Finite Group Databasebeta

← #25119135

Subgroups — #25119135

Order 11008.

892 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144173C211yesmaximal, characteristic
2C2×#14583013C211yesmaximal, characteristic, complemented
3#19143322C211yesmaximal, characteristic, complemented
4#19143320C211yesmaximal, characteristic, complemented
5C22×#13063260C211yesmaximal, characteristic, complemented
6#19135480C211yesmaximal, characteristic, complemented
7#19135342C211yesmaximal, characteristic, complemented
8#19135246C211yesmaximal, characteristic, complemented
9#19135241C211yesmaximal, characteristic, complemented
10#19134895C211yesmaximal, characteristic, complemented
11#19134871C211yesmaximal, characteristic, complemented
12#19134868C211yesmaximal, characteristic, complemented
13#19134473C211yesmaximal, characteristic, complemented
14C22⋊C4×C43⋊C8C211yesmaximal, characteristic, complemented
15C43×#1871C211yesmaximal, characteristic, complemented
16C2×#13063345C2211yescharacteristic
17C2×#13063333C2211yescharacteristic
18C2×#13063332C2211yescharacteristic
19C22×#10621877C2211yescharacteristic
20C23×C43⋊C8C2211yescharacteristic
21#14583410C2211yescharacteristic
22#14583138C411yescharacteristic, complemented
23#14583138C411yescharacteristic, complemented
24#14583133C411yescharacteristic, complemented
25#14583133C411yescharacteristic, complemented
26#14583130C411yescharacteristic, complemented
27#14583130C411yescharacteristic, complemented
28#14583126C411yescharacteristic, complemented
29#14583126C411yescharacteristic, complemented
30#14583013—24no—
31#14582977—21no—
32#14582975—21no—
33#14582971—21no—
34#14582971—21no—
35#14582970—21no—
36#14582968—21no—
37D4×C43⋊C8—21no—
38C8×C22⋊D43—21no—
39C2×#13063260—24no—
40C2×#13063260C2211yescharacteristic
41C2×#13063260C2211yescharacteristic
42C2×#13063260C2211yescharacteristic
43C2×#13063260C2211yescharacteristic
44#14582935C2211yescharacteristic
45#14582927C2211yescharacteristic
46#14582926C2211yescharacteristic
47C2×#13063253C2211yescharacteristic
48C2×#13063253C2211yescharacteristic
49#14582895C2211yescharacteristic
50#14582893C2211yescharacteristic
51#14582867C2211yescharacteristic
52#14582866C2211yescharacteristic
53C2×C22⋊(C43⋊C8)C2211yescharacteristic
54#14582857C2211yescharacteristic
55#14582855C2211yescharacteristic
56C2×C4×C43⋊C8C2211yescharacteristic
57C2×C4×C43⋊C8C2211yescharacteristic
58#14582659C2211yescharacteristic
59#14582659C2211yescharacteristic
60#14582654C2211yescharacteristic
61#14582654C2211yescharacteristic
62C22×M16×C43C2211yescharacteristic
63C43×#525C2211yescharacteristic
64C2×#104×C43C2211yescharacteristic
65C2×#104×C43C2211yescharacteristic
66C4×C22⋊C4×C43C2211yescharacteristic
67C43×#339C2211yescharacteristic
68C43×#339C2211yescharacteristic
69C2×#10621898C2311yescharacteristic
70#13063345—22no—
71#13063345—22no—
72C2×#10621885C2×C411yescharacteristic
73C2×#10621883C2×C411yescharacteristic
74C2×#10621884C2×C411yescharacteristic
75C2×#10621882C2×C411yescharacteristic
76#13063333—22no—
