Finite Group Databasebeta

← #25129591

Subgroups — #25129591

Order 11008.

1462 conjugacy classes of subgroups.

The subgroup lattice has 874 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583220C211yesmaximal, characteristic, complemented
2C2×#14582895C211yesmaximal, characteristic, complemented
3#19138892C211yesmaximal, characteristic, complemented
4#19135831C211yesmaximal, characteristic, complemented
5#19135831C211yesmaximal, characteristic, complemented
6#19135795C211yesmaximal, characteristic, complemented
7#19135788C211yesmaximal, characteristic, complemented
8#19135024C211yesmaximal, characteristic, complemented
9#19134888C211yesmaximal, characteristic, complemented
10#19134856C211yesmaximal, characteristic, complemented
11#19134842C211yesmaximal, characteristic, complemented
12#19134535C211yesmaximal, characteristic, complemented
13#19134526C211yesmaximal, characteristic, complemented
14#19134526C211yesmaximal, characteristic, complemented
15C2×C43×#546C211yesmaximal, characteristic
16C23×C43⋊C8C2211yescharacteristic, complemented
17C2×#13063284C2211yescharacteristic, complemented
18#14583220—24no—
19C2×#13063258C2211yescharacteristic, complemented
20C2×#13063256C2211yescharacteristic, complemented
21#14582895—24no—
22C2×#13063249C2211yescharacteristic, complemented
23C2×#13063249C2211yescharacteristic, complemented
24C2×#13063249C2211yescharacteristic, complemented
25C2×#13063249C2211yescharacteristic, complemented
26C2×#13063246C2211yescharacteristic
27C2×#13063246C2211yescharacteristic
28C2×#13063246C2211yescharacteristic
29C2×#13063246C2211yescharacteristic
30C2×#13063246C2211yescharacteristic
31C2×#13063246C2211yescharacteristic
32C2×#13063246C2211yescharacteristic
33C2×#13063246C2211yescharacteristic
34C2×C22⋊(C43⋊C8)C2211yescharacteristic
35C2×C22⋊(C43⋊C8)C2211yescharacteristic
36C2×C22⋊(C43⋊C8)C2211yescharacteristic, complemented
37#14582827—21no—
38#14582813—21no—
39#14582797C2211yescharacteristic, complemented
40#14582797C2211yescharacteristic, complemented
41#14582787—21no—
42#14582780—21no—
43#14582759C2211yescharacteristic
44#14582759C2211yescharacteristic
45#14582759C2211yescharacteristic, complemented
46#14582661C2211yescharacteristic, complemented
47#14582661C2211yescharacteristic, complemented
48#14582654C2211yescharacteristic, complemented
49#14582654C2211yescharacteristic, complemented
50C22×#41×C43C2211yescharacteristic
51C23×D4×C43C2211yescharacteristic
52C43×#546—24no—
53C43×#546—24no—
54C2×#124×C43C2211yescharacteristic
55C2×#123×C43—21no—
56C2×C22⋊Q8×C43C2211yescharacteristic
57C2×#121×C43—21no—
58C2×#121×C43C2211yescharacteristic
59C2×#120×C43—21no—
60C2×C4×D4×C43C2211yescharacteristic
61C2×C4×D4×C43C2211yescharacteristic
