Finite Group Databasebeta

← #520267

Subgroups — #520267

Order 512.

14596 conjugacy classes of subgroups.

The subgroup lattice has 843 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C24×C22⋊C4C211yesmaximal, characteristic, complemented
2C2×#2846C211yesmaximal, characteristic
3C2×#2358C213yesmaximal, complemented
4C2×C4×#120C211yesmaximal, characteristic, complemented
5C22×#379C211yesmaximal, characteristic, complemented
6#14694C211yesmaximal, characteristic, complemented
7#14693C211yesmaximal, characteristic, complemented
8#14134C213yesmaximal, complemented
9#14127C213yesmaximal, complemented
10#13995C213yesmaximal, complemented
11#13991C213yesmaximal, complemented
12#13971C213yesmaximal, complemented
13#13967C213yesmaximal, complemented
14C22⋊C42C213yesmaximal, complemented
15C4×#379C211yesmaximal, characteristic, complemented
16C27C2211yescharacteristic
17C25×C4C2211yescharacteristic
18C25×C4C2211yescharacteristic
19C22×#120C2213yes—
20C22×#120C2211yescharacteristic
21C22×#120C2213yes—
22C22×C4×D4C2211yescharacteristic, complemented
23C22×C4×D4C2213yescomplemented
24C23×C22⋊C4—224no—
25C23×C22⋊C4C2213yes—
26C23×C22⋊C4C2213yes—
27C23×C22⋊C4C2213yes—
28C23×C22⋊C4C2213yes—
29C23×C22⋊C4C2213yes—
30C23×C22⋊C4C2213yes—
31#2846C4116yescomplemented
32#2358—224no—
33C4×#120—28no—
34C2×#390C2213yescomplemented
35C2×#388C2213yescomplemented
36C2×#388C2213yescomplemented
37C2×#386C2213yescomplemented
38C2×#386C2213yescomplemented
39C2×#386C2213yescomplemented
40C2×#386C2213yescomplemented
41C2×#386C2213yescomplemented
42C2×#385C2213yescomplemented
43C2×#385C2213yescomplemented
44C2×#385C2213yescomplemented
45C2×#385C2213yescomplemented
46C2×#379—28no—
47C2×#379C2211yescharacteristic
48C2×#379C2213yes—
49C2×#379C2213yes—
50C2×#379C2213yes—
51C2×#379C2211yescharacteristic
52C2×#379C2213yes—
53C2×#379C2211yescharacteristic
54C2×C4×C22⋊C4C2213yescomplemented
55C2×C4×C22⋊C4C2213yescomplemented
56C2×C4×C22⋊C4C2213yescomplemented
57C2×C4×C22⋊C4C2213yescomplemented
58#1440C2216yescomplemented
59#1439C2216yescomplemented
60#1439C2216yescomplemented
61#1438C2216yescomplemented
62#1437C2216yescomplemented
63#1437C2216yescomplemented
64C22⋊#95C2216yescomplemented
65C22⋊#95C2213yescomplemented
66C22⋊#95C2213yescomplemented
67C22⋊#95C2213yescomplemented
68C22⋊#95C2213yescomplemented
69C22⋊#95C2213yescomplemented
70C22⋊#95C2213yescomplemented
71C26—212no—
72C26—212no—
73C26—24no—
74C26—24no—
75C26—46no—
76C26—46no—
77C26C2×C418yescomplemented
78C26C2311yescharacteristic
79C26C2313yes—
80C26C2313yes—
81C23×D4C2313yes—
82C23×D4C2311yescharacteristic
83C23×D4C2313yes—
84C24×C4—212no—
