Finite Group Databasebeta

← #25132899

Subgroups — #25132899

Order 11008.

1036 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144388C211yesmaximal, characteristic, complemented
2C4×#13063350C211yesmaximal, characteristic
3#19139769C211yesmaximal, characteristic, complemented
4#19135942C212yesmaximal, complemented
5#19135748C212yesmaximal, complemented
6#19135585C211yesmaximal, characteristic, complemented
7#19135540C211yesmaximal, characteristic, complemented
8#19134971C212yesmaximal
9#19134828C212yesmaximal, complemented
10#19134615C211yesmaximal, characteristic, complemented
11C43×#3503C211yesmaximal, characteristic, complemented
12C2×#13063350C2211yescharacteristic
13C2×C4×D172C2211yescharacteristic
14#14583196—22no—
15#14583186—21no—
16#14583176—21no—
17#14583009—21no—
18#14582997—21no—
19C4×#10621884—21no—
20C4×#10621882—21no—
21#14582942C2212yes—
22#14582942C2211yescharacteristic
23#14582923C2211yescharacteristic
24C2×#13063252C2212yes—
25#14582903C2211yescharacteristic
26#14582903C2212yes—
27#14582900C2211yescharacteristic
28C4×#10621877C2211yescharacteristic
29#14582810—22no—
30#14582800C2212yes—
31#14582764C2212yes—
32#14582756—22no—
33C4×C4⋊Dic43C2211yescharacteristic
34#14582668C2212yes—
35#14582668C2212yes—
36#14582658C2212yes—
37#14582658C2212yes—
38#14582658C2212yes—
39Q82×C43—21no—
40C43×#557—21no—
41C43×#554—21no—
42C43×#554—22no—
43D4×Q8×C43—22no—
44D4×Q8×C43—21no—
45C43×#544—22no—
46C43×#544C2212yes—
47C43×#533—21no—
48C43×#533C2211yescharacteristic
49C2×C4⋊Q8×C43—21no—
50C2×C4⋊Q8×C43C2211yescharacteristic
51C43×#520C2212yes—
52C4×#41×C43C2211yescharacteristic
53C22×D172C2311yescharacteristic
54C22×C4×D43—21no—
55#13063350—22no—
56#13063350Q814yescomplemented
57C2×#10621884—21no—
58C2×#10621882—21no—
59C2×#10621877C2311yescharacteristic
60C2×#10621877C2312yes—
61C2×#10621877C2311yescharacteristic
62C4×D172—21no—
63C4×D172—21no—
64C4×D172—21no—
65C4×D172—21no—
66C2×C4⋊Dic43—21no—
67C2×C4⋊Dic43C2311yescharacteristic
68C2×(C2×D43)⋊C4—21no—
69C2×(C2×D43)⋊C4—24no—
70C2×C4×Dic43C2312yes—
71#13063258—22no—
72#13063258—21no—
73#13063256—22no—
74#13063256—21no—
75C4⋊(C43⋊C8)—21no—
76C4⋊(C43⋊C8)—21no—
77#13063252—24no—
78#13063249—21no—
79#13063246—21no—
80#13063245—22no—
81#13063245—22no—
82#13063245—21no—
83#13063245—21no—
84#13063236—21no—
85C4×C43⋊C8—21no—
86C43⋊#95—21no—
87C43⋊#95—24no—
88C2×#41×C43C2311yescharacteristic
89C22×Q8×C43—22no—
90C22×Q8×C43D412yes—
91C4⋊Q8×C43—22no—
92C4⋊Q8×C43—22no—
93C4⋊Q8×C43—24no—
94C4⋊Q8×C43—22no—
95C4⋊Q8×C43—22no—
96C4⋊Q8×C43—21no—
97C4⋊Q8×C43—21no—
98C4⋊Q8×C43—21no—
99C4⋊Q8×C43—21no—
100C4⋊Q8×C43D411yescharacteristic
101C4⋊Q8×C43D411yescharacteristic
102#125×C43—24no—
103#125×C43—22no—
104#125×C43—22no—
105#125×C43D412yes—
106C22⋊Q8×C43—22no—
107C22⋊Q8×C43—22no—
108C22⋊Q8×C43—24no—
