Finite Group Databasebeta

← #154306

Subgroups — #154306

Order 512.

4090 conjugacy classes of subgroups.

The subgroup lattice has 874 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#388C211yesmaximal, characteristic
2C22×C4×C4⋊C4C211yesmaximal, characteristic, complemented
3C2×#1441C212yesmaximal, complemented
4C2×#1439C212yesmaximal
5C2×#1439C212yesmaximal
6C2×#1437C212yesmaximal
7C2×C4⋊#95C211yesmaximal, characteristic, complemented
8#7557C212yesmaximal, complemented
9#7554C212yesmaximal, complemented
10C23×C4⋊C4C2211yescharacteristic
11C23×C4⋊C4C2212yes—
12C23×C4⋊C4C2212yes—
13C23×C22⋊C4C2211yescharacteristic
14C23×C22⋊C4C2211yescharacteristic
15C23×C22⋊C4C2214yes—
16C23×C22⋊C4C2211yescharacteristic
17C23×C42C2212yes—
18C23×C42C2211yescharacteristic
19C2×#388—24no—
20C2×#388—24no—
21C2×#388C418yescomplemented
22C2×C4×C4⋊C4—24no—
23C2×C4×C4⋊C4—28no—
24C22×#95C2214yes—
25C22×#95C2212yes—
26C22×#95C2212yes—
27C22×#95C2214yes—
28C22×#95C2214yes—
29C22×#95C2211yescharacteristic
30C22×#95C2211yescharacteristic
31C22×#95C2212yes—
32#1441—28no—
33#1439—28no—
34#1439—28no—
35#1437—28no—
36C4⋊#95—24no—
37C26C2311yescharacteristic
38C24×C4C2311yescharacteristic
39C24×C4C2311yescharacteristic
40C24×C4C2314yes—
41C24×C4C2311yescharacteristic
42C24×C4C2314yes—
43C24×C4C2311yescharacteristic
44C24×C4C2311yescharacteristic
45C24×C4C2311yescharacteristic
46C22×C4⋊C4—28no—
47C22×C4⋊C4—24no—
48C22×C4⋊C4—28no—
49C22×C4⋊C4—24no—
50C22×C4⋊C4—24no—
51C22×C4⋊C4—24no—
52C22×C4⋊C4—22no—
53C22×C4⋊C4—22no—
54C22×C4⋊C4—28no—
55C22×C4⋊C4—24no—
56C22×C4⋊C4—24no—
57C22×C4⋊C4—24no—
58C22×C4⋊C4—44no—
59C22×C4⋊C4C2×C414yes—
60C22×C4⋊C4D418yes—
61C22×C22⋊C4—22no—
62C22×C22⋊C4—22no—
63C22×C22⋊C4—22no—
64C22×C22⋊C4—22no—
65C22×C22⋊C4—28no—
66C22×C22⋊C4—24no—
67C22×C22⋊C4—24no—
68C22×C22⋊C4—22no—
69C22×C22⋊C4—22no—
70C22×C22⋊C4—22no—
71C22×C22⋊C4—22no—
72C22×C22⋊C4—28no—
73C22×C22⋊C4—28no—
74C22×C22⋊C4—24no—
75C22×C22⋊C4—24no—
76C22×C22⋊C4—28no—
77C22×C22⋊C4—28no—
78C22×C22⋊C4—44no—
79C22×C22⋊C4—44no—
80C22×C22⋊C4C2×C414yes—
81C22×C22⋊C4C2×C414yes—
82C22×C22⋊C4C2×C414yes—
83C22×C22⋊C4D414yes—
84C22×C22⋊C4Q814yes—
85C22×C42—24no—
86C22×C42—24no—
87C22×C42—28no—
88C22×C42—24no—
89C22×C42—24no—
90C22×C42—24no—
91C22×C42—44no—
92C22×C42C2×C414yes—
93C22×C42D414yes—
94C22×C42D414yes—
95#388—232no—
96C4×C4⋊C4—232no—
97C2×#95—24no—
98C2×#95—24no—
99C2×#95—22no—
100C2×#95—22no—
101C2×#95—22no—
102C2×#95—22no—
103C2×#95—24no—
104C2×#95—24no—
105C2×#95—28no—
106C2×#95—24no—
107C2×#95—28no—
108C2×#95—28no—
109C2×#95—24no—
110C2×#95—28no—
111C2×#95—28no—
112C2×#95—24no—
113C2×#95—28no—
114C2×#95—28no—
115C2×#95—24no—
116C2×#95—44no—
117C2×#95—44no—
118C2×#95C2×C414yes—
