Finite Group Databasebeta

← #25066712

Subgroups — #25066712

Order 11008.

678 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144593C211yesmaximal, characteristic
2#19143672C211yesmaximal, characteristic, complemented
3#19143616C211yesmaximal, characteristic, complemented
4#19133461C211yesmaximal, characteristic, complemented
5#19133424C211yesmaximal, characteristic, complemented
6#19133422C211yesmaximal, characteristic, complemented
7#19133419C211yesmaximal, characteristic, complemented
8#19133418C211yesmaximal, characteristic, complemented
9#19133387C211yesmaximal, characteristic, complemented
10#19133387C211yesmaximal, characteristic, complemented
11#19133372C211yesmaximal, characteristic, complemented
12#19133036C211yesmaximal, characteristic, complemented
13#19133010C211yesmaximal, characteristic, complemented
14#19132893C211yesmaximal, characteristic, complemented
15C43×#1586C211yesmaximal, characteristic, complemented
16#14583446C2211yescharacteristic
17C4×D4×D43C2211yescharacteristic
18#14583214C411yescharacteristic
19#14583211C411yescharacteristic
20#14583178C411yescharacteristic
21#14583177C411yescharacteristic
22#14583093C411yescharacteristic
23#14583092C411yescharacteristic
24#14583034C411yescharacteristic
25#14583031C411yescharacteristic
26C4×D344C2211yescharacteristic
27C4×#10621882C2211yescharacteristic
28C4×#10621882C2211yescharacteristic
29#14582978C2211yescharacteristic, complemented
30#14582968—21no—
31#14582967—21no—
32C8×D172C2211yescharacteristic
33D4×C43⋊C8C2211yescharacteristic
34D4×C43⋊C8C2211yescharacteristic, complemented
35#14582964C2211yescharacteristic
36#14582964C2211yescharacteristic, complemented
37C8×C22⋊D43—21no—
38(C22⋊D43)⋊C8—21no—
39#14582955C2211yescharacteristic
40#14582951C2211yescharacteristic
41#14582950C2211yescharacteristic
42#14582950C2211yescharacteristic
43#14582867—21no—
44#14582864—21no—
45C2×(C2×D43)⋊C8—21no—
46C22⋊C8×D43—21no—
47C4×#10621872C2211yescharacteristic
48#14582651C2211yescharacteristic, complemented
49#14582651C2211yescharacteristic, complemented
50#14582650C2211yescharacteristic, complemented
51#14582628C2211yescharacteristic
52#14582628C2211yescharacteristic, complemented
53D4⋊(C43⋊C8)C2211yescharacteristic
54D4⋊(C43⋊C8)C2211yescharacteristic, complemented
55#14582626C2211yescharacteristic
56#14582626C2211yescharacteristic, complemented
57#14582620C2211yescharacteristic, complemented
58#14582620C2211yescharacteristic, complemented
59C8×C43⋊C8C2211yescharacteristic, complemented
60C4×D8×C43C2211yescharacteristic
61C43×#436C2211yescharacteristic, complemented
62C8×D4×C43C2211yescharacteristic
63C43×#334C2211yescharacteristic, complemented
64C43×D4⋊C8C2211yescharacteristic
65C43×D4⋊C8C2211yescharacteristic, complemented
66C43×#322C2211yescharacteristic, complemented
67C2×#10621898—21no—
68C2×D4×D43C2×C411yescharacteristic
69C22×C4×D43—21no—
70C2×D344C2×C411yescharacteristic
71C2×#10621882C2×C411yescharacteristic
72C2×#10621882C2×C411yescharacteristic
73C2×#10621872—21no—
74C2×#10621872—21no—
75C22×C43⋊C8—21no—
76C22×C43⋊C8—21no—
77C2×C8×D43—21no—
78C2×C8×D43—21no—
79C2×C8×D43—21no—
80#13063324C2×C411yescharacteristic
81#13063321C2×C411yescharacteristic
82#13063311—21no—
83#13063300C2×C411yescharacteristic
84#13063298—21no—
85#13063296C2×C411yescharacteristic
86C4×D172C2311yescharacteristic
87C4×D172C2311yescharacteristic
88D4×Dic43C2×C411yescharacteristic
89#13063287C2×C411yescharacteristic
90C4×C22⋊D43—21no—
91C4×C22⋊D43—21no—
92(C22⋊D43)⋊C4—21no—
93C4⋊C4×D43C2×C411yescharacteristic
94C22⋊C4×D43—21no—
95C42×D43C2311yescharacteristic
96#13063259C2×C411yescharacteristic
97#13063258C2×C411yescharacteristic
