Finite Group Databasebeta

← #25130908

Subgroups — #25130908

Order 11008.

1198 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583451C211yesmaximal, characteristic, complemented
2C2×#14583187C211yesmaximal, characteristic, complemented
3C2×#14583102C211yesmaximal, characteristic, complemented
4#121×Dic43C211yesmaximal, characteristic
5#19135792C211yesmaximal, characteristic, complemented
6#19135788C211yesmaximal, characteristic, complemented
7#19135598C211yesmaximal, characteristic
8#19135541C211yesmaximal, characteristic, complemented
9#19135516C211yesmaximal, characteristic, complemented
10#19134952C211yesmaximal, characteristic, complemented
11#19134947C211yesmaximal, characteristic, complemented
12#19134865C211yesmaximal, characteristic, complemented
13#19134864C211yesmaximal, characteristic, complemented
14#19134573C211yesmaximal, characteristic, complemented
15C43×#2000C211yesmaximal, characteristic
16C22×#10621883C2211yescharacteristic
17#14583451—24no—
18#14583451—24no—
19C2×#13063324C2211yescharacteristic
20C2×#13063323C2211yescharacteristic
21C2×#13063315—21no—
22C2×#13063304C2211yescharacteristic
23C2×#13063302—21no—
24C2×Q8×Dic43C2211yescharacteristic
25C2×#13063290—21no—
26C2×#13063290C2211yescharacteristic
27C2×D4×Dic43—21no—
28C2×D4×Dic43C2211yescharacteristic
29C2×#13063281—21no—
30C22×C4×Dic43C2211yescharacteristic
31#14583187—24no—
32#14583102—24no—
33C2×#13063257C2211yescharacteristic
34C2×#13063256C2211yescharacteristic
35C2×Dic43⋊C8C2211yescharacteristic
36C2×Dic43⋊C8C2211yescharacteristic
37C2×#13063250C2211yescharacteristic
38C2×#13063250C2211yescharacteristic
39C2×#13063249C2211yescharacteristic
40C2×#13063249C2211yescharacteristic
41C2×#13063248C2211yescharacteristic
42C2×#13063246C2211yescharacteristic
43C2×C22⋊(C43⋊C8)C2211yescharacteristic
44#14582802C2211yescharacteristic
45#14582798C2211yescharacteristic
46#14582792—21no—
47#14582779—21no—
48#14582759C2211yescharacteristic
49C4⋊C4×Dic43C2211yescharacteristic
50C22⋊C4×Dic43—21no—
51#14582662C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582661C2211yescharacteristic
54#14582653C2211yescharacteristic
55#14582653C2211yescharacteristic
56C22×SD16×C43C2211yescharacteristic
57C2×C22⋊Q8×C43C2211yescharacteristic
58C2×#121×C43C2211yescharacteristic
59C2×#103×C43C2211yescharacteristic
60C2×#102×C43C2211yescharacteristic
61C2×C22⋊C8×C43C2211yescharacteristic
62C43×#340C2211yescharacteristic
63C22×Dic86—21no—
64C22×Dic86C2311yescharacteristic
65C23×Dic43—21no—
66C23×Dic43D411yescharacteristic
67C23×Dic43D411yescharacteristic
68C2×#10621883—22no—
69C2×#10621883—22no—
70C2×#10621883—41no—
71C22×C43⋊C8C2311yescharacteristic
72C22×C43⋊C8C2311yescharacteristic
73#13063324—22no—
74#13063324D414yescomplemented
75#13063323—22no—
