Finite Group Databasebeta

← #25169383

Subgroups — #25169383

Order 11008.

762 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#19139017C211yesmaximal, characteristic, complemented
2#19135998C211yesmaximal, characteristic, complemented
3#19135969C211yesmaximal, characteristic, complemented
4#19135781C211yesmaximal, characteristic
5#19135781C211yesmaximal, characteristic
6#19135358C211yesmaximal, characteristic, complemented
7#19135320C211yesmaximal, characteristic, complemented
8#19135203C211yesmaximal, characteristic, complemented
9#19135187C211yesmaximal, characteristic, complemented
10#19135177C211yesmaximal, characteristic, complemented
11#19134842C211yesmaximal, characteristic, complemented
12#19134794C211yesmaximal, characteristic, complemented
13#19134690C211yesmaximal, characteristic, complemented
14C4×#13063246C211yesmaximal, characteristic, complemented
15C43×#2363C211yesmaximal, characteristic
16C2×#13063318—21no—
17C2×#13063258C2211yescharacteristic
18C2×#13063256C2211yescharacteristic
19C2×#13063256C2211yescharacteristic
20C2×#13063256C2211yescharacteristic
21C2×C4⋊(C43⋊C8)C2211yescharacteristic
22C2×#13063246C2211yescharacteristic
23C2×#13063246C2211yescharacteristic
24C2×#13063246C2211yescharacteristic
25C2×#13063246C2211yescharacteristic
26C2×C22⋊(C43⋊C8)C2211yescharacteristic
27C2×C22⋊(C43⋊C8)C2211yescharacteristic
28C2×C4×C43⋊C8C2211yescharacteristic
29#14582839—21no—
30#14582824—21no—
31#14582797C2211yescharacteristic
32#14582797C2211yescharacteristic
33#14582784—21no—
34#14582769C2211yescharacteristic
35#14582759C2211yescharacteristic
36#14582759C2211yescharacteristic
37C4×C4⋊Dic43C2211yescharacteristic
38#14582661C2211yescharacteristic
39#14582661C2211yescharacteristic
40#14582661C2211yescharacteristic
41#14582661C2211yescharacteristic
42#14582661C2211yescharacteristic
43#14582661C2211yescharacteristic
44#14582661C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582654C2211yescharacteristic
47#14582654C2211yescharacteristic
48C2×#121×C43C2211yescharacteristic
49C2×C4×D4×C43C2211yescharacteristic
50C2×#117×C43C2211yescharacteristic
51C43×#390—21no—
52C43×#390C2211yescharacteristic
53C43×#389C2211yescharacteristic
54C43×#388—21no—
55C43×#386—21no—
56C4×C4⋊C4×C43C2211yescharacteristic
57C4×C22⋊C4×C43—21no—
58C4×C22⋊C4×C43C2211yescharacteristic
59C22×C43⋊C8C2311yescharacteristic
60C22×C43⋊C8C2311yescharacteristic
61C22×C43⋊C8C2311yescharacteristic
62C22×C43⋊C8C2311yescharacteristic
63#13063318—44no—
64C2×C4⋊Dic43—21no—
65C2×C4⋊Dic43—21no—
66C2×C4⋊Dic43C2311yescharacteristic
67C2×C4⋊Dic43C2311yescharacteristic
68C2×C4⋊Dic43C2311yescharacteristic
69C2×C4⋊Dic43C2311yescharacteristic
70C2×Dic43⋊C4—21no—
71C2×Dic43⋊C4—21no—
72C2×C22⋊Dic43—21no—
73C2×C22⋊Dic43—21no—
74C2×C4×Dic43—21no—
75#13063258—22no—
76#13063256—22no—
77#13063256—22no—
78#13063256—41no—
79C4⋊(C43⋊C8)—22no—
80#13063246—22no—
