Finite Group Databasebeta

← #25139000

Subgroups — #25139000

Order 11008.

1026 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583142C211yesmaximal, characteristic, complemented
2C2×#14582975C211yesmaximal, characteristic, complemented
3C2×#14582940C211yesmaximal, characteristic, complemented
4#19138031C211yesmaximal, characteristic
5#19138020C211yesmaximal, characteristic, complemented
6#19135979C211yesmaximal, characteristic, complemented
7#19135972C211yesmaximal, characteristic, complemented
8#19135795C211yesmaximal, characteristic, complemented
9#19135781C211yesmaximal, characteristic, complemented
10#19135451C211yesmaximal, characteristic, complemented
11#19135329C211yesmaximal, characteristic, complemented
12#19134914C211yesmaximal, characteristic, complemented
13#19134899C211yesmaximal, characteristic, complemented
14#19134628C211yesmaximal, characteristic, complemented
15C2×C43×#468C211yesmaximal, characteristic, complemented
16C22×#10621872C2211yescharacteristic
17C2×#13063301C2211yescharacteristic
18C2×#13063296—21no—
19C2×#13063296C2211yescharacteristic
20C2×C4×C22⋊D43C2211yescharacteristic
21C2×#13063283C2211yescharacteristic
22C2×C4⋊C4×D43C2211yescharacteristic
23#14583142—24no—
24#14582975—24no—
25#14582940—24no—
26C2×#13063259C2211yescharacteristic
27C2×#13063258C2211yescharacteristic
28C2×#13063257C2211yescharacteristic
29C2×#13063256C2211yescharacteristic
30C2×Dic43⋊C8C2211yescharacteristic
31C2×#13063249C2211yescharacteristic
32C2×#13063249C2211yescharacteristic
33C2×#13063246C2211yescharacteristic
34C2×#13063246C2211yescharacteristic
35C2×C22⋊(C43⋊C8)C2211yescharacteristic
36C2×(C2×D43)⋊C8C2211yescharacteristic
37C2×C8×Dic43C2211yescharacteristic
38#14582825—21no—
39#14582822—21no—
40#14582815—21no—
41#14582813—21no—
42#14582806C2211yescharacteristic
43#14582802C2211yescharacteristic
44#14582798C2211yescharacteristic
45#14582798C2211yescharacteristic
46#14582795—21no—
47#14582787—21no—
48#14582775—21no—
49#14582759C2211yescharacteristic
50#14582759C2211yescharacteristic
51#14582662C2211yescharacteristic
52#14582662C2211yescharacteristic
53#14582661C2211yescharacteristic
54#14582661C2211yescharacteristic
55C22×SD16×C43C2211yescharacteristic
56C22×M16×C43C2211yescharacteristic
57C2×C22⋊Q8×C43C2211yescharacteristic
58C2×#121×C43C2211yescharacteristic
59C43×#468—24no—
60C2×#107×C43C2211yescharacteristic
61C2×#103×C43C2211yescharacteristic
62C2×#102×C43C2211yescharacteristic
63C22×C22⋊D43—21no—
64C22×C22⋊D43D411yescharacteristic
65C22×C4×D43—21no—
66C22×C4×D43C2311yescharacteristic
67C2×#10621872—22no—
68C2×#10621872—22no—
69C2×#10621872D414yescomplemented
70C22×C43⋊C8C2311yescharacteristic
71C22×C43⋊C8C2311yescharacteristic
72#13063301—22no—
73#13063301—22no—
74#13063296—22no—
75#13063296—22no—
76#13063296—44no—
