Finite Group Databasebeta

← #25097991

Subgroups — #25097991

Order 11008.

1954 conjugacy classes of subgroups.

The subgroup lattice has 922 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063349C211yesmaximal, characteristic
2C2×#14583371C211yesmaximal, characteristic, complemented
3C2×#14582892C211yesmaximal, characteristic, complemented
4C2×#102×D43C211yesmaximal, characteristic, complemented
5#19137185C211yesmaximal, characteristic, complemented
6#19134946C211yesmaximal, characteristic, complemented
7#19134945C211yesmaximal, characteristic, complemented
8#19134940C211yesmaximal, characteristic, complemented
9#19134930C211yesmaximal, characteristic, complemented
10#19134929C211yesmaximal, characteristic, complemented
11#19134928C211yesmaximal, characteristic, complemented
12#19134927C211yesmaximal, characteristic, complemented
13#19134313C211yesmaximal, characteristic, complemented
14#19134290C211yesmaximal, characteristic, complemented
15C43×#1879C211yesmaximal, characteristic, complemented
16C22×#10621900C2211yescharacteristic
17C22×D4×D43C2211yescharacteristic
18C2×#13063349—24no—
19C2×#13063349—24no—
20C2×#13063349C418yescomplemented
21C22×#10621873C2211yescharacteristic
22C22×#10621883C2211yescharacteristic
23C22×#10621882C2211yescharacteristic
24C22×#10621872C2211yescharacteristic
25C22×C8×D43C2211yescharacteristic
26#14583371—24no—
27#14583371—24no—
28C2×C4×D172C2211yescharacteristic
29C2×D4×Dic43C2211yescharacteristic
30C2×#13063287C2211yescharacteristic
31C2×C4×C22⋊D43—21no—
32C2×(C22⋊D43)⋊C4—21no—
33C2×#13063283C2211yescharacteristic
34C2×#13063282C2211yescharacteristic
35C2×C4⋊C4×D43C2211yescharacteristic
36C22×(C2×D43)⋊C4—21no—
37C2×C22⋊C4×D43—21no—
38#14582892—24no—
39C2×#13063250C2211yescharacteristic, complemented
40C2×#13063248C2211yescharacteristic, complemented
41C2×#13063247C2211yescharacteristic
42C2×#13063246C2211yescharacteristic
43C2×#13063246C2211yescharacteristic, complemented
44C2×#13063245C2211yescharacteristic
45#102×D43—24no—
46#14582805C2211yescharacteristic, complemented
47#14582804C2211yescharacteristic, complemented
48#14582802C2211yescharacteristic, complemented
49#14582775—21no—
50#14582775—21no—
51#14582757—21no—
52#14582757—21no—
53#14582662C2211yescharacteristic, complemented
54#14582661C2211yescharacteristic, complemented
55#14582661C2211yescharacteristic, complemented
56#14582654C2211yescharacteristic, complemented
57#14582653C2211yescharacteristic, complemented
58#14582653C2211yescharacteristic, complemented
59C22×D8×C43C2211yescharacteristic
60C2×C4×D4×C43C2211yescharacteristic
61C2×#102×C43C2211yescharacteristic
62C2×#102×C43C2211yescharacteristic, complemented
