Finite Group Databasebeta

← #25126396

Subgroups — #25126396

Order 11008.

1126 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582936C211yesmaximal, characteristic, complemented
2C2×#14582934C211yesmaximal, characteristic, complemented
3C2×#14582894C211yesmaximal, characteristic
4C2×#14582894C211yesmaximal, characteristic
5#19137084C211yesmaximal, characteristic
6#19137001C211yesmaximal, characteristic, complemented
7#19136143C211yesmaximal, characteristic, complemented
8#19136136C211yesmaximal, characteristic, complemented
9#19136131C211yesmaximal, characteristic, complemented
10#19136125C211yesmaximal, characteristic, complemented
11#19136120C211yesmaximal, characteristic, complemented
12#19136119C211yesmaximal, characteristic, complemented
13#19136115C211yesmaximal, characteristic, complemented
14#336×D43C211yesmaximal, characteristic, complemented
15C43×#2097C211yesmaximal, characteristic, complemented
16C22×#10621902C2211yescharacteristic
17C22×C8×D43C2211yescharacteristic
18C22×C8×D43C2211yescharacteristic
19C2×#13063283C2211yescharacteristic
20C2×#13063283C2211yescharacteristic
21C2×#13063283C2211yescharacteristic
22C2×C42×D43C2211yescharacteristic
23#14582936—24no—
24#14582934—24no—
25C2×#13063259C2211yescharacteristic
26C2×#13063258C2211yescharacteristic
27C2×#13063258C2211yescharacteristic
28C2×#13063257C2211yescharacteristic
29C2×#13063256C2211yescharacteristic
30C2×#13063256C2211yescharacteristic
31#14582894—24no—
32#14582894—24no—
33C2×#13063249C2211yescharacteristic
34C2×#13063249C2211yescharacteristic
35C2×#13063247C2211yescharacteristic
36C2×#13063247C2211yescharacteristic
37C2×#13063245C2211yescharacteristic
38C2×#13063245C2211yescharacteristic
39#14582806C2211yescharacteristic
40#14582801C2211yescharacteristic
41#14582800C2211yescharacteristic
42#14582777—22no—
43#14582768C2211yescharacteristic
44#14582768C2211yescharacteristic
45#14582765C2211yescharacteristic
46#14582758—22no—
47#14582750—22no—
48#14582746—22no—
49#14582654C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52C2×#107×C43C2211yescharacteristic
53C2×#106×C43C2211yescharacteristic
54C2×#103×C43C2211yescharacteristic
55C2×#103×C43C2211yescharacteristic
56C43×#391C2211yescharacteristic
57C43×#382C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C2×#10621902—22no—
60C2×#10621902—22no—
61C2×#10621902—22no—
62C2×#10621902—22no—
63C2×#10621902—22no—
64C2×#10621902Q814yes—
65C22×D172—21no—
66C22×D172C2311yescharacteristic
67C22×C4×D43—21no—
68C22×C4×D43D412yes—
69C22×C4×D43C2311yescharacteristic
70C22×C43⋊C8C2311yescharacteristic
71C22×C43⋊C8C2311yescharacteristic
72C2×C8×D43—22no—
73C2×C8×D43—22no—
74C2×C8×D43—22no—
75C2×C8×D43—22no—
76C2×C8×D43D414yes—
77C2×C8×D43D414yes—
78#13063283—22no—
79#13063283—22no—