109C22⋊Q8×C43—24no—
110C22⋊Q8×C43—21no—
111C22⋊Q8×C43—21no—
112C22⋊Q8×C43—24no—
113C4×Q8×C43—22no—
114C4×Q8×C43—22no—
115C4×Q8×C43—22no—
116C4×Q8×C43—21no—
117C4×Q8×C43—21no—
118C4×Q8×C43D411yescharacteristic
119C4×Q8×C43D411yescharacteristic
120C4×D4×C43—22no—
121C4×D4×C43—21no—
122C4×D4×C43—21no—
123C4×D4×C43—24no—
124C4×D4×C43D411yescharacteristic
125C4×D4×C43D411yescharacteristic
126#117×C43—22no—
127#117×C43—21no—
128#117×C43C2311yescharacteristic
129#117×C43C2312yes—
130C2×C4⋊C4×C43—22no—
131C2×C4⋊C4×C43—22no—
132C2×C4⋊C4×C43D412yes—
133C2×C4⋊C4×C43C2312yes—
134C2×C42×C43—21no—
135C2×C42×C43C2311yescharacteristic
136C23×D43—21no—
137#41×C43—21no—
138#41×C43—21no—
139#41×C43C2×Q812yes—
140#41×C43#4112yes—
141C2×Q8×C43—24no—
142C2×Q8×C43—21no—
143C2×Q8×C43—22no—
144C2×Q8×C43—21no—
145C2×Q8×C43—22no—
146C2×Q8×C43—82no—
147C2×Q8×C43—84no—
148C2×Q8×C43C2×D411yescharacteristic
149C2×D4×C43—21no—
150C2×D4×C43C2×D411yescharacteristic
151C22×C4×C43—21no—
152C22×C4×C43—24no—
153C22×C4×C43—21no—
154C22×C4×C43—21no—
155C22×C4×C43C2×D411yescharacteristic
156C22×C4×C43C2×D414yes—
157C22×C4×C43C2×D411yescharacteristic
158C22×C4×C43C2411yescharacteristic
159C22×Dic43—21no—
160C22×Dic43—22no—
161C2×D172—21no—
162C2×D172—21no—
163C2×D172—21no—
164C2×D172—21no—
165C2×D172—21no—
166C2×D172C2×Q812yescomplemented
167C2×C4×D43—44no—
168C2×C4×D43—41no—
169C2×C4×D43—41no—
170C4⋊C4×C43—24no—
171C4⋊C4×C43—24no—
172C4⋊C4×C43—24no—
173C4⋊C4×C43—24no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—22no—
176C4⋊C4×C43—22no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—22no—
181C4⋊C4×C43—22no—
182C4⋊C4×C43—22no—
183C4⋊C4×C43—22no—
184C4⋊C4×C43C2×D412yes—
185C4⋊C4×C43C2×D412yes—
186C4⋊C4×C43C2×D411yescharacteristic
187C4⋊C4×C43C2×D411yescharacteristic
188C22⋊C4×C43—24no—
189C22⋊C4×C43—21no—
190C22⋊C4×C43—21no—
191C22⋊C4×C43—22no—
192C22⋊C4×C43—21no—
193C42×C43—24no—
194C42×C43—21no—
195C42×C43—21no—
196C42×C43—21no—
197C42×C43—22no—
198C42×C43C2×D411yescharacteristic
199C42×C43C2×D411yescharacteristic
200C42×C43C2×D411yescharacteristic
201C42×C43C2×D411yescharacteristic
202#10621884—24no—
203#10621882—24no—
204(C2×D43)⋊C4—41no—
205(C2×D43)⋊C4—41no—
206(C2×D43)⋊C4—84no—
207C4⋊Dic43—21no—
208C4⋊Dic43—21no—
209C4⋊Dic43—42no—
210C4×Dic43—22no—
211C4×Dic43—22no—
212#10621877—21no—
213#10621877—22no—
214#10621877—21no—
215#10621877—21no—
216#10621877—22no—
217#10621877C2×Q812yescomplemented
218C2×C43⋊C8—21no—
219C2×C43⋊C8—21no—
220C2×C43⋊C8—22no—
221C23×C43—21no—
222C23×C43C22×D411yescharacteristic
223C22×D43—22no—
224C22×D43—42no—
225C22×D43—42no—
226C22×D43—41no—
227C22×D43—41no—
228Q8×C43—21no—
229Q8×C43—44no—
230Q8×C43—42no—
231Q8×C43—42no—
232Q8×C43—82no—
233Q8×C43—84no—
234Q8×C43C22⋊Q812yes—
235D4×C43—22no—
236D4×C43—22no—
237D4×C43—21no—
238D4×C43C22⋊Q812yes—
239C2×C4×C43—21no—
