Finite Group Databasebeta

← #25149851

Subgroups — #25149851

Order 11008.

1238 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583595C211yesmaximal, characteristic, complemented
2C2×#14583253C211yesmaximal, characteristic, complemented
3C2×#14583111C211yesmaximal, characteristic, complemented
4#19135596C211yesmaximal, characteristic, complemented
5#19135596C211yesmaximal, characteristic, complemented
6#19135591C211yesmaximal, characteristic, complemented
7#19135591C211yesmaximal, characteristic, complemented
8#19135552C211yesmaximal, characteristic, complemented
9#19135390C211yesmaximal, characteristic, complemented
10#19134918C211yesmaximal, characteristic, complemented
11#19134913C211yesmaximal, characteristic, complemented
12#19134908C211yesmaximal, characteristic, complemented
13#19134903C211yesmaximal, characteristic, complemented
14C4×#13063245C211yesmaximal, characteristic, complemented
15C43×#2540C211yesmaximal, characteristic, complemented
16C22×#10621884C2211yescharacteristic
17C22×#10621882C2211yescharacteristic
18#14583595—24no—
19#14583595—24no—
20C2×#13063320—21no—
21C2×#13063317C2211yescharacteristic
22C2×#13063307—21no—
23C2×#13063299C2211yescharacteristic
24C2×#13063299C2211yescharacteristic
25C2×#13063297—21no—
26C2×C4×D172C2211yescharacteristic
27C2×(C22⋊D43)⋊C4—21no—
28C2×#13063284C2211yescharacteristic
29C22×C4⋊Dic43C2211yescharacteristic
30#14583253—24no—
31#14583111—24no—
32C2×C4⋊(C43⋊C8)C2211yescharacteristic
33C2×#13063249C2211yescharacteristic
34C2×#13063249C2211yescharacteristic
35C2×#13063249C2211yescharacteristic
36C2×#13063246C2211yescharacteristic
37C2×#13063246C2211yescharacteristic
38C2×#13063246C2211yescharacteristic
39C2×#13063245C2211yescharacteristic
40C2×#13063245C2211yescharacteristic
41C2×C22⋊(C43⋊C8)C2211yescharacteristic
42C2×C22⋊(C43⋊C8)C2211yescharacteristic
43C2×C22⋊(C43⋊C8)C2211yescharacteristic
44C2×C22⋊(C43⋊C8)C2211yescharacteristic
45C2×C4×C43⋊C8C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52C2×#124×C43C2211yescharacteristic
53C2×C22⋊Q8×C43C2211yescharacteristic
54C2×C22⋊Q8×C43C2211yescharacteristic
55C2×#121×C43C2211yescharacteristic
56C2×#121×C43C2211yescharacteristic
57C2×C4×D4×C43C2211yescharacteristic
58C43×#399—21no—
59C43×#392—21no—
60C43×#390—21no—
61C43×#390—21no—
62C4×C4⋊C4×C43C2211yescharacteristic
63C22×D172C2311yescharacteristic
64C22×C22⋊D43—21no—
65C22×C22⋊D43—21no—
66C23×Dic43—21no—
67C22×C4×D43—21no—
68C2×#10621884—22no—
69C2×#10621884—41no—
70C2×#10621884—41no—
71C2×#10621882—22no—
72C2×#10621882—41no—
