Finite Group Databasebeta

← #25062901

Subgroups — #25062901

Order 11008.

996 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
1C2×#14583605C211yesmaximal, characteristic
2#19143632C211yesmaximal, characteristic
3#19143629C211yesmaximal, characteristic
4#19132957C212yesmaximal, complemented
5#19132957C212yesmaximal, complemented
6#19132951C211yesmaximal, characteristic, complemented
7#19132938C211yesmaximal, characteristic, complemented
8#19132923C212yesmaximal, complemented
9#19132918C211yesmaximal, characteristic, complemented
10#324×D43C212yesmaximal, complemented
11C43×#1470C211yesmaximal, characteristic, complemented
12#14583605—21no—
13#14583605—21no—
14#14583605—22no—
15#14583605—22no—
16#14583605—21no—
17#14583605—21no—
18C2×#13063324C411yescharacteristic
19C2×#13063316C411yescharacteristic
20C2×#13063305C412yes—
21C2×#13063303C412yes—
22C2×#13063303C2212yes—
23C2×C4×Dic86C2211yescharacteristic
24C2×C4×D172C2211yescharacteristic
25C2×#13063287C411yescharacteristic
26C2×#13063287C411yescharacteristic
27C2×C4⋊C4×D43C2212yes—
28#14582978—21no—
29#14582976—21no—
30#14582972—22no—
31#14582969—22no—
32C8×D172—21no—
33#14582964—21no—
34#14582956C2211yescharacteristic
35#14582952C2211yescharacteristic
36#14582861C2212yes—
37#14582861C2212yes—
38C22⋊C8×D43C2212yes—
39C22⋊C8×D43C2212yes—
40#14582625C2212yes—
41#14582625C2212yes—
42#14582624C2212yes—
43#14582624C2212yes—
44#14582624C2211yescharacteristic
45#14582624C2211yescharacteristic
46#14582624C2211yescharacteristic
47#14582624C2211yescharacteristic
48C2×#125×C43C2211yescharacteristic
49C43×#432C2211yescharacteristic
50C43×#431C2211yescharacteristic
51C43×#324C2212yes—
52C43×#324C2212yes—
53C22×Dic86C2×C411yescharacteristic
54C22×Dic86C2×C412yes—
55C22×D172C2×C411yescharacteristic
56C22×C4×D43C2×C412yes—
57C22×C4×D43C2×C412yes—
58C22×C4×D43C2312yes—
59C2×#10621872—22no—
60C2×#10621872—22no—
61C2×C8×D43—22no—
62C2×C8×D43—22no—
63#13063324—22no—
64#13063324—21no—
65#13063324—21no—
66#13063316—22no—
67#13063316—21no—
68#13063316—21no—
69#13063305—22no—
70#13063305—22no—
71#13063305—22no—
72#13063305—22no—
73#13063303—22no—
74#13063303—22no—
75#13063303—22no—
76#13063303—22no—
77#13063303—22no—
78#13063303—22no—
79#13063303—22no—
80#13063303—22no—
81C4×Dic86—21no—
82C4×Dic86—21no—
83C4×Dic86—21no—
84C4×Dic86—21no—
85C4×D172D411yescharacteristic
86C4×D172D411yescharacteristic
87C4×D172D412yes—
88C4×D172D412yes—
89C4×D172D411yescharacteristic
90C4×D172D411yescharacteristic
91#13063287—22no—
92#13063287—21no—
93#13063287—21no—
94#13063287—22no—
95#13063287—21no—
96#13063287—21no—
97C2×C4⋊Dic43C2×C412yes—
98C2×C4⋊Dic43C2×C411yescharacteristic
99C2×C4⋊Dic43C2×C411yescharacteristic
100C2×Dic43⋊C4C2×C412yes—
101C2×Dic43⋊C4C2×C412yes—
102C2×Dic43⋊C4C2311yescharacteristic
