Finite Group Databasebeta

← #25102454

Subgroups — #25102454

Order 11008.

1320 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×#14583665C211yesmaximal, characteristic, complemented
2#19143811C211yesmaximal, characteristic
3C2×#14583019C211yesmaximal, characteristic, complemented
4C2×#14583014C211yesmaximal, characteristic, complemented
5#19134925C211yesmaximal, characteristic, complemented
6#19134925C211yesmaximal, characteristic, complemented
7#19134898C211yesmaximal, characteristic, complemented
8#19134869C211yesmaximal, characteristic, complemented
9#19134869C211yesmaximal, characteristic, complemented
10#19134799C211yesmaximal, characteristic, complemented
11#19134538C211yesmaximal, characteristic, complemented
12#19134441C211yesmaximal, characteristic, complemented
13#19134434C211yesmaximal, characteristic, complemented
14#19134376C211yesmaximal, characteristic, complemented
15C43×#2930C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17C2×#13063345C2211yescharacteristic
18C2×#13063345C2211yescharacteristic
19#14583665—24no—
20#14583665—24no—
21C2×#13063333—21no—
22C2×#13063333—21no—
23C2×#13063331C2211yescharacteristic
24C2×#13063331C2211yescharacteristic
25C2×#13063331C2211yescharacteristic
26C2×#13063331C2211yescharacteristic
27C22×#10621877C2211yescharacteristic
28C2×M16×D43—21no—
29C2×M16×D43—21no—
30#14583059C411yescharacteristic, complemented
31#14583059C411yescharacteristic, complemented
32#14583054C411yescharacteristic, complemented
33#14583049C411yescharacteristic, complemented
34#14583042C411yescharacteristic, complemented
35#14583042C411yescharacteristic, complemented
36#14583037C411yescharacteristic, complemented
37#14583032C411yescharacteristic, complemented
38#14583019—24no—
39#14583014—24no—
40C2×#13063260C2211yescharacteristic, complemented
41C2×#13063260C2211yescharacteristic, complemented
42C2×#13063252C2211yescharacteristic, complemented
43C2×#13063252C2211yescharacteristic, complemented
44C2×#13063251C2211yescharacteristic
45C2×#13063251C2211yescharacteristic
46C2×#13063251C2211yescharacteristic
47C2×#13063251C2211yescharacteristic
48#14582893C2211yescharacteristic
49#14582893C2211yescharacteristic
50C2×C22⋊(C43⋊C8)C2211yescharacteristic
51C2×#13063235C2211yescharacteristic, complemented
52C2×C8×Dic43C2211yescharacteristic, complemented
53C4×C22⋊Dic43C2211yescharacteristic
54#14582663C2211yescharacteristic, complemented
55#14582663C2211yescharacteristic, complemented
56#14582658C2211yescharacteristic, complemented
57#14582658C2211yescharacteristic, complemented
58#14582653C2211yescharacteristic, complemented
59#14582653C2211yescharacteristic, complemented
60C2×#131×C43C2211yescharacteristic, complemented
61C22×M16×C43C2211yescharacteristic
62C43×#525C2211yescharacteristic
63C43×#436—21no—
64C43×#436—21no—
65C43×#435—21no—
66C43×#435—21no—
67C43×#424C2211yescharacteristic, complemented
68C43×#408C2211yescharacteristic, complemented
69C43×#407C2211yescharacteristic
