Finite Group Databasebeta

← #25067563

Subgroups — #25067563

Order 11008.

740 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144593C211yesmaximal, characteristic
2#19143334C211yesmaximal, characteristic, complemented
3D4×#10621872C211yesmaximal, characteristic, complemented
4#19133510C211yesmaximal, characteristic, complemented
5#19133506C211yesmaximal, characteristic, complemented
6#19133460C211yesmaximal, characteristic, complemented
7#19133459C211yesmaximal, characteristic, complemented
8#19133459C211yesmaximal, characteristic, complemented
9#19133458C211yesmaximal, characteristic, complemented
10#19133416C211yesmaximal, characteristic, complemented
11#19133364C211yesmaximal, characteristic, complemented
12#19133044C211yesmaximal, characteristic, complemented
13D4⋊C8×D43C211yesmaximal, characteristic, complemented
14#19132883C211yesmaximal, characteristic, complemented
15C43×#1580C211yesmaximal, characteristic, complemented
16C2×#13063331—21no—
17C22×#10621872—21no—
18#14583446C2211yescharacteristic
19C4×D4×D43C2211yescharacteristic
20#14583214C411yescharacteristic
21#14583211C411yescharacteristic
22#14583178C411yescharacteristic
23#14583177C411yescharacteristic
24#14583093C411yescharacteristic
25#14583092C411yescharacteristic
26#14583034C411yescharacteristic
27#14583031C411yescharacteristic
28C4×D344C2211yescharacteristic
29C4×#10621882C2211yescharacteristic
30C4×#10621882C2211yescharacteristic
31#14582978C2211yescharacteristic
32#14582978C2211yescharacteristic, complemented
33#14582977C2211yescharacteristic, complemented
34#14582976C2211yescharacteristic
35#14582973—21no—
36#14582970—21no—
37#14582970—21no—
38#14582967—21no—
39D4×C43⋊C8C2211yescharacteristic
40#14582964C2211yescharacteristic, complemented
41#14582950C2211yescharacteristic
42#14582921C2211yescharacteristic
43C4⋊C8×D43C2211yescharacteristic
44#14582864—21no—
45#14582861—21no—
46C4×#10621872C2211yescharacteristic
47C4×C8×D43C2211yescharacteristic
48#14582650C2211yescharacteristic, complemented
49#14582649C2211yescharacteristic, complemented
50#14582649C2211yescharacteristic, complemented
51#14582628C2211yescharacteristic
52#14582628C2211yescharacteristic, complemented
53D4⋊(C43⋊C8)C2211yescharacteristic
54D4⋊(C43⋊C8)C2211yescharacteristic, complemented
55#14582626C2211yescharacteristic
56#14582626C2211yescharacteristic, complemented
57#14582621C2211yescharacteristic, complemented
58#14582621C2211yescharacteristic, complemented
59#14582621C2211yescharacteristic, complemented
60C4×D8×C43C2211yescharacteristic
61C8×D4×C43C2211yescharacteristic
62C8×D4×C43C2211yescharacteristic, complemented
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
73#13063331—44no—
74C2×#10621877—21no—
75C2×#10621872—21no—
76C2×#10621872—21no—
77C2×#10621872—21no—
78C2×#10621872—21no—
79C2×#10621872—44no—
80C2×#10621872D411yescharacteristic
81C2×#10621872D411yescharacteristic
82C22×C43⋊C8—21no—
83C2×C8×D43—21no—
84C2×C8×D43—21no—
85C2×C8×D43—21no—
86#13063324C2×C411yescharacteristic
87#13063321C2×C411yescharacteristic
88#13063311—21no—
89#13063300C2×C411yescharacteristic
90#13063298—21no—
91#13063296C2×C411yescharacteristic
92C4×D172C2311yescharacteristic
93C4×D172C2311yescharacteristic
94D4×Dic43C2×C411yescharacteristic
95#13063287C2×C411yescharacteristic
96C4×C22⋊D43—21no—
97C4×C22⋊D43—21no—
98(C22⋊D43)⋊C4—21no—
99C4⋊C4×D43C2×C411yescharacteristic
100C22⋊C4×D43—21no—
101C42×D43C2311yescharacteristic
102#13063259C2×C411yescharacteristic
