Finite Group Databasebeta

← #25131338

Subgroups — #25131338

Order 11008.

1150 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583618C211yesmaximal, characteristic, complemented
2C2×#14583102C211yesmaximal, characteristic, complemented
3C2×D8×Dic43C211yesmaximal, characteristic
4#19139515C211yesmaximal, characteristic, complemented
5#19135835C211yesmaximal, characteristic, complemented
6#19135831C211yesmaximal, characteristic, complemented
7#19135670C211yesmaximal, characteristic
8#19135529C211yesmaximal, characteristic, complemented
9#19135395C211yesmaximal, characteristic, complemented
10#19134953C211yesmaximal, characteristic, complemented
11#19134952C211yesmaximal, characteristic, complemented
12#19134852C211yesmaximal, characteristic, complemented
13#19134851C211yesmaximal, characteristic, complemented
14#19134593C211yesmaximal, characteristic, complemented
15C43×#2012C211yesmaximal, characteristic
16C22×#10621883C2211yescharacteristic
17#14583618—24no—
18#14583618—24no—
19C2×#13063323C2211yescharacteristic
20C2×#13063318—21no—
21C2×#13063318—21no—
22C2×#13063312C2211yescharacteristic
23C2×#13063302—21no—
24C2×#13063302—21no—
25C2×Q8×Dic43C2211yescharacteristic
26C2×C4×Dic86C2211yescharacteristic
27C2×C4×Dic86C2211yescharacteristic
28C2×D4×Dic43C2211yescharacteristic
29C2×D4×Dic43C2211yescharacteristic
30C2×#13063281—21no—
31#14583102—24no—
32D8×Dic43—24no—
33C2×#13063259C2211yescharacteristic
34C2×Dic43⋊C8C2211yescharacteristic
35C2×#13063250C2211yescharacteristic
36C2×#13063250C2211yescharacteristic
37C2×#13063249C2211yescharacteristic
38C2×#13063249C2211yescharacteristic
39C2×#13063248C2211yescharacteristic
40C2×#13063246C2211yescharacteristic
41C2×#13063246C2211yescharacteristic
42C2×#13063246C2211yescharacteristic
43C2×C8×Dic43C2211yescharacteristic
44#14582822—21no—
45#14582822—21no—
46#14582802C2211yescharacteristic
47#14582798C2211yescharacteristic
48#14582797C2211yescharacteristic
49#14582768C2211yescharacteristic
50#14582757—21no—
51#14582662C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582654C2211yescharacteristic
54#14582653C2211yescharacteristic
55#14582653C2211yescharacteristic
56C22×SD16×C43C2211yescharacteristic
57C22×D8×C43C2211yescharacteristic
58C2×#124×C43C2211yescharacteristic
59C2×#103×C43C2211yescharacteristic
60C2×#102×C43C2211yescharacteristic
61C43×#390C2211yescharacteristic
62C43×#336C2211yescharacteristic
63C22×Dic86D411yescharacteristic
64C22×Dic86C2311yescharacteristic
65C23×Dic43—21no—
66C23×Dic43—21no—
67C2×#10621883—22no—
68C2×#10621883—22no—
69C2×#10621883—41no—
70C22×C43⋊C8C2311yescharacteristic
71C22×C43⋊C8C2311yescharacteristic
72#13063323—22no—
73#13063323D414yes—
74#13063318—28no—
75#13063318—28no—
76#13063312—22no—
77#13063312—22no—