80#13063283—22no—
81#13063283—22no—
82#13063283—22no—
83#13063283—22no—
84C2×C4⋊Dic43C2311yescharacteristic
85C2×C4⋊Dic43C2311yescharacteristic
86C2×C4⋊Dic43C2311yescharacteristic
87C2×Dic43⋊C4—22no—
88C2×Dic43⋊C4—22no—
89C2×(C2×D43)⋊C4—21no—
90C2×(C2×D43)⋊C4—21no—
91C2×(C2×D43)⋊C4—21no—
92C2×(C2×D43)⋊C4—22no—
93C2×(C2×D43)⋊C4—22no—
94C2×C4×Dic43—21no—
95C2×C4×Dic43—21no—
96C2×C4×Dic43—21no—
97C2×C4×Dic43D412yes—
98C2×C4×Dic43C2311yescharacteristic
99C42×D43—22no—
100C42×D43—22no—
101#13063259—22no—
102#13063258—22no—
103#13063258—22no—
104#13063257—22no—
105#13063256—22no—
106#13063256—22no—
107#13063249—22no—
108#13063249—22no—
109#13063247—22no—
110#13063247—22no—
111#13063245—22no—
112#13063245—22no—
113C43⋊#95—22no—
114C43⋊#95—22no—
115C22×Q8×C43C2311yescharacteristic
116C22×C8×C43C2311yescharacteristic
117C22×C8×C43C2311yescharacteristic
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C4⋊C4×C43C2311yescharacteristic
120C2×C4⋊C4×C43C2311yescharacteristic
121C2×C42×C43C2311yescharacteristic
122#107×C43—22no—
123#106×C43—22no—
124#103×C43—22no—
125#103×C43—22no—
126#95×C43—22no—
127#95×C43—22no—
128C23×D43—21no—
129C23×D43C2×D411yescharacteristic
130C2×Q8×C43—21no—
131C2×Q8×C43—21no—
132C2×Q8×C43—21no—
133C2×Q8×C43—21no—
134C2×Q8×C43—21no—
135C2×Q8×C43C2×Q812yes—
136C22×C4×C43—21no—
137C22×C4×C43—21no—
138C22×C4×C43—21no—
139C22×C4×C43—21no—
140C22×C4×C43C2×D412yes—
141C22×C4×C43C2411yescharacteristic
142C22×Dic43—21no—
143C22×Dic43—21no—
144C22×Dic43—21no—
145C22×Dic43C2×D412yes—
146C22×Dic43C2×D411yescharacteristic
147#10621902—28no—
148#10621902—28no—
149#10621902—44no—
150#10621902—44no—
151C2×D172—21no—
152C2×D172—24no—
153C2×D172—21no—
154C2×D172—21no—
155C2×D172—21no—
156C2×D172—21no—
157C2×D172—42no—
158C2×D172—42no—
159C2×D172C2×Q812yes—
160C2×C4×D43—24no—
161C2×C4×D43—24no—
162C2×C4×D43—24no—
163C2×C4×D43—42no—
164C2×C4×D43—42no—
165C2×C4×D43—42no—
166C2×C4×D43C2×D412yes—
167C2×C4×D43C2×D412yes—
168C2×C4×D43C2×Q812yes—
169C2×C4×D43#4112yes—
170C2×C4×D43#4112yes—
171C2×C4×D43#4112yes—
172C2×C8×C43—21no—
173C2×C8×C43—21no—
174C2×C8×C43—21no—
175C2×C8×C43—21no—
176C2×C8×C43C2×D412yes—
177C2×C8×C43C2×D412yes—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43—21no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43—21no—
184C42×C43—21no—
185C42×C43—21no—
186(C2×D43)⋊C4—44no—
187(C2×D43)⋊C4—44no—
188(C2×D43)⋊C4—42no—
189(C2×D43)⋊C4—42no—
190(C2×D43)⋊C4—42no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197Dic43⋊C4—44no—
198Dic43⋊C4—44no—
199C4×Dic43—21no—
200C4×Dic43—21no—
201C4×Dic43—24no—
202C4×Dic43—42no—
203C4×Dic43—42no—
204C4×Dic43—42no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8C2×D412yes—
210C2×C43⋊C8C2×D412yes—
211C8×D43—28no—
212C8×D43—28no—
213C23×C43C22×D411yescharacteristic
