Finite Group Databasebeta

← #626074

Subgroups — #626074

Order 512.

4080 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2412C212yesmaximal, complemented
2C2×#2618C211yesmaximal, characteristic, complemented
3C2×#2617C211yesmaximal, characteristic
4C2×#2315C211yesmaximal, characteristic, complemented
5C22×#388C211yesmaximal, characteristic, complemented
6#15577C214yesmaximal, complemented
7#15472C214yesmaximal, complemented
8#15403C214yesmaximal, complemented
9#15302C214yesmaximal, complemented
10#14927C212yesmaximal, complemented
11#14921C212yesmaximal, complemented
12#14698C211yesmaximal, characteristic, complemented
13#14697C211yesmaximal, characteristic, complemented
14#14339C211yesmaximal, characteristic, complemented
15#14134C212yesmaximal, complemented
16C22×#123C2212yes—
17C22×#121C2211yescharacteristic
18C22×#120C2212yes—
19C23×C4⋊C4C2211yescharacteristic
20C23×C22⋊C4C2212yes—
21C23×C22⋊C4C2211yescharacteristic
22C23×C22⋊C4C2211yescharacteristic
23C23×C22⋊C4C2211yescharacteristic
24C23×C42C2211yescharacteristic
25#2618—28no—
26#2617—28no—
27#2412—216no—
28C2×#398C2212yescomplemented
29C2×#397C2214yes—
30C2×#397C2212yes—
31C2×#396C2214yescomplemented
32C2×#394C2214yes—
33C2×#394C2212yes—
34C2×#394C2212yes—
35C2×#394C2212yescomplemented
36C2×#392C2212yes—
37#2315—28no—
38C2×#390C2212yescomplemented
39C2×#389C2212yescomplemented
40C2×#388—28no—
41C2×#388C2214yes—
42C2×#388C2214yes—
43C2×#386C2214yes—
44C2×#386C2212yes—
45C2×#386C2212yes—
46C2×#386C2212yes—
47C2×#386C2214yes—
48C2×#386C2212yes—
49C2×#385C2214yes—
50C2×#385C2214yes—
51C2×#385C2212yes—
52C2×#381C2212yes—
53C2×#380C2211yescharacteristic
54C2×#380C2212yes—
55C2×#380C2211yescharacteristic
56C2×#380C2214yes—
57C2×#380C2211yescharacteristic
58C22×#95C2211yescharacteristic
59C22×#95C2211yescharacteristic
60#1443C2214yescomplemented
61#1442C2214yescomplemented
62#1441C2214yescomplemented
63#1441C2212yescomplemented
64#1441C2212yescomplemented
65#1441C2214yescomplemented
66#1441C2214yescomplemented
67#1440C2214yes—
68#1440C2214yescomplemented
69#1439C2214yescomplemented
70#1439C2214yescomplemented
71#1439C2214yescomplemented
72#1438C2214yes—
73#1437C2214yescomplemented
74#1436C2214yescomplemented
75C4⋊#95C2212yescomplemented
76C4⋊#95C2212yescomplemented
77C22⋊#95C2212yes—
78C22⋊#95C2212yes—
79C22⋊#95C2214yes—
80C26C2311yescharacteristic
81C23×D4C2312yes—
82C23×D4C2311yescharacteristic
83C23×D4C2312yes—
84C23×D4C2312yes—
85C24×C4C2311yescharacteristic
86C24×C4C2311yescharacteristic
87C24×C4C2311yescharacteristic
88C24×C4C2314yes—
89C24×C4C2311yescharacteristic
90C24×C4C2311yescharacteristic
91C24×C4C2311yescharacteristic
92C2×#123—28no—
