Finite Group Databasebeta

← #25112612

Subgroups — #25112612

Order 11008.

1384 conjugacy classes of subgroups.

The subgroup lattice has 882 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583702C211yesmaximal, characteristic
2C2×#14583014C211yesmaximal, characteristic, complemented
3#19143468C211yesmaximal, characteristic, complemented
4#19143117C211yesmaximal, characteristic, complemented
5#19135504C211yesmaximal, characteristic, complemented
6#19135458C211yesmaximal, characteristic, complemented
7#19135106C211yesmaximal, characteristic, complemented
8#19135103C211yesmaximal, characteristic, complemented
9#19134971C211yesmaximal, characteristic, complemented
10#19134968C211yesmaximal, characteristic, complemented
11#19134657C211yesmaximal, characteristic, complemented
12#19134549C211yesmaximal, characteristic, complemented
13#19134547C211yesmaximal, characteristic, complemented
14#19134435C211yesmaximal, characteristic, complemented
15C43×#2897C211yesmaximal, characteristic, complemented
16C2×#13063371C2211yescharacteristic
17#14583702—24no—
18#14583702C418yescomplemented
19C2×#13063351—21no—
20C2×#13063351C2211yescharacteristic
21C2×#13063350—21no—
22C2×#13063350C2211yescharacteristic
23C2×#13063345—21no—
24C2×#13063345C2211yescharacteristic
25C22×#10621882—21no—
26C22×#10621882C2211yescharacteristic
27C2×#13063332C2211yescharacteristic
28C2×#13063331C2211yescharacteristic, complemented
29#14583379C2211yescharacteristic, complemented
30#14583014—24no—
31#14582999—21no—
32#14582997—21no—
33C4×#10621885—21no—
34C4×#10621882—21no—
35C2×#13063260C2211yescharacteristic, complemented
36C2×#13063258C2211yescharacteristic, complemented
37C2×#13063252C2211yescharacteristic
38C2×#13063252C2211yescharacteristic, complemented
39C2×#13063251C2211yescharacteristic, complemented
40#14582903C2211yescharacteristic, complemented
41#14582902—21no—
42#14582900C2211yescharacteristic
43#14582900C2211yescharacteristic, complemented
44#14582899—21no—
45#14582898C2211yescharacteristic, complemented
46#14582894—21no—
47C2×#13063247C2211yescharacteristic, complemented
48#102×D43—21no—
49C2×#13063242C2211yescharacteristic, complemented
50C2×#13063241C2211yescharacteristic, complemented
51#14582855C2211yescharacteristic, complemented
52C2×C8×Dic43C2211yescharacteristic, complemented
53#14582802C2211yescharacteristic, complemented
54#14582800C2211yescharacteristic, complemented
55#14582668C2211yescharacteristic, complemented
56#14582667C2211yescharacteristic, complemented
57#14582664C2211yescharacteristic, complemented
58#14582658C2211yescharacteristic, complemented
