Finite Group Databasebeta

← #25105192

Subgroups — #25105192

Order 11008.

1174 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583285C211yesmaximal, characteristic
2C2×#14583009C211yesmaximal, characteristic, complemented
3C2×#14582997C211yesmaximal, characteristic, complemented
4C2×C4×D344C211yesmaximal, characteristic, complemented
5#19137317C211yesmaximal, characteristic, complemented
6#19137302C211yesmaximal, characteristic, complemented
7#19135478C211yesmaximal, characteristic, complemented
8#19135469C211yesmaximal, characteristic, complemented
9#19135458C211yesmaximal, characteristic, complemented
10#19135446C211yesmaximal, characteristic, complemented
11#19135403C211yesmaximal, characteristic, complemented
12#19135399C211yesmaximal, characteristic, complemented
13#19134760C211yesmaximal, characteristic, complemented
14#19134281C211yesmaximal, characteristic, complemented
15C2×C4×SD16×C43C211yesmaximal, characteristic, complemented
16C22×#10621884C2211yescharacteristic
17C22×D344C2211yescharacteristic
18C22×#10621882C2211yescharacteristic
19C2×#13063321C2211yescharacteristic
20C2×#13063314C2211yescharacteristic
21C2×C4×D172C2211yescharacteristic
22C2×C4×D172C2211yescharacteristic
23#14583285C418yescomplemented
24#14583009—24no—
25#14582997—24no—
26C4×D344—24no—
27C2×#13063259C2211yescharacteristic
28C2×#13063258C2211yescharacteristic
29C2×#13063256C2211yescharacteristic
30C2×#13063249C2211yescharacteristic
31C2×#13063247C2211yescharacteristic
32C2×#13063247C2211yescharacteristic
33C2×#13063246C2211yescharacteristic
34C2×#13063245C2211yescharacteristic
35C2×#13063245C2211yescharacteristic
36C2×#13063236C2211yescharacteristic
37C2×#13063235C2211yescharacteristic
38C2×#13063235C2211yescharacteristic
39C2×C8×Dic43C2211yescharacteristic
40C2×C8×Dic43C2211yescharacteristic
41#14582806C2211yescharacteristic
42#14582802C2211yescharacteristic
43#14582800C2211yescharacteristic
44#14582800C2211yescharacteristic
45#14582790—22no—
46#14582778—22no—
47#14582775—22no—
48#14582770—22no—
49#14582768C2211yescharacteristic
50#14582764C2211yescharacteristic
51#14582745C2211yescharacteristic
52C22×SD16×C43C2211yescharacteristic
53C2×C4×Q8×C43C2211yescharacteristic
54C2×C4×D4×C43C2211yescharacteristic
55C4×SD16×C43—24no—
56C2×#106×C43C2211yescharacteristic
57C2×#103×C43C2211yescharacteristic
58C2×#102×C43C2211yescharacteristic
59C2×C4×C8×C43C2211yescharacteristic
60C22×D172C2311yescharacteristic
61C22×D172C2311yescharacteristic
62C22×C22⋊D43—22no—
63C22×C4×D43—21no—
64C22×C4×D43—21no—
65C2×#10621884—22no—
66C2×#10621884—22no—
67C2×#10621884C2×C414yescomplemented
68C2×D344—22no—
69C2×D344—22no—
70C2×D344C2×C414yescomplemented
71C2×#10621882—22no—
72C2×#10621882—22no—
73C2×#10621882C2×C414yescomplemented
74C22×C43⋊C8C2311yescharacteristic
75C22×C43⋊C8C2311yescharacteristic
76#13063321—22no—
77#13063321C2×C414yescomplemented
78#13063314—22no—
79#13063314C2×C414yescomplemented
80C4×D172—22no—
81C4×D172—22no—
82C4×D172—22no—
83C4×D172—22no—
84C2×C4⋊Dic43C2311yescharacteristic
