Finite Group Databasebeta

← #25063027

Subgroups — #25063027

Order 11008.

1332 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#10621900C211yesmaximal, characteristic
2#19143225C211yesmaximal, characteristic, complemented
3C4×M16×D43C211yesmaximal, characteristic, complemented
4#19133043C211yesmaximal, characteristic, complemented
5#19133041C211yesmaximal, characteristic, complemented
6#19133038C211yesmaximal, characteristic, complemented
7#19133031C214yesmaximal, complemented
8#19132974C214yesmaximal, complemented
9C43×#1490C211yesmaximal, characteristic, complemented
10C22×#10621900C411yescharacteristic
11C2×M16×D43—21no—
12C4×#10621900—21no—
13C4×#10621900—21no—
14C4×#10621900—21no—
15C4×#10621900—21no—
16C4×#10621900C412yes—
17C4×#10621900C412yes—
18C4×#10621900C2212yes—
19C4×#10621900C2212yes—
20C2×C4×Dic86C2211yescharacteristic
21C2×#13063290C411yescharacteristic
22C2×D4×Dic43C411yescharacteristic
23C2×C4×C22⋊D43—21no—
24C2×(C22⋊D43)⋊C4—21no—
25C2×#13063283C411yescharacteristic
26C2×#13063281—21no—
27C22×C4×Dic43—21no—
28C2×C42×D43C2211yescharacteristic
29#14582956C2211yescharacteristic
30#14582954—21no—
31#14582951C2212yescomplemented
32#14582949—21no—
33#14582921C2212yescomplemented
34#14582861—21no—
35C4×#10621877C2211yescharacteristic
36#14582851—21no—
37#14582851—21no—
38M16×Dic43—21no—
39C4×#10621872C2212yescomplemented
40#97×D43—21no—
41C4×C8×D43C2212yescomplemented
42#14582631C2214yescomplemented
43#14582629C2214yescomplemented
44D4⋊(C43⋊C8)C2214yescomplemented
45C2×C4×D4×C43C2211yescharacteristic
46C43×#432C2211yescharacteristic
47C4×M16×C43C2211yescharacteristic
48C43×D4⋊C8C2214yescomplemented
49C2×#10621900—28no—
50C2×#10621900—21no—
51C2×#10621900—21no—
52C2×#10621900C2×C412yes—
53C2×#10621900C2×C412yes—
54C22×Dic86C2×C411yescharacteristic
55C22×C22⋊D43—21no—
56C23×Dic43—21no—
57C23×Dic43—21no—
58C22×C4×D43C2×C411yescharacteristic
59C22×C4×D43D411yescharacteristic
60C22×C4×D43D411yescharacteristic
61C2×#10621877—21no—
62C2×#10621872—22no—
63C2×#10621872—22no—
64M16×D43—28no—
65C2×C8×D43—22no—
66C4×Dic86—21no—
67C4×Dic86—21no—
68C4×Dic86C2×C412yes—
69C4×Dic86C2312yes—
70#13063290—21no—
71#13063290—21no—
72#13063290C2×C412yes—
73#13063290C2×C412yes—
74D4×Dic43—21no—
75D4×Dic43—21no—
76D4×Dic43C2×C412yes—
77D4×Dic43C2×C412yes—
78C4×C22⋊D43—22no—
79C4×C22⋊D43—22no—
80C4×C22⋊D43—22no—
81C4×C22⋊D43—22no—
82(C22⋊D43)⋊C4—22no—
83(C22⋊D43)⋊C4—22no—
84(C22⋊D43)⋊C4—22no—
85(C22⋊D43)⋊C4—22no—
86#13063283—21no—
87#13063283—21no—
88#13063283C2×C412yes—
89#13063283C2×C412yes—
90#13063281—22no—
91#13063281—22no—
