Finite Group Databasebeta

← #25104277

Subgroups — #25104277

Order 11008.

936 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583199C211yesmaximal, characteristic
2C4×#13063317C211yesmaximal, characteristic, complemented
3#19135552C211yesmaximal, characteristic, complemented
4#19135363C211yesmaximal, characteristic, complemented
5#19135180C211yesmaximal, characteristic, complemented
6#19135166C211yesmaximal, characteristic, complemented
7#19134856C211yesmaximal, characteristic
8#19134842C211yesmaximal, characteristic
9#19134605C211yesmaximal, characteristic
10#19134493C211yesmaximal, characteristic, complemented
11#19134493C211yesmaximal, characteristic, complemented
12#19134448C211yesmaximal, characteristic, complemented
13#19134420C211yesmaximal, characteristic
14#19134420C211yesmaximal, characteristic
15C42×D4×C43C211yesmaximal, characteristic
16C2×#13063317C2211yescharacteristic
17#14583199C418yescomplemented
18C2×#13063258C2211yescharacteristic
19C2×#13063258C2211yescharacteristic
20C2×#13063256C2211yescharacteristic
21C2×#13063256C2211yescharacteristic
22C2×C4⋊(C43⋊C8)C2211yescharacteristic
23C2×C4⋊(C43⋊C8)C2211yescharacteristic
24C2×#13063246C2211yescharacteristic
25C2×#13063246C2211yescharacteristic
26C2×#13063246C2211yescharacteristic
27C2×#13063246C2211yescharacteristic
28C2×#13063236C2211yescharacteristic
29C2×#13063236C2211yescharacteristic
30#14582797C2211yescharacteristic
31#14582797C2211yescharacteristic
32#14582783—21no—
33#14582783—21no—
34#14582765C2211yescharacteristic
35C4×Dic43⋊C4—21no—
36C4×Dic43⋊C4—21no—
37C4×C4⋊Dic43C2211yescharacteristic
38C4×C4⋊Dic43C2211yescharacteristic
39#14582661C2211yescharacteristic
40#14582661C2211yescharacteristic
41#14582661C2211yescharacteristic
42#14582661C2211yescharacteristic
43#14582661C2211yescharacteristic
44#14582661C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582654C2211yescharacteristic
48#14582654C2211yescharacteristic
49C2×C4×D4×C43C2211yescharacteristic
50C2×C4×D4×C43C2211yescharacteristic
51C2×C4×D4×C43C2211yescharacteristic
52C22×C42×C43—21no—
53C4×C4⋊C4×C43C2211yescharacteristic
54C4×C4⋊C4×C43C2211yescharacteristic
55C4×C4⋊C4×C43C2211yescharacteristic
56C4×C22⋊C4×C43—21no—
57C4×C22⋊C4×C43—21no—
58C4×C22⋊C4×C43—21no—
59C43×C43C2211yescharacteristic
60C22×C43⋊C8C2311yescharacteristic
61C22×C43⋊C8C2311yescharacteristic
62C22×C43⋊C8C2311yescharacteristic
63C22×C43⋊C8C2311yescharacteristic
64#13063317—22no—
65#13063317C2×C414yescomplemented
66C2×C4⋊Dic43C2311yescharacteristic
67C2×C4⋊Dic43C2311yescharacteristic
68C2×C4⋊Dic43C2311yescharacteristic
69C2×C4⋊Dic43C2311yescharacteristic
70C2×Dic43⋊C4—21no—
71C2×Dic43⋊C4—21no—
72C2×Dic43⋊C4—21no—
73C2×Dic43⋊C4—21no—
74C2×C4×Dic43—21no—
75C2×C4×Dic43—21no—
76#13063258—22no—
77#13063258C2×C414yescomplemented
