Finite Group Databasebeta

← #155398

Subgroups — #155398

Order 512.

2902 conjugacy classes of subgroups.

The subgroup lattice has 912 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1446C212yesmaximal
2C2×#1446C211yesmaximal, characteristic
3C2×#1434C212yesmaximal
4#7556C211yesmaximal, characteristic
5#7556C212yesmaximal
6#7556C211yesmaximal, characteristic
7#7556C212yesmaximal
8#7554C212yesmaximal
9#7554C212yesmaximal
10C24×Q8C2211yescharacteristic
11C23×C42C2212yes—
12C22×#95C2212yes—
13C22×#95C2212yes—
14C22×#95C2212yes—
15C22×#95C2212yes—
16C22×#95C2212yes—
17C22×#95C2211yescharacteristic
18C22×#95C2212yes—
19C22×#95C2212yes—
20C22×#95C2212yes—
21C22×#95C2211yescharacteristic
22C22×#95C2211yescharacteristic
23C22×#95C2212yes—
24C22×#95C2212yes—
25C22×#95C2212yes—
26C22×#95C2211yescharacteristic
27C22×#95C2211yescharacteristic
28C22×#95C2212yes—
29C22×#95C2211yescharacteristic
30C22×#95C2212yes—
31#1446—28no—
32#1446C418yescomplemented
33#1434—28no—
34C23×Q8—24no—
35C23×Q8—22no—
36C23×Q8—22no—
37C23×Q8—24no—
38C23×Q8—41no—
39C23×Q8—41no—
40C23×Q8—42no—
41C23×Q8—42no—
42C23×Q8—41no—
43C23×Q8—41no—
44C23×Q8C2×C414yes—
45C24×C4C2311yescharacteristic
46C24×C4C2311yescharacteristic
47C24×C4C2312yes—
48C24×C4C2312yes—
49C24×C4C2312yes—
50C24×C4C2312yes—
51C24×C4C2311yescharacteristic
52C24×C4C2312yes—
53C24×C4C2312yes—
54C22×C42—24no—
55C22×C42—24no—
56C22×C42—24no—
57C22×C42—24no—
58C22×C42—24no—
59C22×C42—42no—
60C22×C42—42no—
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—24no—
80C2×#95—24no—
81C2×#95—24no—
82C2×#95—24no—
83C2×#95—24no—
84C2×#95—24no—
85C2×#95—24no—
86C2×#95—41no—
87C2×#95—42no—
88C2×#95—41no—
89C2×#95—42no—
90C2×#95—41no—
91C2×#95—41no—
92C2×#95—42no—
93C2×#95—42no—
94C2×#95—42no—
95C2×#95—42no—
96C2×#95—42no—
97C2×#95—42no—
98C2×#95—42no—
99C2×#95—41no—
100C2×#95—41no—
101C2×#95—42no—
102C2×#95—42no—
103C2×#95—41no—
104C2×#95—42no—
105C2×#95—42no—
106C2×#95—42no—
107C2×#95—41no—
108C2×#95C2×C418yes—
109C2×#95C2×C414yes—
110C2×#95C2×C418yes—
111C2×#95C2×C414yes—
112C2×#95D418yes—
113C2×#95Q818yescomplemented
114C25C2411yescharacteristic
115C22×Q8—28no—
116C22×Q8—216no—
117C22×Q8—44no—
118C22×Q8—48no—
119C22×Q8—44no—
120C22×Q8—44no—
121C22×Q8—48no—
122C22×Q8—48no—
123C22×Q8—48no—
124C22×Q8—48no—
125C22×Q8—48no—
126C22×Q8—44no—
127C22×Q8—48no—
128C22×Q8—48no—
129C22×Q8—44no—
130C22×Q8—44no—
131C22×Q8—44no—
132C22×Q8—44no—
133C22×Q8—48no—
134C22×Q8—48no—
135C22×Q8—44no—
136C22×Q8—48no—
137C22×Q8—44no—
138C23×C4—22no—
139C23×C4—22no—
140C23×C4—22no—
141C23×C4—22no—
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—21no—
165C23×C4—21no—
166C23×C4—21no—
167C23×C4—21no—
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—21no—
219C23×C4—22no—
220C23×C4—21no—
221C23×C4—21no—
222C23×C4—22no—
223C23×C4—21no—
224C23×C4—22no—
225C23×C4—22no—
226C23×C4—22no—
227C23×C4—22no—
228C23×C4—22no—
229C23×C4—22no—
230C23×C4—22no—
231C23×C4—22no—
232C23×C4—22no—
