Finite Group Databasebeta

← #25063047

Subgroups — #25063047

Order 11008.

1246 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#10621900C211yesmaximal, characteristic
2#19143223C211yesmaximal, characteristic, complemented
3#19143223C211yesmaximal, characteristic, complemented
4#19133031C214yesmaximal, complemented
5#19133026C214yesmaximal, complemented
6#19132991C211yesmaximal, characteristic, complemented
7#19132989C211yesmaximal, characteristic, complemented
8#19132986C211yesmaximal, characteristic, complemented
9C43×#1478C211yesmaximal, characteristic, complemented
10C22×#10621900C411yescharacteristic
11C4×#10621900—21no—
12C4×#10621900—21no—
13C4×#10621900—21no—
14C4×#10621900—21no—
15C4×#10621900C412yes—
16C4×#10621900C412yes—
17C4×#10621900C2212yes—
18C4×#10621900C2212yes—
19C2×C4×Dic86C2211yescharacteristic
20C2×#13063290C411yescharacteristic
21C2×D4×Dic43C411yescharacteristic
22C2×C4×C22⋊D43—21no—
23C2×(C22⋊D43)⋊C4—21no—
24C2×#13063283C411yescharacteristic
25C2×#13063281—21no—
26C22×C4×Dic43—21no—
27C2×C42×D43C2211yescharacteristic
28#14582955—21no—
29#14582955C2212yescomplemented
30#14582953—21no—
31#14582953—21no—
32#14582952C2211yescharacteristic
33#14582952C2211yescharacteristic
34#14582950—21no—
35#14582950C2212yescomplemented
36#14582921—21no—
37#14582921C2212yescomplemented
38#14582861—21no—
39#14582861—21no—
40C4×#10621872—21no—
41C4×#10621872C2212yescomplemented
42#14582631C2214yescomplemented
43#14582629C2214yescomplemented
44D4⋊(C43⋊C8)C2214yescomplemented
45C2×C4×D4×C43C2211yescharacteristic
46C43×#431C2211yescharacteristic
47C43×#431C2211yescharacteristic
48C43×D4⋊C8C2214yescomplemented
49C2×#10621900—24no—
50C2×#10621900—21no—
51C2×#10621900—21no—
52C2×#10621900—24no—
53C2×#10621900C2×C412yes—
54C2×#10621900C2×C412yes—
55C22×Dic86C2×C411yescharacteristic
56C22×C22⋊D43—21no—
57C23×Dic43—21no—
58C23×Dic43—21no—
59C22×C4×D43C2×C411yescharacteristic
60C22×C4×D43D411yescharacteristic
61C22×C4×D43D411yescharacteristic
62C2×#10621872—22no—
63C2×#10621872—22no—
64C4×Dic86—21no—
65C4×Dic86—21no—
66C4×Dic86C2×C412yes—
67C4×Dic86C2312yes—
68#13063290—21no—
69#13063290—21no—
70#13063290C2×C412yes—
71#13063290C2×C412yes—
72D4×Dic43—21no—
73D4×Dic43—21no—
74D4×Dic43C2×C412yes—
75D4×Dic43C2×C412yes—
76C4×C22⋊D43—22no—
77C4×C22⋊D43—22no—
78C4×C22⋊D43—22no—
79C4×C22⋊D43—22no—
80(C22⋊D43)⋊C4—22no—
81(C22⋊D43)⋊C4—22no—
82(C22⋊D43)⋊C4—22no—
83(C22⋊D43)⋊C4—22no—
84#13063283—21no—
85#13063283—21no—
86#13063283C2×C412yes—
87#13063283C2×C412yes—
88#13063281—22no—
