Finite Group Databasebeta

← #4415047

Subgroups — #4415047

Order 512.

4164 conjugacy classes of subgroups.

The subgroup lattice has 873 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2847C211yesmaximal, characteristic
2C22×#385C211yesmaximal, characteristic, complemented
3#16986C212yesmaximal, complemented
4#16562C214yesmaximal, complemented
5#16557C212yesmaximal, complemented
6#16400C212yesmaximal, complemented
7#16261C212yesmaximal, complemented
8#14936C211yesmaximal, characteristic, complemented
9#14927C212yesmaximal, complemented
10#14926C211yesmaximal, characteristic, complemented
11#14911C212yesmaximal, complemented
12#14822C211yesmaximal, characteristic, complemented
13#14729C212yesmaximal, complemented
14#14719C211yesmaximal, characteristic, complemented
15#14718C212yesmaximal, complemented
16#14680C211yesmaximal, characteristic, complemented
17#14622C214yesmaximal, complemented
18C25×C4C2211yescharacteristic
19C22×#123C2212yes—
20C22×#121C2211yescharacteristic
21C22×#121C2211yescharacteristic
22C22×#121C2211yescharacteristic
23C22×#120C2212yes—
24C23×C4⋊C4C2211yescharacteristic
25C23×C4⋊C4C2211yescharacteristic
26C23×C22⋊C4C2211yescharacteristic
27C23×C22⋊C4C2211yescharacteristic
28#2847—28no—
29C2×#400C2212yescomplemented
30C2×#396C2214yescomplemented
31C2×#394C2214yes—
32C2×#394C2212yescomplemented
33C2×#386C2212yes—
34C2×#386C2212yes—
35C2×#386C2212yes—
36C2×#386C2212yes—
37C2×#386C2212yes—
38C2×#386C2212yes—
39C2×#385—28no—
40C2×#385C2212yes—
41C2×#385C2212yes—
42C2×#385C2212yes—
43C2×#385C2212yes—
44C2×#385C2212yes—
45C2×#381C2212yes—
46C2×#380C2211yescharacteristic
47C2×#380C2211yescharacteristic
48C2×#380C2211yescharacteristic
49C2×#380C2212yes—
50C2×#380C2212yes—
51C2×#380C2212yes—
52C2×#379C2212yes—
53C22×#95C2211yescharacteristic
54C22×#95C2211yescharacteristic
55#1445C2212yescomplemented
56#1445C2214yescomplemented
57#1444C2212yescomplemented
58#1444C2212yescomplemented
59#1442C2214yescomplemented
60#1442C2214yescomplemented
61#1441C2214yescomplemented
62#1441C2212yescomplemented
63#1441C2214yescomplemented
64#1441C2214yescomplemented
65#1441C2212yescomplemented
66#1440C2214yes—
67#1440C2214yescomplemented
68#1439C2214yes—
69#1439C2214yes—
70#1439C2214yes—
71#1439C2214yescomplemented
72#1439C2214yescomplemented
73#1439C2214yescomplemented
74#1439C2214yescomplemented
75#1438C2214yes—
76#1438C2214yes—
77#1438C2214yes—
78#1438C2212yescomplemented
79C22⋊#95C2212yes—
80C22⋊#95C2212yes—
81C22⋊#95C2211yescharacteristic
82C22⋊#95C2212yes—
83C22⋊#95C2211yescharacteristic
84C22⋊#95C2212yes—
85C26C2311yescharacteristic
86C23×D4C2312yes—
87C23×D4C2312yes—
88C23×D4C2311yescharacteristic
89C23×D4C2312yes—
90C24×C4—44no—
