Finite Group Databasebeta

← C2×#13998 #514289

Subgroups — C2×#13998 #514289

Order 512.

9562 conjugacy classes of subgroups.

The subgroup lattice has 1002 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#121C211yesmaximal, characteristic
2C22×#390C211yesmaximal, characteristic, complemented
3C22×#390C211yesmaximal, characteristic, complemented
4C22×#390C212yesmaximal, complemented
5C22×#389C211yesmaximal, characteristic, complemented
6C22×#380C211yesmaximal, characteristic, complemented
7C22×C4×C4⋊C4C211yesmaximal, characteristic, complemented
8C22×C4×C22⋊C4C211yesmaximal, characteristic, complemented
9#13998C2116yesmaximal, direct product factor
10C2×#1439C212yesmaximal, complemented
11C2×#1438C212yesmaximal, complemented
12C2×#1437C212yesmaximal, complemented
13C24×D4C2211yescharacteristic
14C24×D4C2212yes—
15C25×C4C2211yescharacteristic
16C22×#121—28no—
17C22×#121—28no—
18C22×#121C4116yescomplemented
19C22×#121C2218yes—
20C23×C4⋊C4C2211yescharacteristic
21C23×C4⋊C4C2212yes—
22C23×C4⋊C4C2211yescharacteristic
23C23×C4⋊C4C2211yescharacteristic
24C23×C22⋊C4C2211yescharacteristic
25C23×C22⋊C4C2212yes—
26C23×C22⋊C4C2212yes—
27C23×C22⋊C4C2212yes—
28C23×C22⋊C4C2212yes—
29C23×C22⋊C4C2212yes—
30C23×C22⋊C4C2211yescharacteristic
31C23×C22⋊C4C2212yes—
32C23×C42C2211yescharacteristic
33C23×C42C2212yes—
34C23×C42C2211yescharacteristic
35C2×#390—28no—
36C2×#390—28no—
37C2×#390—216no—
38C2×#390C2218yescomplemented
39C2×#390C22116yescomplemented
40C2×#390C2218yescomplemented
41C2×#389—28no—
42C2×#389C2218yescomplemented
43C2×#380—28no—
44C2×#380C2218yescomplemented
45C2×C4×C4⋊C4—28no—
46C2×C4×C4⋊C4C2218yescomplemented
47C2×C4×C22⋊C4—28no—
48C2×C4×C22⋊C4C2218yescomplemented
49C22×#95C2212yes—
50C22×#95C2212yes—
51C22×#95C2211yescharacteristic
52C22×#95C2212yes—
53C22×#95C2211yescharacteristic
54#1439C22116yescomplemented
55#1438C22116yescomplemented
56#1437C22116yescomplemented
57C26C2312yes—
58C26C2311yescharacteristic
59C23×D4—28no—
60C23×D4—28no—
61C23×D4—28no—
62C23×D4—28no—
63C23×D4—24no—
64C23×D4—24no—
65C23×D4—24no—
66C23×D4—24no—
67C23×D4—24no—
68C23×D4—24no—
69C23×D4—44no—
70C23×D4—44no—
71C23×D4C2×C418yes—
72C23×D4C2×C4116yes—
73C23×D4C2314yes—
74C23×D4C2318yes—
75C24×C4—24no—
76C24×C4—24no—
77C24×C4—24no—
78C24×C4—24no—
79C24×C4—24no—
80C24×C4—24no—
81C24×C4C2×C418yes—
82C24×C4C2312yes—
83C24×C4C2314yes—
84C24×C4C2311yescharacteristic
85C24×C4C2311yescharacteristic
86C24×C4C2312yes—
87C24×C4C2311yescharacteristic
