Finite Group Databasebeta

← #25105015

Subgroups — #25105015

Order 11008.

1254 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
1C2×#14583270C211yesmaximal, characteristic
2C2×#14582990C211yesmaximal, characteristic, complemented
3C2×SD16×Dic43C211yesmaximal, characteristic, complemented
4C2×#14582986C211yesmaximal, characteristic, complemented
5C2×#14582984C211yesmaximal, characteristic, complemented
6#19137164C211yesmaximal, characteristic, complemented
7#19137159C211yesmaximal, characteristic
8#19135452C211yesmaximal, characteristic, complemented
9#19135449C211yesmaximal, characteristic, complemented
10#19135448C211yesmaximal, characteristic, complemented
11#19135399C211yesmaximal, characteristic
12#19135395C211yesmaximal, characteristic, complemented
13#19134750C211yesmaximal, characteristic, complemented
14C4×C8×Dic43C211yesmaximal, characteristic, complemented
15C43×#1968C211yesmaximal, characteristic, complemented
16C22×#10621873C2211yescharacteristic
17C22×#10621883C2211yescharacteristic
18C22×#10621884C2211yescharacteristic
19C2×#13063323C2211yescharacteristic
20C2×#13063321C2211yescharacteristic
21C2×Q8×Dic43C2211yescharacteristic
22C2×#13063290C2211yescharacteristic
23C2×D4×Dic43C2211yescharacteristic
24C2×#13063287C2211yescharacteristic
25C2×(C22⋊D43)⋊C4—22no—
26#14583270C418yescomplemented
27#14582990—24no—
28SD16×Dic43—24no—
29#14582986—24no—
30#14582984—24no—
31C2×#13063257C2211yescharacteristic
32C2×#13063256C2211yescharacteristic
33C2×#13063256C2211yescharacteristic
34C2×#13063250C2211yescharacteristic
35C2×#13063249C2211yescharacteristic
36C2×#13063248C2211yescharacteristic
37C2×#13063247C2211yescharacteristic
38C2×#13063246C2211yescharacteristic
39C2×#13063245C2211yescharacteristic
40C2×C4×C43⋊C8C2211yescharacteristic
41C2×C8×Dic43C2211yescharacteristic
42C2×C8×Dic43C2211yescharacteristic
43C2×C8×Dic43C2211yescharacteristic
44C2×C8×Dic43C2211yescharacteristic
45#14582805C2211yescharacteristic
46#14582801C2211yescharacteristic
47#14582799—22no—
48#14582796—22no—
49#14582768C2211yescharacteristic
50#14582768C2211yescharacteristic
51#14582750—22no—
52C42×Dic43C2211yescharacteristic
53C22×SD16×C43C2211yescharacteristic
54C2×#106×C43C2211yescharacteristic
55C2×#103×C43C2211yescharacteristic
56C2×#102×C43C2211yescharacteristic
57C2×C4×C8×C43C2211yescharacteristic
58C43×#391C2211yescharacteristic
59C43×#390C2211yescharacteristic
60C22×Dic86C2311yescharacteristic
61C22×D172C2311yescharacteristic
62C22×C22⋊D43—22no—
63C23×Dic43—21no—
64C22×C4×D43—21no—
65C2×#10621873—22no—
66C2×#10621873—22no—