73C2×#10621882—41no—
74C22×C43⋊C8C2311yescharacteristic
75C22×C43⋊C8C2311yescharacteristic
76C22×C43⋊C8C2311yescharacteristic
77C22×C43⋊C8C2311yescharacteristic
78#13063320—28no—
79#13063317—22no—
80#13063317D414yescomplemented
81#13063307—28no—
82#13063299—22no—
83#13063299—22no—
84#13063299—22no—
85#13063299—22no—
86#13063297—28no—
87C4×D172—22no—
88C4×D172D414yescomplemented
89(C22⋊D43)⋊C4—28no—
90#13063284—22no—
91#13063284—22no—
92C2×C4⋊Dic43—21no—
93C2×C4⋊Dic43—22no—
94C2×C4⋊Dic43—22no—
95C2×C4⋊Dic43C2311yescharacteristic
96C2×C4⋊Dic43C2311yescharacteristic
97C2×C4⋊Dic43C2311yescharacteristic
98C2×Dic43⋊C4—21no—
99C2×Dic43⋊C4—21no—
100C2×C22⋊Dic43—21no—
101C2×(C2×D43)⋊C4—21no—
102C2×(C2×D43)⋊C4—21no—
103C2×(C2×D43)⋊C4—21no—
104C2×C4×Dic43—21no—
105C4⋊(C43⋊C8)—22no—
106#13063249—22no—
107#13063249—22no—
108#13063249—22no—
109#13063246—22no—
110#13063246—22no—
111#13063246—22no—
112#13063245—22no—
113#13063245—22no—
114C22⋊(C43⋊C8)—41no—
115C22⋊(C43⋊C8)—41no—
116C22⋊(C43⋊C8)—41no—
117C22⋊(C43⋊C8)—41no—
118C4×C43⋊C8—22no—
119C22×Q8×C43C2311yescharacteristic
120C22×D4×C43—21no—
121C22×D4×C43—21no—
122C22×D4×C43D411yescharacteristic
123C22×D4×C43C2311yescharacteristic
124C23×C4×C43C2311yescharacteristic
125C23×C4×C43C2311yescharacteristic
126#124×C43—22no—
127#124×C43—22no—
128C22⋊Q8×C43—22no—
129C22⋊Q8×C43—22no—
130C22⋊Q8×C43—41no—
131C22⋊Q8×C43—41no—
132#121×C43—22no—
133#121×C43—22no—
134#121×C43—41no—
135#121×C43—41no—
136C4×D4×C43—22no—
137C4×D4×C43—22no—
138C2×C4⋊C4×C43—21no—
139C2×C4⋊C4×C43—21no—
140C2×C4⋊C4×C43D411yescharacteristic
141C2×C4⋊C4×C43C2311yescharacteristic
142C2×C4⋊C4×C43C2311yescharacteristic
143C2×C22⋊C4×C43—21no—
144C2×C22⋊C4×C43—21no—
145C2×C22⋊C4×C43—21no—
146C2×C22⋊C4×C43—21no—
147C2×C22⋊C4×C43—21no—
148C2×C22⋊C4×C43—21no—
149C2×C22⋊C4×C43D411yescharacteristic
150C2×C22⋊C4×C43D411yescharacteristic
151C2×C42×C43—21no—
152C2×C42×C43C2311yescharacteristic
153#95×C43—21no—
154C24×C43—21no—
155C24×C43C2×D411yescharacteristic
156C24×C43C2×D411yescharacteristic
157C23×D43—21no—
158C2×Q8×C43—21no—
159C2×Q8×C43—21no—
160C2×Q8×C43—21no—
161C2×Q8×C43—21no—
162C2×Q8×C43—21no—
163C2×Q8×C43—21no—
164C2×D4×C43—22no—
165C2×D4×C43—22no—
166C2×D4×C43—21no—
167C2×D4×C43—21no—
168C2×D4×C43—21no—
169C2×D4×C43—21no—
170C2×D4×C43—21no—
171C2×D4×C43—21no—
172C2×D4×C43—41no—
173C2×D4×C43—42no—
174C2×D4×C43—42no—
175C2×D4×C43—42no—
176C2×D4×C43—42no—
177C2×D4×C43—81no—
178C2×D4×C43—81no—
179C22×C4×C43—21no—
180C22×C4×C43—21no—
181C22×C4×C43—21no—
182C22×C4×C43—21no—
