Finite Group Databasebeta

← #25130490

Subgroups — #25130490

Order 11008.

1434 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583554C211yesmaximal, characteristic, complemented
2C2×#14583179C211yesmaximal, characteristic, complemented
3#19139508C211yesmaximal, characteristic, complemented
4#19135775C212yesmaximal, complemented
5#19135590C212yesmaximal, complemented
6#19135556C211yesmaximal, characteristic, complemented
7#19135389C211yesmaximal, characteristic, complemented
8#19134909C212yesmaximal, complemented
9#19134781C212yesmaximal, complemented
10#19134595C211yesmaximal, characteristic, complemented
11C2×C4×D8×C43C211yesmaximal, characteristic, complemented
12C22×#10621898—21no—
13#14583554—24no—
14#14583554—24no—
15C2×#13063325C2211yescharacteristic
16C2×#13063307—22no—
17C2×#13063304—21no—
18C2×#13063299—21no—
19C2×#13063296C2212yes—
20C2×#13063296C2212yes—
21C2×C4×D172C2211yescharacteristic
22C2×C4⋊C4×D43C2212yes—
23#14583179—24no—
24C2×#13063258C2212yes—
25C2×C4⋊(C43⋊C8)C2211yescharacteristic
26C2×#13063246C2212yes—
27C2×#13063246C2212yes—
28C2×(C2×D43)⋊C8C2212yes—
29C2×(C2×D43)⋊C8C2212yes—
30#14582815—22no—
31#14582769C2211yescharacteristic
32#14582759—21no—
33#14582756C2212yes—
34#14582662C2212yes—
35#14582662C2212yes—
36#14582661C2212yes—
37C22×D8×C43C2211yescharacteristic
38C2×C4×D4×C43C2211yescharacteristic
39C2×C4×D4×C43C2211yescharacteristic
40C4×D8×C43—24no—
41C2×#107×C43C2211yescharacteristic
42C2×#102×C43C2211yescharacteristic
43C2×#102×C43C2211yescharacteristic
44C2×C4×C8×C43C2211yescharacteristic
45C2×#10621898—28no—
46C2×#10621898—44no—
47C2×#10621898—44no—
48C22×Dic86—21no—
49C22×D172D411yescharacteristic
50C22×C22⋊D43—22no—
51C22×C22⋊D43—22no—
52C22×C4×D43—22no—
53C22×C4×D43C2312yes—
54C22×C43⋊C8C2312yes—
55#13063325—22no—
56#13063325D414yescomplemented
57#13063307—216no—
58#13063304—28no—
59#13063299—44no—
60#13063296—24no—
61#13063296—24no—
62#13063296—24no—
63#13063296—42no—
64C4×D172—22no—
65C4×D172—22no—
66C2×C4⋊Dic43—21no—
67C2×C4⋊Dic43—21no—
68C2×C4⋊Dic43—21no—
69C2×C4⋊Dic43D411yescharacteristic
70C2×C4⋊Dic43C2312yes—
71C2×C4⋊Dic43C2312yes—
72C2×Dic43⋊C4—22no—
73C4⋊C4×D43—24no—
74C4⋊C4×D43—24no—
75C2×C22⋊Dic43—22no—
76C2×C22⋊Dic43—22no—
77C2×(C2×D43)⋊C4—22no—
78C2×(C2×D43)⋊C4D412yes—
79#13063258—24no—
80C4⋊(C43⋊C8)—22no—
81#13063246—24no—
82#13063246—42no—
83(C2×D43)⋊C8—24no—
84(C2×D43)⋊C8—42no—
85C43⋊#95—22no—
86C22×D4×C43C2311yescharacteristic
87C22×D4×C43C2311yescharacteristic
88C23×C4×C43—21no—
89C23×C4×C43—21no—
90C2×D8×C43—22no—
91C2×D8×C43—22no—
92C2×D8×C43—22no—
93C22×C8×C43C2311yescharacteristic
94C22×C8×C43C2311yescharacteristic
95C4×D4×C43—22no—
96C4×D4×C43—22no—
97C4×D4×C43—22no—
98C4×D4×C43D414yescomplemented
99C2×C4⋊C4×C43C2311yescharacteristic
100C2×C4⋊C4×C43C2311yescharacteristic
101C2×C22⋊C4×C43—21no—
