Finite Group Databasebeta

← C23×#14842 #19162468

Subgroups — C23×#14842 #19162468

Order 5888.

1794 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C23×#397C211yesmaximal, characteristic, complemented
2C2×C23×#386C211yesmaximal, characteristic
3C2×C23×#380C211yesmaximal, characteristic, complemented
4C2×C4×C22⋊C4×C23C211yesmaximal, characteristic, complemented
5C23×#1445C211yesmaximal, characteristic, complemented
6C23×#1442C211yesmaximal, characteristic, complemented
7C23×#1440C212yesmaximal, complemented
8C23×#1439C211yesmaximal, characteristic, complemented
9C23×#1438C212yesmaximal
10C23×#1437C212yesmaximal, complemented
11C23×#1434C212yesmaximal, complemented
12C23×D4×C23C2211yescharacteristic
13C24×C4×C23C2211yescharacteristic
14C22×C4⋊C4×C23C2211yescharacteristic
15C22×C4⋊C4×C23C2211yescharacteristic
16C22×C22⋊C4×C23C2211yescharacteristic
17C22×C22⋊C4×C23C2212yes—
18C22×C22⋊C4×C23C2211yescharacteristic
19C22×C22⋊C4×C23C2211yescharacteristic
20C22×C22⋊C4×C23C2212yes—
21C22×C22⋊C4×C23C2212yes—
22C22×C22⋊C4×C23C2212yes—
23C22×C42×C23C2212yes—
24C23×#397—24no—
25C23×#386—24no—
26C23×#380—24no—
27C4×C22⋊C4×C23—24no—
28C2×C23×#95C2211yescharacteristic
29C2×C23×#95C2212yes—
30C2×C23×#95C2212yes—
31C2×C23×#95C2212yes—
32C2×C23×#95C2212yes—
33C2×C23×#95C2211yescharacteristic
34C2×C23×#95C2211yescharacteristic
35C2×C23×#95C2212yes—
36C2×C23×#95C2212yes—
37C2×C23×#95C2212yes—
38C2×C23×#95C2211yescharacteristic
39C25×C23C2311yescharacteristic
40C25×C23C2311yescharacteristic
41C22×D4×C23—22no—
42C22×D4×C23—22no—
43C22×D4×C23—24no—
44C22×D4×C23—22no—
45C22×D4×C23—42no—
46C23×C4×C23—22no—
47C23×C4×C23—22no—
48C23×C4×C23—24no—
49C23×C4×C23—42no—
50C23×C4×C23D414yes—
51C23×C4×C23C2311yescharacteristic
52C23×C4×C23C2311yescharacteristic
53C23×C4×C23C2312yes—
54C23×C4×C23C2312yes—
55C23×C4×C23C2312yes—
56C23×C4×C23C2311yescharacteristic
57C23×C4×C23C2312yes—
58C23×C4×C23C2311yescharacteristic
59C23×C4×C23C2311yescharacteristic
60C2×C4⋊C4×C23—22no—
61C2×C4⋊C4×C23—22no—
62C2×C4⋊C4×C23—22no—
63C2×C4⋊C4×C23—22no—
64C2×C4⋊C4×C23—42no—
65C2×C22⋊C4×C23—24no—
66C2×C22⋊C4×C23—24no—
67C2×C22⋊C4×C23—24no—
68C2×C22⋊C4×C23—24no—
69C2×C22⋊C4×C23—22no—
70C2×C22⋊C4×C23—24no—
71C2×C22⋊C4×C23—24no—
72C2×C22⋊C4×C23—22no—
73C2×C22⋊C4×C23—22no—
74C2×C22⋊C4×C23—24no—
75C2×C22⋊C4×C23—22no—
76C2×C22⋊C4×C23—24no—
77C2×C22⋊C4×C23—22no—
78C2×C22⋊C4×C23—24no—
79C2×C22⋊C4×C23—42no—
80C2×C22⋊C4×C23—42no—
81C2×C22⋊C4×C23—42no—
82C2×C22⋊C4×C23—42no—
83C2×C22⋊C4×C23—42no—
84C2×C42×C23—24no—
85C2×C42×C23—24no—
86C2×C42×C23—42no—
87C23×#95—22no—
88C23×#95—24no—
89C23×#95—22no—
90C23×#95—22no—
91C23×#95—24no—
92C23×#95—24no—
93C23×#95—24no—
94C23×#95—42no—