70C43×#405C2211yescharacteristic, complemented
71C2×#10621898—21no—
72C2×#10621898—21no—
73C2×#10621898—22no—
74C2×#10621898—22no—
75C2×#10621898—22no—
76C2×#10621898—22no—
77C2×#10621898C2×C411yescharacteristic
78C2×#10621898C2×C411yescharacteristic
79C2×#10621898C2311yescharacteristic
80C2×#10621898C2311yescharacteristic
81C22×Dic86C2×C411yescharacteristic
82C22×D172C2×C411yescharacteristic
83C22×C22⋊D43—21no—
84C22×C4×D43—21no—
85#13063345—22no—
86#13063345—22no—
87#13063345—22no—
88#13063345—22no—
89C2×#10621885C2×C411yescharacteristic
90C2×#10621885C2×C411yescharacteristic
91C2×#10621883C2×C411yescharacteristic
92C2×#10621883C2×C411yescharacteristic
93C2×#10621884C2×C411yescharacteristic
94C2×#10621884C2×C411yescharacteristic
95C2×#10621882C2×C411yescharacteristic
96C2×#10621882C2×C411yescharacteristic
97#13063333—28no—
98#13063333—28no—
99#13063331—22no—
100#13063331—22no—
101#13063331—22no—
102#13063331—22no—
103#13063331—22no—
104#13063331—22no—
105#13063331D414yescomplemented
106#13063331D414yescomplemented
107C2×#10621877—21no—
108C2×#10621877—22no—
109C2×#10621877—22no—
110C2×#10621877C2311yescharacteristic
111C2×#10621877C2311yescharacteristic
112C2×#10621872—21no—
113C2×#10621872—21no—
114C2×#10621872—21no—
115C2×#10621872—21no—
116M16×D43—28no—
117M16×D43—28no—
118C22×C43⋊C8—21no—
119C22×C43⋊C8C2311yescharacteristic
120C22×C43⋊C8C2311yescharacteristic
121C2×C8×D43—21no—
122C2×C8×D43—21no—
123C2×C8×D43—21no—
124C2×C8×D43—21no—
125C2×C22⋊Dic43—21no—
126C2×C4×Dic43C2311yescharacteristic
127C2×C4×Dic43C2311yescharacteristic
128#13063260—22no—
129#13063260—22no—
130#13063252—22no—
131#13063252—22no—
132#13063251—22no—
133#13063251—22no—
134#13063251—22no—
135#13063251—22no—
136#13063248C2×C411yescharacteristic
137#13063248C2×C411yescharacteristic
138#13063248C2×C411yescharacteristic
139#13063248C2×C411yescharacteristic
140#13063245C2×C411yescharacteristic
141#13063245C2×C411yescharacteristic
142#13063245C2×C411yescharacteristic
143#13063245C2×C411yescharacteristic
144C22⋊(C43⋊C8)C2×C411yescharacteristic
145C22⋊(C43⋊C8)C2×C411yescharacteristic
146C22⋊(C43⋊C8)C2×C411yescharacteristic
147C22⋊(C43⋊C8)C2×C411yescharacteristic
148#13063235—22no—
149C8×Dic43—22no—
150C43⋊#95—21no—
151C2×#41×C43C2311yescharacteristic
152C23×C4×C43C2311yescharacteristic
153#131×C43—22no—
154#131×C43—22no—
155C2×M16×C43—22no—
156C2×M16×C43—22no—
157C2×M16×C43—21no—
158C2×M16×C43D411yescharacteristic
159C2×M16×C43D411yescharacteristic
160C2×M16×C43D411yescharacteristic
161C2×M16×C43D411yescharacteristic
162C2×M16×C43C2311yescharacteristic
163C2×M16×C43C2311yescharacteristic
164C22×C8×C43—21no—
165C22×C8×C43C2311yescharacteristic
166C22×C8×C43C2311yescharacteristic
167#123×C43—21no—
168C22⋊Q8×C43C2×C411yescharacteristic
169C22⋊Q8×C43C2×C411yescharacteristic
170#121×C43C2×C411yescharacteristic
171#121×C43C2×C411yescharacteristic
172#120×C43—21no—
173C4×D4×C43—21no—
174C4×D4×C43—21no—
175#117×C43C2311yescharacteristic
176C4⋊C8×C43—21no—
