Finite Group Databasebeta

← #364950

Subgroups — #364950

Order 512.

2444 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#460C211yesmaximal, characteristic
2C2×C4×#127C211yesmaximal, characteristic
3C2×#1982C211yesmaximal, characteristic
4C2×#1877C212yesmaximal, complemented
5C2×#1803C211yesmaximal, characteristic, complemented
6C4×#391C211yesmaximal, characteristic, complemented
7#11189C212yesmaximal, complemented
8#11023C212yesmaximal, complemented
9#10849C211yesmaximal, characteristic, complemented
10#10832C211yesmaximal, characteristic, complemented
11#10788C212yesmaximal, complemented
12C23×SD16C2212yes—
13C22×#127C2211yescharacteristic
14C22×C4×Q8C2211yescharacteristic
15C22×C4×D4—21no—
16C22×C4×D4—21no—
17C22×C4×D4C2212yes—
18C2×#460—24no—
19C2×#460—24no—
20C2×#460C418yescomplemented
21C22×C4⋊C8C2211yescharacteristic
22C22×C4⋊C8C2211yescharacteristic
23C22×#103C2212yes—
24C22×#102C2212yes—
25C22×#102C2212yes—
26C22×#102C2212yes—
27C4×#127—24no—
28C4×#127—24no—
29C2×#391C2211yescharacteristic
30C2×#391C2211yescharacteristic
31C2×#390—21no—
32C2×#390—21no—
33C2×#390C2212yes—
34C2×#384C2211yescharacteristic
35C2×C4×C4⋊C4C2211yescharacteristic
36C2×C43C2211yescharacteristic
37#1982—24no—
38#1877—28no—
39#1803—24no—
40C2×#340C2212yes—
41C2×#340C2212yes—
42C2×#340C2212yes—
43C2×#336C2212yes—
44C2×#336C2212yes—
45#1436—21no—
46#1436—21no—
47C4⋊#95C2211yescharacteristic
48C4⋊#95C2211yescharacteristic
49C4×#95—21no—
50C4×#95—21no—
51C23×Q8C2311yescharacteristic
52C23×D4—21no—
53C23×D4—21no—
54C23×D4C2312yes—
55C24×C4—22no—
56C22×SD16—24no—
57C22×SD16—24no—
58C22×SD16—24no—
59C22×SD16—24no—
60C22×SD16—42no—
61C22×SD16—42no—
62C22×SD16C2×C418yescomplemented
63C23×C8C2312yes—
64C23×C8C2312yes—
65C2×#127—22no—
66C2×#127—22no—
67C2×#127—22no—
68C2×#127C2×C414yes—
69C2×#127D414yes—
70C2×#127D414yes—
71C2×C4×Q8—22no—
72C2×C4×Q8—22no—
73C2×C4×Q8—22no—
74C2×C4×Q8—22no—
75C2×C4×Q8—22no—
76C2×C4×Q8C2×C414yescomplemented
77C2×C4×D4—28no—
78C2×C4×D4—28no—
79C2×C4×D4—24no—
80C2×C4×D4—24no—
81C2×C4×D4—24no—
82C2×C4×D4—24no—
83C2×C4×D4—42no—
84C2×C4×D4—42no—
85C2×C4×D4—44no—
86C2×C4×D4—44no—
87C2×C4×D4—44no—
88C2×C4×D4—44no—
89C22×C4⋊C4—21no—
90C22×C4⋊C4—21no—
91C22×C4⋊C4—21no—
92C22×C4⋊C4C2311yescharacteristic
93C22×C4⋊C4C2311yescharacteristic
94C22×C4⋊C4C2312yes—
95C22×C4⋊C4C2311yescharacteristic
96C22×C22⋊C4—22no—
97C22×C22⋊C4—22no—
98C22×C22⋊C4—22no—
99C22×C42—21no—
100C22×C42—21no—
101C22×C42D411yescharacteristic
102C22×C42D411yescharacteristic
103C22×C42D411yescharacteristic
104C22×C42D411yescharacteristic
105C22×C42C2311yescharacteristic
106C22×C42C2311yescharacteristic
107C22×C42C2311yescharacteristic