92#13063281—22no—
93#13063281—22no—
94C2×C4⋊Dic43C2×C411yescharacteristic
95C2×Dic43⋊C4—21no—
96C2×Dic43⋊C4—21no—
97C2×C22⋊Dic43—21no—
98C2×(C2×D43)⋊C4—21no—
99C2×C4×Dic43—21no—
100C2×C4×Dic43—21no—
101C2×C4×Dic43—21no—
102C2×C4×Dic43—22no—
103C2×C4×Dic43—22no—
104C2×C4×Dic43—22no—
105C2×C4×Dic43—22no—
106C2×C4×Dic43C2×C411yescharacteristic
107C2×C4×Dic43D411yescharacteristic
108C2×C4×Dic43D411yescharacteristic
109C42×D43C2×C411yescharacteristic
110C42×D43C2×C411yescharacteristic
111C42×D43D411yescharacteristic
112C42×D43D411yescharacteristic
113C42×D43D411yescharacteristic
114C42×D43D411yescharacteristic
115C42×D43C2311yescharacteristic
116C42×D43C2311yescharacteristic
117C4⋊(C43⋊C8)C2312yes—
118Dic43⋊C8—22no—
119C22⋊(C43⋊C8)—21no—
120(C2×D43)⋊C8—22no—
121#13063236—21no—
122#13063236—21no—
123#13063235—22no—
124C4×C43⋊C8C2312yes—
125C8×Dic43—22no—
126C8×Dic43—22no—
127C22×D4×C43C2×C411yescharacteristic
128C23×C4×C43—21no—
129C2×M16×C43—21no—
130C4×D4×C43—21no—
131C4×D4×C43—21no—
132C4×D4×C43C2×C412yes—
133C4×D4×C43C2312yes—
134C2×C4⋊C4×C43C2×C411yescharacteristic
135C2×C22⋊C4×C43—21no—
136C2×C42×C43C2311yescharacteristic
137C4⋊C8×C43C2312yes—
138C22⋊C8×C43—21no—
139#97×C43—21no—
140#97×C43—21no—
141C4×C8×C43C2312yes—
142C24×C43—21no—
143C23×D43C22⋊C411yescharacteristic
144C2×D4×C43—24no—
145C2×D4×C43—21no—
146C2×D4×C43C22×C412yes—
147C22×C4×C43—22no—
148C22×C4×C43—22no—
149C22×C4×C43—21no—
150C22×C4×C43—44no—
151C22×C4×C43C22×C411yescharacteristic
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43C2×D411yescharacteristic
154C2×C22⋊D43—28no—
155C2×C22⋊D43—22no—
156C2×C22⋊D43—22no—
157C22×Dic43—28no—
158C22×Dic43—22no—
159C22×Dic43—22no—
160C22×Dic43—22no—
161C22×Dic43—22no—
162C22×Dic43—21no—
163C22×Dic43—21no—
164C22×Dic43—44no—
165C22×Dic43C22⋊C411yescharacteristic
166C22×Dic43C22⋊C411yescharacteristic
167C22×Dic43C22⋊C411yescharacteristic
168#10621900—28no—
169#10621900—28no—
170#10621900—24no—
171#10621900—24no—
172#10621900—24no—
173#10621900M1618yescomplemented
174C2×C4×D43—24no—
175C2×C4×D43—24no—
176C2×C4×D43—42no—
177C2×C4×D43C22⋊C411yescharacteristic
178C2×C4×D43C22⋊C411yescharacteristic
179C2×C4×D43C22⋊C411yescharacteristic
180C2×C4×D43C22⋊C411yescharacteristic
181C2×C4×D43C22⋊C411yescharacteristic
182C2×C4×D43C22⋊C411yescharacteristic
183C2×C4×D43C22×C411yescharacteristic
184C2×C4×D43C22×C411yescharacteristic
185C2×C4×D43C2×D411yescharacteristic
186C2×C4×D43C2×D411yescharacteristic
187C2×C4×D43C2×D411yescharacteristic
188C2×C4×D43C2×D411yescharacteristic
189C2×Dic86—21no—
190C2×Dic86—24no—