93C2×#123—28no—
94C2×#123—44no—
95C2×#121—24no—
96C2×#121—24no—
97C2×#121—24no—
98C2×#120—28no—
99C2×#120—28no—
100C2×#120—28no—
101C22×C4⋊C4—24no—
102C22×C4⋊C4—24no—
103C22×C4⋊C4—24no—
104C22×C4⋊C4C2312yes—
105C22×C4⋊C4C2312yes—
106C22×C4⋊C4C2311yescharacteristic
107C22×C4⋊C4C2314yes—
108C22×C4⋊C4C2311yescharacteristic
109C22×C4⋊C4C2311yescharacteristic
110C22×C4⋊C4C2314yes—
111C22×C4⋊C4C2312yes—
112C22×C4⋊C4C2314yes—
113C22×C4⋊C4C2312yes—
114C22×C22⋊C4—24no—
115C22×C22⋊C4—24no—
116C22×C22⋊C4—24no—
117C22×C22⋊C4—24no—
118C22×C22⋊C4—28no—
119C22×C22⋊C4—24no—
120C22×C22⋊C4—28no—
121C22×C22⋊C4—44no—
122C22×C22⋊C4—44no—
123C22×C22⋊C4D418yes—
124C22×C22⋊C4D418yescomplemented
125C22×C22⋊C4C2312yes—
126C22×C22⋊C4C2312yes—
127C22×C22⋊C4C2312yes—
128C22×C22⋊C4C2312yes—
129C22×C22⋊C4C2312yes—
130C22×C22⋊C4C2314yes—
131C22×C22⋊C4C2314yes—
132C22×C22⋊C4C2314yes—
133C22×C22⋊C4C2312yes—
134C22×C22⋊C4C2312yes—
135C22×C22⋊C4C2314yes—
136C22×C22⋊C4C2312yes—
137C22×C22⋊C4C2312yes—
138C22×C22⋊C4C2312yes—
139C22×C22⋊C4C2314yes—
140C22×C22⋊C4C2314yes—
141C22×C22⋊C4C2314yes—
142C22×C42—24no—
143C22×C42—44no—
144C22×C42C2312yes—
145C22×C42C2312yes—
146#398—28no—
147#397—28no—
148#397—216no—
149#396—216no—
150#394—28no—
151#394—28no—
152#394—216no—
153#394—28no—
154#392—28no—
155#390—44no—
156#389—44no—
157#388—216no—
158#388—216no—
159#386—28no—
160#386—28no—
161#386—28no—
162#386—216no—
163#386—48no—
164#386—44no—
165#385—28no—
166#385—216no—
167#385—216no—
168#381—28no—
169#380—24no—
170#380—24no—
171#380—28no—
172#380—216no—
173#380D418yescomplemented
174C2×#95—24no—
175C2×#95—24no—
176C2×#95C2312yes—
177C2×#95C2312yes—
178C2×#95C2312yes—
179C2×#95C2314yes—
180C2×#95C2314yes—
181C2×#95C2314yes—
182C2×#95C2314yes—
183C2×#95C2314yes—
184C2×#95C2314yes—
185C2×#95C2312yes—
186C2×#95C2314yes—
187C2×#95C2314yes—
188C2×#95C2314yes—
189C2×#95C2314yes—
190C2×#95C2314yes—
191C2×#95C2314yes—
192C2×#95C2314yes—
193C2×#95C2312yes—
194C25—22no—
195C25—22no—
196C25—22no—
197C25—22no—
198C25—42no—
199C25—42no—
200C25—42no—
201C25—42no—
202C25C2×D414yes—
203C25C2×D414yes—
204C25#4114yes—
205C25C2412yes—
206C25C2412yes—
207C25C2411yescharacteristic
208C22×D4—24no—
209C22×D4—24no—
210C22×D4—24no—
211C22×D4—24no—
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—22no—
222C22×D4—22no—
223C22×D4—22no—
224C22×D4—42no—
225C22×D4—44no—
226C22×D4—44no—
227C22×D4—44no—
228C22×D4—44no—
229C22×D4—42no—
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—24no—
242C23×C4—22no—
243C23×C4—22no—
244C23×C4—22no—
245C23×C4—28no—
246C23×C4—22no—
247C23×C4—22no—
248C23×C4—28no—
249C23×C4—42no—
250C23×C4—42no—
251C23×C4—42no—
252C23×C4—42no—
