Finite Group Databasebeta

← #357516

Subgroups — #357516

Order 512.

4682 conjugacy classes of subgroups.

The subgroup lattice has 906 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#137C211yesmaximal, characteristic
2C22×#417C211yesmaximal, characteristic
3C22×#419C211yesmaximal, characteristic, complemented
4C2×#2297C211yesmaximal, characteristic
5C22×#391C211yesmaximal, characteristic, complemented
6C2×#1736C211yesmaximal, characteristic, complemented
7C2×#1728C211yesmaximal, characteristic, complemented
8#11024C214yesmaximal, complemented
9#11023C214yesmaximal, complemented
10C23×#41C2211yescharacteristic
11C24×Q8C2211yescharacteristic
12C22×#137—24no—
13C22×#137—24no—
14C22×#137—24no—
15C22×#137—24no—
16C22×#137—24no—
17C22×#137—24no—
18C22×#137C418yescomplemented
19C23×Q16C2212yes—
20C23×SD16C2212yes—
21C23×M16C2211yescharacteristic
22C23×M16C2211yescharacteristic
23C22×#117C2211yescharacteristic
24C23×C4⋊C4C2211yescharacteristic
25C23×C42C2211yescharacteristic
26C2×#417—24no—
27C2×#417—24no—
28C2×#417—24no—
29C2×#419—24no—
30C2×#419—24no—
31C2×#419—24no—
32C22×#103C2214yes—
33C22×#103C2212yes—
34C22×#102C2212yes—
35#2297—24no—
36#2297—24no—
37C2×#391—22no—
38C2×#391—24no—
39C2×#391—24no—
40C2×#391C2214yes—
41C2×#391C2212yes—
42C2×#390C2212yes—
43C2×#386—22no—
44C2×C4×C22⋊C4—22no—
45C22×#95—22no—
46#1736—24no—
47C2×#340C2214yes—
48#1728—24no—
49C2×#336C2214yes—
50C22×#41—22no—
51C22×#41—22no—
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×#41C2×C414yes—
62C22×#41D414yes—
63C22×#41D414yes—
64C23×Q8—22no—
65C23×Q8—21no—
66C23×Q8—22no—
67C23×Q8—22no—
68C23×Q8—22no—
69C23×Q8—22no—
70C23×Q8—22no—
71C23×Q8—22no—
72C23×Q8—22no—
73C23×Q8—22no—
74C23×Q8—22no—
75C23×Q8—22no—
76C23×Q8C2×C414yes—
77C23×Q8D414yes—
78C23×Q8D414yes—
79C23×Q8C2312yes—
80C23×Q8C2311yescharacteristic
81C23×D4—21no—
82C23×D4C2311yescharacteristic
83C24×C4—21no—
84C24×C4—21no—
85C24×C4—21no—
86C24×C4D412yes—
87C24×C4C2311yescharacteristic
88C2×#137—232no—
89C2×#137—232no—
90C2×#137—232no—
91C2×#137—232no—
92C2×#137—232no—
93C2×#137—232no—
94C2×#137—232no—
95C22×Q16—24no—
96C22×Q16—24no—
97C22×Q16—24no—
98C22×Q16—24no—
99C22×Q16—24no—
100C22×Q16—24no—
101C22×Q16C2×C418yescomplemented
102C22×SD16—24no—
103C22×SD16—24no—
104C22×SD16—24no—
105C22×SD16—24no—
106C22×SD16—24no—
107C22×SD16—24no—
108C22×SD16C2×C418yescomplemented
109C22×M16—22no—
110C22×M16—22no—
111C22×M16—22no—
112C22×M16—22no—
113C22×M16—22no—