85C2×C4⋊Dic43C2311yescharacteristic
86C2×Dic43⋊C4—22no—
87C2×C22⋊Dic43—22no—
88C2×(C2×D43)⋊C4—22no—
89C2×(C2×D43)⋊C4—21no—
90C2×(C2×D43)⋊C4—21no—
91C2×(C2×D43)⋊C4—22no—
92C2×(C2×D43)⋊C4—22no—
93C2×C4×Dic43C2311yescharacteristic
94C2×C4×Dic43C2311yescharacteristic
95#13063259—22no—
96#13063258—22no—
97#13063256—22no—
98#13063249—22no—
99#13063247—22no—
100#13063247—22no—
101#13063246—22no—
102#13063245—22no—
103#13063245—22no—
104#13063236D414yescomplemented
105#13063235—22no—
106#13063235C2×C414yescomplemented
107C8×Dic43—22no—
108C8×Dic43—22no—
109C43⋊#95—22no—
110C43⋊#95—22no—
111C43⋊#95D412yes—
112C43⋊#95D412yes—
113C22×Q8×C43C2311yescharacteristic
114C22×D4×C43C2311yescharacteristic
115C23×C4×C43—21no—
116C2×SD16×C43—22no—
117C2×SD16×C43—22no—
118C2×SD16×C43C2×C414yescomplemented
119C22×C8×C43C2311yescharacteristic
120C22×C8×C43C2311yescharacteristic
121C4×Q8×C43—22no—
122C4×Q8×C43—22no—
123C4×D4×C43—22no—
124C4×D4×C43—22no—
125C2×C4⋊C4×C43—21no—
126C2×C4⋊C4×C43C2311yescharacteristic
127C2×C4⋊C4×C43C2311yescharacteristic
128C2×C22⋊C4×C43—21no—
129C2×C42×C43—21no—
130C2×C42×C43C2311yescharacteristic
131#106×C43—22no—
132#103×C43—22no—
133#102×C43—22no—
134C4×C8×C43D414yescomplemented
135C24×C43—21no—
136C23×D43—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×C43—42no—
154C22×C4×C43—82no—
155C22×C4×C43C2×D411yescharacteristic
156C22×C4×C43C2×D411yescharacteristic
157C22×C4×C43C2411yescharacteristic
158C2×C22⋊D43—28no—
159C2×C22⋊D43—82no—
160C2×C22⋊D43—82no—
161C22×Dic43—21no—
162C22×Dic43—21no—
163C22×Dic43C2×D412yes—
164C22×Dic43C2×D412yes—
165C2×D172—21no—
166C2×D172—21no—
167C2×D172—21no—
168C2×D172—21no—
169C2×D172—21no—
170C2×D172—21no—
171C2×D172—21no—
172C2×D172—21no—
173C2×D172—21no—
174C2×D172—21no—
175C2×D172C22×C412yes—
176C2×D172C22×C412yes—
177C2×C4×D43—42no—
178C2×C4×D43—42no—
179C2×C4×D43—82no—
180C2×C4×D43—82no—
181SD16×C43—28no—
182C2×C8×C43—21no—
183C2×C8×C43—21no—
184C2×C8×C43C22×C412yes—
185C2×C8×C43C2×D412yes—
186C2×C8×C43C2×D412yes—
187C2×C8×C43#4112yes—
188C4⋊C4×C43—21no—
189C4⋊C4×C43—21no—
190C4⋊C4×C43—21no—
191C4⋊C4×C43—21no—
192C4⋊C4×C43—42no—
193C22⋊C4×C43—42no—
194C42×C43—42no—
195C42×C43C2×D412yes—
196C42×C43C2×D412yes—
197C22⋊Dic43—82no—
198#10621884—28no—
199#10621882—28no—
200(C2×D43)⋊C4—28no—
201(C2×D43)⋊C4—42no—
202(C2×D43)⋊C4—42no—
203(C2×D43)⋊C4—82no—
204(C2×D43)⋊C4—82no—
205C4⋊Dic43—21no—
206C4⋊Dic43—21no—
207C4⋊Dic43—21no—
208C4⋊Dic43—21no—
209Dic43⋊C4—82no—
210C4×Dic43—21no—
211C4×Dic43—21no—
212C4×Dic43C22×C412yes—
213C4×Dic43#4112yes—
214C2×C43⋊C8—21no—
215C2×C43⋊C8—21no—
216C2×C43⋊C8C22×C412yes—
217C2×C43⋊C8C2×D412yes—
218C2×C43⋊C8C2×D412yes—
219C2×C43⋊C8#4112yes—
220D344—28no—
221C23×C43—22no—
222C23×C43—41no—
223C23×C43—41no—
224C23×C43—42no—
225C23×C43—42no—
226C23×C43C22×D411yescharacteristic
227C22×D43—22no—
228C22×D43—22no—
229C22×D43—41no—
230C22×D43—41no—
231C22×D43—41no—
232C22×D43—41no—
233C22×D43—42no—
234C22×D43—42no—
235C22×D43—42no—
236C22×D43—42no—
237Q8×C43—22no—
238Q8×C43—22no—
239Q8×C43—41no—
240Q8×C43—41no—
241D4×C43—22no—