78#13063302—28no—
79#13063302—44no—
80Q8×Dic43—22no—
81Q8×Dic43—22no—
82C4×Dic86—22no—
83C4×Dic86—22no—
84C4×Dic86—22no—
85C4×Dic86—22no—
86D4×Dic43—22no—
87D4×Dic43—22no—
88D4×Dic43—22no—
89D4×Dic43D414yes—
90#13063281—28no—
91C2×C4⋊Dic43—21no—
92C2×C4⋊Dic43—21no—
93C2×C4⋊Dic43D411yescharacteristic
94C2×C4⋊Dic43C2311yescharacteristic
95C2×C4⋊Dic43C2311yescharacteristic
96C2×C4⋊Dic43C2311yescharacteristic
97C2×Dic43⋊C4—21no—
98C2×Dic43⋊C4—21no—
99C2×Dic43⋊C4—21no—
100C2×Dic43⋊C4—21no—
101C2×Dic43⋊C4—21no—
102C2×Dic43⋊C4—21no—
103C2×Dic43⋊C4D411yescharacteristic
104C2×Dic43⋊C4D411yescharacteristic
105C2×C22⋊Dic43—21no—
106C2×C22⋊Dic43—21no—
107C2×C22⋊Dic43—21no—
108C2×C22⋊Dic43—21no—
109C2×C22⋊Dic43—21no—
110C2×C22⋊Dic43—21no—
111C2×C4×Dic43—21no—
112C2×C4×Dic43—21no—
113C2×C4×Dic43C2311yescharacteristic
114C2×C4×Dic43C2311yescharacteristic
115#13063259—22no—
116Dic43⋊C8—22no—
117#13063250—22no—
118#13063250—22no—
119#13063249—22no—
120#13063249—41no—
121#13063248—41no—
122#13063246—22no—
123#13063246—22no—
124#13063246—41no—
125C8×Dic43—22no—
126C43⋊#95—21no—
127C43⋊#95—21no—
128C22×Q8×C43C2311yescharacteristic
129C22×D4×C43C2311yescharacteristic
130C22×D4×C43C2311yescharacteristic
131C2×SD16×C43—22no—
132C2×SD16×C43—22no—
133C2×SD16×C43—41no—
134C2×D8×C43—22no—
135C2×D8×C43—22no—
136C2×D8×C43—22no—
137C22×C8×C43C2311yescharacteristic
138C22×C8×C43C2311yescharacteristic
139#124×C43—22no—
140#124×C43—22no—
141C2×C4⋊C4×C43C2311yescharacteristic
142C2×C22⋊C4×C43—21no—
143C2×C22⋊C4×C43—21no—
144C2×C22⋊C4×C43—21no—
145C2×C22⋊C4×C43—21no—
146C2×C42×C43C2311yescharacteristic
147#103×C43—22no—
148#102×C43—41no—
149C24×C43—21no—
150C24×C43—21no—
151C2×Q8×C43—21no—
152C2×Q8×C43—21no—
153C2×Q8×C43—21no—
154C2×Q8×C43—21no—
155C2×Q8×C43—21no—
156C2×Q8×C43C2×D412yes—
157C2×D4×C43—21no—
158C2×D4×C43—21no—
159C2×D4×C43—21no—
160C2×D4×C43—21no—
161C2×D4×C43—21no—
162C2×D4×C43—21no—
163C2×D4×C43—21no—
164C2×D4×C43—21no—
165C2×D4×C43—21no—
166C2×D4×C43—21no—
167C2×D4×C43C2×D412yes—
168C2×D4×C43#4112yes—
169C22×C4×C43—21no—
170C22×C4×C43—21no—
171C22×C4×C43C2×D411yescharacteristic
172C22×C4×C43C2×D411yescharacteristic
173C22×C4×C43C2411yescharacteristic
174C22×Dic43—24no—
175C22×Dic43—21no—
176C22×Dic43—21no—
177C22×Dic43—21no—
178C22×Dic43—21no—
179C22×Dic43—42no—
180C22×Dic43—42no—
181C22×Dic43—42no—
182C22×Dic43—42no—
183C22×Dic43—42no—
184C22×Dic43C2×D411yescharacteristic
185C22×Dic43C2×D411yescharacteristic
186C22×Dic43C2×D411yescharacteristic
187C22×Dic43C2×D411yescharacteristic
188C2×Dic86—21no—
189C2×Dic86—21no—
190C2×Dic86—21no—
191C2×Dic86—21no—
192C2×Dic86—21no—
193C2×Dic86—22no—
194C2×Dic86—22no—
195C2×Dic86—22no—
196C2×Dic86C2×D412yes—
197SD16×C43—44no—
198D8×C43—28no—
199C2×C8×C43—21no—
