Finite Group Databasebeta

← #25106249

Subgroups — #25106249

Order 11008.

1200 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147890C211yesmaximal, characteristic
2#423×D43C211yesmaximal, characteristic, complemented
3C4×#13063282C211yesmaximal, characteristic, complemented
4#19135572C211yesmaximal, characteristic, complemented
5#19135571C211yesmaximal, characteristic, complemented
6#19135424C211yesmaximal, characteristic, complemented
7#19134894C214yesmaximal, complemented
8#19134613C214yesmaximal, complemented
9C43×#1962C211yesmaximal, characteristic, complemented
10C2×M16×D43C2212yes—
11#14583456C2211yescharacteristic
12#14583454C411yescharacteristic, complemented
13#14583454C411yescharacteristic, complemented
14#14583447C411yescharacteristic, complemented
15#14583447C411yescharacteristic, complemented
16#14583431—21no—
17#14583431—21no—
18#14583430—21no—
19#14583430—21no—
20#14583428C412yescomplemented
21#14583428C412yescomplemented
22#14583409—21no—
23#14583409—21no—
24#14583406C2212yes—
25#41×Dic43C2212yes—
26C4×#10621900—21no—
27C4×#10621900—21no—
28C2×#13063282—21no—
29C2×C42×D43C2211yescharacteristic
30#14582923C2211yescharacteristic
31#14582922C2212yes—
32#14582921—21no—
33#14582921—21no—
34C4⋊C8×D43—21no—
35C4⋊C8×D43—21no—
36C2×#13063252C2214yes—
37C4×Dic43⋊C4—21no—
38C4×Dic43⋊C4C2212yes—
39C4×(C2×D43)⋊C4—21no—
40C4×(C2×D43)⋊C4C2212yes—
41#14582745—21no—
42C42×Dic43C2211yescharacteristic
43#14582660C2214yes—
44#14582659C2214yes—
45C43×#532C2211yescharacteristic
46C43×#423C2211yescharacteristic
47C2×#104×C43C2214yes—
48C43×C43C2211yescharacteristic
49C2×#10621900—21no—
50C2×#10621900—21no—
51C22×C4×D43D411yescharacteristic
52C22×C4×D43D411yescharacteristic
53C22×C4×D43C2311yescharacteristic
54C2×#10621877C2312yes—
55C2×#10621872—22no—
56M16×D43—44no—
57C2×C8×D43—22no—
58#13063325C2×C411yescharacteristic
59#13063325C2×C411yescharacteristic
60#13063318—22no—
61#13063318—22no—
62#13063317C2×C412yes—
63#13063316—21no—
64#13063316—21no—
65#13063312—21no—
66#13063312—21no—
67#13063307—22no—
68#13063307—22no—
69#13063306—22no—
70#13063305—21no—
71#13063305—21no—
72#13063304—21no—
73#13063304—21no—
74#13063301C2×C412yes—
75#13063301C2×C412yes—
76#13063296—21no—
77#13063296—21no—
78#13063296C2×C412yes—
79#13063296C2×C412yes—
80#13063293—22no—
81Q8×Dic43C2×C412yes—
82Q8×Dic43C2×C412yes—
83C4×Dic86—21no—
84C4×Dic86—21no—
85#13063290—21no—
86#13063290—21no—
87D4×Dic43—22no—
88D4×Dic43—22no—
89D4×Dic43—21no—
90D4×Dic43—21no—
91D4×Dic43C2×C412yes—
92D4×Dic43C2×C412yes—
93C4×C22⋊D43—22no—
94C4×C22⋊D43—22no—
95(C22⋊D43)⋊C4—22no—
96(C22⋊D43)⋊C4—22no—
97#13063284—22no—
98#13063284C2312yes—
99#13063283—21no—
100#13063283—21no—
101#13063282—28no—
102#13063281—22no—
103#13063281—22no—
104C2×Dic43⋊C4—22no—
105C2×(C2×D43)⋊C4—22no—
106C2×C4×Dic43—21no—
107C2×C4×Dic43—22no—
108C2×C4×Dic43—21no—
109C2×C4×Dic43D411yescharacteristic
110C2×C4×Dic43D411yescharacteristic
111C2×C4×Dic43C2312yes—