240C2×C4×C43—22no—
241C2×C4×C43—22no—
242C2×C4×C43—22no—
243C2×C4×C43—22no—
244C2×C4×C43—21no—
245C2×C4×C43—21no—
246C2×C4×C43—24no—
247C2×C4×C43—22no—
248C2×C4×C43—41no—
249C2×C4×C43—42no—
250C2×C4×C43—42no—
251C2×C4×C43—44no—
252C2×C4×C43—84no—
253C2×C4×C43#12011yescharacteristic
254C2×C4×C43#12011yescharacteristic
255C2×C4×C43#12011yescharacteristic
256C2×C4×C43#12011yescharacteristic
257C2×C4×C43C22×D411yescharacteristic
258C2×C4×C43C22×D411yescharacteristic
259C2×C4×C43C22×Q811yescharacteristic
260C2×C4×C43C2×#4111yescharacteristic
261C2×C4×C432−1+411yescharacteristic
262C2×C4×C432−1+411yescharacteristic
263C2×Dic43—42no—
264C2×Dic43—42no—
265C2×Dic43—42no—
266C2×Dic43—41no—
267C2×Dic43—42no—
268D172—22no—
269D172—22no—
270D172—41no—
271D172—41no—
272C4×D43—82no—
273C4×D43—82no—
274C43⋊C8—22no—
275C43⋊C8—41no—
276C43⋊C8—42no—
277#24321—431nomaximal, Sylow
278C22×C43—21no—
279C22×C43—21no—
280C22×C43—22no—
281C22×C43—41no—
282C22×C43—41no—
283C22×C43C2×#12011yescharacteristic
284C22×C43#54811yescharacteristic
285C22×C43D4×Q811yescharacteristic
286C2×D43—44no—
287C2×D43—42no—
288C2×D43—82no—
289C2×D43—81no—
290C2×D43—81no—
291C4×C43—22no—
292C4×C43—21no—
293C4×C43—21no—
294C4×C43—21no—
295C4×C43—41no—
296C4×C43—42no—
297C4×C43—41no—
298C4×C43—44no—
299C4×C43—42no—
300C4×C43#45412yes—
301C4×C43C2×C22⋊Q811yescharacteristic
302C4×C43#53611yescharacteristic
303C4×C43#54811yescharacteristic
304C4×C43D4×Q811yescharacteristic
305Dic43—82no—
306Dic43—81no—
307#3503D4311yescharacteristic, complemented
308#3077—431no—
309C4×AGL(1,ℤ/8)—431no—
310#2563—431no—
311#2061—432no—
312#2027—432no—
313#1997—431no—
314#1986—431no—
315#1883—432no—
316#1860—432no—
317#1806—431no—
318C2×C43—21no—
319C2×C43—21no—
320C2×C43—42no—
321C2×C43#240911yescharacteristic
322C2×C43C2×#45411yescharacteristic
323C2×C43#301911yescharacteristic
324D43—82no—
325C2×AGL(1,ℤ/8)—431no—
326Q82—21no—
327#557—21no—
328#554—21no—
329#554—22no—
330D4×Q8—22no—
331D4×Q8—21no—
332#544—22no—
333#544C2×D4312yes—
334#533—21no—
335#533C2×D4311yescharacteristic
336C2×C4⋊Q8—21no—
337C2×C4⋊Q8C2×D4311yescharacteristic
338#520C2×D4312yes—
339C4×#41C2×D4311yescharacteristic
340C2×C4×D4—431no—
341#478—862no—
342#476—861no—
343#474—861no—
344#442—861no—
345#440—861no—
346C4×SD16—861no—
347C4×D8—861no—
348#428—432no—
349#428—431no—
350#423—431no—
351C2×#104—432no—
352#418—432no—
353#418—431no—
354#417—431no—
355C4×M16—431no—
356#393—862no—
357#390—432no—
358#382—432no—
359#380—862no—
360C4×C4⋊C4—431no—
361#343—432no—
362#343—432no—
363#339—432no—
364#339—432no—
365#339—432no—
366C43#2432111yescharacteristic, complemented, Sylow
367C2×#41C22×D4311yescharacteristic
368C22×Q8—22no—
369C22×Q8C22⋊D4312yes—
370C22×D4—431no—
371C23×C4—861no—
372AGL(1,ℤ/8)—434no—
373AGL(1,ℤ/8)—862no—
374C2×SD16—861no—