88C24×C4C2311yescharacteristic
89C24×C4C2312yes—
90C24×C4C2311yescharacteristic
91C24×C4C2311yescharacteristic
92C2×#121—2128no—
93C2×#121—232no—
94C2×#121—232no—
95C2×#121C2×C4164yescomplemented
96C22×C4⋊C4—24no—
97C22×C4⋊C4—24no—
98C22×C4⋊C4—24no—
99C22×C4⋊C4—28no—
100C22×C4⋊C4—24no—
101C22×C4⋊C4—28no—
102C22×C4⋊C4—24no—
103C22×C4⋊C4—44no—
104C22×C4⋊C4C2×C418yes—
105C22×C4⋊C4D418yes—
106C22×C4⋊C4D418yes—
107C22×C4⋊C4D418yescomplemented
108C22×C4⋊C4C2314yes—
109C22×C4⋊C4C2318yes—
110C22×C4⋊C4C2314yes—
111C22×C4⋊C4C2314yes—
112C22×C22⋊C4—24no—
113C22×C22⋊C4—28no—
114C22×C22⋊C4—28no—
115C22×C22⋊C4—24no—
116C22×C22⋊C4—24no—
117C22×C22⋊C4—24no—
118C22×C22⋊C4—24no—
119C22×C22⋊C4—28no—
120C22×C22⋊C4—28no—
121C22×C22⋊C4—28no—
122C22×C22⋊C4—28no—
123C22×C22⋊C4—28no—
124C22×C22⋊C4—28no—
125C22×C22⋊C4—28no—
126C22×C22⋊C4—28no—
127C22×C22⋊C4—28no—
128C22×C22⋊C4—28no—
129C22×C22⋊C4—44no—
130C22×C22⋊C4—44no—
131C22×C22⋊C4—44no—
132C22×C22⋊C4—44no—
133C22×C22⋊C4—44no—
134C22×C22⋊C4C2×C4116yes—
135C22×C22⋊C4D418yescomplemented
136C22×C22⋊C4C2318yes—
137C22×C22⋊C4C2314yes—
138C22×C22⋊C4C2318yes—
139C22×C22⋊C4C2318yes—
140C22×C22⋊C4C2318yes—
141C22×C22⋊C4C2318yes—
142C22×C22⋊C4C2314yes—
143C22×C22⋊C4C2318yes—
144C22×C42—24no—
145C22×C42—24no—
146C22×C42—24no—
147C22×C42—28no—
148C22×C42—24no—
149C22×C42—28no—
150C22×C42—24no—
151C22×C42—44no—
152C22×C42D418yescomplemented
153C22×C42C2314yes—
154C22×C42C2318yes—
155C22×C42C2314yes—
156#390—232no—
157#390—264no—
158#390—232no—
159#389—232no—
160#380—232no—
161C4×C4⋊C4—232no—
162C4×C22⋊C4—232no—
163C2×#95—24no—
164C2×#95—24no—
165C2×#95—28no—
166C2×#95—28no—
167C2×#95—28no—
168C2×#95C2314yes—
169C2×#95C2318yes—
170C2×#95C2318yes—
171C2×#95C2318yes—
172C2×#95C2314yes—
173C25—22no—
174C25—22no—
175C25—22no—
176C25—22no—
177C25—22no—
178C25—22no—
179C25—22no—
180C25—22no—
181C25—22no—
182C25—22no—
183C25—22no—
184C25—22no—
185C25—24no—
186C25—24no—
187C25—24no—
188C25—24no—
189C25—24no—
190C25—24no—
191C25—24no—
192C25—24no—
193C25—24no—
194C25—24no—
195C25—24no—
196C25—24no—
197C25—24no—
198C25—24no—
199C25C22×C418yes—
200C25C22×C414yes—
201C25C2×D414yes—
202C25#4114yes—
203C25C2414yes—
204C25C2412yes—
205C25C2411yescharacteristic
206C22×D4—264no—
207C22×D4—216no—
208C22×D4—216no—
209C22×D4—264no—
210C22×D4—232no—
211C22×D4—232no—
212C22×D4—232no—
213C22×D4—216no—
214C22×D4—216no—
215C22×D4—28no—
216C22×D4—28no—
217C22×D4—28no—
218C22×D4—28no—
219C22×D4—28no—
220C22×D4—28no—
221C22×D4—432no—
222C22×D4—48no—
