Finite Group Databasebeta

← #372834

Subgroups — #372834

Order 512.

1176 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2511C211yesmaximal, characteristic
2C2×#1916C211yesmaximal, characteristic
3#13804C211yesmaximal, characteristic
4#11373C211yesmaximal, characteristic
5#11208C211yesmaximal, characteristic
6#11077C211yesmaximal, characteristic
7#11052C211yesmaximal, characteristic
8#10932C211yesmaximal, characteristic
9#10932C211yesmaximal, characteristic
10#10932C211yesmaximal, characteristic
11#10926C211yesmaximal, characteristic
12#10884C211yesmaximal, characteristic
13#10849C211yesmaximal, characteristic
14#10807C211yesmaximal, characteristic
15C4×#340C211yesmaximal, characteristic
16C22×C4⋊C8C2211yescharacteristic
17C22×#103C2211yescharacteristic
18C22×#103C2211yescharacteristic
19C22×#103C2211yescharacteristic
20C22×#103C2211yescharacteristic
21C22×C4×C8C2211yescharacteristic
22#2511—24no—
23#2511C418yescomplemented
24C2×#400—21no—
25C2×#400—21no—
26C2×#391C2211yescharacteristic
27C2×#391C2211yescharacteristic
28C2×#391C2211yescharacteristic
29C2×#389C2211yescharacteristic
30C2×#387—21no—
31C2×#387—21no—
32C2×#384C2211yescharacteristic
33C2×#382C2211yescharacteristic
34C2×C4×C4⋊C4C2211yescharacteristic
35C2×C4×C4⋊C4C2211yescharacteristic
36C2×C4×C4⋊C4C2211yescharacteristic
37C2×C4×C4⋊C4C2211yescharacteristic
38C2×C4×C4⋊C4C2211yescharacteristic
39#1916—24no—
40C2×#340C2211yescharacteristic
41C2×#340C2211yescharacteristic
42C2×#340C2211yescharacteristic
43C2×#340C2211yescharacteristic
44C2×#340C2211yescharacteristic
45C2×#340C2211yescharacteristic
46C2×#340C2211yescharacteristic
47C2×#340C2211yescharacteristic
48C2×#340C2211yescharacteristic
49C2×#340C2211yescharacteristic
50C2×#340C2211yescharacteristic
51C2×#340C2211yescharacteristic
52C2×#336C2211yescharacteristic
53C2×#336C2211yescharacteristic
54C2×#336C2211yescharacteristic
55C2×#336C2211yescharacteristic
56#1436—21no—
57#1436—21no—
58C4⋊#95C2211yescharacteristic
59C4⋊#95C2211yescharacteristic
60#1434—21no—
61C4×#95—21no—
62C23×Q8C2311yescharacteristic
63C23×C8C2311yescharacteristic
64C23×C8C2311yescharacteristic
65C23×C8C2311yescharacteristic
66C23×C8C2311yescharacteristic
67C22×C4⋊C4—21no—
68C22×C4⋊C4—21no—
69C22×C4⋊C4—21no—
70C22×C4⋊C4D411yescharacteristic
71C22×C4⋊C4D411yescharacteristic
72C22×C4⋊C4C2311yescharacteristic
73C22×C4⋊C4C2311yescharacteristic
74C22×C4⋊C4C2311yescharacteristic
75C22×C4⋊C4C2311yescharacteristic
76C22×C4⋊C4C2311yescharacteristic
77C22×C4⋊C4C2311yescharacteristic
78C22×C4⋊C4C2311yescharacteristic
79C22×C42—21no—
80C22×C42—21no—
81C22×C42—21no—
82C22×C42—21no—
83C22×C42C2311yescharacteristic
84C22×C42C2311yescharacteristic
85C22×C42C2311yescharacteristic
86C2×C4⋊C8—22no—
87C2×C4⋊C8—22no—
88C2×C4⋊C8—41no—
89C2×#103—22no—
90C2×#103—22no—
91C2×#103—22no—
92C2×#103—22no—
93C2×#103—22no—
94C2×#103—22no—
95C2×#103—22no—
96C2×#103—22no—
97C2×#103—41no—
98C2×#103—41no—
99C2×#103—41no—
100C2×#103—41no—
101C2×C4×C8—22no—
102C2×C4×C8—22no—