62C22×C22⋊C4×C43—21no—
63C22×C43⋊C8—22no—
64C22×C43⋊C8—41no—
65C22×C43⋊C8—41no—
66C22×C43⋊C8C2311yescharacteristic
67C22×C43⋊C8C2311yescharacteristic
68C22×C43⋊C8C2311yescharacteristic
69C22×C43⋊C8C2311yescharacteristic
70#13063284—22no—
71#13063284—22no—
72C2×C4⋊Dic43C2311yescharacteristic
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×Dic43⋊C4—21no—
77C2×Dic43⋊C4—21no—
78C2×C22⋊Dic43—21no—
79C2×C22⋊Dic43—21no—
80C2×C22⋊Dic43—21no—
81C2×C22⋊Dic43—21no—
82C2×C4×Dic43—21no—
83#13063258—22no—
84#13063256—22no—
85#13063249—22no—
86#13063249—22no—
87#13063249—41no—
88#13063249—41no—
89#13063246—22no—
90#13063246—22no—
91#13063246—22no—
92#13063246—22no—
93#13063246—22no—
94#13063246—22no—
95#13063246—41no—
96#13063246—41no—
97C22⋊(C43⋊C8)—22no—
98C22⋊(C43⋊C8)—41no—
99C22⋊(C43⋊C8)—41no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C25×C43—21no—
106C2×#41×C43—22no—
107C2×#41×C43—22no—
108C2×#41×C43—22no—
109C2×#41×C43—41no—
110C2×#41×C43—41no—
111C2×#41×C43D414yes—
112C22×Q8×C43C2311yescharacteristic
113C22×D4×C43—21no—
114C22×D4×C43—21no—
115C22×D4×C43—22no—
116C22×D4×C43—22no—
117C22×D4×C43—22no—
118C22×D4×C43—22no—
119C22×D4×C43—21no—
120C22×D4×C43—41no—
121C22×D4×C43—41no—
122C22×D4×C43D411yescharacteristic
123C22×D4×C43C2311yescharacteristic
124C22×D4×C43C2311yescharacteristic
125C23×C4×C43—21no—
126C23×C4×C43—21no—
127C23×C4×C43C2311yescharacteristic
128C23×C4×C43C2311yescharacteristic
129#124×C43—22no—
130#124×C43—22no—
131#123×C43—28no—
132C22⋊Q8×C43—22no—
133C22⋊Q8×C43—22no—
134#121×C43—28no—
135#121×C43—22no—
136#121×C43D414yes—
137#120×C43—28no—
138C4×D4×C43—22no—
139C4×D4×C43—22no—
140C4×D4×C43—22no—
141C4×D4×C43—22no—
142C2×C4⋊C4×C43—21no—
143C2×C4⋊C4×C43D411yescharacteristic
144C2×C4⋊C4×C43C2311yescharacteristic
145C2×C22⋊C4×C43—28no—
146C2×C22⋊C4×C43—21no—
147C2×C22⋊C4×C43—21no—
148C2×C22⋊C4×C43—21no—
149C2×C22⋊C4×C43—21no—
150C2×C22⋊C4×C43—21no—
151C2×C22⋊C4×C43D411yescharacteristic
152C2×C22⋊C4×C43D411yescharacteristic
153C2×C42×C43C2311yescharacteristic
154C24×C43—21no—
155C24×C43—24no—
156C24×C43—21no—
157C24×C43—42no—
158C24×C43—42no—
159C24×C43—42no—
160C24×C43—42no—
161C24×C43—81no—
162C24×C43—81no—
163C24×C43C2×D411yescharacteristic
164C24×C43C2×D411yescharacteristic
165#41×C43—28no—
166#41×C43—44no—
167#41×C43—44no—
168#41×C43—44no—
169C2×Q8×C43—21no—
170C2×Q8×C43—21no—
171C2×Q8×C43—21no—
172C2×Q8×C43—21no—
173C2×Q8×C43—21no—
174C2×Q8×C43C2×D412yes—
175C2×D4×C43—24no—
176C2×D4×C43—21no—
177C2×D4×C43—21no—
178C2×D4×C43—21no—
179C2×D4×C43—21no—
180C2×D4×C43—22no—
181C2×D4×C43—24no—
182C2×D4×C43—24no—
183C2×D4×C43—22no—
184C2×D4×C43—21no—
185C2×D4×C43—21no—
186C2×D4×C43—21no—
187C2×D4×C43—21no—
188C2×D4×C43—41no—
189C2×D4×C43—42no—
190C2×D4×C43—42no—
