Finite Group Databasebeta

← #358481

Subgroups — #358481

Order 512.

1990 conjugacy classes of subgroups.

The subgroup lattice has 781 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2911C211yesmaximal, characteristic
2C2×#2911C211yesmaximal, characteristic
3#34052C211yesmaximal, characteristic
4C22×#344C211yesmaximal, characteristic
5C2×#1740C211yesmaximal, characteristic
6#20347C211yesmaximal, characteristic
7C2×#1733C211yesmaximal, characteristic
8#11333C218yesmaximal, complemented
9C23×M16C2211yescharacteristic
10C23×M16C2211yescharacteristic
11C22×#117C2211yescharacteristic
12C22×#117C2211yescharacteristic
13C22×#117C2211yescharacteristic
14C22×#117C2211yescharacteristic
15C22×#117C2211yescharacteristic
16#2911—22no—
17#2911—22no—
18#2911—22no—
19#2911—22no—
20#2911—22no—
21#2911—22no—
22#2911—22no—
23#2911C2214yes—
24C2×#428—22no—
25C2×#428—22no—
26C2×#428—22no—
27C2×#428C2214yes—
28C2×#427—22no—
29C2×#427—22no—
30#2317—22no—
31#2317C2214yes—
32#2316—22no—
33#2315—22no—
34#2296—22no—
35#2296—22no—
36#2285—22no—
37C2×#344C418yescomplemented
38C2×#344C2214yes—
39#1740—22no—
40#1740C2214yes—
41C2×#342—22no—
42#1736—22no—
43#1736C2214yes—
44#1735—22no—
45#1733—22no—
46#1733C2214yes—
47C2×#339—22no—
48C24×C4C2311yescharacteristic
49C22×M16—21no—
50C22×M16—21no—
51C22×M16—21no—
52C22×M16—21no—
53C22×M16—21no—
54C22×M16—21no—
55C22×M16—21no—
56C22×M16—22no—
57C22×M16—22no—
58C22×M16—22no—
59C22×M16—22no—
60C22×M16C2×C414yes—
61C22×M16C2×C414yes—
62C22×M16D412yes—
63C22×M16D412yes—
64C22×M16D412yes—
65C22×M16Q814yes—
66C22×M16Q814yes—
67C22×M16C2312yes—
68C22×M16C2312yes—
69C23×C8—21no—
70C23×C8D412yes—
71C2×#117—21no—
72C2×#117—21no—
73C2×#117—22no—
74C2×#117—22no—
75C2×#117—21no—
76C2×#117—21no—
77C2×#117—21no—
78C2×#117—21no—
79C2×#117—21no—
80C2×#117—21no—
81C2×#117—21no—
82C2×#117—22no—
83C2×#117—21no—
84C2×#117—22no—
85C2×#117—21no—
86C2×#117—21no—
87C2×#117—21no—
88C2×#117—21no—
89C2×#117—21no—
90C2×#117—21no—
91C2×#117—21no—
92C2×#117—21no—
93C2×#117—21no—
94C2×#117—21no—
95C2×#117—21no—
96C2×#117—21no—
97C2×#117—21no—
98C2×#117—21no—
99C2×#117—21no—
100C2×#117—21no—
101C2×#117—21no—
102C2×#117—21no—
103C2×#117—21no—
104C2×#117—21no—
105C2×#117—21no—
106C2×#117—21no—
107C2×#117—21no—
108C2×#117—21no—
109C2×#117—21no—
110C2×#117—22no—
111C2×#117C2×C414yes—
112C2×#117D412yes—
113C2×#117D412yes—
114C2×#117D412yes—
115C2×#117D412yes—
116C2×#117D412yes—
117C2×#117Q814yes—
118C2×#117Q814yes—
119C2×#117C2312yes—
120C2×#117C2312yes—
121C2×#117C2312yes—
122C2×#117C2312yes—
123C22×C4⋊C4—21no—
124C22×C4⋊C4—21no—
125C22×C4⋊C4D412yes—
126C22×C4⋊C4D412yes—
127C22×C4⋊C4C2312yes—
128C22×C22⋊C4—21no—