214C22×D43—22no—
215C22×D43—22no—
216C22×D43—22no—
217C22×D43—41no—
218C22×D43—41no—
219C22×D43—42no—
220C22×D43—42no—
221C22×D43C22⋊Q812yes—
222C22×D43#12312yes—
223C22×D43#12712yes—
224Q8×C43—22no—
225Q8×C43—22no—
226Q8×C43—41no—
227Q8×C43—41no—
228C2×C4×C43—22no—
229C2×C4×C43—22no—
230C2×C4×C43—22no—
231C2×C4×C43—22no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—42no—
238C2×C4×C43—42no—
239C2×C4×C43—42no—
240C2×C4×C43C22×D411yescharacteristic
241C2×C4×C43C22×D411yescharacteristic
242C2×C4×C43C22×Q811yescharacteristic
243C2×C4×C43C2×#4111yescharacteristic
244C2×C4×C43C2×#4111yescharacteristic
245C2×C4×C43C2×#4111yescharacteristic
246C2×Dic43—22no—
247C2×Dic43—22no—
248C2×Dic43—41no—
249C2×Dic43—41no—
250C2×Dic43—41no—
251C2×Dic43—42no—
252C2×Dic43—42no—
253C2×Dic43—42no—
254C2×Dic43C22⋊Q812yes—
255C2×Dic43#12312yes—
256C2×Dic43#12712yes—
257C2×Dic43#13514yes—
258D172—22no—
259D172—22no—
260D172—48no—
261D172—41no—
262D172—41no—
263C4×D43—48no—
264C4×D43—48no—
265C4×D43C22⋊Q814yes—
266C4×D43C22⋊Q814yes—
267C4×D43#12314yes—
268C4×D43#12314yes—
269C8×C43—22no—
270C8×C43—22no—
271C43⋊C8—22no—
272C43⋊C8—22no—
273#23730—431nomaximal, Sylow
274C22×C43C2×C22⋊Q811yescharacteristic
275C22×C43C2×#12311yescharacteristic
276C22×C43C2×#12711yescharacteristic
277C22×C43C2×#13512yes—
278C22×C43#57512yes—
279C2×D43—24no—
280C2×D43—24no—
281C2×D43—22no—
282C2×D43—22no—
283C2×D43—44no—
284C2×D43—42no—
285C2×D43—82no—
286C2×D43—81no—
287C2×D43—81no—
288C2×D43#39914yes—
289C4×C43—42no—
290C4×C43—42no—
291C4×C43—81no—
292C4×C43—81no—
293C4×C43—81no—
294C4×C43C2×C22⋊Q811yescharacteristic
295C4×C43C2×C22⋊Q811yescharacteristic
296C4×C43C2×#12311yescharacteristic
297C4×C43C2×#12311yescharacteristic
298Dic43—24no—
299Dic43—81no—
300Dic43—81no—
301Dic43—81no—
302Dic43#39914yes—
303C2×#427—431no—
304C2×#427—431no—
305C2×#416—431no—
306C2×#416—431no—
307#2297—431no—
308#2285—431no—
309#2097—431no—
310#2097D4311yescharacteristic, complemented
311#2096—431no—
312#2095—431no—
313#2094—431no—
314#2093—431no—
315#2092—431no—
316#2092—431no—
317C2×#336—431no—
318C2×C43C2×#39911yescharacteristic
319C2×C43#307612yes—
320C2×C43#309112yes—
321C2×C43#314711yescharacteristic
322C2×C43#315011yescharacteristic
323D43—24no—
324D43—82no—
325C22×#41—431no—
326C23×C8—431no—
327C23×C8—431no—
328C2×#117—431no—
329C2×#117—431no—
330C2×#117—431no—
331C22×C42—431no—
332#427—864no—
333#427—864no—
334C2×#107—431no—
335C2×#107—431no—
336C2×#107—431no—
337C2×#107C2×D4311yescharacteristic
338C2×#106—431no—
339C2×#106—431no—
340C2×#106—431no—
341C2×#106C2×D4311yescharacteristic
342#416—864no—
343#416—864no—
344C2×#103—431no—
345C2×#103—431no—
346C2×#103C2×D4311yescharacteristic
347C2×#103C2×D4311yescharacteristic
348C2×#102—431no—
349C2×#102—431no—