78#13063256—22no—
79#13063256C2×C414yescomplemented
80C4⋊(C43⋊C8)—22no—
81C4⋊(C43⋊C8)C2×C414yescomplemented
82#13063246—22no—
83#13063246—22no—
84#13063246C2×C414yes—
85#13063246C2×C414yes—
86#13063236—22no—
87#13063236—22no—
88C43⋊#95—21no—
89C43⋊#95—21no—
90C43⋊#95—21no—
91C43⋊#95—21no—
92C43⋊#95—21no—
93C43⋊#95—21no—
94C22×D4×C43C2311yescharacteristic
95C23×C4×C43—21no—
96C23×C4×C43—21no—
97C23×C4×C43—21no—
98C4×D4×C43—22no—
99C4×D4×C43—22no—
100C4×D4×C43—22no—
101C4×D4×C43—22no—
102C4×D4×C43C2×C414yes—
103C4×D4×C43Q814yes—
104C2×C4⋊C4×C43C2311yescharacteristic
105C2×C4⋊C4×C43C2311yescharacteristic
106C2×C4⋊C4×C43C2311yescharacteristic
107C2×C22⋊C4×C43—21no—
108C2×C22⋊C4×C43—21no—
109C2×C22⋊C4×C43—21no—
110C2×C42×C43—21no—
111C2×C42×C43—21no—
112C2×C42×C43—21no—
113C2×C42×C43—44no—
114C2×C42×C43D411yescharacteristic
115C2×C42×C43D411yescharacteristic
116C2×C42×C43D411yescharacteristic
117C2×C42×C43D411yescharacteristic
118C2×C42×C43C2311yescharacteristic
119C2×C42×C43C2311yescharacteristic
120C2×C42×C43C2311yescharacteristic
121#95×C43—21no—
122#95×C43—21no—
123#95×C43—21no—
124C24×C43—21no—
125C2×D4×C43—21no—
126C2×D4×C43—21no—
127C2×D4×C43—21no—
128C2×D4×C43C22×C412yes—
129C2×D4×C43C2×Q812yes—
130C2×D4×C43#4112yes—
131C22×C4×C43—24no—
132C22×C4×C43—24no—
133C22×C4×C43—24no—
134C22×C4×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43—42no—
138C22×C4×C43—42no—
139C22×C4×C43—42no—
140C22×C4×C43—42no—
141C22×C4×C43—42no—
142C22×C4×C43—42no—
143C22×C4×C43C2×D411yescharacteristic
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×C43C22×C412yes—
158C4⋊C4×C43C2×Q812yes—
159C4⋊C4×C43#4112yes—
160C22⋊C4×C43—24no—
161C22⋊C4×C43—24no—
162C22⋊C4×C43—24no—
163C42×C43—22no—
164C42×C43—21no—
165C42×C43—21no—
166C42×C43—41no—
167C42×C43—41no—
168C42×C43—41no—
169C42×C43—42no—
170C42×C43—42no—
171C42×C43—42no—
172C42×C43C22×C412yes—
173C42×C43C2×Q812yes—
174C42×C43#4112yes—
175C42×C43#4112yes—
176C4⋊Dic43—21no—
177C4⋊Dic43—21no—
178C4⋊Dic43—21no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43C22×C412yes—
183C4⋊Dic43C22×C412yes—
184Dic43⋊C4—24no—
185Dic43⋊C4—24no—
186Dic43⋊C4—42no—
187Dic43⋊C4—42no—
188C4×Dic43—42no—
189C4×Dic43—42no—
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⋊C8C22×C412yes—
201C2×C43⋊C8C22×C412yes—
202C23×C43—22no—
203C23×C43—22no—
204C23×C43—22no—
205C23×C43—41no—
206C23×C43—41no—
207C23×C43—41no—
208C23×C43—41no—
209C23×C43C22×D411yescharacteristic
210D4×C43—22no—
211D4×C43—22no—
212D4×C43—22no—
213D4×C43C4×Q814yes—
214C2×C4×C43—21no—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—22no—
225C2×C4×C43—22no—
226C2×C4×C43—21no—
227C2×C4×C43—22no—
228C2×C4×C43—21no—
229C2×C4×C43—21no—
230C2×C4×C43—48no—
231C2×C4×C43—48no—
232C2×C4×C43—48no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43C4×D412yes—
