Finite Group Databasebeta

← #354091

Subgroups — #354091

Order 512.

3178 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#417C211yesmaximal, characteristic
2C22×#416C211yesmaximal, characteristic
3C2×#2311C211yesmaximal, characteristic
4C2×#2274C211yesmaximal, characteristic, complemented
5C2×#1736C211yesmaximal, characteristic, complemented
6C22×#340C211yesmaximal, characteristic, complemented
7C2×#1729C211yesmaximal, characteristic, complemented
8#10932C214yesmaximal, complemented
9#10931C214yesmaximal, complemented
10C23×#41C2211yescharacteristic
11C23×M16C2211yescharacteristic
12C24×C8C2211yescharacteristic
13C22×#117C2211yescharacteristic
14C22×#117C2211yescharacteristic
15C23×C4⋊C4C2211yescharacteristic
16C23×C4⋊C4C2211yescharacteristic
17C2×#417—24no—
18C2×#417—24no—
19C2×#417C418yescomplemented
20C2×#416—24no—
21C2×#416—24no—
22C2×#416C418yescomplemented
23C22×#103C2212yes—
24C22×#103C2212yes—
25C22×#102C2212yes—
26C22×#102C2212yes—
27#2311—24no—
28#2311C418yescomplemented
29C2×#391C2212yes—
30C2×#390C2212yes—
31C2×#386—22no—
32C2×#380—22no—
33#2274—24no—
34#2274—24no—
35C2×C4×C4⋊C4—22no—
36C2×C4×C4⋊C4C2214yes—
37C2×C4×C22⋊C4—22no—
38#1736—24no—
39C2×#340—24no—
40C2×#340C2214yes—
41C2×#340C2214yes—
42#1729—24no—
43C2×#336C2214yes—
44C22×#41—22no—
45C22×#41—22no—
46C22×#41—22no—
47C22×#41—22no—
48C22×#41—22no—
49C22×#41—22no—
50C22×#41—22no—
51C22×#41—22no—
52C22×#41—22no—
53C22×#41—22no—
54C22×#41—22no—
55C22×#41C2×C414yes—
56C22×#41C2×C414yes—
57C22×#41C2×C414yes—
58C23×Q8C2311yescharacteristic
59C23×D4—21no—
60C23×D4C2311yescharacteristic
61C24×C4—21no—
62C24×C4—21no—
63C24×C4—21no—
64C24×C4C2311yescharacteristic
65C22×M16—22no—
66C22×M16—22no—
67C22×M16—22no—
68C22×M16—22no—
69C22×M16—22no—
70C22×M16—22no—
71C22×M16C2×C414yes—
72C23×C8—22no—
73C23×C8—22no—
74C23×C8—22no—
75C23×C8—22no—
76C23×C8—22no—
77C23×C8—22no—
78C23×C8C2×C414yes—
79C23×C8C2312yes—
80C23×C8C2312yes—
81C2×#117—22no—
82C2×#117—22no—
83C2×#117—22no—
84C2×#117—22no—
85C2×#117—22no—
86C2×#117—22no—
87C2×#117—22no—
88C2×#117C2×C414yes—
89C2×#117C2×C414yes—
90C2×#117D414yes—
91C2×#117D414yes—
92C2×#117D414yes—
93C22×C4⋊C4—21no—
94C22×C4⋊C4—22no—
95C22×C4⋊C4—22no—
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—21no—
103C22×C4⋊C4C2×C414yes—
104C22×C4⋊C4C2×C414yes—
105C22×C4⋊C4D412yes—
106C22×C4⋊C4D414yes—
107C22×C4⋊C4D414yes—
108C22×C4⋊C4C2312yes—
109C22×C4⋊C4C2312yes—
110C22×C4⋊C4C2312yes—
111C22×C22⋊C4—21no—
112C22×C22⋊C4—24no—
113C22×C22⋊C4D412yes—
114C22×C42—21no—
115C22×C42—24no—
116C22×C42C2312yes—
117#417—232no—
118#416—232no—
119C2×#103—24no—
120C2×#103—24no—
121C2×#103—24no—
122C2×#103—24no—
123C2×#103C2×C418yescomplemented
