Finite Group Databasebeta

← #25140186

Subgroups — #25140186

Order 11008.

1064 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
1C2×#14583234C211yesmaximal, characteristic, complemented
2C2×#14582897C211yesmaximal, characteristic, complemented
3#19137936C211yesmaximal, characteristic
4C4⋊C4×C22⋊D43C211yesmaximal, characteristic, complemented
5#19136121C211yesmaximal, characteristic, complemented
6#19136007C211yesmaximal, characteristic, complemented
7#19135799C211yesmaximal, characteristic, complemented
8#19135781C211yesmaximal, characteristic, complemented
9#19135227C211yesmaximal, characteristic, complemented
10#19135218C211yesmaximal, characteristic, complemented
11#19134889C211yesmaximal, characteristic, complemented
12#19134784C211yesmaximal, characteristic, complemented
13#19134627C211yesmaximal, characteristic, complemented
14#19134532C211yesmaximal, characteristic, complemented
15C43×#1874C211yesmaximal, characteristic, complemented
16C22×#10621900C2211yescharacteristic
17C22×#10621872C2211yescharacteristic
18C2×#13063304C2211yescharacteristic
19C2×C4×C22⋊D43—21no—
20C2×C4×C22⋊D43C2211yescharacteristic
21C2×C4⋊C4×D43C2211yescharacteristic
22#14583234—24no—
23C2×#13063259C2211yescharacteristic
24C2×#13063258C2211yescharacteristic
25C2×#13063258C2211yescharacteristic
26C2×#13063256C2211yescharacteristic
27#14582897—24no—
28C2×#13063250C2211yescharacteristic
29C2×#13063250C2211yescharacteristic
30C2×#13063248C2211yescharacteristic
31C2×#13063248C2211yescharacteristic
32C2×#13063246C2211yescharacteristic
33C2×#13063246C2211yescharacteristic
34C2×C22⋊(C43⋊C8)C2211yescharacteristic
35C2×(C2×D43)⋊C8C2211yescharacteristic
36#14582814—21no—
37#14582807—21no—
38#14582804C2211yescharacteristic
39#14582802C2211yescharacteristic
40#14582794—21no—
41#14582779—21no—
42#14582772—21no—
43#14582771—21no—
44#14582770—21no—
45#14582768C2211yescharacteristic
46#14582759C2211yescharacteristic
47#14582756C2211yescharacteristic
48#14582756C2211yescharacteristic
49C4⋊C4×Dic43C2211yescharacteristic
50#14582662C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582653C2211yescharacteristic
53#14582653C2211yescharacteristic
54C2×#121×C43C2211yescharacteristic
55C22×C4⋊C4×C43C2211yescharacteristic
56C2×#102×C43C2211yescharacteristic
57C2×#102×C43C2211yescharacteristic
58C2×C22⋊C8×C43C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C2×#10621900—22no—
62C2×#10621900—22no—
63C2×#10621900—22no—
64C2×#10621900—22no—
65C2×#10621900—41no—
66C2×#10621900—41no—
67C22×Dic86C2311yescharacteristic
68C22×C22⋊D43—21no—
69C22×C22⋊D43D411yescharacteristic
70C23×Dic43—21no—
71C22×C4×D43—21no—
72C22×C4×D43C2311yescharacteristic
73C2×#10621872—22no—
74C2×#10621872—22no—