103C2×Dic43⋊C4C2311yescharacteristic
104C4⋊C4×D43—22no—
105C4⋊C4×D43—22no—
106C4⋊C4×D43—22no—
107C4⋊C4×D43—22no—
108C2×(C2×D43)⋊C4C2×C412yes—
109C2×(C2×D43)⋊C4C2×C412yes—
110C2×(C2×D43)⋊C4C2×C412yes—
111C2×C4×Dic43C2×C411yescharacteristic
112C2×C4×Dic43C2×C411yescharacteristic
113C4⋊(C43⋊C8)—21no—
114C4⋊(C43⋊C8)—21no—
115C22⋊(C43⋊C8)C2311yescharacteristic
116C22⋊(C43⋊C8)C2312yes—
117C22⋊(C43⋊C8)C2311yescharacteristic
118(C2×D43)⋊C8—22no—
119(C2×D43)⋊C8—22no—
120(C2×D43)⋊C8—22no—
121(C2×D43)⋊C8—22no—
122#13063236—21no—
123C4×C43⋊C8—21no—
124#125×C43—21no—
125#125×C43—21no—
126#125×C43—21no—
127#125×C43—21no—
128C2×C4⋊C4×C43C2×C411yescharacteristic
129C2×C4⋊C4×C43C2×C411yescharacteristic
130C2×C4⋊C4×C43C2×C412yes—
131C2×C4⋊C4×C43C2312yes—
132C2×C42×C43C2311yescharacteristic
133C4⋊C8×C43—21no—
134C4⋊C8×C43—21no—
135C22⋊C8×C43C2311yescharacteristic
136C22⋊C8×C43C2312yes—
137C22⋊C8×C43C2311yescharacteristic
138#97×C43—21no—
139C4×C8×C43—21no—
140C23×D43C22×C412yes—
141C22×C4×C43C22×C412yes—
142C22×C4×C43C22×C411yescharacteristic
143C22×C4×C43C22×C411yescharacteristic
144C22×C4×C43C22×C412yes—
145C22×C4×C43C2411yescharacteristic
146C22×Dic43C22×C411yescharacteristic
147C22×Dic43C22×C411yescharacteristic
148C22×Dic43C22×C411yescharacteristic
149C22×Dic43C22×C411yescharacteristic
150C22×Dic43C22×C412yes—
151C2×D172—24no—
152C2×D172C22⋊C411yescharacteristic
153C2×D172C22⋊C412yes—
154C2×D172C22⋊C411yescharacteristic
155C2×C4×D43—24no—
156C2×C4×D43—22no—
157C2×C4×D43—22no—
158C2×C4×D43—22no—
159C2×C4×D43—22no—
160C2×C4×D43—42no—
161C2×C4×D43—82no—
162C2×C4×D43—82no—
163C2×C4×D43C2×D412yes—
164C2×C4×D43C2×D412yes—
165C2×C4×D43C2×D412yes—
166C2×C4×D43C2×D412yes—
167C2×Dic86—21no—
168C2×Dic86—21no—
169C2×Dic86—22no—
170C2×Dic86—22no—
171C2×Dic86—22no—
172C2×Dic86—41no—
173C2×Dic86—82no—
174C2×C8×C43—21no—
175C2×C8×C43—21no—
176C2×C8×C43—22no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43—22no—
182C4⋊C4×C43—22no—
183C4⋊C4×C43—22no—
184C4⋊C4×C43—22no—
185C42×C43C2×D411yescharacteristic
186C42×C43C2×D411yescharacteristic
187C42×C43C2×D411yescharacteristic
188C42×C43C2×D411yescharacteristic
189(C2×D43)⋊C4—22no—
190(C2×D43)⋊C4—22no—
191(C2×D43)⋊C4—22no—
192(C2×D43)⋊C4—22no—
193(C2×D43)⋊C4C22⋊C412yes—
194(C2×D43)⋊C4C22⋊C412yes—
195(C2×D43)⋊C4C22⋊C412yes—
196(C2×D43)⋊C4C22⋊C412yes—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43—22no—
200C4⋊Dic43—22no—
201C4⋊Dic43C22⋊C412yes—
202C4⋊Dic43C22⋊C411yescharacteristic
203C4⋊Dic43C22⋊C411yescharacteristic
204Dic43⋊C4—21no—
205Dic43⋊C4—21no—
206Dic43⋊C4—21no—
207Dic43⋊C4—21no—
208Dic43⋊C4—22no—
209Dic43⋊C4—22no—
210Dic43⋊C4—22no—
211Dic43⋊C4—22no—
212C4×Dic43—21no—
213C4×Dic43—21no—
214C4×Dic43—21no—
215C4×Dic43—21no—
216C2×C43⋊C8—21no—
217C2×C43⋊C8—21no—
218C2×C43⋊C8—22no—
