Finite Group Databasebeta

← #25105093

Subgroups — #25105093

Order 11008.

1126 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583270C211yesmaximal, characteristic
2C2×#14582999C211yesmaximal, characteristic, complemented
3C2×#14582997C211yesmaximal, characteristic, complemented
4C2×C4×#10621873C211yesmaximal, characteristic, complemented
5#19137317C211yesmaximal, characteristic
6#19137311C211yesmaximal, characteristic, complemented
7#19135477C211yesmaximal, characteristic, complemented
8#19135473C211yesmaximal, characteristic, complemented
9#19135451C211yesmaximal, characteristic, complemented
10#19135447C211yesmaximal, characteristic, complemented
11#19135417C211yesmaximal, characteristic
12#19135413C211yesmaximal, characteristic, complemented
13#19134756C211yesmaximal, characteristic, complemented
14#19134281C211yesmaximal, characteristic, complemented
15C2×C4×SD16×C43C211yesmaximal, characteristic, complemented
16C22×#10621873C2211yescharacteristic
17C22×#10621883C2211yescharacteristic
18C22×#10621884C2211yescharacteristic
19C2×#13063323C2211yescharacteristic
20C2×#13063321C2211yescharacteristic
21C2×C4×Dic86C2211yescharacteristic
22C2×C4×D172C2211yescharacteristic
23#14583270C418yescomplemented
24#14582999—24no—
25#14582997—24no—
26C4×#10621873—24no—
27C2×#13063258C2211yescharacteristic
28C2×#13063258C2211yescharacteristic
29C2×#13063257C2211yescharacteristic
30C2×#13063250C2211yescharacteristic
31C2×#13063249C2211yescharacteristic
32C2×#13063248C2211yescharacteristic
33C2×#13063247C2211yescharacteristic
34C2×#13063246C2211yescharacteristic
35C2×#13063245C2211yescharacteristic
36C2×#13063236C2211yescharacteristic
37C2×#13063235C2211yescharacteristic
38C2×#13063235C2211yescharacteristic
39C2×C8×Dic43C2211yescharacteristic
40C2×C8×Dic43C2211yescharacteristic
41#14582806C2211yescharacteristic
42#14582804C2211yescharacteristic
43#14582802C2211yescharacteristic
44#14582800C2211yescharacteristic
45#14582783—22no—
46#14582780—22no—
47#14582778—22no—
48#14582775—22no—
49#14582764C2211yescharacteristic
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×Dic86C2311yescharacteristic
61C22×D172C2311yescharacteristic
62C22×C22⋊D43—22no—
63C22×C4×D43—21no—
64C2×#10621873—22no—
65C2×#10621873—22no—
66C2×#10621873C2×C414yescomplemented
67C2×#10621883—22no—
68C2×#10621883—22no—
69C2×#10621883C2×C414yescomplemented
70C2×#10621884—22no—
71C2×#10621884—22no—
72C2×#10621884C2×C414yescomplemented
73C22×C43⋊C8C2311yescharacteristic
74C22×C43⋊C8C2311yescharacteristic
75#13063323—22no—
76#13063323C2×C414yescomplemented
77#13063321—22no—
78#13063321C2×C414yes—
79C4×Dic86—22no—
80C4×Dic86—22no—
81C4×D172—22no—
82C4×D172—22no—
83C2×C4⋊Dic43C2311yescharacteristic
84C2×C4⋊Dic43C2311yescharacteristic
85C2×Dic43⋊C4—22no—
86C2×Dic43⋊C4—21no—
