Finite Group Databasebeta

← #25101631

Subgroups — #25101631

Order 11008.

1164 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147892C211yesmaximal, characteristic
2C4×M16×D43C211yesmaximal, characteristic, complemented
3#19136991C211yesmaximal, characteristic, complemented
4#19135540C211yesmaximal, characteristic, complemented
5#19135514C211yesmaximal, characteristic, complemented
6#19135513C211yesmaximal, characteristic, complemented
7#19134896C214yesmaximal, complemented
8#19134404C214yesmaximal, complemented
9C43×#1986C211yesmaximal, characteristic, complemented
10C2×M16×D43C2212yes—
11#14583454C411yescharacteristic, complemented
12#14583454C411yescharacteristic, complemented
13#14583450C411yescharacteristic, complemented
14#14583450C411yescharacteristic, complemented
15#14583449C2211yescharacteristic
16#14583436—21no—
17#14583436—21no—
18#14583435—21no—
19#14583435—21no—
20#14583434C412yescomplemented
21#14583434C412yescomplemented
22#14583412—21no—
23#14583412—21no—
24#14583411C2212yes—
25C4×#10621902—21no—
26C4×#10621902—21no—
27#14583367C2212yes—
28C2×C42×D43C2211yescharacteristic
29C2×#13063253C2214yes—
30C2×#13063251C2214yes—
31C4×#10621877C2211yescharacteristic
32#14582851—21no—
33M16×Dic43C2212yes—
34C4×#10621872—21no—
35#97×D43—21no—
36C4×C8×D43—21no—
37#14582766—21no—
38#14582764—21no—
39#14582761—21no—
40#14582756—21no—
41C4×C4⋊Dic43C2211yescharacteristic
42C4×(C2×D43)⋊C4C2212yes—
43#14582745C2212yes—
44#14582658C2214yes—
45C43×#533C2211yescharacteristic
46C4×M16×C43C2211yescharacteristic
47C4×C4⋊C4×C43C2211yescharacteristic
48C43×#339C2214yes—
49C2×#10621902—21no—
50C2×#10621902—21no—
51C2×#10621898C2312yes—
52C22×C4×D43D411yescharacteristic
53C22×C4×D43D411yescharacteristic
54C22×C4×D43C2311yescharacteristic
55C2×#10621877C2312yes—
56C2×#10621872—22no—
57M16×D43—24no—
58M16×D43—24no—
59C2×C8×D43—22no—
60#13063325C2×C411yescharacteristic
61#13063322C2×C411yescharacteristic
62#13063320—22no—
63#13063320—22no—
64#13063316—21no—
65#13063316—21no—
66#13063314—21no—
67#13063314—21no—
68#13063313C2×C412yes—
69#13063310—22no—
70#13063310—22no—
71#13063309—22no—
72#13063305C2×C412yes—
73#13063305C2×C412yes—
74#13063301—21no—
75#13063301—21no—
76#13063300—21no—
77#13063300—21no—
78#13063300C2×C412yes—
79#13063300C2×C412yes—
80#13063299—21no—
81#13063299—21no—
82#13063295—22no—
83Q8×Dic43—21no—
84Q8×Dic43—21no—
85#13063290C2×C412yes—
86#13063290C2×C412yes—
87C4×D172—22no—
88C4×D172—22no—
89C4×D172—21no—
90C4×D172—21no—
91#13063287—22no—
92#13063287—22no—
93#13063287—21no—
94#13063287—21no—
95#13063287C2×C412yes—