91C24×C4—44no—
92C24×C4—44no—
93C24×C4D418yes—
94C24×C4C2311yescharacteristic
95C24×C4C2311yescharacteristic
96C24×C4C2311yescharacteristic
97C24×C4C2311yescharacteristic
98C24×C4C2311yescharacteristic
99C24×C4C2311yescharacteristic
100C24×C4C2311yescharacteristic
101C24×C4C2311yescharacteristic
102C24×C4C2311yescharacteristic
103C24×C4C2311yescharacteristic
104C2×#123—44no—
105C2×#123—44no—
106C2×#123—44no—
107C2×#121—24no—
108C2×#121—24no—
109C2×#121—24no—
110C2×#121—44no—
111C2×#121—44no—
112C2×#121—44no—
113C2×#120—28no—
114C2×#120—44no—
115C2×#120—44no—
116C22×C4⋊C4—24no—
117C22×C4⋊C4—24no—
118C22×C4⋊C4—44no—
119C22×C4⋊C4—44no—
120C22×C4⋊C4C2312yes—
121C22×C4⋊C4C2312yes—
122C22×C4⋊C4C2311yescharacteristic
123C22×C4⋊C4C2314yes—
124C22×C4⋊C4C2314yes—
125C22×C4⋊C4C2312yes—
126C22×C4⋊C4C2312yes—
127C22×C4⋊C4C2311yescharacteristic
128C22×C4⋊C4C2311yescharacteristic
129C22×C4⋊C4C2314yes—
130C22×C22⋊C4—24no—
131C22×C22⋊C4—28no—
132C22×C22⋊C4—24no—
133C22×C22⋊C4—44no—
134C22×C22⋊C4C2312yes—
135C22×C22⋊C4C2312yes—
136C22×C22⋊C4C2312yes—
137C22×C22⋊C4C2312yes—
138C22×C22⋊C4C2312yes—
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2314yes—
141C22×C22⋊C4C2314yes—
142C22×C22⋊C4C2314yes—
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2312yes—
147C22×C22⋊C4C2312yes—
148C22×C22⋊C4C2312yes—
149C22×C22⋊C4C2314yes—
150C22×C22⋊C4C2314yes—
151C22×C22⋊C4C2314yes—
152#400—44no—
153#396—48no—
154#394—216no—
155#394—44no—
156#386—28no—
157#386—28no—
158#386—28no—
159#386—44no—
160#386—44no—
161#386—44no—
162#385—28no—
163#385—28no—
164#385—28no—
165#385—28no—
166#385—44no—
167#381—44no—
168#380—24no—
169#380—24no—
170#380—24no—
171#380—44no—
172#380—44no—
173#380—44no—
174#379—44no—
175C2×#95—24no—
176C2×#95—24no—
177C2×#95C2314yes—
178C2×#95C2312yes—
179C2×#95C2312yes—
180C2×#95C2312yes—
181C2×#95C2312yes—
182C2×#95C2312yes—
183C2×#95C2312yes—
184C2×#95C2312yes—
185C2×#95C2312yes—
186C2×#95C2312yes—
187C2×#95C2314yes—
188C2×#95C2314yes—
189C2×#95C2314yes—
190C2×#95C2312yes—
191C2×#95C2312yes—
192C2×#95C2314yes—
193C2×#95C2314yes—
194C2×#95C2314yes—
195C2×#95C2314yes—
196C2×#95C2314yes—
197C2×#95C2314yes—
198C2×#95C2314yes—
199C25—24no—
200C25—24no—
201C25—24no—
202C25—24no—
203C25—22no—
204C25—22no—
205C25—42no—
206C25—42no—
207C25C2×D414yes—
208C25C2412yes—
209C25C2411yescharacteristic
210C25C2411yescharacteristic
211C25C2411yescharacteristic
212C22×D4—24no—
213C22×D4—24no—
214C22×D4—24no—
215C22×D4—24no—
216C22×D4—24no—
217C22×D4—24no—
218C22×D4—24no—
219C22×D4—24no—
220C22×D4—24no—
221C22×D4—28no—
222C22×D4—28no—
223C22×D4—22no—
224C22×D4—24no—
225C22×D4—42no—
226C22×D4—42no—
227C22×D4—42no—
228C22×D4—42no—
229C22×D4—42no—
