Finite Group Databasebeta

← #25064071

Subgroups — #25064071

Order 11008.

992 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#533×D43C211yesmaximal, characteristic
2#19143223C211yesmaximal, characteristic
3#19136988C211yesmaximal, characteristic
4#19133160C211yesmaximal, characteristic, complemented
5#19133159C211yesmaximal, characteristic, complemented
6#19133158C211yesmaximal, characteristic, complemented
7#19133126C214yesmaximal
8#19133105C214yesmaximal, complemented
9C43×#1518C211yesmaximal, characteristic, complemented
10#14583456C2211yescharacteristic
11#14583455—21no—
12#14583454C411yescharacteristic, complemented
13#14583454C411yescharacteristic, complemented
14#14583453—21no—
15#14583453C412yescomplemented
16#14583452—21no—
17#14583451—21no—
18#14583451C2212yes—
19C4⋊Q8×D43C411yescharacteristic, complemented
20C4⋊Q8×D43C411yescharacteristic, complemented
21#125×D43—21no—
22C22⋊Q8×D43—21no—
23C22⋊Q8×D43C2212yes—
24C4×Q8×D43—21no—
25C4×Q8×D43C412yescomplemented
26#117×D43—21no—
27C2×C42×D43C2211yescharacteristic
28#14582955—21no—
29#14582953C2212yes—
30#14582952C2211yescharacteristic
31#14582950—21no—
32#14582921—21no—
33#14582861C2212yes—
34C4×#10621872—21no—
35#14582766—21no—
36#14582765C2211yescharacteristic
37#14582761C2212yes—
38#14582756—21no—
39C4⋊C4×Dic43—21no—
40#14582746—21no—
41#14582744C2212yes—
42#14582637C2214yes—
43#14582636C2214yes—
44#14582635C2214yes—
45C43×#533C2211yescharacteristic
46C43×#431C2211yescharacteristic
47C43×#382C2211yescharacteristic
48C43×#328C2214yes—
49C2×Q8×D43—21no—
50C2×Q8×D43C2×C412yes—
51C22×C4×D43D411yescharacteristic
52C22×C4×D43D411yescharacteristic
53C22×C4×D43C2311yescharacteristic
54C2×#10621872—22no—
55#13063325C2×C411yescharacteristic
56#13063325C2×C411yescharacteristic
57#13063324—21no—
58#13063324—21no—
59#13063324—21no—
60#13063324C2×C412yes—
61#13063323—21no—
62#13063323C2×C412yes—
63#13063317—21no—
64#13063316—21no—
65#13063316—21no—
66#13063315—22no—
67#13063315—22no—
68#13063305—21no—
69#13063305C2×C412yes—
70#13063304—21no—
71#13063304C2312yes—
72#13063303—22no—
73#13063303—22no—
74#13063302—22no—
75#13063302—22no—
76#13063301—21no—
77#13063301C2×C412yes—
78Q8×Dic43—21no—
79Q8×Dic43C2×C412yes—
80C4×Dic86—21no—
81C4×Dic86—22no—
82C4×Dic86—22no—
83C4×Dic86C2×C412yes—
84#13063290—21no—
85#13063290—22no—
86#13063290—22no—
87#13063290C2×C412yes—
88#13063284—21no—
89#13063283—21no—
90#13063283—21no—
91#13063282—22no—
92#13063281—22no—
93C2×C4⋊Dic43—21no—
94C4⋊C4×D43—21no—
95C4⋊C4×D43—21no—
96C4⋊C4×D43—21no—
97C4⋊C4×D43—22no—
98C4⋊C4×D43—22no—
99C4⋊C4×D43C2×C412yes—
100C2×(C2×D43)⋊C4—22no—
101C22⋊C4×D43—22no—
102C2×C4×Dic43—22no—
103C2×C4×Dic43D411yescharacteristic
104C2×C4×Dic43D411yescharacteristic
105C2×C4×Dic43C2311yescharacteristic
106C42×D43—22no—
107C42×D43C2×C411yescharacteristic
108C42×D43C2×C411yescharacteristic