96#13063287C2×C412yes—
97(C22⋊D43)⋊C4—22no—
98(C22⋊D43)⋊C4—22no—
99#13063283—21no—
100#13063283—21no—
101#13063283—22no—
102#13063283—22no—
103#13063282—22no—
104C2×C4⋊Dic43—21no—
105C2×(C2×D43)⋊C4—22no—
106C2×C4×Dic43D411yescharacteristic
107C2×C4×Dic43D411yescharacteristic
108C2×C4×Dic43C2312yes—
109C2×C4×Dic43C2311yescharacteristic
110C42×D43—22no—
111C42×D43C2×C411yescharacteristic
112C42×D43C2×C411yescharacteristic
113C42×D43C2×C411yescharacteristic
114C42×D43C2×C411yescharacteristic
115C42×D43D411yescharacteristic
116C42×D43D411yescharacteristic
117C42×D43D411yescharacteristic
118C42×D43D411yescharacteristic
119#13063253—28no—
120#13063251—28no—
121#13063236—21no—
122#13063235—22no—
123C4×C43⋊C8—21no—
124C8×Dic43—22no—
125C43⋊#95—21no—
126C43⋊#95—22no—
127C43⋊#95—22no—
128C43⋊#95—22no—
129C2×M16×C43C2312yes—
130C4⋊Q8×C43C2×C411yescharacteristic
131C4⋊Q8×C43C2×C411yescharacteristic
132#125×C43C2×C412yes—
133C22⋊Q8×C43—21no—
134C22⋊Q8×C43—21no—
135C4×Q8×C43—21no—
136C4×Q8×C43—21no—
137#117×C43C2312yes—
138C2×C4⋊C4×C43—21no—
139C2×C42×C43C2312yes—
140C2×C42×C43C2311yescharacteristic
141#97×C43—21no—
142C4×C8×C43—21no—
143#95×C43—21no—
144C23×D43C2×D411yescharacteristic
145C2×Q8×C43—21no—
146C2×Q8×C43—21no—
147C22×C4×C43—22no—
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2411yescharacteristic
151C2×C22⋊D43—22no—
152C22×Dic43—22no—
153C22×Dic43C2×D411yescharacteristic
154C22×Dic43C2×D411yescharacteristic
155C22×Dic43C2×D411yescharacteristic
156#10621902—44no—
157#10621902—44no—
158#10621898—24no—
159#10621898—24no—
160C2×D172—21no—
161C2×D172—21no—
162C2×D172—22no—
163C2×D172—22no—
164C2×D172C22×C412yes—
165C2×C4×D43—22no—
166C2×C4×D43—22no—
167C2×C4×D43—22no—
168C2×C4×D43—22no—
169C2×C4×D43—22no—
170C2×C4×D43—42no—
171C2×C4×D43—42no—
172C2×C4×D43C22⋊C411yescharacteristic
173C2×C4×D43C22⋊C411yescharacteristic
174C2×C4×D43C22⋊C411yescharacteristic
175C2×C4×D43C22⋊C411yescharacteristic
176C2×C4×D43C22⋊C411yescharacteristic
177C2×C4×D43C22⋊C411yescharacteristic
178C2×C4×D43C22⋊C411yescharacteristic
179C2×C4×D43C22⋊C411yescharacteristic
180C2×C4×D43C22×C411yescharacteristic
181C2×C4×D43C22×C411yescharacteristic
182C2×C4×D43C2×D411yescharacteristic
183C2×C4×D43C2×D411yescharacteristic
184C2×Dic86C22×C412yes—
185M16×C43—22no—
186M16×C43#4114yescomplemented
187C2×C8×C43—22no—
188C4⋊C4×C43—22no—
189C4⋊C4×C43—22no—
190C4⋊C4×C43—21no—
191C4⋊C4×C43—21no—
192C4⋊C4×C43—42no—
193C4⋊C4×C43C22×C412yes—
194C4⋊C4×C43C22×C412yes—
195C22⋊C4×C43—22no—
196C42×C43—22no—
197C42×C43—24no—
198C42×C43C22×C411yescharacteristic