108#460—232no—
109C2×C4⋊C8—22no—
110C2×C4⋊C8—22no—
111C2×C4⋊C8—22no—
112C2×C4⋊C8—22no—
113C2×C4⋊C8—22no—
114C2×C4⋊C8C2×C414yescomplemented
115C2×#103—24no—
116C2×#103—24no—
117C2×#103—42no—
118C2×#102—24no—
119C2×#102—24no—
120C2×#102—24no—
121C2×#102—24no—
122C2×#102—24no—
123C2×#102—24no—
124C2×#102—42no—
125C2×#102—42no—
126C2×#102C2×C418yescomplemented
127#391—22no—
128#391—22no—
129#391—22no—
130#391D414yescomplemented
131#390—28no—
132#390—28no—
133#390—24no—
134#390—24no—
135#384—22no—
136#384D414yes—
137C4×C4⋊C4—22no—
138C4×C4⋊C4—22no—
139C2×#95—21no—
140C2×#95—21no—
141C2×#95—21no—
142C2×#95—21no—
143C2×#95—21no—
144C2×#95—21no—
145C2×#95—21no—
146C2×#95—21no—
147C2×#95—21no—
148C43—22no—
149C43—22no—
150#340—24no—
151#340—24no—
152#340—42no—
153#336—24no—
154#336—42no—
155C25—22no—
156C22×Q8—21no—
157C22×Q8—21no—
158C22×Q8—21no—
159C22×Q8—21no—
160C22×Q8—21no—
161C22×Q8—21no—
162C22×Q8—21no—
163C22×Q8—21no—
164C22×Q8—21no—
165C22×Q8—21no—
166C22×Q8—21no—
167C22×Q8C22×C412yes—
168C22×Q8C2×D412yes—
169C22×Q8#4112yes—
170C22×D4—24no—
171C22×D4—24no—
172C22×D4—24no—
173C22×D4—24no—
174C22×D4—24no—
175C22×D4—24no—
176C22×D4—22no—
177C22×D4—22no—
178C22×D4—22no—
179C22×D4—22no—
180C22×D4—22no—
181C22×D4—22no—
182C22×D4—22no—
183C22×D4—22no—
184C22×D4—22no—
185C22×D4—22no—
186C22×D4—22no—
187C22×D4—42no—
188C22×D4—42no—
189C22×D4—42no—
190C22×D4—42no—
191C22×D4—42no—
192C22×D4—42no—
193C22×D4—42no—
194C22×D4—42no—
195C22×D4C22×C414yes—
196C22×D4C2×D414yes—
197C22×D4C2×D414yes—
198C23×C4—21no—
199C23×C4—28no—
200C23×C4—22no—
201C23×C4—21no—
202C23×C4—21no—
203C23×C4—21no—
204C23×C4—44no—
205C23×C4—44no—
206C23×C4—44no—
207C23×C4—44no—
208C23×C4—44no—
209C23×C4—44no—
210C23×C4C2×D411yescharacteristic
211C23×C4C2×D411yescharacteristic
212C23×C4C2×D411yescharacteristic
213C23×C4C2×D411yescharacteristic
214C23×C4C2×D411yescharacteristic
215C23×C4C2×D411yescharacteristic
216C23×C4C2411yescharacteristic
217C2×SD16—216no—
218C2×SD16—216no—
219C2×SD16—48no—
220C2×SD16—48no—
221C2×SD16—48no—
222C2×SD16—48no—
223C2×SD16—48no—
224C22×C8—22no—
225C22×C8—22no—
226C22×C8—22no—
227C22×C8—22no—
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×C8C22×C414yes—
238#127—28no—
239#127—28no—
240#127—28no—
241#127C22⋊C4116yes—
242C4×Q8—28no—
243C4×Q8—28no—
244C4×Q8—44no—
245C4×Q8—44no—
246C4×D4—48no—
247C4×D4—48no—
248C4×D4—48no—
249C4×D4—48no—
250C4×D4—432no—
251C4×D4—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—22no—
259C2×C4⋊C4—21no—
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—24no—
269C2×C4⋊C4—24no—
270C2×C4⋊C4—24no—
271C2×C4⋊C4—22no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—42no—