76#13063323D414yescomplemented
77#13063315—28no—
78#13063304—22no—
79#13063304—22no—
80#13063302—28no—
81Q8×Dic43—22no—
82Q8×Dic43—22no—
83#13063290—28no—
84#13063290—22no—
85#13063290—22no—
86D4×Dic43—22no—
87D4×Dic43—22no—
88D4×Dic43—44no—
89#13063281—28no—
90C2×C4⋊Dic43—21no—
91C2×C4⋊Dic43—21no—
92C2×C4⋊Dic43C2311yescharacteristic
93C2×C4⋊Dic43C2311yescharacteristic
94C2×C4⋊Dic43C2311yescharacteristic
95C2×Dic43⋊C4—21no—
96C2×Dic43⋊C4—21no—
97C2×Dic43⋊C4—21no—
98C2×Dic43⋊C4—21no—
99C2×Dic43⋊C4—21no—
100C2×C22⋊Dic43—21no—
101C2×C22⋊Dic43—21no—
102C2×C22⋊Dic43—21no—
103C2×C22⋊Dic43—21no—
104C2×C22⋊Dic43—21no—
105C2×C4×Dic43—21no—
106C2×C4×Dic43—21no—
107C2×C4×Dic43—22no—
108C2×C4×Dic43—22no—
109C2×C4×Dic43—21no—
110C2×C4×Dic43D411yescharacteristic
111C2×C4×Dic43D411yescharacteristic
112C2×C4×Dic43C2311yescharacteristic
113C2×C4×Dic43C2311yescharacteristic
114#13063257—22no—
115#13063256—22no—
116Dic43⋊C8—22no—
117Dic43⋊C8—22no—
118#13063250—22no—
119#13063250—41no—
120#13063249—22no—
121#13063249—41no—
122#13063248—22no—
123#13063246—22no—
124C22⋊(C43⋊C8)—41no—
125C43⋊#95—21no—
126C43⋊#95—21no—
127C43⋊#95—21no—
128C22×Q8×C43C2311yescharacteristic
129C22×D4×C43—21no—
130C22×D4×C43C2311yescharacteristic
131C23×C4×C43C2311yescharacteristic
132C2×SD16×C43—22no—
133C2×SD16×C43—22no—
134C2×SD16×C43—41no—
135C22×C8×C43C2311yescharacteristic
136C22×C8×C43C2311yescharacteristic
137C22⋊Q8×C43—22no—
138C22⋊Q8×C43—22no—
139#121×C43—22no—
140#121×C43—22no—
141C2×C4⋊C4×C43—21no—
142C2×C4⋊C4×C43C2311yescharacteristic
143C2×C4⋊C4×C43C2311yescharacteristic
144C2×C22⋊C4×C43—21no—
145C2×C22⋊C4×C43—21no—
146#103×C43—22no—
147#102×C43—22no—
148C22⋊C8×C43—41no—
149C24×C43—21no—
150C24×C43C2×D411yescharacteristic
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—24no—
158C2×D4×C43—21no—
159C2×D4×C43—21no—
160C2×D4×C43—21no—
161C2×D4×C43—21no—
162C2×D4×C43—21no—
163C2×D4×C43—42no—
164C2×D4×C43—42no—
165C2×D4×C43#4112yes—
166C22×C4×C43—21no—
167C22×C4×C43—21no—
168C22×C4×C43—21no—
169C22×C4×C43—21no—
170C22×C4×C43—21no—
171C22×C4×C43—21no—
172C22×C4×C43—21no—
173C22×C4×C43—21no—
174C22×C4×C43—21no—
175C22×C4×C43C2×D411yescharacteristic
176C22×C4×C43C2411yescharacteristic
177C22×Dic43—22no—
178C22×Dic43—22no—
179C22×Dic43—22no—
180C22×Dic43—21no—
181C22×Dic43—21no—
182C22×Dic43—21no—
183C22×Dic43—21no—
184C22×Dic43—41no—
185C22×Dic43—41no—
186C22×Dic43—42no—
187C22×Dic43—42no—
188C22×Dic43—42no—
189C22×Dic43SD1614yescomplemented
190C22×Dic43C2×D411yescharacteristic
191C22×Dic43C2×D411yescharacteristic
192C22×Dic43C2×D411yescharacteristic
193C22×Dic43C2×D411yescharacteristic
194C2×Dic86—21no—
195C2×Dic86—21no—
196C2×Dic86—21no—
197C2×Dic86—21no—
198C2×Dic86—21no—
199C2×Dic86—24no—
200C2×Dic86—42no—
201C2×Dic86—42no—
202C2×Dic86C2×D412yes—
