Finite Group Databasebeta

← C2×#13991 #514281

Subgroups — C2×#13991 #514281

Order 512.

14746 conjugacy classes of subgroups.

The subgroup lattice has 898 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C24×C22⋊C4C211yesmaximal, characteristic
2C22×#388C212yesmaximal, complemented
3C22×#385C211yesmaximal, characteristic, complemented
4C22×#379C211yesmaximal, characteristic
5C22×#379C211yesmaximal, characteristic
6C22×C4×C22⋊C4C211yesmaximal, characteristic, complemented
7#13991C2116yesmaximal, direct product factor
8C2×#1440C212yesmaximal, complemented
9C2×#1439C212yesmaximal, complemented
10C2×#1437C212yesmaximal, complemented
11C2×C22⋊#95C211yesmaximal, characteristic, complemented
12C2×C22⋊#95C211yesmaximal, characteristic, complemented
13C27C2211yescharacteristic
14C25×C4C2211yescharacteristic
15C25×C4C2211yescharacteristic
16C23×C4⋊C4C2212yescomplemented
17C23×C22⋊C4—28no—
18C23×C22⋊C4—216no—
19C23×C22⋊C4C2212yes—
20C23×C22⋊C4C2218yes—
21C23×C22⋊C4C2211yescharacteristic
22C23×C22⋊C4C2212yes—
23C23×C22⋊C4C2212yes—
24C23×C22⋊C4C2211yescharacteristic
25C23×C22⋊C4C2211yescharacteristic
26C23×C22⋊C4C2212yes—
27C23×C22⋊C4C2212yes—
28C23×C22⋊C4C2211yescharacteristic
29C23×C22⋊C4C2212yes—
30C23×C42C2211yescharacteristic, complemented
31C23×C42C2211yescharacteristic, complemented
32C2×#388—216no—
33C2×#388C22116yescomplemented
34C2×#385—28no—
35C2×#385C2218yescomplemented
36C2×#379—28no—
37C2×#379C4116yescomplemented
38C2×#379C2218yes—
39C2×#379C2218yes—
40C2×C4×C22⋊C4—28no—
41C2×C4×C22⋊C4C2218yescomplemented
42C22×#95C2211yescharacteristic, complemented
43C22×#95C2211yescharacteristic, complemented
44C22×#95C2212yescomplemented
45C22×#95C2212yescomplemented
46C22×#95C2212yescomplemented
47C22×#95C2212yescomplemented
48C22×#95C2212yescomplemented
49#1440C22116yescomplemented
50#1439C22116yescomplemented
51#1437C22116yescomplemented
52C22⋊#95C2218yescomplemented
53C22⋊#95C2218yescomplemented
54C26—28no—
55C26—24no—
56C26—28no—
57C26—24no—
58C26—24no—
59C26—24no—
60C26—24no—
61C26—24no—
62C26—44no—
63C26—44no—
64C26C2×C418yes—
65C26C2312yes—
66C26C2314yes—
67C26C2311yescharacteristic
68C24×C4—24no—
69C24×C4—24no—
70C24×C4—24no—
71C24×C4—28no—
72C24×C4—28no—
73C24×C4—24no—
74C24×C4—24no—
75C24×C4—44no—
76C24×C4—44no—
77C24×C4D418yes—
78C24×C4C2312yes—
79C24×C4C2311yescharacteristic
80C24×C4C2311yescharacteristic
81C24×C4C2312yes—
82C24×C4C2312yes—
83C24×C4C2311yescharacteristic
84C24×C4C2311yescharacteristic
85C24×C4C2311yescharacteristic
86C24×C4C2314yes—
87C24×C4C2314yes—
88C24×C4C2311yescharacteristic
