Finite Group Databasebeta

← #25062651

Subgroups — #25062651

Order 11008.

940 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583515C211yesmaximal, characteristic
2#19143679C211yesmaximal, characteristic, complemented
3#19143675C211yesmaximal, characteristic, complemented
4#19132964C211yesmaximal, characteristic, complemented
5#19132963C212yesmaximal, complemented
6#19132948C211yesmaximal, characteristic, complemented
7#19132946C211yesmaximal, characteristic, complemented
8#19132945C212yesmaximal, complemented
9#19132914C212yesmaximal, complemented
10#19132908C212yesmaximal, complemented
11C43×#1473C211yesmaximal, characteristic, complemented
12#14583515—22no—
13#14583515—22no—
14#14583515—22no—
15#14583515—22no—
16C2×#13063324C411yescharacteristic
17C2×#13063320C2211yescharacteristic
18C2×#13063313C2211yescharacteristic
19C2×#13063311C411yescharacteristic
20C2×#13063311C2211yescharacteristic
21C2×#13063310C411yescharacteristic
22C2×#13063309C411yescharacteristic
23C2×#13063305C411yescharacteristic
24C2×#13063303C411yescharacteristic
25C2×#13063302C411yescharacteristic
26C2×#13063298C411yescharacteristic
27C2×C4×Dic86C2211yescharacteristic
28C2×(C22⋊D43)⋊C4C2211yescharacteristic
29C2×#13063283C2211yescharacteristic
30#14583028—22no—
31#14583027—22no—
32C8×Dic86—22no—
33#14583023—22no—
34#14582956C2211yescharacteristic
35#14582953C2212yes—
36#14582952C2211yescharacteristic
37#14582949C2212yes—
38#14582949C2212yes—
39#14582949C2212yes—
40#14582625C2212yes—
41#14582623C2212yes—
42#14582622C2212yes—
43#14582622C2212yes—
44#14582622C2212yes—
45#14582622C2212yes—
46C2×#126×C43C2211yescharacteristic
47C43×#432C2211yescharacteristic
48C43×#431C2211yescharacteristic
49C43×#324C2212yes—
50C43×#323C2212yes—
51C22×Dic86C2×C411yescharacteristic
52C22×Dic86C2×C411yescharacteristic
53C22×Dic86C2×C411yescharacteristic
54C22×D172C2×C411yescharacteristic
55C22×C22⋊D43C2×C411yescharacteristic
56C22×C22⋊D43C2×C411yescharacteristic
57C23×Dic43C2×C411yescharacteristic
58C22×C4×D43C2×C411yescharacteristic
59C22×C4×D43C2×C411yescharacteristic
60#13063324—22no—
61#13063324—22no—
62#13063320—22no—
63#13063320—22no—
64#13063313—21no—
65#13063313—21no—
66#13063313—21no—
67#13063313—21no—
68#13063311—22no—
69#13063311—22no—
70#13063311—22no—
71#13063311—22no—
72#13063310—22no—
73#13063310—22no—
74#13063309—22no—
75#13063309—22no—
76#13063305—22no—
77#13063305—22no—
78#13063303—22no—
79#13063303—22no—
80#13063302—22no—
81#13063302—22no—
82#13063298—22no—
83#13063298—22no—
84C4×Dic86D412yes—
85C4×Dic86D412yes—
86C4×Dic86D412yes—
87C4×Dic86D412yes—
88(C22⋊D43)⋊C4—22no—
89(C22⋊D43)⋊C4—22no—
90#13063283—22no—
91#13063283—22no—
92C2×C4⋊Dic43C2×C411yescharacteristic
93C2×C4⋊Dic43C2×C411yescharacteristic
94C2×C4⋊Dic43C2×C411yescharacteristic
95C2×Dic43⋊C4C2×C411yescharacteristic
96C2×Dic43⋊C4C2×C411yescharacteristic
97C2×Dic43⋊C4C2×C411yescharacteristic
98C2×Dic43⋊C4C2×C411yescharacteristic
99C2×C22⋊Dic43C2×C411yescharacteristic