95C23×#95—42no—
96C23×#95—42no—
97C23×#95D414yescomplemented
98C24×C23—21no—
99C24×C23—22no—
100C24×C23—21no—
101C24×C23—22no—
102C24×C23—21no—
103C24×C23—21no—
104C24×C23—21no—
105C24×C23—21no—
106C24×C23—22no—
107C24×C23—21no—
108C24×C23—21no—
109C24×C23—22no—
110C24×C23—22no—
111C24×C23—21no—
112C24×C23—21no—
113C24×C23—22no—
114C24×C23—21no—
115C24×C23—21no—
116C24×C23—22no—
117C24×C23C2×D412yes—
118C24×C23#4112yes—
119C24×C23#4114yes—
120C24×C23C2411yescharacteristic
121C2×D4×C23—28no—
122C2×D4×C23—48no—
123C2×D4×C23—48no—
124C2×D4×C23—44no—
125C2×D4×C23—44no—
126C22×C4×C23—21no—
127C22×C4×C23—21no—
128C22×C4×C23—22no—
129C22×C4×C23—22no—
130C22×C4×C23—22no—
131C22×C4×C23—22no—
132C22×C4×C23—21no—
133C22×C4×C23—22no—
134C22×C4×C23—22no—
135C22×C4×C23—22no—
136C22×C4×C23—22no—
137C22×C4×C23—22no—
138C22×C4×C23—22no—
139C22×C4×C23—21no—
140C22×C4×C23—22no—
141C22×C4×C23—22no—
142C22×C4×C23—22no—
143C22×C4×C23—22no—
144C22×C4×C23—22no—
145C22×C4×C23—22no—
146C22×C4×C23—22no—
147C22×C4×C23—28no—
148C22×C4×C23—28no—
149C22×C4×C23—21no—
150C22×C4×C23—21no—
151C22×C4×C23—22no—
152C22×C4×C23—22no—
153C22×C4×C23—22no—
154C22×C4×C23—21no—
155C22×C4×C23—21no—
156C22×C4×C23—22no—
157C22×C4×C23—22no—
158C22×C4×C23—22no—
159C22×C4×C23—22no—
160C22×C4×C23—22no—
161C22×C4×C23—22no—
162C22×C4×C23—22no—
163C22×C4×C23—22no—
164C22×C4×C23—22no—
165C22×C4×C23—22no—
166C22×C4×C23—22no—
167C22×C4×C23—22no—
168C22×C4×C23—22no—
169C22×C4×C23—22no—
170C22×C4×C23—22no—
171C22×C4×C23—21no—
172C22×C4×C23—21no—
173C22×C4×C23—44no—
174C22×C4×C23—48no—
175C22×C4×C23—48no—
176C22×C4×C23C2×D414yes—
177C22×C4×C23C2×D412yes—
178C22×C4×C23C2×D412yes—
179C22×C4×C23C2×D412yes—
180C22×C4×C23#4114yes—
181C22×C4×C23#4112yes—
182C22×C4×C23#4112yes—
183C22×C4×C23#4114yes—
184C4⋊C4×C23—44no—
185C4⋊C4×C23—44no—
186C22⋊C4×C23—216no—
187C22⋊C4×C23—48no—
188C22⋊C4×C23—48no—
189C22⋊C4×C23—48no—
190C22⋊C4×C23—44no—
191C22⋊C4×C23—44no—
192C22⋊C4×C23—44no—
193C42×C23—48no—
194#14842C2311yesmaximal, characteristic, direct product factor, Sylow
195C23×C23—22no—
196C23×C23—22no—
197C23×C23—24no—
198C23×C23—22no—
199C23×C23—24no—
200C23×C23—22no—
201C23×C23—22no—
202C23×C23—22no—
203C23×C23—24no—
204C23×C23—24no—
205C23×C23—24no—
206C23×C23—24no—
207C23×C23—22no—
208C23×C23—24no—
209C23×C23—22no—
210C23×C23—24no—
211C23×C23—22no—
212C23×C23—42no—
213C23×C23—42no—
214C23×C23—42no—
215C23×C23—42no—
216C23×C23—42no—
217C23×C23—41no—
218C23×C23—41no—
219C23×C23—42no—
220C23×C23—41no—
221C23×C23—41no—
222C23×C23—41no—
223C23×C23—41no—
224C23×C23—42no—
225C23×C23—41no—
226C23×C23—42no—
227C23×C23—42no—
228C23×C23—41no—
229C23×C23—41no—
230C23×C23—41no—
231C23×C23—42no—
