Finite Group Databasebeta

← #554250

Subgroups — #554250

Order 512.

4518 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2405C211yesmaximal, characteristic
2C2×#2315C211yesmaximal, characteristic, complemented
3C22×#390C211yesmaximal, characteristic
4#14695C212yesmaximal, complemented
5#14536C214yesmaximal, complemented
6#14518C214yesmaximal, complemented
7#14374C214yesmaximal, complemented
8#14360C214yesmaximal, complemented
9#14262C212yesmaximal, complemented
10#14127C211yesmaximal, characteristic, complemented
11#14043C212yesmaximal, complemented
12#13971C212yesmaximal, complemented
13#13869C211yesmaximal, characteristic, complemented
14#13867C211yesmaximal, characteristic
15#13775C211yesmaximal, characteristic, complemented
16C24×D4C2211yescharacteristic
17C22×#123C2212yes—
18C23×C4⋊C4C2211yescharacteristic
19C23×C22⋊C4C2211yescharacteristic
20C23×C22⋊C4C2211yescharacteristic
21C23×C22⋊C4C2211yescharacteristic
22C23×C22⋊C4C2211yescharacteristic
23C23×C22⋊C4C2211yescharacteristic
24C23×C22⋊C4C2211yescharacteristic
25C23×C42C2211yescharacteristic
26#2405C4116yescomplemented
27C2×#394C2214yes—
28#2315—28no—
29C2×#390—28no—
30C2×#390C2214yes—
31C2×#390C2214yes—
32C2×#389C2214yescomplemented
33C2×#388C2214yescomplemented
34C2×#387C2214yescomplemented
35C2×#386C2212yes—
36C2×#386C2212yes—
37C2×#386C2212yes—
38C2×#385C2212yes—
39C2×#385C2212yes—
40C2×#385C2212yes—
41C2×#385C2212yes—
42C2×#385C2212yescomplemented
43C2×#385C2212yescomplemented
44C2×#385C2212yescomplemented
45C2×#381C2212yescomplemented
46C2×#380C2212yescomplemented
47C2×#380C2212yescomplemented
48C2×#379C2211yescharacteristic
49C2×#379C2212yes—
50C2×#379C2211yescharacteristic
51C2×#379C2212yes—
52C2×C4×C22⋊C4C2212yes—
53#1444C2214yescomplemented
54#1441C2214yescomplemented
55#1440C2214yescomplemented
56#1440C2214yescomplemented
57#1439C2214yescomplemented
58#1439C2214yescomplemented
59#1439C2214yescomplemented
60#1439C2214yescomplemented
61#1439C2214yescomplemented
62#1439C2214yescomplemented
63#1438C2214yes—
64#1437C2214yescomplemented
65#1437C2214yescomplemented
66#1437C2214yescomplemented
67#1436C2214yescomplemented
68#1436C2214yescomplemented
69#1436C2214yescomplemented
70#1434C2214yescomplemented
71C22⋊#95C2212yes—
72C22⋊#95C2212yes—
73C22⋊#95C2212yes—
74C22⋊#95C2212yes—
75C22⋊#95C2212yes—
76C22⋊#95C2212yescomplemented
77C22⋊#95C2212yescomplemented
78C26C2311yescharacteristic
79C26C2311yescharacteristic
80C23×D4—24no—
81C23×D4—24no—
82C23×D4—44no—
83C23×D4—44no—
84C23×D4C2×C418yes—
85C23×D4C2312yes—
86C23×D4C2312yes—
87C24×C4C2311yescharacteristic
88C24×C4C2311yescharacteristic
89C24×C4C2311yescharacteristic
90C24×C4C2311yescharacteristic
91C24×C4C2311yescharacteristic
92C24×C4C2311yescharacteristic