77#13063333—41no—
78#13063332—22no—
79#13063332—41no—
80C2×#10621877—21no—
81C2×#10621877—21no—
82C2×#10621877—22no—
83C2×#10621877—41no—
84C2×#10621877C2311yescharacteristic
85C2×#10621877C2311yescharacteristic
86C2×#10621872—21no—
87C22×C43⋊C8—22no—
88C22×C43⋊C8—22no—
89C22×C43⋊C8—21no—
90C22×C43⋊C8—21no—
91C22×C43⋊C8C2×C411yescharacteristic
92C22×C43⋊C8C2×C411yescharacteristic
93C22×C43⋊C8C2×C411yescharacteristic
94C22×C43⋊C8C2×C411yescharacteristic
95C22×C43⋊C8C2311yescharacteristic
96C22×C43⋊C8C2311yescharacteristic
97C22×C43⋊C8C2311yescharacteristic
98C22×C43⋊C8C2311yescharacteristic
99C2×C8×D43—21no—
100#13063308—21no—
101#13063304C2×C411yescharacteristic
102#13063304C2×C411yescharacteristic
103#13063299C2×C411yescharacteristic
104#13063299C2×C411yescharacteristic
105#13063294—21no—
106C4×C22⋊D43—21no—
107C4×C22⋊D43—21no—
108#13063284C2311yescharacteristic
109#13063260—22no—
110#13063260—22no—
111#13063260—22no—
112#13063260D414yescomplemented
113#13063258C2×C411yescharacteristic
114#13063258C2×C411yescharacteristic
115#13063256C2×C411yescharacteristic
116#13063256C2×C411yescharacteristic
117C4⋊(C43⋊C8)—21no—
118C4⋊(C43⋊C8)—21no—
119Dic43⋊C8—21no—
120Dic43⋊C8—21no—
121#13063253—22no—
122#13063253—41no—
123#13063249C2×C411yescharacteristic
124#13063249C2×C411yescharacteristic
125#13063248C2×C411yescharacteristic
126#13063248C2×C411yescharacteristic
127#13063246C2×C411yescharacteristic
128#13063246C2×C411yescharacteristic
129#13063245C2×C411yescharacteristic
130#13063245C2×C411yescharacteristic
131C22⋊(C43⋊C8)—21no—
132C22⋊(C43⋊C8)—21no—
133C22⋊(C43⋊C8)D411yescharacteristic
134C22⋊(C43⋊C8)D411yescharacteristic
135C22⋊(C43⋊C8)D411yescharacteristic
136C22⋊(C43⋊C8)D411yescharacteristic
137(C2×D43)⋊C8—21no—
138(C2×D43)⋊C8—21no—
139#13063236—21no—
140#13063235—21no—
141C4×C43⋊C8—22no—
142C4×C43⋊C8—21no—
143C4×C43⋊C8—22no—
144C8×Dic43—21no—
145C2×#41×C43C2311yescharacteristic
146C23×C4×C43C2311yescharacteristic
147C2×M16×C43—21no—
148C2×M16×C43—22no—
149C2×M16×C43—41no—
150C2×M16×C43C2311yescharacteristic
151C2×M16×C43C2311yescharacteristic
152C22×C8×C43—21no—
153#123×C43—21no—
154C22⋊Q8×C43C2×C411yescharacteristic
155C22⋊Q8×C43C2×C411yescharacteristic
156#121×C43C2×C411yescharacteristic
157#121×C43C2×C411yescharacteristic
158#120×C43—21no—
159C4×D4×C43—21no—
160C4×D4×C43—21no—
161#117×C43C2311yescharacteristic
162C2×C22⋊C4×C43—21no—
163C2×C42×C43C2311yescharacteristic
164C2×C42×C43C2311yescharacteristic
165#104×C43—22no—
166#104×C43—41no—
167#95×C43—21no—
168C24×C43#4111yescharacteristic
169#41×C43—21no—
170#41×C43—21no—
171#41×C43—21no—
172#41×C43—21no—
173C2×Q8×C43C22×C411yescharacteristic
174C2×D4×C43—21no—
175C2×D4×C43—21no—
176C2×D4×C43—21no—
177C2×D4×C43C22×C411yescharacteristic
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×C43C22×C411yescharacteristic
186C22×C4×C43C22×C411yescharacteristic
187C22×C4×C43C2×D411yescharacteristic
188C22×C4×C43C2×D411yescharacteristic
189C22×C4×C43#4111yescharacteristic
190C22×C4×C43C2411yescharacteristic