103#13063258C2×C411yescharacteristic
104#13063258C2×C411yescharacteristic
105C4⋊(C43⋊C8)C2311yescharacteristic
106C4⋊(C43⋊C8)C2311yescharacteristic
107Dic43⋊C8—21no—
108Dic43⋊C8—21no—
109Dic43⋊C8C2×C411yescharacteristic
110Dic43⋊C8C2×C411yescharacteristic
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—
123(C2×D43)⋊C8C2×C411yescharacteristic
124(C2×D43)⋊C8C2×C411yescharacteristic
125#13063235D411yescharacteristic
126#13063235D411yescharacteristic
127C4×C43⋊C8C2311yescharacteristic
128C4×C43⋊C8C2311yescharacteristic
129C4×C43⋊C8C2311yescharacteristic
130C8×Dic43—21no—
131C2×D8×C43C2×C411yescharacteristic
132C22×C8×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
146C23×D43—21no—
147C2×D4×C43C22×C411yescharacteristic
148C2×D4×C43C22×C411yescharacteristic
149C22×C4×C43—21no—
150C22×C4×C43—21no—
151C2×C22⋊D43—21no—
152C2×C22⋊D43—21no—
153C2×C22⋊D43—21no—
154C2×C22⋊D43—21no—
155C22×Dic43—21no—
156D4×D43—22no—
157D4×D43—41no—
158#10621898—42no—
159#10621898—42no—
160C2×D172—21no—
161C2×D172C22×C411yescharacteristic
162C2×D172C22×C411yescharacteristic
163C2×C4×D43—21no—
164C2×C4×D43—21no—
165C2×C4×D43—21no—
166C2×C4×D43—21no—
167C2×C4×D43—42no—
168C2×C4×D43—42no—
169C2×C4×D43C22×C411yescharacteristic
170C2×C4×D43C2×D411yescharacteristic
171C2×C4×D43#4111yescharacteristic
172C2×Dic86—21no—
173D8×C43—22no—
174C2×C8×C43—21no—
175C2×C8×C43—21no—
176C2×C8×C43—21no—
177C2×C8×C43—42no—
178C2×C8×C43—42no—
179C2×C8×C43C22×C411yescharacteristic
180C2×C8×C43C22×C411yescharacteristic
181C2×C8×C43C2×D411yescharacteristic
182C2×C8×C43C2×D411yescharacteristic
183C4⋊C4×C43C22×C411yescharacteristic
184C4⋊C4×C43C22×C411yescharacteristic
185C22⋊C4×C43—21no—
186C22⋊C4×C43—21no—
187C42×C43C2411yescharacteristic
188C22⋊Dic43—21no—
189C22⋊Dic43—21no—
190#10621882—22no—
191#10621882—41no—
192(C2×D43)⋊C4—21no—
193(C2×D43)⋊C4—21no—
194(C2×D43)⋊C4—21no—
195(C2×D43)⋊C4—21no—
196C4⋊Dic43C22×C411yescharacteristic
197C4⋊Dic43C22×C411yescharacteristic
198Dic43⋊C4—21no—
199Dic43⋊C4—21no—
200C4×Dic43C22×C411yescharacteristic
201C4×Dic43C2×D411yescharacteristic
202C4×Dic43#4111yescharacteristic
203#10621877—42no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—42no—
208C2×C43⋊C8C22×C411yescharacteristic
209C2×C43⋊C8C22×C411yescharacteristic
210C2×C43⋊C8C2×D411yescharacteristic
211C2×C43⋊C8C2×D411yescharacteristic
212D344—41no—
213#10621872—22no—
214#10621872—22no—
215#10621872—42no—
216#10621872—42no—
217#10621872—42no—
218#10621872—42no—
219C8×D43—42no—
220C8×D43—42no—
221C8×D43—42no—
222C23×C43—21no—
223C23×C43—21no—
224C22×D43—21no—
225C22×D43—21no—
226C22×D43—42no—
227C22×D43—42no—
228C22×D43—81no—
229C22×D43C4×D411yescharacteristic
230D4×C43—21no—
231D4×C43—21no—
232D4×C43—21no—
233D4×C43#13112yescomplemented
234C2×C4×C43—21no—
235C2×C4×C43—21no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43C23×C411yescharacteristic
241C2×C4×C43C22×D411yescharacteristic
242C2×C4×C43C2×#4111yescharacteristic
243C22⋊D43—42no—
244C22⋊D43—42no—
245C22⋊D43—42no—
246C22⋊D43—81no—
247C2×Dic43—21no—
248C2×Dic43—21no—
249C2×Dic43—42no—
250C2×Dic43C4×D411yescharacteristic
251C2×Dic43C4×D411yescharacteristic
252C2×Dic43C4×D411yescharacteristic
253D172—21no—
254D172—21no—
255D172—21no—
256D172—21no—
257D172—42no—
258C4×D43—21no—
259C4×D43—21no—
260C4×D43—41no—
261C4×D43—42no—
262C4×D43—41no—
263C4×D43—41no—
264C4×D43—41no—
265C4×D43—41no—
266C4×D43—42no—
267C4×D43AGL(1,ℤ/8)12yes—
268C4×D43AGL(1,ℤ/8)12yes—
269Dic86—42no—