89C22×C4⋊C4—28no—
90C22×C4⋊C4—28no—
91C22×C4⋊C4—44no—
92C22×C4⋊C4C2318yescomplemented
93C22×C22⋊C4—2128no—
94C22×C22⋊C4—28no—
95C22×C22⋊C4—24no—
96C22×C22⋊C4—24no—
97C22×C22⋊C4—24no—
98C22×C22⋊C4—28no—
99C22×C22⋊C4—24no—
100C22×C22⋊C4—24no—
101C22×C22⋊C4—28no—
102C22×C22⋊C4—24no—
103C22×C22⋊C4—28no—
104C22×C22⋊C4—28no—
105C22×C22⋊C4—232no—
106C22×C22⋊C4—28no—
107C22×C22⋊C4—28no—
108C22×C22⋊C4—264no—
109C22×C22⋊C4—24no—
110C22×C22⋊C4—28no—
111C22×C22⋊C4—28no—
112C22×C22⋊C4—24no—
113C22×C22⋊C4—24no—
114C22×C22⋊C4—28no—
115C22×C22⋊C4—28no—
116C22×C22⋊C4—44no—
117C22×C22⋊C4—44no—
118C22×C22⋊C4—44no—
119C22×C22⋊C4—44no—
120C22×C22⋊C4C2×C418yes—
121C22×C22⋊C4C2×C418yes—
122C22×C22⋊C4C2×C4116yescomplemented
123C22×C22⋊C4C2×C4116yescomplemented
124C22×C22⋊C4D4116yes—
125C22×C22⋊C4D418yes—
126C22×C22⋊C4C2318yes—
127C22×C22⋊C4C2314yes—
128C22×C22⋊C4C2318yes—
129C22×C22⋊C4C2318yes—
130C22×C22⋊C4C2314yes—
131C22×C22⋊C4C2314yes—
132C22×C22⋊C4C2318yes—
133C22×C22⋊C4C2318yes—
134C22×C22⋊C4C2314yes—
135C22×C22⋊C4C2318yes—
136C22×C42—24no—
137C22×C42—24no—
138C22×C42—28no—
139C22×C42—44no—
140C22×C42C2314yescomplemented
141C22×C42C2314yescomplemented
142#388—264no—
143#385—232no—
144#379—232no—
145#379C2×C4164yescomplemented
146C4×C22⋊C4—232no—
147C2×#95—24no—
148C2×#95—24no—
149C2×#95—28no—
150C2×#95—28no—
151C2×#95—28no—
152C2×#95—44no—
153C2×#95—44no—
154C2×#95C2318yescomplemented
155C2×#95C2318yescomplemented
156C2×#95C2318yescomplemented
157C2×#95C2314yescomplemented
158C2×#95C2314yescomplemented
159C2×#95C2318yescomplemented
160C2×#95C2318yescomplemented
161C25—24no—
162C25—24no—
163C25—24no—
164C25—24no—
165C25—232no—
166C25—232no—
167C25—264no—
168C25—264no—
169C25—232no—
170C25—216no—
171C25—28no—
172C25—24no—
173C25—24no—
174C25—24no—
175C25—216no—
176C25—28no—
177C25—24no—
178C25—24no—
179C25—24no—
180C25—24no—
181C25—24no—
182C25—24no—
183C25—24no—
184C25—24no—
185C25—24no—
186C25—232no—
187C25—232no—
188C25—28no—
189C25—28no—
190C25—28no—
191C25—28no—
192C25—432no—
193C25—48no—
194C25—48no—
195C25—432no—
196C25—432no—
197C25—432no—
198C25—432no—
199C25—432no—
200C25—432no—
201C25—432no—
202C25—432no—
203C25—416no—
204C25—416no—
205C25—432no—
206C25—416no—
207C25—416no—
208C25—416no—
209C25—416no—
210C25C22×C418yes—
211C25C22×C4116yes—
212C25C22×C414yes—
213C25C2×D418yes—
214C25C2×D414yes—
215C25C2×D414yes—
216C25#4118yes—
217C25#4114yes—
218C25#4114yes—
219C25#4114yes—
220C25#4114yes—
221C25C2414yes—
222C25C2412yes—
223C25C2411yescharacteristic
224C23×C4—22no—
225C23×C4—22no—
226C23×C4—24no—
227C23×C4—232no—