253C23×C4—42no—
254C23×C4—44no—
255C23×C4—42no—
256C23×C4—44no—
257C23×C4—42no—
258C23×C4—42no—
259C23×C4—44no—
260C23×C4—42no—
261C23×C4—44no—
262C23×C4—44no—
263C23×C4C2×D414yes—
264C23×C4C2×D414yes—
265C23×C4C2×D414yes—
266C23×C4C2×D414yes—
267C23×C4C2×D414yes—
268C23×C4#4114yes—
269C23×C4C2414yes—
270C23×C4C2412yes—
271C23×C4C2412yes—
272C23×C4C2412yes—
273C23×C4C2412yes—
274C23×C4C2412yes—
275C23×C4C2414yes—
276C23×C4C2412yes—
277C23×C4C2412yes—
278C23×C4C2412yes—
279C23×C4C2411yescharacteristic
280C23×C4C2411yescharacteristic
281#123—432no—
282#121—416no—
283#120—432no—
284C2×C4⋊C4—24no—
285C2×C4⋊C4—24no—
286C2×C4⋊C4—24no—
287C2×C4⋊C4—24no—
288C2×C4⋊C4—22no—
289C2×C4⋊C4—22no—
290C2×C4⋊C4—28no—
291C2×C4⋊C4—28no—
292C2×C4⋊C4—24no—
293C2×C4⋊C4—24no—
294C2×C4⋊C4—22no—
295C2×C4⋊C4—28no—
296C2×C4⋊C4—24no—
297C2×C4⋊C4—28no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—22no—
300C2×C4⋊C4—42no—
301C2×C4⋊C4—44no—
302C2×C4⋊C4—42no—
303C2×C4⋊C4—416no—
304C2×C4⋊C4—42no—
305C2×C4⋊C4—42no—
306C2×C4⋊C4—44no—
307C2×C4⋊C4—44no—
308C2×C4⋊C4—44no—
309C2×C4⋊C4—42no—
310C2×C4⋊C4—44no—
311C2×C4⋊C4—42no—
312C2×C4⋊C4C2×D418yes—
313C2×C22⋊C4—232no—
314C2×C22⋊C4—24no—
315C2×C22⋊C4—28no—
316C2×C22⋊C4—28no—
317C2×C22⋊C4—24no—
318C2×C22⋊C4—232no—
319C2×C22⋊C4—24no—
320C2×C22⋊C4—24no—
321C2×C22⋊C4—24no—
322C2×C22⋊C4—24no—
323C2×C22⋊C4—24no—
324C2×C22⋊C4—24no—
325C2×C22⋊C4—28no—
326C2×C22⋊C4—28no—
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—28no—
338C2×C22⋊C4—24no—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—28no—
341C2×C22⋊C4—28no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—28no—
344C2×C22⋊C4—28no—
345C2×C22⋊C4—24no—
346C2×C22⋊C4—24no—
347C2×C22⋊C4—28no—
348C2×C22⋊C4—28no—
349C2×C22⋊C4—432no—
350C2×C22⋊C4—44no—
351C2×C22⋊C4—44no—
352C2×C22⋊C4—44no—
353C2×C22⋊C4—416no—
354C2×C22⋊C4—44no—
355C2×C22⋊C4—44no—
356C2×C22⋊C4—44no—
357C2×C22⋊C4—44no—
358C2×C22⋊C4—44no—
359C2×C22⋊C4—44no—
360C2×C22⋊C4—44no—
361C2×C22⋊C4—44no—
362C2×C22⋊C4C2×D418yes—
363C2×C22⋊C4C2×D418yes—
364C2×C22⋊C4C2×D418yes—
365C2×C22⋊C4C2×D4116yes—
366C2×C42—24no—
367C2×C42—24no—
368C2×C42—24no—
369C2×C42—24no—
370C2×C42—42no—
371C2×C42—42no—
372C2×C42—416no—
373#95—28no—
374#95—28no—
375#95—28no—
376#95—28no—
377#95—24no—
378#95—28no—
379#95—24no—
380#95—28no—
381#95—28no—
382#95—24no—
383#95—24no—
384#95—28no—
385#95—28no—
386#95—44no—
387#95—44no—
388#95—44no—
389#95—44no—
390#95C2×D418yes—
391C24—22no—
392C24—22no—
393C24—22no—
394C24—22no—
395C24—22no—
396C24—22no—
397C24—24no—
398C24—22no—
399C24—22no—
400C24—24no—
401C24—24no—
402C24—24no—
403C24—28no—
404C24—28no—
405C24—28no—
406C24—28no—
407C24—28no—
408C24—28no—