103C2×C4×C8—41no—
104#400—28no—
105#400—28no—
106#391—22no—
107#391—22no—
108#391—22no—
109#391C2×C414yes—
110#391C2×C414yes—
111#391C2×C414yes—
112#389—22no—
113#389C2×C414yes—
114#387—28no—
115#387—28no—
116#384—22no—
117#384C2×C414yes—
118#382—22no—
119#382—22no—
120C4×C4⋊C4—22no—
121C4×C4⋊C4—22no—
122C4×C4⋊C4—22no—
123C4×C4⋊C4—22no—
124C4×C4⋊C4—22no—
125C4×C4⋊C4—41no—
126C4×C4⋊C4—41no—
127C4×C4⋊C4C2×C414yes—
128C4×C4⋊C4C2×C414yes—
129C4×C4⋊C4D414yes—
130C2×#95—21no—
131C2×#95—21no—
132C2×#95—21no—
133C2×#95—21no—
134C2×#95—21no—
135C2×#95—21no—
136C2×#95—21no—
137C2×#95—21no—
138C2×#95—21no—
139C2×#95—21no—
140C2×#95—21no—
141C2×#95—21no—
142C2×#95—21no—
143C2×#95—21no—
144C2×#95—21no—
145C2×#95—21no—
146C2×#95—21no—
147C2×#95D411yescharacteristic
148C2×#95D411yescharacteristic
149#340—22no—
150#340—22no—
151#340—22no—
152#340—22no—
153#340—22no—
154#340—22no—
155#340—22no—
156#340—22no—
157#340—41no—
158#340—41no—
159#340—41no—
160#340—41no—
161#336—22no—
162#336—22no—
163#336—22no—
164#336—22no—
165C22×Q8—21no—
166C22×Q8—21no—
167C22×Q8—21no—
168C22×Q8—21no—
169C22×Q8—21no—
170C22×Q8—21no—
171C22×Q8—21no—
172C22×Q8—21no—
173C22×Q8—21no—
174C22×Q8—21no—
175C22×Q8—21no—
176C22×Q8—21no—
177C22×Q8—21no—
178C22×Q8C22×C412yes—
179C23×C4—21no—
180C23×C4—21no—
181C23×C4—21no—
182C23×C4—21no—
183C23×C4—21no—
184C23×C4—21no—
185C23×C4—21no—
186C23×C4—21no—
187C23×C4C2×D411yescharacteristic
188C23×C4C2×D411yescharacteristic
189C23×C4C2×D411yescharacteristic
190C23×C4C2×D411yescharacteristic
191C23×C4C2×D411yescharacteristic
192C23×C4C2×D411yescharacteristic
193C23×C4C2411yescharacteristic
194C22×C8—21no—
195C22×C8—21no—
196C22×C8—21no—
197C22×C8—21no—
198C22×C8—21no—
199C22×C8—21no—
200C22×C8—21no—
201C22×C8—21no—
202C22×C8—21no—
203C22×C8—21no—
204C22×C8—21no—
205C22×C8—21no—
206C22×C8—21no—
207C22×C8—21no—
208C22×C8—21no—
209C22×C8—21no—
210C22×C8—21no—
211C22×C8—21no—
212C22×C8—21no—
213C22×C8—21no—
214C22×C8—21no—
215C22×C8—21no—
216C22×C8—21no—
217C22×C8—21no—
218C22×C8—21no—
219C22×C8—21no—
220C22×C8#4112yes—
221C22×C8#4112yes—
222C2×C4⋊C4—22no—
223C2×C4⋊C4—22no—
224C2×C4⋊C4—22no—
225C2×C4⋊C4—22no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—24no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—24no—
261C2×C4⋊C4—24no—
262C2×C4⋊C4—42no—
263C2×C4⋊C4—42no—
264C2×C4⋊C4—81no—
265C2×C4⋊C4—81no—
266C2×C4⋊C4—81no—
267C2×C4⋊C4—81no—
268C2×C4⋊C4C22⋊C414yes—
269C2×C4⋊C4C22⋊C414yes—
270C2×C4⋊C4C22×C412yes—
271C2×C4⋊C4C22×C412yes—
272C2×C4⋊C4C22×C412yes—
273C2×C4⋊C4#4112yes—
274C2×C4⋊C4#4112yes—
275C2×C4⋊C4#4112yes—
276C2×C4⋊C4#4112yes—
277C2×C4⋊C4#4112yes—
278C2×C4⋊C4#4112yes—
279C2×C42—21no—
280C2×C42—21no—
281C2×C42—21no—
282C2×C42—21no—
283C2×C42—21no—
284C2×C42—21no—
285C2×C42—21no—
286C2×C42—21no—
287C2×C42—21no—
288C2×C42—21no—
289C2×C42—21no—
290C2×C42—21no—
291C2×C42—24no—
292C2×C42—24no—
293C2×C42—42no—
294C2×C42—42no—
295C2×C42—42no—
296C2×C42—42no—
297C2×C42—81no—
298C2×C42—81no—
299C2×C42—81no—
300C2×C42—81no—
301C2×C42—81no—