228C23×C4—232no—
229C23×C4—28no—
230C23×C4—24no—
231C23×C4—24no—
232C23×C4—24no—
233C23×C4—24no—
234C23×C4—24no—
235C23×C4—24no—
236C23×C4—22no—
237C23×C4—24no—
238C23×C4—22no—
239C23×C4—22no—
240C23×C4—22no—
241C23×C4—24no—
242C23×C4—22no—
243C23×C4—24no—
244C23×C4—22no—
245C23×C4—24no—
246C23×C4—24no—
247C23×C4—22no—
248C23×C4—22no—
249C23×C4—24no—
250C23×C4—28no—
251C23×C4—28no—
252C23×C4—22no—
253C23×C4—22no—
254C23×C4—24no—
255C23×C4—24no—
256C23×C4—24no—
257C23×C4—24no—
258C23×C4—24no—
259C23×C4—24no—
260C23×C4—24no—
261C23×C4—24no—
262C23×C4—24no—
263C23×C4—24no—
264C23×C4—232no—
265C23×C4—216no—
266C23×C4—216no—
267C23×C4—24no—
268C23×C4—24no—
269C23×C4—28no—
270C23×C4—24no—
271C23×C4—24no—
272C23×C4—24no—
273C23×C4—28no—
274C23×C4—24no—
275C23×C4—24no—
276C23×C4—416no—
277C23×C4—48no—
278C23×C4—48no—
279C23×C4—432no—
280C23×C4—432no—
281C23×C4—432no—
282C23×C4—432no—
283C23×C4—416no—
284C23×C4—416no—
285C23×C4C22×C414yes—
286C23×C4C22×C418yes—
287C23×C4C22×C414yes—
288C23×C4C2×D414yes—
289C23×C4C2×D414yes—
290C23×C4C2×D414yes—
291C23×C4C2×D418yes—
292C23×C4C2×D4116yes—
293C23×C4C2×D414yes—
294C23×C4C2×D418yes—
295C23×C4C2414yes—
296C23×C4C2414yes—
297C23×C4C2412yes—
298C23×C4C2412yes—
299C23×C4C2412yes—
300C23×C4C2412yes—
301C23×C4C2414yes—
302C23×C4C2412yes—
303C23×C4C2412yes—
304C2×C4⋊C4—216no—
305C2×C4⋊C4—216no—
306C2×C4⋊C4—48no—
307C2×C4⋊C4—432no—
308C2×C22⋊C4—264no—
309C2×C22⋊C4—2256no—
310C2×C22⋊C4—232no—
311C2×C22⋊C4—232no—
312C2×C22⋊C4—264no—
313C2×C22⋊C4—232no—
314C2×C22⋊C4—216no—
315C2×C22⋊C4—28no—
316C2×C22⋊C4—28no—
317C2×C22⋊C4—28no—
318C2×C22⋊C4—216no—
319C2×C22⋊C4—28no—
320C2×C22⋊C4—28no—
321C2×C22⋊C4—216no—
322C2×C22⋊C4—28no—
323C2×C22⋊C4—264no—
324C2×C22⋊C4—216no—
325C2×C22⋊C4—216no—
326C2×C22⋊C4—216no—
327C2×C22⋊C4—216no—
328C2×C22⋊C4—28no—
329C2×C22⋊C4—216no—
330C2×C22⋊C4—216no—
331C2×C22⋊C4—28no—
332C2×C22⋊C4—28no—
333C2×C22⋊C4—216no—
334C2×C22⋊C4—216no—
335C2×C22⋊C4—432no—
336C2×C22⋊C4—48no—
337C2×C22⋊C4—48no—
338C2×C22⋊C4—48no—
339C2×C22⋊C4—48no—
340C2×C22⋊C4—432no—
341C2×C22⋊C4—432no—
342C2×C22⋊C4—416no—
343C2×C22⋊C4C22×C4116yes—
344C2×C22⋊C4C22×C4116yes—
345C2×C22⋊C4C22×C4132yescomplemented
346C2×C22⋊C4C22×C4132yescomplemented
347C2×C22⋊C4C2×D4132yes—
348C2×C22⋊C4C2×D4116yes—
349C2×C42—28no—
350C2×C42—28no—
351C2×C42—216no—
352C2×C42—48no—
353C2×C42—416no—
354C2×C42—416no—
355#95—28no—
356#95—28no—
357#95—216no—
358#95—216no—
359#95—216no—
360#95—48no—
361#95—48no—
362C24—216no—
363C24—216no—
364C24—28no—
365C24—28no—
366C24—216no—
367C24—28no—
368C24—28no—
369C24—216no—
370C24—216no—
