Finite Group Databasebeta

← #364905

Subgroups — #364905

Order 512.

2396 conjugacy classes of subgroups.

The subgroup lattice has 857 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C8×D4C211yesmaximal, characteristic, complemented
2C2×#2537C211yesmaximal, characteristic
3C2×#1893C212yesmaximal, complemented
4C2×#1802C211yesmaximal, characteristic, complemented
5C2×C4×#102C211yesmaximal, characteristic, complemented
6#13906C211yesmaximal, characteristic, complemented
7#11199C212yesmaximal, complemented
8#10969C212yesmaximal, complemented
9#10849C211yesmaximal, characteristic, complemented
10#10841C211yesmaximal, characteristic, complemented
11#10721C212yesmaximal, complemented
12C24×C8C2212yes—
13C22×#121—21no—
14C22×#121C2212yes—
15C22×C4×D4C2211yescharacteristic
16C22×C4×D4C2211yescharacteristic
17C2×C8×D4—24no—
18C2×C8×D4—24no—
19C2×C8×D4—24no—
20C22×C4⋊C8C2211yescharacteristic
21C22×#102C2211yescharacteristic
22C22×#102C2212yes—
23C22×#102C2211yescharacteristic
24C22×C22⋊C8C2212yes—
25C22×C4×C8C2211yescharacteristic
26#2537—24no—
27#2537C418yescomplemented
28C2×#394—22no—
29C2×#390—21no—
30C2×#384C2211yescharacteristic
31C2×#384C2211yescharacteristic
32C2×#380—21no—
33C2×#380C2212yes—
34C2×#380C2212yes—
35C2×#380C2212yes—
36C2×C4×C4⋊C4C2211yescharacteristic
37#1893—28no—
38#1802—24no—
39C4×#102—24no—
40C2×#340C2212yes—
41C2×#340C2212yes—
42C2×#340C2212yes—
43C2×#340C2211yescharacteristic
44C2×#340C2211yescharacteristic
45C2×#340C2212yes—
46C2×#340C2212yes—
47#1439—22no—
48C4⋊#95—21no—
49C23×D4—22no—
50C23×D4D411yescharacteristic
51C23×D4C2311yescharacteristic
52C24×C4—21no—
53C24×C4C2312yes—
54C23×C8—24no—
55C23×C8—24no—
56C23×C8—24no—
57C23×C8—24no—
58C23×C8—24no—
59C23×C8—42no—
60C23×C8—42no—
61C23×C8C2311yescharacteristic
62C23×C8C2312yes—
63C23×C8C2311yescharacteristic
64C2×#121—28no—
65C2×#121—24no—
66C2×#121—24no—
67C2×#121—24no—
68C2×#121—42no—
69C2×#121—42no—
70C2×#121—44no—
71C2×#121—44no—
72C2×#121C2×C418yes—
73C2×C4×D4—22no—
74C2×C4×D4—22no—
75C2×C4×D4—22no—
76C2×C4×D4—22no—
77C2×C4×D4—22no—
78C2×C4×D4—22no—
79C2×C4×D4—22no—
80C2×C4×D4—22no—
81C2×C4×D4—22no—
82C2×C4×D4C2×C414yes—
83C2×C4×D4C2×C414yes—
84C2×C4×D4D414yes—
85C22×C4⋊C4—21no—
86C22×C4⋊C4—21no—
87C22×C4⋊C4—21no—
88C22×C4⋊C4—21no—
89C22×C4⋊C4D411yescharacteristic
90C22×C4⋊C4C2312yes—
91C22×C4⋊C4C2311yescharacteristic
92C22×C4⋊C4C2312yes—
93C22×C4⋊C4C2311yescharacteristic
94C22×C4⋊C4C2311yescharacteristic
95C22×C22⋊C4—22no—
96C22×C22⋊C4—21no—
97C22×C22⋊C4—22no—
98C22×C22⋊C4—22no—
99C22×C22⋊C4—22no—
100C22×C22⋊C4D412yes—
101C22×C42—21no—
102C22×C42C2311yescharacteristic
103C8×D4—232no—
104C2×C4⋊C8—22no—
105C2×C4⋊C8—22no—
106C2×C4⋊C8D414yescomplemented
107C2×#102—22no—
108C2×#102—22no—
109C2×#102—22no—
110C2×#102—22no—
111C2×#102—22no—
112C2×#102—24no—
113C2×#102—24no—
114C2×#102—42no—
