Finite Group Databasebeta

← #25102954

Subgroups — #25102954

Order 11008.

980 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583118C211yesmaximal, characteristic
2C2×#14583003C211yesmaximal, characteristic, complemented
3C2×#14582990C211yesmaximal, characteristic
4#19137308C211yesmaximal, characteristic
5#19136959C211yesmaximal, characteristic, complemented
6#19135358C211yesmaximal, characteristic, complemented
7#19135232C211yesmaximal, characteristic, complemented
8#19135225C211yesmaximal, characteristic
9#19134947C211yesmaximal, characteristic
10#19134933C211yesmaximal, characteristic, complemented
11#19134601C211yesmaximal, characteristic, complemented
12#19134454C211yesmaximal, characteristic, complemented
13#19134422C211yesmaximal, characteristic
14#103×Dic43C211yesmaximal, characteristic, complemented
15C43×#1983C211yesmaximal, characteristic
16C22×#10621885C2211yescharacteristic
17C22×#10621883C2211yescharacteristic
18C2×Q8×Dic43C2211yescharacteristic
19C2×C4×Dic86C2211yescharacteristic
20C2×#13063290C2211yescharacteristic
21C2×#13063290C2211yescharacteristic
22C2×D4×Dic43C2211yescharacteristic
23#14583118C418yescomplemented
24#14583003—24no—
25#14582990—24no—
26C2×#13063256C2211yescharacteristic
27C2×#13063256C2211yescharacteristic
28C2×C4⋊(C43⋊C8)C2211yescharacteristic
29C2×#13063250C2211yescharacteristic
30C2×#13063250C2211yescharacteristic
31C2×#13063249C2211yescharacteristic
32C2×#13063246C2211yescharacteristic
33C2×#13063235C2211yescharacteristic
34C2×C8×Dic43C2211yescharacteristic
35#14582806C2211yescharacteristic
36#14582802C2211yescharacteristic
37#14582792—21no—
38#14582792—21no—
39#14582774—21no—
40#14582774—21no—
41#14582769C2211yescharacteristic
42C4⋊C4×Dic43C2211yescharacteristic
43C4⋊C4×Dic43C2211yescharacteristic
44C4×Dic43⋊C4—21no—
45C4×Dic43⋊C4—21no—
46#14582750—21no—
47#14582745C2211yescharacteristic
48#14582744—21no—
49#14582662C2211yescharacteristic
50#14582662C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582653C2211yescharacteristic
54#14582653C2211yescharacteristic
55C2×#124×C43C2211yescharacteristic
56C2×C4⋊C8×C43C2211yescharacteristic
57C2×#103×C43C2211yescharacteristic
58C2×#103×C43C2211yescharacteristic
59C2×#102×C43C2211yescharacteristic
60C2×#102×C43C2211yescharacteristic
61C4×C4⋊C4×C43C2211yescharacteristic
62C22×Dic86C2311yescharacteristic
63C23×Dic43—21no—
64C2×#10621885—22no—
65C2×#10621885—22no—
66C2×#10621885C2×C414yescomplemented
67C2×#10621883—22no—
68C2×#10621883—22no—
69C2×#10621883C2×C414yes—
70C22×C43⋊C8C2311yescharacteristic
71C22×C43⋊C8C2311yescharacteristic
72Q8×Dic43—22no—
73Q8×Dic43—22no—
74C4×Dic86—22no—
75C4×Dic86C2×C414yescomplemented
76#13063290—22no—
77#13063290—22no—
78#13063290—22no—
79#13063290D414yes—
80D4×Dic43—22no—
81D4×Dic43—22no—
82C2×C4⋊Dic43—21no—
83C2×C4⋊Dic43—21no—
84C2×C4⋊Dic43—21no—
85C2×C4⋊Dic43C2311yescharacteristic
86C2×C4⋊Dic43C2311yescharacteristic
