Finite Group Databasebeta

← #25102999

Subgroups — #25102999

Order 11008.

1008 conjugacy classes of subgroups.

The subgroup lattice has 666 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583101C211yesmaximal, characteristic
2C2×#14583002C211yesmaximal, characteristic
3C2×#14582984C211yesmaximal, characteristic
4#19137315C211yesmaximal, characteristic, complemented
5#19136955C211yesmaximal, characteristic
6#19135363C211yesmaximal, characteristic, complemented
7#19135239C211yesmaximal, characteristic, complemented
8#19135232C211yesmaximal, characteristic, complemented
9#19134926C211yesmaximal, characteristic
10#19134926C211yesmaximal, characteristic
11#19134606C211yesmaximal, characteristic
12#19134454C211yesmaximal, characteristic, complemented
13#19134427C211yesmaximal, characteristic, complemented
14#103×Dic43C211yesmaximal, characteristic, complemented
15C43×#1981C211yesmaximal, characteristic, complemented
16C22×#10621884C2211yescharacteristic
17C22×#10621884C2211yescharacteristic
18C2×Q8×Dic43C2211yescharacteristic
19C2×Q8×Dic43C2211yescharacteristic
20C2×C4×D172C2211yescharacteristic
21C2×#13063287C2211yescharacteristic
22C2×#13063287C2211yescharacteristic
23#14583101C418yescomplemented
24#14583002—24no—
25#14582984—24no—
26C2×#13063258C2211yescharacteristic
27C2×#13063256C2211yescharacteristic
28C2×C4⋊(C43⋊C8)C2211yescharacteristic
29C2×#13063249C2211yescharacteristic
30C2×#13063249C2211yescharacteristic
31C2×#13063247C2211yescharacteristic
32C2×#13063247C2211yescharacteristic
33C2×#13063235C2211yescharacteristic
34C2×C8×Dic43C2211yescharacteristic
35#14582806C2211yescharacteristic
36#14582806C2211yescharacteristic
37#14582785—21no—
38#14582785—21no—
39#14582785—21no—
40#14582785—21no—
41#14582765C2211yescharacteristic
42C4⋊C4×Dic43C2211yescharacteristic
43C4⋊C4×Dic43C2211yescharacteristic
44C4×(C2×D43)⋊C4—21no—
45C4×(C2×D43)⋊C4—21no—
46#14582746—21no—
47#14582745C2211yescharacteristic
48#95×D43—21no—
49#14582662C2211yescharacteristic
50#14582662C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582653C2211yescharacteristic
54#14582653C2211yescharacteristic
55C2×C4⋊Q8×C43C2211yescharacteristic
56C2×C4⋊C8×C43C2211yescharacteristic
57C2×#103×C43C2211yescharacteristic
58C2×#103×C43C2211yescharacteristic
59C2×#103×C43C2211yescharacteristic
60C2×#103×C43C2211yescharacteristic
61C4×C4⋊C4×C43C2211yescharacteristic
62C22×D172C2311yescharacteristic
63C22×C4×D43—21no—
64C22×C4×D43—21no—
65C22×C4×D43—21no—
66C2×#10621884—22no—
67C2×#10621884—22no—
68C2×#10621884—22no—
69C2×#10621884—22no—
70C2×#10621884C2×C414yes—
71C2×#10621884C2×C414yes—
72C22×C43⋊C8C2311yescharacteristic
73C22×C43⋊C8C2311yescharacteristic
74Q8×Dic43—22no—
75Q8×Dic43—22no—
76Q8×Dic43—22no—
77Q8×Dic43—22no—
78C4×D172—22no—
79C4×D172C2×C414yes—
80#13063287—22no—
81#13063287—22no—
82#13063287—22no—
83#13063287D414yes—
84C2×C4⋊Dic43—21no—
85C2×C4⋊Dic43—21no—
86C2×C4⋊Dic43C2311yescharacteristic
87C2×C4⋊Dic43C2311yescharacteristic
88C2×C4⋊Dic43C2311yescharacteristic
