Finite Group Databasebeta

← C2×#15126 #608357

Subgroups — C2×#15126 #608357

Order 512.

8934 conjugacy classes of subgroups.

The subgroup lattice has 994 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#121C211yesmaximal, characteristic
2C22×#394C212yesmaximal, complemented
3C22×#390C211yesmaximal, characteristic, complemented
4C22×#390C211yesmaximal, characteristic, complemented
5C22×#389C211yesmaximal, characteristic, complemented
6C22×#380C211yesmaximal, characteristic, complemented
7C22×C4×C22⋊C4C211yesmaximal, characteristic, complemented
8#15126C2116yesmaximal, direct product factor
9C2×#1440C212yesmaximal, complemented
10C2×#1439C212yesmaximal, complemented
11C2×#1438C212yesmaximal, complemented
12C2×C4⋊#95C211yesmaximal, characteristic, complemented
13C24×D4C2211yescharacteristic
14C24×D4C2212yes—
15C25×C4C2211yescharacteristic
16C22×#121—28no—
17C22×#121—28no—
18C22×#121—28no—
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⋊C4C2212yes—
31C23×C22⋊C4C2211yescharacteristic
32C23×C42C2211yescharacteristic
33C23×C42C2211yescharacteristic
34C2×#394—216no—
35C2×#394C22116yescomplemented
36C2×#390—28no—
37C2×#390—28no—
38C2×#390C2218yescomplemented
39C2×#390C2218yescomplemented
40C2×#389—28no—
41C2×#389C2218yescomplemented
42C2×#380—28no—
43C2×#380C2218yescomplemented
44C2×C4×C22⋊C4—28no—
45C2×C4×C22⋊C4C2218yescomplemented
46C22×#95C2212yes—
47C22×#95C2211yescharacteristic
48C22×#95C2212yes—
49C22×#95C2211yescharacteristic
50C22×#95C2212yes—
51C22×#95C2212yes—
52#1440C22116yescomplemented
53#1439C22116yescomplemented
54#1438C22116yescomplemented
55C4⋊#95C2218yescomplemented
56C26C2312yes—
57C26C2311yescharacteristic
58C23×D4—28no—
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×D4D418yes—
72C23×D4C2314yes—
73C23×D4C2318yes—
74C24×C4—24no—
75C24×C4—24no—
76C24×C4—24no—
77C24×C4—24no—
78C24×C4—24no—
79C24×C4—24no—
80C24×C4D418yes—
81C24×C4C2312yes—
82C24×C4C2314yes—
83C24×C4C2311yescharacteristic
84C24×C4C2312yes—
85C24×C4C2311yescharacteristic
86C24×C4C2311yescharacteristic
87C24×C4C2312yes—
88C24×C4C2311yescharacteristic
89C24×C4C2311yescharacteristic
90C24×C4C2311yescharacteristic
91C2×#121—2128no—
92C2×#121—232no—
93C2×#121—232no—
94C2×#121—232no—
95C22×C4⋊C4—24no—
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—24no—
104C22×C4⋊C4—44no—
105C22×C4⋊C4D418yes—
106C22×C4⋊C4D418yescomplemented
107C22×C4⋊C4C2314yes—
108C22×C4⋊C4C2318yes—
109C22×C4⋊C4C2314yes—
110C22×C4⋊C4C2314yes—
111C22×C22⋊C4—28no—
112C22×C22⋊C4—24no—
113C22×C22⋊C4—24no—
114C22×C22⋊C4—24no—
115C22×C22⋊C4—28no—
116C22×C22⋊C4—28no—
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⋊C4D418yescomplemented
135C22×C22⋊C4C2318yes—
136C22×C22⋊C4C2314yes—
137C22×C22⋊C4C2318yes—
138C22×C22⋊C4C2318yes—
139C22×C22⋊C4C2318yes—
140C22×C22⋊C4C2318yes—
141C22×C22⋊C4C2318yes—
142C22×C22⋊C4C2314yes—
143C22×C42—24no—
144C22×C42—24no—
145C22×C42—24no—
146C22×C42—24no—
147C22×C42—24no—
148C22×C42—24no—
