Finite Group Databasebeta

← #154792

Subgroups — #154792

Order 512.

3206 conjugacy classes of subgroups.

The subgroup lattice has 954 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#391C211yesmaximal, characteristic
2C2×#1446C212yesmaximal
3C2×#1441C211yesmaximal, characteristic
4C2×#1436C211yesmaximal, characteristic
5C2×#1434C212yesmaximal
6#7557C212yesmaximal
7#7556C212yesmaximal
8#7556C212yesmaximal
9#7554C212yesmaximal
10C24×Q8C2211yescharacteristic
11C23×C4⋊C4C2211yescharacteristic
12C23×C4⋊C4C2211yescharacteristic
13C23×C42C2211yescharacteristic
14C23×C42C2211yescharacteristic
15C2×#391—24no—
16C2×#391—24no—
17C2×#391C418yescomplemented
18C22×#95C2212yes—
19C22×#95C2212yes—
20C22×#95C2212yes—
21C22×#95C2212yes—
22C22×#95C2212yes—
23C22×#95C2212yes—
24C22×#95C2212yes—
25C22×#95C2212yes—
26C22×#95C2212yes—
27C22×#95C2212yes—
28C22×#95C2212yes—
29C22×#95C2212yes—
30C22×#95C2212yes—
31C22×#95C2212yes—
32C22×#95C2211yescharacteristic
33C22×#95C2211yescharacteristic
34#1446—28no—
35#1441—24no—
36#1436—24no—
37#1434—28no—
38C23×Q8—22no—
39C23×Q8—22no—
40C23×Q8—24no—
41C23×Q8—24no—
42C23×Q8—24no—
43C23×Q8—24no—
44C23×Q8—41no—
45C23×Q8—41no—
46C23×Q8—41no—
47C23×Q8—41no—
48C23×Q8C2×C414yes—
49C24×C4C2312yes—
50C24×C4C2312yes—
51C24×C4C2312yes—
52C24×C4C2311yescharacteristic
53C24×C4C2311yescharacteristic
54C24×C4C2312yes—
55C24×C4C2312yes—
56C24×C4C2312yes—
57C24×C4C2311yescharacteristic
58C22×C4⋊C4—22no—
59C22×C4⋊C4—24no—
60C22×C4⋊C4—41no—
61C22×C4⋊C4—41no—
62C22×C4⋊C4—41no—
63C22×C4⋊C4—41no—
64C22×C4⋊C4—41no—
65C22×C4⋊C4—42no—
66C22×C4⋊C4—41no—
67C22×C4⋊C4C2×C414yes—
68C22×C4⋊C4D414yes—
69C22×C4⋊C4D414yes—
70C22×C42—24no—
71C22×C42—22no—
72C22×C42—22no—
73C22×C42—24no—
74C22×C42—22no—
75C22×C42—24no—
76C22×C42—41no—
77C22×C42—42no—
78C22×C42—41no—
79C22×C42C2×C414yes—
80#391—232no—
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—24no—
96C2×#95—22no—
97C2×#95—24no—
98C2×#95—22no—
99C2×#95—24no—
100C2×#95—24no—
101C2×#95—24no—
102C2×#95—24no—
103C2×#95—24no—
104C2×#95—24no—
105C2×#95—24no—
106C2×#95—24no—
107C2×#95—24no—
108C2×#95—24no—
109C2×#95—24no—
110C2×#95—24no—
111C2×#95—24no—
112C2×#95—24no—
113C2×#95—42no—
114C2×#95—42no—
115C2×#95—42no—
116C2×#95—42no—
117C2×#95—42no—
118C2×#95—42no—
119C2×#95—42no—
120C2×#95—42no—
121C2×#95—41no—
122C2×#95—41no—
123C2×#95—41no—
124C2×#95—41no—
125C2×#95C2×C418yes—
126C2×#95C2×C418yes—
127C2×#95D418yes—
128C2×#95Q818yescomplemented
129C25C2411yescharacteristic
130C22×Q8—28no—
131C22×Q8—28no—
132C22×Q8—216no—
133C22×Q8—28no—
134C22×Q8—216no—
135C22×Q8—216no—
136C22×Q8—44no—
137C22×Q8—44no—
138C22×Q8—48no—
139C22×Q8—48no—
140C22×Q8—48no—
141C22×Q8—48no—
142C22×Q8—48no—
143C22×Q8—48no—
144C22×Q8—48no—