191C2×D4×C43—42no—
192C2×D4×C43—42no—
193C2×D4×C43—44no—
194C2×D4×C43—44no—
195C2×D4×C43—44no—
196C2×D4×C43—44no—
197C2×D4×C43—81no—
198C2×D4×C43—81no—
199C2×D4×C43C2×D412yes—
200C2×D4×C43C2×D412yes—
201C2×D4×C43#4112yes—
202C2×D4×C43#4112yes—
203C22×C4×C43—21no—
204C22×C4×C43—21no—
205C22×C4×C43—21no—
206C22×C4×C43—21no—
207C22×C4×C43—24no—
208C22×C4×C43—24no—
209C22×C4×C43—21no—
210C22×C4×C43—21no—
211C22×C4×C43—21no—
212C22×C4×C43—21no—
213C22×C4×C43—21no—
214C22×C4×C43—21no—
215C22×C4×C43—21no—
216C22×C4×C43—21no—
217C22×C4×C43—42no—
218C22×C4×C43—42no—
219C22×C4×C43—81no—
220C22×C4×C43—81no—
221C22×C4×C43C2×D412yes—
222C22×C4×C43C2×D412yes—
223C22×C4×C43C2×D411yescharacteristic
224C22×C4×C43C2×D411yescharacteristic
225C22×C4×C43C2×D411yescharacteristic
226C22×C4×C43C2×D411yescharacteristic
227C22×C4×C43C2411yescharacteristic
228C22×Dic43—21no—
229C22×Dic43—21no—
230C22×Dic43—21no—
231C22×Dic43—21no—
232C4⋊C4×C43—24no—
233C4⋊C4×C43—22no—
234C4⋊C4×C43—21no—
235C4⋊C4×C43C2×D412yes—
236C22⋊C4×C43—24no—
237C22⋊C4×C43—24no—
238C22⋊C4×C43—24no—
239C22⋊C4×C43—24no—
240C22⋊C4×C43—22no—
241C22⋊C4×C43—24no—
242C22⋊C4×C43—22no—
243C42×C43—21no—
244C42×C43—21no—
245C22⋊Dic43—42no—
246C22⋊Dic43—42no—
247C22⋊Dic43—81no—
248C22⋊Dic43—81no—
249C4⋊Dic43—21no—
250C4⋊Dic43—21no—
251C4⋊Dic43—21no—
252C4⋊Dic43—21no—
253C4⋊Dic43—21no—
254C4⋊Dic43—21no—
255C4⋊Dic43—21no—
256C4⋊Dic43—21no—
257Dic43⋊C4—42no—
258Dic43⋊C4—81no—
259C4×Dic43—42no—
260C2×C43⋊C8—21no—
261C2×C43⋊C8—21no—
262C2×C43⋊C8—21no—
263C2×C43⋊C8—21no—
264C2×C43⋊C8—21no—
265C2×C43⋊C8—21no—
266C2×C43⋊C8—21no—
267C2×C43⋊C8—21no—
268C2×C43⋊C8—21no—
269C2×C43⋊C8—21no—
270C2×C43⋊C8—21no—
271C2×C43⋊C8—21no—
272C2×C43⋊C8—44no—
273C23×C43—21no—
274C23×C43—22no—
275C23×C43—21no—
276C23×C43—21no—
277C23×C43—21no—
278C23×C43—21no—
279C23×C43—22no—
280C23×C43—22no—
281C23×C43—21no—
282C23×C43—21no—
283C23×C43—21no—
284C23×C43—21no—
285C23×C43—21no—
286C23×C43—21no—
287C23×C43—21no—
288C23×C43—22no—
289C23×C43—48no—
290C23×C43—48no—
291C23×C43—41no—
292C23×C43—41no—
293C23×C43—41no—
294C23×C43—41no—
295C23×C43—41no—
296C23×C43—41no—
297C23×C43—41no—
298C23×C43—41no—
299C23×C43—41no—
300C23×C43—41no—
301C23×C43—84no—
302C23×C43—84no—
303C23×C43—84no—
304C23×C43—84no—
305C23×C43—84no—
306C23×C43#12012yes—
307C23×C43#13512yes—
308C23×C43C22×D411yescharacteristic
309Q8×C43—22no—
310Q8×C43—22no—
311Q8×C43—41no—
312Q8×C43—41no—
313D4×C43—22no—
314D4×C43—22no—
315D4×C43—22no—
316D4×C43—22no—
317D4×C43—22no—
318D4×C43—44no—
319D4×C43—48no—
320D4×C43—48no—
321D4×C43—41no—
322D4×C43—41no—
323D4×C43—84no—
324D4×C43#12314yes—
325C2×C4×C43—21no—
326C2×C4×C43—21no—
327C2×C4×C43—22no—
328C2×C4×C43—22no—
329C2×C4×C43—22no—
330C2×C4×C43—22no—