149C22×C42C2314yes—
150C22×C42C2314yes—
151#394—264no—
152#390—232no—
153#390—232no—
154#389—232no—
155#380—232no—
156C4×C22⋊C4—232no—
157C2×#95—28no—
158C2×#95—24no—
159C2×#95—24no—
160C2×#95—28no—
161C2×#95—28no—
162C2×#95—44no—
163C2×#95C2318yes—
164C2×#95C2318yes—
165C2×#95C2314yes—
166C2×#95C2318yes—
167C2×#95C2314yes—
168C2×#95C2318yes—
169C25—22no—
170C25—22no—
171C25—22no—
172C25—22no—
173C25—22no—
174C25—22no—
175C25—22no—
176C25—22no—
177C25—22no—
178C25—22no—
179C25—22no—
180C25—22no—
181C25—24no—
182C25—24no—
183C25—24no—
184C25—24no—
185C25—24no—
186C25—24no—
187C25—24no—
188C25—24no—
189C25—24no—
190C25—24no—
191C25—24no—
192C25—24no—
193C25—24no—
194C25—24no—
195C25C2×D418yes—
196C25C2×D414yes—
197C25C2×D414yes—
198C25#4114yes—
199C25C2414yes—
200C25C2412yes—
201C25C2411yescharacteristic
202C22×D4—264no—
203C22×D4—216no—
204C22×D4—216no—
205C22×D4—216no—
206C22×D4—216no—
207C22×D4—232no—
208C22×D4—232no—
209C22×D4—232no—
210C22×D4—216no—
211C22×D4—28no—
212C22×D4—28no—
213C22×D4—28no—
214C22×D4—28no—
215C22×D4—28no—
216C22×D4—28no—
217C22×D4—48no—
218C22×D4—48no—
219C22×D4—432no—
220C22×D4—432no—
221C22×D4—432no—
222C22×D4—432no—
223C22×D4—432no—
224C22×D4—432no—
225C22×D4—416no—
226C22×D4—416no—
227C22×D4—416no—
228C22×D4—416no—
229C22×D4C2×D4116yes—
230C23×C4—24no—
231C23×C4—22no—
232C23×C4—22no—
233C23×C4—22no—
234C23×C4—22no—
235C23×C4—22no—
236C23×C4—22no—
237C23×C4—24no—
238C23×C4—24no—
239C23×C4—22no—
240C23×C4—22no—
241C23×C4—22no—
242C23×C4—22no—
243C23×C4—24no—
244C23×C4—22no—
245C23×C4—24no—
246C23×C4—22no—
247C23×C4—22no—
248C23×C4—22no—
249C23×C4—22no—
250C23×C4—22no—
251C23×C4—22no—
252C23×C4—24no—
253C23×C4—24no—
254C23×C4—22no—
255C23×C4—22no—
256C23×C4—22no—
257C23×C4—24no—
258C23×C4—22no—
259C23×C4—22no—
260C23×C4—22no—
261C23×C4—22no—
262C23×C4—24no—
263C23×C4—22no—
264C23×C4—22no—
265C23×C4—24no—
266C23×C4—22no—
267C23×C4—24no—
268C23×C4—24no—
269C23×C4—22no—
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×C4C2×D418yes—
293C23×C4C2×D414yes—
294C23×C4C2×D414yes—
295C23×C4C2×D414yes—
296C23×C4C2×D418yes—
297C23×C4C2×D4116yes—
298C23×C4C2×D414yes—
299C23×C4C2×D414yes—
300C23×C4C2×D414yes—
301C23×C4C2×D414yes—
302C23×C4#4114yes—
303C23×C4#4114yes—
304C23×C4#4114yes—
305C23×C4#4114yes—
306C23×C4#4114yes—
307C23×C4C2414yes—
308C23×C4C2414yes—
309C23×C4C2412yes—
310C23×C4C2412yes—
311C23×C4C2412yes—
312C23×C4C2414yes—
313C23×C4C2412yes—
314C23×C4C2412yes—
315C23×C4C2412yes—
316#121—2256no—
317C2×C4⋊C4—232no—
318C2×C4⋊C4—232no—
319C2×C4⋊C4—28no—
320C2×C4⋊C4—28no—
321C2×C4⋊C4—28no—
322C2×C4⋊C4—28no—
323C2×C4⋊C4—28no—
324C2×C4⋊C4—216no—
325C2×C4⋊C4—28no—
326C2×C4⋊C4—216no—
327C2×C4⋊C4—28no—
328C2×C4⋊C4—48no—
329C2×C4⋊C4—432no—
330C2×C4⋊C4—416no—
331C2×C4⋊C4C2×D4116yes—
332C2×C4⋊C4C2×D4116yescomplemented
333C2×C22⋊C4—232no—
334C2×C22⋊C4—264no—
335C2×C22⋊C4—232no—
336C2×C22⋊C4—216no—
337C2×C22⋊C4—28no—
338C2×C22⋊C4—28no—
339C2×C22⋊C4—28no—
340C2×C22⋊C4—216no—