59C2×H(5,𝔽2)×C43C2211yescharacteristic
60C2×#131×C43C2211yescharacteristic, complemented
61C43×#520C2211yescharacteristic, complemented
62C43×#418—21no—
63C43×#418C2211yescharacteristic, complemented
64C43×#417—21no—
65C43×#417C2211yescharacteristic
66C43×#416—21no—
67C43×#416C2211yescharacteristic
68C2×#102×C43—21no—
69C2×#102×C43C2211yescharacteristic, complemented
70#13063371—22no—
71#13063371—22no—
72#13063371—41no—
73#13063371C2×C414yescomplemented
74C2×#10621902—21no—
75C2×#10621898—21no—
76C2×#10621898C2311yescharacteristic
77C22×D172—21no—
78C22×D172C2311yescharacteristic
79C2×D4×D43—21no—
80C2×D4×D43—41no—
81#13063351—22no—
82#13063351—28no—
83#13063351C2×C414yescomplemented
84#13063350—22no—
85#13063350—28no—
86#13063350C2×C414yescomplemented
87#13063345—28no—
88#13063345C2×C414yes—
89#13063345D414yes—
90C2×#10621885D411yescharacteristic
91C2×#10621883—21no—
92C2×#10621883D411yescharacteristic
93C2×#10621884—21no—
94C2×#10621884D411yescharacteristic
95C2×#10621882—21no—
96C2×#10621882—21no—
97C2×#10621882—28no—
98C2×#10621882—21no—
99C2×#10621882—21no—
100C2×#10621882—22no—
101C2×#10621882C2×C414yescomplemented
102C2×#10621882D411yescharacteristic
103#13063332—22no—
104#13063332C2×C414yescomplemented
105#13063331—22no—
106#13063331—41no—
107C2×#10621877—21no—
108C2×#10621877C2311yescharacteristic
109C2×#10621877C2311yescharacteristic
110C2×#10621877C2311yescharacteristic
111C2×#10621872—21no—
112C22×C43⋊C8—21no—
113C22×C43⋊C8C2311yescharacteristic
114C2×C8×D43—21no—
115C4×Dic86—21no—
116C4×D172—21no—
117(C22⋊D43)⋊C4—41no—
118#13063283—21no—
119C2×C4⋊Dic43C2311yescharacteristic
120C4⋊C4×D43—21no—
121C2×C22⋊Dic43—41no—
122C2×(C2×D43)⋊C4—41no—
123C2×C4×Dic43C2311yescharacteristic
124#13063260—22no—
125#13063258—21no—
126#13063258—21no—
127#13063252—22no—
128#13063252—22no—
129#13063251—22no—
130#13063249—21no—
131#13063249—21no—
132#13063248—21no—
133#13063247—21no—
134#13063247—21no—
135#13063246—21no—
136#13063246—21no—
137#13063245—21no—
138#13063245—21no—
139#13063245—21no—
140#13063242—41no—
141#13063241—41no—
142#13063236—21no—
143C4×C43⋊C8—21no—
144C8×Dic43—22no—
145H(5,𝔽2)×C43—22no—
146H(5,𝔽2)×C43—22no—
147H(5,𝔽2)×C43—41no—
148H(5,𝔽2)×C43C2×C414yescomplemented
149C2×#41×C43—21no—
150C2×#41×C43—21no—
151C2×#41×C43C2311yescharacteristic
152C2×#41×C43C2311yescharacteristic
153C22×D4×C43—21no—
154C22×D4×C43—21no—
155C22×D4×C43—41no—
156C22×D4×C43C2311yescharacteristic
157#131×C43—22no—
158#131×C43—41no—
159C2×M16×C43—21no—
160C2×M16×C43C2311yescharacteristic
161C22×C8×C43—21no—
162C22×C8×C43C2311yescharacteristic
163C4×Q8×C43—21no—