67C2×#10621873C2×C414yescomplemented
68C2×#10621883—22no—
69C2×#10621883—22no—
70C2×#10621883C2×C414yescomplemented
71C2×#10621884—22no—
72C2×#10621884—22no—
73C2×#10621884C2×C414yescomplemented
74C22×C43⋊C8C2311yescharacteristic
75C22×C43⋊C8C2311yescharacteristic
76#13063323—22no—
77#13063323C2×C414yescomplemented
78#13063321—22no—
79#13063321C2×C414yes—
80Q8×Dic43—22no—
81Q8×Dic43—22no—
82#13063290—22no—
83#13063290—22no—
84D4×Dic43—22no—
85D4×Dic43—22no—
86#13063287—22no—
87#13063287—22no—
88(C22⋊D43)⋊C4—48no—
89C2×C4⋊Dic43—21no—
90C2×C4⋊Dic43C2311yescharacteristic
91C2×C4⋊Dic43C2311yescharacteristic
92C2×Dic43⋊C4—22no—
93C2×Dic43⋊C4—21no—
94C2×Dic43⋊C4—22no—
95C2×Dic43⋊C4—22no—
96C2×C22⋊Dic43—21no—
97C2×(C2×D43)⋊C4—22no—
98C2×(C2×D43)⋊C4—21no—
99C2×C4×Dic43—21no—
100C2×C4×Dic43—21no—
101C2×C4×Dic43D412yes—
102C2×C4×Dic43D412yes—
103C2×C4×Dic43C2311yescharacteristic
104C2×C4×Dic43C2311yescharacteristic
105#13063257—22no—
106#13063256—22no—
107#13063256—22no—
108#13063250—22no—
109#13063249—22no—
110#13063248—22no—
111#13063247—22no—
112#13063246—22no—
113#13063245—22no—
114C4×C43⋊C8—22no—
115C8×Dic43—22no—
116C8×Dic43C2×C414yescomplemented
117C8×Dic43D414yescomplemented
118C8×Dic43D414yescomplemented
119C43⋊#95—22no—
120C22×Q8×C43C2311yescharacteristic
121C22×D4×C43C2311yescharacteristic
122C2×SD16×C43—22no—
123C2×SD16×C43—22no—
124C2×SD16×C43C2×C414yescomplemented
125C22×C8×C43C2311yescharacteristic
126C22×C8×C43C2311yescharacteristic
127C2×C4⋊C4×C43C2311yescharacteristic
128C2×C4⋊C4×C43C2311yescharacteristic
129C2×C22⋊C4×C43—22no—
130C2×C42×C43C2311yescharacteristic
131#106×C43—22no—
132#103×C43—22no—
133#102×C43—22no—
134C4×C8×C43—22no—
135#95×C43—22no—
136C24×C43—21no—
137C23×D43—21no—
138C2×Q8×C43—21no—
139C2×Q8×C43—21no—
140C2×Q8×C43—21no—
141C2×Q8×C43—21no—
142C2×Q8×C43—21no—
143C2×Q8×C43C22×C412yes—
144C2×D4×C43—21no—
145C2×D4×C43—21no—
146C2×D4×C43—21no—
147C2×D4×C43—21no—
148C2×D4×C43—21no—
149C2×D4×C43C22×C412yes—
150C22×C4×C43—21no—
151C22×C4×C43—21no—
152C22×C4×C43—21no—
153C22×C4×C43C2×D412yes—
154C22×C4×C43C2411yescharacteristic
155C2×C22⋊D43—28no—
156C2×C22⋊D43—44no—
157C2×C22⋊D43—44no—
158C22×Dic43—21no—
159C22×Dic43—21no—
160C22×Dic43—21no—
161C22×Dic43—42no—
162C22×Dic43—44no—
163C22×Dic43C2×D411yescharacteristic
164C22×Dic43C2×D412yes—
165C22×Dic43C2×D411yescharacteristic
166C2×D172—21no—
167C2×D172—21no—
168C2×D172—21no—
169C2×D172—21no—
170C2×D172—21no—
171C2×D172C22×C412yes—
172C2×C4×D43—42no—
173C2×C4×D43—44no—
174C2×Dic86—21no—
175C2×Dic86—21no—
176C2×Dic86—21no—
177C2×Dic86—21no—
178C2×Dic86—21no—
