Finite Group Databasebeta

← #357752

Subgroups — #357752

Order 512.

2758 conjugacy classes of subgroups.

The subgroup lattice has 1028 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#421C211yesmaximal, characteristic
2C2×#2896C211yesmaximal, characteristic
3#34052C211yesmaximal, characteristic, complemented
4#34044C211yesmaximal, characteristic
5C2×#1733C211yesmaximal, characteristic, complemented
6C22×H(3,ℤ/4)C211yesmaximal, characteristic, complemented
7#20335C211yesmaximal, characteristic, complemented
8#11083C218yesmaximal, complemented
9C23×#41C2211yescharacteristic
10C23×M16C2211yescharacteristic
11C23×M16C2211yescharacteristic
12C22×#117C2211yescharacteristic
13C22×#117C2211yescharacteristic
14C22×#117C2211yescharacteristic
15C22×#117C2211yescharacteristic
16C2×#421—24no—
17C2×#421—22no—
18C2×#421C418yescomplemented
19C2×#421C2214yes—
20C22×#104—22no—
21#2896—22no—
22#2896—22no—
23#2896—22no—
24#2896C2214yes—
25C2×#417—22no—
26C2×#419—21no—
27C2×#418—21no—
28C2×#416—22no—
29#2317—22no—
30#2317—22no—
31#2316—22no—
32#2315—22no—
33#2311—22no—
34#2311—22no—
35#2310—21no—
36#2309—21no—
37#2308—22no—
38#2297—22no—
39#2297C2214yes—
40#2296—22no—
41#2296C2214yescomplemented
42#2285—22no—
43#2280—22no—
44#1733—22no—
45#1733C2214yescomplemented
46C2×#339—22no—
47C2×H(3,ℤ/4)—24no—
48C2×H(3,ℤ/4)C2214yescomplemented
49#1729—22no—
50#1729—22no—
51#1728C2214yescomplemented
52C22×#41—21no—
53C22×#41—21no—
54C22×#41—22no—
55C22×#41—22no—
56C22×#41—21no—
57C22×#41—21no—
58C22×#41—21no—
59C22×#41—21no—
60C22×#41—21no—
61C22×#41—22no—
62C22×#41—21no—
63C22×#41—21no—
64C22×#41—21no—
65C22×#41—22no—
66C22×#41—22no—
67C22×#41—22no—
68C22×#41C2×C414yes—
69C22×#41D412yes—
70C22×#41Q814yes—
71C22×#41C2312yes—
72C23×Q8D411yescharacteristic
73C23×D4—21no—
74C23×D4D411yescharacteristic
75C24×C4—21no—
76C24×C4C2311yescharacteristic
77C22×M16—21no—
78C22×M16—21no—
79C22×M16—21no—
80C22×M16—21no—
81C22×M16—21no—
82C22×M16—22no—
83C22×M16—22no—
84C22×M16—22no—
85C22×M16—22no—
86C22×M16—22no—
87C22×M16—21no—
88C22×M16—22no—
89C22×M16—21no—
90C22×M16—21no—
91C22×M16—21no—
92C22×M16—22no—
93C22×M16C2×C414yes—
94C22×M16D412yes—
95C22×M16C2312yes—
96C22×M16C2312yes—
97C23×C8—21no—
98C23×C8D412yes—
99C2×#117—21no—
100C2×#117—21no—
101C2×#117—22no—
102C2×#117—22no—
103C2×#117—21no—
104C2×#117—21no—
105C2×#117—21no—
106C2×#117—21no—
107C2×#117—21no—
108C2×#117—21no—
109C2×#117—21no—
110C2×#117—21no—
111C2×#117—21no—
112C2×#117—21no—
113C2×#117—21no—
114C2×#117—21no—
115C2×#117—21no—