85C24×C4—212no—
86C24×C4—24no—
87C24×C4—24no—
88C24×C4—46no—
89C24×C4—46no—
90C24×C4C2313yes—
91C24×C4C2313yes—
92C24×C4C2311yescharacteristic
93C24×C4C2313yes—
94C24×C4C2313yes—
95C24×C4C2313yes—
96C24×C4C2311yescharacteristic, complemented
97C2×#120—212no—
98C2×#120—24no—
99C2×#120—24no—
100C2×#120—212no—
101C2×#120—46no—
102C2×#120—46no—
103C2×#120C2×C418yescomplemented
104C2×#120C2×C4124yescomplemented
105C2×#120C2×C4124yescomplemented
106C2×C4×D4—212no—
107C2×C4×D4—212no—
108C2×C4×D4—212no—
109C2×C4×D4—46no—
110C22×C4⋊C4C2311yescharacteristic, complemented
111C22×C4⋊C4C2313yescomplemented
112C22×C4⋊C4C2313yescomplemented
113C22×C22⋊C4—2128no—
114C22×C22⋊C4—212no—
115C22×C22⋊C4—212no—
116C22×C22⋊C4—212no—
117C22×C22⋊C4—224no—
118C22×C22⋊C4—224no—
119C22×C22⋊C4—224no—
120C22×C22⋊C4—224no—
121C22×C22⋊C4—212no—
122C22×C22⋊C4—212no—
123C22×C22⋊C4—212no—
124C22×C22⋊C4—212no—
125C22×C22⋊C4—46no—
126C22×C22⋊C4—46no—
127C22×C22⋊C4D4124yescomplemented
128C22×C22⋊C4C2316yes—
129C22×C22⋊C4C2313yes—
130C22×C22⋊C4C2313yes—
131C22×C22⋊C4C2316yes—
132C22×C22⋊C4C2313yes—
133C22×C22⋊C4C2313yes—
134C22×C22⋊C4C2313yes—
135C22×C22⋊C4C2313yes—
136C22×C22⋊C4C2313yes—
137C22×C22⋊C4C2313yes—
138C22×C22⋊C4C2313yes—
139C22×C22⋊C4C2313yes—
140C22×C22⋊C4C2313yes—
141C22×C22⋊C4C2313yes—
142C22×C22⋊C4C2313yes—
143C22×C22⋊C4C2313yes—
144C22×C22⋊C4C2316yes—
145C22×C22⋊C4C2311yescharacteristic
146C22×C22⋊C4C2311yescharacteristic, complemented
147C22×C22⋊C4C2313yescomplemented
148C22×C22⋊C4C2313yescomplemented
149C22×C42C2311yescharacteristic, complemented
150C22×C42C2313yescomplemented
151C22×C42C2313yescomplemented
152#390—212no—
153#388—212no—
154#388—212no—
155#386—212no—
156#386—212no—
157#386—212no—
158#386—212no—
159#386—46no—
160#385—212no—
161#385—212no—
162#385—212no—
163#385—46no—
164#379—24no—
165#379—212no—
166#379—212no—
167#379C2×C418yescomplemented
168#379C2×C4124yescomplemented
169#379C2×C4124yescomplemented
170#379D418yescomplemented
171C4×C22⋊C4—212no—
172C4×C22⋊C4—212no—
173C4×C22⋊C4—212no—
174C4×C22⋊C4—46no—
175C2×#95C2313yescomplemented
176C2×#95C2313yescomplemented
177C2×#95C2313yescomplemented
178C2×#95C2313yescomplemented
179C2×#95C2313yescomplemented
180C2×#95C2313yescomplemented
181C2×#95C2316yescomplemented
182C2×#95C2316yescomplemented
183C2×#95C2316yescomplemented
184C2×#95C2316yescomplemented
185C25—26no—
186C25—26no—
187C25—26no—
188C25—26no—
189C25—232no—
190C25—296no—
191C25—296no—
192C25—212no—
193C25—212no—
194C25—26no—
195C25—26no—
196C25—212no—
197C25—212no—
198C25—26no—
199C25—26no—
200C25—26no—
201C25—26no—
202C25—232no—
203C25—26no—
204C25—26no—
205C25—26no—
