Finite Group Databasebeta

← #357800

Subgroups — #357800

Order 512.

3158 conjugacy classes of subgroups.

The subgroup lattice has 884 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#428C211yesmaximal, characteristic, complemented
2C22×#417C211yesmaximal, characteristic
3C22×#417C211yesmaximal, characteristic
4C2×#2297C211yesmaximal, characteristic
5C2×#1736C211yesmaximal, characteristic, complemented
6C2×#1728C211yesmaximal, characteristic, complemented
7C2×C4⋊#95C211yesmaximal, characteristic, complemented
8#11124C212yesmaximal, complemented
9#11123C212yesmaximal, complemented
10#11122C212yesmaximal, complemented
11#11121C212yesmaximal, complemented
12C23×#41C2211yescharacteristic
13C23×M16C2211yescharacteristic
14C23×M16C2211yescharacteristic
15C22×#117C2211yescharacteristic
16C23×C4⋊C4C2211yescharacteristic
17C23×C4⋊C4C2211yescharacteristic
18C23×C42C2211yescharacteristic
19C2×#428—24no—
20C2×#428—24no—
21C2×#428—24no—
22C22×#107C2212yes—
23C22×#106C2212yes—
24C2×#417—24no—
25C2×#417—24no—
26C2×#417—24no—
27C2×#417—24no—
28C2×#417—24no—
29C2×#417C418yescomplemented
30C22×#103C2212yes—
31C22×#103C2212yes—
32C22×#102C2212yes—
33C22×#102C2212yes—
34#2297—24no—
35#2297—24no—
36C2×#391C2211yescharacteristic
37C2×#391C2211yescharacteristic
38C2×#390C2211yescharacteristic
39C2×#390C2211yescharacteristic
40C2×#386—22no—
41C2×C4×C22⋊C4—22no—
42C22×#95—22no—
43#1736—24no—
44C2×#340C2212yes—
45C2×#340C2212yes—
46#1728—24no—
47C2×#336C2212yes—
48C2×#336C2212yes—
49C4⋊#95—22no—
50C4⋊#95C2212yes—
51C4⋊#95C2212yes—
52C22×#41—22no—
53C22×#41—22no—
54C22×#41—22no—
55C22×#41—22no—
56C22×#41—22no—
57C22×#41—22no—
58C22×#41—22no—
59C22×#41—22no—
60C22×#41—22no—
61C22×#41—22no—
62C22×#41—22no—
63C22×#41C2×C414yes—
64C22×#41D414yes—
65C22×#41Q814yes—
66C23×Q8C2311yescharacteristic
67C23×D4—21no—
68C23×D4C2311yescharacteristic
69C24×C4—21no—
70C24×C4—21no—
71C24×C4—21no—
72C24×C4D412yes—
73C24×C4C2311yescharacteristic
74C22×M16—22no—
75C22×M16—22no—
76C22×M16—22no—
77C22×M16—22no—
78C22×M16—22no—
79C22×M16—22no—
80C22×M16—22no—
81C22×M16—22no—
82C22×M16—22no—
83C22×M16—22no—
84C22×M16C2×C414yes—
85C22×M16D414yes—
86C22×M16D414yes—
87C22×M16D414yes—
88C23×C8C2312yes—
89C23×C8C2312yes—
90C2×#117—22no—
91C2×#117—22no—
92C2×#117—22no—
93C2×#117—22no—
94C2×#117—22no—
95C2×#117D414yes—
96C22×C4⋊C4—22no—
97C22×C4⋊C4—22no—
98C22×C4⋊C4—22no—
99C22×C4⋊C4—22no—
100C22×C4⋊C4—22no—
101C22×C4⋊C4—22no—
102C22×C4⋊C4—22no—
103C22×C4⋊C4—22no—
104C22×C4⋊C4—21no—
105C22×C4⋊C4—21no—
106C22×C4⋊C4—22no—
107C22×C4⋊C4—22no—
108C22×C4⋊C4C2×C414yes—
109C22×C4⋊C4D414yes—
110C22×C4⋊C4C2312yes—
111C22×C4⋊C4C2312yes—
112C22×C4⋊C4C2311yescharacteristic
113C22×C4⋊C4C2311yescharacteristic
114C22×C22⋊C4—21no—
115C22×C22⋊C4—22no—
116C22×C22⋊C4—22no—
117C22×C42—22no—
118C22×C42—22no—