89#13063281—22no—
90#13063281—22no—
91#13063281—22no—
92C2×C4⋊Dic43C2×C411yescharacteristic
93C2×Dic43⋊C4—21no—
94C2×Dic43⋊C4—21no—
95C2×C22⋊Dic43—21no—
96C2×(C2×D43)⋊C4—21no—
97C2×C4×Dic43—21no—
98C2×C4×Dic43—21no—
99C2×C4×Dic43—21no—
100C2×C4×Dic43—22no—
101C2×C4×Dic43—22no—
102C2×C4×Dic43—22no—
103C2×C4×Dic43—22no—
104C2×C4×Dic43C2×C411yescharacteristic
105C2×C4×Dic43D411yescharacteristic
106C2×C4×Dic43D411yescharacteristic
107C42×D43C2×C411yescharacteristic
108C42×D43C2×C411yescharacteristic
109C42×D43D411yescharacteristic
110C42×D43D411yescharacteristic
111C42×D43D411yescharacteristic
112C42×D43D411yescharacteristic
113C42×D43C2311yescharacteristic
114C42×D43C2311yescharacteristic
115C4⋊(C43⋊C8)—21no—
116C4⋊(C43⋊C8)C2312yes—
117Dic43⋊C8—22no—
118Dic43⋊C8—22no—
119C22⋊(C43⋊C8)—21no—
120C22⋊(C43⋊C8)—21no—
121(C2×D43)⋊C8—22no—
122(C2×D43)⋊C8—22no—
123#13063235—22no—
124#13063235—22no—
125C4×C43⋊C8—21no—
126C4×C43⋊C8C2312yes—
127C22×D4×C43C2×C411yescharacteristic
128C23×C4×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×C43C2312yes—
138C22⋊C8×C43—21no—
139C22⋊C8×C43—21no—
140C4×C8×C43—21no—
141C4×C8×C43C2312yes—
142C24×C43—21no—
143C23×D43C22⋊C411yescharacteristic
144C2×D4×C43—21no—
145C2×D4×C43—22no—
146C2×D4×C43M1614yescomplemented
147C2×D4×C43C22×C412yes—
148C22×C4×C43—22no—
149C22×C4×C43—22no—
150C22×C4×C43—21no—
151C22×C4×C43—44no—
152C22×C4×C43C22×C411yescharacteristic
153C22×C4×C43C2×D411yescharacteristic
154C22×C4×C43C2×D411yescharacteristic
155C2×C22⋊D43—28no—
156C2×C22⋊D43—22no—
157C2×C22⋊D43—22no—
158C22×Dic43—28no—
159C22×Dic43—22no—
160C22×Dic43—22no—
161C22×Dic43—22no—
162C22×Dic43—22no—
163C22×Dic43—21no—
164C22×Dic43—21no—
165C22×Dic43—44no—
166C22×Dic43C22⋊C411yescharacteristic
167C22×Dic43C22⋊C411yescharacteristic
168C22×Dic43C22⋊C411yescharacteristic
169#10621900—28no—
170#10621900—28no—
171#10621900—24no—
172#10621900—24no—
173#10621900—24no—
174#10621900—24no—
175C2×C4×D43—22no—
176C2×C4×D43—22no—
177C2×C4×D43—42no—
178C2×C4×D43—42no—
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×D43C22×C411yescharacteristic
186C2×C4×D43C22×C411yescharacteristic
187C2×C4×D43C2×D411yescharacteristic
188C2×C4×D43C2×D411yescharacteristic
189C2×C4×D43C2×D411yescharacteristic
190C2×C4×D43C2×D411yescharacteristic
191C2×Dic86—21no—
192C2×Dic86—22no—
193C2×Dic86M1614yescomplemented
194C2×Dic86C22×C412yes—
195C2×C8×C43—22no—
196C2×C8×C43—22no—
197C4⋊C4×C43—21no—
198C4⋊C4×C43C22×C412yes—
199C22⋊C4×C43—22no—
200C22⋊C4×C43—22no—
201C42×C43C22×C411yescharacteristic