206C25—26no—
207C25—448no—
208C25—46no—
209C25—46no—
210C25—46no—
211C25—46no—
212C25—448no—
213C25—448no—
214C25—448no—
215C25—448no—
216C25—448no—
217C25—448no—
218C25—496no—
219C25C22×C414yes—
220C25C22×C4112yes—
221C25C22×C4112yes—
222C25C2×D414yes—
223C25C2×D4112yes—
224C25#4114yes—
225C25#41112yes—
226C25C2411yescharacteristic
227C25C2413yes—
228C25C2411yescharacteristic
229C25C2413yes—
230C22×D4—26no—
231C22×D4—26no—
232C22×D4—26no—
233C22×D4—26no—
234C22×D4—26no—
235C22×D4—26no—
236C22×D4—26no—
237C22×D4—26no—
238C22×D4—26no—
239C22×D4—26no—
240C22×D4—46no—
241C22×D4—46no—
242C22×D4C22×C4112yes—
243C22×D4C22×C414yescomplemented
244C22×D4C22×C4112yescomplemented
245C23×C4—232no—
246C23×C4—232no—
247C23×C4—26no—
248C23×C4—26no—
249C23×C4—26no—
250C23×C4—26no—
251C23×C4—26no—
252C23×C4—26no—
253C23×C4—212no—
254C23×C4—212no—
255C23×C4—212no—
256C23×C4—212no—
257C23×C4—26no—
258C23×C4—26no—
259C23×C4—26no—
260C23×C4—26no—
261C23×C4—26no—
262C23×C4—26no—
263C23×C4—212no—
264C23×C4—26no—
265C23×C4—22no—
266C23×C4—22no—
267C23×C4—26no—
268C23×C4—46no—
269C23×C4—46no—
270C23×C4—46no—
271C23×C4—46no—
272C23×C4—46no—
273C23×C4—43no—
274C23×C4—43no—
275C23×C4—43no—
276C23×C4—448no—
277C23×C4—448no—
278C23×C4—448no—
279C23×C4—448no—
280C23×C4C2×D4112yes—
281C23×C4C2×D4112yes—
282C23×C4C2411yescharacteristic
283C23×C4C2413yes—
284C23×C4C2411yescharacteristic
285C23×C4C2413yes—
286C23×C4C2413yes—
287C23×C4C2413yes—
288C23×C4C2411yescharacteristic
289C23×C4C2413yes—
290C23×C4C2413yes—
291C23×C4C2411yescharacteristic
292C23×C4C2411yescharacteristic
293#120—232no—
294#120—296no—
295#120—448no—
296C4×D4—448no—
297C4×D4—416no—
298C2×C4⋊C4—26no—
299C2×C4⋊C4—26no—
300C2×C4⋊C4—26no—
301C2×C4⋊C4—26no—
302C2×C4⋊C4—43no—
303C2×C4⋊C4—46no—
304C2×C22⋊C4—296no—
305C2×C22⋊C4—296no—
306C2×C22⋊C4—296no—
307C2×C22⋊C4—212no—
308C2×C22⋊C4—212no—
309C2×C22⋊C4—26no—
310C2×C22⋊C4—26no—
311C2×C22⋊C4—26no—
312C2×C22⋊C4—26no—
313C2×C22⋊C4—26no—
314C2×C22⋊C4—26no—
315C2×C22⋊C4—26no—
316C2×C22⋊C4—26no—
317C2×C22⋊C4—26no—
318C2×C22⋊C4—26no—
319C2×C22⋊C4—26no—
320C2×C22⋊C4—26no—
321C2×C22⋊C4—26no—
322C2×C22⋊C4—26no—
323C2×C22⋊C4—212no—
324C2×C22⋊C4—212no—
325C2×C22⋊C4—212no—
326C2×C22⋊C4—212no—
327C2×C22⋊C4—296no—
328C2×C22⋊C4—26no—
329C2×C22⋊C4—26no—
330C2×C22⋊C4—26no—
331C2×C22⋊C4—26no—
332C2×C22⋊C4—26no—
333C2×C22⋊C4—212no—
334C2×C22⋊C4—26no—
335C2×C22⋊C4—26no—
336C2×C22⋊C4—26no—
337C2×C22⋊C4—212no—
338C2×C22⋊C4—26no—
339C2×C22⋊C4—26no—
340C2×C22⋊C4—26no—
341C2×C22⋊C4—26no—
342C2×C22⋊C4—26no—
343C2×C22⋊C4—26no—
344C2×C22⋊C4—448no—
345C2×C22⋊C4—448no—
346C2×C22⋊C4—46no—
347C2×C22⋊C4—43no—