112C2×C4×Dic43C2311yescharacteristic
113C42×D43C2×C411yescharacteristic
114C42×D43C2×C411yescharacteristic
115C42×D43C2×C411yescharacteristic
116C42×D43C2×C411yescharacteristic
117C42×D43D411yescharacteristic
118C42×D43D411yescharacteristic
119C42×D43D411yescharacteristic
120C42×D43D411yescharacteristic
121C4⋊(C43⋊C8)—21no—
122C4⋊(C43⋊C8)—21no—
123Dic43⋊C8—22no—
124Dic43⋊C8—22no—
125#13063252—44no—
126C43⋊#95—22no—
127C43⋊#95—22no—
128C2×#41×C43C2312yes—
129C2×M16×C43C2312yes—
130C4⋊Q8×C43C2×C411yescharacteristic
131#127×C43C2×C411yescharacteristic
132#124×C43C2×C412yes—
133#121×C43—21no—
134#121×C43—21no—
135C4×D4×C43—21no—
136C4×D4×C43—21no—
137C2×C42×C43—21no—
138C2×C42×C43—21no—
139C2×C42×C43C2312yes—
140C2×C42×C43C2311yescharacteristic
141C4⋊C8×C43—21no—
142C4⋊C8×C43—21no—
143#104×C43—44no—
144C23×D43C2×D411yescharacteristic
145#41×C43—24no—
146#41×C43—24no—
147C2×Q8×C43C22×C412yes—
148C2×D4×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43—22no—
151C2×D4×C43C22×C412yes—
152C22×C4×C43—22no—
153C22×C4×C43—22no—
154C22×C4×C43C2×D411yescharacteristic
155C22×C4×C43C2×D411yescharacteristic
156C22×C4×C43C2411yescharacteristic
157C2×C22⋊D43—22no—
158C2×C22⋊D43—22no—
159C22×Dic43—22no—
160C22×Dic43—22no—
161C22×Dic43—22no—
162C22×Dic43C2×D411yescharacteristic
163C22×Dic43C2×D411yescharacteristic
164C22×Dic43C2×D411yescharacteristic
165#10621900—44no—
166#10621900—44no—
167C2×C4×D43—22no—
168C2×C4×D43—22no—
169C2×C4×D43—24no—
170C2×C4×D43—42no—
171C2×C4×D43C22⋊C411yescharacteristic
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×D43C2×D411yescharacteristic
182C2×C4×D43C2×D411yescharacteristic
183C2×Dic86—21no—
184C2×Dic86—21no—
185M16×C43—24no—
186C2×C8×C43—22no—
187C4⋊C4×C43—21no—
188C4⋊C4×C43—21no—
189C22⋊C4×C43—22no—
190C22⋊C4×C43—22no—
191C42×C43—24no—
192C42×C43—22no—
193C42×C43—22no—
194C42×C43—42no—
195C42×C43C22×C411yescharacteristic
196C42×C43C22×C411yescharacteristic
197C42×C43C2×D411yescharacteristic
198C42×C43C2×D411yescharacteristic
199C22⋊Dic43—22no—
200C22⋊Dic43—22no—
201C22⋊Dic43—22no—
202C22⋊Dic43—22no—
203C22⋊Dic43—22no—
204(C2×D43)⋊C4—28no—
205(C2×D43)⋊C4—22no—
206(C2×D43)⋊C4—22no—
207C4⋊Dic43—21no—
208C4⋊Dic43—21no—
209C4⋊Dic43—22no—
210C4⋊Dic43—22no—
211C4⋊Dic43C22×C412yes—
212C4⋊Dic43C22×C412yes—
213Dic43⋊C4—28no—
214Dic43⋊C4—22no—
215Dic43⋊C4—22no—
216Dic43⋊C4—22no—
217Dic43⋊C4—22no—
218C4×Dic43—24no—
219C4×Dic43—22no—
220C4×Dic43—22no—
221C4×Dic43—22no—
222C4×Dic43—22no—
223C4×Dic43—22no—
224C4×Dic43—42no—
225C4×Dic43C22⋊C411yescharacteristic
226C4×Dic43C22⋊C411yescharacteristic
227C4×Dic43C22⋊C411yescharacteristic
228C4×Dic43C22⋊C411yescharacteristic
229C4×Dic43C22⋊C411yescharacteristic
230C4×Dic43C22⋊C411yescharacteristic
231C4×Dic43C22⋊C411yescharacteristic
232C4×Dic43C22⋊C411yescharacteristic
233C4×Dic43C22×C411yescharacteristic
234C4×Dic43C22×C411yescharacteristic
235C4×Dic43C2×D411yescharacteristic
236C4×Dic43C2×D411yescharacteristic
237#10621877—24no—