116C2×#117—21no—
117C2×#117—21no—
118C2×#117—21no—
119C2×#117—22no—
120C2×#117—22no—
121C2×#117—22no—
122C2×#117—22no—
123C2×#117—21no—
124C2×#117—21no—
125C2×#117—21no—
126C2×#117—21no—
127C2×#117—21no—
128C2×#117—21no—
129C2×#117—21no—
130C2×#117—21no—
131C2×#117C2×C414yes—
132C2×#117D412yes—
133C2×#117D414yes—
134C2×#117D412yes—
135C2×#117D412yes—
136C2×#117C2312yes—
137C2×#117C2312yes—
138C2×#117C2312yes—
139C22×C4⋊C4—21no—
140C22×C4⋊C4—21no—
141C22×C4⋊C4D412yes—
142C22×C4⋊C4D412yes—
143C22×C22⋊C4—21no—
144C22×C22⋊C4—21no—
145C22×C22⋊C4—21no—
146C22×C22⋊C4D412yes—
147C22×C42—21no—
148C22×C42D412yes—
149C22×C42D412yes—
150C22×C42C2312yes—
151#421—216no—
152#421—28no—
153#421C2×C4116yescomplemented
154C2×#104—216no—
155C2×#104—28no—
156#419—24no—
157#419—24no—
158#418—24no—
159#418—24no—
160#417—28no—
161#417—28no—
162#416—28no—
163#416—28no—
164C2×#103—24no—
165C2×#102—24no—
166#391—24no—
167#391—24no—
168#390—24no—
169#390—24no—
170#389—28no—
171#389—28no—
172#386—28no—
173#386—28no—
174#385—28no—
175#385—28no—
176#384—24no—
177#382—24no—
178#381—24no—
179#380—28no—
180#380—28no—
181#379—24no—
182C4×C4⋊C4—28no—
183C4×C22⋊C4—28no—
184#339—28no—
185H(3,ℤ/4)—28no—
186#336—28no—
187C25—21no—
188C25C2×D411yescharacteristic
189C2×#41—24no—
190C2×#41—24no—
191C2×#41—24no—
192C2×#41—24no—
193C2×#41—24no—
194C2×#41—22no—
195C2×#41—22no—
196C2×#41—24no—
197C2×#41—24no—
198C2×#41—24no—
199C2×#41—24no—
200C2×#41—24no—
201C2×#41—24no—
202C2×#41—24no—
203C2×#41—24no—
204C2×#41—22no—
205C2×#41—22no—
206C2×#41—22no—
207C2×#41—22no—
208C2×#41—24no—
209C2×#41—24no—
210C2×#41—24no—
211C2×#41—24no—
212C2×#41—24no—
213C2×#41—24no—
214C2×#41—24no—
215C2×#41—24no—
216C2×#41—24no—
217C2×#41—24no—
218C2×#41—22no—
219C2×#41—22no—
220C2×#41—22no—
221C2×#41—22no—
222C2×#41—22no—
223C2×#41—22no—
224C2×#41—22no—
225C2×#41—22no—
226C2×#41—41no—
227C2×#41—41no—
228C2×#41—41no—
229C2×#41—41no—
230C2×#41—42no—
231C2×#41—42no—
232C2×#41—42no—
233C2×#41—41no—
234C2×#41—41no—
235C2×#41—42no—
236C2×#41—42no—
237C2×#41—42no—
238C2×#41—42no—
239C2×#41—42no—
240C2×#41—42no—
241C2×#41—42no—
242C2×#41—42no—
243C2×#41—42no—
244C2×#41—42no—
245C2×#41—42no—
246C2×#41—42no—
247C2×#41—42no—
248C2×#41—42no—
249C2×#41—42no—
250C2×#41—42no—
251C2×#41—42no—
252C2×#41—41no—
253C2×#41—41no—
254C2×#41C4⋊C418yescomplemented
255C2×#41C22×C414yes—
256C2×#41C2×Q814yes—
257C22×Q8—21no—
258C22×Q8—22no—
259C22×Q8—21no—
260C22×Q8—21no—
261C22×Q8—21no—
262C22×Q8—21no—
263C22×Q8—22no—
264C22×Q8—22no—
