Finite Group Databasebeta

← #156377

Subgroups — #156377

Order 512.

2394 conjugacy classes of subgroups.

The subgroup lattice has 907 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#400C211yesmaximal, characteristic
2C2×#1445C211yesmaximal, characteristic
3C2×#1436C211yesmaximal, characteristic
4#7557C212yesmaximal
5#7556C212yesmaximal
6#7556C212yesmaximal
7#7556C212yesmaximal
8#7556C212yesmaximal
9#7554C212yesmaximal
10C23×C4⋊C4C2211yescharacteristic
11C23×C4⋊C4C2211yescharacteristic
12C23×C42C2211yescharacteristic
13C2×#400—24no—
14C2×#400—24no—
15C2×#400C418yescomplemented
16C22×#95C2212yes—
17C22×#95C2212yes—
18C22×#95C2212yes—
19C22×#95C2212yes—
20C22×#95C2212yes—
21C22×#95C2212yes—
22C22×#95C2212yes—
23C22×#95C2212yes—
24C22×#95C2212yes—
25C22×#95C2212yes—
26C22×#95C2211yescharacteristic
27C22×#95C2211yescharacteristic
28C22×#95C2211yescharacteristic
29C22×#95C2212yes—
30C22×#95C2212yes—
31C22×#95C2212yes—
32C22×#95C2211yescharacteristic
33C22×#95C2212yes—
34#1445—24no—
35#1436—24no—
36C24×C4C2312yes—
37C24×C4C2312yes—
38C24×C4C2312yes—
39C24×C4C2312yes—
40C24×C4C2312yes—
41C24×C4C2311yescharacteristic
42C24×C4C2311yescharacteristic
43C24×C4C2311yescharacteristic
44C24×C4C2312yes—
45C22×C4⋊C4—22no—
46C22×C4⋊C4—22no—
47C22×C4⋊C4—41no—
48C22×C4⋊C4—41no—
49C22×C4⋊C4—41no—
50C22×C4⋊C4—41no—
51C22×C4⋊C4—41no—
52C22×C4⋊C4—41no—
53C22×C4⋊C4—41no—
54C22×C4⋊C4—41no—
55C22×C4⋊C4C2×C414yes—
56C22×C4⋊C4C2×C414yes—
57C22×C4⋊C4D414yes—
58C22×C4⋊C4D414yes—
59C22×C42—22no—
60C22×C42—24no—
61C22×C42—41no—
62C22×C42—42no—
63C22×C42—41no—
64#400—232no—
65C2×#95—24no—
66C2×#95—24no—
67C2×#95—24no—
68C2×#95—24no—
69C2×#95—22no—
70C2×#95—22no—
71C2×#95—24no—
72C2×#95—24no—
73C2×#95—24no—
74C2×#95—24no—
75C2×#95—22no—
76C2×#95—24no—
77C2×#95—24no—
78C2×#95—22no—
79C2×#95—22no—
80C2×#95—24no—
81C2×#95—24no—
82C2×#95—24no—
83C2×#95—24no—
84C2×#95—24no—
85C2×#95—24no—
86C2×#95—24no—
87C2×#95—24no—
88C2×#95—24no—
89C2×#95—24no—
90C2×#95—24no—
91C2×#95—24no—
92C2×#95—24no—
93C2×#95—24no—
94C2×#95—24no—
95C2×#95—42no—
96C2×#95—42no—
97C2×#95—42no—
98C2×#95—42no—
99C2×#95—42no—
100C2×#95—42no—
101C2×#95—41no—
102C2×#95—41no—
103C2×#95—41no—
104C2×#95—41no—
105C2×#95—41no—
106C2×#95—41no—
107C2×#95—42no—
108C2×#95—42no—
109C2×#95—42no—
110C2×#95—42no—
111C2×#95—42no—
112C2×#95—42no—
113C2×#95—42no—
114C2×#95—42no—
115C2×#95—42no—
116C2×#95C2×C418yes—
117C2×#95C2×C418yes—
118C2×#95C2×C414yes—
119C25C2411yescharacteristic
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—21no—
131C23×C4—21no—
132C23×C4—21no—
133C23×C4—21no—
134C23×C4—21no—
135C23×C4—21no—
136C23×C4—21no—
137C23×C4—21no—
138C23×C4—21no—
139C23×C4—21no—
140C23×C4—21no—
141C23×C4—21no—
142C23×C4—22no—
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—22no—
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—22no—
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—22no—
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—22no—
198C23×C4—22no—
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×C4—22no—
212C23×C4—22no—
213C23×C4—22no—
214C23×C4—22no—
215C23×C4—22no—
216C23×C4—22no—
217C23×C4—22no—
218C23×C4—22no—
219C23×C4—22no—
220C23×C4—22no—
221C23×C4—22no—
222C23×C4—22no—
223C23×C4—22no—
224C23×C4—22no—