191C2×C22⋊D43—21no—
192C2×C22⋊D43—21no—
193C2×C22⋊D43—21no—
194#10621898—21no—
195#10621898—21no—
196#10621898—21no—
197#10621898—21no—
198C2×D172C22×C411yescharacteristic
199C2×C4×D43—21no—
200C2×Dic86C22×C411yescharacteristic
201M16×C43—21no—
202M16×C43—21no—
203M16×C43—21no—
204M16×C43—42no—
205M16×C43C2×D412yes—
206C2×C8×C43—21no—
207C2×C8×C43—21no—
208C2×C8×C43—42no—
209C4⋊C4×C43—21no—
210C4⋊C4×C43—21no—
211C4⋊C4×C43C22×C411yescharacteristic
212C4⋊C4×C43C22×C411yescharacteristic
213C22⋊C4×C43—24no—
214C22⋊C4×C43—21no—
215C22⋊C4×C43—21no—
216C22⋊C4×C43—21no—
217C22⋊C4×C43—21no—
218C22⋊C4×C43—21no—
219C42×C43—21no—
220C42×C43—21no—
221C42×C43—21no—
222C42×C43—21no—
223C42×C43—21no—
224C22⋊Dic43—21no—
225C22⋊Dic43—21no—
226C22⋊Dic43—21no—
227#10621885—22no—
228#10621884—22no—
229#10621883—22no—
230#10621882—22no—
231(C2×D43)⋊C4—21no—
232(C2×D43)⋊C4—21no—
233C4⋊Dic43C22×C411yescharacteristic
234C4⋊Dic43C22×C411yescharacteristic
235Dic43⋊C4—21no—
236Dic43⋊C4—21no—
237C4×Dic43—21no—
238#10621877—21no—
239#10621877—21no—
240#10621877—21no—
241#10621877—42no—
242#10621877—42no—
243#10621877C2×D412yes—
244C2×C43⋊C8—21no—
245C2×C43⋊C8—21no—
246C2×C43⋊C8—21no—
247C2×C43⋊C8—21no—
248C2×C43⋊C8—21no—
249C2×C43⋊C8—21no—
250C2×C43⋊C8—21no—
251C2×C43⋊C8—22no—
252C2×C43⋊C8—22no—
253C2×C43⋊C8—22no—
254C2×C43⋊C8—22no—
255C2×C43⋊C8—21no—
256C2×C43⋊C8—42no—
257C2×C43⋊C8—42no—
258C2×C43⋊C8C22×C411yescharacteristic
259C2×C43⋊C8C22×C411yescharacteristic
260C2×C43⋊C8C22×C411yescharacteristic
261C2×C43⋊C8C22×C411yescharacteristic
262C2×C43⋊C8C2×D411yescharacteristic
263C2×C43⋊C8C2×D411yescharacteristic
264C2×C43⋊C8C2×D411yescharacteristic
265C2×C43⋊C8C2×D411yescharacteristic
266C2×C43⋊C8C2×D412yes—
267C2×C43⋊C8#4112yes—
268#10621872—42no—
269C8×D43—42no—
270C23×C43—21no—
271C23×C43—21no—
272C23×C43—22no—
273C23×C43—21no—
274C23×C43—41no—
275C23×C43C4×D411yescharacteristic
276C23×C43C4×D411yescharacteristic
277C23×C43C2×#4111yescharacteristic
278C22×D43—21no—
279Q8×C43—21no—
280Q8×C43—21no—
281D4×C43—21no—
282D4×C43—21no—
283D4×C43—41no—
284D4×C43—41no—
285D4×C43—42no—
286D4×C43—81no—
287C2×C4×C43—21no—
288C2×C4×C43—21no—
289C2×C4×C43—21no—
290C2×C4×C43—21no—
291C2×C4×C43—21no—
292C2×C4×C43—21no—
293C2×C4×C43—21no—
294C2×C4×C43—21no—
295C2×C4×C43—21no—
296C2×C4×C43—21no—
297C2×C4×C43—22no—
298C2×C4×C43—22no—
299C2×C4×C43—21no—
300C2×C4×C43—21no—
301C2×C4×C43—21no—
302C2×C4×C43—41no—
303C2×C4×C43—41no—
304C2×C4×C43—41no—
305C2×C4×C43—41no—
306C2×C4×C43—41no—
307C2×C4×C43—41no—
308C2×C4×C43C4×D411yescharacteristic
309C2×C4×C43C4×D411yescharacteristic
310C2×C4×C43C23×C411yescharacteristic
311C2×C4×C43C22×D411yescharacteristic
312C2×C4×C43C22×D411yescharacteristic
313C2×C4×C43C2×#4111yescharacteristic
314C2×C4×C43H(5,𝔽2)11yescharacteristic
315C2×C4×C432−1+411yescharacteristic
316C22⋊D43—41no—
317C22⋊D43—41no—
318C22⋊D43—42no—
319C22⋊D43—81no—
320C2×Dic43—21no—
321C2×Dic43—21no—
322C2×Dic43—21no—
323D172—21no—
324D172—21no—
325C4×D43—41no—
326C4×D43—41no—
327Dic86—21no—
328Dic86—21no—