89C2×(C2×D43)⋊C4—21no—
90C2×(C2×D43)⋊C4—21no—
91C2×(C2×D43)⋊C4—21no—
92C2×C4×Dic43—21no—
93C2×C4×Dic43—21no—
94C2×C4×Dic43—21no—
95C2×C4×Dic43—21no—
96C2×C4×Dic43C2311yescharacteristic
97C2×C4×Dic43C2311yescharacteristic
98#13063258—22no—
99#13063256—22no—
100C4⋊(C43⋊C8)C2×C414yescomplemented
101#13063249C2×C414yescomplemented
102#13063249C2×C414yescomplemented
103#13063247—22no—
104#13063247—22no—
105#13063235—22no—
106C8×Dic43—22no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C43⋊#95—21no—
113C43⋊#95—21no—
114C43⋊#95—21no—
115C43⋊#95D411yescharacteristic
116C43⋊#95D411yescharacteristic
117C43⋊#95D411yescharacteristic
118C43⋊#95D411yescharacteristic
119C22×Q8×C43C2311yescharacteristic
120C22×Q8×C43C2311yescharacteristic
121C22×C8×C43C2311yescharacteristic
122C22×C8×C43C2311yescharacteristic
123C4⋊Q8×C43—22no—
124C4⋊Q8×C43C2×C414yescomplemented
125C2×C4⋊C4×C43—21no—
126C2×C4⋊C4×C43—21no—
127C2×C4⋊C4×C43C2311yescharacteristic
128C2×C4⋊C4×C43C2311yescharacteristic
129C2×C42×C43—21no—
130C2×C42×C43C2311yescharacteristic
131C4⋊C8×C43—22no—
132#103×C43—22no—
133#103×C43—22no—
134#103×C43—22no—
135#103×C43—22no—
136#95×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×C43—21no—
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43—21no—
147C2×Q8×C43—21no—
148C2×Q8×C43C22×C412yes—
149C2×Q8×C43C22×C412yes—
150C22×C4×C43—21no—
151C22×C4×C43—21no—
152C22×C4×C43—21no—
153C22×C4×C43—21no—
154C22×C4×C43C2×D411yescharacteristic
155C22×C4×C43C2×D411yescharacteristic
156C22×C4×C43C2411yescharacteristic
157C22×Dic43—21no—
158C22×Dic43—21no—
159C22×Dic43—21no—
160C22×Dic43C2×D411yescharacteristic
161C22×Dic43C2×D411yescharacteristic
162C22×Dic43C2×D411yescharacteristic
163C22×Dic43C2×D411yescharacteristic
164C2×D172—21no—
165C2×D172—21no—
166C2×D172—21no—
167C2×D172C22×C412yes—
168C2×D172C2×D412yes—
169C2×D172#4112yes—
170C2×C4×D43—24no—
171C2×C4×D43—24no—
172C2×C4×D43—24no—
173C2×C4×D43—81no—
174C2×C4×D43—81no—
175C2×C4×D43—81no—
176C2×C4×D43—81no—
177C2×C4×D43—81no—
178C2×C4×D43—81no—
179C2×C8×C43—21no—
180C2×C8×C43—21no—
181C2×C8×C43—21no—
182C2×C8×C43—21no—
183C2×C8×C43—21no—
184C2×C8×C43—21no—
185C4⋊C4×C43—24no—
186C4⋊C4×C43—24no—
187C4⋊C4×C43—21no—
188C4⋊C4×C43—21no—
189C4⋊C4×C43C2×D412yes—
190C4⋊C4×C43#4112yes—
191C42×C43—81no—
192C42×C43C22×C412yes—
193C42×C43#4112yes—
194#10621884—28no—
195#10621884—28no—
196(C2×D43)⋊C4—24no—
197(C2×D43)⋊C4—24no—
198(C2×D43)⋊C4—24no—
199C4⋊Dic43—21no—
200C4⋊Dic43—21no—
201C4⋊Dic43—21no—
202C4⋊Dic43—21no—
203C4⋊Dic43—21no—
204C4⋊Dic43—42no—
205C4⋊Dic43—42no—
206C4⋊Dic43C22×C412yes—
207C4×Dic43—21no—
208C4×Dic43—21no—
209C4×Dic43—42no—
210C4×Dic43—42no—
211C4×Dic43—81no—
212C4×Dic43—81no—
213C4×Dic43C2×D412yes—
214C4×Dic43#4112yes—
215C2×C43⋊C8—21no—
216C2×C43⋊C8—21no—
217C2×C43⋊C8—21no—
218C2×C43⋊C8—21no—
219C2×C43⋊C8C22×C412yes—
220C2×C43⋊C8C22×C412yes—
221C23×C43C22×D411yescharacteristic
222C22×D43—22no—
223C22×D43—22no—
224C22×D43—22no—
225C22×D43—41no—
226C22×D43—41no—
227C22×D43—41no—
228C22×D43—41no—