164C4×D4×C43—21no—
165C4×D4×C43—41no—
166#117×C43—21no—
167#117×C43C2311yescharacteristic
168C2×C4⋊C4×C43—21no—
169C2×C4⋊C4×C43C2311yescharacteristic
170#103×C43—21no—
171#103×C43D411yescharacteristic
172#103×C43D411yescharacteristic
173#102×C43—21no—
174#102×C43—21no—
175#102×C43—21no—
176#102×C43—21no—
177#102×C43—21no—
178#102×C43D411yescharacteristic
179#102×C43D411yescharacteristic
180C24×C43—21no—
181C24×C43—41no—
182C23×D43—21no—
183C23×D43—41no—
184#41×C43—21no—
185#41×C43—21no—
186#41×C43—21no—
187#41×C43—21no—
188#41×C43—24no—
189#41×C43—24no—
190#41×C43—42no—
191#41×C43—42no—
192#41×C43C22×C412yes—
193#41×C43C22×C412yes—
194#41×C43C2×D412yes—
195#41×C43#4112yes—
196C2×Q8×C43C2×D411yescharacteristic
197C2×Q8×C43C2×D411yescharacteristic
198C2×D4×C43—21no—
199C2×D4×C43—21no—
200C2×D4×C43—21no—
201C2×D4×C43—24no—
202C2×D4×C43—24no—
203C2×D4×C43—21no—
204C2×D4×C43—21no—
205C2×D4×C43—21no—
206C2×D4×C43—21no—
207C2×D4×C43—41no—
208C2×D4×C43—41no—
209C2×D4×C43—44no—
210C2×D4×C43—42no—
211C2×D4×C43—42no—
212C2×D4×C43—44no—
213C2×D4×C43C22×C412yes—
214C2×D4×C43C2×D411yescharacteristic
215C2×D4×C43C2×D411yescharacteristic
216C22×C4×C43—21no—
217C22×C4×C43—21no—
218C22×C4×C43—21no—
219C22×C4×C43—41no—
220C22×C4×C43—41no—
221C22×C4×C43C2411yescharacteristic
222C2×C22⋊D43—21no—
223C2×C22⋊D43—41no—
224C22×Dic43—21no—
225C22×Dic43—21no—
226#10621902—24no—
227#10621902—42no—
228D4×D43—24no—
229D4×D43—44no—
230D4×D43—42no—
231D4×D43—44no—
232#10621898—21no—
233#10621898—21no—
234#10621898—24no—
235#10621898—42no—
236#10621898C22×C412yes—
237#10621898C2×D412yes—
238C2×D172—21no—
239C2×D172—21no—
240C2×D172—21no—
241C2×D172—21no—
242C2×D172—21no—
243C2×D172—24no—
244C2×D172—41no—
245C2×D172—42no—
246C2×D172C22×C412yes—
247C2×D172C2×D411yescharacteristic
248C2×C4×D43—21no—
249C2×C4×D43—41no—
250C2×C4×D43—41no—
251C2×Dic86C2×D411yescharacteristic
252M16×C43—21no—
253M16×C43—21no—
254M16×C43—42no—
255C2×C8×C43—21no—
256C2×C8×C43—21no—
257C2×C8×C43—21no—
258C2×C8×C43—42no—
259C2×C8×C43C2×D411yescharacteristic
260C2×C8×C43C2×D411yescharacteristic
261C4⋊C4×C43—21no—
262C4⋊C4×C43—21no—
263C4⋊C4×C43—41no—
264C4⋊C4×C43C2×D411yescharacteristic
265C4⋊C4×C43C2×D411yescharacteristic
266C22⋊C4×C43—21no—
267C22⋊C4×C43—41no—
268C42×C43—21no—
269C42×C43—41no—
270C22⋊Dic43—82no—
271#10621885C22⋊C414yescomplemented
272#10621884—24no—
273#10621884C22⋊C414yescomplemented
274#10621883—24no—
275#10621883C22⋊C414yescomplemented
276#10621882—24no—
277#10621882—24no—
278#10621882—24no—
279#10621882—24no—
280#10621882C22⋊C414yescomplemented
281(C2×D43)⋊C4—41no—
282(C2×D43)⋊C4—82no—
