Finite Group Databasebeta

← #25119137

Subgroups — #25119137

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#19144175C211yesmaximal, characteristic
2C2×#14583013C211yesmaximal, characteristic, complemented
3#19143325C211yesmaximal, characteristic, complemented
4#19143323C211yesmaximal, characteristic, complemented
5C2×#108×D43C211yesmaximal, characteristic, complemented
6#19135482C211yesmaximal, characteristic, complemented
7#19135342C211yesmaximal, characteristic, complemented
8#19135244C211yesmaximal, characteristic, complemented
9#19134896C211yesmaximal, characteristic, complemented
10#19134894C211yesmaximal, characteristic, complemented
11#19134872C211yesmaximal, characteristic, complemented
12#19134867C211yesmaximal, characteristic, complemented
13#19134475C211yesmaximal, characteristic, complemented
14#19134365C211yesmaximal, characteristic, complemented
15C43×#1929C211yesmaximal, characteristic, complemented
16C2×#13063345C2211yescharacteristic
17C2×#13063333C2211yescharacteristic
18C2×#13063332C2211yescharacteristic
19C2×M16×D43C2211yescharacteristic
20C2×M16×D43C2211yescharacteristic
21C22×C8×D43C2211yescharacteristic
22#14583411C2211yescharacteristic
23#14583406C2211yescharacteristic
24#14583139C411yescharacteristic, complemented
25#14583139C411yescharacteristic, complemented
26#14583134C411yescharacteristic, complemented
27#14583134C411yescharacteristic, complemented
28#14583131C411yescharacteristic, complemented
29#14583131C411yescharacteristic, complemented
30#14583127C411yescharacteristic, complemented
31#14583127C411yescharacteristic, complemented
32#14583013—24no—
33#14582978—21no—
34#14582974—21no—
35#14582973—21no—
36#14582972—21no—
37#14582972—21no—
38#14582967—21no—
39C8×D172—21no—
40(C22⋊D43)⋊C8—21no—
41C2×#13063261C2211yescharacteristic
42C2×#13063260C2211yescharacteristic
43C2×#13063260C2211yescharacteristic
44#108×D43—24no—
45#14582935C2211yescharacteristic
46#14582927C2211yescharacteristic
47#14582926C2211yescharacteristic
48C2×#13063253C2211yescharacteristic
49C2×#13063252C2211yescharacteristic
50C2×#13063251C2211yescharacteristic
51#14582896C2211yescharacteristic
52#14582865C2211yescharacteristic
53C2×(C2×D43)⋊C8C2211yescharacteristic
54#14582854C2211yescharacteristic
55C2×C4×C43⋊C8C2211yescharacteristic
56C2×C8×Dic43C2211yescharacteristic
57C4×(C2×D43)⋊C4C2211yescharacteristic
58#14582660C2211yescharacteristic
59#14582659C2211yescharacteristic
60#14582658C2211yescharacteristic
61#14582653C2211yescharacteristic
62C2×#108×C43C2211yescharacteristic
63C2×#104×C43C2211yescharacteristic
64C43×#416C2211yescharacteristic
65C43×#408C2211yescharacteristic
66C43×#405C2211yescharacteristic
67C43×#339C2211yescharacteristic
68C43×#336C2211yescharacteristic
69C2×#10621898C2311yescharacteristic
70C22×C4×D43C2311yescharacteristic
71#13063345—22no—
72#13063345—22no—
73C2×#10621885C2×C411yescharacteristic