129C22×C22⋊C4—21no—
130C22×C22⋊C4—21no—
131C22×C22⋊C4—21no—
132C22×C22⋊C4D412yes—
133C22×C42—21no—
134C22×C42—21no—
135C22×C42—21no—
136C22×C42—21no—
137C22×C42—21no—
138#428—28no—
139#428—28no—
140#428—28no—
141#428—28no—
142#428—28no—
143#428—28no—
144#428—28no—
145#428—28no—
146#427—28no—
147#427—28no—
148#427—28no—
149#427—28no—
150C2×#107—24no—
151C2×#107—24no—
152C2×#106—24no—
153C2×#106—24no—
154#389—28no—
155#389—28no—
156#385—28no—
157#385—28no—
158#384—24no—
159#382—24no—
160#380—28no—
161C4×C4⋊C4—28no—
162#344C2×C4116yescomplemented
163#342—28no—
164#340—28no—
165#339—28no—
166C25C2×D411yescharacteristic
167C23×C4—22no—
168C23×C4—22no—
169C23×C4—22no—
170C23×C4—22no—
171C23×C4—41no—
172C23×C4C22×C412yes—
173C23×C4C2×D411yescharacteristic
174C23×C4C2×D411yescharacteristic
175C23×C4C2×D411yescharacteristic
176C23×C4C2×D411yescharacteristic
177C23×C4C2×D411yescharacteristic
178C23×C4C2×D411yescharacteristic
179C23×C4C2×D411yescharacteristic
180C23×C4C2×D411yescharacteristic
181C23×C4C2×D411yescharacteristic
182C23×C4C2×D411yescharacteristic
183C23×C4C2×D411yescharacteristic
184C23×C4C2×Q812yes—
185C23×C4C2×Q812yes—
186C23×C4C2×Q812yes—
187C23×C4C2×Q812yes—
188C23×C4#4112yes—
189C23×C4#4112yes—
190C23×C4#4112yes—
191C23×C4#4111yescharacteristic
192C23×C4#4111yescharacteristic
193C23×C4C2411yescharacteristic
194C2×M16—24no—
195C2×M16—24no—
196C2×M16—24no—
197C2×M16—24no—
198C2×M16—24no—
199C2×M16—24no—
200C2×M16—24no—
201C2×M16—22no—
202C2×M16—22no—
203C2×M16—22no—
204C2×M16—22no—
205C2×M16—24no—
206C2×M16—24no—
207C2×M16—24no—
208C2×M16—24no—
209C2×M16—24no—
210C2×M16—24no—
211C2×M16—24no—
212C2×M16—24no—
213C2×M16—24no—
214C2×M16—24no—
215C2×M16—22no—
216C2×M16—22no—
217C2×M16—22no—
218C2×M16—22no—
219C2×M16—22no—
220C2×M16—22no—
221C2×M16—22no—
222C2×M16C4⋊C418yescomplemented
223C2×M16C4⋊C418yescomplemented
224C2×M16C4⋊C418yescomplemented
225C2×M16C22×C414yes—
226C2×M16C22×C414yes—
227C2×M16C2×D414yes—
228C2×M16C2×Q814yes—
229C2×M16C2×Q814yes—
230C22×C8—24no—
231C22×C8—22no—
232C22×C8—22no—
233C22×C8—22no—
234C22×C8—22no—
235C22×C8—24no—
236C22×C8—24no—
237C22×C8—22no—
238C22×C8C4⋊C418yescomplemented
239C22×C8C2×D414yes—
240#117—24no—
241#117—24no—
242#117—24no—
243#117—24no—
244#117—24no—
245#117—22no—
246#117—22no—
247#117—24no—
248#117—22no—
249#117—24no—
250#117—22no—
251#117—22no—
252#117—22no—
253#117—22no—
254#117—22no—
255#117—22no—
256#117—22no—
257#117—22no—
258#117—22no—
259#117—22no—
260#117—22no—
261#117—22no—
262#117—22no—
263#117—22no—
264#117—22no—
265#117—22no—
266#117—22no—
267#117—24no—
268#117—22no—
269#117—22no—
270#117—22no—
271#117—22no—
272#117—22no—