348C2×C22⋊C4—43no—
349C2×C22⋊C4—46no—
350C2×C22⋊C4—46no—
351C2×C22⋊C4—43no—
352C2×C22⋊C4—46no—
353C2×C22⋊C4C22×C4112yes—
354C2×C22⋊C4C22×C4112yes—
355C2×C22⋊C4C22×C4112yes—
356C2×C22⋊C4C22×C4112yescomplemented
357C2×C22⋊C4C22×C4112yescomplemented
358C2×C22⋊C4C22×C4124yescomplemented
359C2×C22⋊C4C2×D4112yes—
360C2×C22⋊C4C2×D4112yes—
361C2×C22⋊C4C2×D4112yes—
362C2×C22⋊C4C2×D4112yes—
363C2×C22⋊C4C2×D4112yes—
364C2×C22⋊C4C2×D4112yes—
365C2×C42—26no—
366C2×C42—26no—
367C2×C42—26no—
368C2×C42—26no—
369C2×C42—43no—
370C2×C42—46no—
371#95—212no—
372#95—26no—
373#95—26no—
374#95—26no—
375#95—26no—
376#95—26no—
377#95—26no—
378#95—46no—
379#95—46no—
380#95—46no—
381C24—28no—
382C24—224no—
383C24—224no—
384C24—224no—
385C24—248no—
386C24—224no—
387C24—224no—
388C24—224no—
389C24—224no—
390C24—224no—
391C24—224no—
392C24—26no—
393C24—21no—
394C24—26no—
395C24—21no—
396C24—26no—
397C24—23no—
398C24—26no—
399C24—23no—
400C24—224no—
401C24—2256no—
402C24—224no—
403C24—248no—
404C24—248no—
405C24—224no—
406C24—248no—
407C24—224no—
408C24—224no—
409C24—224no—
410C24—224no—
411C24—248no—
412C24—224no—
413C24—224no—
414C24—224no—
415C24—224no—
416C24—26no—
417C24—23no—
418C24—26no—
419C24—23no—
420C24—23no—
421C24—23no—
422C24—26no—
423C24—26no—
424C24—224no—
425C24—224no—
426C24—23no—
427C24—21no—
428C24—23no—
429C24—21no—
430C24—23no—
431C24—23no—
432C24—424no—
433C24—424no—
434C24—412no—
435C24—412no—
436C24—424no—
437C24—4384no—
438C24—424no—
439C24—424no—
440C24—424no—
441C24—424no—
442C24—424no—
443C24—424no—
444C24—424no—
445C24—424no—
446C24—424no—
447C24—424no—
448C24—424no—
449C24—424no—
450C24—424no—
451C24—424no—
452C24—424no—
453C24—424no—
454C24—4128no—
455C24—4128no—
456C24—4384no—
457C24—4384no—
458C24—4384no—
459C24—412no—
460C24—412no—
461C24—424no—
462C24—412no—
463C24—412no—
464C24—412no—
465C24—412no—
466C24C4×D4116yescomplemented
467C24C4×D4148yescomplemented
468C24C23×C412yes—
469C24C23×C416yes—
470C24C23×C412yes—
471C24C23×C416yes—
472C24C22×D416yes—
473C24C22×D416yes—
474C24C22×D416yes—
475C24C22×D416yes—
476C24C2×#4116yes—
477C24C2×#4116yes—
478C24C2×#4116yes—
479C24C2×#4116yes—
480C24H(5,𝔽2)16yes—
481C24H(5,𝔽2)16yes—
482C24C2511yescharacteristic
483C2×D4—224no—
484C2×D4—224no—
485C2×D4—224no—
486C2×D4—224no—
487C2×D4—224no—
488C2×D4—424no—
489C2×D4—44no—
490C2×D4—412no—
491C2×D4—412no—
492C2×D4—412no—
493C2×D4—412no—
494C2×D4—412no—
495C2×D4—86no—
496C2×D4—86no—
497C2×D4—812no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—23no—
501C22×C4—23no—
502C22×C4—224no—
503C22×C4—224no—
504C22×C4—224no—
505C22×C4—224no—
506C22×C4—23no—
507C22×C4—23no—
508C22×C4—23no—