230C22×D4—42no—
231C22×D4—44no—
232C22×D4—44no—
233C23×C4—22no—
234C23×C4—22no—
235C23×C4—24no—
236C23×C4—24no—
237C23×C4—24no—
238C23×C4—24no—
239C23×C4—24no—
240C23×C4—24no—
241C23×C4—24no—
242C23×C4—24no—
243C23×C4—24no—
244C23×C4—24no—
245C23×C4—22no—
246C23×C4—22no—
247C23×C4—24no—
248C23×C4—22no—
249C23×C4—24no—
250C23×C4—24no—
251C23×C4—22no—
252C23×C4—22no—
253C23×C4—22no—
254C23×C4—24no—
255C23×C4—416no—
256C23×C4—416no—
257C23×C4—42no—
258C23×C4—42no—
259C23×C4—416no—
260C23×C4—42no—
261C23×C4—42no—
262C23×C4—42no—
263C23×C4—42no—
264C23×C4—42no—
265C23×C4—42no—
266C23×C4—42no—
267C23×C4—42no—
268C23×C4—42no—
269C23×C4—42no—
270C23×C4—42no—
271C23×C4—42no—
272C23×C4—464no—
273C23×C4C2×D414yes—
274C23×C4C2×D414yes—
275C23×C4C2×D414yes—
276C23×C4C2×D414yes—
277C23×C4C2×D414yes—
278C23×C4C2×D414yes—
279C23×C4C2414yes—
280C23×C4C2414yes—
281C23×C4C2412yes—
282C23×C4C2412yes—
283C23×C4C2412yes—
284C23×C4C2412yes—
285C23×C4C2412yes—
286C23×C4C2411yescharacteristic
287C23×C4C2411yescharacteristic
288C23×C4C2412yes—
289C23×C4C2412yes—
290C23×C4C2411yescharacteristic
291C23×C4C2411yescharacteristic
292#123—432no—
293#121—416no—
294#121—416no—
295#121—416no—
296#120—432no—
297C2×C4⋊C4—24no—
298C2×C4⋊C4—24no—
299C2×C4⋊C4—24no—
300C2×C4⋊C4—24no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—22no—
304C2×C4⋊C4—24no—
305C2×C4⋊C4—28no—
306C2×C4⋊C4—24no—
307C2×C4⋊C4—24no—
308C2×C4⋊C4—28no—
309C2×C4⋊C4—28no—
310C2×C4⋊C4—42no—
311C2×C4⋊C4—42no—
312C2×C4⋊C4—44no—
313C2×C4⋊C4—42no—
314C2×C4⋊C4—42no—
315C2×C4⋊C4—44no—
316C2×C4⋊C4—44no—
317C2×C4⋊C4—44no—
318C2×C4⋊C4—416no—
319C2×C4⋊C4—416no—
320C2×C4⋊C4—44no—
321C2×C4⋊C4—44no—
322C2×C4⋊C4—44no—
323C2×C4⋊C4—44no—
324C2×C22⋊C4—232no—
325C2×C22⋊C4—24no—
326C2×C22⋊C4—24no—
327C2×C22⋊C4—24no—
328C2×C22⋊C4—24no—
329C2×C22⋊C4—24no—
330C2×C22⋊C4—24no—
331C2×C22⋊C4—24no—
332C2×C22⋊C4—24no—
333C2×C22⋊C4—24no—
334C2×C22⋊C4—24no—
335C2×C22⋊C4—24no—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—24no—
338C2×C22⋊C4—24no—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—24no—
341C2×C22⋊C4—24no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—24no—
346C2×C22⋊C4—28no—
347C2×C22⋊C4—28no—
348C2×C22⋊C4—28no—
349C2×C22⋊C4—28no—
350C2×C22⋊C4—28no—
351C2×C22⋊C4—44no—
352C2×C22⋊C4—44no—
353C2×C22⋊C4—42no—
354C2×C22⋊C4—42no—
355C2×C22⋊C4—42no—
356C2×C22⋊C4—42no—
357C2×C22⋊C4—44no—
358C2×C22⋊C4—42no—
359C2×C22⋊C4—42no—
360C2×C22⋊C4—44no—
361C2×C22⋊C4—44no—
362C2×C22⋊C4—44no—
363C2×C22⋊C4—416no—
364C2×C22⋊C4—44no—
365C2×C22⋊C4—44no—
366C2×C22⋊C4—44no—
367C2×C22⋊C4—44no—
368C2×C22⋊C4—44no—
369C2×C22⋊C4—44no—
370C2×C22⋊C4—44no—
371C2×C22⋊C4—44no—
372C2×C22⋊C4—44no—
373C2×C22⋊C4—44no—
374C2×C22⋊C4—44no—