223C22×D4—48no—
224C22×D4—432no—
225C22×D4—432no—
226C22×D4—432no—
227C22×D4—432no—
228C22×D4—416no—
229C22×D4—416no—
230C22×D4—416no—
231C22×D4—416no—
232C22×D4C22×C4116yes—
233C22×D4C22×C4132yes—
234C23×C4—24no—
235C23×C4—22no—
236C23×C4—24no—
237C23×C4—22no—
238C23×C4—24no—
239C23×C4—24no—
240C23×C4—22no—
241C23×C4—22no—
242C23×C4—22no—
243C23×C4—22no—
244C23×C4—22no—
245C23×C4—24no—
246C23×C4—22no—
247C23×C4—22no—
248C23×C4—22no—
249C23×C4—22no—
250C23×C4—24no—
251C23×C4—22no—
252C23×C4—22no—
253C23×C4—22no—
254C23×C4—22no—
255C23×C4—22no—
256C23×C4—22no—
257C23×C4—22no—
258C23×C4—22no—
259C23×C4—24no—
260C23×C4—24no—
261C23×C4—22no—
262C23×C4—22no—
263C23×C4—22no—
264C23×C4—22no—
265C23×C4—22no—
266C23×C4—22no—
267C23×C4—24no—
268C23×C4—22no—
269C23×C4—24no—
270C23×C4—22no—
271C23×C4—22no—
272C23×C4—232no—
273C23×C4—232no—
274C23×C4—232no—
275C23×C4—28no—
276C23×C4—28no—
277C23×C4—28no—
278C23×C4—28no—
279C23×C4—28no—
280C23×C4—28no—
281C23×C4—24no—
282C23×C4—24no—
283C23×C4—24no—
284C23×C4—24no—
285C23×C4—24no—
286C23×C4—24no—
287C23×C4—24no—
288C23×C4—416no—
289C23×C4—416no—
290C23×C4—416no—
291C23×C4—416no—
292C23×C4C22×C414yes—
293C23×C4C22×C4116yes—
294C23×C4C22×C418yes—
295C23×C4C22×C414yes—
296C23×C4C2×D418yes—
297C23×C4C2×D414yes—
298C23×C4C2×D414yes—
299C23×C4C2×D418yes—
300C23×C4C2×D418yes—
301C23×C4C2×D414yes—
302C23×C4C2×D414yes—
303C23×C4C2×D414yes—
304C23×C4C2×D414yes—
305C23×C4C2×D414yes—
306C23×C4C2×D414yes—
307C23×C4#4114yes—
308C23×C4#4114yes—
309C23×C4#4114yes—
310C23×C4#4114yes—
311C23×C4C2414yes—
312C23×C4C2412yes—
313C23×C4C2412yes—
314C23×C4C2414yes—
315C23×C4C2412yes—
316C23×C4C2412yes—
317C23×C4C2414yes—
318C23×C4C2412yes—
319C23×C4C2412yes—
320#121—2256no—
321C2×C4⋊C4—232no—
322C2×C4⋊C4—28no—
323C2×C4⋊C4—28no—
324C2×C4⋊C4—28no—
325C2×C4⋊C4—216no—
326C2×C4⋊C4—28no—
327C2×C4⋊C4—216no—
328C2×C4⋊C4—28no—
329C2×C4⋊C4—48no—
330C2×C4⋊C4—432no—
331C2×C4⋊C4—416no—
332C2×C4⋊C4C22⋊C4164yescomplemented
333C2×C4⋊C4C22×C4116yes—
334C2×C4⋊C4C2×D4116yes—
335C2×C4⋊C4C2×D4116yes—
336C2×C4⋊C4C2×D4116yescomplemented
337C2×C22⋊C4—232no—
338C2×C22⋊C4—28no—
339C2×C22⋊C4—264no—
340C2×C22⋊C4—232no—
341C2×C22⋊C4—216no—
342C2×C22⋊C4—216no—
343C2×C22⋊C4—28no—
344C2×C22⋊C4—28no—
345C2×C22⋊C4—28no—
346C2×C22⋊C4—28no—
347C2×C22⋊C4—216no—
348C2×C22⋊C4—216no—
349C2×C22⋊C4—216no—
350C2×C22⋊C4—216no—
351C2×C22⋊C4—216no—
352C2×C22⋊C4—216no—
353C2×C22⋊C4—216no—
354C2×C22⋊C4—216no—
355C2×C22⋊C4—216no—
356C2×C22⋊C4—216no—
357C2×C22⋊C4—48no—