74C2×#10621883C2×C411yescharacteristic
75C2×#10621884C2×C411yescharacteristic
76C2×#10621882C2×C411yescharacteristic
77#13063333—22no—
78#13063333—41no—
79#13063332—22no—
80#13063332—41no—
81C2×#10621877—21no—
82C2×#10621877C2311yescharacteristic
83C2×#10621877C2311yescharacteristic
84C2×#10621872—21no—
85C2×#10621872—21no—
86C2×#10621872—21no—
87M16×D43—22no—
88M16×D43—22no—
89M16×D43—41no—
90M16×D43—41no—
91C22×C43⋊C8—21no—
92C22×C43⋊C8C2311yescharacteristic
93C22×C43⋊C8C2311yescharacteristic
94C2×C8×D43—22no—
95C2×C8×D43—22no—
96C2×C8×D43—21no—
97C2×C8×D43—21no—
98C2×C8×D43—21no—
99C2×C8×D43C2×C411yescharacteristic
100C2×C8×D43C2×C411yescharacteristic
101C2×C8×D43C2×C411yescharacteristic
102C2×C8×D43C2×C411yescharacteristic
103#13063309—21no—
104#13063306—21no—
105#13063305C2×C411yescharacteristic
106#13063305C2×C411yescharacteristic
107#13063301C2×C411yescharacteristic
108#13063301C2×C411yescharacteristic
109#13063300C2×C411yescharacteristic
110#13063300C2×C411yescharacteristic
111#13063296C2×C411yescharacteristic
112#13063296C2×C411yescharacteristic
113#13063295—21no—
114#13063293—21no—
115C4×D172—21no—
116C4×D172—21no—
117C4×C22⋊D43—21no—
118C4×C22⋊D43—21no—
119#13063284C2311yescharacteristic
120C2×(C2×D43)⋊C4—21no—
121C2×C4×Dic43C2311yescharacteristic
122#13063261—22no—
123#13063260—22no—
124#13063260D414yescomplemented
125#13063258C2×C411yescharacteristic
126#13063258C2×C411yescharacteristic
127#13063256C2×C411yescharacteristic
128#13063256C2×C411yescharacteristic
129C4⋊(C43⋊C8)—21no—
130C4⋊(C43⋊C8)—21no—
131Dic43⋊C8—21no—
132Dic43⋊C8—21no—
133#13063253—22no—
134#13063252—41no—
135#13063251—41no—
136#13063250C2×C411yescharacteristic
137#13063250C2×C411yescharacteristic
138#13063247C2×C411yescharacteristic
139#13063247C2×C411yescharacteristic
140(C2×D43)⋊C8—21no—
141(C2×D43)⋊C8—21no—
142(C2×D43)⋊C8D411yescharacteristic
143(C2×D43)⋊C8D411yescharacteristic
144(C2×D43)⋊C8D411yescharacteristic
145(C2×D43)⋊C8D411yescharacteristic
146#13063235—21no—
147C4×C43⋊C8—22no—
148C8×Dic43—21no—
149C8×Dic43—22no—
150C43⋊#95—21no—
151C2×#41×C43C2311yescharacteristic
152C2×M16×C43C2311yescharacteristic
153C2×M16×C43C2311yescharacteristic
154C22×C8×C43C2311yescharacteristic
155C22×C8×C43C2311yescharacteristic
156#117×C43C2311yescharacteristic
157C2×C42×C43C2311yescharacteristic
158#108×C43—22no—
159#104×C43—22no—
160#103×C43C2×C411yescharacteristic
161#103×C43C2×C411yescharacteristic
162#102×C43C2×C411yescharacteristic
163#102×C43C2×C411yescharacteristic
164C22⋊C8×C43—21no—
165C22⋊C8×C43—21no—
166#97×C43—21no—
167C4×C8×C43—21no—
168C23×D43#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×C43C22×C411yescharacteristic
176C22×C4×C43—21no—
177C22×C4×C43—21no—
178C22×C4×C43C2411yescharacteristic
179C2×C22⋊D43—21no—
180C2×C22⋊D43—21no—
181C2×C22⋊D43—21no—
182C22×Dic43—21no—
183C22×Dic43#4111yescharacteristic