98#13063258C2×C411yescharacteristic
99C4⋊(C43⋊C8)C2311yescharacteristic
100C4⋊(C43⋊C8)C2311yescharacteristic
101Dic43⋊C8C2×C411yescharacteristic
102Dic43⋊C8C2×C411yescharacteristic
103Dic43⋊C8D411yescharacteristic
104Dic43⋊C8D411yescharacteristic
105#13063247C2×C411yescharacteristic
106#13063247C2×C411yescharacteristic
107#13063246C2×C411yescharacteristic
108#13063246C2×C411yescharacteristic
109#13063245C2×C411yescharacteristic
110#13063245C2×C411yescharacteristic
111C22⋊(C43⋊C8)—21no—
112C22⋊(C43⋊C8)—21no—
113(C2×D43)⋊C8—21no—
114(C2×D43)⋊C8—21no—
115(C2×D43)⋊C8—21no—
116(C2×D43)⋊C8—21no—
117(C2×D43)⋊C8—21no—
118(C2×D43)⋊C8—21no—
119(C2×D43)⋊C8C2×C411yescharacteristic
120(C2×D43)⋊C8C2×C411yescharacteristic
121(C2×D43)⋊C8D411yescharacteristic
122(C2×D43)⋊C8D411yescharacteristic
123#13063235—21no—
124#13063235—21no—
125C4×C43⋊C8C2311yescharacteristic
126C4×C43⋊C8C2311yescharacteristic
127C4×C43⋊C8C2311yescharacteristic
128C8×Dic43—21no—
129C2×D8×C43C2×C411yescharacteristic
130C2×M16×C43—21no—
131C22×C8×C43—21no—
132C4×D4×C43C2311yescharacteristic
133C4×D4×C43C2311yescharacteristic
134#107×C43C2×C411yescharacteristic
135C4⋊C8×C43C2311yescharacteristic
136C4⋊C8×C43C2311yescharacteristic
137#102×C43C2×C411yescharacteristic
138#102×C43C2×C411yescharacteristic
139C22⋊C8×C43—21no—
140C22⋊C8×C43—21no—
141C4×C8×C43C2311yescharacteristic
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C23×D43—21no—
145C2×D4×C43C22×C411yescharacteristic
146C2×D4×C43C22×C411yescharacteristic
147C22×C4×C43—21no—
148C22×C4×C43—21no—
149C2×C22⋊D43—21no—
150C2×C22⋊D43—21no—
151C2×C22⋊D43—21no—
152C2×C22⋊D43—21no—
153C22×Dic43—21no—
154D4×D43—22no—
155D4×D43—22no—
156#10621898—81no—
157#10621898—81no—
158C2×D172—21no—
159C2×D172C22×C411yescharacteristic
160C2×D172C22×C411yescharacteristic
161C2×C4×D43—21no—
162C2×C4×D43—21no—
163C2×C4×D43—21no—
164C2×C4×D43—21no—
165C2×C4×D43—81no—
166C2×C4×D43—81no—
167C2×C4×D43C22×C411yescharacteristic
168C2×C4×D43C2×D411yescharacteristic
169C2×C4×D43#4111yescharacteristic
170C2×Dic86—21no—
171D8×C43—22no—
172M16×C43—81no—
173C2×C8×C43—21no—
174C2×C8×C43—21no—
175C2×C8×C43—21no—
176C2×C8×C43—81no—
177C2×C8×C43C22×C411yescharacteristic
178C2×C8×C43C22×C411yescharacteristic
179C2×C8×C43C2×D411yescharacteristic
180C2×C8×C43C2×D411yescharacteristic
181C4⋊C4×C43C22×C411yescharacteristic
182C4⋊C4×C43C22×C411yescharacteristic
183C22⋊C4×C43—21no—
184C22⋊C4×C43—21no—
185C42×C43C2411yescharacteristic
186C22⋊Dic43—21no—
187C22⋊Dic43—21no—
188#10621882—22no—
189#10621882—22no—
190(C2×D43)⋊C4—21no—
191(C2×D43)⋊C4—21no—
192(C2×D43)⋊C4—21no—
193(C2×D43)⋊C4—21no—
194C4⋊Dic43C22×C411yescharacteristic
195C4⋊Dic43C22×C411yescharacteristic
196Dic43⋊C4—21no—
197Dic43⋊C4—21no—
198C4×Dic43C22×C411yescharacteristic
199C4×Dic43C2×D411yescharacteristic
200C4×Dic43#4111yescharacteristic
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—81no—
205C2×C43⋊C8—81no—
206C2×C43⋊C8C22×C411yescharacteristic
207C2×C43⋊C8C22×C411yescharacteristic
208C2×C43⋊C8C2×D411yescharacteristic
209C2×C43⋊C8C2×D411yescharacteristic
210D344—22no—
211#10621872—42no—
212#10621872—81no—
213C8×D43—81no—
214C8×D43—81no—
215C8×D43—81no—
216C23×C43—21no—
217C23×C43—21no—
218C22×D43—21no—
219C22×D43—24no—
220C22×D43—21no—
221C22×D43—81no—
222C22×D43—81no—
223C22×D43C4×D411yescharacteristic
224D4×C43—21no—
225D4×C43—21no—
226D4×C43—21no—
227D4×C43#13112yes—
228C2×C4×C43—21no—
229C2×C4×C43—21no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43C23×C411yescharacteristic
235C2×C4×C43C22×D411yescharacteristic
236C2×C4×C43C2×#4111yescharacteristic
237C22⋊D43—24no—
238C22⋊D43—81no—
239C22⋊D43—81no—
240C22⋊D43—81no—
241C2×Dic43—21no—
