Finite Group Databasebeta

← C23×#24056 #19171682

Subgroups — C23×#24056 #19171682

Order 5888.

1820 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#3484C211yesmaximal, characteristic
2C23×#2849C212yesmaximal, complemented
3C2×C23×#386C211yesmaximal, characteristic, complemented
4C23×#2044C214yesmaximal, complemented
5C23×#1898C212yesmaximal, complemented
6C23×#1867C212yesmaximal, complemented
7C23×#1790C212yesmaximal, complemented
8C23×#1781C211yesmaximal, characteristic, complemented
9C2×C23×H(5,𝔽2)C2211yescharacteristic
10C23×D4×C23C2211yescharacteristic
11C24×C4×C23C2211yescharacteristic, complemented
12C23×#546—22no—
13C23×#546—22no—
14D42×C23—22no—
15D42×C23—22no—
16C23×#535—21no—
17C23×#534—21no—
18C23×#534C2212yes—
19C23×#525—21no—
20C2×C23×#123—22no—
21C2×C23×#120—21no—
22C2×C23×#120C2212yes—
23C23×#518C2211yescharacteristic
24C22×C22⋊C4×C23—21no—
25C22×C22⋊C4×C23C2211yescharacteristic, complemented
26C2×C23×#99C2212yes—
27C2×C23×#99C2214yescomplemented
28C2×C23×#99C2212yescomplemented
29C23×#386—21no—
30C23×#386—21no—
31C23×#386—22no—
32C23×#386C2212yes—
33C23×#386C2212yescomplemented
34C23×#386C2214yescomplemented
35C23×#385—22no—
36C23×#385C2214yescomplemented
37C23×#381—22no—
38C23×#379C2212yescomplemented
39C2×C23×#95—21no—
40C23×#342C2214yescomplemented
41C25×C23D411yescharacteristic
42C25×C23C2311yescharacteristic
43C23×H(5,𝔽2)—24no—
44C23×H(5,𝔽2)—42no—
45C2×#41×C23—21no—
46C2×#41×C23—22no—
47C22×D4×C23—22no—
48C22×D4×C23—22no—
49C22×D4×C23—21no—
50C22×D4×C23—22no—
51C22×D4×C23—21no—
52C22×D4×C23—21no—
53C22×D4×C23—24no—
54C22×D4×C23—42no—
55C22×D4×C23D411yescharacteristic
56C22×D4×C23D411yescharacteristic
57C22×D4×C23D412yes—
58C22×D4×C23D412yes—
59C22×D4×C23C2311yescharacteristic
60C22×D4×C23C2312yes—
61C22×D4×C23C2311yescharacteristic
62C23×C4×C23—21no—
63C23×C4×C23—22no—
64C23×C4×C23—22no—
65C23×C4×C23—21no—
66C23×C4×C23—21no—
67C23×C4×C23—44no—
68C23×C4×C23D411yescharacteristic
69C23×C4×C23C2312yes—
70C23×#127—22no—
71C23×#124—22no—
72C23×#123—22no—
73C23×#123—22no—
74C23×#123—22no—
75C23×#123—48no—
76C23×C22⋊Q8—21no—
77C23×C22⋊Q8—21no—
78C23×#121—21no—
79C23×#121—21no—
80C23×#121—22no—
81C23×#121—22no—
82C23×#121—22no—
83C23×#121—22no—
84C23×#121—22no—
85C23×#121—22no—
86C23×#120—22no—
87C23×#120—22no—
88C23×#120—22no—
89C23×#120—22no—
90C23×#120—22no—
91C23×#120—22no—
92C23×#120—22no—
93C23×#120—22no—
94C23×#120—22no—
95C4×D4×C23—22no—
96C4×D4×C23—22no—
97C4×D4×C23—22no—
98C4×D4×C23—22no—
99C23×#117—21no—
100C2×C4⋊C4×C23—24no—
101C2×C22⋊C4×C23—21no—
102C2×C22⋊C4×C23—21no—
103C2×C22⋊C4×C23—21no—
104C2×C22⋊C4×C23—22no—
105C2×C22⋊C4×C23—22no—
106C2×C22⋊C4×C23—21no—
107C2×C22⋊C4×C23—22no—
108C2×C22⋊C4×C23—22no—
109C2×C22⋊C4×C23—24no—
110C2×C22⋊C4×C23—42no—
111C2×C22⋊C4×C23—44no—
112C2×C22⋊C4×C23D412yes—
113C2×C22⋊C4×C23D412yes—