114C22×M16—22no—
115C22×M16—22no—
116C22×M16—22no—
117C22×M16—22no—
118C22×M16—22no—
119C22×M16C2×C414yes—
120C22×M16D414yes—
121C22×M16D414yes—
122C22×M16D414yes—
123C23×C8C2312yes—
124C23×C8C2312yes—
125C2×#117—22no—
126C2×#117—22no—
127C2×#117—22no—
128C2×#117—22no—
129C2×#117—22no—
130C2×#117D414yes—
131C22×C4⋊C4—22no—
132C22×C4⋊C4—22no—
133C22×C4⋊C4—22no—
134C22×C4⋊C4—22no—
135C22×C4⋊C4—21no—
136C22×C4⋊C4—22no—
137C22×C4⋊C4D414yes—
138C22×C4⋊C4C2312yes—
139C22×C4⋊C4C2312yes—
140C22×C22⋊C4—21no—
141C22×C22⋊C4—24no—
142C22×C42—22no—
143C22×C42—22no—
144C22×C42—22no—
145C22×C42—22no—
146C22×C42—22no—
147C22×C42—21no—
148C22×C42—22no—
149C22×C42D412yes—
150C22×C42C2312yes—
151#419—232no—
152#417—232no—
153C2×#103—28no—
154C2×#103—24no—
155C2×#103—28no—
156C2×#103—24no—
157C2×#103—28no—
158C2×#103—24no—
159C2×#102—24no—
160C2×#102—24no—
161C2×#102—24no—
162#391—216no—
163#391—28no—
164#391—24no—
165#391—28no—
166#391—24no—
167#390—24no—
168#390—24no—
169#386—216no—
170C4×C22⋊C4—216no—
171C2×#95—216no—
172C2×#95—28no—
173C2×#95—24no—
174#340—28no—
175#336—28no—
176C25—21no—
177C25C2×D411yescharacteristic
178C2×#41—28no—
179C2×#41—28no—
180C2×#41—28no—
181C2×#41—28no—
182C2×#41—28no—
183C2×#41—28no—
184C2×#41—28no—
185C2×#41—28no—
186C2×#41—28no—
187C2×#41—28no—
188C2×#41—28no—
189C2×#41—28no—
190C2×#41—28no—
191C2×#41—28no—
192C2×#41—28no—
193C2×#41—44no—
194C2×#41—44no—
195C2×#41—44no—
196C2×#41—44no—
197C2×#41—44no—
198C2×#41—44no—
199C2×#41—44no—
200C2×#41—44no—
201C2×#41—44no—
202C2×#41—44no—
203C2×#41—44no—
204C2×#41—44no—
205C2×#41C22⋊C4116yes—
206C22×Q8—24no—
207C22×Q8—28no—
208C22×Q8—24no—
209C22×Q8—24no—
210C22×Q8—28no—
211C22×Q8—28no—
212C22×Q8—22no—
213C22×Q8—21no—
214C22×Q8—22no—
215C22×Q8—22no—
216C22×Q8—21no—
217C22×Q8—21no—
218C22×Q8—28no—
219C22×Q8—28no—
220C22×Q8—28no—
221C22×Q8—28no—
222C22×Q8—28no—
223C22×Q8—28no—
224C22×Q8—28no—
225C22×Q8—28no—
226C22×Q8—28no—
227C22×Q8—28no—
228C22×Q8—28no—
229C22×Q8—28no—
230C22×Q8—22no—
231C22×Q8—22no—
232C22×Q8—22no—
233C22×Q8—22no—
234C22×Q8—21no—
235C22×Q8—21no—
236C22×Q8—21no—
237C22×Q8—21no—
238C22×Q8—22no—
239C22×Q8—22no—
240C22×Q8—21no—
241C22×Q8—21no—
242C22×Q8—22no—
243C22×Q8—22no—
244C22×Q8—21no—
245C22×Q8—21no—
246C22×Q8—42no—
247C22×Q8—44no—
248C22×Q8—42no—
249C22×Q8—42no—
250C22×Q8—44no—
251C22×Q8—44no—
252C22×Q8—44no—
253C22×Q8—44no—
254C22×Q8—44no—
255C22×Q8—44no—
256C22×Q8—44no—
257C22×Q8—44no—
258C22×Q8—44no—
259C22×Q8—44no—