329C8×C43—22no—
330C8×C43—41no—
331C43⋊C8—21no—
332C43⋊C8—21no—
333C43⋊C8—21no—
334C43⋊C8—21no—
335C43⋊C8—22no—
336C43⋊C8—21no—
337C43⋊C8—21no—
338C43⋊C8—41no—
339C43⋊C8C4×D412yes—
340C43⋊C8C4×D412yes—
341#23018—431nomaximal, Sylow
342C22×C43—21no—
343C22×C43—21no—
344C22×C43—21no—
345C22×C43—21no—
346C22×C43—21no—
347C22×C43—21no—
348C22×C43—21no—
349C22×C43—42no—
350C22×C43—42no—
351C22×C43—41no—
352C22×C43—41no—
353C22×C43—41no—
354C22×C43#44312yescomplemented
355C22×C43C2×C4×D411yescharacteristic
356C22×C43#54811yescharacteristic
357C22×C43#55311yescharacteristic
358C2×D43—41no—
359C2×D43—41no—
360C2×D43—41no—
361C4×C43—21no—
362C4×C43—21no—
363C4×C43—42no—
364C4×C43—42no—
365C4×C43—41no—
366C4×C43—41no—
367C4×C43—41no—
368C4×C43C2×C4×D411yescharacteristic
369C4×C43#52011yescharacteristic
370C4×C43D4211yescharacteristic
371C4×C43#54711yescharacteristic
372Dic43—41no—
373Dic43—41no—
374Dic43—41no—
375#3050—431no—
376C2×#443—431no—
377#2933—431no—
378#2933—431no—
379C22×#108—431no—
380#1974—431no—
381#1945—431no—
382#1929—431no—
383#1929—431no—
384#1871—431no—
385#1871D4311yescharacteristic, complemented
386#1866—431no—
387#1866—431no—
388#1772—431no—
389C8×C22⋊C4—431no—
390C2×C43—21no—
391C2×C43—21no—
392C2×C43—22no—
393C2×C43—41no—
394C2×C43—81no—
395C2×C43#236111yescharacteristic
396C2×C43C2×#44311yescharacteristic
397C2×C43#295711yescharacteristic
398D43—81no—
399C2×#135—431no—
400C2×#131—431no—
401C2×#131—431no—
402C22×M16—431no—
403C22×M16C2×D4311yescharacteristic
404C23×C8—431no—
405#525—431no—
406#525C2×D4311yescharacteristic
407#467—431no—
408#467—431no—
409#466—431no—
410#466—431no—
411#465—431no—
412#465—431no—
413#465—431no—
414#465—431no—
415#443—864no—
416#436—861no—
417#436—861no—
418#435—861no—
419#435—861no—
420#435—861no—
421#435—861no—
422C8×D4—861no—
423C8×D4—861no—
424C2×#108—431no—
425C2×#108—431no—
426C2×#108—431no—
427C2×#108—431no—
428C2×#108—864no—
429#427—431no—
430#424—431no—
431#424—431no—
432C2×#104—431no—
433C2×#104—431no—
434C2×#104C2×D4311yescharacteristic
435C2×#104C2×D4311yescharacteristic
436#416—431no—
437#416—431no—
438#408—431no—
439#408—431no—
440C2×C22⋊C8—431no—
441#405—431no—
442#405—431no—
443C2×C4×C8—431no—
444C2×C4×C8—431no—
445C4×C22⋊C4C2×D4311yescharacteristic
446#339—431no—
447#339—431no—
448#339C2×D4311yescharacteristic
449#339C2×D4311yescharacteristic
450#336—431no—
451#336—431no—
452C43#2301811yescharacteristic, complemented, Sylow
453C2×#41—431no—
454C2×#41C22×D4311yescharacteristic
455C23×C4C22×D4311yescharacteristic
456#135—862no—
457#135—862no—
458C2×Q16—431no—
459C2×SD16—431no—
460C2×SD16—431no—
461C2×D8—431no—
462#131—862no—
463#131—862no—
464#131—1721no—
465#131—1721no—
466C2×M16—21no—
467C2×M16—22no—
468C2×M16—41no—
469C2×M16—431no—
470C2×M16—431no—
471C2×M16—861no—
472C2×M16—861no—
473C2×M16—861no—
474C2×M16—862no—
475C2×M16—1721no—
476C2×M16C22×D4311yescharacteristic
477C2×M16C22×D4311yescharacteristic
478C22×C8—21no—
479C22×C8—431no—
480C22×C8—431no—
481C22×C8—431no—
482C22×C8—431no—