179C2×Dic86C22×C412yes—
180SD16×C43—28no—
181C2×C8×C43—21no—
182C2×C8×C43—21no—
183C2×C8×C43C22×C412yes—
184C2×C8×C43C2×D412yes—
185C2×C8×C43C2×D412yes—
186C2×C8×C43#4112yes—
187C4⋊C4×C43—21no—
188C4⋊C4×C43—21no—
189C4⋊C4×C43—21no—
190C4⋊C4×C43—21no—
191C22⋊C4×C43—44no—
192C42×C43—21no—
193C42×C43—21no—
194C22⋊Dic43—42no—
195#10621884—28no—
196#10621883—28no—
197(C2×D43)⋊C4—44no—
198(C2×D43)⋊C4—42no—
199C4⋊Dic43—21no—
200C4⋊Dic43—21no—
201C4⋊Dic43—21no—
202C4⋊Dic43—21no—
203C4⋊Dic43—42no—
204Dic43⋊C4—28no—
205Dic43⋊C4—42no—
206Dic43⋊C4—44no—
207Dic43⋊C4—44no—
208C4×Dic43—24no—
209C4×Dic43—42no—
210C4×Dic43—42no—
211C4×Dic43SD1618yescomplemented
212C4×Dic43C22×C412yes—
213C4×Dic43C2×D412yes—
214C4×Dic43C2×D412yes—
215C4×Dic43#4112yes—
216C2×C43⋊C8—21no—
217C2×C43⋊C8—21no—
218C2×C43⋊C8C22×C412yes—
219C2×C43⋊C8C2×D412yes—
220C2×C43⋊C8C2×D412yes—
221C2×C43⋊C8#4112yes—
222#10621873—28no—
223C23×C43—22no—
224C23×C43—41no—
225C23×C43—41no—
226C23×C43—42no—
227C23×C43—42no—
228C23×C43C22×D411yescharacteristic
229C22×D43—22no—
230C22×D43—41no—
231C22×D43—41no—
232C22×D43—42no—
233C22×D43—42no—
234Q8×C43—22no—
235Q8×C43—22no—
236Q8×C43—41no—
237Q8×C43—41no—
238D4×C43—22no—
239D4×C43—22no—
240D4×C43—41no—
241D4×C43—41no—
242C2×C4×C43—22no—
243C2×C4×C43—22no—
244C2×C4×C43—22no—
245C2×C4×C43—41no—
246C2×C4×C43—41no—
247C2×C4×C43—41no—
248C2×C4×C43—41no—
249C2×C4×C43—42no—
250C2×C4×C43—42no—
251C2×C4×C43C2×SD1614yes—
252C2×C4×C43C23×C411yescharacteristic
253C2×C4×C43C22×D411yescharacteristic
254C2×C4×C43C22×D411yescharacteristic
255C2×C4×C43C2×#4111yescharacteristic
256C2×C4×C43C2×#4111yescharacteristic
257C2×C4×C43C2×#4111yescharacteristic
258C22⋊D43—416no—
259C2×Dic43—22no—
260C2×Dic43—22no—
261C2×Dic43—41no—
262C2×Dic43—41no—
263C2×Dic43—41no—
264C2×Dic43—41no—
265C2×Dic43—42no—
266C2×Dic43—42no—
267C2×Dic43—84no—
268C2×Dic43C4×D414yes—
269C2×Dic43#12712yes—
270C2×Dic43#12712yes—
271C2×Dic43C2×SD1614yes—
272C2×Dic43C2×SD1614yes—
273C2×Dic43#13514yes—
274D172—22no—
275D172—22no—
276D172—41no—
277D172—41no—
278C4×D43—84no—
279Dic86—22no—
280Dic86—22no—
281Dic86—41no—
282Dic86—41no—
283C8×C43—22no—
284C8×C43C4×D414yescomplemented
285C43⋊C8—22no—
286C43⋊C8C4×D414yescomplemented
287C4×#492—431nomaximal, Sylow
288C22×C43—42no—
289C22×C43—44no—
290C22×C43—81no—
291C22×C43—81no—
292C22×C43—82no—
293C22×C43C2×C4×D411yescharacteristic
294C22×C43C2×#12711yescharacteristic
295C22×C43#53211yescharacteristic
296C22×C43C22×SD1612yes—
297C22×C43C2×#13512yes—
298C2×D43—42no—
299C2×D43—44no—
300C2×D43—81no—
301C2×D43—81no—
302C2×D43—82no—
303C4×C43—24no—