124C2×#103C2×C418yescomplemented
125C2×#102—24no—
126C2×#102—24no—
127C2×#102—24no—
128C2×#102—24no—
129C2×#102C2×C418yescomplemented
130C2×#102C2×C418yescomplemented
131#391—24no—
132#391C2×C418yescomplemented
133#390—24no—
134#390C2×C418yescomplemented
135#386—216no—
136#380—216no—
137C4×C4⋊C4—216no—
138C4×C4⋊C4—28no—
139C4×C4⋊C4—28no—
140C4×C22⋊C4—216no—
141C2×#95—24no—
142C2×#95—24no—
143#340—28no—
144#340—28no—
145#336—28no—
146C25—21no—
147C25C2×D411yescharacteristic
148C2×#41—28no—
149C2×#41—28no—
150C2×#41—28no—
151C2×#41—28no—
152C2×#41—28no—
153C2×#41—28no—
154C2×#41—28no—
155C2×#41—28no—
156C2×#41—28no—
157C2×#41—28no—
158C2×#41—28no—
159C2×#41—28no—
160C2×#41—28no—
161C2×#41—28no—
162C2×#41—28no—
163C2×#41—44no—
164C2×#41—44no—
165C2×#41—44no—
166C2×#41—44no—
167C2×#41—44no—
168C2×#41—44no—
169C2×#41—44no—
170C2×#41—44no—
171C2×#41—44no—
172C2×#41—44no—
173C2×#41—44no—
174C2×#41—44no—
175C2×#41C42116yescomplemented
176C22×Q8—21no—
177C22×Q8—21no—
178C22×Q8—21no—
179C22×Q8—21no—
180C22×Q8—21no—
181C22×Q8—21no—
182C22×Q8—21no—
183C22×Q8—21no—
184C22×Q8—21no—
185C22×Q8—21no—
186C22×Q8—21no—
187C22×Q8C22×C412yes—
188C22×Q8C22×C412yes—
189C22×Q8C22×C412yes—
190C22×D4—24no—
191C22×D4—24no—
192C22×D4—24no—
193C22×D4—21no—
194C22×D4—21no—
195C22×D4—21no—
196C22×D4—21no—
197C22×D4—21no—
198C22×D4—21no—
199C22×D4—21no—
200C22×D4—21no—
201C22×D4—21no—
202C22×D4—21no—
203C22×D4—21no—
204C22×D4—42no—
205C22×D4—42no—
206C22×D4—42no—
207C22×D4—42no—
208C22×D4C22×C412yes—
209C22×D4C22×C412yes—
210C22×D4C22×C412yes—
211C23×C4—22no—
212C23×C4—22no—
213C23×C4—21no—
214C23×C4—24no—
215C23×C4—24no—
216C23×C4—24no—
217C23×C4—24no—
218C23×C4—24no—
219C23×C4—24no—
220C23×C4—22no—
221C23×C4—24no—
222C23×C4—42no—
223C23×C4—42no—
224C23×C4—42no—
225C23×C4—42no—
226C23×C4—42no—
227C23×C4—42no—
228C23×C4—82no—
229C23×C4—82no—
230C23×C4—82no—
231C23×C4—82no—
232C23×C4C22×C412yes—
233C23×C4C22×C412yes—
234C23×C4C22×C412yes—
235C23×C4C2×D414yes—
236C23×C4C2×D411yescharacteristic
237C23×C4C2×D412yes—
238C23×C4C2×D412yes—
239C23×C4C2×D412yes—
240C23×C4C2×D412yes—
241C23×C4C2×D412yes—
242C23×C4#4112yes—
243C23×C4#4112yes—
244C23×C4#4112yes—
245C23×C4#4112yes—
246C23×C4#4112yes—
247C23×C4#4112yes—
248C23×C4C2411yescharacteristic
249C2×M16—28no—
250C2×M16—28no—
251C2×M16—28no—
252C2×M16—44no—
253C2×M16—44no—
254C2×M16—44no—
255C2×M16—44no—
256C22×C8—28no—
257C22×C8—28no—
258C22×C8—28no—
259C22×C8—22no—
260C22×C8—22no—
261C22×C8—22no—
262C22×C8—22no—
263C22×C8—22no—
264C22×C8—22no—
265C22×C8—22no—
266C22×C8—22no—
267C22×C8—22no—
268C22×C8—22no—
269C22×C8—22no—
270C22×C8—22no—
271C22×C8—44no—
272C22×C8—44no—
273C22×C8—44no—
274C22×C8—44no—
275C22×C8C22×C414yes—
276C22×C8C22×C414yes—
