Finite Group Databasebeta

← #25125406

Subgroups — #25125406

Order 11008.

1010 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582897C211yesmaximal, characteristic
2C2×#14582892C211yesmaximal, characteristic
3#19137220C211yesmaximal, characteristic, complemented
4#19137185C211yesmaximal, characteristic
5#19136017C211yesmaximal, characteristic, complemented
6#19136014C211yesmaximal, characteristic, complemented
7#19136011C211yesmaximal, characteristic, complemented
8#19136007C211yesmaximal, characteristic, complemented
9#19136005C211yesmaximal, characteristic, complemented
10#19136001C211yesmaximal, characteristic, complemented
11#19135998C211yesmaximal, characteristic, complemented
12#19134313C211yesmaximal, characteristic, complemented
13#340×D43C211yesmaximal, characteristic, complemented
14#19134290C211yesmaximal, characteristic, complemented
15C43×#2073C211yesmaximal, characteristic, complemented
16C22×#10621900C2211yescharacteristic
17C22×#10621872C2211yescharacteristic
18C22×C8×D43C2211yescharacteristic
19C2×#13063283C2211yescharacteristic
20C2×#13063282C2211yescharacteristic
21C2×C4⋊C4×D43C2211yescharacteristic
22C2×C4⋊C4×D43C2211yescharacteristic
23#14582897—24no—
24#14582892—24no—
25C2×#13063250C2211yescharacteristic
26C2×#13063250C2211yescharacteristic
27C2×#13063248C2211yescharacteristic
28C2×#13063248C2211yescharacteristic
29C2×#13063246C2211yescharacteristic
30C2×#13063246C2211yescharacteristic
31#14582805C2211yescharacteristic
32#14582804C2211yescharacteristic
33#14582802C2211yescharacteristic
34#14582796—21no—
35#14582796—21no—
36#14582775—21no—
37#14582775—21no—
38#14582773—21no—
39#14582773—21no—
40#14582769C2211yescharacteristic
41#14582768C2211yescharacteristic
42#14582764C2211yescharacteristic
43#14582757—21no—
44#14582757—21no—
45#14582662C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582654C2211yescharacteristic
52#14582653C2211yescharacteristic
53#14582653C2211yescharacteristic
54C2×#102×C43C2211yescharacteristic
55C2×#102×C43C2211yescharacteristic
56C43×#390C2211yescharacteristic
57C43×#382C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C43×#336C2211yescharacteristic
61C2×#10621900—22no—
62C2×#10621900—22no—
63C2×#10621900—22no—
64C2×#10621900—22no—
65C2×#10621900—22no—
66C2×#10621900D414yes—
67C22×Dic86C2311yescharacteristic
68C22×C22⋊D43—21no—
69C23×Dic43—21no—
70C22×C4×D43—21no—
71C22×C4×D43—21no—
72C22×C4×D43C2311yescharacteristic
73C2×#10621872—22no—
74C2×#10621872—22no—
75C2×#10621872—22no—
76C22×C43⋊C8C2311yescharacteristic
77C22×C43⋊C8C2311yescharacteristic
78C2×C8×D43—22no—
79C2×C8×D43—22no—
80C2×C8×D43—22no—
81#13063283—22no—
82#13063283—22no—
83#13063282—22no—
84#13063282—22no—
85C2×C4⋊Dic43—21no—
86C2×C4⋊Dic43—21no—
87C2×C4⋊Dic43C2311yescharacteristic
88C2×C4⋊Dic43C2311yescharacteristic
89C2×C4⋊Dic43C2311yescharacteristic
90C2×Dic43⋊C4—21no—
91C2×Dic43⋊C4—21no—
92C2×Dic43⋊C4—21no—
93C2×Dic43⋊C4—21no—
94C2×Dic43⋊C4D411yescharacteristic
95C2×Dic43⋊C4D411yescharacteristic
96C4⋊C4×D43—22no—
97C4⋊C4×D43—22no—
98C4⋊C4×D43—22no—
99C4⋊C4×D43—22no—
100C2×C22⋊Dic43—21no—
101C2×C22⋊Dic43—21no—
