Finite Group Databasebeta

← #554243

Subgroups — #554243

Order 512.

5042 conjugacy classes of subgroups.

The subgroup lattice has 865 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2405C211yesmaximal, characteristic
2C2×#2315C211yesmaximal, characteristic, complemented
3C22×#386C211yesmaximal, characteristic
4#14693C212yesmaximal, complemented
5#14535C214yesmaximal, complemented
6#14517C214yesmaximal, complemented
7#14373C214yesmaximal, complemented
8#14359C214yesmaximal, complemented
9#14265C212yesmaximal, complemented
10#14127C211yesmaximal, characteristic, complemented
11#14044C212yesmaximal, complemented
12#13971C212yesmaximal, complemented
13#13869C211yesmaximal, characteristic, complemented
14#13867C211yesmaximal, characteristic
15#13775C211yesmaximal, characteristic, complemented
16C24×D4C2211yescharacteristic
17C25×C4C2211yescharacteristic
18C22×#123C2212yes—
19C23×C22⋊C4C2211yescharacteristic
20C23×C22⋊C4C2211yescharacteristic
21C23×C22⋊C4C2211yescharacteristic
22C23×C22⋊C4C2211yescharacteristic
23C23×C22⋊C4C2211yescharacteristic
24#2405C4116yescomplemented
25C2×#394C2214yes—
26#2315—28no—
27C2×#388C2214yescomplemented
28C2×#386—28no—
29C2×#386C2214yes—
30C2×#386C2214yes—
31C2×#386C2212yes—
32C2×#386C2212yes—
33C2×#386C2212yes—
34C2×#385C2212yes—
35C2×#385C2212yes—
36C2×#385C2212yes—
37C2×#385C2212yes—
38C2×#385C2212yescomplemented
39C2×#385C2212yescomplemented
40C2×#385C2214yescomplemented
41C2×#385C2214yescomplemented
42C2×#385C2212yescomplemented
43C2×#381C2212yescomplemented
44C2×#380C2212yescomplemented
45C2×#380C2212yescomplemented
46C2×#379C2211yescharacteristic
47C2×#379C2212yes—
48C2×#379C2211yescharacteristic
49C2×#379C2212yes—
50C2×C4×C22⋊C4C2212yes—
51C22×#95C2211yescharacteristic
52C22×#95C2211yescharacteristic
53#1445C2214yescomplemented
54#1443C2214yescomplemented
55#1442C2214yescomplemented
56#1442C2214yescomplemented
57#1441C2214yescomplemented
58#1441C2214yescomplemented
59#1440C2214yescomplemented
60#1440C2214yescomplemented
61#1439C2214yescomplemented
62#1439C2214yescomplemented
63#1438C2214yes—
64#1437C2214yescomplemented
65#1437C2214yescomplemented
66#1437C2214yescomplemented
67#1436C2214yescomplemented
68C4⋊#95C2214yescomplemented
69C22⋊#95C2212yes—
70C22⋊#95C2212yes—
71C22⋊#95C2212yes—
72C22⋊#95C2212yes—
73C22⋊#95C2212yes—
74C22⋊#95C2212yescomplemented
75C22⋊#95C2214yescomplemented
76C22⋊#95C2214yescomplemented
77C22⋊#95C2212yescomplemented
78C26C2311yescharacteristic
79C26C2311yescharacteristic
80C23×D4—24no—
81C23×D4—24no—
82C23×D4—44no—
83C23×D4—44no—
84C23×D4C2×C418yes—
85C23×D4C2312yes—
86C23×D4C2312yes—
87C24×C4—24no—
88C24×C4—44no—
89C24×C4—44no—
90C24×C4—44no—
91C24×C4C2311yescharacteristic
92C24×C4C2314yes—
93C24×C4C2311yescharacteristic