93C24×C4C2311yescharacteristic
94C24×C4C2311yescharacteristic
95C24×C4C2311yescharacteristic
96C2×#123—44no—
97C2×#123—44no—
98C2×#123C2×C4116yescomplemented
99C22×C4⋊C4—24no—
100C22×C4⋊C4—44no—
101C22×C4⋊C4C2314yes—
102C22×C4⋊C4C2314yes—
103C22×C4⋊C4C2312yes—
104C22×C4⋊C4C2312yes—
105C22×C4⋊C4C2312yes—
106C22×C4⋊C4C2312yes—
107C22×C4⋊C4C2314yes—
108C22×C22⋊C4—24no—
109C22×C22⋊C4—24no—
110C22×C22⋊C4—24no—
111C22×C22⋊C4—24no—
112C22×C22⋊C4—24no—
113C22×C22⋊C4—24no—
114C22×C22⋊C4—44no—
115C22×C22⋊C4—44no—
116C22×C22⋊C4—44no—
117C22×C22⋊C4—44no—
118C22×C22⋊C4—44no—
119C22×C22⋊C4C2×C418yes—
120C22×C22⋊C4D418yes—
121C22×C22⋊C4C2312yes—
122C22×C22⋊C4C2312yes—
123C22×C22⋊C4C2312yes—
124C22×C22⋊C4C2312yes—
125C22×C22⋊C4C2314yes—
126C22×C22⋊C4C2312yes—
127C22×C22⋊C4C2312yes—
128C22×C22⋊C4C2312yes—
129C22×C22⋊C4C2312yes—
130C22×C22⋊C4C2314yes—
131C22×C22⋊C4C2312yes—
132C22×C22⋊C4C2312yes—
133C22×C22⋊C4C2314yes—
134C22×C22⋊C4C2314yes—
135C22×C22⋊C4C2312yes—
136C22×C22⋊C4C2314yes—
137C22×C22⋊C4C2314yes—
138C22×C22⋊C4C2312yes—
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2312yes—
141C22×C42—24no—
142C22×C42—44no—
143C22×C42C2314yes—
144C22×C42C2314yes—
145#394C2×C4132yescomplemented
146#390—216no—
147#390—216no—
148#389—48no—
149#388—48no—
150#387—48no—
151#386—44no—
152#386—44no—
153#386C2×C4116yescomplemented
154#385—28no—
155#385—28no—
156#385—28no—
157#385—28no—
158#385—44no—
159#385—44no—
160#385C2×C4116yescomplemented
161#381—44no—
162#380—28no—
163#380—28no—
164#379—24no—
165#379—44no—
166#379C2×C418yes—
167#379C2×C4116yescomplemented
168C4×C22⋊C4—44no—
169C2×#95C2314yes—
170C2×#95C2314yes—
171C2×#95C2314yes—
172C2×#95C2314yes—
173C2×#95C2312yes—
174C2×#95C2312yes—
175C2×#95C2312yes—
176C2×#95C2312yes—
177C2×#95C2314yes—
178C2×#95C2314yes—
179C2×#95C2314yes—
180C2×#95C2314yes—
181C2×#95C2314yes—
182C2×#95C2314yes—
183C2×#95C2314yes—
184C2×#95C2314yes—
185C2×#95C2314yes—
186C25—24no—
187C25—24no—
188C25—22no—
189C25—22no—
190C25—24no—
191C25—24no—
192C25—42no—
193C25—42no—
194C25—42no—
195C25—42no—
196C25—42no—
197C25—42no—
198C25—42no—
199C25—42no—
200C25C22×C414yes—
201C25C22×C414yes—
202C25C2×D414yes—
203C25#4114yes—
204C25C2412yes—
205C25C2411yescharacteristic
206C25C2411yescharacteristic
207C25C2411yescharacteristic
208C22×D4—232no—
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—432no—
218C22×D4—42no—
219C22×D4—42no—
220C22×D4—42no—
221C22×D4—42no—
222C22×D4—416no—
223C22×D4—416no—
224C22×D4—432no—
225C22×D4C22×C418yes—
226C22×D4C22×C418yes—
227C23×C4—22no—
228C23×C4—22no—
229C23×C4—24no—
230C23×C4—24no—
231C23×C4—22no—
232C23×C4—24no—
233C23×C4—22no—
234C23×C4—22no—
235C23×C4—22no—
236C23×C4—22no—
237C23×C4—24no—
238C23×C4—24no—
239C23×C4—22no—
240C23×C4—24no—
