescharacteristic
640C2#1914307511yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC23×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1467C2
socleC22×C43C22×C22⋊C4
prime radicalC22×D172C2×C4
cosocleC22×C4×C43C24
hypercenter#1467D43
hypocenterC43#17420
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
2. #19143254C2semidirect
3. #19132965C2semidirect
4. #19132963C2semidirect
5. #19132957C2semidirect
6. #19132937C2semidirect
8. #19132919C2semidirect
9. #19132917C2semidirect
11. C43×#1467C2semidirect
320. #1467D43semidirect
371. C43#17420semidirect

Maximal subgroups

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

subgroupindex
C2×#145836212
#191432542
#191329652
#191329632
#191329572
#191329372
#191329322
#191329192
#191329172
#191329122
C43×#14672
#1742043