100C2×(C2×D43)⋊C4C2×C411yescharacteristic
101C2×(C2×D43)⋊C4C2×C411yescharacteristic
102C2×(C2×D43)⋊C4C2×C411yescharacteristic
103C2×(C2×D43)⋊C4C2×C411yescharacteristic
104C2×(C2×D43)⋊C4C2×C411yescharacteristic
105C2×(C2×D43)⋊C4C2×C411yescharacteristic
106C2×(C2×D43)⋊C4C2311yescharacteristic
107C2×(C2×D43)⋊C4C2311yescharacteristic
108C2×C4×Dic43C2×C411yescharacteristic
109C2×C4×Dic43C2311yescharacteristic
110C2×C4×Dic43C2311yescharacteristic
111C4⋊(C43⋊C8)—21no—
112C4⋊(C43⋊C8)—21no—
113Dic43⋊C8—22no—
114Dic43⋊C8—22no—
115Dic43⋊C8—22no—
116Dic43⋊C8—22no—
117C22⋊(C43⋊C8)C2312yes—
118C22⋊(C43⋊C8)C2312yes—
119#13063236—21no—
120#13063235—22no—
121C4×C43⋊C8—21no—
122C8×Dic43—22no—
123C8×Dic43—22no—
124C8×Dic43—22no—
125#126×C43—21no—
126#126×C43—21no—
127#126×C43—21no—
128#126×C43—21no—
129C2×C4⋊C4×C43C2×C411yescharacteristic
130C2×C4⋊C4×C43C2×C411yescharacteristic
131C2×C4⋊C4×C43C2311yescharacteristic
132C2×C22⋊C4×C43C2×C411yescharacteristic
133C2×C22⋊C4×C43C2×C411yescharacteristic
134C2×C22⋊C4×C43C2311yescharacteristic
135C2×C42×C43C2311yescharacteristic
136C4⋊C8×C43—21no—
137C4⋊C8×C43—21no—
138C22⋊C8×C43C2312yes—
139C22⋊C8×C43C2312yes—
140#97×C43—21no—
141C4×C8×C43—21no—
142C24×C43C22×C411yescharacteristic
143C23×D43C22×C411yescharacteristic
144C23×D43C22×C411yescharacteristic
145C22×C4×C43C22×C411yescharacteristic
146C22×C4×C43C22×C411yescharacteristic
147C22×C4×C43C22×C411yescharacteristic
148C22×C4×C43C22×C411yescharacteristic
149C22×C4×C43C22×C411yescharacteristic
150C22×C4×C43C2411yescharacteristic
151C2×C22⋊D43—22no—
152C2×C22⋊D43—22no—
153C2×C22⋊D43—24no—
154C2×C22⋊D43—81no—
155C22×Dic43—22no—
156C22×Dic43—81no—
157C22×Dic43C22×C411yescharacteristic
158C22×Dic43C22×C411yescharacteristic
159C22×Dic43C22×C411yescharacteristic
160C22×Dic43C22×C411yescharacteristic
161C22×Dic43C22×C411yescharacteristic
162C22×Dic43C22×C411yescharacteristic
163C2×D172—21no—
164C2×D172—21no—
165C2×D172—81no—
166C2×C4×D43—22no—
167C2×C4×D43—24no—
168C2×C4×D43—22no—
169C2×C4×D43—81no—
170C2×Dic86—24no—
171C2×Dic86—21no—
172C2×Dic86—21no—
173C2×Dic86—22no—
174C2×Dic86—81no—
175C2×Dic86—81no—
176C2×Dic86C22⋊C412yes—
177C2×Dic86C22⋊C412yes—
178C2×C8×C43—22no—
179C2×C8×C43—22no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43—21no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43—21no—
184C4⋊C4×C43—21no—
185C4⋊C4×C43—21no—
186C22⋊C4×C43—21no—
187C22⋊C4×C43—21no—
188C22⋊C4×C43—21no—
189C22⋊C4×C43—21no—
190C22⋊C4×C43—21no—
191C22⋊C4×C43—21no—
192C42×C43C2×D411yescharacteristic
193C42×C43C2×D411yescharacteristic
194C42×C43C2×D411yescharacteristic
195C42×C43C2×D411yescharacteristic
196C22⋊Dic43—22no—
197(C2×D43)⋊C4—21no—
198(C2×D43)⋊C4—21no—
199(C2×D43)⋊C4—21no—
200(C2×D43)⋊C4—21no—
201(C2×D43)⋊C4—21no—
202(C2×D43)⋊C4—21no—
203(C2×D43)⋊C4—21no—
204(C2×D43)⋊C4—21no—
205(C2×D43)⋊C4—22no—
206(C2×D43)⋊C4—22no—
207(C2×D43)⋊C4—22no—
208(C2×D43)⋊C4—22no—
209C4⋊Dic43—22no—
210C4⋊Dic43—22no—
