Finite Group Databasebeta

← #364889

Subgroups — #364889

Order 512.

2472 conjugacy classes of subgroups.

The subgroup lattice has 870 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#459C211yesmaximal, characteristic
2C2×#2366C211yesmaximal, characteristic, complemented
3C2×#1957C211yesmaximal, characteristic, complemented
4C2×#1879C212yesmaximal, complemented
5C2×C4×#102C211yesmaximal, characteristic, complemented
6#13906C211yesmaximal, characteristic, complemented
7#11189C212yesmaximal, complemented
8#11022C212yesmaximal, complemented
9#10849C211yesmaximal, characteristic, complemented
10#10834C211yesmaximal, characteristic, complemented
11#10788C212yesmaximal, complemented
12C23×D8C2212yes—
13C22×#127C2211yescharacteristic
14C22×C4×D4—21no—
15C22×C4×D4C2211yescharacteristic
16C22×C4×D4C2212yes—
17C2×#459—24no—
18C2×#459—24no—
19C2×#459C418yescomplemented
20C22×C4⋊C8C2211yescharacteristic
21C22×#102C2211yescharacteristic
22C22×#102C2212yes—
23C22×#102C2212yes—
24C22×#102C2212yes—
25C22×#102C2211yescharacteristic
26C22×C4×C8C2211yescharacteristic
27#2366—24no—
28#2366—24no—
29C2×#390—21no—
30C2×#390C2212yes—
31C2×#390C2212yes—
32C2×#386—22no—
33C2×#384C2211yescharacteristic
34C2×#380—21no—
35C2×#380—21no—
36C2×C4×C4⋊C4C2211yescharacteristic
37C2×C4×C4⋊C4C2211yescharacteristic
38#1957—24no—
39#1879—28no—
40C4×#102—24no—
41C2×#340C2211yescharacteristic
42C2×#340C2212yes—
43C2×#340C2211yescharacteristic
44C2×#340C2212yes—
45C2×#336C2212yes—
46C2×#336C2212yes—
47#1439—22no—
48C4⋊#95C2212yes—
49C23×D4—21no—
50C23×D4—21no—
51C23×D4C2312yes—
52C23×D4C2311yescharacteristic
53C24×C4—21no—
54C24×C4—22no—
55C22×D8—24no—
56C22×D8—24no—
57C22×D8—24no—
58C22×D8—24no—
59C22×D8—42no—
60C22×D8—42no—
61C22×D8C2×C418yescomplemented
62C23×C8C2312yes—
63C23×C8C2311yescharacteristic
64C23×C8C2311yescharacteristic
65C2×#127—22no—
66C2×#127—22no—
67C2×#127—22no—
68C2×#127C2×C414yes—
69C2×#127D414yes—
70C2×#127D414yes—
71C2×C4×D4—28no—
72C2×C4×D4—24no—
73C2×C4×D4—24no—
74C2×C4×D4—24no—
75C2×C4×D4—24no—
76C2×C4×D4—22no—
77C2×C4×D4—22no—
78C2×C4×D4—22no—
79C2×C4×D4—22no—
80C2×C4×D4—22no—
81C2×C4×D4—42no—
82C2×C4×D4—42no—
83C2×C4×D4—44no—
84C2×C4×D4—44no—
85C2×C4×D4C2×C414yescomplemented
86C22×C4⋊C4—21no—
87C22×C4⋊C4—21no—
88C22×C4⋊C4D411yescharacteristic
89C22×C4⋊C4D411yescharacteristic
90C22×C4⋊C4C2312yes—
91C22×C4⋊C4C2311yescharacteristic
92C22×C4⋊C4C2311yescharacteristic
93C22×C4⋊C4C2311yescharacteristic
94C22×C22⋊C4—22no—
95C22×C22⋊C4—21no—
96C22×C22⋊C4—22no—
97C22×C22⋊C4—22no—
98C22×C22⋊C4—22no—
99C22×C22⋊C4—22no—
100C22×C42—21no—
101C22×C42C2312yes—
102C22×C42C2311yescharacteristic
103#459—232no—
104C2×C4⋊C8—22no—
105C2×C4⋊C8—22no—
106C2×C4⋊C8C2×C414yescomplemented
107C2×#102—24no—
108C2×#102—24no—