276C2×C4⋊C4—42no—
277C2×C4⋊C4—42no—
278C2×C4⋊C4—42no—
279C2×C4⋊C4—42no—
280C2×C4⋊C4—42no—
281C2×C4⋊C4C22×C412yes—
282C2×C4⋊C4C2×D414yes—
283C2×C4⋊C4C2×D412yes—
284C2×C4⋊C4#4112yes—
285C2×C22⋊C4—28no—
286C2×C22⋊C4—28no—
287C2×C22⋊C4—28no—
288C2×C22⋊C4—44no—
289C2×C22⋊C4—44no—
290C2×C22⋊C4—44no—
291C2×C22⋊C4—44no—
292C2×C22⋊C4—44no—
293C2×C22⋊C4—44no—
294C2×C42—22no—
295C2×C42—22no—
296C2×C42—22no—
297C2×C42—22no—
298C2×C42—22no—
299C2×C42—21no—
300C2×C42—21no—
301C2×C42—21no—
302C2×C42—21no—
303C2×C42—24no—
304C2×C42—22no—
305C2×C42—22no—
306C2×C42—22no—
307C2×C42—22no—
308C2×C42—21no—
309C2×C42—21no—
310C2×C42—21no—
311C2×C42—21no—
312C2×C42—21no—
313C2×C42—21no—
314C2×C42—41no—
315C2×C42—41no—
316C2×C42—42no—
317C2×C42—42no—
318C2×C42—42no—
319C2×C42—42no—
320C2×C42—42no—
321C2×C42SD1614yescomplemented
322C2×C42C22×C412yes—
323C2×C42C2×D412yes—
324C2×C42C2×D412yes—
325C2×C42C2×D412yes—
326C2×C42C2×D412yes—
327C2×C42#4112yes—
328C2×C42#4112yes—
329C2×C42#4112yes—
330C4⋊C8—28no—
331C4⋊C8—44no—
332#103—48no—
333#102—216no—
334#102—48no—
335#102—48no—
336#95—24no—
337#95—24no—
338#95—24no—
339#95—24no—
340#95—42no—
341#95—42no—
342#95—42no—
343#95—42no—
344#95—42no—
345C24—24no—
346C24—24no—
347C24—24no—
348C24—42no—
349C24—42no—
350C24—42no—
351C24—42no—
352C24—42no—
353C24—42no—
354C24—42no—
355C24—42no—
356C24—42no—
357C24—42no—
358C24—42no—
359C24—42no—
360C24C22×D411yescharacteristic
361C2×Q8—22no—
362C2×Q8—22no—
363C2×Q8—22no—
364C2×Q8—22no—
365C2×Q8—22no—
366C2×Q8—22no—
367C2×Q8—22no—
368C2×Q8—22no—
369C2×Q8—22no—
370C2×Q8—22no—
371C2×Q8—22no—
372C2×Q8—22no—
373C2×Q8—22no—
374C2×Q8—22no—
375C2×Q8—22no—
376C2×Q8—41no—
377C2×Q8—41no—
378C2×Q8—41no—
379C2×Q8—41no—
380C2×Q8—41no—
381C2×Q8—41no—
382C2×Q8—41no—
383C2×Q8—41no—
384C2×Q8—41no—
385C2×Q8—41no—
386C2×Q8—41no—
387C2×Q8—41no—
388C2×Q8C4×D414yescomplemented
389C2×D4—24no—
390C2×D4—24no—
391C2×D4—24no—
392C2×D4—24no—
393C2×D4—24no—
394C2×D4—24no—
395C2×D4—24no—
396C2×D4—24no—
397C2×D4—24no—
398C2×D4—24no—
399C2×D4—24no—
400C2×D4—24no—
401C2×D4—24no—
402C2×D4—24no—
403C2×D4—24no—
404C2×D4—216no—
405C2×D4—216no—
406C2×D4—48no—
407C2×D4—48no—
408C2×D4—48no—
409C2×D4—48no—
410C2×D4—48no—
411C2×D4—48no—
412C2×D4—42no—
413C2×D4—42no—
414C2×D4—42no—
415C2×D4—42no—
416C2×D4—42no—
417C2×D4—42no—
418C2×D4—42no—
419C2×D4—42no—
420C2×D4—42no—
421C2×D4—42no—
422C2×D4—42no—
423C2×D4—42no—
424C2×D4—48no—
425C2×D4—48no—
426C2×D4—48no—
427C2×D4—48no—
428C2×D4—48no—
429C2×D4—48no—
430C2×D4C2×C22⋊C418yes—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—22no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—22no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—22no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—22no—