202C42×C43C2×D411yescharacteristic
203C42×C43C2×D411yescharacteristic
204C42×C43C2411yescharacteristic
205C22⋊Dic43—22no—
206C22⋊Dic43—22no—
207(C2×D43)⋊C4—22no—
208(C2×D43)⋊C4—22no—
209C4⋊Dic43—21no—
210C4⋊Dic43C22×C412yes—
211Dic43⋊C4—22no—
212Dic43⋊C4—22no—
213Dic43⋊C4—22no—
214Dic43⋊C4—22no—
215C4×Dic43—22no—
216C4×Dic43—22no—
217C4×Dic43—22no—
218C4×Dic43—22no—
219C4×Dic43—22no—
220C4×Dic43—22no—
221C4×Dic43C22⋊C411yescharacteristic
222C4×Dic43C22⋊C411yescharacteristic
223C4×Dic43C22⋊C411yescharacteristic
224C4×Dic43C22⋊C411yescharacteristic
225C4×Dic43C22⋊C411yescharacteristic
226C4×Dic43C22⋊C411yescharacteristic
227C4×Dic43C22×C411yescharacteristic
228C4×Dic43C22×C411yescharacteristic
229C4×Dic43C2×D411yescharacteristic
230C4×Dic43C2×D411yescharacteristic
231C4×Dic43C2×D411yescharacteristic
232C4×Dic43C2×D411yescharacteristic
233C2×C43⋊C8—22no—
234C2×C43⋊C8—22no—
235#10621872—44no—
236#10621872—44no—
237C23×C43—22no—
238C23×C43—24no—
239C23×C43—42no—
240C23×C43—42no—
241C23×C43C2×C22⋊C411yescharacteristic
242C22×D43—22no—
243C22×D43—41no—
244C22×D43—41no—
245C22×D43C2×C22⋊C411yescharacteristic
246C22×D43C2×C22⋊C411yescharacteristic
247D4×C43—22no—
248D4×C43—24no—
249D4×C43C2×M1614yes—
250C2×C4×C43—22no—
251C2×C4×C43—22no—
252C2×C4×C43—41no—
253C2×C4×C43—44no—
254C2×C4×C43—42no—
255C2×C4×C43—44no—
256C2×C4×C43C2×C22⋊C411yescharacteristic
257C2×C4×C43C2×C22⋊C411yescharacteristic
258C2×C4×C43C2×C22⋊C411yescharacteristic
259C2×C4×C43C2×M1612yes—
260C2×C4×C43C2×M1612yes—
261C2×C4×C43C23×C411yescharacteristic
262C2×C4×C43C22×D411yescharacteristic
263C2×C4×C43C22×D411yescharacteristic
264C22⋊D43—28no—
265C22⋊D43—28no—
266C2×Dic43—28no—
267C2×Dic43—28no—
268C2×Dic43—22no—
269C2×Dic43—24no—
270C2×Dic43—22no—
271C2×Dic43—22no—
272C2×Dic43—22no—
273C2×Dic43—41no—
274C2×Dic43—44no—
275C2×Dic43—42no—
276C2×Dic43—44no—
277C2×Dic43C2×C22⋊C411yescharacteristic
278C2×Dic43C2×C22⋊C411yescharacteristic
279C2×Dic43C2×C22⋊C411yescharacteristic
280C2×Dic43C2×C22⋊C411yescharacteristic
281C2×Dic43C2×C22⋊C411yescharacteristic
282C2×Dic43C2×C22⋊C411yescharacteristic
283C4×D43—21no—
284C4×D43—21no—
285C4×D43—21no—
286C4×D43—21no—
287C4×D43—22no—
288C4×D43—22no—
289C4×D43—22no—
290C4×D43—22no—
291C4×D43—22no—
292C4×D43—22no—
293C4×D43—41no—
294C4×D43—41no—
295C4×D43—41no—
296C4×D43—41no—
297Dic86—22no—
298Dic86—24no—
299Dic86C2×M1614yes—
300C8×C43—42no—
301C8×C43—42no—
302C43⋊C8—42no—
303C43⋊C8—42no—
304#17450—431nomaximal, Sylow
305C22×C43—21no—
306C22×C43—21no—
307C22×C43—24no—
308C22×C43—48no—
