Finite Group Databasebeta

← #25067301

Subgroups — #25067301

Order 11008.

726 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145171C211yesmaximal, characteristic
2#19143304C211yesmaximal, characteristic, complemented
3#19143302C211yesmaximal, characteristic, complemented
4#19133427C211yesmaximal, characteristic, complemented
5#19133426C211yesmaximal, characteristic, complemented
6#19133425C211yesmaximal, characteristic, complemented
7#19133424C211yesmaximal, characteristic, complemented
8#19133423C211yesmaximal, characteristic, complemented
9#19133422C211yesmaximal, characteristic, complemented
10#19133421C211yesmaximal, characteristic, complemented
11#19133352C211yesmaximal, characteristic, complemented
12#19133044C211yesmaximal, characteristic, complemented
13#19133044C211yesmaximal, characteristic, complemented
14#322×D43C211yesmaximal, characteristic, complemented
15C43×#1581C211yesmaximal, characteristic, complemented
16C2×#13063333—21no—
17C2×#13063331—21no—
18#14583446C2211yescharacteristic
19#14583446C2211yescharacteristic
20#14583303C411yescharacteristic
21#14583274C411yescharacteristic
22#14583244C411yescharacteristic
23#14583244C411yescharacteristic
24#14583136C411yescharacteristic
25#14583134C411yescharacteristic
26#14583134C411yescharacteristic
27#14583132C411yescharacteristic
28C4×D344C2211yescharacteristic
29C4×#10621882C2211yescharacteristic
30C4×#10621882C2211yescharacteristic
31#14582978C2211yescharacteristic
32#14582977C2211yescharacteristic
33#14582976C2211yescharacteristic
34#14582975—21no—
35#14582974—21no—
36C8×D172C2211yescharacteristic
37D4×C43⋊C8C2211yescharacteristic
38#14582964C2211yescharacteristic
39C8×C22⋊D43—21no—
40(C22⋊D43)⋊C8—21no—
41#14582921C2211yescharacteristic
42#14582921C2211yescharacteristic
43#14582864—21no—
44#14582864—21no—
45C4×C8×D43C2211yescharacteristic
46C4×C8×D43C2211yescharacteristic
47C4×C8×D43C2211yescharacteristic
48#14582652C2211yescharacteristic
49#14582651C2211yescharacteristic
50#14582651C2211yescharacteristic
51#14582628C2211yescharacteristic
52#14582628C2211yescharacteristic
53D4⋊(C43⋊C8)C2211yescharacteristic
54D4⋊(C43⋊C8)C2211yescharacteristic
55#14582626C2211yescharacteristic
56#14582626C2211yescharacteristic
57#14582621C2211yescharacteristic
58#14582621C2211yescharacteristic
59#14582620C2211yescharacteristic
60C4×D8×C43C2211yescharacteristic
61C43×#436C2211yescharacteristic
62C8×D4×C43C2211yescharacteristic
63C43×#335C2211yescharacteristic
64C43×D4⋊C8C2211yescharacteristic
65C43×D4⋊C8C2211yescharacteristic
66C43×#322C2211yescharacteristic
67C2×#10621898—21no—
68C2×#10621898—21no—
69C2×D344C2×C411yescharacteristic
70C2×#10621882C2×C411yescharacteristic
71C2×#10621882C2×C411yescharacteristic
72#13063333—44no—
73#13063331—44no—
74C2×#10621877—21no—
75C2×#10621872—21no—
76C2×#10621872—21no—
77C2×#10621872—21no—
78C2×#10621872—21no—
79C22×C43⋊C8—21no—
80C2×C8×D43—21no—
81C2×C8×D43—21no—