277#117—28no—
278#117—28no—
279#117—28no—
280#117—28no—
281#117—28no—
282#117—28no—
283#117—28no—
284#117C22⋊C4116yescomplemented
285C2×C4⋊C4—28no—
286C2×C4⋊C4—24no—
287C2×C4⋊C4—24no—
288C2×C4⋊C4—24no—
289C2×C4⋊C4—28no—
290C2×C4⋊C4—24no—
291C2×C4⋊C4—28no—
292C2×C4⋊C4—24no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4—22no—
295C2×C4⋊C4—22no—
296C2×C4⋊C4—22no—
297C2×C4⋊C4—22no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—28no—
300C2×C4⋊C4—28no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—22no—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—24no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—42no—
308C2×C4⋊C4—42no—
309C2×C4⋊C4—44no—
310C2×C4⋊C4—44no—
311C2×C4⋊C4C22⋊C418yes—
312C2×C4⋊C4C22⋊C4116yescomplemented
313C2×C4⋊C4C22×C414yes—
314C2×C4⋊C4C22×C414yes—
315C2×C4⋊C4C22×C414yes—
316C2×C4⋊C4C2×D414yes—
317C2×C4⋊C4C2×D414yes—
318C2×C4⋊C4C2×D414yes—
319C2×C4⋊C4C2×D414yes—
320C2×C22⋊C4—24no—
321C2×C22⋊C4—24no—
322C2×C22⋊C4—24no—
323C2×C22⋊C4—24no—
324C2×C22⋊C4—24no—
325C2×C22⋊C4—216no—
326C2×C22⋊C4—84no—
327C2×C22⋊C4—84no—
328C2×C22⋊C4C22⋊C418yes—
329C2×C42—24no—
330C2×C42—24no—
331C2×C42—24no—
332C2×C42—22no—
333C2×C42—22no—
334C2×C42—22no—
335C2×C42—22no—
336C2×C42—216no—
337C2×C42—84no—
338C2×C42—84no—
339C2×C42C22×C414yes—
340C2×C42C2×D414yes—
341#103—216no—
342#103—216no—
343#102—216no—
344#102—216no—
345#95—216no—
346#95—216no—
347C24—22no—
348C24—22no—
349C24—22no—
350C24—22no—
351C24—22no—
352C24—22no—
353C24—22no—
354C24—41no—
355C24—41no—
356C24—41no—
357C24—41no—
358C24—42no—
359C24—42no—
360C24—42no—
361C24—42no—
362C24C2×C22⋊C412yes—
363C24C4×D412yes—
364C24C4×D412yes—
365C24#12012yes—
366C24#12112yes—
367C24#12112yes—
368C24#12312yes—
369C24C22×D411yescharacteristic
370#41—232no—
371#41—232no—
372#41—416no—
373#41—416no—
374#41—416no—
375#41—416no—
376#41—416no—
377#41—416no—
378C2×Q8—22no—
379C2×Q8—22no—
380C2×Q8—22no—
381C2×Q8—22no—
382C2×Q8—22no—
383C2×Q8—22no—
384C2×Q8—22no—
385C2×Q8—22no—
386C2×Q8—22no—
387C2×Q8—22no—
388C2×Q8—22no—
389C2×Q8—22no—
390C2×Q8—22no—
391C2×Q8—22no—
392C2×Q8—22no—
393C2×Q8—41no—
394C2×Q8—41no—
395C2×Q8—41no—
396C2×Q8—41no—
397C2×Q8—41no—
398C2×Q8—41no—
399C2×Q8—41no—
400C2×Q8—41no—
401C2×Q8—41no—
402C2×Q8—41no—
403C2×Q8—41no—
404C2×Q8—41no—
405C2×Q8C2×C4214yes—
406C2×D4—216no—
407C2×D4—22no—
408C2×D4—22no—
409C2×D4—22no—
410C2×D4—22no—
411C2×D4—22no—
412C2×D4—22no—
413C2×D4—22no—
414C2×D4—22no—
415C2×D4—22no—
416C2×D4—22no—
417C2×D4—22no—
418C2×D4—22no—
419C2×D4—22no—
420C2×D4—22no—
421C2×D4—22no—
422C2×D4—48no—
423C2×D4—48no—
424C2×D4—48no—
425C2×D4—48no—
426C2×D4—48no—
427C2×D4—48no—
428C2×D4—41no—
429C2×D4—41no—
430C2×D4—41no—
431C2×D4—41no—
432C2×D4—41no—