341C2×C22⋊C4—216no—
342C2×C22⋊C4—28no—
343C2×C22⋊C4—28no—
344C2×C22⋊C4—216no—
345C2×C22⋊C4—216no—
346C2×C22⋊C4—216no—
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—48no—
355C2×C22⋊C4—48no—
356C2×C22⋊C4—48no—
357C2×C22⋊C4—48no—
358C2×C22⋊C4—48no—
359C2×C22⋊C4—432no—
360C2×C22⋊C4—432no—
361C2×C22⋊C4—432no—
362C2×C22⋊C4—432no—
363C2×C22⋊C4—432no—
364C2×C22⋊C4C2×D4116yescomplemented
365C2×C42—28no—
366C2×C42—28no—
367C2×C42—28no—
368C2×C42—28no—
369C2×C42—28no—
370C2×C42—28no—
371C2×C42—416no—
372C2×C42—416no—
373#95—28no—
374#95—28no—
375#95—216no—
376#95—216no—
377#95—216no—
378#95—48no—
379C24—28no—
380C24—28no—
381C24—28no—
382C24—28no—
383C24—28no—
384C24—28no—
385C24—28no—
386C24—28no—
387C24—28no—
388C24—28no—
389C24—28no—
390C24—28no—
391C24—28no—
392C24—28no—
393C24—28no—
394C24—28no—
395C24—28no—
396C24—28no—
397C24—22no—
398C24—22no—
399C24—22no—
400C24—22no—
401C24—22no—
402C24—22no—
403C24—22no—
404C24—22no—
405C24—22no—
406C24—22no—
407C24—22no—
408C24—22no—
409C24—216no—
410C24—216no—
411C24—216no—
412C24—216no—
413C24—216no—
414C24—216no—
415C24—216no—
416C24—24no—
417C24—24no—
418C24—24no—
419C24—24no—
420C24—24no—
421C24—24no—
422C24—24no—
423C24—24no—
424C24—24no—
425C24—24no—
426C24—24no—
427C24—24no—
428C24—24no—
429C24—24no—
430C24—44no—
431C24—44no—
432C24—44no—
433C24—44no—
434C24—44no—
435C24—44no—
436C24—44no—
437C24—44no—
438C24—44no—
439C24—44no—
440C24—44no—
441C24—44no—
442C24—44no—
443C24—44no—
444C24—44no—
445C24—44no—
446C24—48no—
447C24—48no—
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—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#121116yes—
475C24C22×D418yes—
476C24C22×D414yes—
477C24C22×D414yes—
478C24C22×D412yes—
479C24C22×D412yes—
480C24C22×D412yes—
481C24C22×D412yes—
482C24C22×D412yes—
483C24C2×#4114yes—
484C24C2×#4112yes—
485C24C2×#4112yes—
486C24C2×#4112yes—
487C24C2×#4112yes—
488C24C2×#4112yes—
489C24C2×#4112yes—
490C24H(5,𝔽2)12yes—
491C24H(5,𝔽2)12yes—
492C24H(5,𝔽2)12yes—
493C242−1+412yes—
494C24C2511yescharacteristic
495C2×D4—264no—
496C2×D4—232no—
497C2×D4—232no—
498C2×D4—232no—
499C2×D4—432no—
500C2×D4—432no—
501C2×D4—432no—
502C2×D4—432no—
503C2×D4—4256no—
504C2×D4—432no—
505C2×D4—432no—
506C2×D4—416no—
507C2×D4—416no—
508C2×D4—416no—
509C2×D4—416no—
510C2×D4—4128no—
511C22×C4—28no—
512C22×C4—216no—
513C22×C4—28no—
514C22×C4—28no—
515C22×C4—216no—
516C22×C4—28no—
517C22×C4—28no—
518C22×C4—28no—
519C22×C4—28no—
520C22×C4—28no—
521C22×C4—28no—
522C22×C4—216no—
523C22×C4—28no—
524C22×C4—216no—
525C22×C4—28no—
526C22×C4—28no—
527C22×C4—216no—
528C22×C4—216no—
529C22×C4—28no—
530C22×C4—28no—
531C22×C4—28no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—24no—
539C22×C4—24no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—24no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—24no—
549C22×C4—24no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—24no—
557C22×C4—24no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—24no—