265C22×Q8C4⋊C414yescomplemented
266C22×Q8C2×D412yes—
267C22×D4—24no—
268C22×D4—22no—
269C22×D4—24no—
270C22×D4—22no—
271C22×D4—21no—
272C22×D4—21no—
273C22×D4—21no—
274C22×D4—21no—
275C22×D4—21no—
276C22×D4—22no—
277C22×D4—22no—
278C22×D4—22no—
279C22×D4—41no—
280C22×D4—41no—
281C22×D4—41no—
282C22×D4—41no—
283C22×D4—42no—
284C22×D4—42no—
285C22×D4C4⋊C414yescomplemented
286C22×D4C2×D412yes—
287C23×C4—21no—
288C23×C4—22no—
289C23×C4—24no—
290C23×C4—22no—
291C23×C4—24no—
292C23×C4—22no—
293C23×C4—22no—
294C23×C4—22no—
295C23×C4—41no—
296C23×C4—41no—
297C23×C4—42no—
298C23×C4—42no—
299C23×C4—41no—
300C23×C4—41no—
301C23×C4C22×C412yes—
302C23×C4C2×D414yes—
303C23×C4C2×D411yescharacteristic
304C23×C4C2×D411yescharacteristic
305C23×C4C2×D412yes—
306C23×C4C2×D411yescharacteristic
307C23×C4C2×D411yescharacteristic
308C23×C4C2×D411yescharacteristic
309C23×C4C2×D411yescharacteristic
310C23×C4C2×D411yescharacteristic
311C23×C4C2×D411yescharacteristic
312C23×C4C2×D411yescharacteristic
313C23×C4C2×D411yescharacteristic
314C23×C4C2×D411yescharacteristic
315C23×C4C2×Q812yes—
316C23×C4#4111yescharacteristic
317C23×C4#4111yescharacteristic
318C23×C4#4112yes—
319C23×C4#4112yes—
320C23×C4#4112yes—
321C23×C4#4112yes—
322C23×C4#4112yes—
323C23×C4C2411yescharacteristic
324C2×M16—24no—
325C2×M16—22no—
326C2×M16—22no—
327C2×M16—24no—
328C2×M16—24no—
329C2×M16—22no—
330C2×M16—22no—
331C2×M16—22no—
332C2×M16—22no—
333C2×M16—22no—
334C2×M16—22no—
335C2×M16—22no—
336C2×M16—24no—
337C2×M16—24no—
338C2×M16—24no—
339C2×M16—24no—
340C2×M16—22no—
341C2×M16—22no—
342C2×M16—22no—
343C2×M16—22no—
344C2×M16—42no—
345C2×M16—42no—
346C2×M16—42no—
347C2×M16—42no—
348C2×M16—42no—
349C2×M16—42no—
350C2×M16—42no—
351C2×M16—42no—
352C2×M16—42no—
353C2×M16—42no—
354C2×M16—42no—
355C2×M16—42no—
356C2×M16—42no—
357C2×M16—41no—
358C2×M16—41no—
359C2×M16C22×C414yes—
360C22×C8—24no—
361C22×C8—22no—
362C22×C8—22no—
363C22×C8—24no—
364C22×C8—24no—
365C22×C8—22no—
366C22×C8—42no—
367C22×C8—41no—
368C22×C8—41no—
369C22×C8C2×D414yes—
370#117—24no—
371#117—24no—
372#117—24no—
373#117—24no—
374#117—24no—
375#117—22no—
376#117—22no—
377#117—24no—
378#117—24no—
379#117—22no—
380#117—22no—
381#117—22no—
382#117—22no—
383#117—22no—
384#117—22no—
385#117—22no—
386#117—22no—
387#117—22no—
388#117—22no—
389#117—22no—
390#117—22no—
391#117—41no—
392#117—41no—
393#117—41no—
394#117—41no—
395#117—41no—
396#117—41no—
397#117—41no—
398#117—41no—
399#117—41no—
400#117—41no—
401#117—41no—
402#117—41no—
403#117—41no—
404#117—41no—