115C2×#102D414yescomplemented
116C2×C22⋊C8—24no—
117C2×C22⋊C8—24no—
118C2×C22⋊C8—24no—
119C2×C4×C8—22no—
120C2×C4×C8—22no—
121C2×C4×C8D414yescomplemented
122#394—216no—
123#390—44no—
124#384—22no—
125#384—22no—
126#384—22no—
127#384C2×C414yes—
128#380—24no—
129#380—28no—
130#380—24no—
131#380—24no—
132#380—42no—
133#380—42no—
134#380C2×C418yes—
135C4×C4⋊C4—22no—
136C4×C4⋊C4—22no—
137C2×#95—22no—
138C2×#95—22no—
139C2×#95—22no—
140C2×#95—21no—
141#340—24no—
142#340—24no—
143#340—22no—
144#340—22no—
145#340—24no—
146#340—42no—
147#340—42no—
148C25—21no—
149C25C2×D412yes—
150C22×D4—28no—
151C22×D4—22no—
152C22×D4—22no—
153C22×D4—22no—
154C22×D4—22no—
155C22×D4—21no—
156C22×D4—21no—
157C22×D4—21no—
158C22×D4—21no—
159C22×D4—21no—
160C22×D4—21no—
161C22×D4—21no—
162C22×D4—21no—
163C22×D4—21no—
164C22×D4—21no—
165C22×D4—21no—
166C22×D4—44no—
167C22×D4—44no—
168C22×D4—44no—
169C22×D4—44no—
170C22×D4—82no—
171C22×D4—82no—
172C22×D4C22⋊C414yes—
173C22×D4D814yes—
174C22×D4SD1614yes—
175C22×D4C22×C412yes—
176C22×D4C2×D412yes—
177C22×D4#4112yes—
178C23×C4—22no—
179C23×C4—22no—
180C23×C4—22no—
181C23×C4—22no—
182C23×C4—22no—
183C23×C4—22no—
184C23×C4—22no—
185C23×C4—22no—
186C23×C4—22no—
187C23×C4—22no—
188C23×C4—22no—
189C23×C4—22no—
190C23×C4—21no—
191C23×C4—22no—
192C23×C4—21no—
193C23×C4—21no—
194C23×C4—24no—
195C23×C4—22no—
196C23×C4—42no—
197C23×C4—42no—
198C23×C4—42no—
199C23×C4—42no—
200C23×C4—42no—
201C23×C4—42no—
202C23×C4C22×C414yes—
203C23×C4C2×D412yes—
204C23×C4C2×D414yes—
205C23×C4C2×D411yescharacteristic
206C23×C4C2×D411yescharacteristic
207C23×C4C2411yescharacteristic
208C22×C8—21no—
209C22×C8—21no—
210C22×C8—21no—
211C22×C8—21no—
212C22×C8—216no—
213C22×C8—22no—
214C22×C8—22no—
215C22×C8—22no—
216C22×C8—21no—
217C22×C8—21no—
218C22×C8—22no—
219C22×C8—21no—
220C22×C8—21no—
221C22×C8—22no—
222C22×C8—22no—
223C22×C8—21no—
224C22×C8—21no—
225C22×C8—48no—
226C22×C8—48no—
227C22×C8—48no—
228C22×C8—48no—
229C22×C8—48no—
230C22×C8—48no—
231C22×C8C2×D414yes—
232C22×C8C2×D412yes—
233C22×C8C2×D412yes—
234C22×C8C2×D412yes—
235C22×C8#4112yes—
236#121—216no—
237#121—48no—
238#121—48no—
239#121—48no—
240#121—432no—
241C4×D4—28no—
242C4×D4—28no—
243C4×D4—28no—
244C4×D4—28no—
245C4×D4—28no—
246C4×D4—28no—
247C4×D4—44no—
248C4×D4—44no—
249C2×C4⋊C4—22no—
250C2×C4⋊C4—22no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—22no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—22no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—22no—
264C2×C4⋊C4—22no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—24no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—22no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—22no—
273C2×C4⋊C4—22no—
274C2×C4⋊C4—22no—
275C2×C4⋊C4—22no—
276C2×C4⋊C4—22no—
277C2×C4⋊C4—22no—
278C2×C4⋊C4—24no—
279C2×C4⋊C4—42no—
280C2×C4⋊C4—42no—