242C2×Dic43—21no—
243C2×Dic43—81no—
244C2×Dic43C4×D411yescharacteristic
245C2×Dic43C4×D411yescharacteristic
246C2×Dic43C4×D411yescharacteristic
247D172—21no—
248D172—21no—
249D172—21no—
250D172—81no—
251D172#13112yes—
252C4×D43—21no—
253C4×D43—21no—
254C4×D43—21no—
255C4×D43—21no—
256C4×D43—41no—
257C4×D43—41no—
258C4×D43—41no—
259C4×D43—41no—
260C4×D43—41no—
261C4×D43—81no—
262C4×D43—81no—
263Dic86—81no—
264C8×C43—22no—
265C8×C43—21no—
266C8×C43—21no—
267C8×C43—21no—
268C8×C43—21no—
269C8×C43—41no—
270C8×C43—41no—
271C43⋊C8—21no—
272C43⋊C8—21no—
273C43⋊C8—21no—
274C43⋊C8—21no—
275C43⋊C8—41no—
276C43⋊C8—41no—
277C43⋊C8—41no—
278#17922—431nomaximal, Sylow
279C22×C43—22no—
280C22×C43—41no—
281C22×C43—41no—
282C22×C43—41no—
283C22×C43—41no—
284C22×C43—41no—
285C22×C43C2×C4×D411yescharacteristic
286C2×D43—21no—
287C2×D43—22no—
288C2×D43—21no—
289C2×D43—21no—
290C2×D43—41no—
291C2×D43—41no—
292C2×D43—41no—
293C2×D43—41no—
294C2×D43—41no—
295C2×D43—84no—
296C4×C43—21no—
297C4×C43—41no—
298C4×C43—41no—
299C4×C43C2×#13111yescharacteristic
300C4×C43C2×#13111yescharacteristic
301C4×C43#57611yescharacteristic
302C4×C43#57611yescharacteristic
303Dic43—21no—
304Dic43—21no—
305Dic43—21no—
306Dic43—41no—
307Dic43—41no—
308#3100—431no—
309#2981—431no—
310#2972—431no—
311#1586—431no—
312#1586D4311yescharacteristic, complemented
313#1581—431no—
314#1581—431no—
315#1580—431no—
316#1580—431no—
317C8×D8—431no—
318C8×D8—431no—
319#1572—431no—
320#1490—431no—
321#1484—431no—
322#1453—431no—
323C2×C43—42no—
324C2×C43—81no—
325C2×C43#292911yescharacteristic
326C2×C43#294811yescharacteristic
327C2×C43#295611yescharacteristic
328D43—41no—
329D43—42no—
330D43—81no—
331#532—431no—
332C2×C4×D4—431no—
333#480—431no—
334#480—431no—
335#474—431no—
336#474—431no—
337#459—431no—
338#459—431no—
339#447—431no—
340#447—431no—
341C4×D8—431no—
342C4×D8—431no—
343C4×D8—431no—
344C4×D8C2×D4311yescharacteristic
345#436—431no—
346#436C2×D4311yescharacteristic, complemented
347#435—861no—
348#435—861no—
349C8×D4—431no—
350C8×D4—431no—
351C8×D4—431no—
352C8×D4—431no—
353C8×D4—431no—
354C8×D4—861no—
355C8×D4—861no—
356C8×D4C2×D4311yescharacteristic
357#432—431no—
358#431—431no—
359#431—431no—
360#431—431no—
361#408—861no—
362#408—861no—
363C2×C22⋊C8—861no—
364C2×C22⋊C8—861no—
365C4×M16—431no—
366#335—431no—
367#335—431no—
368#334—431no—
369#334C2×D4311yescharacteristic, complemented
370D4⋊C8—431no—
371D4⋊C8—431no—
372D4⋊C8—431no—
373D4⋊C8—431no—
374D4⋊C8—431no—
375D4⋊C8—431no—
376D4⋊C8C2×D4311yescharacteristic
377D4⋊C8C2×D4311yescharacteristic, complemented
378#322—431no—
379#322—431no—
380#322C2×D4311yescharacteristic, complemented
381C82—431no—
382C43#1792211yescharacteristic, complemented, Sylow
383C2×#41—861no—
384C22×D4—431no—
385C23×C4—861no—
386C2×D8—431no—
387C2×D8—431no—
388C2×D8—431no—
389C2×D8C4×D4311yescharacteristic
390C2×M16—21no—
391C2×M16—861no—
392C2×M16—861no—
393C22×C8—21no—
394C22×C8—861no—
395C22×C8—861no—
396C22×C8—861no—
397C22×C8—861no—
398C22×C8—861no—
399C4⋊Q8—431no—
400#127—431no—
401#124—861no—
402#121—431no—
403#121—431no—
404#121—861no—
405C4×D4—431no—
406C4×D4—431no—
407C4×D4—431no—
408C4×D4—431no—
409C4×D4—861no—
410C4×D4—861no—
411C4×D4—861no—
412C4×D4C22×D4311yescharacteristic
413C4×D4C22×D4311yescharacteristic
414C2×C4⋊C4—431no—
415C2×C22⋊C4—861no—
416C2×C42—431no—
417#107—431no—
418#107—431no—
419#107—431no—
420#107C4×D4311yescharacteristic
421C4⋊C8—431no—
422C4⋊C8—431no—
423C4⋊C8—431no—
424C4⋊C8—431no—
425C4⋊C8—431no—
426C4⋊C8—431no—
427C4⋊C8C22×D4311yescharacteristic
428C4⋊C8C22×D4311yescharacteristic
429#102—431no—
430#102—431no—
431#102—431no—
432#102—431no—
433#102—431no—