102C2×(C2×D43)⋊C4—21no—
103C2×(C2×D43)⋊C4D411yescharacteristic
104C2×(C2×D43)⋊C4D411yescharacteristic
105C2×C4×Dic43—21no—
106C2×C4×Dic43C2311yescharacteristic
107#13063250—22no—
108#13063250—22no—
109#13063248—22no—
110#13063248—22no—
111#13063246—22no—
112#13063246—22no—
113C43⋊#95—21no—
114C43⋊#95—21no—
115C43⋊#95—21no—
116C43⋊#95—21no—
117C43⋊#95—21no—
118C43⋊#95—21no—
119C22×D4×C43C2311yescharacteristic
120C22×C8×C43C2311yescharacteristic
121C22×C8×C43C2311yescharacteristic
122C2×C4⋊C4×C43C2311yescharacteristic
123C2×C4⋊C4×C43C2311yescharacteristic
124C2×C4⋊C4×C43C2311yescharacteristic
125C2×C22⋊C4×C43—21no—
126C2×C22⋊C4×C43—21no—
127C2×C42×C43C2311yescharacteristic
128#102×C43—22no—
129#102×C43—22no—
130#95×C43—21no—
131#95×C43—21no—
132C24×C43—21no—
133C23×D43C2×D411yescharacteristic
134C2×D4×C43—21no—
135C2×D4×C43—21no—
136C2×D4×C43—21no—
137C2×D4×C43—21no—
138C2×D4×C43—21no—
139C2×D4×C43C2×D412yes—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43—21no—
143C22×C4×C43C2×D411yescharacteristic
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2411yescharacteristic
146C2×C22⋊D43—24no—
147C2×C22⋊D43—42no—
148C2×C22⋊D43—42no—
149C22×Dic43—24no—
150C22×Dic43—21no—
151C22×Dic43—21no—
152C22×Dic43—21no—
153C22×Dic43—21no—
154C22×Dic43—42no—
155C22×Dic43—42no—
156C22×Dic43C2×D411yescharacteristic
157C22×Dic43C2×D411yescharacteristic
158C22×Dic43C2×D411yescharacteristic
159#10621900—28no—
160#10621900—28no—
161#10621900—44no—
162#10621900—44no—
163C2×C4×D43—42no—
164C2×C4×D43—42no—
165C2×C4×D43—81no—
166C2×C4×D43—81no—
167C2×C4×D43—81no—
168C2×C4×D43—81no—
169C2×C4×D43C2×D412yes—
170C2×C4×D43#4112yes—
171C2×C4×D43#4112yes—
172C2×C4×D43#4112yes—
173C2×C4×D43#4112yes—
174C2×C4×D43#4112yes—
175C2×Dic86—21no—
176C2×Dic86—21no—
177C2×Dic86—21no—
178C2×Dic86—21no—
179C2×Dic86—21no—
180C2×Dic86C2×D412yes—
181C2×C8×C43—21no—
182C2×C8×C43—21no—
183C2×C8×C43—21no—
184C2×C8×C43—21no—
185C2×C8×C43—21no—
186C2×C8×C43—21no—
187C4⋊C4×C43—21no—
188C4⋊C4×C43—21no—
189C4⋊C4×C43—21no—
190C4⋊C4×C43—21no—
191C4⋊C4×C43—21no—
192C4⋊C4×C43—21no—
193C22⋊C4×C43—81no—
194C22⋊C4×C43—81no—
195C42×C43—21no—
196C42×C43—21no—
197C22⋊Dic43—81no—
198C22⋊Dic43—81no—
199(C2×D43)⋊C4—22no—
200(C2×D43)⋊C4—22no—
201(C2×D43)⋊C4—42no—
202C4⋊Dic43—21no—
203C4⋊Dic43—21no—
204C4⋊Dic43—21no—
205C4⋊Dic43—21no—
206C4⋊Dic43—21no—
207C4⋊Dic43—21no—
208C4⋊Dic43—81no—
209C4⋊Dic43—81no—
210Dic43⋊C4—22no—
211Dic43⋊C4—22no—
212Dic43⋊C4—42no—
213Dic43⋊C4—42no—
214Dic43⋊C4—81no—
215Dic43⋊C4—81no—
216C4×Dic43—21no—
217C4×Dic43—21no—
218C4×Dic43—42no—
219C2×C43⋊C8—21no—
220C2×C43⋊C8—21no—
221C2×C43⋊C8—21no—
222C2×C43⋊C8—21no—
223C2×C43⋊C8—21no—
224C2×C43⋊C8—21no—
225#10621872—44no—
226C8×D43—44no—
227C23×C43—22no—
228C23×C43—41no—
229C23×C43—41no—
230C23×C43—41no—
231C23×C43—41no—
232C23×C43—41no—
233C23×C43—41no—
234C23×C43C22×D411yescharacteristic
235C22×D43—21no—
236C22×D43—21no—
237C22×D43—21no—
238C22×D43—21no—
239C22×D43#12112yes—
240C22×D43#12312yes—
241C22×D43#12412yes—
242D4×C43—22no—
243D4×C43—22no—
244D4×C43—41no—
245D4×C43—41no—
246C2×C4×C43—21no—
247C2×C4×C43—21no—