82C2×C8×D43—21no—
83C2×C8×D43C2×C411yescharacteristic
84C2×C8×D43C2×C411yescharacteristic
85C2×C8×D43D411yescharacteristic
86C2×C8×D43D411yescharacteristic
87#13063324C2×C411yescharacteristic
88#13063324C2×C411yescharacteristic
89#13063321C2×C411yescharacteristic
90#13063321C2×C411yescharacteristic
91#13063311—21no—
92#13063311—21no—
93#13063300C2×C411yescharacteristic
94#13063300C2×C411yescharacteristic
95#13063298—21no—
96#13063298—21no—
97#13063296C2×C411yescharacteristic
98#13063296C2×C411yescharacteristic
99C4×D172C2311yescharacteristic
100C4×D172C2311yescharacteristic
101C4×C22⋊D43—21no—
102C4×C22⋊D43—21no—
103C42×D43C2311yescharacteristic
104#13063259C2×C411yescharacteristic
105#13063258C2×C411yescharacteristic
106#13063258C2×C411yescharacteristic
107C4⋊(C43⋊C8)C2311yescharacteristic
108C4⋊(C43⋊C8)C2311yescharacteristic
109Dic43⋊C8—21no—
110Dic43⋊C8—21no—
111#13063247C2×C411yescharacteristic
112#13063247C2×C411yescharacteristic
113#13063246C2×C411yescharacteristic
114#13063246C2×C411yescharacteristic
115#13063245C2×C411yescharacteristic
116#13063245C2×C411yescharacteristic
117C22⋊(C43⋊C8)—21no—
118C22⋊(C43⋊C8)—21no—
119(C2×D43)⋊C8—21no—
120(C2×D43)⋊C8—21no—
121(C2×D43)⋊C8—21no—
122(C2×D43)⋊C8—21no—
123C4×C43⋊C8C2311yescharacteristic
124C4×C43⋊C8C2311yescharacteristic
125C4×C43⋊C8C2311yescharacteristic
126C8×Dic43—21no—
127C8×Dic43C2×C411yescharacteristic
128C8×Dic43C2×C411yescharacteristic
129C8×Dic43D411yescharacteristic
130C8×Dic43D411yescharacteristic
131C2×D8×C43C2×C411yescharacteristic
132C2×M16×C43—21no—
133C22×C8×C43—21no—
134C4×D4×C43C2311yescharacteristic
135C4×D4×C43C2311yescharacteristic
136#107×C43C2×C411yescharacteristic
137C4⋊C8×C43C2311yescharacteristic
138C4⋊C8×C43C2311yescharacteristic
139#102×C43C2×C411yescharacteristic
140#102×C43C2×C411yescharacteristic
141C22⋊C8×C43—21no—
142C22⋊C8×C43—21no—
143C4×C8×C43C2311yescharacteristic
144C4×C8×C43C2311yescharacteristic
145C4×C8×C43C2311yescharacteristic
146C2×D4×C43C22×C411yescharacteristic
147C2×D4×C43C22×C411yescharacteristic
148C22×C4×C43—21no—
149C22×C4×C43—21no—
150C2×C22⋊D43—21no—
151C2×C22⋊D43—21no—
152C2×C22⋊D43—21no—
153C2×C22⋊D43—21no—
154C2×C22⋊D43—21no—
155C2×C22⋊D43—21no—
156#10621898—42no—
157#10621898—42no—
158#10621898—42no—
159#10621898—42no—
160C2×D172—21no—
161C2×D172—21no—
162C2×D172C22×C411yescharacteristic
163C2×D172C22×C411yescharacteristic
164C2×C4×D43—21no—
165C2×C4×D43—21no—
166C2×C4×D43C22×C411yescharacteristic
167C2×C4×D43C2×D411yescharacteristic
168C2×C4×D43#4111yescharacteristic
169C2×Dic86—21no—
170C2×Dic86—21no—
171D8×C43—41no—
172M16×C43—42no—
173C2×C8×C43—21no—
174C2×C8×C43—21no—
175C2×C8×C43—21no—
176C2×C8×C43—42no—
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—41no—
189#10621882—41no—
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
201#10621877—42no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—42no—
206C2×C43⋊C8C22×C411yescharacteristic