232C23×C23—42no—
233C23×C23—42no—
234C23×C23—41no—
235C23×C23—42no—
236C23×C23—42no—
237C23×C23—42no—
238C23×C23—42no—
239C23×C23—41no—
240C23×C23#12414yes—
241C23×C23C22×D411yescharacteristic
242C23×C23C22×D411yescharacteristic
243C23×C23C2×#4111yescharacteristic
244C23×C23C2×#4112yes—
245C23×C23C2×#4112yes—
246C23×C23C2×#4112yes—
247C23×C23C2×#4111yescharacteristic
248C23×C23C2×#4111yescharacteristic
249C23×C23H(5,𝔽2)12yes—
250C23×C23H(5,𝔽2)11yescharacteristic
251C23×C23H(5,𝔽2)11yescharacteristic
252D4×C23—416no—
253C2×C4×C23—22no—
254C2×C4×C23—22no—
255C2×C4×C23—22no—
256C2×C4×C23—22no—
257C2×C4×C23—24no—
258C2×C4×C23—24no—
259C2×C4×C23—24no—
260C2×C4×C23—24no—
261C2×C4×C23—24no—
262C2×C4×C23—24no—
263C2×C4×C23—22no—
264C2×C4×C23—24no—
265C2×C4×C23—24no—
266C2×C4×C23—24no—
267C2×C4×C23—24no—
268C2×C4×C23—24no—
269C2×C4×C23—416no—
270C2×C4×C23—41no—
271C2×C4×C23—42no—
272C2×C4×C23—41no—
273C2×C4×C23—42no—
274C2×C4×C23—42no—
275C2×C4×C23—42no—
276C2×C4×C23—42no—
277C2×C4×C23—42no—
278C2×C4×C23—42no—
279C2×C4×C23—42no—
280C2×C4×C23—42no—
281C2×C4×C23—41no—
282C2×C4×C23—42no—
283C2×C4×C23—41no—
284C2×C4×C23—42no—
285C2×C4×C23—42no—
286C2×C4×C23—41no—
287C2×C4×C23—41no—
288C2×C4×C23—42no—
289C2×C4×C23—41no—
290C2×C4×C23—42no—
291C2×C4×C23—42no—
292C2×C4×C23—42no—
293C2×C4×C23—42no—
294C2×C4×C23—41no—
295C2×C4×C23—42no—
296C2×C4×C23—42no—
297C2×C4×C23—42no—
298C2×C4×C23—42no—
299C2×C4×C23—42no—
300C2×C4×C23—42no—
301C2×C4×C23—42no—
302C2×C4×C23—42no—
303C2×C4×C23—42no—
304C2×C4×C23—42no—
305C2×C4×C23#12114yes—
306C2×C4×C23#12314yes—
307C2×#397C2×C2311yescharacteristic, complemented
308C2×#386C2×C2311yescharacteristic
309C2×#380C2×C2311yescharacteristic, complemented
310C2×C4×C22⋊C4C2×C2311yescharacteristic, complemented
311#1445C2×C2311yescharacteristic, complemented
312#1442C2×C2311yescharacteristic, complemented
313#1440C2×C2312yescomplemented
314#1439C2×C2311yescharacteristic, complemented
315#1438C2×C2312yes—
316#1437C2×C2312yescomplemented
317#1434C2×C2312yescomplemented
318C22×C23—24no—
319C22×C23—24no—
320C22×C23—24no—
321C22×C23—44no—
322C22×C23—42no—
323C22×C23—42no—
324C22×C23—42no—
325C22×C23—42no—
326C22×C23—44no—
327C22×C23—44no—
328C22×C23—44no—
329C22×C23—42no—
330C22×C23—44no—
331C22×C23—42no—
332C22×C23—42no—
333C22×C23—44no—
334C22×C23—81no—
335C22×C23—81no—
336C22×C23—81no—
337C22×C23—82no—
338C22×C23—81no—
339C22×C23—82no—
340C22×C23C2×#12111yescharacteristic
341C22×C23C2×#12311yescharacteristic
342C22×C23#52511yescharacteristic
343C22×C23#52512yes—
344C22×C23C2×#12411yescharacteristic
345C22×C23#52912yes—
346C22×C23#52912yes—
347C22×C23#52912yes—
348C22×C23#53211yescharacteristic
349C22×C23#53411yescharacteristic