219#10621872—82no—
220#10621872—82no—
221C8×D43—82no—
222C8×D43—82no—
223C23×C43C23×C411yescharacteristic
224C22×D43—22no—
225C22×D43—22no—
226C22×D43—24no—
227C22×D43—42no—
228C22×D43C2×C22⋊C412yes—
229C22×D43C2×C22⋊C412yes—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—22no—
233C2×C4×C43—22no—
234C2×C4×C43—22no—
235C2×C4×C43—22no—
236C2×C4×C43—22no—
237C2×C4×C43—41no—
238C2×C4×C43—42no—
239C2×C4×C43C2×C22⋊C411yescharacteristic
240C2×C4×C43C2×C22⋊C411yescharacteristic
241C2×C4×C43C2×C22⋊C411yescharacteristic
242C2×C4×C43C2×C22⋊C411yescharacteristic
243C2×C4×C43C22×D411yescharacteristic
244C2×C4×C43C22×D411yescharacteristic
245C2×Dic43—21no—
246C2×Dic43—21no—
247C2×Dic43—21no—
248C2×Dic43—21no—
249C2×Dic43—21no—
250C2×Dic43—21no—
251C2×Dic43—21no—
252C2×Dic43—42no—
253C2×Dic43—41no—
254C2×Dic43—41no—
255C2×Dic43C2×C22⋊C412yes—
256C2×Dic43C2×C22⋊C412yes—
257C2×Dic43#13112yes—
258D172—24no—
259D172—22no—
260D172#10114yes—
261C4×D43—42no—
262C4×D43—42no—
263C4×D43—42no—
264C4×D43—42no—
265C4×D43—44no—
266C4×D43—44no—
267C4×D43—82no—
268C4×D43—82no—
269Dic86—42no—
270Dic86—42no—
271Dic86—82no—
272Dic86—82no—
273C8×C43—41no—
274C8×C43—42no—
275C8×C43—41no—
276C43⋊C8—41no—
277C43⋊C8—42no—
278C43⋊C8—41no—
279#17426—431nomaximal, Sylow
280C22×C43—21no—
281C22×C43—21no—
282C22×C43C22×C22⋊C411yescharacteristic
283C22×C43C2×#13111yescharacteristic
284C22×C43#56811yescharacteristic
285C2×D43—22no—
286C2×D43—22no—
287C2×D43—22no—
288C2×D43—22no—
289C2×D43—22no—
290C2×D43—44no—
291C2×D43—44no—
292C2×D43C2×#10114yes—
293C4×C43—21no—
294C4×C43—21no—
295C4×C43—21no—
296C4×C43—21no—
297C4×C43—21no—
298C4×C43—42no—
299C4×C43—42no—
300C4×C43C2×#10112yes—
301Dic43—22no—
302Dic43—22no—
303Dic43—22no—
304Dic43—41no—
305Dic43—41no—
306Dic43—41no—
307C2×#554—431no—
308#2974—431no—
309#2974—431no—
310#1472—432no—
311#1472—432no—
312#1470—431no—
313#1470D4311yescharacteristic, complemented
314#1467—431no—
315#1463—432no—
316#1461—431no—
317C2×#324—432no—
318C2×C43—21no—
319C2×C43—21no—
320C2×C43#288011yescharacteristic
321C2×C43#288311yescharacteristic
322C2×C43C22×#10111yescharacteristic
323D43—24no—
324D43—42no—
325#554—861no—
326#554—861no—
327#554—862no—
328#554—862no—
329#554—861no—
330#554—861no—
331C2×C4⋊Q8—431no—
332C2×#125—431no—
333C2×#125C2×D4311yescharacteristic
334C2×C22⋊Q8—432no—
335C2×C22⋊Q8—432no—
336C2×C22⋊Q8—432no—
337C2×C4×Q8—431no—
338C2×C4×D4—431no—
339C2×C4×D4—431no—
340C2×C4×D4—431no—
341C22×C4⋊C4—432no—
342#436—861no—
343#436—861no—
344#435—862no—
345#435—862no—
346C8×D4—861no—
347C8×D4—861no—
348#432—431no—
349#432C2×D4311yescharacteristic
350#431—431no—
351#431C2×D4311yescharacteristic
352#407—432no—
353#407—432no—
354C2×C22⋊C8—432no—
355C2×C22⋊C8—432no—
356#324—432no—
357#324—432no—
358#324—431no—
359#324—432no—
