Finite Group Databasebeta

← #25063062

Subgroups — #25063062

Order 11008.

1248 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#10621900C211yesmaximal, characteristic
2#19143226C211yesmaximal, characteristic, complemented
3#432×D43C211yesmaximal, characteristic, complemented
4#19133043C211yesmaximal, characteristic, complemented
5#19133041C211yesmaximal, characteristic, complemented
6#19133038C211yesmaximal, characteristic, complemented
7#19133026C214yesmaximal, complemented
8#19132979C214yesmaximal, complemented
9C43×#1490C211yesmaximal, 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#14582956C2211yescharacteristic
29#14582955C2212yescomplemented
30#14582954—21no—
31#14582954—21no—
32#14582954—21no—
33#14582953—21no—
34#14582950C2212yescomplemented
35#14582950C2212yescomplemented
36#14582922—21no—
37C4⋊C8×D43C2212yescomplemented
38#14582862—21no—
39C22⋊C8×D43—21no—
40C4×#10621877C2211yescharacteristic
41#97×D43—21no—
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×C8×D43—22no—
63C4×Dic86—21no—
64C4×Dic86—21no—
65C4×Dic86C2×C412yes—
66C4×Dic86C2312yes—
67#13063290—21no—
68#13063290—21no—
69#13063290C2×C412yes—
70#13063290C2×C412yes—
71D4×Dic43—21no—
72D4×Dic43—21no—
73D4×Dic43C2×C412yes—
74D4×Dic43C2×C412yes—
75C4×C22⋊D43—22no—
76C4×C22⋊D43—22no—
77C4×C22⋊D43—22no—
78C4×C22⋊D43—22no—
79(C22⋊D43)⋊C4—22no—
80(C22⋊D43)⋊C4—22no—
81(C22⋊D43)⋊C4—22no—
82(C22⋊D43)⋊C4—22no—
83#13063283—21no—
84#13063283—21no—
85#13063283C2×C412yes—
86#13063283C2×C412yes—
87#13063281—22no—
88#13063281—22no—
89#13063281—22no—
90#13063281—22no—
91C2×C4⋊Dic43C2×C411yescharacteristic
92C2×Dic43⋊C4—21no—
93C2×Dic43⋊C4—21no—
94C2×C22⋊Dic43—21no—
95C2×(C2×D43)⋊C4—21no—
96C2×C4×Dic43—21no—
97C2×C4×Dic43—21no—
98C2×C4×Dic43—21no—
99C2×C4×Dic43—22no—
100C2×C4×Dic43—22no—
101C2×C4×Dic43—22no—
102C2×C4×Dic43—22no—
103C2×C4×Dic43C2×C411yescharacteristic
104C2×C4×Dic43D411yescharacteristic
105C2×C4×Dic43D411yescharacteristic
106C42×D43C2×C411yescharacteristic
107C42×D43C2×C411yescharacteristic
108C42×D43D411yescharacteristic
109C42×D43D411yescharacteristic
110C42×D43D411yescharacteristic
111C42×D43D411yescharacteristic
112C42×D43C2311yescharacteristic
113C42×D43C2311yescharacteristic
114C4⋊(C43⋊C8)C2312yes—
115Dic43⋊C8—22no—
116Dic43⋊C8—22no—
117Dic43⋊C8—22no—
118C22⋊(C43⋊C8)—21no—
119(C2×D43)⋊C8—22no—
120(C2×D43)⋊C8—22no—
121(C2×D43)⋊C8—22no—
122#13063236—21no—
123#13063236—21no—
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×C43C2312yes—
137C22⋊C8×C43—21no—
138#97×C43—21no—
139#97×C43—21no—
140C4×C8×C43C2312yes—
141C24×C43—21no—
142C23×D43C22⋊C411yescharacteristic
143C2×D4×C43—24no—
144C2×D4×C43—21no—
145C2×D4×C43C22×C412yes—