483C22×C8—431no—
484C22×C8—431no—
485C22×C8—431no—
486C22×C8—431no—
487C22×C8—861no—
488C22×C8—862no—
489C22×C8—862no—
490C22×C8—861no—
491C22×C8—861no—
492#123—21no—
493#123—861no—
494C22⋊Q8—431no—
495C22⋊Q8—431no—
496C22⋊Q8C4×D4311yescharacteristic
497C22⋊Q8C4×D4311yescharacteristic
498#121—431no—
499#121—431no—
500#121C4×D4311yescharacteristic
501#121C4×D4311yescharacteristic
502#120—21no—
503#120—861no—
504C4×D4—21no—
505C4×D4—21no—
506C4×D4—861no—
507C4×D4—861no—
508#117—431no—
509#117C22×D4311yescharacteristic
510C2×C22⋊C4—21no—
511C2×C42C22×D4311yescharacteristic
512C2×C42C22×D4311yescharacteristic
513#108—434no—
514#108—862no—
515#108—862no—
516#108—862no—
517#107—431no—
518#107—431no—
519#106—431no—
520#106—431no—
521C4⋊C8—861no—
522C4⋊C8—861no—
523C4⋊C8—861no—
524C4⋊C8—861no—
525#104—22no—
526#104—41no—
527#104—862no—
528#104—1721no—
529#103—431no—
530#103—431no—
531#103—431no—
532#103—431no—
533#102—431no—
534#102—431no—
535#102—431no—
536#102—431no—
537C22⋊C8—431no—
538C22⋊C8—431no—
539C22⋊C8—431no—
540C22⋊C8—431no—
541C22⋊C8—861no—
542C22⋊C8—861no—
543C22⋊C8—861no—
544C22⋊C8—861no—
545#97—861no—
546#97—861no—
547C4×C8—862no—
548C4×C8—862no—
549C4×C8—861no—
550C4×C8—861no—
551#95—21no—
552C24#1062190011yescharacteristic
553#41—21no—
554#41—21no—
555#41—21no—
556#41—21no—
557#41—861no—
558#41—861no—
559#41—861no—
560#41—861no—
561C2×Q8—431no—
562C2×Q8C2×C4×D4311yescharacteristic
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—431no—
567C2×D4—861no—
568C2×D4—861no—
569C2×D4—861no—
570C2×D4C2×C4×D4311yescharacteristic
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—861no—
579C22×C4C2×C4×D4311yescharacteristic
580C22×C4C2×C4×D4311yescharacteristic
581C22×C4D4×D4311yescharacteristic
582C22×C4D4×D4311yescharacteristic
583C22×C4#1062190011yescharacteristic
584C22×C4C23×D4311yescharacteristic
585Q16—862no—
586SD16—862no—
587SD16—862no—
588D8—862no—
589M16—21no—
590M16—21no—
591M16—21no—
592M16—42no—
593M16—432no—
594M16—861no—
595M16—861no—
596M16—861no—
597M16—1722no—
598M16—1722no—
599M16—1722no—
600M16D4×D4312yes—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—42no—
604C2×C8—431no—
605C2×C8—431no—
606C2×C8—432no—
607C2×C8—432no—
608C2×C8—431no—
609C2×C8—431no—
610C2×C8—431no—
611C2×C8—431no—
612C2×C8—431no—
613C2×C8—431no—
614C2×C8—862no—
615C2×C8—862no—
616C2×C8—862no—
617C2×C8—862no—
618C2×C8—861no—
619C2×C8—861no—
620C2×C8—861no—
621C2×C8—861no—
622C2×C8—861no—
623C2×C8—861no—
624C2×C8—861no—
625C2×C8—861no—
626C2×C8—1722no—
627C2×C8—1722no—
628C2×C8—1722no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—431no—
632C4⋊C4—431no—
633C4⋊C4—861no—
634C4⋊C4—861no—
635C4⋊C4C2×C4×D4311yescharacteristic
636C4⋊C4C2×C4×D4311yescharacteristic
637C22⋊C4—24no—
638C22⋊C4—21no—
639C22⋊C4—21no—
640C22⋊C4—21no—
641C22⋊C4—21no—
642C22⋊C4—21no—
643C22⋊C4—861no—
644C22⋊C4—861no—
645C22⋊C4—861no—
646C22⋊C4—861no—
647C22⋊C4—861no—
648C42—21no—
649C42—21no—
650C42—21no—
651C42—21no—
652C42—21no—
653C42—861no—
654C23—21no—
655C23—21no—
656C23—22no—