350C22×C23#53511yescharacteristic
351C22×C23#53812yes—
352C22×C23#54012yes—
353C22×C23#54612yes—
354C22×C23#54611yescharacteristic
355C22×C23#55011yescharacteristic
356C22×C23#55112yes—
357C22×C23#55112yes—
358C22×C23#55112yes—
359C22×C23#55311yescharacteristic
360C22×C23#55312yes—
361C22×C23#55312yes—
362C22×C23#55511yescharacteristic
363C4×C23—24no—
364C4×C23—24no—
365C4×C23—42no—
366C4×C23—44no—
367C4×C23—44no—
368C4×C23—81no—
369C4×C23—82no—
370C4×C23—82no—
371C4×C23—81no—
372C23×D4C22×C2311yescharacteristic
373C24×C4C22×C2311yescharacteristic
374C22×C4⋊C4C22×C2311yescharacteristic
375C22×C4⋊C4C22×C2311yescharacteristic
376C22×C22⋊C4C22×C2311yescharacteristic
377C22×C22⋊C4C22×C2311yescharacteristic
378C22×C22⋊C4C22×C2312yes—
379C22×C22⋊C4C22×C2311yescharacteristic
380C22×C22⋊C4C22×C2312yes—
381C22×C22⋊C4C22×C2312yes—
382C22×C22⋊C4C22×C2312yes—
383C22×C42C22×C2312yes—
384#397—24no—
385#386—24no—
386#380—24no—
387C4×C22⋊C4—24no—
388C2×#95C22×C2312yes—
389C2×#95C22×C2311yescharacteristic
390C2×#95C22×C2312yes—
391C2×#95C22×C2312yes—
392C2×#95C22×C2312yes—
393C2×#95C22×C2311yescharacteristic
394C2×#95C22×C2311yescharacteristic
395C2×#95C22×C2312yes—
396C2×#95C22×C2312yes—
397C2×#95C22×C2312yes—
398C2×#95C22×C2311yescharacteristic
399C2×C23—44no—
400C2×C23—82no—
401C2×C23#239511yescharacteristic
402C2×C23#241211yescharacteristic
403C2×C23#241411yescharacteristic
404C2×C23#245712yes—
405C2×C23#246712yes—
406C2×C23#250411yescharacteristic
407C2×C23#253112yes—
408C2×C23#256111yescharacteristic
409C2×C23#257812yes—
410C2×C23#266111yescharacteristic
411C2×C23#285011yescharacteristic
412C25C23×C2311yescharacteristic
413C25C23×C2311yescharacteristic
414C22×D4—22no—
415C22×D4—22no—
416C22×D4—24no—
417C22×D4—22no—
418C22×D4—42no—
419C23×C4—22no—
420C23×C4—22no—
421C23×C4—24no—
422C23×C4—42no—
423C23×C4D4×C2314yes—
424C23×C4C23×C2312yes—
425C23×C4C23×C2312yes—
426C23×C4C23×C2311yescharacteristic
427C23×C4C23×C2311yescharacteristic
428C23×C4C23×C2312yes—
429C23×C4C23×C2312yes—
430C23×C4C23×C2311yescharacteristic
431C23×C4C23×C2311yescharacteristic
432C23×C4C23×C2311yescharacteristic
433C2×C4⋊C4—22no—
434C2×C4⋊C4—22no—
435C2×C4⋊C4—22no—
436C2×C4⋊C4—22no—
437C2×C4⋊C4—42no—
438C2×C22⋊C4—24no—
439C2×C22⋊C4—24no—
440C2×C22⋊C4—24no—
441C2×C22⋊C4—24no—
442C2×C22⋊C4—22no—
443C2×C22⋊C4—24no—
444C2×C22⋊C4—24no—
445C2×C22⋊C4—22no—
446C2×C22⋊C4—22no—
447C2×C22⋊C4—24no—
448C2×C22⋊C4—22no—
449C2×C22⋊C4—24no—
450C2×C22⋊C4—22no—
451C2×C22⋊C4—24no—
452C2×C22⋊C4—42no—
453C2×C22⋊C4—42no—
454C2×C22⋊C4—42no—
455C2×C22⋊C4—42no—
456C2×C22⋊C4—42no—
457C2×C42—24no—
458C2×C42—24no—
459C2×C42—42no—
460#95—22no—
461#95—24no—
462#95—22no—
463#95—22no—