119C22×C42—22no—
120C22×C42—21no—
121C22×C42—22no—
122C22×C42—22no—
123C22×C42—22no—
124C22×C42D412yes—
125C22×C42C2311yescharacteristic
126C22×C42C2311yescharacteristic
127#428—232no—
128C2×#107—24no—
129C2×#107—24no—
130C2×#107—24no—
131C2×#106—24no—
132C2×#106—24no—
133C2×#106—24no—
134#417—232no—
135#417—232no—
136C2×#103—24no—
137C2×#103—24no—
138C2×#103—24no—
139C2×#103—24no—
140C2×#103—24no—
141C2×#103C2×C418yescomplemented
142C2×#102—24no—
143C2×#102—24no—
144C2×#102—24no—
145C2×#102—24no—
146C2×#102—24no—
147C2×#102C2×C418yescomplemented
148#391—22no—
149#391—22no—
150#391—22no—
151#391—22no—
152#390—22no—
153#390—22no—
154#390—22no—
155#390—22no—
156#386—216no—
157C4×C22⋊C4—216no—
158C2×#95—22no—
159C2×#95—22no—
160C2×#95—24no—
161C2×#95—24no—
162C2×#95—48no—
163#340—24no—
164#340—24no—
165#336—24no—
166#336—24no—
167C25—21no—
168C25C2×D411yescharacteristic
169C2×#41—28no—
170C2×#41—28no—
171C2×#41—28no—
172C2×#41—28no—
173C2×#41—28no—
174C2×#41—28no—
175C2×#41—28no—
176C2×#41—28no—
177C2×#41—28no—
178C2×#41—28no—
179C2×#41—28no—
180C2×#41—28no—
181C2×#41—28no—
182C2×#41—28no—
183C2×#41—28no—
184C2×#41—44no—
185C2×#41—44no—
186C2×#41—44no—
187C2×#41—44no—
188C2×#41—44no—
189C2×#41—44no—
190C2×#41—44no—
191C2×#41—44no—
192C2×#41—44no—
193C2×#41—44no—
194C2×#41—44no—
195C2×#41—44no—
196C2×#41C4⋊C4116yes—
197C22×Q8—21no—
198C22×Q8—21no—
199C22×Q8—21no—
200C22×Q8—21no—
201C22×Q8—21no—
202C22×Q8—21no—
203C22×Q8—21no—
204C22×Q8—21no—
205C22×Q8—21no—
206C22×Q8—21no—
207C22×Q8—21no—
208C22×Q8C22×C412yes—
209C22×Q8C2×D412yes—
210C22×Q8C2×Q812yes—
211C22×D4—24no—
212C22×D4—24no—
213C22×D4—24no—
214C22×D4—21no—
215C22×D4—21no—
216C22×D4—21no—
217C22×D4—21no—
218C22×D4—21no—
219C22×D4—21no—
220C22×D4—21no—
221C22×D4—21no—
222C22×D4—21no—
223C22×D4—21no—
224C22×D4—21no—
225C22×D4—42no—
226C22×D4—42no—
227C22×D4—42no—
228C22×D4—42no—
229C22×D4C22×C412yes—
230C22×D4C2×D412yes—
231C22×D4C2×Q812yes—
232C23×C4—24no—
233C23×C4—21no—
234C23×C4—24no—
235C23×C4—24no—
236C23×C4—24no—
237C23×C4—24no—
238C23×C4—24no—
239C23×C4—24no—
240C23×C4—24no—
241C23×C4—24no—
242C23×C4—24no—
243C23×C4—21no—
244C23×C4—21no—
245C23×C4—22no—
246C23×C4—22no—
247C23×C4—42no—
248C23×C4—42no—
249C23×C4—42no—
250C23×C4—42no—
251C23×C4—42no—
252C23×C4—42no—
253C23×C4—44no—
254C23×C4—44no—
255C23×C4—44no—
256C23×C4—44no—
257C23×C4—42no—
258C23×C4—42no—
259C23×C4—42no—
260C23×C4—42no—
261C23×C4C22×C412yes—
262C23×C4C2×D412yes—
263C23×C4C2×D412yes—
264C23×C4C2×D412yes—
265C23×C4C2×D412yes—
266C23×C4C2×D412yes—
267C23×C4C2×D412yes—
268C23×C4C2×D412yes—
269C23×C4C2×D411yescharacteristic
270C23×C4C2×D412yes—
271C23×C4C2×Q812yes—
272C23×C4#4112yes—
273C23×C4#4112yes—
274C23×C4#4112yes—
275C23×C4#4112yes—
276C23×C4#4112yes—
277C23×C4#4112yes—
278C23×C4C2411yescharacteristic
279C2×M16—28no—