225C23×C4—22no—
226C23×C4C22×C414yes—
227C23×C4C22×C414yes—
228C23×C4C22×C412yes—
229C23×C4C22×C412yes—
230C23×C4C22×C412yes—
231C23×C4C2×D412yes—
232C23×C4C2×D412yes—
233C23×C4C2×D412yes—
234C23×C4C2×D412yes—
235C23×C4C2×D412yes—
236C23×C4C2×D412yes—
237C23×C4#4114yes—
238C23×C4#4114yes—
239C23×C4#4114yes—
240C23×C4#4114yes—
241C23×C4#4114yes—
242C23×C4#4114yes—
243C2×C4⋊C4—28no—
244C2×C4⋊C4—44no—
245C2×C4⋊C4—44no—
246C2×C4⋊C4—44no—
247C2×C4⋊C4—44no—
248C2×C4⋊C4—44no—
249C2×C4⋊C4—44no—
250C2×C4⋊C4—44no—
251C2×C4⋊C4—44no—
252C2×C4⋊C4—44no—
253C2×C4⋊C4—44no—
254C2×C4⋊C4—44no—
255C2×C4⋊C4—44no—
256C2×C4⋊C4C22⋊C4116yes—
257C2×C42—48no—
258C2×C42—44no—
259C2×C42—44no—
260C2×C42—48no—
261C2×C42—44no—
262#95—216no—
263#95—28no—
264#95—216no—
265#95—216no—
266#95—48no—
267#95—48no—
268#95—48no—
269#95—48no—
270#95—48no—
271#95—48no—
272#95—44no—
273#95—44no—
274#95—44no—
275#95—48no—
276#95—48no—
277#95—48no—
278#95—48no—
279#95—48no—
280C24C23×C411yescharacteristic
281C24C22×D411yescharacteristic
282C24C22×D411yescharacteristic
283C24C2×#4112yes—
284C24C2×#4112yes—
285C24C2×#4112yes—
286C24C2×#4112yes—
287C24C2×#4112yes—
288C24C2×#4112yes—
289C24H(5,𝔽2)11yescharacteristic
290C24H(5,𝔽2)11yescharacteristic
291C24H(5,𝔽2)11yescharacteristic
292C24H(5,𝔽2)11yescharacteristic
293C24H(5,𝔽2)12yes—
294C24H(5,𝔽2)12yes—
295C242−1+412yes—
296C242−1+412yes—
297C242−1+412yes—
298C242−1+412yes—
299C22×C4—24no—
300C22×C4—24no—
301C22×C4—22no—
302C22×C4—22no—
303C22×C4—22no—
304C22×C4—22no—
305C22×C4—22no—
306C22×C4—22no—
307C22×C4—22no—
308C22×C4—22no—
309C22×C4—22no—
310C22×C4—22no—
311C22×C4—24no—
312C22×C4—24no—
313C22×C4—24no—
314C22×C4—24no—
315C22×C4—24no—
316C22×C4—24no—
317C22×C4—22no—
318C22×C4—22no—
319C22×C4—22no—
320C22×C4—22no—
321C22×C4—22no—
322C22×C4—22no—
323C22×C4—22no—
324C22×C4—22no—
325C22×C4—22no—
326C22×C4—22no—
327C22×C4—22no—
328C22×C4—22no—
329C22×C4—24no—
330C22×C4—24no—
331C22×C4—24no—
332C22×C4—24no—
333C22×C4—24no—
334C22×C4—24no—
335C22×C4—24no—
336C22×C4—24no—
337C22×C4—24no—
338C22×C4—24no—
339C22×C4—24no—
340C22×C4—24no—
341C22×C4—24no—
342C22×C4—24no—
343C22×C4—24no—
344C22×C4—24no—
345C22×C4—24no—
346C22×C4—24no—
347C22×C4—24no—
348C22×C4—24no—
349C22×C4—24no—
350C22×C4—24no—
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—24no—
384C22×C4—24no—
385C22×C4—24no—
386C22×C4—24no—
387C22×C4—24no—
388C22×C4—24no—
389C22×C4—24no—
390C22×C4—42no—
391C22×C4—42no—
392C22×C4—42no—
393C22×C4—42no—
394C22×C4—42no—
395C22×C4—42no—
396C22×C4—42no—
397C22×C4—42no—
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—41no—
417C22×C4—41no—
418C22×C4—42no—
419C22×C4—42no—
420C22×C4—42no—
421C22×C4—42no—
422C22×C4—41no—
423C22×C4—41no—
424C22×C4—42no—
425C22×C4—41no—
426C22×C4—41no—
427C22×C4—42no—
428C22×C4—42no—
429C22×C4—42no—
430C22×C4—42no—
431C22×C4—42no—
432C22×C4—41no—
433C22×C4—41no—
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—42no—
446C22×C4—42no—
447C22×C4—42no—
448C22×C4—42no—
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—42no—
463C22×C4—42no—
464C22×C4—42no—
465C22×C4—42no—
466C22×C4—42no—
467C22×C4—42no—
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—42no—
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—42no—