405#117—41no—
406#117—41no—
407#117—41no—
408#117—41no—
409#117—42no—
410#117—42no—
411#117—42no—
412#117—42no—
413#117—41no—
414#117—41no—
415#117—41no—
416#117—41no—
417#117—41no—
418#117—41no—
419#117C22⋊C418yescomplemented
420#117C22×C414yes—
421#117C2×D414yes—
422C2×C4⋊C4—24no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—24no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—22no—
428C2×C4⋊C4—22no—
429C2×C4⋊C4—22no—
430C2×C4⋊C4—22no—
431C2×C4⋊C4—22no—
432C2×C4⋊C4—22no—
433C2×C4⋊C4—22no—
434C2×C4⋊C4—22no—
435C2×C4⋊C4—22no—
436C2×C4⋊C4—22no—
437C2×C4⋊C4—22no—
438C2×C4⋊C4—22no—
439C2×C4⋊C4—216no—
440C2×C4⋊C4—42no—
441C2×C4⋊C4—42no—
442C2×C4⋊C4C2×D414yes—
443C2×C22⋊C4—24no—
444C2×C22⋊C4—22no—
445C2×C22⋊C4—24no—
446C2×C22⋊C4—22no—
447C2×C22⋊C4—22no—
448C2×C22⋊C4—22no—
449C2×C22⋊C4—22no—
450C2×C22⋊C4—22no—
451C2×C22⋊C4—22no—
452C2×C22⋊C4—22no—
453C2×C22⋊C4—22no—
454C2×C22⋊C4—22no—
455C2×C22⋊C4—22no—
456C2×C22⋊C4—22no—
457C2×C22⋊C4—216no—
458C2×C22⋊C4—41no—
459C2×C22⋊C4—41no—
460C2×C22⋊C4—41no—
461C2×C22⋊C4—41no—
462C2×C22⋊C4—42no—
463C2×C22⋊C4—42no—
464C2×C42—22no—
465C2×C42—24no—
466C2×C42—24no—
467C2×C42—24no—
468C2×C42—22no—
469C2×C42—22no—
470C2×C42—22no—
471C2×C42—22no—
472C2×C42—22no—
473C2×C42—22no—
474C2×C42—22no—
475C2×C42—22no—
476C2×C42—22no—
477C2×C42—41no—
478C2×C42—41no—
479C2×C42—41no—
480C2×C42—41no—
481C2×C42C22⋊C418yescomplemented
482C2×C42C2×D414yes—
483C2×C42C2×D414yes—
484#104—232no—
485#103—216no—
486#102—216no—
487#95—216no—
488#95—216no—
489C24—22no—
490C24—24no—
491C24—41no—
492C24—41no—
493C24—42no—
494C24—82no—
495C24—84no—
496C24C4×D412yes—
497C24#12011yescharacteristic
498C24#12011yescharacteristic
499C24#12011yescharacteristic
500C24#12011yescharacteristic
501C24#12111yescharacteristic
502C24#12111yescharacteristic
503C24#12112yes—
504C24C22⋊Q812yes—
505C24#12412yes—
506C24C22×D411yescharacteristic
507#41—24no—
508#41—24no—
509#41—24no—
510#41—24no—
511#41—24no—
512#41—24no—
513#41—24no—
514#41—24no—
515#41—28no—
516#41—28no—
517#41—28no—
518#41—28no—
519#41—42no—
520#41—42no—
521#41—42no—
522#41—42no—
523#41—42no—
524#41—42no—
525#41—42no—
526#41—42no—
527#41—44no—
528#41—44no—
529#41—44no—
530#41—44no—
531#41—44no—
532#41—44no—
533#41—44no—
534#41—44no—
535#41—44no—
536#41—44no—
537#41—44no—
538#41—44no—
539#41—44no—
540#41—44no—
541#41—44no—
542#41—44no—
543#41—44no—
544#41—44no—
545#41—44no—
546#41—44no—
547C2×Q8—22no—
548C2×Q8—24no—
549C2×Q8—22no—
550C2×Q8—22no—
551C2×Q8—22no—
552C2×Q8—22no—
553C2×Q8—24no—