184#10621898—21no—
185#10621898—21no—
186#10621898—21no—
187#10621898—21no—
188C2×D172—21no—
189C2×D172—21no—
190C2×D172C22×C411yescharacteristic
191C2×C4×D43—21no—
192C2×C4×D43—21no—
193C2×C4×D43—21no—
194C2×C4×D43—21no—
195C2×C4×D43—21no—
196C2×C4×D43C22×C411yescharacteristic
197C2×C4×D43C22×C411yescharacteristic
198C2×C4×D43C2×D411yescharacteristic
199C2×C4×D43C2×D411yescharacteristic
200C2×Dic86C22×C411yescharacteristic
201M16×C43—21no—
202M16×C43—21no—
203M16×C43—21no—
204M16×C43C2×D412yes—
205C2×C8×C43—21no—
206C2×C8×C43—21no—
207C2×C8×C43—21no—
208C2×C8×C43—21no—
209C2×C8×C43—21no—
210C2×C8×C43—21no—
211C2×C8×C43C22×C411yescharacteristic
212C2×C8×C43C22×C411yescharacteristic
213C2×C8×C43C2×D411yescharacteristic
214C2×C8×C43C2×D411yescharacteristic
215C4⋊C4×C43C22×C411yescharacteristic
216C4⋊C4×C43C22×C411yescharacteristic
217C22⋊C4×C43—21no—
218C42×C43—21no—
219C42×C43—21no—
220C42×C43—21no—
221C22⋊Dic43—21no—
222C22⋊Dic43—21no—
223C22⋊Dic43—21no—
224#10621885—22no—
225#10621884—22no—
226#10621883—22no—
227#10621882—22no—
228(C2×D43)⋊C4—24no—
229(C2×D43)⋊C4—21no—
230(C2×D43)⋊C4—21no—
231(C2×D43)⋊C4—21no—
232(C2×D43)⋊C4—21no—
233(C2×D43)⋊C4—21no—
234(C2×D43)⋊C4—21no—
235C4⋊Dic43—21no—
236C4⋊Dic43—21no—
237C4⋊Dic43C22×C411yescharacteristic
238C4⋊Dic43C22×C411yescharacteristic
239Dic43⋊C4—21no—
240Dic43⋊C4—21no—
241C4×Dic43—21no—
242C4×Dic43—21no—
243C4×Dic43—21no—
244#10621877—21no—
245#10621877—21no—
246#10621877—21no—
247#10621877—42no—
248#10621877C2×D412yes—
249C2×C43⋊C8—21no—
250C2×C43⋊C8—21no—
251C2×C43⋊C8—21no—
252C2×C43⋊C8—21no—
253C2×C43⋊C8—42no—
254C2×C43⋊C8C22×C411yescharacteristic
255C2×C43⋊C8C22×C411yescharacteristic
256C2×C43⋊C8C2×D411yescharacteristic
257C2×C43⋊C8C2×D411yescharacteristic
258C2×C43⋊C8C2×D412yes—
259C2×C43⋊C8#4112yes—
260#10621872—42no—
261#10621872—42no—
262#10621872—42no—
263C8×D43—22no—
264C8×D43—22no—
265C8×D43—22no—
266C8×D43—22no—
267C8×D43—42no—
268C8×D43—42no—
269C8×D43—42no—
270C23×C43—21no—
271C23×C43C2×#4111yescharacteristic
272C22×D43—21no—
273C22×D43—21no—
274C22×D43—22no—
275C22×D43—21no—
276C22×D43—41no—
277C22×D43C4×D411yescharacteristic
278C22×D43C4×D411yescharacteristic
279Q8×C43—21no—
280Q8×C43—21no—
281D4×C43—21no—
282D4×C43—21no—
283D4×C43—41no—
284D4×C43—41no—
285C2×C4×C43—22no—
286C2×C4×C43—21no—
287C2×C4×C43—21no—
288C2×C4×C43—21no—
289C2×C4×C43—41no—
290C2×C4×C43—41no—
291C2×C4×C43—41no—
292C2×C4×C43—41no—
293C2×C4×C43C23×C411yescharacteristic
294C2×C4×C43C22×D411yescharacteristic
295C2×C4×C43C22×D411yescharacteristic
296C2×C4×C43C2×#4111yescharacteristic
297C2×C4×C43H(5,𝔽2)11yescharacteristic
298C2×C4×C432−1+411yescharacteristic
299C22⋊D43—41no—
300C22⋊D43—41no—
301C22⋊D43—42no—
302C22⋊D43—81no—
303C2×Dic43—21no—
304C2×Dic43—21no—
305C2×Dic43—22no—
306C2×Dic43—21no—
307C2×Dic43—21no—
308C2×Dic43—21no—
309C2×Dic43—41no—
310C2×Dic43—41no—
311C2×Dic43C4×D411yescharacteristic
