Finite Group Databasebeta

← #25147547

Subgroups — #25147547

Order 11008.

1118 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583150C211yesmaximal, characteristic, complemented
2C2×#14583130C211yesmaximal, characteristic, complemented
3C2×#14583111C211yesmaximal, characteristic, complemented
4C2×#14582971C211yesmaximal, characteristic, complemented
5#19139508C211yesmaximal, characteristic, complemented
6#19135788C211yesmaximal, characteristic, complemented
7#19135781C211yesmaximal, characteristic, complemented
8#19135596C211yesmaximal, characteristic, complemented
9#19135591C211yesmaximal, characteristic, complemented
10#19135412C211yesmaximal, characteristic, complemented
11#19135358C211yesmaximal, characteristic, complemented
12#19135029C211yesmaximal, characteristic, complemented
13#19135024C211yesmaximal, characteristic, complemented
14#19134423C211yesmaximal, characteristic, complemented
15C43×#2540C211yesmaximal, characteristic, complemented
16C22×#10621884C2211yescharacteristic
17C22×#10621882C2211yescharacteristic
18C22×#10621877C2211yescharacteristic
19C23×C43⋊C8C2211yescharacteristic
20C2×#13063299C2211yescharacteristic
21C2×#13063299C2211yescharacteristic
22C2×#13063296—21no—
23C2×C4×D172C2211yescharacteristic
24#14583150—24no—
25#14583130—24no—
26#14583111—24no—
27#14582971—24no—
28C2×#13063256C2211yescharacteristic
29C2×#13063256C2211yescharacteristic
30C2×C4⋊(C43⋊C8)C2211yescharacteristic
31C2×#13063249C2211yescharacteristic
32C2×#13063249C2211yescharacteristic
33C2×#13063249C2211yescharacteristic
34C2×#13063246C2211yescharacteristic
35C2×#13063246C2211yescharacteristic
36C2×#13063246C2211yescharacteristic
37C2×#13063245C2211yescharacteristic
38C2×#13063245C2211yescharacteristic
39C2×C22⋊(C43⋊C8)C2211yescharacteristic
40C2×C22⋊(C43⋊C8)C2211yescharacteristic
41C2×#13063236C2211yescharacteristic
42#14582815—21no—
43#14582815—21no—
44#14582769C2211yescharacteristic
45#14582759C2211yescharacteristic
46#14582759C2211yescharacteristic
47#14582756—21no—
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—
66C22×C4×D43—21no—
67C2×#10621884—22no—
68C2×#10621884—22no—
69C2×#10621884—41no—
70C2×#10621882—22no—
71C2×#10621882—22no—
72C2×#10621882—41no—
73C2×#10621877—22no—
74C2×#10621877—22no—
75C2×#10621877—41no—
76C22×C43⋊C8—22no—
77C22×C43⋊C8—22no—
78C22×C43⋊C8—41no—
79C22×C43⋊C8C2311yescharacteristic
80C22×C43⋊C8C2311yescharacteristic
81C22×C43⋊C8C2311yescharacteristic
82C22×C43⋊C8C2311yescharacteristic
83#13063299—22no—
84#13063299—22no—
85#13063299—41no—
86#13063299—41no—
87#13063296—44no—
88C4×D172—22no—
89C4×D172—22no—
90C2×C4⋊Dic43—21no—
91C2×C4⋊Dic43—21no—
92C2×C4⋊Dic43C2311yescharacteristic
93C2×C4⋊Dic43C2311yescharacteristic
94C2×C4⋊Dic43C2311yescharacteristic
95C2×C22⋊Dic43—21no—
96C2×C22⋊Dic43—21no—
97C2×(C2×D43)⋊C4—21no—