554C2×Q8—24no—
555C2×Q8—24no—
556C2×Q8—24no—
557C2×Q8—41no—
558C2×Q8—41no—
559C2×Q8—42no—
560C2×Q8—42no—
561C2×Q8—42no—
562C2×Q8—42no—
563C2×Q8—42no—
564C2×Q8C2×C4⋊C414yes—
565C2×D4—24no—
566C2×D4—24no—
567C2×D4—28no—
568C2×D4—22no—
569C2×D4—22no—
570C2×D4—22no—
571C2×D4—22no—
572C2×D4—22no—
573C2×D4—24no—
574C2×D4—24no—
575C2×D4—24no—
576C2×D4—24no—
577C2×D4—24no—
578C2×D4—42no—
579C2×D4—42no—
580C2×D4—42no—
581C2×D4—42no—
582C2×D4—44no—
583C2×D4—44no—
584C2×D4—44no—
585C2×D4—44no—
586C2×D4—42no—
587C2×D4—42no—
588C2×D4—44no—
589C2×D4—44no—
590C2×D4—44no—
591C2×D4—44no—
592C2×D4—44no—
593C2×D4—41no—
594C2×D4—41no—
595C2×D4—42no—
596C2×D4—42no—
597C2×D4—42no—
598C2×D4—42no—
599C2×D4—42no—
600C2×D4C2×C4⋊C414yes—
601C22×C4—22no—
602C22×C4—24no—
603C22×C4—24no—
604C22×C4—28no—
605C22×C4—24no—
606C22×C4—24no—
607C22×C4—28no—
608C22×C4—24no—
609C22×C4—24no—
610C22×C4—24no—
611C22×C4—24no—
612C22×C4—24no—
613C22×C4—41no—
614C22×C4—41no—
615C22×C4—42no—
616C22×C4—42no—
617C22×C4—42no—
618C22×C4—42no—
619C22×C4—42no—
620C22×C4—44no—
621C22×C4—44no—
622C22×C4—44no—
623C22×C4—44no—
624C22×C4—42no—
625C22×C4—42no—
626C22×C4—44no—
627C22×C4—44no—
628C22×C4—44no—
629C22×C4—44no—
630C22×C4—44no—
631C22×C4—42no—
632C22×C4—42no—
633C22×C4—44no—
634C22×C4—84no—
635C22×C4—84no—
636C22×C4—84no—
637C22×C4—84no—
638C22×C4C2×C22⋊C412yes—
639C22×C4C2×C22⋊C412yes—
640C22×C4C2×C4⋊C412yes—
641C22×C4C2×C4⋊C412yes—
642C22×C4#11712yes—
643C22×C4#11712yes—
644C22×C4C4×D412yes—
645C22×C4C4×D412yes—
646C22×C4C4×D412yes—
647C22×C4C4×D412yes—
648C22×C4C4×D412yes—
649C22×C4C4×D412yes—
650C22×C4C4×D412yes—
651C22×C4#12011yescharacteristic
652C22×C4#12011yescharacteristic
653C22×C4#12011yescharacteristic
654C22×C4#12011yescharacteristic
655C22×C4#12011yescharacteristic
656C22×C4#12011yescharacteristic
657C22×C4#12011yescharacteristic
658C22×C4#12011yescharacteristic
659C22×C4#12111yescharacteristic
660C22×C4#12111yescharacteristic
661C22×C4#12111yescharacteristic
662C22×C4#12111yescharacteristic
663C22×C4#12112yes—
664C22×C4#12112yes—
665C22×C4#12112yes—
666C22×C4#12112yes—
667C22×C4#12111yescharacteristic
668C22×C4#12111yescharacteristic
669C22×C4#12111yescharacteristic
670C22×C4#12111yescharacteristic
671C22×C4#12112yes—
672C22×C4#12112yes—
673C22×C4#12112yes—
674C22×C4#12112yes—
675C22×C4#12112yes—
676C22×C4#12111yescharacteristic
677C22×C4#12111yescharacteristic
678C22×C4C22⋊Q812yes—
679C22×C4C22⋊Q812yes—
680C22×C4C22⋊Q812yes—
681C22×C4C22⋊Q812yes—
682C22×C4C22⋊Q812yes—
683C22×C4C22⋊Q812yes—