63C43×#390C2211yescharacteristic, complemented
64C43×#340C2211yescharacteristic, complemented
65C43×#336C2211yescharacteristic, complemented
66C24×D43—21no—
67C2×#10621900—22no—
68C2×#10621900—22no—
69C2×#10621900—22no—
70C2×#10621900—22no—
71C2×#10621900—22no—
72C2×#10621900C2×C414yescomplemented
73C22×Dic86C2311yescharacteristic
74C22×D172C2311yescharacteristic
75C22×C22⋊D43—21no—
76C22×C22⋊D43—21no—
77C2×D4×D43—22no—
78C2×D4×D43—22no—
79C2×D4×D43—22no—
80C2×D4×D43C2×C414yes—
81C2×D4×D43D414yes—
82C2×D4×D43D414yes—
83C23×Dic43—21no—
84C23×Dic43—21no—
85C22×C4×D43—21no—
86C22×C4×D43—21no—
87C22×C4×D43—21no—
88C22×C4×D43C2311yescharacteristic
89#13063349—232no—
90C2×#10621873—22no—
91C2×#10621873—22no—
92C2×#10621873C2×C414yescomplemented
93C2×#10621883—22no—
94C2×#10621883—22no—
95C2×#10621883C2×C414yescomplemented
96C2×#10621882—22no—
97C2×#10621882—22no—
98C2×#10621882C2×C414yescomplemented
99C2×#10621872—22no—
100C2×#10621872—22no—
101C2×#10621872C2×C414yescomplemented
102C22×C43⋊C8C2311yescharacteristic
103C22×C43⋊C8C2311yescharacteristic
104C2×C8×D43—22no—
105C2×C8×D43—22no—
106C2×C8×D43—22no—
107C4×D172—22no—
108C4×D172—22no—
109D4×Dic43—22no—
110D4×Dic43—22no—
111#13063287—22no—
112#13063287—22no—
113C4×C22⋊D43—28no—
114(C22⋊D43)⋊C4—28no—
115#13063283—22no—
116#13063283D414yes—
117#13063282—22no—
118#13063282—22no—
119C2×C4⋊Dic43C2311yescharacteristic
120C2×C4⋊Dic43C2311yescharacteristic
121C2×Dic43⋊C4—21no—
122C2×Dic43⋊C4D411yescharacteristic
123C2×Dic43⋊C4D411yescharacteristic
124C4⋊C4×D43—22no—
125C4⋊C4×D43—22no—
126C2×C22⋊Dic43—21no—
127C2×C22⋊Dic43—21no—
128C2×C22⋊Dic43—21no—
129C2×(C2×D43)⋊C4—28no—
130C2×(C2×D43)⋊C4—21no—
131C2×(C2×D43)⋊C4—21no—
132C2×(C2×D43)⋊C4—21no—
133C2×(C2×D43)⋊C4D411yescharacteristic
134C2×(C2×D43)⋊C4D411yescharacteristic
135C22⋊C4×D43—28no—
136C2×C4×Dic43—21no—
137C2×C4×Dic43C2311yescharacteristic
138#13063250—22no—
139#13063248—22no—
140#13063247—22no—
141#13063246—22no—
142#13063246—22no—
143#13063245—22no—
144C43⋊#95—21no—
145C43⋊#95—21no—
146C43⋊#95—21no—
147C43⋊#95—21no—
148C22×D4×C43C2311yescharacteristic
149C22×D4×C43C2311yescharacteristic
150C23×C4×C43—21no—
151C2×D8×C43—22no—
152C2×D8×C43—22no—
153C2×D8×C43C2×C414yescomplemented
154C22×C8×C43C2311yescharacteristic
155C22×C8×C43C2311yescharacteristic
156C4×D4×C43—22no—
157C4×D4×C43—22no—
158C2×C4⋊C4×C43C2311yescharacteristic
159C2×C4⋊C4×C43C2311yescharacteristic
160C2×C22⋊C4×C43—21no—
161C2×C22⋊C4×C43—21no—
162C2×C22⋊C4×C43—21no—
163C2×C42×C43C2311yescharacteristic
164#102×C43—22no—
165#102×C43—22no—
166C24×C43—21no—
167C24×C43—21no—
168C23×D43—21no—
169C23×D43—24no—
170C23×D43—24no—
