Finite Group Databasebeta

← #154028

Subgroups — #154028

Order 512.

2606 conjugacy classes of subgroups.

The subgroup lattice has 885 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1445C211yesmaximal, characteristic
2C2×#1436C212yesmaximal
3C2×#1434C212yesmaximal
4#7556C211yesmaximal, characteristic
5#7556C212yesmaximal
6#7556C212yesmaximal
7#7554C211yesmaximal, characteristic
8#7554C212yesmaximal
9#7554C212yesmaximal
10C23×C4⋊C4C2211yescharacteristic
11C23×C42C2211yescharacteristic
12C23×C42C2212yes—
13C22×#95C2212yes—
14C22×#95C2212yes—
15C22×#95C2211yescharacteristic
16C22×#95C2212yes—
17C22×#95C2212yes—
18C22×#95C2212yes—
19C22×#95C2212yes—
20C22×#95C2212yes—
21C22×#95C2212yes—
22C22×#95C2212yes—
23C22×#95C2212yes—
24C22×#95C2211yescharacteristic
25C22×#95C2212yes—
26C22×#95C2211yescharacteristic
27C22×#95C2211yescharacteristic
28C22×#95C2212yes—
29C22×#95C2212yes—
30C22×#95C2211yescharacteristic
31#1445C418yescomplemented
32#1436C4116yescomplemented
33#1434—28no—
34C24×C4C2312yes—
35C24×C4C2312yes—
36C24×C4C2311yescharacteristic
37C24×C4C2312yes—
38C24×C4C2311yescharacteristic
39C24×C4C2312yes—
40C24×C4C2311yescharacteristic
41C24×C4C2312yes—
42C24×C4C2312yes—
43C22×C4⋊C4—41no—
44C22×C4⋊C4—42no—
45C22×C4⋊C4—41no—
46C22×C4⋊C4C2×C418yes—
47C22×C4⋊C4C2×C414yes—
48C22×C42—24no—
49C22×C42—24no—
50C22×C42—24no—
51C22×C42—22no—
52C22×C42—42no—
53C22×C42—42no—
54C22×C42—42no—
55C22×C42—42no—
56C22×C42—41no—
57C22×C42—42no—
58C22×C42—41no—
59C22×C42C2×C418yes—
60C2×#95—24no—
61C2×#95—24no—
62C2×#95—24no—
63C2×#95—24no—
64C2×#95—24no—
65C2×#95—24no—
66C2×#95—24no—
67C2×#95—24no—
68C2×#95—24no—
69C2×#95—24no—
70C2×#95—24no—
71C2×#95—24no—
72C2×#95—24no—
73C2×#95—24no—
74C2×#95—24no—
75C2×#95—24no—
76C2×#95—24no—
77C2×#95—24no—
78C2×#95—24no—
79C2×#95—41no—
80C2×#95—42no—
81C2×#95—41no—
82C2×#95—42no—
83C2×#95—42no—
84C2×#95—42no—
85C2×#95—42no—
86C2×#95—42no—
87C2×#95—42no—
88C2×#95—41no—
89C2×#95—41no—
90C2×#95—42no—
91C2×#95—42no—
92C2×#95—42no—
93C2×#95—42no—
94C2×#95—41no—
95C2×#95—42no—
96C2×#95—42no—
97C2×#95—42no—
98C2×#95—42no—
99C2×#95—41no—
100C2×#95—42no—
101C2×#95C2×C418yes—
102C2×#95C2×C418yes—
103C2×#95C2×C418yes—
104C2×#95C2×C418yes—
105C2×#95C2×C418yes—
106C2×#95C2×C418yes—
107C2×#95C2×C418yes—
108C2×#95C2×C414yes—
109C2×#95C2×C414yes—
110C2×#95D414yes—
111C25C2411yescharacteristic
112C23×C4—22no—
113C23×C4—22no—
114C23×C4—22no—
115C23×C4—22no—
116C23×C4—22no—
117C23×C4—22no—
118C23×C4—22no—
119C23×C4—22no—
120C23×C4—22no—
121C23×C4—22no—
122C23×C4—22no—
123C23×C4—22no—
124C23×C4—22no—
125C23×C4—22no—
126C23×C4—22no—
127C23×C4—22no—
128C23×C4—22no—
129C23×C4—22no—
130C23×C4—22no—
131C23×C4—22no—
132C23×C4—22no—
133C23×C4—22no—