87C2×C22⋊Dic43—22no—
88C2×(C2×D43)⋊C4—21no—
89C2×(C2×D43)⋊C4—22no—
90C2×C4×Dic43—21no—
91C2×C4×Dic43C2311yescharacteristic
92C2×C4×Dic43C2311yescharacteristic
93#13063258—22no—
94#13063258—22no—
95#13063257—22no—
96#13063250—22no—
97#13063249—22no—
98#13063248—22no—
99#13063247—22no—
100#13063246—22no—
101#13063245—22no—
102#13063236D414yescomplemented
103#13063235—22no—
104#13063235—22no—
105C8×Dic43—22no—
106C8×Dic43C2×C414yescomplemented
107C43⋊#95—22no—
108C43⋊#95—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—
137C2×Q8×C43—21no—
138C2×Q8×C43—21no—
139C2×Q8×C43—21no—
140C2×Q8×C43—21no—
141C2×Q8×C43—21no—
142C2×Q8×C43C22×C412yes—
143C2×D4×C43—21no—
144C2×D4×C43—21no—
145C2×D4×C43—21no—
146C2×D4×C43—21no—
147C2×D4×C43—21no—
148C2×D4×C43C22×C412yes—
149C22×C4×C43—21no—
150C22×C4×C43—21no—
151C22×C4×C43—21no—
152C22×C4×C43—42no—
153C22×C4×C43—82no—
154C22×C4×C43C2×D411yescharacteristic
155C22×C4×C43C2×D411yescharacteristic
156C22×C4×C43C2411yescharacteristic
157C2×C22⋊D43—28no—
158C2×C22⋊D43—82no—
159C2×C22⋊D43—82no—
160C22×Dic43—21no—
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×D172C22×C412yes—
171C2×C4×D43—42no—
172C2×C4×D43—82no—
173C2×Dic86—21no—
174C2×Dic86—21no—
175C2×Dic86—21no—
176C2×Dic86—21no—
177C2×Dic86—21no—
178C2×Dic86C22×C412yes—
179SD16×C43—28no—
180C2×C8×C43—21no—
181C2×C8×C43—21no—
182C2×C8×C43C22×C412yes—
183C2×C8×C43C2×D412yes—
184C2×C8×C43C2×D412yes—
185C2×C8×C43#4112yes—
186C4⋊C4×C43—21no—
187C4⋊C4×C43—21no—
188C4⋊C4×C43—21no—
189C4⋊C4×C43—21no—
190C4⋊C4×C43—42no—
191C22⋊C4×C43—42no—
192C42×C43—42no—
193C42×C43C2×D412yes—
194C42×C43C2×D412yes—
195C22⋊Dic43—82no—
196#10621884—28no—
197#10621883—28no—
198(C2×D43)⋊C4—42no—
199(C2×D43)⋊C4—82no—
200C4⋊Dic43—21no—
201C4⋊Dic43—21no—
202C4⋊Dic43—21no—
203C4⋊Dic43—21no—
204Dic43⋊C4—28no—
205Dic43⋊C4—42no—
206C4×Dic43—21no—
207C4×Dic43—21no—
208C4×Dic43—42no—
209C4×Dic43C22×C412yes—
210C4×Dic43#4112yes—
211C2×C43⋊C8—21no—
212C2×C43⋊C8—21no—
213C2×C43⋊C8C22×C412yes—
214C2×C43⋊C8C2×D412yes—
215C2×C43⋊C8C2×D412yes—
216C2×C43⋊C8#4112yes—
217#10621873—28no—
218C23×C43—22no—
219C23×C43—41no—
220C23×C43—41no—
221C23×C43—42no—
222C23×C43—42no—
223C23×C43C22×D411yescharacteristic
224C22×D43—22no—
225C22×D43—41no—
226C22×D43—41no—
227C22×D43—42no—
228C22×D43—42no—
229Q8×C43—22no—
230Q8×C43—22no—
231Q8×C43—41no—
232Q8×C43—41no—
233D4×C43—22no—
234D4×C43—22no—
235D4×C43—41no—
236D4×C43—41no—
237C2×C4×C43—22no—
238C2×C4×C43—22no—
239C2×C4×C43—22no—
240C2×C4×C43—41no—
241C2×C4×C43—41no—
242C2×C4×C43—41no—
243C2×C4×C43—41no—
244C2×C4×C43—42no—
245C2×C4×C43—42no—
246C2×C4×C43—84no—
247C2×C4×C43#12712yes—
248C2×C4×C43#12712yes—
249C2×C4×C43C23×C411yescharacteristic
250C2×C4×C43C22×D411yescharacteristic
251C2×C4×C43C22×D411yescharacteristic
252C2×C4×C43C2×#4111yescharacteristic