434#102—431no—
435#102C4×D4311yescharacteristic
436#102C4×D4311yescharacteristic
437C22⋊C8—21no—
438C22⋊C8—21no—
439C22⋊C8—431no—
440C22⋊C8—431no—
441C22⋊C8—431no—
442C22⋊C8—431no—
443C22⋊C8—861no—
444C22⋊C8—861no—
445C22⋊C8—861no—
446C22⋊C8—861no—
447C22⋊C8—861no—
448C22⋊C8—861no—
449C22⋊C8—861no—
450C22⋊C8—861no—
451#97—861no—
452#97—861no—
453C4×C8—431no—
454C4×C8—431no—
455C4×C8—431no—
456C4×C8—861no—
457C4×C8C22×D4311yescharacteristic
458C4×C8C22×D4311yescharacteristic
459C4×C8C22×D4311yescharacteristic
460C24—861no—
461#41—3441no—
462#41—3441no—
463C2×Q8—861no—
464C2×D4—431no—
465C2×D4—431no—
466C2×D4—861no—
467C2×D4—861no—
468C2×D4—861no—
469C2×D4—861no—
470C2×D4—862no—
471C2×D4—862no—
472C2×D4—861no—
473C2×D4C2×C4×D4311yescharacteristic
474C2×D4C2×C4×D4311yescharacteristic
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—431no—
478C22×C4—431no—
479C22×C4—431no—
480C22×C4—861no—
481C22×C4—861no—
482C22×C4—861no—
483C22×C4—861no—
484C22×C4—861no—
485C22×C4—3441no—
486C22×C4—3441no—
487D8—22no—
488D8—862no—
489D8—862no—
490D8—862no—
491M16—81no—
492M16—3441no—
493M16—1722no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—81no—
498C2×C8—431no—
499C2×C8—431no—
500C2×C8—431no—
501C2×C8—431no—
502C2×C8—861no—
503C2×C8—861no—
504C2×C8—861no—
505C2×C8—3441no—
506C2×C8—3441no—
507C2×C8—3441no—
508C2×C8—3441no—
509C2×C8—3441no—
510C2×C8C2×C4×D4311yescharacteristic
511C2×C8C2×C4×D4311yescharacteristic
512C2×C8D4×D4311yescharacteristic
513C2×C8D4×D4311yescharacteristic
514C4⋊C4—431no—
515C4⋊C4—431no—
516C4⋊C4—861no—
517C4⋊C4—861no—
518C4⋊C4C2×C4×D4311yescharacteristic
519C4⋊C4C2×C4×D4311yescharacteristic
520C22⋊C4—21no—
521C22⋊C4—21no—
522C22⋊C4—861no—
523C22⋊C4—861no—
524C22⋊C4—861no—
525C22⋊C4—861no—
526C22⋊C4—861no—
527C22⋊C4—861no—
528C42—431no—
529C42—431no—
530C42—431no—
531C42C23×D4311yescharacteristic
532C23—21no—
533C23—21no—
534C23—431no—
535C23—864no—
536C23—861no—
537C23—861no—
538C23—3441no—
539C23—3441no—
540Q8—3441no—
541D4—21no—
542D4—21no—
543D4—21no—
544D4—432no—
545D4—864no—
546D4—861no—
547D4—861no—
548D4—861no—
549D4—3441no—
550D4—3441no—
551D4—3441no—
552D4—3441no—
553D4#1306333312yes—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—431no—
561C2×C4—431no—
562C2×C4—431no—
563C2×C4—861no—
564C2×C4—861no—
565C2×C4—861no—
566C2×C4—861no—
567C2×C4—861no—
568C2×C4—861no—
569C2×C4—3441no—
570C2×C4—3441no—
571C2×C4—3441no—
572C2×C4—1721no—
573C2×C4—1721no—
574C2×C4—1721no—
575C2×C4—1721no—
576C2×C4—1721no—
577C2×C4C22×C4×D4311yescharacteristic
578C2×C4C2×D4×D4311yescharacteristic
579C2×C4#41×D4311yescharacteristic
580C8—22no—
581C8—21no—
582C8—21no—
583C8—21no—
584C8—21no—
585C8—41no—
586C8—41no—
587C8—861no—
588C8—861no—
589C8—861no—
590C8—861no—
591C8—1721no—
592C8—1721no—
593C8—1721no—
594C22—22no—
595C22—41no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22—41no—
600C22—861no—
601C22—861no—
602C22—861no—
603C22—862no—
604C22—3444no—
605C22—1721no—
606C22—1721no—
607C22—1721no—
608C22—1721no—
609C22—1721no—
610C22C4×D4×D4311yescharacteristic
611C4—21no—
612C4—41no—
613C4—41no—
614C4—861no—
615C4—861no—
616C4—861no—
617C4—1721no—
618C4—1721no—
619C4#131×D4311yescharacteristic
620C4C2×#1306333311yescharacteristic
621C4#1458370311yescharacteristic
622C4#1458370311yescharacteristic
623C2—42no—
624C2—81no—
625C2—3441no—
626C2—1721no—
627C2—1722no—
628C2#1914328611yescharacteristic
629C2#1914344411yescharacteristic
630C2#1914350011yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1586C2
socleC22×C43C2×C4×D4
prime radical#19144593C2
cosocleC42×C43C24
hypercenter#1586D43
hypocenterC43#17922
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1586