77C4×C22⋊D43—22no—
78C4×C22⋊D43—22no—
79#13063283—22no—
80#13063283—41no—
81C2×C4⋊Dic43—21no—
82C2×C4⋊Dic43—21no—
83C2×C4⋊Dic43C2311yescharacteristic
84C2×C4⋊Dic43C2311yescharacteristic
85C2×C4⋊Dic43C2311yescharacteristic
86C2×C4⋊Dic43C2311yescharacteristic
87C2×Dic43⋊C4—21no—
88C2×Dic43⋊C4—21no—
89C2×Dic43⋊C4D411yescharacteristic
90C4⋊C4×D43—22no—
91C4⋊C4×D43—41no—
92C2×C22⋊Dic43—21no—
93C2×C22⋊Dic43—21no—
94C2×C22⋊Dic43—21no—
95C2×C22⋊Dic43—21no—
96C2×C22⋊Dic43—21no—
97C2×C22⋊Dic43D411yescharacteristic
98C2×(C2×D43)⋊C4—21no—
99C2×(C2×D43)⋊C4—21no—
100C2×(C2×D43)⋊C4D411yescharacteristic
101C2×C4×Dic43—21no—
102C2×C4×Dic43C2311yescharacteristic
103#13063259—22no—
104#13063258—22no—
105#13063257—22no—
106#13063256—22no—
107Dic43⋊C8—22no—
108#13063249—22no—
109#13063249—41no—
110#13063246—22no—
111#13063246—41no—
112C22⋊(C43⋊C8)—22no—
113(C2×D43)⋊C8—22no—
114C8×Dic43—22no—
115C43⋊#95—21no—
116C43⋊#95—21no—
117C43⋊#95—21no—
118C43⋊#95—21no—
119C43⋊#95—21no—
120C43⋊#95—21no—
121C22×Q8×C43C2311yescharacteristic
122C22×D4×C43—21no—
123C22×D4×C43C2311yescharacteristic
124C23×C4×C43C2311yescharacteristic
125C2×SD16×C43—22no—
126C2×SD16×C43—22no—
127C2×SD16×C43—22no—
128C2×M16×C43—22no—
129C2×M16×C43—22no—
130C2×M16×C43—22no—
131C22×C8×C43C2311yescharacteristic
132C22×C8×C43C2311yescharacteristic
133C22⋊Q8×C43—22no—
134C22⋊Q8×C43—41no—
135#121×C43—22no—
136#121×C43—41no—
137C2×C4⋊C4×C43—21no—
138C2×C4⋊C4×C43C2311yescharacteristic
139C2×C4⋊C4×C43C2311yescharacteristic
140C2×C22⋊C4×C43—21no—
141C2×C22⋊C4×C43—21no—
142#107×C43D414yescomplemented
143#103×C43—22no—
144#102×C43—22no—
145C24×C43—21no—
146C24×C43C2×D411yescharacteristic
147C23×D43C2×D411yescharacteristic
148C2×Q8×C43—21no—
149C2×Q8×C43—21no—
150C2×Q8×C43—21no—
151C2×Q8×C43—21no—
152C2×Q8×C43—21no—
153C2×Q8×C43—21no—
154C2×D4×C43—21no—
155C2×D4×C43—21no—
156C2×D4×C43—21no—
157C2×D4×C43—21no—
158C2×D4×C43—21no—
159C2×D4×C43—21no—
160C2×D4×C43—42no—
161C2×D4×C43—42no—
162C2×D4×C43—81no—
163C22×C4×C43—21no—
164C22×C4×C43—21no—
165C22×C4×C43—21no—
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×C43C2×D411yescharacteristic
173C22×C4×C43C2411yescharacteristic
174C2×C22⋊D43—22no—
175C2×C22⋊D43—22no—
176C2×C22⋊D43—41no—
177C2×C22⋊D43—42no—
178C2×C22⋊D43—42no—
179C2×C22⋊D43—42no—
180C22×Dic43—21no—
181C22×Dic43—21no—
182C22×Dic43—21no—
183C22×Dic43—21no—
184C22×Dic43C2×D411yescharacteristic
185C22×Dic43C2×D411yescharacteristic
186C22×Dic43C2×D411yescharacteristic
187C2×C4×D43—21no—
188C2×C4×D43—21no—
189C2×C4×D43—21no—
190C2×C4×D43—21no—
191C2×C4×D43—42no—
192C2×C4×D43—42no—
193C2×C4×D43—81no—
194C2×C4×D43C2×D412yes—
195C2×C4×D43#4112yes—
196SD16×C43—44no—
197M16×C43—44no—
198C2×C8×C43—21no—
199C2×C8×C43—21no—
200C2×C8×C43—21no—
201C2×C8×C43C2×D412yes—
202C2×C8×C43C2×D412yes—