280C2×M16—28no—
281C2×M16—28no—
282C2×M16—28no—
283C2×M16—28no—
284C2×M16—28no—
285C2×M16—28no—
286C2×M16—28no—
287C2×M16—28no—
288C2×M16—44no—
289C2×M16—44no—
290C2×M16—44no—
291C2×M16—44no—
292C2×M16C22⋊C4116yescomplemented
293C22×C8—22no—
294C22×C8—22no—
295C22×C8—22no—
296C22×C8—22no—
297C22×C8—22no—
298C22×C8—22no—
299C22×C8—22no—
300C22×C8—22no—
301C22×C8—22no—
302C22×C8—22no—
303C22×C8C22×C414yes—
304C22×C8C2×D414yes—
305C22×C8C2×D414yes—
306C22×C8C2×D414yes—
307#117—28no—
308#117—28no—
309#117—44no—
310#117—44no—
311C2×C4⋊C4—28no—
312C2×C4⋊C4—28no—
313C2×C4⋊C4—28no—
314C2×C4⋊C4—28no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—22no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—21no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4—24no—
332C2×C4⋊C4—24no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—42no—
338C2×C4⋊C4—44no—
339C2×C4⋊C4—44no—
340C2×C4⋊C4—44no—
341C2×C4⋊C4—42no—
342C2×C4⋊C4—44no—
343C2×C4⋊C4—42no—
344C2×C4⋊C4—42no—
345C2×C4⋊C4C22×C414yes—
346C2×C4⋊C4C2×D414yes—
347C2×C4⋊C4C2×D412yes—
348C2×C4⋊C4C2×D412yes—
349C2×C22⋊C4—28no—
350C2×C22⋊C4—28no—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—44no—
353C2×C22⋊C4—44no—
354C2×C22⋊C4—42no—
355C2×C22⋊C4—42no—
356C2×C22⋊C4—44no—
357C2×C22⋊C4—44no—
358C2×C42—24no—
359C2×C42—24no—
360C2×C42—24no—
361C2×C42—24no—
362C2×C42—21no—
363C2×C42—21no—
364C2×C42—21no—
365C2×C42—21no—
366C2×C42—21no—
367C2×C42—21no—
368C2×C42—21no—
369C2×C42—21no—
370C2×C42—21no—
371C2×C42—21no—
372C2×C42—21no—
373C2×C42—21no—
374C2×C42—42no—
375C2×C42—44no—
376C2×C42—44no—
377C2×C42—44no—
378C2×C42—44no—
379C2×C42—42no—
380#107—216no—
381#106—216no—
382#103—216no—
383#103—216no—
384#102—216no—
385#102—216no—
386#95—28no—
387#95—28no—
388#95—48no—
389#95—48no—
390C24—22no—
391C24—22no—
392C24—22no—
393C24—22no—
394C24—22no—
395C24—22no—
396C24—22no—
397C24—41no—
398C24—41no—
399C24—41no—
400C24—41no—
401C24—42no—
402C24—42no—
403C24—42no—
404C24—42no—
405C24C4×D412yes—
406C24#12012yes—
407C24#12112yes—
408C24#12112yes—
409C24C22⋊Q812yes—
410C24#12312yes—
411C24#12712yes—
412C24C22×D411yescharacteristic
413#41—232no—
414#41—232no—
415#41—416no—
416#41—416no—
417#41—416no—
418#41—416no—
419#41—416no—
420#41—416no—
421C2×Q8—22no—
422C2×Q8—22no—
423C2×Q8—22no—
424C2×Q8—22no—
425C2×Q8—22no—
426C2×Q8—22no—
427C2×Q8—22no—
428C2×Q8—22no—
429C2×Q8—22no—
430C2×Q8—22no—
431C2×Q8—22no—
432C2×Q8—22no—
433C2×Q8—22no—
434C2×Q8—22no—
435C2×Q8—22no—
436C2×Q8—41no—
437C2×Q8—41no—
438C2×Q8—41no—
439C2×Q8—41no—
440C2×Q8—41no—
441C2×Q8—41no—
442C2×Q8—41no—
443C2×Q8—41no—
444C2×Q8—41no—
445C2×Q8—41no—
446C2×Q8—41no—
447C2×Q8—41no—
448C2×Q8C2×C4⋊C414yes—
449C2×D4—216no—
450C2×D4—22no—
451C2×D4—22no—
452C2×D4—22no—
453C2×D4—22no—
454C2×D4—22no—
455C2×D4—22no—
456C2×D4—22no—
457C2×D4—22no—
458C2×D4—22no—