562C22×C4—22no—
563C22×C4—24no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—24no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—24no—
570C22×C4—22no—
571C22×C4—24no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—232no—
575C22×C4—232no—
576C22×C4—232no—
577C22×C4—24no—
578C22×C4—24no—
579C22×C4—24no—
580C22×C4—24no—
581C22×C4—24no—
582C22×C4—24no—
583C22×C4—24no—
584C22×C4—44no—
585C22×C4—44no—
586C22×C4—44no—
587C22×C4—44no—
588C22×C4—44no—
589C22×C4—44no—
590C22×C4—48no—
591C22×C4—44no—
592C22×C4—44no—
593C22×C4—48no—
594C22×C4—44no—
595C22×C4—44no—
596C22×C4—48no—
597C22×C4—44no—
598C22×C4—44no—
599C22×C4—48no—
600C22×C4—48no—
601C22×C4—48no—
602C22×C4—44no—
603C22×C4—44no—
604C22×C4—48no—
605C22×C4—44no—
606C22×C4—44no—
607C22×C4—44no—
608C22×C4—44no—
609C22×C4—48no—
610C22×C4—44no—
611C22×C4—44no—
612C22×C4—416no—
613C22×C4—416no—
614C22×C4—416no—
615C22×C4—416no—
616C22×C4—4128no—
617C22×C4—48no—
618C22×C4—48no—
619C22×C4—48no—
620C22×C4—48no—
621C22×C4—48no—
622C22×C4—48no—
623C22×C4—48no—
624C22×C4#120116yes—
625C22×C4#121116yes—
626C22×C4#121116yes—
627C22×C4#121116yes—
628C22×C4#123116yes—
629C22×C4#123116yes—
630C22×C4#124116yes—
631C22×C4C22×D414yes—
632C22×C4C22×D414yes—
633C22×C4C22×D418yes—
634C22×C4C22×D418yes—
635C22×C4C22×D414yes—
636C22×C4C22×D414yes—
637C22×C4C22×D414yes—
638C22×C4C22×D414yes—
639C22×C4C22×D414yes—
640C22×C4C2×#4114yes—
641C22×C4C2×#4114yes—
642C22×C4C2×#4114yes—
643C22×C4C2×#4114yes—
644C22×C4C2×#4114yes—
645C4⋊C4—232no—
646C4⋊C4—232no—
647C4⋊C4—432no—
648C4⋊C4—416no—
649C22⋊C4—232no—
650C22⋊C4—264no—
651C22⋊C4—232no—
652C22⋊C4—432no—
653C22⋊C4—432no—
654C22⋊C4—432no—
655C22⋊C4—432no—
656C22⋊C4—432no—
657C42—416no—
658C42—416no—
659C23—232no—
660C23—24no—
661C23—232no—
662C23—24no—
663C23—24no—
664C23—24no—
665C23—24no—
666C23—24no—
667C23—232no—
668C23—24no—
669C23—24no—
670C23—24no—
671C23—24no—
672C23—24no—
673C23—24no—
674C23—24no—
675C23—24no—
676C23—24no—
677C23—24no—
678C23—24no—
679C23—24no—
680C23—28no—
681C23—28no—
682C23—28no—
683C23—28no—
684C23—28no—
685C23—28no—
686C23—28no—
687C23—416no—
688C23—416no—
689C23—416no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—416no—
695C23—416no—
696C23—416no—
697C23—416no—
698C23—416no—
699C23—416no—
700C23—416no—
701C23—42no—
702C23—42no—
703C23—42no—
704C23—42no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—42no—
709C23—42no—
710C23—42no—
711C23—42no—
712C23—42no—
713C23—416no—
714C23—416no—
715C23—432no—
716C23—432no—
717C23—432no—
718C23—44no—
719C23—44no—
720C23—44no—
721C23—44no—
722C23—44no—
723C23—44no—
724C23—44no—
725C23—44no—
726C23—44no—
727C23—44no—
728C23—432no—
729C23—432no—
730C23—44no—
731C23—44no—
732C23—432no—
733C23—432no—
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—816no—
751C23—816no—
752C23—816no—
753C23—816no—
754C23—816no—
755C23—816no—
756C23—816no—
757C23—816no—
758C23C2×#12014yes—
759C23C2×#12118yes—
760C23C2×#12114yes—
