Finite Group Databasebeta

← #25147284

Subgroups — #25147284

Order 11008.

980 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583291C211yesmaximal, characteristic
2C2×#14583121C211yesmaximal, characteristic
3C2×#14583106C211yesmaximal, characteristic, complemented
4C2×#14583101C211yesmaximal, characteristic
5#19137664C211yesmaximal, characteristic
6#19135917C211yesmaximal, characteristic, complemented
7#19135910C211yesmaximal, characteristic
8#19135695C211yesmaximal, characteristic, complemented
9#19135678C211yesmaximal, characteristic
10#19135519C211yesmaximal, characteristic, complemented
11#19135319C211yesmaximal, characteristic, complemented
12#19134939C211yesmaximal, characteristic, complemented
13#19134932C211yesmaximal, characteristic
14#19134425C211yesmaximal, characteristic, complemented
15C43×#2546C211yesmaximal, characteristic, complemented
16C22×#10621885C2211yescharacteristic
17C22×#10621885C2211yescharacteristic
18C22×#10621885C2211yescharacteristic
19C22×#10621884C2211yescharacteristic
20C22×#10621884C2211yescharacteristic
21C22×#10621884C2211yescharacteristic
22C2×#13063313C2211yescharacteristic
23C2×C4×Dic86C2211yescharacteristic
24C2×C4×D172C2211yescharacteristic
25#14583291—24no—
26#14583121—24no—
27#14583106—24no—
28#14583101—24no—
29C2×C4⋊(C43⋊C8)C2211yescharacteristic
30C2×C4⋊(C43⋊C8)C2211yescharacteristic
31C2×C4⋊(C43⋊C8)C2211yescharacteristic
32C2×#13063249C2211yescharacteristic
33C2×#13063249C2211yescharacteristic
34C2×#13063249C2211yescharacteristic
35C2×#13063249C2211yescharacteristic
36C2×#13063249C2211yescharacteristic
37C2×#13063249C2211yescharacteristic
38C2×#13063248C2211yescharacteristic
39C2×#13063245C2211yescharacteristic
40C2×#13063236C2211yescharacteristic
41#14582805C2211yescharacteristic
42#14582801C2211yescharacteristic
43#14582789—21no—
44#14582788—21no—
45#14582770—21no—
46C4×C4⋊Dic43C2211yescharacteristic
47#14582746—21no—
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582654C2211yescharacteristic
51#14582654C2211yescharacteristic
52C2×C4⋊Q8×C43C2211yescharacteristic
53C2×C4⋊Q8×C43C2211yescharacteristic
54C2×C4⋊Q8×C43C2211yescharacteristic
55C2×C4×Q8×C43C2211yescharacteristic
56C43×#398—21no—
57C43×#398—21no—
58C43×#391C2211yescharacteristic
59C43×#391C2211yescharacteristic
60C43×#389—21no—
61C43×#389—21no—
62C4×C4⋊C4×C43C2211yescharacteristic
63C22×Dic86C2311yescharacteristic
64C22×D172C2311yescharacteristic
65C22×C4×D43—21no—
66C2×#10621885—22no—
67C2×#10621885—22no—
68C2×#10621885—22no—
69C2×#10621885—22no—
70C2×#10621885—22no—
71C2×#10621885—22no—
72C2×#10621885—41no—
73C2×#10621885—41no—
74C2×#10621885—41no—
75C2×#10621884—22no—
76C2×#10621884—22no—