146C22×C4×C43—22no—
147C22×C4×C43—22no—
148C22×C4×C43—21no—
149C22×C4×C43—44no—
150C22×C4×C43C22×C411yescharacteristic
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43C2×D411yescharacteristic
153C2×C22⋊D43—28no—
154C2×C22⋊D43—22no—
155C2×C22⋊D43—22no—
156C22×Dic43—28no—
157C22×Dic43—22no—
158C22×Dic43—22no—
159C22×Dic43—22no—
160C22×Dic43—22no—
161C22×Dic43—21no—
162C22×Dic43—21no—
163C22×Dic43—44no—
164C22×Dic43C22⋊C411yescharacteristic
165C22×Dic43C22⋊C411yescharacteristic
166C22×Dic43C22⋊C411yescharacteristic
167#10621900—28no—
168#10621900—28no—
169#10621900—24no—
170#10621900—24no—
171#10621900—24no—
172#10621900M1618yescomplemented
173C2×C4×D43—24no—
174C2×C4×D43—42no—
175C2×C4×D43—42no—
176C2×C4×D43C22⋊C411yescharacteristic
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×D43C2×D411yescharacteristic
185C2×C4×D43C2×D411yescharacteristic
186C2×C4×D43C2×D411yescharacteristic
187C2×C4×D43C2×D411yescharacteristic
188C2×Dic86—21no—
189C2×Dic86—24no—
190C2×Dic86C22×C412yes—
191M16×C43—42no—
192C2×C8×C43—22no—
193C2×C8×C43—22no—
194C4⋊C4×C43—21no—
195C4⋊C4×C43C22×C412yes—
196C22⋊C4×C43—22no—
197C22⋊C4×C43—22no—
198C42×C43C22×C411yescharacteristic
199C42×C43C2×D411yescharacteristic
200C42×C43C2×D411yescharacteristic
201C42×C43C2411yescharacteristic
202C22⋊Dic43—22no—
203C22⋊Dic43—22no—
204(C2×D43)⋊C4—22no—
205(C2×D43)⋊C4—22no—
206C4⋊Dic43—21no—
207C4⋊Dic43C22×C412yes—
208Dic43⋊C4—22no—
209Dic43⋊C4—22no—
210Dic43⋊C4—22no—
211Dic43⋊C4—22no—
212C4×Dic43—22no—
213C4×Dic43—22no—
214C4×Dic43—22no—
215C4×Dic43—22no—
216C4×Dic43—22no—
217C4×Dic43—22no—
218C4×Dic43C22⋊C411yescharacteristic
219C4×Dic43C22⋊C411yescharacteristic
220C4×Dic43C22⋊C411yescharacteristic
221C4×Dic43C22⋊C411yescharacteristic
222C4×Dic43C22⋊C411yescharacteristic
223C4×Dic43C22⋊C411yescharacteristic
224C4×Dic43C22×C411yescharacteristic
225C4×Dic43C22×C411yescharacteristic
226C4×Dic43C2×D411yescharacteristic
227C4×Dic43C2×D411yescharacteristic
228C4×Dic43C2×D411yescharacteristic
229C4×Dic43C2×D411yescharacteristic
230#10621877—42no—
231C2×C43⋊C8—22no—
232C2×C43⋊C8—22no—
233C8×D43—44no—
234C23×C43—24no—
235C23×C43—22no—
236C23×C43—42no—
237C23×C43—42no—
238C23×C43C2×C22⋊C411yescharacteristic
239C22×D43—22no—
240C22×D43—22no—
241C22×D43—41no—
242C22×D43C2×C22⋊C411yescharacteristic
243C22×D43C2×C22⋊C411yescharacteristic
244D4×C43—24no—
245D4×C43—22no—
246D4×C43C2×M1614yes—
247C2×C4×C43—22no—
248C2×C4×C43—22no—
249C2×C4×C43—22no—
250C2×C4×C43—22no—
251C2×C4×C43—44no—
252C2×C4×C43—42no—
253C2×C4×C43—44no—
254C2×C4×C43C2×C22⋊C411yescharacteristic
255C2×C4×C43C2×C22⋊C411yescharacteristic
256C2×C4×C43C2×C22⋊C411yescharacteristic
257C2×C4×C43C23×C411yescharacteristic