260C22×Q8—42no—
261C22×Q8—44no—
262C22×Q8C22⋊C4116yescomplemented
263C22×Q8C22×C414yes—
264C22×Q8C22×C412yes—
265C22×Q8C2×D414yes—
266C22×Q8C2×D414yes—
267C22×Q8C2×D412yes—
268C22×Q8C2×D412yes—
269C22×D4—24no—
270C22×D4—24no—
271C22×D4—24no—
272C22×D4—21no—
273C22×D4—21no—
274C22×D4—21no—
275C22×D4—21no—
276C22×D4—21no—
277C22×D4—21no—
278C22×D4—21no—
279C22×D4—21no—
280C22×D4—21no—
281C22×D4—21no—
282C22×D4—21no—
283C22×D4—42no—
284C22×D4—42no—
285C22×D4—42no—
286C22×D4—42no—
287C22×D4C22×C412yes—
288C22×D4C2×D412yes—
289C22×D4C2×D412yes—
290C23×C4—24no—
291C23×C4—24no—
292C23×C4—24no—
293C23×C4—24no—
294C23×C4—21no—
295C23×C4—22no—
296C23×C4—24no—
297C23×C4—24no—
298C23×C4—24no—
299C23×C4—28no—
300C23×C4—24no—
301C23×C4—24no—
302C23×C4—24no—
303C23×C4—22no—
304C23×C4—22no—
305C23×C4—44no—
306C23×C4—42no—
307C23×C4—42no—
308C23×C4—42no—
309C23×C4—42no—
310C23×C4—42no—
311C23×C4—42no—
312C23×C4—42no—
313C23×C4—42no—
314C23×C4—48no—
315C23×C4—42no—
316C23×C4—42no—
317C23×C4C22×C412yes—
318C23×C4C2×D414yes—
319C23×C4C2×D412yes—
320C23×C4C2×D412yes—
321C23×C4C2×D412yes—
322C23×C4C2×D412yes—
323C23×C4C2×D412yes—
324C23×C4C2×D412yes—
325C23×C4C2×D411yescharacteristic
326C23×C4C2×D412yes—
327C23×C4C2×D412yes—
328C23×C4C2×D412yes—
329C23×C4#4112yes—
330C23×C4#4112yes—
331C23×C4#4112yes—
332C23×C4#4112yes—
333C23×C4C2411yescharacteristic
334#137—2256no—
335C2×Q16—216no—
336C2×Q16—216no—
337C2×Q16—216no—
338C2×Q16—216no—
339C2×Q16—216no—
340C2×Q16—216no—
341C2×Q16—216no—
342C2×SD16—216no—
343C2×SD16—216no—
344C2×SD16—216no—
345C2×SD16—216no—
346C2×SD16—216no—
347C2×SD16—216no—
348C2×SD16—216no—
349C2×M16—28no—
350C2×M16—28no—
351C2×M16—28no—
352C2×M16—28no—
353C2×M16—28no—
354C2×M16—28no—
355C2×M16—28no—
356C2×M16—28no—
357C2×M16—28no—
358C2×M16—44no—
359C2×M16—44no—
360C2×M16—44no—
361C2×M16—44no—
362C2×M16C22⋊C4116yescomplemented
363C22×C8—22no—
364C22×C8—22no—
365C22×C8—22no—
366C22×C8—22no—
367C22×C8—22no—
368C22×C8—22no—
369C22×C8—22no—
370C22×C8—22no—
371C22×C8—22no—
372C22×C8—22no—
373C22×C8C22×C414yes—
374C22×C8C2×D414yes—
375C22×C8C2×D414yes—
376C22×C8C2×D414yes—
377#117—28no—
378#117—28no—
379#117—44no—
380#117—44no—
381C2×C4⋊C4—28no—
382C2×C4⋊C4—28no—
383C2×C4⋊C4—22no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4—22no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4—24no—
392C2×C4⋊C4—22no—
393C2×C4⋊C4—22no—
394C2×C4⋊C4—44no—
395C2×C4⋊C4—44no—
396C2×C4⋊C4—42no—
397C2×C4⋊C4—42no—