102C2×C22⋊C4×C43—21no—
103C2×C42×C43C2311yescharacteristic
104#107×C43—22no—
105#102×C43—22no—
106#102×C43—22no—
107C4×C8×C43—22no—
108C24×C43—21no—
109C24×C43—21no—
110C23×D43C2×D412yes—
111C2×D4×C43—21no—
112C2×D4×C43—21no—
113C2×D4×C43—21no—
114C2×D4×C43—21no—
115C2×D4×C43—21no—
116C2×D4×C43—21no—
117C2×D4×C43—21no—
118C2×D4×C43—21no—
119C2×D4×C43—21no—
120C2×D4×C43—21no—
121C2×D4×C43C2×D412yes—
122C2×D4×C43#4112yescomplemented
123C22×C4×C43—24no—
124C22×C4×C43—21no—
125C22×C4×C43—21no—
126C22×C4×C43—42no—
127C22×C4×C43—42no—
128C22×C4×C43—42no—
129C22×C4×C43—42no—
130C22×C4×C43—42no—
131C22×C4×C43C2×D411yescharacteristic
132C22×C4×C43C2×D411yescharacteristic
133C22×C4×C43C2411yescharacteristic
134C2×C22⋊D43—28no—
135C2×C22⋊D43—44no—
136C2×C22⋊D43—44no—
137C2×C22⋊D43—44no—
138C2×C22⋊D43—44no—
139C2×C22⋊D43—82no—
140C22×Dic43—22no—
141C22×Dic43—22no—
142C22×Dic43C2×D412yes—
143#10621898—432no—
144C2×D172—22no—
145C2×D172—22no—
146C2×D172D814yescomplemented
147C2×C4×D43—28no—
148C2×C4×D43—22no—
149C2×C4×D43—22no—
150C2×C4×D43—22no—
151C2×C4×D43—22no—
152C2×C4×D43—22no—
153C2×C4×D43—22no—
154C2×C4×D43—44no—
155C2×C4×D43—44no—
156C2×Dic86—24no—
157C2×Dic86—42no—
158C2×Dic86—42no—
159D8×C43—28no—
160C2×C8×C43—21no—
161C2×C8×C43—21no—
162C2×C8×C43—21no—
163C2×C8×C43—21no—
164C2×C8×C43—21no—
165C2×C8×C43#4112yescomplemented
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43C2×D412yes—
170C22⋊C4×C43—24no—
171C22⋊C4×C43—42no—
172C42×C43C2×D412yes—
173C42×C43C2×D412yes—
174C22⋊Dic43—28no—
175C22⋊Dic43—44no—
176(C2×D43)⋊C4—24no—
177(C2×D43)⋊C4—44no—
178C4⋊Dic43—24no—
179C4⋊Dic43—22no—
180C4⋊Dic43—22no—
181C4⋊Dic43—22no—
182C4⋊Dic43—22no—
183C4⋊Dic43—42no—
184C4⋊Dic43—81no—
185C4⋊Dic43C2×D414yes—
186Dic43⋊C4—28no—
187C2×C43⋊C8—22no—
188C2×C43⋊C8—22no—
189C2×C43⋊C8—22no—
190C23×C43—22no—
191C23×C43—22no—
192C23×C43—41no—
193C23×C43—41no—
194C23×C43—41no—
195C23×C43—41no—
196C23×C43—41no—
197C23×C43—41no—
198C23×C43—41no—
199C23×C43—41no—
200C23×C43—41no—
201C23×C43—41no—
202C23×C43—41no—
203C23×C43—41no—
204C23×C43C22×D411yescharacteristic
205C22×D43—22no—
206C22×D43—22no—
207C22×D43—22no—
208C22×D43—22no—
209C22×D43—22no—
210C22×D43—22no—
211C22×D43C2×D814yes—
212D4×C43—22no—
213D4×C43—22no—
214D4×C43—22no—
215D4×C43—22no—
216D4×C43—41no—
217D4×C43—41no—
218D4×C43—41no—
219D4×C43—41no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—22no—
223C2×C4×C43—41no—
224C2×C4×C43—41no—
225C2×C4×C43—48no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—84no—
230C2×C4×C43#12012yes—
231C2×C4×C43#12012yes—
232C2×C4×C43C2×D812yes—
233C2×C4×C43AGL(1,ℤ/8)12yes—
234C2×C4×C43C22×D411yescharacteristic
235C2×C4×C43C22×D411yescharacteristic
236C2×C4×C43C2×#4111yescharacteristic
237C2×C4×C43C2×#4111yescharacteristic
238C2×C4×C43H(5,𝔽2)11yescharacteristic
239C2×C4×C432−1+411yescharacteristic