509C22×C4—23no—
510C22×C4—23no—
511C22×C4—23no—
512C22×C4—23no—
513C22×C4—26no—
514C22×C4—26no—
515C22×C4—26no—
516C22×C4—23no—
517C22×C4—23no—
518C22×C4—23no—
519C22×C4—23no—
520C22×C4—23no—
521C22×C4—23no—
522C22×C4—23no—
523C22×C4—26no—
524C22×C4—26no—
525C22×C4—26no—
526C22×C4—26no—
527C22×C4—26no—
528C22×C4—23no—
529C22×C4—23no—
530C22×C4—23no—
531C22×C4—23no—
532C22×C4—224no—
533C22×C4—224no—
534C22×C4—23no—
535C22×C4—23no—
536C22×C4—21no—
537C22×C4—23no—
538C22×C4—26no—
539C22×C4—23no—
540C22×C4—26no—
541C22×C4—23no—
542C22×C4—412no—
543C22×C4—412no—
544C22×C4—412no—
545C22×C4—424no—
546C22×C4—424no—
547C22×C4—424no—
548C22×C4—424no—
549C22×C4—424no—
550C22×C4—424no—
551C22×C4—424no—
552C22×C4—424no—
553C22×C4—412no—
554C22×C4—412no—
555C22×C4—424no—
556C22×C4—4128no—
557C22×C4—4128no—
558C22×C4—412no—
559C22×C4—412no—
560C22×C4—412no—
561C22×C4—412no—
562C22×C4—44no—
563C22×C4—412no—
564C22×C4—44no—
565C22×C4—86no—
566C22×C4—86no—
567C22×C4—86no—
568C22×C4—812no—
569C22×C4C23×C412yes—
570C22×C4C23×C416yes—
571C22×C4C23×C416yes—
572C22×C4C22×D416yes—
573C22×C4C22×D416yes—
574C22×C4C22×D416yes—
575C22×C4C22×D412yes—
576C22×C4C22×D416yes—
577C22×C4C22×D416yes—
578C4⋊C4—412no—
579C4⋊C4—44no—
580C4⋊C4—86no—
581C22⋊C4—248no—
582C22⋊C4—224no—
583C22⋊C4—224no—
584C22⋊C4—224no—
585C22⋊C4—224no—
586C22⋊C4—224no—
587C22⋊C4—224no—
588C22⋊C4—224no—
589C22⋊C4—224no—
590C22⋊C4—224no—
591C22⋊C4—224no—
592C22⋊C4—424no—
593C22⋊C4—412no—
594C22⋊C4—412no—
595C22⋊C4—412no—
596C22⋊C4—424no—
597C22⋊C4—412no—
598C22⋊C4—412no—
599C22⋊C4—44no—
600C22⋊C4—86no—
601C22⋊C4#120116yescomplemented
602C42—412no—
603C42—44no—
604C42—86no—
605C23—232no—
606C23—232no—
607C23—232no—
608C23—296no—
609C23—296no—
610C23—296no—
611C23—296no—
612C23—22no—
613C23—212no—
614C23—212no—
615C23—26no—
616C23—26no—
617C23—26no—
618C23—212no—
619C23—26no—
620C23—212no—
621C23—26no—
622C23—212no—
623C23—212no—
624C23—26no—
625C23—212no—
626C23—26no—
627C23—26no—
628C23—26no—
629C23—212no—
630C23—212no—
631C23—26no—
632C23—26no—
633C23—212no—
634C23—212no—
635C23—212no—
636C23—212no—
637C23—296no—
638C23—296no—
639C23—26no—
640C23—212no—
641C23—212no—
642C23—26no—
643C23—26no—
644C23—26no—
645C23—212no—
646C23—26no—
647C23—26no—
648C23—26no—
649C23—26no—
650C23—26no—
651C23—26no—
652C23—212no—
653C23—296no—
654C23—22no—
655C23—26no—
656C23—26no—
657C23—448no—
658C23—448no—
659C23—496no—
660C23—448no—
661C23—448no—
662C23—496no—
663C23—496no—
664C23—496no—
665C23—496no—
666C23—496no—
667C23—448no—
668C23—41024no—
669C23—448no—
670C23—496no—
671C23—448no—
672C23—448no—
673C23—496no—
674C23—448no—
675C23—448no—