358C2×C22⋊C4—48no—
359C2×C22⋊C4—48no—
360C2×C22⋊C4—48no—
361C2×C22⋊C4—48no—
362C2×C22⋊C4—432no—
363C2×C22⋊C4—432no—
364C2×C22⋊C4—432no—
365C2×C22⋊C4—432no—
366C2×C22⋊C4—432no—
367C2×C22⋊C4C22×C4132yes—
368C2×C22⋊C4C2×D4116yescomplemented
369C2×C42—232no—
370C2×C42—28no—
371C2×C42—28no—
372C2×C42—28no—
373C2×C42—216no—
374C2×C42—28no—
375C2×C42—216no—
376C2×C42—28no—
377C2×C42—48no—
378C2×C42—432no—
379C2×C42—416no—
380C2×C42C2×D4116yescomplemented
381#95—28no—
382#95—28no—
383#95—216no—
384#95—216no—
385#95—216no—
386C24—28no—
387C24—28no—
388C24—28no—
389C24—28no—
390C24—28no—
391C24—28no—
392C24—28no—
393C24—28no—
394C24—28no—
395C24—28no—
396C24—28no—
397C24—28no—
398C24—28no—
399C24—28no—
400C24—28no—
401C24—28no—
402C24—28no—
403C24—28no—
404C24—22no—
405C24—22no—
406C24—22no—
407C24—22no—
408C24—22no—
409C24—22no—
410C24—22no—
411C24—22no—
412C24—22no—
413C24—22no—
414C24—22no—
415C24—22no—
416C24—216no—
417C24—216no—
418C24—216no—
419C24—216no—
420C24—216no—
421C24—216no—
422C24—216no—
423C24—24no—
424C24—24no—
425C24—24no—
426C24—24no—
427C24—24no—
428C24—24no—
429C24—24no—
430C24—24no—
431C24—24no—
432C24—24no—
433C24—24no—
434C24—24no—
435C24—24no—
436C24—24no—
437C24—44no—
438C24—44no—
439C24—44no—
440C24—44no—
441C24—44no—
442C24—44no—
443C24—44no—
444C24—44no—
445C24—44no—
446C24—44no—
447C24—44no—
448C24—44no—
449C24—44no—
450C24—44no—
451C24—44no—
452C24—44no—
453C24—48no—
454C24—48no—
455C24—48no—
456C24—48no—
457C24—48no—
458C24—48no—
459C24—48no—
460C24—48no—
461C24—48no—
462C24—48no—
463C24—48no—
464C24—48no—
465C24—48no—
466C24—48no—
467C24—48no—
468C24—48no—
469C24—48no—
470C24—48no—
471C24—48no—
472C24—48no—
473C24—48no—
474C24—48no—
475C24—48no—
476C24—48no—
477C24—48no—
478C24—48no—
479C24—48no—
480C24—48no—
481C24C4×D4116yes—
482C24C23×C418yes—
483C24C23×C414yes—
484C24C23×C412yes—
485C24C22×D414yes—
486C24C22×D412yes—
487C24C22×D412yes—
488C24C22×D412yes—
489C24C22×D412yes—
490C24C22×D412yes—
491C24C2×#4114yes—
492C24C2×#4112yes—
493C24C2×#4112yes—
494C24C2×#4112yes—
495C24C2×#4112yes—
496C24C2×#4112yes—
497C24H(5,𝔽2)12yes—
498C24H(5,𝔽2)12yes—
499C24H(5,𝔽2)12yes—
500C242−1+412yes—
501C24C2511yescharacteristic
502C2×D4—264no—
503C2×D4—264no—
504C2×D4—232no—
505C2×D4—232no—
506C2×D4—232no—
507C2×D4—432no—
508C2×D4—4256no—
509C2×D4—432no—
510C2×D4—432no—
511C2×D4—432no—
512C2×D4—432no—
513C2×D4—416no—
514C2×D4—416no—
515C2×D4—416no—
516C2×D4—416no—
517C2×D4—4128no—
518C22×C4—216no—
519C22×C4—216no—