119C2×#95C2×C414yes—
120C2×#95D418yes—
121C25—21no—
122C25—21no—
123C25—22no—
124C25—22no—
125C25—21no—
126C25—21no—
127C25—22no—
128C25—22no—
129C25—24no—
130C25—24no—
131C25—22no—
132C25—22no—
133C25—22no—
134C25—22no—
135C25C22×C412yes—
136C25C2×D412yes—
137C25C2×Q812yes—
138C25C2411yescharacteristic
139C23×C4—22no—
140C23×C4—22no—
141C23×C4—24no—
142C23×C4—24no—
143C23×C4—22no—
144C23×C4—22no—
145C23×C4—22no—
146C23×C4—22no—
147C23×C4—22no—
148C23×C4—22no—
149C23×C4—21no—
150C23×C4—21no—
151C23×C4—24no—
152C23×C4—22no—
153C23×C4—24no—
154C23×C4—24no—
155C23×C4—21no—
156C23×C4—21no—
157C23×C4—24no—
158C23×C4—22no—
159C23×C4—24no—
160C23×C4—24no—
161C23×C4—24no—
162C23×C4—24no—
163C23×C4—24no—
164C23×C4—24no—
165C23×C4—22no—
166C23×C4—24no—
167C23×C4—22no—
168C23×C4—24no—
169C23×C4—21no—
170C23×C4—21no—
171C23×C4—24no—
172C23×C4—21no—
173C23×C4—21no—
174C23×C4—22no—
175C23×C4—22no—
176C23×C4—24no—
177C23×C4—24no—
178C23×C4—22no—
179C23×C4—24no—
180C23×C4—24no—
181C23×C4—22no—
182C23×C4—22no—
183C23×C4—24no—
184C23×C4—22no—
185C23×C4—24no—
186C23×C4—24no—
187C23×C4—24no—
188C23×C4—24no—
189C23×C4—24no—
190C23×C4—24no—
191C23×C4—24no—
192C23×C4—24no—
193C23×C4—24no—
194C23×C4—22no—
195C23×C4—22no—
196C23×C4—24no—
197C23×C4C22×C412yes—
198C23×C4C22×C412yes—
199C23×C4C22×C412yes—
200C23×C4C22×C412yes—
201C23×C4C22×C412yes—
202C23×C4C22×C412yes—
203C23×C4C2×D412yes—
204C23×C4C2×D418yes—
205C23×C4C2×D418yes—
206C23×C4C2×D412yes—
207C23×C4C2×D412yes—
208C23×C4C2×D412yes—
209C23×C4C2×D412yes—
210C23×C4C2×D412yes—
211C23×C4C2×D412yes—
212C23×C4C2×D412yes—
213C23×C4C2×D414yes—
214C23×C4C2×D414yes—
215C23×C4C2×Q812yes—
216C23×C4C2×Q812yes—
217C23×C4#4118yes—
218C23×C4#4118yes—
219C23×C4#4112yes—
220C23×C4#4112yes—
221C23×C4#4114yes—
222C23×C4#4114yes—
223C2×C4⋊C4—216no—
224C2×C4⋊C4—232no—
225C2×C4⋊C4—216no—
226C2×C4⋊C4—232no—
227C2×C4⋊C4—216no—
228C2×C4⋊C4—216no—
229C2×C4⋊C4—28no—
230C2×C4⋊C4—216no—
231C2×C4⋊C4—416no—
232C2×C4⋊C4—416no—
233C2×C4⋊C4—48no—
234C2×C4⋊C4—48no—
235C2×C4⋊C4—48no—
236C2×C4⋊C4—44no—
237C2×C4⋊C4—44no—
238C2×C22⋊C4—28no—
239C2×C22⋊C4—28no—
240C2×C22⋊C4—28no—
241C2×C22⋊C4—28no—
242C2×C22⋊C4—28no—
243C2×C22⋊C4—28no—
244C2×C22⋊C4—232no—
245C2×C22⋊C4—28no—
246C2×C22⋊C4—28no—
247C2×C22⋊C4—216no—
248C2×C22⋊C4—216no—
249C2×C22⋊C4—416no—
250C2×C22⋊C4—416no—
251C2×C22⋊C4—416no—
252C2×C22⋊C4—416no—
253C2×C22⋊C4—416no—
254C2×C22⋊C4—44no—
255C2×C22⋊C4—416no—
256C2×C22⋊C4—48no—
257C2×C22⋊C4—48no—
258C2×C22⋊C4—44no—
259C2×C22⋊C4—44no—
260C2×C22⋊C4—44no—
261C2×C22⋊C4C4⋊C4116yescomplemented
262C2×C42—216no—
263C2×C42—28no—
264C2×C42—216no—
265C2×C42—28no—
266C2×C42—216no—
267C2×C42—416no—
268C2×C42—416no—
269C2×C42—48no—
270C2×C42—48no—
