Finite Group Databasebeta

← #25125468

Subgroups — #25125468

Order 11008.

1166 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×#14582940C211yesmaximal, characteristic, complemented
2C2×#14582861C211yesmaximal, characteristic
3#19136977C211yesmaximal, characteristic
4#380×D43C211yesmaximal, characteristic
5#19136033C211yesmaximal, characteristic, complemented
6#19136032C211yesmaximal, characteristic, complemented
7#19136030C211yesmaximal, characteristic, complemented
8#19136028C211yesmaximal, characteristic, complemented
9#19136026C211yesmaximal, characteristic, complemented
10#19136022C211yesmaximal, characteristic, complemented
11#19136019C211yesmaximal, characteristic, complemented
12#19134313C211yesmaximal, characteristic, complemented
13#19134313C211yesmaximal, characteristic, complemented
14#19134313C211yesmaximal, characteristic, complemented
15C43×#2076C211yesmaximal, characteristic, complemented
16C23×C4×D43C2211yescharacteristic
17C22×#10621872C2211yescharacteristic
18C22×#10621872C2211yescharacteristic
19C2×#13063283C2211yescharacteristic
20C2×#13063283C2211yescharacteristic
21C2×C4⋊C4×D43C2211yescharacteristic
22C2×C4⋊C4×D43C2211yescharacteristic
23C2×C22⋊C4×D43—21no—
24#14582940—24no—
25C2×#13063258C2211yescharacteristic, complemented
26C2×#13063257C2211yescharacteristic, complemented
27C2×#13063256C2211yescharacteristic, complemented
28#14582861—24no—
29C2×C22⋊(C43⋊C8)C2211yescharacteristic
30C2×(C2×D43)⋊C8C2211yescharacteristic
31C2×(C2×D43)⋊C8C2211yescharacteristic
32#14582761—21no—
33#14582759C2211yescharacteristic
34#14582759C2211yescharacteristic
35#14582758—21no—
36#14582757—21no—
37#14582756C2211yescharacteristic
38#14582756C2211yescharacteristic
39#14582756C2211yescharacteristic
40#14582756C2211yescharacteristic
41#14582754—21no—
42C22⋊C4×Dic43—21no—
43#14582746—21no—
44#95×D43—21no—
45#14582662C2211yescharacteristic, complemented
46#14582662C2211yescharacteristic, complemented
47#14582662C2211yescharacteristic, complemented
48#14582661C2211yescharacteristic, complemented
49#14582661C2211yescharacteristic, complemented
50#14582661C2211yescharacteristic, complemented
51#14582661C2211yescharacteristic, complemented
52#14582661C2211yescharacteristic, complemented
53#14582661C2211yescharacteristic, complemented
54C2×#107×C43C2211yescharacteristic, complemented
55C2×C22⋊C8×C43C2211yescharacteristic
56C43×#380C2211yescharacteristic
57C43×#380C2211yescharacteristic
58C43×#340C2211yescharacteristic, complemented
59C43×#340C2211yescharacteristic, complemented
60C43×#340C2211yescharacteristic, complemented
61C24×D43D411yescharacteristic
62C23×Dic43D411yescharacteristic
63C22×C4×D43—22no—
64C22×C4×D43—22no—
65C22×C4×D43—22no—
66C22×C4×D43—22no—
67C22×C4×D43—22no—
68C22×C4×D43—22no—
69C22×C4×D43—21no—
70C22×C4×D43—21no—
71C22×C4×D43D411yescharacteristic