177C4⋊C8×C43—21no—
178C22⋊C8×C43—21no—
179C22⋊C8×C43—21no—
180C22⋊C8×C43—21no—
181C22⋊C8×C43—21no—
182#97×C43—21no—
183C4×C8×C43—21no—
184C24×C43#4111yescharacteristic
185C23×D43—21no—
186#41×C43—21no—
187#41×C43—21no—
188#41×C43—21no—
189#41×C43—21no—
190C2×Q8×C43C22×C411yescharacteristic
191C2×D4×C43—21no—
192C2×D4×C43—21no—
193C2×D4×C43—21no—
194C2×D4×C43C22×C411yescharacteristic
195C22×C4×C43—21no—
196C22×C4×C43—21no—
197C22×C4×C43—21no—
198C22×C4×C43—21no—
199C22×C4×C43—21no—
200C22×C4×C43C22×C411yescharacteristic
201C22×C4×C43C22×C411yescharacteristic
202C22×C4×C43C2×D411yescharacteristic
203C22×C4×C43C2×D411yescharacteristic
204C22×C4×C43#4111yescharacteristic
205C22×C4×C43C2411yescharacteristic
206C2×C22⋊D43—24no—
207C2×C22⋊D43—24no—
208C2×C22⋊D43—21no—
209C2×C22⋊D43—21no—
210C2×C22⋊D43—21no—
211C2×C22⋊D43—21no—
212C22×Dic43—21no—
213C22×Dic43—21no—
214C22×Dic43—21no—
215#10621898—24no—
216#10621898—24no—
217#10621898—24no—
218#10621898—24no—
219#10621898—21no—
220#10621898—21no—
221#10621898—21no—
222#10621898—21no—
223#10621898—22no—
224#10621898—22no—
225#10621898—22no—
226#10621898—22no—
227#10621898C2×D412yes—
228#10621898C2×D412yes—
229#10621898#4112yes—
230#10621898#4112yes—
231C2×D172—21no—
232C2×D172—22no—
233C2×D172—22no—
234C2×D172C22×C411yescharacteristic
235C2×D172C22×C411yescharacteristic
236C2×C4×D43—24no—
237C2×C4×D43—24no—
238C2×C4×D43—21no—
239C2×C4×D43—21no—
240C2×C4×D43—21no—
241C2×C4×D43—21no—
242C2×Dic86—21no—
243C2×Dic86—22no—
244C2×Dic86—22no—
245C2×Dic86C22×C411yescharacteristic
246C2×Dic86C22×C411yescharacteristic
247M16×C43—22no—
248M16×C43—22no—
249M16×C43—22no—
250M16×C43—22no—
251M16×C43—21no—
252M16×C43—21no—
253M16×C43—21no—
254M16×C43—21no—
255M16×C43—42no—
256C2×C8×C43—21no—
257C2×C8×C43—21no—
258C2×C8×C43—21no—
259C2×C8×C43—21no—
260C2×C8×C43—42no—
261C2×C8×C43C2×D412yes—
262C2×C8×C43C2×D412yes—
263C2×C8×C43C2×D411yescharacteristic
264C2×C8×C43C2×D411yescharacteristic
265C2×C8×C43C2×D411yescharacteristic
266C2×C8×C43C2×D411yescharacteristic
267C4⋊C4×C43—21no—
268C4⋊C4×C43—21no—
269C4⋊C4×C43C22×C411yescharacteristic
270C4⋊C4×C43C22×C411yescharacteristic
271C22⋊C4×C43—21no—
272C22⋊C4×C43—21no—
273C22⋊C4×C43—21no—
274C22⋊C4×C43—21no—
275C22⋊C4×C43—21no—
276C42×C43—21no—
277C22⋊Dic43—42no—
278#10621885—22no—
279#10621885—22no—
280#10621884—22no—
281#10621884—22no—
282#10621883—22no—
283#10621883—22no—
284#10621882—22no—
285#10621882—22no—
286C4×Dic43—21no—
287C4×Dic43—21no—
288C4×Dic43—21no—
289C4×Dic43—21no—
290#10621877—24no—
291#10621877—21no—
292#10621877—21no—
293#10621877C2×D412yes—
294#10621877C2×D412yes—
295C2×C43⋊C8—24no—
296C2×C43⋊C8—21no—
297C2×C43⋊C8—21no—
298C2×C43⋊C8—21no—
299C2×C43⋊C8—21no—
300C2×C43⋊C8—21no—
301C2×C43⋊C8—21no—
302C2×C43⋊C8C22×C411yescharacteristic
303C2×C43⋊C8C22×C411yescharacteristic
304C2×C43⋊C8C22×C411yescharacteristic
305C2×C43⋊C8C22×C411yescharacteristic
306#10621872—24no—
307#10621872—24no—
308#10621872—24no—
309#10621872—24no—