203SD16×C43—44no—
204C2×C8×C43—21no—
205C2×C8×C43—21no—
206C2×C8×C43—21no—
207C2×C8×C43—21no—
208C2×C8×C43—21no—
209C2×C8×C43—21no—
210C4⋊C4×C43—24no—
211C4⋊C4×C43—21no—
212C4⋊C4×C43—21no—
213C4⋊C4×C43C2×D412yes—
214C4⋊C4×C43#4112yes—
215C22⋊C4×C43—24no—
216C22⋊C4×C43—24no—
217C22⋊Dic43—24no—
218C22⋊Dic43—42no—
219C22⋊Dic43—42no—
220C22⋊Dic43—42no—
221C22⋊Dic43—42no—
222#10621883—44no—
223C4⋊Dic43—24no—
224C4⋊Dic43—21no—
225C4⋊Dic43—21no—
226C4⋊Dic43—21no—
227C4⋊Dic43—21no—
228C4⋊Dic43—21no—
229C4⋊Dic43—42no—
230C4⋊Dic43C2×D412yes—
231Dic43⋊C4—24no—
232Dic43⋊C4—24no—
233Dic43⋊C4—24no—
234Dic43⋊C4—24no—
235Dic43⋊C4—24no—
236C4×Dic43—24no—
237C4×Dic43—24no—
238C4×Dic43—21no—
239C4×Dic43—21no—
240C4×Dic43—22no—
241C4×Dic43—22no—
242C4×Dic43—42no—
243C4×Dic43C2×D412yes—
244C4×Dic43C2×D412yes—
245C2×C43⋊C8—21no—
246C2×C43⋊C8—21no—
247C2×C43⋊C8—21no—
248C2×C43⋊C8—21no—
249C2×C43⋊C8—21no—
250C2×C43⋊C8—21no—
251C23×C43—21no—
252C23×C43—21no—
253C23×C43—21no—
254C23×C43—21no—
255C23×C43—21no—
256C23×C43—21no—
257C23×C43—22no—
258C23×C43—41no—
259C23×C43—41no—
260C23×C43—41no—
261C23×C43—41no—
262C23×C43—41no—
263C23×C43—41no—
264C23×C43C2×SD1612yes—
265C23×C43C22×D411yescharacteristic
266Q8×C43—22no—
267Q8×C43—22no—
268Q8×C43—41no—
269Q8×C43—41no—
270D4×C43—22no—
271D4×C43—22no—
272D4×C43—48no—
273D4×C43—41no—
274D4×C43—41no—
275C2×C4×C43—21no—
276C2×C4×C43—22no—
277C2×C4×C43—22no—
278C2×C4×C43—21no—
279C2×C4×C43—22no—
280C2×C4×C43—21no—
281C2×C4×C43—41no—
282C2×C4×C43—41no—
283C2×C4×C43—41no—
284C2×C4×C43—41no—
285C2×C4×C43—41no—
286C2×C4×C43—41no—
287C2×C4×C43—41no—
288C2×C4×C43—41no—
289C2×C4×C43—41no—
290C2×C4×C43—41no—
291C2×C4×C43C22×D411yescharacteristic
292C2×C4×C43C22×D411yescharacteristic
293C2×C4×C43C2×#4111yescharacteristic
294C2×C4×C43C2×#4111yescharacteristic
295C2×C4×C43H(5,𝔽2)11yescharacteristic
296C2×C4×C432−1+411yescharacteristic
297C2×Dic43—21no—
298C2×Dic43—21no—
299C2×Dic43—21no—
300C2×Dic43—21no—
301C2×Dic43—28no—
302C2×Dic43—21no—
303C2×Dic43—22no—
304C2×Dic43—22no—
305C2×Dic43—21no—
306C2×Dic43—21no—
307C2×Dic43—44no—
308C2×Dic43—41no—
309C2×Dic43—41no—
310C2×Dic43—41no—
311C2×Dic43—41no—
312C2×Dic43—41no—
313C2×Dic43—41no—
314C2×Dic43—41no—
315C2×Dic43—41no—
316C2×Dic43—41no—
317C2×Dic43—41no—
318C2×Dic43—84no—
319C2×Dic43#12012yes—
320C2×Dic43#12012yes—
321C2×Dic43C2×SD1612yes—
322C2×Dic43C2×SD1612yes—
323C2×Dic43#13712yes—
324Dic86—22no—
325Dic86—22no—
326Dic86—48no—
327Dic86—41no—
328Dic86—41no—
329C8×C43—41no—
330C8×C43—41no—
331C43⋊C8—41no—
332C43⋊C8—41no—
333#24151—431nomaximal, Sylow
334C22×C43—22no—
335C22×C43—22no—
336C22×C43—22no—
337C22×C43—41no—
338C22×C43—41no—
339C22×C43—41no—
340C22×C43—41no—
341C22×C43—42no—
342C22×C43—42no—
343C22×C43—42no—
344C22×C43—81no—
345C22×C43—81no—
346C22×C43—81no—