145C22×Q8—48no—
146C22×Q8—44no—
147C22×Q8—44no—
148C22×Q8—44no—
149C22×Q8—44no—
150C22×Q8—48no—
151C22×Q8—44no—
152C22×Q8—44no—
153C23×C4—22no—
154C23×C4—22no—
155C23×C4—21no—
156C23×C4—21no—
157C23×C4—21no—
158C23×C4—21no—
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—21no—
186C23×C4—21no—
187C23×C4—21no—
188C23×C4—21no—
189C23×C4—21no—
190C23×C4—21no—
191C23×C4—22no—
192C23×C4—21no—
193C23×C4—21no—
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×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×C4—22no—
239C23×C4—22no—
240C23×C4—22no—
241C23×C4—22no—
242C23×C4—22no—
243C23×C4—22no—
244C23×C4—22no—
245C23×C4—22no—
246C23×C4—22no—
247C23×C4—22no—
248C23×C4—22no—
249C23×C4—22no—
250C23×C4—22no—
251C23×C4—22no—
252C23×C4—22no—
253C23×C4C22×C412yes—
254C23×C4C22×C412yes—
255C23×C4C22×C414yes—
256C23×C4C22×C414yes—
257C23×C4C22×C412yes—
258C23×C4C2×D414yes—
259C23×C4C2×D412yes—
260C23×C4C2×D412yes—
261C23×C4C2×D412yes—
262C23×C4C2×D412yes—
263C23×C4C2×D414yes—
264C23×C4C2×D412yes—
265C23×C4C2×D412yes—
266C23×C4C2×D414yes—
267C23×C4C2×Q814yes—
268C23×C4C2×Q814yes—
269C23×C4C2×Q814yes—
270C23×C4#4114yes—
271C23×C4#4114yes—
272C23×C4#4114yes—
273C23×C4#4114yes—
274C23×C4#4114yes—
275C23×C4#4114yes—
276C2×C4⋊C4—44no—
277C2×C4⋊C4—44no—
278C2×C4⋊C4—44no—
279C2×C4⋊C4—44no—
280C2×C4⋊C4—44no—
281C2×C4⋊C4—44no—
282C2×C4⋊C4—48no—
283C2×C4⋊C4—44no—
284C2×C4⋊C4—44no—
285C2×C4⋊C4—48no—
286C2×C4⋊C4—44no—
287C2×C4⋊C4C22⋊C4116yes—
288C2×C42—28no—
289C2×C42—216no—
290C2×C42—48no—
291C2×C42—44no—
292C2×C42—44no—
293C2×C42—48no—
294C2×C42—44no—
295C2×C42—48no—
296C2×C42—44no—
297C2×C42—44no—
298#95—216no—
299#95—216no—
300#95—216no—
301#95—216no—
302#95—216no—
303#95—48no—
304#95—48no—
305#95—48no—
306#95—48no—
307#95—48no—
308#95—48no—
309#95—48no—
310#95—48no—
311#95—44no—
312#95—44no—
313#95—48no—
314C24C23×C411yescharacteristic
315C24C22×D411yescharacteristic
316C24C22×D411yescharacteristic
317C24C22×D412yes—
318C24C22×Q812yes—
319C24C2×#4112yes—
320C24C2×#4112yes—
321C24C2×#4112yes—
322C24C2×#4112yes—
323C24C2×#4112yes—
324C24C2×#4112yes—
325C24H(5,𝔽2)11yescharacteristic
326C24H(5,𝔽2)11yescharacteristic
327C24H(5,𝔽2)11yescharacteristic
328C24H(5,𝔽2)11yescharacteristic
329C24H(5,𝔽2)12yes—
330C242−1+412yes—
331C242−1+412yes—
332C242−1+412yes—
333C2×Q8—232no—
334C2×Q8—432no—
335C2×Q8—432no—
336C2×Q8—416no—
337C2×Q8—416no—
338C2×Q8—416no—
339C2×Q8—432no—
340C2×Q8—432no—
341C2×Q8—416no—
342C2×Q8—416no—
343C2×Q8—416no—
344C22×C4—24no—
345C22×C4—22no—
346C22×C4—22no—
347C22×C4—22no—
348C22×C4—22no—
349C22×C4—24no—
350C22×C4—22no—
351C22×C4—22no—
352C22×C4—22no—
353C22×C4—22no—
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—22no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—22no—