199C42×C43C22×C411yescharacteristic
200C42×C43C2×D411yescharacteristic
201C42×C43C2×D411yescharacteristic
202(C2×D43)⋊C4—22no—
203(C2×D43)⋊C4—22no—
204(C2×D43)⋊C4—22no—
205(C2×D43)⋊C4—22no—
206(C2×D43)⋊C4—22no—
207(C2×D43)⋊C4—22no—
208(C2×D43)⋊C4—22no—
209(C2×D43)⋊C4—22no—
210(C2×D43)⋊C4—44no—
211C4⋊Dic43—21no—
212C4⋊Dic43—21no—
213C4⋊Dic43—22no—
214C4⋊Dic43—22no—
215C4⋊Dic43—42no—
216Dic43⋊C4—22no—
217Dic43⋊C4—22no—
218C4×Dic43—22no—
219C4×Dic43—22no—
220C4×Dic43—24no—
221C4×Dic43C22⋊C411yescharacteristic
222C4×Dic43C22⋊C411yescharacteristic
223C4×Dic43C22⋊C411yescharacteristic
224C4×Dic43C22⋊C411yescharacteristic
225C4×Dic43C22⋊C411yescharacteristic
226C4×Dic43C22⋊C411yescharacteristic
227C4×Dic43C22⋊C411yescharacteristic
228C4×Dic43C22⋊C411yescharacteristic
229C4×Dic43C22×C411yescharacteristic
230C4×Dic43C22×C411yescharacteristic
231C4×Dic43C2×D411yescharacteristic
232C4×Dic43C2×D411yescharacteristic
233#10621877—22no—
234#10621877#4114yescomplemented
235C2×C43⋊C8—22no—
236#10621872—28no—
237C8×D43—28no—
238C23×C43C22×D411yescharacteristic
239C22×D43—21no—
240C22×D43—21no—
241C22×D43—22no—
242C22×D43—22no—
243C22×D43—41no—
244C22×D43C2×C22⋊C411yescharacteristic
245C22×D43C2×C22⋊C411yescharacteristic
246Q8×C43—42no—
247Q8×C43—42no—
248C2×C4×C43—22no—
249C2×C4×C43—22no—
250C2×C4×C43—22no—
251C2×C4×C43—41no—
252C2×C4×C43—42no—
253C2×C4×C43—42no—
254C2×C4×C43—42no—
255C2×C4×C43C2×C22⋊C411yescharacteristic
256C2×C4×C43C2×C22⋊C411yescharacteristic
257C2×C4×C43C2×C22⋊C411yescharacteristic
258C2×C4×C43C2×C22⋊C411yescharacteristic
259C2×C4×C43C23×C411yescharacteristic
260C2×C4×C43C22×D411yescharacteristic
261C2×C4×C43C2×#4112yes—
262C2×C4×C43C2×#4112yes—
263C22⋊D43—42no—
264C22⋊D43—42no—
265C2×Dic43—21no—
266C2×Dic43—21no—
267C2×Dic43—22no—
268C2×Dic43—41no—
269C2×Dic43—41no—
270C2×Dic43—42no—
271C2×Dic43—42no—
272C2×Dic43—42no—
273C2×Dic43C2×C22⋊C411yescharacteristic
274C2×Dic43C2×C22⋊C411yescharacteristic
275C2×Dic43C2×C22⋊C411yescharacteristic
276C2×Dic43C2×C22⋊C411yescharacteristic
277C2×Dic43C2×C22⋊C411yescharacteristic
278C2×Dic43C2×C22⋊C411yescharacteristic
279D172—24no—
280D172—42no—
281D172—44no—
282D172—44no—
283D172—42no—
284C4×D43—22no—
285C4×D43—22no—
286C4×D43—22no—
287C4×D43—22no—
288C4×D43—22no—
289C4×D43—22no—
290C4×D43—22no—
291C4×D43—22no—
292C4×D43—41no—
293C4×D43—41no—
294C4×D43—41no—
295C4×D43—41no—
296C4×D43—44no—
297C4×D43—44no—
298C4×D43—44no—
299Dic86—24no—
300C8×C43—24no—
301C43⋊C8—24no—
302#21383—431nomaximal, Sylow
303C22×C43—21no—
304C22×C43—21no—
305C22×C43C22×C22⋊C411yescharacteristic