398C2×C4⋊C4C2×D414yes—
399C2×C4⋊C4C2×D414yes—
400C2×C22⋊C4—216no—
401C2×C22⋊C4—24no—
402C2×C22⋊C4—48no—
403C2×C22⋊C4—42no—
404C2×C22⋊C4—42no—
405C2×C22⋊C4—48no—
406C2×C42—24no—
407C2×C42—24no—
408C2×C42—24no—
409C2×C42—24no—
410C2×C42—22no—
411C2×C42—22no—
412C2×C42—22no—
413C2×C42—22no—
414C2×C42—22no—
415C2×C42—22no—
416C2×C42—44no—
417C2×C42—42no—
418C2×C42—44no—
419C2×C42—44no—
420C2×C42—42no—
421C2×C42—44no—
422#103—216no—
423#103—232no—
424#102—216no—
425#95—232no—
426#95—216no—
427C24—24no—
428C24—24no—
429C24—22no—
430C24—22no—
431C24—22no—
432C24—41no—
433C24—41no—
434C24—41no—
435C24—41no—
436C24—44no—
437C24—44no—
438C24C4×D412yes—
439C24#12012yes—
440C24#12012yes—
441C24#12112yes—
442C24#12112yes—
443C24#12112yes—
444C24#12712yes—
445C24C22×D411yescharacteristic
446#41—232no—
447#41—232no—
448#41—416no—
449#41—416no—
450#41—416no—
451#41—416no—
452#41—416no—
453#41—416no—
454C2×Q8—24no—
455C2×Q8—22no—
456C2×Q8—24no—
457C2×Q8—22no—
458C2×Q8—24no—
459C2×Q8—22no—
460C2×Q8—216no—
461C2×Q8—24no—
462C2×Q8—24no—
463C2×Q8—22no—
464C2×Q8—22no—
465C2×Q8—24no—
466C2×Q8—24no—
467C2×Q8—22no—
468C2×Q8—22no—
469C2×Q8—24no—
470C2×Q8—22no—
471C2×Q8—24no—
472C2×Q8—24no—
473C2×Q8—24no—
474C2×Q8—24no—
475C2×Q8—22no—
476C2×Q8—22no—
477C2×Q8—22no—
478C2×Q8—22no—
479C2×Q8—24no—
480C2×Q8—24no—
481C2×Q8—22no—
482C2×Q8—22no—
483C2×Q8—24no—
484C2×Q8—22no—
485C2×Q8—232no—
486C2×Q8—232no—
487C2×Q8—42no—
488C2×Q8—41no—
489C2×Q8—42no—
490C2×Q8—42no—
491C2×Q8—42no—
492C2×Q8—42no—
493C2×Q8—42no—
494C2×Q8—42no—
495C2×Q8—41no—
496C2×Q8—41no—
497C2×Q8—41no—
498C2×Q8—41no—
499C2×Q8—41no—
500C2×Q8—41no—
501C2×Q8—42no—
502C2×Q8—42no—
503C2×Q8—41no—
504C2×Q8—41no—
505C2×Q8—42no—
506C2×Q8—42no—
507C2×Q8—41no—
508C2×Q8—41no—
509C2×Q8—42no—
510C2×Q8—41no—
511C2×Q8—416no—
512C2×Q8—48no—
513C2×Q8—416no—
514C2×Q8—48no—
515C2×Q8—48no—
516C2×Q8—48no—
517C2×Q8—48no—
518C2×Q8—416no—
519C2×Q8—48no—
520C2×Q8—416no—
521C2×Q8—416no—
522C2×Q8—416no—
523C2×Q8C2×C22⋊C418yes—
524C2×Q8C2×C22⋊C414yes—
525C2×D4—216no—
526C2×D4—22no—
527C2×D4—22no—
528C2×D4—22no—
529C2×D4—22no—
530C2×D4—22no—
531C2×D4—22no—
532C2×D4—22no—
533C2×D4—22no—
534C2×D4—22no—
535C2×D4—22no—
536C2×D4—22no—
537C2×D4—22no—
538C2×D4—22no—
539C2×D4—22no—
540C2×D4—22no—
541C2×D4—48no—
542C2×D4—48no—
543C2×D4—48no—
544C2×D4—48no—
545C2×D4—48no—
546C2×D4—48no—
547C2×D4—41no—
548C2×D4—41no—
549C2×D4—41no—
550C2×D4—41no—
551C2×D4—41no—
552C2×D4—41no—
553C2×D4—41no—