183C22×C4×C43—21no—
184C22×C4×C43—21no—
185C22×C4×C43—21no—
186C22×C4×C43—21no—
187C22×C4×C43—21no—
188C22×C4×C43—21no—
189C22×C4×C43—21no—
190C22×C4×C43—21no—
191C22×C4×C43—21no—
192C22×C4×C43—21no—
193C22×C4×C43—21no—
194C22×C4×C43C2×D411yescharacteristic
195C22×C4×C43C2×D411yescharacteristic
196C22×C4×C43C2×D411yescharacteristic
197C22×C4×C43C2×D411yescharacteristic
198C22×C4×C43C2411yescharacteristic
199C2×C22⋊D43—24no—
200C2×C22⋊D43—24no—
201C2×C22⋊D43—42no—
202C2×C22⋊D43—42no—
203C2×C22⋊D43—81no—
204C2×C22⋊D43—81no—
205C22×Dic43—24no—
206C22×Dic43—21no—
207C22×Dic43—21no—
208C22×Dic43—21no—
209C22×Dic43—81no—
210C22×Dic43—81no—
211C2×D172—21no—
212C2×D172—21no—
213C2×D172—21no—
214C2×D172—21no—
215C2×D172—21no—
216C2×D172C2×D412yes—
217C2×C4×D43—24no—
218C2×C4×D43—81no—
219C2×C4×D43—81no—
220C4⋊C4×C43—22no—
221C4⋊C4×C43—21no—
222C4⋊C4×C43—21no—
223C4⋊C4×C43—42no—
224C4⋊C4×C43—42no—
225C4⋊C4×C43#4112yes—
226C4⋊C4×C43#4112yes—
227C22⋊C4×C43—22no—
228C22⋊C4×C43—22no—
229C22⋊C4×C43—42no—
230C22⋊C4×C43—42no—
231C22⋊C4×C43—42no—
232C22⋊C4×C43—42no—
233C22⋊C4×C43—42no—
234C22⋊C4×C43—42no—
235C42×C43—81no—
236C42×C43C2×D412yes—
237C42×C43C2×D412yes—
238C22⋊Dic43—24no—
239#10621884—44no—
240#10621882—44no—
241(C2×D43)⋊C4—24no—
242(C2×D43)⋊C4—24no—
243(C2×D43)⋊C4—24no—
244C4⋊Dic43—24no—
245C4⋊Dic43—21no—
246C4⋊Dic43—21no—
247C4⋊Dic43—21no—
248C4⋊Dic43C2×D412yes—
249C4⋊Dic43C2×D412yes—
250C4⋊Dic43C2×D412yes—
251Dic43⋊C4—24no—
252Dic43⋊C4—24no—
253C4×Dic43—24no—
254C2×C43⋊C8—21no—
255C2×C43⋊C8—21no—
256C2×C43⋊C8—21no—
257C2×C43⋊C8—21no—
258C2×C43⋊C8—21no—
259C2×C43⋊C8—21no—
260C2×C43⋊C8—21no—
261C2×C43⋊C8—21no—
262C2×C43⋊C8—21no—
263C2×C43⋊C8—21no—
264C2×C43⋊C8—21no—
265C2×C43⋊C8—21no—
266C23×C43—21no—
267C23×C43—21no—
268C23×C43—21no—
269C23×C43—21no—
270C23×C43—21no—
271C23×C43—21no—
272C23×C43—21no—
273C23×C43—21no—
274C23×C43—21no—
275C23×C43—21no—
276C23×C43—21no—
277C23×C43—21no—
278C23×C43—21no—
279C23×C43—41no—
280C23×C43—41no—
281C23×C43—41no—
282C23×C43—41no—
283C23×C43—41no—
284C23×C43—41no—
285C23×C43—41no—
286C23×C43#13512yes—
287C23×C43C22×D411yescharacteristic
288C22×D43—22no—
289C22×D43—41no—
290C22×D43—41no—
291C22×D43—41no—
292C22×D43—41no—
293C22×D43—41no—
294C22×D43—41no—
295Q8×C43—41no—
296Q8×C43—41no—
297Q8×C43—41no—
298Q8×C43—41no—
299D4×C43—44no—
300D4×C43—41no—
301D4×C43—41no—
302D4×C43—41no—
303D4×C43—41no—
304D4×C43—84no—
305D4×C43—84no—
306C2×C4×C43—21no—
307C2×C4×C43—21no—
308C2×C4×C43—21no—
309C2×C4×C43—21no—
310C2×C4×C43—21no—
311C2×C4×C43—21no—
312C2×C4×C43—22no—
