Finite Group Databasebeta

← #412020

Subgroups — #412020

Order 512.

2238 conjugacy classes of subgroups.

The subgroup lattice has 913 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2856C211yesmaximal, characteristic
2C2×#2034C212yesmaximal, complemented
3C2×#1982C211yesmaximal, characteristic, complemented
4C2×#1982C211yesmaximal, characteristic, complemented
5C2×#1948C211yesmaximal, characteristic, complemented
6C2×#1797C211yesmaximal, characteristic, complemented
7C4×#380C211yesmaximal, characteristic, complemented
8#11189C212yesmaximal, complemented
9#11121C212yesmaximal, complemented
10#10969C212yesmaximal, complemented
11#10849C211yesmaximal, characteristic, complemented
12C22×#127C2211yescharacteristic
13C22×#121—21no—
14C22×#121—21no—
15C22×#121C2212yes—
16C23×C42C2211yescharacteristic
17C22×#106C2212yes—
18C22×C4⋊C8C2211yescharacteristic
19C22×C4⋊C8C2211yescharacteristic
20C22×#102C2212yes—
21C22×#102C2212yes—
22C22×#102C2212yes—
23C22×#102C2212yes—
24C22×C22⋊C8C2212yes—
25#2856—24no—
26#2856—24no—
27C2×#390—21no—
28C2×#390—21no—
29C2×#390C2212yes—
30C2×#384C2211yescharacteristic
31C2×#380C2211yescharacteristic
32C2×#380C2211yescharacteristic
33C2×C4×C4⋊C4C2211yescharacteristic
34C2×C4×C4⋊C4C2211yescharacteristic
35C2×C4×C22⋊C4—21no—
36#2034—28no—
37#1982—24no—
38#1982—24no—
39#1948—24no—
40#1797—24no—
41C2×#340C2212yes—
42C2×#340C2212yes—
43C2×#340C2212yes—
44C2×#336C2212yes—
45C4⋊#95C2211yescharacteristic
46C4⋊#95C2211yescharacteristic
47#1434—21no—
48C22⋊#95—21no—
49C4×#95—21no—
50C23×D4—22no—
51C23×D4—21no—
52C23×D4—21no—
53C23×D4C2312yes—
54C24×C4D411yescharacteristic
55C24×C4D411yescharacteristic
56C24×C4C2311yescharacteristic
57C23×C8C2312yes—
58C23×C8C2312yes—
59C2×#127—22no—
60C2×#127—22no—
61C2×#127—22no—
62C2×#127—22no—
63C2×#127—22no—
64C2×#127D414yes—
65C2×#121—28no—
66C2×#121—28no—
67C2×#121—24no—
68C2×#121—24no—
69C2×#121—24no—
70C2×#121—24no—
71C2×#121—42no—
72C2×#121—42no—
73C2×#121—44no—
74C2×#121—44no—
75C2×#121—44no—
76C2×#121—44no—
77C22×C4⋊C4—21no—
78C22×C4⋊C4—21no—
79C22×C4⋊C4C2311yescharacteristic
80C22×C4⋊C4C2311yescharacteristic
81C22×C4⋊C4C2312yes—
82C22×C4⋊C4C2311yescharacteristic
83C22×C4⋊C4C2311yescharacteristic
84C22×C22⋊C4—21no—
85C22×C22⋊C4—21no—
86C22×C22⋊C4—22no—
87C22×C22⋊C4—22no—
88C22×C22⋊C4—22no—
89C22×C42—22no—
90C22×C42—22no—
91C22×C42—22no—
92C22×C42—22no—
93C22×C42—22no—
94C22×C42—22no—
95C22×C42—21no—
96C22×C42—21no—
97C22×C42D411yescharacteristic
98C22×C42D411yescharacteristic
99C22×C42C2311yescharacteristic
100C22×C42C2311yescharacteristic
101C2×#106—24no—
102C2×#106—24no—
103C2×#106—42no—
104C2×C4⋊C8—22no—
105C2×C4⋊C8—22no—
106C2×C4⋊C8—22no—
107C2×C4⋊C8—22no—
108C2×C4⋊C8—22no—
109C2×C4⋊C8D414yescomplemented
110C2×#102—24no—
111C2×#102—24no—
112C2×#102—24no—
113C2×#102—24no—