109C42×D43C2×C411yescharacteristic
110C42×D43C2×C411yescharacteristic
111C42×D43D411yescharacteristic
112C42×D43D411yescharacteristic
113C42×D43D411yescharacteristic
114C42×D43D411yescharacteristic
115C4⋊(C43⋊C8)—21no—
116Dic43⋊C8—22no—
117C22⋊(C43⋊C8)C2312yes—
118(C2×D43)⋊C8—22no—
119#13063235—22no—
120C4×C43⋊C8—21no—
121C43⋊#95—21no—
122C43⋊#95—22no—
123C43⋊#95—22no—
124C43⋊#95C2312yes—
125C4⋊Q8×C43C2×C411yescharacteristic
126C4⋊Q8×C43C2×C411yescharacteristic
127#125×C43—21no—
128C22⋊Q8×C43—21no—
129C22⋊Q8×C43C2312yes—
130C4×Q8×C43—21no—
131C4×Q8×C43C2×C412yes—
132#117×C43—21no—
133C2×C4⋊C4×C43—21no—
134C2×C42×C43C2311yescharacteristic
135C4⋊C8×C43—21no—
136C22⋊C8×C43C2312yes—
137C4×C8×C43—21no—
138#95×C43—21no—
139#95×C43C2312yes—
140C23×D43C2×D411yescharacteristic
141C2×Q8×C43—21no—
142C2×Q8×C43C22×C412yes—
143C22×C4×C43—22no—
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43C2411yescharacteristic
147C22×Dic43—22no—
148C22×Dic43C2×D411yescharacteristic
149C22×Dic43C2×D411yescharacteristic
150C22×Dic43C2×D411yescharacteristic
151Q8×D43—44no—
152Q8×D43—44no—
153C2×C4×D43—22no—
154C2×C4×D43—22no—
155C2×C4×D43—22no—
156C2×C4×D43—22no—
157C2×C4×D43—42no—
158C2×C4×D43—42no—
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×D43C22⋊C411yescharacteristic
166C2×C4×D43C22⋊C411yescharacteristic
167C2×C4×D43C22×C411yescharacteristic
168C2×C4×D43C22×C411yescharacteristic
169C2×C4×D43C2×D411yescharacteristic
170C2×C4×D43C2×D411yescharacteristic
171C2×Dic86—21no—
172C2×Dic86—22no—
173C2×Dic86—22no—
174C2×Dic86C22×C412yes—
175C2×C8×C43—22no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—22no—
180C4⋊C4×C43—22no—
181C4⋊C4×C43—42no—
182C4⋊C4×C43C22×C412yes—
183C22⋊C4×C43—22no—
184C42×C43—22no—
185C42×C43C22×C411yescharacteristic
186C42×C43C22×C411yescharacteristic
187C42×C43C2×D411yescharacteristic
188C42×C43C2×D411yescharacteristic
189C22⋊Dic43—22no—
190(C2×D43)⋊C4—22no—
191(C2×D43)⋊C4—22no—
192(C2×D43)⋊C4—44no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—22no—
197C4⋊Dic43—22no—
198C4⋊Dic43—42no—
199C4⋊Dic43C22×C412yes—
200Dic43⋊C4—22no—
201Dic43⋊C4—22no—
202Dic43⋊C4—22no—
203Dic43⋊C4—22no—
204Dic43⋊C4—22no—
205Dic43⋊C4—22no—
206Dic43⋊C4—22no—
207Dic43⋊C4—22no—
208C4×Dic43—22no—
209C4×Dic43—22no—
210C4×Dic43—22no—
211C4×Dic43—44no—
212C4×Dic43C22⋊C411yescharacteristic
213C4×Dic43C22⋊C411yescharacteristic
214C4×Dic43C22⋊C411yescharacteristic
215C4×Dic43C22⋊C411yescharacteristic
216C4×Dic43C22⋊C411yescharacteristic
217C4×Dic43C22⋊C411yescharacteristic
218C4×Dic43C22⋊C411yescharacteristic
219C4×Dic43C22⋊C411yescharacteristic
220C4×Dic43C22×C411yescharacteristic
221C4×Dic43C22×C411yescharacteristic
222C4×Dic43C2×D411yescharacteristic
223C4×Dic43C2×D411yescharacteristic
224C2×C43⋊C8—22no—
225#10621872—44no—
226C23×C43C22×D411yescharacteristic
227C22×D43—21no—
