Finite Group Databasebeta

← #25102442

Subgroups — #25102442

Order 11008.

1342 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#131×D43C211yesmaximal, characteristic, complemented
2#19143815C211yesmaximal, characteristic
3C2×#14583020C211yesmaximal, characteristic, complemented
4C2×#14583018C211yesmaximal, characteristic, complemented
5#19143288C211yesmaximal, characteristic, complemented
6#19134922C211yesmaximal, characteristic, complemented
7#19134921C211yesmaximal, characteristic, complemented
8#19134896C211yesmaximal, characteristic, complemented
9#19134869C211yesmaximal, characteristic, complemented
10#19134798C211yesmaximal, characteristic, complemented
11#19134537C211yesmaximal, characteristic, complemented
12#19134442C211yesmaximal, characteristic, complemented
13#19134436C211yesmaximal, characteristic, complemented
14#19134370C211yesmaximal, characteristic, complemented
15C43×#1866C211yesmaximal, characteristic, complemented
16C2×#41×D43C2211yescharacteristic
17C2×#13063347C2211yescharacteristic
18C2×#13063345C2211yescharacteristic
19C2×#13063333—21no—
20C2×#13063333C2211yescharacteristic
21C2×#13063333C2211yescharacteristic, complemented
22C2×#13063332C2211yescharacteristic
23C2×#13063331—21no—
24C2×#13063331C2211yescharacteristic
25#131×D43—24no—
26#131×D43—24no—
27C2×M16×D43—21no—
28C2×M16×D43C2211yescharacteristic
29C22×C8×D43—21no—
30C22×C8×D43C2211yescharacteristic
31#14583411C2211yescharacteristic
32#14583064C411yescharacteristic, complemented
33#14583062C411yescharacteristic, complemented
34#14583056C411yescharacteristic, complemented
35#14583051C411yescharacteristic, complemented
36#14583047C411yescharacteristic, complemented
37#14583045C411yescharacteristic, complemented
38#14583039C411yescharacteristic, complemented
39#14583034C411yescharacteristic, complemented
40#14583020—24no—
41#14583018—24no—
42#14582969—21no—
43#14582969—21no—
44#14582964—21no—
45#14582964—21no—
46C2×#13063260C2211yescharacteristic, complemented
47C2×#13063253C2211yescharacteristic
48C2×#13063253C2211yescharacteristic, complemented
49C2×#13063252C2211yescharacteristic
50C2×#13063251C2211yescharacteristic
51C2×#13063251C2211yescharacteristic, complemented
52#14582893C2211yescharacteristic
53#14582865C2211yescharacteristic, complemented
54#14582862C2211yescharacteristic
55C2×(C2×D43)⋊C8C2211yescharacteristic
56#14582855C2211yescharacteristic, complemented
57C2×#13063236C2211yescharacteristic, complemented
58C2×#13063235C2211yescharacteristic, complemented
59C4×(C2×D43)⋊C4C2211yescharacteristic
60#14582664C2211yescharacteristic, complemented
61#14582663C2211yescharacteristic, complemented