281C2×C4⋊C4—42no—
282C2×C4⋊C4—42no—
283C2×C4⋊C4—42no—
284C2×C4⋊C4—42no—
285C2×C4⋊C4—81no—
286C2×C4⋊C4—81no—
287C2×C4⋊C4—81no—
288C2×C4⋊C4—81no—
289C2×C4⋊C4C22⋊C414yes—
290C2×C4⋊C4C22×C412yes—
291C2×C4⋊C4C22×C414yes—
292C2×C4⋊C4C2×D412yes—
293C2×C4⋊C4#4112yes—
294C2×C22⋊C4—24no—
295C2×C22⋊C4—24no—
296C2×C22⋊C4—28no—
297C2×C22⋊C4—24no—
298C2×C22⋊C4—28no—
299C2×C22⋊C4—44no—
300C2×C22⋊C4—44no—
301C2×C22⋊C4—44no—
302C2×C22⋊C4—44no—
303C2×C22⋊C4—42no—
304C2×C22⋊C4—42no—
305C2×C22⋊C4—44no—
306C2×C22⋊C4—44no—
307C2×C22⋊C4—44no—
308C2×C22⋊C4—44no—
309C2×C22⋊C4—82no—
310C2×C22⋊C4—82no—
311C2×C22⋊C4C22⋊C418yes—
312C2×C42—42no—
313C2×C42—42no—
314C2×C42—42no—
315C2×C42C22×C412yes—
316C2×C42C2×D412yes—
317C2×C42C2×D412yes—
318C2×C42C2×D412yes—
319C2×C42#4112yes—
320C2×C42#4112yes—
321C4⋊C8—28no—
322#102—28no—
323#102—28no—
324#102—48no—
325C22⋊C8—216no—
326C4×C8—28no—
327#95—28no—
328#95—44no—
329#95—44no—
330#95—42no—
331C24—22no—
332C24—22no—
333C24—22no—
334C24—22no—
335C24—22no—
336C24—22no—
337C24—22no—
338C24—22no—
339C24—22no—
340C24—22no—
341C24—22no—
342C24—22no—
343C24—22no—
344C24—22no—
345C24—22no—
346C24—41no—
347C24—41no—
348C24—41no—
349C24—41no—
350C24—41no—
351C24—41no—
352C24—41no—
353C24—41no—
354C24—41no—
355C24—41no—
356C24—41no—
357C24—41no—
358C24C2×C22⋊C414yes—
359C24C2×D814yes—
360C24C2×SD1614yes—
361C24C22×D411yescharacteristic
362C2×D4—22no—
363C2×D4—22no—
364C2×D4—22no—
365C2×D4—22no—
366C2×D4—22no—
367C2×D4—22no—
368C2×D4—22no—
369C2×D4—22no—
370C2×D4—22no—
371C2×D4—22no—
372C2×D4—22no—
373C2×D4—22no—
374C2×D4—22no—
375C2×D4—22no—
376C2×D4—22no—
377C2×D4—28no—
378C2×D4—28no—
379C2×D4—28no—
380C2×D4—28no—
381C2×D4—28no—
382C2×D4—28no—
383C2×D4—416no—
384C2×D4—416no—
385C2×D4—41no—
386C2×D4—41no—
387C2×D4—41no—
388C2×D4—41no—
389C2×D4—41no—
390C2×D4—41no—
391C2×D4—41no—
392C2×D4—41no—
393C2×D4—41no—
394C2×D4—41no—
395C2×D4—41no—
396C2×D4—41no—
397C2×D4—88no—
398C2×D4—88no—
399C2×D4—88no—
400C2×D4—88no—
401C2×D4—88no—
402C2×D4#102116yescomplemented
403C2×D4C4×D414yes—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—24no—
415C22×C4—24no—
416C22×C4—24no—
417C22×C4—24no—
418C22×C4—24no—
419C22×C4—24no—
420C22×C4—24no—
421C22×C4—24no—
422C22×C4—24no—
423C22×C4—24no—
424C22×C4—24no—
425C22×C4—24no—
426C22×C4—22no—
427C22×C4—24no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—42no—
431C22×C4—42no—
432C22×C4—42no—
433C22×C4—42no—
434C22×C4—42no—
435C22×C4—42no—
436C22×C4—42no—
437C22×C4—42no—
438C22×C4—42no—
439C22×C4—42no—
440C22×C4—42no—
441C22×C4—42no—
442C22×C4—42no—
443C22×C4—42no—
444C22×C4—42no—
445C22×C4—42no—
446C22×C4—41no—
447C22×C4—41no—
448C22×C4—41no—
449C22×C4—41no—
450C22×C4—42no—
451C22×C4—42no—
452C22×C4—41no—
453C22×C4—41no—
454C22×C4—41no—
455C22×C4—41no—
456C22×C4—41no—
457C22×C4—42no—
458C22×C4—41no—
459C22×C4—42no—
460C22×C4—41no—