191C2×Dic86C22×C412yes—
192M16×C43—24no—
193C2×C8×C43—22no—
194C2×C8×C43—22no—
195C4⋊C4×C43—21no—
196C4⋊C4×C43C22×C412yes—
197C22⋊C4×C43—22no—
198C22⋊C4×C43—22no—
199C42×C43C22×C411yescharacteristic
200C42×C43C2×D411yescharacteristic
201C42×C43C2×D411yescharacteristic
202C42×C43C2411yescharacteristic
203C22⋊Dic43—22no—
204C22⋊Dic43—22no—
205(C2×D43)⋊C4—22no—
206(C2×D43)⋊C4—22no—
207C4⋊Dic43—21no—
208C4⋊Dic43C22×C412yes—
209Dic43⋊C4—22no—
210Dic43⋊C4—22no—
211Dic43⋊C4—22no—
212Dic43⋊C4—22no—
213C4×Dic43—22no—
214C4×Dic43—22no—
215C4×Dic43—22no—
216C4×Dic43—22no—
217C4×Dic43—22no—
218C4×Dic43—22no—
219C4×Dic43C22⋊C411yescharacteristic
220C4×Dic43C22⋊C411yescharacteristic
221C4×Dic43C22⋊C411yescharacteristic
222C4×Dic43C22⋊C411yescharacteristic
223C4×Dic43C22⋊C411yescharacteristic
224C4×Dic43C22⋊C411yescharacteristic
225C4×Dic43C22×C411yescharacteristic
226C4×Dic43C22×C411yescharacteristic
227C4×Dic43C2×D411yescharacteristic
228C4×Dic43C2×D411yescharacteristic
229C4×Dic43C2×D411yescharacteristic
230C4×Dic43C2×D411yescharacteristic
231#10621877—24no—
232C2×C43⋊C8—22no—
233C2×C43⋊C8—22no—
234#10621872—28no—
235#10621872—44no—
236C8×D43—28no—
237C23×C43—24no—
238C23×C43—22no—
239C23×C43—42no—
240C23×C43—42no—
241C23×C43C2×C22⋊C411yescharacteristic
242C22×D43—22no—
243C22×D43—22no—
244C22×D43—41no—
245C22×D43C2×C22⋊C411yescharacteristic
246C22×D43C2×C22⋊C411yescharacteristic
247D4×C43—24no—
248D4×C43—22no—
249D4×C43C2×M1614yescomplemented
250C2×C4×C43—22no—
251C2×C4×C43—22no—
252C2×C4×C43—22no—
253C2×C4×C43—22no—
254C2×C4×C43—44no—
255C2×C4×C43—42no—
256C2×C4×C43—44no—
257C2×C4×C43C2×C22⋊C411yescharacteristic
258C2×C4×C43C2×C22⋊C411yescharacteristic
259C2×C4×C43C2×C22⋊C411yescharacteristic
260C2×C4×C43C23×C411yescharacteristic
261C2×C4×C43C22×D411yescharacteristic
262C2×C4×C43C22×D411yescharacteristic
263C22⋊D43—28no—
264C22⋊D43—28no—
265C2×Dic43—24no—
266C2×Dic43—28no—
267C2×Dic43—22no—
268C2×Dic43—22no—
269C2×Dic43—28no—
270C2×Dic43—22no—
271C2×Dic43—41no—
272C2×Dic43—42no—
273C2×Dic43—44no—
274C2×Dic43—44no—
275C2×Dic43#10414yes—
276C2×Dic43C2×C22⋊C411yescharacteristic
277C2×Dic43C2×C22⋊C411yescharacteristic
278C2×Dic43C2×C22⋊C411yescharacteristic
279C2×Dic43C2×C22⋊C411yescharacteristic
280C2×Dic43C2×C22⋊C411yescharacteristic
281C2×Dic43C2×C22⋊C411yescharacteristic
282C4×D43—22no—
283C4×D43—22no—
284C4×D43—22no—
285C4×D43—22no—
286C4×D43—22no—
287C4×D43—22no—
288C4×D43—22no—
289C4×D43—22no—
290C4×D43—22no—
291C4×D43—41no—
292C4×D43—41no—
293C4×D43C2×M1614yes—
294Dic86—24no—
295Dic86—22no—
296Dic86C2×M1614yescomplemented