203C2×C8×C43#4112yes—
204C4⋊C4×C43—21no—
205C4⋊C4×C43—21no—
206C4⋊C4×C43—42no—
207C4⋊C4×C43C2×D412yes—
208C4⋊C4×C43C2×D412yes—
209C22⋊C4×C43—42no—
210C22⋊C4×C43—42no—
211C22⋊Dic43—22no—
212C22⋊Dic43—42no—
213C22⋊Dic43—42no—
214C22⋊Dic43—42no—
215C22⋊Dic43—42no—
216C22⋊Dic43—81no—
217(C2×D43)⋊C4—22no—
218(C2×D43)⋊C4—42no—
219(C2×D43)⋊C4—42no—
220C4⋊Dic43—21no—
221C4⋊Dic43—21no—
222C4⋊Dic43—21no—
223C4⋊Dic43—21no—
224C4⋊Dic43—21no—
225C4⋊Dic43—21no—
226C4⋊Dic43—21no—
227C4⋊Dic43—21no—
228C4⋊Dic43—42no—
229C4⋊Dic43—42no—
230Dic43⋊C4—22no—
231Dic43⋊C4—42no—
232Dic43⋊C4—42no—
233C4×Dic43—21no—
234C4×Dic43—21no—
235C4×Dic43—42no—
236C2×C43⋊C8—21no—
237C2×C43⋊C8—21no—
238C2×C43⋊C8—21no—
239C2×C43⋊C8—21no—
240C2×C43⋊C8—21no—
241C2×C43⋊C8C2×D412yes—
242#10621872—28no—
243C23×C43—21no—
244C23×C43—21no—
245C23×C43—21no—
246C23×C43—21no—
247C23×C43—21no—
248C23×C43—21no—
249C23×C43—21no—
250C23×C43—41no—
251C23×C43—41no—
252C23×C43—41no—
253C23×C43—41no—
254C23×C43—41no—
255C23×C43—41no—
256C23×C43—41no—
257C23×C43C22×D411yescharacteristic
258C22×D43—21no—
259C22×D43—21no—
260C22×D43—21no—
261C22×D43—21no—
262C22×D43—21no—
263C22×D43—21no—
264C22×D43#12112yes—
265Q8×C43—41no—
266Q8×C43—41no—
267Q8×C43—41no—
268Q8×C43—41no—
269D4×C43—41no—
270D4×C43—41no—
271D4×C43—41no—
272D4×C43—41no—
273D4×C43—84no—
274C2×C4×C43—21no—
275C2×C4×C43—22no—
276C2×C4×C43—22no—
277C2×C4×C43—21no—
278C2×C4×C43—21no—
279C2×C4×C43—41no—
280C2×C4×C43—41no—
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×C43C22×D411yescharacteristic
291C2×C4×C43C22×D411yescharacteristic
292C2×C4×C43C2×#4111yescharacteristic
293C2×C4×C43C2×#4111yescharacteristic
294C2×C4×C43H(5,𝔽2)11yescharacteristic
295C2×C4×C432−1+411yescharacteristic
296C22⋊D43—44no—
297C22⋊D43—84no—
298C2×Dic43—21no—
299C2×Dic43—21no—
300C2×Dic43—21no—
301C2×Dic43—21no—
302C2×Dic43—21no—
303C2×Dic43—21no—
304C2×Dic43—21no—
305C2×Dic43—41no—
306C2×Dic43—41no—
307C2×Dic43—41no—
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#12112yes—
318C2×Dic43AGL(1,ℤ/8)12yes—
319C4×D43—22no—
320C4×D43—22no—
321C4×D43—22no—
322C4×D43—22no—
323C4×D43—84no—
324C8×C43—41no—
325C8×C43#12114yescomplemented
326C43⋊C8—22no—
327C43⋊C8—41no—
328#24794—431nomaximal, Sylow
329C22×C43—41no—
330C22×C43—41no—
331C22×C43—41no—
332C22×C43—41no—
333C22×C43—41no—
334C22×C43—41no—
335C22×C43—41no—
336C22×C43—81no—
337C22×C43—81no—
338C22×C43—81no—
339C22×C43—81no—
340C22×C43—81no—
341C22×C43—81no—
342C22×C43—81no—
343C22×C43C2×#12111yescharacteristic
344C22×C43D4211yescharacteristic
345C22×C43#54711yescharacteristic
346C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
347C22×C43#57511yescharacteristic
348C22×C43#57711yescharacteristic
349C22×C43#57811yescharacteristic
350C2×D43—22no—
351C2×D43—22no—
352C2×D43—22no—
353C2×D43—41no—
