Finite Group Databasebeta

← #25063337

Subgroups — #25063337

Order 11008.

1036 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583431C211yesmaximal, characteristic
2#19143223C211yesmaximal, characteristic, complemented
3#423×D43C211yesmaximal, characteristic, complemented
4#19133057C214yesmaximal, complemented
5#19133025C211yesmaximal, characteristic, complemented
6#19133023C211yesmaximal, characteristic, complemented
7#19133020C211yesmaximal, characteristic, complemented
8#19133005C214yesmaximal, complemented
9C43×#1486C211yesmaximal, characteristic, complemented
10C2×M16×D43—21no—
11#14583431—21no—
12#14583431—21no—
13#14583431—21no—
14#14583431—21no—
15#14583431C412yes—
16#14583431C412yes—
17#14583431C2212yes—
18#14583431C2212yes—
19C2×#13063318—21no—
20C2×#13063316C411yescharacteristic
21C2×#13063312C411yescharacteristic
22C2×#13063307—21no—
23C2×#13063305C411yescharacteristic
24C2×#13063296C411yescharacteristic
25C2×C4×Dic86C2211yescharacteristic
26C2×C4×C22⋊D43—21no—
27C2×#13063284—21no—
28C2×C42×D43C2211yescharacteristic
29#14582955—21no—
30#14582953—21no—
31#14582952C2211yescharacteristic
32#14582950C2212yescomplemented
33#14582923C2211yescharacteristic
34#14582922—21no—
35#14582921—21no—
36#14582921—21no—
37#14582921C2212yescomplemented
38C4⋊C8×D43—21no—
39C4⋊C8×D43C2212yescomplemented
40#14582861—21no—
41C4×#10621872C2212yescomplemented
42#14582631C2214yescomplemented
43#14582629C2214yescomplemented
44D4⋊(C43⋊C8)C2214yescomplemented
45C2×C4×D4×C43C2211yescharacteristic
46C43×#431C2211yescharacteristic
47C43×#423C2211yescharacteristic
48C43×D4⋊C8C2214yescomplemented
49C22×Dic86C2×C411yescharacteristic
50C22×C22⋊D43—21no—
51C22×C4×D43C2×C411yescharacteristic
52C22×C4×D43D411yescharacteristic
53C22×C4×D43D411yescharacteristic
54C2×#10621877—21no—
55C2×#10621872—22no—
56C2×#10621872—22no—
57M16×D43—44no—
58C2×C8×D43—22no—
59#13063318—22no—
60#13063318—22no—
61#13063318—22no—
62#13063318—22no—
63#13063316—21no—
64#13063316—21no—
65#13063316C2×C412yes—
66#13063316C2×C412yes—
67#13063312—21no—
68#13063312—21no—
69#13063312C2×C412yes—
70#13063312C2×C412yes—
71#13063307—22no—
72#13063307—22no—
73#13063307—22no—
74#13063307—22no—
75#13063305—21no—
76#13063305—21no—
77#13063305C2×C412yes—
78#13063305C2×C412yes—
79#13063296—21no—
80#13063296—21no—
81#13063296C2×C412yes—
82#13063296C2×C412yes—
83C4×Dic86—21no—
84C4×Dic86—21no—
85C4×Dic86C2×C412yes—
86C4×Dic86C2312yes—
87C4×C22⋊D43—22no—
88C4×C22⋊D43—22no—
89C4×C22⋊D43—22no—
90C4×C22⋊D43—22no—
91#13063284—22no—
92#13063284—22no—
93#13063284—22no—
94#13063284—22no—
95C2×C4⋊Dic43—21no—
96C2×C4⋊Dic43—21no—
97C2×C4⋊Dic43C2×C411yescharacteristic
98C2×Dic43⋊C4—21no—
99C2×Dic43⋊C4—21no—
100C2×C22⋊Dic43—21no—
101C2×C22⋊Dic43—21no—
102C2×C22⋊Dic43—21no—
103C2×(C2×D43)⋊C4—21no—
104C2×C4×Dic43—21no—
105C2×C4×Dic43C2×C411yescharacteristic
106C2×C4×Dic43D411yescharacteristic
107C2×C4×Dic43D411yescharacteristic
108C42×D43C2×C411yescharacteristic
109C42×D43C2×C411yescharacteristic