273#117—22no—
274#117—22no—
275#117—22no—
276#117—22no—
277#117—41no—
278#117—41no—
279#117—41no—
280#117—41no—
281#117—41no—
282#117—41no—
283#117—41no—
284#117—41no—
285#117—41no—
286#117—41no—
287#117—41no—
288#117—41no—
289#117—41no—
290#117—41no—
291#117—41no—
292#117—41no—
293#117—41no—
294#117—41no—
295#117—41no—
296#117—41no—
297#117—42no—
298#117—42no—
299#117—42no—
300#117—41no—
301#117—41no—
302#117—41no—
303#117—41no—
304#117C4⋊C418yes—
305#117C22×C414yes—
306#117C2×Q814yes—
307#117C2×Q814yes—
308C2×C4⋊C4—24no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—24no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—22no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—24no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—216no—
330C2×C4⋊C4—42no—
331C2×C4⋊C4—41no—
332C2×C4⋊C4C2×D414yes—
333C2×C4⋊C4C2×D414yes—
334C2×C4⋊C4C2×D414yes—
335C2×C22⋊C4—22no—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—24no—
338C2×C22⋊C4—22no—
339C2×C22⋊C4—22no—
340C2×C22⋊C4—22no—
341C2×C22⋊C4—22no—
342C2×C22⋊C4—22no—
343C2×C22⋊C4—22no—
344C2×C22⋊C4—22no—
345C2×C22⋊C4—41no—
346C2×C22⋊C4—41no—
347C2×C22⋊C4—41no—
348C2×C22⋊C4—41no—
349C2×C22⋊C4—41no—
350C2×C22⋊C4—41no—
351C2×C22⋊C4—42no—
352C2×C22⋊C4—41no—
353C2×C22⋊C4—41no—
354C2×C22⋊C4—41no—
355C2×C22⋊C4—41no—
356C2×C22⋊C4—41no—
357C2×C22⋊C4—41no—
358C2×C22⋊C4—41no—
359C2×C22⋊C4C4⋊C418yes—
360C2×C22⋊C4C2×D414yes—
361C2×C42—24no—
362C2×C42—22no—
363C2×C42—24no—
364C2×C42—22no—
365C2×C42—24no—
366C2×C42—22no—
367C2×C42—22no—
368C2×C42—22no—
369C2×C42—22no—
370C2×C42—22no—
371C2×C42—22no—
372C2×C42—22no—
373C2×C42—41no—
374C2×C42—41no—
375C2×C42—41no—
376C2×C42—41no—
377C2×C42—41no—
378C2×C42—41no—
379C2×C42—41no—
380C2×C42—41no—
381C2×C42—41no—
382C2×C42—41no—
383C2×C42—42no—
384C2×C42—41no—
385C2×C42—41no—
386C2×C42—41no—
387#107—216no—
388#107—216no—
389#106—216no—
390#106—216no—
391#95—216no—
392C24—82no—
393C24C2×C4⋊C412yes—
394C24#12011yescharacteristic
395C24#12011yescharacteristic
396C24#12111yescharacteristic
397C24#12111yescharacteristic
398C24C22⋊Q812yes—
399C24#12312yes—
400C24#12711yescharacteristic
401C24#12711yescharacteristic
402C24C4⋊Q812yes—
403C24C22×D411yescharacteristic
404C22×C4—24no—
405C22×C4—28no—
406C22×C4—24no—
407C22×C4—24no—
408C22×C4—24no—
409C22×C4—42no—
410C22×C4—42no—
411C22×C4—42no—
412C22×C4—42no—
413C22×C4—42no—
414C22×C4—42no—
415C22×C4—42no—
416C22×C4—44no—
417C22×C4—84no—
418C22×C4—84no—
419C22×C4—84no—
420C22×C4—84no—
421C22×C4—84no—
422C22×C4C2×C4⋊C412yes—
423C22×C4C2×C4⋊C412yes—
424C22×C4C2×C4⋊C412yes—
425C22×C4C2×C4⋊C412yes—
426C22×C4C2×C4⋊C412yes—
427C22×C4C4×D412yes—
428C22×C4C4×D412yes—