304C4×C43—42no—
305C4×C43—81no—
306C4×C43—81no—
307C4×C43C2×C4×D411yescharacteristic
308C4×C43C2×C4×D411yescharacteristic
309C4×C43#53211yescharacteristic
310C4×C43#53211yescharacteristic
311Dic43—22no—
312Dic43—42no—
313Dic43—81no—
314Dic43—81no—
315Dic43C4×SD1618yescomplemented
316Dic43#49214yescomplemented
317C2×#492—431no—
318C2×C4×SD16—431no—
319C2×C4×SD16—431no—
320C2×C4×SD16—431no—
321C2×C4×SD16—431no—
322C4×C4⋊Q8—431no—
323C4×#127—431no—
324#1968—431no—
325#1968—431no—
326#1968—431no—
327#1968D4311yescharacteristic, complemented
328#1957—431no—
329#1956—431no—
330#1844—431no—
331C42×C8—431no—
332C2×C43—82no—
333C2×C43C4×#12711yescharacteristic
334C2×C43C2×C4×SD1612yes—
335C2×C43C2×#49211yescharacteristic
336C2×C43#314711yescharacteristic
337C2×C43#316712yes—
338D43—82no—
339C22×SD16—431no—
340C22×SD16—431no—
341C22×SD16—431no—
342C22×SD16C2×D4311yescharacteristic
343C2×C4⋊Q8—431no—
344C2×#127—431no—
345C2×C4×Q8—431no—
346C2×C4×Q8—431no—
347C2×C4×D4—431no—
348C2×C4×D4—431no—
349C2×C4×D4—862no—
350#492—438no—
351C4×SD16—864no—
352C4×SD16—864no—
353C4×SD16—864no—
354C4×SD16—864no—
355C2×#106—431no—
356C2×#106—431no—
357C2×#106—431no—
358C2×#106C2×D4311yescharacteristic
359C2×#103—431no—
360C2×#103—431no—
361C2×#103—431no—
362C2×#103C2×D4311yescharacteristic
363C2×#102—431no—
364C2×#102—431no—
365C2×#102—431no—
366C2×#102C2×D4311yescharacteristic
367C2×C4×C8—431no—
368C2×C4×C8—431no—
369C2×C4×C8—431no—
370C2×C4×C8—431no—
371C2×C4×C8—431no—
372C2×C4×C8C2×D4311yescharacteristic
373#391—431no—
374#391C2×D4311yescharacteristic
375#390—431no—
376#390—862no—
377#390C2×D4311yescharacteristic
378#389—862no—
379#384—431no—
380#384—431no—
381C4×C4⋊C4—862no—
382C43—431no—
383C43C4×#49211yescharacteristic, complemented, Sylow
384C22×Q8—431no—
385C22×Q8C22×D4311yescharacteristic
386C22×D4—431no—
387C22×D4—862no—
388C22×D4C22×D4311yescharacteristic
389C23×C4—861no—
390C23×C4—861no—
391C2×SD16—22no—
392C2×SD16—22no—
393C2×SD16—434no—
394C2×SD16—434no—
395C2×SD16—434no—
396C2×SD16—862no—
397C2×SD16—862no—
398C2×SD16—862no—
399C2×SD16—862no—
400C2×SD16—862no—
401C2×SD16—862no—
402C2×SD16C4×D4314yescomplemented
403C22×C8—431no—
404C22×C8—431no—
405C22×C8C22×D4311yescharacteristic
406C22×C8C22×D4311yescharacteristic
407C4⋊Q8—434no—
408C4⋊Q8—862no—
409#127—434no—
410#127—862no—
411C4×Q8—862no—
412C4×Q8—862no—
413C4×Q8—862no—
414C4×Q8—862no—
415C4×D4—862no—
416C4×D4—862no—
417C4×D4—862no—
418C4×D4—862no—
419C4×D4—1728no—
420C2×C4⋊C4—431no—
421C2×C4⋊C4—431no—
422C2×C4⋊C4—862no—
423C2×C4⋊C4—862no—
424C2×C4⋊C4—861no—
425C2×C4⋊C4—861no—