306C22×C43#53211yescharacteristic
307C22×C43#53211yescharacteristic
308C2×D43—21no—
309C2×D43—21no—
310C2×D43—21no—
311C2×D43—21no—
312C2×D43—21no—
313C2×D43—42no—
314C2×D43—42no—
315C2×D43—42no—
316C2×D43—42no—
317C2×D43—42no—
318C2×D43#42112yes—
319C4×C43—21no—
320C4×C43—21no—
321C4×C43—21no—
322C4×C43—42no—
323C4×C43—42no—
324C4×C43—82no—
325C4×C43#42112yes—
326C4×C43C4×#4112yes—
327C4×C43#52512yes—
328Dic43—21no—
329Dic43—21no—
330Dic43—21no—
331Dic43—21no—
332Dic43—21no—
333Dic43—21no—
334Dic43—42no—
335Dic43—82no—
336#3444—431no—
337C2×C4×M16—431no—
338#2283—431no—
339#1986—431no—
340#1986D4311yescharacteristic, complemented
341#1980—431no—
342#1980—431no—
343#1871—434no—
344#1759—434no—
345C2×C43—21no—
346C2×C43—21no—
347C2×C43#229711yescharacteristic
348C2×C43C2×#42111yescharacteristic
349C2×C43C2×#42111yescharacteristic
350D43—22no—
351D43—41no—
352D43—82no—
353C22×M16—432no—
354#533—431no—
355#533—431no—
356#533C2×D4311yescharacteristic
357#532—431no—
358#532—431no—
359#532—431no—
360#529—432no—
361#529—432no—
362#529—861no—
363#529—861no—
364#529—861no—
365#529—861no—
366#525—432no—
367#525—861no—
368#525—861no—
369C4×#41—432no—
370C4×#41—861no—
371C4×#41—861no—
372C22×C42—431no—
373C2×#104—434no—
374C2×#104—434no—
375C4×M16—432no—
376C4×M16—431no—
377C4×M16—861no—
378C4×M16—861no—
379C4×M16C2×D4311yescharacteristic
380C2×#97—861no—
381C2×C4×C8—861no—
382#383—861no—
383#382—861no—
384#381—861no—
385#380—861no—
386C4×C4⋊C4—431no—
387C4×C4⋊C4C2×D4311yescharacteristic
388C4×C22⋊C4—432no—
389#376—432no—
390#339—434no—
391#339C2×D4314yes—
392C43#2138311yescharacteristic, complemented, Sylow
393C2×#41—432no—
394C2×#41—861no—
395C2×#41—861no—
396C23×C4—431no—
397C23×C4—431no—
398C23×C4—431no—
399C2×M16—432no—
400C2×M16—862no—
401C2×M16—864no—
402C2×M16—864no—
403C2×M16C22×D4312yes—
404C22×C8—862no—
405C4⋊Q8—431no—
406C4⋊Q8C4×D4311yescharacteristic
407C4⋊Q8C4×D4311yescharacteristic
408#127—431no—
409#126—862no—
410#126—862no—
411#125—861no—
412#125—861no—
413#125C4×D4312yes—
414#124—432no—
415#124—861no—
416#124—861no—
417#123—862no—
418#123—862no—
419#123—862no—
420C22⋊Q8—21no—
421C22⋊Q8—21no—
422C22⋊Q8—432no—
423C22⋊Q8—432no—
424C22⋊Q8—861no—
425C22⋊Q8—861no—
426#121—432no—
427#121—432no—
428#121—861no—
429#121—861no—
430#121—861no—
431#121—861no—
432#120—862no—
433C4×Q8—21no—
434C4×Q8—21no—
435C4×Q8—432no—
436C4×Q8—432no—
437C4×Q8—861no—
438C4×Q8—861no—
439C4×D4—432no—
440C4×D4—432no—
441C4×D4—862no—
442C4×D4—862no—
443C4×D4—861no—
444C4×D4—861no—
445C4×D4—862no—
446C4×D4—862no—
447C4×D4—862no—
448C4×D4—862no—
449C4×D4—861no—