110C42×D43D411yescharacteristic
111C42×D43D411yescharacteristic
112C42×D43D411yescharacteristic
113C42×D43D411yescharacteristic
114C42×D43C2311yescharacteristic
115C42×D43C2311yescharacteristic
116C4⋊(C43⋊C8)—21no—
117C4⋊(C43⋊C8)—21no—
118C4⋊(C43⋊C8)C2312yes—
119Dic43⋊C8—22no—
120Dic43⋊C8—22no—
121Dic43⋊C8—22no—
122C22⋊(C43⋊C8)—21no—
123(C2×D43)⋊C8—22no—
124#13063235—22no—
125C4×C43⋊C8C2312yes—
126C22×D4×C43C2×C411yescharacteristic
127C23×C4×C43—21no—
128C2×M16×C43—21no—
129C4×D4×C43—21no—
130C4×D4×C43—21no—
131C4×D4×C43C2×C412yes—
132C4×D4×C43C2312yes—
133C2×C4⋊C4×C43C2×C411yescharacteristic
134C2×C22⋊C4×C43—21no—
135C2×C42×C43C2311yescharacteristic
136C4⋊C8×C43—21no—
137C4⋊C8×C43—21no—
138C4⋊C8×C43C2312yes—
139C22⋊C8×C43—21no—
140C4×C8×C43C2312yes—
141C24×C43—21no—
142C23×D43C22⋊C411yescharacteristic
143C2×D4×C43—21no—
144C2×D4×C43—42no—
145C2×D4×C43C22×C412yes—
146C22×C4×C43—22no—
147C22×C4×C43—22no—
148C22×C4×C43—21no—
149C22×C4×C43—42no—
150C22×C4×C43—42no—
151C22×C4×C43C22×C411yescharacteristic
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43C2×D411yescharacteristic
154C2×C22⋊D43—22no—
155C2×C22⋊D43—22no—
156C2×C22⋊D43—44no—
157C22×Dic43—21no—
158C22×Dic43—21no—
159C22×Dic43C22⋊C411yescharacteristic
160C22×Dic43C22⋊C411yescharacteristic
161C22×Dic43C22⋊C411yescharacteristic
162C2×C4×D43—22no—
163C2×C4×D43—22no—
164C2×C4×D43—42no—
165C2×C4×D43—42no—
166C2×C4×D43C22⋊C411yescharacteristic
167C2×C4×D43C22⋊C411yescharacteristic
168C2×C4×D43C22⋊C411yescharacteristic
169C2×C4×D43C22⋊C411yescharacteristic
170C2×C4×D43C22⋊C411yescharacteristic
171C2×C4×D43C22⋊C411yescharacteristic
172C2×C4×D43C22×C411yescharacteristic
173C2×C4×D43C22×C411yescharacteristic
174C2×C4×D43C2×D411yescharacteristic
175C2×C4×D43C2×D411yescharacteristic
176C2×C4×D43C2×D411yescharacteristic
177C2×C4×D43C2×D411yescharacteristic
178C2×Dic86—21no—
179C2×Dic86—42no—
180C2×Dic86C22×C412yes—
181M16×C43—42no—
182C2×C8×C43—22no—
183C2×C8×C43—22no—
184C4⋊C4×C43—21no—
185C4⋊C4×C43C22×C412yes—
186C22⋊C4×C43—22no—
187C22⋊C4×C43—22no—
188C42×C43C22×C411yescharacteristic
189C42×C43C2×D411yescharacteristic
190C42×C43C2×D411yescharacteristic
191C42×C43C2411yescharacteristic
192C22⋊Dic43—22no—
193C22⋊Dic43—22no—
194C22⋊Dic43—22no—
195C22⋊Dic43—22no—
196C22⋊Dic43—22no—
197C22⋊Dic43—22no—
198(C2×D43)⋊C4—22no—
199(C2×D43)⋊C4—22no—
200C4⋊Dic43—21no—
201C4⋊Dic43—22no—
202C4⋊Dic43—22no—
203C4⋊Dic43—22no—
204C4⋊Dic43—22no—
205C4⋊Dic43C22×C412yes—
206Dic43⋊C4—22no—
207Dic43⋊C4—22no—
208Dic43⋊C4—22no—
209Dic43⋊C4—22no—
210C4×Dic43—22no—
211C4×Dic43—22no—
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×Dic43C2×D411yescharacteristic
221C4×Dic43C2×D411yescharacteristic
222C4×Dic43C2×D411yescharacteristic
223C4×Dic43C2×D411yescharacteristic
224#10621877—42no—
225C2×C43⋊C8—22no—
226C2×C43⋊C8—22no—
227#10621872—44no—
228#10621872—44no—
229C8×D43—44no—
230C23×C43—22no—
231C23×C43—42no—
232C23×C43—42no—
233C23×C43—42no—
234C23×C43C2×C22⋊C411yescharacteristic
235C22×D43—22no—
236C22×D43—22no—