114C2×#102—24no—
115C2×#102—24no—
116C2×#102—24no—
117C2×#102—24no—
118C2×#102—42no—
119C2×#102—42no—
120C2×#102—42no—
121C2×#102—42no—
122C2×C22⋊C8—24no—
123C2×C22⋊C8—24no—
124C2×C22⋊C8—42no—
125#390—28no—
126#390—28no—
127#390—24no—
128#390—24no—
129#384—22no—
130#384D414yes—
131#380—22no—
132#380—22no—
133#380—22no—
134#380D414yescomplemented
135C4×C4⋊C4—22no—
136C4×C4⋊C4—22no—
137C4×C4⋊C4—22no—
138C4×C4⋊C4—22no—
139C4×C22⋊C4—44no—
140C2×#95—21no—
141C2×#95—21no—
142C2×#95—21no—
143C2×#95—21no—
144C2×#95—21no—
145C2×#95—21no—
146C2×#95—21no—
147C2×#95—21no—
148#340—24no—
149#340—24no—
150#340—42no—
151#336—24no—
152C25—22no—
153C25C2×D411yescharacteristic
154C22×D4—28no—
155C22×D4—24no—
156C22×D4—24no—
157C22×D4—22no—
158C22×D4—22no—
159C22×D4—22no—
160C22×D4—22no—
161C22×D4—22no—
162C22×D4—22no—
163C22×D4—22no—
164C22×D4—22no—
165C22×D4—22no—
166C22×D4—22no—
167C22×D4—22no—
168C22×D4—22no—
169C22×D4—22no—
170C22×D4—42no—
171C22×D4—42no—
172C22×D4—42no—
173C22×D4—42no—
174C22×D4—44no—
175C22×D4—44no—
176C22×D4—44no—
177C22×D4—44no—
178C22×D4—44no—
179C22×D4—44no—
180C22×D4—42no—
181C22×D4—42no—
182C22×D4—42no—
183C22×D4—42no—
184C22×D4—42no—
185C22×D4—42no—
186C22×D4—42no—
187C22×D4—42no—
188C22×D4C2×D414yes—
189C23×C4—22no—
190C23×C4—22no—
191C23×C4—22no—
192C23×C4—22no—
193C23×C4—22no—
194C23×C4—22no—
195C23×C4—22no—
196C23×C4—22no—
197C23×C4—22no—
198C23×C4—21no—
199C23×C4—21no—
200C23×C4—21no—
201C23×C4—21no—
202C23×C4—21no—
203C23×C4—21no—
204C23×C4—21no—
205C23×C4—21no—
206C23×C4—21no—
207C23×C4—21no—
208C23×C4—21no—
209C23×C4—21no—
210C23×C4—22no—
211C23×C4—21no—
212C23×C4—21no—
213C23×C4—21no—
214C23×C4—21no—
215C23×C4—22no—
216C23×C4—22no—
217C23×C4—41no—
218C23×C4—41no—
219C23×C4SD1614yes—
220C23×C4C2×D411yescharacteristic
221C23×C4C2×D412yes—
222C23×C4C2×D411yescharacteristic
223C23×C4C2×D411yescharacteristic
224C23×C4C2×D411yescharacteristic
225C23×C4C2×D411yescharacteristic
226C23×C4#4112yes—
227C23×C4C2411yescharacteristic
228C22×C8—22no—
229C22×C8—22no—
230C22×C8—22no—
231C22×C8—22no—
232C22×C8—22no—
233C22×C8—22no—
234C22×C8—22no—
235C22×C8—22no—
236C22×C8—22no—
237C22×C8—22no—
238C22×C8—22no—
239C22×C8—22no—
240C22×C8—22no—
241C22×C8C2×D414yes—
242#127—28no—
243#127—28no—
244#127—44no—
245#127—44no—
246#121—48no—
247#121—48no—
248#121—48no—
249#121—48no—
250#121—432no—
251#121—432no—
252C2×C4⋊C4—22no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—22no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—22no—
263C2×C4⋊C4—22no—
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—21no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—24no—
273C2×C4⋊C4—24no—
274C2×C4⋊C4—22no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—21no—
277C2×C4⋊C4—21no—
278C2×C4⋊C4—21no—
279C2×C4⋊C4—42no—
280C2×C4⋊C4—42no—