354C2×D43—41no—
355C2×D43—41no—
356C2×D43—41no—
357C4×C43—41no—
358C4×C43—42no—
359C4×C43—42no—
360C4×C43—81no—
361C4×C43C2×#12111yescharacteristic
362C4×C43#53711yescharacteristic
363C4×C43#54811yescharacteristic
364C4×C43#55311yescharacteristic
365Dic43—22no—
366Dic43—22no—
367Dic43—41no—
368Dic43—81no—
369Dic43—81no—
370Dic43—81no—
371Dic43—81no—
372C2×#468—431no—
373C2×#468D4311yescharacteristic, complemented
374C2×#436—431no—
375C2×#428—431no—
376#2416—431no—
377#2415—431no—
378#2067—431no—
379#2066—431no—
380#2036—431no—
381#2034—431no—
382#1968—431no—
383#1942—431no—
384#1875—431no—
385#1872—431no—
386#1809—431no—
387C2×C43—81no—
388C2×C43—161no—
389C2×C43#241611yescharacteristic
390C2×C43#305511yescharacteristic
391C2×C43#306311yescharacteristic
392C2×C43#327211yescharacteristic
393C2×C43#327711yescharacteristic
394C2×C43#335111yescharacteristic
395C2×C43#335311yescharacteristic
396D43—42no—
397C22×SD16C2×D4311yescharacteristic
398C22×M16—431no—
399C22×M16C2×D4311yescharacteristic
400C2×C22⋊Q8—431no—
401C2×C22⋊Q8C2×D4311yescharacteristic
402C2×#121—431no—
403C2×#121—861no—
404C2×#121C2×D4311yescharacteristic
405C2×C4×D4—431no—
406C2×#117—431no—
407C22×C4⋊C4—431no—
408#468—24no—
409#468—864no—
410#436—864no—
411#428—864no—
412C2×#107—431no—
413C2×#107—431no—
414C2×#107C2×D4311yescharacteristic
415C2×#106—431no—
416C2×#106—431no—
417C2×C4⋊C8—431no—
418C2×#103—431no—
419C2×#103—431no—
420C2×#103C2×D4311yescharacteristic
421C2×#102—431no—
422C2×#102—431no—
423C2×#102C2×D4311yescharacteristic
424C2×C22⋊C8—431no—
425C2×C22⋊C8—431no—
426C2×C4×C8—431no—
427#397—861no—
428#396—861no—
429#394—861no—
430#394—861no—
431#391—431no—
432#390—431no—
433#389—431no—
434#389—431no—
435#389—861no—
436#388—861no—
437#386—861no—
438#380—431no—
439#380—431no—
440#340—431no—
441#340—431no—
442#340—431no—
443#340—431no—
444C43#2479411yescharacteristic, complemented, Sylow
445C22×Q8C22×D4311yescharacteristic
446C22×D4—21no—
447C22×D4—431no—
448C22×D4—861no—
449C22×D4C22×D4311yescharacteristic
450C23×C4—431no—
451C23×C4—861no—
452C23×C4C22×D4311yescharacteristic
453C2×SD16—22no—
454C2×SD16—22no—
455C2×SD16—22no—
456C2×M16—22no—
457C2×M16—22no—
458C2×M16—22no—
459C2×M16—434no—
460C2×M16—862no—
461C2×M16—862no—
462C22×C8—431no—
463C22×C8—431no—
464C22×C8C22×D4311yescharacteristic
465C22×C8C22×D4311yescharacteristic
466C22⋊Q8—22no—
467C22⋊Q8—41no—
468C22⋊Q8—862no—
469C22⋊Q8—862no—
470#121—22no—
471#121—41no—
472#121—862no—
473#121—862no—
474#121—1724no—
475C4×D4—862no—
476C4×D4—862no—
477#117—862no—
478#117—1721no—
479C2×C4⋊C4—21no—
480C2×C4⋊C4—431no—
481C2×C4⋊C4—431no—
482C2×C4⋊C4—431no—
483C2×C4⋊C4—431no—
484C2×C4⋊C4—431no—
485C2×C4⋊C4—862no—
486C2×C4⋊C4—861no—
487C2×C4⋊C4—861no—
488C2×C4⋊C4—861no—
489C2×C4⋊C4—861no—
490C2×C4⋊C4—1721no—