258C2×C4×C43C22×D411yescharacteristic
259C2×C4×C43C22×D411yescharacteristic
260C22⋊D43—28no—
261C22⋊D43—28no—
262C2×Dic43—24no—
263C2×Dic43—28no—
264C2×Dic43—22no—
265C2×Dic43—22no—
266C2×Dic43—22no—
267C2×Dic43—28no—
268C2×Dic43—22no—
269C2×Dic43—41no—
270C2×Dic43—44no—
271C2×Dic43—44no—
272C2×Dic43—42no—
273C2×Dic43C2×C22⋊C411yescharacteristic
274C2×Dic43C2×C22⋊C411yescharacteristic
275C2×Dic43C2×C22⋊C411yescharacteristic
276C2×Dic43C2×C22⋊C411yescharacteristic
277C2×Dic43C2×C22⋊C411yescharacteristic
278C2×Dic43C2×C22⋊C411yescharacteristic
279C4×D43—22no—
280C4×D43—22no—
281C4×D43—22no—
282C4×D43—22no—
283C4×D43—22no—
284C4×D43—41no—
285C4×D43—41no—
286C4×D43—41no—
287C4×D43—41no—
288C4×D43—41no—
289C4×D43—41no—
290C4×D43C2×M1614yes—
291Dic86—24no—
292Dic86—22no—
293Dic86C2×M1614yes—
294C8×C43—42no—
295C8×C43—42no—
296C43⋊C8—42no—
297C43⋊C8—42no—
298#17452—431nomaximal, Sylow
299C22×C43—21no—
300C22×C43—21no—
301C22×C43—24no—
302C22×C43—48no—
303C22×C43—42no—
304C22×C43—42no—
305C22×C43#42112yes—
306C22×C43C22×C22⋊C411yescharacteristic
307C2×D43—21no—
308C2×D43—21no—
309C2×D43—21no—
310C2×D43—21no—
311C2×D43—21no—
312C2×D43—44no—
313C2×D43#40712yes—
314C4×C43—21no—
315C4×C43—21no—
316C4×C43—21no—
317C4×C43—21no—
318C4×C43—42no—
319C4×C43C22×M1612yes—
320C4×C43#57512yes—
321Dic43—24no—
322Dic43—21no—
323Dic43—21no—
324Dic43—21no—
325Dic43—21no—
326Dic43—21no—
327Dic43—42no—
328Dic43#40712yes—
329C2×C4×#41—431no—
330#2920—431no—
331C2×#432—431no—
332#1491—431no—
333#1491—431no—
334#1490—431no—
335#1490D4311yescharacteristic, complemented
336#1488—434no—
337#1477—434no—
338C2×C43—22no—
339C2×C43—44no—
340C2×C43C2×#40711yescharacteristic
341C2×C43#289611yescharacteristic
342C2×C43C2×#42111yescharacteristic
343D43—22no—
344D43—41no—
345C22×#41—431no—
346C4×#41—432no—
347C4×#41—432no—
348C4×#41—432no—
349C4×#41—432no—
350C4×#41—861no—
351C4×#41—861no—
352C4×#41—861no—
353C4×#41—861no—
354C2×C4×Q8—431no—
355C2×C4×Q8—431no—
356C2×C4×D4—431no—
357C2×C4×D4—861no—
358C2×C4×D4—861no—
359C2×C4×D4C2×D4311yescharacteristic
360C2×#117—431no—
361C2×#117—861no—
362C22×C42—431no—
363C22×C42—861no—
364#432—431no—
365#432—432no—
366#432—861no—
367#432—861no—
368#432—861no—
369#432—861no—
370#432C2×D4311yescharacteristic
371#431—432no—
372#431—432no—
373#423—861no—
374C2×C4⋊C8—432no—
375#407—861no—
376C2×C22⋊C8—861no—
377C4×M16—431no—
378C4×M16C2×D4311yescharacteristic
379C2×#97—861no—
380Q8⋊C8—434no—
381Q8⋊C8—434no—
382D4⋊C8—434no—
383D4⋊C8C2×D4314yescomplemented
384C43#1745211yescharacteristic, complemented, Sylow
385C2×#41—432no—
386C2×#41—432no—
387C2×#41—861no—
388C2×#41—861no—
389C2×#41—868no—
390C22×Q8—431no—
391C22×D4—861no—