114C2×C22⋊C4×C23C2312yes—
115C2×C22⋊C4×C23C2314yes—
116C2×C22⋊C4×C23C2312yes—
117C23×#99—24no—
118C23×#99—42no—
119C23×#99—44no—
120C23×#95—22no—
121C23×#95—22no—
122C23×#95—24no—
123C23×#95—24no—
124C24×C23—22no—
125C24×C23—22no—
126C24×C23—21no—
127C24×C23—22no—
128C24×C23—21no—
129C24×C23—21no—
130C24×C23—42no—
131C24×C23—42no—
132C24×C23—41no—
133C24×C23—42no—
134C24×C23—42no—
135C24×C23C2×D411yescharacteristic
136C24×C23C2×D412yes—
137C24×C23C2×D412yes—
138C24×C23C2×D411yescharacteristic
139C24×C23C2×D412yes—
140C24×C23C2×D411yescharacteristic
141C24×C23C2×D411yescharacteristic
142C24×C23C2411yescharacteristic
143#41×C23—48no—
144#41×C23—42no—
145#41×C23—42no—
146C2×Q8×C23—21no—
147C2×D4×C23—22no—
148C2×D4×C23—22no—
149C2×D4×C23—22no—
150C2×D4×C23—21no—
151C2×D4×C23—22no—
152C2×D4×C23—22no—
153C2×D4×C23—22no—
154C2×D4×C23—22no—
155C2×D4×C23—22no—
156C2×D4×C23—22no—
157C2×D4×C23—22no—
158C2×D4×C23—22no—
159C2×D4×C23—22no—
160C2×D4×C23—24no—
161C2×D4×C23—22no—
162C2×D4×C23—24no—
163C2×D4×C23—22no—
164C2×D4×C23—22no—
165C2×D4×C23—22no—
166C2×D4×C23—22no—
167C2×D4×C23—22no—
168C2×D4×C23—41no—
169C2×D4×C23—41no—
170C2×D4×C23—48no—
171C2×D4×C23—48no—
172C2×D4×C23—48no—
173C2×D4×C23—42no—
174C2×D4×C23—42no—
175C2×D4×C23—44no—
176C2×D4×C23—44no—
177C2×D4×C23—82no—
178C2×D4×C23—82no—
179C2×D4×C23#4114yes—
180C22×C4×C23—21no—
181C22×C4×C23—24no—
182C22×C4×C23—22no—
183C22×C4×C23—28no—
184C22×C4×C23—21no—
185C22×C4×C23—21no—
186C22×C4×C23—22no—
187C22×C4×C23—24no—
188C22×C4×C23—21no—
189C22×C4×C23—21no—
190C22×C4×C23—22no—
191C22×C4×C23—24no—
192C22×C4×C23—22no—
193C22×C4×C23—44no—
194C22×C4×C23—41no—
195C22×C4×C23—44no—
196C22×C4×C23—48no—
197C22×C4×C23—42no—
198C22×C4×C23—44no—
199C22×C4×C23—42no—
200C22×C4×C23—41no—
201C22×C4×C23—41no—
202C22×C4×C23—42no—
203C22×C4×C23—42no—
204C22×C4×C23—42no—
205C22×C4×C23C2×D412yes—
206C22×C4×C23C2×D411yescharacteristic
207C22×C4×C23C2×D411yescharacteristic
208C22×C4×C23C2×D412yes—
209C22×C4×C23C2×D412yes—
210C4⋊C4×C23—21no—
211C4⋊C4×C23—21no—
212C4⋊C4×C23—22no—
213C4⋊C4×C23—22no—
214C4⋊C4×C23—48no—
215C22⋊C4×C23—22no—
216C22⋊C4×C23—22no—
217C22⋊C4×C23—22no—
218C22⋊C4×C23—22no—
219C22⋊C4×C23—22no—
220C22⋊C4×C23—22no—
221C22⋊C4×C23—22no—
222C22⋊C4×C23—22no—
223C22⋊C4×C23—22no—
224C22⋊C4×C23—22no—
225C22⋊C4×C23—22no—
226C22⋊C4×C23—24no—
227C22⋊C4×C23—24no—
228C22⋊C4×C23—24no—
229C22⋊C4×C23—44no—
230C22⋊C4×C23—44no—
231C22⋊C4×C23—48no—
232C22⋊C4×C23—44no—
233C22⋊C4×C23—42no—
234C22⋊C4×C23—44no—
235C42×C23—22no—
236#24056C2311yesmaximal, characteristic, direct product factor, Sylow
237C23×C23—21no—
238C23×C23—21no—
239C23×C23—22no—
240C23×C23—22no—
241C23×C23—21no—
242C23×C23—21no—
243C23×C23—21no—
244C23×C23—24no—
245C23×C23—24no—
246C23×C23—24no—
247C23×C23—24no—
248C23×C23—21no—
249C23×C23—21no—
250C23×C23—22no—
251C23×C23—21no—