87C2×C4⋊Dic43C2311yescharacteristic
88C2×Dic43⋊C4—21no—
89C2×Dic43⋊C4—21no—
90C2×Dic43⋊C4—21no—
91C2×C22⋊Dic43—21no—
92C2×C22⋊Dic43—21no—
93C2×C22⋊Dic43—21no—
94C2×C4×Dic43—21no—
95C2×C4×Dic43—21no—
96C2×C4×Dic43—21no—
97C2×C4×Dic43—21no—
98C2×C4×Dic43—21no—
99C2×C4×Dic43—21no—
100C2×C4×Dic43C2311yescharacteristic
101C2×C4×Dic43C2311yescharacteristic
102#13063256—22no—
103#13063256—22no—
104C4⋊(C43⋊C8)C2×C414yescomplemented
105#13063250—22no—
106#13063250—22no—
107#13063249C2×C414yescomplemented
108#13063246C2×C414yes—
109#13063235—22no—
110C8×Dic43—22no—
111C43⋊#95—21no—
112C43⋊#95—21no—
113C43⋊#95—21no—
114C43⋊#95—21no—
115C43⋊#95D411yescharacteristic
116C43⋊#95D411yescharacteristic
117C43⋊#95D411yescharacteristic
118C43⋊#95D411yescharacteristic
119C22×Q8×C43C2311yescharacteristic
120C22×D4×C43C2311yescharacteristic
121C22×C8×C43C2311yescharacteristic
122C22×C8×C43C2311yescharacteristic
123#124×C43—22no—
124#124×C43C2×C414yes—
125C2×C4⋊C4×C43C2311yescharacteristic
126C2×C4⋊C4×C43C2311yescharacteristic
127C2×C22⋊C4×C43—21no—
128C2×C22⋊C4×C43—21no—
129C2×C42×C43—21no—
130C2×C42×C43C2311yescharacteristic
131C4⋊C8×C43—22no—
132#103×C43—22no—
133#103×C43—22no—
134#102×C43—22no—
135#102×C43—22no—
136#95×C43—21no—
137C24×C43—21no—
138C2×Q8×C43—21no—
139C2×Q8×C43—21no—
140C2×Q8×C43—21no—
141C2×Q8×C43—21no—
142C2×Q8×C43—21no—
143C2×Q8×C43C22×C412yes—
144C2×D4×C43—21no—
145C2×D4×C43—21no—
146C2×D4×C43—21no—
147C2×D4×C43—21no—
148C2×D4×C43—21no—
149C2×D4×C43C22×C412yes—
150C22×C4×C43—21no—
151C22×C4×C43—21no—
152C22×C4×C43—21no—
153C22×C4×C43C2×D411yescharacteristic
154C22×C4×C43C2×D411yescharacteristic
155C22×C4×C43C2411yescharacteristic
156C22×Dic43—21no—
157C22×Dic43—21no—
158C22×Dic43—21no—
159C22×Dic43—21no—
160C22×Dic43—42no—
161C22×Dic43—81no—
162C22×Dic43—81no—
163C22×Dic43C2×D411yescharacteristic
164C22×Dic43C2×D411yescharacteristic
165C22×Dic43C2×D411yescharacteristic
166C22×Dic43C2×D411yescharacteristic
167C2×Dic86—21no—
168C2×Dic86—21no—
169C2×Dic86—21no—
170C2×Dic86C22×C412yes—
171C2×Dic86C2×D412yes—
172C2×Dic86#4112yes—
173C2×C8×C43—21no—
174C2×C8×C43—21no—
175C2×C8×C43—21no—
176C2×C8×C43—21no—
177C2×C8×C43—21no—
178C2×C8×C43—21no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43C2×D412yes—
182C4⋊C4×C43#4112yes—
183C22⋊C4×C43—24no—
184C22⋊C4×C43—24no—
185C42×C43—81no—
186C42×C43C22×C412yes—
187C42×C43#4112yes—
188C22⋊Dic43—42no—
189C22⋊Dic43—81no—
190C22⋊Dic43—81no—
191#10621885—28no—
192#10621883—28no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—42no—
199C4⋊Dic43—81no—
200C4⋊Dic43—81no—
201C4⋊Dic43C22×C412yes—
202Dic43⋊C4—24no—
203Dic43⋊C4—24no—
204Dic43⋊C4—24no—
205C4×Dic43—24no—
206C4×Dic43—24no—
207C4×Dic43—21no—
208C4×Dic43—21no—
209C4×Dic43—24no—
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×C43—22no—
222C23×C43—41no—
223C23×C43—41no—
224C23×C43—41no—
225C23×C43—41no—
226C23×C43—41no—