347C22×C43—81no—
348C22×C43C2×#12011yescharacteristic
349C22×C43#52511yescharacteristic
350C22×C43#53711yescharacteristic
351C22×C43C22×SD1611yescharacteristic
352C22×C43C2×#13711yescharacteristic
353C22×C43#57511yescharacteristic
354C22×C43#57511yescharacteristic
355C4×C43—42no—
356C4×C43—41no—
357C4×C43—42no—
358C4×C43—42no—
359C4×C43#54611yescharacteristic
360C4×C43#54711yescharacteristic
361C4×C43#54811yescharacteristic
362C4×C43#55011yescharacteristic
363Dic43—22no—
364Dic43—22no—
365Dic43—42no—
366Dic43—42no—
367Dic43—41no—
368Dic43—81no—
369Dic43—81no—
370Dic43#44814yes—
371C2×#533—431no—
372C2×#476—431no—
373C2×#461—431no—
374C4×#121—431no—
375#2035—431no—
376#2035—431no—
377#2000—431no—
378#2000D4311yescharacteristic
379#1987—431no—
380#1981—431no—
381#1880—431no—
382#1880—431no—
383#1865—431no—
384#1865—431no—
385#1797—431no—
386C2×C43—42no—
387C2×C43—82no—
388C2×C43#240711yescharacteristic
389C2×C43C2×#44811yescharacteristic
390C2×C43#300511yescharacteristic
391C2×C43#310111yescharacteristic
392C2×C43#311611yescharacteristic
393C2×C43#324611yescharacteristic
394C2×C43#325211yescharacteristic
395C22×SD16—431no—
396C22×SD16C2×D4311yescharacteristic
397#533—864no—
398#533—864no—
399C2×C4⋊Q8—431no—
400C2×C4⋊Q8—431no—
401C2×#125—861no—
402C2×C22⋊Q8—431no—
403C2×C22⋊Q8—861no—
404C2×C22⋊Q8C2×D4311yescharacteristic
405C2×#121C2×D4311yescharacteristic
406C2×C4×Q8—431no—
407C2×C4×Q8—431no—
408C2×C4×Q8—861no—
409C2×C4×D4—431no—
410C2×C4×D4—861no—
411C2×#117—861no—
412C22×C42—431no—
413#476—864no—
414#461—864no—
415C2×#106—431no—
416C2×#106—431no—
417C2×C4⋊C8—431no—
418C2×C4⋊C8—431no—
419C2×#103—431no—
420C2×#103—431no—
421C2×#103—431no—
422C2×#103—431no—
423C2×#103—431no—
424C2×#103C2×D4311yescharacteristic
425C2×#102—431no—
426C2×#102C2×D4311yescharacteristic
427C2×C22⋊C8—431no—
428C2×C22⋊C8C2×D4311yescharacteristic
429#390—431no—
430#389—431no—
431#388—861no—
432#386—861no—
433#380—431no—
434C4×C4⋊C4—431no—
435C4×C22⋊C4—861no—
436#340—431no—
437#340—431no—
438#340—431no—
439#340C2×D4311yescharacteristic
440#336—431no—
441#336—431no—
442C43#2415111yescharacteristic, complemented, Sylow
443C22×Q8—431no—
444C22×Q8—861no—
445C22×Q8C22×D4311yescharacteristic
446C22×D4—21no—
447C22×D4C22×D4311yescharacteristic
448C23×C4—431no—
449C23×C4—431no—
450C23×C4—861no—
451C23×C4C22×D4311yescharacteristic
452C2×SD16—22no—
453C2×SD16—22no—
454C2×SD16—41no—
455C2×SD16—862no—
456C2×SD16—862no—
457C2×SD16—1721no—
458C22×C8—431no—
459C22×C8—431no—
460C22×C8C22×D4311yescharacteristic
461C22×C8C22×D4311yescharacteristic
462C4⋊Q8—434no—
463C4⋊Q8—434no—
464C4⋊Q8—862no—
465C4⋊Q8—862no—
466#125—868no—
467C22⋊Q8—22no—
468C22⋊Q8—22no—
469C22⋊Q8—868no—
470C22⋊Q8—862no—
471C22⋊Q8—862no—
472#121—22no—
473#121—22no—
474C4×Q8—862no—