283C4⋊Dic43—21no—
284C4⋊Dic43—21no—
285Dic43⋊C4—41no—
286C4×Dic43—21no—
287C4×Dic43—21no—
288C4×Dic43—41no—
289#10621877—21no—
290#10621877—24no—
291#10621877—21no—
292#10621877—21no—
293#10621877—21no—
294#10621877—21no—
295#10621877C22×C412yes—
296C2×C43⋊C8—21no—
297C2×C43⋊C8—24no—
298C2×C43⋊C8—21no—
299C2×C43⋊C8—21no—
300C2×C43⋊C8C22×C412yes—
301C2×C43⋊C8C2×D412yes—
302C2×C43⋊C8C2×D411yescharacteristic
303C2×C43⋊C8C2×D411yescharacteristic
304#10621872—42no—
305C8×D43—42no—
306C23×C43—21no—
307C23×C43—21no—
308C23×C43—22no—
309C23×C43—44no—
310C23×C43—41no—
311C23×C43—41no—
312C23×C43—81no—
313C23×C43—81no—
314C23×C43—161no—
315C23×C43—161no—
316C23×C43H(5,𝔽2)11yescharacteristic
317C22×D43—21no—
318C22×D43—22no—
319C22×D43—44no—
320C22×D43—41no—
321C22×D43—41no—
322C22×D43—81no—
323C22×D43—81no—
324C22×D43—161no—
325C22×D43—161no—
326Q8×C43—21no—
327Q8×C43—21no—
328Q8×C43C2×C22⋊C412yes—
329Q8×C43C4×D412yes—
330D4×C43—22no—
331D4×C43—22no—
332D4×C43—22no—
333D4×C43—22no—
334D4×C43—22no—
335D4×C43—22no—
336D4×C43—21no—
337D4×C43—21no—
338D4×C43—44no—
339D4×C43—44no—
340D4×C43—41no—
341D4×C43—41no—
342D4×C43C2×C22⋊C412yes—
343D4×C43C4×D412yes—
344C2×C4×C43—21no—
345C2×C4×C43—21no—
346C2×C4×C43—22no—
347C2×C4×C43—22no—
348C2×C4×C43—22no—
349C2×C4×C43—22no—
350C2×C4×C43—21no—
351C2×C4×C43—21no—
352C2×C4×C43—44no—
353C2×C4×C43—41no—
354C2×C4×C43—81no—
355C2×C4×C43—161no—
356C2×C4×C43C23×C411yescharacteristic
357C2×C4×C43C22×D411yescharacteristic
358C2×C4×C43C22×D411yescharacteristic
359C2×C4×C43C22×D411yescharacteristic
360C2×C4×C43C2×#4111yescharacteristic
361C2×C4×C43H(5,𝔽2)11yescharacteristic
362C22⋊D43—22no—
363C22⋊D43—22no—
364C22⋊D43—44no—
365C2×Dic43—21no—
366C2×Dic43—22no—
367C2×Dic43—41no—
368C2×Dic43—41no—
369C2×Dic43—41no—
370C2×Dic43—81no—
371D172—22no—
372D172—22no—
373D172—21no—
374D172—44no—
375D172—41no—
376D172—41no—
377D172C2×C22⋊C412yes—
378C4×D43—22no—
379C4×D43—22no—
380C4×D43—44no—
381C4×D43—161no—
382Dic86—21no—
383Dic86C2×C22⋊C412yes—
384C8×C43—21no—
385C8×C43—21no—
386C8×C43—41no—
387C43⋊C8—22no—
388C43⋊C8—41no—
389C43⋊C8—41no—
390C43⋊C8C2×C22⋊C412yes—
391C43⋊C8C2×C22⋊C412yes—
392#22466—431nomaximal, Sylow
393C22×C43—21no—
394C22×C43—21no—
395C22×C43—22no—
396C22×C43—22no—
397C22×C43—41no—
398C22×C43—41no—
399C22×C43—41no—
400C22×C43—41no—
401C22×C43—42no—
402C22×C43—82no—
403C22×C43—81no—
404C22×C43—81no—
405C22×C43—161no—
406C22×C43—164no—
407C22×C43#51811yescharacteristic
408C22×C43D4211yescharacteristic
409C22×C43#54611yescharacteristic
410C2×D43—22no—
411C2×D43—41no—
412C2×D43—41no—
413C2×D43—42no—
414C2×D43—81no—
415C2×D43—81no—