75C2×#10621872—41no—
76C22×C43⋊C8C2311yescharacteristic
77C22×C43⋊C8C2311yescharacteristic
78#13063304—22no—
79#13063304—41no—
80C4×C22⋊D43—22no—
81C4×C22⋊D43—22no—
82C4×C22⋊D43—44no—
83C2×C4⋊Dic43C2311yescharacteristic
84C2×C4⋊Dic43C2311yescharacteristic
85C2×C4⋊Dic43C2311yescharacteristic
86C2×Dic43⋊C4—21no—
87C2×Dic43⋊C4—21no—
88C2×Dic43⋊C4—21no—
89C2×Dic43⋊C4—21no—
90C2×Dic43⋊C4D411yescharacteristic
91C4⋊C4×D43—22no—
92C4⋊C4×D43—41no—
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—41no—
104#13063258—22no—
105#13063258—22no—
106#13063256—41no—
107#13063250—22no—
108#13063250—41no—
109#13063248—22no—
110#13063248D414yescomplemented
111#13063246—22no—
112#13063246—22no—
113C22⋊(C43⋊C8)—22no—
114(C2×D43)⋊C8—22no—
115C43⋊#95—21no—
116C43⋊#95—21no—
117C43⋊#95—21no—
118C43⋊#95—21no—
119C43⋊#95—21no—
120C43⋊#95—21no—
121C22×D4×C43—21no—
122C22×D4×C43C2311yescharacteristic
123C23×C4×C43—21no—
124C23×C4×C43C2311yescharacteristic
125C22×C8×C43C2311yescharacteristic
126C22×C8×C43C2311yescharacteristic
127#121×C43—22no—
128#121×C43—41no—
129C2×C4⋊C4×C43—22no—
130C2×C4⋊C4×C43—21no—
131C2×C4⋊C4×C43—41no—
132C2×C4⋊C4×C43C2311yescharacteristic
133C2×C4⋊C4×C43C2311yescharacteristic
134C2×C4⋊C4×C43C2311yescharacteristic
135C2×C22⋊C4×C43—21no—
136#102×C43—22no—
137#102×C43—41no—
138C22⋊C8×C43—41no—
139C24×C43—21no—
140C24×C43C2×D411yescharacteristic
141C23×D43C2×D411yescharacteristic
142C2×D4×C43—21no—
143C2×D4×C43—21no—
144C2×D4×C43—21no—
145C2×D4×C43—21no—
146C2×D4×C43—21no—
147C2×D4×C43—42no—
148C2×D4×C43—42no—
149C2×D4×C43—81no—
150C2×D4×C43#4112yes—
151C22×C4×C43—21no—
152C22×C4×C43—21no—
153C22×C4×C43—21no—
154C22×C4×C43—21no—
155C22×C4×C43—21no—
156C22×C4×C43—21no—
157C22×C4×C43—21no—
158C22×C4×C43—21no—
159C22×C4×C43—21no—
160C22×C4×C43—42no—
161C22×C4×C43—42no—
162C22×C4×C43—81no—
163C22×C4×C43C2×D411yescharacteristic
164C22×C4×C43C2411yescharacteristic
165C2×C22⋊D43—22no—
166C2×C22⋊D43—22no—
167C2×C22⋊D43—22no—
168C2×C22⋊D43—42no—
169C2×C22⋊D43—42no—
170C2×C22⋊D43—42no—
171C22×Dic43—21no—
172C22×Dic43—21no—
173C22×Dic43—21no—
174C22×Dic43—21no—
175C22×Dic43—42no—
176C22×Dic43—42no—
177C22×Dic43—42no—
178C22×Dic43C2×D411yescharacteristic
179C22×Dic43C2×D411yescharacteristic
180C22×Dic43C2×D411yescharacteristic
181#10621900—28no—
182#10621900—44no—
183#10621900—44no—
184#10621900—44no—
185C2×C4×D43—21no—
186C2×C4×D43—21no—
187C2×C4×D43—21no—
188C2×C4×D43—21no—
189C2×C4×D43—42no—
190C2×C4×D43—42no—
191C2×C4×D43—81no—
192C2×C4×D43#4112yes—
193C2×C4×D43#4112yes—
194C2×Dic86—21no—
195C2×Dic86—21no—
196C2×Dic86—21no—
197C2×Dic86—21no—
198C2×Dic86—21no—
199C2×Dic86C2×D412yes—
200C2×C8×C43—21no—
201C2×C8×C43—21no—
202C2×C8×C43—21no—