134C23×C4—22no—
135C23×C4—22no—
136C23×C4—21no—
137C23×C4—22no—
138C23×C4—21no—
139C23×C4—22no—
140C23×C4—22no—
141C23×C4—22no—
142C23×C4—21no—
143C23×C4—22no—
144C23×C4—22no—
145C23×C4—22no—
146C23×C4—22no—
147C23×C4—22no—
148C23×C4—22no—
149C23×C4—22no—
150C23×C4—22no—
151C23×C4—21no—
152C23×C4—22no—
153C23×C4—22no—
154C23×C4—22no—
155C23×C4—22no—
156C23×C4—22no—
157C23×C4—22no—
158C23×C4—22no—
159C23×C4—22no—
160C23×C4—21no—
161C23×C4—22no—
162C23×C4—22no—
163C23×C4—22no—
164C23×C4—22no—
165C23×C4—22no—
166C23×C4—22no—
167C23×C4—22no—
168C23×C4—22no—
169C23×C4—21no—
170C23×C4—22no—
171C23×C4—22no—
172C23×C4—22no—
173C23×C4—22no—
174C23×C4—22no—
175C23×C4—22no—
176C23×C4—22no—
177C23×C4—22no—
178C23×C4—22no—
179C23×C4—22no—
180C23×C4—22no—
181C23×C4—22no—
182C23×C4—22no—
183C23×C4—22no—
184C23×C4—22no—
185C23×C4—22no—
186C23×C4—22no—
187C23×C4—22no—
188C23×C4—22no—
189C23×C4—22no—
190C23×C4—22no—
191C23×C4—22no—
192C23×C4—22no—
193C23×C4—22no—
194C23×C4—22no—
195C23×C4—22no—
196C23×C4—22no—
197C23×C4—21no—
198C23×C4—21no—
199C23×C4—22no—
200C23×C4—22no—
201C23×C4—22no—
202C23×C4—22no—
203C23×C4—22no—
204C23×C4—22no—
205C23×C4—22no—
206C23×C4—22no—
207C23×C4—22no—
208C23×C4—22no—
209C23×C4—22no—
210C23×C4—22no—
211C23×C4C22×C414yes—
212C23×C4C22×C414yes—
213C23×C4C22×C412yes—
214C23×C4C22×C414yes—
215C23×C4C22×C414yes—
216C23×C4C22×C414yes—
217C23×C4C22×C412yes—
218C23×C4C22×C414yes—
219C23×C4C22×C414yes—
220C23×C4C22×C414yes—
221C23×C4C22×C412yes—
222C23×C4C22×C414yes—
223C23×C4C2×D412yes—
224C23×C4C2×D414yes—
225C23×C4#4114yes—
226C23×C4#4114yes—
227C23×C4#4114yes—
228C23×C4#4114yes—
229C23×C4#4114yes—
230C23×C4#4112yes—
231C2×C4⋊C4—48no—
232C2×C4⋊C4—44no—
233C2×C4⋊C4—44no—
234C2×C4⋊C4—48no—
235C2×C4⋊C4C42116yescomplemented
236C2×C42—216no—
237C2×C42—48no—
238C2×C42—48no—
239C2×C42—48no—
240C2×C42—44no—
241C2×C42—48no—
242C2×C42—48no—
243C2×C42—48no—
244C2×C42—48no—
245C2×C42—48no—
246C2×C42—44no—
247C2×C42—44no—
248#95—216no—
249#95—216no—
250#95—216no—
251#95—216no—
252#95—48no—
253#95—48no—
254#95—44no—
255#95—44no—
256#95—48no—
257#95—44no—
258#95—48no—
259#95—48no—
260#95—48no—
261#95—48no—
262#95—44no—
263#95—48no—
264#95—48no—
265#95—44no—
266C24C23×C412yes—
267C24C23×C411yescharacteristic
268C24C22×D411yescharacteristic
269C24C2×#4112yes—
270C24C2×#4112yes—
271C24C2×#4112yes—
272C24C2×#4112yes—
273C24C2×#4112yes—
274C24C2×#4111yescharacteristic
275C24H(5,𝔽2)11yescharacteristic
276C24H(5,𝔽2)12yes—
277C24H(5,𝔽2)11yescharacteristic
278C24H(5,𝔽2)11yescharacteristic
279C24H(5,𝔽2)12yes—
280C24H(5,𝔽2)12yes—
281C242−1+412yes—
282C242−1+412yes—
283C242−1+412yes—
284C242−1+411yescharacteristic
285C22×C4—24no—
286C22×C4—24no—
287C22×C4—24no—