228C22×D43—21no—
229C22×D43—22no—
230C22×D43—41no—
231C22×D43C2×C22⋊C411yescharacteristic
232C22×D43C2×C22⋊C411yescharacteristic
233Q8×C43—42no—
234Q8×C43—42no—
235C2×C4×C43—22no—
236C2×C4×C43—22no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—42no—
240C2×C4×C43—42no—
241C2×C4×C43—42no—
242C2×C4×C43C2×C22⋊C411yescharacteristic
243C2×C4×C43C2×C22⋊C411yescharacteristic
244C2×C4×C43C2×C22⋊C411yescharacteristic
245C2×C4×C43C2×C22⋊C411yescharacteristic
246C2×C4×C43#13712yes—
247C2×C4×C43#13712yes—
248C2×C4×C43C23×C411yescharacteristic
249C2×C4×C43C22×D411yescharacteristic
250C2×Dic43—21no—
251C2×Dic43—21no—
252C2×Dic43—22no—
253C2×Dic43—22no—
254C2×Dic43—22no—
255C2×Dic43—41no—
256C2×Dic43—42no—
257C2×Dic43—42no—
258C2×Dic43—42no—
259C2×Dic43C2×C22⋊C411yescharacteristic
260C2×Dic43C2×C22⋊C411yescharacteristic
261C2×Dic43C2×C22⋊C411yescharacteristic
262C2×Dic43C2×C22⋊C411yescharacteristic
263C2×Dic43C2×C22⋊C411yescharacteristic
264C2×Dic43C2×C22⋊C411yescharacteristic
265C4×D43—22no—
266C4×D43—22no—
267C4×D43—22no—
268C4×D43—22no—
269C4×D43—22no—
270C4×D43—22no—
271C4×D43—22no—
272C4×D43—22no—
273C4×D43—41no—
274C4×D43—41no—
275C4×D43—41no—
276C4×D43—41no—
277C4×D43—44no—
278C4×D43—44no—
279Dic86—44no—
280Dic86—42no—
281Dic86—44no—
282Dic86—42no—
283C8×C43—42no—
284C43⋊C8—42no—
285#17590—431nomaximal, Sylow
286C22×C43—21no—
287C22×C43—21no—
288C22×C43C22×C22⋊C411yescharacteristic
289C22×C43C2×#13711yescharacteristic
290C22×C43C2×#13711yescharacteristic
291C2×D43—21no—
292C2×D43—21no—
293C2×D43—21no—
294C2×D43—21no—
295C2×D43—21no—
296C2×D43—42no—
297C2×D43—42no—
298C2×D43#41012yes—
299C4×C43—21no—
300C4×C43—21no—
301C4×C43—21no—
302C4×C43—21no—
303C4×C43—42no—
304C4×C43—42no—
305C4×C43—82no—
306C4×C43#41912yes—
307C4×C43#41912yes—
308Dic43—21no—
309Dic43—21no—
310Dic43—21no—
311Dic43—21no—
312Dic43—21no—
313Dic43—42no—
314Dic43—42no—
315Dic43—82no—
316Dic43#42112yes—
317C2×#533—431no—
318#2920—431no—
319#2283—431no—
320#1518—431no—
321#1518—431no—
322#1518—431no—
323#1518D4311yescharacteristic, complemented
324#1511—434no—
325#1506—434no—
326C2×C43—21no—
327C2×C43—21no—
328C2×C43C2×#41011yescharacteristic
329C2×C43C2×#41911yescharacteristic
330C2×C43C2×#42111yescharacteristic
331D43—22no—
332D43—41no—
333#533—431no—
334#533—431no—
335#533—432no—
336#533—432no—
337#533—431no—
338#533—861no—
339#533—861no—
340#533—861no—
341#533—861no—
342#533C2×D4311yescharacteristic
343C2×C4⋊Q8—431no—
344C2×C4⋊Q8—431no—
345C2×#125—861no—
346C2×C22⋊Q8—432no—
347C2×C22⋊Q8—861no—
348C2×C4×Q8—432no—
349C2×C4×Q8—861no—
350C2×#117—861no—
351C22×C42—431no—
352#432—432no—
353#432—861no—
354#431—431no—
355#431—861no—
356#431C2×D4311yescharacteristic
357#423—861no—
358#407—432no—
359C4×M16—861no—
360#383—861no—
361#382—431no—
362#382C2×D4311yescharacteristic
363#381—432no—
364#380—861no—