94C24×C4C2311yescharacteristic
95C24×C4C2311yescharacteristic
96C24×C4C2311yescharacteristic
97C24×C4C2311yescharacteristic
98C24×C4C2311yescharacteristic
99C24×C4C2311yescharacteristic
100C24×C4C2311yescharacteristic
101C2×#123—44no—
102C2×#123—44no—
103C2×#123C2×C4116yescomplemented
104C22×C4⋊C4C2314yes—
105C22×C4⋊C4C2312yes—
106C22×C4⋊C4C2312yes—
107C22×C4⋊C4C2312yes—
108C22×C4⋊C4C2312yes—
109C22×C4⋊C4C2314yes—
110C22×C22⋊C4—24no—
111C22×C22⋊C4—24no—
112C22×C22⋊C4—24no—
113C22×C22⋊C4—24no—
114C22×C22⋊C4—24no—
115C22×C22⋊C4—44no—
116C22×C22⋊C4—44no—
117C22×C22⋊C4—44no—
118C22×C22⋊C4—44no—
119C22×C22⋊C4C2×C418yescomplemented
120C22×C22⋊C4D418yes—
121C22×C22⋊C4C2312yes—
122C22×C22⋊C4C2312yes—
123C22×C22⋊C4C2312yes—
124C22×C22⋊C4C2312yes—
125C22×C22⋊C4C2314yes—
126C22×C22⋊C4C2314yes—
127C22×C22⋊C4C2312yes—
128C22×C22⋊C4C2312yes—
129C22×C22⋊C4C2312yes—
130C22×C22⋊C4C2312yes—
131C22×C22⋊C4C2314yes—
132C22×C22⋊C4C2312yes—
133C22×C22⋊C4C2312yes—
134C22×C22⋊C4C2314yes—
135C22×C22⋊C4C2314yes—
136C22×C22⋊C4C2312yes—
137C22×C22⋊C4C2312yes—
138C22×C22⋊C4C2312yes—
139C22×C22⋊C4C2312yes—
140C22×C42C2314yes—
141#394C2×C4132yescomplemented
142#388—48no—
143#386—216no—
144#386—216no—
145#386—44no—
146#386—44no—
147#386C2×C4116yescomplemented
148#385—28no—
149#385—28no—
150#385—28no—
151#385—28no—
152#385—48no—
153#385—44no—
154#385—48no—
155#385—44no—
156#385C2×C4116yescomplemented
157#381—44no—
158#380—28no—
159#380—28no—
160#379—24no—
161#379—44no—
162#379C2×C4116yescomplemented
163#379C2×C418yescomplemented
164C4×C22⋊C4—44no—
165C2×#95—24no—
166C2×#95—24no—
167C2×#95C2314yes—
168C2×#95C2312yes—
169C2×#95C2312yes—
170C2×#95C2312yes—
171C2×#95C2314yes—
172C2×#95C2312yes—
173C2×#95C2314yes—
174C2×#95C2314yes—
175C2×#95C2314yes—
176C2×#95C2314yes—
177C2×#95C2314yes—
178C2×#95C2314yes—
179C2×#95C2314yes—
180C2×#95C2314yes—
181C2×#95C2314yes—
182C2×#95C2314yes—
183C2×#95C2314yes—
184C2×#95C2314yes—
185C2×#95C2314yes—
186C25—22no—
187C25—22no—
188C25—24no—
189C25—24no—
190C25—24no—
191C25—24no—
192C25—24no—
193C25—24no—
194C25—42no—
195C25—42no—
196C25—42no—
197C25—42no—
198C25—42no—
199C25—42no—
200C25C22×C414yes—
201C25C22×C414yes—
202C25C2×D414yes—
203C25#4114yes—
204C25C2411yescharacteristic
205C25C2411yescharacteristic
206C25C2412yes—
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—42no—
218C22×D4—42no—
219C22×D4—42no—
220C22×D4—42no—
221C22×D4—432no—
222C22×D4—416no—
223C22×D4—416no—
224C22×D4—432no—
225C22×D4C22×C418yes—
226C22×D4C22×C418yes—
227C23×C4—22no—
228C23×C4—22no—
229C23×C4—22no—
230C23×C4—24no—
231C23×C4—22no—
232C23×C4—22no—
233C23×C4—22no—
234C23×C4—22no—
235C23×C4—24no—
236C23×C4—24no—
237C23×C4—22no—
238C23×C4—28no—
239C23×C4—24no—
240C23×C4—22no—
241C23×C4—22no—
242C23×C4—24no—
