Finite Group Databasebeta

← #25066529

Subgroups — #25066529

Order 11008.

766 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144593C211yesmaximal, characteristic
2#19143302C211yesmaximal, characteristic, complemented
3C8×D4×D43C211yesmaximal, characteristic, complemented
4#19133462C211yesmaximal, characteristic, complemented
5#19133460C211yesmaximal, characteristic, complemented
6#19133458C211yesmaximal, characteristic, complemented
7#19133456C211yesmaximal, characteristic, complemented
8#19133420C211yesmaximal, characteristic, complemented
9#19133417C211yesmaximal, characteristic, complemented
10#19133417C211yesmaximal, characteristic, complemented
11#19133364C211yesmaximal, characteristic, complemented
12#19133018C211yesmaximal, characteristic, complemented
13#19132992C211yesmaximal, characteristic, complemented
14#19132886C211yesmaximal, characteristic, complemented
15C43×#1580C211yesmaximal, characteristic, complemented
16C2×#13063331—21no—
17C22×C8×D43—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#14582977C2211yescharacteristic, complemented
32#14582976C2211yescharacteristic, complemented
33#14582974—21no—
34C8×D172C2211yescharacteristic
35C8×D172C2211yescharacteristic, complemented
36D4×C43⋊C8C2211yescharacteristic
37#14582964C2211yescharacteristic
38C8×C22⋊D43—21no—
39C8×C22⋊D43—21no—
40(C22⋊D43)⋊C8—21no—
41#14582950C2211yescharacteristic
42#14582950C2211yescharacteristic
43#14582921C2211yescharacteristic
44C4⋊C8×D43C2211yescharacteristic
45#14582864—21no—
46C22⋊C8×D43—21no—
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#14582620C2211yescharacteristic, 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—
77C22×C43⋊C8—21no—
78C2×C8×D43—21no—
79C2×C8×D43—21no—
80C2×C8×D43—21no—
81C2×C8×D43—21no—
82C2×C8×D43—44no—
83C2×C8×D43D411yescharacteristic
84C2×C8×D43D411yescharacteristic
85#13063324C2×C411yescharacteristic
86#13063321C2×C411yescharacteristic
87#13063311—21no—
88#13063300C2×C411yescharacteristic
89#13063298—21no—
90#13063296C2×C411yescharacteristic
91C4×D172C2311yescharacteristic
92C4×D172C2311yescharacteristic
93D4×Dic43C2×C411yescharacteristic
94#13063287C2×C411yescharacteristic
95C4×C22⋊D43—21no—
96C4×C22⋊D43—21no—
97(C22⋊D43)⋊C4—21no—
98C4⋊C4×D43C2×C411yescharacteristic
99C22⋊C4×D43—21no—
100C42×D43C2311yescharacteristic
101#13063259C2×C411yescharacteristic
102#13063258C2×C411yescharacteristic
103#13063258C2×C411yescharacteristic
104C4⋊(C43⋊C8)C2311yescharacteristic
105C4⋊(C43⋊C8)C2311yescharacteristic
106Dic43⋊C8—21no—
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)⋊C8—21no—
124(C2×D43)⋊C8C2×C411yescharacteristic
125(C2×D43)⋊C8C2×C411yescharacteristic
126C4×C43⋊C8C2311yescharacteristic
127C4×C43⋊C8C2311yescharacteristic
128C4×C43⋊C8C2311yescharacteristic
129C8×Dic43D411yescharacteristic
130C8×Dic43D411yescharacteristic
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—22no—
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—22no—
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—22no—
213#10621872—42no—
214#10621872—42no—
215C8×D43—22no—
216C8×D43—22no—