375C2×C22⋊C4#4118yes—
376#95—24no—
377#95—24no—
378#95—24no—
379#95—24no—
380#95—24no—
381#95—24no—
382#95—24no—
383#95—28no—
384#95—24no—
385#95—24no—
386#95—44no—
387#95—42no—
388#95—42no—
389#95—44no—
390#95—44no—
391#95—44no—
392#95—44no—
393#95—44no—
394#95—44no—
395#95—44no—
396#95—44no—
397#95—44no—
398C24—22no—
399C24—22no—
400C24—22no—
401C24—22no—
402C24—232no—
403C24—28no—
404C24—28no—
405C24—28no—
406C24—22no—
407C24—21no—
408C24—21no—
409C24—22no—
410C24—22no—
411C24—22no—
412C24—22no—
413C24—22no—
414C24—22no—
415C24—22no—
416C24—22no—
417C24—22no—
418C24—21no—
419C24—21no—
420C24—28no—
421C24—28no—
422C24—22no—
423C24—24no—
424C24—24no—
425C24—22no—
426C24—22no—
427C24—22no—
428C24—24no—
429C24—22no—
430C24—22no—
431C24—24no—
432C24—22no—
433C24—44no—
434C24—44no—
435C24—48no—
436C24—416no—
437C24—48no—
438C24—48no—
439C24—416no—
440C24—48no—
441C24—416no—
442C24—48no—
443C24—48no—
444C24C22×D412yes—
445C24C22×D412yes—
446C24C22×D412yes—
447C24C2×#4114yes—
448C24H(5,𝔽2)14yes—
449C24H(5,𝔽2)14yes—
450C24H(5,𝔽2)12yes—
451C242−1+414yes—
452C242−1+412yes—
453C24C2511yescharacteristic
454C2×D4—44no—
455C2×D4—44no—
456C2×D4—48no—
457C2×D4—48no—
458C2×D4—48no—
459C2×D4—48no—
460C2×D4—48no—
461C2×D4—48no—
462C2×D4—48no—
463C2×D4—48no—
464C2×D4—48no—
465C2×D4—48no—
466C2×D4—48no—
467C2×D4—48no—
468C2×D4—48no—
469C2×D4—44no—
470C2×D4—88no—
471C2×D4—88no—
472C2×D4—88no—
473C2×D4—88no—
474C2×D4—88no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—28no—
480C22×C4—28no—
481C22×C4—28no—
482C22×C4—28no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—24no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—24no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—28no—
500C22×C4—28no—
501C22×C4—28no—
502C22×C4—28no—
503C22×C4—28no—
504C22×C4—28no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—24no—
511C22×C4—24no—
512C22×C4—24no—
513C22×C4—24no—
514C22×C4—24no—
515C22×C4—24no—
516C22×C4—24no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—24no—
521C22×C4—22no—
522C22×C4—24no—
523C22×C4—24no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—24no—
528C22×C4—24no—
529C22×C4—24no—
530C22×C4—24no—
531C22×C4—24no—
532C22×C4—24no—
533C22×C4—24no—
534C22×C4—24no—
535C22×C4—22no—
536C22×C4—24no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—24no—
542C22×C4—24no—
543C22×C4—22no—
544C22×C4—24no—
545C22×C4—22no—
546C22×C4—44no—
547C22×C4—44no—
548C22×C4—44no—
549C22×C4—44no—
550C22×C4—44no—
551C22×C4—44no—
552C22×C4—44no—
553C22×C4—44no—
554C22×C4—44no—
555C22×C4—44no—
556C22×C4—416no—
557C22×C4—48no—
558C22×C4—416no—
559C22×C4—48no—
560C22×C4—416no—
561C22×C4—416no—
562C22×C4—416no—
563C22×C4—416no—
564C22×C4—44no—