426C2×C4⋊C4—862no—
427C2×C4⋊C4C22×D4311yescharacteristic
428C2×C4⋊C4C22×D4311yescharacteristic
429C2×C22⋊C4—22no—
430C2×C22⋊C4—861no—
431C2×C22⋊C4—861no—
432C2×C22⋊C4—862no—
433C2×C42—432no—
434C2×C42—431no—
435C2×C42—431no—
436C2×C42—432no—
437C2×C42—861no—
438C2×C42—861no—
439C2×C42C22×D4311yescharacteristic
440#106—22no—
441#106—862no—
442#106—862no—
443#106—862no—
444#103—22no—
445#103—862no—
446#103—862no—
447#103—862no—
448#102—22no—
449#102—862no—
450#102—862no—
451#102—862no—
452C4×C8—22no—
453C4×C8—434no—
454C4×C8—434no—
455C4×C8—434no—
456C4×C8—862no—
457C4×C8—862no—
458#95—22no—
459#95—862no—
460C24—21no—
461C24—861no—
462C2×Q8—21no—
463C2×Q8—21no—
464C2×Q8—21no—
465C2×Q8—21no—
466C2×Q8—21no—
467C2×Q8—432no—
468C2×Q8—861no—
469C2×Q8—861no—
470C2×Q8—861no—
471C2×Q8—861no—
472C2×Q8—861no—
473C2×Q8C2×C4×D4312yes—
474C2×D4—21no—
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4—432no—
480C2×D4—868no—
481C2×D4—861no—
482C2×D4—861no—
483C2×D4—861no—
484C2×D4—861no—
485C2×D4—861no—
486C2×D4—1724no—
487C2×D4—1724no—
488C2×D4C2×C4×D4312yes—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—431no—
493C22×C4—432no—
494C22×C4—431no—
495C22×C4—861no—
496C22×C4—861no—
497C22×C4—861no—
498C22×C4—1722no—
499C22×C4—1724no—
500C22×C4—1722no—
501C22×C4—1724no—
502C22×C4D4×D4312yes—
503C22×C4C23×D4311yescharacteristic
504SD16—28no—
505SD16—868no—
506SD16—868no—
507SD16—868no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—432no—
511C2×C8—432no—
512C2×C8—432no—
513C2×C8—432no—
514C2×C8—861no—
515C2×C8—861no—
516C2×C8C2×C4×D4312yes—
517C2×C8D4×D4312yes—
518C2×C8D4×D4312yes—
519C2×C8#1062190012yes—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—868no—
525C4⋊C4—861no—
526C4⋊C4—861no—
527C4⋊C4—861no—
528C4⋊C4—861no—
529C4⋊C4—1724no—
530C4⋊C4—1722no—
531C4⋊C4—1722no—
532C4⋊C4—1724no—
533C22⋊C4—44no—
534C22⋊C4—1722no—
535C22⋊C4—1722no—
536C22⋊C4—1724no—
537C42—21no—
538C42—21no—
539C42—438no—
540C42—432no—
541C42—432no—
542C42—432no—
543C42—432no—
544C42—864no—
545C42—1722no—
546C42—1722no—
547C23—22no—
548C23—42no—
549C23—42no—
550C23—41no—
551C23—41no—
552C23—862no—
553C23—1722no—
554C23—1722no—
555C23—1721no—
556C23—1721no—
557C23C2×D4×D4311yescharacteristic
558Q8—22no—
559Q8—22no—
560Q8—41no—
561Q8—41no—
562Q8—862no—
563Q8—862no—
564Q8—1721no—
565Q8—1721no—
566D4—22no—
567D4—22no—
568D4—41no—
569D4—41no—
570D4—862no—
571D4—862no—
572D4—17216no—
573D4—1721no—
574D4—1721no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—434no—
585C2×C4—434no—
586C2×C4—434no—
587C2×C4—434no—
588C2×C4—432no—
589C2×C4—432no—
590C2×C4—862no—