302C2×C42—81no—
303C2×C42C22×C412yes—
304C2×C42C22×C412yes—
305C2×C42C22×C412yes—
306C2×C42C2×D412yes—
307C2×C42C2×D412yes—
308C2×C42C2×D412yes—
309C4⋊C8—44no—
310#103—44no—
311#103—44no—
312#103—44no—
313#103—44no—
314C4×C8—44no—
315#95—24no—
316#95—24no—
317#95—24no—
318#95—24no—
319#95—24no—
320#95—24no—
321#95—24no—
322#95—24no—
323#95—24no—
324#95—24no—
325#95—24no—
326#95—42no—
327#95—42no—
328#95—42no—
329#95—42no—
330#95—81no—
331#95—81no—
332#95C22⋊C414yes—
333#95C22⋊C414yes—
334C24C22×D411yescharacteristic
335C2×Q8—22no—
336C2×Q8—22no—
337C2×Q8—22no—
338C2×Q8—22no—
339C2×Q8—22no—
340C2×Q8—22no—
341C2×Q8—41no—
342C2×Q8—41no—
343C2×Q8—41no—
344C2×Q8—41no—
345C2×Q8—41no—
346C2×Q8—41no—
347C2×Q8—41no—
348C2×Q8—41no—
349C2×Q8—41no—
350C2×Q8—41no—
351C2×Q8—41no—
352C2×Q8—41no—
353C2×Q8—41no—
354C2×Q8—41no—
355C2×Q8—41no—
356C2×Q8—41no—
357C2×Q8—41no—
358C2×Q8—41no—
359C2×Q8—41no—
360C2×Q8—41no—
361C2×Q8—41no—
362C2×Q8—41no—
363C22×C4—21no—
364C22×C4—21no—
365C22×C4—21no—
366C22×C4—21no—
367C22×C4—21no—
368C22×C4—21no—
369C22×C4—21no—
370C22×C4—21no—
371C22×C4—21no—
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—22no—
375C22×C4—21no—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—22no—
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—22no—
382C22×C4—21no—
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—21no—
387C22×C4—21no—
388C22×C4—21no—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—41no—
406C22×C4—41no—
407C22×C4—41no—
408C22×C4—41no—
409C22×C4—41no—
410C22×C4—41no—
411C22×C4—41no—
412C22×C4—41no—
413C22×C4—41no—
414C22×C4—41no—
415C22×C4—41no—
416C22×C4—41no—
417C22×C4—41no—
418C22×C4—41no—
419C22×C4—41no—
420C22×C4—41no—
421C22×C4—41no—
422C22×C4—41no—
423C22×C4—41no—
424C22×C4—41no—
425C22×C4—41no—
426C22×C4—41no—
427C22×C4—41no—
428C22×C4—41no—
429C22×C4—41no—
430C22×C4—41no—
431C22×C4—41no—
432C22×C4—41no—
433C22×C4—41no—
434C22×C4—41no—
435C22×C4—41no—
436C22×C4—41no—
437C22×C4—41no—
438C22×C4—41no—
439C22×C4—41no—
440C22×C4—41no—
441C22×C4—41no—
442C22×C4—41no—
443C22×C4—41no—
444C22×C4—41no—
445C22×C4—41no—
446C22×C4—41no—
447C22×C4—41no—
448C22×C4—41no—
449C22×C4—41no—
450C22×C4—41no—
451C22×C4C2×C22⋊C412yes—
452C22×C4C2×C22⋊C412yes—
453C22×C4C2×C22⋊C412yes—
454C22×C4C2×C22⋊C412yes—
455C22×C4C2×C22⋊C412yes—
456C22×C4C2×C22⋊C412yes—
457C22×C4#13512yes—
458C22×C4#13512yes—
459C22×C4#13712yes—
460C22×C4#13712yes—
461C22×C4C23×C411yescharacteristic
462C22×C4C22×D411yescharacteristic
463C22×C4C2×#4111yescharacteristic
464C22×C4C2×#4111yescharacteristic
465C22×C4C2×#4111yescharacteristic
466C22×C4C2×#4111yescharacteristic
467C22×C4C2×#4111yescharacteristic
468C22×C4C2×#4111yescharacteristic
469C22×C4C2×#4111yescharacteristic
470C22×C4C2×#4111yescharacteristic
471C22×C4H(5,𝔽2)11yescharacteristic
472C22×C4H(5,𝔽2)11yescharacteristic
473C22×C42−1+411yescharacteristic
474C22×C42−1+411yescharacteristic
475C2×C8—22no—
476C2×C8—22no—
477C2×C8—22no—
478C2×C8—22no—
479C2×C8—22no—
480C2×C8—22no—
481C2×C8—41no—