233C23×C4—22no—
234C23×C4—22no—
235C23×C4—22no—
236C23×C4—22no—
237C23×C4—22no—
238C23×C4C22×C412yes—
239C23×C4C22×C412yes—
240C23×C4C22×C412yes—
241C23×C4C22×C414yes—
242C23×C4C22×C414yes—
243C23×C4C2×D414yes—
244C23×C4C2×D414yes—
245C23×C4C2×D414yes—
246C23×C4C2×Q814yes—
247C23×C4C2×Q814yes—
248C23×C4C2×Q814yes—
249C23×C4#4114yes—
250C23×C4#4112yes—
251C23×C4#4112yes—
252C23×C4#4114yes—
253C23×C4#4114yes—
254C23×C4#4114yes—
255C23×C4#4114yes—
256C23×C4#4114yes—
257C2×C42—216no—
258C2×C42—48no—
259C2×C42—48no—
260C2×C42—48no—
261C2×C42—48no—
262C2×C42—48no—
263C2×C42—48no—
264#95—216no—
265#95—216no—
266#95—44no—
267#95—48no—
268#95—44no—
269#95—48no—
270#95—44no—
271#95—48no—
272#95—48no—
273#95—48no—
274#95—48no—
275#95—48no—
276#95—44no—
277#95—48no—
278#95—48no—
279#95—44no—
280#95—48no—
281#95—44no—
282#95—48no—
283C24C23×C411yescharacteristic
284C24C22×D412yes—
285C24C22×Q812yes—
286C24C2×#4111yescharacteristic
287C24C2×#4111yescharacteristic
288C24C2×#4112yes—
289C24C2×#4112yes—
290C24C2×#4112yes—
291C24C2×#4112yes—
292C24C2×#4112yes—
293C24C2×#4112yes—
294C24H(5,𝔽2)11yescharacteristic
295C24H(5,𝔽2)12yes—
296C24H(5,𝔽2)11yescharacteristic
297C24H(5,𝔽2)12yes—
298C24H(5,𝔽2)11yescharacteristic
299C24H(5,𝔽2)11yescharacteristic
300C242−1+412yes—
301C242−1+412yes—
302C2×Q8—432no—
303C2×Q8—416no—
304C2×Q8—416no—
305C2×Q8—432no—
306C2×Q8—416no—
307C2×Q8—416no—
308C2×Q8—416no—
309C2×Q8—432no—
310C2×Q8—432no—
311C2×Q8—416no—
312C2×Q8—416no—
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—22no—
323C22×C4—22no—
324C22×C4—24no—
325C22×C4—24no—
326C22×C4—24no—
327C22×C4—24no—
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—24no—
337C22×C4—24no—
338C22×C4—24no—
339C22×C4—24no—
340C22×C4—24no—
341C22×C4—24no—
342C22×C4—24no—
343C22×C4—22no—
344C22×C4—22no—
345C22×C4—22no—
346C22×C4—22no—
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—24no—
391C22×C4—24no—
392C22×C4—24no—
393C22×C4—24no—
394C22×C4—24no—
395C22×C4—24no—
396C22×C4—24no—
397C22×C4—24no—
398C22×C4—22no—
399C22×C4—24no—
400C22×C4—22no—
401C22×C4—24no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—24no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—24no—
408C22×C4—24no—
409C22×C4—24no—
410C22×C4—24no—
411C22×C4—24no—
412C22×C4—24no—
413C22×C4—24no—
414C22×C4—24no—
415C22×C4—24no—
416C22×C4—24no—
417C22×C4—24no—
418C22×C4—24no—
419C22×C4—24no—
420C22×C4—24no—
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—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—41no—
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—41no—
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—41no—
488C22×C4—42no—
489C22×C4—42no—
490C22×C4—42no—
491C22×C4—42no—
492C22×C4—41no—
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—41no—
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—41no—
546C22×C4—42no—
547C22×C4—41no—
548C22×C4—42no—
549C22×C4—42no—
550C22×C4—42no—
551C22×C4—41no—
552C22×C4—41no—
553C22×C4—42no—