248C2×C4×C43—21no—
249C2×C4×C43—21no—
250C2×C4×C43—21no—
251C2×C4×C43—21no—
252C2×C4×C43—41no—
253C2×C4×C43—41no—
254C2×C4×C43—41no—
255C2×C4×C43—41no—
256C2×C4×C43—41no—
257C2×C4×C43—41no—
258C2×C4×C43—41no—
259C2×C4×C43—41no—
260C2×C4×C43—41no—
261C2×C4×C43C22×D411yescharacteristic
262C2×C4×C43C2×#4111yescharacteristic
263C2×C4×C43C2×#4111yescharacteristic
264C2×C4×C43C2×#4111yescharacteristic
265C2×C4×C43C2×#4111yescharacteristic
266C2×C4×C43C2×#4111yescharacteristic
267C22⋊D43—48no—
268C2×Dic43—22no—
269C2×Dic43—21no—
270C2×Dic43—21no—
271C2×Dic43—21no—
272C2×Dic43—21no—
273C2×Dic43—21no—
274C2×Dic43—21no—
275C2×Dic43—41no—
276C2×Dic43—41no—
277C2×Dic43—48no—
278C2×Dic43—41no—
279C2×Dic43—41no—
280C2×Dic43—41no—
281C2×Dic43—41no—
282C2×Dic43—41no—
283C2×Dic43—41no—
284C2×Dic43—41no—
285C2×Dic43—41no—
286C2×Dic43—41no—
287C2×Dic43#12112yes—
288C2×Dic43#12312yes—
289C2×Dic43#12412yes—
290C4×D43—84no—
291C4×D43—84no—
292C4×D43#12314yes—
293C4×D43#12314yes—
294C4×D43#12614yes—
295C4×D43#12614yes—
296Dic86—22no—
297Dic86—22no—
298Dic86—41no—
299Dic86—41no—
300C8×C43—41no—
301C8×C43—41no—
302C43⋊C8—41no—
303C43⋊C8—41no—
304#23634—431nomaximal, Sylow
305C22×C43—42no—
306C22×C43—42no—
307C22×C43—42no—
308C22×C43—81no—
309C22×C43—81no—
310C22×C43—81no—
311C22×C43—81no—
312C22×C43C2×#12111yescharacteristic
313C22×C43C2×#12311yescharacteristic
314C22×C43C2×#12411yescharacteristic
315C22×C43#57611yescharacteristic
316C22×C43#57711yescharacteristic
317C22×C43#57711yescharacteristic
318C22×C43#57811yescharacteristic
319C2×D43—22no—
320C2×D43—22no—
321C2×D43—22no—
322C2×D43—22no—
323C2×D43—22no—
324C2×D43—22no—
325C2×D43#39714yes—
326C4×C43—41no—
327C4×C43—41no—
328C4×C43—81no—
329C4×C43—81no—
330C4×C43—81no—
331C4×C43C2×#12311yescharacteristic
332C4×C43C2×#12311yescharacteristic
333C4×C43C2×#12611yescharacteristic
334C4×C43C2×#12611yescharacteristic
335Dic43—41no—
336Dic43—41no—
337Dic43—42no—
338Dic43—81no—
339Dic43—81no—
340Dic43—81no—
341Dic43#39714yes—
342C2×#417—431no—
343C2×#416—431no—
344#2317—431no—
345#2311—431no—
346#2074—431no—
347#2074—431no—
348#2073—431no—
349#2073D4311yescharacteristic, complemented
350#2072—431no—
351#2072—431no—
352#2071—431no—
353#2071—431no—
354#1736—431no—
355C2×#340—431no—
356#1729—431no—
357C2×C43—82no—
358C2×C43C2×#39711yescharacteristic
359C2×C43#304511yescharacteristic
360C2×C43#304611yescharacteristic
361C2×C43#309811yescharacteristic
362C2×C43#309911yescharacteristic
363C2×C43#313611yescharacteristic
364C2×C43#313711yescharacteristic
365D43—24no—
366C22×#41—431no—
367C22×M16—431no—
368C23×C8—431no—
369C2×#117—431no—
370C2×#117—431no—
371C22×C4⋊C4—431no—
372C22×C4⋊C4—431no—
373#417—864no—
374#416—864no—
375C2×#103—431no—
376C2×#103—431no—
377C2×#103—431no—
378C2×#103—431no—
379C2×#102—431no—
380C2×#102—431no—
381C2×#102C2×D4311yescharacteristic
382C2×#102C2×D4311yescharacteristic
383#391—431no—
384#391—431no—
385#390—431no—
386#390C2×D4311yescharacteristic
387#389—861no—
388#389—861no—
389#386—861no—
390#386—861no—
391#385—861no—
392#385—861no—
393#384—431no—
394#384—431no—
395#382—431no—