360#324—431no—
361#324—431no—
362#324—431no—
363#324—432no—
364#324C2×D4312yes—
365#324C2×D4312yes—
366C43#1742611yescharacteristic, complemented, Sylow
367C22×Q8—431no—
368C22×Q8—432no—
369C22×D4—431no—
370C23×C4—432no—
371C23×C4—432no—
372C23×C4—432no—
373C2×M16—862no—
374C2×M16—862no—
375C22×C8—862no—
376C22×C8—862no—
377C4⋊Q8—862no—
378C4⋊Q8—861no—
379C4⋊Q8—861no—
380#125—21no—
381#125—21no—
382#125—21no—
383#125—21no—
384#125—862no—
385#125—861no—
386#125—861no—
387C22⋊Q8—862no—
388C22⋊Q8—862no—
389C22⋊Q8—862no—
390C22⋊Q8—862no—
391C22⋊Q8—862no—
392C22⋊Q8—862no—
393C22⋊Q8—862no—
394C22⋊Q8—862no—
395C22⋊Q8—862no—
396C22⋊Q8—862no—
397C22⋊Q8—862no—
398C22⋊Q8—862no—
399C4×Q8—861no—
400C4×Q8—861no—
401C4×Q8—861no—
402C4×Q8—861no—
403C4×D4—431no—
404C4×D4—431no—
405C4×D4—432no—
406C4×D4—432no—
407C4×D4—431no—
408C4×D4—431no—
409C4×D4—861no—
410C4×D4—862no—
411C4×D4—861no—
412C4×D4—861no—
413C4×D4—862no—
414C4×D4—861no—
415C2×C4⋊C4—431no—
416C2×C4⋊C4—432no—
417C2×C4⋊C4—432no—
418C2×C4⋊C4—431no—
419C2×C4⋊C4—432no—
420C2×C4⋊C4—431no—
421C2×C4⋊C4—431no—
422C2×C4⋊C4—862no—
423C2×C4⋊C4—862no—
424C2×C4⋊C4—862no—
425C2×C4⋊C4—862no—
426C2×C4⋊C4C4×D4311yescharacteristic
427C2×C4⋊C4C4×D4311yescharacteristic
428C2×C4⋊C4C4×D4312yes—
429C2×C4⋊C4C22×D4312yes—
430C2×C22⋊C4—432no—
431C2×C22⋊C4—432no—
432C2×C22⋊C4—432no—
433C2×C42—431no—
434C2×C42—431no—
435C2×C42C22×D4311yescharacteristic
436C4⋊C8—21no—
437C4⋊C8—21no—
438C4⋊C8—861no—
439C4⋊C8—861no—
440C22⋊C8—431no—
441C22⋊C8—432no—
442C22⋊C8—431no—
443C22⋊C8—862no—
444C22⋊C8—862no—
445C22⋊C8—862no—
446C22⋊C8—862no—
447C22⋊C8C22×D4311yescharacteristic
448C22⋊C8C22×D4312yes—
449C22⋊C8C22×D4311yescharacteristic
450#97—21no—
451#97—861no—
452C4×C8—21no—
453C4×C8—861no—
454C24—432no—
455C2×Q8—862no—
456C2×Q8—862no—
457C2×Q8—862no—
458C2×Q8—861no—
459C2×Q8—861no—
460C2×Q8—3442no—
461C2×Q8—1721no—
462C2×D4—431no—
463C2×D4—432no—
464C2×D4—431no—
465C2×D4—864no—
466C22×C4—431no—
467C22×C4—432no—
468C22×C4—432no—
469C22×C4—432no—
470C22×C4—432no—
471C22×C4—432no—
472C22×C4—431no—
473C22×C4—431no—
474C22×C4—431no—
475C22×C4—864no—
476C22×C4—862no—
477C22×C4—862no—
478C22×C4—862no—
479C22×C4—862no—
480C22×C4—3442no—
481C22×C4—3442no—
482C22×C4—1722no—
483C22×C4C2×C4×D4312yes—
484C22×C4C2×C4×D4311yescharacteristic
485C22×C4C2×C4×D4311yescharacteristic
486C22×C4C2×C4×D4312yes—
487C22×C4C23×D4311yescharacteristic
488M16—3442no—
489M16—3442no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—22no—
493C2×C8—861no—
494C2×C8—861no—
495C2×C8—862no—
496C2×C8—3442no—
497C2×C8—3442no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—22no—
503C4⋊C4—22no—
504C4⋊C4—22no—
505C4⋊C4—22no—
506C4⋊C4—432no—
507C4⋊C4—431no—
508C4⋊C4—431no—
509C4⋊C4—862no—
510C4⋊C4—862no—
511C4⋊C4—862no—
512C4⋊C4—862no—
513C4⋊C4—862no—