72C22×C4×D43D411yescharacteristic
73C22×C4×D43C2311yescharacteristic
74C22×C4×D43C2311yescharacteristic
75C2×#10621872—22no—
76C2×#10621872—22no—
77C2×#10621872—22no—
78C2×#10621872—22no—
79C2×#10621872—22no—
80C2×#10621872D414yes—
81C22×C43⋊C8C2311yescharacteristic
82C22×C43⋊C8C2311yescharacteristic
83#13063283—22no—
84#13063283—22no—
85#13063283—22no—
86#13063283—22no—
87C2×C4⋊Dic43C2311yescharacteristic
88C2×C4⋊Dic43C2311yescharacteristic
89C2×C4⋊Dic43C2311yescharacteristic
90C2×C4⋊Dic43C2311yescharacteristic
91C2×Dic43⋊C4—21no—
92C2×Dic43⋊C4—21no—
93C4⋊C4×D43—22no—
94C4⋊C4×D43—22no—
95C4⋊C4×D43—22no—
96C4⋊C4×D43—22no—
97C2×C22⋊Dic43—21no—
98C2×C22⋊Dic43—21no—
99C2×(C2×D43)⋊C4—21no—
100C2×(C2×D43)⋊C4—21no—
101C2×(C2×D43)⋊C4—21no—
102C2×(C2×D43)⋊C4—21no—
103C2×(C2×D43)⋊C4—21no—
104C2×(C2×D43)⋊C4—21no—
105C22⋊C4×D43—44no—
106C2×C4×Dic43—21no—
107C2×C4×Dic43—21no—
108#13063258—22no—
109#13063257—22no—
110#13063256—22no—
111C22⋊(C43⋊C8)—22no—
112(C2×D43)⋊C8—22no—
113(C2×D43)⋊C8—22no—
114C43⋊#95—21no—
115C43⋊#95—21no—
116C43⋊#95—21no—
117C43⋊#95—21no—
118C43⋊#95—21no—
119C43⋊#95—21no—
120C23×C4×C43C2311yescharacteristic
121C22×C8×C43C2311yescharacteristic
122C22×C8×C43C2311yescharacteristic
123C2×C4⋊C4×C43C2311yescharacteristic
124C2×C4⋊C4×C43C2311yescharacteristic
125C2×C4⋊C4×C43C2311yescharacteristic
126C2×C4⋊C4×C43C2311yescharacteristic
127C2×C22⋊C4×C43—21no—
128C2×C22⋊C4×C43—21no—
129#107×C43—22no—
130C22⋊C8×C43—22no—
131#95×C43—21no—
132#95×C43—21no—
133C24×C43C2×D411yescharacteristic
134C23×D43—22no—
135C23×D43—22no—
136C23×D43—22no—
137C23×D43—22no—
138C23×D43—22no—
139C23×D43—41no—
140C23×D43—41no—
141C23×D43C2×D411yescharacteristic
142C23×D43C2×D411yescharacteristic
143C22×C4×C43—21no—
144C22×C4×C43—21no—
145C22×C4×C43—21no—
146C22×C4×C43—21no—
147C22×C4×C43—21no—
148C22×C4×C43—21no—
149C22×C4×C43—21no—
150C22×C4×C43—21no—
151C22×C4×C43—21no—
152C22×C4×C43—21no—
153C22×C4×C43C2×D411yescharacteristic
154C22×C4×C43C2411yescharacteristic
155C22×Dic43—22no—
156C22×Dic43—22no—
157C22×Dic43—22no—
158C22×Dic43—21no—
159C22×Dic43—21no—
160C22×Dic43—21no—
161C22×Dic43—21no—
162C22×Dic43C2×D411yescharacteristic
163C22×Dic43C2×D411yescharacteristic
164C2×C4×D43—21no—
165C2×C4×D43—21no—
166C2×C4×D43—21no—
167C2×C4×D43—21no—
168C2×C4×D43—21no—
169C2×C4×D43—21no—
170C2×C4×D43—22no—
171C2×C4×D43—22no—
172C2×C4×D43—22no—
173C2×C4×D43—22no—
174C2×C4×D43—22no—
175C2×C4×D43—22no—
176C2×C4×D43—42no—
177C2×C4×D43—42no—
178C2×C4×D43—42no—
179C2×C4×D43—42no—
180C2×C4×D43—44no—
181C2×C4×D43—44no—
182C2×C4×D43—44no—
183C2×C4×D43—44no—
184C2×C4×D43—42no—
185C2×C4×D43—42no—
186C2×C4×D43C2×D412yes—
187C2×C4×D43#4112yes—
188C2×C4×D43#4112yes—
189C2×C4×D43#4112yes—
190C2×C4×D43#4112yes—
191C2×C4×D43#4112yes—
192C2×C8×C43—21no—
193C2×C8×C43—21no—
194C2×C8×C43—21no—
195C2×C8×C43—21no—
196C2×C8×C43—21no—
197C2×C8×C43C2×D412yes—