240C2×C4×C43C4×D412yes—
241C2×C4×C43C22⋊Q812yes—
242C2×C4×C43C22⋊Q812yes—
243C2×C4×C43AGL(1,ℤ/8)12yes—
244C2×C4×C43C23×C411yescharacteristic
245C2×C4×C43C22×Q811yescharacteristic
246C2×C4×C43C2×#4111yescharacteristic
247C2×C4×C43C2×#4111yescharacteristic
248C2×C4×C43C2×#4111yescharacteristic
249C2×C4×C43C2×#4111yescharacteristic
250C2×Dic43—22no—
251C2×Dic43—22no—
252C2×Dic43—41no—
253C2×Dic43—41no—
254C2×Dic43—41no—
255C2×Dic43—41no—
256C2×Dic43—41no—
257C2×Dic43—41no—
258C2×Dic43—41no—
259C2×Dic43—41no—
260C2×Dic43—41no—
261C2×Dic43—41no—
262C43⋊C8—22no—
263C43⋊C8—22no—
264C43⋊C8—41no—
265C43⋊C8—41no—
266#21617—431nomaximal, Sylow
267C22×C43—24no—
268C22×C43—42no—
269C22×C43—42no—
270C22×C43—42no—
271C22×C43—42no—
272C22×C43—42no—
273C22×C43—42no—
274C22×C43C2×C4×D411yescharacteristic
275C22×C43C2×C22⋊Q811yescharacteristic
276C22×C43#52511yescharacteristic
277C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
278C22×C43#57511yescharacteristic
279C22×C43#57511yescharacteristic
280C22×C43#57511yescharacteristic
281C4×C43—22no—
282C4×C43—22no—
283C4×C43—22no—
284C4×C43—22no—
285C4×C43—22no—
286C4×C43—42no—
287C4×C43—41no—
288C4×C43—42no—
289C4×C43—42no—
290C4×C43C2×C4×Q811yescharacteristic
291C4×C43C4×#4111yescharacteristic
292C4×C43#52911yescharacteristic
293C4×C43#53311yescharacteristic
294Dic43—42no—
295Dic43—42no—
296Dic43—81no—
297Dic43—81no—
298C2×#478—431no—
299C4×#125—431no—
300C42×D4D4311yescharacteristic
301#1989—431no—
302#1949—431no—
303#1920—431no—
304#1918—431no—
305#1864—431no—
306#1862—431no—
307#1804—431no—
308#1776—431no—
309#1776—431no—
310#1767—431no—
311#1762—431no—
312#1762—431no—
313C2×C43—44no—
314C2×C43C4×C22⋊Q811yescharacteristic
315C2×C43#294311yescharacteristic
316C2×C43C4×AGL(1,ℤ/8)11yescharacteristic
317C2×C43#307711yescharacteristic
318C2×C43#308011yescharacteristic
319C2×C43#311111yescharacteristic
320C2×C43#311411yescharacteristic
321C2×#125—431no—
322C2×C4×D4C2×D4311yescharacteristic
323C2×C4×D4C2×D4311yescharacteristic
324C2×C4×D4C2×D4311yescharacteristic
325C22×C42—21no—
326#478—438no—
327C2×#107—431no—
328C2×#107—431no—
329C2×#106—431no—
330C2×#106—431no—
331C2×C4⋊C8—431no—
332C2×C4⋊C8—431no—
333C2×#102—431no—
334C2×#102—431no—
335C2×#102—431no—
336C2×#102—431no—
337C2×#97—431no—
338C2×#97—431no—
339#389—431no—
340#389—431no—
341#387—861no—
342#387—861no—
343#382—431no—
344C4×C4⋊C4—431no—
345C4×C4⋊C4—431no—
346C4×C4⋊C4—861no—
347C4×C4⋊C4—861no—
348C4×C4⋊C4C2×D4311yescharacteristic
349C4×C4⋊C4C2×D4311yescharacteristic
350C4×C4⋊C4C2×D4311yescharacteristic
351C4×C22⋊C4—21no—
352C4×C22⋊C4—21no—
353C4×C22⋊C4—21no—
354C43C2×D4311yescharacteristic
355#340—431no—
356#340—431no—
357#340—431no—
358#340—431no—
359#340—431no—
360#340—431no—
361#340—431no—
362#340—431no—
363#336—431no—
364#336—431no—