62#14582658C2211yescharacteristic, complemented
63#14582653C2211yescharacteristic, complemented
64C2×#131×C43C2211yescharacteristic
65C2×#108×C43C2211yescharacteristic, complemented
66C43×#424C2211yescharacteristic, complemented
67C2×#104×C43C2211yescharacteristic
68C43×#416C2211yescharacteristic
69C43×#339C2211yescharacteristic, complemented
70C43×#336C2211yescharacteristic, complemented
71C2×#10621902C2×C411yescharacteristic
72C2×#10621898—21no—
73C2×#10621898C2311yescharacteristic
74C2×#10621898C2311yescharacteristic
75C2×#10621900—21no—
76C2×#10621900C2×C411yescharacteristic
77#41×D43—22no—
78#41×D43—22no—
79#41×D43—22no—
80#41×D43—22no—
81C2×Q8×D43C2×C411yescharacteristic
82C2×D4×D43—21no—
83C2×D4×D43C2×C411yescharacteristic
84C22×C4×D43—21no—
85C22×C4×D43C2311yescharacteristic
86#13063347—22no—
87#13063347—22no—
88#13063345—22no—
89#13063345—22no—
90C2×Dic172C2×C411yescharacteristic
91C2×#10621885C2×C411yescharacteristic
92C2×#10621873C2×C411yescharacteristic
93C2×#10621873C2×C411yescharacteristic
94C2×#10621883C2×C411yescharacteristic
95C2×#10621884C2×C411yescharacteristic
96C2×D344C2×C411yescharacteristic
97C2×#10621882C2×C411yescharacteristic
98#13063333—28no—
99#13063333—22no—
100#13063333—22no—
101#13063333—22no—
102#13063333D414yescomplemented
103#13063332—22no—
104#13063332D414yescomplemented
105#13063331—28no—
106#13063331—22no—
107#13063331—22no—
108C2×#10621877—21no—
109C2×#10621877C2311yescharacteristic
110C2×#10621877C2311yescharacteristic
111C2×#10621872—21no—
112C2×#10621872—21no—
113C2×#10621872—21no—
114C2×#10621872—21no—
115M16×D43—28no—
116M16×D43—22no—
117M16×D43—22no—
118C22×C43⋊C8—21no—
119C22×C43⋊C8C2311yescharacteristic
120C22×C43⋊C8C2311yescharacteristic
121C2×C8×D43—28no—
122C2×C8×D43—21no—
123C2×C8×D43—21no—
124C2×C8×D43—21no—
125C2×C8×D43—22no—
126C2×C8×D43—22no—
127C2×C8×D43—21no—
128C2×C8×D43D411yescharacteristic
129C2×C8×D43D411yescharacteristic
130C2×C8×D43D411yescharacteristic
131C2×C8×D43D411yescharacteristic
132#13063309—21no—
133#13063305C2×C411yescharacteristic
134#13063305C2×C411yescharacteristic
135#13063300C2×C411yescharacteristic
136#13063300C2×C411yescharacteristic
137#13063295—21no—
138C4×D172—21no—
139C4×D172—21no—
140C2×(C2×D43)⋊C4—21no—
141C2×C4×Dic43C2311yescharacteristic
142#13063260—22no—
143#13063253—22no—
144#13063253—22no—
145#13063252—22no—
146#13063251—22no—
147#13063251—22no—
148#13063248C2×C411yescharacteristic
149#13063248C2×C411yescharacteristic
150#13063245C2×C411yescharacteristic
151#13063245C2×C411yescharacteristic
152(C2×D43)⋊C8—21no—
153(C2×D43)⋊C8—21no—
154(C2×D43)⋊C8—21no—
155(C2×D43)⋊C8—21no—
156(C2×D43)⋊C8C2×C411yescharacteristic