241C23×C4—22no—
242C23×C4—22no—
243C23×C4—24no—
244C23×C4—42no—
245C23×C4—42no—
246C23×C4—42no—
247C23×C4—42no—
248C23×C4—42no—
249C23×C4—42no—
250C23×C4—42no—
251C23×C4—42no—
252C23×C4—42no—
253C23×C4—42no—
254C23×C4—42no—
255C23×C4—42no—
256C23×C4—42no—
257C23×C4—42no—
258C23×C4—42no—
259C23×C4—42no—
260C23×C4—42no—
261C23×C4C22×C414yes—
262C23×C4C22×C414yes—
263C23×C4C22×C414yes—
264C23×C4C2×D414yes—
265C23×C4C2×D414yes—
266C23×C4C2414yes—
267C23×C4C2412yes—
268C23×C4C2412yes—
269C23×C4C2412yes—
270C23×C4C2414yes—
271C23×C4C2412yes—
272C23×C4C2412yes—
273C23×C4C2412yes—
274C23×C4C2412yes—
275C23×C4C2412yes—
276C23×C4C2412yes—
277#123—432no—
278C2×C4⋊C4—28no—
279C2×C4⋊C4—28no—
280C2×C4⋊C4—28no—
281C2×C4⋊C4—28no—
282C2×C4⋊C4—24no—
283C2×C4⋊C4—24no—
284C2×C4⋊C4—24no—
285C2×C4⋊C4—24no—
286C2×C4⋊C4—44no—
287C2×C4⋊C4—416no—
288C2×C4⋊C4—44no—
289C2×C4⋊C4—44no—
290C2×C4⋊C4—44no—
291C2×C4⋊C4—44no—
292C2×C4⋊C4—44no—
293C2×C4⋊C4—44no—
294C2×C4⋊C4—44no—
295C2×C4⋊C4C22×C4116yes—
296C2×C22⋊C4—232no—
297C2×C22⋊C4—24no—
298C2×C22⋊C4—24no—
299C2×C22⋊C4—24no—
300C2×C22⋊C4—24no—
301C2×C22⋊C4—24no—
302C2×C22⋊C4—24no—
303C2×C22⋊C4—24no—
304C2×C22⋊C4—24no—
305C2×C22⋊C4—24no—
306C2×C22⋊C4—24no—
307C2×C22⋊C4—24no—
308C2×C22⋊C4—24no—
309C2×C22⋊C4—24no—
310C2×C22⋊C4—24no—
311C2×C22⋊C4—24no—
312C2×C22⋊C4—28no—
313C2×C22⋊C4—28no—
314C2×C22⋊C4—24no—
315C2×C22⋊C4—24no—
316C2×C22⋊C4—28no—
317C2×C22⋊C4—24no—
318C2×C22⋊C4—24no—
319C2×C22⋊C4—416no—
320C2×C22⋊C4—42no—
321C2×C22⋊C4—42no—
322C2×C22⋊C4—42no—
323C2×C22⋊C4—42no—
324C2×C22⋊C4—44no—
325C2×C22⋊C4—42no—
326C2×C22⋊C4—42no—
327C2×C22⋊C4—44no—
328C2×C22⋊C4—44no—
329C2×C22⋊C4—42no—
330C2×C22⋊C4—42no—
331C2×C22⋊C4—42no—
332C2×C22⋊C4—44no—
333C2×C22⋊C4—42no—
334C2×C22⋊C4—44no—
335C2×C22⋊C4—44no—
336C2×C22⋊C4—42no—
337C2×C22⋊C4—42no—
338C2×C22⋊C4—44no—
339C2×C22⋊C4—416no—
340C2×C22⋊C4—416no—
341C2×C22⋊C4—416no—
342C2×C22⋊C4—416no—
343C2×C22⋊C4—42no—
344C2×C22⋊C4—44no—
345C2×C22⋊C4—44no—
346C2×C22⋊C4—44no—
347C2×C22⋊C4—42no—
348C2×C22⋊C4—42no—
349C2×C22⋊C4—42no—
350C2×C22⋊C4—44no—
351C2×C22⋊C4—44no—
352C2×C22⋊C4—44no—
353C2×C22⋊C4C22×C418yes—
354C2×C22⋊C4C22×C418yes—
355C2×C22⋊C4C22×C418yes—
356C2×C22⋊C4C22×C418yes—
357C2×C22⋊C4C22×C4116yes—
358C2×C22⋊C4C22×C418yes—
359C2×C22⋊C4C22×C4116yes—
360C2×C22⋊C4C2×D418yes—
361C2×C22⋊C4C2×D418yes—
362C2×C42—28no—
363C2×C42—28no—
364C2×C42—44no—
365C2×C42—416no—
366C2×C42—44no—
367C2×C42—44no—
368C2×C42—44no—
369#95—24no—
370#95—24no—
371#95—24no—
372#95—24no—
373#95—28no—
374#95—28no—
375#95—28no—
376#95—28no—
377#95—44no—
378#95—44no—
379#95—44no—
380#95—44no—
381#95—44no—
382#95—44no—
383#95—44no—
384#95—44no—
385#95C22×C4116yes—
386C24—22no—
387C24—22no—
388C24—22no—
389C24—22no—
390C24—22no—
391C24—22no—