475C4×Q8—868no—
476C4×Q8—862no—
477C4×Q8—862no—
478C4×Q8—862no—
479C4×D4—862no—
480C4×D4—862no—
481C4×D4—1724no—
482#117—868no—
483C2×C4⋊C4—21no—
484C2×C4⋊C4—431no—
485C2×C4⋊C4—431no—
486C2×C4⋊C4—431no—
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×C4⋊C4C22×D4311yescharacteristic
496C2×C22⋊C4—21no—
497C2×C22⋊C4—21no—
498C2×C22⋊C4—861no—
499C2×C22⋊C4—861no—
500C2×C22⋊C4—861no—
501C2×C22⋊C4—861no—
502C2×C22⋊C4—861no—
503C2×C42—431no—
504C2×C42—431no—
505C2×C42—431no—
506C2×C42—431no—
507C2×C42—862no—
508C2×C42—862no—
509C2×C42—861no—
510C2×C42—861no—
511C2×C42—861no—
512#106—862no—
513#106—862no—
514C4⋊C8—862no—
515C4⋊C8—862no—
516#103—22no—
517#103—862no—
518#103—862no—
519#103—862no—
520#103—1721no—
521#103—1721no—
522#102—22no—
523#102—862no—
524C22⋊C8—41no—
525C22⋊C8—1721no—
526#95—861no—
527#95—861no—
528#95—861no—
529C24—21no—
530C24D4×D4311yescharacteristic
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8—21no—
534C2×Q8—21no—
535C2×Q8—21no—
536C2×Q8—432no—
537C2×Q8—864no—
538C2×Q8—861no—
539C2×Q8—861no—
540C2×Q8—861no—
541C2×Q8—861no—
542C2×Q8—861no—
543C2×Q8—1722no—
544C2×Q8—1722no—
545C2×Q8D4×D4312yes—
546C2×D4—24no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—42no—
553C2×D4—42no—
554C2×D4#1062190012yes—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—431no—
565C22×C4—434no—
566C22×C4—431no—
567C22×C4—431no—
568C22×C4—431no—
569C22×C4—862no—
570C22×C4—862no—
571C22×C4—862no—
572C22×C4—861no—
573C22×C4—861no—
574C22×C4—861no—
575C22×C4—861no—
576C22×C4—1722no—
577C22×C4—1722no—
578C22×C4—1722no—
579C22×C4—1721no—
580C22×C4—1721no—
581C22×C4D4×D4311yescharacteristic
582C22×C4C23×D4311yescharacteristic
583SD16—44no—
584SD16—1724no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—861no—
592C2×C8—861no—
593C2×C8—861no—
594C2×C8—861no—
595C2×C8—861no—
596C2×C8—861no—
597C4⋊C4—24no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—432no—
601C4⋊C4—864no—
602C4⋊C4—864no—
603C4⋊C4—864no—
604C4⋊C4—864no—
605C4⋊C4—864no—
606C4⋊C4—864no—
607C4⋊C4—861no—
608C4⋊C4—861no—
609C4⋊C4—861no—
610C4⋊C4—861no—
611C4⋊C4—861no—
612C4⋊C4—1722no—
613C4⋊C4D4×D4312yes—
614C4⋊C4#1062190012yes—
615C22⋊C4—24no—
616C22⋊C4—24no—
617C22⋊C4—864no—
618C22⋊C4—1722no—
619C22⋊C4—1722no—
620C22⋊C4—1722no—
621C22⋊C4—1722no—
622C42—432no—
623C42—432no—
624C42—862no—
625C42—862no—
626C42—864no—
627C42—864no—
628C42—861no—
629C42—861no—
630C42—1722no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—22no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23SD16×D4312yes—
645C23C2×D4×D4311yescharacteristic
646Q8—22no—
647Q8—22no—
648Q8—41no—
649Q8—41no—
650Q8—862no—
651Q8—862no—
652Q8—1728no—
653Q8—1721no—
654Q8—1721no—
655D4—22no—
656D4—22no—
657D4—48no—
658D4—41no—
659D4—41no—
660C2×C4—21no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—21no—