313C2×C4×C43—22no—
314C2×C4×C43—21no—
315C2×C4×C43—21no—
316C2×C4×C43—21no—
317C2×C4×C43—21no—
318C2×C4×C43—41no—
319C2×C4×C43—41no—
320C2×C4×C43—41no—
321C2×C4×C43—41no—
322C2×C4×C43—41no—
323C2×C4×C43—41no—
324C2×C4×C43—41no—
325C2×C4×C43—41no—
326C2×C4×C43—41no—
327C2×C4×C43—41no—
328C2×C4×C43—41no—
329C2×C4×C43—41no—
330C2×C4×C43—41no—
331C2×C4×C43—41no—
332C2×C4×C43—41no—
333C2×C4×C43#12012yes—
334C2×C4×C43#12012yes—
335C2×C4×C43C22×D411yescharacteristic
336C2×C4×C43C22×D411yescharacteristic
337C2×C4×C43C2×#4111yescharacteristic
338C2×C4×C43C2×#4111yescharacteristic
339C2×C4×C43H(5,𝔽2)11yescharacteristic
340C2×C4×C43H(5,𝔽2)11yescharacteristic
341C22⋊D43—48no—
342C22⋊D43—84no—
343C2×Dic43—22no—
344C2×Dic43—22no—
345C2×Dic43—22no—
346C2×Dic43—41no—
347C2×Dic43—41no—
348C2×Dic43—41no—
349C2×Dic43—41no—
350C2×Dic43—41no—
351C2×Dic43—41no—
352C2×Dic43—84no—
353D172—22no—
354D172—22no—
355D172—41no—
356D172—41no—
357C4×D43—84no—
358C43⋊C8—41no—
359C43⋊C8—41no—
360C43⋊C8—41no—
361C43⋊C8—41no—
362#25575—431nomaximal, Sylow
363C22×C43—22no—
364C22×C43—22no—
365C22×C43—22no—
366C22×C43—41no—
367C22×C43—41no—
368C22×C43—41no—
369C22×C43—41no—
370C22×C43—41no—
371C22×C43—41no—
372C22×C43—41no—
373C22×C43—41no—
374C22×C43—41no—
375C22×C43—41no—
376C22×C43—41no—
377C22×C43—81no—
378C22×C43—81no—
379C22×C43—81no—
380C22×C43—81no—
381C22×C43—81no—
382C22×C43—81no—
383C22×C43—81no—
384C22×C43C2×#12011yescharacteristic
385C22×C43#54611yescharacteristic
386C22×C43#54611yescharacteristic
387C22×C43C2×#13511yescharacteristic
388C22×C43#57511yescharacteristic
389C22×C43#57611yescharacteristic
390C22×C43#57711yescharacteristic
391C2×D43—42no—
392C2×D43—42no—
393C2×D43—42no—
394C2×D43—81no—
395C2×D43—81no—
396C2×D43—81no—
397C2×D43—81no—
398C4×C43—22no—
399C4×C43—22no—
400C4×C43—41no—
401C4×C43—41no—
402C4×C43—42no—
403C4×C43—42no—
404C4×C43—81no—
405C4×C43#53211yescharacteristic
406C4×C43#53511yescharacteristic
407C4×C43#55011yescharacteristic
408C4×C43#55011yescharacteristic
409Dic43—42no—
410Dic43—42no—
411Dic43—42no—
412C2×#553—431no—
413C2×#488—431no—
414C2×#463—431no—
415#2540D4311yescharacteristic, complemented
416#2000—431no—
417#2000—431no—
418#1999—431no—
419#1999—431no—
420#1989—431no—
421#1954—431no—
422#1875—431no—
423#1874—431no—
424#1873—431no—
425#1872—431no—
426C4×#102—431no—
427C2×C43—42no—
428C2×C43—81no—
429C2×C43—161no—
430C2×C43#243111yescharacteristic
431C2×C43#300211yescharacteristic
432C2×C43#301211yescharacteristic
433C2×C43#329711yescharacteristic
434C2×C43#330111yescharacteristic