684C22×C4C22⋊Q812yes—
685C22×C4C22⋊Q812yes—
686C22×C4C22⋊Q812yes—
687C22×C4C22⋊Q812yes—
688C22×C4C22⋊Q812yes—
689C22×C4#12312yes—
690C22×C4#12312yes—
691C22×C4#12312yes—
692C22×C4#12312yes—
693C22×C4#12312yes—
694C22×C4#12312yes—
695C22×C4#12312yes—
696C22×C4#12312yes—
697C22×C4#12312yes—
698C22×C4#12312yes—
699C22×C4#12412yes—
700C22×C4#12412yes—
701C22×C4#12412yes—
702C22×C4#12412yes—
703C22×C4#12412yes—
704C22×C4#12612yes—
705C22×C4#12612yes—
706C22×C4#12612yes—
707C22×C4#12612yes—
708C22×C4#12711yescharacteristic
709C22×C4#12711yescharacteristic
710C22×C4#12711yescharacteristic
711C22×C4#12711yescharacteristic
712C22×C4C23×C411yescharacteristic
713C22×C4C22×D411yescharacteristic
714C22×C4C22×D411yescharacteristic
715C22×C4C22×D411yescharacteristic
716C22×C4C22×D411yescharacteristic
717C22×C4C22×D411yescharacteristic
718C22×C4C22×D411yescharacteristic
719C22×C4C22×Q811yescharacteristic
720C22×C4C2×#4111yescharacteristic
721C22×C4C2×#4111yescharacteristic
722C22×C4C2×#4111yescharacteristic
723C22×C4C2×#4111yescharacteristic
724C22×C4C2×#4111yescharacteristic
725C22×C4C2×#4111yescharacteristic
726M16—24no—
727M16—24no—
728M16—42no—
729M16—42no—
730M16—42no—
731M16—42no—
732M16—42no—
733M16—42no—
734M16—44no—
735M16—44no—
736M16—44no—
737M16—44no—
738C2×C8—24no—
739C2×C8—24no—
740C2×C8—24no—
741C2×C8—24no—
742C2×C8—42no—
743C2×C8—42no—
744C2×C8—44no—
745C2×C8—44no—
746C2×C8—44no—
747C2×C8—44no—
748C4⋊C4—24no—
749C4⋊C4—24no—
750C4⋊C4—28no—
751C4⋊C4—24no—
752C4⋊C4—24no—
753C4⋊C4—42no—
754C4⋊C4—42no—
755C4⋊C4—42no—
756C4⋊C4—42no—
757C4⋊C4—42no—
758C4⋊C4—42no—
759C4⋊C4—42no—
760C4⋊C4—42no—
761C4⋊C4—44no—
762C4⋊C4—816no—
763C22⋊C4—24no—
764C22⋊C4—24no—
765C22⋊C4—28no—
766C22⋊C4—42no—
767C22⋊C4—42no—
768C22⋊C4—42no—
769C22⋊C4—42no—
770C22⋊C4—42no—
771C22⋊C4—42no—
772C22⋊C4—42no—
773C22⋊C4—42no—
774C22⋊C4—42no—
775C22⋊C4—42no—
776C22⋊C4—44no—
777C22⋊C4—816no—
778C42—24no—
779C42—28no—
780C42—24no—
781C42—24no—
782C42—42no—
783C42—42no—
784C42—42no—
785C42—42no—
786C42—42no—
787C42—42no—
788C42—42no—
789C42—42no—
790C42—44no—
791C42C2×C22⋊C418yes—
792C23—24no—
793C23—42no—
794C23—42no—
795C23—42no—
796C23—42no—
797C23—42no—
798C23—42no—
799C23—42no—
800C23—48no—
801C23—42no—
802C23—42no—
803C23—44no—
804C23—44no—
805C23—84no—
806C23—84no—
807C23—82no—
808C23—82no—
809C23—82no—
810C23—82no—
811C23—88no—
812C23—88no—
813C23#38512yes—
814C23#38512yes—
815C23#38612yes—
816C23#38612yes—
817C23#38812yes—
818C23#38812yes—
819C23#39211yescharacteristic
820C23#39211yescharacteristic