591C2×C4—862no—
592C2×C4—3444no—
593C2×C4—3444no—
594C2×C4—1722no—
595C2×C4—1722no—
596C2×C4—1721no—
597C2×C4—1721no—
598C2×C4—1721no—
599C2×C4—1721no—
600C2×C4SD16×D4314yes—
601C2×C4C22×C4×D4311yescharacteristic
602C2×C4C2×D4×D4311yescharacteristic
603C2×C4C2×D4×D4311yescharacteristic
604C2×C4#41×D4311yescharacteristic
605C2×C4#41×D4311yescharacteristic
606C2×C4C2×#1062190011yescharacteristic
607C8—22no—
608C8—434no—
609C8—862no—
610C8(C22⋊D43)⋊C414yescomplemented
611C22—42no—
612C22—44no—
613C22—81no—
614C22—81no—
615C22—82no—
616C22—3441no—
617C22—3441no—
618C22—3442no—
619C22—1722no—
620C22—1724no—
621C22C4×D4×D4311yescharacteristic
622C22#127×D4311yescharacteristic
623C22#1458344411yescharacteristic
624C22C2×SD16×D4312yes—
625C22#135×D4312yes—
626C4—24no—
627C4—42no—
628C4—81no—
629C4—81no—
630C4—434no—
631C4—438no—
632C4—862no—
633C4—3441no—
634C4—3441no—
635C4—1722no—
636C4C4×D4×D4311yescharacteristic
637C4C2×(C22⋊D43)⋊C411yescharacteristic
638C4#1458344411yescharacteristic
639C4#1458344811yescharacteristic
640C2—82no—
641C2—3442no—
642C2#1913715911yescharacteristic
643C2C4×SD16×D4312yes—
644C2#492×D4311yescharacteristic
645C2#1914502011yescharacteristic
646C2#1914514912yes—
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1968C2
socleC23×C43C22×D4
prime radicalC2×#13063321C22
cosocleC22×C4×C43C24
hypercenter#1968D43
hypocenterC43C4×#492
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1968

Complements

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

NH ≅ G/Ntype
2. C2×#14582990C2semidirect
3. C2×SD16×Dic43C2semidirect
4. C2×#14582986C2semidirect
5. C2×#14582984C2semidirect
6. #19137164C2semidirect
8. #19135452C2semidirect
9. #19135449C2semidirect
10. #19135448C2semidirect
12. #19135395C2semidirect
13. #19134750C2semidirect
14. C4×C8×Dic43C2semidirect
15. C43×#1968C2semidirect
26. #14583270C4semidirect
67. C2×#10621873C2×C4semidirect
70. C2×#10621883C2×C4semidirect
73. C2×#10621884C2×C4semidirect
77. #13063323C2×C4semidirect
116. C8×Dic43C2×C4semidirect
117. C8×Dic43D4semidirect
118. C8×Dic43D4semidirect
124. C2×SD16×C43C2×C4semidirect
211. C4×Dic43SD16semidirect
284. C8×C43C4×D4semidirect
286. C43⋊C8C4×D4semidirect
315. Dic43C4×SD16semidirect
316. Dic43#492semidirect
327. #1968D43semidirect
383. C43C4×#492semidirect
402. C2×SD16C4×D43semidirect
610. C8(C22⋊D43)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×#145832702
C2×#145829902
C2×SD16×Dic432
C2×#145829862
C2×#145829842
#191371642
#191371592
#191354522
#191354492
#191354482
#191353992
#191353952
#191347502
C4×C8×Dic432
C43×#19682
C4×#49243