554C2×D4—41no—
555C2×D4—41no—
556C2×D4—41no—
557C2×D4—41no—
558C2×D4—41no—
559C2×D4C2×C22⋊C414yes—
560C22×C4—216no—
561C22×C4—22no—
562C22×C4—24no—
563C22×C4—24no—
564C22×C4—22no—
565C22×C4—24no—
566C22×C4—24no—
567C22×C4—24no—
568C22×C4—22no—
569C22×C4—24no—
570C22×C4—24no—
571C22×C4—24no—
572C22×C4—24no—
573C22×C4—216no—
574C22×C4—216no—
575C22×C4—24no—
576C22×C4—24no—
577C22×C4—416no—
578C22×C4—416no—
579C22×C4—48no—
580C22×C4—41no—
581C22×C4—42no—
582C22×C4—41no—
583C22×C4—41no—
584C22×C4—42no—
585C22×C4—42no—
586C22×C4—41no—
587C22×C4—42no—
588C22×C4—48no—
589C22×C4—48no—
590C22×C4—48no—
591C22×C4—48no—
592C22×C4—48no—
593C22×C4—48no—
594C22×C4—48no—
595C22×C4—48no—
596C22×C4—48no—
597C22×C4—48no—
598C22×C4—48no—
599C22×C4—48no—
600C22×C4—48no—
601C22×C4—416no—
602C22×C4—42no—
603C22×C4—42no—
604C22×C4—42no—
605C22×C4—42no—
606C22×C4—44no—
607C22×C4—44no—
608C22×C4—48no—
609C22×C4—48no—
610C22×C4—88no—
611C22×C4—88no—
612C22×C4C2×C22⋊C414yes—
613C22×C4C2×C22⋊C414yes—
614C22×C4C2×C22⋊C414yes—
615C22×C4C4×D414yes—
616C22×C4C4×D414yes—
617C22×C4C4×D414yes—
618C22×C4C4×D412yes—
619C22×C4#12014yes—
620C22×C4#12014yes—
621C22×C4#12014yes—
622C22×C4#12014yes—
623C22×C4#12014yes—
624C22×C4#12014yes—
625C22×C4#12012yes—
626C22×C4#12012yes—
627C22×C4#12114yes—
628C22×C4#12114yes—
629C22×C4#12114yes—
630C22×C4#12114yes—
631C22×C4#12114yes—
632C22×C4#12114yes—
633C22×C4#12114yes—
634C22×C4#12114yes—
635C22×C4#12114yes—
636C22×C4#12112yes—
637C22×C4#12112yes—
638C22×C4#12112yes—
639C22×C4#12314yes—
640C22×C4#12314yes—
641C22×C4#12314yes—
642C22×C4#12314yes—
643C22×C4#12414yes—
644C22×C4#12414yes—
645C22×C4#12714yes—
646C22×C4#12712yes—
647C22×C4#13718yescomplemented
648C22×C4C23×C411yescharacteristic
649C22×C4C22×D411yescharacteristic
650C22×C4C22×D411yescharacteristic
651C22×C4C22×D411yescharacteristic
652C22×C4C22×D411yescharacteristic
653C22×C4C22×D411yescharacteristic
654C22×C4C22×D411yescharacteristic
655C22×C4C22×D411yescharacteristic
656C22×C4C22×D411yescharacteristic
657C22×C4C22×D411yescharacteristic
658C22×C4C2×#4111yescharacteristic
659C22×C4C2×#4111yescharacteristic
660C22×C4C2×#4111yescharacteristic
661C22×C4C2×#4111yescharacteristic
662Q16—264no—
663SD16—264no—
664M16—232no—
665M16—416no—
666C2×C8—24no—
667C2×C8—24no—
668C2×C8—24no—
669C2×C8—24no—
670C2×C8—24no—
671C2×C8—24no—
672C2×C8—24no—
673C2×C8—24no—
674C2×C8—24no—
675C2×C8—42no—
676C2×C8—42no—
677C2×C8—42no—
678C2×C8—42no—