554C22×C4—41no—
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×C4—42no—
575C22×C4—42no—
576C22×C4—41no—
577C22×C4—42no—
578C22×C4—42no—
579C22×C4—41no—
580C22×C4—42no—
581C22×C4—42no—
582C22×C4—42no—
583C22×C4#11714yes—
584C22×C4C4×D418yes—
585C22×C4C4×Q818yes—
586C22×C4C22⋊Q818yes—
587C22×C4#12418yes—
588C42—432no—
589C23C2×#11711yescharacteristic
590C23C2×C4×D412yes—
591C23C2×C4×Q812yes—
592C23C4×#4111yescharacteristic
593C23C4×#4111yescharacteristic
594C23C4×#4112yes—
595C23#51811yescharacteristic
596C23#51811yescharacteristic
597C23#51812yes—
598C23#51911yescharacteristic
599C23#51911yescharacteristic
600C23C2×C22⋊Q812yes—
601C23#52512yes—
602C23C2×#12412yes—
603C23#52912yes—
604C23#52912yes—
605C23#52912yes—
606C23#52912yes—
607C23#52912yes—
608C23#53212yes—
609C23#53312yes—
610C23#53312yes—
611C23#53312yes—
612C23#53412yes—
613C23#53512yes—
614C23#53811yescharacteristic
615C23#53811yescharacteristic
616C23#53811yescharacteristic
617C23#53811yescharacteristic
618C23#53812yes—
619C23#53812yes—
620C23#53912yes—
621C23#53912yes—
622C23#53912yes—
623C23#53912yes—
624C23#54212yes—
625C23#54212yes—
626C23#54212yes—
627C23#54212yes—
628C23#54212yes—
629C23#54212yes—
630C23#54412yes—
631C23#54412yes—
632C23D4211yescharacteristic
633C23#54612yes—
634C23#54612yes—
635C23#54612yes—
636C23#54712yes—
637C23#54712yes—
638C23#54812yes—
639C23D4×Q812yes—
640C23#55111yescharacteristic
641C23#55112yes—
642C23#55112yes—
643C23#55112yes—
644C23#55112yes—
645C23#55112yes—
646C23#55112yes—
647C23#55111yescharacteristic
648C23#55112yes—
649C23#55111yescharacteristic
650C23#55112yes—
651C23#55112yes—
652C23#55212yes—
653C23#55212yes—
654C23#55212yes—
655C23#55412yes—
656C23#55412yes—
657C23#55412yes—
658C23#55412yes—
659C23#55412yes—
660C23#55512yes—
661C23#55512yes—
662C23#55511yescharacteristic
663C23#55512yes—
664C23#55512yes—
665C23#55612yes—
666C23#55612yes—
667C23#55612yes—
668C23#55612yes—
669C23#55712yes—
670C23Q8211yescharacteristic
671C23#56011yescharacteristic
672C23#56012yes—
673C23H(3,𝔽4)11yescharacteristic
674C23#56312yes—
675C23#56312yes—
676Q8—464no—
677C2×C4—28no—
678C2×C4—28no—
679C2×C4—24no—
680C2×C4—28no—
681C2×C4—28no—
682C2×C4—28no—
683C2×C4—28no—
684C2×C4—28no—
685C2×C4—28no—
686C2×C4—28no—
687C2×C4—28no—
688C2×C4—28no—
689C2×C4—28no—
690C2×C4—28no—
691C2×C4—44no—
692C2×C4—44no—
693C2×C4—44no—
694C2×C4—44no—
695C2×C4—44no—
696C2×C4—44no—
697C2×C4—44no—
698C2×C4—44no—
699C2×C4—44no—
700C2×C4—44no—
701C2×C4—44no—
702C2×C4—44no—
703C2×C4—44no—
704C2×C4—44no—
705C2×C4—44no—
706C2×C4—44no—
707C2×C4—44no—
708C2×C4—42no—
709C2×C4—44no—
710C2×C4—44no—
711C2×C4—42no—
712C2×C4—44no—
713C2×C4—44no—
714C2×C4—44no—
715C2×C4—42no—
716C2×C4—44no—
717C2×C4—42no—
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—42no—
732C2×C4—44no—
733C2×C4—42no—
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—44no—
752C2×C4—44no—
753C2×C4—42no—
754C2×C4—44no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—44no—