77C2×#10621884—22no—
78C2×#10621884—22no—
79C2×#10621884—22no—
80C2×#10621884—22no—
81C2×#10621884—41no—
82C2×#10621884—41no—
83C2×#10621884—41no—
84C22×C43⋊C8C2311yescharacteristic
85C22×C43⋊C8C2311yescharacteristic
86C22×C43⋊C8C2311yescharacteristic
87C22×C43⋊C8C2311yescharacteristic
88#13063313—22no—
89#13063313D414yes—
90C4×Dic86—22no—
91C4×Dic86—41no—
92C4×D172—22no—
93C4×D172—41no—
94C2×C4⋊Dic43C2311yescharacteristic
95C2×C4⋊Dic43C2311yescharacteristic
96C2×Dic43⋊C4—21no—
97C2×(C2×D43)⋊C4—21no—
98C2×(C2×D43)⋊C4—21no—
99C2×(C2×D43)⋊C4—21no—
100C2×(C2×D43)⋊C4—21no—
101C2×(C2×D43)⋊C4—21no—
102C2×C4×Dic43—21no—
103C2×C4×Dic43—21no—
104C4⋊(C43⋊C8)—22no—
105C4⋊(C43⋊C8)—22no—
106C4⋊(C43⋊C8)—22no—
107#13063249—22no—
108#13063249—22no—
109#13063249—22no—
110#13063249—41no—
111#13063249—41no—
112#13063249D414yes—
113#13063248—22no—
114#13063245—22no—
115#13063236—22no—
116C43⋊#95—21no—
117C43⋊#95—21no—
118C43⋊#95—21no—
119C22×Q8×C43C2311yescharacteristic
120C22×Q8×C43C2311yescharacteristic
121C22×Q8×C43C2311yescharacteristic
122C4⋊Q8×C43—22no—
123C4⋊Q8×C43—22no—
124C4⋊Q8×C43—22no—
125C4⋊Q8×C43—22no—
126C4⋊Q8×C43—41no—
127C4⋊Q8×C43—41no—
128C4×Q8×C43—22no—
129C4×Q8×C43—22no—
130C2×C4⋊C4×C43—21no—
131C2×C4⋊C4×C43—21no—
132C2×C4⋊C4×C43—21no—
133C2×C4⋊C4×C43—21no—
134C2×C4⋊C4×C43—21no—
135C2×C4⋊C4×C43—21no—
136C2×C4⋊C4×C43—21no—
137C2×C4⋊C4×C43D411yescharacteristic
138C2×C4⋊C4×C43D411yescharacteristic
139C2×C4⋊C4×C43C2311yescharacteristic
140C2×C42×C43—21no—
141C2×C42×C43C2311yescharacteristic
142C2×C42×C43C2311yescharacteristic
143C2×C42×C43C2311yescharacteristic
144#95×C43—21no—
145#95×C43—21no—
146#95×C43—21no—
147#95×C43—21no—
148#95×C43D411yescharacteristic
149#95×C43D411yescharacteristic
150C23×D43—21no—
151C2×Q8×C43—21no—
152C2×Q8×C43—21no—
153C2×Q8×C43—21no—
154C2×Q8×C43—21no—
155C2×Q8×C43—21no—
156C2×Q8×C43—21no—
157C2×Q8×C43—21no—
158C2×Q8×C43—21no—
159C2×Q8×C43—21no—
160C2×Q8×C43—21no—
161C2×Q8×C43—21no—
162C2×Q8×C43—21no—
163C2×Q8×C43—21no—
164C2×Q8×C43—21no—
165C2×Q8×C43—21no—
166C2×Q8×C43—21no—
167C2×Q8×C43—21no—
168C2×Q8×C43C2×D412yes—
169C22×C4×C43—21no—
170C22×C4×C43—21no—
171C22×C4×C43—21no—
172C22×C4×C43—21no—
173C22×C4×C43C2×D411yescharacteristic
174C22×C4×C43C2×D411yescharacteristic
175C22×C4×C43C2×D411yescharacteristic
176C22×C4×C43C2×D411yescharacteristic
177C22×C4×C43C2×D411yescharacteristic
178C22×C4×C43C2×D411yescharacteristic
179C22×C4×C43C2411yescharacteristic
180C22×Dic43—21no—
181C22×Dic43—21no—
182C22×Dic43—21no—
183C2×D172—21no—
184C2×D172—21no—
185C2×D172—21no—
186C2×D172—21no—
187C2×D172—21no—
188C2×D172C2×D412yes—
189C2×C4×D43—42no—
190C2×C4×D43—42no—
191C2×C4×D43—81no—