243C23×C4—28no—
244C23×C4—28no—
245C23×C4—42no—
246C23×C4—42no—
247C23×C4—42no—
248C23×C4—44no—
249C23×C4—44no—
250C23×C4—44no—
251C23×C4—44no—
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×C4—42no—
262C23×C4—42no—
263C23×C4—42no—
264C23×C4—42no—
265C23×C4—42no—
266C23×C4—42no—
267C23×C4—42no—
268C23×C4—416no—
269C23×C4—416no—
270C23×C4—416no—
271C23×C4—464no—
272C23×C4C22×C414yes—
273C23×C4C22×C414yescomplemented
274C23×C4C22×C414yescomplemented
275C23×C4C2×D414yes—
276C23×C4C2×D414yes—
277C23×C4C2414yes—
278C23×C4C2412yes—
279C23×C4C2412yes—
280C23×C4C2412yes—
281C23×C4C2414yes—
282C23×C4C2412yes—
283C23×C4C2412yes—
284C23×C4C2412yes—
285C23×C4C2412yes—
286C23×C4C2412yes—
287C23×C4C2412yes—
288#123—432no—
289C2×C4⋊C4—24no—
290C2×C4⋊C4—24no—
291C2×C4⋊C4—24no—
292C2×C4⋊C4—24no—
293C2×C4⋊C4—28no—
294C2×C4⋊C4—44no—
295C2×C4⋊C4—44no—
296C2×C4⋊C4—44no—
297C2×C4⋊C4—44no—
298C2×C4⋊C4—44no—
299C2×C4⋊C4—44no—
300C2×C4⋊C4—44no—
301C2×C4⋊C4—44no—
302C2×C4⋊C4C22×C4116yescomplemented
303C2×C22⋊C4—232no—
304C2×C22⋊C4—24no—
305C2×C22⋊C4—24no—
306C2×C22⋊C4—24no—
307C2×C22⋊C4—24no—
308C2×C22⋊C4—28no—
309C2×C22⋊C4—28no—
310C2×C22⋊C4—24no—
311C2×C22⋊C4—24no—
312C2×C22⋊C4—24no—
313C2×C22⋊C4—24no—
314C2×C22⋊C4—24no—
315C2×C22⋊C4—24no—
316C2×C22⋊C4—24no—
317C2×C22⋊C4—24no—
318C2×C22⋊C4—24no—
319C2×C22⋊C4—28no—
320C2×C22⋊C4—24no—
321C2×C22⋊C4—24no—
322C2×C22⋊C4—28no—
323C2×C22⋊C4—24no—
324C2×C22⋊C4—24no—
325C2×C22⋊C4—24no—
326C2×C22⋊C4—24no—
327C2×C22⋊C4—28no—
328C2×C22⋊C4—28no—
329C2×C22⋊C4—416no—
330C2×C22⋊C4—42no—
331C2×C22⋊C4—42no—
332C2×C22⋊C4—42no—
333C2×C22⋊C4—42no—
334C2×C22⋊C4—44no—
335C2×C22⋊C4—42no—
336C2×C22⋊C4—42no—
337C2×C22⋊C4—42no—
338C2×C22⋊C4—42no—
339C2×C22⋊C4—44no—
340C2×C22⋊C4—42no—
341C2×C22⋊C4—42no—
342C2×C22⋊C4—42no—
343C2×C22⋊C4—44no—
344C2×C22⋊C4—42no—
345C2×C22⋊C4—416no—
346C2×C22⋊C4—416no—
347C2×C22⋊C4—416no—
348C2×C22⋊C4—42no—
349C2×C22⋊C4—44no—
350C2×C22⋊C4—44no—
351C2×C22⋊C4—44no—
352C2×C22⋊C4—42no—
353C2×C22⋊C4—44no—
354C2×C22⋊C4—42no—
355C2×C22⋊C4—42no—
356C2×C22⋊C4C22×C418yes—
357C2×C22⋊C4C22×C4116yes—
358C2×C22⋊C4C22×C418yes—
359C2×C22⋊C4C22×C4116yes—
360C2×C22⋊C4C22×C418yescomplemented
361C2×C22⋊C4C22×C418yescomplemented
362C2×C22⋊C4C22×C418yescomplemented
363C2×C22⋊C4C2×D418yes—
364C2×C22⋊C4C2×D418yes—
365C2×C42—44no—
366C2×C42—44no—
367C2×C42—44no—
368#95—28no—
369#95—28no—
370#95—24no—
371#95—24no—
372#95—24no—
373#95—24no—
374#95—28no—
375#95—44no—
376#95—44no—
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#95—44no—
386#95C22×C4116yescomplemented
387C24—22no—
388C24—22no—
389C24—22no—
390C24—22no—
391C24—28no—
392C24—28no—
393C24—216no—
394C24—28no—
395C24—216no—
396C24—22no—
397C24—22no—
398C24—22no—
399C24—22no—
400C24—22no—
401C24—24no—
402C24—22no—