157(C2×D43)⋊C8C2×C411yescharacteristic
158(C2×D43)⋊C8C2×C411yescharacteristic
159(C2×D43)⋊C8C2×C411yescharacteristic
160#13063236—22no—
161#13063236—21no—
162#13063235—22no—
163C4×C43⋊C8—21no—
164C43⋊#95—21no—
165C2×#41×C43C2311yescharacteristic
166#131×C43—22no—
167#131×C43—22no—
168C2×M16×C43—21no—
169C2×M16×C43C2311yescharacteristic
170C2×M16×C43C2311yescharacteristic
171C22×C8×C43—21no—
172C22×C8×C43C2311yescharacteristic
173C22×C8×C43C2311yescharacteristic
174#117×C43C2311yescharacteristic
175C2×C42×C43C2311yescharacteristic
176#108×C43—22no—
177C4⋊C8×C43—21no—
178C4⋊C8×C43—21no—
179#104×C43—22no—
180#103×C43C2×C411yescharacteristic
181#103×C43C2×C411yescharacteristic
182#102×C43C2×C411yescharacteristic
183#102×C43C2×C411yescharacteristic
184C23×D43—21no—
185C23×D43#4111yescharacteristic
186#41×C43—21no—
187#41×C43—21no—
188#41×C43C2×D412yes—
189#41×C43#4112yes—
190C2×Q8×C43C22×C411yescharacteristic
191C2×D4×C43—21no—
192C2×D4×C43C22×C411yescharacteristic
193C22×C4×C43—21no—
194C22×C4×C43—21no—
195C22×C4×C43C2411yescharacteristic
196C2×C22⋊D43—21no—
197C2×C22⋊D43—21no—
198C2×C22⋊D43—21no—
199C2×C22⋊D43—21no—
200C22×Dic43—21no—
201C22×Dic43—21no—
202C22×Dic43#4111yescharacteristic
203#10621902—22no—
204#10621902—22no—
205Q8×D43—22no—
206Q8×D43—22no—
207#10621900—24no—
208#10621900—24no—
209#10621900—22no—
210#10621900—22no—
211D4×D43—24no—
212D4×D43—24no—
213D4×D43—22no—
214D4×D43—22no—
215#10621898—24no—
216#10621898—24no—
217#10621898—21no—
218#10621898—21no—
219#10621898—21no—
220#10621898—21no—
221#10621898—21no—
222#10621898—21no—
223#10621898C2×D412yes—
224#10621898#4112yes—
225C2×D172—21no—
226C2×D172—21no—
227C2×D172—21no—
228C2×D172C22×C411yescharacteristic
229C2×D172C22×C411yescharacteristic
230C2×C4×D43—24no—
231C2×C4×D43—24no—
232C2×C4×D43—21no—
233C2×C4×D43—21no—
234C2×C4×D43—21no—
235C2×C4×D43—21no—
236C2×C4×D43—21no—
237C2×C4×D43—21no—
238C2×C4×D43—21no—
239C2×C4×D43—21no—
240C2×C4×D43C22×C411yescharacteristic
241C2×C4×D43C22×C411yescharacteristic
242C2×C4×D43C2×D411yescharacteristic
243C2×C4×D43C2×D411yescharacteristic
244C2×Dic86—21no—
245C2×Dic86C22×C411yescharacteristic
246C2×Dic86C22×C411yescharacteristic
247M16×C43—24no—
248M16×C43—21no—
249M16×C43—21no—
250M16×C43—21no—
251M16×C43C2×D412yes—
252C2×C8×C43—24no—
253C2×C8×C43—21no—
254C2×C8×C43—21no—
255C2×C8×C43—21no—
256C2×C8×C43—21no—
257C2×C8×C43—21no—
258C2×C8×C43—21no—
259C2×C8×C43C22×C411yescharacteristic
260C2×C8×C43C22×C411yescharacteristic
261C2×C8×C43C2×D411yescharacteristic
262C2×C8×C43C2×D411yescharacteristic
263C4⋊C4×C43C22×C411yescharacteristic
264C4⋊C4×C43C22×C411yescharacteristic
265C22⋊C4×C43—21no—
266C42×C43—21no—
267C42×C43—21no—