482C2×C8—41no—
483C2×C8—41no—
484C2×C8—41no—
485C2×C8—41no—
486C2×C8—41no—
487C2×C8—41no—
488C2×C8—41no—
489C2×C8—41no—
490C2×C8—41no—
491C2×C8—41no—
492C2×C8—41no—
493C2×C8—41no—
494C2×C8—41no—
495C2×C8—41no—
496C2×C8—41no—
497C2×C8—41no—
498C2×C8—41no—
499C2×C8—41no—
500C2×C8—41no—
501C2×C8—41no—
502C2×C8—41no—
503C4⋊C4—22no—
504C4⋊C4—22no—
505C4⋊C4—22no—
506C4⋊C4—28no—
507C4⋊C4—28no—
508C4⋊C4—22no—
509C4⋊C4—22no—
510C4⋊C4—22no—
511C4⋊C4—22no—
512C4⋊C4—22no—
513C4⋊C4—22no—
514C4⋊C4—22no—
515C4⋊C4—22no—
516C4⋊C4—22no—
517C4⋊C4—22no—
518C4⋊C4—22no—
519C4⋊C4—22no—
520C4⋊C4—41no—
521C4⋊C4—41no—
522C4⋊C4—41no—
523C4⋊C4—41no—
524C4⋊C4—41no—
525C4⋊C4—41no—
526C4⋊C4—41no—
527C4⋊C4—41no—
528C4⋊C4—41no—
529C4⋊C4—41no—
530C4⋊C4—41no—
531C4⋊C4—41no—
532C4⋊C4—48no—
533C4⋊C4—84no—
534C4⋊C4—84no—
535C4⋊C4#12614yes—
536C42—22no—
537C42—22no—
538C42—22no—
539C42—22no—
540C42—22no—
541C42—22no—
542C42—22no—
543C42—22no—
544C42—22no—
545C42—22no—
546C42—22no—
547C42—22no—
548C42—84no—
549C42—84no—
550C42—84no—
551C42—84no—
552C23C22×C22⋊C411yescharacteristic
553C23#52511yescharacteristic
554C23#52511yescharacteristic
555C23#54611yescharacteristic
556C23#54711yescharacteristic
557C23#54811yescharacteristic
558C23#55011yescharacteristic
559C23C2×#13511yescharacteristic
560C23C2×#13511yescharacteristic
561C23C2×#13711yescharacteristic
562C23C2×#13711yescharacteristic
563C23#57611yescharacteristic
564C23#57711yescharacteristic
565C23#57711yescharacteristic
566C23#57811yescharacteristic
567Q8—42no—
568Q8—42no—
569Q8—42no—
570Q8—42no—
571Q8—81no—
572Q8—81no—
573Q8—81no—
574Q8—81no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—24no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—42no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—42no—
610C2×C4—42no—
611C2×C4—41no—
612C2×C4—42no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—42no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—42no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—42no—
623C2×C4—42no—
624C2×C4—42no—
625C2×C4—42no—
626C2×C4—42no—
627C2×C4—42no—
628C2×C4—42no—
629C2×C4—42no—
630C2×C4—42no—
631C2×C4—42no—
632C2×C4—42no—
633C2×C4—42no—
634C2×C4—42no—
635C2×C4—42no—
636C2×C4—42no—
637C2×C4—42no—
638C2×C4—42no—
639C2×C4—42no—
640C2×C4—42no—
641C2×C4—42no—
642C2×C4—42no—
643C2×C4—81no—
644C2×C4—81no—
645C2×C4—81no—
646C2×C4—81no—
647C2×C4—81no—
648C2×C4—81no—
649C2×C4—81no—
650C2×C4—81no—
651C2×C4—81no—
652C2×C4—81no—
653C2×C4—81no—
654C2×C4—81no—
655C2×C4—81no—
656C2×C4—81no—
657C2×C4—81no—
658C2×C4—81no—
659C2×C4—81no—
660C2×C4—81no—
661C2×C4—81no—
662C2×C4—81no—
663C2×C4—81no—
664C2×C4—81no—
665C2×C4—81no—
666C2×C4—81no—
667C2×C4—81no—
668C2×C4—81no—
669C2×C4—81no—
670C2×C4—81no—
671C2×C4#41614yes—
672C2×C4#41914yes—
673C2×C4C4×#4111yescharacteristic
674C2×C4C4×#4111yescharacteristic
675C2×C4C4×#4111yescharacteristic
676C2×C4C4×#4111yescharacteristic
677C2×C4#52011yescharacteristic
678C2×C4#52011yescharacteristic
679C2×C4C2×#12611yescharacteristic