491C2×C4⋊C4C22×D4311yescharacteristic
492C2×C4⋊C4C22×D4311yescharacteristic
493C2×C22⋊C4—21no—
494C2×C22⋊C4—21no—
495C2×C22⋊C4—431no—
496C2×C22⋊C4—431no—
497C2×C22⋊C4—861no—
498C2×C22⋊C4—861no—
499C2×C22⋊C4—861no—
500C2×C22⋊C4—861no—
501C2×C22⋊C4—861no—
502C2×C22⋊C4—861no—
503C2×C22⋊C4—861no—
504C2×C42—431no—
505C2×C42—861no—
506#107—862no—
507#107—862no—
508#107C22⋊D4314yescomplemented
509#106—862no—
510#106—862no—
511C4⋊C8—862no—
512#103—22no—
513#103—862no—
514#103—1721no—
515#102—22no—
516#102—862no—
517#102—1721no—
518C22⋊C8—862no—
519C22⋊C8—862no—
520C4×C8—862no—
521#95—861no—
522#95—861no—
523#95—861no—
524#95—861no—
525#95—861no—
526#95—861no—
527C24—21no—
528C24—431no—
529C24D4×D4311yescharacteristic
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8—21no—
534C2×Q8—21no—
535C2×Q8—21no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—42no—
543C2×D4—42no—
544C2×D4—81no—
545C2×D4—862no—
546C2×D4—862no—
547C2×D4—1721no—
548C2×D4—1722no—
549C2×D4—1722no—
550C2×D4—1722no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—431no—
561C22×C4—431no—
562C22×C4—432no—
563C22×C4—432no—
564C22×C4—431no—
565C22×C4—861no—
566C22×C4—861no—
567C22×C4—861no—
568C22×C4—861no—
569C22×C4—861no—
570C22×C4—861no—
571C22×C4—861no—
572C22×C4—861no—
573C22×C4—3441no—
574C22×C4—1722no—
575C22×C4—1722no—
576C22×C4D4×D4311yescharacteristic
577C22×C4C23×D4311yescharacteristic
578SD16—44no—
579M16—44no—
580M16—868no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—432no—
585C2×C8—861no—
586C2×C8—861no—
587C2×C8—861no—
588C2×C8—861no—
589C2×C8—861no—
590C2×C8D4×D4312yes—
591C2×C8#1062190012yes—
592C2×C8C2×C22⋊D4312yes—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—42no—
596C4⋊C4—862no—
597C4⋊C4—861no—
598C4⋊C4—861no—
599C4⋊C4—861no—
600C4⋊C4—861no—
601C4⋊C4—861no—
602C4⋊C4—861no—
603C4⋊C4—861no—
604C4⋊C4—861no—
605C4⋊C4—1722no—
606C4⋊C4—1722no—
607C4⋊C4—1722no—
608C4⋊C4—1722no—
609C4⋊C4C2×C22⋊D4312yes—
610C4⋊C4C2×C22⋊D4312yes—
611C22⋊C4—42no—
612C22⋊C4—42no—
613C22⋊C4—862no—
614C22⋊C4—862no—
615C22⋊C4—3441no—
616C22⋊C4—1722no—
617C22⋊C4—1722no—
618C22⋊C4—1722no—
619C22⋊C4—1722no—
620C22⋊C4—1722no—
621C22⋊C4—1722no—
622C42—861no—
623C42—861no—
624C42—1722no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—432no—
640C23—861no—
641C23—861no—
642C23—861no—
643C23—861no—
644C23—861no—
645C23—861no—
646C23C2×D4×D4311yescharacteristic
647Q8—41no—
648Q8—41no—
649Q8—41no—
650Q8—41no—
651D4—41no—
652D4—41no—
653D4—41no—
654D4—41no—
655D4—84no—
656D4—3444no—
657D4—1724no—
658C2×C4—21no—
659C2×C4—22no—
660C2×C4—21no—
661C2×C4—22no—
662C2×C4—21no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
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—432no—
675C2×C4—432no—
676C2×C4—861no—
677C2×C4—861no—
678C2×C4—861no—
679C2×C4—861no—
680C2×C4—862no—