200C2×C8×C43—21no—
201C2×C8×C43—21no—
202C2×C8×C43—21no—
203C2×C8×C43—21no—
204C2×C8×C43#4112yes—
205C4⋊C4×C43—21no—
206C4⋊C4×C43—21no—
207C22⋊C4×C43—24no—
208C22⋊C4×C43—24no—
209C22⋊C4×C43—42no—
210C22⋊C4×C43—81no—
211C42×C43—21no—
212C42×C43—21no—
213C22⋊Dic43—24no—
214C22⋊Dic43—24no—
215C22⋊Dic43—24no—
216C22⋊Dic43—42no—
217C22⋊Dic43—42no—
218C22⋊Dic43—81no—
219#10621883—44no—
220C4⋊Dic43—24no—
221C4⋊Dic43—21no—
222C4⋊Dic43—22no—
223C4⋊Dic43—21no—
224C4⋊Dic43—21no—
225C4⋊Dic43—21no—
226C4⋊Dic43—21no—
227C4⋊Dic43—42no—
228C4⋊Dic43C2×D412yes—
229Dic43⋊C4—24no—
230Dic43⋊C4—24no—
231Dic43⋊C4—24no—
232Dic43⋊C4—22no—
233Dic43⋊C4—22no—
234Dic43⋊C4—42no—
235Dic43⋊C4—42no—
236Dic43⋊C4—81no—
237C4×Dic43—24no—
238C4×Dic43—24no—
239C4×Dic43—21no—
240C4×Dic43—21no—
241C4×Dic43C2×D412yes—
242C4×Dic43C2×D412yes—
243C2×C43⋊C8—21no—
244C2×C43⋊C8—21no—
245C2×C43⋊C8—21no—
246C2×C43⋊C8—21no—
247C2×C43⋊C8—21no—
248C2×C43⋊C8—21no—
249C23×C43—22no—
250C23×C43—22no—
251C23×C43—41no—
252C23×C43—41no—
253C23×C43—41no—
254C23×C43—41no—
255C23×C43—41no—
256C23×C43—41no—
257C23×C43—41no—
258C23×C43—41no—
259C23×C43—41no—
260C23×C43—41no—
261C23×C43—41no—
262C23×C43—41no—
263C23×C43C22×D411yescharacteristic
264Q8×C43—22no—
265Q8×C43—22no—
266Q8×C43—41no—
267Q8×C43—41no—
268D4×C43—22no—
269D4×C43—22no—
270D4×C43—22no—
271D4×C43—22no—
272D4×C43—41no—
273D4×C43—41no—
274D4×C43—41no—
275D4×C43—41no—
276C2×C4×C43—21no—
277C2×C4×C43—22no—
278C2×C4×C43—21no—
279C2×C4×C43—21no—
280C2×C4×C43—21no—
281C2×C4×C43—21no—
282C2×C4×C43—21no—
283C2×C4×C43—41no—
284C2×C4×C43—41no—
285C2×C4×C43—41no—
286C2×C4×C43—41no—
287C2×C4×C43—41no—
288C2×C4×C43C22×D411yescharacteristic
289C2×C4×C43C22×D411yescharacteristic
290C2×C4×C43C2×#4111yescharacteristic
291C2×C4×C43C2×#4111yescharacteristic
292C2×C4×C43H(5,𝔽2)11yescharacteristic
293C2×C4×C432−1+411yescharacteristic
294C2×Dic43—21no—
295C2×Dic43—21no—
296C2×Dic43—21no—
297C2×Dic43—22no—
298C2×Dic43—22no—
299C2×Dic43—21no—
300C2×Dic43—21no—
301C2×Dic43—21no—
302C2×Dic43—21no—
303C2×Dic43—21no—
304C2×Dic43—41no—
305C2×Dic43—41no—
306C2×Dic43—41no—
307C2×Dic43—41no—
308C2×Dic43—48no—
309C2×Dic43—41no—
310C2×Dic43—41no—
311C2×Dic43—41no—
312C2×Dic43—41no—
313C2×Dic43—41no—
314C2×Dic43—41no—
315C2×Dic43—84no—
316C2×Dic43#12012yes—
317C2×Dic43#12012yes—
318C2×Dic43#13512yes—
319C2×Dic43AGL(1,ℤ/8)12yes—
320Dic86—22no—
321Dic86—22no—
322Dic86—41no—
323Dic86—41no—
324Dic86—44no—
325C8×C43—22no—
326C8×C43—41no—
327C43⋊C8—41no—
328C43⋊C8—41no—
329#24185—431nomaximal, Sylow
330C22×C43—42no—
331C22×C43—42no—
332C22×C43—42no—
333C22×C43—42no—
334C22×C43—42no—
335C22×C43—42no—
336C22×C43—81no—
337C22×C43—81no—
338C22×C43—81no—
339C22×C43—81no—
340C22×C43—81no—
341C22×C43—81no—
342C22×C43—81no—
343C22×C43—81no—