679C2×C8C2×C22⋊C418yes—
680C4⋊C4—24no—
681C4⋊C4—24no—
682C4⋊C4—24no—
683C4⋊C4—24no—
684C4⋊C4—42no—
685C4⋊C4—42no—
686C4⋊C4—42no—
687C4⋊C4—42no—
688C4⋊C4—48no—
689C22⋊C4—432no—
690C22⋊C4—48no—
691C42—42no—
692C42—42no—
693C42—42no—
694C42—42no—
695C42—48no—
696C42—48no—
697C23—24no—
698C23—24no—
699C23—28no—
700C23—24no—
701C23—24no—
702C23—28no—
703C23—28no—
704C23—24no—
705C23—24no—
706C23—28no—
707C23—24no—
708C23—42no—
709C23—42no—
710C23—42no—
711C23—42no—
712C23—48no—
713C23—48no—
714C23—44no—
715C23—44no—
716C23—42no—
717C23—42no—
718C23—82no—
719C23—82no—
720C23—82no—
721C23—82no—
722C23—84no—
723C23—84no—
724C23#38614yes—
725C23#38614yes—
726C23#39014yes—
727C23#39214yes—
728C23#39214yes—
729C23#39214yes—
730C23#39414yes—
731C23C2×C4×D411yescharacteristic
732C23C2×#12011yescharacteristic
733C23C2×#12011yescharacteristic
734C23C2×#12111yescharacteristic
735C23C2×#12111yescharacteristic
736C23C2×#12111yescharacteristic
737C23C2×#12711yescharacteristic
738C23C2×#13714yes—
739C23#57514yes—
740Q8—28no—
741Q8—24no—
742Q8—28no—
743Q8—24no—
744Q8—44no—
745Q8—42no—
746Q8—44no—
747Q8—44no—
748Q8—44no—
749Q8—42no—
750Q8—42no—
751Q8—42no—
752Q8—432no—
753Q8—44no—
754Q8—42no—
755Q8—44no—
756Q8—42no—
757D4—24no—
758D4—24no—
759D4—432no—
760D4—42no—
761D4—42no—
762D4—42no—
763D4—42no—
764D4—42no—
765D4—42no—
766C2×C4—28no—
767C2×C4—28no—
768C2×C4—24no—
769C2×C4—28no—
770C2×C4—28no—
771C2×C4—432no—
772C2×C4—44no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—44no—
777C2×C4—44no—
778C2×C4—44no—
779C2×C4—42no—
780C2×C4—44no—
781C2×C4—432no—
782C2×C4—44no—
783C2×C4—44no—
784C2×C4—42no—
785C2×C4—44no—
786C2×C4—44no—
787C2×C4—42no—
788C2×C4—44no—
789C2×C4—432no—
790C2×C4—44no—
791C2×C4—44no—
792C2×C4—48no—
793C2×C4—48no—
794C2×C4—816no—
795C2×C4—82no—
796C2×C4—82no—
797C2×C4—84no—
798C2×C4—84no—
799C2×C4—84no—
800C2×C4#37918yes—
801C2×C4#38614yes—
802C2×C4#38614yes—
803C2×C4#38618yes—
804C2×C4#38618yes—
805C2×C4#39014yes—
806C2×C4#39018yes—
807C2×C4#39218yes—
808C2×C4#39214yes—
809C2×C4#39214yes—
810C2×C4#39214yes—
811C2×C4#39418yes—
812C2×C4#39418yes—
813C2×C4#39418yes—
814C2×C4#39414yes—
815C2×C4C22×C22⋊C411yescharacteristic
816C2×C4C22×C22⋊C411yescharacteristic
817C2×C4C22×C22⋊C411yescharacteristic
818C2×C4C2×C4×D411yescharacteristic
819C2×C4C2×C4×D411yescharacteristic
820C2×C4C2×C4×D411yescharacteristic
821C2×C4C2×#12011yescharacteristic
822C2×C4C2×#12011yescharacteristic
823C2×C4C2×#12011yescharacteristic