392C24—22no—
393C24—22no—
394C24—22no—
395C24—22no—
396C24—22no—
397C24—22no—
398C24—22no—
399C24—22no—
400C24—22no—
401C24—22no—
402C24—216no—
403C24—28no—
404C24—28no—
405C24—216no—
406C24—28no—
407C24—22no—
408C24—22no—
409C24—24no—
410C24—24no—
411C24—22no—
412C24—22no—
413C24—22no—
414C24—22no—
415C24—24no—
416C24—24no—
417C24—216no—
418C24—44no—
419C24—48no—
420C24—48no—
421C24—44no—
422C24—44no—
423C24—48no—
424C24—48no—
425C24—48no—
426C24—44no—
427C24—48no—
428C24—44no—
429C24—44no—
430C24—44no—
431C24—48no—
432C24—44no—
433C24—48no—
434C24—44no—
435C24—44no—
436C24—48no—
437C24—88no—
438C24—88no—
439C24—88no—
440C24—88no—
441C24—88no—
442C24—88no—
443C24—88no—
444C24—88no—
445C24C4×D4116yes—
446C24C23×C414yes—
447C24C23×C412yes—
448C24C23×C412yes—
449C24C23×C412yes—
450C24C22×D412yes—
451C24C22×D412yes—
452C24C22×D412yes—
453C24C2×#4112yes—
454C24C2×#4112yes—
455C24C2×#4112yes—
456C24H(5,𝔽2)14yes—
457C242−1+414yes—
458C24C2511yescharacteristic
459C2×D4—216no—
460C2×D4—216no—
461C2×D4—216no—
462C2×D4—216no—
463C2×D4—48no—
464C2×D4—48no—
465C2×D4—48no—
466C2×D4—48no—
467C2×D4—48no—
468C2×D4—48no—
469C2×D4—48no—
470C2×D4—48no—
471C2×D4—48no—
472C2×D4—48no—
473C2×D4—4128no—
474C22×C4—28no—
475C22×C4—28no—
476C22×C4—216no—
477C22×C4—28no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—216no—
483C22×C4—28no—
484C22×C4—28no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—24no—
491C22×C4—24no—
492C22×C4—24no—
493C22×C4—24no—
494C22×C4—24no—
495C22×C4—22no—
496C22×C4—24no—
497C22×C4—24no—
498C22×C4—24no—
499C22×C4—22no—
500C22×C4—24no—
501C22×C4—24no—
502C22×C4—24no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—24no—
507C22×C4—24no—
508C22×C4—24no—
509C22×C4—24no—
510C22×C4—24no—
511C22×C4—28no—
512C22×C4—28no—
513C22×C4—28no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—24no—
518C22×C4—24no—
519C22×C4—24no—
520C22×C4—24no—
521C22×C4—24no—
522C22×C4—24no—
523C22×C4—24no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—24no—
527C22×C4—24no—
528C22×C4—24no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—24no—
534C22×C4—24no—
535C22×C4—24no—
536C22×C4—44no—
537C22×C4—44no—
538C22×C4—44no—
539C22×C4—44no—
540C22×C4—48no—
541C22×C4—48no—
542C22×C4—416no—
543C22×C4—44no—
544C22×C4—416no—
545C22×C4—44no—
546C22×C4—44no—
547C22×C4—44no—
548C22×C4—44no—
549C22×C4—44no—
550C22×C4—44no—
551C22×C4—82no—
552C22×C4—82no—
553C22×C4—82no—
554C22×C4—82no—
555C22×C4—84no—
556C22×C4—84no—
557C22×C4—88no—
558C22×C4—82no—
559C22×C4—82no—
560C22×C4—82no—
561C22×C4—82no—
562C22×C4—88no—
563C22×C4—88no—
564C22×C4—88no—
565C22×C4C23×C414yes—
566C22×C4C23×C418yes—
567C22×C4C23×C414yes—
568C22×C4C23×C414yes—
569C22×C4C22×D414yes—
570C22×C4C22×D414yes—
571C22×C4H(5,𝔽2)14yes—