435C2×C43#332211yescharacteristic
436C2×C43#332611yescharacteristic
437D43—82no—
438C22×SD16—431no—
439C22×D8—431no—
440#553—864no—
441#553—864no—
442C2×#126—861no—
443C2×#125—431no—
444C2×#124C2×D4311yescharacteristic
445C2×#123—861no—
446C2×C22⋊Q8C2×D4311yescharacteristic
447C2×C22⋊Q8C2×D4311yescharacteristic
448C2×#121—431no—
449C2×#121—431no—
450C2×#121—861no—
451C2×#121C2×D4311yescharacteristic
452C2×#121C2×D4311yescharacteristic
453C2×C4×D4—431no—
454C2×C4×D4—861no—
455C2×C4×D4C2×D4311yescharacteristic
456C2×#117—431no—
457C22×C4⋊C4—431no—
458#488—864no—
459#463—864no—
460C2×C4⋊C8—431no—
461C2×#103—431no—
462C2×#103—431no—
463C2×#103—431no—
464C2×#102—431no—
465C2×#102—431no—
466C2×#102—431no—
467C2×#102—431no—
468C2×#102—431no—
469C2×C22⋊C8—431no—
470C2×C22⋊C8—431no—
471C2×C22⋊C8—431no—
472C2×C22⋊C8—431no—
473C2×C4×C8—431no—
474#399—21no—
475#392—21no—
476#390—21no—
477#390—21no—
478C4×C4⋊C4C2×D4311yescharacteristic
479#340—431no—
480#340—431no—
481#340—431no—
482#340—431no—
483#340—431no—
484#340—431no—
485C43#2557511yescharacteristic, complemented, Sylow
486C22×Q8C22×D4311yescharacteristic
487C22×D4—21no—
488C22×D4—21no—
489C22×D4—431no—
490C22×D4—861no—
491C22×D4—861no—
492C22×D4C22⋊D4311yescharacteristic
493C22×D4C22×D4311yescharacteristic
494C23×C4—861no—
495C23×C4—861no—
496C23×C4C22×D4311yescharacteristic
497C23×C4C22×D4311yescharacteristic
498C2×SD16—862no—
499C2×SD16—1721no—
500C2×SD16—1721no—
501C2×D8—862no—
502C2×D8—1721no—
503C2×D8—1721no—
504C22×C8—431no—
505C22×C8—431no—
506C22×C8—431no—
507C22×C8—431no—
508#126—868no—
509#125—434no—
510#125—862no—
511#124—22no—
512#124—22no—
513#123—868no—
514C22⋊Q8—22no—
515C22⋊Q8—22no—
516C22⋊Q8—41no—
517C22⋊Q8—41no—
518#121—22no—
519#121—22no—
520#121—41no—
521#121—41no—
522#121—862no—
523#121—862no—
524#121—862no—
525#121—862no—
526#121—868no—
527C4×D4—22no—
528C4×D4—22no—
529C4×D4—434no—
530C4×D4—868no—
531C4×D4—862no—
532#117—862no—
533#117—862no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—431no—
537C2×C4⋊C4—431no—
538C2×C4⋊C4—431no—
539C2×C4⋊C4—862no—
540C2×C4⋊C4—862no—
541C2×C4⋊C4—861no—
542C2×C4⋊C4—861no—
543C2×C4⋊C4—861no—
544C2×C4⋊C4C22⋊D4311yescharacteristic
545C2×C4⋊C4C22×D4311yescharacteristic
546C2×C4⋊C4C22×D4311yescharacteristic
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—861no—
554C2×C22⋊C4—861no—
555C2×C22⋊C4—861no—
556C2×C22⋊C4—861no—
557C2×C22⋊C4C22⋊D4311yescharacteristic
558C2×C22⋊C4C22⋊D4311yescharacteristic
559C2×C42—21no—
560C2×C42—861no—
561C2×C42C22×D4311yescharacteristic