227C23×C43—41no—
228C23×C43C22×D411yescharacteristic
229Q8×C43—22no—
230Q8×C43—22no—
231Q8×C43—41no—
232Q8×C43—41no—
233D4×C43—22no—
234D4×C43—22no—
235D4×C43—41no—
236D4×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—41no—
245C2×C4×C43—41no—
246C2×C4×C43—41no—
247C2×C4×C43—41no—
248C2×C4×C43—41no—
249C2×C4×C43—41no—
250C2×C4×C43C4×D412yes—
251C2×C4×C43C4×D412yes—
252C2×C4×C43C23×C411yescharacteristic
253C2×C4×C43C22×D411yescharacteristic
254C2×C4×C43C2×#4111yescharacteristic
255C2×C4×C43C2×#4111yescharacteristic
256C2×C4×C43C2×#4111yescharacteristic
257C2×C4×C43C2×#4111yescharacteristic
258C2×Dic43—22no—
259C2×Dic43—22no—
260C2×Dic43—22no—
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—84no—
281C2×Dic43#12112yes—
282C2×Dic43#12112yes—
283Dic86—22no—
284Dic86—22no—
285Dic86—22no—
286Dic86C4×D414yes—
287C8×C43—41no—
288C8×C43—41no—
289C43⋊C8—22no—
290C43⋊C8—22no—
291#21511—431nomaximal, Sylow
292C22×C43—42no—
293C22×C43—42no—
294C22×C43—42no—
295C22×C43—81no—
296C22×C43—81no—
297C22×C43—81no—
298C22×C43—81no—
299C22×C43C2×C4×D411yescharacteristic
300C22×C43C2×#12111yescharacteristic
301C22×C43#52511yescharacteristic
302C22×C43#57711yescharacteristic
303C22×C43#57711yescharacteristic
304C22×C43#57711yescharacteristic
305C22×C43#57811yescharacteristic
306C4×C43—22no—
307C4×C43—22no—
308C4×C43—42no—
309C4×C43—42no—
310C4×C43—42no—
311C4×C43C2×C4×D411yescharacteristic
312C4×C43C4×#4111yescharacteristic
313C4×C43#52911yescharacteristic
314C4×C43#53211yescharacteristic
315Dic43—22no—
316Dic43—22no—
317Dic43—24no—
318Dic43—41no—
319Dic43—41no—
320Dic43—42no—
321Dic43—81no—
322Dic43—81no—
323C2×#464—431no—
324C2×#441—431no—
325C2×C4×SD16—431no—
326#2326—431no—
327#2276—431no—
328#1983D4311yescharacteristic
329#1948—431no—
330#1927—431no—
331#1926—431no—
332#1880—431no—
333#1878—431no—
334#1803—431no—
335#1768—431no—
336#1762—431no—
337C4×#103—431no—
338C2×C43—82no—
339C2×C43C4×#12111yescharacteristic
340C2×C43#294711yescharacteristic
341C2×C43#295211yescharacteristic
342C2×C43#304311yescharacteristic
343C2×C43#304611yescharacteristic
344C2×C43#312111yescharacteristic
345C2×C43#312511yescharacteristic
346C22×Q16—431no—
347C22×SD16—431no—
348C2×#124C2×D4311yescharacteristic
349C2×C4×Q8—431no—
350C2×C4×Q8—431no—
351C2×C4×Q8—431no—
352C2×C4×Q8—431no—
353C2×C4×D4—431no—
354#464—438no—
355#441—864no—
356C4×SD16—864no—
357C2×#106—431no—
358C2×#106—431no—
359C2×C4⋊C8—431no—
360C2×C4⋊C8C2×D4311yescharacteristic
361C2×#103—431no—
362C2×#103—431no—
363C2×#103—431no—
364C2×#103C2×D4311yescharacteristic
365C2×#103C2×D4311yescharacteristic
366C2×#102—431no—
367C2×#102C2×D4311yescharacteristic
368C2×#102C2×D4311yescharacteristic
369C2×#97—431no—
370C2×C4×C8—431no—
371#391—431no—
372#390—431no—
373#388—861no—
374#388—861no—
375#385—861no—
376#385—861no—
377#384—431no—
378C4×C4⋊C4—431no—
379C4×C4⋊C4—431no—
380C4×C4⋊C4—861no—
381C4×C4⋊C4—861no—