98C2×(C2×D43)⋊C4—21no—
99C2×(C2×D43)⋊C4—21no—
100#13063256—22no—
101#13063256—22no—
102C4⋊(C43⋊C8)D414yescomplemented
103#13063249—22no—
104#13063249—22no—
105#13063249—41no—
106#13063246—22no—
107#13063246—22no—
108#13063246—41no—
109#13063245—22no—
110#13063245D414yescomplemented
111C22⋊(C43⋊C8)—22no—
112C22⋊(C43⋊C8)—22no—
113#13063236—22no—
114C43⋊#95—21no—
115C43⋊#95—21no—
116C22×Q8×C43C2311yescharacteristic
117C22×D4×C43—21no—
118C22×D4×C43—21no—
119C22×D4×C43D411yescharacteristic
120C22×D4×C43C2311yescharacteristic
121C23×C4×C43C2311yescharacteristic
122C23×C4×C43C2311yescharacteristic
123#124×C43—22no—
124#124×C43—22no—
125C22⋊Q8×C43—22no—
126C22⋊Q8×C43—22no—
127C22⋊Q8×C43—41no—
128C22⋊Q8×C43—41no—
129#121×C43—22no—
130#121×C43—22no—
131#121×C43—41no—
132#121×C43—41no—
133C4×D4×C43—22no—
134C4×D4×C43—22no—
135C2×C4⋊C4×C43—21no—
136C2×C4⋊C4×C43—21no—
137C2×C4⋊C4×C43D411yescharacteristic
138C2×C4⋊C4×C43C2311yescharacteristic
139C2×C4⋊C4×C43C2311yescharacteristic
140C2×C22⋊C4×C43—21no—
141C2×C22⋊C4×C43—21no—
142C2×C22⋊C4×C43—21no—
143C2×C22⋊C4×C43—21no—
144C2×C22⋊C4×C43—21no—
145C2×C22⋊C4×C43—21no—
146C2×C22⋊C4×C43D411yescharacteristic
147C2×C22⋊C4×C43D411yescharacteristic
148C2×C42×C43—21no—
149C2×C42×C43C2311yescharacteristic
150#95×C43—21no—
151C24×C43—21no—
152C24×C43C2×D411yescharacteristic
153C24×C43C2×D411yescharacteristic
154C23×D43—21no—
155C2×Q8×C43—21no—
156C2×Q8×C43—21no—
157C2×Q8×C43—21no—
158C2×Q8×C43—21no—
159C2×Q8×C43—21no—
160C2×Q8×C43—21no—
161C2×D4×C43—22no—
162C2×D4×C43—22no—
163C2×D4×C43—21no—
164C2×D4×C43—21no—
165C2×D4×C43—21no—
166C2×D4×C43—21no—
167C2×D4×C43—21no—
168C2×D4×C43—21no—
169C2×D4×C43—41no—
170C2×D4×C43—42no—
171C2×D4×C43—42no—
172C2×D4×C43—42no—
173C2×D4×C43—42no—
174C2×D4×C43—81no—
175C2×D4×C43—81no—
176C22×C4×C43—21no—
177C22×C4×C43—21no—
178C22×C4×C43—21no—
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×C43C2×D411yescharacteristic
192C22×C4×C43C2×D411yescharacteristic
193C22×C4×C43C2×D411yescharacteristic
194C22×C4×C43C2×D411yescharacteristic
195C22×C4×C43C2411yescharacteristic
196C2×C22⋊D43—42no—
197C2×C22⋊D43—42no—
198C2×C22⋊D43—42no—
199C2×C22⋊D43—42no—
200C2×C22⋊D43—81no—
201C2×C22⋊D43—81no—
202C22×Dic43—21no—
203C22×Dic43—21no—
204C22×Dic43—21no—
205C2×D172—21no—
206C2×D172—21no—
207C2×D172—21no—
208C2×D172—21no—
209C2×D172—21no—
210C2×D172C2×D412yes—
211C2×C4×D43—42no—
212C2×C4×D43—42no—
213C2×C4×D43—42no—
214C4⋊C4×C43—22no—
215C4⋊C4×C43—21no—
216C4⋊C4×C43—21no—
217C4⋊C4×C43—42no—
218C4⋊C4×C43—42no—
219C4⋊C4×C43C2×D412yes—
220C4⋊C4×C43#4112yes—
221C22⋊C4×C43—22no—
222C22⋊C4×C43—22no—
223C22⋊C4×C43—42no—
224C22⋊C4×C43—42no—
225C22⋊C4×C43—42no—
226C22⋊C4×C43—42no—
227C22⋊C4×C43—42no—
228C22⋊C4×C43—42no—
229C42×C43—81no—
230C42×C43C2×D412yes—
231C42×C43#4112yes—
232C22⋊Dic43—42no—