433C2×D4—41no—
434C2×D4—41no—
435C2×D4—41no—
436C2×D4—41no—
437C2×D4—41no—
438C2×D4—41no—
439C2×D4—41no—
440C2×D4C2×C4214yes—
441C22×C4—22no—
442C22×C4—24no—
443C22×C4—24no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—24no—
447C22×C4—24no—
448C22×C4—24no—
449C22×C4—24no—
450C22×C4—24no—
451C22×C4—24no—
452C22×C4—24no—
453C22×C4—24no—
454C22×C4—24no—
455C22×C4—24no—
456C22×C4—216no—
457C22×C4—216no—
458C22×C4—24no—
459C22×C4—41no—
460C22×C4—41no—
461C22×C4—41no—
462C22×C4—41no—
463C22×C4—42no—
464C22×C4—44no—
465C22×C4—42no—
466C22×C4—44no—
467C22×C4—42no—
468C22×C4—42no—
469C22×C4—48no—
470C22×C4—48no—
471C22×C4—48no—
472C22×C4—48no—
473C22×C4—48no—
474C22×C4—48no—
475C22×C4—42no—
476C22×C4—42no—
477C22×C4—44no—
478C22×C4—44no—
479C22×C4—48no—
480C22×C4—88no—
481C22×C4—88no—
482C22×C4—84no—
483C22×C4—84no—
484C22×C4—88no—
485C22×C4—84no—
486C22×C4—84no—
487C22×C4—88no—
488C22×C4C2×C4214yes—
489C22×C4C2×C22⋊C418yes—
490C22×C4C2×C22⋊C414yes—
491C22×C4C2×C22⋊C414yes—
492C22×C4C2×C22⋊C412yes—
493C22×C4#11714yes—
494C22×C4#11714yes—
495C22×C4#11714yes—
496C22×C4C4×D414yes—
497C22×C4C4×D414yes—
498C22×C4C4×D414yes—
499C22×C4C4×D414yes—
500C22×C4C4×D414yes—
501C22×C4C4×D414yes—
502C22×C4C4×D414yes—
503C22×C4C4×D414yes—
504C22×C4C4×D414yes—
505C22×C4C4×D414yes—
506C22×C4C4×D412yes—
507C22×C4C4×D412yes—
508C22×C4#12012yes—
509C22×C4#12114yes—
510C22×C4#12114yes—
511C22×C4#12114yes—
512C22×C4#12114yes—
513C22×C4#12112yes—
514C22×C4#12112yes—
515C22×C4#12314yes—
516C22×C4#12314yes—
517C22×C4#12312yes—
518C22×C4#12414yes—
519C22×C4#12414yes—
520C22×C4#12414yes—
521C22×C4#12614yes—
522C22×C4#12614yes—
523C22×C4#12714yes—
524C22×C4C23×C411yescharacteristic
525C22×C4C23×C411yescharacteristic
526C22×C4C23×C411yescharacteristic
527C22×C4C22×D411yescharacteristic
528C22×C4C22×D411yescharacteristic
529C22×C4C22×D411yescharacteristic
530C22×C4C22×D411yescharacteristic
531C22×C4C22×D411yescharacteristic
532C22×C4C2×#4111yescharacteristic
533C22×C4C2×#4111yescharacteristic
534C22×C4C2×#4111yescharacteristic
535C22×C4C2×#4111yescharacteristic
536C22×C4C2×#4111yescharacteristic
537C22×C4C2×#4111yescharacteristic
538M16—416no—
539C2×C8—24no—
540C2×C8—24no—
541C2×C8—24no—
542C2×C8—24no—
543C2×C8—24no—
544C2×C8—24no—
545C2×C8—42no—
546C2×C8—42no—
547C2×C8—42no—
548C2×C8—42no—
549C2×C8—42no—
550C2×C8—42no—
551C2×C8—42no—
552C2×C8—42no—
553C2×C8—416no—
554C4⋊C4—24no—
555C4⋊C4—24no—
556C4⋊C4—24no—
557C4⋊C4—24no—
558C4⋊C4—24no—
559C4⋊C4—24no—
560C4⋊C4—216no—
561C4⋊C4—216no—
562C4⋊C4—24no—
563C4⋊C4—24no—
564C4⋊C4—42no—
565C4⋊C4—42no—
566C4⋊C4—48no—
567C4⋊C4C2×C22⋊C418yes—
568C4⋊C4C2×C22⋊C418yes—
569C22⋊C4—216no—
570C22⋊C4—216no—
571C22⋊C4—816no—
572C42—24no—