365C4×C4⋊C4—861no—
366C4×C22⋊C4—861no—
367#376—432no—
368#328—434no—
369#328—434no—
370#328—434no—
371#328C2×D4314yes—
372C43#1759011yescharacteristic, complemented, Sylow
373C22×Q8—432no—
374C22×Q8—861no—
375C23×C4—431no—
376C23×C4—431no—
377C23×C4—431no—
378C2×M16—862no—
379C4⋊Q8—432no—
380C4⋊Q8—432no—
381C4⋊Q8—431no—
382C4⋊Q8—431no—
383C4⋊Q8—861no—
384C4⋊Q8—861no—
385C4⋊Q8—861no—
386C4⋊Q8—861no—
387C4⋊Q8C4×D4311yescharacteristic
388C4⋊Q8C4×D4311yescharacteristic
389#125—21no—
390#125—862no—
391#125—862no—
392#125—861no—
393#125—861no—
394#125—861no—
395C22⋊Q8—21no—
396C22⋊Q8—432no—
397C22⋊Q8—432no—
398C22⋊Q8—432no—
399C22⋊Q8—862no—
400C22⋊Q8—862no—
401C22⋊Q8—862no—
402C22⋊Q8—862no—
403C22⋊Q8—861no—
404C22⋊Q8—861no—
405C22⋊Q8—861no—
406C22⋊Q8C22×D4312yes—
407C4×Q8—21no—
408C4×Q8—432no—
409C4×Q8—432no—
410C4×Q8—432no—
411C4×Q8—862no—
412C4×Q8—862no—
413C4×Q8—862no—
414C4×Q8—861no—
415C4×Q8—862no—
416C4×Q8—861no—
417C4×Q8—861no—
418C4×Q8C4×D4312yes—
419#117—21no—
420#117—862no—
421#117—862no—
422#117—861no—
423#117—861no—
424#117—861no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—432no—
427C2×C4⋊C4—861no—
428C2×C4⋊C4—861no—
429C2×C4⋊C4—862no—
430C2×C4⋊C4—862no—
431C2×C4⋊C4—861no—
432C2×C4⋊C4—861no—
433C2×C22⋊C4—862no—
434C2×C22⋊C4—862no—
435C2×C42—431no—
436C2×C42—431no—
437C2×C42—431no—
438C2×C42—431no—
439C2×C42—431no—
440C2×C42—431no—
441C2×C42—431no—
442C2×C42—431no—
443C2×C42—431no—
444C2×C42—431no—
445C2×C42—431no—
446C2×C42—862no—
447C2×C42—862no—
448C2×C42C22×D4311yescharacteristic
449C4⋊C8—21no—
450C4⋊C8—862no—
451C4⋊C8—861no—
452C22⋊C8—432no—
453C22⋊C8—862no—
454C22⋊C8C22×D4312yes—
455#97—862no—
456C4×C8—21no—
457C4×C8—861no—
458#95—21no—
459#95—432no—
460#95—862no—
461#95—862no—
462#95—861no—
463#95C22×D4312yes—
464C24—431no—
465C2×Q8—21no—
466C2×Q8—432no—
467C2×Q8—862no—
468C2×Q8—862no—
469C2×Q8—861no—
470C2×Q8—1724no—
471C2×Q8—1724no—
472C2×Q8C2×C4×D4312yes—
473C22×C4—22no—
474C22×C4—431no—
475C22×C4—431no—
476C22×C4—431no—
477C22×C4—431no—
478C22×C4—431no—
479C22×C4—431no—
480C22×C4—431no—
481C22×C4—431no—
482C22×C4—431no—
483C22×C4—431no—
484C22×C4—431no—
485C22×C4—431no—
486C22×C4—431no—
487C22×C4—431no—
488C22×C4—431no—
489C22×C4—862no—
490C22×C4—862no—
491C22×C4—862no—
492C22×C4—862no—
493C22×C4—862no—
494C22×C4—1722no—
495C22×C4—1722no—
496C22×C4D4×D4311yescharacteristic
497C22×C4D4×D4311yescharacteristic
498C22×C4C23×D4311yescharacteristic
499M16—1724no—
500C2×C8—22no—
501C2×C8—862no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—22no—
506C4⋊C4—22no—
507C4⋊C4—42no—
508C4⋊C4—432no—
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—
519C4⋊C4—862no—
520C4⋊C4—861no—
521C4⋊C4—862no—
522C4⋊C4—1722no—
523C4⋊C4C2×C4×D4312yes—
524C22⋊C4—22no—
525C22⋊C4—862no—
526C22⋊C4—862no—
527C22⋊C4—862no—
528C22⋊C4—1724no—
529C42—22no—
530C42—431no—
531C42—431no—