520C22×C4—28no—
521C22×C4—28no—
522C22×C4—28no—
523C22×C4—216no—
524C22×C4—216no—
525C22×C4—216no—
526C22×C4—216no—
527C22×C4—28no—
528C22×C4—28no—
529C22×C4—28no—
530C22×C4—22no—
531C22×C4—24no—
532C22×C4—22no—
533C22×C4—24no—
534C22×C4—22no—
535C22×C4—24no—
536C22×C4—24no—
537C22×C4—22no—
538C22×C4—28no—
539C22×C4—28no—
540C22×C4—28no—
541C22×C4—28no—
542C22×C4—28no—
543C22×C4—216no—
544C22×C4—28no—
545C22×C4—28no—
546C22×C4—28no—
547C22×C4—216no—
548C22×C4—28no—
549C22×C4—28no—
550C22×C4—28no—
551C22×C4—216no—
552C22×C4—28no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—24no—
560C22×C4—22no—
561C22×C4—24no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—24no—
572C22×C4—24no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—24no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—24no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—232no—
584C22×C4—232no—
585C22×C4—232no—
586C22×C4—24no—
587C22×C4—24no—
588C22×C4—24no—
589C22×C4—24no—
590C22×C4—24no—
591C22×C4—24no—
592C22×C4—24no—
593C22×C4—44no—
594C22×C4—44no—
595C22×C4—44no—
596C22×C4—44no—
597C22×C4—44no—
598C22×C4—44no—
599C22×C4—48no—
600C22×C4—44no—
601C22×C4—44no—
602C22×C4—48no—
603C22×C4—48no—
604C22×C4—44no—
605C22×C4—44no—
606C22×C4—44no—
607C22×C4—44no—
608C22×C4—48no—
609C22×C4—44no—
610C22×C4—44no—
611C22×C4—44no—
612C22×C4—44no—
613C22×C4—416no—
614C22×C4—416no—
615C22×C4—416no—
616C22×C4—416no—
617C22×C4—4128no—
618C22×C4—48no—
619C22×C4—48no—
620C22×C4—48no—
621C22×C4—48no—
622C22×C4—48no—
623C22×C4—48no—
624C22×C4—48no—
625C22×C4C2×C22⋊C4132yes—
626C22×C4C2×C22⋊C4116yes—
627C22×C4C4×D4116yes—
628C22×C4C4×D4116yes—
629C22×C4#121116yes—
630C22×C4#121116yes—
631C22×C4#121116yescomplemented
632C22×C4#124116yes—
633C22×C4#127116yes—
634C22×C4C23×C414yes—
635C22×C4C23×C418yes—
636C22×C4C23×C414yes—
637C22×C4C22×D414yes—
638C22×C4C22×D418yes—
639C22×C4C22×D414yes—
640C22×C4C22×D418yes—
641C22×C4C22×D418yes—
642C22×C4C22×D414yes—
643C22×C4C22×D414yes—
644C22×C4C22×D414yes—
645C22×C4C22×D414yes—
646C22×C4C22×D414yes—
647C22×C4C22×D414yes—
648C22×C4C2×#4114yes—
649C22×C4C2×#4114yes—
650C22×C4C2×#4114yes—
651C22×C4C2×#4114yes—
652C4⋊C4—232no—
653C4⋊C4—432no—
654C4⋊C4—416no—
655C4⋊C4C2×C22⋊C4164yescomplemented
656C22⋊C4—232no—
657C22⋊C4—264no—
658C22⋊C4—232no—
659C22⋊C4—432no—
660C22⋊C4—432no—
661C22⋊C4—432no—
662C22⋊C4—432no—
663C22⋊C4—432no—
664C42—232no—
665C42—432no—
666C42—416no—
667C23—232no—
668C23—232no—
669C23—24no—
670C23—24no—
671C23—24no—