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—22no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—24no—
402C22×C4—24no—
403C22×C4—24no—
404C22×C4—24no—
405C22×C4—24no—
406C22×C4—24no—
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—24no—
422C22×C4—24no—
423C22×C4—24no—
424C22×C4—24no—
425C22×C4—24no—
426C22×C4—24no—
427C22×C4—24no—
428C22×C4—24no—
429C22×C4—24no—
430C22×C4—24no—
431C22×C4—24no—
432C22×C4—24no—
433C22×C4—24no—
434C22×C4—24no—
435C22×C4—24no—
436C22×C4—24no—
437C22×C4—24no—
438C22×C4—24no—
439C22×C4—24no—
440C22×C4—24no—
441C22×C4—24no—
442C22×C4—24no—
443C22×C4—24no—
444C22×C4—24no—
445C22×C4—24no—
446C22×C4—24no—
447C22×C4—24no—
448C22×C4—24no—
449C22×C4—24no—
450C22×C4—24no—
451C22×C4—24no—
452C22×C4—24no—
453C22×C4—24no—
454C22×C4—24no—
455C22×C4—24no—
456C22×C4—24no—
457C22×C4—24no—
458C22×C4—24no—
459C22×C4—24no—
460C22×C4—24no—
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—41no—
506C22×C4—41no—
507C22×C4—42no—
508C22×C4—41no—
509C22×C4—41no—
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—41no—
522C22×C4—42no—
523C22×C4—41no—
524C22×C4—42no—
525C22×C4—42no—
526C22×C4—41no—
527C22×C4—41no—
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×C4—42no—
575C22×C4—42no—
576C22×C4—42no—
577C22×C4—42no—
578C22×C4—42no—
579C22×C4—42no—
580C22×C4—42no—
581C22×C4—42no—
582C22×C4—42no—
583C22×C4—42no—
584C22×C4—42no—
585C22×C4—42no—
586C22×C4—42no—
587C22×C4—42no—
588C22×C4—42no—
589C22×C4—42no—
590C22×C4—42no—
591C22×C4—42no—
592C22×C4—42no—
593C22×C4—42no—
594C22×C4—42no—
595C22×C4—42no—
596C22×C4—42no—
597C22×C4—42no—
598C22×C4—42no—
599C22×C4—42no—
600C22×C4—42no—
601C22×C4—42no—
602C22×C4—42no—
603C22×C4—42no—
604C22×C4—42no—
605C22×C4—42no—
606C22×C4—42no—
607C22×C4—42no—
608C22×C4—42no—
609C22×C4—42no—
610C22×C4—42no—
611C22×C4—42no—
612C22×C4—42no—
613C22×C4C2×C22⋊C414yes—
614C22×C4C2×C22⋊C414yes—
615C22×C4C2×C22⋊C414yes—
616C22×C4#11718yes—
617C22×C4C4×D418yes—
618C22×C4C4×Q818yes—
619C22×C4#12118yes—
620C22×C4C22⋊Q818yes—
621C22×C4#12414yes—
622C22×C4#12714yes—
623C4⋊C4—416no—
624C4⋊C4—416no—
625C42—416no—
626C42—416no—
627C23C22×C22⋊C411yescharacteristic
628C23C2×#11712yes—
629C23C2×C4×D412yes—
630C23C2×C4×Q812yes—
631C23C4×#4112yes—
632C23#51811yescharacteristic
633C23#51811yescharacteristic
634C23#51912yes—
635C23#52012yes—
636C23C2×#12112yes—
637C23C2×C22⋊Q812yes—
638C23#52511yescharacteristic
639C23#52511yescharacteristic
640C23#52512yes—
641C23#52512yes—
642C23C2×#12411yescharacteristic
643C23#52912yes—
644C23#52912yes—
645C23#52912yes—
646C23C2×#12711yescharacteristic
647C23#53312yes—
648C23#53312yes—
649C23#53312yes—
650C23#53411yescharacteristic
651C23#53411yescharacteristic