676C23—448no—
677C23—46no—
678C23—46no—
679C23—46no—
680C23—46no—
681C23—46no—
682C23—46no—
683C23—46no—
684C23—46no—
685C23—41no—
686C23—43no—
687C23—43no—
688C23—43no—
689C23—43no—
690C23—43no—
691C23—43no—
692C23—43no—
693C23—46no—
694C23C2×C4×D4112yes—
695C23C2×C4×D4112yes—
696C23C2×C4×D4112yes—
697C23C2×C4×D4112yes—
698C23#518112yes—
699C23C2×#12014yes—
700C23#525112yes—
701C23D42112yes—
702C23#546112yes—
703C23#546112yes—
704C23#551112yes—
705C23C24×C411yescharacteristic
706C23C23×D413yes—
707C23C23×D411yescharacteristic
708C23C22×#4113yes—
709C23C22×#4111yescharacteristic
710C23C2×H(5,𝔽2)13yes—
711C23C2×H(5,𝔽2)13yes—
712D4—448no—
713D4—416no—
714D4—824no—
715C2×C4—26no—
716C2×C4—26no—
717C2×C4—26no—
718C2×C4—26no—
719C2×C4—26no—
720C2×C4—26no—
721C2×C4—26no—
722C2×C4—26no—
723C2×C4—212no—
724C2×C4—26no—
725C2×C4—26no—
726C2×C4—26no—
727C2×C4—26no—
728C2×C4—26no—
729C2×C4—26no—
730C2×C4—212no—
731C2×C4—26no—
732C2×C4—26no—
733C2×C4—26no—
734C2×C4—448no—
735C2×C4—448no—
736C2×C4—448no—
737C2×C4—448no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—43no—
741C2×C4—43no—
742C2×C4—43no—
743C2×C4—46no—
744C2×C4—46no—
745C2×C4—43no—
746C2×C4—43no—
747C2×C4—43no—
748C2×C4—43no—
749C2×C4—43no—
750C2×C4—43no—
751C2×C4—46no—
752C2×C4—46no—
753C2×C4—43no—
754C2×C4—46no—
755C2×C4—46no—
756C2×C4—41no—
757C2×C4—43no—
758C2×C4—43no—
759C2×C4—43no—
760C2×C4—46no—
761C2×C4—43no—
762C2×C4—43no—
763C2×C4—46no—
764C2×C4—88no—
765C2×C4—824no—
766C2×C4—88no—
767C2×C4C2×#12014yes—
768C2×C4C2×#12014yes—
769C22—2128no—
770C22—212no—
771C22—212no—
772C22—224no—
773C22—212no—
774C22—24no—
775C22—212no—
776C22—224no—
777C22—212no—
778C22—224no—
779C22—212no—
780C22—212no—
781C22—224no—
782C22—212no—
783C22—212no—
784C22—212no—
785C22—24no—
786C22—212no—
787C22—212no—
788C22—212no—
789C22—4192no—
790C22—4192no—
791C22—46no—
792C22—412no—
793C22—46no—
794C22—46no—
795C22—412no—
796C22—412no—
797C22—412no—
798C22—46no—
799C22—46no—
800C22—46no—
801C22—42no—
802C22—83no—
803C22—81no—
804C22—83no—
805C22—81no—
806C22C4×#12018yescomplemented
807C22#2358124yescomplemented
808C22C22×C4×D411yescharacteristic
809C22C22×C4×D413yes—
810C22C2×#51813yes—
811C22C22×#12011yescharacteristic
812C22C2×#52513yes—
813C22C2×D4213yes—
814C22C2×#54613yes—
815C22C2×#54613yes—
816C22C2×#55113yes—
817C22#348413yes—
818C22#348413yes—
819C22#349016yes—
820C4—24no—
821C4—24no—
822C4—46no—
823C4—46no—
824C4—46no—
825C4—46no—
826C4—42no—
827C4—46no—
828C4—42no—
829C4—83no—
830C4—81no—
831C2—224no—
832C2—28no—
833C2—412no—
834C2—82no—
835C2C2×C4×#12011yescharacteristic
836C2C2×#235813yes—
837C2#3419813yes—
838C2D4×#12011yescharacteristic