233C22⋊Dic43—42no—
234#10621884—44no—
235#10621882—44no—
236(C2×D43)⋊C4—42no—
237(C2×D43)⋊C4—42no—
238(C2×D43)⋊C4—42no—
239C4⋊Dic43—21no—
240C4⋊Dic43—21no—
241C4⋊Dic43—21no—
242C4⋊Dic43—21no—
243C4⋊Dic43—21no—
244C4⋊Dic43—21no—
245C4⋊Dic43—42no—
246C4⋊Dic43—81no—
247#10621877—44no—
248C2×C43⋊C8—21no—
249C2×C43⋊C8—21no—
250C2×C43⋊C8—21no—
251C2×C43⋊C8—21no—
252C2×C43⋊C8—21no—
253C2×C43⋊C8—21no—
254C2×C43⋊C8—21no—
255C2×C43⋊C8—21no—
256C2×C43⋊C8—21no—
257C2×C43⋊C8—44no—
258C2×C43⋊C8C2×D412yes—
259C2×C43⋊C8C2×D412yes—
260C2×C43⋊C8C2×D412yes—
261C23×C43—21no—
262C23×C43—21no—
263C23×C43—21no—
264C23×C43—21no—
265C23×C43—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—41no—
275C23×C43—41no—
276C23×C43—41no—
277C23×C43—41no—
278C23×C43—41no—
279C23×C43—41no—
280C23×C43—41no—
281C23×C43AGL(1,ℤ/8)12yes—
282C23×C43C22×D411yescharacteristic
283C22×D43—22no—
284C22×D43—41no—
285C22×D43—41no—
286C22×D43—41no—
287C22×D43—41no—
288C22×D43—41no—
289C22×D43—41no—
290Q8×C43—41no—
291Q8×C43—41no—
292Q8×C43—41no—
293Q8×C43—41no—
294D4×C43—44no—
295D4×C43—41no—
296D4×C43—41no—
297D4×C43—41no—
298D4×C43—41no—
299D4×C43—84no—
300D4×C43—84no—
301C2×C4×C43—21no—
302C2×C4×C43—21no—
303C2×C4×C43—21no—
304C2×C4×C43—21no—
305C2×C4×C43—21no—
306C2×C4×C43—21no—
307C2×C4×C43—21no—
308C2×C4×C43—21no—
309C2×C4×C43—22no—
310C2×C4×C43—22no—
311C2×C4×C43—21no—
312C2×C4×C43—21no—
313C2×C4×C43—41no—
314C2×C4×C43—41no—
315C2×C4×C43—41no—
316C2×C4×C43—41no—
317C2×C4×C43—41no—
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#12112yes—
329C2×C4×C43#12112yes—
330C2×C4×C43C22×D411yescharacteristic
331C2×C4×C43C22×D411yescharacteristic
332C2×C4×C43C2×#4111yescharacteristic
333C2×C4×C43C2×#4111yescharacteristic
334C2×C4×C43H(5,𝔽2)11yescharacteristic
335C2×C4×C43H(5,𝔽2)11yescharacteristic
336C22⋊D43—84no—
337C22⋊D43—84no—
338C2×Dic43—41no—
339C2×Dic43—41no—
340C2×Dic43—41no—
341C2×Dic43—41no—
342C2×Dic43—41no—
343C2×Dic43—41no—
344C2×Dic43—41no—
345C2×Dic43—41no—
346C2×Dic43—41no—
347D172—22no—
348D172—22no—
349D172—41no—
350D172—41no—
351C4×D43—84no—
352C43⋊C8—22no—
353C43⋊C8—22no—
354C43⋊C8—22no—
355C43⋊C8—41no—
356#25401—431nomaximal, Sylow
357C22×C43—22no—
358C22×C43—22no—
359C22×C43—22no—
360C22×C43—41no—
361C22×C43—41no—
362C22×C43—41no—
363C22×C43—41no—
364C22×C43—41no—
365C22×C43—41no—
366C22×C43—41no—
367C22×C43—41no—
368C22×C43—41no—
369C22×C43—41no—
370C22×C43—41no—
371C22×C43—81no—
372C22×C43—81no—
373C22×C43—81no—
374C22×C43—81no—
375C22×C43—81no—
376C22×C43—81no—
377C22×C43—81no—
378C22×C43C2×#12111yescharacteristic
379C22×C43D4211yescharacteristic
380C22×C43#54611yescharacteristic
381C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
382C22×C43#57511yescharacteristic
383C22×C43#57711yescharacteristic
384C22×C43#57711yescharacteristic
385C2×D43—42no—