429C22×C4C4×D412yes—
430C22×C4C4×D412yes—
431C22×C4C4×D412yes—
432C22×C4C4×D412yes—
433C22×C4C4×Q812yes—
434C22×C4C4×Q812yes—
435C22×C4#12011yescharacteristic
436C22×C4#12011yescharacteristic
437C22×C4#12011yescharacteristic
438C22×C4#12011yescharacteristic
439C22×C4#12011yescharacteristic
440C22×C4#12011yescharacteristic
441C22×C4#12011yescharacteristic
442C22×C4#12011yescharacteristic
443C22×C4#12011yescharacteristic
444C22×C4#12011yescharacteristic
445C22×C4#12111yescharacteristic
446C22×C4#12111yescharacteristic
447C22×C4#12111yescharacteristic
448C22×C4#12111yescharacteristic
449C22×C4#12111yescharacteristic
450C22×C4#12111yescharacteristic
451C22×C4#12111yescharacteristic
452C22×C4#12111yescharacteristic
453C22×C4#12111yescharacteristic
454C22×C4#12111yescharacteristic
455C22×C4C22⋊Q812yes—
456C22×C4C22⋊Q812yes—
457C22×C4C22⋊Q812yes—
458C22×C4C22⋊Q812yes—
459C22×C4C22⋊Q812yes—
460C22×C4C22⋊Q812yes—
461C22×C4C22⋊Q812yes—
462C22×C4C22⋊Q812yes—
463C22×C4C22⋊Q812yes—
464C22×C4C22⋊Q812yes—
465C22×C4C22⋊Q812yes—
466C22×C4C22⋊Q812yes—
467C22×C4C22⋊Q812yes—
468C22×C4C22⋊Q812yes—
469C22×C4C22⋊Q812yes—
470C22×C4C22⋊Q812yes—
471C22×C4C22⋊Q812yes—
472C22×C4#12312yes—
473C22×C4#12312yes—
474C22×C4#12312yes—
475C22×C4#12312yes—
476C22×C4#12312yes—
477C22×C4#12512yes—
478C22×C4#12512yes—
479C22×C4#12512yes—
480C22×C4#12512yes—
481C22×C4#12512yes—
482C22×C4#12512yes—
483C22×C4#12711yescharacteristic
484C22×C4#12711yescharacteristic
485C22×C4C4⋊Q812yes—
486C22×C4C4⋊Q812yes—
487C22×C4C4⋊Q812yes—
488C22×C4C4⋊Q812yes—
489C22×C4C4⋊Q812yes—
490C22×C4C4⋊Q812yes—
491C22×C4C4⋊Q812yes—
492C22×C4C4⋊Q812yes—
493C22×C4C4⋊Q812yes—
494C22×C4C4⋊Q812yes—
495C22×C4C4⋊Q812yes—
496C22×C4C23×C411yescharacteristic
497C22×C4C22×D411yescharacteristic
498C22×C4C22×D411yescharacteristic
499C22×C4C22×D411yescharacteristic
500C22×C4C22×D411yescharacteristic
501C22×C4C22×D411yescharacteristic
502C22×C4C22×Q811yescharacteristic
503C22×C4C22×Q811yescharacteristic
504C22×C4C22×Q811yescharacteristic
505C22×C4C22×Q811yescharacteristic
506C22×C4C2×#4111yescharacteristic
507C22×C4C2×#4111yescharacteristic
508C22×C4C2×#4111yescharacteristic
509C22×C4C2×#4111yescharacteristic
510M16—24no—
511M16—24no—
512M16—24no—
513M16—24no—
514M16—24no—
515M16—24no—
516M16—24no—
517M16—28no—
518M16—28no—
519M16—28no—
520M16—28no—
521M16C2×C4⋊C418yes—
522C2×C8—24no—
523C2×C8—24no—
524C2×C8—24no—
525C2×C8—24no—
526C2×C8—24no—
527C2×C8—28no—
528C2×C8—28no—
529C2×C8—28no—
530C2×C8—28no—
531C2×C8C2×C4⋊C418yes—
532C4⋊C4—24no—
533C4⋊C4—24no—
534C4⋊C4—28no—
535C4⋊C4—24no—
536C4⋊C4—24no—
537C4⋊C4—24no—
538C4⋊C4—24no—
539C4⋊C4—24no—
540C4⋊C4—24no—
541C4⋊C4—24no—