309C22×C43—42no—
310C22×C43—42no—
311C22×C43#40712yes—
312C22×C43C22×C22⋊C411yescharacteristic
313C2×D43—21no—
314C2×D43—21no—
315C2×D43—21no—
316C2×D43—21no—
317C2×D43—21no—
318C2×D43—21no—
319C2×D43—44no—
320C4×C43—21no—
321C4×C43—21no—
322C4×C43—21no—
323C4×C43—42no—
324C4×C43#40712yes—
325C4×C43C22×M1611yescharacteristic
326C4×C43C22×M1611yescharacteristic
327C4×C43#57512yes—
328Dic43—24no—
329Dic43—21no—
330Dic43—21no—
331Dic43—21no—
332Dic43—21no—
333Dic43—21no—
334Dic43—42no—
335Dic43#42112yes—
336C2×C4×#41—431no—
337#2920—431no—
338#2920—431no—
339#1489—434no—
340#1488—434no—
341#1479—431no—
342#1479—431no—
343#1478—431no—
344#1478D4311yescharacteristic, complemented
345C2×C43—22no—
346C2×C43—44no—
347C2×C43C2×#40711yescharacteristic
348C2×C43#289611yescharacteristic
349C2×C43C2×#42111yescharacteristic
350D43—41no—
351D43—41no—
352C22×#41—431no—
353C4×#41—432no—
354C4×#41—432no—
355C4×#41—432no—
356C4×#41—432no—
357C4×#41—861no—
358C4×#41—861no—
359C4×#41—861no—
360C4×#41—861no—
361C2×C4×Q8—431no—
362C2×C4×Q8—431no—
363C2×C4×D4—431no—
364C2×C4×D4—861no—
365C2×C4×D4—861no—
366C2×C4×D4C2×D4311yescharacteristic
367C2×#117—431no—
368C2×#117—861no—
369C22×C42—431no—
370C22×C42—861no—
371#432—432no—
372#432—861no—
373#432—861no—
374#432—861no—
375#431—431no—
376#431—432no—
377#431—431no—
378#431—861no—
379#431C2×D4311yescharacteristic
380#431C2×D4311yescharacteristic
381#423—432no—
382#423—861no—
383#407—861no—
384#407—861no—
385C4×M16—432no—
386C4×M16—861no—
387Q8⋊C8—434no—
388Q8⋊C8—434no—
389D4⋊C8—434no—
390D4⋊C8C2×D4314yescomplemented
391C43#1745011yescharacteristic, complemented, Sylow
392C2×#41—432no—
393C2×#41—432no—
394C2×#41—861no—
395C2×#41—861no—
396C2×#41—864no—
397C2×#41—864no—
398C22×Q8—431no—
399C22×D4—861no—
400C22×D4C4×D4311yescharacteristic
401C23×C4—21no—
402C23×C4—431no—
403C23×C4—431no—
404C23×C4—431no—
405C23×C4—861no—
406C23×C4—861no—
407C2×M16—862no—
408C2×M16—862no—
409C4×Q8—432no—
410C4×Q8—432no—
411C4×Q8—432no—
412C4×Q8—432no—
413C4×Q8—861no—
414C4×Q8—861no—
415C4×Q8—861no—
416C4×Q8—861no—
417C4×D4—21no—
418C4×D4—21no—
419C4×D4—432no—
420C4×D4—432no—
421C4×D4—861no—
422C4×D4—861no—
423C4×D4—862no—
424C4×D4—862no—
425C4×D4—862no—
426C4×D4—862no—
427C4×D4—862no—
428C4×D4—862no—
429C4×D4—862no—
430C4×D4—862no—
431C4×D4C4×D4312yes—
432C4×D4C22×D4312yes—
433#117—432no—
434#117—432no—
435#117—862no—
436#117—862no—
437#117—862no—
438#117—862no—
439#117—861no—
440#117—861no—
441C2×C4⋊C4—431no—
442C2×C4⋊C4—861no—
443C2×C4⋊C4—861no—
444C2×C4⋊C4C4×D4311yescharacteristic