81#13063246—22no—
82#13063246—22no—
83#13063246—41no—
84C22⋊(C43⋊C8)—22no—
85C22⋊(C43⋊C8)—41no—
86C4×C43⋊C8—41no—
87C43⋊#95—21no—
88C43⋊#95—21no—
89C43⋊#95—21no—
90C43⋊#95—21no—
91C43⋊#95—21no—
92C22×D4×C43—21no—
93C22×D4×C43C2311yescharacteristic
94C23×C4×C43—21no—
95C23×C4×C43C2311yescharacteristic
96#121×C43—22no—
97#121×C43—22no—
98C4×D4×C43—22no—
99C4×D4×C43—41no—
100#117×C43—22no—
101#117×C43—41no—
102C2×C4⋊C4×C43—21no—
103C2×C4⋊C4×C43C2311yescharacteristic
104C2×C4⋊C4×C43C2311yescharacteristic
105C2×C4⋊C4×C43C2311yescharacteristic
106C2×C22⋊C4×C43—21no—
107C2×C22⋊C4×C43—21no—
108C2×C22⋊C4×C43—21no—
109C2×C22⋊C4×C43—21no—
110C2×C22⋊C4×C43—21no—
111C2×C22⋊C4×C43D411yescharacteristic
112C2×C22⋊C4×C43D411yescharacteristic
113C2×C42×C43—21no—
114C2×C42×C43—21no—
115C2×C42×C43C2311yescharacteristic
116C2×C42×C43C2311yescharacteristic
117#95×C43—21no—
118#95×C43—21no—
119#95×C43D411yescharacteristic
120#95×C43D411yescharacteristic
121C24×C43—21no—
122C24×C43C2×D411yescharacteristic
123C2×D4×C43—24no—
124C2×D4×C43—21no—
125C2×D4×C43—21no—
126C2×D4×C43—21no—
127C2×D4×C43—21no—
128C2×D4×C43—21no—
129C2×D4×C43—81no—
130C2×D4×C43—81no—
131C2×D4×C43#4112yes—
132C22×C4×C43—21no—
133C22×C4×C43—21no—
134C22×C4×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43—21no—
138C22×C4×C43—21no—
139C22×C4×C43—21no—
140C22×C4×C43—21no—
141C22×C4×C43—42no—
142C22×C4×C43—42no—
143C22×C4×C43—81no—
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43C2×D411yescharacteristic
147C22×C4×C43C2×D411yescharacteristic
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43C2411yescharacteristic
150C22×Dic43—21no—
151C22×Dic43—21no—
152C22×Dic43—21no—
153C22×Dic43—21no—
154C4⋊C4×C43—21no—
155C4⋊C4×C43—21no—
156C4⋊C4×C43—21no—
157C4⋊C4×C43—21no—
158C4⋊C4×C43—81no—
159C4⋊C4×C43#4112yes—
160C4⋊C4×C43#4112yes—
161C22⋊C4×C43—24no—
162C22⋊C4×C43—22no—
163C22⋊C4×C43—22no—
164C22⋊C4×C43—42no—
165C22⋊C4×C43—42no—
166C22⋊C4×C43—42no—
167C22⋊C4×C43—81no—
168C42×C43—21no—
169C42×C43—21no—
170C42×C43—21no—
171C42×C43—21no—
172C42×C43—42no—
173C42×C43—81no—
174C22⋊Dic43—42no—
175C22⋊Dic43—42no—
176C4⋊Dic43—21no—
177C4⋊Dic43—21no—
178C4⋊Dic43—21no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43—42no—
185C4⋊Dic43—42no—
186Dic43⋊C4—42no—
187Dic43⋊C4—42no—
188C4×Dic43—42no—
189C2×C43⋊C8—21no—
190C2×C43⋊C8—21no—
191C2×C43⋊C8—21no—
192C2×C43⋊C8—21no—
193C2×C43⋊C8—21no—
194C2×C43⋊C8—21no—
195C2×C43⋊C8—21no—
196C2×C43⋊C8—21no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8#4112yes—
201C23×C43—22no—
202C23×C43—21no—
203C23×C43—21no—
204C23×C43—21no—
205C23×C43—21no—
206C23×C43—21no—
207C23×C43—21no—
208C23×C43—21no—
209C23×C43—41no—
210C23×C43—41no—
211C23×C43—41no—
212C23×C43—41no—
213C23×C43—41no—
214C23×C43—41no—
215C23×C43C22×D411yescharacteristic
216D4×C43—22no—
217D4×C43—22no—
218D4×C43—41no—
219D4×C43—41no—