217C8×D43—42no—
218C8×D43—42no—
219C8×D43—42no—
220C8×D43—42no—
221C23×C43—21no—
222C23×C43—21no—
223C22×D43—24no—
224C22×D43—21no—
225C22×D43—21no—
226C22×D43—42no—
227C22×D43—42no—
228C22×D43C4×D411yescharacteristic
229D4×C43—21no—
230D4×C43—21no—
231D4×C43—21no—
232D4×C43#13112yescomplemented
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43C23×C411yescharacteristic
240C2×C4×C43C22×D411yescharacteristic
241C2×C4×C43C2×#4111yescharacteristic
242C22⋊D43—24no—
243C22⋊D43—42no—
244C22⋊D43—42no—
245C22⋊D43—42no—
246C2×Dic43—21no—
247C2×Dic43—21no—
248C2×Dic43—42no—
249C2×Dic43C4×D411yescharacteristic
250C2×Dic43C4×D411yescharacteristic
251C2×Dic43C4×D411yescharacteristic
252D172—21no—
253D172—21no—
254D172—21no—
255D172—42no—
256D172#13112yescomplemented
257C4×D43—21no—
258C4×D43—21no—
259C4×D43—41no—
260C4×D43—42no—
261C4×D43—41no—
262C4×D43—41no—
263C4×D43—41no—
264C4×D43—41no—
265C4×D43—42no—
266C4×D43AGL(1,ℤ/8)12yes—
267C4×D43AGL(1,ℤ/8)12yes—
268Dic86—42no—
269C8×C43—21no—
270C8×C43—21no—
271C8×C43—21no—
272C8×C43—21no—
273C8×C43—41no—
274C8×C43—41no—
275C8×C43—41no—
276C43⋊C8—21no—
277C43⋊C8—21no—
278C43⋊C8—21no—
279C43⋊C8—21no—
280C43⋊C8—41no—
281C43⋊C8—41no—
282C43⋊C8—41no—
283#17907—431nomaximal, Sylow
284C22×C43—22no—
285C22×C43—41no—
286C22×C43—41no—
287C22×C43—41no—
288C22×C43—41no—
289C22×C43—41no—
290C22×C43C2×C4×D411yescharacteristic
291C2×D43—21no—
292C2×D43—21no—
293C2×D43—22no—
294C2×D43—48no—
295C2×D43—41no—
296C2×D43—41no—
297C2×D43—41no—
298C2×D43—41no—
299C2×D43—41no—
300C2×D43#44212yes—
301C4×C43—21no—
302C4×C43—41no—
303C4×C43—41no—
304C4×C43C2×#13111yescharacteristic
305C4×C43C2×#13111yescharacteristic
306C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
307C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
308Dic43—21no—
309Dic43—21no—
310Dic43—41no—
311Dic43—41no—
312Dic43#44212yes—
313#3100—431no—
314#2931—431no—
315C2×C8×D4—431no—
316#1586—431no—
317#1586—431no—
318#1586—431no—
319#1586—431no—
320#1580—431no—
321#1580—431no—
322#1580—431no—
323#1580D4311yescharacteristic, complemented
324#1570—431no—
325#1486—431no—
326#1480—431no—
327#1452—431no—
328C2×C43—42no—
329C2×C43—81no—
330C2×C43#292911yescharacteristic
331C2×C43C2×#44211yescharacteristic
332C2×C43#295511yescharacteristic
333D43—22no—
334D43—42no—
335D43—81no—
336C2×#131—861no—
337C23×C8—861no—
338#532—431no—
339C2×C4×D4—431no—
340#480—431no—
341#480—431no—
342#474—431no—
343#474—431no—
344#459—431no—
345#459—431no—
346#447—431no—
347#447—431no—
348C4×D8—431no—
349C4×D8—431no—
350C4×D8—431no—
351C4×D8C2×D4311yescharacteristic
352#436—431no—
353#436—431no—
354#436—861no—
355C8×D4—431no—
356C8×D4—431no—
357C8×D4—431no—
358C8×D4—431no—
359C8×D4—861no—
360C8×D4—861no—
361C8×D4—861no—
362C8×D4C2×D4311yescharacteristic
363C8×D4C2×D4311yescharacteristic, complemented
364#431—431no—
365#431—431no—
366#423—431no—
367C2×C4⋊C8—431no—
368#408—861no—
369C2×C22⋊C8—861no—
370C2×C4×C8—431no—
371#334—431no—
372#334—431no—
373#334—431no—
374#334C2×D4311yescharacteristic, complemented
375D4⋊C8—431no—
376D4⋊C8—431no—
377D4⋊C8—431no—