344C22×C43C2×#12011yescharacteristic
345C22×C43#54811yescharacteristic
346C22×C43#55011yescharacteristic
347C22×C43C2×#13511yescharacteristic
348C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
349C22×C43#57711yescharacteristic
350C22×C43#57811yescharacteristic
351C4×C43—42no—
352C4×C43—41no—
353C4×C43—41no—
354C4×C43—81no—
355C4×C43#52511yescharacteristic
356C4×C43#53711yescharacteristic
357C4×C43#54611yescharacteristic
358C4×C43#54711yescharacteristic
359Dic43—22no—
360Dic43—42no—
361Dic43—41no—
362Dic43—42no—
363Dic43—41no—
364Dic43—81no—
365Dic43—81no—
366Dic43#44914yes—
367C2×#556—431no—
368C2×#461—431no—
369C2×C4×D8—431no—
370#2538—431no—
371#2042—431no—
372#2042—431no—
373#2012—431no—
374#2012D4311yescharacteristic
375#1984—431no—
376#1956—431no—
377#1880—431no—
378#1880—431no—
379#1863—431no—
380#1863—431no—
381#1802—431no—
382C2×C43—82no—
383C2×C43—82no—
384C2×C43#240711yescharacteristic
385C2×C43C2×#44911yescharacteristic
386C2×C43#301311yescharacteristic
387C2×C43#336011yescharacteristic
388C2×C43#336711yescharacteristic
389C2×C43#339311yescharacteristic
390C2×C43#339711yescharacteristic
391C22×SD16—431no—
392C22×SD16C2×D4311yescharacteristic
393C22×D8C2×D4311yescharacteristic
394#556—864no—
395#556—864no—
396C2×C4⋊Q8—431no—
397C2×#126—861no—
398C2×#126—861no—
399C2×#124—431no—
400C2×#124C2×D4311yescharacteristic
401C2×C22⋊Q8—861no—
402C2×C22⋊Q8—861no—
403C2×C4×Q8—431no—
404C2×C4×Q8—431no—
405C2×C4×Q8—431no—
406C2×C4×D4—431no—
407C2×C4×D4—431no—
408C2×#117—861no—
409#461—864no—
410C4×D8—864no—
411C2×#107—431no—
412C2×C4⋊C8—431no—
413C2×#103—431no—
414C2×#103—431no—
415C2×#103—431no—
416C2×#103—431no—
417C2×#103—431no—
418C2×#103C2×D4311yescharacteristic
419C2×#102—431no—
420C2×#102—431no—
421C2×#102—431no—
422C2×#102C2×D4311yescharacteristic
423C2×C4×C8—431no—
424#396—861no—
425#396—861no—
426#390—431no—
427#390C2×D4311yescharacteristic
428#389—431no—
429#389—431no—
430#384—431no—
431#380—861no—
432#340—431no—
433#340—431no—
434#336—431no—
435#336—431no—
436#336—431no—
437#336C2×D4311yescharacteristic
438C43#2418511yescharacteristic, complemented, Sylow
439C22×Q8—431no—
440C22×Q8—431no—
441C22×Q8C22×D4311yescharacteristic
442C22×D4C22×D4311yescharacteristic
443C22×D4C22×D4311yescharacteristic
444C23×C4—861no—
445C23×C4—861no—
446C2×SD16—22no—
447C2×SD16—22no—
448C2×SD16—41no—
449C2×SD16—862no—
450C2×SD16—862no—
451C2×SD16—1721no—
452C2×D8—22no—
453C2×D8—22no—
454C2×D8—22no—
455C22×C8—431no—
456C22×C8—431no—
457C22×C8C22×D4311yescharacteristic
458C22×C8C22×D4311yescharacteristic
459C4⋊Q8—434no—
460C4⋊Q8—862no—
461#126—868no—
462#126—868no—
463#124—22no—
464#124—22no—
465#124—862no—
466#124—862no—
467C22⋊Q8—868no—
468C22⋊Q8—1724no—
469C4×Q8—862no—
470C4×Q8—862no—