542C4⋊C4—42no—
543C4⋊C4—42no—
544C4⋊C4—42no—
545C4⋊C4—42no—
546C4⋊C4—42no—
547C4⋊C4—42no—
548C4⋊C4—42no—
549C4⋊C4—44no—
550C4⋊C4—816no—
551C22⋊C4—24no—
552C22⋊C4—28no—
553C22⋊C4—24no—
554C22⋊C4—42no—
555C22⋊C4—42no—
556C22⋊C4—42no—
557C22⋊C4—42no—
558C22⋊C4—42no—
559C22⋊C4—42no—
560C22⋊C4—42no—
561C22⋊C4—42no—
562C22⋊C4—42no—
563C22⋊C4—42no—
564C22⋊C4—42no—
565C22⋊C4—42no—
566C22⋊C4—42no—
567C22⋊C4—44no—
568C22⋊C4C2×C4⋊C418yes—
569C42—24no—
570C42—24no—
571C42—28no—
572C42—24no—
573C42—42no—
574C42—42no—
575C42—42no—
576C42—42no—
577C42—42no—
578C42—42no—
579C42—42no—
580C42—42no—
581C42—42no—
582C42—42no—
583C42—42no—
584C42—42no—
585C42—42no—
586C42—44no—
587C23—42no—
588C23—42no—
589C23—42no—
590C23—42no—
591C23—42no—
592C23—42no—
593C23—42no—
594C23—82no—
595C23—82no—
596C23—82no—
597C23—82no—
598C23#38412yes—
599C23#38412yes—
600C23#38512yes—
601C23#38512yes—
602C23#38912yes—
603C23#38912yes—
604C23#39211yescharacteristic
605C23#39211yescharacteristic
606C23#39211yescharacteristic
607C23#39211yescharacteristic
608C23#39512yes—
609C23#39512yes—
610C23#39812yes—
611C23#39812yes—
612C23#39912yes—
613C23#39912yes—
614C23C22×C4⋊C411yescharacteristic
615C23C2×#12011yescharacteristic
616C23C2×#12111yescharacteristic
617C23C2×C22⋊Q811yescharacteristic
618C23C2×#12311yescharacteristic
619C23C2×#12711yescharacteristic
620C23C2×C4⋊Q811yescharacteristic
621C2×C4—28no—
622C2×C4—48no—
623C2×C4—48no—
624C2×C4—48no—
625C2×C4—44no—
626C2×C4—44no—
627C2×C4—44no—
628C2×C4—44no—
629C2×C4—88no—
630C2×C4—84no—
631C2×C4—84no—
632C2×C4—84no—
633C2×C4—84no—
634C2×C4—84no—
635C2×C4—84no—
636C2×C4—84no—
637C2×C4—88no—
638C2×C4—84no—
639C2×C4#38412yes—
640C2×C4#38412yes—
641C2×C4#38512yes—
642C2×C4#38512yes—
643C2×C4#38512yes—
644C2×C4#38512yes—
645C2×C4#38512yes—
646C2×C4#38512yes—
647C2×C4#38512yes—
648C2×C4#38512yes—
649C2×C4#38512yes—
650C2×C4#38512yes—
651C2×C4#38912yes—
652C2×C4#38912yes—
653C2×C4#38912yes—
654C2×C4#38912yes—
655C2×C4#38912yes—
656C2×C4#38912yes—
657C2×C4#38912yes—
658C2×C4#38912yes—
659C2×C4#38912yes—
660C2×C4#38912yes—
661C2×C4#39211yescharacteristic
662C2×C4#39211yescharacteristic
663C2×C4#39211yescharacteristic
664C2×C4#39211yescharacteristic
665C2×C4#39512yes—
666C2×C4#39512yes—
667C2×C4#39512yes—
668C2×C4#39512yes—
669C2×C4#39512yes—
670C2×C4#39512yes—
671C2×C4#39512yes—
672C2×C4#39512yes—
673C2×C4#39512yes—
674C2×C4#39512yes—
675C2×C4#39812yes—
676C2×C4#39812yes—
677C2×C4#39812yes—
678C2×C4#39812yes—
679C2×C4#39812yes—
680C2×C4#39812yes—
681C2×C4#39812yes—
682C2×C4#39812yes—
683C2×C4#39812yes—
684C2×C4#39812yes—
685C2×C4#39912yes—
686C2×C4#39912yes—
687C2×C4C22×C4⋊C411yescharacteristic