237C22×D43—41no—
238C22×D43C2×C22⋊C411yescharacteristic
239C22×D43C2×C22⋊C411yescharacteristic
240D4×C43—24no—
241D4×C43—42no—
242C2×C4×C43—22no—
243C2×C4×C43—22no—
244C2×C4×C43—41no—
245C2×C4×C43—42no—
246C2×C4×C43—42no—
247C2×C4×C43—42no—
248C2×C4×C43—44no—
249C2×C4×C43C2×C22⋊C411yescharacteristic
250C2×C4×C43C2×C22⋊C411yescharacteristic
251C2×C4×C43C2×C22⋊C411yescharacteristic
252C2×C4×C43AGL(1,ℤ/8)12yes—
253C2×C4×C43#13712yes—
254C2×C4×C43C23×C411yescharacteristic
255C2×C4×C43C22×D411yescharacteristic
256C2×C4×C43C22×D411yescharacteristic
257C22⋊D43—44no—
258C22⋊D43—44no—
259C2×Dic43—22no—
260C2×Dic43—22no—
261C2×Dic43—22no—
262C2×Dic43—41no—
263C2×Dic43—41no—
264C2×Dic43—42no—
265C2×Dic43—42no—
266C2×Dic43C2×C22⋊C411yescharacteristic
267C2×Dic43C2×C22⋊C411yescharacteristic
268C2×Dic43C2×C22⋊C411yescharacteristic
269C2×Dic43C2×C22⋊C411yescharacteristic
270C2×Dic43C2×C22⋊C411yescharacteristic
271C2×Dic43C2×C22⋊C411yescharacteristic
272C4×D43—22no—
273C4×D43—22no—
274C4×D43—22no—
275C4×D43—22no—
276C4×D43—21no—
277C4×D43—21no—
278C4×D43—21no—
279C4×D43—21no—
280C4×D43—22no—
281C4×D43—22no—
282C4×D43—41no—
283C4×D43—41no—
284C4×D43—41no—
285C4×D43—41no—
286Dic86—24no—
287Dic86—42no—
288C8×C43—42no—
289C8×C43—42no—
290C43⋊C8—42no—
291C43⋊C8—42no—
292#17492—431nomaximal, Sylow
293C22×C43—21no—
294C22×C43—21no—
295C22×C43—42no—
296C22×C43—42no—
297C22×C43—42no—
298C22×C43—84no—
299C22×C43#41712yes—
300C22×C43C22×C22⋊C411yescharacteristic
301C2×D43—21no—
302C2×D43—21no—
303C2×D43—21no—
304C2×D43—21no—
305C2×D43—21no—
306C2×D43—44no—
307C2×D43#42112yes—
308C4×C43—21no—
309C4×C43—21no—
310C4×C43—21no—
311C4×C43—42no—
312C4×C43#41712yes—
313C4×C43#56812yes—
314C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
315C4×C43C2×#13711yescharacteristic
316Dic43—21no—
317Dic43—21no—
318Dic43—21no—
319Dic43—21no—
320Dic43—21no—
321Dic43—21no—
322Dic43—42no—
323Dic43—42no—
324C2×#529—431no—
325#2920—431no—
326C2×#423—431no—
327#1495—434no—
328#1487—431no—
329#1487—431no—
330#1486—431no—
331#1486D4311yescharacteristic, complemented
332#1483—434no—
333C2×C43—22no—
334C2×C43—82no—
335C2×C43#287911yescharacteristic
336C2×C43C2×#41711yescharacteristic
337C2×C43C2×#42111yescharacteristic
338D43—22no—
339D43—41no—
340C22×M16—861no—
341#529—432no—
342#529—432no—
343#529—432no—
344#529—432no—
345#529—861no—
346#529—861no—
347#529—861no—
348#529—861no—
349C2×#126—861no—
350C2×#125—431no—
351C2×#124—431no—
352C2×#123—861no—
353C2×C22⋊Q8—431no—
354C2×#121—431no—
355C2×C4×Q8—431no—
356C2×C4×D4—861no—
357C2×C4×D4C2×D4311yescharacteristic
358C2×#117—861no—
359C22×C42—431no—
360#432—861no—
361#432—861no—
362#431—431no—
363#431—432no—
364#431C2×D4311yescharacteristic
365#423—431no—
366#423—432no—
367#423—861no—
368#423—861no—
369#423—861no—
370#423C2×D4311yescharacteristic
371C2×C4⋊C8—432no—
372C2×C4⋊C8—861no—
373#407—861no—
374C4×M16—432no—
375Q8⋊C8—434no—
376Q8⋊C8—434no—
377D4⋊C8—434no—
378D4⋊C8C2×D4314yescomplemented
379C43#1749211yescharacteristic, complemented, Sylow