171C23×D43—24no—
172C23×D43—81no—
173C23×D43—81no—
174C23×D43—81no—
175C23×D43—81no—
176C23×D43C2×D411yescharacteristic
177C2×D4×C43—21no—
178C2×D4×C43—21no—
179C2×D4×C43—21no—
180C2×D4×C43—21no—
181C2×D4×C43—21no—
182C2×D4×C43—21no—
183C2×D4×C43—21no—
184C2×D4×C43—21no—
185C2×D4×C43C22×C412yes—
186C2×D4×C43C22×C412yes—
187C2×D4×C43C2×D412yes—
188C2×D4×C43C2×D412yes—
189C22×C4×C43—24no—
190C22×C4×C43—21no—
191C22×C4×C43—21no—
192C22×C4×C43—81no—
193C22×C4×C43—81no—
194C22×C4×C43C2×D411yescharacteristic
195C22×C4×C43C2×D411yescharacteristic
196C22×C4×C43C2411yescharacteristic
197C2×C22⋊D43—24no—
198C2×C22⋊D43—24no—
199C2×C22⋊D43—24no—
200C2×C22⋊D43—24no—
201C2×C22⋊D43—42no—
202C2×C22⋊D43—42no—
203C22×Dic43—24no—
204C22×Dic43—24no—
205C22×Dic43—21no—
206C22×Dic43—21no—
207C22×Dic43—21no—
208C22×Dic43—42no—
209C22×Dic43—42no—
210C22×Dic43—81no—
211C22×Dic43—81no—
212C22×Dic43C2×D411yescharacteristic
213C22×Dic43C2×D411yescharacteristic
214C22×Dic43C2×D411yescharacteristic
215#10621900—28no—
216#10621900—28no—
217#10621900—44no—
218#10621900—44no—
219D4×D43—28no—
220D4×D43—28no—
221D4×D43—28no—
222D4×D43C22⋊C4116yescomplemented
223C2×D172—21no—
224C2×D172—21no—
225C2×D172—21no—
226C2×D172C22×C412yes—
227C2×D172C2×D412yes—
228C2×D172C2×D412yes—
229C2×C4×D43—24no—
230C2×C4×D43—24no—
231C2×C4×D43—42no—
232C2×C4×D43—81no—
233C2×C4×D43—81no—
234C2×C4×D43—81no—
235C2×C4×D43—81no—
236C2×C4×D43—81no—
237C2×C4×D43—81no—
238C2×C4×D43C22×C412yes—
239C2×C4×D43C2×D412yes—
240C2×C4×D43C2×D412yes—
241C2×C4×D43C2×D412yes—
242C2×C4×D43#4112yes—
243C2×C4×D43#4112yes—
244C2×Dic86—21no—
245C2×Dic86—21no—
246C2×Dic86—21no—
247C2×Dic86—21no—
248C2×Dic86—21no—
249C2×Dic86C22×C412yes—
250D8×C43—28no—
251C2×C8×C43—21no—
252C2×C8×C43—21no—
253C2×C8×C43—21no—
254C2×C8×C43—21no—
255C2×C8×C43—21no—
256C2×C8×C43C22×C412yes—
257C4⋊C4×C43—21no—
258C4⋊C4×C43—21no—
259C4⋊C4×C43—21no—
260C4⋊C4×C43C2×D412yes—
261C22⋊C4×C43—24no—
262C22⋊C4×C43—81no—
263C22⋊C4×C43—81no—
264C42×C43—21no—
265C42×C43—21no—
266C22⋊Dic43—24no—
267C22⋊Dic43—81no—
268C22⋊Dic43—81no—
269#10621883—28no—
270#10621882—28no—
271(C2×D43)⋊C4—24no—
272(C2×D43)⋊C4—24no—
273(C2×D43)⋊C4—22no—
274(C2×D43)⋊C4—24no—
275(C2×D43)⋊C4—22no—
276C4⋊Dic43—21no—
277C4⋊Dic43—21no—
278C4⋊Dic43—21no—
279C4⋊Dic43C2×D412yes—
280Dic43⋊C4—22no—
281Dic43⋊C4—22no—
282Dic43⋊C4—42no—
283C4×Dic43—21no—
284C4×Dic43—21no—
285C4×Dic43—24no—
286C2×C43⋊C8—21no—
287C2×C43⋊C8—21no—
288C2×C43⋊C8—21no—
289C2×C43⋊C8—21no—
290C2×C43⋊C8—21no—
291C2×C43⋊C8C22×C412yes—
292#10621873—28no—
293#10621872—28no—
294C8×D43—44no—
295C23×C43—22no—
296C23×C43—22no—
297C23×C43—22no—
298C23×C43—22no—
299C23×C43—41no—