403C24—24no—
404C24—22no—
405C24—22no—
406C24—22no—
407C24—22no—
408C24—22no—
409C24—22no—
410C24—22no—
411C24—22no—
412C24—24no—
413C24—24no—
414C24—22no—
415C24—22no—
416C24—216no—
417C24—28no—
418C24—28no—
419C24—216no—
420C24—216no—
421C24—48no—
422C24—44no—
423C24—48no—
424C24—44no—
425C24—44no—
426C24—48no—
427C24—48no—
428C24—44no—
429C24—48no—
430C24—416no—
431C24—416no—
432C24—416no—
433C24—416no—
434C24—44no—
435C24—44no—
436C24—48no—
437C24—44no—
438C24—44no—
439C24—48no—
440C24—88no—
441C24—88no—
442C24—88no—
443C24—88no—
444C24C4×D4116yes—
445C24C23×C412yes—
446C24C23×C412yes—
447C24C23×C414yes—
448C24C23×C412yes—
449C24C22×D412yes—
450C24C22×D412yes—
451C24C22×D412yes—
452C24C2×#4112yes—
453C24C2×#4112yes—
454C24C2×#4112yes—
455C24H(5,𝔽2)14yes—
456C24H(5,𝔽2)14yes—
457C24H(5,𝔽2)14yes—
458C242−1+414yes—
459C24C2511yescharacteristic
460C2×D4—216no—
461C2×D4—216no—
462C2×D4—216no—
463C2×D4—216no—
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—48no—
474C2×D4—4128no—
475C22×C4—28no—
476C22×C4—28no—
477C22×C4—28no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—24no—
486C22×C4—24no—
487C22×C4—24no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—24no—
492C22×C4—24no—
493C22×C4—24no—
494C22×C4—24no—
495C22×C4—24no—
496C22×C4—24no—
497C22×C4—24no—
498C22×C4—24no—
499C22×C4—22no—
500C22×C4—24no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—24no—
507C22×C4—24no—
508C22×C4—24no—
509C22×C4—24no—
510C22×C4—28no—
511C22×C4—28no—
512C22×C4—28no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—24no—
517C22×C4—24no—
518C22×C4—24no—
519C22×C4—24no—
520C22×C4—22no—
521C22×C4—24no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—24no—
525C22×C4—24no—
526C22×C4—24no—
527C22×C4—24no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—24no—
532C22×C4—24no—
533C22×C4—24no—
534C22×C4—24no—
535C22×C4—44no—
536C22×C4—44no—
537C22×C4—48no—
538C22×C4—416no—
539C22×C4—44no—
540C22×C4—48no—
541C22×C4—48no—
542C22×C4—44no—
543C22×C4—416no—
544C22×C4—416no—
545C22×C4—416no—
546C22×C4—416no—
547C22×C4—416no—
548C22×C4—44no—
549C22×C4—416no—
550C22×C4—416no—
551C22×C4—44no—
552C22×C4—44no—
553C22×C4—48no—
554C22×C4—4128no—
555C22×C4—416no—
556C22×C4—44no—
557C22×C4—44no—
558C22×C4—44no—
559C22×C4—44no—
560C22×C4—44no—
561C22×C4—44no—
562C22×C4—82no—
563C22×C4—82no—
564C22×C4—82no—
565C22×C4—82no—
566C22×C4—84no—
567C22×C4—84no—
568C22×C4—88no—
569C22×C4—82no—
570C22×C4—82no—
571C22×C4—82no—
572C22×C4—82no—
573C22×C4—88no—
574C22×C4—88no—
575C22×C4—88no—
576C22×C4C23×C414yes—
577C22×C4C23×C414yes—
578C22×C4C23×C418yes—
579C22×C4C23×C414yes—
580C22×C4C22×D414yes—
581C22×C4C22×D414yes—
582C22×C4H(5,𝔽2)14yes—
583C4⋊C4—416no—
584C4⋊C4—84no—
585C4⋊C4—84no—
586C4⋊C4—84no—
587C4⋊C4—84no—