207C2×C43⋊C8C22×C411yescharacteristic
208C2×C43⋊C8C2×D411yescharacteristic
209C2×C43⋊C8C2×D411yescharacteristic
210D344—41no—
211#10621872—42no—
212#10621872—42no—
213#10621872—42no—
214#10621872—42no—
215C8×D43—22no—
216C8×D43—41no—
217C8×D43—41no—
218C8×D43—42no—
219C8×D43—42no—
220C8×D43—42no—
221C8×D43D814yescomplemented
222C23×C43—21no—
223C23×C43—21no—
224C22×D43—21no—
225C22×D43—21no—
226C22×D43C4×D411yescharacteristic
227D4×C43—21no—
228D4×C43—21no—
229D4×C43—21no—
230D4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43C23×C411yescharacteristic
238C2×C4×C43C22×D411yescharacteristic
239C2×C4×C43C2×#4111yescharacteristic
240C22⋊D43—42no—
241C22⋊D43—42no—
242C22⋊D43—42no—
243C22⋊D43—42no—
244C22⋊D43—42no—
245C22⋊D43—42no—
246C2×Dic43—21no—
247C2×Dic43—21no—
248C2×Dic43C4×D411yescharacteristic
249C2×Dic43C4×D411yescharacteristic
250C2×Dic43C4×D411yescharacteristic
251D172—21no—
252D172—21no—
253D172—21no—
254D172—21no—
255D172—42no—
256D172—42no—
257C4×D43—21no—
258C4×D43—21no—
259C4×D43—22no—
260C4×D43—41no—
261C4×D43—41no—
262C4×D43—41no—
263C4×D43—41no—
264C4×D43C2×D812yes—
265C4×D43#13512yes—
266Dic86—42no—
267Dic86—42no—
268C8×C43—21no—
269C8×C43—21no—
270C8×C43—21no—
271C8×C43—41no—
272C8×C43—41no—
273C8×C43—41no—
274C8×C43C2×D812yes—
275C43⋊C8—21no—
276C43⋊C8—21no—
277C43⋊C8—21no—
278C43⋊C8—41no—
279C43⋊C8—41no—
280C43⋊C8—41no—
281C43⋊C8C2×D812yes—
282#17975—431nomaximal, Sylow
283C22×C43—41no—
284C22×C43—41no—
285C22×C43—41no—
286C22×C43—41no—
287C22×C43—41no—
288C22×C43—41no—
289C22×C43C2×C4×D411yescharacteristic
290C2×D43—21no—
291C2×D43—21no—
292C2×D43—41no—
293C2×D43—41no—
294C2×D43—41no—
295C2×D43—41no—
296C2×D43—41no—
297C2×D43—41no—
298C2×D43C4×D812yes—
299C4×C43—21no—
300C4×C43—41no—
301C4×C43—41no—
302C4×C43#56811yescharacteristic
303C4×C43#56811yescharacteristic
304C4×C43C22×D811yescharacteristic
305C4×C43C2×#13511yescharacteristic
306Dic43—21no—
307Dic43—41no—
308Dic43—41no—
309Dic43C4×D812yes—
310Dic43#44412yes—
311#3169—431no—
312#2931—431no—
313#2931—431no—
314#1581—431no—
315#1581—431no—
316#1581—431no—
317#1581—431no—
318#1581—431no—
319#1581—431no—
320#1581—431no—
321#1581D4311yescharacteristic, complemented
322#1567—431no—
323#1492—431no—
324#1492—431no—
325C2×#322—431no—
326C2×C43—81no—
327C2×C43—81no—
328C2×C43#293211yescharacteristic
329C2×C43C2×C4×D811yescharacteristic
330C2×C43C2×#44411yescharacteristic
331D43—22no—
332D43—81no—
333D43—81no—
334C2×#131—861no—
335C2×#131—861no—
336#532—431no—
337#532—431no—
338#500—431no—
339#493—431no—
340#486—431no—
341#486—431no—
342#466—431no—
343#466—431no—
344#466—431no—
345#466—431no—
346C4×D8—431no—
347C4×D8—431no—
348C4×D8—431no—
349C4×D8C2×D4311yescharacteristic
350#436—431no—
351#436—431no—
352#436—431no—
353#436—861no—
354#436—861no—
355#436C2×D4311yescharacteristic
356C8×D4—431no—
357C8×D4—431no—
358C8×D4—431no—
359C8×D4—861no—
360C8×D4—861no—
361C8×D4C2×D4311yescharacteristic