198C4⋊C4×C43—21no—
199C4⋊C4×C43—21no—
200C4⋊C4×C43—21no—
201C4⋊C4×C43—21no—
202C4⋊C4×C43—21no—
203C4⋊C4×C43—21no—
204C4⋊C4×C43—21no—
205C4⋊C4×C43—21no—
206C22⋊C4×C43—42no—
207C22⋊C4×C43—42no—
208C22⋊Dic43—42no—
209C22⋊Dic43—42no—
210(C2×D43)⋊C4—42no—
211(C2×D43)⋊C4—42no—
212(C2×D43)⋊C4—42no—
213(C2×D43)⋊C4—42no—
214(C2×D43)⋊C4—42no—
215(C2×D43)⋊C4—42no—
216C4⋊Dic43—21no—
217C4⋊Dic43—21no—
218C4⋊Dic43—21no—
219C4⋊Dic43—21no—
220C4⋊Dic43—21no—
221C4⋊Dic43—21no—
222C4⋊Dic43—21no—
223C4⋊Dic43—21no—
224Dic43⋊C4—42no—
225Dic43⋊C4—42no—
226C4×Dic43—42no—
227C4×Dic43—42no—
228C2×C43⋊C8—21no—
229C2×C43⋊C8—21no—
230C2×C43⋊C8—21no—
231C2×C43⋊C8—21no—
232C2×C43⋊C8—21no—
233C2×C43⋊C8C2×D412yes—
234#10621872—28no—
235#10621872—44no—
236C23×C43—21no—
237C23×C43—21no—
238C23×C43—21no—
239C23×C43—21no—
240C23×C43—21no—
241C23×C43—21no—
242C23×C43#13712yes—
243C23×C43C22×D411yescharacteristic
244C22×D43—21no—
245C22×D43—21no—
246C22×D43—21no—
247C22×D43—21no—
248C22×D43—28no—
249C22×D43—21no—
250C22×D43—21no—
251C22×D43—21no—
252C22×D43—21no—
253C22×D43—21no—
254C22×D43—21no—
255C22×D43—44no—
256C22×D43—44no—
257C22×D43—44no—
258C22×D43—44no—
259C22×D43—44no—
260C22×D43—44no—
261C22×D43#12112yes—
262C22×D43#12312yes—
263C22×D43#12312yes—
264C22×D43AGL(1,ℤ/8)12yes—
265C2×C4×C43—21no—
266C2×C4×C43—21no—
267C2×C4×C43—21no—
268C2×C4×C43—41no—
269C2×C4×C43—41no—
270C2×C4×C43—41no—
271C2×C4×C43—41no—
272C2×C4×C43—41no—
273C2×C4×C43—41no—
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×C43C22×D411yescharacteristic
285C2×C4×C43C2×#4111yescharacteristic
286C2×C4×C43C2×#4111yescharacteristic
287C2×C4×C43C2×#4111yescharacteristic
288C2×C4×C43C2×#4111yescharacteristic
289C2×C4×C43C2×#4111yescharacteristic
290C2×Dic43—21no—
291C2×Dic43—21no—
292C2×Dic43—21no—
293C2×Dic43—44no—
294C2×Dic43—41no—
295C2×Dic43—41no—
296C2×Dic43—41no—
297C2×Dic43—41no—
298C2×Dic43—41no—
299C2×Dic43—41no—
300C2×Dic43—41no—
301C2×Dic43—41no—
302C2×Dic43—41no—
303C2×Dic43—41no—
304C2×Dic43—41no—
305C2×Dic43—41no—
306C2×Dic43#12112yes—
307C2×Dic43#12312yes—
308C2×Dic43#12312yes—
309C4×D43—44no—
310C4×D43—41no—
311C4×D43—41no—
312C4×D43—41no—
313C4×D43—41no—
314C4×D43—44no—
315C4×D43—84no—
316C4×D43—84no—
317C4×D43#12314yes—
318C4×D43#12414yes—
319C4×D43#12614yes—
320C4×D43#12614yes—
321C8×C43—22no—
322C8×C43—41no—
323C43⋊C8—22no—
324C43⋊C8—41no—
325#23642—431nomaximal, Sylow
326C22×C43—22no—
327C22×C43—22no—
328C22×C43—22no—
329C22×C43—41no—
330C22×C43—41no—
331C22×C43—41no—
332C22×C43—41no—
333C22×C43C2×#12111yescharacteristic
334C22×C43C2×#12311yescharacteristic
335C22×C43C2×#12311yescharacteristic
336C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
337C22×C43C2×#13711yescharacteristic
338C22×C43#57511yescharacteristic
339C22×C43#57511yescharacteristic
340C2×D43—22no—
341C2×D43—22no—
342C2×D43—22no—
343C2×D43—22no—
344C2×D43—22no—