203C2×C8×C43—21no—
204C2×C8×C43—21no—
205C2×C8×C43—21no—
206C4⋊C4×C43—21no—
207C4⋊C4×C43—21no—
208C4⋊C4×C43—21no—
209C4⋊C4×C43—21no—
210C4⋊C4×C43—21no—
211C4⋊C4×C43—42no—
212C4⋊C4×C43C2×D412yes—
213C22⋊C4×C43—42no—
214C22⋊Dic43—22no—
215C22⋊Dic43—42no—
216C22⋊Dic43—42no—
217C22⋊Dic43—42no—
218C22⋊Dic43—81no—
219(C2×D43)⋊C4—22no—
220(C2×D43)⋊C4—42no—
221(C2×D43)⋊C4—81no—
222C4⋊Dic43—21no—
223C4⋊Dic43—21no—
224C4⋊Dic43—21no—
225C4⋊Dic43—21no—
226C4⋊Dic43—21no—
227C4⋊Dic43—21no—
228Dic43⋊C4—22no—
229Dic43⋊C4—42no—
230Dic43⋊C4—42no—
231Dic43⋊C4—42no—
232Dic43⋊C4—81no—
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—44no—
243C23×C43—21no—
244C23×C43—21no—
245C23×C43—21no—
246C23×C43—21no—
247C23×C43—21no—
248C23×C43—21no—
249C23×C43—22no—
250C23×C43—41no—
251C23×C43—41no—
252C23×C43—41no—
253C23×C43—41no—
254C23×C43—41no—
255C23×C43—41no—
256C23×C43#13712yes—
257C23×C43C22×D411yescharacteristic
258C22×D43—21no—
259C22×D43—21no—
260C22×D43—21no—
261C22×D43—21no—
262C22×D43—21no—
263C22×D43—21no—
264C22×D43#12312yes—
265D4×C43—22no—
266D4×C43—22no—
267D4×C43—41no—
268D4×C43—41no—
269D4×C43—84no—
270C2×C4×C43—21no—
271C2×C4×C43—21no—
272C2×C4×C43—22no—
273C2×C4×C43—21no—
274C2×C4×C43—41no—
275C2×C4×C43—41no—
276C2×C4×C43—41no—
277C2×C4×C43—41no—
278C2×C4×C43—41no—
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—84no—
287C2×C4×C43C22×D411yescharacteristic
288C2×C4×C43C2×#4111yescharacteristic
289C2×C4×C43C2×#4111yescharacteristic
290C2×C4×C43C2×#4111yescharacteristic
291C2×C4×C43H(5,𝔽2)11yescharacteristic
292C2×C4×C43H(5,𝔽2)11yescharacteristic
293C22⋊D43—28no—
294C22⋊D43—48no—
295C2×Dic43—21no—
296C2×Dic43—21no—
297C2×Dic43—21no—
298C2×Dic43—21no—
299C2×Dic43—21no—
300C2×Dic43—22no—
301C2×Dic43—21no—
302C2×Dic43—21no—
303C2×Dic43—48no—
304C2×Dic43—41no—
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#12312yes—
316C2×Dic43AGL(1,ℤ/8)12yes—
317C4×D43—22no—
318C4×D43—22no—
319C4×D43—22no—
320C4×D43—22no—
321C4×D43—84no—
322Dic86—22no—
323Dic86—22no—
324Dic86—41no—
325Dic86—41no—
326C8×C43—41no—
327C8×C43—41no—
328C43⋊C8—22no—
329C43⋊C8—41no—
330#24883—431nomaximal, Sylow
331C22×C43—22no—
332C22×C43—22no—
333C22×C43—22no—
334C22×C43—41no—
335C22×C43—41no—
336C22×C43—41no—
337C22×C43—41no—
338C22×C43—42no—
339C22×C43—42no—
340C22×C43—42no—
341C22×C43—81no—
342C22×C43—81no—
343C22×C43—81no—
344C22×C43—81no—
345C22×C43C2×#12311yescharacteristic
346C22×C43D4211yescharacteristic
347C22×C43#54611yescharacteristic
348C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
349C22×C43C2×#13711yescharacteristic
350C22×C43#57611yescharacteristic
351C22×C43#57811yescharacteristic
352C2×D43—22no—
353C2×D43—22no—
354C2×D43—22no—
355C2×D43—41no—
356C2×D43—41no—