300C23×C43—41no—
301C23×C43—41no—
302C23×C43—41no—
303C23×C43—41no—
304C23×C43—41no—
305C23×C43—41no—
306C23×C43—41no—
307C23×C43—41no—
308C23×C43—41no—
309C23×C43C22×D411yescharacteristic
310C22×D43—21no—
311C22×D43—21no—
312C22×D43—21no—
313C22×D43—21no—
314C22×D43—22no—
315C22×D43—22no—
316C22×D43—22no—
317C22×D43—216no—
318C22×D43—41no—
319C22×D43—41no—
320C22×D43—41no—
321C22×D43—41no—
322C22×D43—84no—
323C22×D43—84no—
324C22×D43—84no—
325C22×D43—84no—
326C22×D43—84no—
327C22×D43—84no—
328C22×D43C4×D412yes—
329C22×D43#12012yes—
330C22×D43#12112yes—
331D4×C43—22no—
332D4×C43—22no—
333D4×C43—22no—
334D4×C43—22no—
335D4×C43—22no—
336D4×C43—41no—
337D4×C43—41no—
338D4×C43C2×C22⋊C414yes—
339C2×C4×C43—22no—
340C2×C4×C43—21no—
341C2×C4×C43—21no—
342C2×C4×C43—21no—
343C2×C4×C43—21no—
344C2×C4×C43—21no—
345C2×C4×C43—21no—
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×C43C23×C411yescharacteristic
353C2×C4×C43C22×D411yescharacteristic
354C2×C4×C43C22×D411yescharacteristic
355C2×C4×C43C22×D411yescharacteristic
356C2×C4×C43C2×#4111yescharacteristic
357C2×C4×C43C2×#4111yescharacteristic
358C22⋊D43—216no—
359C22⋊D43—48no—
360C2×Dic43—22no—
361C2×Dic43—21no—
362C2×Dic43—21no—
363C2×Dic43—22no—
364C2×Dic43—21no—
365C2×Dic43—21no—
366C2×Dic43—21no—
367C2×Dic43—21no—
368C2×Dic43—41no—
369C2×Dic43—41no—
370C2×Dic43—41no—
371C2×Dic43—41no—
372C2×Dic43—48no—
373C2×Dic43—41no—
374C2×Dic43—41no—
375C2×Dic43—41no—
376C2×Dic43—84no—
377C2×Dic43C4×D412yes—
378C2×Dic43#12012yes—
379C2×Dic43#12112yes—
380D172—22no—
381D172—22no—
382D172—22no—
383D172C2×C22⋊C414yes—
384C4×D43—84no—
385C4×D43—84no—
386C4×D43—84no—
387C4×D43C2×C22⋊C414yes—
388C4×D43C4×D414yes—
389C4×D43#12114yes—
390C4×D43#12314yes—
391Dic86—22no—
392Dic86—22no—
393Dic86—41no—
394Dic86—41no—
395C8×C43—22no—
396C8×C43—41no—
397C43⋊C8—22no—
398C43⋊C8—41no—
399#20929—431nomaximal, Sylow
400C22×C43—24no—
401C22×C43—42no—
402C22×C43—42no—
403C22×C43—42no—
404C22×C43—42no—
405C22×C43—42no—
406C22×C43—42no—
407C22×C43—42no—
408C22×C43—42no—
409C22×C43—42no—
410C22×C43—81no—
411C22×C43—81no—
412C22×C43—81no—
413C22×C43—81no—
414C22×C43C2×C4×D411yescharacteristic
415C22×C43C2×#12011yescharacteristic
416C22×C43C2×#12111yescharacteristic
417C22×C43#57611yescharacteristic
418C22×C43#57611yescharacteristic
419C22×C43#57711yescharacteristic
420C22×C43#57711yescharacteristic
421C2×D43—22no—
422C2×D43—22no—
423C2×D43—22no—
424C2×D43—22no—
425C2×D43—22no—
426C2×D43—22no—
427C2×D43—24no—
428C2×D43—42no—
429C2×D43—42no—
430C2×D43—42no—
431C2×D43—42no—
432C2×D43—42no—
433C2×D43—42no—
434C2×D43—816no—
435C2×D43#38614yes—
436C4×C43—41no—
437C4×C43—42no—
438C4×C43—41no—