345C2×D43—22no—
346C2×D43—22no—
347C2×D43—22no—
348C2×D43—22no—
349C2×D43—416no—
350C2×D43—41no—
351C2×D43—41no—
352C2×D43—41no—
353C2×D43—41no—
354C2×D43#39714yes—
355C4×C43—41no—
356C4×C43—81no—
357C4×C43—81no—
358C4×C43—81no—
359C4×C43—81no—
360C4×C43C2×#12311yescharacteristic
361C4×C43C2×#12411yescharacteristic
362C4×C43C2×#12611yescharacteristic
363C4×C43C2×#12611yescharacteristic
364Dic43—41no—
365Dic43—81no—
366Dic43—81no—
367Dic43—81no—
368Dic43—81no—
369Dic43#39714yes—
370C2×#428—431no—
371C2×#407—431no—
372#2280—431no—
373C2×#380—431no—
374#2077—431no—
375#2077—431no—
376#2077—431no—
377#2077—431no—
378#2076—431no—
379#2076D4311yescharacteristic, complemented
380#2075—431no—
381#2075—431no—
382#1736—431no—
383#1736—431no—
384#1736—431no—
385C2×C43—42no—
386C2×C43C2×#39711yescharacteristic
387C2×C43#305511yescharacteristic
388C2×C43#305611yescharacteristic
389C2×C43#309211yescharacteristic
390C2×C43#309311yescharacteristic
391C2×C43#309411yescharacteristic
392C2×C43#309511yescharacteristic
393D43—24no—
394D43—42no—
395C24×C4—431no—
396C22×M16—431no—
397C22×M16—431no—
398C2×#117—431no—
399C2×#117—431no—
400C22×C4⋊C4—431no—
401C22×C4⋊C4—431no—
402C22×C22⋊C4—861no—
403#428—864no—
404C2×#107—431no—
405C2×#107C2×D4311yescharacteristic, complemented
406C2×#106—431no—
407C2×#106—431no—
408#407—864no—
409C2×C22⋊C8—431no—
410C2×C22⋊C8—431no—
411C2×C22⋊C8—431no—
412C2×C22⋊C8C2×D4311yescharacteristic
413#381—861no—
414#380—431no—
415#380—431no—
416#380—431no—
417#380—431no—
418#380—431no—
419#380—431no—
420#380—861no—
421#380—861no—
422#380C2×D4311yescharacteristic
423#380C2×D4311yescharacteristic
424#379—861no—
425C4×C22⋊C4—861no—
426C4×C22⋊C4—861no—
427C2×#95—861no—
428#340—431no—
429#340—431no—
430#340—431no—
431#340—431no—
432#340—431no—
433#340—431no—
434#340—431no—
435#340—431no—
436#340—431no—
437#340C2×D4311yescharacteristic, complemented
438#340C2×D4311yescharacteristic, complemented
439#340C2×D4311yescharacteristic, complemented
440C43#2364211yescharacteristic, complemented, Sylow
441C25—431no—
442C23×C4—431no—
443C23×C4—431no—
444C23×C4—431no—
445C23×C4—431no—
446C23×C4—431no—
447C23×C4—862no—
448C23×C4—862no—
449C23×C4—862no—
450C23×C4—862no—
451C23×C4—862no—
452C23×C4—862no—
453C23×C4—861no—
454C23×C4—861no—
455C23×C4C22×D4311yescharacteristic
456C2×M16—434no—
457C2×M16—862no—
458C2×M16—862no—
459C2×M16—862no—
460C2×M16—862no—
461C2×M16—862no—
462C22×C8—431no—
463C22×C8—431no—
464C22×C8C22×D4311yescharacteristic
465C22×C8C22×D4311yescharacteristic
466#117—862no—
467#117—862no—
468#117—862no—
469#117—862no—
470C2×C4⋊C4—431no—
471C2×C4⋊C4—431no—
472C2×C4⋊C4—431no—
473C2×C4⋊C4—431no—
474C2×C4⋊C4—862no—
475C2×C4⋊C4—862no—
476C2×C4⋊C4—862no—
477C2×C4⋊C4—862no—
478C2×C4⋊C4—861no—
479C2×C4⋊C4—861no—
480C2×C4⋊C4C22×D4311yescharacteristic
481C2×C4⋊C4C22×D4311yescharacteristic