310C8×D43—24no—
311C8×D43—24no—
312C8×D43—24no—
313C8×D43—24no—
314C23×C43—21no—
315C23×C43—21no—
316C23×C43—21no—
317C23×C43—41no—
318C23×C43—41no—
319C23×C43C4×D411yescharacteristic
320C23×C43C4×D411yescharacteristic
321C23×C43C2×#4111yescharacteristic
322C22×D43—21no—
323C22×D43—21no—
324C22×D43—24no—
325C22×D43—81no—
326C22×D43—81no—
327Q8×C43—21no—
328Q8×C43—21no—
329D4×C43—21no—
330D4×C43—21no—
331D4×C43—41no—
332D4×C43—41no—
333D4×C43—81no—
334D4×C43—81no—
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—21no—
343C2×C4×C43—21no—
344C2×C4×C43—21no—
345C2×C4×C43—21no—
346C2×C4×C43—21no—
347C2×C4×C43—21no—
348C2×C4×C43—41no—
349C2×C4×C43—41no—
350C2×C4×C43C4×D411yescharacteristic
351C2×C4×C43C4×D411yescharacteristic
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—24no—
359C22⋊D43—24no—
360C22⋊D43—22no—
361C22⋊D43—22no—
362C22⋊D43—22no—
363C22⋊D43—22no—
364C2×Dic43—24no—
365C2×Dic43—21no—
366C2×Dic43—21no—
367C2×Dic43—22no—
368C2×Dic43—41no—
369C2×Dic43—41no—
370C2×Dic43—41no—
371C2×Dic43—41no—
372C2×Dic43—41no—
373D172—24no—
374D172—21no—
375D172—21no—
376D172C4×D412yes—
377D172C4×D412yes—
378C4×D43—24no—
379C4×D43—24no—
380C4×D43—22no—
381C4×D43—22no—
382C4×D43—22no—
383C4×D43—22no—
384Dic86—24no—
385Dic86—21no—
386Dic86—21no—
387Dic86C4×D412yes—
388Dic86C4×D412yes—
389C8×C43—21no—
390C8×C43—21no—
391C8×C43—41no—
392C8×C43—41no—
393C8×C43#12012yes—
394C8×C43#12012yes—
395C43⋊C8—21no—
396C43⋊C8—21no—
397C43⋊C8—21no—
398C43⋊C8—21no—
399C43⋊C8—22no—
400C43⋊C8—22no—
401#21468—431nomaximal, Sylow
402C22×C43—21no—
403C22×C43—21no—
404C22×C43—21no—
405C22×C43—21no—
406C22×C43—21no—
407C22×C43—21no—
408C22×C43—21no—
409C22×C43—21no—
410C22×C43—41no—
411C22×C43—41no—
412C22×C43—41no—
413C22×C43—81no—
414C22×C43—81no—
415C22×C43C2×C4×D411yescharacteristic
416C22×C43#52511yescharacteristic
417C22×C43#52511yescharacteristic
418C2×D43—22no—
419C2×D43—22no—
420C2×D43—41no—
421C2×D43—41no—
422C2×D43—41no—
423C2×D43—41no—
424C2×D43—84no—
425C4×C43—21no—
426C4×C43—21no—
427C4×C43—41no—
428C4×C43—41no—
429C4×C43—41no—
430C4×C43C2×C4×D411yescharacteristic
431C4×C43C2×C4×D411yescharacteristic
432C4×C43C2×#12011yescharacteristic
433C4×C43#52511yescharacteristic
434Dic43—22no—
435Dic43—22no—
436Dic43—42no—
437Dic43—81no—
438C2×#568—431no—
439#3002—431no—
440C2×#444—431no—
441C2×#443—431no—
442#2930D4311yescharacteristic, complemented
443#1876—431no—
444#1876—431no—
445#1871—431no—
446#1866—431no—
447#1866—431no—
448#1855—431no—
449#1789—431no—
450#1765—431no—
451#1764—431no—
452#1753—431no—
453C2×C43—21no—
454C2×C43—21no—
455C2×C43—41no—
456C2×C43—41no—
457C2×C43—81no—
458C2×C43C4×#12011yescharacteristic
459C2×C43#295611yescharacteristic
460C2×C43#295711yescharacteristic
461D43—42no—
462D43—42no—
463C22×#41—431no—
464C2×#135—431no—
465C2×#135—431no—
466#568—864no—
467#568—864no—
468C2×#131—431no—
469C2×#131—431no—
470C2×#131—431no—
471C2×#131—431no—
472C2×#131—861no—
473C2×#131—861no—