471C4×Q8—862no—
472C4×Q8—862no—
473C4×Q8—862no—
474C4×Q8—862no—
475C4×D4—434no—
476C4×D4—862no—
477C4×D4—862no—
478C4×D4—862no—
479#117—868no—
480C2×C4⋊C4—431no—
481C2×C4⋊C4—431no—
482C2×C4⋊C4—431no—
483C2×C4⋊C4—431no—
484C2×C4⋊C4—431no—
485C2×C4⋊C4—431no—
486C2×C4⋊C4—861no—
487C2×C4⋊C4—861no—
488C2×C4⋊C4—861no—
489C2×C4⋊C4—861no—
490C2×C4⋊C4—861no—
491C2×C4⋊C4—861no—
492C2×C4⋊C4—861no—
493C2×C4⋊C4—861no—
494C2×C4⋊C4C22×D4311yescharacteristic
495C2×C22⋊C4—21no—
496C2×C22⋊C4—21no—
497C2×C22⋊C4—21no—
498C2×C22⋊C4—21no—
499C2×C22⋊C4—861no—
500C2×C22⋊C4—861no—
501C2×C22⋊C4—861no—
502C2×C22⋊C4—861no—
503C2×C22⋊C4—861no—
504C2×C22⋊C4—861no—
505C2×C42—431no—
506C2×C42—431no—
507C2×C42—861no—
508C2×C42—861no—
509C2×C42C22×D4311yescharacteristic
510#107—862no—
511C4⋊C8—862no—
512#103—22no—
513#103—862no—
514#103—862no—
515#103—862no—
516#103—1721no—
517#103—1721no—
518#102—41no—
519#102—862no—
520#102—862no—
521#102—1721no—
522C4×C8—862no—
523#95—861no—
524#95—861no—
525C24—21no—
526C24—21no—
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—432no—
533C2×Q8—862no—
534C2×Q8—862no—
535C2×Q8—862no—
536C2×Q8—861no—
537C2×Q8—861no—
538C2×Q8—861no—
539C2×Q8—861no—
540C2×Q8—861no—
541C2×Q8D4×D4312yes—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4D4×D4312yes—
553C2×D4#1062190012yes—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—431no—
557C22×C4—431no—
558C22×C4—431no—
559C22×C4—431no—
560C22×C4—864no—
561C22×C4—861no—
562C22×C4—861no—
563C22×C4—861no—
564C22×C4—861no—
565C22×C4—1722no—
566C22×C4—1722no—
567C22×C4—1722no—
568C22×C4—1722no—
569C22×C4—1722no—
570C22×C4D4×D4311yescharacteristic
571C22×C4D4×D4311yescharacteristic
572C22×C4C23×D4311yescharacteristic
573SD16—44no—
574SD16—1724no—
575D8—28no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—861no—
582C2×C8—861no—
583C2×C8—861no—
584C2×C8—861no—
585C2×C8—861no—
586C2×C8—861no—
587C2×C8#1062190012yes—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—432no—
591C4⋊C4—862no—
592C4⋊C4—862no—
593C4⋊C4—862no—
594C4⋊C4—864no—
595C4⋊C4—864no—
596C4⋊C4—864no—
597C4⋊C4—864no—
598C4⋊C4—861no—
599C4⋊C4—861no—
600C4⋊C4—861no—
601C4⋊C4—861no—
602C4⋊C4—861no—
603C4⋊C4—3441no—
604C4⋊C4—1722no—
605C4⋊C4—1722no—
606C4⋊C4—1722no—
607C22⋊C4—24no—
608C22⋊C4—24no—
609C22⋊C4—42no—
610C22⋊C4—81no—
611C22⋊C4—864no—
612C22⋊C4—864no—
613C22⋊C4—864no—
614C22⋊C4—3441no—
615C22⋊C4—1722no—
616C22⋊C4—1722no—
617C42—21no—
618C42—21no—
619C42—432no—
620C42—432no—
621C42—864no—
622C42—864no—
623C42—861no—
624C42—861no—
625C23—22no—
626C23—22no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23C2×D4×D4311yescharacteristic
640Q8—22no—
641Q8—22no—
642Q8—41no—
643Q8—41no—
644Q8—862no—
645Q8—862no—
646Q8—1724no—
647Q8—1721no—
648Q8—1721no—
649D4—22no—
650D4—22no—