371C24—216no—
372C24—216no—
373C24—216no—
374C24—216no—
375C24—216no—
376C24—216no—
377C24—216no—
378C24—24no—
379C24—24no—
380C24—24no—
381C24—24no—
382C24—232no—
383C24—232no—
384C24—264no—
385C24—2256no—
386C24—216no—
387C24—264no—
388C24—232no—
389C24—216no—
390C24—216no—
391C24—216no—
392C24—216no—
393C24—216no—
394C24—216no—
395C24—216no—
396C24—216no—
397C24—216no—
398C24—216no—
399C24—216no—
400C24—216no—
401C24—216no—
402C24—216no—
403C24—216no—
404C24—216no—
405C24—216no—
406C24—24no—
407C24—24no—
408C24—24no—
409C24—24no—
410C24—24no—
411C24—24no—
412C24—24no—
413C24—24no—
414C24—24no—
415C24—24no—
416C24—24no—
417C24—24no—
418C24—232no—
419C24—232no—
420C24—432no—
421C24—4256no—
422C24—4256no—
423C24—432no—
424C24—432no—
425C24—432no—
426C24—432no—
427C24—432no—
428C24—432no—
429C24—432no—
430C24—432no—
431C24—4128no—
432C24—4128no—
433C24—4128no—
434C24—416no—
435C24—416no—
436C24—432no—
437C24—4256no—
438C24—4256no—
439C24—4128no—
440C24—4128no—
441C24—416no—
442C24—48no—
443C24—416no—
444C24—48no—
445C24—416no—
446C24—48no—
447C24—416no—
448C24—48no—
449C24—48no—
450C24—48no—
451C24—48no—
452C24—48no—
453C24—48no—
454C24—48no—
455C24—48no—
456C24—48no—
457C24—48no—
458C24—48no—
459C24—48no—
460C24—48no—
461C24—4128no—
462C24#117116yes—
463C24C4×D4132yes—
464C24C4×D4116yes—
465C24C4×D4116yes—
466C24#121116yes—
467C24#123116yes—
468C24#124116yes—
469C24#126116yes—
470C24C23×C418yes—
471C24C23×C414yes—
472C24C23×C412yes—
473C24C22×D418yes—
474C24C22×D414yes—
475C24C22×D414yes—
476C24C22×D412yes—
477C24C22×D414yes—
478C24C22×D412yes—
479C24C2×#4118yes—
480C24C2×#4114yes—
481C24C2×#4114yes—
482C24C2×#4114yes—
483C24C2×#4114yes—
484C24C2×#4112yes—
485C24C2×#4112yes—
486C24C2×#4112yes—
487C24C2×#4112yes—
488C24C2×#4114yes—
489C24H(5,𝔽2)14yes—
490C24H(5,𝔽2)14yes—
491C24C2511yescharacteristic
492C22×C4—28no—
493C22×C4—28no—
494C22×C4—216no—
495C22×C4—216no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—24no—
499C22×C4—232no—
500C22×C4—28no—
501C22×C4—216no—
502C22×C4—216no—
503C22×C4—28no—
504C22×C4—216no—
505C22×C4—216no—
506C22×C4—216no—
507C22×C4—28no—
508C22×C4—216no—
509C22×C4—28no—
510C22×C4—28no—
511C22×C4—232no—
512C22×C4—28no—
513C22×C4—28no—
514C22×C4—216no—
515C22×C4—216no—
516C22×C4—216no—
517C22×C4—216no—
518C22×C4—22no—
519C22×C4—24no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—24no—
524C22×C4—24no—
525C22×C4—24no—
526C22×C4—24no—
527C22×C4—24no—
528C22×C4—24no—
529C22×C4—24no—
530C22×C4—22no—
531C22×C4—24no—
532C22×C4—22no—
533C22×C4—24no—