474C2×#131C2×D4311yescharacteristic, complemented
475C22×M16—431no—
476C22×M16—861no—
477C22×M16—861no—
478C22×M16C2×D4311yescharacteristic
479#525C2×D4311yescharacteristic
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#443—864no—
490#436—21no—
491#436—21no—
492#435—21no—
493#435—21no—
494C2×#108—431no—
495C2×#108—431no—
496#424C2×D4311yescharacteristic, complemented
497C2×#104—431no—
498C2×#104—431no—
499C2×#104—431no—
500C2×#104—431no—
501C2×#104—431no—
502C2×#104—431no—
503#416—431no—
504#416—431no—
505#408C2×D4311yescharacteristic, complemented
506#407C2×D4311yescharacteristic
507C2×C22⋊C8—431no—
508#405C2×D4311yescharacteristic, complemented
509C2×#97—431no—
510C2×C4×C8—431no—
511C4×C22⋊C4—431no—
512#341—431no—
513#341—431no—
514#339—431no—
515#339—431no—
516#336—431no—
517#336—431no—
518C43#2146811yescharacteristic, complemented, Sylow
519C2×#41—431no—
520C2×#41—431no—
521C2×#41—431no—
522C2×#41—431no—
523C2×#41—862no—
524C2×#41—862no—
525C2×#41—862no—
526C2×#41—862no—
527C2×#41—861no—
528C2×#41—861no—
529C2×#41C22×D4311yescharacteristic
530C22×Q8—431no—
531C22×D4—431no—
532C22×D4—861no—
533C23×C4—861no—
534C23×C4C22×D4311yescharacteristic
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—862no—
554#131—862no—
555#131—868no—
556#131—868no—
557#131—862no—
558#131—862no—
559C2×M16—22no—
560C2×M16—22no—
561C2×M16—21no—
562C2×M16—431no—
563C2×M16—431no—
564C2×M16—868no—
565C2×M16—868no—
566C2×M16—862no—
567C2×M16—862no—
568C2×M16—861no—
569C2×M16—861no—
570C2×M16—861no—
571C2×M16—861no—
572C2×M16—861no—
573C2×M16C22⋊D4311yescharacteristic
574C2×M16C22⋊D4311yescharacteristic
575C2×M16C22⋊D4311yescharacteristic
576C2×M16C22⋊D4311yescharacteristic
577C2×M16C22×D4311yescharacteristic
578C2×M16C22×D4311yescharacteristic
579C22×C8—21no—
580C22×C8—431no—
581C22×C8—431no—
582C22×C8—861no—
583C22×C8—861no—
584C22×C8—861no—
585C22×C8—861no—
586C22×C8—861no—
587C22×C8C22×D4311yescharacteristic
588C22×C8C22×D4311yescharacteristic
589#123—21no—
590C22⋊Q8C4×D4311yescharacteristic
591C22⋊Q8C4×D4311yescharacteristic
592#121C4×D4311yescharacteristic
593#121C4×D4311yescharacteristic
594#120—21no—
595C4×D4—21no—
596C4×D4—21no—
597#117C22×D4311yescharacteristic
598C2×C22⋊C4—861no—
599C2×C42—431no—
600C2×C42—431no—
601#108—862no—
602#108—862no—
603C4⋊C8—21no—
604C4⋊C8—21no—
605#104—862no—
606#104—862no—
607#104—862no—
608#104—862no—
609#104—862no—
610#104—862no—
611#103—431no—
612#103—431no—
613#103—431no—
614#103—431no—
615#102—431no—
616#102—431no—
617#102—431no—
618#102—431no—
619C22⋊C8—21no—
620C22⋊C8—21no—
621C22⋊C8—21no—
622C22⋊C8—21no—
623C22⋊C8—431no—
624C22⋊C8—431no—
625C22⋊C8—431no—
626C22⋊C8—431no—
627#97—21no—
628#97—862no—
629C4×C8—21no—
630C4×C8—862no—
631#95—861no—
632C24—861no—
633C24#1062189811yescharacteristic
634#41—21no—
635#41—21no—
636#41—21no—
637#41—21no—
638#41—432no—
639#41—432no—
640#41—432no—
641#41—432no—
642#41—862no—
643#41—862no—
644#41—862no—
645#41—862no—
646#41—864no—
647#41—864no—
648#41—864no—