588C4⋊C4—88no—
589C22⋊C4—216no—
590C22⋊C4—216no—
591C22⋊C4—232no—
592C22⋊C4—216no—
593C22⋊C4—48no—
594C22⋊C4—48no—
595C22⋊C4—416no—
596C22⋊C4—48no—
597C22⋊C4—48no—
598C22⋊C4—416no—
599C22⋊C4—48no—
600C22⋊C4—48no—
601C22⋊C4—48no—
602C22⋊C4—48no—
603C22⋊C4—48no—
604C22⋊C4—84no—
605C22⋊C4—84no—
606C22⋊C4—88no—
607C22⋊C4—88no—
608C42—88no—
609C23—24no—
610C23—24no—
611C23—22no—
612C23—22no—
613C23—22no—
614C23—22no—
615C23—24no—
616C23—24no—
617C23—28no—
618C23—28no—
619C23—28no—
620C23—28no—
621C23—232no—
622C23—24no—
623C23—24no—
624C23—24no—
625C23—24no—
626C23—24no—
627C23—24no—
628C23—28no—
629C23—28no—
630C23—24no—
631C23—24no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—24no—
637C23—24no—
638C23—22no—
639C23—22no—
640C23—24no—
641C23—24no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—24no—
649C23—24no—
650C23—24no—
651C23—24no—
652C23—24no—
653C23—24no—
654C23—28no—
655C23—28no—
656C23—28no—
657C23—28no—
658C23—232no—
659C23—416no—
660C23—416no—
661C23—464no—
662C23—416no—
663C23—416no—
664C23—416no—
665C23—464no—
666C23—416no—
667C23—416no—
668C23—416no—
669C23—42no—
670C23—42no—
671C23—44no—
672C23—42no—
673C23—42no—
674C23—44no—
675C23—44no—
676C23—44no—
677C23—44no—
678C23—44no—
679C23—44no—
680C23—44no—
681C23—44no—
682C23—44no—
683C23—44no—
684C23—44no—
685C23—44no—
686C23—44no—
687C23—88no—
688C23—88no—
689C23—88no—
690C23—832no—
691C23—832no—
692C23—88no—
693C23C2×C4×D414yes—
694C23C2×C4×D414yes—
695C23C2×C4×D414yes—
696C23#51818yes—
697C23#52018yes—
698C23#53414yes—
699C23#53614yes—
700C23#53918yes—
701C23C24×C411yescharacteristic
702C23C23×D411yescharacteristic
703C23C22×#4111yescharacteristic
704C23C2×H(5,𝔽2)12yes—
705C23C2×H(5,𝔽2)12yes—
706C23C2×H(5,𝔽2)12yes—
707C23C2×H(5,𝔽2)12yes—
708C23C2×2−1+412yes—
709C23#58512yes—
710D4—432no—
711D4—432no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—24no—
715C2×C4—28no—
716C2×C4—28no—
717C2×C4—24no—
718C2×C4—24no—
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—24no—
728C2×C4—24no—
729C2×C4—28no—
730C2×C4—416no—
731C2×C4—416no—
732C2×C4—416no—
733C2×C4—464no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
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—44no—
754C2×C4—44no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—44no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—44no—
766C2×C4—44no—
767C2×C4—44no—
768C2×C4—44no—
769C2×C4—44no—
770C2×C4—44no—
771C2×C4—44no—
772C2×C4—44no—
773C2×C4—44no—
774C2×C4—44no—
775C2×C4—44no—
776C2×C4—44no—
777C2×C4—88no—
778C2×C4—88no—
779C2×C4—88no—
780C2×C4—88no—
781C2×C4—88no—
782C2×C4—88no—
783C22—24no—
784C22—24no—
785C22—24no—
786C22—24no—
787C22—216no—
788C22—216no—
789C22—24no—
790C22—24no—
791C22—24no—
792C22—24no—
793C22—24no—
794C22—28no—
795C22—24no—