229Q8×C43—22no—
230Q8×C43—22no—
231Q8×C43—22no—
232Q8×C43—22no—
233Q8×C43—41no—
234Q8×C43—41no—
235Q8×C43—41no—
236Q8×C43—41no—
237C2×C4×C43—21no—
238C2×C4×C43—21no—
239C2×C4×C43—21no—
240C2×C4×C43—21no—
241C2×C4×C43—22no—
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—41no—
250C2×C4×C43—41no—
251C2×C4×C43—41no—
252C2×C4×C43—41no—
253C2×C4×C43C4×D412yes—
254C2×C4×C43C4×D412yes—
255C2×C4×C43C23×C411yescharacteristic
256C2×C4×C43C22×D411yescharacteristic
257C2×C4×C43C2×#4111yescharacteristic
258C2×C4×C43C2×#4111yescharacteristic
259C2×C4×C43C2×#4111yescharacteristic
260C2×C4×C43C2×#4111yescharacteristic
261C2×Dic43—21no—
262C2×Dic43—21no—
263C2×Dic43—21no—
264C2×Dic43—21no—
265C2×Dic43—22no—
266C2×Dic43—21no—
267C2×Dic43—21no—
268C2×Dic43—21no—
269C2×Dic43—21no—
270C2×Dic43—21no—
271C2×Dic43—21no—
272C2×Dic43—41no—
273C2×Dic43—41no—
274C2×Dic43—41no—
275C2×Dic43—41no—
276C2×Dic43—41no—
277C2×Dic43—41no—
278C2×Dic43—41no—
279C2×Dic43—41no—
280C2×Dic43#12112yes—
281C2×Dic43#12112yes—
282D172—22no—
283D172—22no—
284D172—22no—
285D172C4×D414yes—
286C4×D43—84no—
287C4×D43—84no—
288C4×D43—84no—
289C8×C43—41no—
290C8×C43—41no—
291C43⋊C8—22no—
292C43⋊C8—22no—
293#21514—431nomaximal, Sylow
294C22×C43C2×C4×D411yescharacteristic
295C22×C43C2×#12111yescharacteristic
296C22×C43#52511yescharacteristic
297C22×C43#57711yescharacteristic
298C22×C43#57711yescharacteristic
299C22×C43#57711yescharacteristic
300C22×C43#57811yescharacteristic
301C2×D43—24no—
302C2×D43—42no—
303C2×D43—42no—
304C2×D43—42no—
305C2×D43—42no—
306C2×D43—42no—
307C2×D43—42no—
308C4×C43—22no—
309C4×C43—22no—
310C4×C43—42no—
311C4×C43—42no—
312C4×C43—42no—
313C4×C43—42no—
314C4×C43C2×C4×D411yescharacteristic
315C4×C43C4×#4111yescharacteristic
316C4×C43#52911yescharacteristic
317C4×C43#53211yescharacteristic
318Dic43—22no—
319Dic43—22no—
320Dic43—41no—
321Dic43—41no—
322Dic43—42no—
323Dic43—81no—
324Dic43—81no—
325C2×#461—431no—
326C2×#440—431no—
327C2×C4×SD16—431no—
328#2327—431no—
329#2275—431no—
330#1981D4311yescharacteristic, complemented
331#1949—431no—
332#1928—431no—
333#1927—431no—
334#1877—431no—
335#1877—431no—
336#1804—431no—
337#1768—431no—
338#1763—431no—
339C4×#103—431no—
340C2×C43C4×#12111yescharacteristic
341C2×C43#294711yescharacteristic
342C2×C43#294911yescharacteristic
343C2×C43#304211yescharacteristic
344C2×C43#304611yescharacteristic
345C2×C43#312011yescharacteristic
346C2×C43#312311yescharacteristic
347D43—44no—
348C22×SD16—431no—
349C22×SD16—431no—
350C2×C4⋊Q8C2×D4311yescharacteristic
351C2×C4×Q8—431no—
352C2×C4×Q8—431no—
353C2×C4×D4—431no—
354C2×C4×D4—431no—
355C2×C4×D4—431no—
356#461—438no—
357#440—864no—
358C4×SD16—864no—
359C2×#107—431no—
360C2×#106—431no—
361C2×C4⋊C8—431no—
362C2×C4⋊C8C2×D4311yescharacteristic
363C2×#103—431no—
364C2×#103—431no—
365C2×#103C2×D4311yescharacteristic
366C2×#103C2×D4311yescharacteristic
367C2×#103C2×D4311yescharacteristic
368C2×#103C2×D4311yescharacteristic
369C2×#102—431no—
370C2×#102—431no—
371C2×#97—431no—
372C2×C4×C8—431no—