378D4⋊C8—431no—
379D4⋊C8—431no—
380D4⋊C8—431no—
381D4⋊C8C2×D4311yescharacteristic
382D4⋊C8C2×D4311yescharacteristic, complemented
383#322—431no—
384#322—431no—
385#322—431no—
386#322C2×D4311yescharacteristic, complemented
387C43#1790711yescharacteristic, complemented, Sylow
388C2×#41—861no—
389C22×D4—431no—
390C23×C4—861no—
391C2×D8—431no—
392C2×D8—431no—
393C2×D8—431no—
394C2×D8C4×D4311yescharacteristic
395#131—1724no—
396C2×M16—861no—
397C2×M16—861no—
398C2×M16—861no—
399C22×C8—21no—
400C22×C8—21no—
401C22×C8—431no—
402C22×C8—431no—
403C22×C8—861no—
404C22×C8—861no—
405C22×C8—861no—
406C22×C8—861no—
407C22×C8—861no—
408C22×C8—1724no—
409C4⋊Q8—431no—
410#127—431no—
411#124—861no—
412#121—431no—
413#121—431no—
414#121—861no—
415C4×D4—431no—
416C4×D4—431no—
417C4×D4—431no—
418C4×D4—431no—
419C4×D4—861no—
420C4×D4—861no—
421C4×D4—861no—
422C4×D4C22×D4311yescharacteristic
423C4×D4C22×D4311yescharacteristic
424C2×C4⋊C4—431no—
425C2×C22⋊C4—861no—
426C2×C42—431no—
427#107—431no—
428#107—431no—
429#107—431no—
430#107C4×D4311yescharacteristic
431C4⋊C8—431no—
432C4⋊C8—431no—
433C4⋊C8—431no—
434C4⋊C8—431no—
435C4⋊C8—861no—
436C4⋊C8—861no—
437C4⋊C8—861no—
438C4⋊C8C22×D4311yescharacteristic
439C4⋊C8C22×D4311yescharacteristic
440#102—431no—
441#102—431no—
442#102—431no—
443#102—431no—
444#102—431no—
445#102—431no—
446#102C4×D4311yescharacteristic
447#102C4×D4311yescharacteristic
448C22⋊C8—21no—
449C22⋊C8—21no—
450C22⋊C8—431no—
451C22⋊C8—431no—
452C22⋊C8—861no—
453C22⋊C8—861no—
454C22⋊C8—861no—
455C22⋊C8—861no—
456C22⋊C8—861no—
457C22⋊C8—861no—
458C22⋊C8—861no—
459C4×C8—431no—
460C4×C8—431no—
461C4×C8—431no—
462C4×C8—431no—
463C4×C8—431no—
464C4×C8C22×D4311yescharacteristic
465C4×C8C22×D4311yescharacteristic
466C4×C8C22×D4311yescharacteristic
467C24—861no—
468#41—1722no—
469#41—1722no—
470C2×Q8—861no—
471C2×D4—431no—
472C2×D4—431no—
473C2×D4—861no—
474C2×D4—861no—
475C2×D4—861no—
476C2×D4—861no—
477C2×D4—862no—
478C2×D4—862no—
479C2×D4—861no—
480C2×D4C2×C4×D4311yescharacteristic
481C2×D4C2×C4×D4311yescharacteristic
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—431no—
485C22×C4—431no—
486C22×C4—431no—
487C22×C4—861no—
488C22×C4—861no—
489C22×C4—861no—
490C22×C4—861no—
491C22×C4—861no—
492C22×C4—1722no—
493C22×C4—1722no—
494D8—22no—
495D8—862no—
496D8—862no—
497D8—862no—
498M16—1722no—
499M16—1722no—
500M16—1722no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—42no—
505C2×C8—42no—
506C2×C8—431no—
507C2×C8—431no—
508C2×C8—431no—
509C2×C8—431no—
510C2×C8—862no—
511C2×C8—862no—
512C2×C8—861no—
513C2×C8—861no—
514C2×C8—861no—
515C2×C8—1722no—
516C2×C8—1722no—
517C2×C8—1722no—
518C2×C8—1722no—
519C2×C8—1722no—
520C2×C8C2×C4×D4311yescharacteristic
521C2×C8C2×C4×D4311yescharacteristic
522C2×C8D4×D4311yescharacteristic
523C2×C8D4×D4311yescharacteristic
524C4⋊C4—431no—
525C4⋊C4—431no—
526C4⋊C4—861no—
527C4⋊C4—861no—
528C4⋊C4C2×C4×D4311yescharacteristic
529C4⋊C4C2×C4×D4311yescharacteristic
530C22⋊C4—21no—
531C22⋊C4—21no—
532C22⋊C4—861no—
533C22⋊C4—861no—
534C22⋊C4—861no—
535C22⋊C4—861no—
536C22⋊C4—861no—
537C22⋊C4—861no—