439C4×C43—81no—
440C4×C43C22×C22⋊C411yescharacteristic
441C4×C43C2×C4×D411yescharacteristic
442C4×C43C2×#12111yescharacteristic
443C4×C43C2×#12311yescharacteristic
444Dic43—41no—
445Dic43—42no—
446Dic43—41no—
447Dic43—42no—
448Dic43—81no—
449Dic43#38614yes—
450C22×AGL(1,ℤ/8)—431no—
451C2×#518—431no—
452C2×#416—431no—
453C22×#102—431no—
454#2311—431no—
455#1879—431no—
456#1879—431no—
457#1879—431no—
458#1879D4311yescharacteristic, complemented
459#1877—431no—
460#1877—431no—
461#1877—431no—
462#1877—431no—
463#1736—431no—
464#1729—431no—
465C2×C43—44no—
466C2×C43—82no—
467C2×C43C2×#38611yescharacteristic
468C2×C43#294611yescharacteristic
469C2×C43#294611yescharacteristic
470C2×C43#301211yescharacteristic
471C2×C43#301211yescharacteristic
472C2×C43#304111yescharacteristic
473C2×C43#304211yescharacteristic
474D43—24no—
475D43—44no—
476C22×#41—431no—
477C23×D4—431no—
478C2×AGL(1,ℤ/8)—438no—
479C2×AGL(1,ℤ/8)—864no—
480C2×AGL(1,ℤ/8)—864no—
481C22×SD16—431no—
482C22×SD16—431no—
483C22×D8—431no—
484C22×D8C2×D4311yescharacteristic
485C22×M16—431no—
486C23×C8—431no—
487#518—864no—
488#518—864no—
489C2×C4×D4—431no—
490C2×C4×D4—431no—
491C2×C4×D4—431no—
492C2×C4×D4—861no—
493C2×C4×D4—861no—
494C2×C4×D4C2×D4311yescharacteristic
495C2×#117—431no—
496C2×#117—431no—
497C22×C4⋊C4—431no—
498C22×C22⋊C4—861no—
499C22×C22⋊C4—861no—
500#416—864no—
501C2×#103—431no—
502C2×#103—431no—
503C2×#102—431no—
504C2×#102—431no—
505C2×#102—431no—
506C2×#102—431no—
507C2×#102—864no—
508C2×#102C2×D4311yescharacteristic
509C2×#102C2×D4311yescharacteristic, complemented
510#391—431no—
511#391—431no—
512#390—431no—
513#390C2×D4311yescharacteristic, complemented
514#386—861no—
515#386—861no—
516#380—861no—
517#380—861no—
518#340—431no—
519#340—431no—
520#340—431no—
521#340C2×D4311yescharacteristic, complemented
522#336—431no—
523#336—431no—
524#336—431no—
525#336C2×D4311yescharacteristic, complemented
526C43#2092911yescharacteristic, complemented, Sylow
527C25—861no—
528C2×#41—434no—
529C2×#41—862no—
530C2×#41—862no—
531C2×#41—862no—
532C2×#41—862no—
533C2×#41—862no—
534C22×Q8—431no—
535C22×D4—434no—
536C22×D4—434no—
537C22×D4—434no—
538C22×D4—431no—
539C22×D4—862no—
540C22×D4—862no—
541C22×D4—862no—
542C22×D4—861no—
543C22×D4—861no—
544C22×D4C22×D4311yescharacteristic
545C22×D4C22×D4311yescharacteristic
546C23×C4—21no—
547C23×C4—431no—
548C23×C4—861no—
549C23×C4—861no—
550C23×C4—861no—
551C23×C4—861no—
552C23×C4—861no—
553AGL(1,ℤ/8)—8632no—
554C2×SD16—434no—
555C2×SD16—434no—
556C2×SD16—862no—
557C2×SD16—862no—
558C2×SD16—862no—
559C2×SD16—862no—
560C2×D8—22no—
561C2×D8—22no—
562C2×D8—434no—
563C2×D8—862no—
564C2×D8—862no—