649#41—864no—
650#41—861no—
651#41—861no—
652#41—861no—
653#41—861no—
654C2×Q8—431no—
655C2×Q8—431no—
656C2×Q8—862no—
657C2×Q8—862no—
658C2×Q8—861no—
659C2×Q8C2×C4×D4311yescharacteristic
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—431no—
664C2×D4—431no—
665C2×D4—862no—
666C2×D4—862no—
667C2×D4—864no—
668C2×D4—864no—
669C2×D4—861no—
670C2×D4—861no—
671C2×D4—861no—
672C2×D4—861no—
673C2×D4—861no—
674C2×D4C2×C4×D4311yescharacteristic
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—864no—
681C22×C4—864no—
682C22×C4—861no—
683C22×C4—861no—
684C22×C4—861no—
685C22×C4—861no—
686C22×C4—861no—
687C22×C4—861no—
688C22×C4—861no—
689C22×C4C2×C4×D4311yescharacteristic
690C22×C4C2×C4×D4311yescharacteristic
691C22×C4#1062189811yescharacteristic
692C22×C4C2×C22⋊D4311yescharacteristic
693C22×C4C2×C22⋊D4311yescharacteristic
694C22×C4C23×D4311yescharacteristic
695Q16—862no—
696Q16—862no—
697SD16—862no—
698SD16—862no—
699SD16—862no—
700SD16—862no—
701D8—862no—
702D8—862no—
703M16—22no—
704M16—22no—
705M16—22no—
706M16—22no—
707M16—21no—
708M16—21no—
709M16—21no—
710M16—21no—
711M16—42no—
712M16—432no—
713M16—432no—
714M16—864no—
715M16—864no—
716M16—864no—
717M16—861no—
718M16—861no—
719M16—864no—
720M16—864no—
721C2×C8—21no—
722C2×C8—21no—
723C2×C8—21no—
724C2×C8—21no—
725C2×C8—42no—
726C2×C8—431no—
727C2×C8—431no—
728C2×C8—431no—
729C2×C8—431no—
730C2×C8—864no—
731C2×C8—864no—
732C2×C8—864no—
733C2×C8—861no—
734C2×C8—861no—
735C2×C8—861no—
736C2×C8—861no—
737C2×C8—861no—
738C2×C8—861no—
739C2×C8—864no—
740C2×C8—864no—
741C2×C8D4×D4312yes—
742C2×C8D4×D4312yes—
743C2×C8C2×C22⋊D4311yescharacteristic
744C2×C8C2×C22⋊D4311yescharacteristic
745C2×C8C2×C22⋊D4311yescharacteristic
746C2×C8C2×C22⋊D4311yescharacteristic
747C4⋊C4—21no—
748C4⋊C4—21no—
749C4⋊C4C2×C4×D4311yescharacteristic
750C4⋊C4C2×C4×D4311yescharacteristic
751C22⋊C4—21no—
752C22⋊C4—21no—
753C22⋊C4—21no—
754C22⋊C4—21no—
755C22⋊C4—21no—
756C22⋊C4—1722no—
757C42—21no—
758C42—861no—
759C42—861no—
760C42—861no—
761C42—861no—
762C23—21no—
763C23—21no—
764C23—21no—
765C23—41no—
766C23—41no—
767C23—864no—
768C23—861no—
769C23—861no—
770C23—3441no—
771C23—3441no—
772C23C4×C22⋊D4311yescharacteristic
773C23C4×C22⋊D4311yescharacteristic
774C23C2×#1062189811yescharacteristic
775Q8—21no—
776Q8—21no—
777Q8—432no—
778Q8—432no—
779Q8—864no—
780Q8—861no—
781Q8—861no—
782D4—21no—
783D4—21no—
784D4—41no—
785D4—41no—
786D4—81no—
787D4—81no—
788D4—432no—
789D4—432no—
790D4—864no—
791D4—864no—
792D4—864no—
793D4—862no—
794D4—862no—
795D4—862no—
796D4—862no—
797D4—861no—
798D4—861no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—864no—
815C2×C4—864no—
816C2×C4—864no—
817C2×C4—861no—
818C2×C4—861no—
819C2×C4—862no—
820C2×C4—862no—
821C2×C4—862no—
822C2×C4—862no—
823C2×C4—862no—
824C2×C4—1721no—
825C2×C4—1721no—
826C2×C4—1721no—
827C2×C4—1721no—
828C2×C4—1721no—
829C2×C4C4×C22⋊D4311yescharacteristic
830C2×C4C4×C22⋊D4311yescharacteristic
831C2×C4C22×C4×D4311yescharacteristic