396#382C2×D4311yescharacteristic
397#380—861no—
398#380—861no—
399#340—431no—
400#340—431no—
401#340—431no—
402#340—431no—
403#340—431no—
404#340—431no—
405#340C2×D4311yescharacteristic
406#340C2×D4311yescharacteristic
407#336—431no—
408#336—431no—
409#336—431no—
410#336C2×D4311yescharacteristic
411C43#2363411yescharacteristic, complemented, Sylow
412C2×#41—434no—
413C2×#41—862no—
414C2×#41—862no—
415C2×#41—862no—
416C2×#41—862no—
417C2×#41—862no—
418C22×Q8—431no—
419C22×D4—861no—
420C22×D4C22×D4311yescharacteristic
421C23×C4—431no—
422C23×C4—861no—
423C23×C4—861no—
424C23×C4—861no—
425C2×M16—862no—
426C2×M16—862no—
427C2×M16—862no—
428C22×C8—431no—
429C22×C8—431no—
430C22×C8—862no—
431C22×C8—862no—
432C22×C8—862no—
433C22×C8C22×D4311yescharacteristic
434C22×C8C22×D4311yescharacteristic
435#117—862no—
436#117—862no—
437#117—862no—
438#117—862no—
439C2×C4⋊C4—431no—
440C2×C4⋊C4—431no—
441C2×C4⋊C4—431no—
442C2×C4⋊C4—431no—
443C2×C4⋊C4—431no—
444C2×C4⋊C4—862no—
445C2×C4⋊C4—862no—
446C2×C4⋊C4—862no—
447C2×C4⋊C4—862no—
448C2×C4⋊C4—861no—
449C2×C4⋊C4—861no—
450C2×C4⋊C4—861no—
451C2×C4⋊C4—861no—
452C2×C4⋊C4—861no—
453C2×C4⋊C4—861no—
454C2×C4⋊C4C22×D4311yescharacteristic
455C2×C4⋊C4C22×D4311yescharacteristic
456C2×C4⋊C4C22×D4311yescharacteristic
457C2×C22⋊C4—21no—
458C2×C22⋊C4—21no—
459C2×C22⋊C4—431no—
460C2×C22⋊C4—431no—
461C2×C22⋊C4—861no—
462C2×C22⋊C4—861no—
463C2×C22⋊C4—861no—
464C2×C42—431no—
465C2×C42—861no—
466C2×C42C22×D4311yescharacteristic
467#103—862no—
468#103—862no—
469#103—862no—
470#103—862no—
471#102—22no—
472#102—22no—
473#102—862no—
474#102—862no—
475#95—21no—
476#95—21no—
477#95—861no—
478#95—861no—
479#95—861no—
480#95—861no—
481#95—861no—
482#95—861no—
483C24—21no—
484C24—431no—
485#41—868no—
486#41—868no—
487#41—1724no—
488#41—1724no—
489C2×Q8—432no—
490C2×Q8—861no—
491C2×Q8—861no—
492C2×Q8—861no—
493C2×Q8—861no—
494C2×Q8—861no—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—21no—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—864no—
501C2×D4—1722no—
502C2×D4—1722no—
503C2×D4D4×D4312yes—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—431no—
508C22×C4—432no—
509C22×C4—432no—
510C22×C4—432no—
511C22×C4—432no—
512C22×C4—432no—
513C22×C4—432no—
514C22×C4—431no—
515C22×C4—431no—
516C22×C4—864no—
517C22×C4—861no—
518C22×C4—861no—
519C22×C4—861no—
520C22×C4—861no—
521C22×C4—3441no—
522C22×C4—3441no—
523C22×C4—3441no—
524C22×C4—3441no—
525C22×C4—1722no—
526C22×C4—1722no—
527C22×C4—1722no—
528C22×C4—1722no—
529C22×C4D4×D4311yescharacteristic
530C22×C4D4×D4311yescharacteristic
531C22×C4C23×D4311yescharacteristic
532M16—1724no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—861no—
540C2×C8—861no—
541C2×C8—861no—
542C2×C8—861no—
543C2×C8—861no—
544C2×C8—861no—
545C2×C8—1724no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—862no—
553C4⋊C4—862no—
554C4⋊C4—861no—
555C4⋊C4—861no—
556C4⋊C4—861no—
557C4⋊C4—861no—
558C4⋊C4—861no—
559C4⋊C4—861no—
560C4⋊C4—3441no—
561C4⋊C4—3441no—
562C4⋊C4—3441no—
563C4⋊C4—3441no—
564C4⋊C4—1722no—
565C4⋊C4—1722no—
566C22⋊C4—81no—
567C22⋊C4—81no—
568C22⋊C4—862no—
569C22⋊C4—862no—
570C22⋊C4—3441no—