271C2×C42C22⋊C4116yescomplemented
272#95—28no—
273#95—28no—
274#95—216no—
275#95—416no—
276#95—416no—
277#95—416no—
278#95—48no—
279#95—48no—
280C24—22no—
281C24—22no—
282C24—24no—
283C24—24no—
284C24—24no—
285C24—24no—
286C24—24no—
287C24—24no—
288C24—22no—
289C24—22no—
290C24—22no—
291C24—22no—
292C24—28no—
293C24—28no—
294C24—24no—
295C24—24no—
296C24—24no—
297C24—24no—
298C24—24no—
299C24—24no—
300C24—24no—
301C24—24no—
302C24—41no—
303C24—42no—
304C24—44no—
305C24—42no—
306C24—41no—
307C24—42no—
308C24—42no—
309C24—44no—
310C24—41no—
311C24—44no—
312C24—44no—
313C24—44no—
314C24—41no—
315C24—42no—
316C24—42no—
317C24—44no—
318C24—41no—
319C24—41no—
320C24—41no—
321C24—41no—
322C24—42no—
323C24—42no—
324C24—44no—
325C24—44no—
326C24—44no—
327C24—44no—
328C24—44no—
329C24—44no—
330C24—42no—
331C24—42no—
332C24—44no—
333C24—42no—
334C24—44no—
335C24—42no—
336C24—44no—
337C24—42no—
338C24—44no—
339C24—42no—
340C24—42no—
341C24—42no—
342C24—44no—
343C24—44no—
344C24C2×C4⋊C414yes—
345C24C23×C411yescharacteristic
346C24C22×D411yescharacteristic
347C24C22×D411yescharacteristic
348C24C22×D411yescharacteristic
349C24C22×D412yes—
350C24C22×D412yes—
351C24C22×Q811yescharacteristic
352C24C2×#4111yescharacteristic
353C24C2×#4111yescharacteristic
354C24C2×#4112yes—
355C24C2×#4112yes—
356C24C2×#4114yes—
357C24C2×#4114yes—
358C24H(5,𝔽2)12yes—
359C24H(5,𝔽2)12yes—
360C242−1+412yes—
361C242−1+412yes—
362C22×C4—24no—
363C22×C4—24no—
364C22×C4—24no—
365C22×C4—24no—
366C22×C4—24no—
367C22×C4—24no—
368C22×C4—22no—
369C22×C4—22no—
370C22×C4—24no—
371C22×C4—24no—
372C22×C4—28no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—24no—
376C22×C4—24no—
377C22×C4—28no—
378C22×C4—28no—
379C22×C4—24no—
380C22×C4—28no—
381C22×C4—24no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—24no—
387C22×C4—24no—
388C22×C4—24no—
389C22×C4—24no—
390C22×C4—28no—
391C22×C4—24no—
392C22×C4—28no—
393C22×C4—24no—
394C22×C4—24no—
395C22×C4—28no—
396C22×C4—24no—
397C22×C4—28no—
398C22×C4—24no—
399C22×C4—24no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—24no—
403C22×C4—24no—
404C22×C4—28no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—28no—
408C22×C4—28no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—28no—
412C22×C4—28no—
413C22×C4—28no—
414C22×C4—28no—
415C22×C4—28no—
416C22×C4—28no—
417C22×C4—28no—
418C22×C4—24no—
419C22×C4—28no—
420C22×C4—28no—
421C22×C4—28no—
422C22×C4—28no—
423C22×C4—28no—
424C22×C4—28no—
425C22×C4—24no—
426C22×C4—28no—
427C22×C4—28no—
428C22×C4—24no—
429C22×C4—24no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—24no—
433C22×C4—24no—
434C22×C4—24no—
435C22×C4—24no—
436C22×C4—24no—
437C22×C4—24no—
438C22×C4—28no—
439C22×C4—28no—