382C4×C4⋊C4—861no—
383C4×C4⋊C4C2×D4311yescharacteristic
384#376—431no—
385#376—861no—
386#340—431no—
387#340—431no—
388#340—431no—
389#340—431no—
390#336—431no—
391#336—431no—
392C43#2151111yescharacteristic, complemented, Sylow
393C22×Q8—431no—
394C22×Q8C22×D4311yescharacteristic
395C22×D4C22×D4311yescharacteristic
396C23×C4—861no—
397C2×Q16—434no—
398C2×Q16—862no—
399C2×Q16—862no—
400C2×SD16—434no—
401C2×SD16—862no—
402C2×SD16—862no—
403C22×C8—431no—
404C22×C8—431no—
405C22×C8C22×D4311yescharacteristic
406C22×C8C22×D4311yescharacteristic
407#124—22no—
408#124C4×D4314yes—
409C4×Q8—434no—
410C4×Q8—434no—
411C4×Q8—862no—
412C4×Q8—862no—
413C4×Q8—862no—
414C4×Q8—862no—
415C4×Q8—862no—
416C4×Q8—862no—
417C4×D4—862no—
418C4×D4—862no—
419C2×C4⋊C4—431no—
420C2×C4⋊C4—431no—
421C2×C4⋊C4—431no—
422C2×C4⋊C4—861no—
423C2×C4⋊C4—861no—
424C2×C4⋊C4—861no—
425C2×C4⋊C4—861no—
426C2×C4⋊C4—861no—
427C2×C4⋊C4—861no—
428C2×C4⋊C4C22×D4311yescharacteristic
429C2×C4⋊C4C22×D4311yescharacteristic
430C2×C22⋊C4—21no—
431C2×C22⋊C4—21no—
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×C42—861no—
443C2×C42—861no—
444C2×C42C22×D4311yescharacteristic
445#106—862no—
446#106—862no—
447C4⋊C8—22no—
448C4⋊C8—434no—
449#103—22no—
450#103—22no—
451#103—434no—
452#103—862no—
453#103—862no—
454#102—22no—
455#102—22no—
456#102—434no—
457#97—862no—
458C4×C8—862no—
459#95—21no—
460#95—431no—
461#95—431no—
462#95—431no—
463#95—431no—
464#95—861no—
465#95—861no—
466#95—861no—
467#95—861no—
468C24—21no—
469C2×Q8—21no—
470C2×Q8—21no—
471C2×Q8—21no—
472C2×Q8—21no—
473C2×Q8—21no—
474C2×Q8—432no—
475C2×Q8—432no—
476C2×Q8—432no—
477C2×Q8—861no—
478C2×Q8—861no—
479C2×Q8—861no—
480C2×Q8C2×C4×D4312yes—
481C2×D4—21no—
482C2×D4—21no—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4—21no—
486C2×D4C2×C4×D4312yes—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—431no—
491C22×C4—431no—
492C22×C4—431no—
493C22×C4—431no—
494C22×C4—861no—
495C22×C4—861no—
496C22×C4—861no—
497C22×C4—861no—
498C22×C4—3441no—
499C22×C4—3441no—
500C22×C4—1722no—
501C22×C4D4×D4311yescharacteristic
502C22×C4D4×D4311yescharacteristic
503C22×C4C23×D4311yescharacteristic
504Q16—868no—
505SD16—868no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—432no—
513C2×C8—432no—
514C2×C8—861no—
515C2×C8—861no—
516C2×C8—861no—
517C2×C8—861no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—432no—
521C4⋊C4—864no—
522C4⋊C4—864no—
523C4⋊C4—864no—
524C4⋊C4—861no—
525C4⋊C4—861no—
526C4⋊C4—861no—
527C4⋊C4—861no—
528C4⋊C4—861no—
529C4⋊C4—3441no—
530C4⋊C4—3441no—
531C4⋊C4—1722no—
532C4⋊C4D4×D4312yes—
533C4⋊C4#1062190012yes—
534C22⋊C4—24no—
535C22⋊C4—24no—
536C22⋊C4—3441no—
537C22⋊C4—3441no—
538C22⋊C4—1722no—
539C42—81no—
540C42—432no—
541C42—432no—
542C42—864no—
543C42—864no—
544C42—864no—
545C42—861no—
546C42—861no—
547C42—3441no—
548C42—3441no—
549C42—1722no—
550C42C2×C4×D4312yes—
551C42#1062190012yes—
552C23—22no—
