Finite Group Databasebeta

← #25125408

Subgroups — #25125408

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×#14582899C211yesmaximal, characteristic
2C2×#14582894C211yesmaximal, characteristic
3#19137216C211yesmaximal, characteristic, complemented
4#19137186C211yesmaximal, characteristic
5#19136016C211yesmaximal, characteristic, complemented
6#19136013C211yesmaximal, characteristic, complemented
7#19136012C211yesmaximal, characteristic, complemented
8#19136010C211yesmaximal, characteristic, complemented
9#19136006C211yesmaximal, characteristic, complemented
10#19136002C211yesmaximal, characteristic, complemented
11#19135999C211yesmaximal, characteristic, complemented
12#19134313C211yesmaximal, characteristic, complemented
13#340×D43C211yesmaximal, characteristic, complemented
14#19134290C211yesmaximal, characteristic, complemented
15C43×#2072C211yesmaximal, characteristic, complemented
16C22×#10621902C2211yescharacteristic
17C22×#10621872C2211yescharacteristic
18C22×C8×D43C2211yescharacteristic
19C2×#13063283C2211yescharacteristic
20C2×#13063282C2211yescharacteristic
21C2×C4⋊C4×D43C2211yescharacteristic
22C2×C4⋊C4×D43C2211yescharacteristic
23#14582899—24no—
24#14582894—24no—
25C2×#13063249C2211yescharacteristic
26C2×#13063249C2211yescharacteristic
27C2×#13063247C2211yescharacteristic
28C2×#13063247C2211yescharacteristic
29C2×#13063245C2211yescharacteristic
30C2×#13063245C2211yescharacteristic
31#14582806C2211yescharacteristic
32#14582801C2211yescharacteristic
33#14582800C2211yescharacteristic
34#14582794—21no—
35#14582794—21no—
36#14582777—21no—
37#14582777—21no—
38#14582770—21no—
39#14582770—21no—
40#14582768C2211yescharacteristic
41#14582765C2211yescharacteristic
42#14582764C2211yescharacteristic
43#14582758—21no—
44#14582758—21no—
45#14582662C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582654C2211yescharacteristic
52#14582653C2211yescharacteristic
53#14582653C2211yescharacteristic
54C2×#103×C43C2211yescharacteristic
55C2×#103×C43C2211yescharacteristic
56C43×#391C2211yescharacteristic
57C43×#384C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C43×#336C2211yescharacteristic
61C2×#10621902—22no—
62C2×#10621902—22no—
63C2×#10621902—22no—
64C2×#10621902—22no—
65C2×#10621902—22no—
66C2×#10621902D414yes—
67C22×D172—21no—
68C22×D172C2311yescharacteristic
69C22×C4×D43—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⋊Dic43C2311yescharacteristic
86C2×C4⋊Dic43C2311yescharacteristic
87C2×C4⋊Dic43C2311yescharacteristic
88C2×Dic43⋊C4—21no—
89C2×Dic43⋊C4—21no—
90C2×Dic43⋊C4—21no—
91C2×Dic43⋊C4—21no—
92C2×Dic43⋊C4D411yescharacteristic
93C2×Dic43⋊C4D411yescharacteristic
94C4⋊C4×D43—22no—
95C4⋊C4×D43—22no—
96C4⋊C4×D43—22no—
97C4⋊C4×D43—22no—
98C2×(C2×D43)⋊C4—21no—
99C2×(C2×D43)⋊C4—21no—
100C2×(C2×D43)⋊C4—21no—
101C2×(C2×D43)⋊C4—21no—
102C2×(C2×D43)⋊C4—21no—
103C2×(C2×D43)⋊C4D411yescharacteristic
104C2×(C2×D43)⋊C4D411yescharacteristic
105C2×C4×Dic43—21no—
106C2×C4×Dic43C2311yescharacteristic
107#13063249—22no—
108#13063249—22no—
109#13063247—22no—
110#13063247—22no—
111#13063245—22no—
112#13063245—22no—
113C43⋊#95—21no—
114C43⋊#95—21no—
115C43⋊#95—21no—
116C43⋊#95—21no—
117C43⋊#95—21no—