514C4⋊C4—862no—
515C4⋊C4—861no—
516C4⋊C4—861no—
517C4⋊C4—861no—
518C4⋊C4—861no—
519C4⋊C4—861no—
520C4⋊C4—861no—
521C22⋊C4—432no—
522C22⋊C4—432no—
523C22⋊C4—432no—
524C22⋊C4—432no—
525C22⋊C4—862no—
526C22⋊C4—862no—
527C22⋊C4—862no—
528C22⋊C4—862no—
529C42—861no—
530C42—861no—
531C42—861no—
532C42—861no—
533C42D4×D4311yescharacteristic
534C42D4×D4311yescharacteristic
535C42D4×D4311yescharacteristic
536C42D4×D4311yescharacteristic
537C23—432no—
538C23—432no—
539C23—864no—
540C23—862no—
541C23—862no—
542C23—1722no—
543C23C22×C4×D4311yescharacteristic
544Q8—3442no—
545Q8—3442no—
546Q8—1722no—
547Q8—1722no—
548D4—434no—
549D4—864no—
550D4—862no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—41no—
559C2×C4—42no—
560C2×C4—432no—
561C2×C4—432no—
562C2×C4—432no—
563C2×C4—861no—
564C2×C4—861no—
565C2×C4—861no—
566C2×C4—861no—
567C2×C4—861no—
568C2×C4—861no—
569C2×C4—861no—
570C2×C4—3442no—
571C2×C4—3442no—
572C2×C4—1722no—
573C2×C4—1722no—
574C2×C4—1722no—
575C2×C4—1722no—
576C2×C4—1724no—
577C2×C4—1724no—
578C2×C4—1722no—
579C2×C4—1721no—
580C2×C4—1721no—
581C2×C4C22⋊C4×D4311yescharacteristic
582C2×C4C22⋊C4×D4311yescharacteristic
583C2×C4C22⋊C4×D4311yescharacteristic
584C2×C4C22⋊C4×D4311yescharacteristic
585C2×C4C2×D4×D4311yescharacteristic
586C2×C4C2×D4×D4311yescharacteristic
587C8—41no—
588C8—42no—
589C8—41no—
590C8—1721no—
591C8—1722no—
592C8—1721no—
593C22—21no—
594C22—21no—
595C22—434no—
596C22—862no—
597C22—862no—
598C22—862no—
599C22—862no—
600C22—862no—
601C22—1724no—
602C22—1724no—
603C22C2×C22⋊C4×D4311yescharacteristic
604C22#131×D4311yescharacteristic
605C22#1458366411yescharacteristic
606C4—21no—
607C4—21no—
608C4—21no—
609C4—21no—
610C4—21no—
611C4—42no—
612C4—42no—
613C4—862no—
614C4—862no—
615C4—862no—
616C4—1721no—
617C4—1721no—
618C4—1721no—
619C4#101×D4312yes—
620C2—21no—
621C2—21no—
622C2—864no—
623C2—1722no—
624C2#1914304311yescharacteristic
625C2#1914305411yescharacteristic
626C2C2×#101×D4311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC23×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1470C2
socleC22×C43C22×C22⋊C4
prime radicalC22×D172C2×C4
cosocleC22×C4×C43C24
hypercenter#1470D43
hypocenterC43#17426
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1470

Complements

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

NH ≅ G/Ntype
4. #19132957C2semidirect
5. #19132957C2semidirect
6. #19132951C2semidirect
7. #19132938C2semidirect
8. #19132923C2semidirect
9. #19132918C2semidirect
10. #324×D43C2semidirect
11. C43×#1470C2semidirect
313. #1470D43semidirect
366. C43#17426semidirect

Maximal subgroups

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

subgroupindex
C2×#145836052
#191436322
#191436292
#191329572
#191329512
#191329382
#191329232
#191329182
#324×D432
C43×#14702
#1742643