331C2×C4×C43—21no—
332C2×C4×C43—21no—
333C2×C4×C43—22no—
334C2×C4×C43—22no—
335C2×C4×C43—21no—
336C2×C4×C43—21no—
337C2×C4×C43—21no—
338C2×C4×C43—21no—
339C2×C4×C43—21no—
340C2×C4×C43—21no—
341C2×C4×C43—21no—
342C2×C4×C43—48no—
343C2×C4×C43—41no—
344C2×C4×C43—41no—
345C2×C4×C43—41no—
346C2×C4×C43—41no—
347C2×C4×C43—41no—
348C2×C4×C43—41no—
349C2×C4×C43—41no—
350C2×C4×C43—41no—
351C2×C4×C43—84no—
352C2×C4×C43#12012yes—
353C2×C4×C43C22×D411yescharacteristic
354C2×C4×C43C22×D411yescharacteristic
355C2×C4×C43C2×#4111yescharacteristic
356C2×C4×C43C2×#4111yescharacteristic
357C2×C4×C43H(5,𝔽2)11yescharacteristic
358C2×C4×C43H(5,𝔽2)11yescharacteristic
359C2×Dic43—41no—
360C2×Dic43—41no—
361C2×Dic43—41no—
362C2×Dic43—41no—
363C2×Dic43—41no—
364C2×Dic43—41no—
365C2×Dic43—41no—
366C2×Dic43—41no—
367C2×Dic43—41no—
368C2×Dic43—41no—
369C2×Dic43—41no—
370C2×Dic43—41no—
371C43⋊C8—41no—
372C43⋊C8—41no—
373C43⋊C8—41no—
374C43⋊C8—41no—
375#24037—431nomaximal, Sylow
376C22×C43—24no—
377C22×C43—22no—
378C22×C43—22no—
379C22×C43—22no—
380C22×C43—22no—
381C22×C43—22no—
382C22×C43—22no—
383C22×C43—41no—
384C22×C43—42no—
385C22×C43—41no—
386C22×C43—42no—
387C22×C43—41no—
388C22×C43—42no—
389C22×C43—41no—
390C22×C43—42no—
391C22×C43—41no—
392C22×C43—41no—
393C22×C43—42no—
394C22×C43—41no—
395C22×C43—41no—
396C22×C43—42no—
397C22×C43—42no—
398C22×C43—42no—
399C22×C43—42no—
400C22×C43—816no—
401C22×C43—81no—
402C22×C43—81no—
403C22×C43—81no—
404C22×C43—81no—
405C22×C43C2×#12011yescharacteristic
406C22×C43#54611yescharacteristic
407C22×C43#54611yescharacteristic
408C22×C43C2×#13511yescharacteristic
409C22×C43#57511yescharacteristic
410C22×C43#57611yescharacteristic
411C22×C43#57711yescharacteristic
412C4×C43—22no—
413C4×C43—41no—
414C4×C43—42no—
415C4×C43—41no—
416C4×C43—41no—
417C4×C43—42no—
418C4×C43C2×#12311yescharacteristic
419C4×C43#53411yescharacteristic
420C4×C43#54611yescharacteristic
421C4×C43#54611yescharacteristic
422Dic43—81no—
423Dic43—81no—
424Dic43—81no—
425Dic43—81no—
426C2×#546D4311yescharacteristic
427C2×#482—431no—
428C2×#416—431no—
429#2485—431no—
430#2042—431no—
431#2042—431no—
432#2036—431no—
433#2035—431no—
434#1893—431no—
435#1869—431no—
436#1864—431no—
437#1862—431no—
438#1788—431no—
439#1786—431no—
440#1786—431no—
441C2×C43—42no—
442C2×C43—42no—
443C2×C43—44no—
444C2×C43—82no—
445C2×C43#240511yescharacteristic
446C2×C43#300211yescharacteristic
447C2×C43#301211yescharacteristic
448C2×C43#329611yescharacteristic
449C2×C43#329711yescharacteristic
450C2×C43#331111yescharacteristic
451C2×C43#331911yescharacteristic
452C22×#41C2×D4311yescharacteristic
453C23×D4C2×D4311yescharacteristic
454C23×C8—431no—
455#546—24no—
456#546—24no—
457C2×#124C2×D4311yescharacteristic
458C2×#123—21no—