839C2#3609813yes—
840C2#3615211yescharacteristic
841C2#3615813yes—
subgroupG/H
center, Frattini, socle, cosocleC24C25
commutatorC23C24×C4
prime radicalC2×#2846C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C24×C22⋊C4C2semidirect
3. C2×#2358C2semidirect
4. C2×C4×#120C2semidirect
5. C22×#379C2semidirect
6. #14694C2semidirect
7. #14693C2semidirect
8. #14134C2semidirect
9. #14127C2semidirect
10. #13995C2semidirect
11. #13991C2semidirect
12. #13971C2semidirect
13. #13967C2semidirect
14. C22⋊C42C2semidirect
15. C4×#379C2semidirect
22. C22×C4×D4C22semidirect
23. C22×C4×D4C22semidirect
31. #2846C4semidirect
34. C2×#390C22semidirect
35. C2×#388C22semidirect
36. C2×#388C22semidirect
37. C2×#386C22semidirect
38. C2×#386C22semidirect
39. C2×#386C22semidirect
40. C2×#386C22semidirect
41. C2×#386C22semidirect
42. C2×#385C22semidirect
43. C2×#385C22semidirect
44. C2×#385C22semidirect
45. C2×#385C22semidirect
54. C2×C4×C22⋊C4C22semidirect
55. C2×C4×C22⋊C4C22semidirect
56. C2×C4×C22⋊C4C22semidirect
57. C2×C4×C22⋊C4C22semidirect
58. #1440C22semidirect
59. #1439C22semidirect
60. #1439C22semidirect
61. #1438C22semidirect
62. #1437C22semidirect
63. #1437C22semidirect
64. C22⋊#95C22semidirect
65. C22⋊#95C22semidirect
66. C22⋊#95C22semidirect
67. C22⋊#95C22semidirect
68. C22⋊#95C22semidirect
69. C22⋊#95C22semidirect
70. C22⋊#95C22semidirect
77. C26C2×C4semidirect
96. C24×C4C23semidirect
103. C2×#120C2×C4semidirect
104. C2×#120C2×C4semidirect
105. C2×#120C2×C4semidirect
110. C22×C4⋊C4C23semidirect
111. C22×C4⋊C4C23semidirect
112. C22×C4⋊C4C23semidirect
127. C22×C22⋊C4D4semidirect
146. C22×C22⋊C4C23semidirect
147. C22×C22⋊C4C23semidirect
148. C22×C22⋊C4C23semidirect
149. C22×C42C23semidirect
150. C22×C42C23semidirect
151. C22×C42C23semidirect
167. #379C2×C4semidirect
168. #379C2×C4semidirect
169. #379C2×C4semidirect
170. #379D4semidirect
175. C2×#95C23semidirect
176. C2×#95C23semidirect
177. C2×#95C23semidirect
178. C2×#95C23semidirect
179. C2×#95C23semidirect
180. C2×#95C23semidirect
181. C2×#95C23semidirect
182. C2×#95C23semidirect
183. C2×#95C23semidirect
184. C2×#95C23semidirect
243. C22×D4C22×C4semidirect
244. C22×D4C22×C4semidirect
356. C2×C22⋊C4C22×C4semidirect
357. C2×C22⋊C4C22×C4semidirect
358. C2×C22⋊C4C22×C4semidirect
466. C24C4×D4semidirect
467. C24C4×D4semidirect
601. C22⋊C4#120semidirect
806. C22C4×#120semidirect
807. C22#2358semidirect

Maximal subgroups

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

subgroupindex
C24×C22⋊C42
C2×#28462
C2×#23582
C2×C4×#1202
C22×#3792
#146942
#146932
#141342
#141272
#139952
#139912
#139712
#139672
C22⋊C422
C4×#3792