380C22×Q8—431no—
381C22×D4—861no—
382C22×D4C4×D4311yescharacteristic
383C23×C4—21no—
384C23×C4—431no—
385C23×C4—431no—
386C23×C4—431no—
387C2×M16—21no—
388C2×M16—862no—
389C2×M16—862no—
390C2×M16—861no—
391C2×M16—1724no—
392C22×C8—862no—
393#126—862no—
394#126—862no—
395#126—862no—
396#126—862no—
397#125—432no—
398#125—432no—
399#125—861no—
400#125—861no—
401#124—432no—
402#124—432no—
403#124—861no—
404#124—861no—
405#123—862no—
406#123—862no—
407#123—862no—
408#123—862no—
409C22⋊Q8—432no—
410C22⋊Q8—432no—
411C22⋊Q8—861no—
412C22⋊Q8—861no—
413#121—432no—
414#121—432no—
415#121—861no—
416#121—861no—
417C4×Q8—432no—
418C4×Q8—432no—
419C4×Q8—861no—
420C4×Q8—861no—
421C4×D4—21no—
422C4×D4—21no—
423C4×D4—862no—
424C4×D4—862no—
425C4×D4—862no—
426C4×D4—862no—
427C4×D4C4×D4312yes—
428C4×D4C22×D4312yes—
429#117—862no—
430#117—862no—
431#117—862no—
432#117—862no—
433C2×C4⋊C4—431no—
434C2×C4⋊C4—861no—
435C2×C4⋊C4—861no—
436C2×C4⋊C4—861no—
437C2×C4⋊C4—861no—
438C2×C4⋊C4C4×D4311yescharacteristic
439C2×C22⋊C4—21no—
440C2×C22⋊C4—861no—
441C2×C22⋊C4—861no—
442C2×C22⋊C4—861no—
443C2×C22⋊C4—861no—
444C2×C42—431no—
445C2×C42—431no—
446C2×C42—431no—
447C2×C42—431no—
448C2×C42—431no—
449C2×C42—431no—
450C2×C42—431no—
451C2×C42—431no—
452C2×C42—431no—
453C2×C42—431no—
454C2×C42—431no—
455C2×C42—861no—
456C2×C42C22×D4311yescharacteristic
457C4⋊C8—21no—
458C4⋊C8—21no—
459C4⋊C8—432no—
460C4⋊C8—862no—
461C4⋊C8—862no—
462C4⋊C8—862no—
463C4⋊C8—861no—
464C4⋊C8—861no—
465C4⋊C8C22×D4312yes—
466C22⋊C8—21no—
467C22⋊C8—862no—
468C22⋊C8—861no—
469#97—862no—
470C4×C8—432no—
471C4×C8C22×D4312yes—
472C24—21no—
473C24—431no—
474C2×Q8—432no—
475C2×Q8—861no—
476C2×Q8—1722no—
477C2×D4—21no—
478C2×D4—42no—
479C2×D4—862no—
480C2×D4—862no—
481C2×D4—1724no—
482C2×D4C2×C4×D4312yes—
483C22×C4—21no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—42no—
487C22×C4—42no—
488C22×C4—431no—
489C22×C4—431no—
490C22×C4—431no—
491C22×C4—431no—
492C22×C4—431no—
493C22×C4—431no—
494C22×C4—431no—
495C22×C4—431no—
496C22×C4—431no—
497C22×C4—431no—
498C22×C4—431no—
499C22×C4—431no—
500C22×C4—431no—
501C22×C4—431no—
502C22×C4—431no—
503C22×C4—862no—
504C22×C4—862no—
505C22×C4—861no—
506C22×C4—861no—
507C22×C4—1722no—
508C22×C4—1722no—
509C22×C4C2×C4×D4311yescharacteristic
510C22×C4D4×D4311yescharacteristic
511C22×C4D4×D4311yescharacteristic
512M16—42no—
513M16—1724no—
514M16—1724no—
515M16—1722no—
516C2×C8—22no—
517C2×C8—22no—
518C2×C8—862no—
519C2×C8—862no—
520C2×C8—1724no—
521C4⋊C4—21no—
522C4⋊C4—432no—
523C4⋊C4—862no—
524C4⋊C4—862no—
525C4⋊C4—862no—
526C4⋊C4—862no—
527C4⋊C4—862no—
528C4⋊C4—862no—
529C4⋊C4—861no—
530C4⋊C4—862no—
531C4⋊C4—862no—
532C4⋊C4C2×C4×D4312yes—
533C22⋊C4—22no—
534C22⋊C4—22no—
535C22⋊C4—862no—
536C22⋊C4—862no—
537C22⋊C4—862no—
538C22⋊C4—862no—
539C22⋊C4—862no—
540C22⋊C4—862no—
541C22⋊C4—862no—
542C22⋊C4—862no—
543C42—431no—
544C42—431no—
545C42—431no—
546C42—431no—
547C42—431no—
548C42—431no—
549C42—431no—
550C42—431no—
551C42—431no—