373#391—431no—
374#391—431no—
375#387—861no—
376#387—861no—
377#387—861no—
378#387—861no—
379#382—431no—
380C4×C4⋊C4—431no—
381C4×C4⋊C4—431no—
382C4×C4⋊C4C2×D4311yescharacteristic
383C4×C22⋊C4—861no—
384C4×C22⋊C4—861no—
385C4×C22⋊C4—861no—
386#376—431no—
387C2×#95—861no—
388#340—431no—
389#340—431no—
390#340—431no—
391#340—431no—
392#336—431no—
393#336—431no—
394C43#2151411yescharacteristic, complemented, Sylow
395C22×Q8C22×D4311yescharacteristic
396C22×Q8C22×D4311yescharacteristic
397C22×D4—431no—
398C23×C4—861no—
399C23×C4—861no—
400C23×C4—861no—
401C2×SD16—434no—
402C2×SD16—434no—
403C2×SD16—862no—
404C2×SD16—862no—
405C2×SD16—862no—
406C2×SD16—862no—
407C22×C8—431no—
408C22×C8—431no—
409C22×C8C22×D4311yescharacteristic
410C22×C8C22×D4311yescharacteristic
411C4⋊Q8—22no—
412C4⋊Q8C4×D4314yescomplemented
413C4×Q8—862no—
414C4×Q8—862no—
415C4×Q8—862no—
416C4×Q8—862no—
417C4×D4—434no—
418C4×D4—434no—
419C4×D4—862no—
420C4×D4—862no—
421C4×D4—862no—
422C4×D4—862no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—431no—
426C2×C4⋊C4—431no—
427C2×C4⋊C4—431no—
428C2×C4⋊C4—861no—
429C2×C4⋊C4—861no—
430C2×C4⋊C4C22×D4311yescharacteristic
431C2×C4⋊C4C22×D4311yescharacteristic
432C2×C22⋊C4—861no—
433C2×C22⋊C4—861no—
434C2×C22⋊C4—861no—
435C2×C42—21no—
436C2×C42—431no—
437C2×C42—431no—
438C2×C42—861no—
439C2×C42—861no—
440C2×C42—861no—
441C2×C42—861no—
442C2×C42C22×D4311yescharacteristic
443#107—862no—
444#106—862no—
445C4⋊C8—22no—
446C4⋊C8—434no—
447#103—22no—
448#103—22no—
449#103—22no—
450#103—22no—
451#103—434no—
452#103—434no—
453#102—862no—
454#102—862no—
455#97—862no—
456C4×C8—862no—
457#95—21no—
458#95—431no—
459#95—431no—
460#95—431no—
461#95—431no—
462#95—861no—
463#95—861no—
464#95—861no—
465#95—861no—
466#95—861no—
467#95—861no—
468#95—861no—
469#95—861no—
470C24—861no—
471C2×Q8—21no—
472C2×Q8—21no—
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8C2×C4×D4312yes—
482C2×Q8C2×C4×D4312yes—
483C2×D4—432no—
484C2×D4—432no—
485C2×D4—432no—
486C2×D4—861no—
487C2×D4—861no—
488C2×D4—861no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—431no—
494C22×C4—431no—
495C22×C4—431no—
496C22×C4—431no—
497C22×C4—864no—
498C22×C4—864no—
499C22×C4—861no—
500C22×C4—864no—
501C22×C4—861no—
502C22×C4—861no—
503C22×C4—3441no—
504C22×C4—3441no—
505C22×C4—3441no—
506C22×C4—3441no—
507C22×C4—3441no—
508C22×C4—3441no—
509C22×C4D4×D4311yescharacteristic
510C22×C4D4×D4311yescharacteristic
511C22×C4C23×D4311yescharacteristic
512SD16—868no—
513SD16—868no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—432no—
521C2×C8—432no—
522C2×C8—861no—
523C2×C8—861no—
524C2×C8—861no—
525C2×C8—861no—
526C4⋊C4—24no—
527C4⋊C4—24no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—432no—
531C4⋊C4—861no—
532C4⋊C4—861no—
533C4⋊C4—861no—
534C4⋊C4—861no—
535C4⋊C4—861no—
536C4⋊C4—1722no—
537C4⋊C4—1722no—
538C4⋊C4D4×D4312yes—
539C4⋊C4#1062190012yes—
540C22⋊C4—864no—
541C22⋊C4—864no—
542C22⋊C4—864no—
543C42—81no—
544C42—432no—
545C42—432no—
546C42—861no—
547C42—861no—