220D4×C43—84no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—22no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—22no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
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×C43—41no—
241C2×C4×C43—41no—
242C2×C4×C43—41no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43—41no—
247C2×C4×C43—84no—
248C2×C4×C43#13512yes—
249C2×C4×C43AGL(1,ℤ/8)12yes—
250C2×C4×C43C2×#4111yescharacteristic
251C2×C4×C43C2×#4111yescharacteristic
252C2×C4×C43C2×#4111yescharacteristic
253C2×C4×C43C2×#4111yescharacteristic
254C2×C4×C43H(5,𝔽2)11yescharacteristic
255C2×C4×C432−1+411yescharacteristic
256C2×Dic43—41no—
257C2×Dic43—41no—
258C2×Dic43—41no—
259C2×Dic43—41no—
260C2×Dic43—41no—
261C2×Dic43—41no—
262C2×Dic43—41no—
263C2×Dic43—41no—
264C2×Dic43—41no—
265C2×Dic43—41no—
266C2×Dic43—41no—
267C2×Dic43—41no—
268C43⋊C8—22no—
269C43⋊C8—41no—
270C43⋊C8—41no—
271C43⋊C8—41no—
272#27039—431nomaximal, Sylow
273C22×C43—41no—
274C22×C43—41no—
275C22×C43—41no—
276C22×C43—42no—
277C22×C43—41no—
278C22×C43—42no—
279C22×C43—41no—
280C22×C43—42no—
281C22×C43—41no—
282C22×C43—41no—
283C22×C43—81no—
284C22×C43—81no—
285C22×C43—81no—
286C22×C43—81no—
287C22×C43#52511yescharacteristic
288C22×C43#54611yescharacteristic
289C22×C43#54711yescharacteristic
290C22×C43C2×#13511yescharacteristic
291C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
292C22×C43#57711yescharacteristic
293C22×C43#57711yescharacteristic
294C4×C43—22no—
295C4×C43—22no—
296C4×C43—41no—
297C4×C43—42no—
298C4×C43—41no—
299C4×C43—41no—
300C4×C43—42no—
301C4×C43—81no—
302C4×C43#52911yescharacteristic
303C4×C43#53911yescharacteristic
304C4×C43#55311yescharacteristic
305C4×C43#55611yescharacteristic
306Dic43—81no—
307Dic43—81no—
308Dic43—81no—
309Dic43—81no—
310#2496—431no—
311#2363D4311yescharacteristic
312#2071—431no—
313#2065—431no—
314#2034—431no—
315#2034—431no—
316#1948—431no—
317#1941—431no—
318#1923—431no—
319#1921—431no—
320#1920—431no—
321#1862—431no—
322#1854—431no—
323#1825—431no—
324C4×#102—431no—
325C2×C43—81no—
326C2×C43—82no—
327C2×C43#246611yescharacteristic
328C2×C43#310611yescharacteristic
329C2×C43#312311yescharacteristic
330C2×C43#330411yescharacteristic
331C2×C43#330611yescharacteristic
332C2×C43#333711yescharacteristic
333C2×C43#335411yescharacteristic
334C2×#126—861no—
335C2×#121C2×D4311yescharacteristic
336C2×C4×D4C2×D4311yescharacteristic
337C2×#117C2×D4311yescharacteristic
338C2×#107—431no—
339C2×#106—431no—
340C2×#106—431no—
341C2×#106—431no—
342C2×C4⋊C8—431no—
343C2×#102—431no—
344C2×#102—431no—
345C2×#102—431no—
346C2×#102—431no—
347C2×C22⋊C8—431no—
348C2×C22⋊C8—431no—
349C2×C4×C8—431no—
350#400—861no—
351#397—861no—
352#390—21no—
353#390C2×D4311yescharacteristic
354#389—431no—
355#389—431no—
356#389C2×D4311yescharacteristic
357#388—21no—
358#387—861no—
359#386—21no—
360#384—431no—
361#380—431no—
362#380—431no—