288C22×C4—24no—
289C22×C4—24no—
290C22×C4—24no—
291C22×C4—24no—
292C22×C4—24no—
293C22×C4—24no—
294C22×C4—24no—
295C22×C4—24no—
296C22×C4—24no—
297C22×C4—24no—
298C22×C4—24no—
299C22×C4—24no—
300C22×C4—24no—
301C22×C4—24no—
302C22×C4—24no—
303C22×C4—24no—
304C22×C4—24no—
305C22×C4—24no—
306C22×C4—22no—
307C22×C4—22no—
308C22×C4—24no—
309C22×C4—22no—
310C22×C4—24no—
311C22×C4—24no—
312C22×C4—24no—
313C22×C4—24no—
314C22×C4—24no—
315C22×C4—24no—
316C22×C4—24no—
317C22×C4—24no—
318C22×C4—24no—
319C22×C4—24no—
320C22×C4—24no—
321C22×C4—24no—
322C22×C4—24no—
323C22×C4—24no—
324C22×C4—24no—
325C22×C4—24no—
326C22×C4—24no—
327C22×C4—22no—
328C22×C4—24no—
329C22×C4—24no—
330C22×C4—24no—
331C22×C4—24no—
332C22×C4—24no—
333C22×C4—24no—
334C22×C4—24no—
335C22×C4—24no—
336C22×C4—22no—
337C22×C4—24no—
338C22×C4—22no—
339C22×C4—24no—
340C22×C4—24no—
341C22×C4—24no—
342C22×C4—24no—
343C22×C4—22no—
344C22×C4—24no—
345C22×C4—24no—
346C22×C4—24no—
347C22×C4—24no—
348C22×C4—24no—
349C22×C4—24no—
350C22×C4—22no—
351C22×C4—24no—
352C22×C4—24no—
353C22×C4—24no—
354C22×C4—24no—
355C22×C4—24no—
356C22×C4—24no—
357C22×C4—24no—
358C22×C4—24no—
359C22×C4—24no—
360C22×C4—24no—
361C22×C4—24no—
362C22×C4—24no—
363C22×C4—24no—
364C22×C4—24no—
365C22×C4—24no—
366C22×C4—24no—
367C22×C4—24no—
368C22×C4—24no—
369C22×C4—24no—
370C22×C4—24no—
371C22×C4—24no—
372C22×C4—24no—
373C22×C4—24no—
374C22×C4—24no—
375C22×C4—24no—
376C22×C4—24no—
377C22×C4—24no—
378C22×C4—24no—
379C22×C4—24no—
380C22×C4—24no—
381C22×C4—24no—
382C22×C4—24no—
383C22×C4—22no—
384C22×C4—24no—
385C22×C4—24no—
386C22×C4—24no—
387C22×C4—22no—
388C22×C4—24no—
389C22×C4—24no—
390C22×C4—24no—
391C22×C4—22no—
392C22×C4—24no—
393C22×C4—24no—
394C22×C4—24no—
395C22×C4—24no—
396C22×C4—24no—
397C22×C4—24no—
398C22×C4—42no—
399C22×C4—42no—
400C22×C4—42no—
401C22×C4—42no—
402C22×C4—42no—
403C22×C4—42no—
404C22×C4—42no—
405C22×C4—42no—
406C22×C4—42no—
407C22×C4—42no—
408C22×C4—42no—
409C22×C4—42no—
410C22×C4—42no—
411C22×C4—42no—
412C22×C4—42no—
413C22×C4—42no—
414C22×C4—42no—
415C22×C4—42no—
416C22×C4—42no—
417C22×C4—42no—
418C22×C4—42no—
419C22×C4—42no—
420C22×C4—42no—
421C22×C4—42no—
422C22×C4—42no—
423C22×C4—42no—
424C22×C4—42no—
425C22×C4—42no—
426C22×C4—42no—
427C22×C4—42no—
428C22×C4—42no—
429C22×C4—42no—
430C22×C4—42no—
431C22×C4—42no—
432C22×C4—42no—
433C22×C4—42no—
434C22×C4—42no—
435C22×C4—42no—
436C22×C4—42no—
437C22×C4—42no—
438C22×C4—42no—
439C22×C4—42no—
440C22×C4—42no—
441C22×C4—42no—
442C22×C4—42no—
443C22×C4—42no—
444C22×C4—42no—
445C22×C4—41no—
446C22×C4—41no—
447C22×C4—42no—
448C22×C4—41no—
449C22×C4—42no—
450C22×C4—42no—
451C22×C4—42no—
452C22×C4—42no—
453C22×C4—42no—
454C22×C4—42no—
455C22×C4—42no—
456C22×C4—42no—