440C22×C4—28no—
441C22×C4—28no—
442C22×C4—28no—
443C22×C4—28no—
444C22×C4—28no—
445C22×C4—44no—
446C22×C4—42no—
447C22×C4—44no—
448C22×C4—41no—
449C22×C4—44no—
450C22×C4—41no—
451C22×C4—44no—
452C22×C4—44no—
453C22×C4—41no—
454C22×C4—41no—
455C22×C4—42no—
456C22×C4—44no—
457C22×C4—44no—
458C22×C4—44no—
459C22×C4—44no—
460C22×C4—44no—
461C22×C4—44no—
462C22×C4—42no—
463C22×C4—44no—
464C22×C4—44no—
465C22×C4—42no—
466C22×C4—42no—
467C22×C4—44no—
468C22×C4—42no—
469C22×C4—44no—
470C22×C4—44no—
471C22×C4—41no—
472C22×C4—44no—
473C22×C4—44no—
474C22×C4—44no—
475C22×C4—44no—
476C22×C4—42no—
477C22×C4—42no—
478C22×C4—44no—
479C22×C4—42no—
480C22×C4—41no—
481C22×C4—44no—
482C22×C4—42no—
483C22×C4—42no—
484C22×C4—44no—
485C22×C4—41no—
486C22×C4—41no—
487C22×C4—44no—
488C22×C4—44no—
489C22×C4—44no—
490C22×C4—41no—
491C22×C4—41no—
492C22×C4—44no—
493C22×C4—44no—
494C22×C4—42no—
495C22×C4—42no—
496C22×C4—44no—
497C22×C4—44no—
498C22×C4—44no—
499C22×C4—41no—
500C22×C4—41no—
501C22×C4—42no—
502C22×C4—44no—
503C22×C4—44no—
504C22×C4—44no—
505C22×C4—44no—
506C22×C4—44no—
507C22×C4—44no—
508C22×C4—44no—
509C22×C4—44no—
510C22×C4—44no—
511C22×C4—44no—
512C22×C4—44no—
513C22×C4—44no—
514C22×C4—44no—
515C22×C4—44no—
516C22×C4—44no—
517C22×C4—44no—
518C22×C4—44no—
519C22×C4—44no—
520C22×C4—44no—
521C22×C4—44no—
522C22×C4—44no—
523C22×C4C2×C22⋊C414yes—
524C22×C4C2×C22⋊C414yes—
525C22×C4C2×C22⋊C414yes—
526C22×C4C2×C4⋊C414yes—
527C22×C4C2×C4⋊C414yes—
528C22×C4#11714yes—
529C22×C4C4×D418yes—
530C22×C4C4×D418yes—
531C22×C4#12014yes—
532C22×C4#121116yes—
533C22×C4#12114yes—
534C22×C4#12114yes—
535C22×C4#12118yes—
536C22×C4#12118yes—
537C22×C4C22⋊Q814yes—
538C22×C4C22⋊Q814yes—
539C22×C4#12314yes—
540C22×C4#12414yes—
541C22×C4#12714yes—
542C4⋊C4—264no—
543C4⋊C4—432no—
544C4⋊C4—416no—
545C22⋊C4—232no—
546C22⋊C4—464no—
547C22⋊C4—416no—
548C22⋊C4—416no—
549C42—232no—
550C42—432no—
551C23—28no—
552C23—28no—
553C23—24no—
554C23—28no—
555C23—42no—
556C23—42no—
557C23—42no—
558C23—48no—
559C23—48no—
560C23—44no—
561C23—44no—
562C23—48no—
563C23—48no—
564C23—44no—
565C23—44no—
566C23—44no—
567C23—44no—
568C23—42no—
569C23—42no—
570C23—44no—
571C23—44no—
572C23—48no—
573C23—48no—
574C23—48no—
575C23—48no—
576C23—48no—
577C23—48no—
578C23—42no—
579C23—42no—
580C23—44no—
581C23—44no—
582C23—42no—
583C23—42no—
584C23—42no—
585C23—42no—
586C23—42no—
587C23—42no—
588C23—42no—
589C23—44no—
590C23—48no—
591C23—48no—
592C23—82no—
593C23—82no—
594C23—82no—
595C23—84no—
596C23—82no—
597C23—82no—
598C23—82no—
599C23—82no—
600C23—82no—
601C23—82no—
602C23—82no—
603C23—82no—
604C23—84no—
605C23—84no—
606C23—82no—
607C23—84no—
608C23—84no—
609C23—82no—
610C23—84no—
611C23—84no—