416C2×D43—82no—
417C2×D43—164no—
418C2×D43—161no—
419C4×C43—22no—
420C4×C43—22no—
421C4×C43—41no—
422C4×C43—41no—
423C4×C43—81no—
424C4×C43C22×C22⋊C411yescharacteristic
425C4×C43C2×C4×D411yescharacteristic
426C4×C43D4211yescharacteristic
427C4×C43#54611yescharacteristic
428Dic43—22no—
429Dic43—42no—
430Dic43—81no—
431C2×#576—431no—
432C2×#443—431no—
433#2951—431no—
434#2897—431no—
435#2897D4311yescharacteristic, complemented
436#1978—431no—
437#1970—431no—
438#1907—431no—
439#1907—431no—
440#1883—431no—
441#1883—431no—
442#1816—431no—
443#1792—431no—
444#1792—431no—
445#1764—431no—
446C2×C43—21no—
447C2×C43—21no—
448C2×C43—42no—
449C2×C43—42no—
450C2×C43—82no—
451C2×C43D4×C22⋊C411yescharacteristic
452C2×C43#329011yescharacteristic
453C2×C43#329211yescharacteristic
454D43—42no—
455D43—82no—
456C2×H(5,𝔽2)—431no—
457C2×H(5,𝔽2)C2×D4311yescharacteristic
458#576—438no—
459#576—864no—
460C2×AGL(1,ℤ/8)—431no—
461C2×AGL(1,ℤ/8)—431no—
462C2×AGL(1,ℤ/8)—861no—
463C2×AGL(1,ℤ/8)—861no—
464C2×#135—431no—
465C2×#135—861no—
466C22×D8—431no—
467C22×D8—861no—
468C2×#131—431no—
469C2×#131—431no—
470C2×#131C2×D4311yescharacteristic, complemented
471#520—431no—
472#520C2×D4311yescharacteristic, complemented
473#443—864no—
474#440—861no—
475#440—861no—
476C4×Q16—861no—
477C4×D8—861no—
478C2×#108—431no—
479C2×#107—431no—
480C2×#104—431no—
481C2×#104—431no—
482C2×#104—431no—
483#418—21no—
484#418—431no—
485#418—861no—
486#418C2×D4311yescharacteristic, complemented
487#417—21no—
488#417—431no—
489#417—431no—
490#417—431no—
491#417—861no—
492#417C2×D4311yescharacteristic
493#416—21no—
494#416—861no—
495#416C2×D4311yescharacteristic
496C2×#102—21no—
497C2×#102—431no—
498C2×#102—861no—
499C2×#102C2×D4311yescharacteristic, complemented
500C2×#100—431no—
501C2×#100—431no—
502#405—431no—
503C2×C4×C8—431no—
504#390—431no—
505#390—431no—
506#343—431no—
507#343—431no—
508#341—431no—
509#339—431no—
510C43#2246611yescharacteristic, complemented, Sylow
511H(5,𝔽2)—22no—
512H(5,𝔽2)—22no—
513H(5,𝔽2)—41no—
514H(5,𝔽2)—434no—
515H(5,𝔽2)—862no—
516H(5,𝔽2)—862no—
517H(5,𝔽2)—1721no—
518H(5,𝔽2)C4×D4314yescomplemented
519C2×#41—21no—
520C2×#41—21no—
521C2×#41—431no—
522C2×#41—861no—
523C2×#41—861no—
524C2×#41C22×D4311yescharacteristic
525C2×#41C22×D4311yescharacteristic
526C22×D4—21no—
527C22×D4—21no—
528C22×D4—41no—
529C22×D4—431no—
530C22×D4—861no—
531C22×D4—861no—
532C22×D4—1721no—
533C22×D4C22×D4311yescharacteristic
534AGL(1,ℤ/8)—434no—
535AGL(1,ℤ/8)—434no—
536AGL(1,ℤ/8)—868no—
537AGL(1,ℤ/8)—868no—
538AGL(1,ℤ/8)—862no—
539AGL(1,ℤ/8)—862no—
540#135—434no—
541#135—434no—
542#135—868no—