281C2×C4⋊C4—42no—
282C2×C4⋊C4—42no—
283C2×C4⋊C4C2×D414yes—
284C2×C4⋊C4C2×D412yes—
285C2×C4⋊C4C2×D412yes—
286C2×C4⋊C4#4112yes—
287C2×C4⋊C4#4112yes—
288C2×C22⋊C4—28no—
289C2×C22⋊C4—28no—
290C2×C22⋊C4—28no—
291C2×C22⋊C4—24no—
292C2×C22⋊C4—24no—
293C2×C22⋊C4—44no—
294C2×C22⋊C4—44no—
295C2×C22⋊C4—44no—
296C2×C22⋊C4—42no—
297C2×C22⋊C4—42no—
298C2×C22⋊C4—42no—
299C2×C22⋊C4—42no—
300C2×C22⋊C4—44no—
301C2×C22⋊C4—44no—
302C2×C22⋊C4—44no—
303C2×C42—22no—
304C2×C42—22no—
305C2×C42—22no—
306C2×C42—22no—
307C2×C42—22no—
308C2×C42—22no—
309C2×C42—21no—
310C2×C42—21no—
311C2×C42—21no—
312C2×C42—21no—
313C2×C42—21no—
314C2×C42—21no—
315C2×C42—44no—
316C2×C42—44no—
317C2×C42—44no—
318C2×C42—44no—
319C2×C42—42no—
320C2×C42—42no—
321C2×C42—42no—
322C2×C42—42no—
323C2×C42—42no—
324C2×C42—42no—
325C2×C42C2×D412yes—
326C2×C42C2×D412yes—
327C2×C42C2×D412yes—
328C2×C42#4112yes—
329C2×C42#4112yes—
330C2×C42#4112yes—
331#106—48no—
332C4⋊C8—28no—
333C4⋊C8—44no—
334#102—48no—
335#102—48no—
336#102—48no—
337#102—48no—
338C22⋊C8—48no—
339#95—24no—
340#95—24no—
341#95—42no—
342#95—42no—
343#95—42no—
344#95—42no—
345#95—42no—
346#95—42no—
347C24—21no—
348C24—21no—
349C24—21no—
350C24—21no—
351C24—21no—
352C24—21no—
353C24—21no—
354C24—21no—
355C24—21no—
356C24—21no—
357C24—21no—
358C24—21no—
359C24—24no—
360C24—42no—
361C24—42no—
362C24—42no—
363C24—42no—
364C24—42no—
365C24—42no—
366C24—42no—
367C24—42no—
368C24—42no—
369C24—42no—
370C24—42no—
371C24—42no—
372C24—42no—
373C24—42no—
374C24#12112yes—
375C24C2×SD1612yes—
376C24AGL(1,ℤ/8)12yes—
377C24C22×D411yescharacteristic
378C2×D4—24no—
379C2×D4—24no—
380C2×D4—24no—
381C2×D4—24no—
382C2×D4—24no—
383C2×D4—24no—
384C2×D4—48no—
385C2×D4—48no—
386C2×D4—416no—
387C2×D4—416no—
388C2×D4—416no—
389C2×D4—42no—
390C2×D4—42no—
391C2×D4—42no—
392C2×D4—42no—
393C2×D4—42no—
394C2×D4—42no—
395C2×D4—42no—
396C2×D4—42no—
397C2×D4—42no—
398C2×D4—42no—
399C2×D4—42no—
400C2×D4—42no—
401C2×D4—42no—
402C2×D4—42no—
403C2×D4—42no—
404C2×D4—42no—
405C2×D4—42no—
406C2×D4—42no—
407C2×D4—42no—
408C2×D4—42no—
409C2×D4—42no—
410C2×D4—42no—
411C2×D4—48no—
412C2×D4—48no—
413C2×D4—48no—
414C2×D4—48no—
415C2×D4—84no—
416C2×D4—84no—
417C2×D4—84no—
418C2×D4—84no—
419C2×D4—88no—
420C2×D4—88no—
421C2×D4—88no—
422C2×D4—88no—
423C2×D4—84no—
424C2×D4—84no—
425C2×D4—84no—
426C2×D4—84no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—28no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
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—22no—
461C22×C4—22no—
462C22×C4—28no—
463C22×C4—28no—
464C22×C4—28no—
465C22×C4—24no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—44no—
471C22×C4—44no—
472C22×C4—44no—
473C22×C4—44no—
474C22×C4—44no—
475C22×C4—41no—
476C22×C4—41no—
477C22×C4—41no—
478C22×C4—41no—
479C22×C4—41no—
480C22×C4—41no—