565C22×C4—44no—
566C22×C4—4128no—
567C22×C4—416no—
568C22×C4—44no—
569C22×C4—44no—
570C22×C4—44no—
571C22×C4—44no—
572C22×C4—44no—
573C22×C4—44no—
574C22×C4—44no—
575C22×C4—44no—
576C22×C4—48no—
577C22×C4—48no—
578C22×C4—88no—
579C22×C4C22×D412yes—
580C22×C4C22×D412yes—
581C22×C4C22×D412yes—
582C22×C4C22×D412yes—
583C22×C4C2×#4114yes—
584C22×C4C2×#4114yes—
585C22×C4H(5,𝔽2)14yes—
586C22×C4H(5,𝔽2)14yes—
587C4⋊C4—48no—
588C4⋊C4—48no—
589C4⋊C4—44no—
590C4⋊C4—44no—
591C4⋊C4—416no—
592C4⋊C4—48no—
593C4⋊C4—48no—
594C4⋊C4—44no—
595C4⋊C4—88no—
596C4⋊C4—88no—
597C22⋊C4—216no—
598C22⋊C4—216no—
599C22⋊C4—48no—
600C22⋊C4—48no—
601C22⋊C4—48no—
602C22⋊C4—48no—
603C22⋊C4—48no—
604C22⋊C4—48no—
605C22⋊C4—416no—
606C22⋊C4—48no—
607C22⋊C4—48no—
608C22⋊C4—48no—
609C22⋊C4—48no—
610C22⋊C4—88no—
611C22⋊C4—88no—
612C22⋊C4—88no—
613C22⋊C4—88no—
614C22⋊C4—88no—
615C23—22no—
616C23—22no—
617C23—22no—
618C23—22no—
619C23—28no—
620C23—28no—
621C23—24no—
622C23—24no—
623C23—28no—
624C23—24no—
625C23—28no—
626C23—24no—
627C23—232no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—28no—
641C23—28no—
642C23—24no—
643C23—28no—
644C23—24no—
645C23—24no—
646C23—28no—
647C23—24no—
648C23—416no—
649C23—416no—
650C23—416no—
651C23—416no—
652C23—416no—
653C23—464no—
654C23—464no—
655C23—44no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—44no—
663C23—44no—
664C23—42no—
665C23—44no—
666C23—42no—
667C23—416no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—44no—
676C23—44no—
677C23—44no—
678C23—44no—
679C23—44no—
680C23—44no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—44no—
686C23—44no—
687C23—44no—
688C23—44no—
689C23—44no—
690C23—44no—
691C23#52514yes—
692C23#53414yes—
693C23#53514yes—
694C23#53614yes—
695C23#53714yes—
696C23#56018yes—
697C23#56218yes—
698C23C23×D411yescharacteristic
699C23C22×#4112yes—
700C23C2×H(5,𝔽2)12yes—
701C23C2×H(5,𝔽2)12yes—
702C23C2×H(5,𝔽2)12yes—
703C23C2×H(5,𝔽2)12yes—
704C23C2×H(5,𝔽2)11yescharacteristic
705C23C2×2−1+412yes—
706C23C2×2−1+411yescharacteristic
707D4—88no—
708D4—816no—
709D4—816no—
710D4—816no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—28no—
716C2×C4—28no—
717C2×C4—24no—
718C2×C4—24no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—24no—
726C2×C4—28no—
727C2×C4—24no—
728C2×C4—416no—
729C2×C4—416no—
730C2×C4—416no—
731C2×C4—416no—
732C2×C4—416no—
733C2×C4—416no—
734C2×C4—416no—
735C2×C4—416no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—44no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—44no—
744C2×C4—44no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—44no—
761C2×C4—44no—
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—42no—
772C2×C4—42no—
773C2×C4—44no—
774C2×C4—42no—