543C2×Q16—431no—
544C2×SD16—431no—
545C2×SD16—431no—
546C2×SD16—861no—
547C2×SD16—861no—
548C2×D8—431no—
549C2×D8—434no—
550C2×D8—861no—
551C2×D8—861no—
552C2×D8—862no—
553C2×D8—868no—
554C2×D8—861no—
555C2×D8—861no—
556#131—22no—
557#131—41no—
558#131—434no—
559#131—862no—
560#131—862no—
561#131—1721no—
562C2×M16—21no—
563C2×M16—431no—
564C2×M16—431no—
565C2×M16—431no—
566C2×M16—861no—
567C2×M16—861no—
568C2×M16C22×D4311yescharacteristic
569C22×C8—21no—
570C22×C8—431no—
571C22×C8—861no—
572C22×C8—861no—
573C22×C8C22×D4311yescharacteristic
574C4×Q8—21no—
575C4×Q8—861no—
576C4×D4—21no—
577C4×D4—41no—
578C4×D4—861no—
579C4×D4—1721no—
580#117—21no—
581#117—861no—
582#117C22×D4311yescharacteristic
583C2×C4⋊C4—21no—
584C2×C4⋊C4—431no—
585C2×C4⋊C4—861no—
586C2×C4⋊C4C22×D4311yescharacteristic
587C2×C22⋊C4—1721no—
588C2×C22⋊C4—1721no—
589C2×C42—431no—
590#108—862no—
591#107—861no—
592#107—861no—
593#104—862no—
594#104—862no—
595#104—862no—
596#103—21no—
597#103—861no—
598#103—861no—
599#103—861no—
600#103C22⋊D4311yescharacteristic
601#103C22⋊D4311yescharacteristic
602#102—21no—
603#102—21no—
604#102—21no—
605#102—21no—
606#102—21no—
607#102—861no—
608#102—861no—
609#102—861no—
610#102—861no—
611#102—861no—
612#102—861no—
613#102—861no—
614#102C22⋊D4311yescharacteristic
615#102C22⋊D4311yescharacteristic
616#100—1721no—
617#100—1721no—
618#97—861no—
619C4×C8—861no—
620C4×C8—862no—
621C24—21no—
622C24—41no—
623C24—861no—
624C24—1721no—
625#41—21no—
626#41—21no—
627#41—21no—
628#41—21no—
629#41—24no—
630#41—24no—
631#41—42no—
632#41—42no—
633#41—432no—
634#41—432no—
635#41—864no—
636#41—861no—
637#41—861no—
638#41—864no—
639#41—1722no—
640#41—1722no—
641#41C2×C4×D4312yes—
642#41C2×C4×D4312yes—
643#41#1062189812yes—
644#41D4×D4312yes—
645C2×Q8—431no—
646C2×Q8D4×D4311yescharacteristic
647C2×Q8C2×C22⋊D4311yescharacteristic
648C2×D4—21no—
649C2×D4—21no—
650C2×D4—24no—
651C2×D4—24no—
652C2×D4—21no—
653C2×D4—21no—
654C2×D4—21no—
655C2×D4—21no—
656C2×D4—21no—
657C2×D4—42no—
658C2×D4—42no—
659C2×D4—41no—
660C2×D4—41no—
661C2×D4—44no—
662C2×D4—44no—
663C2×D4—432no—
664C2×D4—431no—
665C2×D4—864no—
666C2×D4—861no—
667C2×D4—864no—
668C2×D4—861no—
669C2×D4—861no—
670C2×D4—861no—
671C2×D4—861no—
672C2×D4—861no—
673C2×D4—1722no—
674C2×D4—1721no—
675C2×D4—1722no—
676C2×D4—1721no—
677C2×D4—1724no—
678C2×D4—1724no—
679C2×D4C2×C4×D4312yes—
680C2×D4D4×D4311yescharacteristic
681C2×D4C2×C22⋊D4311yescharacteristic
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—41no—
686C22×C4—41no—
687C22×C4—861no—
688C22×C4—861no—
689C22×C4—861no—
690C22×C4—1721no—
691C22×C4—1721no—