386C2×D43—42no—
387C2×D43—42no—
388C2×D43—81no—
389C2×D43—81no—
390C2×D43—81no—
391C2×D43—81no—
392C4×C43—22no—
393C4×C43—22no—
394C4×C43—41no—
395C4×C43—41no—
396C4×C43—42no—
397C4×C43—42no—
398C4×C43—81no—
399C4×C43#53211yescharacteristic
400C4×C43#54011yescharacteristic
401C4×C43D4211yescharacteristic
402C4×C43#55011yescharacteristic
403Dic43—81no—
404Dic43—81no—
405Dic43—81no—
406C2×#469—431no—
407C2×#465—431no—
408C2×#463—431no—
409C2×#435—431no—
410#2540D4311yescharacteristic, complemented
411#2537—431no—
412#2035—431no—
413#2034—431no—
414#2000—431no—
415#1999—431no—
416#1959—431no—
417#1948—431no—
418#1894—431no—
419#1893—431no—
420#1762—431no—
421C2×C43—42no—
422C2×C43—81no—
423C2×C43—161no—
424C2×C43#242811yescharacteristic
425C2×C43#305511yescharacteristic
426C2×C43#306011yescharacteristic
427C2×C43#326511yescharacteristic
428C2×C43#326711yescharacteristic
429C2×C43#330611yescharacteristic
430C2×C43#332111yescharacteristic
431D43—82no—
432C22×SD16—431no—
433C22×D8—431no—
434C22×M16—431no—
435C23×C8—431no—
436C2×#124C2×D4311yescharacteristic
437C2×C22⋊Q8C2×D4311yescharacteristic
438C2×C22⋊Q8C2×D4311yescharacteristic
439C2×#121—431no—
440C2×#121—431no—
441C2×#121—861no—
442C2×#121C2×D4311yescharacteristic
443C2×#121C2×D4311yescharacteristic
444C2×C4×D4—431no—
445C2×C4×D4C2×D4311yescharacteristic
446#469—864no—
447#465—864no—
448#463—864no—
449#435—864no—
450C2×#106—431no—
451C2×#106—431no—
452C2×C4⋊C8—431no—
453C2×#103—431no—
454C2×#103—431no—
455C2×#103—431no—
456C2×#102—431no—
457C2×#102—431no—
458C2×#102—431no—
459C2×#102—431no—
460C2×#102—431no—
461C2×C22⋊C8—431no—
462C2×C22⋊C8—431no—
463C2×#97—431no—
464#399—21no—
465#394—861no—
466#394—861no—
467#392—21no—
468#390—21no—
469#390—21no—
470#384—431no—
471#380—431no—
472#380—431no—
473#380—861no—
474C4×C4⋊C4C2×D4311yescharacteristic
475#340—431no—
476#340—431no—
477#340—431no—
478#340—431no—
479C43#2540111yescharacteristic, complemented, Sylow
480C22×Q8C22×D4311yescharacteristic
481C22×D4—21no—
482C22×D4—21no—
483C22×D4—431no—
484C22×D4—861no—
485C22×D4—861no—
486C22×D4C22⋊D4311yescharacteristic
487C22×D4C22×D4311yescharacteristic
488C23×C4—861no—
489C23×C4C22×D4311yescharacteristic
490C23×C4C22×D4311yescharacteristic
491C2×SD16—862no—
492C2×SD16—862no—
493C2×SD16—1721no—
494C2×D8—862no—
495C2×D8—862no—
496C2×D8—1721no—
497C2×M16—862no—
498C2×M16—862no—
499C2×M16—1721no—
500C22×C8—431no—
501C22×C8—431no—
502C22×C8—431no—
503C22×C8—431no—
504C22×C8—862no—
505C22×C8—862no—
506C22×C8—1721no—
507#124—22no—
508#124—22no—
509C22⋊Q8—22no—
510C22⋊Q8—22no—
511C22⋊Q8—41no—
512C22⋊Q8—41no—
513#121—22no—
514#121—22no—
515#121—41no—
516#121—41no—
517#121—862no—
518#121—862no—
519#121—1721no—
520#121—1721no—
521#121—1724no—
522C4×D4—22no—
523C4×D4—22no—
524C4×D4—862no—
525C4×D4—862no—