118C43⋊#95—21no—
119C22×Q8×C43C2311yescharacteristic
120C22×C8×C43C2311yescharacteristic
121C22×C8×C43C2311yescharacteristic
122C2×C4⋊C4×C43—21no—
123C2×C4⋊C4×C43—21no—
124C2×C4⋊C4×C43C2311yescharacteristic
125C2×C4⋊C4×C43C2311yescharacteristic
126C2×C4⋊C4×C43C2311yescharacteristic
127C2×C42×C43C2311yescharacteristic
128#103×C43—22no—
129#103×C43—22no—
130#95×C43—21no—
131#95×C43—21no—
132C23×D43—21no—
133C23×D43C2×D411yescharacteristic
134C2×Q8×C43—21no—
135C2×Q8×C43—21no—
136C2×Q8×C43—21no—
137C2×Q8×C43—21no—
138C2×Q8×C43—21no—
139C2×Q8×C43C2×D412yes—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43—21no—
143C22×C4×C43—21no—
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43C2411yescharacteristic
147C22×Dic43—21no—
148C22×Dic43—21no—
149C22×Dic43—21no—
150C22×Dic43C2×D411yescharacteristic
151C22×Dic43C2×D411yescharacteristic
152C22×Dic43C2×D411yescharacteristic
153#10621902—28no—
154#10621902—28no—
155#10621902—44no—
156#10621902—44no—
157C2×D172—21no—
158C2×D172—24no—
159C2×D172—21no—
160C2×D172—21no—
161C2×D172—21no—
162C2×D172—21no—
163C2×D172—42no—
164C2×D172—42no—
165C2×D172C2×D412yes—
166C2×C4×D43—24no—
167C2×C4×D43—42no—
168C2×C4×D43—42no—
169C2×C4×D43—42no—
170C2×C4×D43—42no—
171C2×C4×D43—81no—
172C2×C4×D43—81no—
173C2×C4×D43—81no—
174C2×C4×D43—81no—
175C2×C4×D43C2×D412yes—
176C2×C4×D43#4112yes—
177C2×C4×D43#4112yes—
178C2×C4×D43#4112yes—
179C2×C4×D43#4112yes—
180C2×C4×D43#4112yes—
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—
193C4⋊C4×C43—81no—
194C4⋊C4×C43—81no—
195C42×C43—21no—
196C42×C43—21no—
197(C2×D43)⋊C4—22no—
198(C2×D43)⋊C4—22no—
199(C2×D43)⋊C4—42no—
200(C2×D43)⋊C4—81no—
201(C2×D43)⋊C4—81no—
202(C2×D43)⋊C4—81no—
203(C2×D43)⋊C4—81no—
204C4⋊Dic43—21no—
205C4⋊Dic43—21no—
206C4⋊Dic43—21no—
207C4⋊Dic43—21no—
208C4⋊Dic43—21no—
209C4⋊Dic43—21no—
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×C43C22×D411yescharacteristic
228C22×D43—21no—
229C22×D43—21no—
230C22×D43—21no—
231C22×D43—21no—
232C22×D43—22no—
233C22×D43—41no—
234C22×D43—41no—
235C22×D43—41no—
236C22×D43—41no—
237C22×D43—41no—
238C22×D43—41no—
239C22×D43#12112yes—
240C22×D43#12312yes—
241C22×D43#12412yes—
242Q8×C43—22no—
243Q8×C43—22no—
244Q8×C43—41no—
245Q8×C43—41no—
246C2×C4×C43—22no—
247C2×C4×C43—21no—
248C2×C4×C43—21no—
249C2×C4×C43—21no—
250C2×C4×C43—21no—
251C2×C4×C43—21no—
252C2×C4×C43—21no—
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×C43—41no—
262C2×C4×C43—41no—
263C2×C4×C43—41no—
264C2×C4×C43C22×D411yescharacteristic
265C2×C4×C43C2×#4111yescharacteristic
266C2×C4×C43C2×#4111yescharacteristic
267C2×C4×C43C2×#4111yescharacteristic
268C2×C4×C43C2×#4111yescharacteristic
269C2×C4×C43C2×#4111yescharacteristic
270C2×Dic43—21no—
271C2×Dic43—21no—
272C2×Dic43—21no—
273C2×Dic43—21no—
274C2×Dic43—21no—
275C2×Dic43—21no—
276C2×Dic43—41no—
277C2×Dic43—41no—
278C2×Dic43—41no—
279C2×Dic43—41no—
280C2×Dic43—41no—
281C2×Dic43—41no—
282C2×Dic43—41no—
283C2×Dic43—41no—
284C2×Dic43—41no—
285C2×Dic43#12112yes—
286C2×Dic43#12312yes—
287C2×Dic43#12412yes—
288D172—22no—
289D172—22no—
290D172—48no—
291D172—41no—
292D172—41no—
293C4×D43—48no—
294C4×D43—84no—
295C4×D43—84no—
296C4×D43#12314yes—