362#423—431no—
363#423—431no—
364#408—861no—
365#408—861no—
366C2×C4×C8—431no—
367C2×C4×C8—431no—
368C2×C4×C8—431no—
369#335—431no—
370#335—431no—
371#335—431no—
372#335C2×D4311yescharacteristic
373D4⋊C8—431no—
374D4⋊C8—431no—
375D4⋊C8—431no—
376D4⋊C8—431no—
377D4⋊C8—431no—
378D4⋊C8—431no—
379D4⋊C8C2×D4311yescharacteristic
380D4⋊C8C2×D4311yescharacteristic
381#322—431no—
382#322—431no—
383#322—431no—
384#322C2×D4311yescharacteristic
385C43#1797511yescharacteristic, complemented, Sylow
386C2×#41—861no—
387C2×#41—861no—
388C2×D8—431no—
389C2×D8—431no—
390C2×D8—431no—
391C2×D8C4×D4311yescharacteristic
392#131—1724no—
393#131—1724no—
394C2×M16—21no—
395C2×M16—861no—
396C2×M16—861no—
397C2×M16—861no—
398C2×M16—861no—
399C2×M16—861no—
400C22×C8—21no—
401C22×C8—431no—
402C22×C8—431no—
403C22×C8—431no—
404C22×C8—431no—
405C22×C8—861no—
406C22×C8—861no—
407C22×C8—861no—
408C22×C8—861no—
409C4⋊Q8—431no—
410C4⋊Q8—431no—
411#127—431no—
412#127—431no—
413#124—861no—
414#124—861no—
415#121—431no—
416#121—431no—
417#121—431no—
418#121—431no—
419#121—861no—
420#121—861no—
421C4×D4—431no—
422C4×D4—431no—
423C4×D4—861no—
424C4×D4—861no—
425C4×D4C22×D4311yescharacteristic
426C4×D4C22×D4311yescharacteristic
427C2×C42—431no—
428#107—431no—
429#107—431no—
430#107—431no—
431#107C4×D4311yescharacteristic
432C4⋊C8—431no—
433C4⋊C8—431no—
434C4⋊C8—861no—
435C4⋊C8—861no—
436C4⋊C8C22×D4311yescharacteristic
437C4⋊C8C22×D4311yescharacteristic
438#102—431no—
439#102—431no—
440#102—431no—
441#102—431no—
442#102—431no—
443#102—431no—
444#102C4×D4311yescharacteristic
445#102C4×D4311yescharacteristic
446C22⋊C8—21no—
447C22⋊C8—21no—
448C22⋊C8—861no—
449C22⋊C8—861no—
450C22⋊C8—861no—
451C22⋊C8—861no—
452C22⋊C8—861no—
453C22⋊C8—861no—
454C4×C8—431no—
455C4×C8—431no—
456C4×C8—431no—
457C4×C8—431no—
458C4×C8—431no—
459C4×C8—431no—
460C4×C8—431no—
461C4×C8—861no—
462C4×C8C22×D4311yescharacteristic
463C4×C8C22×D4311yescharacteristic
464C4×C8C22×D4311yescharacteristic
465#41—1722no—
466#41—1722no—
467#41—1722no—
468#41—1722no—
469C2×Q8—861no—
470C2×Q8—861no—
471C2×D4—431no—
472C2×D4—431no—
473C2×D4—861no—
474C2×D4—861no—
475C2×D4—861no—
476C2×D4—861no—
477C2×D4—861no—
478C2×D4—861no—
479C2×D4—861no—
480C2×D4—861no—
481C2×D4C2×C4×D4311yescharacteristic
482C2×D4C2×C4×D4311yescharacteristic
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—431no—
486C22×C4—431no—
487C22×C4—431no—
488C22×C4—861no—
489C22×C4—861no—
490D8—41no—
491D8—1721no—
492D8—1721no—
493D8—1721no—
494M16—42no—
495M16—1722no—
496M16—1722no—
497M16—1722no—
498M16—1722no—
499M16—1722no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—42no—
504C2×C8—431no—
505C2×C8—434no—
506C2×C8—431no—
507C2×C8—431no—
508C2×C8—431no—
509C2×C8—862no—
510C2×C8—861no—
511C2×C8—861no—
512C2×C8—861no—
513C2×C8—1721no—
514C2×C8—1721no—
515C2×C8—1722no—
516C2×C8—1722no—
517C2×C8—1722no—
518C2×C8—1722no—
519C2×C8C2×C4×D4311yescharacteristic
520C2×C8C2×C4×D4311yescharacteristic