253C2×C4×C43C2×#4111yescharacteristic
254C2×C4×C43C2×#4111yescharacteristic
255C22⋊D43—88no—
256C2×Dic43—22no—
257C2×Dic43—22no—
258C2×Dic43—22no—
259C2×Dic43—22no—
260C2×Dic43—22no—
261C2×Dic43—22no—
262C2×Dic43—41no—
263C2×Dic43—41no—
264C2×Dic43—41no—
265C2×Dic43—41no—
266C2×Dic43—42no—
267C2×Dic43—42no—
268C2×Dic43C4×D414yes—
269D172—22no—
270D172—22no—
271D172—41no—
272D172—41no—
273C4×D43—84no—
274Dic86—22no—
275Dic86—22no—
276Dic86—41no—
277Dic86—41no—
278C8×C43—22no—
279C8×C43C4×D414yes—
280C43⋊C8—22no—
281C43⋊C8C4×D414yes—
282#21695—431nomaximal, Sylow
283C22×C43—42no—
284C22×C43—44no—
285C22×C43—81no—
286C22×C43—81no—
287C22×C43—82no—
288C22×C43C2×C4×D411yescharacteristic
289C22×C43C2×#12711yescharacteristic
290C22×C43#53211yescharacteristic
291C22×C43#57712yes—
292C22×C43#57712yes—
293C2×D43—42no—
294C2×D43—44no—
295C2×D43—81no—
296C2×D43—81no—
297C2×D43—82no—
298C4×C43—22no—
299C4×C43—22no—
300C4×C43—42no—
301C4×C43—81no—
302C4×C43—81no—
303C4×C43C2×C4×D411yescharacteristic
304C4×C43C2×C4×D411yescharacteristic
305C4×C43#53211yescharacteristic
306C4×C43#53211yescharacteristic
307Dic43—24no—
308Dic43—42no—
309Dic43—42no—
310Dic43—81no—
311Dic43—81no—
312C2×#492—431no—
313C2×#440—431no—
314C2×#440—431no—
315C2×C4×SD16—431no—
316C2×C4×SD16D4311yescharacteristic, complemented
317#2328—431no—
318#2327—431no—
319#1973—431no—
320#1973—431no—
321#1968—431no—
322#1968—431no—
323#1961—431no—
324#1960—431no—
325#1846—431no—
326#1726—431no—
327C2×C43—82no—
328C2×C43C4×#12711yescharacteristic
329C2×C43#294912yes—
330C2×C43#315411yescharacteristic
331C2×C43#315411yescharacteristic
332C2×C43#317412yes—
333D43—82no—
334C22×SD16—431no—
335C22×SD16—431no—
336C22×SD16—431no—
337C22×SD16C2×D4311yescharacteristic
338C2×C4⋊Q8—431no—
339C2×#127—431no—
340C2×C4×Q8—431no—
341C2×C4×Q8C2×D4311yescharacteristic
342C2×C4×D4—431no—
343C2×C4×D4C2×D4311yescharacteristic
344#492—438no—
345#440—864no—
346#440—864no—
347C4×SD16—24no—
348C4×SD16—864no—
349C2×#107—431no—
350C2×#107—431no—
351C2×#106—431no—
352C2×#106C2×D4311yescharacteristic
353C2×#103—431no—
354C2×#103—431no—
355C2×#103—431no—
356C2×#103C2×D4311yescharacteristic
357C2×#102—431no—
358C2×#102—431no—
359C2×#102—431no—
360C2×#102C2×D4311yescharacteristic
361C2×#97—431no—
362C2×#97—431no—
363C2×#97—431no—
364C2×C4×C8—431no—
365C2×C4×C8—431no—
366C2×C4×C8C2×D4311yescharacteristic
367#391—431no—
368#391—431no—
369#390—431no—
370#390—431no—
371#387—862no—
372#387—862no—
373#386—862no—
374#386—862no—
375#382—431no—
376#382—431no—
377#376—431no—
378C43#2169511yescharacteristic, complemented, Sylow
379C22×Q8—431no—
380C22×Q8C22×D4311yescharacteristic
381C22×D4—431no—
382C22×D4—862no—
383C22×D4C22×D4311yescharacteristic
384C23×C4—21no—
385C23×C4—861no—
386C2×SD16—22no—
387C2×SD16—22no—