350C2×#102—431no—
351C2×#102—431no—
352#391—431no—
353#391C2×D4311yescharacteristic
354#390—431no—
355#390—431no—
356#386—862no—
357#384—431no—
358#384—431no—
359#382—431no—
360#382C2×D4311yescharacteristic
361#380—862no—
362C4×C4⋊C4—862no—
363C4×C22⋊C4—862no—
364#336—431no—
365#336—431no—
366#336—431no—
367#336C2×D4311yescharacteristic
368C43#2373011yescharacteristic, complemented, Sylow
369C2×#41—434no—
370C2×#41—862no—
371C2×#41—862no—
372C2×#41—862no—
373C2×#41—862no—
374C2×#41—862no—
375C22×Q8C22×D4311yescharacteristic
376C22×D4—431no—
377C22×D4—861no—
378C23×C4—431no—
379C23×C4—432no—
380C23×C4—861no—
381C22×C8—431no—
382C22×C8—431no—
383C22×C8—434no—
384C22×C8—434no—
385C22×C8—862no—
386C22×C8—862no—
387C22×C8—862no—
388C22×C8—862no—
389C22×C8C22×D4311yescharacteristic
390C22×C8C22×D4311yescharacteristic
391#117—862no—
392#117—862no—
393#117—862no—
394#117—862no—
395#117—862no—
396#117—862no—
397C2×C4⋊C4—431no—
398C2×C4⋊C4—431no—
399C2×C4⋊C4—431no—
400C2×C4⋊C4—862no—
401C2×C4⋊C4—862no—
402C2×C4⋊C4C22×D4311yescharacteristic
403C2×C4⋊C4C22×D4311yescharacteristic
404C2×C4⋊C4C22×D4311yescharacteristic
405C2×C22⋊C4—862no—
406C2×C22⋊C4—861no—
407C2×C22⋊C4—861no—
408C2×C22⋊C4—861no—
409C2×C22⋊C4—862no—
410C2×C42—432no—
411C2×C42—431no—
412C2×C42—862no—
413C2×C42—862no—
414C2×C42—861no—
415C2×C42—861no—
416C2×C42—861no—
417C2×C42C22×D4311yescharacteristic
418#107—22no—
419#107—862no—
420#107—862no—
421#107—862no—
422#106—22no—
423#106—862no—
424#106—862no—
425#106—862no—
426#103—22no—
427#103—22no—
428#103—862no—
429#103—862no—
430#102—862no—
431#102—862no—
432#102—862no—
433#102—862no—
434#95—22no—
435#95—22no—
436#95—862no—
437#95—862no—
438C24—431no—
439C24—861no—
440#41—868no—
441#41—868no—
442#41—1724no—
443#41—1724no—
444C2×Q8—21no—
445C2×Q8—21no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8Q8×D4312yes—
450C2×D4—432no—
451C2×D4—864no—
452C2×D4—861no—
453C2×D4—861no—
454C2×D4—861no—
455C2×D4—861no—
456C2×D4—861no—
457C2×D4—1722no—
458C2×D4—1722no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—431no—
464C22×C4—432no—
465C22×C4—432no—
466C22×C4—432no—
467C22×C4—432no—
468C22×C4—432no—
469C22×C4—432no—
470C22×C4—432no—
471C22×C4—864no—
472C22×C4—864no—
473C22×C4—864no—
474C22×C4—861no—
475C22×C4—861no—
476C22×C4—861no—
477C22×C4—1722no—
478C22×C4—1722no—
479C22×C4—1722no—
480C22×C4D4×D4312yes—
481C22×C4C23×D4311yescharacteristic
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—432no—
487C2×C8—432no—
488C2×C8—868no—
489C2×C8—868no—
490C2×C8—861no—
491C2×C8—861no—
492C2×C8—861no—
493C2×C8—861no—
494C2×C8D4×D4312yes—
495C2×C8D4×D4312yes—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—861no—
503C4⋊C4—861no—
504C4⋊C4—861no—
505C4⋊C4—861no—
506C4⋊C4—861no—
507C4⋊C4—861no—
508C4⋊C4—1724no—