461C22×C4—24no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—416no—
465C22×C4—416no—
466C22×C4—416no—
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—42no—
476C22×C4—42no—
477C22×C4—41no—
478C22×C4—41no—
479C22×C4—42no—
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—42no—
489C22×C4—42no—
490C22×C4—42no—
491C22×C4—41no—
492C22×C4—41no—
493C22×C4—41no—
494C22×C4—41no—
495C22×C4—88no—
496C22×C4—88no—
497C22×C4—88no—
498C22×C4—88no—
499C22×C4C4×D412yes—
500C22×C4C4×D412yes—
501C22×C4#12012yes—
502C22×C4#12012yes—
503C22×C4#12112yes—
504C22×C4#12112yes—
505C22×C4#12112yes—
506C22×C4#12112yes—
507C22×C4C2×SD1612yes—
508C22×C4C2×SD1612yes—
509C22×C4C2×SD1612yes—
510C22×C4#13512yes—
511C22×C4AGL(1,ℤ/8)12yes—
512C22×C4AGL(1,ℤ/8)12yes—
513C22×C4AGL(1,ℤ/8)12yes—
514C22×C4#13712yes—
515C22×C4C23×C411yescharacteristic
516C22×C4C22×D411yescharacteristic
517C22×C4C22×D411yescharacteristic
518C22×C4C22×D411yescharacteristic
519C22×C4C22×D411yescharacteristic
520C22×C4C2×#4111yescharacteristic
521C22×C4C2×#4111yescharacteristic
522C22×C4C2×#4111yescharacteristic
523C22×C4C2×#4111yescharacteristic
524C22×C4C2×#4111yescharacteristic
525C22×C4H(5,𝔽2)11yescharacteristic
526C22×C4H(5,𝔽2)11yescharacteristic
527C22×C4H(5,𝔽2)11yescharacteristic
528C22×C42−1+411yescharacteristic
529SD16—432no—
530C2×C8—24no—
531C2×C8—24no—
532C2×C8—24no—
533C2×C8—42no—
534C2×C8—42no—
535C2×C8—42no—
536C2×C8—42no—
537C2×C8—42no—
538C2×C8—42no—
539C2×C8—42no—
540C2×C8—42no—
541C2×C8—42no—
542C2×C8—42no—
543C2×C8—42no—
544C4⋊C4—22no—
545C4⋊C4—22no—
546C4⋊C4—22no—
547C4⋊C4—24no—
548C4⋊C4—22no—
549C4⋊C4—24no—
550C4⋊C4—22no—
551C4⋊C4—22no—
552C4⋊C4—48no—
553C4⋊C4—41no—
554C4⋊C4—41no—
555C4⋊C4—42no—
556C4⋊C4—41no—
557C4⋊C4—42no—
558C4⋊C4—41no—
559C4⋊C4—41no—
560C4⋊C4—41no—
561C4⋊C4—48no—
562C4⋊C4—48no—
563C22⋊C4—416no—
564C22⋊C4—416no—
565C22⋊C4—416no—
566C42—28no—
567C42—22no—
568C42—22no—
569C42—22no—
570C42—22no—
571C42—28no—
572C42—44no—
573C42—41no—
574C42—41no—
575C42—41no—
576C42—41no—
577C42—48no—
578C42—44no—
579C42—84no—
580C42C2×C22⋊C414yes—
581C42C4×D414yes—
582C42#12114yes—
583C42#12314yes—
584C23—28no—
585C23—44no—
586C23—44no—
587C23—44no—
588C23—44no—
589C23—44no—
590C23—44no—
591C23—44no—
592C23—44no—
593C23—44no—
594C23—44no—
595C23—44no—
596C23—44no—
597C23—44no—
598C23—44no—
599C23—44no—
600C23—44no—
601C23—44no—
602C23—44no—
603C23—82no—
604C23—82no—
605C23—82no—
606C23—82no—
607C23—82no—
608C23—82no—
609C23—82no—
610C23—82no—
611C23—82no—
612C23—82no—
613C23—82no—
614C23—82no—
615C23—82no—
616C23—82no—
617C23—82no—
618C23—82no—
619C23C2×C4×D411yescharacteristic