664C2×C4—22no—
665C2×C4—21no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—432no—
677C2×C4—432no—
678C2×C4—432no—
679C2×C4—432no—
680C2×C4—432no—
681C2×C4—868no—
682C2×C4—861no—
683C2×C4—861no—
684C2×C4—861no—
685C2×C4—861no—
686C2×C4—861no—
687C2×C4—862no—
688C2×C4—862no—
689C2×C4—861no—
690C2×C4—861no—
691C2×C4—3444no—
692C2×C4—1724no—
693C2×C4—1721no—
694C2×C4—1721no—
695C2×C4—1721no—
696C2×C4—1721no—
697C2×C4—1721no—
698C2×C4—1721no—
699C2×C4—1721no—
700C2×C4—1721no—
701C2×C4—1721no—
702C2×C4—1721no—
703C2×C4C2×D4×D4311yescharacteristic
704C2×C4C2×D4×D4311yescharacteristic
705C2×C4C2×#1062190011yescharacteristic
706C2×C4C2×#1062190011yescharacteristic
707C2×C4#1306337011yescharacteristic
708C2×C4#1306337211yescharacteristic
709C8—41no—
710C8—41no—
711C8—1721no—
712C8—1721no—
713C22—22no—
714C22—22no—
715C22—22no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—42no—
721C22—42no—
722C22—42no—
723C22—81no—
724C22—81no—
725C22—81no—
726C22—81no—
727C22#120×D4311yescharacteristic
728C22#1458340511yescharacteristic
729C22#1458347611yescharacteristic
730C22C2×SD16×D4311yescharacteristic
731C22#137×D4311yescharacteristic
732C22#1458369511yescharacteristic
733C22#1458369611yescharacteristic
734C4—41no—
735C4—42no—
736C4—42no—
737C4—42no—
738C4—434no—
739C4—862no—
740C4—862no—
741C4—3441no—
742C4—3441no—
743C4—1722no—
744C4—1721no—
745C4—1722no—
746C4#1458353611yescharacteristic
747C4#1458354911yescharacteristic
748C4#1458355511yescharacteristic
749C4#1458356911yescharacteristic
750C2—42no—
751C2—82no—
752C2#1913793311yescharacteristic
753C2#448×D4311yescharacteristic
754C2#1914383311yescharacteristic
755C2#1914459811yescharacteristic
756C2#1914475011yescharacteristic
757C2#1914590611yescharacteristic
758C2#1914596111yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2000C2
socleC23×C43C22×D4
prime radicalC2×#121×C43C22
hypercenter#2000D43
hypocenterC43#24151
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2000

Complements

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

NH ≅ G/Ntype
1. C2×#14583451C2semidirect
2. C2×#14583187C2semidirect
3. C2×#14583102C2semidirect
5. #19135792C2semidirect
6. #19135788C2semidirect
8. #19135541C2semidirect
9. #19135516C2semidirect
10. #19134952C2semidirect
11. #19134947C2semidirect
12. #19134865C2semidirect
13. #19134864C2semidirect
14. #19134573C2semidirect
74. #13063324D4semidirect
76. #13063323D4semidirect
189. C22×Dic43SD16semidirect
442. C43#24151semidirect

Maximal subgroups

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

subgroupindex
C2×#145834512
C2×#145831872
C2×#145831022
#121×Dic432
#191357922
#191357882
#191355982
#191355412
#191355162
#191349522
#191349472
#191348652
#191348642
#191345732
C43×#20002
#2415143