464#95—24no—
465#95—24no—
466#95—24no—
467#95—42no—
468#95—42no—
469#95—42no—
470#95D4×C2314yescomplemented
471C23#1484211yescharacteristic, direct product factor, Sylow
472C24—21no—
473C24—22no—
474C24—22no—
475C24—21no—
476C24—21no—
477C24—21no—
478C24—21no—
479C24—21no—
480C24—22no—
481C24—21no—
482C24—21no—
483C24—21no—
484C24—22no—
485C24—22no—
486C24—22no—
487C24—21no—
488C24—21no—
489C24—21no—
490C24—22no—
491C24C2×D4×C2312yes—
492C24#41×C2312yes—
493C24#41×C2314yes—
494C24C24×C2311yescharacteristic
495C2×D4—28no—
496C2×D4—48no—
497C2×D4—48no—
498C2×D4—44no—
499C2×D4—44no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—21no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—21no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—28no—
522C22×C4—28no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—21no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—44no—
548C22×C4—48no—
549C22×C4—48no—
550C22×C4C2×D4×C2314yes—
551C22×C4C2×D4×C2312yes—
552C22×C4C2×D4×C2312yes—
553C22×C4C2×D4×C2312yes—
554C22×C4#41×C2312yes—
555C22×C4#41×C2314yes—
556C22×C4#41×C2312yes—
557C22×C4#41×C2314yes—
558C4⋊C4—44no—
559C4⋊C4—44no—
560C22⋊C4—216no—
561C22⋊C4—48no—
562C22⋊C4—48no—
563C22⋊C4—48no—
564C22⋊C4—44no—
565C22⋊C4—44no—
566C22⋊C4—44no—
567C42—48no—
568C23—24no—
569C23—24no—
570C23—24no—
571C23—24no—
572C23—22no—
573C23—22no—
574C23—24no—
575C23—22no—
576C23—24no—
577C23—22no—
578C23—22no—
579C23—22no—
580C23—24no—
581C23—22no—
582C23—22no—
583C23—24no—
584C23—22no—
585C23—41no—
586C23—42no—
587C23—41no—
588C23—41no—
589C23—42no—
590C23—42no—
591C23—42no—
592C23—42no—
593C23—42no—
594C23—41no—
595C23—41no—
596C23—42no—
597C23—42no—
598C23—42no—
599C23—42no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23—42no—
604C23—41no—
605C23—42no—
606C23—42no—
607C23—41no—
608C23—41no—
609C23—41no—
610C23—42no—
611C23—42no—
612C23—42no—
613C23C23×#12414yes—
614C23C22×D4×C2311yescharacteristic
615C23C22×D4×C2311yescharacteristic
616C23C2×#41×C2311yescharacteristic
617C23C2×#41×C2312yes—
618C23C2×#41×C2311yescharacteristic
619C23C2×#41×C2311yescharacteristic
620C23C2×#41×C2312yes—
621C23C2×#41×C2312yes—
622C23C23×H(5,𝔽2)11yescharacteristic
623C23C23×H(5,𝔽2)12yes—
624C23C23×H(5,𝔽2)11yescharacteristic
625D4—416no—
626C2×C4—24no—
627C2×C4—24no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—24no—
633C2×C4—24no—
634C2×C4—24no—
635C2×C4—24no—
636C2×C4—24no—
637C2×C4—22no—
638C2×C4—24no—
639C2×C4—24no—
640C2×C4—24no—
641C2×C4—24no—
642C2×C4—416no—
643C2×C4—42no—
644C2×C4—42no—
645C2×C4—42no—
646C2×C4—42no—
647C2×C4—42no—
648C2×C4—42no—
649C2×C4—41no—
650C2×C4—42no—
651C2×C4—41no—
652C2×C4—42no—