392C22×D4C4×D4311yescharacteristic
393C23×C4—21no—
394C23×C4—431no—
395C23×C4—431no—
396C23×C4—431no—
397C23×C4—861no—
398C23×C4—861no—
399C2×M16—21no—
400C2×M16—861no—
401C22×C8—862no—
402C4×Q8—432no—
403C4×Q8—432no—
404C4×Q8—432no—
405C4×Q8—432no—
406C4×Q8—861no—
407C4×Q8—861no—
408C4×Q8—861no—
409C4×Q8—861no—
410C4×D4—21no—
411C4×D4—21no—
412C4×D4—432no—
413C4×D4—432no—
414C4×D4—861no—
415C4×D4—861no—
416C4×D4—862no—
417C4×D4—862no—
418C4×D4—862no—
419C4×D4—862no—
420C4×D4—862no—
421C4×D4—862no—
422C4×D4—862no—
423C4×D4—862no—
424C4×D4C4×D4312yes—
425C4×D4C22×D4312yes—
426#117—432no—
427#117—432no—
428#117—862no—
429#117—862no—
430#117—862no—
431#117—862no—
432#117—861no—
433#117—861no—
434C2×C4⋊C4—431no—
435C2×C4⋊C4—861no—
436C2×C4⋊C4—861no—
437C2×C4⋊C4C4×D4311yescharacteristic
438C2×C22⋊C4—21no—
439C2×C22⋊C4—861no—
440C2×C22⋊C4—861no—
441C2×C42—431no—
442C2×C42—431no—
443C2×C42—431no—
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—862no—
453C2×C42—862no—
454C2×C42—862no—
455C2×C42—862no—
456C2×C42—861no—
457C2×C42—861no—
458C2×C42—861no—
459C2×C42C22×D4311yescharacteristic
460C4⋊C8—432no—
461C4⋊C8—862no—
462C4⋊C8—862no—
463C4⋊C8—862no—
464C4⋊C8C22×D4312yes—
465C22⋊C8—21no—
466C22⋊C8—862no—
467C22⋊C8—862no—
468C22⋊C8—862no—
469C22⋊C8—861no—
470#97—21no—
471#97—21no—
472#97—862no—
473#97—861no—
474#97—861no—
475C4×C8—432no—
476C4×C8C22×D4312yes—
477C24—21no—
478C24—431no—
479#41—438no—
480#41—864no—
481#41—864no—
482#41—868no—
483#41—868no—
484#41—864no—
485C2×Q8—432no—
486C2×Q8—864no—
487C2×Q8—861no—
488C2×D4—24no—
489C2×D4—21no—
490C2×D4—862no—
491C2×D4—862no—
492C2×D4—868no—
493C2×D4C2×C4×D4312yes—
494C22×C4—21no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—44no—
498C22×C4—431no—
499C22×C4—431no—
500C22×C4—431no—
501C22×C4—431no—
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—864no—
514C22×C4—862no—
515C22×C4—862no—
516C22×C4—862no—
517C22×C4—862no—
518C22×C4—868no—
519C22×C4—861no—
520C22×C4—861no—
521C22×C4—1722no—
522C22×C4—1722no—
523C22×C4—1724no—
524C22×C4C2×C4×D4311yescharacteristic
525C22×C4D4×D4311yescharacteristic
526C22×C4D4×D4311yescharacteristic
527M16—42no—
528M16—1722no—
529C2×C8—22no—
530C2×C8—22no—
531C2×C8—862no—
532C2×C8—862no—
533C2×C8—1724no—
534C4⋊C4—21no—
535C4⋊C4—432no—
536C4⋊C4—862no—
537C4⋊C4—862no—
538C4⋊C4—861no—
539C4⋊C4—862no—
540C4⋊C4—862no—
541C4⋊C4C2×C4×D4312yes—
542C22⋊C4—22no—
543C22⋊C4—22no—
544C22⋊C4—862no—
545C22⋊C4—862no—
546C22⋊C4—862no—
547C22⋊C4—862no—
548C42—431no—
549C42—431no—
550C42—431no—
551C42—431no—
552C42—431no—
553C42—431no—
554C42—431no—
555C42—431no—
556C42—431no—
557C42—431no—
558C42—431no—
559C42—431no—
560C42—862no—
561C42—862no—
562C42—862no—