240C22⋊D43—416no—
241C22⋊D43—88no—
242C2×Dic43—22no—
243C2×Dic43—24no—
244C2×Dic43—22no—
245C2×Dic43—22no—
246C2×Dic43—42no—
247C2×Dic43—42no—
248C2×Dic43—42no—
249C2×Dic43—42no—
250C2×Dic43—42no—
251D172—28no—
252C4×D43—416no—
253C4×D43—42no—
254C4×D43—42no—
255C4×D43—42no—
256C4×D43—42no—
257Dic86—48no—
258C8×C43—22no—
259C8×C43—41no—
260C43⋊C8—42no—
261#24116—431nomaximal, Sylow
262C22×C43—42no—
263C22×C43—42no—
264C22×C43—42no—
265C22×C43—42no—
266C22×C43—42no—
267C22×C43—42no—
268C22×C43—81no—
269C22×C43—81no—
270C22×C43—81no—
271C22×C43—81no—
272C22×C43—81no—
273C22×C43—81no—
274C22×C43—81no—
275C22×C43—81no—
276C22×C43C2×#12011yescharacteristic
277C22×C43#54611yescharacteristic
278C22×C43#54711yescharacteristic
279C22×C43C22×D811yescharacteristic
280C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
281C22×C43#57711yescharacteristic
282C22×C43#57811yescharacteristic
283C2×D43—24no—
284C2×D43—24no—
285C2×D43—24no—
286C2×D43—42no—
287C2×D43—42no—
288C2×D43—42no—
289C2×D43—42no—
290C4×C43—22no—
291C4×C43—42no—
292C4×C43—81no—
293C4×C43#44714yes—
294C4×C43#52511yescharacteristic
295C4×C43#53711yescharacteristic
296C4×C43#54811yescharacteristic
297C4×C43#55011yescharacteristic
298Dic43—42no—
299Dic43—44no—
300Dic43—82no—
301C2×#547—431no—
302C2×#474—431no—
303C2×C4×D8D4311yescharacteristic, complemented
304#2537—431no—
305#2033—432no—
306#1999—432no—
307#1990—431no—
308#1954—431no—
309#1874—432no—
310#1852—432no—
311#1802—431no—
312C2×C43—82no—
313C2×C43—82no—
314C2×C43#240711yescharacteristic
315C2×C43C2×#44711yescharacteristic
316C2×C43#301311yescharacteristic
317C2×C43#329411yescharacteristic
318C2×C43#333011yescharacteristic
319C2×C43#333411yescharacteristic
320C2×C43#335411yescharacteristic
321D43—44no—
322C22×#41—861no—
323C22×D8C2×D4311yescharacteristic
324#547—864no—
325#547—864no—
326C2×C4⋊Q8—431no—
327C2×#123—862no—
328C2×C22⋊Q8—861no—
329C2×#121—432no—
330C2×#121—432no—
331C2×#121—861no—
332C2×C4×D4—431no—
333C2×C4×D4C2×D4311yescharacteristic
334C2×C4×D4C2×D4311yescharacteristic
335C22×C4⋊C4—432no—
336#474—864no—
337C4×D8—24no—
338C2×#107—432no—
339C2×#107C2×D4311yescharacteristic
340C2×C4⋊C8—431no—
341C2×#102—432no—
342C2×#102—432no—
343C2×#102C2×D4311yescharacteristic
344C2×#102C2×D4311yescharacteristic
345C2×C22⋊C8—432no—
346C2×C22⋊C8—432no—
347C2×C4×C8C2×D4311yescharacteristic
348#394—862no—
349#384—431no—
350#380—432no—
351#380—861no—
352#340—432no—
353#340—432no—
354#340—432no—
355C43#2411611yescharacteristic, complemented, Sylow
356C2×#41—868no—
357C2×#41—1724no—
358C2×#41—1724no—
359C22×Q8—861no—
360C22×D4—431no—
361C22×D4—862no—
362C22×D4—862no—
363C22×D4C22×D4311yescharacteristic
364C22×D4C22×D4311yescharacteristic
365C23×C4—21no—
366C23×C4—21no—
367C23×C4—432no—
368C23×C4—862no—
369C2×D8—22no—
370C2×D8—22no—
371C2×D8—22no—