109C2×#102—22no—
110C2×#102—22no—
111C2×#102—22no—
112C2×#102—22no—
113C2×#102—22no—
114C2×#102—24no—
115C2×#102—24no—
116C2×#102—24no—
117C2×#102—24no—
118C2×#102—42no—
119C2×#102—42no—
120C2×#102C2×C418yescomplemented
121C2×#102D414yescomplemented
122C2×C4×C8—22no—
123C2×C4×C8—22no—
124C2×C4×C8—22no—
125#390—28no—
126#390—24no—
127#390—24no—
128#390—24no—
129#390—42no—
130#386—216no—
131#384—22no—
132#384—22no—
133#380—44no—
134#380—44no—
135C4×C4⋊C4—22no—
136C4×C4⋊C4—22no—
137C4×C4⋊C4—22no—
138C4×C4⋊C4D414yes—
139C2×#95—21no—
140C2×#95—22no—
141C2×#95—22no—
142C2×#95D412yes—
143#340—24no—
144#340—22no—
145#340—22no—
146#340—42no—
147#336—24no—
148#336—42no—
149C25—21no—
150C25—22no—
151C22×D4—24no—
152C22×D4—24no—
153C22×D4—24no—
154C22×D4—24no—
155C22×D4—24no—
156C22×D4—24no—
157C22×D4—21no—
158C22×D4—21no—
159C22×D4—22no—
160C22×D4—21no—
161C22×D4—22no—
162C22×D4—21no—
163C22×D4—22no—
164C22×D4—22no—
165C22×D4—21no—
166C22×D4—21no—
167C22×D4—22no—
168C22×D4—21no—
169C22×D4—22no—
170C22×D4—22no—
171C22×D4—22no—
172C22×D4—22no—
173C22×D4—21no—
174C22×D4—21no—
175C22×D4—22no—
176C22×D4—21no—
177C22×D4—22no—
178C22×D4—21no—
179C22×D4—42no—
180C22×D4—42no—
181C22×D4—42no—
182C22×D4—42no—
183C22×D4—81no—
184C22×D4—81no—
185C22×D4—81no—
186C22×D4—81no—
187C22×D4C22×C414yes—
188C22×D4C22×C412yes—
189C22×D4C2×D414yes—
190C22×D4C2×D414yes—
191C22×D4C2×D412yes—
192C22×D4#4112yes—
193C23×C4—21no—
194C23×C4—21no—
195C23×C4—21no—
196C23×C4—28no—
197C23×C4—24no—
198C23×C4—22no—
199C23×C4—44no—
200C23×C4—44no—
201C23×C4—44no—
202C23×C4—42no—
203C23×C4—42no—
204C23×C4—44no—
205C23×C4—42no—
206C23×C4—42no—
207C23×C4—42no—
208C23×C4—42no—
209C23×C4—82no—
210C23×C4—82no—
211C23×C4C2×D412yes—
212C23×C4C2×D412yes—
213C23×C4C2×D411yescharacteristic
214C23×C4C2×D411yescharacteristic
215C23×C4C2411yescharacteristic
216C2×D8—216no—
217C2×D8—216no—
218C2×D8—48no—
219C2×D8—48no—
220C2×D8—48no—
221C2×D8—48no—
222C2×D8—48no—
223C22×C8—22no—
224C22×C8—22no—
225C22×C8—22no—
226C22×C8—21no—
227C22×C8—21no—
228C22×C8—21no—
229C22×C8—21no—
230C22×C8—22no—
231C22×C8—21no—
232C22×C8—21no—
233C22×C8—21no—
234C22×C8—21no—
235C22×C8—22no—
236C22×C8—22no—
237C22×C8—21no—
238C22×C8—21no—
239C22×C8—21no—
240C22×C8—21no—
241C22×C8C22×C414yes—
242C22×C8C2×D412yes—
243C22×C8#4112yes—
244#127—28no—
245#127—28no—
246#127—28no—
247#127C22⋊C4116yescomplemented
248C4×D4—28no—
249C4×D4—28no—
250C4×D4—48no—
251C4×D4—48no—
252C4×D4—48no—
253C4×D4—432no—
254C4×D4—48no—
255C4×D4—44no—
256C4×D4—44no—
257C2×C4⋊C4—22no—
258C2×C4⋊C4—22no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—22no—
271C2×C4⋊C4—22no—
272C2×C4⋊C4—22no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—22no—
276C2×C4⋊C4—22no—
277C2×C4⋊C4—22no—
278C2×C4⋊C4—22no—