242D4×C43—22no—
243D4×C43—41no—
244D4×C43—41no—
245C2×C4×C43—22no—
246C2×C4×C43—22no—
247C2×C4×C43—22no—
248C2×C4×C43—41no—
249C2×C4×C43—41no—
250C2×C4×C43—41no—
251C2×C4×C43—41no—
252C2×C4×C43—42no—
253C2×C4×C43—42no—
254C2×C4×C43—84no—
255C2×C4×C43#12712yes—
256C2×C4×C43#12712yes—
257C2×C4×C43C23×C411yescharacteristic
258C2×C4×C43C22×D411yescharacteristic
259C2×C4×C43C22×D411yescharacteristic
260C2×C4×C43C2×#4111yescharacteristic
261C2×C4×C43C2×#4111yescharacteristic
262C2×C4×C43C2×#4111yescharacteristic
263C22⋊D43—88no—
264C2×Dic43—22no—
265C2×Dic43—22no—
266C2×Dic43—22no—
267C2×Dic43—22no—
268C2×Dic43—22no—
269C2×Dic43—41no—
270C2×Dic43—41no—
271C2×Dic43—42no—
272C2×Dic43—42no—
273C2×Dic43C4×D414yes—
274D172—22no—
275D172—22no—
276D172—22no—
277D172—22no—
278D172—41no—
279D172—41no—
280D172—41no—
281D172—41no—
282C4×D43—84no—
283C4×D43—84no—
284C8×C43—22no—
285C8×C43C4×D414yes—
286C43⋊C8—22no—
287C43⋊C8C4×D414yes—
288#21704—431nomaximal, Sylow
289C22×C43—42no—
290C22×C43—44no—
291C22×C43—81no—
292C22×C43—81no—
293C22×C43—82no—
294C22×C43C2×C4×D411yescharacteristic
295C22×C43C2×#12711yescharacteristic
296C22×C43#53211yescharacteristic
297C22×C43#57612yes—
298C22×C43#57712yes—
299C2×D43—42no—
300C2×D43—42no—
301C2×D43—44no—
302C2×D43—44no—
303C2×D43—81no—
304C2×D43—81no—
305C2×D43—81no—
306C2×D43—81no—
307C2×D43—82no—
308C2×D43—82no—
309C4×C43—22no—
310C4×C43—22no—
311C4×C43—42no—
312C4×C43—81no—
313C4×C43—81no—
314C4×C43C2×C4×D411yescharacteristic
315C4×C43C2×C4×D411yescharacteristic
316C4×C43#53211yescharacteristic
317C4×C43#53211yescharacteristic
318Dic43—24no—
319Dic43—42no—
320Dic43—81no—
321Dic43—81no—
322C2×#496—431no—
323C2×#442—431no—
324C2×#440—431no—
325C2×C4×SD16D4311yescharacteristic, complemented
326C2×C4×D8—431no—
327#2328—431no—
328#2326—431no—
329#1973—431no—
330#1972—431no—
331#1970—431no—
332#1968—431no—
333#1958—431no—
334#1957—431no—
335#1847—431no—
336#1726—431no—
337C2×C43—82no—
338C2×C43C4×#12711yescharacteristic
339C2×C43#294612yes—
340C2×C43#315411yescharacteristic
341C2×C43#315511yescharacteristic
342C2×C43#317912yes—
343D43—82no—
344D43—82no—
345C22×SD16—431no—
346C22×SD16C2×D4311yescharacteristic
347C22×D8—431no—
348C22×D8—431no—
349C2×#127—431no—
350C2×#124—431no—
351C2×C4×Q8C2×D4311yescharacteristic
352C2×C4×D4—431no—
353C2×C4×D4—431no—
354C2×C4×D4C2×D4311yescharacteristic
355#496—438no—
356#442—864no—
357#440—864no—
358C4×SD16—24no—
359C4×D8—864no—
360C2×#107—431no—
361C2×#107—431no—
362C2×#106—431no—
363C2×#106C2×D4311yescharacteristic
364C2×#103—431no—
365C2×#103C2×D4311yescharacteristic
366C2×#102—431no—
367C2×#102—431no—
368C2×#102—431no—
369C2×#102—431no—
370C2×#102—431no—
371C2×#102C2×D4311yescharacteristic
372C2×#97—431no—
373C2×#97—431no—
374C2×#97—431no—
375C2×C4×C8—431no—
376C2×C4×C8—431no—
377C2×C4×C8C2×D4311yescharacteristic
378#391—431no—
379#390—431no—
380#390—431no—
381#390—431no—
382#388—862no—
383#386—862no—
384#386—862no—
385#385—862no—
386#384—431no—
387#382—431no—
388#376—431no—
389C43#2170411yescharacteristic, complemented, Sylow