461C22×C4—41no—
462C22×C4—41no—
463C22×C4—41no—
464C22×C4—41no—
465C22×C4—42no—
466C22×C4—41no—
467C22×C4—42no—
468C22×C4—41no—
469C22×C4—41no—
470C22×C4—48no—
471C22×C4—48no—
472C22×C4—48no—
473C22×C4—42no—
474C22×C4—42no—
475C22×C4—42no—
476C22×C4—42no—
477C22×C4—42no—
478C22×C4—42no—
479C22×C4—42no—
480C22×C4—84no—
481C22×C4—84no—
482C22×C4—84no—
483C22×C4—84no—
484C22×C4C2×C22⋊C414yes—
485C22×C4C2×C22⋊C412yes—
486C22×C4C2×C22⋊C412yes—
487C22×C4#12112yes—
488C22×C4#12112yes—
489C22×C4#12112yes—
490C22×C4#12112yes—
491C22×C4C2×D812yes—
492C22×C4C2×SD1612yes—
493C22×C4#13512yes—
494C22×C4#13512yes—
495C22×C4C23×C411yescharacteristic
496C22×C4C22×D411yescharacteristic
497C22×C4C22×D411yescharacteristic
498C22×C4C22×D411yescharacteristic
499C22×C4C22×D411yescharacteristic
500C22×C4C2×#4111yescharacteristic
501C22×C4C2×#4111yescharacteristic
502C22×C4C2×#4111yescharacteristic
503C22×C4C2×#4111yescharacteristic
504C22×C4C2×#4111yescharacteristic
505C22×C4H(5,𝔽2)11yescharacteristic
506C22×C4H(5,𝔽2)11yescharacteristic
507C22×C4H(5,𝔽2)11yescharacteristic
508C22×C42−1+411yescharacteristic
509C2×C8—22no—
510C2×C8—22no—
511C2×C8—22no—
512C2×C8—22no—
513C2×C8—22no—
514C2×C8—22no—
515C2×C8—22no—
516C2×C8—24no—
517C2×C8—22no—
518C2×C8—22no—
519C2×C8—24no—
520C2×C8—24no—
521C2×C8—432no—
522C2×C8—42no—
523C2×C8—42no—
524C2×C8—42no—
525C2×C8—41no—
526C2×C8—42no—
527C2×C8—41no—
528C2×C8—41no—
529C2×C8—41no—
530C2×C8#12114yescomplemented
531C4⋊C4—28no—
532C4⋊C4—22no—
533C4⋊C4—22no—
534C4⋊C4—24no—
535C4⋊C4—24no—
536C4⋊C4—22no—
537C4⋊C4—22no—
538C4⋊C4—22no—
539C4⋊C4—22no—
540C4⋊C4—41no—
541C4⋊C4—41no—
542C4⋊C4—41no—
543C4⋊C4—41no—
544C4⋊C4—42no—
545C4⋊C4—42no—
546C4⋊C4—41no—
547C4⋊C4—41no—
548C4⋊C4—48no—
549C4⋊C4—42no—
550C4⋊C4—42no—
551C4⋊C4—42no—
552C4⋊C4—42no—
553C4⋊C4—84no—
554C4⋊C4—84no—
555C4⋊C4—84no—
556C22⋊C4—216no—
557C22⋊C4—416no—
558C22⋊C4—416no—
559C22⋊C4—48no—
560C22⋊C4—88no—
561C22⋊C4—88no—
562C42—84no—
563C42C4×D414yes—
564C42C4×D414yes—
565C42#12014yes—
566C42#12314yes—
567C23—24no—
568C23—24no—
569C23—24no—
570C23—24no—
571C23—24no—
572C23—24no—
573C23—24no—
574C23—24no—
575C23—24no—
576C23—24no—
577C23—24no—
578C23—24no—
579C23—24no—
580C23—24no—
581C23—24no—
582C23—24no—
583C23—24no—
584C23—24no—
585C23—24no—
586C23—42no—
587C23—42no—
588C23—42no—
589C23—42no—
590C23—42no—
591C23—42no—
592C23—42no—
593C23—42no—
594C23—42no—
595C23—42no—
596C23—42no—
597C23—42no—
598C23—42no—
599C23—42no—
600C23—42no—
601C23—42no—
602C23—42no—
603C23—42no—
604C23—42no—
605C23—42no—
606C23—42no—
607C23—42no—
608C23—42no—
609C23—42no—
610C23—42no—
611C23—42no—
612C23—42no—
613C23—42no—
614C23—42no—
615C23—42no—
616C23—42no—
617C23—42no—
618C23—42no—
619C23—42no—
620C23—81no—
621C23—81no—
622C23—81no—
623C23—81no—
624C23—81no—
625C23—81no—
626C23—81no—
627C23—81no—
628C23—81no—
629C23—81no—