192C2×Dic86—21no—
193C2×Dic86—21no—
194C2×Dic86—21no—
195C2×Dic86—21no—
196C2×Dic86—21no—
197C2×Dic86C2×D412yes—
198C4⋊C4×C43—22no—
199C4⋊C4×C43—22no—
200C4⋊C4×C43—21no—
201C4⋊C4×C43—21no—
202C4⋊C4×C43—42no—
203C4⋊C4×C43—42no—
204C4⋊C4×C43—42no—
205C4⋊C4×C43—42no—
206C4⋊C4×C43—42no—
207C4⋊C4×C43—42no—
208C4⋊C4×C43—42no—
209C42×C43—21no—
210C42×C43—21no—
211C42×C43—21no—
212C42×C43—21no—
213C42×C43—42no—
214C42×C43C2×D412yes—
215C42×C43#4112yes—
216#10621885—44no—
217#10621885—44no—
218#10621885—44no—
219#10621884—44no—
220#10621884—44no—
221#10621884—44no—
222(C2×D43)⋊C4—24no—
223(C2×D43)⋊C4—24no—
224(C2×D43)⋊C4—42no—
225(C2×D43)⋊C4—42no—
226(C2×D43)⋊C4—81no—
227C4⋊Dic43—21no—
228C4⋊Dic43—21no—
229C4⋊Dic43—21no—
230C4⋊Dic43C2×D412yes—
231Dic43⋊C4—42no—
232C4×Dic43—42no—
233C4×Dic43—81no—
234C2×C43⋊C8—21no—
235C2×C43⋊C8—21no—
236C2×C43⋊C8—21no—
237C2×C43⋊C8—21no—
238C2×C43⋊C8—21no—
239C2×C43⋊C8—21no—
240C2×C43⋊C8—21no—
241C2×C43⋊C8—21no—
242C2×C43⋊C8—21no—
243C2×C43⋊C8—21no—
244C2×C43⋊C8C2×D412yes—
245C2×C43⋊C8#4112yes—
246C23×C43C22×D411yescharacteristic
247C22×D43—22no—
248C22×D43—41no—
249C22×D43—41no—
250C22×D43—41no—
251C22×D43—41no—
252C22×D43—41no—
253C22×D43—41no—
254Q8×C43—22no—
255Q8×C43—22no—
256Q8×C43—41no—
257Q8×C43—41no—
258Q8×C43—41no—
259Q8×C43—41no—
260Q8×C43—41no—
261Q8×C43—41no—
262Q8×C43—41no—
263Q8×C43—41no—
264Q8×C43—41no—
265Q8×C43—41no—
266C2×C4×C43—21no—
267C2×C4×C43—21no—
268C2×C4×C43—21no—
269C2×C4×C43—21no—
270C2×C4×C43—21no—
271C2×C4×C43—21no—
272C2×C4×C43—21no—
273C2×C4×C43—21no—
274C2×C4×C43—21no—
275C2×C4×C43—21no—
276C2×C4×C43—22no—
277C2×C4×C43—21no—
278C2×C4×C43—21no—
279C2×C4×C43—21no—
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×C43—41no—
292C2×C4×C43#12112yes—
293C2×C4×C43#12112yes—
294C2×C4×C43#13712yes—
295C2×C4×C43#13712yes—
296C2×C4×C43C22×D411yescharacteristic
297C2×C4×C43C22×D411yescharacteristic
298C2×C4×C43C2×#4111yescharacteristic
299C2×C4×C43C2×#4111yescharacteristic
300C2×C4×C43H(5,𝔽2)11yescharacteristic
301C2×C4×C43H(5,𝔽2)11yescharacteristic
302C2×Dic43—22no—
303C2×Dic43—22no—
304C2×Dic43—41no—
305C2×Dic43—41no—
306C2×Dic43—41no—
307C2×Dic43—41no—
308C2×Dic43—41no—
309C2×Dic43—41no—
310C2×Dic43—41no—
311D172—22no—
312D172—22no—
313D172—41no—
314D172—41no—
315C4×D43—84no—
316Dic86—22no—
317Dic86—22no—
318Dic86—41no—
319Dic86—41no—
320C43⋊C8—22no—
321C43⋊C8—22no—
322C43⋊C8—41no—
323C43⋊C8—41no—
324#25382—431nomaximal, Sylow
325C22×C43C2×#12111yescharacteristic
326C22×C43D4211yescharacteristic
327C22×C43#55011yescharacteristic
328C22×C43C2×#13711yescharacteristic
329C22×C43C2×#13711yescharacteristic
330C22×C43#57711yescharacteristic
331C22×C43#57811yescharacteristic