573C42—24no—
574C42—24no—
575C42—24no—
576C42—216no—
577C42—816no—
578C23—24no—
579C23—24no—
580C23—24no—
581C23—24no—
582C23—24no—
583C23—24no—
584C23—24no—
585C23—24no—
586C23—24no—
587C23—24no—
588C23—22no—
589C23—22no—
590C23—22no—
591C23—22no—
592C23—24no—
593C23—24no—
594C23—24no—
595C23—44no—
596C23—44no—
597C23—44no—
598C23—44no—
599C23—44no—
600C23—44no—
601C23—42no—
602C23—42no—
603C23—42no—
604C23—42no—
605C23—42no—
606C23—42no—
607C23—82no—
608C23—82no—
609C23—82no—
610C23—82no—
611C23—81no—
612C23—81no—
613C23—81no—
614C23—81no—
615C23—82no—
616C23—82no—
617C23C4×C22⋊C414yes—
618C23#38614yes—
619C23#38614yes—
620C23#38614yes—
621C23#38814yes—
622C23#38814yes—
623C23#39014yes—
624C23C22×C22⋊C411yescharacteristic
625C23C2×C4×D411yescharacteristic
626C23C2×C4×D411yescharacteristic
627C23C2×#12011yescharacteristic
628C23C2×#12111yescharacteristic
629C23C2×#12111yescharacteristic
630C23C2×#12311yescharacteristic
631C23#57612yes—
632C23#57712yes—
633C23#57712yes—
634C23#57812yes—
635Q8—24no—
636Q8—24no—
637Q8—42no—
638Q8—42no—
639Q8—42no—
640Q8—42no—
641Q8—42no—
642Q8—42no—
643D4—24no—
644D4—24no—
645D4—432no—
646D4—42no—
647D4—42no—
648D4—42no—
649D4—42no—
650D4—42no—
651D4—42no—
652C2×C4—28no—
653C2×C4—28no—
654C2×C4—24no—
655C2×C4—28no—
656C2×C4—28no—
657C2×C4—28no—
658C2×C4—44no—
659C2×C4—44no—
660C2×C4—48no—
661C2×C4—44no—
662C2×C4—44no—
663C2×C4—44no—
664C2×C4—44no—
665C2×C4—48no—
666C2×C4—44no—
667C2×C4—44no—
668C2×C4—44no—
669C2×C4—44no—
670C2×C4—44no—
671C2×C4—44no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—432no—
679C2×C4—48no—
680C2×C4—44no—
681C2×C4—816no—
682C2×C4—816no—
683C2×C4—82no—
684C2×C4—82no—
685C2×C4—84no—
686C2×C4C4×C22⋊C414yes—
687C2×C4C4×C22⋊C418yes—
688C2×C4C4×C22⋊C418yes—
689C2×C4#38614yes—
690C2×C4#38614yes—
691C2×C4#38614yes—
692C2×C4#38814yes—
693C2×C4#38814yes—
694C2×C4#38818yes—
695C2×C4#38818yes—
696C2×C4#38818yes—
697C2×C4#38818yes—
698C2×C4#39014yes—
699C2×C4#39018yes—
700C2×C4#39018yes—
701C2×C4C22×C4211yescharacteristic
702C2×C4C22×C22⋊C411yescharacteristic
703C2×C4C22×C22⋊C411yescharacteristic
704C2×C4C2×#11711yescharacteristic
705C2×C4C2×#11711yescharacteristic
706C2×C4C2×#11711yescharacteristic
707C2×C4C2×C4×D411yescharacteristic
708C2×C4C2×C4×D411yescharacteristic
709C2×C4C2×C4×D411yescharacteristic
710C2×C4C2×C4×D411yescharacteristic
711C2×C4C2×C4×D411yescharacteristic
712C2×C4C2×C4×D411yescharacteristic
713C2×C4C2×C4×D411yescharacteristic
714C2×C4C2×C4×D411yescharacteristic
715C2×C4C2×C4×D411yescharacteristic
716C2×C4C2×C4×D411yescharacteristic
717C2×C4C2×#12111yescharacteristic
718C2×C4C2×#12111yescharacteristic
719C2×C4C2×#12111yescharacteristic
720C2×C4C2×#12111yescharacteristic