390C22×Q8C22×D4311yescharacteristic
391C22×D4—431no—
392C22×D4—431no—
393C22×D4—862no—
394C22×D4C22×D4311yescharacteristic
395C23×C4—21no—
396C23×C4—861no—
397C23×C4—861no—
398C2×SD16—22no—
399C2×SD16—22no—
400C2×SD16—434no—
401C2×SD16—862no—
402C2×SD16—862no—
403C2×SD16C4×D4314yescomplemented
404C2×D8—434no—
405C2×D8—434no—
406C2×D8—862no—
407C2×D8—862no—
408C2×D8—862no—
409C2×D8—862no—
410C22×C8—431no—
411C22×C8—431no—
412C22×C8C22×D4311yescharacteristic
413C22×C8C22×D4311yescharacteristic
414#127—434no—
415#127—862no—
416#124—434no—
417#124—862no—
418C4×Q8—22no—
419C4×Q8—22no—
420C4×D4—22no—
421C4×D4—22no—
422C4×D4—862no—
423C4×D4—862no—
424C4×D4—862no—
425C4×D4—862no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—431no—
428C2×C4⋊C4—431no—
429C2×C4⋊C4—862no—
430C2×C4⋊C4C22×D4311yescharacteristic
431C2×C4⋊C4C22×D4311yescharacteristic
432C2×C22⋊C4—21no—
433C2×C22⋊C4—862no—
434C2×C22⋊C4—862no—
435C2×C22⋊C4—862no—
436C2×C22⋊C4—862no—
437C2×C22⋊C4—861no—
438C2×C22⋊C4—861no—
439C2×C42—21no—
440C2×C42—431no—
441C2×C42—431no—
442C2×C42C22×D4311yescharacteristic
443#107—862no—
444#107—862no—
445#106—22no—
446#106—862no—
447#103—22no—
448#103—862no—
449#102—22no—
450#102—862no—
451#102—862no—
452#102—862no—
453#102—862no—
454#102—862no—
455#97—434no—
456#97—434no—
457#97—862no—
458C4×C8—862no—
459C4×C8—862no—
460C4×C8C22⋊D4314yescomplemented
461#95—432no—
462#95—432no—
463#95—862no—
464#95—862no—
465C24—21no—
466C24—861no—
467C24—861no—
468C2×Q8—21no—
469C2×Q8—21no—
470C2×Q8—21no—
471C2×Q8—21no—
472C2×Q8—21no—
473C2×Q8C2×C4×D4312yes—
474C2×D4—21no—
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4—432no—
480C2×D4—432no—
481C2×D4—868no—
482C2×D4—861no—
483C2×D4—861no—
484C2×D4—861no—
485C2×D4—861no—
486C2×D4—861no—
487C2×D4—861no—
488C2×D4—861no—
489C2×D4—861no—
490C2×D4—861no—
491C2×D4—861no—
492C2×D4—3442no—
493C2×D4—3442no—
494C2×D4C2×C4×D4312yes—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—42no—
499C22×C4—82no—
500C22×C4—432no—
501C22×C4—432no—
502C22×C4—861no—
503C22×C4—861no—
504C22×C4—3442no—
505C22×C4—3442no—
506C22×C4—1722no—
507C22×C4—1722no—
508C22×C4D4×D4311yescharacteristic
509C22×C4D4×D4311yescharacteristic
510C22×C4C23×D4311yescharacteristic
511SD16—28no—
512SD16—868no—
513D8—868no—
514D8—868no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—432no—
518C2×C8—432no—
519C2×C8—432no—
520C2×C8—432no—
521C2×C8—861no—
522C2×C8—861no—
523C2×C8C2×C4×D4312yes—
524C2×C8#1062189812yes—
525C2×C8C2×C22⋊D4312yes—
526C2×C8C2×C22⋊D4312yes—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—42no—
532C4⋊C4—861no—
533C4⋊C4—861no—
534C4⋊C4—861no—
535C4⋊C4—861no—
536C4⋊C4—3442no—
537C22⋊C4—42no—
538C22⋊C4—868no—
539C22⋊C4—3442no—
540C22⋊C4—3442no—
541C22⋊C4—3442no—
542C22⋊C4—1722no—
543C22⋊C4—1722no—
544C42—42no—
545C42—432no—
546C42—432no—
547C42—861no—
548C42—861no—
549C42D4×D4312yes—
550C42C2×C22⋊D4312yes—
551C23—22no—
552C23—41no—
553C23—42no—
554C23—41no—
555C23—42no—
556C23—862no—
557C23—862no—
558C23—1721no—
559C23—1721no—
560C23—1722no—