238C2×C43⋊C8—22no—
239#10621872—44no—
240C8×D43—44no—
241C23×C43—22no—
242C23×C43C22×D411yescharacteristic
243C22×D43—22no—
244C22×D43—22no—
245C22×D43—41no—
246C22×D43C2×C22⋊C411yescharacteristic
247C22×D43C2×C22⋊C411yescharacteristic
248Q8×C43—24no—
249D4×C43—24no—
250D4×C43—44no—
251D4×C43—42no—
252D4×C43—42no—
253C2×C4×C43—22no—
254C2×C4×C43—22no—
255C2×C4×C43—24no—
256C2×C4×C43—22no—
257C2×C4×C43—42no—
258C2×C4×C43—42no—
259C2×C4×C43—42no—
260C2×C4×C43—42no—
261C2×C4×C43C2×C22⋊C411yescharacteristic
262C2×C4×C43C2×C22⋊C411yescharacteristic
263C2×C4×C43C2×C22⋊C411yescharacteristic
264C2×C4×C43C2×C22⋊C411yescharacteristic
265C2×C4×C43C23×C411yescharacteristic
266C2×C4×C43C22×D411yescharacteristic
267C2×C4×C43H(5,𝔽2)12yes—
268C2×C4×C432−1+412yes—
269C22⋊D43—44no—
270C22⋊D43—44no—
271C2×Dic43—22no—
272C2×Dic43—22no—
273C2×Dic43—24no—
274C2×Dic43—22no—
275C2×Dic43—22no—
276C2×Dic43—41no—
277C2×Dic43—44no—
278C2×Dic43—42no—
279C2×Dic43—42no—
280C2×Dic43—44no—
281C2×Dic43C2×C22⋊C411yescharacteristic
282C2×Dic43C2×C22⋊C411yescharacteristic
283C2×Dic43C2×C22⋊C411yescharacteristic
284C2×Dic43C2×C22⋊C411yescharacteristic
285C2×Dic43C2×C22⋊C411yescharacteristic
286C2×Dic43C2×C22⋊C411yescharacteristic
287C4×D43—22no—
288C4×D43—22no—
289C4×D43—22no—
290C4×D43—21no—
291C4×D43—21no—
292C4×D43—21no—
293C4×D43—21no—
294C4×D43—22no—
295C4×D43—22no—
296C4×D43—22no—
297C4×D43—22no—
298C4×D43—41no—
299C4×D43—41no—
300C4×D43#10414yescomplemented
301Dic86—42no—
302Dic86—42no—
303C8×C43—42no—
304C43⋊C8—42no—
305#21856—431nomaximal, Sylow
306C22×C43—21no—
307C22×C43—21no—
308C22×C43—42no—
309C22×C43—42no—
310C22×C43—42no—
311C22×C43C22×C22⋊C411yescharacteristic
312C22×C43#53712yes—
313C2×D43—21no—
314C2×D43—21no—
315C2×D43—21no—
316C2×D43—21no—
317C2×D43—21no—
318C2×D43—44no—
319C2×D43C2×#10412yes—
320C4×C43—21no—
321C4×C43—21no—
322C4×C43—44no—
323C4×C43—42no—
324C4×C43C2×#10412yes—
325C4×C43#42112yes—
326C4×C43#52012yes—
327C4×C43#53511yescharacteristic
328C4×C43#53611yescharacteristic
329Dic43—21no—
330Dic43—21no—
331Dic43—21no—
332Dic43—21no—
333Dic43—21no—
334Dic43—44no—
335Dic43—42no—
336Dic43—42no—
337Dic43C2×#10412yes—
338#3444—431no—
339C2×#423—431no—
340C4×#117—431no—
341#1994—431no—
342#1994—431no—
343#1962—431no—
344#1962D4311yescharacteristic, complemented
345#1871—434no—
346#1806—434no—
347C2×C43—22no—
348C2×C43—82no—
349C2×C43#231111yescharacteristic
350C2×C43C22×#10411yescharacteristic
351C2×C43C2×#42111yescharacteristic
352D43—22no—
353D43—41no—
354C22×M16—432no—
355#533—431no—
356#533—431no—
357#533—431no—
358#532—431no—
359#532—431no—
360#532C2×D4311yescharacteristic
361#529—432no—
362#529—432no—
363#529—861no—
364#529—861no—
365#529—861no—
366#529—861no—
367#525—432no—
368#525—861no—
369#525—861no—
370C4×#41—432no—
371C4×#41—861no—
372C4×#41—861no—
373C2×#117—861no—
374C22×C42—431no—
375#423—432no—
376#423—431no—
377#423—861no—
378#423—861no—
379#423C2×D4311yescharacteristic
380C2×C4⋊C8—861no—