357C2×D43—41no—
358C2×D43—41no—
359C4×C43—41no—
360C4×C43—42no—
361C4×C43—81no—
362C4×C43—81no—
363C4×C43#52511yescharacteristic
364C4×C43#53811yescharacteristic
365C4×C43#54611yescharacteristic
366C4×C43#55111yescharacteristic
367Dic43—22no—
368Dic43—22no—
369Dic43—41no—
370Dic43—42no—
371Dic43—81no—
372Dic43—81no—
373Dic43—81no—
374C2×#484—431no—
375C2×#417—431no—
376#2407—431no—
377D4×C4⋊C4—431no—
378#2093—431no—
379#2072—431no—
380#2036—431no—
381#2034—431no—
382#1927—431no—
383#1925—431no—
384#1874D4311yescharacteristic, complemented
385#1870—431no—
386#1852—431no—
387#1809—431no—
388#1788—431no—
389C2×C43—42no—
390C2×C43—82no—
391C2×C43#241811yescharacteristic
392C2×C43#309211yescharacteristic
393C2×C43#309811yescharacteristic
394C2×C43#327011yescharacteristic
395C2×C43#327411yescharacteristic
396C2×C43#331411yescharacteristic
397C2×C43#333011yescharacteristic
398D43—42no—
399C22×#41—431no—
400C22×M16—431no—
401C2×C22⋊Q8—431no—
402C2×#121C2×D4311yescharacteristic
403C2×C4×D4—431no—
404C2×C4×D4—861no—
405C22×C4⋊C4—431no—
406C22×C4⋊C4C2×D4311yescharacteristic
407#484—864no—
408C2×#107—431no—
409C2×#107—431no—
410C2×#107—431no—
411C2×#106—431no—
412#417—864no—
413C2×#103—431no—
414C2×#103—431no—
415C2×#103—431no—
416C2×#103—431no—
417C2×#102—431no—
418C2×#102—431no—
419C2×#102C2×D4311yescharacteristic
420C2×#102C2×D4311yescharacteristic
421C2×C22⋊C8—431no—
422C2×C22⋊C8—431no—
423C2×C22⋊C8C2×D4311yescharacteristic
424#394—861no—
425#392—861no—
426#391—431no—
427#390—431no—
428#389—861no—
429#386—861no—
430#385—861no—
431#385—861no—
432#385—861no—
433#384—431no—
434#380—431no—
435#380—431no—
436#380—431no—
437C4×C4⋊C4—431no—
438#340—431no—
439#340—431no—
440#340C2×D4311yescharacteristic
441#340C2×D4311yescharacteristic
442#336—431no—
443#336—431no—
444C43#2488311yescharacteristic, complemented, Sylow
445C2×#41—862no—
446C2×#41—862no—
447C2×#41—862no—
448C2×#41—862no—
449C2×#41—1721no—
450C2×#41—1721no—
451C22×Q8—431no—
452C22×D4—21no—
453C22×D4—431no—
454C22×D4—861no—
455C22×D4C22×D4311yescharacteristic
456C23×C4—21no—
457C23×C4—431no—
458C23×C4—861no—
459C23×C4—861no—
460C23×C4C22×D4311yescharacteristic
461C2×M16—862no—
462C2×M16—862no—
463C2×M16—1721no—
464C22×C8—431no—
465C22×C8—431no—
466C22×C8C22×D4311yescharacteristic
467C22×C8C22×D4311yescharacteristic
468C22⋊Q8—862no—
469C22⋊Q8—1721no—
470#121—22no—
471#121—41no—
472C4×D4—862no—
473C4×D4—862no—
474C4×D4—1724no—
475C2×C4⋊C4—22no—
476C2×C4⋊C4—21no—
477C2×C4⋊C4—41no—
478C2×C4⋊C4—431no—
479C2×C4⋊C4—431no—
480C2×C4⋊C4—431no—
481C2×C4⋊C4—431no—
482C2×C4⋊C4—862no—
483C2×C4⋊C4—861no—
484C2×C4⋊C4—861no—
485C2×C4⋊C4—861no—
486C2×C4⋊C4—861no—
487C2×C4⋊C4—1721no—
488C2×C4⋊C4C22×D4311yescharacteristic