561C23—1722no—
562C23—1721no—
563C23—1721no—
564C23—1722no—
565C23—1722no—
566C23C2×D4×D4311yescharacteristic
567Q8—22no—
568Q8—22no—
569Q8—41no—
570Q8—41no—
571D4—22no—
572D4—22no—
573D4—41no—
574D4—41no—
575D4—862no—
576D4—862no—
577D4—862no—
578D4—862no—
579D4—3448no—
580D4—1721no—
581D4—1721no—
582D4—1721no—
583D4—1721no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—84no—
594C2×C4—434no—
595C2×C4—862no—
596C2×C4—862no—
597C2×C4—862no—
598C2×C4—862no—
599C2×C4—862no—
600C2×C4—3444no—
601C2×C4—3444no—
602C2×C4—1721no—
603C2×C4—1721no—
604C2×C4—1722no—
605C2×C4—1722no—
606C2×C4#1306332112yes—
607C2×C4#1306332112yes—
608C2×C4C22×C4×D4311yescharacteristic
609C2×C4C2×D4×D4311yescharacteristic
610C2×C4C22×C22⋊D4311yescharacteristic
611C2×C4#41×D4311yescharacteristic
612C2×C4#41×D4311yescharacteristic
613C2×C4C2×#1062189811yescharacteristic
614C8—22no—
615C8—434no—
616C8—862no—
617C8C4×C22⋊D4314yes—
618C22—42no—
619C22—44no—
620C22—82no—
621C22—81no—
622C22—81no—
623C22—3442no—
624C22—3442no—
625C22—3441no—
626C22—3441no—
627C22—3441no—
628C22—3441no—
629C22—1722no—
630C22—1722no—
631C22—1724no—
632C22—1724no—
633C22C4×D4×D4311yescharacteristic
634C22C2×#1306332111yescharacteristic
635C22#1458344611yescharacteristic
636C22#1458370112yes—
637C22#1458370512yes—
638C4—22no—
639C4—22no—
640C4—42no—
641C4—81no—
642C4—81no—
643C4—864no—
644C4—3441no—
645C4—3441no—
646C4—1722no—
647C4C4×D4×D4311yescharacteristic
648C4C2×C4×C22⋊D4311yescharacteristic
649C4#1458344511yescharacteristic
650C4#1458344611yescharacteristic
651C2—82no—
652C2—3442no—
653C2—3442no—
654C2C4×#1306332111yescharacteristic
655C2#1914342212yes—
656C2#1914506511yescharacteristic
657C2#1914508211yescharacteristic
658C2#1914527412yes—
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C4×SD16×C43C2
socleC23×C43C22×D4
prime radicalC2×#14583285C2
cosocleC22×C4×C43C24
hypercenterC2×C4×SD16D43
hypocenterC43#21704
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×SD16

Complements

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

NH ≅ G/Ntype
2. C2×#14583009C2semidirect
3. C2×#14582997C2semidirect
4. C2×C4×D344C2semidirect
5. #19137317C2semidirect
6. #19137302C2semidirect
7. #19135478C2semidirect
8. #19135469C2semidirect
9. #19135458C2semidirect
10. #19135446C2semidirect
11. #19135403C2semidirect
12. #19135399C2semidirect
13. #19134760C2semidirect
14. #19134281C2semidirect
15. C2×C4×SD16×C43C2semidirect
23. #14583285C4semidirect
67. C2×#10621884C2×C4semidirect
70. C2×D344C2×C4semidirect
73. C2×#10621882C2×C4semidirect
77. #13063321C2×C4semidirect
79. #13063314C2×C4semidirect
104. #13063236D4semidirect
106. #13063235C2×C4semidirect
118. C2×SD16×C43C2×C4semidirect
134. C4×C8×C43D4semidirect
325. C2×C4×SD16D43semidirect
389. C43#21704semidirect
403. C2×SD16C4×D43semidirect
460. C4×C8C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145832852
C2×#145830092
C2×#145829972
C2×C4×D3442
#191373172
#191373022
#191354782
#191354692
#191354582
#191354462
#191354032
#191353992
#191347602
#191342812
C2×C4×SD16×C432
#2170443