509C4⋊C4—1724no—
510C22⋊C4—1724no—
511C22⋊C4—1724no—
512C22⋊C4—1722no—
513C22⋊C4—1722no—
514C22⋊C4—1722no—
515C42—21no—
516C42—21no—
517C42—864no—
518C42—861no—
519C42—861no—
520C42—1722no—
521C42—1722no—
522C42—1722no—
523C23—432no—
524C23—432no—
525C23—432no—
526C23—862no—
527C23—862no—
528C23—862no—
529C23—1721no—
530C23—1722no—
531C23—1721no—
532C23—1722no—
533C23C2×D4×D4311yescharacteristic
534Q8—22no—
535Q8—22no—
536Q8—41no—
537Q8—41no—
538D4—862no—
539D4—862no—
540D4—1728no—
541D4—1721no—
542D4—1721no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—42no—
555C2×C4—432no—
556C2×C4—432no—
557C2×C4—432no—
558C2×C4—434no—
559C2×C4—434no—
560C2×C4—434no—
561C2×C4—434no—
562C2×C4—434no—
563C2×C4—862no—
564C2×C4—862no—
565C2×C4—1728no—
566C2×C4—1728no—
567C2×C4—1722no—
568C2×C4—1721no—
569C2×C4—1721no—
570C2×C4—1721no—
571C2×C4—1722no—
572C2×C4—1722no—
573C2×C4C2×D4×D4311yescharacteristic
574C2×C4C2×D4×D4311yescharacteristic
575C2×C4C2×Q8×D4311yescharacteristic
576C2×C4#41×D4311yescharacteristic
577C2×C4#41×D4311yescharacteristic
578C2×C4#41×D4311yescharacteristic
579C8—22no—
580C8—22no—
581C8—862no—
582C8—862no—
583C22—434no—
584C22—862no—
585C22—864no—
586C22—862no—
587C22—864no—
588C22—3441no—
589C22—3442no—
590C22—3441no—
591C22—1722no—
592C22—1724no—
593C22C22⋊Q8×D4311yescharacteristic
594C22#123×D4311yescharacteristic
595C22#127×D4311yescharacteristic
596C22#135×D4312yes—
597C22#1458369812yes—
598C4—42no—
599C4—42no—
600C4—81no—
601C4—81no—
602C4—81no—
603C4—434no—
604C4—864no—
605C4—3441no—
606C4—3441no—
607C4—3441no—
608C4C22⋊Q8×D4311yescharacteristic
609C4C22⋊Q8×D4311yescharacteristic
610C4#123×D4311yescharacteristic
611C4#123×D4311yescharacteristic
612C2—864no—
613C2—3442no—
614C2#399×D4311yescharacteristic
615C2#1914438212yes—
616C2#1914451312yes—
617C2#1914502011yescharacteristic
618C2#1914503911yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2097C2
socleC23×C43C22×D4
prime radicalC22×#10621902C22
hypercenter#2097D43
hypocenterC43#23730
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2097

Complements

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

NH ≅ G/Ntype
1. C2×#14582936C2semidirect
2. C2×#14582934C2semidirect
6. #19137001C2semidirect
7. #19136143C2semidirect
8. #19136136C2semidirect
9. #19136131C2semidirect
10. #19136125C2semidirect
11. #19136120C2semidirect
12. #19136119C2semidirect
13. #19136115C2semidirect
14. #336×D43C2semidirect
15. C43×#2097C2semidirect
310. #2097D43semidirect
368. C43#23730semidirect

Maximal subgroups

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

subgroupindex
C2×#145829362
C2×#145829342
C2×#145828942
#191370842
#191370012
#191361432
#191361362
#191361312
#191361252
#191361202
#191361192
#191361152
#336×D432
C43×#20972
#2373043