372C22×C8—432no—
373C22×C8C22×D4311yescharacteristic
374C22×C8C22×D4311yescharacteristic
375C4⋊Q8—434no—
376C4⋊Q8—862no—
377#123—8616no—
378C22⋊Q8—868no—
379#121—864no—
380#121—864no—
381#121—864no—
382#121—1722no—
383#121—1724no—
384C4×D4—22no—
385C4×D4—22no—
386C4×D4—22no—
387C4×D4—862no—
388C4×D4—862no—
389C4×D4C22⋊D4314yescomplemented
390C2×C4⋊C4—432no—
391C2×C4⋊C4—431no—
392C2×C4⋊C4—432no—
393C2×C4⋊C4—864no—
394C2×C4⋊C4—862no—
395C2×C4⋊C4—861no—
396C2×C4⋊C4—864no—
397C2×C4⋊C4—861no—
398C2×C4⋊C4—861no—
399C2×C4⋊C4C22×D4311yescharacteristic
400C2×C4⋊C4C22×D4311yescharacteristic
401C2×C22⋊C4—21no—
402C2×C22⋊C4—21no—
403C2×C22⋊C4—432no—
404C2×C22⋊C4—862no—
405C2×C22⋊C4—862no—
406C2×C22⋊C4—862no—
407C2×C42C22×D4311yescharacteristic
408#107—22no—
409#107—864no—
410C4⋊C8—862no—
411#102—22no—
412#102—22no—
413#102—864no—
414#102—1722no—
415C22⋊C8—864no—
416C22⋊C8—1722no—
417C4×C8—22no—
418#95—862no—
419C24—21no—
420C24—21no—
421C24—432no—
422#41—17232no—
423C2×Q8—864no—
424C2×Q8—1722no—
425C2×Q8—1722no—
426C2×D4—21no—
427C2×D4—21no—
428C2×D4—21no—
429C2×D4—21no—
430C2×D4—21no—
431C2×D4—21no—
432C2×D4—21no—
433C2×D4—21no—
434C2×D4—21no—
435C2×D4—21no—
436C2×D4—434no—
437C2×D4—868no—
438C2×D4—862no—
439C2×D4—862no—
440C2×D4—3442no—
441C2×D4—1724no—
442C2×D4—1724no—
443C2×D4—1724no—
444C2×D4—1724no—
445C2×D4#1062189812yescomplemented
446C2×D4C2×C22⋊D4312yes—
447C22×C4—21no—
448C22×C4—24no—
449C22×C4—21no—
450C22×C4—42no—
451C22×C4—42no—
452C22×C4—42no—
453C22×C4—42no—
454C22×C4—42no—
455C22×C4—432no—
456C22×C4—868no—
457C22×C4—862no—
458C22×C4—862no—
459C22×C4—862no—
460C22×C4—862no—
461C22×C4—862no—
462C22×C4—862no—
463C22×C4—862no—
464C22×C4—862no—
465C22×C4—1724no—
466C22×C4—1724no—
467C22×C4D4×D4311yescharacteristic
468C22×C4D4×D4311yescharacteristic
469C22×C4C23×D4311yescharacteristic
470D8—28no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—862no—
477C2×C8—862no—
478C2×C8—862no—
479C2×C8#1062189812yescomplemented
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—434no—
484C4⋊C4—868no—
485C4⋊C4—862no—
486C4⋊C4—864no—
487C4⋊C4—862no—
488C4⋊C4—862no—
489C4⋊C4—862no—
490C4⋊C4—3441no—
491C4⋊C4—1722no—
492C4⋊C4C2×C22⋊D4312yes—
493C22⋊C4—24no—
494C22⋊C4—42no—
495C22⋊C4—868no—
496C22⋊C4—864no—
497C22⋊C4—1724no—
498C22⋊C4—1724no—
499C42D4×D4312yes—
500C42C2×C22⋊D4312yes—
501C23—22no—
502C23—22no—
503C23—41no—
504C23—41no—
505C23—41no—
506C23—41no—
507C23—41no—
508C23—41no—
509C23—41no—
510C23—41no—
511C23—41no—
512C23—41no—
513C23—41no—
514C23—41no—
515C23—434no—
516C23—862no—
517C23—862no—
518C23—862no—
519C23—862no—
520C23—862no—
521C23—862no—
522C23C2×D4×D4311yescharacteristic
523Q8—1728no—
524D4—22no—
525D4—22no—
526D4—22no—
527D4—22no—
528D4—41no—
529D4—41no—
530D4—41no—
531D4—41no—
532D4—868no—
533D4—3448no—