Complements

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

NH ≅ G/Ntype
2. #19143672C2semidirect
3. #19143616C2semidirect
4. #19133461C2semidirect
5. #19133424C2semidirect
6. #19133422C2semidirect
7. #19133419C2semidirect
8. #19133418C2semidirect
9. #19133387C2semidirect
10. #19133387C2semidirect
11. #19133372C2semidirect
12. #19133036C2semidirect
13. #19133010C2semidirect
14. #19132893C2semidirect
15. C43×#1586C2semidirect
29. #14582978C22semidirect
34. D4×C43⋊C8C22semidirect
36. #14582964C22semidirect
48. #14582651C22semidirect
49. #14582651C22semidirect
50. #14582650C22semidirect
52. #14582628C22semidirect
54. D4⋊(C43⋊C8)C22semidirect
56. #14582626C22semidirect
57. #14582620C22semidirect
58. #14582620C22semidirect
59. C8×C43⋊C8C22semidirect
61. C43×#436C22semidirect
63. C43×#334C22semidirect
65. C43×D4⋊C8C22semidirect
66. C43×#322C22semidirect
312. #1586D43semidirect
346. #436C2×D43semidirect
369. #334C2×D43semidirect
377. D4⋊C8C2×D43semidirect
380. #322C2×D43semidirect
382. C43#17922semidirect

Maximal subgroups

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

subgroupindex
#191445932
#191436722
#191436162
#191334612
#191334242
#191334222
#191334192
#191334182
#191333872
#191333722
#191330362
#191330102
#191328932
C43×#15862
#1792243