538C42—431no—
539C42—431no—
540C42—431no—
541C42C23×D4311yescharacteristic
542C23—21no—
543C23—21no—
544C23—431no—
545C23—864no—
546C23—861no—
547C23—861no—
548C23—1722no—
549C23—1722no—
550Q8—1722no—
551D4—21no—
552D4—21no—
553D4—21no—
554D4—432no—
555D4—864no—
556D4—861no—
557D4—861no—
558D4—861no—
559D4—1722no—
560D4—1722no—
561D4—1722no—
562D4—1722no—
563D4#1306333112yescomplemented
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—431no—
571C2×C4—432no—
572C2×C4—432no—
573C2×C4—431no—
574C2×C4—431no—
575C2×C4—861no—
576C2×C4—861no—
577C2×C4—861no—
578C2×C4—861no—
579C2×C4—1721no—
580C2×C4—1722no—
581C2×C4—1722no—
582C2×C4—1722no—
583C2×C4—1721no—
584C2×C4—1721no—
585C2×C4—1721no—
586C2×C4—1721no—
587C2×C4C22×C4×D4311yescharacteristic
588C2×C4C2×D4×D4311yescharacteristic
589C2×C4#41×D4311yescharacteristic
590C8—21no—
591C8—21no—
592C8—21no—
593C8—21no—
594C8—41no—
595C8—41no—
596C8—41no—
597C8—861no—
598C8—861no—
599C8—861no—
600C8—861no—
601C8—1721no—
602C8—1721no—
603C8—1721no—
604C22—22no—
605C22—41no—
606C22—41no—
607C22—41no—
608C22—41no—
609C22—41no—
610C22—432no—
611C22—861no—
612C22—861no—
613C22—862no—
614C22—1728no—
615C22—1721no—
616C22—1721no—
617C22—1721no—
618C22—1721no—
619C22—1721no—
620C22C4×D4×D4311yescharacteristic
621C4—21no—
622C4—41no—
623C4—41no—
624C4—432no—
625C4—861no—
626C4—861no—
627C4—1721no—
628C4—1721no—
629C4#131×D4311yescharacteristic
630C4C2×#1306333111yescharacteristic
631C4AGL(1,ℤ/8)×D4311yescharacteristic
632C4AGL(1,ℤ/8)×D4311yescharacteristic
633C2—42no—
634C2—81no—
635C2—862no—
636C2—3441no—
637C2—1722no—
638C2#1914328411yescharacteristic
639C2#442×D4311yescharacteristic
640C2#1914349511yescharacteristic
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#17907
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. #19143302C2semidirect
3. C8×D4×D43C2semidirect
4. #19133462C2semidirect
5. #19133460C2semidirect
6. #19133458C2semidirect
7. #19133456C2semidirect
8. #19133420C2semidirect
9. #19133417C2semidirect
10. #19133417C2semidirect
11. #19133364C2semidirect
12. #19133018C2semidirect
13. #19132992C2semidirect
14. #19132886C2semidirect
15. C43×#1580C2semidirect
31. #14582977C22semidirect
32. #14582976C22semidirect
35. C8×D172C22semidirect
48. #14582650C22semidirect
49. #14582649C22semidirect
50. #14582649C22semidirect
52. #14582628C22semidirect
54. D4⋊(C43⋊C8)C22semidirect
56. #14582626C22semidirect
57. #14582621C22semidirect
58. #14582621C22semidirect
59. #14582620C22semidirect
62. C8×D4×C43C22semidirect
63. C43×#334C22semidirect
65. C43×D4⋊C8C22semidirect
66. C43×#322C22semidirect
232. D4×C43#131semidirect
256. D172#131semidirect
323. #1580D43semidirect
363. C8×D4C2×D43semidirect
374. #334C2×D43semidirect
382. D4⋊C8C2×D43semidirect
386. #322C2×D43semidirect
387. C43#17907semidirect
563. D4#13063331semidirect

Maximal subgroups

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

subgroupindex
#191445932
#191433022
C8×D4×D432
#191334622
#191334602
#191334582
#191334562
#191334202
#191334172
#191333642
#191330182
#191329922
#191328862
C43×#15802
#1790743