363C4×C4⋊C4—431no—
364C4×C4⋊C4C2×D4311yescharacteristic
365C4×C22⋊C4—21no—
366C4×C22⋊C4C2×D4311yescharacteristic
367#340—431no—
368#340—431no—
369#340—431no—
370#340—431no—
371#340—431no—
372#340—431no—
373#340—431no—
374#340—431no—
375#336—431no—
376#336—431no—
377C43#2703911yescharacteristic, complemented, Sylow
378C22×D4—21no—
379C22×D4C22×D4311yescharacteristic
380C23×C4—21no—
381C23×C4C22×D4311yescharacteristic
382C22×C8—431no—
383C22×C8—431no—
384C22×C8—431no—
385C22×C8—431no—
386#126—1724no—
387#121—22no—
388#121—22no—
389C4×D4—22no—
390C4×D4—41no—
391#117—22no—
392#117—41no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—431no—
395C2×C4⋊C4—431no—
396C2×C4⋊C4—431no—
397C2×C4⋊C4—431no—
398C2×C4⋊C4—861no—
399C2×C4⋊C4—861no—
400C2×C4⋊C4—861no—
401C2×C4⋊C4—861no—
402C2×C4⋊C4C22×D4311yescharacteristic
403C2×C4⋊C4C22×D4311yescharacteristic
404C2×C4⋊C4C22×D4311yescharacteristic
405C2×C22⋊C4—21no—
406C2×C22⋊C4—21no—
407C2×C22⋊C4—21no—
408C2×C22⋊C4—21no—
409C2×C22⋊C4—21no—
410C2×C22⋊C4—861no—
411C2×C22⋊C4—861no—
412C2×C22⋊C4C22⋊D4311yescharacteristic
413C2×C22⋊C4C22⋊D4311yescharacteristic
414C2×C42—21no—
415C2×C42—21no—
416C2×C42—861no—
417C2×C42C22×D4311yescharacteristic
418C2×C42C22×D4311yescharacteristic
419#107—862no—
420#106—862no—
421#106—862no—
422#106—1721no—
423C4⋊C8—862no—
424#102—862no—
425#102—862no—
426#102—862no—
427#102—1721no—
428C22⋊C8—862no—
429C22⋊C8—1721no—
430C4×C8—1721no—
431#95—21no—
432#95—21no—
433#95—861no—
434#95—861no—
435#95—861no—
436#95—861no—
437#95—861no—
438#95C22⋊D4311yescharacteristic
439#95C22⋊D4311yescharacteristic
440C24—21no—
441C24C2×C22⋊D4311yescharacteristic
442C2×D4—24no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—21no—
448C2×D4—81no—
449C2×D4—81no—
450C2×D4#1062189812yes—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—42no—
461C22×C4—42no—
462C22×C4—81no—
463C22×C4—861no—
464C22×C4—861no—
465C22×C4—861no—
466C22×C4—861no—
467C22×C4C2×C22⋊D4311yescharacteristic
468C22×C4C2×C22⋊D4311yescharacteristic
469C22×C4C2×C22⋊D4311yescharacteristic
470C22×C4C2×C22⋊D4311yescharacteristic
471C22×C4C2×C22⋊D4311yescharacteristic
472C22×C4C23×D4311yescharacteristic
473C2×C8—432no—
474C2×C8—861no—
475C2×C8—861no—
476C2×C8—861no—
477C2×C8—861no—
478C2×C8—861no—
479C2×C8—861no—
480C2×C8—861no—
481C2×C8—861no—
482C2×C8—861no—
483C2×C8—861no—
484C2×C8—861no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—81no—
490C4⋊C4—861no—
491C4⋊C4—861no—
492C4⋊C4—861no—
493C4⋊C4—861no—
494C4⋊C4—861no—
495C4⋊C4—861no—
496C4⋊C4—861no—
497C4⋊C4—861no—
498C4⋊C4—1722no—
499C4⋊C4—1722no—
500C4⋊C4—1722no—
501C4⋊C4—1722no—
502C4⋊C4#1062189812yes—
503C4⋊C4#1062190012yes—
504C22⋊C4—24no—
505C22⋊C4—22no—
506C22⋊C4—22no—
507C22⋊C4—42no—
508C22⋊C4—42no—
509C22⋊C4—42no—
510C22⋊C4—81no—
511C22⋊C4—1722no—
512C22⋊C4—1722no—
513C42—21no—
514C42—21no—
515C42—21no—
516C42—21no—
517C42—42no—