268C42×C43—21no—
269#10621885—22no—
270#10621884—22no—
271#10621883—22no—
272#10621882—22no—
273(C2×D43)⋊C4—21no—
274(C2×D43)⋊C4—21no—
275(C2×D43)⋊C4—21no—
276(C2×D43)⋊C4—21no—
277(C2×D43)⋊C4—42no—
278C4⋊Dic43—21no—
279C4⋊Dic43—21no—
280C4×Dic43—21no—
281C4×Dic43—21no—
282#10621877—21no—
283#10621877—24no—
284#10621877—21no—
285#10621877—21no—
286#10621877C2×D412yes—
287C2×C43⋊C8—21no—
288C2×C43⋊C8—21no—
289C2×C43⋊C8—21no—
290C2×C43⋊C8—24no—
291C2×C43⋊C8—21no—
292C2×C43⋊C8C22×C411yescharacteristic
293C2×C43⋊C8C22×C411yescharacteristic
294C2×C43⋊C8C2×D411yescharacteristic
295C2×C43⋊C8C2×D412yes—
296C2×C43⋊C8C2×D411yescharacteristic
297C2×C43⋊C8C2×D412yes—
298Dic172—22no—
299D344—22no—
300#10621873—22no—
301#10621873—22no—
302#10621872—24no—
303#10621872—24no—
304#10621872—24no—
305#10621872—42no—
306C8×D43—24no—
307C8×D43—24no—
308C8×D43—22no—
309C8×D43—24no—
310C8×D43—22no—
311C8×D43—22no—
312C8×D43—22no—
313C8×D43—42no—
314C23×C43—21no—
315C23×C43C2×#4111yescharacteristic
316C22×D43—24no—
317C22×D43—21no—
318C22×D43—21no—
319C22×D43—21no—
320C22×D43—22no—
321C22×D43—21no—
322C22×D43—41no—
323C22×D43—42no—
324C22×D43—42no—
325C22×D43C4×D411yescharacteristic
326C22×D43C4×D411yescharacteristic
327Q8×C43—21no—
328Q8×C43C4×D412yes—
329D4×C43—22no—
330D4×C43—22no—
331D4×C43—21no—
332D4×C43C4×D412yes—
333C2×C4×C43—21no—
334C2×C4×C43—22no—
335C2×C4×C43—22no—
336C2×C4×C43—21no—
337C2×C4×C43—21no—
338C2×C4×C43—41no—
339C2×C4×C43—41no—
340C2×C4×C43—41no—
341C2×C4×C43C23×C411yescharacteristic
342C2×C4×C43C22×D411yescharacteristic
343C2×C4×C43C22×D411yescharacteristic
344C2×C4×C43C22×D411yescharacteristic
345C2×C4×C43C2×#4111yescharacteristic
346C2×C4×C43C2×#4111yescharacteristic
347C22⋊D43—24no—
348C22⋊D43—24no—
349C22⋊D43—22no—
350C22⋊D43—22no—
351C22⋊D43—41no—
352C22⋊D43—41no—
353C2×Dic43—24no—
354C2×Dic43—21no—
355C2×Dic43—21no—
356C2×Dic43—21no—
357C2×Dic43—21no—
358C2×Dic43—41no—
359C2×Dic43—41no—
360C2×Dic43—41no—
361C2×Dic43C4×D411yescharacteristic
362C2×Dic43C4×D411yescharacteristic
363D172—24no—
364D172—21no—
365D172—21no—
366D172—21no—
367D172—42no—
368D172—42no—
369D172C4×D412yes—
370C4×D43—24no—
371C4×D43—24no—
372C4×D43—21no—
373C4×D43—21no—
374C4×D43—21no—
375C4×D43—21no—
376C4×D43—21no—
377C4×D43—22no—
378C4×D43—21no—
379C4×D43—21no—
380C4×D43—22no—
381C4×D43—21no—
382C4×D43—41no—
383C4×D43—41no—
384Dic86—24no—
385Dic86—21no—
386Dic86—21no—
387Dic86—21no—
388Dic86C4×D412yes—
389C8×C43—21no—
390C8×C43—21no—
391C8×C43—21no—
392C8×C43—22no—
393C8×C43—21no—
394C8×C43—41no—
395C43⋊C8—21no—
396C43⋊C8—21no—
397C43⋊C8—22no—
398C43⋊C8—41no—
399C43⋊C8#12012yes—
400C43⋊C8#12012yes—
401#21467—431nomaximal, Sylow