279C2×C4⋊C4—22no—
280C2×C4⋊C4—22no—
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⋊C4D814yescomplemented
288C2×C4⋊C4C22×C412yes—
289C2×C4⋊C4C2×D412yes—
290C2×C4⋊C4C2×D412yes—
291C2×C4⋊C4C2×D412yes—
292C2×C4⋊C4#4112yes—
293C2×C22⋊C4—28no—
294C2×C22⋊C4—28no—
295C2×C22⋊C4—24no—
296C2×C22⋊C4—28no—
297C2×C22⋊C4—44no—
298C2×C22⋊C4—44no—
299C2×C22⋊C4—44no—
300C2×C22⋊C4—42no—
301C2×C22⋊C4—42no—
302C2×C22⋊C4—44no—
303C2×C22⋊C4—44no—
304C2×C22⋊C4—44no—
305C2×C22⋊C4—44no—
306C2×C22⋊C4—44no—
307C2×C22⋊C4—82no—
308C2×C22⋊C4—82no—
309C2×C22⋊C4—82no—
310C2×C22⋊C4—82no—
311C2×C42—24no—
312C2×C42—22no—
313C2×C42—22no—
314C2×C42—22no—
315C2×C42—22no—
316C2×C42—22no—
317C2×C42—22no—
318C2×C42—42no—
319C2×C42—42no—
320C2×C42C22×C412yes—
321C2×C42C2×D412yes—
322C2×C42C2×D412yes—
323C2×C42C2×D412yes—
324C2×C42#4112yes—
325C2×C42#4112yes—
326C4⋊C8—28no—
327#102—28no—
328#102—216no—
329#102—28no—
330#102—48no—
331#102—48no—
332C4×C8—44no—
333#95—24no—
334#95—24no—
335#95—44no—
336#95—44no—
337C24—22no—
338C24—24no—
339C24—24no—
340C24—24no—
341C24—22no—
342C24—22no—
343C24—41no—
344C24—41no—
345C24—42no—
346C24—42no—
347C24—41no—
348C24—42no—
349C24—41no—
350C24—42no—
351C24—41no—
352C24—42no—
353C24—41no—
354C24—42no—
355C24—41no—
356C24—42no—
357C24—41no—
358C24—42no—
359C24—41no—
360C24—41no—
361C24—42no—
362C24—42no—
363C24—42no—
364C24—42no—
365C24—41no—
366C24—41no—
367C24C22×D411yescharacteristic
368C2×D4—22no—
369C2×D4—22no—
370C2×D4—24no—
371C2×D4—24no—
372C2×D4—24no—
373C2×D4—22no—
374C2×D4—22no—
375C2×D4—24no—
376C2×D4—24no—
377C2×D4—22no—
378C2×D4—22no—
379C2×D4—24no—
380C2×D4—24no—
381C2×D4—22no—
382C2×D4—22no—
383C2×D4—22no—
384C2×D4—24no—
385C2×D4—24no—
386C2×D4—22no—
387C2×D4—22no—
388C2×D4—24no—
389C2×D4—24no—
390C2×D4—22no—
391C2×D4—22no—
392C2×D4—24no—
393C2×D4—24no—
394C2×D4—24no—
395C2×D4—24no—
396C2×D4—22no—
397C2×D4—22no—
398C2×D4—216no—
399C2×D4—216no—
400C2×D4—41no—
401C2×D4—42no—
402C2×D4—41no—
403C2×D4—42no—
404C2×D4—42no—
405C2×D4—42no—
406C2×D4—42no—
407C2×D4—41no—
408C2×D4—41no—
409C2×D4—42no—
410C2×D4—41no—
411C2×D4—42no—
412C2×D4—41no—
413C2×D4—42no—
414C2×D4—41no—
415C2×D4—41no—
416C2×D4—41no—
417C2×D4—41no—
418C2×D4—42no—
419C2×D4—42no—
420C2×D4—41no—
421C2×D4—42no—
422C2×D4—42no—
423C2×D4—41no—
424C2×D4—48no—
425C2×D4—48no—
426C2×D4—48no—
427C2×D4—48no—
428C2×D4—48no—
429C2×D4—48no—
430C2×D4—84no—
431C2×D4—84no—
432C2×D4—84no—
433C2×D4—84no—
434C2×D4—84no—
435C2×D4—84no—
436C2×D4C2×C22⋊C418yes—
437C2×D4C4×D414yescomplemented
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—416no—
461C22×C4—416no—
462C22×C4—41no—
463C22×C4—41no—
464C22×C4—41no—
465C22×C4—41no—
466C22×C4—41no—
467C22×C4—41no—
468C22×C4—41no—
469C22×C4—41no—
470C22×C4—41no—
471C22×C4—41no—
472C22×C4—41no—