620C23C2×#12011yescharacteristic
621C23C2×#12111yescharacteristic
622C23C2×#12111yescharacteristic
623C23#52511yescharacteristic
624C23#53511yescharacteristic
625C23#53711yescharacteristic
626C23C22×SD1611yescharacteristic
627C23C2×#13511yescharacteristic
628C23C2×AGL(1,ℤ/8)11yescharacteristic
629C23C2×AGL(1,ℤ/8)11yescharacteristic
630C23C2×AGL(1,ℤ/8)11yescharacteristic
631C23C2×#13711yescharacteristic
632C23#57511yescharacteristic
633C23#57511yescharacteristic
634Q8—24no—
635Q8—24no—
636Q8—42no—
637Q8—42no—
638Q8—42no—
639Q8—42no—
640Q8—42no—
641Q8—42no—
642D4—28no—
643D4—28no—
644D4—432no—
645D4—44no—
646D4—44no—
647D4—432no—
648D4—44no—
649D4—44no—
650D4—44no—
651D4—44no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—24no—
674C2×C4—42no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—44no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—44no—
698C2×C4—44no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—832no—
705C2×C4—82no—
706C2×C4—81no—
707C2×C4—81no—
708C2×C4—82no—
709C2×C4—81no—
710C2×C4—81no—
711C2×C4—81no—
712C2×C4—81no—
713C2×C4—81no—
714C2×C4—81no—
715C2×C4—82no—
716C2×C4—81no—
717C2×C4—81no—
718C2×C4—81no—
719C2×C4—81no—
720C2×C4—82no—
721C2×C4#38614yes—
722C2×C4#38614yes—
723C2×C4C4×SD1614yes—
724C2×C4#44014yes—
725C2×C4#45014yes—
726C2×C4#45214yes—
727C2×C4#46014yescomplemented
728C2×C4#46114yes—
729C2×C4#46314yes—
730C2×C4C22×C22⋊C411yescharacteristic
731C2×C4C2×C4×D411yescharacteristic
732C2×C4C2×C4×D411yescharacteristic
733C2×C4C4×#4111yescharacteristic
734C2×C4#51811yescharacteristic
735C2×C4#52011yescharacteristic
736C2×C4C2×#12111yescharacteristic
737C2×C4C2×#12311yescharacteristic
738C2×C4#52911yescharacteristic
739C2×C4#53211yescharacteristic
740C2×C4#54011yescharacteristic
741C2×C4#54211yescharacteristic
742C2×C4D4211yescharacteristic
743C2×C4D4211yescharacteristic
744C2×C4D4211yescharacteristic
745C2×C4#54611yescharacteristic
746C2×C4#54611yescharacteristic
747C2×C4#54611yescharacteristic
748C2×C4#54611yescharacteristic
749C2×C4#54611yescharacteristic
750C2×C4#54711yescharacteristic
751C2×C4#54711yescharacteristic
752C2×C4#54711yescharacteristic
753C2×C4#54811yescharacteristic
754C2×C4#55011yescharacteristic
755C2×C4#55311yescharacteristic
756C2×C4#55311yescharacteristic
757C2×C4#55511yescharacteristic
758C8—44no—
759C8—82no—
760C22—48no—
761C22—48no—
762C22—48no—
763C22—84no—
764C22—84no—
765C22—84no—
766C22—84no—
767C22—84no—
768C22—84no—
769C22—84no—
770C22—84no—
771C22—84no—
772C22—84no—
773C22—84no—
774C22—84no—
775C22C2×#38611yescharacteristic
776C22C4×#12111yescharacteristic
777C22#232411yescharacteristic
778C22#240711yescharacteristic