332C2×D43—42no—
333C2×D43—42no—
334C2×D43—42no—
335C2×D43—81no—
336C2×D43—81no—
337C2×D43—81no—
338C2×D43—81no—
339C4×C43—22no—
340C4×C43—22no—
341C4×C43—22no—
342C4×C43—22no—
343C4×C43—42no—
344C4×C43—41no—
345C4×C43—41no—
346C4×C43—81no—
347C4×C43—81no—
348C4×C43—81no—
349C4×C43#53211yescharacteristic
350C4×C43#54011yescharacteristic
351C4×C43D4211yescharacteristic
352C4×C43#54611yescharacteristic
353Dic43—42no—
354Dic43—42no—
355Dic43—81no—
356C2×#497—431no—
357C2×#464—431no—
358C2×#462—431no—
359C2×#461—431no—
360#2546D4311yescharacteristic, complemented
361#2367—431no—
362#2056—431no—
363#2055—431no—
364#2016—431no—
365#2013—431no—
366#1981—431no—
367#1940—431no—
368#1878—431no—
369#1877—431no—
370#1763—431no—
371C2×C43#242811yescharacteristic
372C2×C43#303911yescharacteristic
373C2×C43#304611yescharacteristic
374C2×C43#326611yescharacteristic
375C2×C43#327011yescharacteristic
376C2×C43#339811yescharacteristic
377C2×C43#340011yescharacteristic
378D43—82no—
379C22×Q16—431no—
380C22×Q16—431no—
381C22×Q16—431no—
382C22×SD16—431no—
383C22×SD16—431no—
384C22×SD16—431no—
385C2×C4⋊Q8C2×D4311yescharacteristic
386C2×C4⋊Q8C2×D4311yescharacteristic
387C2×C4⋊Q8C2×D4311yescharacteristic
388C2×#124—431no—
389C2×C4×Q8—431no—
390C2×C4×Q8C2×D4311yescharacteristic
391C2×C4×D4—431no—
392#497—864no—
393#464—864no—
394#462—864no—
395#461—864no—
396C2×C4⋊C8—431no—
397C2×C4⋊C8—431no—
398C2×C4⋊C8—431no—
399C2×#103—431no—
400C2×#103—431no—
401C2×#103—431no—
402C2×#103—431no—
403C2×#103—431no—
404C2×#103—431no—
405C2×#103—431no—
406C2×#102—431no—
407C2×#97—431no—
408#398—21no—
409#398—21no—
410#391—431no—
411#391C2×D4311yescharacteristic
412#391C2×D4311yescharacteristic
413#390—431no—
414#389—21no—
415#389—21no—
416#388—861no—
417#388—861no—
418#385—861no—
419C4×C4⋊C4—431no—
420C4×C4⋊C4C2×D4311yescharacteristic
421C4×C22⋊C4—861no—
422#340—431no—
423#340—431no—
424#336—431no—
425#336—431no—
426C43#2538211yescharacteristic, complemented, Sylow
427C22×Q8—431no—
428C22×Q8C22×D4311yescharacteristic
429C22×Q8C22×D4311yescharacteristic
430C22×Q8C22×D4311yescharacteristic
431C22×D4—431no—
432C23×C4—861no—
433C2×Q16—862no—
434C2×Q16—862no—
435C2×Q16—862no—
436C2×Q16—862no—
437C2×Q16—862no—
438C2×Q16—862no—
439C2×Q16—1721no—
440C2×Q16—1721no—
441C2×Q16—1721no—
442C2×SD16—862no—
443C2×SD16—862no—
444C2×SD16—862no—
445C2×SD16—862no—
446C2×SD16—862no—
447C2×SD16—862no—
448C2×SD16—1721no—
449C2×SD16—1721no—
450C2×SD16—1721no—
451C22×C8—431no—
452C22×C8—431no—
453C22×C8—431no—
454C22×C8—431no—
455C4⋊Q8—22no—
456C4⋊Q8—22no—
457C4⋊Q8—22no—
458C4⋊Q8—22no—
459C4⋊Q8—41no—
460C4⋊Q8—41no—
461#124—434no—
462#124—862no—
463C4×Q8—22no—