489C2×C4⋊C4C22×D4311yescharacteristic
490C2×C4⋊C4C22×D4311yescharacteristic
491C2×C22⋊C4—21no—
492C2×C22⋊C4—431no—
493C2×C22⋊C4—431no—
494C2×C22⋊C4—861no—
495C2×C22⋊C4—861no—
496C2×C22⋊C4—861no—
497C2×C22⋊C4—861no—
498C2×C22⋊C4—861no—
499C2×C22⋊C4—861no—
500C2×C42—431no—
501C2×C42—861no—
502#107—862no—
503#107—862no—
504#107—1721no—
505#106—1721no—
506#103—434no—
507#103—862no—
508#103—862no—
509#103—1721no—
510#102—22no—
511#102—41no—
512#102—862no—
513#102—862no—
514C22⋊C8—41no—
515C22⋊C8—862no—
516C22⋊C8—862no—
517#95—861no—
518#95—861no—
519#95—861no—
520#95—861no—
521#95—861no—
522#95—861no—
523C24—21no—
524C24—431no—
525C24D4×D4311yescharacteristic
526#41—868no—
527#41—1724no—
528#41—1724no—
529#41—1724no—
530C2×Q8—432no—
531C2×Q8—861no—
532C2×Q8—861no—
533C2×Q8—861no—
534C2×Q8—861no—
535C2×Q8—861no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—42no—
542C2×D4—42no—
543C2×D4—81no—
544C2×D4—862no—
545C2×D4—862no—
546C2×D4—862no—
547C2×D4—1722no—
548C2×D4—1722no—
549C2×D4—1722no—
550C2×D4#1062189812yes—
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—42no—
561C22×C4—42no—
562C22×C4—81no—
563C22×C4—431no—
564C22×C4—431no—
565C22×C4—432no—
566C22×C4—432no—
567C22×C4—431no—
568C22×C4—861no—
569C22×C4—861no—
570C22×C4—861no—
571C22×C4—861no—
572C22×C4—861no—
573C22×C4—861no—
574C22×C4—861no—
575C22×C4—861no—
576C22×C4—3441no—
577C22×C4—1722no—
578C22×C4—1722no—
579C22×C4—1722no—
580C22×C4—1722no—
581C22×C4—1722no—
582C22×C4D4×D4311yescharacteristic
583C22×C4C23×D4311yescharacteristic
584M16—1724no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—432no—
592C2×C8—861no—
593C2×C8—861no—
594C2×C8—861no—
595C2×C8—861no—
596C2×C8—861no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—42no—
603C4⋊C4—862no—
604C4⋊C4—861no—
605C4⋊C4—861no—
606C4⋊C4—861no—
607C4⋊C4—861no—
608C4⋊C4—861no—
609C4⋊C4—861no—
610C4⋊C4—3441no—
611C4⋊C4—1722no—
612C4⋊C4—1722no—
613C4⋊C4—1722no—
614C4⋊C4D4×D4312yes—
615C22⋊C4—42no—
616C22⋊C4—862no—
617C22⋊C4—862no—
618C22⋊C4—3441no—
619C22⋊C4—3441no—
620C22⋊C4—1722no—
621C22⋊C4—1722no—
622C22⋊C4—1722no—
623C22⋊C4—1722no—
624C42—861no—
625C42—861no—
626C42—1722no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—22no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—432no—
641C23—861no—
642C23—861no—
643C23—861no—
644C23—861no—
645C23—861no—
646C23—861no—
647C23#1306335412yes—
648C23C2×D4×D4311yescharacteristic
649Q8—862no—
650Q8—862no—
651Q8—1721no—
652Q8—1721no—
653D4—22no—
654D4—22no—
655D4—41no—
656D4—41no—
657D4—84no—
658D4—868no—
659D4—1728no—
660C2×C4—21no—
661C2×C4—22no—
662C2×C4—21no—
663C2×C4—21no—
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—41no—
675C2×C4—41no—