297C8×C43—24no—
298C8×C43—42no—
299C43⋊C8—24no—
300C43⋊C8—42no—
301#17447—431nomaximal, Sylow
302C22×C43—21no—
303C22×C43—21no—
304C22×C43—24no—
305C22×C43—48no—
306C22×C43—42no—
307C22×C43—42no—
308C22×C43C2×#10412yes—
309C22×C43C22×C22⋊C411yescharacteristic
310C2×D43—21no—
311C2×D43—21no—
312C2×D43—21no—
313C2×D43—21no—
314C2×D43—21no—
315C2×D43—44no—
316C2×D43#40712yes—
317C4×C43—21no—
318C4×C43—21no—
319C4×C43—21no—
320C4×C43—21no—
321C4×C43—42no—
322C4×C43C22×M1612yes—
323C4×C43#57512yes—
324Dic43—24no—
325Dic43—21no—
326Dic43—21no—
327Dic43—21no—
328Dic43—42no—
329Dic43#40712yes—
330Dic43C2×#10412yes—
331Dic43C2×#10412yes—
332C2×C4×#41—431no—
333#2920—431no—
334C2×C4×M16—431no—
335#1491—431no—
336#1491—431no—
337#1490—431no—
338#1490D4311yescharacteristic, complemented
339#1489—434no—
340#1476—434no—
341C2×C43—22no—
342C2×C43—44no—
343C2×C43C2×#40711yescharacteristic
344C2×C43#289611yescharacteristic
345C2×C43C22×#10411yescharacteristic
346D43—22no—
347D43—41no—
348C22×#41—431no—
349C22×M16—861no—
350C4×#41—432no—
351C4×#41—432no—
352C4×#41—432no—
353C4×#41—432no—
354C4×#41—861no—
355C4×#41—861no—
356C4×#41—861no—
357C4×#41—861no—
358C2×C4×Q8—431no—
359C2×C4×Q8—431no—
360C2×C4×D4—431no—
361C2×C4×D4—861no—
362C2×C4×D4—861no—
363C2×C4×D4C2×D4311yescharacteristic
364C2×#117—431no—
365C2×#117—861no—
366C22×C42—431no—
367C22×C42—861no—
368#432—431no—
369#432—861no—
370#432C2×D4311yescharacteristic
371#431—432no—
372#431—861no—
373#423—432no—
374#407—861no—
375C4×M16—431no—
376C4×M16—432no—
377C4×M16—861no—
378C4×M16—861no—
379C4×M16—861no—
380C4×M16C2×D4311yescharacteristic
381C2×#97—861no—
382C2×C4×C8—432no—
383Q8⋊C8—434no—
384Q8⋊C8—434no—
385D4⋊C8—434no—
386D4⋊C8C2×D4314yescomplemented
387C43#1744711yescharacteristic, complemented, Sylow
388C2×#41—432no—
389C2×#41—432no—
390C2×#41—861no—
391C2×#41—861no—
392C2×#41—868no—
393C22×Q8—431no—
394C22×D4—861no—
395C22×D4C4×D4311yescharacteristic
396C23×C4—21no—
397C23×C4—431no—
398C23×C4—431no—
399C23×C4—431no—
400C23×C4—861no—
401C23×C4—861no—
402C2×M16—21no—
403C2×M16—862no—
404C2×M16—862no—
405C2×M16—868no—
406C2×M16—861no—
407C22×C8—862no—
408C4×Q8—432no—
409C4×Q8—432no—
410C4×Q8—432no—
411C4×Q8—432no—
412C4×Q8—861no—
413C4×Q8—861no—
414C4×Q8—861no—
415C4×Q8—861no—
416C4×D4—21no—
417C4×D4—21no—
418C4×D4—432no—
419C4×D4—432no—
420C4×D4—861no—
421C4×D4—861no—
422C4×D4—862no—
423C4×D4—862no—
424C4×D4—862no—
425C4×D4—862no—
426C4×D4—862no—
427C4×D4—862no—
428C4×D4—862no—
429C4×D4—862no—
430C4×D4C4×D4312yes—
431C4×D4C22×D4312yes—
432#117—432no—
433#117—432no—
434#117—862no—