565C2×D8C4×D4314yescomplemented
566C2×M16—434no—
567C2×M16—862no—
568C2×M16—862no—
569C22×C8—431no—
570C22×C8—431no—
571C22×C8—862no—
572C22×C8—862no—
573C22×C8—862no—
574C22×C8C22×D4311yescharacteristic
575C22×C8C22×D4311yescharacteristic
576C4×D4—22no—
577C4×D4—22no—
578C4×D4—862no—
579C4×D4—862no—
580C4×D4—868no—
581C4×D4—862no—
582C4×D4—862no—
583C4×D4—868no—
584C4×D4—862no—
585C4×D4—862no—
586#117—434no—
587#117—862no—
588#117—862no—
589#117—862no—
590C2×C4⋊C4—431no—
591C2×C4⋊C4—431no—
592C2×C4⋊C4—431no—
593C2×C4⋊C4—431no—
594C2×C4⋊C4—862no—
595C2×C4⋊C4—862no—
596C2×C4⋊C4—861no—
597C2×C4⋊C4C22×D4311yescharacteristic
598C2×C4⋊C4C22×D4311yescharacteristic
599C2×C22⋊C4—21no—
600C2×C22⋊C4—21no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—431no—
603C2×C22⋊C4—431no—
604C2×C22⋊C4—868no—
605C2×C22⋊C4—861no—
606C2×C22⋊C4—861no—
607C2×C22⋊C4—868no—
608C2×C22⋊C4—861no—
609C2×C22⋊C4—861no—
610C2×C22⋊C4—861no—
611C2×C22⋊C4—861no—
612C2×C42—431no—
613C2×C42—861no—
614C2×C42C22×D4311yescharacteristic
615#103—862no—
616#103—862no—
617#102—22no—
618#102—22no—
619#102—862no—
620#102—862no—
621#102—862no—
622#102—862no—
623#95—861no—
624#95—861no—
625#95—861no—
626#95—861no—
627C24—21no—
628C24—21no—
629C24—431no—
630C24—864no—
631C24—864no—
632C24—864no—
633C24—861no—
634C24—3441no—
635C24—3441no—
636C24—3441no—
637C24—3441no—
638#41—868no—
639#41—868no—
640#41—1724no—
641#41—1724no—
642C2×Q8—432no—
643C2×Q8—861no—
644C2×Q8—861no—
645C2×Q8—861no—
646C2×Q8—861no—
647C2×Q8—861no—
648C2×D4—21no—
649C2×D4—21no—
650C2×D4—21no—
651C2×D4—21no—
652C2×D4—21no—
653C2×D4—21no—
654C2×D4—21no—
655C2×D4—21no—
656C2×D4—4316no—
657C2×D4—432no—
658C2×D4—432no—
659C2×D4—432no—
660C2×D4—868no—
661C2×D4—868no—
662C2×D4—868no—
663C2×D4—864no—
664C2×D4—864no—
665C2×D4—864no—
666C2×D4—864no—
667C2×D4—861no—
668C2×D4—861no—
669C2×D4—861no—
670C2×D4—1722no—
671C2×D4—1722no—
672C2×D4C2×C4×D4312yes—
673C2×D4C2×C4×D4312yes—
674C2×D4D4×D4312yes—
675C2×D4D4×D4312yes—
676C22×C4—21no—
677C22×C4—24no—
678C22×C4—21no—
679C22×C4—81no—
680C22×C4—81no—
681C22×C4—431no—
682C22×C4—432no—
683C22×C4—432no—
684C22×C4—432no—
685C22×C4—432no—
686C22×C4—432no—
687C22×C4—432no—
688C22×C4—431no—
689C22×C4—431no—
690C22×C4—864no—
691C22×C4—864no—
692C22×C4—864no—
693C22×C4—864no—
694C22×C4—861no—
695C22×C4—861no—
696C22×C4—861no—
697C22×C4—3441no—
698C22×C4—3441no—
699C22×C4—3441no—
700C22×C4—3441no—
701C22×C4—3441no—
702C22×C4—3441no—
703C22×C4—3441no—
704C22×C4—3441no—
705C22×C4—1722no—
706C22×C4—1722no—
707C22×C4—1722no—
708C22×C4D4×D4311yescharacteristic
709C22×C4D4×D4311yescharacteristic
710C22×C4C23×D4311yescharacteristic
711SD16—868no—
712SD16—868no—