676C2×C4—84no—
677C2×C4—432no—
678C2×C4—432no—
679C2×C4—861no—
680C2×C4—861no—
681C2×C4—861no—
682C2×C4—861no—
683C2×C4—862no—
684C2×C4—862no—
685C2×C4—862no—
686C2×C4—862no—
687C2×C4—861no—
688C2×C4—861no—
689C2×C4—861no—
690C2×C4—862no—
691C2×C4—3444no—
692C2×C4—1728no—
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×C4—1721no—
704C2×C4C2×D4×D4311yescharacteristic
705C2×C4#41×D4311yescharacteristic
706C2×C4#41×D4311yescharacteristic
707C2×C4C2×#1062189811yescharacteristic
708C2×C4#1306337011yescharacteristic
709C2×C4#1306337011yescharacteristic
710C8—41no—
711C8—41no—
712C8—862no—
713C8—1721no—
714C22—22no—
715C22—22no—
716C22—22no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—41no—
721C22—42no—
722C22—42no—
723C22—42no—
724C22—81no—
725C22—81no—
726C22—81no—
727C22—81no—
728C22—862no—
729C22—862no—
730C22—862no—
731C22—1721no—
732C22—1721no—
733C22—1721no—
734C22—1721no—
735C22#123×D4311yescharacteristic
736C22#1458353111yescharacteristic
737C22#1458353911yescharacteristic
738C22AGL(1,ℤ/8)×D4311yescharacteristic
739C22C2×#1306335411yescharacteristic
740C22#1458370011yescharacteristic
741C22#1458371511yescharacteristic
742C4—41no—
743C4—42no—
744C4—81no—
745C4—81no—
746C4—862no—
747C4—862no—
748C4—3441no—
749C4—3441no—
750C4—3441no—
751C4—1722no—
752C4—1721no—
753C4#1458340811yescharacteristic
754C4#1458348111yescharacteristic
755C4#1458354611yescharacteristic
756C4#1458357811yescharacteristic
757C2—42no—
758C2—82no—
759C2—1722no—
760C2#1913805611yescharacteristic
761C2#1914451711yescharacteristic
762C2#1914456811yescharacteristic
763C2#1914615811yescharacteristic
764C2#1914621311yescharacteristic
765C2#1914667211yescharacteristic
766C2#1914689611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1874C2
socleC23×C43C22×D4
prime radical#19137936C2
hypercenter#1874D43
hypocenterC43#24883
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1874

Complements

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

NH ≅ G/Ntype
1. C2×#14583234C2semidirect
2. C2×#14582897C2semidirect
4. C4⋊C4×C22⋊D43C2semidirect
5. #19136121C2semidirect
6. #19136007C2semidirect
7. #19135799C2semidirect
8. #19135781C2semidirect
9. #19135227C2semidirect
10. #19135218C2semidirect
11. #19134889C2semidirect
12. #19134784C2semidirect
13. #19134627C2semidirect
14. #19134532C2semidirect
15. C43×#1874C2semidirect
110. #13063248D4semidirect
384. #1874D43semidirect
444. C43#24883semidirect

Maximal subgroups

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

subgroupindex
C2×#145832342
C2×#145828972
#191379362
C4⋊C4×C22⋊D432
#191361212
#191360072
#191357992
#191357812
#191352272
#191352182
#191348892
#191347842
#191346272
#191345322
C43×#18742
#2488343