211C4⋊Dic43C22⋊C412yes—
212C4⋊Dic43C22⋊C412yes—
213Dic43⋊C4—22no—
214Dic43⋊C4—22no—
215Dic43⋊C4C22⋊C412yes—
216Dic43⋊C4C22⋊C412yes—
217Dic43⋊C4C22⋊C412yes—
218Dic43⋊C4C22⋊C412yes—
219C4×Dic43—22no—
220C4×Dic43C2×D412yes—
221C4×Dic43C2×D412yes—
222C4×Dic43C2×D412yes—
223C4×Dic43C2×D412yes—
224C2×C43⋊C8—22no—
225C2×C43⋊C8—22no—
226C23×C43—21no—
227C23×C43—22no—
228C23×C43—41no—
229C23×C43—41no—
230C23×C43C23×C411yescharacteristic
231C22×D43—21no—
232C22×D43—21no—
233C22×D43—22no—
234C22×D43—22no—
235C22×D43—41no—
236C22×D43—41no—
237C22×D43—41no—
238C22×D43—41no—
239C2×C4×C43—22no—
240C2×C4×C43—21no—
241C2×C4×C43—21no—
242C2×C4×C43—21no—
243C2×C4×C43—22no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43—41no—
247C2×C4×C43—41no—
248C2×C4×C43C2×C22⋊C411yescharacteristic
249C2×C4×C43C2×C22⋊C411yescharacteristic
250C2×C4×C43C2×C22⋊C411yescharacteristic
251C2×C4×C43C2×C22⋊C411yescharacteristic
252C2×C4×C43C22×D411yescharacteristic
253C2×C4×C43C22×D411yescharacteristic
254C22⋊D43—44no—
255C22⋊D43—82no—
256C2×Dic43—22no—
257C2×Dic43—21no—
258C2×Dic43—21no—
259C2×Dic43—41no—
260C2×Dic43—41no—
261C2×Dic43—41no—
262C2×Dic43—41no—
263C2×Dic43—82no—
264C2×Dic43C2×C22⋊C412yes—
265C2×Dic43C2×C22⋊C412yes—
266C2×Dic43C2×C22⋊C412yes—
267C2×Dic43C2×C22⋊C412yes—
268C2×Dic43#13114yes—
269D172—81no—
270D172—81no—
271C4×D43—44no—
272C4×D43—82no—
273Dic86—24no—
274Dic86—24no—
275Dic86—82no—
276Dic86—81no—
277Dic86—81no—
278C8×C43—42no—
279C8×C43—42no—
280C43⋊C8—42no—
281C43⋊C8—42no—
282#17390—431nomaximal, Sylow
283C22×C43—21no—
284C22×C43—21no—
285C22×C43—41no—
286C22×C43—41no—
287C22×C43—41no—
288C22×C43—82no—
289C22×C43C22×C22⋊C411yescharacteristic
290C22×C43C2×#13112yes—
291C2×D43—41no—
292C2×D43—41no—
293C2×D43—41no—
294C2×D43—41no—
295C2×D43—41no—
296C2×D43—41no—
297C2×D43—82no—
298C2×D43—82no—
299C4×C43—21no—
300C4×C43—21no—
301C4×C43—21no—
302C4×C43—21no—
303C4×C43—21no—
304C4×C43—21no—
305C4×C43—41no—
306C4×C43—41no—
307C4×C43—41no—
308Dic43—22no—
309Dic43—22no—
310Dic43—22no—
311Dic43—41no—
312Dic43—41no—
313Dic43#40814yes—
314C2×#542—431no—
315#2983—431no—
316#2982—431no—
317#1473—432no—
318#1473—431no—
319#1473D4311yescharacteristic, complemented
320#1469—431no—
321#1469—431no—
322#1469—432no—
323#1460—432no—
324#1458—432no—
325C2×C43—22no—
326C2×C43—81no—
327C2×C43C2×#40811yescharacteristic
328C2×C43#288411yescharacteristic
329C2×C43#288811yescharacteristic
330D43—81no—
331D43—81no—
332#542—862no—
333#542—862no—
334#542—862no—
335#542—862no—
336C2×C4⋊Q8—431no—
337C2×#126—431no—
338C2×#126C2×D4311yescharacteristic
339C2×#124—431no—
340C2×#124—431no—
341C2×#124—431no—
342C2×#123—431no—
343C2×#123—431no—
344C2×C22⋊Q8—431no—
345C2×C22⋊Q8—431no—
346C2×C22⋊Q8—431no—
347C2×#121—431no—
348C2×C4×Q8—431no—
349C2×C4×D4—431no—
350C2×#117—431no—
351#446—862no—
352#446—862no—
353C8×Q8—862no—
354C8×Q8—862no—
355#432—431no—
356#432—432no—
357#432C2×D4311yescharacteristic
358#431—431no—
359#431—432no—