464C4×Q8—22no—
465C4×Q8—862no—
466C4×Q8—1721no—
467C4×D4—862no—
468C4×D4—1721no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4—21no—
471C2×C4⋊C4—21no—
472C2×C4⋊C4—21no—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—21no—
475C2×C4⋊C4—21no—
476C2×C4⋊C4—431no—
477C2×C4⋊C4—431no—
478C2×C4⋊C4—861no—
479C2×C4⋊C4C22⋊D4311yescharacteristic
480C2×C4⋊C4C22⋊D4311yescharacteristic
481C2×C4⋊C4C22×D4311yescharacteristic
482C2×C22⋊C4—861no—
483C2×C22⋊C4—861no—
484C2×C22⋊C4—861no—
485C2×C22⋊C4—861no—
486C2×C22⋊C4—861no—
487C2×C42—21no—
488C2×C42—861no—
489C2×C42—861no—
490C2×C42C22×D4311yescharacteristic
491C2×C42C22×D4311yescharacteristic
492C2×C42C22×D4311yescharacteristic
493C4⋊C8—862no—
494C4⋊C8—862no—
495C4⋊C8—862no—
496#103—434no—
497#103—862no—
498#103—862no—
499#103—862no—
500#103—862no—
501#103—1721no—
502#103—1721no—
503#102—862no—
504#97—862no—
505#95—21no—
506#95—21no—
507#95—21no—
508#95—21no—
509#95—861no—
510#95—861no—
511#95—861no—
512#95C22⋊D4311yescharacteristic
513#95C22⋊D4311yescharacteristic
514C24—861no—
515C2×Q8—21no—
516C2×Q8—21no—
517C2×Q8—21no—
518C2×Q8—21no—
519C2×Q8—21no—
520C2×Q8—21no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—432no—
533C2×Q8—861no—
534C2×Q8—861no—
535C2×Q8—861no—
536C2×Q8—861no—
537C2×Q8—861no—
538C2×Q8D4×D4312yes—
539C2×D4—432no—
540C2×D4—861no—
541C2×D4—861no—
542C2×D4—861no—
543C2×D4—861no—
544C2×D4—861no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—861no—
550C22×C4—861no—
551C22×C4—861no—
552C22×C4—3441no—
553C22×C4—1722no—
554C22×C4—1722no—
555C22×C4C2×C22⋊D4311yescharacteristic
556C22×C4C2×C22⋊D4311yescharacteristic
557C22×C4C2×C22⋊D4311yescharacteristic
558C22×C4C2×C22⋊D4311yescharacteristic
559C22×C4C2×C22⋊D4311yescharacteristic
560C22×C4C2×C22⋊D4311yescharacteristic
561C22×C4C23×D4311yescharacteristic
562Q16—1724no—
563Q16—1724no—
564Q16—1724no—
565SD16—1724no—
566SD16—1724no—
567SD16—1724no—
568C2×C8—432no—
569C2×C8—432no—
570C2×C8—861no—
571C2×C8—861no—
572C2×C8—861no—
573C2×C8—861no—
574C2×C8—861no—
575C2×C8—861no—
576C2×C8—861no—
577C2×C8—861no—
578C2×C8—861no—
579C2×C8—861no—
580C4⋊C4—22no—
581C4⋊C4—22no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—42no—
585C4⋊C4—42no—
586C4⋊C4—42no—
587C4⋊C4—42no—
588C4⋊C4—42no—
589C4⋊C4—42no—
590C4⋊C4—42no—
591C4⋊C4—432no—
592C4⋊C4—861no—
593C4⋊C4—861no—
594C4⋊C4—861no—
595C4⋊C4—1722no—
596C22⋊C4—864no—
597C22⋊C4—864no—
598C22⋊C4—3441no—
599C22⋊C4—1722no—
600C22⋊C4—1722no—
601C42—21no—
602C42—21no—
603C42—21no—
604C42—21no—
605C42—42no—
606C42—3441no—
607C42—1722no—
608C42D4×D4312yes—
609C42#1062190012yes—
610C23—862no—
611C23—1721no—
612C23—1721no—
613C23—1721no—
614C23—1721no—
615C23—1721no—