482C2×C4⋊C4C22×D4311yescharacteristic
483C2×C4⋊C4C22×D4311yescharacteristic
484C2×C22⋊C4—21no—
485C2×C22⋊C4—21no—
486C2×C22⋊C4—861no—
487C2×C22⋊C4—861no—
488C2×C22⋊C4—861no—
489C2×C22⋊C4—861no—
490C2×C22⋊C4—861no—
491C2×C22⋊C4—861no—
492C2×C22⋊C4—861no—
493C2×C22⋊C4—861no—
494C2×C22⋊C4—1724no—
495C2×C42—861no—
496C2×C42—861no—
497#107—22no—
498#107—862no—
499#106—862no—
500#106—862no—
501C22⋊C8—22no—
502C22⋊C8—862no—
503C22⋊C8—862no—
504C22⋊C8—862no—
505#95—21no—
506#95—21no—
507#95—861no—
508#95—861no—
509#95—861no—
510#95—861no—
511#95—861no—
512#95—861no—
513C24—431no—
514C24—431no—
515C24—862no—
516C24—862no—
517C24—862no—
518C24—862no—
519C24—862no—
520C24—1721no—
521C24—1721no—
522C24D4×D4311yescharacteristic
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—431no—
534C22×C4—432no—
535C22×C4—432no—
536C22×C4—432no—
537C22×C4—432no—
538C22×C4—432no—
539C22×C4—432no—
540C22×C4—431no—
541C22×C4—862no—
542C22×C4—862no—
543C22×C4—862no—
544C22×C4—862no—
545C22×C4—862no—
546C22×C4—862no—
547C22×C4—862no—
548C22×C4—862no—
549C22×C4—862no—
550C22×C4—861no—
551C22×C4—861no—
552C22×C4—861no—
553C22×C4—861no—
554C22×C4—861no—
555C22×C4—861no—
556C22×C4—861no—
557C22×C4—861no—
558C22×C4—861no—
559C22×C4—861no—
560C22×C4—1724no—
561C22×C4—1724no—
562C22×C4—1724no—
563C22×C4—1724no—
564C22×C4—1722no—
565C22×C4—1722no—
566C22×C4—1722no—
567C22×C4—1722no—
568C22×C4—1722no—
569C22×C4—1722no—
570C22×C4D4×D4311yescharacteristic
571C22×C4C23×D4311yescharacteristic
572M16—868no—
573M16—1724no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—432no—
580C2×C8—861no—
581C2×C8—861no—
582C2×C8—861no—
583C2×C8—861no—
584C2×C8—861no—
585C2×C8D4×D4312yes—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—861no—
595C4⋊C4—861no—
596C4⋊C4—861no—
597C4⋊C4—861no—
598C4⋊C4—861no—
599C4⋊C4—861no—
600C4⋊C4—861no—
601C4⋊C4—861no—
602C4⋊C4—1722no—
603C4⋊C4—1722no—
604C22⋊C4—42no—
605C22⋊C4—42no—
606C22⋊C4—1722no—
607C22⋊C4—1722no—
608C22⋊C4—1722no—
609C22⋊C4—1722no—
610C22⋊C4—1722no—
611C22⋊C4—1722no—
612C22⋊C4—1722no—
613C22⋊C4—1722no—
614C42—1722no—
615C42—1722no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—432no—
623C23—432no—
624C23—432no—
625C23—432no—
626C23—868no—
627C23—861no—
628C23—861no—
629C23—861no—
630C23—861no—
631C23—861no—
632C23—861no—
633C23—861no—
634C23—861no—
635C23—861no—
636C23—861no—
637C23—1724no—
638C23—1724no—
639C23—1724no—
640C23—1724no—
641C23—1724no—
642C23—1724no—
643C23#1306335712yes—
644C23C2×D4×D4311yescharacteristic
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—432no—
665C2×C4—432no—
666C2×C4—432no—
667C2×C4—434no—
668C2×C4—434no—
669C2×C4—434no—
670C2×C4—434no—
671C2×C4—861no—
672C2×C4—861no—
673C2×C4—861no—
674C2×C4—3444no—
675C2×C4—3444no—
676C2×C4—1724no—
677C2×C4—1724no—
678C2×C4—1724no—
679C2×C4—1721no—
680C2×C4—1721no—
681C2×C4—1721no—
682C2×C4—1721no—