526C2×C4⋊C4—21no—
527C2×C4⋊C4—21no—
528C2×C4⋊C4—431no—
529C2×C4⋊C4—431no—
530C2×C4⋊C4—431no—
531C2×C4⋊C4—861no—
532C2×C4⋊C4—861no—
533C2×C4⋊C4C22⋊D4311yescharacteristic
534C2×C4⋊C4C22×D4311yescharacteristic
535C2×C4⋊C4C22×D4311yescharacteristic
536C2×C22⋊C4—21no—
537C2×C22⋊C4—21no—
538C2×C22⋊C4—21no—
539C2×C22⋊C4—21no—
540C2×C22⋊C4—21no—
541C2×C22⋊C4—21no—
542C2×C22⋊C4—861no—
543C2×C22⋊C4—861no—
544C2×C22⋊C4—861no—
545C2×C22⋊C4—861no—
546C2×C22⋊C4—861no—
547C2×C22⋊C4C22⋊D4311yescharacteristic
548C2×C22⋊C4C22⋊D4311yescharacteristic
549C2×C42—21no—
550C2×C42C22×D4311yescharacteristic
551#106—862no—
552#106—862no—
553C4⋊C8—434no—
554#103—862no—
555#103—862no—
556#103—1721no—
557#102—434no—
558#102—862no—
559#102—862no—
560#102—862no—
561#102—1721no—
562C22⋊C8—862no—
563C22⋊C8—862no—
564#97—862no—
565#95—21no—
566#95—861no—
567#95—861no—
568C24—21no—
569C24—861no—
570C24C2×C22⋊D4311yescharacteristic
571C24C2×C22⋊D4311yescharacteristic
572C2×Q8—21no—
573C2×Q8—21no—
574C2×Q8—21no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×D4—22no—
579C2×D4—22no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—41no—
587C2×D4—42no—
588C2×D4—42no—
589C2×D4—42no—
590C2×D4—42no—
591C2×D4—81no—
592C2×D4—81no—
593C2×D4—432no—
594C2×D4—861no—
595C2×D4—861no—
596C2×D4—861no—
597C2×D4—861no—
598C2×D4—861no—
599C2×D4—3441no—
600C2×D4—3441no—
601C2×D4—1722no—
602C2×D4—1722no—
603C2×D4—1722no—
604C2×D4—1722no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—861no—
621C22×C4—861no—
622C22×C4—861no—
623C22×C4—1722no—
624C22×C4—1722no—
625C22×C4—1722no—
626C22×C4C2×C22⋊D4311yescharacteristic
627C22×C4C2×C22⋊D4311yescharacteristic
628C22×C4C2×C22⋊D4311yescharacteristic
629C22×C4C2×C22⋊D4311yescharacteristic
630C22×C4C23×D4311yescharacteristic
631SD16—1724no—
632D8—1724no—
633M16—1724no—
634C2×C8—432no—
635C2×C8—432no—
636C2×C8—432no—
637C2×C8—861no—
638C2×C8—861no—
639C2×C8—861no—
640C2×C8—861no—
641C2×C8—861no—
642C2×C8—861no—
643C2×C8—861no—
644C2×C8—861no—
645C2×C8—861no—
646C2×C8—1724no—
647C4⋊C4—22no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—42no—
651C4⋊C4—42no—
652C4⋊C4—861no—
653C4⋊C4—861no—
654C4⋊C4—861no—
655C4⋊C4—861no—
656C4⋊C4—861no—
657C4⋊C4—861no—
658C4⋊C4—3441no—
659C4⋊C4—1722no—
660C4⋊C4D4×D4312yes—
661C4⋊C4#1062190012yes—
662C22⋊C4—22no—
663C22⋊C4—22no—
664C22⋊C4—42no—
665C22⋊C4—42no—
666C22⋊C4—42no—
667C22⋊C4—42no—
668C22⋊C4—42no—
669C22⋊C4—42no—
670C22⋊C4—1722no—
671C22⋊C4—1722no—
672C22⋊C4—1722no—
673C22⋊C4—1722no—
674C22⋊C4—1722no—
675C42—81no—
676C42D4×D4312yes—
677C42#1062190012yes—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—41no—
697C23—41no—
698C23—862no—
699C23—1721no—
700C23—1721no—
701C23—1721no—
702C23—1721no—
703C23—1721no—
704C23—1721no—
705C23#1306335012yes—
706C23C22×C22⋊D4311yescharacteristic
707Q8—41no—
708Q8—41no—