450C4×D4—861no—
451#117—862no—
452#117—862no—
453#117—862no—
454#117—861no—
455#117—861no—
456#117C22×D4312yes—
457C2×C4⋊C4—21no—
458C2×C4⋊C4—861no—
459C2×C22⋊C4—862no—
460C2×C42—431no—
461C2×C42—431no—
462C2×C42—431no—
463C2×C42—431no—
464C2×C42—431no—
465C2×C42—431no—
466C2×C42—431no—
467C2×C42—431no—
468C2×C42—431no—
469C2×C42—431no—
470C2×C42—431no—
471C2×C42—432no—
472C2×C42—862no—
473C2×C42C22×D4312yes—
474C2×C42C22×D4311yescharacteristic
475#104—868no—
476#104—868no—
477#97—21no—
478#97—862no—
479#97—861no—
480C4×C8—21no—
481C4×C8—862no—
482C4×C8—861no—
483#95—21no—
484#95—862no—
485#95—862no—
486#95—862no—
487#95—861no—
488C24—431no—
489#41—864no—
490#41—864no—
491#41—1724no—
492#41—1724no—
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8—432no—
496C2×D4—432no—
497C2×D4—862no—
498C2×D4—862no—
499C2×D4—862no—
500C2×D4—861no—
501C2×D4—861no—
502C22×C4—22no—
503C22×C4—431no—
504C22×C4—431no—
505C22×C4—431no—
506C22×C4—431no—
507C22×C4—431no—
508C22×C4—431no—
509C22×C4—431no—
510C22×C4—431no—
511C22×C4—431no—
512C22×C4—431no—
513C22×C4—431no—
514C22×C4—431no—
515C22×C4—431no—
516C22×C4—431no—
517C22×C4—431no—
518C22×C4—862no—
519C22×C4—862no—
520C22×C4—862no—
521C22×C4—862no—
522C22×C4—862no—
523C22×C4—862no—
524C22×C4—1722no—
525C22×C4—1722no—
526C22×C4D4×D4311yescharacteristic
527C22×C4D4×D4311yescharacteristic
528C22×C4C23×D4311yescharacteristic
529M16—22no—
530M16—434no—
531M16—868no—
532M16—862no—
533M16#1062190214yescomplemented
534C2×C8—22no—
535C2×C8—868no—
536C2×C8—862no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—22no—
540C4⋊C4—22no—
541C4⋊C4—42no—
542C4⋊C4—862no—
543C4⋊C4—862no—
544C4⋊C4—862no—
545C4⋊C4—862no—
546C4⋊C4—861no—
547C4⋊C4—861no—
548C4⋊C4—1722no—
549C4⋊C4C2×C4×D4312yes—
550C4⋊C4C2×C4×D4312yes—
551C22⋊C4—22no—
552C22⋊C4—862no—
553C22⋊C4—862no—
554C22⋊C4—862no—
555C22⋊C4—862no—
556C22⋊C4—862no—
557C22⋊C4—862no—
558C22⋊C4—862no—
559C22⋊C4—862no—
560C22⋊C4—1724no—
561C42—22no—
562C42—24no—
563C42—431no—
564C42—431no—
565C42—431no—
566C42—431no—
567C42—431no—
568C42—431no—
569C42—431no—
570C42—431no—
571C42—431no—
572C42—431no—
573C42—431no—
574C42—431no—
575C42—862no—
576C42—862no—
577C42—864no—
578C42C2×C4×D4311yescharacteristic
579C42C2×C4×D4311yescharacteristic
580C42D4×D4311yescharacteristic
581C42D4×D4311yescharacteristic
582C23—431no—
583C23—431no—
584C23—862no—
585C23—861no—
586C23—861no—
587C23—862no—
588C23—1721no—
589C23C2×D4×D4311yescharacteristic
590Q8—42no—
591Q8—42no—
592Q8—864no—
593D4—864no—
594D4—1722no—
595D4—1724no—
596D4—1724no—
597D4—1722no—
598D4—1722no—