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—42no—
543C22×C4—42no—
544C22×C4—42no—
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—42no—
554C22×C4—42no—
555C22×C4—42no—
556C22×C4—42no—
557C22×C4—42no—
558C22×C4—42no—
559C22×C4—42no—
560C22×C4—42no—
561C22×C4—42no—
562C22×C4—42no—
563C22×C4—42no—
564C22×C4—42no—
565C22×C4—42no—
566C22×C4—42no—
567C22×C4—42no—
568C22×C4—42no—
569C22×C4—42no—
570C22×C4—42no—
571C22×C4—42no—
572C22×C4—42no—
573C22×C4—42no—
574C22×C4C2×C22⋊C414yes—
575C22×C4C2×C22⋊C414yes—
576C22×C4C2×C22⋊C414yes—
577C22×C4#12618yes—
578C4⋊C4—416no—
579C4⋊C4—416no—
580C42—416no—
581C23C22×C22⋊C411yescharacteristic
582C23C4×#4111yescharacteristic
583C23C4×#4112yes—
584C23C4×#4112yes—
585C23C4×#4111yescharacteristic
586C23#51811yescharacteristic
587C23#51811yescharacteristic
588C23#51911yescharacteristic
589C23#51911yescharacteristic
590C23#52012yes—
591C23#52012yes—
592C23#52512yes—
593C23C2×#12612yes—
594C23#52912yes—
595C23#52912yes—
596C23#52912yes—
597C23#53212yes—
598C23#53411yescharacteristic
599C23#53411yescharacteristic
600C23#53411yescharacteristic
601C23#53411yescharacteristic
602C23#53612yes—
603C23#53612yes—
604C23#53812yes—
605C23#53812yes—
606C23#53812yes—
607C23#53812yes—
608C23#53912yes—
609C23#53912yes—
610C23#53912yes—
611C23#53912yes—
612C23#53912yes—
613C23#53912yes—
614C23#53912yes—
615C23#53912yes—
616C23#53912yes—
617C23#53912yes—
618C23#54012yes—
619C23#54112yes—
620C23#54112yes—
621C23#54112yes—
622C23#54112yes—
623C23#54112yes—
624C23#54212yes—
625C23#54212yes—
626C23#54212yes—
627C23#54212yes—
628C23#54212yes—
629C23#54212yes—
630C23#54212yes—
631C23#54212yes—
632C23#54612yes—
633C23#54612yes—
634C23#54712yes—
635C23#54712yes—
636C23#54812yes—
637C23#54812yes—
638C23#55012yes—
639C23#55012yes—
640C23#55112yes—
641C23#55112yes—
642C23#55112yes—
643C23#55111yescharacteristic
644C23#55212yes—
645C23#55212yes—
646C23#55212yes—
647C23#55212yes—
648C23#55212yes—
649C23#55212yes—
650C23#55312yes—
651C23#55312yes—
652C23#55312yes—
653C23#55511yescharacteristic
654C23#55511yescharacteristic
655C23#55612yes—
656C23#55612yes—
657C23#55911yescharacteristic
658C23#56011yescharacteristic
659C23H(3,𝔽4)11yescharacteristic
660C23#56212yes—
661C23#56212yes—
662C23#56212yes—
663C23#56312yes—
664C23#56312yes—
665C23#56311yescharacteristic
666C23#56311yescharacteristic
667C23#56412yes—
668C2×C4—24no—
669C2×C4—24no—
670C2×C4—24no—
671C2×C4—24no—
672C2×C4—28no—
673C2×C4—28no—
674C2×C4—28no—
675C2×C4—28no—
676C2×C4—28no—
677C2×C4—24no—
678C2×C4—44no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—44no—
684C2×C4—44no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—44no—
690C2×C4—44no—
691C2×C4—44no—
692C2×C4—44no—
693C2×C4—44no—
694C2×C4—44no—
695C2×C4—44no—
696C2×C4—44no—
697C2×C4—44no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—44no—
701C2×C4—44no—
702C2×C4—44no—
703C2×C4—44no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—44no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—44no—
712C2×C4—44no—
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—44no—
727C2×C4—44no—
728C2×C4—44no—
729C2×C4—44no—
730C2×C4—44no—
731C2×C4—44no—
732C2×C4—44no—
733C2×C4—44no—
734C2×C4—44no—
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—44no—
745C2×C4—44no—