365C43#2161711yescharacteristic, complemented, Sylow
366C22×D4C22×D4311yescharacteristic
367C23×C4—21no—
368C23×C4—21no—
369C23×C4—21no—
370C22×C8—431no—
371C22×C8—431no—
372C22×C8—431no—
373C22×C8—431no—
374#125—434no—
375#125—862no—
376C4×D4—22no—
377C4×D4—22no—
378C4×D4—22no—
379C4×D4—22no—
380C4×D4Dic8614yes—
381C4×D4C4×D4314yes—
382C2×C4⋊C4—431no—
383C2×C4⋊C4—431no—
384C2×C4⋊C4—431no—
385C2×C4⋊C4—431no—
386C2×C4⋊C4—861no—
387C2×C4⋊C4—861no—
388C2×C4⋊C4—861no—
389C2×C4⋊C4—861no—
390C2×C4⋊C4C22×D4311yescharacteristic
391C2×C4⋊C4C22×D4311yescharacteristic
392C2×C4⋊C4C22×D4311yescharacteristic
393C2×C22⋊C4—21no—
394C2×C22⋊C4—21no—
395C2×C22⋊C4—21no—
396C2×C42—21no—
397C2×C42—21no—
398C2×C42—21no—
399C2×C42—44no—
400C2×C42—861no—
401C2×C42—861no—
402C2×C42C22⋊D4311yescharacteristic
403C2×C42C22⋊D4311yescharacteristic
404C2×C42C22⋊D4311yescharacteristic
405C2×C42C22⋊D4311yescharacteristic
406C2×C42C22×D4311yescharacteristic
407C2×C42C22×D4311yescharacteristic
408C2×C42C22×D4311yescharacteristic
409#107—434no—
410#107—862no—
411#106—434no—
412#106—862no—
413C4⋊C8—434no—
414C4⋊C8—862no—
415#102—434no—
416#102—434no—
417#102—862no—
418#102—862no—
419#97—862no—
420#97—862no—
421#95—21no—
422#95—21no—
423#95—21no—
424#95—861no—
425#95—861no—
426#95—861no—
427#95—861no—
428#95—861no—
429#95—861no—
430C24—21no—
431C2×D4—21no—
432C2×D4—21no—
433C2×D4—21no—
434C2×D4C2×Dic8612yes—
435C2×D4C2×C4×D4312yes—
436C2×D4#1062189812yes—
437C22×C4—24no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—24no—
442C22×C4—24no—
443C22×C4—42no—
444C22×C4—42no—
445C22×C4—42no—
446C22×C4—42no—
447C22×C4—42no—
448C22×C4—42no—
449C22×C4—861no—
450C22×C4—861no—
451C22×C4—861no—
452C22×C4—861no—
453C22×C4C2×C22⋊D4311yescharacteristic
454C22×C4C2×C22⋊D4311yescharacteristic
455C22×C4C2×C22⋊D4311yescharacteristic
456C22×C4C2×C22⋊D4311yescharacteristic
457C22×C4C2×C22⋊D4311yescharacteristic
458C22×C4C2×C22⋊D4311yescharacteristic
459C22×C4C23×D4311yescharacteristic
460C2×C8—432no—
461C2×C8—432no—
462C2×C8—861no—
463C2×C8—861no—
464C2×C8—861no—
465C2×C8—861no—
466C2×C8—861no—
467C2×C8—861no—
468C2×C8—861no—
469C2×C8—861no—
470C2×C8—861no—
471C2×C8—861no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—432no—
476C4⋊C4—432no—
477C4⋊C4—864no—
478C4⋊C4—864no—
479C4⋊C4—861no—
480C4⋊C4—861no—
481C4⋊C4—861no—
482C4⋊C4—861no—
483C4⋊C4—861no—
484C4⋊C4—861no—
485C4⋊C4—1722no—
486C4⋊C4—1722no—
487C4⋊C4C2×Dic8612yes—
488C4⋊C4C2×C4×D4312yes—
489C4⋊C4#1062189812yes—
490C22⋊C4—24no—
491C22⋊C4—24no—
492C22⋊C4—24no—
493C42—22no—
494C42—21no—
495C42—21no—
496C42—41no—
497C42—41no—
498C42—41no—
499C42—42no—
500C42—42no—
501C42—42no—
502C42—1722no—
503C42—1722no—
504C42C2×Dic8612yes—
505C42C2×C4×D4312yes—
506C42#1062189812yes—
507C42#1062189812yes—
508C23—22no—
509C23—22no—
510C23—22no—
511C23—41no—