473C22×C4—41no—
474C22×C4—41no—
475C22×C4—41no—
476C22×C4—41no—
477C22×C4—41no—
478C22×C4—48no—
479C22×C4—48no—
480C22×C4—48no—
481C22×C4—42no—
482C22×C4—42no—
483C22×C4—42no—
484C22×C4—42no—
485C22×C4—42no—
486C22×C4—42no—
487C22×C4—42no—
488C22×C4—88no—
489C22×C4—88no—
490C22×C4—88no—
491C22×C4—88no—
492C22×C4—88no—
493C22×C4—84no—
494C22×C4—84no—
495C22×C4—84no—
496C22×C4—84no—
497C22×C4C4×D412yes—
498C22×C4C4×D412yes—
499C22×C4#12012yes—
500C22×C4#12012yes—
501C22×C4#12112yes—
502C22×C4#12112yes—
503C22×C4C2×D814yes—
504C22×C4C2×D812yes—
505C22×C4#13512yes—
506C22×C4AGL(1,ℤ/8)12yes—
507C22×C4AGL(1,ℤ/8)12yes—
508C22×C4C23×C411yescharacteristic
509C22×C4C22×D411yescharacteristic
510C22×C4C22×D411yescharacteristic
511C22×C4C22×D411yescharacteristic
512C22×C4C22×D411yescharacteristic
513C22×C4C2×#4111yescharacteristic
514C22×C4C2×#4111yescharacteristic
515C22×C4C2×#4111yescharacteristic
516C22×C4C2×#4111yescharacteristic
517C22×C4C2×#4111yescharacteristic
518C22×C4H(5,𝔽2)11yescharacteristic
519C22×C4H(5,𝔽2)11yescharacteristic
520C22×C4H(5,𝔽2)11yescharacteristic
521C22×C42−1+411yescharacteristic
522D8—432no—
523C2×C8—24no—
524C2×C8—24no—
525C2×C8—24no—
526C2×C8—22no—
527C2×C8—22no—
528C2×C8—22no—
529C2×C8—22no—
530C2×C8—22no—
531C2×C8—22no—
532C2×C8—41no—
533C2×C8—41no—
534C2×C8—41no—
535C2×C8—41no—
536C2×C8—42no—
537C2×C8—42no—
538C2×C8—41no—
539C2×C8—42no—
540C2×C8—42no—
541C2×C8—41no—
542C2×C8—41no—
543C2×C8—41no—
544C4⋊C4—22no—
545C4⋊C4—22no—
546C4⋊C4—22no—
547C4⋊C4—28no—
548C4⋊C4—22no—
549C4⋊C4—22no—
550C4⋊C4—22no—
551C4⋊C4—22no—
552C4⋊C4—41no—
553C4⋊C4—41no—
554C4⋊C4—41no—
555C4⋊C4—41no—
556C4⋊C4—44no—
557C4⋊C4—42no—
558C4⋊C4—42no—
559C4⋊C4—42no—
560C4⋊C4—42no—
561C4⋊C4—84no—
562C4⋊C4—84no—
563C4⋊C4#12114yes—
564C22⋊C4—416no—
565C22⋊C4—416no—
566C22⋊C4—48no—
567C22⋊C4—88no—
568C22⋊C4—88no—
569C22⋊C4—88no—
570C42—42no—
571C42—42no—
572C42—42no—
573C42—42no—
574C42—48no—
575C42C2×C22⋊C414yes—
576C42C4×D414yes—
577C42#12114yes—
578C42#12314yes—
579C23—24no—
580C23—28no—
581C23—42no—
582C23—42no—
583C23—42no—
584C23—42no—
585C23—44no—
586C23—42no—
587C23—44no—
588C23—42no—
589C23—44no—
590C23—44no—
591C23—42no—
592C23—42no—
593C23—44no—
594C23—42no—
595C23—44no—
596C23—42no—
597C23—44no—
598C23—42no—
599C23—44no—
600C23—44no—
601C23—44no—
602C23—42no—
603C23—42no—
604C23—44no—
605C23—44no—
606C23—44no—
607C23—44no—
608C23—42no—
609C23—42no—
610C23—42no—
611C23—42no—
612C23—44no—
613C23—44no—
614C23—44no—
615C23—44no—
616C23—42no—
617C23—82no—
618C23—81no—
619C23—82no—
620C23—82no—
621C23—82no—
622C23—82no—
623C23—81no—
624C23—82no—
625C23—81no—
626C23—82no—
627C23—82no—
628C23—81no—
629C23—81no—
630C23—82no—
631C23—81no—
632C23—81no—
633C23—81no—
634C23—81no—
635C23—82no—
636C23—82no—