775C2×C4—42no—
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—88no—
787C2×C4—88no—
788C2×C4#53414yes—
789C2×C4#53414yes—
790C22—24no—
791C22—24no—
792C22—24no—
793C22—24no—
794C22—24no—
795C22—216no—
796C22—216no—
797C22—24no—
798C22—24no—
799C22—24no—
800C22—24no—
801C22—24no—
802C22—24no—
803C22—24no—
804C22—464no—
805C22—42no—
806C22—42no—
807C22—42no—
808C22—42no—
809C22—42no—
810C22—42no—
811C22—42no—
812C22—42no—
813C22—48no—
814C22—48no—
815C22—48no—
816C22—48no—
817C22—82no—
818C22—82no—
819C22—82no—
820C22—82no—
821C22—82no—
822C22—82no—
823C22—84no—
824C22—84no—
825C22—84no—
826C22—84no—
827C22—82no—
828C22#281318yes—
829C22C2×#52511yescharacteristic
830C22C2×#53411yescharacteristic
831C22C2×#53411yescharacteristic
832C22C2×#53411yescharacteristic
833C22C2×#53511yescharacteristic
834C22C2×#53611yescharacteristic
835C22C2×#53711yescharacteristic
836C22#349214yes—
837C22#351914yes—
838C22#351912yes—
839C22#352012yes—
840C22C2×#56012yes—
841C22C2×#56212yes—
842C22#353214yes—
843C22#353612yes—
844C22#353614yes—
845C22#353812yes—
846C4—24no—
847C4—24no—
848C4—44no—
849C4—44no—
850C4—42no—
851C4—42no—
852C4—82no—
853C4—82no—
854C4—82no—
855C4—82no—
856C4—82no—
857C4—84no—
858C4—84no—
859C2—28no—
860C2—44no—
861C2—44no—
862C2—162no—
863C2#3505711yescharacteristic
864C2#3507611yescharacteristic
865C2#3507711yescharacteristic
866C2C2×#281311yescharacteristic
867C2#3743611yescharacteristic
868C2#3744211yescharacteristic
869C2#3745111yescharacteristic
870C2#4574314yes—
871C2#4574514yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC2×#2847C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C22×#385C2semidirect
3. #16986C2semidirect
4. #16562C2semidirect
5. #16557C2semidirect
6. #16400C2semidirect
7. #16261C2semidirect
8. #14936C2semidirect
9. #14927C2semidirect
10. #14926C2semidirect
11. #14911C2semidirect
12. #14822C2semidirect
13. #14729C2semidirect
14. #14719C2semidirect
15. #14718C2semidirect
16. #14680C2semidirect
17. #14622C2semidirect
29. C2×#400C22semidirect
30. C2×#396C22semidirect
32. C2×#394C22semidirect
55. #1445C22semidirect
56. #1445C22semidirect
57. #1444C22semidirect
58. #1444C22semidirect
59. #1442C22semidirect
60. #1442C22semidirect
61. #1441C22semidirect
62. #1441C22semidirect
63. #1441C22semidirect
64. #1441C22semidirect
65. #1441C22semidirect
67. #1440C22semidirect
71. #1439C22semidirect
72. #1439C22semidirect
73. #1439C22semidirect
74. #1439C22semidirect
78. #1438C22semidirect

Maximal subgroups

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

subgroupindex
C2×#28472
C22×#3852
#169862
#165622
#165572
#164002
#162612
#149362
#149272
#149262
#149112
#148222
#147292
#147192
#147182
#146802
#146222