553C23—41no—
554C23—41no—
555C23—41no—
556C23—41no—
557C23—41no—
558C23—41no—
559C23C2×D4×D4311yescharacteristic
560Q8—22no—
561Q8—22no—
562Q8—41no—
563Q8—41no—
564Q8—434no—
565Q8—862no—
566Q8—862no—
567Q8—862no—
568D4—22no—
569D4—22no—
570D4—41no—
571D4—41no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—432no—
586C2×C4—432no—
587C2×C4—862no—
588C2×C4—862no—
589C2×C4—862no—
590C2×C4—861no—
591C2×C4—861no—
592C2×C4—861no—
593C2×C4—861no—
594C2×C4—862no—
595C2×C4—861no—
596C2×C4—861no—
597C2×C4—861no—
598C2×C4—861no—
599C2×C4—861no—
600C2×C4—861no—
601C2×C4—3444no—
602C2×C4—1721no—
603C2×C4—1721no—
604C2×C4—1721no—
605C2×C4—1721no—
606C2×C4—1721no—
607C2×C4—1721no—
608C2×C4—1721no—
609C2×C4—1721no—
610C2×C4(C22⋊D43)⋊C412yes—
611C2×C4(C22⋊D43)⋊C412yes—
612C2×C4C22×C4×D4311yescharacteristic
613C2×C4C2×D4×D4311yescharacteristic
614C2×C4#41×D4311yescharacteristic
615C2×C4#41×D4311yescharacteristic
616C2×C4C2×#1062190011yescharacteristic
617C2×C4C2×#1062190011yescharacteristic
618C8—41no—
619C8—41no—
620C8—862no—
621C8—862no—
622C22—42no—
623C22—42no—
624C22—42no—
625C22—81no—
626C22—81no—
627C22—81no—
628C22—81no—
629C22C2×(C22⋊D43)⋊C411yescharacteristic
630C22#121×D4311yescharacteristic
631C22#1458340911yescharacteristic
632C22#1458370611yescharacteristic
633C22#1458370811yescharacteristic
634C22#1458370911yescharacteristic
635C22#1458371311yescharacteristic
636C4—22no—
637C4—22no—
638C4—42no—
639C4—42no—
640C4—42no—
641C4—864no—
642C4—862no—
643C4—862no—
644C4—3441no—
645C4—3441no—
646C4—1722no—
647C4—1721no—
648C4—1721no—
649C4C4×D4×D4311yescharacteristic
650C4C4×#1062190011yescharacteristic
651C4#1458342811yescharacteristic
652C4#1458344711yescharacteristic
653C2—82no—
654C2#1913711111yescharacteristic
655C2#1914344111yescharacteristic
656C2#1914347411yescharacteristic
657C2#1914411411yescharacteristic
658C2#1914414611yescharacteristic
659C2#1914482311yescharacteristic
660C2#1914486911yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1983C2
socleC23×C43C22×D4
prime radicalC22×D4×C43C23
cosocleC22×C4×C43C24
hypercenter#1983D43
hypocenterC43#21511
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1983

Complements

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

NH ≅ G/Ntype
2. C2×#14583003C2semidirect
5. #19136959C2semidirect
6. #19135358C2semidirect
7. #19135232C2semidirect
10. #19134933C2semidirect
11. #19134601C2semidirect
12. #19134454C2semidirect
14. #103×Dic43C2semidirect
23. #14583118C4semidirect
66. C2×#10621885C2×C4semidirect
75. C4×Dic86C2×C4semidirect
104. C4⋊(C43⋊C8)C2×C4semidirect
107. #13063249C2×C4semidirect
392. C43#21511semidirect

Maximal subgroups

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

subgroupindex
C2×#145831182
C2×#145830032
C2×#145829902
#191373082
#191369592
#191353582
#191352322
#191352252
#191349472
#191349332
#191346012
#191344542
#191344222
#103×Dic432
C43×#19832
#2151143