572C22×C4H(5,𝔽2)14yes—
573C22×C4H(5,𝔽2)14yes—
574C4⋊C4—232no—
575C4⋊C4—416no—
576C4⋊C4—84no—
577C4⋊C4—84no—
578C4⋊C4—84no—
579C4⋊C4—84no—
580C4⋊C4—88no—
581C22⋊C4—216no—
582C22⋊C4—216no—
583C22⋊C4—216no—
584C22⋊C4—48no—
585C22⋊C4—48no—
586C22⋊C4—48no—
587C22⋊C4—416no—
588C22⋊C4—48no—
589C22⋊C4—416no—
590C22⋊C4—416no—
591C22⋊C4—48no—
592C22⋊C4—48no—
593C22⋊C4—416no—
594C22⋊C4—48no—
595C22⋊C4—48no—
596C22⋊C4—48no—
597C22⋊C4—84no—
598C22⋊C4—84no—
599C22⋊C4—88no—
600C22⋊C4—88no—
601C42—416no—
602C42—88no—
603C23—24no—
604C23—24no—
605C23—22no—
606C23—22no—
607C23—22no—
608C23—22no—
609C23—24no—
610C23—24no—
611C23—28no—
612C23—28no—
613C23—28no—
614C23—28no—
615C23—24no—
616C23—24no—
617C23—24no—
618C23—24no—
619C23—24no—
620C23—24no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—24no—
626C23—24no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—24no—
636C23—24no—
637C23—24no—
638C23—24no—
639C23—232no—
640C23—24no—
641C23—24no—
642C23—24no—
643C23—28no—
644C23—28no—
645C23—416no—
646C23—416no—
647C23—416no—
648C23—416no—
649C23—44no—
650C23—44no—
651C23—44no—
652C23—44no—
653C23—44no—
654C23—44no—
655C23—44no—
656C23—44no—
657C23—416no—
658C23—42no—
659C23—42no—
660C23—44no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—44no—
668C23—44no—
669C23—44no—
670C23—44no—
671C23—44no—
672C23—44no—
673C23—44no—
674C23—44no—
675C23—44no—
676C23—88no—
677C23—88no—
678C23—88no—
679C23—88no—
680C23—832no—
681C23—832no—
682C23—832no—
683C23—88no—
684C23—88no—
685C23—88no—
686C23—88no—
687C23—832no—
688C23C2×C4×D414yes—
689C23C2×C4×D414yes—
690C23C2×C4×D414yes—
691C23#52018yes—
692C23#53414yes—
693C23#53614yes—
694C23#53918yes—
695C23C24×C411yescharacteristic
696C23C23×D411yescharacteristic
697C23C22×#4111yescharacteristic
698C23C2×H(5,𝔽2)12yes—
699C23C2×H(5,𝔽2)12yes—
700C23C2×H(5,𝔽2)12yes—
701C23C2×H(5,𝔽2)12yes—
702C23C2×2−1+412yes—
703C23#58512yes—
704D4—432no—
705D4—432no—
706C2×C4—232no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—24no—
715C2×C4—28no—
716C2×C4—28no—
717C2×C4—28no—
718C2×C4—28no—
719C2×C4—28no—
720C2×C4—24no—
721C2×C4—24no—
722C2×C4—24no—
723C2×C4—24no—
724C2×C4—24no—
725C2×C4—24no—
726C2×C4—24no—
727C2×C4—28no—
728C2×C4—416no—
729C2×C4—416no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
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—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—44no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—44no—
758C2×C4—44no—
759C2×C4—44no—
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—88no—
770C2×C4—88no—
771C2×C4—88no—
772C2×C4—88no—
773C2×C4—88no—
774C2×C4—88no—
775C2×C4#51818yes—
776C22—24no—
777C22—24no—
778C22—24no—
779C22—24no—
780C22—24no—
781C22—216no—
782C22—216no—