252C23×C23—21no—
253C23×C23—24no—
254C23×C23—42no—
255C23×C23—41no—
256C23×C23—41no—
257C23×C23—42no—
258C23×C23—41no—
259C23×C23—41no—
260C23×C23—42no—
261C23×C23—42no—
262C23×C23—48no—
263C23×C23—48no—
264C23×C23—41no—
265C23×C23—41no—
266C23×C23—41no—
267C23×C23—41no—
268C23×C23—48no—
269C23×C23—42no—
270C23×C23—42no—
271C23×C23—42no—
272C23×C23—42no—
273C23×C23—42no—
274C23×C23—81no—
275C23×C23—81no—
276C23×C23—84no—
277C23×C23—81no—
278C23×C23—81no—
279C23×C23#12012yes—
280C23×C23#12011yescharacteristic
281C23×C23#12011yescharacteristic
282C23×C23#12312yescomplemented
283C23×C23C22×D411yescharacteristic
284C23×C23C22×D412yes—
285C23×C23C2×#4112yes—
286C23×C23H(5,𝔽2)12yes—
287Q8×C23—42no—
288D4×C23—28no—
289D4×C23—44no—
290D4×C23—42no—
291D4×C23—44no—
292D4×C23—44no—
293D4×C23—42no—
294D4×C23—42no—
295D4×C23—44no—
296D4×C23—44no—
297D4×C23—44no—
298D4×C23—44no—
299D4×C23—82no—
300D4×C23—82no—
301D4×C23—82no—
302D4×C23—82no—
303C2×C4×C23—21no—
304C2×C4×C23—21no—
305C2×C4×C23—24no—
306C2×C4×C23—28no—
307C2×C4×C23—22no—
308C2×C4×C23—22no—
309C2×C4×C23—22no—
310C2×C4×C23—21no—
311C2×C4×C23—21no—
312C2×C4×C23—21no—
313C2×C4×C23—24no—
314C2×C4×C23—42no—
315C2×C4×C23—42no—
316C2×C4×C23—44no—
317C2×C4×C23—44no—
318C2×C4×C23—42no—
319C2×C4×C23—44no—
320C2×C4×C23—48no—
321C2×C4×C23—42no—
322C2×C4×C23—42no—
323C2×C4×C23—44no—
324C2×C4×C23—42no—
325C2×C4×C23—42no—
326C2×C4×C23—44no—
327C2×C4×C23—42no—
328C2×C4×C23—44no—
329C2×C4×C23—42no—
330C2×C4×C23—42no—
331C2×C4×C23—44no—
332C2×C4×C23—81no—
333C2×C4×C23—81no—
334C2×C4×C23—84no—
335C2×C4×C23#12312yescomplemented
336#3484C2×C2311yescharacteristic
337#2849C2×C2312yescomplemented
338C2×#386C2×C2311yescharacteristic, complemented
339#2044C2×C2314yescomplemented
340#1898C2×C2312yescomplemented
341#1867C2×C2312yescomplemented
342#1790C2×C2312yescomplemented
343#1781C2×C2311yescharacteristic, complemented
344C22×C23—24no—
345C22×C23—24no—
346C22×C23—21no—
347C22×C23—21no—
348C22×C23—22no—
349C22×C23—21no—
350C22×C23—21no—
351C22×C23—22no—
352C22×C23—21no—
353C22×C23—21no—
354C22×C23—22no—
355C22×C23—22no—
356C22×C23—22no—
357C22×C23—22no—
358C22×C23—42no—
359C22×C23—42no—
360C22×C23—48no—
361C22×C23—48no—
362C22×C23—42no—
363C22×C23—42no—
364C22×C23—42no—
365C22×C23—42no—
366C22×C23—41no—
367C22×C23—41no—
368C22×C23—42no—
369C22×C23—41no—
370C22×C23—42no—
371C22×C23—41no—
372C22×C23—42no—
373C22×C23—41no—
374C22×C23—81no—
375C22×C23—84no—
376C22×C23—84no—
377C22×C23—84no—
378C22×C23—81no—
379C22×C23—162no—
380C22×C23B(4,𝔽2)12yes—
381C22×C23#45812yes—
382C22×C23C2×#12011yescharacteristic
383C22×C23C2×#12311yescharacteristic
384C22×C23#53411yescharacteristic
385C22×C23#54614yes—
386C4×C23—22no—
387C4×C23—41no—
388C4×C23—42no—
389C4×C23—44no—
390C4×C23—42no—
391C4×C23—42no—
392C4×C23—84no—
393C4×C23—82no—