445C2×C22⋊C4—21no—
446C2×C22⋊C4—861no—
447C2×C22⋊C4—861no—
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—431no—
459C2×C42—862no—
460C2×C42—862no—
461C2×C42—862no—
462C2×C42—862no—
463C2×C42—861no—
464C2×C42—861no—
465C2×C42—861no—
466C2×C42C22×D4311yescharacteristic
467C4⋊C8—21no—
468C4⋊C8—432no—
469C4⋊C8—862no—
470C4⋊C8—862no—
471C4⋊C8—861no—
472C4⋊C8C22×D4312yes—
473C22⋊C8—21no—
474C22⋊C8—21no—
475C22⋊C8—862no—
476C22⋊C8—862no—
477C22⋊C8—861no—
478C22⋊C8—861no—
479#97—862no—
480#97—862no—
481C4×C8—21no—
482C4×C8—432no—
483C4×C8—861no—
484C4×C8C22×D4312yes—
485C24—21no—
486C24—431no—
487#41—864no—
488#41—864no—
489#41—868no—
490#41—868no—
491#41—864no—
492#41—864no—
493C2×Q8—434no—
494C2×Q8—432no—
495C2×Q8—861no—
496C2×Q8—862no—
497C2×D4—21no—
498C2×D4—22no—
499C2×D4—862no—
500C2×D4—862no—
501C2×D4—868no—
502C2×D4#1062187214yescomplemented
503C2×D4C2×C4×D4312yes—
504C22×C4—21no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—44no—
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—431no—
518C22×C4—431no—
519C22×C4—431no—
520C22×C4—431no—
521C22×C4—431no—
522C22×C4—431no—
523C22×C4—862no—
524C22×C4—862no—
525C22×C4—862no—
526C22×C4—862no—
527C22×C4—868no—
528C22×C4—861no—
529C22×C4—862no—
530C22×C4—862no—
531C22×C4—861no—
532C22×C4—1722no—
533C22×C4—1722no—
534C22×C4—1724no—
535C22×C4C2×C4×D4311yescharacteristic
536C22×C4D4×D4311yescharacteristic
537C22×C4D4×D4311yescharacteristic
538M16—1724no—
539M16—1724no—
540C2×C8—22no—
541C2×C8—22no—
542C2×C8—862no—
543C2×C8—862no—
544C4⋊C4—21no—
545C4⋊C4—432no—
546C4⋊C4—862no—
547C4⋊C4—862no—
548C4⋊C4—861no—
549C4⋊C4—862no—
550C4⋊C4—862no—
551C4⋊C4C2×C4×D4312yes—
552C22⋊C4—22no—
553C22⋊C4—22no—
554C22⋊C4—862no—
555C22⋊C4—862no—
556C22⋊C4—862no—
557C22⋊C4—862no—
558C42—431no—
559C42—431no—
560C42—431no—
561C42—431no—
562C42—431no—
563C42—431no—
564C42—431no—
565C42—431no—
566C42—431no—
567C42—431no—
568C42—431no—
569C42—431no—
570C42—862no—
571C42—862no—
572C42—862no—
573C42—862no—
574C42—862no—
575C42—862no—
576C42C2×C4×D4311yescharacteristic
577C42D4×D4311yescharacteristic
578C42D4×D4311yescharacteristic
579C42C23×D4311yescharacteristic
580C23—22no—
581C23—24no—
582C23—42no—
583C23—42no—
584C23—431no—
585C23—431no—
586C23—862no—
587C23—1721no—
588C23—1721no—
589C23C22⋊C4×D4311yescharacteristic
590Q8—434no—
591Q8—864no—
592Q8—862no—
593D4—24no—
594D4—22no—
595D4—868no—
596D4—868no—
597D4C2×#1062187214yes—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—41no—
601C2×C4—44no—
602C2×C4—42no—