312C2×Dic43C4×D411yescharacteristic
313D172—21no—
314D172—21no—
315D172—42no—
316D172—81no—
317C4×D43—21no—
318C4×D43—21no—
319C4×D43—21no—
320C4×D43—21no—
321C4×D43—21no—
322C4×D43—21no—
323C4×D43—21no—
324C4×D43—21no—
325C4×D43—41no—
326C4×D43—41no—
327Dic86—21no—
328Dic86—21no—
329C8×C43—21no—
330C8×C43—21no—
331C8×C43—22no—
332C8×C43—21no—
333C8×C43—21no—
334C8×C43—41no—
335C43⋊C8—21no—
336C43⋊C8—22no—
337C43⋊C8—21no—
338C43⋊C8—41no—
339C43⋊C8C4×D412yes—
340C43⋊C8C4×D412yes—
341#23018—431nomaximal, Sylow
342C22×C43—21no—
343C22×C43—21no—
344C22×C43—41no—
345C22×C43—41no—
346C22×C43—41no—
347C22×C43C2×C4×D411yescharacteristic
348C22×C43#54811yescharacteristic
349C22×C43#55311yescharacteristic
350C2×D43—21no—
351C2×D43—21no—
352C2×D43—21no—
353C2×D43—21no—
354C2×D43—21no—
355C2×D43—42no—
356C2×D43—42no—
357C2×D43—41no—
358C2×D43—41no—
359C2×D43—41no—
360C2×D43#44312yescomplemented
361C4×C43—42no—
362C4×C43—41no—
363C4×C43—41no—
364C4×C43—41no—
365C4×C43C2×C4×D411yescharacteristic
366C4×C43#52011yescharacteristic
367C4×C43D4211yescharacteristic
368C4×C43#54711yescharacteristic
369Dic43—21no—
370Dic43—21no—
371Dic43—42no—
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#1929D4311yescharacteristic, complemented
384#1871—431no—
385#1871—431no—
386#1866—431no—
387#1866—431no—
388#1772—431no—
389C8×C22⋊C4—431no—
390C2×C43—21no—
391C2×C43—21no—
392C2×C43—81no—
393C2×C43#236111yescharacteristic
394C2×C43C2×#44311yescharacteristic
395C2×C43#295711yescharacteristic
396D43—22no—
397D43—41no—
398D43—81no—
399C2×#135—431no—
400C2×#131—431no—
401C2×#131—431no—
402C22×M16—431no—
403C22×M16—431no—
404C23×C8—431no—
405#525—431no—
406#525—431no—
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—864no—
428C2×#108C2×D4311yescharacteristic
429#427—431no—
430#424—431no—
431#424—431no—
432C2×#104—431no—
433C2×#104—431no—
434C2×#104—431no—
435C2×#104C2×D4311yescharacteristic
436#416—431no—
437#416C2×D4311yescharacteristic
438#408—431no—
439#408C2×D4311yescharacteristic
440C2×C22⋊C8—431no—
441#405—431no—
442#405C2×D4311yescharacteristic
443C2×C4×C8—431no—
444C2×C4×C8—431no—
445C4×C22⋊C4—431no—
446#339—431no—
447#339—431no—
448#339—431no—
449#339C2×D4311yescharacteristic
450#336—431no—
451#336C2×D4311yescharacteristic
452C43#2301811yescharacteristic, complemented, Sylow
453C2×#41—431no—
454C2×#41C22×D4311yescharacteristic
455C23×C4—431no—
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—431no—
467C2×M16—431no—
468C2×M16—861no—
469C2×M16—861no—
470C2×M16—861no—
471C2×M16—861no—
472C2×M16—862no—
473C2×M16—862no—
474C2×M16—1721no—
475C2×M16—1721no—
476C2×M16C22×D4311yescharacteristic
477C2×M16C22×D4311yescharacteristic
478C22×C8—431no—
479C22×C8—431no—
480C22×C8—431no—
481C22×C8—431no—
482C22×C8—431no—
483C22×C8—431no—
484C22×C8—862no—
485C22×C8—862no—
486C22×C8—861no—
487C22×C8—861no—
488C22×C8—861no—