672C23—24no—
673C23—24no—
674C23—24no—
675C23—24no—
676C23—24no—
677C23—24no—
678C23—24no—
679C23—24no—
680C23—24no—
681C23—24no—
682C23—24no—
683C23—24no—
684C23—24no—
685C23—24no—
686C23—24no—
687C23—232no—
688C23—28no—
689C23—28no—
690C23—28no—
691C23—28no—
692C23—28no—
693C23—28no—
694C23—28no—
695C23—416no—
696C23—416no—
697C23—416no—
698C23—42no—
699C23—42no—
700C23—42no—
701C23—416no—
702C23—416no—
703C23—42no—
704C23—42no—
705C23—42no—
706C23—416no—
707C23—416no—
708C23—42no—
709C23—42no—
710C23—42no—
711C23—42no—
712C23—42no—
713C23—42no—
714C23—42no—
715C23—42no—
716C23—42no—
717C23—42no—
718C23—416no—
719C23—416no—
720C23—416no—
721C23—416no—
722C23—416no—
723C23—432no—
724C23—432no—
725C23—432no—
726C23—432no—
727C23—432no—
728C23—44no—
729C23—44no—
730C23—44no—
731C23—44no—
732C23—44no—
733C23—44no—
734C23—44no—
735C23—44no—
736C23—44no—
737C23—44no—
738C23—44no—
739C23—44no—
740C23—44no—
741C23—44no—
742C23—44no—
743C23—44no—
744C23—44no—
745C23—44no—
746C23—44no—
747C23—44no—
748C23—44no—
749C23—44no—
750C23—44no—
751C23—44no—
752C23—44no—
753C23—44no—
754C23—44no—
755C23—44no—
756C23—432no—
757C23—432no—
758C23—816no—
759C23—816no—
760C23—816no—
761C23—816no—
762C23—816no—
763C23—816no—
764C23—816no—
765C23—816no—
766C23C22×C22⋊C414yes—
767C23C2×C4×D418yes—
768C23C2×C4×D414yes—
769C23C2×C4×D414yes—
770C23C2×C4×D414yes—
771C23C4×#4114yes—
772C23#51814yes—
773C23#52014yes—
774C23C2×#12114yes—
775C23C2×#12114yes—
776C23C2×#12114yes—
777C23#52514yes—
778C23C2×#12414yes—
779C23#52914yes—
780C23C2×#12714yes—
781C23#53214yes—
782C23#53514yes—
783C23#53714yes—
784C23#54014yes—
785C23#54214yes—
786C23D4214yes—
787C23D4214yes—
788C23D4214yes—
789C23#54614yes—
790C23#54614yes—
791C23#54614yes—
792C23#54714yes—
793C23#54814yes—
794C23#54814yes—
795C23#54814yes—
796C23#55014yes—
797C23#55014yes—
798C23#55014yes—
799C23#55314yes—
800C23#55314yes—
801C23#55514yes—
802C23C24×C411yescharacteristic
803C23C23×D411yescharacteristic
804C23C23×D411yescharacteristic
805C23C23×D411yescharacteristic
806C23C23×D411yescharacteristic
807C23C23×D411yescharacteristic
808C23C22×#4111yescharacteristic
809C23C22×#4111yescharacteristic
810C23C22×#4111yescharacteristic
811C23C22×#4111yescharacteristic
812C23C22×#4111yescharacteristic
813C23C2×H(5,𝔽2)11yescharacteristic
814C23C2×H(5,𝔽2)11yescharacteristic
815C23C2×H(5,𝔽2)11yescharacteristic
816C23C2×2−1+411yescharacteristic
817D4—4128no—
818D4—464no—
819C2×C4—264no—
820C2×C4—28no—
821C2×C4—28no—