612C23—82no—
613C23—82no—
614C23—82no—
615C23—84no—
616C23C22×C22⋊C411yescharacteristic
617C23C22×C4⋊C411yescharacteristic
618C23C2×#11711yescharacteristic
619C23C2×C4×D412yes—
620C23C2×C4×D412yes—
621C23C4×#4112yes—
622C23C4×#4112yes—
623C23#52012yes—
624C23#52012yes—
625C23C2×#12011yescharacteristic
626C23C2×#12112yes—
627C23C2×#12114yes—
628C23C2×#12112yes—
629C23C2×#12111yescharacteristic
630C23C2×#12111yescharacteristic
631C23C2×C22⋊Q811yescharacteristic
632C23C2×C22⋊Q811yescharacteristic
633C23C2×#12311yescharacteristic
634C23#52514yes—
635C23#52512yes—
636C23#52512yes—
637C23#52514yes—
638C23C2×#12411yescharacteristic
639C23#52914yes—
640C23#52914yes—
641C23#52914yes—
642C23C2×#12711yescharacteristic
643C23#53212yes—
644C23#53214yes—
645C23#53212yes—
646C23#53314yes—
647C23#53511yescharacteristic
648C23#53511yescharacteristic
649C23#53611yescharacteristic
650C23#53611yescharacteristic
651C23#53712yes—
652C23#53712yes—
653C23#53814yes—
654C23#53914yes—
655C23#54114yes—
656C23#54214yes—
657C23D4212yes—
658C23D4212yes—
659C23#54612yes—
660C23#54614yes—
661C23#54614yes—
662C23#54712yes—
663C23#54712yes—
664C23#54712yes—
665C23#54714yes—
666C23#54812yes—
667C23#54814yes—
668C23D4×Q812yes—
669C23D4×Q812yes—
670C23#55012yes—
671C23#55114yes—
672C23#55214yes—
673C23#55212yes—
674C23#55312yes—
675C23#55412yes—
676C23#55412yes—
677C23#55512yes—
678C23#55614yes—
679C23#55612yes—
680C23#55914yes—
681C2×C4—24no—
682C2×C4—24no—
683C2×C4—28no—
684C2×C4—28no—
685C2×C4—28no—
686C2×C4—28no—
687C2×C4—28no—
688C2×C4—28no—
689C2×C4—216no—
690C2×C4—24no—
691C2×C4—24no—
692C2×C4—28no—
693C2×C4—28no—
694C2×C4—28no—
695C2×C4—28no—
696C2×C4—28no—
697C2×C4—24no—
698C2×C4—24no—
699C2×C4—28no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—24no—
704C2×C4—216no—
705C2×C4—216no—
706C2×C4—28no—
707C2×C4—216no—
708C2×C4—216no—
709C2×C4—24no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—44no—
713C2×C4—48no—
714C2×C4—48no—
715C2×C4—48no—
716C2×C4—48no—
717C2×C4—48no—
718C2×C4—48no—
719C2×C4—48no—
720C2×C4—48no—
721C2×C4—48no—
722C2×C4—48no—
723C2×C4—44no—
724C2×C4—48no—
725C2×C4—44no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—48no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—48no—
733C2×C4—48no—
734C2×C4—48no—
735C2×C4—48no—
736C2×C4—48no—
737C2×C4—48no—
738C2×C4—48no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—48no—
745C2×C4—48no—
746C2×C4—82no—
747C2×C4—82no—
748C2×C4—82no—
749C2×C4—82no—
750C2×C4—82no—
751C2×C4—84no—
752C2×C4—84no—
753C2×C4—84no—
754C2×C4—84no—
755C2×C4—84no—
756C2×C4—84no—
757C2×C4—82no—
758C2×C4—84no—
759C2×C4—82no—
760C2×C4—82no—
761C2×C4—84no—
762C2×C4#38018yes—
763C2×C4#38618yes—
764C2×C4#39018yes—