713D8—28no—
714D8—868no—
715M16—868no—
716C2×C8—21no—
717C2×C8—21no—
718C2×C8—21no—
719C2×C8—21no—
720C2×C8—21no—
721C2×C8—432no—
722C2×C8—861no—
723C2×C8—861no—
724C2×C8—861no—
725C2×C8—861no—
726C2×C8—861no—
727C2×C8—1724no—
728C2×C8C2×C4×D4312yes—
729C4⋊C4—21no—
730C4⋊C4—21no—
731C4⋊C4—21no—
732C4⋊C4—432no—
733C4⋊C4—862no—
734C4⋊C4—862no—
735C4⋊C4—861no—
736C4⋊C4—861no—
737C4⋊C4—861no—
738C4⋊C4—1722no—
739C4⋊C4D4×D4312yes—
740C22⋊C4—24no—
741C22⋊C4—81no—
742C22⋊C4—81no—
743C22⋊C4—862no—
744C22⋊C4—862no—
745C22⋊C4—864no—
746C22⋊C4—864no—
747C22⋊C4—864no—
748C22⋊C4—864no—
749C22⋊C4—3441no—
750C22⋊C4—3441no—
751C42—21no—
752C42—21no—
753C42—864no—
754C42—861no—
755C42—861no—
756C23—22no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—41no—
761C23—41no—
762C23—41no—
763C23—41no—
764C23—41no—
765C23—41no—
766C23—41no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—432no—
771C23—432no—
772C23—432no—
773C23—8616no—
774C23—861no—
775C23—861no—
776C23—861no—
777C23—861no—
778C23—862no—
779C23—862no—
780C23—862no—
781C23—3444no—
782C23—3444no—
783C23—3444no—
784C23—3444no—
785C23—3444no—
786C23—3444no—
787C23—1721no—
788C23—1721no—
789C23—1721no—
790C23—1721no—
791C23C2×D4×D4311yescharacteristic
792Q8—862no—
793Q8—862no—
794Q8—1721no—
795Q8—1721no—
796D4—22no—
797D4—22no—
798D4—22no—
799D4—22no—
800D4—22no—
801D4—41no—
802D4—41no—
803D4—434no—
804D4—8616no—
805D4—862no—
806D4—862no—
807D4—862no—
808D4—1728no—
809D4C22⋊C4×D4314yes—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—22no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—84no—
823C2×C4—432no—
824C2×C4—432no—
825C2×C4—432no—
826C2×C4—434no—
827C2×C4—434no—
828C2×C4—434no—
829C2×C4—434no—
830C2×C4—862no—
831C2×C4—862no—
832C2×C4—861no—
833C2×C4—861no—
834C2×C4—861no—
835C2×C4—861no—
836C2×C4—861no—
837C2×C4—861no—
838C2×C4—3444no—
839C2×C4—3444no—
840C2×C4—3444no—
841C2×C4—3444no—
842C2×C4—1728no—
843C2×C4—1721no—
844C2×C4—1721no—
845C2×C4—1721no—
846C2×C4—1721no—
847C2×C4—1721no—
848C2×C4—1721no—
849C2×C4—1721no—
850C2×C4C22×C4×D4311yescharacteristic
851C2×C4C2×D4×D4311yescharacteristic
852C2×C4C2×D4×D4311yescharacteristic
853C2×C4C2×D4×D4311yescharacteristic
854C2×C4#41×D4311yescharacteristic
855C2×C4#41×D4311yescharacteristic
856C8—22no—
857C8—41no—
858C8—862no—
859C8—1721no—
860C22—24no—
861C22—42no—
862C22—42no—
863C22—42no—
864C22—42no—
865C22—42no—
866C22—42no—
867C22—42no—
868C22—42no—
869C22—42no—
870C22—81no—
871C22—81no—
872C22—81no—
873C22—81no—
874C22—434no—
875C22—862no—
876C22—862no—
877C22—862no—
878C22—862no—
879C22—862no—
880C22—862no—
881C22—864no—
882C22—34416no—
883C22—1722no—
884C22—1722no—
885C22—1722no—