692C22×C4C23×D4311yescharacteristic
693Q16—434no—
694SD16—434no—
695SD16—434no—
696SD16—864no—
697SD16—864no—
698D8—434no—
699D8—864no—
700D8—864no—
701D8—864no—
702D8—864no—
703M16—21no—
704M16—21no—
705M16—42no—
706M16—432no—
707M16—864no—
708M16—861no—
709M16—861no—
710M16—861no—
711M16—861no—
712M16—861no—
713M16—1722no—
714C2×C8—21no—
715C2×C8—21no—
716C2×C8—21no—
717C2×C8—42no—
718C2×C8—432no—
719C2×C8—431no—
720C2×C8—432no—
721C2×C8—431no—
722C2×C8—864no—
723C2×C8—861no—
724C2×C8—861no—
725C2×C8—861no—
726C2×C8—1722no—
727C2×C8C2×C22⋊D4311yescharacteristic
728C2×C8C2×C22⋊D4311yescharacteristic
729C4⋊C4—21no—
730C4⋊C4—21no—
731C4⋊C4—41no—
732C4⋊C4—861no—
733C4⋊C4—861no—
734C4⋊C4—1721no—
735C4⋊C4C2×C22⋊D4311yescharacteristic
736C4⋊C4C2×C22⋊D4311yescharacteristic
737C22⋊C4—21no—
738C22⋊C4—41no—
739C22⋊C4—3442no—
740C22⋊C4—3442no—
741C22⋊C4—1721no—
742C42—21no—
743C42—41no—
744C42—861no—
745C42—861no—
746C42—1721no—
747C23—21no—
748C23—21no—
749C23—22no—
750C23—44no—
751C23—41no—
752C23—41no—
753C23—81no—
754C23—81no—
755C23—161no—
756C23—161no—
757C23—861no—
758C23—862no—
759C23—3441no—
760C23—3441no—
761C23—1724no—
762C23—1721no—
763C23—1721no—
764C23—6881no—
765C23—6881no—
766C23#1306337011yescharacteristic
767Q8—21no—
768Q8—21no—
769Q8—432no—
770Q8—861no—
771Q8C22⋊C4×D4312yes—
772Q8C4×C22⋊D4312yes—
773D4—22no—
774D4—22no—
775D4—22no—
776D4—22no—
777D4—22no—
778D4—22no—
779D4—21no—
780D4—21no—
781D4—44no—
782D4—44no—
783D4—41no—
784D4—41no—
785D4—432no—
786D4—862no—
787D4—862no—
788D4—862no—
789D4—862no—
790D4—861no—
791D4—1724no—
792D4—1724no—
793D4—1721no—
794D4—1721no—
795D4C22⋊C4×D4312yes—
796D4C4×C22⋊D4312yes—
797C2×C4—21no—
798C2×C4—21no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—44no—
806C2×C4—41no—
807C2×C4—81no—
808C2×C4—161no—
809C2×C4—861no—
810C2×C4—862no—
811C2×C4—862no—
812C2×C4—862no—
813C2×C4—3441no—
814C2×C4—1724no—
815C2×C4—1721no—
816C2×C4—1721no—
817C2×C4—1721no—
818C2×C4—6881no—
819C2×C4C22×C4×D4311yescharacteristic
820C2×C4C2×D4×D4311yescharacteristic
821C2×C4C2×D4×D4311yescharacteristic
822C2×C4C22×C22⋊D4311yescharacteristic
823C2×C4C2×#1062189811yescharacteristic
824C2×C4#1306337011yescharacteristic
825C8—21no—
826C8—21no—
827C8—41no—
828C8—432no—
829C8—432no—
830C8—862no—
831C8—1721no—
832C8—1721no—
833C22—21no—
834C22—21no—
835C22—22no—
836C22—22no—
837C22—41no—
838C22—41no—
839C22—41no—
840C22—41no—
841C22—42no—
842C22—82no—
843C22—81no—
844C22—81no—
845C22—161no—
846C22—164no—
847C22—862no—
848C22—3442no—
849C22—3441no—
850C22—3441no—
851C22—1722no—
852C22—1721no—
853C22—1721no—
854C22—6881no—
855C22—6884no—