360#431—432no—
361#431—432no—
362#431C2×D4311yescharacteristic
363#324—432no—
364#324C2×D4312yes—
365#323—432no—
366#323—432no—
367#323—432no—
368#323—432no—
369#323—432no—
370#323C2×D4312yes—
371C43#1739011yescharacteristic, complemented, Sylow
372C22×Q8—431no—
373C22×Q8—431no—
374C22×Q8—431no—
375C22×D4—431no—
376C22×D4—431no—
377C22×D4—431no—
378C23×C4—431no—
379C23×C4—431no—
380C23×C4—431no—
381C4⋊Q8—862no—
382C4⋊Q8—862no—
383#126—21no—
384#126—21no—
385#126—21no—
386#126—21no—
387#126—862no—
388#126—862no—
389#124—862no—
390#124—862no—
391#124—862no—
392#124—862no—
393#124—861no—
394#124—861no—
395#124—861no—
396#124—861no—
397#123—862no—
398#123—862no—
399#123—862no—
400#123—862no—
401C22⋊Q8—862no—
402C22⋊Q8—862no—
403C22⋊Q8—862no—
404C22⋊Q8—862no—
405C22⋊Q8—862no—
406C22⋊Q8—862no—
407#121—862no—
408#121—862no—
409C4×Q8—432no—
410C4×Q8—432no—
411C4×Q8—432no—
412C4×Q8—432no—
413C4×D4—862no—
414C4×D4—862no—
415#117—862no—
416#117—862no—
417C2×C4⋊C4—431no—
418C2×C4⋊C4—431no—
419C2×C4⋊C4—431no—
420C2×C4⋊C4—431no—
421C2×C4⋊C4—431no—
422C2×C4⋊C4—431no—
423C2×C4⋊C4—431no—
424C2×C4⋊C4C4×D4311yescharacteristic
425C2×C4⋊C4C4×D4311yescharacteristic
426C2×C4⋊C4C22×D4311yescharacteristic
427C2×C22⋊C4—431no—
428C2×C22⋊C4—431no—
429C2×C22⋊C4—431no—
430C2×C22⋊C4—431no—
431C2×C22⋊C4—431no—
432C2×C22⋊C4—431no—
433C2×C22⋊C4—431no—
434C2×C22⋊C4—431no—
435C2×C22⋊C4—431no—
436C2×C22⋊C4C4×D4311yescharacteristic
437C2×C22⋊C4C4×D4311yescharacteristic
438C2×C22⋊C4C22×D4311yescharacteristic
439C2×C42—431no—
440C2×C42—431no—
441C2×C42—431no—
442C2×C42C22×D4311yescharacteristic
443C4⋊C8—21no—
444C4⋊C8—21no—
445C4⋊C8—862no—
446C4⋊C8—862no—
447C4⋊C8—862no—
448C4⋊C8—862no—
449C4⋊C8—861no—
450C4⋊C8—861no—
451C22⋊C8—432no—
452C22⋊C8—432no—
453C22⋊C8C22×D4312yes—
454C22⋊C8C22×D4312yes—
455#97—21no—
456#97—862no—
457#97—861no—
458C4×C8—21no—
459C4×C8—862no—
460C4×C8—862no—
461C4×C8—862no—
462C4×C8—861no—
463C24—431no—
464C24—431no—
465C24C2×C4×D4311yescharacteristic
466C2×Q8—432no—
467C2×Q8—432no—
468C2×Q8—864no—
469C2×Q8—862no—
470C2×Q8—861no—
471C2×Q8—861no—
472C2×Q8—3441no—
473C2×Q8—3441no—
474C2×D4—862no—
475C2×D4—862no—
476C2×D4—864no—
477C2×D4—861no—
478C2×D4—861no—
479C2×D4—3441no—
480C2×D4—3441no—
481C22×C4—431no—
482C22×C4—431no—
483C22×C4—431no—
484C22×C4—431no—
485C22×C4—431no—
486C22×C4—431no—
487C22×C4—862no—
488C22×C4—862no—
489C22×C4—864no—
490C22×C4—862no—
491C22×C4—3441no—
492C22×C4—3441no—
493C22×C4C2×C4×D4311yescharacteristic
494C22×C4C2×C4×D4311yescharacteristic
495C22×C4C2×C4×D4311yescharacteristic
496C22×C4C2×C4×D4311yescharacteristic
497C22×C4C2×C4×D4311yescharacteristic
498C22×C4C23×D4311yescharacteristic
499C2×C8—22no—
500C2×C8—22no—
501C2×C8—862no—
502C2×C8—862no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—432no—
510C4⋊C4—432no—
511C4⋊C4—432no—
512C4⋊C4—432no—
513C4⋊C4—432no—
514C4⋊C4—432no—
515C4⋊C4—862no—
516C4⋊C4—862no—
517C4⋊C4—862no—
518C4⋊C4—862no—
519C22⋊C4—21no—