886C22—1722no—
887C22—1722no—
888C22—1722no—
889C22C4×D4×D4311yescharacteristic
890C22#120×D4311yescharacteristic
891C22#121×D4311yescharacteristic
892C22#1458370011yescharacteristic
893C22#1458370311yescharacteristic
894C22#1458370611yescharacteristic
895C22#1458370911yescharacteristic
896C4—41no—
897C4—42no—
898C4—41no—
899C4—81no—
900C4—434no—
901C4—3441no—
902C4—1721no—
903C4—1721no—
904C4—1722no—
905C4—1722no—
906C4C2×C22⋊C4×D4311yescharacteristic
907C4C4×D4×D4311yescharacteristic
908C4#121×D4311yescharacteristic
909C4#123×D4311yescharacteristic
910C2—44no—
911C2—82no—
912C2—864no—
913C2—1724no—
914C2#386×D4311yescharacteristic
915C2#1914342011yescharacteristic
916C2#1914342411yescharacteristic
917C2#1914389411yescharacteristic
918C2#1914389711yescharacteristic
919C2#1914409311yescharacteristic
920C2#1914410511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1879C2
socleC23×C43C22×D4
prime radicalC22×#13063349C2
cosocleC22×C4×C43C24
hypercenter#1879D43
hypocenterC43#20929
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1879

Complements

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

NH ≅ G/Ntype
2. C2×#14583371C2semidirect
3. C2×#14582892C2semidirect
4. C2×#102×D43C2semidirect
5. #19137185C2semidirect
6. #19134946C2semidirect
7. #19134945C2semidirect
8. #19134940C2semidirect
9. #19134930C2semidirect
10. #19134929C2semidirect
11. #19134928C2semidirect
12. #19134927C2semidirect
13. #19134313C2semidirect
14. #19134290C2semidirect
15. C43×#1879C2semidirect
20. C2×#13063349C4semidirect
39. C2×#13063250C22semidirect
40. C2×#13063248C22semidirect
43. C2×#13063246C22semidirect
46. #14582805C22semidirect
47. #14582804C22semidirect
48. #14582802C22semidirect
53. #14582662C22semidirect
54. #14582661C22semidirect
55. #14582661C22semidirect
56. #14582654C22semidirect
57. #14582653C22semidirect
58. #14582653C22semidirect
62. C2×#102×C43C22semidirect
63. C43×#390C22semidirect
64. C43×#340C22semidirect
65. C43×#336C22semidirect
72. C2×#10621900C2×C4semidirect
92. C2×#10621873C2×C4semidirect
95. C2×#10621883C2×C4semidirect
98. C2×#10621882C2×C4semidirect
101. C2×#10621872C2×C4semidirect
153. C2×D8×C43C2×C4semidirect
222. D4×D43C22⋊C4semidirect
458. #1879D43semidirect
509. C2×#102C2×D43semidirect
513. #390C2×D43semidirect
521. #340C2×D43semidirect
525. #336C2×D43semidirect
526. C43#20929semidirect
565. C2×D8C4×D43semidirect

Maximal subgroups

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

subgroupindex
C22×#130633492
C2×#145833712
C2×#145828922
C2×#102×D432
#191371852
#191349462
#191349452
#191349402
#191349302
#191349292
#191349282
#191349272
#191343132
#191342902
C43×#18792
#2092943