822C2×C4—24no—
823C2×C4—232no—
824C2×C4—24no—
825C2×C4—24no—
826C2×C4—28no—
827C2×C4—28no—
828C2×C4—28no—
829C2×C4—28no—
830C2×C4—24no—
831C2×C4—24no—
832C2×C4—24no—
833C2×C4—24no—
834C2×C4—24no—
835C2×C4—24no—
836C2×C4—24no—
837C2×C4—24no—
838C2×C4—28no—
839C2×C4—24no—
840C2×C4—24no—
841C2×C4—24no—
842C2×C4—24no—
843C2×C4—28no—
844C2×C4—24no—
845C2×C4—24no—
846C2×C4—28no—
847C2×C4—24no—
848C2×C4—42no—
849C2×C4—42no—
850C2×C4—42no—
851C2×C4—416no—
852C2×C4—42no—
853C2×C4—42no—
854C2×C4—42no—
855C2×C4—44no—
856C2×C4—42no—
857C2×C4—42no—
858C2×C4—432no—
859C2×C4—44no—
860C2×C4—44no—
861C2×C4—42no—
862C2×C4—42no—
863C2×C4—42no—
864C2×C4—42no—
865C2×C4—42no—
866C2×C4—44no—
867C2×C4—42no—
868C2×C4—42no—
869C2×C4—42no—
870C2×C4—416no—
871C2×C4—416no—
872C2×C4—416no—
873C2×C4—464no—
874C2×C4—44no—
875C2×C4—44no—
876C2×C4—44no—
877C2×C4—44no—
878C2×C4—44no—
879C2×C4—44no—
880C2×C4—44no—
881C2×C4—816no—
882C2×C4#390164yescomplemented
883C2×C4C22×C22⋊C4116yes—
884C2×C4C22×C22⋊C418yes—
885C2×C4C2×C4×D418yes—
886C2×C4C2×C4×D418yes—
887C2×C4C2×#12118yes—
888C2×C4C2×#12118yes—
889C2×C4C2×#12118yescomplemented
890C2×C4C2×#12418yes—
891C2×C4C2×#12718yes—
892C22—28no—
893C22—28no—
894C22—28no—
895C22—44no—
896C22—44no—
897C22—44no—
898C22—44no—
899C22—44no—
900C22—44no—
901C22—44no—
902C22—44no—
903C22—44no—
904C22—464no—
905C22—44no—
906C22—44no—
907C22—44no—
908C22—48no—
909C22—48no—
910C22—48no—
911C22—48no—
912C22—48no—
913C22—48no—
914C22—48no—
915C22—84no—
916C22—84no—
917C22—84no—
918C22—84no—
919C22—84no—
920C22—84no—
921C22—864no—
922C22—84no—
923C22—84no—
924C22C2×#39018yes—
925C22C4×#12118yes—
926C22#232418yes—
927C22D4×C22⋊C418yes—
928C22#234118yes—
929C22#236118yes—
930C22#236318yes—
931C22#241418yes—
932C22#241618yes—
933C22#242618yes—
934C22#242818yes—
935C22#249018yes—
936C22#249118yes—
937C22#254018yes—
938C22#254118yes—
939C22C23×C22⋊C411yescharacteristic
940C22C22×C4×D411yescharacteristic
941C22C22×C4×D411yescharacteristic
942C22C22×C4×D411yescharacteristic
943C22C2×C4×#4111yescharacteristic
944C22C2×#51811yescharacteristic
945C22C2×#52011yescharacteristic
946C22C22×#12111yescharacteristic
947C22C22×#12111yescharacteristic
948C22C22×#12111yescharacteristic
949C22C2×#52511yescharacteristic
950C22C22×#12411yescharacteristic
951C22C2×#52911yescharacteristic
952C22C22×#12711yescharacteristic
953C22C2×#53211yescharacteristic
954C22C2×#53511yescharacteristic
955C22C2×#53711yescharacteristic
956C22C2×#54011yescharacteristic