375C2×D8—861no—
376C2×M16—431no—
377C2×M16—431no—
378C2×M16—432no—
379C4⋊Q8—22no—
380C4⋊Q8—22no—
381C4⋊Q8—24no—
382C4⋊Q8—22no—
383C4⋊Q8—22no—
384C4⋊Q8—21no—
385C4⋊Q8—21no—
386C4⋊Q8—21no—
387C4⋊Q8—21no—
388C4⋊Q8C22⋊D4311yescharacteristic
389C4⋊Q8C22⋊D4311yescharacteristic
390#125—24no—
391#125—22no—
392#125—22no—
393#125C22⋊D4312yes—
394C22⋊Q8—22no—
395C22⋊Q8—22no—
396C22⋊Q8—24no—
397C22⋊Q8—24no—
398C22⋊Q8—21no—
399C22⋊Q8—21no—
400C22⋊Q8—24no—
401C4×Q8—22no—
402C4×Q8—22no—
403C4×Q8—22no—
404C4×Q8—21no—
405C4×Q8—21no—
406C4×Q8C22⋊D4311yescharacteristic
407C4×Q8C22⋊D4311yescharacteristic
408C4×D4—22no—
409C4×D4—21no—
410C4×D4—21no—
411C4×D4—24no—
412C4×D4—861no—
413C4×D4—861no—
414C4×D4—861no—
415C4×D4—861no—
416C4×D4C22⋊D4311yescharacteristic
417C4×D4C22⋊D4311yescharacteristic
418#117—22no—
419#117—21no—
420#117C22×D4311yescharacteristic
421#117C22×D4312yes—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—431no—
425C2×C4⋊C4—861no—
426C2×C4⋊C4C22⋊D4312yes—
427C2×C4⋊C4C22×D4312yes—
428C2×C22⋊C4—864no—
429C2×C22⋊C4—861no—
430C2×C42—21no—
431C2×C42—432no—
432C2×C42C22×D4311yescharacteristic
433#107—861no—
434#107—862no—
435#106—861no—
436#106—862no—
437C4⋊C8—861no—
438C4⋊C8—861no—
439#104—864no—
440#103—861no—
441#102—861no—
442#102—861no—
443#102—861no—
444#102—862no—
445#102—862no—
446#97—861no—
447C4×C8—861no—
448#95—861no—
449#95—864no—
450C24—861no—
451#41—21no—
452#41—21no—
453#41Q8×D4312yes—
454#41#1062190212yes—
455C2×Q8—24no—
456C2×Q8—21no—
457C2×Q8—22no—
458C2×Q8—21no—
459C2×Q8—22no—
460C2×Q8—82no—
461C2×Q8—84no—
462C2×Q8C2×C22⋊D4311yescharacteristic
463C2×D4—21no—
464C2×D4—432no—
465C2×D4—861no—
466C2×D4—861no—
467C2×D4—861no—
468C2×D4—861no—
469C2×D4—861no—
470C2×D4C2×C22⋊D4311yescharacteristic
471C22×C4—21no—
472C22×C4—24no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—861no—
476C22×C4—862no—
477C22×C4—1724no—
478C22×C4—1721no—
479C22×C4—1721no—
480C22×C4C2×C22⋊D4311yescharacteristic
481C22×C4C2×C22⋊D4314yes—
482C22×C4C2×C22⋊D4311yescharacteristic
483C22×C4C23×D4311yescharacteristic
484SD16—864no—
485D8—864no—
486M16—432no—
487M16—861no—
488M16—862no—
489M16—862no—
490M16—861no—
491M16—861no—
492C2×C8—861no—
493C2×C8—861no—
494C2×C8—862no—
495C4⋊C4—24no—
496C4⋊C4—24no—
497C4⋊C4—24no—
498C4⋊C4—24no—
499C4⋊C4—21no—
500C4⋊C4—22no—
501C4⋊C4—22no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—22no—
506C4⋊C4—22no—
507C4⋊C4—22no—
508C4⋊C4—22no—
509C4⋊C4—861no—
510C4⋊C4—861no—
511C4⋊C4—1722no—
512C4⋊C4C2×C22⋊D4312yes—
513C4⋊C4C2×C22⋊D4311yescharacteristic
514C4⋊C4C2×C22⋊D4312yes—
515C4⋊C4C2×C22⋊D4311yescharacteristic
516C22⋊C4—24no—
517C22⋊C4—22no—
518C22⋊C4—21no—
519C22⋊C4—21no—
520C22⋊C4—21no—
521C22⋊C4—3444no—
522C22⋊C4—1721no—
523C22⋊C4—1721no—
524C42—24no—
525C42—21no—
526C42—21no—
527C42—21no—
528C42—22no—
529C42—862no—
530C42—862no—