402C22×C43—21no—
403C22×C43—21no—
404C22×C43—22no—
405C22×C43—41no—
406C22×C43—41no—
407C22×C43C2×C4×D411yescharacteristic
408C22×C43#52511yescharacteristic
409C22×C43#52511yescharacteristic
410C2×D43—21no—
411C2×D43—21no—
412C2×D43—21no—
413C2×D43—21no—
414C2×D43—22no—
415C2×D43—21no—
416C2×D43—42no—
417C2×D43—42no—
418C2×D43—48no—
419C2×D43—41no—
420C2×D43—41no—
421C2×D43—41no—
422C2×D43—41no—
423C2×D43—41no—
424C2×D43#44412yescomplemented
425C4×C43—22no—
426C4×C43—41no—
427C4×C43—41no—
428C4×C43—81no—
429C4×C43C2×C4×D411yescharacteristic
430C4×C43C2×C4×D411yescharacteristic
431C4×C43C2×#12011yescharacteristic
432C4×C43#52511yescharacteristic
433Dic43—21no—
434Dic43—22no—
435Dic43—21no—
436Dic43—41no—
437Dic43—81no—
438C22×#131—431no—
439#3002—431no—
440C2×#444—431no—
441C2×#444—431no—
442#2929—431no—
443#1876—431no—
444#1876—431no—
445#1871—431no—
446#1866—431no—
447#1866D4311yescharacteristic, complemented
448#1855—431no—
449#1789—431no—
450#1765—431no—
451#1765—431no—
452#1752—431no—
453C2×C43—21no—
454C2×C43—21no—
455C2×C43—42no—
456C2×C43C4×#12011yescharacteristic
457C2×C43C2×#44411yescharacteristic
458C2×C43#295511yescharacteristic
459D43—22no—
460D43—41no—
461D43—42no—
462D43—81no—
463C22×#41—431no—
464C2×#135—431no—
465C2×#135—431no—
466C2×#131—431no—
467C2×#131—431no—
468C2×#131—431no—
469C2×#131—431no—
470C2×#131—861no—
471C2×#131—861no—
472C2×#131—864no—
473C2×#131—864no—
474C2×#131C2×D4311yescharacteristic
475C22×M16—431no—
476C22×M16—861no—
477C23×C8—431no—
478C23×C8—861no—
479#525—431no—
480#452—431no—
481#452—431no—
482#451—431no—
483#450—431no—
484#449—431no—
485#449—431no—
486#448—431no—
487#447—431no—
488#444—864no—
489#444—864no—
490#435—861no—
491#435—861no—
492C8×D4—861no—
493C8×D4—861no—
494C2×#108—431no—
495C2×#108C2×D4311yescharacteristic, complemented
496#424C2×D4311yescharacteristic, complemented
497C2×#104—431no—
498C2×#104—431no—
499C2×#104—431no—
500C2×#104—431no—
501C2×#104—431no—
502C2×#104C2×D4311yescharacteristic
503#416—431no—
504#416C2×D4311yescharacteristic
505#408—431no—
506#407—431no—
507C2×C22⋊C8—431no—
508#405—431no—
509C2×#97—431no—
510C2×#97—431no—
511C4×C22⋊C4—431no—
512#341—431no—
513#341—431no—
514#339—431no—
515#339C2×D4311yescharacteristic, complemented
516#336—431no—
517#336C2×D4311yescharacteristic, complemented
518C43#2146711yescharacteristic, complemented, Sylow
519C2×#41—431no—
520C2×#41—431no—
521C2×#41—431no—
522C2×#41—431no—
523C2×#41—861no—
524C2×#41—861no—
525C2×#41—862no—
526C2×#41—862no—
527C2×#41—862no—
528C2×#41—862no—
529C2×#41C22×D4311yescharacteristic
530C22×Q8—431no—
531C22×D4—431no—
532C22×D4—861no—
533C23×C4—431no—
534C23×C4—861no—