534C22×C4—24no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—24no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—24no—
541C22×C4—24no—
542C22×C4—24no—
543C22×C4—24no—
544C22×C4—24no—
545C22×C4—24no—
546C22×C4—24no—
547C22×C4—24no—
548C22×C4—24no—
549C22×C4—24no—
550C22×C4—232no—
551C22×C4—24no—
552C22×C4—24no—
553C22×C4—24no—
554C22×C4—24no—
555C22×C4—24no—
556C22×C4—24no—
557C22×C4—24no—
558C22×C4—416no—
559C22×C4—4128no—
560C22×C4—432no—
561C22×C4—432no—
562C22×C4—432no—
563C22×C4—432no—
564C22×C4—4128no—
565C22×C4—416no—
566C22×C4—44no—
567C22×C4—44no—
568C22×C4—416no—
569C22×C4—48no—
570C22×C4—44no—
571C22×C4—48no—
572C22×C4—44no—
573C22×C4—44no—
574C22×C4—44no—
575C22×C4—44no—
576C22×C4—44no—
577C22×C4—48no—
578C22×C4—48no—
579C22×C4—48no—
580C22×C4—48no—
581C22×C4—48no—
582C22×C4—48no—
583C22×C4—48no—
584C22×C4—48no—
585C22×C4—48no—
586C22×C4—48no—
587C22×C4—48no—
588C22×C4—48no—
589C22×C4—48no—
590C22×C4—48no—
591C22×C4—48no—
592C22×C4—48no—
593C22×C4—48no—
594C22×C4—48no—
595C22×C4—48no—
596C22×C4#120116yes—
597C22×C4C23×C414yes—
598C22×C4C23×C418yes—
599C22×C4C23×C414yes—
600C22×C4C22×D414yes—
601C22×C4C22×D414yes—
602C22×C4C22×D418yes—
603C22×C4C22×D414yes—
604C22×C4C22×D418yes—
605C22×C4C22×D414yes—
606C4⋊C4—432no—
607C22⋊C4—264no—
608C22⋊C4—232no—
609C22⋊C4—232no—
610C22⋊C4—264no—
611C22⋊C4—232no—
612C22⋊C4—264no—
613C22⋊C4—432no—
614C22⋊C4—432no—
615C22⋊C4—432no—
616C22⋊C4—416no—
617C42—416no—
618C42—416no—
619C23—232no—
620C23—264no—
621C23—264no—
622C23—28no—
623C23—28no—
624C23—232no—
625C23—24no—
626C23—232no—
627C23—24no—
628C23—28no—
629C23—24no—
630C23—24no—
631C23—28no—
632C23—28no—
633C23—28no—
634C23—28no—
635C23—28no—
636C23—28no—
637C23—28no—
638C23—28no—
639C23—28no—
640C23—264no—
641C23—264no—
642C23—232no—
643C23—232no—
644C23—232no—
645C23—2128no—
646C23—264no—
647C23—264no—
648C23—28no—
649C23—28no—
650C23—28no—
651C23—28no—
652C23—28no—
653C23—28no—
654C23—28no—
655C23—28no—
656C23—28no—
657C23—28no—
658C23—28no—
659C23—28no—
660C23—28no—
661C23—28no—
662C23—28no—
663C23—28no—
664C23—28no—
665C23—28no—
666C23—264no—
667C23—4128no—
668C23—4128no—
669C23—464no—
670C23—464no—
671C23—464no—
672C23—4128no—
673C23—4128no—
674C23—464no—
675C23—41024no—
676C23—464no—
677C23—432no—
678C23—432no—
679C23—432no—
680C23—432no—
681C23—432no—
682C23—44no—
683C23—44no—
684C23—44no—
685C23—44no—
686C23—44no—
687C23—44no—
688C23—44no—
689C23—44no—
690C23—44no—
691C23—44no—
692C23—44no—
693C23—44no—
694C23—44no—
695C23—44no—
696C23—44no—
697C23—44no—
698C23—432no—
699C23—432no—
700C23—432no—
701C23—432no—
702C23—432no—