599D4—1722no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—41no—
604C2×C4—42no—
605C2×C4—42no—
606C2×C4—42no—
607C2×C4—431no—
608C2×C4—431no—
609C2×C4—431no—
610C2×C4—431no—
611C2×C4—431no—
612C2×C4—431no—
613C2×C4—862no—
614C2×C4—862no—
615C2×C4—861no—
616C2×C4—861no—
617C2×C4—862no—
618C2×C4—862no—
619C2×C4—862no—
620C2×C4—862no—
621C2×C4—862no—
622C2×C4—862no—
623C2×C4—862no—
624C2×C4—1721no—
625C2×C4—1721no—
626C2×C4—1721no—
627C2×C4—1721no—
628C2×C4—1724no—
629C2×C4—1724no—
630C2×C4—1721no—
631C2×C4—1721no—
632C2×C4—1722no—
633C2×C4—1722no—
634C2×C4—1722no—
635C2×C4—1724no—
636C2×C4C22⋊C4×D4311yescharacteristic
637C2×C4C22⋊C4×D4311yescharacteristic
638C2×C4C22⋊C4×D4311yescharacteristic
639C2×C4C22⋊C4×D4311yescharacteristic
640C2×C4C22×C4×D4311yescharacteristic
641C2×C4C2×D4×D4311yescharacteristic
642C2×C4#41×D4312yes—
643C2×C4C2×#1062190212yes—
644C8—24no—
645C8—864no—
646C22—21no—
647C22—21no—
648C22—432no—
649C22—861no—
650C22—861no—
651C22—861no—
652C22—861no—
653C22—861no—
654C22—1722no—
655C22—1722no—
656C22—1722no—
657C22—1722no—
658C22—1722no—
659C22C2×C22⋊C4×D4311yescharacteristic
660C22#1458344811yescharacteristic
661C22#1458345011yescharacteristic
662C4—21no—
663C4—21no—
664C4—21no—
665C4—42no—
666C4—42no—
667C4—82no—
668C4—861no—
669C4—861no—
670C4—861no—
671C4—861no—
672C4—861no—
673C4—861no—
674C4—3442no—
675C4—1722no—
676C4#1458291412yes—
677C4C4×#1062190212yes—
678C4#1458341212yes—
679C2—21no—
680C2—21no—
681C2—862no—
682C2—3442no—
683C2—1721no—
684C2#1913708411yescharacteristic
685C2#421×D4311yescharacteristic
686C2C2×#1458291411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1986C2
socleC22×C43C22×C22⋊C4
prime radical#19147892C2
cosocleC22×C4×C43C24
hypercenter#1986D43
hypocenterC43#21383
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1986

Complements

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

NH ≅ G/Ntype
2. C4×M16×D43C2semidirect
3. #19136991C2semidirect
4. #19135540C2semidirect
5. #19135514C2semidirect
6. #19135513C2semidirect
7. #19134896C2semidirect
8. #19134404C2semidirect
9. C43×#1986C2semidirect
11. #14583454C4semidirect
12. #14583454C4semidirect
13. #14583450C4semidirect
14. #14583450C4semidirect
20. #14583434C4semidirect
21. #14583434C4semidirect
186. M16×C43#41semidirect
234. #10621877#41semidirect
340. #1986D43semidirect
392. C43#21383semidirect
533. M16#10621902semidirect

Maximal subgroups

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

subgroupindex
#191478922
C4×M16×D432
#191369912
#191355402
#191355142
#191355132
#191348962
#191344042
C43×#19862
#2138343