630C23—81no—
631C23—81no—
632C23—81no—
633C23—81no—
634C23—81no—
635C23—81no—
636C23C2×#10218yes—
637C23C22×C22⋊C411yescharacteristic
638C23C2×#12111yescharacteristic
639C23C2×#12111yescharacteristic
640C23D4211yescharacteristic
641C23#54611yescharacteristic
642C23#54611yescharacteristic
643C23#54711yescharacteristic
644C23C22×D811yescharacteristic
645C23C22×SD1611yescharacteristic
646C23C2×#13511yescharacteristic
647C23C2×#13511yescharacteristic
648C23#57611yescharacteristic
649C23#57711yescharacteristic
650C23#57711yescharacteristic
651C23#57811yescharacteristic
652D4—24no—
653D4—232no—
654D4—24no—
655D4—42no—
656D4—42no—
657D4—42no—
658D4—42no—
659D4—42no—
660D4—42no—
661D4—832no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—24no—
669C2×C4—24no—
670C2×C4—24no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—44no—
676C2×C4—44no—
677C2×C4—44no—
678C2×C4—44no—
679C2×C4—44no—
680C2×C4—44no—
681C2×C4—44no—
682C2×C4—44no—
683C2×C4—44no—
684C2×C4—42no—
685C2×C4—44no—
686C2×C4—42no—
687C2×C4—44no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—81no—
696C2×C4—81no—
697C2×C4—82no—
698C2×C4—82no—
699C2×C4—81no—
700C2×C4—82no—
701C2×C4—82no—
702C2×C4—81no—
703C2×C4—81no—
704C2×C4—81no—
705C2×C4—81no—
706C2×C4—81no—
707C2×C4—81no—
708C2×C4—81no—
709C2×C4—81no—
710C2×C4—81no—
711C2×C4—816no—
712C2×C4—82no—
713C2×C4—82no—
714C2×C4—82no—
715C2×C4—82no—
716C2×C4—82no—
717C2×C4—82no—
718C2×C4—82no—
719C2×C4#38614yes—
720C2×C4#38614yes—
721C2×C4C2×#10214yes—
722C2×C4#41614yes—
723C2×C4#46514yes—
724C2×C4#46514yes—
725C2×C4#46614yes—
726C2×C4#46614yes—
727C2×C4C2×C4×D411yescharacteristic
728C2×C4C2×C4×D411yescharacteristic
729C2×C4C2×C4×D411yescharacteristic
730C2×C4C4×#4111yescharacteristic
731C2×C4#51811yescharacteristic
732C2×C4#52011yescharacteristic
733C2×C4C2×#12011yescharacteristic
734C2×C4C2×#12111yescharacteristic
735C2×C4C2×#12311yescharacteristic
736C2×C4#52511yescharacteristic
737C2×C4#52911yescharacteristic
738C2×C4#53211yescharacteristic
739C2×C4#53511yescharacteristic
740C2×C4#53711yescharacteristic
741C2×C4#54011yescharacteristic
742C2×C4#54211yescharacteristic
743C2×C4D4211yescharacteristic
744C2×C4D4211yescharacteristic
745C2×C4#54611yescharacteristic
746C2×C4#54611yescharacteristic
747C2×C4#54611yescharacteristic
748C2×C4#54711yescharacteristic
749C2×C4#54711yescharacteristic
750C2×C4#54811yescharacteristic
751C2×C4#55011yescharacteristic
752C2×C4#55311yescharacteristic
753C2×C4#55311yescharacteristic
754C2×C4#55511yescharacteristic
755C8—24no—
756C8—42no—
757C8—44no—
758C22—28no—
759C22—28no—
760C22—28no—
761C22—44no—
762C22—44no—
763C22—44no—
764C22—44no—
765C22—44no—
766C22—44no—
767C22—44no—
768C22—44no—
769C22—44no—
770C22—44no—
771C22—44no—
772C22—44no—
773C22—44no—
774C22—44no—
775C22—44no—
776C22—82no—
777C22—82no—
778C22—82no—