381C2×C4⋊C8—861no—
382C2×#104—434no—
383C2×#104C2×D4314yes—
384C4×C4⋊C4—432no—
385C4×C4⋊C4—861no—
386C4×C22⋊C4—432no—
387C4×C22⋊C4—861no—
388#376—861no—
389C43—431no—
390C43C2×D4311yescharacteristic
391#339—434no—
392#339—434no—
393C43#2185611yescharacteristic, complemented, Sylow
394C2×#41—861no—
395C2×#41—861no—
396C2×#41C22×D4312yes—
397C23×C4—431no—
398C23×C4—431no—
399C23×C4—431no—
400C2×M16—432no—
401C2×M16—862no—
402C2×M16—1724no—
403C2×M16C22×D4312yes—
404C22×C8—862no—
405C4⋊Q8—431no—
406C4⋊Q8—431no—
407C4⋊Q8C4×D4311yescharacteristic
408#127C4×D4311yescharacteristic
409#126—862no—
410#126—862no—
411#125—432no—
412#125—861no—
413#125—861no—
414#124—861no—
415#124—861no—
416#124C4×D4312yes—
417#123—862no—
418#123—862no—
419#123—862no—
420C22⋊Q8—432no—
421C22⋊Q8—432no—
422C22⋊Q8—861no—
423C22⋊Q8—861no—
424C22⋊Q8—861no—
425C22⋊Q8—861no—
426#121—21no—
427#121—21no—
428#121—432no—
429#121—432no—
430#121—861no—
431#121—861no—
432#120—862no—
433C4×Q8—432no—
434C4×Q8—432no—
435C4×Q8—861no—
436C4×Q8—861no—
437C4×Q8—861no—
438C4×Q8—861no—
439C4×D4—21no—
440C4×D4—21no—
441C4×D4—432no—
442C4×D4—432no—
443C4×D4—861no—
444C4×D4—861no—
445C4×D4—862no—
446C4×D4—862no—
447C4×D4—862no—
448C4×D4—862no—
449C4×D4—862no—
450C4×D4—862no—
451#117—432no—
452#117—868no—
453#117—862no—
454#117—862no—
455#117—862no—
456#117—861no—
457#117—861no—
458C2×C4⋊C4—862no—
459C2×C22⋊C4—862no—
460C2×C42—21no—
461C2×C42—21no—
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—431no—
472C2×C42—431no—
473C2×C42—432no—
474C2×C42—862no—
475C2×C42—861no—
476C2×C42—861no—
477C2×C42C22×D4312yes—
478C2×C42C22×D4311yescharacteristic
479C4⋊C8—21no—
480C4⋊C8—21no—
481C4⋊C8—862no—
482C4⋊C8—862no—
483C4⋊C8—861no—
484C4⋊C8—861no—
485#104—44no—
486#104—1724no—
487#95—862no—
488#95—862no—
489C24—431no—
490#41—24no—
491#41—24no—
492#41—1724no—
493#41—1724no—
494C2×Q8—861no—
495C2×Q8—861no—
496C2×Q8C2×C4×D4312yes—
497C2×D4—22no—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—862no—
501C2×D4—862no—
502C2×D4C2×C4×D4312yes—
503C22×C4—22no—
504C22×C4—22no—
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—431no—
519C22×C4—431no—
520C22×C4—864no—
521C22×C4—862no—
522C22×C4—862no—
523C22×C4—862no—
524C22×C4—862no—
525C22×C4—862no—
526C22×C4—1722no—
527C22×C4D4×D4311yescharacteristic
528C22×C4D4×D4311yescharacteristic
529C22×C4C23×D4311yescharacteristic
530M16—24no—
531M16—864no—
532M16—1724no—
533C2×C8—22no—
534C2×C8—862no—
535C2×C8—1724no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—432no—
539C4⋊C4—432no—
540C4⋊C4—862no—
541C4⋊C4—862no—
542C4⋊C4—862no—
543C4⋊C4—862no—
544C4⋊C4—868no—
545C4⋊C4—861no—
546C4⋊C4—861no—
547C4⋊C4—862no—
548C4⋊C4—862no—
549C22⋊C4—22no—
550C22⋊C4—22no—
551C22⋊C4—862no—
552C22⋊C4—862no—
553C22⋊C4—868no—
554C22⋊C4—862no—
555C22⋊C4—862no—
556C22⋊C4—862no—
557C22⋊C4—862no—
558C22⋊C4—862no—
559C42—24no—
560C42—22no—
561C42—22no—
562C42—42no—
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—
578C42—862no—