270C8×C43—21no—
271C8×C43—21no—
272C8×C43—21no—
273C8×C43—21no—
274C8×C43—41no—
275C8×C43—41no—
276C8×C43—41no—
277C43⋊C8—22no—
278C43⋊C8—21no—
279C43⋊C8—21no—
280C43⋊C8—21no—
281C43⋊C8—21no—
282C43⋊C8—41no—
283C43⋊C8—41no—
284#18001—431nomaximal, Sylow
285C22×C43—22no—
286C22×C43—41no—
287C22×C43—41no—
288C22×C43—41no—
289C22×C43—41no—
290C22×C43—41no—
291C22×C43C2×C4×D411yescharacteristic
292C2×D43—21no—
293C2×D43—21no—
294C2×D43—41no—
295C2×D43—41no—
296C2×D43—41no—
297C2×D43—41no—
298C2×D43—41no—
299C2×D43—41no—
300C2×D43—84no—
301C2×D43#44212yes—
302C4×C43—21no—
303C4×C43—41no—
304C4×C43—41no—
305C4×C43C2×#13111yescharacteristic
306C4×C43#56811yescharacteristic
307C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
308C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
309Dic43—21no—
310Dic43—21no—
311Dic43—41no—
312Dic43—41no—
313Dic43#44212yes—
314#3100—431no—
315#2935—431no—
316D4×M16—431no—
317#1594—431no—
318#1594—431no—
319#1586—431no—
320#1586—431no—
321#1586—431no—
322#1586—431no—
323#1580—431no—
324#1580D4311yescharacteristic, complemented
325#1570—431no—
326#1492—431no—
327C2×D4⋊C8—431no—
328#1451—431no—
329C2×C43—42no—
330C2×C43—81no—
331C2×C43#293311yescharacteristic
332C2×C43C2×#44211yescharacteristic
333C2×C43#295611yescharacteristic
334D43—22no—
335D43—81no—
336D43—81no—
337C2×#131—861no—
338C22×M16—861no—
339#532—431no—
340C2×C4×D4—431no—
341#480—431no—
342#480—431no—
343#474—431no—
344#474—431no—
345#459—431no—
346#459—431no—
347#447—431no—
348#447—431no—
349C4×D8—431no—
350C4×D8—431no—
351C4×D8—431no—
352C4×D8C2×D4311yescharacteristic
353#436—431no—
354#436—431no—
355#436—431no—
356#436—431no—
357#435—861no—
358#435—861no—
359#435—861no—
360#435—861no—
361C8×D4—431no—
362C8×D4—431no—
363C8×D4C2×D4311yescharacteristic
364C8×D4C2×D4311yescharacteristic, complemented
365#431—431no—
366#423—431no—
367C2×C4⋊C8—431no—
368#408—861no—
369#407—861no—
370C4×M16—431no—
371C2×C4×C8—431no—
372#334—431no—
373#334—431no—
374#334—431no—
375#334C2×D4311yescharacteristic, complemented
376D4⋊C8—431no—
377D4⋊C8—431no—
378D4⋊C8—431no—
379D4⋊C8—431no—
380D4⋊C8—431no—
381D4⋊C8—431no—
382D4⋊C8C2×D4311yescharacteristic
383D4⋊C8C2×D4311yescharacteristic, complemented
384#322—431no—
385#322—431no—
386#322—431no—
387#322C2×D4311yescharacteristic, complemented
388C43#1800111yescharacteristic, complemented, Sylow
389C2×#41—861no—
390C22×D4—431no—
391C23×C4—861no—
392C2×D8—431no—
393C2×D8—431no—
394C2×D8—431no—
395C2×D8C4×D4311yescharacteristic
396#131—1724no—
397C2×M16—431no—
398C2×M16—431no—
399C2×M16—861no—
400C2×M16—861no—
401C2×M16—861no—
402C2×M16—861no—
403C2×M16—861no—
404C2×M16—1724no—
405C22×C8—21no—
406C22×C8—21no—
407C22×C8—861no—
408C22×C8—861no—
409C22×C8—861no—
410C22×C8—861no—
411C4⋊Q8—431no—
412#127—431no—
413#124—861no—
414#121—431no—
415#121—431no—
416#121—861no—
417C4×D4—431no—
418C4×D4—431no—
419C4×D4—431no—
420C4×D4—431no—
421C4×D4—861no—
422C4×D4—861no—
423C4×D4—861no—
424C4×D4C22×D4311yescharacteristic
425C4×D4C22×D4311yescharacteristic
426C2×C4⋊C4—431no—
427C2×C22⋊C4—861no—
428C2×C42—431no—
429#107—431no—
430#107—431no—
431#107—431no—
432#107C4×D4311yescharacteristic
433C4⋊C8—431no—
434C4⋊C8—431no—
435C4⋊C8—431no—
436C4⋊C8—431no—
437C4⋊C8—861no—
438C4⋊C8—861no—
439C4⋊C8C22×D4311yescharacteristic
440C4⋊C8C22×D4311yescharacteristic
441#102—431no—
442#102—431no—
443#102—431no—
444#102—431no—
445#102—431no—
446#102—431no—
447#102C4×D4311yescharacteristic