518C42—81no—
519C42—1722no—
520C23—22no—
521C23—21no—
522C23—21no—
523C23—21no—
524C23—21no—
525C23—21no—
526C23—21no—
527C23—21no—
528C23—41no—
529C23—41no—
530C23—41no—
531C23—41no—
532C23—41no—
533C23—41no—
534C23C22×C22⋊D4311yescharacteristic
535D4—22no—
536D4—22no—
537D4—41no—
538D4—41no—
539D4—84no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—22no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—22no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—84no—
567C2×C4—1721no—
568C2×C4—1721no—
569C2×C4—1721no—
570C2×C4—1721no—
571C2×C4—1721no—
572C2×C4—1721no—
573C2×C4—1721no—
574C2×C4—1721no—
575C2×C4—1721no—
576C2×C4—1721no—
577C2×C4—1721no—
578C2×C4—1721no—
579C2×C4#1306334512yes—
580C2×C4#1306335012yes—
581C2×C4#41×D4311yescharacteristic
582C2×C4C2×#1062190011yescharacteristic
583C2×C4C2×#1062189811yescharacteristic
584C2×C4C2×#1062189811yescharacteristic
585C2×C4#1306337011yescharacteristic
586C2×C4#1306337211yescharacteristic
587C8—862no—
588C8—1721no—
589C8—1721no—
590C8—1721no—
591C22—41no—
592C22—41no—
593C22—41no—
594C22—42no—
595C22—41no—
596C22—42no—
597C22—41no—
598C22—41no—
599C22—42no—
600C22—41no—
601C22—81no—
602C22—81no—
603C22—81no—
604C22—81no—
605C22#1458341011yescharacteristic
606C22#1458354311yescharacteristic
607C22#1458354811yescharacteristic
608C22C2×#1306334511yescharacteristic
609C22C2×#1306335011yescharacteristic
610C22#1458371011yescharacteristic
611C22#1458371011yescharacteristic
612C4—22no—
613C4—22no—
614C4—41no—
615C4—42no—
616C4—41no—
617C4—42no—
618C4—41no—
619C4—81no—
620C4—3441no—
621C4—3441no—
622C4—3441no—
623C4—3441no—
624C4#1458342911yescharacteristic
625C4#1458349111yescharacteristic
626C4#1458359911yescharacteristic
627C4#1458361911yescharacteristic
628C2—81no—
629C2—82no—
630C2#1913862511yescharacteristic
631C2#1914465511yescharacteristic
632C2#1914484711yescharacteristic
633C2#1914653411yescharacteristic
634C2#1914655611yescharacteristic
635C2#1914696811yescharacteristic
636C2#1914718411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2363C2
socleC23×C43C22×D4
prime radicalC2×#121×C43C22
hypercenter#2363D43
hypocenterC43#27039
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2363

Complements

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

NH ≅ G/Ntype
1. #19139017C2semidirect
2. #19135998C2semidirect
3. #19135969C2semidirect
6. #19135358C2semidirect
7. #19135320C2semidirect
8. #19135203C2semidirect
9. #19135187C2semidirect
10. #19135177C2semidirect
11. #19134842C2semidirect
12. #19134794C2semidirect
13. #19134690C2semidirect
14. C4×#13063246C2semidirect
377. C43#27039semidirect

Maximal subgroups

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

subgroupindex
#191390172
#191359982
#191359692
#191357812
#191353582
#191353202
#191352032
#191351872
#191351772
#191348422
#191347942
#191346902
C4×#130632462
C43×#23632
#2703943