534D4—17216no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—22no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—48no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—84no—
545C2×C4—862no—
546C2×C4—862no—
547C2×C4—864no—
548C2×C4—862no—
549C2×C4—17216no—
550C2×C4—1722no—
551C2×C4—1722no—
552C2×C4—1722no—
553C2×C4—1722no—
554C2×C4—1722no—
555C2×C4—1722no—
556C2×C4—1722no—
557C2×C4—1722no—
558C2×C4—1722no—
559C2×C4#1306329312yes—
560C2×C4#1306329312yes—
561C2×C4D8×D4312yes—
562C2×C4#1306334912yes—
563C2×C4C2×D4×D4311yescharacteristic
564C2×C4C22×C22⋊D4311yescharacteristic
565C2×C4C2×#1062189811yescharacteristic
566C2×C4C2×#1062189811yescharacteristic
567C2×C4#1306337111yescharacteristic
568C2×C4#1306337211yescharacteristic
569C8—22no—
570C8—41no—
571C8—1722no—
572C22—42no—
573C22—42no—
574C22—42no—
575C22—42no—
576C22—42no—
577C22—42no—
578C22—81no—
579C22—81no—
580C22—81no—
581C22—81no—
582C22—81no—
583C22—81no—
584C22—81no—
585C22—81no—
586C22—864no—
587C22—864no—
588C22—864no—
589C22—1722no—
590C22—1722no—
591C22—1722no—
592C22—1722no—
593C22C2×#1306329311yescharacteristic
594C22#1458354511yescharacteristic
595C22#1458355411yescharacteristic
596C22C2×D8×D4311yescharacteristic
597C22C2×#1306334911yescharacteristic
598C22#1458370611yescharacteristic
599C22#1458371311yescharacteristic
600C4—22no—
601C4—42no—
602C4—81no—
603C4—3442no—
604C4—1724no—
605C4—1722no—
606C4#1458303114yes—
607C4#1458341011yescharacteristic
608C4#1458347711yescharacteristic
609C4#1458355811yescharacteristic
610C4#1458357011yescharacteristic
611C2—82no—
612C2—82no—
613C2—1724no—
614C2#1913794011yescharacteristic
615C2C2×#1458303111yescharacteristic
616C2#1914390611yescharacteristic
617C2#1914641011yescharacteristic
618C2#1914690211yescharacteristic
619C2#1914694411yescharacteristic
620C2#1914719211yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C4×D8×C43C2
socleC23×C43C22×D4
hypercenterC2×C4×D8D43
hypocenterC43#24116
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×D8

Complements

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

NH ≅ G/Ntype
1. C2×#14583554C2semidirect
2. C2×#14583179C2semidirect
3. #19139508C2semidirect
4. #19135775C2semidirect
5. #19135590C2semidirect
6. #19135556C2semidirect
7. #19135389C2semidirect
8. #19134909C2semidirect
9. #19134781C2semidirect
10. #19134595C2semidirect
11. C2×C4×D8×C43C2semidirect
56. #13063325D4semidirect
98. C4×D4×C43D4semidirect
122. C2×D4×C43#41semidirect
146. C2×D172D8semidirect
165. C2×C8×C43#41semidirect
303. C2×C4×D8D43semidirect
355. C43#24116semidirect
389. C4×D4C22⋊D43semidirect
445. C2×D4#10621898semidirect
479. C2×C8#10621898semidirect

Maximal subgroups

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

subgroupindex
C2×#145835542
C2×#145831792
#191395082
#191357752
#191355902
#191355562
#191353892
#191349092
#191347812
#191345952
C2×C4×D8×C432
#2411643