459C2×D4—22no—
460C2×D4—22no—
461C2×D4—22no—
462C2×D4—22no—
463C2×D4—22no—
464C2×D4—22no—
465C2×D4—48no—
466C2×D4—48no—
467C2×D4—48no—
468C2×D4—48no—
469C2×D4—48no—
470C2×D4—48no—
471C2×D4—41no—
472C2×D4—41no—
473C2×D4—41no—
474C2×D4—41no—
475C2×D4—41no—
476C2×D4—41no—
477C2×D4—41no—
478C2×D4—41no—
479C2×D4—41no—
480C2×D4—41no—
481C2×D4—41no—
482C2×D4—41no—
483C2×D4C2×C4⋊C414yes—
484C22×C4—216no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—216no—
501C22×C4—24no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—24no—
505C22×C4—48no—
506C22×C4—48no—
507C22×C4—48no—
508C22×C4—48no—
509C22×C4—48no—
510C22×C4—41no—
511C22×C4—41no—
512C22×C4—41no—
513C22×C4—41no—
514C22×C4—48no—
515C22×C4—48no—
516C22×C4—48no—
517C22×C4—48no—
518C22×C4—48no—
519C22×C4—48no—
520C22×C4—48no—
521C22×C4—416no—
522C22×C4—416no—
523C22×C4—42no—
524C22×C4—41no—
525C22×C4—41no—
526C22×C4—42no—
527C22×C4—41no—
528C22×C4—41no—
529C22×C4—42no—
530C22×C4—42no—
531C22×C4—44no—
532C22×C4—44no—
533C22×C4—42no—
534C22×C4—42no—
535C22×C4—42no—
536C22×C4—42no—
537C22×C4—44no—
538C22×C4—44no—
539C22×C4—48no—
540C22×C4—48no—
541C22×C4—84no—
542C22×C4—84no—
543C22×C4—84no—
544C22×C4—84no—
545C22×C4—88no—
546C22×C4—88no—
547C22×C4C2×C22⋊C414yes—
548C22×C4C2×C4⋊C414yes—
549C22×C4#11714yes—
550C22×C4C4×D414yes—
551C22×C4C4×D414yes—
552C22×C4C4×D414yes—
553C22×C4C4×D412yes—
554C22×C4#12014yes—
555C22×C4#12014yes—
556C22×C4#12012yes—
557C22×C4#12114yes—
558C22×C4#12114yes—
559C22×C4#12114yes—
560C22×C4#12114yes—
561C22×C4#12114yes—
562C22×C4#12114yes—
563C22×C4#12112yes—
564C22×C4#12112yes—
565C22×C4C22⋊Q814yes—
566C22×C4C22⋊Q814yes—
567C22×C4C22⋊Q814yes—
568C22×C4C22⋊Q814yes—
569C22×C4C22⋊Q814yes—
570C22×C4C22⋊Q812yes—
571C22×C4#12314yes—
572C22×C4#12314yes—
573C22×C4#12314yes—
574C22×C4#12314yes—
575C22×C4#12312yes—
576C22×C4#12414yes—
577C22×C4#12414yes—
578C22×C4#12414yes—
579C22×C4#12614yes—
580C22×C4#12614yes—
581C22×C4#12712yes—
582C22×C4AGL(1,ℤ/8)14yes—
583C22×C4#13714yes—
584C22×C4C23×C411yescharacteristic
585C22×C4C22×D411yescharacteristic
586C22×C4C22×D411yescharacteristic
587C22×C4C22×D411yescharacteristic
588C22×C4C22×D411yescharacteristic
589C22×C4C22×D411yescharacteristic
590C22×C4C22×D411yescharacteristic
591C22×C4C22×Q811yescharacteristic
592C22×C4C2×#4111yescharacteristic
593C22×C4C2×#4111yescharacteristic
594C22×C4C2×#4111yescharacteristic
595C22×C4C2×#4111yescharacteristic
596C22×C4C2×#4111yescharacteristic
597C22×C4C2×#4111yescharacteristic
598M16—232no—
599M16—416no—
600C2×C8—24no—
601C2×C8—24no—
602C2×C8—24no—
603C2×C8—24no—
604C2×C8—24no—
605C2×C8—24no—
606C2×C8—24no—
607C2×C8—24no—
608C2×C8—24no—
609C2×C8—42no—
610C2×C8—42no—
611C2×C8—42no—
612C2×C8—42no—
613C2×C8C2×C22⋊C418yes—
614C4⋊C4—24no—
615C4⋊C4—24no—
616C4⋊C4—24no—
617C4⋊C4—22no—
618C4⋊C4—24no—