616C23—1721no—
617C23C22×C22⋊D4311yescharacteristic
618Q8—22no—
619Q8—22no—
620Q8—41no—
621Q8—41no—
622Q8—41no—
623Q8—41no—
624Q8—41no—
625Q8—41no—
626Q8—41no—
627Q8—41no—
628Q8—41no—
629Q8—41no—
630Q8—862no—
631Q8—862no—
632Q8—1721no—
633Q8—1721no—
634D4—862no—
635D4—862no—
636D4—1721no—
637D4—1721no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—22no—
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—862no—
665C2×C4—862no—
666C2×C4—3444no—
667C2×C4—1721no—
668C2×C4—1721no—
669C2×C4—1721no—
670C2×C4—1721no—
671C2×C4—1721no—
672C2×C4—1721no—
673C2×C4—1721no—
674C2×C4#1306329612yes—
675C2×C4#1306329612yes—
676C2×C4#1306335612yes—
677C2×C4#1306335612yes—
678C2×C4C2×D4×D4311yescharacteristic
679C2×C4C2×D4×D4311yescharacteristic
680C2×C4#41×D4311yescharacteristic
681C2×C4C2×#1062190011yescharacteristic
682C2×C4#1306337011yescharacteristic
683C2×C4#1306337111yescharacteristic
684C8—862no—
685C8—862no—
686C8—1721no—
687C8—1721no—
688C22—3441no—
689C22—3441no—
690C22—3441no—
691C22—3441no—
692C22—1722no—
693C22—1722no—
694C22—1722no—
695C22C2×#1306329611yescharacteristic
696C22D4×C22⋊D4311yescharacteristic
697C22#1458356811yescharacteristic
698C22C2×#1306335611yescharacteristic
699C22C2×#1306335611yescharacteristic
700C22#1458370711yescharacteristic
701C22#1458371411yescharacteristic
702C4—22no—
703C4—22no—
704C4—22no—
705C4—22no—
706C4—41no—
707C4—42no—
708C4—41no—
709C4—81no—
710C4—81no—
711C4—81no—
712C4—3441no—
713C4—1722no—
714C4—1722no—
715C4#1458344411yescharacteristic
716C4#1458350211yescharacteristic
717C4#1458353311yescharacteristic
718C4#1458354611yescharacteristic
719C2—3442no—
720C2#1913817911yescharacteristic
721C2#1914407811yescharacteristic
722C2#1914414111yescharacteristic
723C2#1914610611yescharacteristic
724C2#1914616611yescharacteristic
725C2#1914762211yescharacteristic
726C2#1914764411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2546C2
socleC23×C43C22×D4
prime radicalC22×D172C23
hypercenter#2546D43
hypocenterC43#25382
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2546

Complements

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

NH ≅ G/Ntype
3. C2×#14583106C2semidirect
6. #19135917C2semidirect
8. #19135695C2semidirect
10. #19135519C2semidirect
11. #19135319C2semidirect
12. #19134939C2semidirect
14. #19134425C2semidirect
15. C43×#2546C2semidirect
360. #2546D43semidirect
426. C43#25382semidirect

Maximal subgroups

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

subgroupindex
C2×#145832912
C2×#145831212
C2×#145831062
C2×#145831012
#191376642
#191359172
#191359102
#191356952
#191356782
#191355192
#191353192
#191349392
#191349322
#191344252
C43×#25462
#2538243