297C4×D43#12314yes—
298C4×D43#12614yes—
299C4×D43#12614yes—
300C8×C43—41no—
301C8×C43—41no—
302C43⋊C8—41no—
303C43⋊C8—41no—
304#23634—431nomaximal, Sylow
305C22×C43C2×#12111yescharacteristic
306C22×C43C2×#12311yescharacteristic
307C22×C43C2×#12411yescharacteristic
308C22×C43#57611yescharacteristic
309C22×C43#57711yescharacteristic
310C22×C43#57711yescharacteristic
311C22×C43#57811yescharacteristic
312C2×D43—22no—
313C2×D43—22no—
314C2×D43—22no—
315C2×D43—22no—
316C2×D43—22no—
317C2×D43—22no—
318C2×D43—42no—
319C2×D43—42no—
320C2×D43—42no—
321C2×D43—81no—
322C2×D43—81no—
323C2×D43—81no—
324C2×D43—81no—
325C2×D43#39714yes—
326C4×C43—41no—
327C4×C43—41no—
328C4×C43—42no—
329C4×C43—81no—
330C4×C43—81no—
331C4×C43—81no—
332C4×C43C2×#12311yescharacteristic
333C4×C43C2×#12311yescharacteristic
334C4×C43C2×#12611yescharacteristic
335C4×C43C2×#12611yescharacteristic
336Dic43—41no—
337Dic43—41no—
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#2073—431no—
350#2072—431no—
351#2072D4311yescharacteristic, complemented
352#2071—431no—
353#2071—431no—
354#1736—431no—
355C2×#340—431no—
356#1729—431no—
357C2×C43C2×#39711yescharacteristic
358C2×C43#304511yescharacteristic
359C2×C43#304611yescharacteristic
360C2×C43#309811yescharacteristic
361C2×C43#309911yescharacteristic
362C2×C43#313611yescharacteristic
363C2×C43#313711yescharacteristic
364D43—24no—
365D43—82no—
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×#103C2×D4311yescharacteristic
378C2×#103C2×D4311yescharacteristic
379C2×#102—431no—
380C2×#102—431no—
381C2×#102—431no—
382C2×#102—431no—
383#391—431no—
384#391C2×D4311yescharacteristic
385#390—431no—
386#390—431no—
387#389—861no—
388#389—861no—
389#386—861no—
390#386—861no—
391#385—861no—
392#385—861no—
393#384—431no—
394#384C2×D4311yescharacteristic
395#382—431no—
396#382—431no—
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×Q8C22×D4311yescharacteristic
419C22×D4—431no—
420C22×D4—861no—
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—21no—
440C2×C4⋊C4—21no—
441C2×C4⋊C4—431no—
442C2×C4⋊C4—431no—
443C2×C4⋊C4—431no—
444C2×C4⋊C4—431no—
445C2×C4⋊C4—431no—
446C2×C4⋊C4—862no—
447C2×C4⋊C4—862no—
448C2×C4⋊C4—862no—
449C2×C4⋊C4—862no—
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—431no—
458C2×C22⋊C4—431no—
459C2×C22⋊C4—861no—
460C2×C22⋊C4—861no—
461C2×C22⋊C4—861no—
462C2×C22⋊C4—861no—
463C2×C22⋊C4—861no—
464C2×C42—431no—
465C2×C42—861no—
466C2×C42C22×D4311yescharacteristic
467#103—22no—
468#103—22no—
469#103—862no—
470#103—862no—
471#102—862no—
472#102—862no—
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—431no—
484C24—861no—
485#41—868no—
486#41—868no—
487#41—1724no—
488#41—1724no—
489C2×Q8—21no—
490C2×Q8—21no—
491C2×Q8—21no—
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8D4×D4312yes—
495C2×D4—432no—
496C2×D4—864no—
497C2×D4—861no—
498C2×D4—861no—
499C2×D4—861no—
500C2×D4—861no—
501C2×D4—861no—
502C2×D4—1722no—
503C2×D4—1722no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—431no—
509C22×C4—432no—
510C22×C4—432no—
511C22×C4—432no—
512C22×C4—432no—
513C22×C4—432no—
514C22×C4—432no—
515C22×C4—431no—
516C22×C4—431no—
517C22×C4—864no—