779C22#240811yescharacteristic
780C22#253511yescharacteristic
781C22#253711yescharacteristic
782C22C2×C4×SD1611yescharacteristic
783C22C2×#44011yescharacteristic
784C22C4×AGL(1,ℤ/8)11yescharacteristic
785C22C4×AGL(1,ℤ/8)11yescharacteristic
786C22C2×#45011yescharacteristic
787C22C2×#45211yescharacteristic
788C22#300311yescharacteristic
789C22#300511yescharacteristic
790C22C2×#46111yescharacteristic
791C22C2×#46311yescharacteristic
792C22C2×#46011yescharacteristic
793C22#303511yescharacteristic
794C22#303611yescharacteristic
795C22#303611yescharacteristic
796C22#303711yescharacteristic
797C22#303811yescharacteristic
798C22#310311yescharacteristic
799C22#310611yescharacteristic
800C22#311211yescharacteristic
801C22#311511yescharacteristic
802C22#320811yescharacteristic
803C22#321211yescharacteristic
804C22#321611yescharacteristic
805C22#321711yescharacteristic
806C22#324611yescharacteristic
807C22#324711yescharacteristic
808C22#325111yescharacteristic
809C22#325411yescharacteristic
810C4—24no—
811C4—24no—
812C4—42no—
813C4—42no—
814C4—44no—
815C4—42no—
816C4—82no—
817C4—84no—
818C4—82no—
819C4—82no—
820C4#187718yescomplemented
821C4D4×C22⋊C411yescharacteristic
822C4#233911yescharacteristic
823C4#236111yescharacteristic
824C4#236311yescharacteristic
825C4#242011yescharacteristic
826C4#242211yescharacteristic
827C4#242711yescharacteristic
828C4#242811yescharacteristic
829C2—88no—
830C2#1397011yescharacteristic
831C2C2×#187711yescharacteristic
832C2#2092511yescharacteristic
833C2C4×#46011yescharacteristic
834C2#2150511yescharacteristic
835C2#2214711yescharacteristic
836C2#2215311yescharacteristic
837C2#2415411yescharacteristic
838C2#2415611yescharacteristic
839C2#2421111yescharacteristic
840C2#2421311yescharacteristic
841C2#2815811yescharacteristic
842C2#2816011yescharacteristic
843C2#2825211yescharacteristic
844C2#2825311yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC22×#127C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×C43 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
4. C2×#1877C2semidirect
5. C2×#1803C2semidirect
6. C4×#391C2semidirect
7. #11189C2semidirect
8. #11023C2semidirect
9. #10849C2semidirect
10. #10832C2semidirect
11. #10788C2semidirect
20. C2×#460C4semidirect
62. C22×SD16C2×C4semidirect
76. C2×C4×Q8C2×C4semidirect
114. C2×C4⋊C8C2×C4semidirect
126. C2×#102C2×C4semidirect
130. #391D4semidirect
321. C2×C42SD16semidirect
388. C2×Q8C4×D4semidirect
727. C2×C4#460semidirect
820. C4#1877semidirect

Maximal subgroups

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

subgroupindex
C22×#4602
C2×C4×#1272
C2×#19822
C2×#18772
C2×#18032
C4×#3912
#111892
#110232
#108492
#108322
#107882