394C2×H(5,𝔽2)C22×C2311yescharacteristic
395C23×D4C22×C2311yescharacteristic
396C24×C4C22×C2311yescharacteristic, complemented
397#546—22no—
398#546—22no—
399D42—22no—
400D42—22no—
401#535—21no—
402#534—21no—
403#534C22×C2312yes—
404#525—21no—
405C2×#123—22no—
406C2×#120—21no—
407C2×#120C22×C2312yes—
408#518C22×C2311yescharacteristic
409C22×C22⋊C4—21no—
410C22×C22⋊C4C22×C2311yescharacteristic, complemented
411C2×#99C22×C2312yes—
412C2×#99C22×C2314yescomplemented
413C2×#99C22×C2312yescomplemented
414#386—22no—
415#386—21no—
416#386—21no—
417#386C22×C2312yes—
418#386C22×C2314yescomplemented
419#386C22×C2312yescomplemented
420#385—22no—
421#385C22×C2314yescomplemented
422#381—22no—
423#379C22×C2312yescomplemented
424C2×#95—21no—
425#342C22×C2314yescomplemented
426C2×C23—21no—
427C2×C23—24no—
428C2×C23—21no—
429C2×C23—22no—
430C2×C23—22no—
431C2×C23—42no—
432C2×C23—42no—
433C2×C23—81no—
434C2×C23—82no—
435C2×C23#240511yescharacteristic
436C2×C23C2×B(4,𝔽2)11yescharacteristic
437C2×C23C2×#45811yescharacteristic
438C25D4×C2311yescharacteristic
439C25C23×C2311yescharacteristic
440H(5,𝔽2)—24no—
441H(5,𝔽2)—42no—
442C2×#41—21no—
443C2×#41—22no—
444C22×D4—21no—
445C22×D4—22no—
446C22×D4—22no—
447C22×D4—22no—
448C22×D4—21no—
449C22×D4—21no—
450C22×D4—24no—
451C22×D4—42no—
452C22×D4D4×C2311yescharacteristic
453C22×D4D4×C2311yescharacteristic
454C22×D4D4×C2312yes—
455C22×D4D4×C2312yes—
456C22×D4C23×C2312yes—
457C22×D4C23×C2311yescharacteristic
458C22×D4C23×C2311yescharacteristic
459C23×C4—21no—
460C23×C4—22no—
461C23×C4—21no—
462C23×C4—22no—
463C23×C4—21no—
464C23×C4—44no—
465C23×C4D4×C2311yescharacteristic
466C23×C4C23×C2312yes—
467#127—22no—
468#124—22no—
469#123—22no—
470#123—22no—
471#123—22no—
472#123—48no—
473C22⋊Q8—21no—
474C22⋊Q8—21no—
475#121—21no—
476#121—21no—
477#121—22no—
478#121—22no—
479#121—22no—
480#121—22no—
481#121—22no—
482#121—22no—
483#120—22no—
484#120—22no—
485#120—22no—
486#120—22no—
487#120—22no—
488#120—22no—
489#120—22no—
490#120—22no—
491#120—22no—
492C4×D4—22no—
493C4×D4—22no—
494C4×D4—22no—
495C4×D4—22no—
496#117—21no—
497C2×C4⋊C4—24no—
498C2×C22⋊C4—21no—
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—22no—
502C2×C22⋊C4—22no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—22no—
505C2×C22⋊C4—24no—
506C2×C22⋊C4—22no—
507C2×C22⋊C4—42no—
508C2×C22⋊C4—44no—
509C2×C22⋊C4D4×C2312yes—
510C2×C22⋊C4D4×C2312yes—
511C2×C22⋊C4C23×C2312yes—
512C2×C22⋊C4C23×C2314yes—
513C2×C22⋊C4C23×C2312yes—
514#99—24no—
515#99—42no—
516#99—44no—
517#95—22no—
518#95—22no—
519#95—24no—
520#95—24no—
521C23#2405611yescharacteristic, direct product factor, Sylow
522C24—22no—
523C24—22no—
524C24—21no—
525C24—22no—
526C24—21no—
527C24—21no—
528C24—42no—
529C24—42no—
530C24—41no—
531C24—42no—
532C24—42no—
533C24C2×D4×C2311yescharacteristic
534C24C2×D4×C2312yes—
535C24C2×D4×C2312yes—