457C22×C4—42no—
458C22×C4—42no—
459C22×C4—42no—
460C22×C4—42no—
461C22×C4—42no—
462C22×C4—41no—
463C22×C4—41no—
464C22×C4—42no—
465C22×C4—42no—
466C22×C4—41no—
467C22×C4—41no—
468C22×C4—42no—
469C22×C4—42no—
470C22×C4—42no—
471C22×C4—42no—
472C22×C4—42no—
473C22×C4—42no—
474C22×C4—42no—
475C22×C4—42no—
476C22×C4—42no—
477C22×C4—42no—
478C22×C4—42no—
479C22×C4—42no—
480C22×C4—41no—
481C22×C4—42no—
482C22×C4—42no—
483C22×C4—42no—
484C22×C4—42no—
485C22×C4—42no—
486C22×C4—42no—
487C22×C4—42no—
488C22×C4—42no—
489C22×C4—42no—
490C22×C4—42no—
491C22×C4—42no—
492C22×C4—42no—
493C22×C4—42no—
494C22×C4—42no—
495C22×C4—42no—
496C22×C4—42no—
497C22×C4—42no—
498C22×C4—42no—
499C22×C4—42no—
500C22×C4—42no—
501C22×C4—42no—
502C22×C4—42no—
503C22×C4—42no—
504C22×C4—42no—
505C22×C4—42no—
506C22×C4—42no—
507C22×C4—42no—
508C22×C4—42no—
509C22×C4—42no—
510C22×C4—42no—
511C22×C4—42no—
512C22×C4—42no—
513C22×C4—42no—
514C22×C4—42no—
515C22×C4—42no—
516C22×C4—42no—
517C22×C4—42no—
518C22×C4—42no—
519C22×C4—42no—
520C22×C4—42no—
521C22×C4—42no—
522C22×C4—41no—
523C22×C4—42no—
524C22×C4—42no—
525C22×C4—42no—
526C22×C4—42no—
527C22×C4—42no—
528C22×C4—42no—
529C22×C4—42no—
530C22×C4—42no—
531C22×C4—42no—
532C22×C4—42no—
533C22×C4—42no—
534C22×C4—42no—
535C22×C4—42no—
536C22×C4—42no—
537C22×C4—42no—
538C22×C4—42no—
539C22×C4—42no—
540C22×C4—42no—
541C22×C4—42no—
542C22×C4—41no—
543C22×C4—42no—
544C22×C4—41no—
545C22×C4—42no—
546C22×C4—42no—
547C22×C4—42no—
548C22×C4—42no—
549C22×C4—42no—
550C22×C4—42no—
551C22×C4—42no—
552C22×C4—42no—
553C22×C4—41no—
554C22×C4C2×C4214yes—
555C22×C4C2×C4218yes—
556C22×C4#11718yes—
557C22×C4#11718yes—
558C22×C4C4×D414yes—
559C22×C4C4×D418yes—
560C4⋊C4—416no—
561C42—432no—
562C42—416no—
563C23C22×C4211yescharacteristic
564C23C2×#11712yes—
565C23C2×#11712yes—
566C23C2×C4×D412yes—
567C23C2×C4×D411yescharacteristic
568C23C4×#4112yes—
569C23C4×#4112yes—
570C23C4×#4112yes—
571C23C4×#4111yescharacteristic
572C23C4×#4112yes—
573C23C4×#4112yes—
574C23#51812yes—
575C23#51812yes—
576C23#51812yes—
577C23#51811yescharacteristic
578C23#51811yescharacteristic
579C23#51811yescharacteristic
580C23#51912yes—
581C23#51912yes—
582C23#51912yes—
583C23#52012yes—
584C23#52012yes—
585C23#52011yescharacteristic
586C23#52012yes—
587C23#52012yes—
588C23#53411yescharacteristic
589C23#53512yes—
590C23#53711yescharacteristic
591C23#53812yes—
592C23#53812yes—
593C23#53812yes—
594C23#53812yes—
595C23#53811yescharacteristic
596C23#53912yes—
597C23#53912yes—
598C23#53912yes—
599C23#53912yes—
600C23#53912yes—
601C23#53912yes—
602C23#53911yescharacteristic
603C23#54012yes—
604C23#54012yes—
605C23#54012yes—
606C23#54112yes—
607C23#54112yes—
608C23#54112yes—
609C23#54212yes—