562C4⋊C8—862no—
563#103—862no—
564#103—862no—
565#103—862no—
566#102—862no—
567#102—862no—
568#102—862no—
569#102—862no—
570#102—862no—
571C22⋊C8—1721no—
572C22⋊C8—1721no—
573C22⋊C8—1721no—
574C22⋊C8—1721no—
575C4×C8—862no—
576#95—21no—
577C24—21no—
578C24—861no—
579C24C2×C22⋊D4311yescharacteristic
580C24C2×C22⋊D4311yescharacteristic
581C2×Q8—21no—
582C2×Q8—21no—
583C2×Q8—21no—
584C2×Q8—21no—
585C2×Q8—21no—
586C2×Q8—21no—
587C2×D4—22no—
588C2×D4—22no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—41no—
596C2×D4—42no—
597C2×D4—42no—
598C2×D4—42no—
599C2×D4—42no—
600C2×D4—81no—
601C2×D4—81no—
602C2×D4—432no—
603C2×D4—864no—
604C2×D4—864no—
605C2×D4—861no—
606C2×D4—861no—
607C2×D4—861no—
608C2×D4—861no—
609C2×D4—861no—
610C2×D4—3441no—
611C2×D4—3441no—
612C2×D4—1722no—
613C2×D4—1722no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—864no—
630C22×C4—861no—
631C22×C4—861no—
632C22×C4—861no—
633C22×C4—864no—
634C22×C4—3441no—
635C22×C4—3441no—
636C22×C4—3441no—
637C22×C4—3441no—
638C22×C4C2×C22⋊D4311yescharacteristic
639C22×C4C2×C22⋊D4311yescharacteristic
640C22×C4C2×C22⋊D4311yescharacteristic
641C22×C4C2×C22⋊D4311yescharacteristic
642C22×C4C23×D4311yescharacteristic
643SD16—1724no—
644D8—1724no—
645C2×C8—861no—
646C2×C8—861no—
647C2×C8—861no—
648C2×C8—861no—
649C2×C8—861no—
650C2×C8—861no—
651C2×C8—861no—
652C2×C8—861no—
653C2×C8—861no—
654C2×C8—861no—
655C2×C8—861no—
656C2×C8—861no—
657C4⋊C4—22no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—42no—
661C4⋊C4—42no—
662C4⋊C4—432no—
663C4⋊C4—432no—
664C4⋊C4—432no—
665C4⋊C4—864no—
666C4⋊C4—864no—
667C4⋊C4—864no—
668C4⋊C4—861no—
669C4⋊C4—861no—
670C4⋊C4—861no—
671C4⋊C4#1062190012yes—
672C4⋊C4#1062190012yes—
673C22⋊C4—22no—
674C22⋊C4—22no—
675C22⋊C4—42no—
676C22⋊C4—42no—
677C22⋊C4—42no—
678C22⋊C4—42no—
679C22⋊C4—42no—
680C22⋊C4—42no—
681C22⋊C4—864no—
682C22⋊C4—864no—
683C22⋊C4—864no—
684C22⋊C4—864no—
685C42—81no—
686C42—864no—
687C42D4×D4312yes—
688C42D4×D4312yes—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—862no—
710C23—1721no—
711C23—1721no—
712C23—1721no—
713C23—1721no—
714C23—1721no—
715C23—1721no—
716C23#1306334512yes—
717C23C22×C22⋊D4311yescharacteristic
718Q8—41no—
719Q8—41no—
720Q8—41no—
721Q8—41no—
722D4—44no—
723D4—41no—
724D4—41no—
725D4—41no—
726D4—41no—
727D4—84no—
728D4—84no—
729D4—862no—
730D4—862no—
731D4—3444no—
732D4—1728no—
733D4—1721no—
734D4—1721no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—862no—
763C2×C4—862no—
764C2×C4—862no—
765C2×C4—3444no—
766C2×C4—3444no—
767C2×C4—1721no—