459C2×C22⋊Q8C2×D4311yescharacteristic
460C2×#121—21no—
461C2×#121C2×D4311yescharacteristic
462C2×#120—21no—
463C2×C4×D4C2×D4311yescharacteristic
464C2×C4×D4C2×D4311yescharacteristic
465C2×#117—431no—
466C22×C22⋊C4—21no—
467#482—864no—
468C2×#107—431no—
469C2×#106—431no—
470#416—864no—
471C2×#103—431no—
472C2×#103—431no—
473C2×#103—431no—
474C2×#103—431no—
475C2×#102—431no—
476C2×#102—431no—
477C2×#102—431no—
478C2×#102—431no—
479C2×#102—431no—
480C2×#102—431no—
481C2×#102—431no—
482C2×#102—431no—
483C2×C22⋊C8—431no—
484C2×C22⋊C8—431no—
485C2×C22⋊C8—431no—
486#397—861no—
487#394—861no—
488#389—431no—
489#389—431no—
490#388—861no—
491#387—861no—
492#380—431no—
493#380—431no—
494#380—431no—
495#340—431no—
496#340—431no—
497#336—431no—
498#336—431no—
499C43#2403711yescharacteristic, complemented, Sylow
500C25—21no—
501C2×#41—22no—
502C2×#41—22no—
503C2×#41—22no—
504C2×#41—41no—
505C2×#41—41no—
506C2×#41C22⋊D4314yes—
507C22×Q8C22×D4311yescharacteristic
508C22×D4—21no—
509C22×D4—21no—
510C22×D4—22no—
511C22×D4—22no—
512C22×D4—22no—
513C22×D4—22no—
514C22×D4—21no—
515C22×D4—41no—
516C22×D4—41no—
517C22×D4C22⋊D4311yescharacteristic
518C22×D4C22×D4311yescharacteristic
519C22×D4C22×D4311yescharacteristic
520C23×C4—21no—
521C23×C4—21no—
522C23×C4C22×D4311yescharacteristic
523C23×C4C22×D4311yescharacteristic
524C22×C8—431no—
525C22×C8—431no—
526C22×C8—431no—
527C22×C8—431no—
528C22×C8—862no—
529C22×C8—1721no—
530C22×C8—1721no—
531#124—22no—
532#124—22no—
533#123—28no—
534C22⋊Q8—22no—
535C22⋊Q8—22no—
536#121—28no—
537#121—22no—
538#121C22⋊D4314yes—
539#120—28no—
540C4×D4—22no—
541C4×D4—22no—
542C4×D4—22no—
543C4×D4—22no—
544#117—862no—
545#117—862no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4—431no—
548C2×C4⋊C4—431no—
549C2×C4⋊C4—431no—
550C2×C4⋊C4—431no—
551C2×C4⋊C4—861no—
552C2×C4⋊C4—861no—
553C2×C4⋊C4C22⋊D4311yescharacteristic
554C2×C4⋊C4C22×D4311yescharacteristic
555C2×C22⋊C4—28no—
556C2×C22⋊C4—21no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—21no—
561C2×C22⋊C4—861no—
562C2×C22⋊C4—861no—
563C2×C22⋊C4—861no—
564C2×C22⋊C4—861no—
565C2×C22⋊C4C22⋊D4311yescharacteristic
566C2×C22⋊C4C22⋊D4311yescharacteristic
567C2×C42—861no—
568C2×C42C22×D4311yescharacteristic
569#107—862no—
570#106—862no—
571#103—862no—
572#103—862no—
573#103—1721no—
574#103—1721no—
575#102—862no—
576#102—862no—
577#102—862no—
578#102—862no—
579#102—862no—
580#102—862no—
581#102—1721no—
582#102—1721no—
583C22⋊C8—862no—
584C22⋊C8—1721no—
585C22⋊C8—1721no—
586#95—861no—
587#95—861no—
588#95—861no—
589#95—861no—
590#95—861no—
591C24—21no—
592C24—24no—
593C24—21no—
594C24—42no—
595C24—42no—
596C24—42no—
597C24—42no—
598C24—81no—
599C24—81no—
600C24C2×C22⋊D4311yescharacteristic
601C24C2×C22⋊D4311yescharacteristic