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—81no—
553C4⋊C4—81no—
554C4⋊C4—862no—
555C4⋊C4—862no—
556C4⋊C4—861no—
557C4⋊C4—861no—
558C4⋊C4—861no—
559C4⋊C4—861no—
560C4⋊C4—861no—
561C4⋊C4—861no—
562C4⋊C4—3441no—
563C4⋊C4—3441no—
564C4⋊C4—1722no—
565C4⋊C4—1722no—
566C22⋊C4—862no—
567C22⋊C4—862no—
568C22⋊C4—3441no—
569C22⋊C4—3441no—
570C22⋊C4—3441no—
571C22⋊C4—3441no—
572C22⋊C4—1722no—
573C42—21no—
574C42—21no—
575C42—861no—
576C42—861no—
577C42—1722no—
578C23—432no—
579C23—432no—
580C23—432no—
581C23—861no—
582C23—861no—
583C23—861no—
584C23—861no—
585C23—862no—
586C23—1721no—
587C23—1721no—
588C23—1721no—
589C23—1721no—
590C23—1721no—
591C23—1721no—
592C23C2×D4×D4311yescharacteristic
593Q8—22no—
594Q8—22no—
595Q8—41no—
596Q8—41no—
597D4—862no—
598D4—862no—
599D4—1728no—
600D4—1721no—
601D4—1721no—
602C2×C4—22no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
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—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—432no—
621C2×C4—432no—
622C2×C4—432no—
623C2×C4—434no—
624C2×C4—434no—
625C2×C4—434no—
626C2×C4—434no—
627C2×C4—861no—
628C2×C4—861no—
629C2×C4—861no—
630C2×C4—861no—
631C2×C4—861no—
632C2×C4—861no—
633C2×C4—3444no—
634C2×C4—3444no—
635C2×C4—1728no—
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—434no—
656C22—862no—
657C22—862no—
658C22—862no—
659C22—862no—
660C22—862no—
661C22—862no—
662C22—3441no—
663C22—3441no—
664C22—3441no—
665C22—3441no—
666C22—1722no—
667C22—1722no—
668C22—1722no—
669C22#121×D4311yescharacteristic
670C22#123×D4311yescharacteristic
671C22#124×D4311yescharacteristic
672C22#1458370311yescharacteristic
673C22#1458370511yescharacteristic
674C22#1458370811yescharacteristic
675C22#1458371211yescharacteristic
676C4—42no—
677C4—41no—
678C4—41no—
679C4—81no—
680C4—81no—
681C4—81no—
682C4—434no—
683C4—3441no—
684C4—3441no—
685C4—3441no—
686C4—1721no—
687C4—1721no—
688C4#123×D4311yescharacteristic
689C4#123×D4311yescharacteristic
690C4#126×D4311yescharacteristic
691C4#126×D4311yescharacteristic
692C2—864no—
693C2—3442no—
694C2#397×D4311yescharacteristic
695C2#1914413111yescharacteristic
696C2#1914414211yescharacteristic
697C2#1914457411yescharacteristic
698C2#1914457911yescharacteristic
699C2#1914494611yescharacteristic
700C2#1914495511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2072C2
socleC23×C43C22×D4
prime radicalC22×#10621902C22
hypercenter#2072D43
hypocenterC43#23634
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2072

Complements

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

NH ≅ G/Ntype
3. #19137216C2semidirect
5. #19136016C2semidirect
6. #19136013C2semidirect
7. #19136012C2semidirect
8. #19136010C2semidirect
9. #19136006C2semidirect
10. #19136002C2semidirect
11. #19135999C2semidirect
12. #19134313C2semidirect
13. #340×D43C2semidirect
14. #19134290C2semidirect
15. C43×#2072C2semidirect
351. #2072D43semidirect
411. C43#23634semidirect

Maximal subgroups

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

subgroupindex
C2×#145828992
C2×#145828942
#191372162
#191371862
#191360162
#191360132
#191360122
#191360102
#191360062
#191360022
#191359992
#191343132
#340×D432
#191342902
C43×#20722
#2363443