409C24—22no—
410C24—22no—
411C24—22no—
412C24—22no—
413C24—22no—
414C24—24no—
415C24—22no—
416C24—22no—
417C24—24no—
418C24—24no—
419C24—24no—
420C24—44no—
421C24—48no—
422C24—44no—
423C24—44no—
424C24—44no—
425C24—48no—
426C24—48no—
427C24—48no—
428C24—84no—
429C24—84no—
430C24—84no—
431C24—84no—
432C24—84no—
433C24—84no—
434C24—84no—
435C24—84no—
436C24#121116yes—
437C24C22×D414yes—
438C24C22×D414yes—
439C24C22×D412yes—
440C24C22×D412yes—
441C24C22×D412yes—
442C24C2×#4114yes—
443C24C2×#4112yes—
444C24C2×#4112yes—
445C24H(5,𝔽2)12yes—
446C242−1+412yes—
447C24C2511yescharacteristic
448C2×D4—48no—
449C2×D4—416no—
450C2×D4—416no—
451C2×D4—48no—
452C2×D4—48no—
453C2×D4—48no—
454C2×D4—48no—
455C2×D4—48no—
456C2×D4—48no—
457C2×D4—48no—
458C2×D4—48no—
459C2×D4—48no—
460C2×D4—44no—
461C2×D4—82no—
462C2×D4—82no—
463C2×D4—84no—
464C2×D4—84no—
465C2×D4—84no—
466C2×D4—84no—
467C2×D4—84no—
468C2×D4—88no—
469C2×D4—88no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—28no—
475C22×C4—28no—
476C22×C4—28no—
477C22×C4—28no—
478C22×C4—28no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—24no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—24no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—24no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—24no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—24no—
503C22×C4—24no—
504C22×C4—24no—
505C22×C4—22no—
506C22×C4—24no—
507C22×C4—28no—
508C22×C4—22no—
509C22×C4—24no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—24no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—24no—
525C22×C4—22no—
526C22×C4—24no—
527C22×C4—24no—
528C22×C4—24no—
529C22×C4—22no—
530C22×C4—24no—
531C22×C4—24no—
532C22×C4—24no—
533C22×C4—24no—
534C22×C4—24no—
535C22×C4—24no—
536C22×C4—24no—
537C22×C4—44no—
538C22×C4—44no—
539C22×C4—48no—
540C22×C4—48no—
541C22×C4—48no—
542C22×C4—44no—
543C22×C4—44no—
544C22×C4—48no—
545C22×C4—48no—
546C22×C4—416no—
547C22×C4—44no—
548C22×C4—48no—
549C22×C4—44no—
550C22×C4—44no—
551C22×C4—44no—
552C22×C4—44no—
553C22×C4—44no—
554C22×C4—44no—
555C22×C4—44no—
556C22×C4—44no—
557C22×C4—416no—
558C22×C4—44no—
559C22×C4—44no—
560C22×C4—88no—
561C22×C4—88no—
562C22×C4—88no—
563C22×C4—84no—
564C22×C4—84no—
565C22×C4—84no—
566C22×C4—84no—
567C22×C4—88no—
568C22×C4—88no—
569C22×C4#121116yes—
570C22×C4C22×D414yes—
571C22×C4C22×D414yes—
572C22×C4C22×D414yes—
573C22×C4C22×D418yes—
574C22×C4C22×D412yes—
575C22×C4C22×D412yes—
576C22×C4C22×D412yes—
577C22×C4C22×D412yes—
578C22×C4C2×#4112yes—
579C22×C4C2×#4112yes—
580C22×C4H(5,𝔽2)14yes—
581C4⋊C4—48no—
582C4⋊C4—416no—
583C4⋊C4—48no—
584C4⋊C4—48no—
585C4⋊C4—44no—
586C4⋊C4—82no—
587C4⋊C4—82no—
588C4⋊C4—84no—