388C2×SD16—434no—
389C2×SD16—434no—
390C2×SD16—434no—
391C2×SD16—862no—
392C2×SD16—862no—
393C2×SD16—862no—
394C2×SD16—862no—
395C2×SD16—862no—
396C2×SD16—862no—
397C2×SD16C4×D4314yescomplemented
398C22×C8—431no—
399C22×C8—431no—
400C22×C8C22×D4311yescharacteristic
401C22×C8C22×D4311yescharacteristic
402C4⋊Q8—434no—
403C4⋊Q8—862no—
404#127—434no—
405#127—862no—
406C4×Q8—22no—
407C4×Q8—22no—
408C4×Q8—862no—
409C4×Q8—862no—
410C4×D4—22no—
411C4×D4—22no—
412C4×D4—862no—
413C4×D4—862no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—431no—
416C2×C4⋊C4—431no—
417C2×C4⋊C4—862no—
418C2×C4⋊C4—861no—
419C2×C4⋊C4C22×D4311yescharacteristic
420C2×C4⋊C4C22×D4311yescharacteristic
421C2×C22⋊C4—21no—
422C2×C22⋊C4—862no—
423C2×C22⋊C4—862no—
424C2×C22⋊C4—861no—
425C2×C42—21no—
426C2×C42—431no—
427C2×C42—431no—
428C2×C42—861no—
429C2×C42C22×D4311yescharacteristic
430#107—862no—
431#107—862no—
432#106—22no—
433#106—862no—
434#103—22no—
435#103—862no—
436#103—862no—
437#103—862no—
438#102—22no—
439#102—862no—
440#102—862no—
441#102—862no—
442#97—434no—
443#97—862no—
444#97—862no—
445C4×C8—434no—
446C4×C8—862no—
447C4×C8C22⋊D4314yescomplemented
448#95—432no—
449#95—432no—
450#95—862no—
451#95—862no—
452#95—862no—
453#95—862no—
454C24—21no—
455C24—861no—
456C2×Q8—21no—
457C2×Q8—21no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×Q8—21no—
461C2×Q8—432no—
462C2×Q8—861no—
463C2×Q8—861no—
464C2×Q8—861no—
465C2×Q8—861no—
466C2×Q8—861no—
467C2×Q8C2×C4×D4312yes—
468C2×D4—21no—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4—21no—
473C2×D4—432no—
474C2×D4—868no—
475C2×D4—861no—
476C2×D4—861no—
477C2×D4—861no—
478C2×D4—861no—
479C2×D4—861no—
480C2×D4—3442no—
481C2×D4—3442no—
482C2×D4C2×C4×D4312yes—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—42no—
487C22×C4—82no—
488C22×C4—432no—
489C22×C4—432no—
490C22×C4—861no—
491C22×C4—861no—
492C22×C4—861no—
493C22×C4—3442no—
494C22×C4—1722no—
495C22×C4D4×D4311yescharacteristic
496C22×C4D4×D4311yescharacteristic
497C22×C4C23×D4311yescharacteristic
498SD16—28no—
499SD16—868no—
500SD16—868no—
501SD16—868no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—432no—
505C2×C8—432no—
506C2×C8—432no—
507C2×C8—432no—
508C2×C8—861no—
509C2×C8—861no—
510C2×C8C2×C4×D4312yes—
511C2×C8#1062189812yes—
512C2×C8C2×C22⋊D4312yes—
513C2×C8C2×C22⋊D4312yes—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—42no—
519C4⋊C4—868no—
520C4⋊C4—861no—
521C4⋊C4—861no—
522C4⋊C4—861no—
523C4⋊C4—861no—
524C4⋊C4—1722no—
525C22⋊C4—42no—
526C22⋊C4—3442no—
527C22⋊C4—3442no—
528C22⋊C4—1722no—
529C42—42no—
530C42—432no—
531C42—432no—
532C42—861no—
533C42—861no—
534C42—1722no—
535C42D4×D4312yes—
536C42C2×C22⋊D4312yes—
537C23—22no—
538C23—41no—
539C23—41no—
540C23—42no—
541C23—42no—
542C23—862no—
543C23—1721no—
544C23—1721no—
545C23—1722no—