602#41—28no—
603#41—44no—
604#41—44no—
605#41—44no—
606C2×Q8—21no—
607C2×Q8—21no—
608C2×Q8—21no—
609C2×Q8—21no—
610C2×Q8—21no—
611C2×Q8C2×C22⋊D4312yes—
612C2×D4—24no—
613C2×D4—22no—
614C2×D4—24no—
615C2×D4—22no—
616C2×D4—24no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—41no—
626C2×D4—42no—
627C2×D4—42no—
628C2×D4—44no—
629C2×D4—44no—
630C2×D4—44no—
631C2×D4—42no—
632C2×D4—42no—
633C2×D4—44no—
634C2×D4—81no—
635C2×D4—81no—
636C2×D4#1062190012yes—
637C2×D4#1062190012yes—
638C2×D4C2×C22⋊D4312yes—
639C2×D4C2×C22⋊D4312yes—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—24no—
647C22×C4—24no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—42no—
655C22×C4—42no—
656C22×C4—81no—
657C22×C4—81no—
658C22×C4—861no—
659C22×C4—861no—
660C22×C4—861no—
661C22×C4—861no—
662C22×C4C2×C22⋊D4311yescharacteristic
663C22×C4C2×C22⋊D4311yescharacteristic
664C22×C4C2×C22⋊D4311yescharacteristic
665C22×C4C2×C22⋊D4311yescharacteristic
666C22×C4C2×C22⋊D4312yes—
667C22×C4C2×C22⋊D4312yes—
668C22×C4C23×D4311yescharacteristic
669C2×C8—861no—
670C2×C8—861no—
671C2×C8—861no—
672C2×C8—861no—
673C2×C8—861no—
674C2×C8—861no—
675C2×C8—861no—
676C2×C8—861no—
677C2×C8—861no—
678C2×C8—861no—
679C2×C8—861no—
680C2×C8—861no—
681C2×C8—1724no—
682C4⋊C4—24no—
683C4⋊C4—22no—
684C4⋊C4—21no—
685C4⋊C4—861no—
686C4⋊C4—861no—
687C4⋊C4—861no—
688C4⋊C4—861no—
689C4⋊C4—861no—
690C4⋊C4—861no—
691C4⋊C4—861no—
692C4⋊C4—861no—
693C4⋊C4—3441no—
694C4⋊C4—1722no—
695C4⋊C4C2×C22⋊D4312yes—
696C22⋊C4—24no—
697C22⋊C4—24no—
698C22⋊C4—24no—
699C22⋊C4—24no—
700C22⋊C4—22no—
701C22⋊C4—22no—
702C22⋊C4—24no—
703C22⋊C4—3441no—
704C22⋊C4—3441no—
705C22⋊C4—1722no—
706C22⋊C4—1722no—
707C42—21no—
708C42—21no—
709C42—1722no—
710C23—21no—
711C23—22no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—22no—
724C23—22no—
725C23—22no—
726C23—48no—
727C23—48no—
728C23—41no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23—84no—
739C23—84no—
740C23—84no—
741C23—84no—
742C23—84no—
743C23#1306329412yes—
744C23#1306334512yes—
745C23C22×C22⋊D4311yescharacteristic
746Q8—22no—
747Q8—22no—
748Q8—41no—
749Q8—41no—
750D4—22no—
751D4—22no—
752D4—22no—
753D4—22no—
754D4—22no—
755D4—44no—
756D4—48no—
757D4—48no—
758D4—41no—
759D4—41no—
760D4—84no—
761D4#1306330614yes—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—48no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—84no—
789C2×C4—1721no—
790C2×C4—1721no—
791C2×C4—1721no—
792C2×C4—1721no—
793C2×C4—1721no—
794C2×C4—1721no—
795C2×C4—1721no—
796C2×C4—1721no—
797C2×C4—1721no—
798C2×C4—1721no—
799C2×C4—1721no—
800C2×C4—1721no—
801C2×C4#1306329412yes—
802C2×C4C22×C22⋊D4311yescharacteristic
803C2×C4C22×C22⋊D4311yescharacteristic
804C2×C4C2×#1062190011yescharacteristic