768C2×C4—1721no—
769C2×C4—1721no—
770C2×C4—1721no—
771C2×C4—1721no—
772C2×C4—1721no—
773C2×C4#1306329312yes—
774C2×C4#1306329312yes—
775C2×C4C2×D4×D4311yescharacteristic
776C2×C4C2×D4×D4311yescharacteristic
777C2×C4C2×#1062190011yescharacteristic
778C2×C4C2×#1062190011yescharacteristic
779C2×C4#1306337011yescharacteristic
780C2×C4#1306337011yescharacteristic
781C8—1721no—
782C8—1721no—
783C8—1721no—
784C8—1721no—
785C22—22no—
786C22—22no—
787C22—22no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22—41no—
797C22—41no—
798C22—41no—
799C22—81no—
800C22—81no—
801C22—81no—
802C22—81no—
803C22—81no—
804C22—81no—
805C22—81no—
806C22—3441no—
807C22—3441no—
808C22—3441no—
809C22—3441no—
810C22—1722no—
811C22—1722no—
812C22—1722no—
813C22C2×#1306329311yescharacteristic
814C22#1458354311yescharacteristic
815C22#1458354311yescharacteristic
816C22C2×#1306334511yescharacteristic
817C22#1458369711yescharacteristic
818C22#1458370211yescharacteristic
819C22#1458370711yescharacteristic
820C4—22no—
821C4—22no—
822C4—42no—
823C4—41no—
824C4—41no—
825C4—42no—
826C4—81no—
827C4—1722no—
828C4—1722no—
829C4—1722no—
830C4#1458344711yescharacteristic
831C4#1458346211yescharacteristic
832C4#1458356911yescharacteristic
833C4#1458356911yescharacteristic
834C2—42no—
835C2—81no—
836C2—161no—
837C2—3442no—
838C2#1913821111yescharacteristic
839C2#1914381111yescharacteristic
840C2#1914389611yescharacteristic
841C2#1914644511yescharacteristic
842C2#1914649711yescharacteristic
843C2#1914679611yescharacteristic
844C2#1914684811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2540C2
socleC23×C43C22×D4
hypercenter#2540D43
hypocenterC43#25575
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2540

Complements

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

NH ≅ G/Ntype
1. C2×#14583595C2semidirect
2. C2×#14583253C2semidirect
3. C2×#14583111C2semidirect
4. #19135596C2semidirect
5. #19135596C2semidirect
6. #19135591C2semidirect
7. #19135591C2semidirect
8. #19135552C2semidirect
9. #19135390C2semidirect
10. #19134918C2semidirect
11. #19134913C2semidirect
12. #19134908C2semidirect
13. #19134903C2semidirect
14. C4×#13063245C2semidirect
15. C43×#2540C2semidirect
80. #13063317D4semidirect
88. C4×D172D4semidirect
415. #2540D43semidirect
485. C43#25575semidirect

Maximal subgroups

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

subgroupindex
C2×#145835952
C2×#145832532
C2×#145831112
#191355962
#191355912
#191355522
#191353902
#191349182
#191349132
#191349082
#191349032
C4×#130632452
C43×#25402
#2557543