680C2×C4#52911yescharacteristic
681C2×C4#52911yescharacteristic
682C2×C4#52911yescharacteristic
683C2×C4#53211yescharacteristic
684C2×C4#53211yescharacteristic
685C2×C4#53811yescharacteristic
686C2×C4#53911yescharacteristic
687C2×C4#54111yescharacteristic
688C2×C4#54211yescharacteristic
689C2×C4#54611yescharacteristic
690C2×C4#54711yescharacteristic
691C2×C4#54811yescharacteristic
692C2×C4#55011yescharacteristic
693C2×C4#55111yescharacteristic
694C2×C4#55111yescharacteristic
695C2×C4#55211yescharacteristic
696C2×C4#55211yescharacteristic
697C2×C4#55311yescharacteristic
698C2×C4#55311yescharacteristic
699C2×C4#55611yescharacteristic
700C2×C4#55611yescharacteristic
701C8—42no—
702C8—42no—
703C8—81no—
704C8—81no—
705C22#229711yescharacteristic
706C22#233911yescharacteristic
707C22#234111yescharacteristic
708C22#246711yescharacteristic
709C22#246911yescharacteristic
710C22#247911yescharacteristic
711C22#248111yescharacteristic
712C22C2×#41611yescharacteristic
713C22C2×#41911yescharacteristic
714C22#289711yescharacteristic
715C22#289811yescharacteristic
716C22#310711yescharacteristic
717C22#310711yescharacteristic
718C22#310711yescharacteristic
719C22#310711yescharacteristic
720C22#311811yescharacteristic
721C22#312111yescharacteristic
722C22#312411yescharacteristic
723C22#312511yescharacteristic
724C22#329611yescharacteristic
725C22#330011yescharacteristic
726C22#331411yescharacteristic
727C22#331611yescharacteristic
728C22#333611yescharacteristic
729C22#333711yescharacteristic
730C22#334411yescharacteristic
731C22#334611yescharacteristic
732C22#336111yescharacteristic
733C22#336511yescharacteristic
734C22#337211yescharacteristic
735C22#337411yescharacteristic
736C22#339411yescharacteristic
737C22#339611yescharacteristic
738C22#339811yescharacteristic
739C22#340011yescharacteristic
740C4—24no—
741C4—24no—
742C4—42no—
743C4—42no—
744C4—44no—
745C4—42no—
746C4—42no—
747C4—82no—
748C4—82no—
749C4—82no—
750C4—82no—
751C4—82no—
752C4—82no—
753C4—82no—
754C4C4×#12611yescharacteristic
755C4#233411yescharacteristic
756C4#237311yescharacteristic
757C4#237311yescharacteristic
758C4#251211yescharacteristic
759C4#251911yescharacteristic
760C4#255411yescharacteristic
761C4#256011yescharacteristic
762C2#1410111yescharacteristic
763C2#2138911yescharacteristic
764C2#2139711yescharacteristic
765C2#2248611yescharacteristic
766C2#2249711yescharacteristic
767C2#2254311yescharacteristic
768C2#2254711yescharacteristic
769C2#2707311yescharacteristic
770C2#2707711yescharacteristic
771C2#2713711yescharacteristic
772C2#2714111yescharacteristic
773C2#2749711yescharacteristic
774C2#2750111yescharacteristic
775C2#2756111yescharacteristic
776C2#2756511yescharacteristic
subgroupG/H
center, socle, prime radicalC24C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
23. #2511C4semidirect

Maximal subgroups

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

subgroupindex
C2×#25112
C2×#19162
#138042
#113732
#112082
#110772
#110522
#109322
#109262
#108842
#108492
#108072
C4×#3402