489C22×C8—861no—
490C22×C8C22×D4311yescharacteristic
491C22×C8C22×D4311yescharacteristic
492#123—861no—
493#123—861no—
494C22⋊Q8—431no—
495C22⋊Q8—431no—
496C22⋊Q8—431no—
497C22⋊Q8—431no—
498#121—431no—
499#121—431no—
500#121—431no—
501#121—431no—
502#120—861no—
503#120—861no—
504C4×D4—861no—
505C4×D4—861no—
506C4×D4—861no—
507C4×D4—861no—
508#117—431no—
509#117C22×D4311yescharacteristic
510C2×C22⋊C4—861no—
511C2×C42—431no—
512C2×C42C22×D4311yescharacteristic
513#108—22no—
514#108—434no—
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—862no—
527#104—1721no—
528#104—1721no—
529#103—431no—
530#103—431no—
531#103C4×D4311yescharacteristic
532#103C4×D4311yescharacteristic
533#102—431no—
534#102—431no—
535#102C4×D4311yescharacteristic
536#102C4×D4311yescharacteristic
537C22⋊C8—21no—
538C22⋊C8—21no—
539C22⋊C8—431no—
540C22⋊C8—431no—
541C22⋊C8—431no—
542C22⋊C8—431no—
543C22⋊C8—861no—
544C22⋊C8—861no—
545#97—21no—
546#97—861no—
547C4×C8—21no—
548C4×C8—862no—
549C4×C8—862no—
550C4×C8—861no—
551#95—861no—
552C24—431no—
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—431no—
565C2×D4—861no—
566C2×D4—861no—
567C2×D4—861no—
568C2×D4—861no—
569C2×D4—861no—
570C2×D4C2×C4×D4311yescharacteristic
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—431no—
574C22×C4—431no—
575C22×C4—431no—
576C22×C4—431no—
577C22×C4—431no—
578C22×C4—861no—
579C22×C4—861no—
580C22×C4—861no—
581C22×C4—861no—
582C22×C4—861no—
583C22×C4—861no—
584C22×C4C23×D4311yescharacteristic
585Q16—862no—
586SD16—862no—
587SD16—862no—
588D8—862no—
589M16—21no—
590M16—21no—
591M16—21no—
592M16—432no—
593M16—861no—
594M16—861no—
595M16—861no—
596M16—1722no—
597M16—1722no—
598M16—1722no—
599M16—1722no—
600M16D4×D4312yes—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—431no—
608C2×C8—431no—
609C2×C8—432no—
610C2×C8—432no—
611C2×C8—431no—
612C2×C8—431no—
613C2×C8—862no—
614C2×C8—862no—
615C2×C8—862no—
616C2×C8—862no—
617C2×C8—861no—
618C2×C8—861no—
619C2×C8—861no—
620C2×C8—861no—
621C2×C8—1722no—
622C2×C8—1722no—
623C2×C8—1722no—
624C2×C8—1722no—
625C2×C8C2×C4×D4311yescharacteristic
626C2×C8C2×C4×D4311yescharacteristic
627C2×C8D4×D4311yescharacteristic
628C2×C8D4×D4311yescharacteristic
629C4⋊C4—431no—
630C4⋊C4—431no—
631C4⋊C4—861no—
632C4⋊C4—861no—
633C4⋊C4—861no—
634C4⋊C4—861no—
635C4⋊C4C2×C4×D4311yescharacteristic
636C4⋊C4C2×C4×D4311yescharacteristic
637C22⋊C4—21no—
638C22⋊C4—861no—
639C22⋊C4—861no—
640C22⋊C4—861no—
641C22⋊C4—861no—
642C22⋊C4—861no—
643C22⋊C4—861no—
644C22⋊C4—864no—
645C22⋊C4—861no—
646C22⋊C4—861no—
647C22⋊C4—861no—
648C42—21no—
649C42—21no—
650C42—21no—
651C42—861no—
652C42—861no—
653C42—861no—
654C23—21no—
655C23—431no—
656C23—431no—
657C23—862no—
658C23—861no—
659C23—861no—
660C23—861no—
661C23—1721no—
662C23#41×D4311yescharacteristic
663Q8—21no—
664Q8—21no—
665Q8—861no—
666Q8—861no—
667D4—21no—
668D4—21no—
669D4—41no—
670D4—41no—
671D4—861no—