546C23—1722no—
547C23C2×D4×D4311yescharacteristic
548Q8—22no—
549Q8—22no—
550Q8—41no—
551Q8—41no—
552Q8—862no—
553Q8—862no—
554Q8—1721no—
555Q8—1721no—
556D4—22no—
557D4—22no—
558D4—41no—
559D4—41no—
560D4—862no—
561D4—862no—
562D4—3448no—
563D4—1721no—
564D4—1721no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—84no—
575C2×C4—434no—
576C2×C4—862no—
577C2×C4—862no—
578C2×C4—862no—
579C2×C4—862no—
580C2×C4—862no—
581C2×C4—862no—
582C2×C4—3444no—
583C2×C4—1721no—
584C2×C4—1721no—
585C2×C4—1722no—
586C2×C4—1722no—
587C2×C4—1721no—
588C2×C4—1721no—
589C2×C4#1306332112yes—
590C2×C4#1306332112yes—
591C2×C4C22×C4×D4311yescharacteristic
592C2×C4C2×D4×D4311yescharacteristic
593C2×C4C22×C22⋊D4311yescharacteristic
594C2×C4#41×D4311yescharacteristic
595C2×C4#41×D4311yescharacteristic
596C2×C4C2×#1062189811yescharacteristic
597C8—22no—
598C8—434no—
599C8—862no—
600C8C4×C22⋊D4314yes—
601C22—44no—
602C22—42no—
603C22—82no—
604C22—81no—
605C22—81no—
606C22—3442no—
607C22—3441no—
608C22—3441no—
609C22—1724no—
610C22—1722no—
611C22C4×D4×D4311yescharacteristic
612C22C2×#1306332111yescharacteristic
613C22#1458344611yescharacteristic
614C22#1458370512yes—
615C22#1458370612yes—
616C4—22no—
617C4—22no—
618C4—42no—
619C4—81no—
620C4—81no—
621C4—864no—
622C4—3441no—
623C4—3441no—
624C4—1722no—
625C4—1722no—
626C4C4×D4×D4311yescharacteristic
627C4C2×C4×C22⋊D4311yescharacteristic
628C4#1458344511yescharacteristic
629C4#1458344611yescharacteristic
630C2—82no—
631C2—3442no—
632C2C4×#1306332111yescharacteristic
633C2#1914344912yes—
634C2#1914506511yescharacteristic
635C2#1914507211yescharacteristic
636C2#1914521912yes—
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C4×SD16×C43C2
socleC23×C43C22×D4
prime radicalC2×#13063321C22
cosocleC22×C4×C43C24
hypercenterC2×C4×SD16D43
hypocenterC43#21695
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×#14582999C2semidirect
3. C2×#14582997C2semidirect
4. C2×C4×#10621873C2semidirect
6. #19137311C2semidirect
7. #19135477C2semidirect
8. #19135473C2semidirect
9. #19135451C2semidirect
10. #19135447C2semidirect
12. #19135413C2semidirect
13. #19134756C2semidirect
14. #19134281C2semidirect
15. C2×C4×SD16×C43C2semidirect
23. #14583270C4semidirect
66. C2×#10621873C2×C4semidirect
69. C2×#10621883C2×C4semidirect
72. C2×#10621884C2×C4semidirect
76. #13063323C2×C4semidirect
102. #13063236D4semidirect
106. C8×Dic43C2×C4semidirect
118. C2×SD16×C43C2×C4semidirect
134. C4×C8×C43D4semidirect
316. C2×C4×SD16D43semidirect
378. C43#21695semidirect
397. C2×SD16C4×D43semidirect
447. C4×C8C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145832702
C2×#145829992
C2×#145829972
C2×C4×#106218732
#191373172
#191373112
#191354772
#191354732
#191354512
#191354472
#191354172
#191354132
#191347562
#191342812
C2×C4×SD16×C432
#2169543