610C23#54212yes—
611C23#54212yes—
612C23#54212yes—
613C23#54212yes—
614C23#54612yes—
615C23#54712yes—
616C23#54712yes—
617C23#54812yes—
618C23#55112yes—
619C23#55112yes—
620C23#55111yescharacteristic
621C23#55112yes—
622C23#55111yescharacteristic
623C23#55212yes—
624C23#55212yes—
625C23#55212yes—
626C23#55212yes—
627C23#55212yes—
628C23#55212yes—
629C23#55212yes—
630C23#55312yes—
631C23#55312yes—
632C23#55312yes—
633C23#55312yes—
634C23#55312yes—
635C23#55612yes—
636C23#55612yes—
637C23#55912yes—
638C23#55911yescharacteristic
639C23#55911yescharacteristic
640C23H(3,𝔽4)11yescharacteristic
641C23#56212yes—
642C23#56212yes—
643C23#56212yes—
644C23#56312yes—
645C23#56312yes—
646C23#56311yescharacteristic
647C23#56311yescharacteristic
648C23#56311yescharacteristic
649C23#56312yes—
650C2×C4—28no—
651C2×C4—28no—
652C2×C4—28no—
653C2×C4—24no—
654C2×C4—28no—
655C2×C4—28no—
656C2×C4—28no—
657C2×C4—28no—
658C2×C4—28no—
659C2×C4—28no—
660C2×C4—28no—
661C2×C4—28no—
662C2×C4—28no—
663C2×C4—28no—
664C2×C4—24no—
665C2×C4—28no—
666C2×C4—44no—
667C2×C4—44no—
668C2×C4—44no—
669C2×C4—44no—
670C2×C4—44no—
671C2×C4—44no—
672C2×C4—44no—
673C2×C4—44no—
674C2×C4—44no—
675C2×C4—44no—
676C2×C4—44no—
677C2×C4—44no—
678C2×C4—44no—
679C2×C4—44no—
680C2×C4—44no—
681C2×C4—44no—
682C2×C4—44no—
683C2×C4—44no—
684C2×C4—44no—
685C2×C4—44no—
686C2×C4—44no—
687C2×C4—44no—
688C2×C4—44no—
689C2×C4—44no—
690C2×C4—44no—
691C2×C4—44no—
692C2×C4—42no—
693C2×C4—44no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—44no—
697C2×C4—44no—
698C2×C4—44no—
699C2×C4—42no—
700C2×C4—44no—
701C2×C4—44no—
702C2×C4—44no—
703C2×C4—44no—
704C2×C4—44no—
705C2×C4—42no—
706C2×C4—44no—
707C2×C4—42no—
708C2×C4—44no—
709C2×C4—44no—
710C2×C4—44no—
711C2×C4—44no—
712C2×C4—42no—
713C2×C4—44no—
714C2×C4—44no—
715C2×C4—44no—
716C2×C4—44no—
717C2×C4—44no—
718C2×C4—44no—
719C2×C4—44no—
720C2×C4—44no—
721C2×C4—44no—
722C2×C4—44no—
723C2×C4—44no—
724C2×C4—44no—
725C2×C4—44no—
726C2×C4—42no—
727C2×C4—44no—
728C2×C4—44no—
729C2×C4—44no—
730C2×C4—44no—
731C2×C4—44no—
732C2×C4—44no—
733C2×C4—44no—
734C2×C4—42no—
735C2×C4—44no—
736C2×C4—44no—
737C2×C4—44no—
738C2×C4—44no—
739C2×C4—44no—
740C2×C4—44no—
741C2×C4—44no—
742C2×C4—44no—
743C2×C4—44no—
744C2×C4—42no—
745C2×C4—44no—
746C2×C4—44no—
747C2×C4—42no—
748C2×C4—44no—
749C2×C4—82no—
750C2×C4—82no—
751C2×C4—82no—
752C2×C4—82no—
753C2×C4—82no—
754C2×C4—82no—
755C2×C4—82no—
756C2×C4—82no—
757C2×C4—82no—
758C2×C4—82no—
759C2×C4—82no—
760C2×C4—82no—
761C2×C4—82no—
762C2×C4—82no—
763C2×C4—82no—
764C2×C4—82no—
765C2×C4—82no—
766C2×C4—82no—
767C2×C4—82no—
768C2×C4—82no—
769C22C4×#11712yes—
770C22C42×D411yescharacteristic
771C22#227311yescharacteristic
772C22#227511yescharacteristic