435#117—862no—
436#117—862no—
437#117—862no—
438#117—861no—
439#117—861no—
440C2×C4⋊C4—431no—
441C2×C4⋊C4—861no—
442C2×C4⋊C4—861no—
443C2×C4⋊C4C4×D4311yescharacteristic
444C2×C22⋊C4—21no—
445C2×C22⋊C4—861no—
446C2×C22⋊C4—861no—
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—431no—
456C2×C42—431no—
457C2×C42—431no—
458C2×C42—862no—
459C2×C42—862no—
460C2×C42—862no—
461C2×C42—862no—
462C2×C42—861no—
463C2×C42—861no—
464C2×C42—861no—
465C2×C42C22×D4311yescharacteristic
466C4⋊C8—432no—
467C4⋊C8—862no—
468C4⋊C8C22×D4312yes—
469C22⋊C8—21no—
470C22⋊C8—862no—
471C22⋊C8—861no—
472#97—21no—
473#97—21no—
474#97—862no—
475#97—861no—
476#97—861no—
477C4×C8—432no—
478C4×C8—862no—
479C4×C8—862no—
480C4×C8C22×D4312yes—
481C24—21no—
482C24—431no—
483#41—438no—
484#41—864no—
485#41—864no—
486#41—868no—
487#41—868no—
488#41—864no—
489C2×Q8—432no—
490C2×Q8—864no—
491C2×Q8—861no—
492C2×D4—24no—
493C2×D4—21no—
494C2×D4—862no—
495C2×D4—862no—
496C2×D4—868no—
497C2×D4C2×C4×D4312yes—
498C22×C4—21no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—44no—
502C22×C4—431no—
503C22×C4—431no—
504C22×C4—431no—
505C22×C4—431no—
506C22×C4—431no—
507C22×C4—431no—
508C22×C4—431no—
509C22×C4—431no—
510C22×C4—431no—
511C22×C4—431no—
512C22×C4—431no—
513C22×C4—431no—
514C22×C4—431no—
515C22×C4—431no—
516C22×C4—431no—
517C22×C4—864no—
518C22×C4—864no—
519C22×C4—862no—
520C22×C4—862no—
521C22×C4—862no—
522C22×C4—862no—
523C22×C4—868no—
524C22×C4—861no—
525C22×C4—861no—
526C22×C4—1722no—
527C22×C4—1724no—
528C22×C4C2×C4×D4311yescharacteristic
529C22×C4D4×D4311yescharacteristic
530C22×C4D4×D4311yescharacteristic
531M16—24no—
532M16—868no—
533M16—864no—
534M16—1724no—
535C2×C8—22no—
536C2×C8—22no—
537C2×C8—868no—
538C2×C8—862no—
539C2×C8—862no—
540C4⋊C4—21no—
541C4⋊C4—432no—
542C4⋊C4—862no—
543C4⋊C4—862no—
544C4⋊C4—861no—
545C4⋊C4—862no—
546C4⋊C4—862no—
547C4⋊C4C2×C4×D4312yes—
548C22⋊C4—22no—
549C22⋊C4—22no—
550C22⋊C4—862no—
551C22⋊C4—862no—
552C22⋊C4—862no—
553C22⋊C4—862no—
554C42—431no—
555C42—431no—
556C42—431no—
557C42—431no—
558C42—431no—
559C42—431no—
560C42—431no—
561C42—431no—
562C42—431no—
563C42—431no—
564C42—431no—
565C42—431no—
566C42—862no—
567C42—862no—
568C42—862no—
569C42—862no—
570C42—862no—
571C42—862no—
572C42C2×C4×D4311yescharacteristic
573C42D4×D4311yescharacteristic
574C42D4×D4311yescharacteristic
575C42C23×D4311yescharacteristic
576C23—24no—
577C23—22no—
578C23—42no—
579C23—42no—
580C23—431no—
581C23—431no—
582C23—862no—
583C23—862no—
584C23—1721no—
585C23C22⋊C4×D4311yescharacteristic
586Q8—434no—
587Q8—864no—
588Q8—862no—