619C4⋊C4—22no—
620C4⋊C4—22no—
621C4⋊C4—22no—
622C4⋊C4—41no—
623C4⋊C4—41no—
624C4⋊C4—42no—
625C4⋊C4—42no—
626C4⋊C4—42no—
627C4⋊C4—41no—
628C4⋊C4—41no—
629C4⋊C4—42no—
630C4⋊C4—48no—
631C4⋊C4—48no—
632C22⋊C4—416no—
633C22⋊C4—416no—
634C22⋊C4—48no—
635C42—41no—
636C42—41no—
637C42—41no—
638C42—41no—
639C42—41no—
640C42—41no—
641C42—41no—
642C42—41no—
643C42—48no—
644C42—48no—
645C23—24no—
646C23—24no—
647C23—24no—
648C23—24no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—24no—
654C23—24no—
655C23—24no—
656C23—24no—
657C23—24no—
658C23—24no—
659C23—24no—
660C23—24no—
661C23—24no—
662C23—44no—
663C23—44no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—44no—
669C23—44no—
670C23—44no—
671C23—44no—
672C23—42no—
673C23—42no—
674C23—82no—
675C23—82no—
676C23—81no—
677C23—81no—
678C23—81no—
679C23—81no—
680C23—82no—
681C23—82no—
682C23—82no—
683C23—82no—
684C23#38514yes—
685C23#38814yes—
686C23#39014yes—
687C23#39214yes—
688C23#39414yes—
689C23#39614yes—
690C23#39914yes—
691C23C2×C4×D411yescharacteristic
692C23C2×#12011yescharacteristic
693C23C2×#12111yescharacteristic
694C23C2×#12111yescharacteristic
695C23C2×C22⋊Q811yescharacteristic
696C23C2×#12311yescharacteristic
697C23C2×#12711yescharacteristic
698C23C2×AGL(1,ℤ/8)12yes—
699C23C2×#13712yes—
700C23#57512yes—
701C23#57512yes—
702Q8—24no—
703Q8—24no—
704Q8—42no—
705Q8—42no—
706Q8—42no—
707Q8—42no—
708Q8—42no—
709Q8—42no—
710D4—24no—
711D4—24no—
712D4—432no—
713D4—42no—
714D4—42no—
715D4—42no—
716D4—42no—
717D4—42no—
718D4—42no—
719C2×C4—24no—
720C2×C4—24no—
721C2×C4—24no—
722C2×C4—24no—
723C2×C4—24no—
724C2×C4—24no—
725C2×C4—24no—
726C2×C4—432no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
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—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—432no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—44no—
745C2×C4—48no—
746C2×C4—44no—
747C2×C4—44no—
748C2×C4—48no—
749C2×C4—44no—
750C2×C4—816no—
751C2×C4—816no—
752C2×C4—81no—
753C2×C4—82no—
754C2×C4—82no—
755C2×C4—81no—
756C2×C4—81no—
757C2×C4—81no—
758C2×C4—82no—
759C2×C4—82no—
760C2×C4—84no—
761C2×C4—82no—
762C2×C4—82no—
763C2×C4—84no—
764C2×C4#38018yes—
765C2×C4#38514yes—
766C2×C4#38518yes—
767C2×C4#38618yes—
768C2×C4#38814yes—
769C2×C4#38818yes—
770C2×C4#39014yes—
771C2×C4#39214yes—
772C2×C4#39318yes—
773C2×C4#39418yes—
774C2×C4#39414yes—
775C2×C4#39618yes—
776C2×C4#39614yes—
777C2×C4#39718yes—
778C2×C4#39914yes—
779C2×C4C22×C22⋊C411yescharacteristic
780C2×C4C22×C4⋊C411yescharacteristic
781C2×C4C2×#11711yescharacteristic
782C2×C4C2×C4×D411yescharacteristic
783C2×C4C2×C4×D411yescharacteristic
784C2×C4C2×C4×D411yescharacteristic
785C2×C4C2×#12011yescharacteristic
786C2×C4C2×#12011yescharacteristic
787C2×C4C2×#12111yescharacteristic
788C2×C4C2×#12111yescharacteristic