548C42—3441no—
549C42—3441no—
550C42—1722no—
551C42—1722no—
552C42C2×C4×D4312yes—
553C42#1062190012yes—
554C23—862no—
555C23—862no—
556C23—862no—
557C23—1721no—
558C23—1721no—
559C23—1721no—
560C23—1721no—
561C23C2×D4×D4311yescharacteristic
562Q8—22no—
563Q8—22no—
564Q8—22no—
565Q8—22no—
566Q8—41no—
567Q8—41no—
568Q8—41no—
569Q8—41no—
570D4—434no—
571D4—862no—
572D4—862no—
573D4—862no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—432no—
591C2×C4—432no—
592C2×C4—861no—
593C2×C4—861no—
594C2×C4—861no—
595C2×C4—861no—
596C2×C4—862no—
597C2×C4—861no—
598C2×C4—861no—
599C2×C4—861no—
600C2×C4—861no—
601C2×C4—861no—
602C2×C4—861no—
603C2×C4—3444no—
604C2×C4—3444no—
605C2×C4—3444no—
606C2×C4—1721no—
607C2×C4—1721no—
608C2×C4—1721no—
609C2×C4—1721no—
610C2×C4—1721no—
611C2×C4—1721no—
612C2×C4—1721no—
613C2×C4—1721no—
614C2×C4(C22⋊D43)⋊C412yes—
615C2×C4(C22⋊D43)⋊C412yes—
616C2×C4C22×C4×D4311yescharacteristic
617C2×C4C2×D4×D4311yescharacteristic
618C2×C4#41×D4311yescharacteristic
619C2×C4#41×D4311yescharacteristic
620C2×C4C2×#1062190011yescharacteristic
621C2×C4C2×#1062190011yescharacteristic
622C8—41no—
623C8—41no—
624C8—862no—
625C8—862no—
626C22—864no—
627C22—1722no—
628C22—1722no—
629C22—1722no—
630C22—1722no—
631C22—1722no—
632C22—1722no—
633C22C2×(C22⋊D43)⋊C411yescharacteristic
634C22#121×D4311yescharacteristic
635C22#1458340911yescharacteristic
636C22#1458370511yescharacteristic
637C22#1458370811yescharacteristic
638C22#1458370811yescharacteristic
639C22#1458371211yescharacteristic
640C4—22no—
641C4—22no—
642C4—42no—
643C4—42no—
644C4—42no—
645C4—42no—
646C4—862no—
647C4—862no—
648C4—3441no—
649C4—3441no—
650C4—1722no—
651C4—1721no—
652C4—1721no—
653C4C4×D4×D4311yescharacteristic
654C4C4×#1062190011yescharacteristic
655C4#1458342811yescharacteristic
656C4#1458344711yescharacteristic
657C2—1724no—
658C2#1913711111yescharacteristic
659C2#1914343211yescharacteristic
660C2#1914345011yescharacteristic
661C2#1914410211yescharacteristic
662C2#1914414211yescharacteristic
663C2#1914480811yescharacteristic
664C2#1914484511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1981C2
socleC23×C43C22×D4
prime radicalC22×D172C23
cosocleC22×C4×C43C24
hypercenter#1981D43
hypocenterC43#21514
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1981

Complements

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

NH ≅ G/Ntype
4. #19137315C2semidirect
6. #19135363C2semidirect
7. #19135239C2semidirect
8. #19135232C2semidirect
12. #19134454C2semidirect
13. #19134427C2semidirect
14. #103×Dic43C2semidirect
15. C43×#1981C2semidirect
23. #14583101C4semidirect
100. C4⋊(C43⋊C8)C2×C4semidirect
101. #13063249C2×C4semidirect
102. #13063249C2×C4semidirect
124. C4⋊Q8×C43C2×C4semidirect
330. #1981D43semidirect
394. C43#21514semidirect
412. C4⋊Q8C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145831012
C2×#145830022
C2×#145829842
#191373152
#191369552
#191353632
#191352392
#191352322
#191349262
#191346062
#191344542
#191344272
#103×Dic432
C43×#19812
#2151443