805C2×C4C2×#1062190011yescharacteristic
806C2×C4#1306337011yescharacteristic
807C2×C4#1306337011yescharacteristic
808C8—1721no—
809C8—1721no—
810C8—1721no—
811C8—1721no—
812C22—22no—
813C22—24no—
814C22—22no—
815C22—22no—
816C22—22no—
817C22—22no—
818C22—22no—
819C22—41no—
820C22—42no—
821C22—41no—
822C22—41no—
823C22—42no—
824C22—41no—
825C22—42no—
826C22—41no—
827C22—42no—
828C22—42no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—42no—
833C22—42no—
834C22—42no—
835C22—42no—
836C22—816no—
837C22—81no—
838C22—81no—
839C22—81no—
840C22—81no—
841C22C2×#1306329411yescharacteristic
842C22#1458354311yescharacteristic
843C22#1458354311yescharacteristic
844C22C2×#1306334511yescharacteristic
845C22#1458369711yescharacteristic
846C22#1458370211yescharacteristic
847C22#1458371011yescharacteristic
848C4—22no—
849C4—41no—
850C4—42no—
851C4—41no—
852C4—41no—
853C4—42no—
854C4—3441no—
855C4—3441no—
856C4—3441no—
857C4—3441no—
858C4C2×#1306330611yescharacteristic
859C4#1458345811yescharacteristic
860C4#1458354311yescharacteristic
861C4#1458354311yescharacteristic
862C2—42no—
863C2—42no—
864C2—44no—
865C2—82no—
866C2#1913791811yescharacteristic
867C2#1914381311yescharacteristic
868C2#1914389911yescharacteristic
869C2#1914643011yescharacteristic
870C2#1914644511yescharacteristic
871C2#1914663111yescharacteristic
872C2#1914675111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
Fitting, prime radicalC2×C43×#546C2
socleC23×C43C22×D4
hypercenterC2×#546D43
hypocenterC43#24037
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#546

Complements

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

NH ≅ G/Ntype
1. C2×#14583220C2semidirect
2. C2×#14582895C2semidirect
3. #19138892C2semidirect
4. #19135831C2semidirect
5. #19135831C2semidirect
6. #19135795C2semidirect
7. #19135788C2semidirect
8. #19135024C2semidirect
9. #19134888C2semidirect
10. #19134856C2semidirect
11. #19134842C2semidirect
12. #19134535C2semidirect
13. #19134526C2semidirect
14. #19134526C2semidirect
16. C23×C43⋊C8C22semidirect
17. C2×#13063284C22semidirect
19. C2×#13063258C22semidirect
20. C2×#13063256C22semidirect
22. C2×#13063249C22semidirect
23. C2×#13063249C22semidirect
24. C2×#13063249C22semidirect
25. C2×#13063249C22semidirect
36. C2×C22⋊(C43⋊C8)C22semidirect
39. #14582797C22semidirect
40. #14582797C22semidirect
45. #14582759C22semidirect
46. #14582661C22semidirect
47. #14582661C22semidirect
48. #14582654C22semidirect
49. #14582654C22semidirect
499. C43#24037semidirect

Maximal subgroups

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

subgroupindex
C2×#145832202
C2×#145828952
#191388922
#191358312
#191357952
#191357882
#191350242
#191348882
#191348562
#191348422
#191345352
#191345262
C2×C43×#5462
#2403743