535#135—862no—
536#135—862no—
537#135—862no—
538#135—862no—
539C2×Q16—431no—
540C2×Q16—431no—
541C2×SD16—431no—
542C2×SD16—431no—
543C2×SD16—431no—
544C2×SD16—431no—
545C2×D8—431no—
546C2×D8—431no—
547#131—22no—
548#131—22no—
549#131—434no—
550#131—434no—
551#131—862no—
552#131—862no—
553#131—868no—
554#131—862no—
555#131—862no—
556#131—862no—
557#131—862no—
558#131—868no—
559C2×M16—21no—
560C2×M16—431no—
561C2×M16—431no—
562C2×M16—861no—
563C2×M16—861no—
564C2×M16—861no—
565C2×M16—861no—
566C2×M16—862no—
567C2×M16—868no—
568C2×M16—862no—
569C2×M16—861no—
570C2×M16C22×D4311yescharacteristic
571C2×M16C22×D4311yescharacteristic
572C22×C8—21no—
573C22×C8—431no—
574C22×C8—431no—
575C22×C8—431no—
576C22×C8—431no—
577C22×C8—431no—
578C22×C8—431no—
579C22×C8—862no—
580C22×C8—862no—
581C22×C8—861no—
582C22×C8—861no—
583C22×C8—861no—
584C22×C8—868no—
585C22×C8—861no—
586C22×C8—861no—
587C22×C8C22×D4311yescharacteristic
588C22×C8C22×D4311yescharacteristic
589#123—861no—
590C22⋊Q8—431no—
591C22⋊Q8—431no—
592#121—431no—
593#121—431no—
594#120—861no—
595C4×D4—861no—
596C4×D4—861no—
597#117C22×D4311yescharacteristic
598C2×C22⋊C4—861no—
599C2×C42—431no—
600C2×C42C22×D4311yescharacteristic
601#108—22no—
602#108—862no—
603C4⋊C8—21no—
604C4⋊C8—21no—
605#104—22no—
606#104—862no—
607#104—862no—
608#104—862no—
609#104—862no—
610#104—862no—
611#103—431no—
612#103—431no—
613#103C4×D4311yescharacteristic
614#103C4×D4311yescharacteristic
615#102—431no—
616#102—431no—
617#102C4×D4311yescharacteristic
618#102C4×D4311yescharacteristic
619C22⋊C8—431no—
620C22⋊C8—431no—
621C22⋊C8—431no—
622C22⋊C8—431no—
623C22⋊C8—861no—
624C22⋊C8—861no—
625C22⋊C8—861no—
626C22⋊C8—861no—
627#97—862no—
628#97—861no—
629#97—862no—
630C4×C8—861no—
631#95—861no—
632C24—431no—
633C24—861no—
634#41—21no—
635#41—21no—
636#41—432no—
637#41—432no—
638#41—864no—
639#41—864no—
640#41—862no—
641#41—864no—
642#41—864no—
643#41—862no—
644#41—862no—
645#41—862no—
646#41—861no—
647#41—861no—
648#41—861no—
649#41—861no—
650#41—861no—
651#41—861no—
652#41D4×D4312yes—
653#41#1062190212yes—
654C2×Q8—431no—
655C2×Q8—431no—
656C2×Q8—861no—
657C2×Q8—862no—
658C2×Q8—862no—
659C2×Q8C2×C4×D4311yescharacteristic
660C2×D4—21no—
661C2×D4—431no—
662C2×D4—431no—
663C2×D4—861no—
664C2×D4—861no—
665C2×D4—861no—
666C2×D4—861no—
667C2×D4—862no—
668C2×D4—864no—
669C2×D4—864no—
670C2×D4—861no—
671C2×D4—861no—
672C2×D4—862no—
673C2×D4—861no—
674C2×D4C2×C4×D4311yescharacteristic
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—431no—
678C22×C4—431no—
679C22×C4—431no—
680C22×C4—431no—
681C22×C4—431no—
682C22×C4—861no—
683C22×C4—861no—
684C22×C4—864no—
685C22×C4—864no—
686C22×C4—861no—