448#102C4×D4311yescharacteristic
449C22⋊C8—21no—
450C22⋊C8—21no—
451C22⋊C8—431no—
452C22⋊C8—431no—
453C22⋊C8—861no—
454C22⋊C8—861no—
455C22⋊C8—861no—
456C22⋊C8—861no—
457C22⋊C8—861no—
458C22⋊C8—861no—
459#97—431no—
460#97—431no—
461C4×C8—431no—
462C4×C8—431no—
463C4×C8—431no—
464C4×C8—861no—
465C4×C8C22×D4311yescharacteristic
466C4×C8C22×D4311yescharacteristic
467C4×C8C22×D4311yescharacteristic
468C24—861no—
469#41—1722no—
470#41—1722no—
471C2×Q8—861no—
472C2×D4—431no—
473C2×D4—431no—
474C2×D4—861no—
475C2×D4—861no—
476C2×D4—861no—
477C2×D4—861no—
478C2×D4—862no—
479C2×D4—861no—
480C2×D4—1721no—
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—
490C22×C4—861no—
491C22×C4—861no—
492C22×C4—861no—
493C22×C4—1722no—
494C22×C4—1722no—
495D8—22no—
496D8—862no—
497D8—1721no—
498D8—1721no—
499M16—862no—
500M16—862no—
501M16—1722no—
502M16—1722no—
503M16—1722no—
504M16—1722no—
505M16—1722no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—42no—
510C2×C8—42no—
511C2×C8—431no—
512C2×C8—431no—
513C2×C8—431no—
514C2×C8—431no—
515C2×C8—861no—
516C2×C8—861no—
517C2×C8—861no—
518C2×C8—1722no—
519C2×C8—1722no—
520C2×C8—1722no—
521C2×C8—1722no—
522C2×C8C2×C4×D4311yescharacteristic
523C2×C8C2×C4×D4311yescharacteristic
524C2×C8D4×D4311yescharacteristic
525C2×C8D4×D4311yescharacteristic
526C4⋊C4—431no—
527C4⋊C4—431no—
528C4⋊C4—861no—
529C4⋊C4—861no—
530C4⋊C4C2×C4×D4311yescharacteristic
531C4⋊C4C2×C4×D4311yescharacteristic
532C22⋊C4—21no—
533C22⋊C4—21no—
534C22⋊C4—861no—
535C22⋊C4—861no—
536C22⋊C4—861no—
537C22⋊C4—861no—
538C22⋊C4—861no—
539C22⋊C4—861no—
540C42—431no—
541C42—431no—
542C42—431no—
543C42C23×D4311yescharacteristic
544C23—21no—
545C23—21no—
546C23—431no—
547C23—861no—
548C23—861no—
549C23—3441no—
550C23—1722no—
551C23—1722no—
552Q8—1722no—
553D4—21no—
554D4—21no—
555D4—21no—
556D4—861no—
557D4—861no—
558D4—861no—
559D4—861no—
560D4—3441no—
561D4—1722no—
562D4—1722no—
563D4—1722no—
564D4—1722no—
565D4#1306333112yescomplemented
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—431no—
573C2×C4—432no—
574C2×C4—432no—
575C2×C4—431no—
576C2×C4—431no—
577C2×C4—861no—
578C2×C4—861no—
579C2×C4—861no—
580C2×C4—861no—
581C2×C4—1721no—
582C2×C4—1722no—
583C2×C4—1722no—
584C2×C4—1722no—
585C2×C4—1721no—
586C2×C4—1721no—
587C2×C4—1721no—
588C2×C4—1721no—
589C2×C4C22×C4×D4311yescharacteristic
590C2×C4C2×D4×D4311yescharacteristic
591C2×C4#41×D4311yescharacteristic
592C8—21no—
593C8—21no—
594C8—21no—
595C8—21no—
596C8—41no—
597C8—41no—
598C8—41no—
599C8—862no—
600C8—861no—
601C8—861no—
602C8—861no—
603C8—861no—
604C8—1721no—
605C8—1721no—
606C22—22no—
607C22—41no—
608C22—41no—
609C22—41no—
610C22—41no—
611C22—41no—
612C22—432no—
613C22—861no—
614C22—861no—
615C22—3444no—
616C22—1721no—
617C22—1721no—
618C22—1721no—
619C22—1721no—
620C22—1721no—
621C22—1721no—
622C22C4×D4×D4311yescharacteristic
623C4—21no—
624C4—41no—
625C4—41no—
626C4—432no—
627C4—861no—
628C4—861no—
629C4—1721no—
630C4—1721no—
631C4C2×#1306333111yescharacteristic
632C4#1458366411yescharacteristic
633C4AGL(1,ℤ/8)×D4311yescharacteristic
634C4AGL(1,ℤ/8)×D4311yescharacteristic
635C2—42no—
636C2—81no—
637C2—862no—
638C2—3441no—
639C2—3441no—
640C2#1914331511yescharacteristic
641C2#442×D4311yescharacteristic
642C2#1914350311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1580C2
socleC22×C43C2×C4×D4
prime radical#19144593C2
cosocleC42×C43C24
hypercenter#1580D43
hypocenterC43#18001
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1580