657C23—21no—
658C23—41no—
659C23—861no—
660C23(C22⋊D43)⋊C411yescharacteristic
661C23(C22⋊D43)⋊C411yescharacteristic
662C23C2×#1062190011yescharacteristic
663Q8—21no—
664Q8—21no—
665Q8—861no—
666Q8—861no—
667D4—21no—
668D4—21no—
669D4—41no—
670D4—41no—
671D4—42no—
672D4—81no—
673D4—861no—
674D4—861no—
675D4—3441no—
676D4—1721no—
677D4—1721no—
678D4—1722no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—861no—
701C2×C4—861no—
702C2×C4—861no—
703C2×C4—1721no—
704C2×C4—1721no—
705C2×C4(C22⋊D43)⋊C411yescharacteristic
706C2×C4(C22⋊D43)⋊C411yescharacteristic
707C2×C4C22×C4×D4311yescharacteristic
708C2×C4C2×D4×D4311yescharacteristic
709C2×C4C2×D4×D4311yescharacteristic
710C2×C4#41×D4311yescharacteristic
711C2×C4#1306337011yescharacteristic
712C2×C4#1306337211yescharacteristic
713C8—22no—
714C8—41no—
715C8—432no—
716C8—432no—
717C8—861no—
718C8—861no—
719C8—861no—
720C8—861no—
721C8—862no—
722C8—861no—
723C8—861no—
724C8—1721no—
725C22—21no—
726C22—21no—
727C22—21no—
728C22—21no—
729C22—21no—
730C22—21no—
731C22—21no—
732C22—42no—
733C22—42no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—1721no—
738C22—1721no—
739C22—1721no—
740C22#1458301312yescomplemented
741C22C2×(C22⋊D43)⋊C411yescharacteristic
742C22#1458355511yescharacteristic
743C22#1458359211yescharacteristic
744C4—21no—
745C4—21no—
746C4—42no—
747C4—42no—
748C4—41no—
749C4—41no—
750C4—41no—
751C4—1721no—
752C4—1721no—
753C4—1721no—
754C4C4×D4×D4311yescharacteristic
755C4#1458337811yescharacteristic
756C4#1458353111yescharacteristic
757C4#1458354711yescharacteristic
758C2—21no—
759C2—21no—
760C2—22no—
761C2—41no—
762C2—81no—
763C2—3441no—
764C2#1913760611yescharacteristic
765C2C2×#1458301311yescharacteristic
766C2#1914350811yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1871C2
socleC22×C43C2×C4×D4
prime radical#19144173C2
cosocleC22×C4×C43C24
hypercenter#1871D43
hypocenterC43#23018
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1871

Complements

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

NH ≅ G/Ntype
2. C2×#14583013C2semidirect
3. #19143322C2semidirect
4. #19143320C2semidirect
5. C22×#13063260C2semidirect
6. #19135480C2semidirect
7. #19135342C2semidirect
8. #19135246C2semidirect
9. #19135241C2semidirect
10. #19134895C2semidirect
11. #19134871C2semidirect
12. #19134868C2semidirect
13. #19134473C2semidirect
14. C22⋊C4×C43⋊C8C2semidirect
15. C43×#1871C2semidirect
22. #14583138C4semidirect
23. #14583138C4semidirect
24. #14583133C4semidirect
25. #14583133C4semidirect
26. #14583130C4semidirect
27. #14583130C4semidirect
28. #14583126C4semidirect
29. #14583126C4semidirect
112. #13063260D4semidirect
354. C22×C43#443semidirect
385. #1871D43semidirect
452. C43#23018semidirect
740. C22#14583013semidirect

Maximal subgroups

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

subgroupindex
#191441732
C2×#145830132
#191433222
#191433202
C22×#130632602
#191354802
#191353422
#191352462
#191352412
#191348952
#191348712
#191348682
#191344732
C22⋊C4×C43⋊C82
C43×#18712
#2301843