687C22×C4—861no—
688C22×C4—861no—
689C22×C4—861no—
690C22×C4—861no—
691C22×C4—861no—
692C22×C4—861no—
693C22×C4—861no—
694C22×C4C23×D4311yescharacteristic
695Q16—862no—
696Q16—862no—
697SD16—862no—
698SD16—862no—
699SD16—862no—
700SD16—862no—
701D8—862no—
702D8—862no—
703M16—24no—
704M16—21no—
705M16—21no—
706M16—21no—
707M16—432no—
708M16—864no—
709M16—864no—
710M16—864no—
711M16—864no—
712M16—861no—
713M16—861no—
714M16—861no—
715M16—1722no—
716M16D4×D4312yes—
717C2×C8—24no—
718C2×C8—21no—
719C2×C8—21no—
720C2×C8—21no—
721C2×C8—21no—
722C2×C8—21no—
723C2×C8—21no—
724C2×C8—432no—
725C2×C8—432no—
726C2×C8—431no—
727C2×C8—431no—
728C2×C8—431no—
729C2×C8—431no—
730C2×C8—862no—
731C2×C8—862no—
732C2×C8—862no—
733C2×C8—862no—
734C2×C8—864no—
735C2×C8—864no—
736C2×C8—864no—
737C2×C8—864no—
738C2×C8—861no—
739C2×C8—861no—
740C2×C8—861no—
741C2×C8—861no—
742C2×C8—1722no—
743C2×C8C2×C4×D4311yescharacteristic
744C2×C8C2×C4×D4311yescharacteristic
745C2×C8D4×D4311yescharacteristic
746C2×C8D4×D4311yescharacteristic
747C4⋊C4—861no—
748C4⋊C4—861no—
749C4⋊C4C2×C4×D4311yescharacteristic
750C4⋊C4C2×C4×D4311yescharacteristic
751C22⋊C4—21no—
752C22⋊C4—861no—
753C22⋊C4—861no—
754C22⋊C4—861no—
755C22⋊C4—861no—
756C22⋊C4—1722no—
757C42—21no—
758C42—21no—
759C42—21no—
760C42—861no—
761C42—861no—
762C23—21no—
763C23—431no—
764C23—431no—
765C23—862no—
766C23—864no—
767C23—861no—
768C23—861no—
769C23—861no—
770C23—861no—
771C23—1721no—
772C23—1722no—
773C23—1722no—
774C23#41×D4311yescharacteristic
775Q8—21no—
776Q8—432no—
777Q8—864no—
778Q8—861no—
779Q8—861no—
780Q8—861no—
781Q8#1306328712yes—
782D4—22no—
783D4—22no—
784D4—21no—
785D4—432no—
786D4—864no—
787D4—864no—
788D4—864no—
789D4—862no—
790D4—862no—
791D4—861no—
792D4—861no—
793D4—861no—
794D4—1722no—
795D4—1722no—
796D4—1721no—
797D4—1721no—
798D4#1306328712yes—
799C2×C4—21no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—431no—
808C2×C4—431no—
809C2×C4—864no—
810C2×C4—864no—
811C2×C4—864no—
812C2×C4—861no—
813C2×C4—861no—
814C2×C4—861no—
815C2×C4—861no—
816C2×C4—861no—
817C2×C4—861no—
818C2×C4—861no—
819C2×C4—861no—
820C2×C4—861no—
821C2×C4—862no—
822C2×C4—861no—
823C2×C4—861no—
824C2×C4—862no—
825C2×C4—861no—
826C2×C4—1721no—
827C2×C4—1721no—
828C2×C4—1721no—
829C2×C4—1721no—
830C2×C4—1721no—
831C2×C4C22×C4×D4311yescharacteristic
832C2×C4C2×D4×D4311yescharacteristic
833C2×C4C2×D4×D4311yescharacteristic
834C2×C4C2×D4×D4311yescharacteristic
835C2×C4#41×D4311yescharacteristic
836C2×C4C2×#1062190211yescharacteristic
837C8—21no—
838C8—21no—
839C8—21no—
840C8—22no—
841C8—21no—
842C8—41no—
843C8—432no—
844C8—432no—
845C8—861no—
846C8—861no—
847C8—862no—
848C8—1721no—