532C42—431no—
533C42—431no—
534C42—431no—
535C42—431no—
536C42—431no—
537C42—431no—
538C42—431no—
539C42—431no—
540C42—431no—
541C42—431no—
542C42—862no—
543C42—862no—
544C42—862no—
545C42—1724no—
546C42C2×C4×D4311yescharacteristic
547C42C2×C4×D4311yescharacteristic
548C42D4×D4311yescharacteristic
549C42D4×D4311yescharacteristic
550C23—431no—
551C23—431no—
552C23—862no—
553C23—861no—
554C23—861no—
555C23—1721no—
556C23C2×D4×D4311yescharacteristic
557Q8—42no—
558Q8—42no—
559Q8—1722no—
560Q8—1722no—
561Q8—1724no—
562Q8—1724no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—431no—
571C2×C4—431no—
572C2×C4—431no—
573C2×C4—431no—
574C2×C4—431no—
575C2×C4—431no—
576C2×C4—862no—
577C2×C4—862no—
578C2×C4—862no—
579C2×C4—862no—
580C2×C4—862no—
581C2×C4—861no—
582C2×C4—861no—
583C2×C4—862no—
584C2×C4—862no—
585C2×C4—862no—
586C2×C4—862no—
587C2×C4—862no—
588C2×C4—862no—
589C2×C4—1721no—
590C2×C4—1721no—
591C2×C4—1721no—
592C2×C4—1721no—
593C2×C4—1724no—
594C2×C4—1724no—
595C2×C4—1721no—
596C2×C4—1722no—
597C2×C4—1722no—
598C2×C4—1722no—
599C2×C4C22⋊C4×D4311yescharacteristic
600C2×C4C22⋊C4×D4311yescharacteristic
601C2×C4C22⋊C4×D4311yescharacteristic
602C2×C4C22⋊C4×D4311yescharacteristic
603C2×C4#1306335412yes—
604C2×C4#1306335712yes—
605C2×C4C22×C4×D4311yescharacteristic
606C2×C4C2×D4×D4311yescharacteristic
607C8—42no—
608C8—1722no—
609C22—21no—
610C22—21no—
611C22—432no—
612C22—861no—
613C22—861no—
614C22—861no—
615C22—861no—
616C22—861no—
617C22—1722no—
618C22—1722no—
619C22C2×C22⋊C4×D4311yescharacteristic
620C22C2×#1306335411yescharacteristic
621C22C2×#1306335711yescharacteristic
622C4—21no—
623C4—21no—
624C4—21no—
625C4—21no—
626C4—42no—
627C4—42no—
628C4—82no—
629C4—432no—
630C4—861no—
631C4—861no—
632C4—861no—
633C4—861no—
634C4—861no—
635C4—3442no—
636C4—1722no—
637C4—1722no—
638C4#1458290612yes—
639C4#1458290612yes—
640C2—21no—
641C2—21no—
642C2—862no—
643C2—1721no—
644C2#410×D4311yescharacteristic
645C2C2×#1458290611yescharacteristic
646C2#421×D4311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1518C2
socleC22×C43C22×C22⋊C4
prime radicalC23×D43C2×D4
cosocleC22×C4×C43C24
hypercenter#1518D43
hypocenterC43#17590
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1518

Complements

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

NH ≅ G/Ntype
4. #19133160C2semidirect
5. #19133159C2semidirect
6. #19133158C2semidirect
8. #19133105C2semidirect
9. C43×#1518C2semidirect
12. #14583454C4semidirect
13. #14583454C4semidirect
15. #14583453C4semidirect
19. C4⋊Q8×D43C4semidirect
20. C4⋊Q8×D43C4semidirect
25. C4×Q8×D43C4semidirect
323. #1518D43semidirect
372. C43#17590semidirect

Maximal subgroups

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

subgroupindex
#533×D432
#191432232
#191369882
#191331602
#191331592
#191331582
#191331262
#191331052
C43×#15182
#1759043