552C42—431no—
553C42—431no—
554C42—431no—
555C42—862no—
556C42—862no—
557C42C2×C4×D4311yescharacteristic
558C42D4×D4311yescharacteristic
559C42D4×D4311yescharacteristic
560C42C23×D4311yescharacteristic
561C23—22no—
562C23—42no—
563C23—42no—
564C23—42no—
565C23—431no—
566C23—431no—
567C23—862no—
568C23—862no—
569C23—1721no—
570C23C22⋊C4×D4311yescharacteristic
571Q8—864no—
572Q8—1722no—
573D4—24no—
574D4—42no—
575D4—1724no—
576D4—1724no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—41no—
580C2×C4—42no—
581C2×C4—44no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—431no—
585C2×C4—431no—
586C2×C4—431no—
587C2×C4—431no—
588C2×C4—431no—
589C2×C4—431no—
590C2×C4—862no—
591C2×C4—862no—
592C2×C4—862no—
593C2×C4—862no—
594C2×C4—862no—
595C2×C4—862no—
596C2×C4—862no—
597C2×C4—861no—
598C2×C4—861no—
599C2×C4—861no—
600C2×C4—861no—
601C2×C4—862no—
602C2×C4—862no—
603C2×C4—1721no—
604C2×C4—1721no—
605C2×C4—1721no—
606C2×C4—1721no—
607C2×C4—1721no—
608C2×C4—1721no—
609C2×C4—1722no—
610C2×C4—1722no—
611C2×C4C22⋊C4×D4311yescharacteristic
612C2×C4C22⋊C4×D4311yescharacteristic
613C2×C4C22⋊C4×D4311yescharacteristic
614C2×C4#1306334912yes—
615C2×C4#1306335412yes—
616C2×C4C22×C4×D4311yescharacteristic
617C2×C4C2×D4×D4311yescharacteristic
618C2×C4C2×D4×D4311yescharacteristic
619C8—42no—
620C8—42no—
621C8—1722no—
622C8—1722no—
623C22—21no—
624C22—21no—
625C22—42no—
626C22—42no—
627C22—42no—
628C22—84no—
629C22—432no—
630C22—861no—
631C22—861no—
632C22—861no—
633C22—861no—
634C22—861no—
635C22—1724no—
636C22#1458289712yes—
637C22C2×C22⋊C4×D4311yescharacteristic
638C4—21no—
639C4—21no—
640C4—21no—
641C4—42no—
642C4—861no—
643C4—861no—
644C4—861no—
645C4—861no—
646C4—861no—
647C4—861no—
648C4—1722no—
649C4—1722no—
650C4#1458289712yes—
651C4#1458366512yes—
652C4C2×#1306334911yescharacteristic
653C4C2×#1306335411yescharacteristic
654C2—22no—
655C2—82no—
656C2—862no—
657C2—1721no—
658C2#1914303811yescharacteristic
659C2C2×#1458289711yescharacteristic
660C2#421×D4311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1486C2
socleC22×C43C22×C22⋊C4
prime radicalC2×#13063296C4
cosocleC42×C43C24
hypercenter#1486D43
hypocenterC43#17492
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1486

Complements

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

NH ≅ G/Ntype
2. #19143223C2semidirect
3. #423×D43C2semidirect
4. #19133057C2semidirect
5. #19133025C2semidirect
6. #19133023C2semidirect
7. #19133020C2semidirect
8. #19133005C2semidirect
9. C43×#1486C2semidirect
32. #14582950C22semidirect
37. #14582921C22semidirect
39. C4⋊C8×D43C22semidirect
41. C4×#10621872C22semidirect
42. #14582631C22semidirect
43. #14582629C22semidirect
44. D4⋊(C43⋊C8)C22semidirect
48. C43×D4⋊C8C22semidirect
331. #1486D43semidirect
378. D4⋊C8C2×D43semidirect
379. C43#17492semidirect

Maximal subgroups

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

subgroupindex
C2×#145834312
#191432232
#423×D432
#191330572
#191330252
#191330232
#191330202
#191330052
C43×#14862
#1749243