563C42—862no—
564C42—862no—
565C42—862no—
566C42C2×C4×D4311yescharacteristic
567C42D4×D4311yescharacteristic
568C42D4×D4311yescharacteristic
569C42C23×D4311yescharacteristic
570C23—24no—
571C23—22no—
572C23—42no—
573C23—42no—
574C23—431no—
575C23—431no—
576C23—862no—
577C23—862no—
578C23—1721no—
579C23C22⋊C4×D4311yescharacteristic
580Q8—434no—
581Q8—864no—
582Q8—862no—
583D4—24no—
584D4—22no—
585D4—868no—
586D4—868no—
587D4M16×D4314yes—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—44no—
593C2×C4—42no—
594C2×C4—44no—
595C2×C4—431no—
596C2×C4—434no—
597C2×C4—431no—
598C2×C4—431no—
599C2×C4—431no—
600C2×C4—431no—
601C2×C4—431no—
602C2×C4—862no—
603C2×C4—862no—
604C2×C4—862no—
605C2×C4—868no—
606C2×C4—864no—
607C2×C4—868no—
608C2×C4—862no—
609C2×C4—862no—
610C2×C4—862no—
611C2×C4—862no—
612C2×C4—862no—
613C2×C4—862no—
614C2×C4—1721no—
615C2×C4—1721no—
616C2×C4—1721no—
617C2×C4—1721no—
618C2×C4—1721no—
619C2×C4—1721no—
620C2×C4—1721no—
621C2×C4—1724no—
622C2×C4—1724no—
623C2×C4—1722no—
624C2×C4C22⋊C4×D4311yescharacteristic
625C2×C4C22⋊C4×D4311yescharacteristic
626C2×C4C22⋊C4×D4311yescharacteristic
627C2×C4C22×C4×D4311yescharacteristic
628C2×C4C2×D4×D4311yescharacteristic
629C2×C4C2×D4×D4311yescharacteristic
630C8—42no—
631C8—42no—
632C8—1722no—
633C8—1722no—
634C22—21no—
635C22—21no—
636C22—24no—
637C22—48no—
638C22—42no—
639C22—42no—
640C22—432no—
641C22—861no—
642C22—861no—
643C22—861no—
644C22—861no—
645C22—861no—
646C22—1724no—
647C22#1458291412yes—
648C22C2×C22⋊C4×D4311yescharacteristic
649C4—21no—
650C4—21no—
651C4—21no—
652C4—21no—
653C4—42no—
654C4—432no—
655C4—861no—
656C4—864no—
657C4—861no—
658C4—861no—
659C4—861no—
660C4—861no—
661C4—1722no—
662C4C2×M16×D4312yes—
663C4#1458369512yes—
664C2—22no—
665C2—44no—
666C2—862no—
667C2—1721no—
668C2#407×D4311yescharacteristic
669C2#1914310911yescharacteristic
670C2C2×#1458291411yescharacteristic
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#17452
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. #19143226C2semidirect
3. #432×D43C2semidirect
4. #19133043C2semidirect
5. #19133041C2semidirect
6. #19133038C2semidirect
7. #19133026C2semidirect
8. #19132979C2semidirect
9. C43×#1490C2semidirect
29. #14582955C22semidirect
34. #14582950C22semidirect
35. #14582950C22semidirect
37. C4⋊C8×D43C22semidirect
42. #14582631C22semidirect
43. #14582629C22semidirect
44. D4⋊(C43⋊C8)C22semidirect
48. C43×D4⋊C8C22semidirect
172. #10621900M16semidirect
335. #1490D43semidirect
383. D4⋊C8C2×D43semidirect
384. C43#17452semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#106219002
#191432262
#432×D432
#191330432
#191330412
#191330382
#191330262
#191329792
C43×#14902
#1745243