688C2×C4C22×C4⋊C411yescharacteristic
689C2×C4C2×C4×D411yescharacteristic
690C2×C4C2×C4×D411yescharacteristic
691C2×C4C2×C4×D411yescharacteristic
692C2×C4C2×C4×Q811yescharacteristic
693C2×C4C2×#12011yescharacteristic
694C2×C4C2×#12011yescharacteristic
695C2×C4C2×#12111yescharacteristic
696C2×C4C2×#12111yescharacteristic
697C2×C4C2×C22⋊Q811yescharacteristic
698C2×C4C2×C22⋊Q811yescharacteristic
699C2×C4C2×C22⋊Q811yescharacteristic
700C2×C4C2×C22⋊Q811yescharacteristic
701C2×C4C2×C22⋊Q811yescharacteristic
702C2×C4C2×C22⋊Q811yescharacteristic
703C2×C4C2×C22⋊Q811yescharacteristic
704C2×C4C2×C22⋊Q811yescharacteristic
705C2×C4C2×#12311yescharacteristic
706C2×C4C2×#12311yescharacteristic
707C2×C4C2×#12511yescharacteristic
708C2×C4C2×#12511yescharacteristic
709C2×C4C2×#12511yescharacteristic
710C2×C4C2×C4⋊Q811yescharacteristic
711C2×C4C2×C4⋊Q811yescharacteristic
712C2×C4C2×C4⋊Q811yescharacteristic
713C2×C4C2×C4⋊Q811yescharacteristic
714C2×C4C2×C4⋊Q811yescharacteristic
715C8—28no—
716C8—28no—
717C22—22no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—22no—
724C22—42no—
725C22—42no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22—42no—
731C22—42no—
732C22—42no—
733C22—42no—
734C22—42no—
735C22—42no—
736C22—42no—
737C22—42no—
738C22—42no—
739C22—42no—
740C22#144412yes—
741C22#144412yes—
742C22#144412yes—
743C22#144412yes—
744C22C2×#38411yescharacteristic
745C22C2×#38511yescharacteristic
746C22C2×#38911yescharacteristic
747C22C2×#39211yescharacteristic
748C22C2×#39511yescharacteristic
749C22C2×#39811yescharacteristic
750C22C2×#39911yescharacteristic
751C4—48no—
752C4—84no—
753C4—84no—
754C4—84no—
755C4—84no—
756C4#144412yes—
757C4#144412yes—
758C4#144412yes—
759C4#144412yes—
760C4C2×#38511yescharacteristic
761C4C2×#38511yescharacteristic
762C4C2×#38911yescharacteristic
763C4C2×#38911yescharacteristic
764C4C2×#39511yescharacteristic
765C4C2×#39511yescharacteristic
766C4C2×#39811yescharacteristic
767C4C2×#39811yescharacteristic
768C2—21no—
769C2—21no—
770C2—21no—
771C2—21no—
772C2—22no—
773C2—22no—
774C2—22no—
775C2—22no—
776C2—21no—
777C2—21no—
778C2C2×#144411yescharacteristic
779C2#2341212yes—
subgroupG/H
centerC2×C4#392
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
socleC22C2×#392
prime radicalC25C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4 ◁ C24×C4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
8. #11333C2semidirect
37. C2×#344C4semidirect
162. #344C2×C4semidirect
222. C2×M16C4⋊C4semidirect
223. C2×M16C4⋊C4semidirect
224. C2×M16C4⋊C4semidirect
238. C22×C8C4⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×#29112
#340522
C22×#3442
C2×#17402
#203472
C2×#17332
#113332