681C2×C4—862no—
682C2×C4—862no—
683C2×C4—862no—
684C2×C4—861no—
685C2×C4—861no—
686C2×C4—861no—
687C2×C4—3444no—
688C2×C4—1721no—
689C2×C4—1721no—
690C2×C4—1721no—
691C2×C4—1721no—
692C2×C4—1721no—
693C2×C4—1721no—
694C2×C4—1721no—
695C2×C4—1721no—
696C2×C4—1721no—
697C2×C4—1721no—
698C2×C4—1721no—
699C2×C4—1721no—
700C2×C4C2×D4×D4311yescharacteristic
701C2×C4C22×C22⋊D4311yescharacteristic
702C2×C4#41×D4311yescharacteristic
703C2×C4C2×#1062190011yescharacteristic
704C2×C4#1306337011yescharacteristic
705C2×C4#1306337211yescharacteristic
706C8—41no—
707C8—862no—
708C8—1721no—
709C8#1306329614yescomplemented
710C22—41no—
711C22—41no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—81no—
718C22—81no—
719C22—81no—
720C22—81no—
721C22—81no—
722C22—81no—
723C22—81no—
724C22—862no—
725C22—862no—
726C22—862no—
727C22—1721no—
728C22—1721no—
729C22—1721no—
730C22—1721no—
731C22#121×D4311yescharacteristic
732C22D4×C22⋊D4311yescharacteristic
733C22#1458354911yescharacteristic
734C22AGL(1,ℤ/8)×D4311yescharacteristic
735C22#1458369811yescharacteristic
736C22#1458370911yescharacteristic
737C22#1458371511yescharacteristic
738C4—42no—
739C4—42no—
740C4—41no—
741C4—81no—
742C4—862no—
743C4—862no—
744C4—3441no—
745C4—3441no—
746C4—3441no—
747C4—3441no—
748C4—1721no—
749C4C2×#1306329611yescharacteristic
750C4#1458347811yescharacteristic
751C4#1458355611yescharacteristic
752C4#1458359611yescharacteristic
753C2—81no—
754C2—161no—
755C2—1722no—
756C2#1913803111yescharacteristic
757C2#1914420911yescharacteristic
758C2#1914428111yescharacteristic
759C2#1914618911yescharacteristic
760C2#1914624611yescharacteristic
761C2#1914716111yescharacteristic
762C2#1914717411yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#468C2
socleC23×C43C22×D4
prime radical#19138031C2
hypercenterC2×#468D43
hypocenterC43#24794
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#468

Complements

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

NH ≅ G/Ntype
1. C2×#14583142C2semidirect
2. C2×#14582975C2semidirect
3. C2×#14582940C2semidirect
5. #19138020C2semidirect
6. #19135979C2semidirect
7. #19135972C2semidirect
8. #19135795C2semidirect
9. #19135781C2semidirect
10. #19135451C2semidirect
11. #19135329C2semidirect
12. #19134914C2semidirect
13. #19134899C2semidirect
14. #19134628C2semidirect
15. C2×C43×#468C2semidirect
69. C2×#10621872D4semidirect
142. #107×C43D4semidirect
325. C8×C43#121semidirect
373. C2×#468D43semidirect
444. C43#24794semidirect
508. #107C22⋊D43semidirect
709. C8#13063296semidirect

Maximal subgroups

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

subgroupindex
C2×#145831422
C2×#145829752
C2×#145829402
#191380312
#191380202
#191359792
#191359722
#191357952
#191357812
#191354512
#191353292
#191349142
#191348992
#191346282
C2×C43×#4682
#2479443