703C23—432no—
704C23—432no—
705C23—464no—
706C23#388164yescomplemented
707C23C2×#11718yes—
708C23C2×#11714yes—
709C23C2×C4×D4116yes—
710C23C2×C4×D418yes—
711C23C2×C4×D418yes—
712C23C2×C4×D414yes—
713C23C2×C4×D418yes—
714C23C2×C4×D414yes—
715C23#51818yes—
716C23C2×#12014yes—
717C23C2×#12118yes—
718C23C2×#12114yes—
719C23C2×#12318yes—
720C23C2×#12314yes—
721C23#52518yes—
722C23#52514yes—
723C23C2×#12418yes—
724C23C2×#12414yes—
725C23C2×#12618yes—
726C23C2×#12614yes—
727C23#53414yes—
728C23#53514yes—
729C23#53818yes—
730C23D4218yes—
731C23#54618yes—
732C23#54618yes—
733C23#54618yes—
734C23#54618yes—
735C23#55118yes—
736C23#55118yes—
737C23#55118yes—
738C23C24×C411yescharacteristic
739C23C23×D411yescharacteristic
740C23C23×D412yes—
741C23C23×D411yescharacteristic
742C23C22×#4111yescharacteristic
743C23C22×#4111yescharacteristic
744C23C22×#4111yescharacteristic
745C23C22×#4111yescharacteristic
746C23C22×#4112yes—
747C23C2×H(5,𝔽2)12yes—
748C23C2×H(5,𝔽2)12yes—
749C2×C4—232no—
750C2×C4—24no—
751C2×C4—24no—
752C2×C4—28no—
753C2×C4—28no—
754C2×C4—24no—
755C2×C4—28no—
756C2×C4—28no—
757C2×C4—24no—
758C2×C4—28no—
759C2×C4—28no—
760C2×C4—28no—
761C2×C4—24no—
762C2×C4—28no—
763C2×C4—24no—
764C2×C4—24no—
765C2×C4—24no—
766C2×C4—24no—
767C2×C4—28no—
768C2×C4—28no—
769C2×C4—28no—
770C2×C4—28no—
771C2×C4—464no—
772C2×C4—464no—
773C2×C4—416no—
774C2×C4—432no—
775C2×C4—416no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—416no—
779C2×C4—432no—
780C2×C4—44no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—44no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—42no—
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—416no—
801C2×C4—416no—
802C2×C4—44no—
803C2×C4—44no—
804C2×C4—44no—
805C2×C4—44no—
806C2×C4—44no—
807C2×C4—44no—
808C2×C4—44no—
809C2×C4—816no—
810C2×C4C2×#12018yes—
811C22—28no—
812C22—28no—
813C22—216no—
814C22—216no—
815C22—28no—
816C22—216no—
817C22—216no—
818C22—28no—
819C22—2128no—
820C22—28no—
821C22—28no—
822C22—216no—
823C22—216no—
824C22—216no—
825C22—4256no—
826C22—48no—
827C22—48no—
828C22—48no—
829C22—48no—
830C22—48no—
831C22—48no—
832C22—48no—
833C22—48no—
834C22—48no—
835C22—48no—
836C22—4128no—
837C22—48no—
838C22—48no—
839C22C2×#38818yes—
840C22C2×#388116yescomplemented
841C22C4×#12018yes—
842C22#232118yes—
843C22#2342116yes—
844C22#2358116yes—
845C22#240518yes—
846C22#240818yes—
847C22#2472116yes—
848C22#2480116yes—
849C22#248218yes—
850C22#253418yes—
851C22C22×#11711yescharacteristic
852C22C22×C4×D411yescharacteristic
853C22C22×C4×D412yes—
854C22C22×C4×D411yescharacteristic