796C22—216no—
797C22—24no—
798C22—24no—
799C22—464no—
800C22—44no—
801C22—44no—
802C22—42no—
803C22—42no—
804C22—44no—
805C22—42no—
806C22—42no—
807C22—44no—
808C22—42no—
809C22—42no—
810C22—48no—
811C22—48no—
812C22—48no—
813C22—48no—
814C22—48no—
815C22—48no—
816C22—48no—
817C22—44no—
818C22—42no—
819C22—44no—
820C22—42no—
821C22—832no—
822C22#232218yes—
823C22C22×C4×D411yescharacteristic
824C22C2×#51812yes—
825C22C2×#52012yes—
826C22C4×H(5,𝔽2)12yes—
827C22C2×#53411yescharacteristic
828C22C2×#53611yescharacteristic
829C22C2×#53912yes—
830C22#348411yescharacteristic
831C22#348411yescharacteristic
832C22#348411yescharacteristic
833C22#348511yescharacteristic
834C22#349012yes—
835C22#350512yes—
836C22#353214yes—
837C22#353414yes—
838C22#353514yes—
839C22#353614yes—
840C4—44no—
841C4—44no—
842C4—44no—
843C4—44no—
844C4—48no—
845C4—44no—
846C4—44no—
847C4—82no—
848C4—82no—
849C4—84no—
850C4—82no—
851C2—28no—
852C2—48no—
853C2—44no—
854C2—44no—
855C2C2×#232211yescharacteristic
856C2#3419811yescharacteristic
857C2#3426411yescharacteristic
858C2#3445614yes—
859C2#3671411yescharacteristic
860C2#3671811yescharacteristic
861C2#3672011yescharacteristic
862C2#3677514yes—
863C2#3711711yescharacteristic
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. #14693C2semidirect
5. #14535C2semidirect
6. #14517C2semidirect
7. #14373C2semidirect
8. #14359C2semidirect
9. #14265C2semidirect
10. #14127C2semidirect
11. #14044C2semidirect
12. #13971C2semidirect
13. #13869C2semidirect
15. #13775C2semidirect
24. #2405C4semidirect
27. C2×#388C22semidirect
38. C2×#385C22semidirect
39. C2×#385C22semidirect
40. C2×#385C22semidirect
41. C2×#385C22semidirect
42. C2×#385C22semidirect
43. C2×#381C22semidirect
44. C2×#380C22semidirect
45. C2×#380C22semidirect
53. #1445C22semidirect
54. #1443C22semidirect
55. #1442C22semidirect
56. #1442C22semidirect
57. #1441C22semidirect
58. #1441C22semidirect
59. #1440C22semidirect
60. #1440C22semidirect
61. #1439C22semidirect
62. #1439C22semidirect
64. #1437C22semidirect
65. #1437C22semidirect
66. #1437C22semidirect
67. #1436C22semidirect
68. C4⋊#95C22semidirect
74. C22⋊#95C22semidirect
75. C22⋊#95C22semidirect
76. C22⋊#95C22semidirect
77. C22⋊#95C22semidirect
103. C2×#123C2×C4semidirect
119. C22×C22⋊C4C2×C4semidirect
141. #394C2×C4semidirect
147. #386C2×C4semidirect
156. #385C2×C4semidirect
162. #379C2×C4semidirect
163. #379C2×C4semidirect
273. C23×C4C22×C4semidirect
274. C23×C4C22×C4semidirect
302. C2×C4⋊C4C22×C4semidirect
360. C2×C22⋊C4C22×C4semidirect
361. C2×C22⋊C4C22×C4semidirect
362. C2×C22⋊C4C22×C4semidirect
386. #95C22×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×#3862
#146932
#145352
#145172
#143732
#143592
#142652
#141272
#140442
#139712
#138692
#138672
#137752