765C22—44no—
766C22—416no—
767C22—44no—
768C22—44no—
769C22—84no—
770C22—84no—
771C22—84no—
772C22—88no—
773C22—82no—
774C22—82no—
775C22—82no—
776C22—82no—
777C22—84no—
778C22—84no—
779C22—84no—
780C22—84no—
781C22—84no—
782C22C2×#38011yescharacteristic
783C22C2×#38611yescharacteristic
784C22C2×#39011yescharacteristic
785C22#229612yes—
786C22#229711yescharacteristic
787C22#229711yescharacteristic
788C22#229812yes—
789C22C4×#12114yes—
790C22#231111yescharacteristic
791C22#231111yescharacteristic
792C22#233414yes—
793C22D4×C4⋊C412yes—
794C22D4×C4⋊C412yes—
795C22#235212yes—
796C22#235412yes—
797C22#235914yes—
798C22#236714yes—
799C22#239212yes—
800C22#239212yes—
801C22#239612yes—
802C22#239612yes—
803C22#240811yescharacteristic
804C22#240911yescharacteristic
805C22#241112yes—
806C22#241312yes—
807C22#241612yes—
808C22#241712yes—
809C22#242414yes—
810C22#242514yes—
811C22#242614yes—
812C22#242914yes—
813C22#243012yes—
814C22#245514yes—
815C22#245914yes—
816C22#246114yes—
817C22#246514yes—
818C22#246914yes—
819C22#247814yes—
820C22#248611yescharacteristic
821C22#248711yescharacteristic
822C22#249812yes—
823C22#251914yes—
824C22#253214yes—
825C22#253712yes—
826C22#253812yes—
827C22#254012yes—
828C22#254111yescharacteristic
829C22#254211yescharacteristic
830C22#254412yes—
831C22#254512yes—
832C22#254711yescharacteristic
833C22#255414yes—
834C22#255614yes—
835C22#256311yescharacteristic
836C22#258914yes—
837C22#259212yes—
838C22#259614yes—
839C22#263612yes—
840C22#263712yes—
841C22#266212yes—
842C22#266412yes—
843C22#284712yes—
844C22#285012yes—
845C22#285412yes—
846C22#285612yes—
847C4—28no—
848C4—28no—
849C4—28no—
850C4—44no—
851C4—416no—
852C4—82no—
853C4—82no—
854C4—88no—
855C2—84no—
856C2#1385211yescharacteristic
857C2#1387211yescharacteristic
858C2#1390611yescharacteristic
859C2#1411214yes—
860C2#1411914yes—
861C2#1413511yescharacteristic
862C2#1415311yescharacteristic
863C2#1429111yescharacteristic
864C2#1469811yescharacteristic
865C2#1480612yes—
866C2#1480812yes—
867C2#1481512yes—
868C2#1486612yes—
869C2#1487012yes—
870C2#1487712yes—
871C2#1508112yes—
872C2#1510312yes—
subgroupG/H
center, Frattini, socle, cosocleC25C24
commutatorC24C23×C4
prime radicalC26C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C25 ◁ G
LECSG ▷ C25 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C22×C4×C4⋊C4C2semidirect
3. C2×#1441C2semidirect
7. C2×C4⋊#95C2semidirect
8. #7557C2semidirect
9. #7554C2semidirect
21. C2×#388C4semidirect
261. C2×C22⋊C4C4⋊C4semidirect
271. C2×C42C22⋊C4semidirect

Maximal subgroups

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

subgroupindex
C22×#3882
C22×C4×C4⋊C42
C2×#14412
C2×#14392
C2×#14372
C2×C4⋊#952
#75572
#75542