957C22C2×#54211yescharacteristic
958C22C2×D4211yescharacteristic
959C22C2×D4211yescharacteristic
960C22C2×D4211yescharacteristic
961C22C2×#54611yescharacteristic
962C22C2×#54611yescharacteristic
963C22C2×#54611yescharacteristic
964C22C2×#54711yescharacteristic
965C22C2×#54811yescharacteristic
966C22C2×#54811yescharacteristic
967C22C2×#54811yescharacteristic
968C22C2×#55011yescharacteristic
969C22C2×#55011yescharacteristic
970C22C2×#55011yescharacteristic
971C22C2×#55311yescharacteristic
972C22C2×#55311yescharacteristic
973C22C2×#55511yescharacteristic
974C4—216no—
975C4—28no—
976C4—44no—
977C4—44no—
978C4—48no—
979C4—44no—
980C4—44no—
981C4—84no—
982C4C2×#390116yescomplemented
983C2—48no—
984C2—88no—
985C2#13998116yesdirect product factor
986C2C22×#39011yescharacteristic
987C2C2×C4×#12111yescharacteristic
988C2C2×#232411yescharacteristic
989C2C2×D4×C22⋊C411yescharacteristic
990C2C2×#234111yescharacteristic
991C2C2×#236111yescharacteristic
992C2C2×#236311yescharacteristic
993C2C2×#241611yescharacteristic
994C2C2×#242811yescharacteristic
995C2C2×#242611yescharacteristic
996C2C2×#241411yescharacteristic
997C2C2×#249111yescharacteristic
998C2C2×#249011yescharacteristic
999C2C2×#254011yescharacteristic
1000C2C2×#254111yescharacteristic
subgroupG/H
center, socleC25C24
commutatorC23C24×C4
Frattini, cosocleC24C25
prime radicalC23×#121C2
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×#390C2semidirect
3. C22×#390C2semidirect
4. C22×#390C2semidirect
5. C22×#389C2semidirect
6. C22×#380C2semidirect
7. C22×C4×C4⋊C4C2semidirect
8. C22×C4×C22⋊C4C2semidirect
9. #13998C2direct (N × H)
10. C2×#1439C2semidirect
11. C2×#1438C2semidirect
12. C2×#1437C2semidirect
18. C22×#121C4semidirect
38. C2×#390C22semidirect
39. C2×#390C22semidirect
40. C2×#390C22semidirect
42. C2×#389C22semidirect
44. C2×#380C22semidirect
46. C2×C4×C4⋊C4C22semidirect
48. C2×C4×C22⋊C4C22semidirect
54. #1439C22semidirect
55. #1438C22semidirect
56. #1437C22semidirect
95. C2×#121C2×C4semidirect
107. C22×C4⋊C4D4semidirect
135. C22×C22⋊C4D4semidirect
152. C22×C42D4semidirect
332. C2×C4⋊C4C22⋊C4semidirect
336. C2×C4⋊C4C2×D4semidirect
368. C2×C22⋊C4C2×D4semidirect
380. C2×C42C2×D4semidirect
631. C22×C4#121semidirect
655. C4⋊C4C2×C22⋊C4semidirect
882. C2×C4#390semidirect
889. C2×C4C2×#121semidirect
982. C4C2×#390semidirect
985. C2#13998direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#1212
C22×#3902
C22×#3892
C22×#3802
C22×C4×C4⋊C42
C22×C4×C22⋊C42
#139982
C2×#14392
C2×#14382
C2×#14372