821C23#39211yescharacteristic
822C23#39211yescharacteristic
823C23#39312yes—
824C23#39312yes—
825C23#39412yes—
826C23#39412yes—
827C23#39612yes—
828C23#39612yes—
829C23C2×C4×D411yescharacteristic
830C23C2×#12011yescharacteristic
831C23C2×#12011yescharacteristic
832C23C2×#12111yescharacteristic
833C23C2×#12111yescharacteristic
834C23C2×C22⋊Q811yescharacteristic
835C23C2×#12411yescharacteristic
836Q8—24no—
837Q8—24no—
838Q8—42no—
839Q8—42no—
840Q8—44no—
841Q8—44no—
842D4—24no—
843D4—24no—
844D4—44no—
845D4—44no—
846D4—48no—
847D4—48no—
848D4—44no—
849D4—44no—
850D4—42no—
851D4—42no—
852D4—44no—
853D4—44no—
854C2×C4—24no—
855C2×C4—28no—
856C2×C4—48no—
857C2×C4—42no—
858C2×C4—42no—
859C2×C4—44no—
860C2×C4—44no—
861C2×C4—44no—
862C2×C4—44no—
863C2×C4—48no—
864C2×C4—48no—
865C2×C4—44no—
866C2×C4—44no—
867C2×C4—48no—
868C2×C4—48no—
869C2×C4—48no—
870C2×C4—48no—
871C2×C4—48no—
872C2×C4—44no—
873C2×C4—44no—
874C2×C4—44no—
875C2×C4—88no—
876C2×C4—84no—
877C2×C4—84no—
878C2×C4—88no—
879C2×C4#38012yes—
880C2×C4#38012yes—
881C2×C4#38012yes—
882C2×C4#38012yes—
883C2×C4#38512yes—
884C2×C4#38512yes—
885C2×C4#38512yes—
886C2×C4#38512yes—
887C2×C4#38512yes—
888C2×C4#38512yes—
889C2×C4#38612yes—
890C2×C4#38612yes—
891C2×C4#38812yes—
892C2×C4#38812yes—
893C2×C4#38812yes—
894C2×C4#38812yes—
895C2×C4#38812yes—
896C2×C4#38812yes—
897C2×C4#39012yes—
898C2×C4#39012yes—
899C2×C4#39012yes—
900C2×C4#39012yes—
901C2×C4#39211yescharacteristic
902C2×C4#39211yescharacteristic
903C2×C4#39211yescharacteristic
904C2×C4#39211yescharacteristic
905C2×C4#39312yes—
906C2×C4#39312yes—
907C2×C4#39412yes—
908C2×C4#39412yes—
909C2×C4#39412yes—
910C2×C4#39412yes—
911C2×C4#39412yes—
912C2×C4#39412yes—
913C2×C4#39612yes—
914C2×C4#39612yes—
915C2×C4#39612yes—
916C2×C4#39612yes—
917C2×C4#39612yes—
918C2×C4#39612yes—
919C2×C4#39712yes—
920C2×C4#39712yes—
921C2×C4#39712yes—
922C2×C4#39712yes—
923C2×C4#39912yes—
924C2×C4#39912yes—
925C2×C4#39912yes—
926C2×C4#39912yes—
927C2×C4C22×C22⋊C411yescharacteristic
928C2×C4C22×C4⋊C411yescharacteristic
929C2×C4C2×#11711yescharacteristic
930C2×C4C2×C4×D411yescharacteristic
931C2×C4C2×C4×D411yescharacteristic
932C2×C4C2×C4×D411yescharacteristic
933C2×C4C2×#12011yescharacteristic
934C2×C4C2×#12111yescharacteristic
935C2×C4C2×#12111yescharacteristic
936C2×C4C2×#12111yescharacteristic
937C2×C4C2×#12111yescharacteristic
938C2×C4C2×#12111yescharacteristic
939C2×C4C2×#12111yescharacteristic
940C2×C4C2×C22⋊Q811yescharacteristic
941C2×C4C2×C22⋊Q811yescharacteristic