856C22#1458337211yescharacteristic
857C22D4×C22⋊D4311yescharacteristic
858C22#1458353911yescharacteristic
859C4—22no—
860C4—22no—
861C4—41no—
862C4—41no—
863C4—81no—
864C4—862no—
865C4—3441no—
866C4—1722no—
867C4C2×C22⋊C4×D4311yescharacteristic
868C4C2×C4×C22⋊D4311yescharacteristic
869C4D4×C22⋊D4311yescharacteristic
870C4#1458353911yescharacteristic
871C2—21no—
872C2—21no—
873C2—42no—
874C2—42no—
875C2—82no—
876C2—3442no—
877C2—1722no—
878C2C22⋊C4×C22⋊D4311yescharacteristic
879C2#1914637511yescharacteristic
880C2#1914639211yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#2897C2
socleC22×C43D42
prime radicalC2×#14583702C2
cosocleC22×C4×C43C24
hypercenter#2897D43
hypocenterC43#22466
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #2897

Complements

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

NH ≅ G/Ntype
2. C2×#14583014C2semidirect
3. #19143468C2semidirect
4. #19143117C2semidirect
5. #19135504C2semidirect
6. #19135458C2semidirect
7. #19135106C2semidirect
8. #19135103C2semidirect
9. #19134971C2semidirect
10. #19134968C2semidirect
11. #19134657C2semidirect
12. #19134549C2semidirect
13. #19134547C2semidirect
14. #19134435C2semidirect
15. C43×#2897C2semidirect
18. #14583702C4semidirect
28. C2×#13063331C22semidirect
29. #14583379C22semidirect
35. C2×#13063260C22semidirect
36. C2×#13063258C22semidirect
38. C2×#13063252C22semidirect
39. C2×#13063251C22semidirect
40. #14582903C22semidirect
43. #14582900C22semidirect
45. #14582898C22semidirect
47. C2×#13063247C22semidirect
49. C2×#13063242C22semidirect
50. C2×#13063241C22semidirect
51. #14582855C22semidirect
52. C2×C8×Dic43C22semidirect
53. #14582802C22semidirect
54. #14582800C22semidirect
55. #14582668C22semidirect
56. #14582667C22semidirect
57. #14582664C22semidirect
58. #14582658C22semidirect
60. C2×#131×C43C22semidirect
61. C43×#520C22semidirect
63. C43×#418C22semidirect
69. C2×#102×C43C22semidirect
73. #13063371C2×C4semidirect
83. #13063351C2×C4semidirect
86. #13063350C2×C4semidirect
101. C2×#10621882C2×C4semidirect
104. #13063332C2×C4semidirect
148. H(5,𝔽2)×C43C2×C4semidirect
271. #10621885C22⋊C4semidirect
273. #10621884C22⋊C4semidirect
275. #10621883C22⋊C4semidirect
280. #10621882C22⋊C4semidirect
435. #2897D43semidirect
470. C2×#131C2×D43semidirect
472. #520C2×D43semidirect
486. #418C2×D43semidirect
499. C2×#102C2×D43semidirect
510. C43#22466semidirect
518. H(5,𝔽2)C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145837022
C2×#145830142
#191434682
#191431172
#191355042
#191354582
#191351062
#191351032
#191349712
#191349682
#191346572
#191345492
#191345472
#191344352
C43×#28972
#2246643