824C2×C4C2×#12011yescharacteristic
825C2×C4C2×#12011yescharacteristic
826C2×C4C2×#12011yescharacteristic
827C2×C4C2×#12111yescharacteristic
828C2×C4C2×#12111yescharacteristic
829C2×C4C2×#12111yescharacteristic
830C2×C4C2×#12111yescharacteristic
831C2×C4C2×#12111yescharacteristic
832C2×C4C2×#12111yescharacteristic
833C2×C4C2×#12111yescharacteristic
834C2×C4C2×#12111yescharacteristic
835C2×C4C2×#12111yescharacteristic
836C2×C4C2×#12311yescharacteristic
837C2×C4C2×#12311yescharacteristic
838C2×C4C2×#12311yescharacteristic
839C2×C4C2×#12311yescharacteristic
840C2×C4C2×#12411yescharacteristic
841C2×C4C2×#12411yescharacteristic
842C2×C4C2×#12711yescharacteristic
843C8—28no—
844C8—44no—
845C22—28no—
846C22—28no—
847C22—24no—
848C22—24no—
849C22—28no—
850C22—28no—
851C22—28no—
852C22—28no—
853C22—44no—
854C22—48no—
855C22—84no—
856C22—84no—
857C22—82no—
858C22—82no—
859C22—84no—
860C22—84no—
861C22—84no—
862C22#143818yes—
863C22C2×#38611yescharacteristic
864C22C2×#38611yescharacteristic
865C22C2×#39011yescharacteristic
866C22C2×#39211yescharacteristic
867C22C2×#39211yescharacteristic
868C22C2×#39211yescharacteristic
869C22C2×#39411yescharacteristic
870C22C4×#13714yes—
871C22#300412yes—
872C22#300512yes—
873C22#300714yes—
874C22#303714yes—
875C22#303912yes—
876C22#304012yes—
877C22#305614yes—
878C22#315212yes—
879C22#315312yes—
880C4—44no—
881C4—48no—
882C4—48no—
883C4—84no—
884C4—84no—
885C4#143818yes—
886C4C2×#37911yescharacteristic
887C4C2×#38611yescharacteristic
888C4C2×#38611yescharacteristic
889C4C2×#39011yescharacteristic
890C4C2×#39211yescharacteristic
891C4C2×#39411yescharacteristic
892C4C2×#39411yescharacteristic
893C4C2×#39411yescharacteristic
894C2—28no—
895C2—84no—
896C2C2×#143811yescharacteristic
897C2#2092612yes—
898C2#2092712yes—
899C2#2123712yes—
900C2#2339212yes—
901C2#2342912yes—
902C2#2343111yescharacteristic
903C2#2343211yescharacteristic
904C2#2354712yes—
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
3. C22×#419C2semidirect
5. C22×#391C2semidirect
6. C2×#1736C2semidirect
7. C2×#1728C2semidirect
8. #11024C2semidirect
9. #11023C2semidirect
18. C22×#137C4semidirect
101. C22×Q16C2×C4semidirect
108. C22×SD16C2×C4semidirect
262. C22×Q8C22⋊C4semidirect
362. C2×M16C22⋊C4semidirect
647. C22×C4#137semidirect

Maximal subgroups

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

subgroupindex
C23×#1372
C22×#4172
C22×#4192
C2×#22972
C22×#3912
C2×#17362
C2×#17282
#110242
#110232