481C22×C4—41no—
482C22×C4—41no—
483C22×C4—41no—
484C22×C4—41no—
485C22×C4—41no—
486C22×C4—41no—
487C22×C4—41no—
488C22×C4—41no—
489C22×C4—41no—
490C22×C4—41no—
491C22×C4—44no—
492C22×C4—44no—
493C22×C4—44no—
494C22×C4—44no—
495C22×C4—44no—
496C22×C4—41no—
497C22×C4—41no—
498C22×C4—41no—
499C22×C4—41no—
500C22×C4—42no—
501C22×C4—42no—
502C22×C4—41no—
503C22×C4—41no—
504C22×C4—41no—
505C22×C4—41no—
506C22×C4—42no—
507C22×C4—41no—
508C22×C4—41no—
509C22×C4—41no—
510C22×C4—41no—
511C22×C4—41no—
512C22×C4—41no—
513C22×C4—41no—
514C22×C4—41no—
515C22×C4—41no—
516C22×C4—41no—
517C22×C4—42no—
518C22×C4—42no—
519C22×C4—42no—
520C22×C4—41no—
521C22×C4—41no—
522C22×C4—41no—
523C22×C4—41no—
524C22×C4—41no—
525C22×C4—41no—
526C22×C4#12012yes—
527C22×C4#12012yes—
528C22×C4#12112yes—
529C22×C4#12112yes—
530C22×C4#12112yes—
531C22×C4#12312yes—
532C22×C4#12312yes—
533C22×C4C2×SD1612yes—
534C22×C4C2×SD1612yes—
535C22×C4#13512yes—
536C22×C4AGL(1,ℤ/8)12yes—
537C22×C4AGL(1,ℤ/8)12yes—
538C22×C4AGL(1,ℤ/8)12yes—
539C22×C4C22×D411yescharacteristic
540C22×C4C22×D411yescharacteristic
541C22×C4C22×D411yescharacteristic
542C22×C4C22×D411yescharacteristic
543C22×C4C2×#4111yescharacteristic
544C22×C4C2×#4111yescharacteristic
545C22×C4C2×#4111yescharacteristic
546C22×C4C2×#4111yescharacteristic
547C22×C4C2×#4111yescharacteristic
548C22×C4C2×#4111yescharacteristic
549C22×C4H(5,𝔽2)11yescharacteristic
550C22×C4H(5,𝔽2)11yescharacteristic
551C22×C4H(5,𝔽2)11yescharacteristic
552C22×C42−1+411yescharacteristic
553C2×C8—24no—
554C2×C8—24no—
555C2×C8—24no—
556C2×C8—42no—
557C2×C8—42no—
558C2×C8—42no—
559C2×C8—42no—
560C2×C8—42no—
561C2×C8—42no—
562C2×C8—42no—
563C2×C8—42no—
564C2×C8—42no—
565C2×C8—42no—
566C2×C8—42no—
567C4⋊C4—22no—
568C4⋊C4—22no—
569C4⋊C4—22no—
570C4⋊C4—24no—
571C4⋊C4—22no—
572C4⋊C4—22no—
573C4⋊C4—24no—
574C4⋊C4—22no—
575C4⋊C4—22no—
576C4⋊C4—22no—
577C4⋊C4—48no—
578C4⋊C4—42no—
579C4⋊C4—41no—
580C4⋊C4—41no—
581C4⋊C4—42no—
582C4⋊C4—41no—
583C4⋊C4—41no—
584C4⋊C4—41no—
585C4⋊C4—41no—
586C4⋊C4—41no—
587C4⋊C4—41no—
588C4⋊C4—48no—
589C22⋊C4—416no—
590C22⋊C4—416no—
591C22⋊C4—416no—
592C22⋊C4—48no—
593C22⋊C4—48no—
594C42—41no—
595C42—41no—
596C42—41no—
597C42—41no—
598C42—44no—
599C42—44no—
600C42—84no—
601C42—84no—
602C42#12114yes—
603C42#12114yes—
604C42#12314yes—
605C42#12414yes—
606C23—22no—
607C23—22no—
608C23—22no—
609C23—22no—
610C23—22no—
611C23—22no—
612C23—22no—
613C23—22no—
614C23—22no—
615C23—22no—
616C23—22no—
617C23—22no—
618C23—22no—
619C23—22no—
620C23—22no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—44no—
641C23—44no—
642C23—44no—
643C23—44no—
644C23—44no—
645C23—44no—
646C23—44no—
647C23—82no—
648C23—82no—
649C23—82no—
650C23—82no—
651C23—82no—
652C23—82no—
653C23—82no—
654C23—82no—
655C23—82no—
656C23—82no—
657C23—82no—
658C23—82no—
659C23—82no—