579C42—862no—
580C42—862no—
581C42—1722no—
582C42C2×C4×D4311yescharacteristic
583C42C2×C4×D4311yescharacteristic
584C42D4×D4311yescharacteristic
585C42D4×D4311yescharacteristic
586C23—22no—
587C23—431no—
588C23—431no—
589C23—862no—
590C23—862no—
591C23—1721no—
592C23C2×D4×D4311yescharacteristic
593Q8—24no—
594Q8—1722no—
595Q8—1722no—
596D4—24no—
597D4—44no—
598D4—42no—
599D4—42no—
600D4—1724no—
601D4—1724no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—24no—
605C2×C4—22no—
606C2×C4—42no—
607C2×C4—42no—
608C2×C4—42no—
609C2×C4—42no—
610C2×C4—431no—
611C2×C4—434no—
612C2×C4—431no—
613C2×C4—431no—
614C2×C4—431no—
615C2×C4—431no—
616C2×C4—431no—
617C2×C4—862no—
618C2×C4—862no—
619C2×C4—862no—
620C2×C4—862no—
621C2×C4—862no—
622C2×C4—862no—
623C2×C4—862no—
624C2×C4—862no—
625C2×C4—862no—
626C2×C4—861no—
627C2×C4—861no—
628C2×C4—861no—
629C2×C4—861no—
630C2×C4—864no—
631C2×C4—862no—
632C2×C4—862no—
633C2×C4—1721no—
634C2×C4—1721no—
635C2×C4—1724no—
636C2×C4—1721no—
637C2×C4—1724no—
638C2×C4—1722no—
639C2×C4—1722no—
640C2×C4C22⋊C4×D4311yescharacteristic
641C2×C4C22⋊C4×D4311yescharacteristic
642C2×C4C22⋊C4×D4311yescharacteristic
643C2×C4C22⋊C4×D4311yescharacteristic
644C2×C4C22×C4×D4311yescharacteristic
645C2×C4C2×D4×D4311yescharacteristic
646C2×C4#1306337012yes—
647C2×C4#1306337212yes—
648C8—42no—
649C8—1722no—
650C22—21no—
651C22—21no—
652C22—42no—
653C22—42no—
654C22—42no—
655C22—432no—
656C22—861no—
657C22—861no—
658C22—861no—
659C22—861no—
660C22—861no—
661C22—1724no—
662C22C2×C22⋊C4×D4311yescharacteristic
663C22#1458347812yes—
664C4—21no—
665C4—21no—
666C4—44no—
667C4—42no—
668C4—432no—
669C4—861no—
670C4—861no—
671C4—861no—
672C4—861no—
673C4—861no—
674C4—1724no—
675C4—1722no—
676C4—1722no—
677C4#104×D4312yes—
678C4#1458291412yes—
679C4#1458337812yes—
680C4#1458346211yescharacteristic
681C4#1458346911yescharacteristic
682C2—22no—
683C2—82no—
684C2—862no—
685C2—1721no—
686C2#1913718511yescharacteristic
687C2C2×#104×D4311yescharacteristic
688C2C2×#1458291411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1962C2
socleC22×C43C22×C22⋊C4
prime radical#19147890C2
cosocleC22×C4×C43C24
hypercenter#1962D43
hypocenterC43#21856
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1962

Complements

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

NH ≅ G/Ntype
2. #423×D43C2semidirect
3. C4×#13063282C2semidirect
4. #19135572C2semidirect
5. #19135571C2semidirect
6. #19135424C2semidirect
7. #19134894C2semidirect
8. #19134613C2semidirect
9. C43×#1962C2semidirect
12. #14583454C4semidirect
13. #14583454C4semidirect
14. #14583447C4semidirect
15. #14583447C4semidirect
20. #14583428C4semidirect
21. #14583428C4semidirect
300. C4×D43#104semidirect
344. #1962D43semidirect
393. C43#21856semidirect

Maximal subgroups

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

subgroupindex
#191478902
#423×D432
C4×#130632822
#191355722
#191355712
#191354242
#191348942
#191346132
C43×#19622
#2185643