783C22—24no—
784C22—24no—
785C22—24no—
786C22—24no—
787C22—24no—
788C22—24no—
789C22—24no—
790C22—42no—
791C22—42no—
792C22—42no—
793C22—42no—
794C22—42no—
795C22—42no—
796C22—42no—
797C22—42no—
798C22—48no—
799C22—48no—
800C22—48no—
801C22—48no—
802C22—44no—
803C22—44no—
804C22—48no—
805C22—48no—
806C22—44no—
807C22—832no—
808C22—832no—
809C22—82no—
810C22—82no—
811C22—82no—
812C22—82no—
813C22—84no—
814C22—84no—
815C22#232218yes—
816C22C22×C4×D411yescharacteristic
817C22C2×#51812yes—
818C22C2×#52012yes—
819C22C4×H(5,𝔽2)12yes—
820C22C2×#53411yescharacteristic
821C22C2×#53611yescharacteristic
822C22C2×#53912yes—
823C22#348411yescharacteristic
824C22#348411yescharacteristic
825C22#348411yescharacteristic
826C22#348511yescharacteristic
827C22#349012yes—
828C22#350512yes—
829C22#353614yes—
830C22#354214yes—
831C22#354314yes—
832C22#356114yes—
833C4—28no—
834C4—44no—
835C4—44no—
836C4—44no—
837C4—44no—
838C4—48no—
839C4—44no—
840C4—82no—
841C4—82no—
842C4—82no—
843C4—84no—
844C2—28no—
845C2—44no—
846C2—44no—
847C2—84no—
848C2C2×#232211yescharacteristic
849C2#3419811yescharacteristic
850C2#3426411yescharacteristic
851C2#3447614yes—
852C2#3671511yescharacteristic
853C2#3671811yescharacteristic
854C2#3680714yes—
855C2#3696611yescharacteristic
856C2#3723211yescharacteristic
subgroupG/H
center, Frattini, socle, cosocleC24C25
commutatorC23C24×C4
prime radicalC24×D4C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#2315C2semidirect
4. #14695C2semidirect
5. #14536C2semidirect
6. #14518C2semidirect
7. #14374C2semidirect
8. #14360C2semidirect
9. #14262C2semidirect
10. #14127C2semidirect
11. #14043C2semidirect
12. #13971C2semidirect
13. #13869C2semidirect
15. #13775C2semidirect
26. #2405C4semidirect
32. C2×#389C22semidirect
33. C2×#388C22semidirect
34. C2×#387C22semidirect
42. C2×#385C22semidirect
43. C2×#385C22semidirect
44. C2×#385C22semidirect
45. C2×#381C22semidirect
46. C2×#380C22semidirect
47. C2×#380C22semidirect
53. #1444C22semidirect
54. #1441C22semidirect
55. #1440C22semidirect
56. #1440C22semidirect
57. #1439C22semidirect
58. #1439C22semidirect
59. #1439C22semidirect
60. #1439C22semidirect
61. #1439C22semidirect
62. #1439C22semidirect
64. #1437C22semidirect
65. #1437C22semidirect
66. #1437C22semidirect
67. #1436C22semidirect
68. #1436C22semidirect
69. #1436C22semidirect
70. #1434C22semidirect
76. C22⋊#95C22semidirect
77. C22⋊#95C22semidirect
98. C2×#123C2×C4semidirect
145. #394C2×C4semidirect
153. #386C2×C4semidirect
160. #385C2×C4semidirect
167. #379C2×C4semidirect

Maximal subgroups

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

subgroupindex
C2×#24052
C2×#23152
C22×#3902
#146952
#145362
#145182
#143742
#143602
#142622
#141272
#140432
#139712
#138692
#138672
#137752