761C23C2×#12114yes—
762C23C2×#12114yes—
763C23C2×#12114yes—
764C23C2×#12314yes—
765C23C2×#12314yes—
766C23#52514yes—
767C23C2×#12414yes—
768C23#52914yes—
769C23#52914yes—
770C23#53214yes—
771C23#53214yes—
772C23#53514yes—
773C23#53714yes—
774C23#54014yes—
775C23#54014yes—
776C23#54214yes—
777C23#54214yes—
778C23D4214yes—
779C23D4214yes—
780C23D4214yes—
781C23#54614yes—
782C23#54614yes—
783C23#54614yes—
784C23#54614yes—
785C23#54714yes—
786C23#54714yes—
787C23#54814yes—
788C23#54814yes—
789C23#55014yes—
790C23#55014yes—
791C23#55314yes—
792C23#55314yes—
793C23#55514yes—
794C23C23×D411yescharacteristic
795C23C23×D411yescharacteristic
796C23C23×D411yescharacteristic
797C23C23×D411yescharacteristic
798C23C23×D411yescharacteristic
799C23C22×#4111yescharacteristic
800C23C22×#4111yescharacteristic
801C23C22×#4111yescharacteristic
802C23C22×#4111yescharacteristic
803C23C22×#4111yescharacteristic
804C23C22×#4111yescharacteristic
805C23C2×H(5,𝔽2)11yescharacteristic
806C23C2×H(5,𝔽2)11yescharacteristic
807C23C2×H(5,𝔽2)11yescharacteristic
808C23C2×2−1+411yescharacteristic
809D4—4128no—
810D4—464no—
811C2×C4—24no—
812C2×C4—28no—
813C2×C4—24no—
814C2×C4—24no—
815C2×C4—28no—
816C2×C4—24no—
817C2×C4—24no—
818C2×C4—24no—
819C2×C4—24no—
820C2×C4—24no—
821C2×C4—24no—
822C2×C4—28no—
823C2×C4—24no—
824C2×C4—28no—
825C2×C4—24no—
826C2×C4—24no—
827C2×C4—28no—
828C2×C4—28no—
829C2×C4—24no—
830C2×C4—24no—
831C2×C4—24no—
832C2×C4—416no—
833C2×C4—416no—
834C2×C4—42no—
835C2×C4—42no—
836C2×C4—416no—
837C2×C4—432no—
838C2×C4—42no—
839C2×C4—42no—
840C2×C4—42no—
841C2×C4—42no—
842C2×C4—44no—
843C2×C4—42no—
844C2×C4—42no—
845C2×C4—416no—
846C2×C4—416no—
847C2×C4—44no—
848C2×C4—42no—
849C2×C4—42no—
850C2×C4—44no—
851C2×C4—42no—
852C2×C4—42no—
853C2×C4—432no—
854C2×C4—44no—
855C2×C4—44no—
856C2×C4—44no—
857C2×C4—42no—
858C2×C4—42no—
859C2×C4—44no—
860C2×C4—42no—
861C2×C4—42no—
862C2×C4—44no—
863C2×C4—42no—
864C2×C4—42no—
865C2×C4—42no—
866C2×C4—42no—
867C2×C4—464no—
868C2×C4—44no—
869C2×C4—44no—
870C2×C4—44no—
871C2×C4—44no—
872C2×C4—44no—
873C2×C4—44no—
874C2×C4—44no—
875C2×C4—816no—
876C2×C4#394164yescomplemented
877C2×C4C2×#12018yes—
878C2×C4C2×#12118yes—
879C2×C4C2×#12118yes—
880C2×C4C2×#12118yes—
881C2×C4C2×#12318yes—
882C2×C4C2×#12318yes—
883C2×C4C2×#12418yes—
884C22—28no—
885C22—28no—
886C22—28no—
887C22—464no—
888C22—44no—
889C22—44no—
890C22—44no—
891C22—44no—
892C22—44no—
893C22—44no—
894C22—44no—
895C22—44no—
896C22—44no—
897C22—44no—
898C22—44no—
899C22—44no—
900C22—48no—
901C22—48no—
902C22—48no—
903C22—48no—
904C22—48no—
905C22—48no—
906C22—48no—
907C22—84no—
908C22—864no—
909C22—84no—
910C22—84no—
911C22—84no—
912C22—84no—
913C22—84no—
914C22—84no—
915C22—84no—
916C22C2×#39418yes—
917C22#240718yes—
918C22#240818yes—
919C22#241418yes—
920C22#241618yes—
921C22#242018yes—
922C22#242218yes—
923C22#242618yes—
924C22#242718yes—
925C22#242818yes—
926C22#242818yes—
927C22#249018yes—
928C22#249118yes—