603C2×C4—44no—
604C2×C4—431no—
605C2×C4—431no—
606C2×C4—431no—
607C2×C4—431no—
608C2×C4—431no—
609C2×C4—431no—
610C2×C4—862no—
611C2×C4—862no—
612C2×C4—862no—
613C2×C4—868no—
614C2×C4—868no—
615C2×C4—862no—
616C2×C4—862no—
617C2×C4—864no—
618C2×C4—862no—
619C2×C4—862no—
620C2×C4—861no—
621C2×C4—861no—
622C2×C4—861no—
623C2×C4—861no—
624C2×C4—862no—
625C2×C4—862no—
626C2×C4—862no—
627C2×C4—1721no—
628C2×C4—1721no—
629C2×C4—1721no—
630C2×C4—1721no—
631C2×C4—1724no—
632C2×C4—1721no—
633C2×C4—1724no—
634C2×C4—1722no—
635C2×C4C22⋊C4×D4311yescharacteristic
636C2×C4C22⋊C4×D4311yescharacteristic
637C2×C4C22⋊C4×D4311yescharacteristic
638C2×C4M16×D4312yes—
639C2×C4C2×#1062187212yes—
640C2×C4C22×C4×D4311yescharacteristic
641C2×C4C2×D4×D4311yescharacteristic
642C2×C4C2×D4×D4311yescharacteristic
643C8—42no—
644C8—42no—
645C8—1722no—
646C8—1722no—
647C22—21no—
648C22—21no—
649C22—24no—
650C22—48no—
651C22—42no—
652C22—42no—
653C22—861no—
654C22—861no—
655C22—861no—
656C22—861no—
657C22—861no—
658C22—861no—
659C22—1724no—
660C22#1458286112yes—
661C22C2×C22⋊C4×D4311yescharacteristic
662C4—21no—
663C4—21no—
664C4—21no—
665C4—42no—
666C4—432no—
667C4—861no—
668C4—861no—
669C4—864no—
670C4—861no—
671C4—861no—
672C4—861no—
673C4—1722no—
674C4#1458286112yes—
675C4C2×M16×D4311yescharacteristic
676C4C22×#1062187211yescharacteristic
677C4#1458369512yes—
678C2—22no—
679C2—44no—
680C2—1721no—
681C2—1721no—
682C2C2×#1458286111yescharacteristic
683C2#1914310911yescharacteristic
684C2#421×D4311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1478C2
socleC22×C43C22×C22⋊C4
prime radicalC22×#10621900C4
cosocleC42×C43C24
hypercenter#1478D43
hypocenterC43#17450
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1478

Complements

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

NH ≅ G/Ntype
2. #19143223C2semidirect
3. #19143223C2semidirect
4. #19133031C2semidirect
5. #19133026C2semidirect
6. #19132991C2semidirect
7. #19132989C2semidirect
8. #19132986C2semidirect
9. C43×#1478C2semidirect
29. #14582955C22semidirect
35. #14582950C22semidirect
37. #14582921C22semidirect
41. C4×#10621872C22semidirect
42. #14582631C22semidirect
43. #14582629C22semidirect
44. D4⋊(C43⋊C8)C22semidirect
48. C43×D4⋊C8C22semidirect
146. C2×D4×C43M16semidirect
193. C2×Dic86M16semidirect
344. #1478D43semidirect
390. D4⋊C8C2×D43semidirect
391. C43#17450semidirect
502. C2×D4#10621872semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#106219002
#191432232
#191330312
#191330262
#191329912
#191329892
#191329862
C43×#14782
#1745043