589C4⋊C4—88no—
590C4⋊C4—88no—
591C22⋊C4—232no—
592C22⋊C4—216no—
593C22⋊C4—216no—
594C22⋊C4—216no—
595C22⋊C4—416no—
596C22⋊C4—416no—
597C22⋊C4—416no—
598C22⋊C4—48no—
599C22⋊C4—48no—
600C22⋊C4—48no—
601C22⋊C4—48no—
602C22⋊C4—48no—
603C22⋊C4—84no—
604C22⋊C4—84no—
605C22⋊C4—88no—
606C22⋊C4—88no—
607C22⋊C4—88no—
608C42—48no—
609C42—48no—
610C23—24no—
611C23—24no—
612C23—22no—
613C23—22no—
614C23—22no—
615C23—22no—
616C23—24no—
617C23—24no—
618C23—24no—
619C23—24no—
620C23—24no—
621C23—24no—
622C23—24no—
623C23—24no—
624C23—24no—
625C23—24no—
626C23—24no—
627C23—24no—
628C23—28no—
629C23—28no—
630C23—24no—
631C23—24no—
632C23—24no—
633C23—24no—
634C23—24no—
635C23—24no—
636C23—24no—
637C23—24no—
638C23—28no—
639C23—28no—
640C23—232no—
641C23—416no—
642C23—416no—
643C23—44no—
644C23—44no—
645C23—44no—
646C23—44no—
647C23—44no—
648C23—44no—
649C23—44no—
650C23—44no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—44no—
655C23—44no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—44no—
665C23—44no—
666C23—44no—
667C23—44no—
668C23—44no—
669C23—44no—
670C23—44no—
671C23—44no—
672C23—44no—
673C23—44no—
674C23—88no—
675C23—88no—
676C23—816no—
677C23—88no—
678C23—88no—
679C23—816no—
680C23—816no—
681C23—816no—
682C23C2×#12118yes—
683C23C2×#12114yes—
684C23C2×#12114yes—
685C23#53714yes—
686C23D4214yes—
687C23#54714yes—
688C23#54814yes—
689C23#55314yes—
690C23C23×D411yescharacteristic
691C23C23×D411yescharacteristic
692C23C23×D411yescharacteristic
693C23C22×#4111yescharacteristic
694C23C22×#4111yescharacteristic
695C23C2×H(5,𝔽2)11yescharacteristic
696C23C2×H(5,𝔽2)12yes—
697C23C2×2−1+411yescharacteristic
698C23#58512yes—
699C23#58512yes—
700C23#58512yes—
701D4—88no—
702D4—816no—
703D4—816no—
704D4—816no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—24no—
715C2×C4—24no—
716C2×C4—28no—
717C2×C4—24no—
718C2×C4—24no—
719C2×C4—24no—
720C2×C4—24no—
721C2×C4—24no—
722C2×C4—24no—
723C2×C4—28no—
724C2×C4—24no—
725C2×C4—28no—
726C2×C4—24no—
727C2×C4—24no—
728C2×C4—416no—
729C2×C4—416no—
730C2×C4—416no—
731C2×C4—42no—
732C2×C4—416no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—44no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—44no—
744C2×C4—44no—
745C2×C4—44no—
746C2×C4—42no—
747C2×C4—44no—
748C2×C4—42no—
749C2×C4—44no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—44no—
757C2×C4—44no—
758C2×C4—44no—
759C2×C4—44no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—44no—
771C2×C4—44no—
772C2×C4—44no—
773C2×C4—44no—
774C2×C4—44no—
775C2×C4—44no—
776C2×C4—44no—
777C2×C4—44no—
778C2×C4—44no—
779C2×C4—88no—
780C2×C4—832no—
781C2×C4—88no—
782C2×C4C2×#12114yes—
783C2×C4C2×#12114yes—
784C22—24no—