683C2×C4—1721no—
684C2×C4—1721no—
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×C4#41×D4311yescharacteristic
697C2×C4#41×D4311yescharacteristic
698C2×C4#41×D4311yescharacteristic
699C2×C4#41×D4311yescharacteristic
700C2×C4#41×D4311yescharacteristic
701C8—22no—
702C8—41no—
703C8—862no—
704C8—1721no—
705C22—22no—
706C22—22no—
707C22—22no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—41no—
712C22—434no—
713C22—862no—
714C22—862no—
715C22—862no—
716C22—862no—
717C22—862no—
718C22—862no—
719C22—862no—
720C22—862no—
721C22—862no—
722C22—17216no—
723C22—1721no—
724C22—1721no—
725C22—1721no—
726C22—1721no—
727C22#121×D4311yescharacteristic
728C22#123×D4311yescharacteristic
729C22#123×D4311yescharacteristic
730C22AGL(1,ℤ/8)×D4311yescharacteristic
731C22C2×#1306335711yescharacteristic
732C22#1458369511yescharacteristic
733C22#1458369611yescharacteristic
734C4—41no—
735C4—81no—
736C4—81no—
737C4—81no—
738C4—81no—
739C4—434no—
740C4—3441no—
741C4—3441no—
742C4—3441no—
743C4—3441no—
744C4—1721no—
745C4#123×D4311yescharacteristic
746C4#124×D4311yescharacteristic
747C4#126×D4311yescharacteristic
748C4#126×D4311yescharacteristic
749C2—42no—
750C2—864no—
751C2—1722no—
752C2#397×D4311yescharacteristic
753C2#1914421311yescharacteristic
754C2#1914422211yescharacteristic
755C2#1914452211yescharacteristic
756C2#1914452311yescharacteristic
757C2#1914453411yescharacteristic
758C2#1914454011yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2076C2
socleC23×C43C22×D4
prime radicalC24×D43D4
hypercenter#2076D43
hypocenterC43#23642
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2076

Complements

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

NH ≅ G/Ntype
1. C2×#14582940C2semidirect
5. #19136033C2semidirect
6. #19136032C2semidirect
7. #19136030C2semidirect
8. #19136028C2semidirect
9. #19136026C2semidirect
10. #19136022C2semidirect
11. #19136019C2semidirect
12. #19134313C2semidirect
13. #19134313C2semidirect
14. #19134313C2semidirect
15. C43×#2076C2semidirect
25. C2×#13063258C22semidirect
26. C2×#13063257C22semidirect
27. C2×#13063256C22semidirect
45. #14582662C22semidirect
46. #14582662C22semidirect
47. #14582662C22semidirect
48. #14582661C22semidirect
49. #14582661C22semidirect
50. #14582661C22semidirect
51. #14582661C22semidirect
52. #14582661C22semidirect
53. #14582661C22semidirect
54. C2×#107×C43C22semidirect
58. C43×#340C22semidirect
59. C43×#340C22semidirect
60. C43×#340C22semidirect
379. #2076D43semidirect
405. C2×#107C2×D43semidirect
437. #340C2×D43semidirect
438. #340C2×D43semidirect
439. #340C2×D43semidirect
440. C43#23642semidirect

Maximal subgroups

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

subgroupindex
C2×#145829402
C2×#145828612
#191369772
#380×D432
#191360332
#191360322
#191360302
#191360282
#191360262
#191360222
#191360192
#191343132
C43×#20762
#2364243