536C24C2×D4×C2311yescharacteristic
537C24C2×D4×C2312yes—
538C24C2×D4×C2311yescharacteristic
539C24C2×D4×C2311yescharacteristic
540C24C24×C2311yescharacteristic
541#41—48no—
542#41—42no—
543#41—42no—
544C2×Q8—21no—
545C2×D4—22no—
546C2×D4—22no—
547C2×D4—22no—
548C2×D4—21no—
549C2×D4—22no—
550C2×D4—22no—
551C2×D4—22no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—22no—
555C2×D4—22no—
556C2×D4—22no—
557C2×D4—22no—
558C2×D4—24no—
559C2×D4—22no—
560C2×D4—24no—
561C2×D4—22no—
562C2×D4—22no—
563C2×D4—22no—
564C2×D4—22no—
565C2×D4—22no—
566C2×D4—41no—
567C2×D4—41no—
568C2×D4—48no—
569C2×D4—48no—
570C2×D4—48no—
571C2×D4—42no—
572C2×D4—42no—
573C2×D4—44no—
574C2×D4—44no—
575C2×D4—82no—
576C2×D4—82no—
577C2×D4#41×C2314yes—
578C22×C4—21no—
579C22×C4—24no—
580C22×C4—22no—
581C22×C4—28no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—22no—
585C22×C4—24no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—22no—
589C22×C4—24no—
590C22×C4—22no—
591C22×C4—44no—
592C22×C4—41no—
593C22×C4—44no—
594C22×C4—48no—
595C22×C4—42no—
596C22×C4—44no—
597C22×C4—42no—
598C22×C4—41no—
599C22×C4—41no—
600C22×C4—42no—
601C22×C4—42no—
602C22×C4—42no—
603C22×C4C2×D4×C2312yes—
604C22×C4C2×D4×C2311yescharacteristic
605C22×C4C2×D4×C2311yescharacteristic
606C22×C4C2×D4×C2312yes—
607C22×C4C2×D4×C2312yes—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—22no—
611C4⋊C4—22no—
612C4⋊C4—48no—
613C22⋊C4—22no—
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—22no—
617C22⋊C4—22no—
618C22⋊C4—22no—
619C22⋊C4—22no—
620C22⋊C4—22no—
621C22⋊C4—22no—
622C22⋊C4—22no—
623C22⋊C4—22no—
624C22⋊C4—24no—
625C22⋊C4—24no—
626C22⋊C4—24no—
627C22⋊C4—44no—
628C22⋊C4—44no—
629C22⋊C4—48no—
630C22⋊C4—42no—
631C22⋊C4—44no—
632C22⋊C4—44no—
633C42—22no—
634C23—22no—
635C23—22no—
636C23—21no—
637C23—21no—
638C23—24no—
639C23—24no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—24no—
644C23—24no—
645C23—21no—
646C23—21no—
647C23—22no—
648C23—21no—
649C23—21no—
650C23—24no—
651C23—42no—
652C23—41no—
653C23—41no—
654C23—42no—
655C23—41no—
656C23—41no—
657C23—42no—
658C23—42no—
659C23—48no—
660C23—48no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—48no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—81no—
672C23—81no—
673C23—84no—
674C23—81no—
675C23—81no—
676C23C23×#12012yes—
677C23C23×#12011yescharacteristic
678C23C23×#12011yescharacteristic
679C23C23×#12312yescomplemented
680C23C22×D4×C2311yescharacteristic
681C23C22×D4×C2312yes—
682C23C2×#41×C2312yes—
683C23C23×H(5,𝔽2)12yes—
684Q8—42no—
685D4—28no—
686D4—44no—
687D4—42no—
688D4—44no—
689D4—44no—
690D4—44no—
691D4—44no—
692D4—42no—
693D4—42no—
694D4—44no—
695D4—44no—
696D4—82no—
697D4—82no—
698D4—82no—
699D4—82no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—24no—
703C2×C4—28no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—24no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—44no—