660C23—82no—
661C23—82no—
662C23—82no—
663C23—82no—
664C23—82no—
665C23—82no—
666C23—82no—
667C23—82no—
668C23—82no—
669C23—82no—
670C23—82no—
671C23—82no—
672C23—82no—
673C23—82no—
674C23—82no—
675C23#46014yes—
676C23C2×#12011yescharacteristic
677C23C2×#12111yescharacteristic
678C23C2×#12111yescharacteristic
679C23C2×#12311yescharacteristic
680C23#52511yescharacteristic
681C23#53511yescharacteristic
682C23#53711yescharacteristic
683C23C22×SD1611yescharacteristic
684C23C2×#13511yescharacteristic
685C23C2×AGL(1,ℤ/8)11yescharacteristic
686C23C2×AGL(1,ℤ/8)11yescharacteristic
687C23C2×AGL(1,ℤ/8)11yescharacteristic
688C23C2×AGL(1,ℤ/8)11yescharacteristic
689C23#57511yescharacteristic
690C23#57511yescharacteristic
691D4—44no—
692D4—44no—
693D4—44no—
694D4—44no—
695D4—816no—
696D4—832no—
697D4—82no—
698D4—82no—
699D4—82no—
700D4—82no—
701D4—816no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—416no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—416no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—44no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—44no—
749C2×C4—44no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—82no—
755C2×C4—81no—
756C2×C4—81no—
757C2×C4—81no—
758C2×C4—81no—
759C2×C4—82no—
760C2×C4—81no—
761C2×C4—81no—
762C2×C4—81no—
763C2×C4—81no—
764C2×C4—81no—
765C2×C4—81no—
766C2×C4—81no—
767C2×C4—81no—
768C2×C4—82no—
769C2×C4—82no—
770C2×C4—81no—
771C2×C4—81no—
772C2×C4—81no—
773C2×C4—81no—
774C2×C4#39414yes—
775C2×C4#39414yes—
776C2×C4#44914yes—
777C2×C4#45014yes—
778C2×C4#46514yes—
779C2×C4#46914yes—
780C2×C4#48114yes—
781C2×C4#48214yes—
782C2×C4C2×#12111yescharacteristic
783C2×C4C2×#12111yescharacteristic
784C2×C4C2×#12311yescharacteristic
785C2×C4C2×#12411yescharacteristic
786C2×C4#52911yescharacteristic
787C2×C4#52911yescharacteristic
788C2×C4#53211yescharacteristic
789C2×C4#53211yescharacteristic
790C2×C4#54011yescharacteristic
791C2×C4#54011yescharacteristic
792C2×C4#54211yescharacteristic
793C2×C4#54211yescharacteristic
794C2×C4D4211yescharacteristic
795C2×C4D4211yescharacteristic
796C2×C4D4211yescharacteristic
797C2×C4#54611yescharacteristic
798C2×C4#54611yescharacteristic
799C2×C4#54611yescharacteristic
800C2×C4#54611yescharacteristic
801C2×C4#54711yescharacteristic
802C2×C4#54711yescharacteristic
803C2×C4#54811yescharacteristic
804C2×C4#54811yescharacteristic
805C2×C4#55011yescharacteristic
806C2×C4#55011yescharacteristic
807C2×C4#55311yescharacteristic
808C2×C4#55311yescharacteristic
809C2×C4#55511yescharacteristic
810C8—44no—
811C8—82no—
812C22—24no—
813C22—24no—
814C22—24no—
815C22—42no—
816C22—42no—
817C22—42no—
818C22—42no—
819C22—42no—
820C22—42no—
821C22—42no—
822C22—42no—
823C22—42no—
824C22—42no—
825C22—42no—
826C22—42no—
827C22—84no—
828C22—84no—
829C22—84no—
830C22—84no—
831C22—84no—