652C23#53411yescharacteristic
653C23#53411yescharacteristic
654C23#53612yes—
655C23#53712yes—
656C23#53812yes—
657C23#53812yes—
658C23#54112yes—
659C23#54112yes—
660C23#54112yes—
661C23#54212yes—
662C23#54212yes—
663C23#54212yes—
664C23#54212yes—
665C23#54212yes—
666C23#54212yes—
667C23#54212yes—
668C23#54412yes—
669C23#54412yes—
670C23#54612yes—
671C23#54612yes—
672C23#54612yes—
673C23#54612yes—
674C23#54612yes—
675C23#54612yes—
676C23#54612yes—
677C23#54712yes—
678C23#54712yes—
679C23#54712yes—
680C23#54812yes—
681C23#54812yes—
682C23#54812yes—
683C23D4×Q812yes—
684C23D4×Q812yes—
685C23D4×Q812yes—
686C23#55112yes—
687C23#55112yes—
688C23#55112yes—
689C23#55112yes—
690C23#55111yescharacteristic
691C23#55111yescharacteristic
692C23#55212yes—
693C23#55212yes—
694C23#55212yes—
695C23#55212yes—
696C23#55412yes—
697C23#55412yes—
698C23#55412yes—
699C23#55512yes—
700C23#55511yescharacteristic
701C23#55612yes—
702C23#55612yes—
703C23#55612yes—
704C23#55612yes—
705C23#55712yes—
706C23Q8211yescharacteristic
707C23#55912yes—
708C23H(3,𝔽4)11yescharacteristic
709C23#56212yes—
710C23#56311yescharacteristic
711C23#56311yescharacteristic
712C23#56311yescharacteristic
713C23#56312yes—
714Q8—464no—
715C2×C4—24no—
716C2×C4—24no—
717C2×C4—24no—
718C2×C4—28no—
719C2×C4—28no—
720C2×C4—28no—
721C2×C4—28no—
722C2×C4—24no—
723C2×C4—24no—
724C2×C4—24no—
725C2×C4—24no—
726C2×C4—24no—
727C2×C4—28no—
728C2×C4—28no—
729C2×C4—28no—
730C2×C4—28no—
731C2×C4—28no—
732C2×C4—28no—
733C2×C4—28no—
734C2×C4—28no—
735C2×C4—28no—
736C2×C4—28no—
737C2×C4—28no—
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—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—44no—
754C2×C4—44no—
755C2×C4—44no—
756C2×C4—44no—
757C2×C4—42no—
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—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—44no—
775C2×C4—44no—
776C2×C4—44no—
777C2×C4—44no—
778C2×C4—44no—
779C2×C4—44no—
780C2×C4—44no—
781C2×C4—44no—
782C2×C4—44no—
783C2×C4—44no—
784C2×C4—44no—
785C2×C4—44no—
786C2×C4—44no—
787C2×C4—44no—
788C2×C4—44no—
789C2×C4—44no—
790C2×C4—44no—
791C2×C4—44no—
792C2×C4—44no—
793C2×C4—44no—
794C2×C4—44no—
795C2×C4—44no—
796C2×C4—44no—
797C2×C4—44no—
798C2×C4—44no—
799C2×C4—44no—
800C2×C4—44no—
801C2×C4—44no—
802C2×C4—44no—
803C2×C4—44no—
804C2×C4—44no—
805C2×C4—44no—
806C2×C4—44no—
807C2×C4—44no—
808C2×C4—44no—
809C2×C4—44no—
810C2×C4—44no—
811C2×C4—44no—
812C2×C4—44no—
813C2×C4—82no—
814C2×C4—82no—
815C2×C4—82no—
816C2×C4—82no—
817C2×C4—82no—
818C2×C4—82no—
819C2×C4—82no—
820C2×C4—82no—
821C2×C4—82no—
822C2×C4—82no—
823C2×C4—82no—
824C2×C4—82no—
825C2×C4—82no—
826C2×C4—82no—
827C2×C4—82no—
828C2×C4—82no—
829C2×C4—82no—
830C2×C4—82no—
831C2×C4—82no—
832C2×C4—82no—