714C2×C4—44no—
715C2×C4—42no—
716C2×C4—44no—
717C2×C4—48no—
718C2×C4—42no—
719C2×C4—44no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—44no—
724C2×C4—42no—
725C2×C4—44no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—44no—
729C2×C4—81no—
730C2×C4—81no—
731C2×C4—84no—
732C2×C4C23×#12312yescomplemented
733C22—24no—
734C22—24no—
735C22—21no—
736C22—21no—
737C22—22no—
738C22—21no—
739C22—21no—
740C22—22no—
741C22—21no—
742C22—21no—
743C22—22no—
744C22—22no—
745C22—22no—
746C22—22no—
747C22—42no—
748C22—42no—
749C22—48no—
750C22—48no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—41no—
756C22—41no—
757C22—42no—
758C22—41no—
759C22—42no—
760C22—41no—
761C22—42no—
762C22—41no—
763C22—81no—
764C22—84no—
765C22—84no—
766C22—81no—
767C22—84no—
768C22—162no—
769C22C23×B(4,𝔽2)12yes—
770C22C23×#45812yes—
771C22C2×C23×#12011yescharacteristic
772C22C2×C23×#12311yescharacteristic
773C22C23×#53411yescharacteristic
774C22C23×#54614yes—
775C4—22no—
776C4—41no—
777C4—42no—
778C4—44no—
779C4—42no—
780C4—42no—
781C4—82no—
782C4—84no—
783C2—21no—
784C2—24no—
785C2—21no—
786C2—22no—
787C2—22no—
788C2—42no—
789C2—42no—
790C2—81no—
791C2—82no—
792C2C23×#240511yescharacteristic
793C2C2×C23×B(4,𝔽2)11yescharacteristic
794C2C2×C23×#45811yescharacteristic
subgroupG/H
center, socleC22×C23C2×#120
commutator, Frattini, cosocleC24C24×C23
prime radicalC23×#3484C2
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C23 ◁ C25×C23 ◁ G

Complements

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

NH ≅ G/Ntype
2. C23×#2849C2semidirect
3. C2×C23×#386C2semidirect
4. C23×#2044C2semidirect
5. C23×#1898C2semidirect
6. C23×#1867C2semidirect
7. C23×#1790C2semidirect
8. C23×#1781C2semidirect
11. C24×C4×C23C22semidirect
25. C22×C22⋊C4×C23C22semidirect
27. C2×C23×#99C22semidirect
28. C2×C23×#99C22semidirect
33. C23×#386C22semidirect
34. C23×#386C22semidirect
36. C23×#385C22semidirect
38. C23×#379C22semidirect
40. C23×#342C22semidirect
236. #24056C23direct (N × H)
282. C23×C23#123semidirect
335. C2×C4×C23#123semidirect
337. #2849C2×C23semidirect
338. C2×#386C2×C23semidirect
339. #2044C2×C23semidirect
340. #1898C2×C23semidirect
341. #1867C2×C23semidirect
342. #1790C2×C23semidirect
343. #1781C2×C23semidirect
396. C24×C4C22×C23semidirect
410. C22×C22⋊C4C22×C23semidirect
412. C2×#99C22×C23semidirect
413. C2×#99C22×C23semidirect
418. #386C22×C23semidirect
419. #386C22×C23semidirect
421. #385C22×C23semidirect
423. #379C22×C23semidirect
425. #342C22×C23semidirect
521. C23#24056direct (N × H)
679. C23C23×#123semidirect
732. C2×C4C23×#123semidirect

Maximal subgroups

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

subgroupindex
C23×#34842
C23×#28492
C2×C23×#3862
C23×#20442
C23×#18982
C23×#18672
C23×#17902
C23×#17812
#2405623