746C2×C4—44no—
747C2×C4—44no—
748C2×C4—44no—
749C2×C4—44no—
750C2×C4—44no—
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—
769C2×C4—82no—
770C2×C4—82no—
771C2×C4—82no—
772C2×C4—82no—
773C2×C4—82no—
774C2×C4—82no—
775C2×C4—82no—
776C2×C4—82no—
777C2×C4—82no—
778C2×C4—82no—
779C2×C4—82no—
780C2×C4—82no—
781C2×C4—82no—
782C2×C4—82no—
783C2×C4—82no—
784C2×C4—82no—
785C2×C4—82no—
786C2×C4—82no—
787C2×C4—82no—
788C2×C4—82no—
789C2×C4—82no—
790C2×C4—82no—
791C22#229711yescharacteristic
792C22C4×#12612yes—
793C22#230811yescharacteristic
794C22#231011yescharacteristic
795C22#233211yescharacteristic
796C22#233211yescharacteristic
797C22#233211yescharacteristic
798C22#233211yescharacteristic
799C22#233412yes—
800C22#233512yes—
801C22#233612yes—
802C22#233612yes—
803C22#233712yes—
804C22#233912yes—
805C22#234112yes—
806C22#237112yes—
807C22#237211yescharacteristic
808C22#237312yes—
809C22#237312yes—
810C22#237411yescharacteristic
811C22#237611yescharacteristic
812C22#237911yescharacteristic
813C22#238212yes—
814C22#246712yes—
815C22#246912yes—
816C22#247912yes—
817C22#248112yes—
818C22#249312yes—
819C22#249512yes—
820C22#251212yes—
821C22#251912yes—
822C22#252912yes—
823C22#255412yes—
824C22#256012yes—
825C22#257512yes—
826C22#263812yes—
827C22#263812yes—
828C22#264312yes—
829C22#264512yes—
830C22#264912yes—
831C22#265012yes—
832C22#265212yes—
833C22#265212yes—
834C22#265412yes—
835C22#265512yes—
836C22#266312yes—
837C22#266312yes—
838C22#269012yes—
839C22#269012yes—
840C22#269412yes—
841C22#269412yes—
842C22#269711yescharacteristic
843C22#270112yes—
844C22#270812yes—
845C22#270911yescharacteristic
846C22#271711yescharacteristic
847C22#271912yes—
848C22#271912yes—
849C22#272112yes—
850C22#272112yes—
851C22#272411yescharacteristic
852C22#273012yes—
853C22#273012yes—
854C22#273111yescharacteristic
855C22#273111yescharacteristic
856C22#273311yescharacteristic
857C22#273311yescharacteristic
858C22#273912yes—
859C22#274312yes—
860C22#274412yes—
861C22#274512yes—
862C22#274612yes—
863C22#275812yes—
864C22#276412yes—
865C22#276712yes—
866C22#276712yes—
867C22#277012yes—
868C22#277612yes—
869C22#277712yes—
870C22#277912yes—
871C22#278212yes—
872C22#278312yes—
873C22#279812yes—
874C22#282712yes—
875C22#283212yes—
876C22#283912yes—
877C22#283912yes—
878C4—48no—
879C4—44no—
880C4—44no—
881C4—44no—
882C4—84no—
883C4—84no—
884C4—84no—
885C4—84no—
886C4—84no—
887C2#1410112yes—
888C2#1425211yescharacteristic
889C2#1429211yescharacteristic
890C2#1433412yes—
891C2#1447412yes—
892C2#1449211yescharacteristic
893C2#1450511yescharacteristic
894C2#1460812yes—
895C2#1461211yescharacteristic
896C2#1461411yescharacteristic
897C2#1465411yescharacteristic
898C2#1641412yes—
899C2#1641812yes—
900C2#1649612yes—
901C2#1664112yes—
902C2#1686712yes—
903C2#1686912yes—
904C2#1687512yes—
905C2#1691112yes—
subgroupG/H
center, Frattini, socle, prime radical, cosocleC25C24
commutatorC24C23×C4
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C25 ◁ G
LECSG ▷ C25 ▷ C1

Complements

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

NH ≅ G/Ntype
15. C2×#400C4semidirect

Maximal subgroups

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

subgroupindex
C22×#4002
C2×#14452
C2×#14362
#75572
#75562
#75542