855C22C2×#51812yes—
856C22C22×#12011yescharacteristic
857C22C22×#12111yescharacteristic
858C22C22×#12311yescharacteristic
859C22C2×#52511yescharacteristic
860C22C2×#52512yes—
861C22C22×#12411yescharacteristic
862C22C22×#12611yescharacteristic
863C22C2×#53411yescharacteristic
864C22C2×#53511yescharacteristic
865C22C2×#53812yes—
866C22C2×D4212yes—
867C22C2×#54612yes—
868C22C2×#54612yes—
869C22C2×#54612yes—
870C22C2×#54612yes—
871C22C2×#55112yes—
872C22C2×#55112yes—
873C22C2×#55112yes—
874C4—28no—
875C4—44no—
876C4—44no—
877C4—48no—
878C4—44no—
879C4—44no—
880C4—48no—
881C4—44no—
882C4—84no—
883C2—216no—
884C2—416no—
885C2#13991116yesdirect product factor
886C2C22×#38811yescharacteristic
887C2C2×C4×#12011yescharacteristic
888C2C2×#232111yescharacteristic
889C2C2×#234212yes—
890C2C2×#235812yes—
891C2C2×#240511yescharacteristic
892C2C2×#247212yes—
893C2C2×#248012yes—
894C2C2×#240811yescharacteristic
895C2C2×#248211yescharacteristic
896C2C2×#253411yescharacteristic
subgroupG/H
center, socleC25C24
commutatorC23C24×C4
Frattini, cosocleC24C25
prime radicalC27C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C25 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C22×#388C2semidirect
3. C22×#385C2semidirect
6. C22×C4×C22⋊C4C2semidirect
7. #13991C2direct (N × H)
8. C2×#1440C2semidirect
9. C2×#1439C2semidirect
10. C2×#1437C2semidirect
11. C2×C22⋊#95C2semidirect
12. C2×C22⋊#95C2semidirect
16. C23×C4⋊C4C22semidirect
30. C23×C42C22semidirect
31. C23×C42C22semidirect
33. C2×#388C22semidirect
35. C2×#385C22semidirect
37. C2×#379C4semidirect
41. C2×C4×C22⋊C4C22semidirect
42. C22×#95C22semidirect
43. C22×#95C22semidirect
44. C22×#95C22semidirect
45. C22×#95C22semidirect
46. C22×#95C22semidirect
47. C22×#95C22semidirect
48. C22×#95C22semidirect
49. #1440C22semidirect
50. #1439C22semidirect
51. #1437C22semidirect
52. C22⋊#95C22semidirect
53. C22⋊#95C22semidirect
92. C22×C4⋊C4C23semidirect
122. C22×C22⋊C4C2×C4semidirect
123. C22×C22⋊C4C2×C4semidirect
140. C22×C42C23semidirect
141. C22×C42C23semidirect
145. #379C2×C4semidirect
154. C2×#95C23semidirect
155. C2×#95C23semidirect
156. C2×#95C23semidirect
157. C2×#95C23semidirect
158. C2×#95C23semidirect
159. C2×#95C23semidirect
160. C2×#95C23semidirect
345. C2×C22⋊C4C22×C4semidirect
346. C2×C22⋊C4C22×C4semidirect
706. C23#388semidirect
840. C22C2×#388semidirect
885. C2#13991direct (N × H)

Maximal subgroups

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

subgroupindex
C24×C22⋊C42
C22×#3882
C22×#3852
C22×#3792
C22×C4×C22⋊C42
#139912
C2×#14402
C2×#14392
C2×#14372
C2×C22⋊#952