709Q8—41no—
710Q8—41no—
711D4—44no—
712D4—41no—
713D4—41no—
714D4—41no—
715D4—41no—
716D4—84no—
717D4—84no—
718D4—862no—
719D4—862no—
720D4—3444no—
721D4—3444no—
722D4—1721no—
723D4—1721no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—22no—
732C2×C4—21no—
733C2×C4—22no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—3444no—
752C2×C4—1721no—
753C2×C4—1721no—
754C2×C4—1721no—
755C2×C4—1721no—
756C2×C4—1721no—
757C2×C4—1721no—
758C2×C4—1721no—
759C2×C4—1721no—
760C2×C4—1721no—
761C2×C4#1306329712yes—
762C2×C4#1306329712yes—
763C2×C4C2×D4×D4311yescharacteristic
764C2×C4C2×D4×D4311yescharacteristic
765C2×C4C2×#1062190011yescharacteristic
766C2×C4C2×#1062190011yescharacteristic
767C2×C4#1306337011yescharacteristic
768C2×C4#1306337011yescharacteristic
769C8—862no—
770C8—862no—
771C8—862no—
772C8—1721no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—81no—
788C22—81no—
789C22—81no—
790C22—81no—
791C22—81no—
792C22—81no—
793C22—81no—
794C22—3441no—
795C22—3441no—
796C22—3441no—
797C22—3441no—
798C22—1722no—
799C22—1722no—
800C22—1722no—
801C22C2×#1306329711yescharacteristic
802C22D4×C22⋊D4311yescharacteristic
803C22#1458354311yescharacteristic
804C22C2×#1306335011yescharacteristic
805C22#1458369711yescharacteristic
806C22#1458370711yescharacteristic
807C22#1458371011yescharacteristic
808C4—22no—
809C4—22no—
810C4—42no—
811C4—42no—
812C4—41no—
813C4—41no—
814C4—81no—
815C4—3441no—
816C4—3441no—
817C4—3441no—
818C4#1458344711yescharacteristic
819C4#1458350311yescharacteristic
820C4#1458353411yescharacteristic
821C4#1458356911yescharacteristic
822C2—42no—
823C2—81no—
824C2—161no—
825C2—3442no—
826C2#1913818611yescharacteristic
827C2#1914421611yescharacteristic
828C2#1914425411yescharacteristic
829C2#1914609111yescharacteristic
830C2#1914611611yescharacteristic
831C2#1914655611yescharacteristic
832C2#1914678111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2540C2
socleC23×C43C22×D4
hypercenter#2540D43
hypocenterC43#25401
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×#14583150C2semidirect
2. C2×#14583130C2semidirect
3. C2×#14583111C2semidirect
4. C2×#14582971C2semidirect
5. #19139508C2semidirect
6. #19135788C2semidirect
7. #19135781C2semidirect
8. #19135596C2semidirect
9. #19135591C2semidirect
10. #19135412C2semidirect
11. #19135358C2semidirect
12. #19135029C2semidirect
13. #19135024C2semidirect
14. #19134423C2semidirect
15. C43×#2540C2semidirect
102. C4⋊(C43⋊C8)D4semidirect
110. #13063245D4semidirect
410. #2540D43semidirect
479. C43#25401semidirect

Maximal subgroups

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

subgroupindex
C2×#145831502
C2×#145831302
C2×#145831112
C2×#145829712
#191395082
#191357882
#191357812
#191355962
#191355912
#191354122
#191353582
#191350292
#191350242
#191344232
C43×#25402
#2540143