789C2×C4C2×#12111yescharacteristic
790C2×C4C2×#12111yescharacteristic
791C2×C4C2×#12111yescharacteristic
792C2×C4C2×#12111yescharacteristic
793C2×C4C2×C22⋊Q811yescharacteristic
794C2×C4C2×C22⋊Q811yescharacteristic
795C2×C4C2×C22⋊Q811yescharacteristic
796C2×C4C2×C22⋊Q811yescharacteristic
797C2×C4C2×C22⋊Q811yescharacteristic
798C2×C4C2×#12311yescharacteristic
799C2×C4C2×#12311yescharacteristic
800C2×C4C2×#12311yescharacteristic
801C2×C4C2×#12311yescharacteristic
802C2×C4C2×#12411yescharacteristic
803C2×C4C2×#12411yescharacteristic
804C2×C4C2×#12411yescharacteristic
805C2×C4C2×#12611yescharacteristic
806C2×C4C2×#12611yescharacteristic
807C8—28no—
808C8—44no—
809C22—28no—
810C22—28no—
811C22—24no—
812C22—24no—
813C22—28no—
814C22—24no—
815C22—24no—
816C22—28no—
817C22—24no—
818C22—24no—
819C22—44no—
820C22—48no—
821C22—84no—
822C22—84no—
823C22—82no—
824C22—82no—
825C22—82no—
826C22—82no—
827C22—84no—
828C22—82no—
829C22—82no—
830C22#143918yes—
831C22C2×#38511yescharacteristic
832C22C2×#38811yescharacteristic
833C22C2×#39011yescharacteristic
834C22C2×#39211yescharacteristic
835C22C2×#39411yescharacteristic
836C22C2×#39611yescharacteristic
837C22C2×#39911yescharacteristic
838C22C4×AGL(1,ℤ/8)12yes—
839C22C4×#13712yes—
840C22#300612yes—
841C22#300712yes—
842C22#303612yes—
843C22#303712yes—
844C22#305512yes—
845C22#305612yes—
846C22#307912yes—
847C22#308012yes—
848C22#309212yes—
849C22#309312yes—
850C22#315111yescharacteristic
851C22#315211yescharacteristic
852C22#315311yescharacteristic
853C22#315311yescharacteristic
854C4—44no—
855C4—44no—
856C4—44no—
857C4—82no—
858C4—84no—
859C4—82no—
860C4—84no—
861C4#143918yes—
862C4C2×#38011yescharacteristic
863C4C2×#38511yescharacteristic
864C4C2×#38611yescharacteristic
865C4C2×#38811yescharacteristic
866C4C2×#39311yescharacteristic
867C4C2×#39411yescharacteristic
868C4C2×#39611yescharacteristic
869C4C2×#39711yescharacteristic
870C2—28no—
871C2—84no—
872C2C2×#143911yescharacteristic
873C2#2087512yes—
874C2#2105912yes—
875C2#2123611yescharacteristic
876C2#2123711yescharacteristic
877C2#2342811yescharacteristic
878C2#2342911yescharacteristic
879C2#2348212yes—
880C2#2361712yes—
881C2#2373311yescharacteristic
882C2#2373411yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC23×#41C22
LCSG ▷ C22×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
1. C22×#428C2semidirect
5. C2×#1736C2semidirect
6. C2×#1728C2semidirect
7. C2×C4⋊#95C2semidirect
8. #11124C2semidirect
9. #11123C2semidirect
10. #11122C2semidirect
11. #11121C2semidirect
29. C2×#417C4semidirect
141. C2×#103C2×C4semidirect
147. C2×#102C2×C4semidirect
292. C2×M16C22⋊C4semidirect

Maximal subgroups

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

subgroupindex
C22×#4282
C22×#4172
C2×#22972
C2×#17362
C2×#17282
C2×C4⋊#952
#111242
#111232
#111222
#111212