785C22—24no—
786C22—24no—
787C22—28no—
788C22—24no—
789C22—24no—
790C22—28no—
791C22—24no—
792C22—28no—
793C22—28no—
794C22—28no—
795C22—28no—
796C22—28no—
797C22—44no—
798C22—44no—
799C22—48no—
800C22—44no—
801C22—44no—
802C22—48no—
803C22—48no—
804C22—48no—
805C22—832no—
806C22—82no—
807C22—82no—
808C22—82no—
809C22—84no—
810C22—82no—
811C22—82no—
812C22—82no—
813C22—84no—
814C22—82no—
815C22—84no—
816C22—84no—
817C22#241618yes—
818C22C22×#12111yescharacteristic
819C22C22×#12111yescharacteristic
820C22C2×#53711yescharacteristic
821C22#344912yes—
822C22#345912yes—
823C22C2×D4211yescharacteristic
824C22C2×#54711yescharacteristic
825C22C2×#54811yescharacteristic
826C22C2×#55311yescharacteristic
827C22#348411yescharacteristic
828C22#348511yescharacteristic
829C22#348511yescharacteristic
830C22#348511yescharacteristic
831C22#349112yes—
832C22#349612yes—
833C22#349612yes—
834C22#350012yes—
835C22#350512yes—
836C22#351012yes—
837C22#353412yes—
838C22#353512yes—
839C22#356012yes—
840C22#356412yes—
841C4—24no—
842C4—24no—
843C4—44no—
844C4—44no—
845C4—44no—
846C4—44no—
847C4—48no—
848C4—82no—
849C4—82no—
850C4—82no—
851C4—82no—
852C4—84no—
853C2—28no—
854C2—48no—
855C2—162no—
856C2C2×#241611yescharacteristic
857C2#3498411yescharacteristic
858C2#3508911yescharacteristic
859C2#3535811yescharacteristic
860C2#3561711yescharacteristic
861C2#3670911yescharacteristic
862C2#3696011yescharacteristic
863C2#3935412yes—
864C2#3942212yes—
865C2#3948212yes—
866C2#3955012yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC2×#2617C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#2412C2semidirect
2. C2×#2618C2semidirect
4. C2×#2315C2semidirect
5. C22×#388C2semidirect
6. #15577C2semidirect
7. #15472C2semidirect
8. #15403C2semidirect
9. #15302C2semidirect
10. #14927C2semidirect
11. #14921C2semidirect
12. #14698C2semidirect
13. #14697C2semidirect
14. #14339C2semidirect
15. #14134C2semidirect
28. C2×#398C22semidirect
31. C2×#396C22semidirect
35. C2×#394C22semidirect
38. C2×#390C22semidirect
39. C2×#389C22semidirect
60. #1443C22semidirect
61. #1442C22semidirect
62. #1441C22semidirect
63. #1441C22semidirect
64. #1441C22semidirect
65. #1441C22semidirect
66. #1441C22semidirect
68. #1440C22semidirect
69. #1439C22semidirect
70. #1439C22semidirect
71. #1439C22semidirect
73. #1437C22semidirect
74. #1436C22semidirect
75. C4⋊#95C22semidirect
76. C4⋊#95C22semidirect
124. C22×C22⋊C4D4semidirect
173. #380D4semidirect

Maximal subgroups

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

subgroupindex
C2×#24122
C2×#26182
C2×#26172
C2×#23152
C22×#3882
#155772
#154722
#154032
#153022
#149272
#149212
#146982
#146972
#143392
#141342