672D4—861no—
673D4—3441no—
674D4—3441no—
675D4—1722no—
676D4—1722no—
677D4—1721no—
678D4—1721no—
679C2×C4—22no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—431no—
688C2×C4—431no—
689C2×C4—861no—
690C2×C4—861no—
691C2×C4—861no—
692C2×C4—861no—
693C2×C4—861no—
694C2×C4—861no—
695C2×C4—861no—
696C2×C4—861no—
697C2×C4—861no—
698C2×C4—861no—
699C2×C4—862no—
700C2×C4—861no—
701C2×C4—861no—
702C2×C4—861no—
703C2×C4—1721no—
704C2×C4—1721no—
705C2×C4—1721no—
706C2×C4—1721no—
707C2×C4C22×C4×D4311yescharacteristic
708C2×C4C2×D4×D4311yescharacteristic
709C2×C4C2×D4×D4311yescharacteristic
710C2×C4#41×D4311yescharacteristic
711C2×C4#1306337111yescharacteristic
712C2×C4#1306337211yescharacteristic
713C8—21no—
714C8—21no—
715C8—22no—
716C8—21no—
717C8—21no—
718C8—41no—
719C8—432no—
720C8—432no—
721C8—861no—
722C8—861no—
723C8—862no—
724C8—1721no—
725C22—21no—
726C22—21no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22—432no—
731C22—861no—
732C22—861no—
733C22—861no—
734C22—861no—
735C22—861no—
736C22—1722no—
737C22—1722no—
738C22—1721no—
739C22—1721no—
740C22—1721no—
741C22C4×D4×D4311yescharacteristic
742C22#1458355711yescharacteristic
743C22#1458360011yescharacteristic
744C4—42no—
745C4—41no—
746C4—41no—
747C4—41no—
748C4—861no—
749C4—861no—
750C4—1722no—
751C4—1721no—
752C4—1721no—
753C4—1721no—
754C4C4×D4×D4311yescharacteristic
755C4#1458337911yescharacteristic
756C4#1458353311yescharacteristic
757C4#1458354711yescharacteristic
758C2—21no—
759C2—21no—
760C2—81no—
761C2—862no—
762C2—3441no—
763C2—1721no—
764C2#1913760811yescharacteristic
765C2#443×D4311yescharacteristic
766C2#1914350911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1929C2
socleC22×C43C2×C4×D4
prime radical#19144175C2
cosocleC22×C4×C43C24
hypercenter#1929D43
hypocenterC43#23018
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1929

Complements

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

NH ≅ G/Ntype
2. C2×#14583013C2semidirect
3. #19143325C2semidirect
4. #19143323C2semidirect
5. C2×#108×D43C2semidirect
6. #19135482C2semidirect
7. #19135342C2semidirect
8. #19135244C2semidirect
9. #19134896C2semidirect
10. #19134894C2semidirect
11. #19134872C2semidirect
12. #19134867C2semidirect
13. #19134475C2semidirect
14. #19134365C2semidirect
15. C43×#1929C2semidirect
24. #14583139C4semidirect
25. #14583139C4semidirect
26. #14583134C4semidirect
27. #14583134C4semidirect
28. #14583131C4semidirect
29. #14583131C4semidirect
30. #14583127C4semidirect
31. #14583127C4semidirect
124. #13063260D4semidirect
360. C2×D43#443semidirect
383. #1929D43semidirect
452. C43#23018semidirect

Maximal subgroups

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

subgroupindex
#191441752
C2×#145830132
#191433252
#191433232
C2×#108×D432
#191354822
#191353422
#191352442
#191348962
#191348942
#191348722
#191348672
#191344752
#191343652
C43×#19292
#2301843