758C2×C4—44no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—44no—
763C2×C4—44no—
764C2×C4—44no—
765C2×C4—44no—
766C2×C4—44no—
767C2×C4—44no—
768C2×C4—44no—
769C2×C4—44no—
770C2×C4—44no—
771C2×C4—44no—
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—
791C2×C4—82no—
792C2×C4—82no—
793C2×C4—82no—
794C2×C4—82no—
795C2×C4—82no—
796C22#229512yes—
797C22C4×C22⋊Q812yes—
798C22C4×#12412yes—
799C22#231211yescharacteristic
800C22#232112yes—
801C22#233112yes—
802C22#233211yescharacteristic
803C22#233211yescharacteristic
804C22#233212yes—
805C22#234212yes—
806C22#235611yescharacteristic
807C22#235611yescharacteristic
808C22#235811yescharacteristic
809C22#236212yes—
810C22#236512yes—
811C22#236812yes—
812C22#236812yes—
813C22#236911yescharacteristic
814C22#237212yes—
815C22#237211yescharacteristic
816C22#237211yescharacteristic
817C22#237511yescharacteristic
818C22#238111yescharacteristic
819C22#243812yes—
820C22#243912yes—
821C22#244912yes—
822C22#245112yes—
823C22#247412yes—
824C22#247412yes—
825C22#247712yes—
826C22#248812yes—
827C22#248812yes—
828C22#249112yes—
829C22#249212yes—
830C22#252012yes—
831C22#252112yes—
832C22#252312yes—
833C22#252712yes—
834C22#252712yes—
835C22#253212yes—
836C22#253212yes—
837C22#255612yes—
838C22#256012yes—
839C22#256112yes—
840C22#256312yes—
841C22#256412yes—
842C22#257212yes—
843C22#257212yes—
844C22#257211yescharacteristic
845C22#257211yescharacteristic
846C22#257412yes—
847C22#257412yes—
848C22#257412yes—
849C22#257412yes—
850C22#258611yescharacteristic
851C22#258611yescharacteristic
852C22#258812yes—
853C22#258812yes—
854C22#260512yes—
855C22#261012yes—
856C22#261212yes—
857C22#266811yescharacteristic
858C22#267011yescharacteristic
859C22#268512yes—
860C22#269712yes—
861C22#271712yes—
862C22#272012yes—
863C22#272312yes—
864C22#272912yes—
865C22#273511yescharacteristic
866C22#273611yescharacteristic
867C22#273712yes—
868C22#273712yes—
869C22#273712yes—
870C22#273712yes—
871C22#274212yes—
872C22#274512yes—
873C22#274512yes—
874C22#274512yes—
875C22#275912yes—
876C22#276312yes—
877C22#277412yes—
878C22#277512yes—
879C22#277512yes—
880C22#278512yes—
881C22#279212yes—
882C22#280512yes—
883C4—44no—
884C4—48no—
885C4—48no—
886C4—48no—
887C4—48no—
888C4—82no—
889C4—84no—
890C4—82no—
891C4—84no—
892C2#1405812yes—
893C2#1409012yes—
894C2#1416211yescharacteristic
895C2#1421911yescharacteristic
896C2#1423211yescharacteristic
897C2#1424312yes—
898C2#1436611yescharacteristic
899C2#1448911yescharacteristic
900C2#1456112yes—
901C2#1459911yescharacteristic
902C2#1460911yescharacteristic
903C2#1577012yes—
904C2#1577212yes—
905C2#1586112yes—
906C2#1586212yes—
907C2#1593012yes—
908C2#1593112yes—
909C2#1613712yes—
910C2#1618512yes—
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
32. #1446C4semidirect
113. C2×#95Q8semidirect

Maximal subgroups

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

subgroupindex
C2×#14462
C2×#14342
#75562
#75542