832C2×C4C2×D4×D4311yescharacteristic
833C2×C4C2×D4×D4311yescharacteristic
834C2×C4C22×C22⋊D4311yescharacteristic
835C2×C4#41×D4311yescharacteristic
836C2×C4#41×D4311yescharacteristic
837C8—21no—
838C8—21no—
839C8—41no—
840C8—41no—
841C8—861no—
842C8—861no—
843C8—861no—
844C8—861no—
845C8—862no—
846C8—862no—
847C8#1306329312yes—
848C8#1306329312yes—
849C22—21no—
850C22—21no—
851C22—21no—
852C22—21no—
853C22—21no—
854C22—21no—
855C22—21no—
856C22—21no—
857C22—41no—
858C22—41no—
859C22—41no—
860C22—81no—
861C22—81no—
862C22—862no—
863C22—862no—
864C22—3444no—
865C22—1721no—
866C22—1721no—
867C22—1721no—
868C22—1721no—
869C22C2×C4×C22⋊D4311yescharacteristic
870C22#1458340811yescharacteristic
871C22#1458340811yescharacteristic
872C4—21no—
873C4—21no—
874C4—41no—
875C4—41no—
876C4—41no—
877C4—862no—
878C4—862no—
879C4—3441no—
880C4—1722no—
881C4C4×D4×D4311yescharacteristic
882C4C4×D4×D4311yescharacteristic
883C4C2×#1306329311yescharacteristic
884C4#1458340611yescharacteristic
885C2—21no—
886C2—21no—
887C2—41no—
888C2—41no—
889C2—81no—
890C2—1722no—
891C2—1722no—
892C2C4×#1306329311yescharacteristic
893C2#1914350211yescharacteristic
894C2#1914351011yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#2930C2
socleC22×C43C2×C4×D4
prime radical#19143811C2
cosocleC22×C4×C43C24
hypercenter#2930D43
hypocenterC43#21468
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C22×M16 ◁ #2930

Complements

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

NH ≅ G/Ntype
1. C2×#14583665C2semidirect
3. C2×#14583019C2semidirect
4. C2×#14583014C2semidirect
5. #19134925C2semidirect
6. #19134925C2semidirect
7. #19134898C2semidirect
8. #19134869C2semidirect
9. #19134869C2semidirect
10. #19134799C2semidirect
11. #19134538C2semidirect
12. #19134441C2semidirect
13. #19134434C2semidirect
14. #19134376C2semidirect
15. C43×#2930C2semidirect
30. #14583059C4semidirect
31. #14583059C4semidirect
32. #14583054C4semidirect
33. #14583049C4semidirect
34. #14583042C4semidirect
35. #14583042C4semidirect
36. #14583037C4semidirect
37. #14583032C4semidirect
40. C2×#13063260C22semidirect
41. C2×#13063260C22semidirect
42. C2×#13063252C22semidirect
43. C2×#13063252C22semidirect
51. C2×#13063235C22semidirect
52. C2×C8×Dic43C22semidirect
54. #14582663C22semidirect
55. #14582663C22semidirect
56. #14582658C22semidirect
57. #14582658C22semidirect
58. #14582653C22semidirect
59. #14582653C22semidirect
60. C2×#131×C43C22semidirect
67. C43×#424C22semidirect
68. C43×#408C22semidirect
70. C43×#405C22semidirect
105. #13063331D4semidirect
106. #13063331D4semidirect
442. #2930D43semidirect
474. C2×#131C2×D43semidirect
496. #424C2×D43semidirect
505. #408C2×D43semidirect
508. #405C2×D43semidirect
518. C43#21468semidirect

Maximal subgroups

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

subgroupindex
C2×#145836652
#191438112
C2×#145830192
C2×#145830142
#191349252
#191348982
#191348692
#191347992
#191345382
#191344412
#191344342
#191343762
C43×#29302
#2146843