779C22—82no—
780C22—82no—
781C22—82no—
782C22—82no—
783C22—82no—
784C22—82no—
785C22—82no—
786C22—82no—
787C22—82no—
788C22C2×#38611yescharacteristic
789C22D4×C22⋊C411yescharacteristic
790C22#233911yescharacteristic
791C22#242711yescharacteristic
792C22#242811yescharacteristic
793C22#253511yescharacteristic
794C22#253711yescharacteristic
795C22C22×#10211yescharacteristic
796C22C2×#41611yescharacteristic
797C22#289711yescharacteristic
798C22#289811yescharacteristic
799C22C2×#46511yescharacteristic
800C22C2×#46511yescharacteristic
801C22C2×#46611yescharacteristic
802C22C2×#46611yescharacteristic
803C22#306011yescharacteristic
804C22#306111yescharacteristic
805C22#306211yescharacteristic
806C22#306311yescharacteristic
807C22D4×D811yescharacteristic
808C22D4×SD1611yescharacteristic
809C22#328311yescharacteristic
810C22#328411yescharacteristic
811C22#329411yescharacteristic
812C22#329411yescharacteristic
813C22#329511yescharacteristic
814C22#329811yescharacteristic
815C22#330211yescharacteristic
816C22#330311yescharacteristic
817C22#330311yescharacteristic
818C22#330511yescharacteristic
819C22#333411yescharacteristic
820C22#333511yescharacteristic
821C22#334011yescharacteristic
822C22#334111yescharacteristic
823C4—24no—
824C4—44no—
825C4—82no—
826C4—84no—
827C4—82no—
828C4—82no—
829C4—162no—
830C4#189318yescomplemented
831C4C4×#12111yescharacteristic
832C4#232411yescharacteristic
833C4#236111yescharacteristic
834C4#236311yescharacteristic
835C4#240711yescharacteristic
836C4#240811yescharacteristic
837C4#242011yescharacteristic
838C4#242211yescharacteristic
839C2—48no—
840C2—84no—
841C2#1397011yescharacteristic
842C2C2×#189311yescharacteristic
843C2#2097611yescharacteristic
844C2D4×#10211yescharacteristic
845C2#2241711yescharacteristic
846C2#2248511yescharacteristic
847C2#2248911yescharacteristic
848C2#2533811yescharacteristic
849C2#2533911yescharacteristic
850C2#2538411yescharacteristic
851C2#2538511yescharacteristic
852C2#2814011yescharacteristic
853C2#2814111yescharacteristic
854C2#2822311yescharacteristic
855C2#2822711yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC2×#2537C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C22×C4×D4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C22×C8×D4C2semidirect
3. C2×#1893C2semidirect
4. C2×#1802C2semidirect
5. C2×C4×#102C2semidirect
6. #13906C2semidirect
7. #11199C2semidirect
8. #10969C2semidirect
9. #10849C2semidirect
10. #10841C2semidirect
11. #10721C2semidirect
27. #2537C4semidirect
106. C2×C4⋊C8D4semidirect
115. C2×#102D4semidirect
121. C2×C4×C8D4semidirect
402. C2×D4#102semidirect
530. C2×C8#121semidirect
830. C4#1893semidirect

Maximal subgroups

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

subgroupindex
C22×C8×D42
C2×#25372
C2×#18932
C2×#18022
C2×C4×#1022
#139062
#111992
#109692
#108492
#108412
#107212