637C23—82no—
638C23—82no—
639C23—81no—
640C23—81no—
641C23—82no—
642C23—81no—
643C23—81no—
644C23—81no—
645C23—82no—
646C23—81no—
647C23—82no—
648C23—81no—
649C23C2×C4×D411yescharacteristic
650C23C2×#12011yescharacteristic
651C23C2×#12111yescharacteristic
652C23D4211yescharacteristic
653C23#54611yescharacteristic
654C23#54811yescharacteristic
655C23#55011yescharacteristic
656C23C22×D811yescharacteristic
657C23C2×#13511yescharacteristic
658C23C2×AGL(1,ℤ/8)11yescharacteristic
659C23C2×AGL(1,ℤ/8)11yescharacteristic
660C23#57611yescharacteristic
661C23#57611yescharacteristic
662C23#57711yescharacteristic
663C23#57711yescharacteristic
664D4—24no—
665D4—28no—
666D4—28no—
667D4—24no—
668D4—42no—
669D4—44no—
670D4—42no—
671D4—432no—
672D4—44no—
673D4—42no—
674D4—44no—
675D4—42no—
676D4—44no—
677D4—42no—
678D4—42no—
679D4—44no—
680D4—44no—
681D4—816no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—24no—
689C2×C4—24no—
690C2×C4—24no—
691C2×C4—24no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—832no—
716C2×C4—81no—
717C2×C4—81no—
718C2×C4—81no—
719C2×C4—81no—
720C2×C4—81no—
721C2×C4—81no—
722C2×C4—81no—
723C2×C4—81no—
724C2×C4—816no—
725C2×C4—82no—
726C2×C4—82no—
727C2×C4—82no—
728C2×C4—82no—
729C2×C4—82no—
730C2×C4—82no—
731C2×C4—82no—
732C2×C4#38614yes—
733C2×C4#38614yes—
734C2×C4C4×D814yes—
735C2×C4#44214yes—
736C2×C4#44714yes—
737C2×C4#44914yes—
738C2×C4#45914yes—
739C2×C4#46314yes—
740C2×C4C22×C22⋊C411yescharacteristic
741C2×C4C2×C4×D411yescharacteristic
742C2×C4C2×C4×D411yescharacteristic
743C2×C4C4×#4111yescharacteristic
744C2×C4#51811yescharacteristic
745C2×C4#52011yescharacteristic
746C2×C4C2×#12111yescharacteristic
747C2×C4C2×#12111yescharacteristic
748C2×C4C2×#12311yescharacteristic
749C2×C4#52511yescharacteristic
750C2×C4#52911yescharacteristic
751C2×C4#53211yescharacteristic
752C2×C4#53511yescharacteristic
753C2×C4#53711yescharacteristic
754C2×C4#54011yescharacteristic
755C2×C4#54211yescharacteristic
756C2×C4D4211yescharacteristic
757C2×C4D4211yescharacteristic
758C2×C4#54611yescharacteristic
759C2×C4#54611yescharacteristic
760C2×C4#54611yescharacteristic
761C2×C4#54611yescharacteristic
762C2×C4#54711yescharacteristic
763C2×C4#54711yescharacteristic
764C2×C4#54711yescharacteristic
765C2×C4#55311yescharacteristic
766C2×C4#55311yescharacteristic
767C2×C4#55511yescharacteristic
768C8—44no—
769C8—42no—
770C8—42no—
771C22—44no—
772C22—48no—
773C22—48no—
774C22—48no—
775C22—44no—
776C22—44no—
777C22—82no—
778C22—84no—
779C22—82no—
780C22—84no—
781C22—82no—
782C22—84no—
783C22—82no—
784C22—84no—
785C22—82no—
786C22—84no—
787C22—82no—
788C22—84no—
789C22—84no—
790C22—82no—
791C22—84no—
792C22—82no—
793C22—82no—
794C22—82no—
795C22—84no—
796C22—84no—
797C22—82no—
798C22—84no—
799C22—82no—