531C42C2×C22⋊D4311yescharacteristic
532C42C2×C22⋊D4311yescharacteristic
533C42C2×C22⋊D4311yescharacteristic
534C42C2×C22⋊D4311yescharacteristic
535C23—21no—
536C23—862no—
537C23—1722no—
538C23—1722no—
539C23—1721no—
540C23—1721no—
541C23C22×C22⋊D4311yescharacteristic
542Q8—21no—
543Q8—44no—
544Q8—42no—
545Q8—42no—
546Q8—82no—
547Q8—84no—
548Q8#1306330112yes—
549D4—22no—
550D4—22no—
551D4—21no—
552D4—862no—
553D4—862no—
554D4—1721no—
555D4—1721no—
556D4#1306330112yes—
557C2×C4—21no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—24no—
565C2×C4—22no—
566C2×C4—41no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—44no—
570C2×C4—84no—
571C2×C4—3442no—
572C2×C4—3442no—
573C2×C4—1722no—
574C2×C4—1722no—
575C2×C4—1722no—
576C2×C4—1722no—
577C2×C4—1721no—
578C2×C4#1306329411yescharacteristic
579C2×C4#1306329411yescharacteristic
580C2×C4#1306329411yescharacteristic
581C2×C4#1306329411yescharacteristic
582C2×C4C22×C22⋊D4311yescharacteristic
583C2×C4C22×C22⋊D4311yescharacteristic
584C2×C4C2×Q8×D4311yescharacteristic
585C2×C4C2×#1062190211yescharacteristic
586C2×C4#1306337311yescharacteristic
587C2×C4#1306337311yescharacteristic
588C8—862no—
589C8—1722no—
590C8—1721no—
591C22—21no—
592C22—21no—
593C22—22no—
594C22—41no—
595C22—41no—
596C22—3442no—
597C22—3441no—
598C22—3441no—
599C22—1724no—
600C22—1722no—
601C22C2×#1306329411yescharacteristic
602C22#1458356011yescharacteristic
603C22Q8×C22⋊D4311yescharacteristic
604C4—21no—
605C4—21no—
606C4—22no—
607C4—21no—
608C4—41no—
609C4—44no—
610C4—42no—
611C4—41no—
612C4—42no—
613C4—3442no—
614C4—3441no—
615C4#1458307212yes—
616C4C2×#1306330111yescharacteristic
617C4#1458347311yescharacteristic
618C4#1458356011yescharacteristic
619C4Q8×C22⋊D4311yescharacteristic
620C2—21no—
621C2—21no—
622C2—42no—
623C2—3442no—
624C2#1913795411yescharacteristic
625C2C2×#1458307211yescharacteristic
626C2#1914395211yescharacteristic
subgroupG/H
centerC22C2×#13063294
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#3503C2
socleC22×C43C2×#120
prime radicalC2×#13063350C22
hypercenter#3503D43
hypocenterC43#24321
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3503

Complements

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

NH ≅ G/Ntype
1. #19144388C2semidirect
3. #19139769C2semidirect
4. #19135942C2semidirect
5. #19135748C2semidirect
6. #19135585C2semidirect
7. #19135540C2semidirect
9. #19134828C2semidirect
10. #19134615C2semidirect
11. C43×#3503C2semidirect
56. #13063350Q8semidirect
166. C2×D172C2×Q8semidirect
217. #10621877C2×Q8semidirect
307. #3503D43semidirect
366. C43#24321semidirect

Maximal subgroups

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

subgroupindex
#191443882
C4×#130633502
#191397692
#191359422
#191357482
#191355852
#191355402
#191349712
#191348282
#191346152
C43×#35032
#2432143