929C22#262418yes—
930C22#285418yes—
931C22C22×#12011yescharacteristic
932C22C22×#12111yescharacteristic
933C22C22×#12111yescharacteristic
934C22C22×#12111yescharacteristic
935C22C22×#12111yescharacteristic
936C22C22×#12311yescharacteristic
937C22C22×#12311yescharacteristic
938C22C2×#52511yescharacteristic
939C22C22×#12411yescharacteristic
940C22C2×#52911yescharacteristic
941C22C2×#52911yescharacteristic
942C22C2×#53211yescharacteristic
943C22C2×#53211yescharacteristic
944C22C2×#53511yescharacteristic
945C22C2×#53711yescharacteristic
946C22C2×#54011yescharacteristic
947C22C2×#54011yescharacteristic
948C22C2×#54211yescharacteristic
949C22C2×#54211yescharacteristic
950C22C2×D4211yescharacteristic
951C22C2×D4211yescharacteristic
952C22C2×D4211yescharacteristic
953C22C2×#54611yescharacteristic
954C22C2×#54611yescharacteristic
955C22C2×#54611yescharacteristic
956C22C2×#54611yescharacteristic
957C22C2×#54711yescharacteristic
958C22C2×#54711yescharacteristic
959C22C2×#54811yescharacteristic
960C22C2×#54811yescharacteristic
961C22C2×#55011yescharacteristic
962C22C2×#55011yescharacteristic
963C22C2×#55311yescharacteristic
964C22C2×#55311yescharacteristic
965C22C2×#55511yescharacteristic
966C4—44no—
967C4—48no—
968C4—44no—
969C4—48no—
970C4—44no—
971C4—44no—
972C4—44no—
973C4—84no—
974C4C2×#394116yescomplemented
975C2—48no—
976C2—88no—
977C2#15126116yesdirect product factor
978C2C22×#39411yescharacteristic
979C2C2×#262411yescharacteristic
980C2C2×#240811yescharacteristic
981C2C2×#241611yescharacteristic
982C2C2×#242211yescharacteristic
983C2C2×#242811yescharacteristic
984C2C2×#242811yescharacteristic
985C2C2×#242011yescharacteristic
986C2C2×#242711yescharacteristic
987C2C2×#242611yescharacteristic
988C2C2×#240711yescharacteristic
989C2C2×#241411yescharacteristic
990C2C2×#249111yescharacteristic
991C2C2×#249011yescharacteristic
992C2C2×#285411yescharacteristic
subgroupG/H
center, socleC25C24
commutator, Frattini, cosocleC24C25
prime radicalC23×#121C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C25 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C22×#394C2semidirect
3. C22×#390C2semidirect
4. C22×#390C2semidirect
5. C22×#389C2semidirect
6. C22×#380C2semidirect
7. C22×C4×C22⋊C4C2semidirect
8. #15126C2direct (N × H)
9. C2×#1440C2semidirect
10. C2×#1439C2semidirect
11. C2×#1438C2semidirect
12. C2×C4⋊#95C2semidirect
35. C2×#394C22semidirect
38. C2×#390C22semidirect
39. C2×#390C22semidirect
41. C2×#389C22semidirect
43. C2×#380C22semidirect
45. C2×C4×C22⋊C4C22semidirect
52. #1440C22semidirect
53. #1439C22semidirect
54. #1438C22semidirect
55. C4⋊#95C22semidirect
106. C22×C4⋊C4D4semidirect
134. C22×C22⋊C4D4semidirect
332. C2×C4⋊C4C2×D4semidirect
364. C2×C22⋊C4C2×D4semidirect
876. C2×C4#394semidirect
974. C4C2×#394semidirect
977. C2#15126direct (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×#3942
C22×#3902
C22×#3892
C22×#3802
C22×C4×C22⋊C42
#151262
C2×#14402
C2×#14392
C2×#14382
C2×C4⋊#952