800C22—84no—
801C22C2×#38611yescharacteristic
802C22#236111yescharacteristic
803C22#236311yescharacteristic
804C22#240711yescharacteristic
805C22#240811yescharacteristic
806C22#242711yescharacteristic
807C22#242811yescharacteristic
808C22C2×C4×D811yescharacteristic
809C22C2×#44211yescharacteristic
810C22#294611yescharacteristic
811C22#294611yescharacteristic
812C22C2×#44711yescharacteristic
813C22C2×#44911yescharacteristic
814C22#301211yescharacteristic
815C22#301211yescharacteristic
816C22C2×#45911yescharacteristic
817C22C2×#46311yescharacteristic
818C22#304111yescharacteristic
819C22#304211yescharacteristic
820C22#327211yescharacteristic
821C22#327411yescharacteristic
822C22D4×D811yescharacteristic
823C22#328411yescharacteristic
824C22#329411yescharacteristic
825C22#330511yescharacteristic
826C22#332511yescharacteristic
827C22#333211yescharacteristic
828C22#335811yescharacteristic
829C22#336111yescharacteristic
830C22#336611yescharacteristic
831C22#337311yescharacteristic
832C22#339111yescharacteristic
833C22#339411yescharacteristic
834C22#339711yescharacteristic
835C22#339911yescharacteristic
836C4—24no—
837C4—44no—
838C4—44no—
839C4—82no—
840C4—82no—
841C4—82no—
842C4—162no—
843C4#187918yescomplemented
844C4C4×#12111yescharacteristic
845C4#232411yescharacteristic
846C4D4×C22⋊C411yescharacteristic
847C4#233911yescharacteristic
848C4#242011yescharacteristic
849C4#242211yescharacteristic
850C4#253511yescharacteristic
851C4#253711yescharacteristic
852C2—88no—
853C2—84no—
854C2#1397011yescharacteristic
855C2C2×#187911yescharacteristic
856C2#2092911yescharacteristic
857C2#2299511yescharacteristic
858C2#2300111yescharacteristic
859C2#2309311yescharacteristic
860C2#2309911yescharacteristic
861C2#2418411yescharacteristic
862C2#2418611yescharacteristic
863C2#2423611yescharacteristic
864C2#2423811yescharacteristic
865C2#2531811yescharacteristic
866C2#2532111yescharacteristic
867C2#2536411yescharacteristic
868C2#2536711yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC22×#459C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#2366C2semidirect
3. C2×#1957C2semidirect
4. C2×#1879C2semidirect
5. C2×C4×#102C2semidirect
6. #13906C2semidirect
7. #11189C2semidirect
8. #11022C2semidirect
9. #10849C2semidirect
10. #10834C2semidirect
11. #10788C2semidirect
19. C2×#459C4semidirect
61. C22×D8C2×C4semidirect
85. C2×C4×D4C2×C4semidirect
106. C2×C4⋊C8C2×C4semidirect
120. C2×#102C2×C4semidirect
121. C2×#102D4semidirect
247. #127C22⋊C4semidirect
287. C2×C4⋊C4D8semidirect
437. C2×D4C4×D4semidirect
843. C4#1879semidirect

Maximal subgroups

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

subgroupindex
C22×#4592
C2×#23662
C2×#19572
C2×#18792
C2×C4×#1022
#139062
#111892
#110222
#108492
#108342
#107882