832C22—84no—
833C22—84no—
834C22—162no—
835C22—162no—
836C22—162no—
837C22—162no—
838C22—162no—
839C22—162no—
840C22—162no—
841C22—162no—
842C22C2×#39411yescharacteristic
843C22#240711yescharacteristic
844C22#240811yescharacteristic
845C22#241411yescharacteristic
846C22#241611yescharacteristic
847C22#262411yescharacteristic
848C22#285411yescharacteristic
849C22C2×#45011yescharacteristic
850C22C2×#44911yescharacteristic
851C22#300311yescharacteristic
852C22#300511yescharacteristic
853C22C2×#46011yescharacteristic
854C22#303511yescharacteristic
855C22#303611yescharacteristic
856C22#303811yescharacteristic
857C22C2×#46511yescharacteristic
858C22C2×#46911yescharacteristic
859C22#305511yescharacteristic
860C22#305511yescharacteristic
861C22C2×#48211yescharacteristic
862C22C2×#48111yescharacteristic
863C22#309411yescharacteristic
864C22#309411yescharacteristic
865C22#310311yescharacteristic
866C22#310611yescharacteristic
867C22#310911yescharacteristic
868C22#311511yescharacteristic
869C22#320811yescharacteristic
870C22#321211yescharacteristic
871C22#321411yescharacteristic
872C22#321711yescharacteristic
873C22#324611yescharacteristic
874C22#324711yescharacteristic
875C22#325111yescharacteristic
876C22#325311yescharacteristic
877C4—24no—
878C4—42no—
879C4—42no—
880C4—42no—
881C4—82no—
882C4—82no—
883C4—82no—
884C4—84no—
885C4—82no—
886C4#203418yescomplemented
887C4#242011yescharacteristic
888C4#242211yescharacteristic
889C4#242611yescharacteristic
890C4#242711yescharacteristic
891C4#242811yescharacteristic
892C4#242811yescharacteristic
893C4#249011yescharacteristic
894C4#249111yescharacteristic
895C2—44no—
896C2—164no—
897C2#1512611yescharacteristic
898C2C2×#203411yescharacteristic
899C2#2348011yescharacteristic
900C2#2415211yescharacteristic
901C2#2415411yescharacteristic
902C2#2421011yescharacteristic
903C2#2421111yescharacteristic
904C2#2465311yescharacteristic
905C2#2465811yescharacteristic
906C2#2475311yescharacteristic
907C2#2475811yescharacteristic
908C2#2992111yescharacteristic
909C2#2992511yescharacteristic
910C2#3310711yescharacteristic
911C2#3311311yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC23×C4C24
prime radicalC2×#2856C2
LCSG ▷ C23×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C23×C42 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#2034C2semidirect
3. C2×#1982C2semidirect
4. C2×#1982C2semidirect
5. C2×#1948C2semidirect
6. C2×#1797C2semidirect
7. C4×#380C2semidirect
8. #11189C2semidirect
9. #11121C2semidirect
10. #10969C2semidirect
11. #10849C2semidirect
109. C2×C4⋊C8D4semidirect
134. #380D4semidirect
886. C4#2034semidirect

Maximal subgroups

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

subgroupindex
C2×#28562
C2×#20342
C2×#19822
C2×#19482
C2×#17972
C4×#3802
#111892
#111212
#109692
#108492