521C2×C8D4×D4311yescharacteristic
522C2×C8D4×D4311yescharacteristic
523C4⋊C4—431no—
524C4⋊C4—431no—
525C4⋊C4—861no—
526C4⋊C4—861no—
527C4⋊C4C2×C4×D4311yescharacteristic
528C4⋊C4C2×C4×D4311yescharacteristic
529C22⋊C4—21no—
530C22⋊C4—21no—
531C22⋊C4—861no—
532C22⋊C4—861no—
533C22⋊C4—861no—
534C22⋊C4—861no—
535C22⋊C4—861no—
536C22⋊C4—861no—
537C42—431no—
538C42—431no—
539C42—431no—
540C42C23×D4311yescharacteristic
541C23—21no—
542C23—21no—
543C23—431no—
544C23—861no—
545C23—861no—
546Q8—1722no—
547Q8—1722no—
548D4—21no—
549D4—21no—
550D4—21no—
551D4—21no—
552D4—861no—
553D4—861no—
554D4—861no—
555D4—861no—
556D4—1722no—
557D4—1722no—
558D4—1722no—
559D4—1722no—
560D4—1722no—
561D4—1722no—
562D4—1722no—
563D4—1722no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—431no—
571C2×C4—431no—
572C2×C4—432no—
573C2×C4—432no—
574C2×C4—431no—
575C2×C4—862no—
576C2×C4—861no—
577C2×C4—861no—
578C2×C4—861no—
579C2×C4—861no—
580C2×C4—1721no—
581C2×C4—1721no—
582C2×C4—1721no—
583C2×C4—1721no—
584C2×C4C22×C4×D4311yescharacteristic
585C2×C4C2×D4×D4311yescharacteristic
586C2×C4#41×D4311yescharacteristic
587C8—21no—
588C8—21no—
589C8—21no—
590C8—41no—
591C8—41no—
592C8—41no—
593C8—432no—
594C8—861no—
595C8—861no—
596C8—861no—
597C8—1721no—
598C8—1721no—
599C8—1721no—
600C8D8×D4312yes—
601C22—41no—
602C22—41no—
603C22—41no—
604C22—41no—
605C22—41no—
606C22—41no—
607C22—432no—
608C22—861no—
609C22—861no—
610C22—1721no—
611C22—1721no—
612C22—1721no—
613C22—1721no—
614C22—1721no—
615C22—1721no—
616C22C4×D4×D4311yescharacteristic
617C4—21no—
618C4—41no—
619C4—41no—
620C4—432no—
621C4—432no—
622C4—861no—
623C4—1721no—
624C4—1721no—
625C4#1458366411yescharacteristic
626C4#1458366511yescharacteristic
627C4C2×D8×D4311yescharacteristic
628C4#135×D4311yescharacteristic
629C2—81no—
630C2—81no—
631C2—862no—
632C2—3441no—
633C2—3441no—
634C2#1914330911yescharacteristic
635C2C4×D8×D4311yescharacteristic
636C2#444×D4311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1581C2
socleC22×C43C2×C4×D4
prime radical#19145171C2
cosocleC42×C43C24
hypercenter#1581D43
hypocenterC43#17975
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1581

Complements

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

NH ≅ G/Ntype
2. #19143304C2semidirect
3. #19143302C2semidirect
4. #19133427C2semidirect
5. #19133426C2semidirect
6. #19133425C2semidirect
7. #19133424C2semidirect
8. #19133423C2semidirect
9. #19133422C2semidirect
10. #19133421C2semidirect
11. #19133352C2semidirect
12. #19133044C2semidirect
13. #19133044C2semidirect
14. #322×D43C2semidirect
15. C43×#1581C2semidirect
221. C8×D43D8semidirect
321. #1581D43semidirect
385. C43#17975semidirect

Maximal subgroups

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

subgroupindex
#191451712
#191433042
#191433022
#191334272
#191334262
#191334252
#191334242
#191334232
#191334222
#191334212
#191333522
#191330442
#322×D432
C43×#15812
#1797543