653C2×C4—42no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—42no—
658C2×C4—42no—
659C2×C4—41no—
660C2×C4—42no—
661C2×C4—41no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—41no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—41no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4C23×#12114yes—
679C2×C4C23×#12314yes—
680C22—24no—
681C22—24no—
682C22—24no—
683C22—42no—
684C22—42no—
685C22—42no—
686C22—44no—
687C22—44no—
688C22—44no—
689C22—44no—
690C22—42no—
691C22—42no—
692C22—44no—
693C22—42no—
694C22—44no—
695C22—42no—
696C22—81no—
697C22—81no—
698C22—82no—
699C22—81no—
700C22—82no—
701C22—81no—
702C22C2×C23×#12111yescharacteristic
703C22C2×C23×#12311yescharacteristic
704C22C23×#52511yescharacteristic
705C22C23×#52512yes—
706C22C2×C23×#12411yescharacteristic
707C22C23×#52912yes—
708C22C23×#52912yes—
709C22C23×#52912yes—
710C22C23×#53211yescharacteristic
711C22C23×#53411yescharacteristic
712C22C23×#53511yescharacteristic
713C22C23×#53812yes—
714C22C23×#54012yes—
715C22C23×#54612yes—
716C22C23×#54611yescharacteristic
717C22C23×#55011yescharacteristic
718C22C23×#55112yes—
719C22C23×#55112yes—
720C22C23×#55112yes—
721C22C23×#55311yescharacteristic
722C22C23×#55312yes—
723C22C23×#55312yes—
724C22C23×#55511yescharacteristic
725C4—24no—
726C4—24no—
727C4—44no—
728C4—44no—
729C4—42no—
730C4—82no—
731C4—82no—
732C4—81no—
733C4—81no—
734C2—44no—
735C2—82no—
736C2C23×#239511yescharacteristic
737C2C23×#241211yescharacteristic
738C2C23×#241411yescharacteristic
739C2C23×#245712yes—
740C2C23×#246712yes—
741C2C23×#250411yescharacteristic
742C2C23×#253112yes—
743C2C23×#256111yescharacteristic
744C2C23×#257812yes—
745C2C23×#266111yescharacteristic
746C2C23×#285011yescharacteristic
subgroupG/H
center, socleC24×C23C24
commutator, Frattini, cosocleC24C24×C23
prime radicalC23×D4×C23C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C23 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C23×#397C2semidirect
3. C2×C23×#380C2semidirect
4. C2×C4×C22⋊C4×C23C2semidirect
5. C23×#1445C2semidirect
6. C23×#1442C2semidirect
7. C23×#1440C2semidirect
8. C23×#1439C2semidirect
10. C23×#1437C2semidirect
11. C23×#1434C2semidirect
97. C23×#95D4semidirect
194. #14842C23direct (N × H)
307. C2×#397C2×C23semidirect
309. C2×#380C2×C23semidirect
310. C2×C4×C22⋊C4C2×C23semidirect
311. #1445C2×C23semidirect
312. #1442C2×C23semidirect
313. #1440C2×C23semidirect
314. #1439C2×C23semidirect
316. #1437C2×C23semidirect
317. #1434C2×C23semidirect
470. #95D4×C23semidirect
471. C23#14842direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C23×#3972
C2×C23×#3862
C2×C23×#3802
C2×C4×C22⋊C4×C232
C23×#14452
C23×#14422
C23×#14402
C23×#14392
C23×#14382
C23×#14372
C23×#14342
#1484223