833C2×C4—82no—
834C2×C4—82no—
835C2×C4—82no—
836C2×C4—82no—
837C2×C4#39018yes—
838C22#228011yescharacteristic
839C22C2×#39011yescharacteristic
840C22#229512yes—
841C22C4×C22⋊Q812yes—
842C22#230811yescharacteristic
843C22#232012yes—
844C22#232312yes—
845C22#233112yes—
846C22#233712yes—
847C22#233912yes—
848C22Q8×C22⋊C412yes—
849C22#234212yes—
850C22#234212yes—
851C22#235512yes—
852C22#235612yes—
853C22#236012yes—
854C22#236212yes—
855C22#236911yescharacteristic
856C22#237211yescharacteristic
857C22#237911yescharacteristic
858C22#238111yescharacteristic
859C22#241512yes—
860C22#241712yes—
861C22#242712yes—
862C22#242912yes—
863C22#243812yes—
864C22#243912yes—
865C22#245012yes—
866C22#245112yes—
867C22#245812yes—
868C22#245812yes—
869C22#245912yes—
870C22#246212yes—
871C22#246212yes—
872C22#246512yes—
873C22#246512yes—
874C22#246512yes—
875C22#246912yes—
876C22#246912yes—
877C22#247412yes—
878C22#247712yes—
879C22#248912yes—
880C22#249212yes—
881C22#252012yes—
882C22#252712yes—
883C22#253212yes—
884C22#253212yes—
885C22#253412yes—
886C22#253412yes—
887C22#253911yescharacteristic
888C22#253911yescharacteristic
889C22#254012yes—
890C22#254212yes—
891C22#256111yescharacteristic
892C22#256111yescharacteristic
893C22#258612yes—
894C22#258912yes—
895C22#260512yes—
896C22#261212yes—
897C22#268411yescharacteristic
898C22#268411yescharacteristic
899C22#268612yes—
900C22#268612yes—
901C22#269812yes—
902C22#270012yes—
903C22#270212yes—
904C22#270412yes—
905C22#271212yes—
906C22#271312yes—
907C22#271512yes—
908C22#271612yes—
909C22#271711yescharacteristic
910C22#271711yescharacteristic
911C22#272912yes—
912C22#272912yes—
913C22#273111yescharacteristic
914C22#273111yescharacteristic
915C22#273411yescharacteristic
916C22#273411yescharacteristic
917C22#275412yes—
918C22#275512yes—
919C22#275812yes—
920C22#275912yes—
921C22#276212yes—
922C22#276212yes—
923C22#276312yes—
924C22#276412yes—
925C4—28no—
926C4—48no—
927C4—44no—
928C4—44no—
929C4—48no—
930C4—48no—
931C4—84no—
932C4—84no—
933C4—84no—
934C2#1390311yescharacteristic
935C2#1392712yes—
936C2#1399712yes—
937C2#1405912yes—
938C2#1409012yes—
939C2#1437812yes—
940C2#1438012yes—
941C2#1445011yescharacteristic
942C2#1447311yescharacteristic
943C2#1582412yes—
944C2#1582512yes—
945C2#1583212yes—
946C2#1583311yescharacteristic
947C2#1585411yescharacteristic
948C2#1585611yescharacteristic
949C2#1585712yes—
950C2#1586012yes—
951C2#1586712yes—
952C2#1588411yescharacteristic
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
17. C2×#391C4semidirect
128. C2×#95Q8semidirect

Maximal subgroups

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

subgroupindex
C22×#3912
C2×#14462
C2×#14412
C2×#14362
C2×#14342
#75572
#75562
#75542