773C22#227612yes—
774C22#231312yes—
775C22#231412yes—
776C22#231812yes—
777C22#232012yes—
778C22#232112yes—
779C22#232412yes—
780C22#232511yescharacteristic
781C22#232811yescharacteristic
782C22#233212yes—
783C22#233212yes—
784C22#233311yescharacteristic
785C22#233312yes—
786C22#233412yes—
787C22#233412yes—
788C22#233512yes—
789C22#233512yes—
790C22#233512yes—
791C22#233612yes—
792C22#233612yes—
793C22#233711yescharacteristic
794C22#234312yes—
795C22#234412yes—
796C22#235212yes—
797C22#235312yes—
798C22#235312yes—
799C22#235612yes—
800C22#235712yes—
801C22#235712yes—
802C22#235912yes—
803C22#235912yes—
804C22#236212yes—
805C22#236212yes—
806C22#237112yes—
807C22#237112yes—
808C22#237312yes—
809C22#237312yes—
810C22#237411yescharacteristic
811C22#237412yes—
812C22#237411yescharacteristic
813C22#237812yes—
814C22#237812yes—
815C22#237812yes—
816C22#237911yescharacteristic
817C22#237912yes—
818C22#238111yescharacteristic
819C22#238112yes—
820C22#270812yes—
821C22#271012yes—
822C22#271112yes—
823C22#271211yescharacteristic
824C22#271812yes—
825C22#272211yescharacteristic
826C22#272312yes—
827C22#272411yescharacteristic
828C22#272512yes—
829C22#272811yescharacteristic
830C22#273611yescharacteristic
831C22#273812yes—
832C22#273912yes—
833C22#274012yes—
834C22#274112yes—
835C22#275012yes—
836C22#275012yes—
837C22#275112yes—
838C22#275312yes—
839C22#275412yes—
840C22#275812yes—
841C22#276512yes—
842C22#276612yes—
843C22#277012yes—
844C22#277112yes—
845C22#277111yescharacteristic
846C22#277212yes—
847C22#277312yes—
848C22#277312yes—
849C22#277712yes—
850C22#277712yes—
851C22#278612yes—
852C22#278712yes—
853C22#278712yes—
854C22#278911yescharacteristic
855C22#279411yescharacteristic
856C4—48no—
857C4—48no—
858C4—48no—
859C4—48no—
860C4—44no—
861C4—44no—
862C4—82no—
863C4—84no—
864C4—84no—
865C2#1378712yes—
866C2#1379111yescharacteristic
867C2#1380711yescharacteristic
868C2#1381512yes—
869C2#1383411yescharacteristic
870C2#1438412yes—
871C2#1438812yes—
872C2#1441212yes—
873C2#1441612yes—
874C2#1448012yes—
875C2#1448112yes—
876C2#1449012yes—
877C2#1449112yes—
878C2#1457711yescharacteristic
879C2#1457812yes—
880C2#1459011yescharacteristic
881C2#1460611yescharacteristic
882C2#1460712yes—
883C2#1461311yescharacteristic
subgroupG/H
center, Frattini, socle, prime radical, cosocleC25C24
commutatorC23C22×C42
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C25 ◁ G
LECSG ▷ C25 ▷ C1

Complements

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

NH ≅ G/Ntype
31. #1445C4semidirect
32. #1436C4semidirect
235. C2×C4⋊C4C42semidirect

Maximal subgroups

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

subgroupindex
C2×#14452
C2×#14362
C2×#14342
#75562
#75542