651D4—22no—
652D4—22no—
653D4—41no—
654D4—41no—
655D4—41no—
656D4—41no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—22no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—432no—
670C2×C4—432no—
671C2×C4—432no—
672C2×C4—432no—
673C2×C4—861no—
674C2×C4—861no—
675C2×C4—861no—
676C2×C4—862no—
677C2×C4—861no—
678C2×C4—862no—
679C2×C4—861no—
680C2×C4—861no—
681C2×C4—861no—
682C2×C4—861no—
683C2×C4—3444no—
684C2×C4—1728no—
685C2×C4—1721no—
686C2×C4—1721no—
687C2×C4—1721no—
688C2×C4—1721no—
689C2×C4—1721no—
690C2×C4—1721no—
691C2×C4—1721no—
692C2×C4—1721no—
693C2×C4—1721no—
694C2×C4—1721no—
695C2×C4C2×D4×D4311yescharacteristic
696C2×C4C2×D4×D4311yescharacteristic
697C2×C4C2×#1062190011yescharacteristic
698C2×C4C2×#1062190011yescharacteristic
699C2×C4#1306337011yescharacteristic
700C2×C4#1306337211yescharacteristic
701C8—22no—
702C8—41no—
703C8—1721no—
704C8—1721no—
705C22—42no—
706C22—42no—
707C22—42no—
708C22—42no—
709C22—42no—
710C22—42no—
711C22—81no—
712C22—81no—
713C22—81no—
714C22—81no—
715C22—81no—
716C22—81no—
717C22—81no—
718C22—81no—
719C22#120×D4311yescharacteristic
720C22#1458355511yescharacteristic
721C22#1458356911yescharacteristic
722C22#135×D4311yescharacteristic
723C22AGL(1,ℤ/8)×D4311yescharacteristic
724C22#1458370911yescharacteristic
725C22#1458371311yescharacteristic
726C4—41no—
727C4—42no—
728C4—41no—
729C4—81no—
730C4—434no—
731C4—862no—
732C4—3441no—
733C4—3441no—
734C4—1721no—
735C4—1722no—
736C4—1722no—
737C4—1721no—
738C4#1458340511yescharacteristic
739C4#1458347611yescharacteristic
740C4#1458353611yescharacteristic
741C4#1458354911yescharacteristic
742C2—82no—
743C2—82no—
744C2#1913793311yescharacteristic
745C2#449×D4311yescharacteristic
746C2#1914390811yescharacteristic
747C2#1914723911yescharacteristic
748C2#1914730811yescharacteristic
749C2#1914758011yescharacteristic
750C2#1914761211yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2012C2
socleC23×C43C22×D4
prime radicalC22×D8×C43C22
hypercenter#2012D43
hypocenterC43#24185
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2012

Complements

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

NH ≅ G/Ntype
1. C2×#14583618C2semidirect
2. C2×#14583102C2semidirect
4. #19139515C2semidirect
5. #19135835C2semidirect
6. #19135831C2semidirect
8. #19135529C2semidirect
9. #19135395C2semidirect
10. #19134953C2semidirect
11. #19134952C2semidirect
12. #19134852C2semidirect
13. #19134851C2semidirect
14. #19134593C2semidirect
438. C43#24185semidirect

Maximal subgroups

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

subgroupindex
C2×#145836182
C2×#145831022
C2×D8×Dic432
#191395152
#191358352
#191358312
#191356702
#191355292
#191353952
#191349532
#191349522
#191348522
#191348512
#191345932
C43×#20122
#2418543