Complements

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

NH ≅ G/Ntype
2. #19143334C2semidirect
3. D4×#10621872C2semidirect
4. #19133510C2semidirect
5. #19133506C2semidirect
6. #19133460C2semidirect
7. #19133459C2semidirect
8. #19133459C2semidirect
9. #19133458C2semidirect
10. #19133416C2semidirect
11. #19133364C2semidirect
12. #19133044C2semidirect
13. D4⋊C8×D43C2semidirect
14. #19132883C2semidirect
15. C43×#1580C2semidirect
32. #14582978C22semidirect
33. #14582977C22semidirect
40. #14582964C22semidirect
48. #14582650C22semidirect
49. #14582649C22semidirect
50. #14582649C22semidirect
52. #14582628C22semidirect
54. D4⋊(C43⋊C8)C22semidirect
56. #14582626C22semidirect
57. #14582621C22semidirect
58. #14582621C22semidirect
59. #14582621C22semidirect
62. C8×D4×C43C22semidirect
63. C43×#334C22semidirect
65. C43×D4⋊C8C22semidirect
66. C43×#322C22semidirect
233. D4×C43#131semidirect
324. #1580D43semidirect
364. C8×D4C2×D43semidirect
375. #334C2×D43semidirect
383. D4⋊C8C2×D43semidirect
387. #322C2×D43semidirect
388. C43#18001semidirect
565. D4#13063331semidirect

Maximal subgroups

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

subgroupindex
#191445932
#191433342
D4×#106218722
#191335102
#191335062
#191334602
#191334592
#191334582
#191334162
#191333642
#191330442
D4⋊C8×D432
#191328832
C43×#15802
#1800143