721C2×C4C2×#12311yescharacteristic
722C2×C4C2×#12311yescharacteristic
723C2×C4C2×#12411yescharacteristic
724C2×C4C2×#12411yescharacteristic
725C2×C4C2×#12411yescharacteristic
726C2×C4C2×#12611yescharacteristic
727C2×C4C2×#12611yescharacteristic
728C2×C4C2×#12711yescharacteristic
729C8—44no—
730C8—44no—
731C22—24no—
732C22—24no—
733C22—28no—
734C22—24no—
735C22—24no—
736C22—28no—
737C22—28no—
738C22—24no—
739C22—24no—
740C22—28no—
741C22—48no—
742C22—44no—
743C22—82no—
744C22—82no—
745C22—84no—
746C22—82no—
747C22—82no—
748C22—84no—
749C22—82no—
750C22—82no—
751C22—84no—
752C22#143718yes—
753C22C2×C4×C22⋊C411yescharacteristic
754C22C2×#38611yescharacteristic
755C22C2×#38611yescharacteristic
756C22C2×#38611yescharacteristic
757C22C2×#38811yescharacteristic
758C22C2×#38811yescharacteristic
759C22C2×#39011yescharacteristic
760C22#289712yes—
761C22#289812yes—
762C22#294612yes—
763C22#294712yes—
764C22#295112yes—
765C22#295212yes—
766C22#301212yes—
767C22#301312yes—
768C22#304111yescharacteristic
769C22#304211yescharacteristic
770C22#304311yescharacteristic
771C22#304411yescharacteristic
772C22#304512yes—
773C22#304612yes—
774C22#309812yes—
775C22#309912yes—
776C4—48no—
777C4—44no—
778C4—48no—
779C4—48no—
780C4—84no—
781C4#143718yes—
782C4C2×C4×C22⋊C411yescharacteristic
783C4C2×C4×C22⋊C411yescharacteristic
784C4C2×#38811yescharacteristic
785C4C2×#38811yescharacteristic
786C4C2×#38811yescharacteristic
787C4C2×#38811yescharacteristic
788C4C2×#39011yescharacteristic
789C4C2×#39011yescharacteristic
790C2—28no—
791C2—84no—
792C2C2×#143711yescharacteristic
793C2#2041512yes—
794C2#2091512yes—
795C2#2092911yescharacteristic
796C2#2093011yescharacteristic
797C2#2093712yes—
798C2#2106212yes—
799C2#2106711yescharacteristic
800C2#2106811yescharacteristic
801C2#2126211yescharacteristic
802C2#2126311yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutatorC2×C4C22×C42
Frattini, cosocleC23×C4C24
prime radicalC23×#41C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C22×#117 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
4. C2×#2274C2semidirect
5. C2×#1736C2semidirect
6. C22×#340C2semidirect
7. C2×#1729C2semidirect
8. #10932C2semidirect
9. #10931C2semidirect
19. C2×#417C4semidirect
22. C2×#416C4semidirect
28. #2311C4semidirect
123. C2×#103C2×C4semidirect
124. C2×#103C2×C4semidirect
129. C2×#102C2×C4semidirect
130. C2×#102C2×C4semidirect
132. #391C2×C4semidirect
134. #390C2×C4semidirect
175. C2×#41C42semidirect
284. #117C22⋊C4semidirect
312. C2×C4⋊C4C22⋊C4semidirect

Maximal subgroups

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

subgroupindex
C22×#4172
C22×#4162
C2×#23112
C2×#22742
C2×#17362
C22×#3402
C2×#17292
#109322
#109312