571C22⋊C4—3441no—
572C22⋊C4—1722no—
573C42—21no—
574C42—21no—
575C42—861no—
576C42—861no—
577C42—1722no—
578C23—22no—
579C23—41no—
580C23—41no—
581C23—41no—
582C23—41no—
583C23—41no—
584C23—41no—
585C23—432no—
586C23—432no—
587C23—432no—
588C23—861no—
589C23—861no—
590C23—861no—
591C23—861no—
592C23C2×D4×D4311yescharacteristic
593Q8—862no—
594Q8—862no—
595Q8—1721no—
596Q8—1721no—
597D4—22no—
598D4—22no—
599D4—41no—
600D4—41no—
601D4—1728no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—432no—
618C2×C4—432no—
619C2×C4—432no—
620C2×C4—434no—
621C2×C4—434no—
622C2×C4—434no—
623C2×C4—434no—
624C2×C4—862no—
625C2×C4—861no—
626C2×C4—861no—
627C2×C4—861no—
628C2×C4—861no—
629C2×C4—861no—
630C2×C4—861no—
631C2×C4—3444no—
632C2×C4—3444no—
633C2×C4—1728no—
634C2×C4—1721no—
635C2×C4—1721no—
636C2×C4—1721no—
637C2×C4—1721no—
638C2×C4—1721no—
639C2×C4—1721no—
640C2×C4—1721no—
641C2×C4—1721no—
642C2×C4—1721no—
643C2×C4—1721no—
644C2×C4—1721no—
645C2×C4C2×D4×D4311yescharacteristic
646C2×C4#41×D4311yescharacteristic
647C2×C4#41×D4311yescharacteristic
648C2×C4#41×D4311yescharacteristic
649C2×C4#41×D4311yescharacteristic
650C2×C4#41×D4311yescharacteristic
651C8—41no—
652C8—41no—
653C8—1721no—
654C8—1721no—
655C22—42no—
656C22—42no—
657C22—42no—
658C22—81no—
659C22—81no—
660C22—81no—
661C22—81no—
662C22—434no—
663C22—862no—
664C22—862no—
665C22—862no—
666C22—862no—
667C22—862no—
668C22—862no—
669C22#121×D4311yescharacteristic
670C22#123×D4311yescharacteristic
671C22#124×D4311yescharacteristic
672C22#1458370311yescharacteristic
673C22#1458370611yescharacteristic
674C22#1458370911yescharacteristic
675C22#1458371311yescharacteristic
676C4—41no—
677C4—41no—
678C4—81no—
679C4—81no—
680C4—81no—
681C4—434no—
682C4—3441no—
683C4—3441no—
684C4—3441no—
685C4—1722no—
686C4—1721no—
687C4—1721no—
688C4#123×D4311yescharacteristic
689C4#123×D4311yescharacteristic
690C4#126×D4311yescharacteristic
691C4#126×D4311yescharacteristic
692C2—82no—
693C2—864no—
694C2#397×D4311yescharacteristic
695C2#1914413511yescharacteristic
696C2#1914414611yescharacteristic
697C2#1914457011yescharacteristic
698C2#1914458711yescharacteristic
699C2#1914495011yescharacteristic
700C2#1914495911yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2073C2
socleC23×C43C22×D4
prime radicalC22×#10621900C22
hypercenter#2073D43
hypocenterC43#23634
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2073

Complements

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

NH ≅ G/Ntype
3. #19137220C2semidirect
5. #19136017C2semidirect
6. #19136014C2semidirect
7. #19136011C2semidirect
8. #19136007C2semidirect
9. #19136005C2semidirect
10. #19136001C2semidirect
11. #19135998C2semidirect
12. #19134313C2semidirect
13. #340×D43C2semidirect
14. #19134290C2semidirect
15. C43×#2073C2semidirect
349. #2073D43semidirect
411. C43#23634semidirect

Maximal subgroups

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

subgroupindex
C2×#145828972
C2×#145828922
#191372202
#191371852
#191360172
#191360142
#191360112
#191360072
#191360052
#191360012
#191359982
#191343132
#340×D432
#191342902
C43×#20732
#2363443