589D4—24no—
590D4—22no—
591D4—868no—
592D4—868no—
593D4M16×D4314yescomplemented
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—44no—
599C2×C4—42no—
600C2×C4—44no—
601C2×C4—431no—
602C2×C4—431no—
603C2×C4—431no—
604C2×C4—434no—
605C2×C4—434no—
606C2×C4—431no—
607C2×C4—431no—
608C2×C4—431no—
609C2×C4—862no—
610C2×C4—862no—
611C2×C4—862no—
612C2×C4—862no—
613C2×C4—862no—
614C2×C4—862no—
615C2×C4—862no—
616C2×C4—868no—
617C2×C4—864no—
618C2×C4—868no—
619C2×C4—862no—
620C2×C4—862no—
621C2×C4—862no—
622C2×C4—862no—
623C2×C4—862no—
624C2×C4—1721no—
625C2×C4—1721no—
626C2×C4—1724no—
627C2×C4—1724no—
628C2×C4—1721no—
629C2×C4—1722no—
630C2×C4C22⋊C4×D4311yescharacteristic
631C2×C4C22⋊C4×D4311yescharacteristic
632C2×C4C22⋊C4×D4311yescharacteristic
633C2×C4C22×C4×D4311yescharacteristic
634C2×C4C2×D4×D4311yescharacteristic
635C2×C4C2×D4×D4311yescharacteristic
636C8—24no—
637C8—42no—
638C8—864no—
639C8—1722no—
640C22—21no—
641C22—21no—
642C22—24no—
643C22—48no—
644C22—42no—
645C22—42no—
646C22—432no—
647C22—861no—
648C22—861no—
649C22—861no—
650C22—861no—
651C22—861no—
652C22—1724no—
653C22#104×D4312yes—
654C22C2×C22⋊C4×D4311yescharacteristic
655C4—21no—
656C4—21no—
657C4—21no—
658C4—21no—
659C4—42no—
660C4—432no—
661C4—432no—
662C4—432no—
663C4—861no—
664C4—864no—
665C4—861no—
666C4—861no—
667C4—1722no—
668C4C2×M16×D4312yes—
669C4#1458369512yes—
670C2—22no—
671C2—44no—
672C2—862no—
673C2—1721no—
674C2#407×D4311yescharacteristic
675C2#1914310911yescharacteristic
676C2C2×#104×D4311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1490C2
socleC22×C43C22×C22⋊C4
prime radicalC22×#10621900C4
cosocleC42×C43C24
hypercenter#1490D43
hypocenterC43#17447
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1490

Complements

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

NH ≅ G/Ntype
2. #19143225C2semidirect
3. C4×M16×D43C2semidirect
4. #19133043C2semidirect
5. #19133041C2semidirect
6. #19133038C2semidirect
7. #19133031C2semidirect
8. #19132974C2semidirect
9. C43×#1490C2semidirect
31. #14582951C22semidirect
33. #14582921C22semidirect
39. C4×#10621872C22semidirect
41. C4×C8×D43C22semidirect
42. #14582631C22semidirect
43. #14582629C22semidirect
44. D4⋊(C43⋊C8)C22semidirect
48. C43×D4⋊C8C22semidirect
173. #10621900M16semidirect
249. D4×C43C2×M16semidirect
296. Dic86C2×M16semidirect
338. #1490D43semidirect
386. D4⋊C8C2×D43semidirect
387. C43#17447semidirect
593. D4M16×D43semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#106219002
#191432252
C4×M16×D432
#191330432
#191330412
#191330382
#191330312
#191329742
C43×#14902
#1744743