512C23—41no—
513C23—41no—
514C23—41no—
515C23C22×C22⋊D4311yescharacteristic
516D4—22no—
517D4—22no—
518D4—22no—
519D4C4×Dic8614yes—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—21no—
533C2×C4—22no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—48no—
537C2×C4—48no—
538C2×C4—48no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—862no—
546C2×C4—862no—
547C2×C4—1721no—
548C2×C4—1721no—
549C2×C4—1721no—
550C2×C4—1721no—
551C2×C4—1721no—
552C2×C4—1721no—
553C2×C4—1721no—
554C2×C4—1721no—
555C2×C4—1721no—
556C2×C4—1721no—
557C2×C4C4×C22⋊D4312yes—
558C2×C4C4×C22⋊D4312yes—
559C2×C4#1306330412yes—
560C2×C4#1306330412yes—
561C2×C4#1306335112yes—
562C2×C4C22×C4×D4311yescharacteristic
563C2×C4C22×Dic8611yescharacteristic
564C2×C4C2×#1062189811yescharacteristic
565C2×C4C2×#1062189811yescharacteristic
566C2×C4C2×#1062189811yescharacteristic
567C2×C4C2×#1062189811yescharacteristic
568C8—862no—
569C8—862no—
570C8—1721no—
571C8—1721no—
572C22—24no—
573C22—42no—
574C22—42no—
575C22—42no—
576C22—42no—
577C22—42no—
578C22—42no—
579C22C2×C4×C22⋊D4311yescharacteristic
580C22C2×#1306330411yescharacteristic
581C22#1458341011yescharacteristic
582C22C2×#1306335111yescharacteristic
583C22#1458369711yescharacteristic
584C22#1458369711yescharacteristic
585C22#1458369711yescharacteristic
586C4—22no—
587C4—22no—
588C4—22no—
589C4—22no—
590C4—22no—
591C4—41no—
592C4—42no—
593C4—42no—
594C4—42no—
595C4—3441no—
596C4—3441no—
597C4—1722no—
598C4—1722no—
599C4C2×C4×Dic8611yescharacteristic
600C4C4×#1062189811yescharacteristic
601C4#1458343311yescharacteristic
602C4#1458345611yescharacteristic
603C2—44no—
604C2C4×#1306330411yescharacteristic
605C2#1914339311yescharacteristic
606C2C4×#1306335111yescharacteristic
607C2#1914439211yescharacteristic
608C2#1914441711yescharacteristic
609C2#1914470411yescharacteristic
610C2#1914473311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC42×D4×C43C2
socleC23×C43C22×D4
prime radicalC22×D4×C43C23
cosocleC22×C4×C43C24
hypercenterC42×D4D43
hypocenterC43#21617
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C43 ◁ C42×D4

Complements

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

NH ≅ G/Ntype
2. C4×#13063317C2semidirect
3. #19135552C2semidirect
4. #19135363C2semidirect
5. #19135180C2semidirect
6. #19135166C2semidirect
10. #19134493C2semidirect
11. #19134493C2semidirect
12. #19134448C2semidirect
17. #14583199C4semidirect
65. #13063317C2×C4semidirect
77. #13063258C2×C4semidirect
79. #13063256C2×C4semidirect
81. C4⋊(C43⋊C8)C2×C4semidirect
365. C43#21617semidirect

Maximal subgroups

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

subgroupindex
C2×#145831992
C4×#130633172
#191355522
#191353632
#191351802
#191351662
#191348562
#191348422
#191346052
#191344932
#191344482
#191344202
C42×D4×C432
#2161743