849C22—21no—
850C22—21no—
851C22—22no—
852C22—41no—
853C22—41no—
854C22—432no—
855C22—861no—
856C22—861no—
857C22—861no—
858C22—861no—
859C22—862no—
860C22—861no—
861C22—1722no—
862C22—1722no—
863C22—1728no—
864C22—1721no—
865C22—1721no—
866C22—1721no—
867C22—1721no—
868C22—1721no—
869C22C4×D4×D4311yescharacteristic
870C22#1458340711yescharacteristic
871C22#1458341211yescharacteristic
872C4—22no—
873C4—41no—
874C4—41no—
875C4—81no—
876C4—861no—
877C4—861no—
878C4—862no—
879C4—3441no—
880C4—1721no—
881C4C4×D4×D4311yescharacteristic
882C4C2×#1306328711yescharacteristic
883C4#120×D4311yescharacteristic
884C4#1458341211yescharacteristic
885C2—21no—
886C2—21no—
887C2—42no—
888C2—862no—
889C2—3441no—
890C2—1721no—
891C2—1722no—
892C2#1913709611yescharacteristic
893C2#444×D4311yescharacteristic
894C2#1914349311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1866C2
socleC22×C43C2×C4×D4
prime radical#19143815C2
cosocleC22×C4×C43C24
hypercenter#1866D43
hypocenterC43#21467
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1866

Complements

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

NH ≅ G/Ntype
1. C2×#131×D43C2semidirect
3. C2×#14583020C2semidirect
4. C2×#14583018C2semidirect
5. #19143288C2semidirect
6. #19134922C2semidirect
7. #19134921C2semidirect
8. #19134896C2semidirect
9. #19134869C2semidirect
10. #19134798C2semidirect
11. #19134537C2semidirect
12. #19134442C2semidirect
13. #19134436C2semidirect
14. #19134370C2semidirect
15. C43×#1866C2semidirect
21. C2×#13063333C22semidirect
32. #14583064C4semidirect
33. #14583062C4semidirect
34. #14583056C4semidirect
35. #14583051C4semidirect
36. #14583047C4semidirect
37. #14583045C4semidirect
38. #14583039C4semidirect
39. #14583034C4semidirect
46. C2×#13063260C22semidirect
48. C2×#13063253C22semidirect
51. C2×#13063251C22semidirect
53. #14582865C22semidirect
56. #14582855C22semidirect
57. C2×#13063236C22semidirect
58. C2×#13063235C22semidirect
60. #14582664C22semidirect
61. #14582663C22semidirect
62. #14582658C22semidirect
63. #14582653C22semidirect
65. C2×#108×C43C22semidirect
66. C43×#424C22semidirect
69. C43×#339C22semidirect
70. C43×#336C22semidirect
102. #13063333D4semidirect
104. #13063332D4semidirect
424. C2×D43#444semidirect
447. #1866D43semidirect
495. C2×#108C2×D43semidirect
496. #424C2×D43semidirect
515. #339C2×D43semidirect
517. #336C2×D43semidirect
518. C43#21467semidirect

Maximal subgroups

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

subgroupindex
C2×#131×D432
#191438152
C2×#145830202
C2×#145830182
#191432882
#191349222
#191349212
#191348962
#191348692
#191347982
#191345372
#191344422
#191344362
#191343702
C43×#18662
#2146743