942C2×C4C2×C22⋊Q811yescharacteristic
943C2×C4C2×C22⋊Q811yescharacteristic
944C2×C4C2×C22⋊Q811yescharacteristic
945C2×C4C2×#12311yescharacteristic
946C2×C4C2×#12311yescharacteristic
947C2×C4C2×#12311yescharacteristic
948C2×C4C2×#12311yescharacteristic
949C2×C4C2×#12311yescharacteristic
950C2×C4C2×#12411yescharacteristic
951C2×C4C2×#12411yescharacteristic
952C2×C4C2×#12611yescharacteristic
953C2×C4C2×#12611yescharacteristic
954C2×C4C2×#12711yescharacteristic
955C8—44no—
956C8—44no—
957C22—22no—
958C22—22no—
959C22—22no—
960C22—22no—
961C22—22no—
962C22—22no—
963C22—22no—
964C22—42no—
965C22—42no—
966C22—42no—
967C22—42no—
968C22—41no—
969C22—41no—
970C22—41no—
971C22—41no—
972C22—42no—
973C22—42no—
974C22—42no—
975C22—42no—
976C22—42no—
977C22—42no—
978C22—42no—
979C22—42no—
980C22—48no—
981C22—44no—
982C22—84no—
983C22—88no—
984C22—88no—
985C22—84no—
986C22#143912yes—
987C22#143912yes—
988C22#143912yes—
989C22#143912yes—
990C22C2×#38511yescharacteristic
991C22C2×#38611yescharacteristic
992C22C2×#38811yescharacteristic
993C22C2×#39211yescharacteristic
994C22C2×#39311yescharacteristic
995C22C2×#39411yescharacteristic
996C22C2×#39611yescharacteristic
997C4—48no—
998C4—44no—
999C4—84no—
1000C4—84no—
1001C4—84no—
1002C4#143912yes—
1003C4#143912yes—
1004C4#143912yes—
1005C4#143912yes—
1006C4C2×#38011yescharacteristic
1007C4C2×#38511yescharacteristic
1008C4C2×#38811yescharacteristic
1009C4C2×#39011yescharacteristic
1010C4C2×#39411yescharacteristic
1011C4C2×#39611yescharacteristic
1012C4C2×#39711yescharacteristic
1013C4C2×#39911yescharacteristic
1014C2—21no—
1015C2—21no—
1016C2—21no—
1017C2—22no—
1018C2—22no—
1019C2—21no—
1020C2—21no—
1021C2—22no—
1022C2—22no—
1023C2—21no—
1024C2—84no—
1025C2C2×#143911yescharacteristic
1026C2#2341412yes—
subgroupG/H
centerC2×C4C2×#127
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
socleC22C2×#392
prime radicalC23×#41C22
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
3. #34052C2semidirect
5. C2×#1733C2semidirect
6. C22×H(3,ℤ/4)C2semidirect
7. #20335C2semidirect
8. #11083C2semidirect
18. C2×#421C4semidirect
41. #2296C22semidirect
45. #1733C22semidirect
48. C2×H(3,ℤ/4)C22semidirect
51. #1728C22semidirect
153. #421C2×C4semidirect
254. C2×#41C4⋊C4semidirect
265. C22×Q8C4⋊C4semidirect
285. C22×D4C4⋊C4semidirect
419. #117C22⋊C4semidirect
481. C2×C42C22⋊C4semidirect

Maximal subgroups

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

subgroupindex
C22×#4212
C2×#28962
#340522
#340442
C2×#17332
C22×H(3,ℤ/4)2
#203352
#110832