520C22⋊C4—21no—
521C22⋊C4—21no—
522C22⋊C4—21no—
523C22⋊C4—21no—
524C22⋊C4—21no—
525C22⋊C4—862no—
526C22⋊C4—862no—
527C22⋊C4—862no—
528C22⋊C4—862no—
529C22⋊C4—862no—
530C22⋊C4—861no—
531C22⋊C4—861no—
532C22⋊C4—861no—
533C22⋊C4—861no—
534C22⋊C4—861no—
535C22⋊C4—861no—
536C22⋊C4—861no—
537C22⋊C4—861no—
538C42—432no—
539C42—432no—
540C42—432no—
541C42—432no—
542C42—862no—
543C42D4×D4311yescharacteristic
544C42D4×D4311yescharacteristic
545C42D4×D4311yescharacteristic
546C42D4×D4311yescharacteristic
547C23—21no—
548C23—22no—
549C23—41no—
550C23—41no—
551C23—862no—
552C23—862no—
553C23—861no—
554C23—861no—
555C23—1721no—
556C23—1721no—
557C23—1721no—
558C23—1721no—
559C23C22×C4×D4311yescharacteristic
560Q8—864no—
561Q8—864no—
562Q8—3441no—
563Q8—3441no—
564Q8—3442no—
565D4—3441no—
566D4—3441no—
567D4—3442no—
568D4—1724no—
569C2×C4—22no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—22no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—432no—
579C2×C4—434no—
580C2×C4—432no—
581C2×C4—432no—
582C2×C4—432no—
583C2×C4—862no—
584C2×C4—861no—
585C2×C4—861no—
586C2×C4—3442no—
587C2×C4—3442no—
588C2×C4—1724no—
589C2×C4—1721no—
590C2×C4—1721no—
591C2×C4—1721no—
592C2×C4—1721no—
593C2×C4C22⋊C4×D4311yescharacteristic
594C2×C4C22⋊C4×D4311yescharacteristic
595C2×C4C22⋊C4×D4311yescharacteristic
596C2×C4C22⋊C4×D4311yescharacteristic
597C2×C4C2×D4×D4311yescharacteristic
598C2×C4C2×D4×D4311yescharacteristic
599C8—42no—
600C8—42no—
601C8—1722no—
602C8—1722no—
603C22—21no—
604C22—21no—
605C22—41no—
606C22—41no—
607C22—41no—
608C22—82no—
609C22—3442no—
610C22—3442no—
611C22—1721no—
612C22—1721no—
613C22—1721no—
614C22—1721no—
615C22—1721no—
616C22—1721no—
617C22C2×C22⋊C4×D4311yescharacteristic
618C22#131×D4312yes—
619C4—21no—
620C4—21no—
621C4—21no—
622C4—21no—
623C4—21no—
624C4—21no—
625C4—41no—
626C4—41no—
627C4—41no—
628C4—434no—
629C4—862no—
630C4—862no—
631C4—862no—
632C4—1721no—
633C4—1721no—
634C2—22no—
635C2—81no—
636C2—3441no—
637C2—3441no—
638C2#408×D4311yescharacteristic
639C2#1914305711yescharacteristic
640C2#1914307211yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC23×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1473C2
socleC22×C43C22×C22⋊C4
prime radicalC2×#13063298C4
cosocleC22×C4×C43C24
hypercenter#1473D43
hypocenterC43#17390
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1473

Complements

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

NH ≅ G/Ntype
2. #19143679C2semidirect
3. #19143675C2semidirect
4. #19132964C2semidirect
5. #19132963C2semidirect
6. #19132948C2semidirect
7. #19132946C2semidirect
8. #19132945C2semidirect
9. #19132914C2semidirect
10. #19132908C2semidirect
11. C43×#1473C2semidirect
319. #1473D43semidirect
371. C43#17390semidirect

Maximal subgroups

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

subgroupindex
C2×#145835152
#191436792
#191436752
#191329642
#191329632
#191329482
#191329462
#191329452
#191329142
#191329082
C43×#14732
#1739043