Finite Group Databasebeta

← C2×#11083 #357751

Subgroups — C2×#11083 #357751

Order 512.

3006 conjugacy classes of subgroups.

The subgroup lattice has 1047 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#421C211yesmaximal, characteristic
2C2×#2896C211yesmaximal, characteristic
3C2×#2297C211yesmaximal, characteristic
4C2×#2296C211yesmaximal, characteristic, complemented
5C2×#1733C211yesmaximal, characteristic, complemented
6C22×H(3,ℤ/4)C211yesmaximal, characteristic, complemented
7C2×#1728C211yesmaximal, characteristic, complemented
8#11083C218yesmaximal, direct product factor
9C23×#41C2211yescharacteristic
10C23×M16C2211yescharacteristic
11C23×M16C2211yescharacteristic
12C22×#117C2211yescharacteristic
13C22×#117C2211yescharacteristic
14C22×#117C2211yescharacteristic
15C23×C42C2211yescharacteristic
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#2297—22no—
30#2297—22no—
31#2297—22no—
32#2297C2214yes—
33#2296—22no—
34#2296—22no—
35#2296—22no—
36#2296C2214yescomplemented
37C2×#391—21no—
38C2×#390—21no—
39C2×#389—22no—
40C2×#386—22no—
41C2×#385—22no—
42C2×C4×C4⋊C4—22no—
43C2×C4×C22⋊C4—22no—
44#1733—22no—
45#1733C2214yescomplemented
46C2×#339—22no—
47C2×H(3,ℤ/4)—24no—
48C2×H(3,ℤ/4)C2214yescomplemented
49#1728—22no—
50#1728C2214yescomplemented
51C2×#336—22no—
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×C4D412yes—
77C24×C4C2311yescharacteristic
78C22×M16—21no—
79C22×M16—21no—
80C22×M16—21no—
81C22×M16—21no—
82C22×M16—21no—
83C22×M16—22no—
84C22×M16—22no—
85C22×M16—22no—
86C22×M16—22no—
87C22×M16—22no—
88C22×M16—21no—
89C22×M16—22no—
90C22×M16—21no—
91C22×M16—21no—
92C22×M16—21no—
93C22×M16—22no—
94C22×M16C2×C414yes—
95C22×M16D412yes—
96C22×M16C2312yes—
97C22×M16C2312yes—
98C23×C8—21no—
99C23×C8D412yes—
100C2×#117—21no—
101C2×#117—21no—
102C2×#117—22no—
103C2×#117—22no—
104C2×#117—21no—
105C2×#117—21no—
106C2×#117—21no—
107C2×#117—21no—
108C2×#117—22no—
109C2×#117—22no—
110C2×#117—22no—
111C2×#117—22no—
112C2×#117—21no—
113C2×#117—21no—
114C2×#117—21no—
115C2×#117—21no—
116C2×#117—21no—
117C2×#117—21no—
118C2×#117—21no—
119C2×#117—21no—
120C2×#117C2×C414yes—
121C2×#117D412yes—
122C2×#117D414yes—
123C2×#117D412yes—
124C2×#117D412yes—
125C2×#117C2312yes—
126C2×#117C2312yes—
127C2×#117C2312yes—
128C22×C4⋊C4—21no—
129C22×C4⋊C4—24no—
130C22×C4⋊C4—21no—
131C22×C4⋊C4D412yes—
132C22×C22⋊C4—21no—
133C22×C22⋊C4—24no—
134C22×C22⋊C4—21no—
135C22×C22⋊C4—21no—
136C22×C42—21no—
137C22×C42—21no—
138C22×C42—21no—
139C22×C42—21no—
140C22×C42—21no—
141C22×C42—21no—
142C22×C42—21no—
143C22×C42—21no—
144C22×C42—21no—
145C22×C42—21no—
146C22×C42—21no—
147C22×C42—21no—
148C22×C42—21no—
149C22×C42D412yes—
150C22×C42D412yes—
151C22×C42D412yes—
152C22×C42C2312yes—
153#421—216no—
154#421—28no—
155#421C2×C4116yescomplemented
156C2×#104—216no—
157C2×#104—28no—
158#419—24no—
159#419—24no—
160#418—24no—
161#418—24no—
162#417—28no—
163#417—28no—
164#416—28no—
165#416—28no—
166C2×#103—24no—
167C2×#102—24no—
168#391—24no—
169#391—24no—
170#390—24no—
171#390—24no—
172#389—28no—
173#389—28no—
174#386—28no—
175#386—28no—
176#385—28no—
177#385—28no—
178C4×C4⋊C4—28no—
179C4×C4⋊C4—28no—
180C4×C22⋊C4—28no—
181C4×C22⋊C4—28no—
182C2×#95—24no—
183C2×#95—24no—
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—22no—
288C23×C4—22no—
289C23×C4—22no—
290C23×C4—21no—
291C23×C4—22no—
292C23×C4—24no—
293C23×C4—22no—
294C23×C4—24no—
295C23×C4—22no—
296C23×C4—22no—
297C23×C4—22no—
298C23×C4—22no—
299C23×C4—22no—
300C23×C4—22no—
301C23×C4—48no—
302C23×C4—41no—
303C23×C4—41no—
304C23×C4—42no—
305C23×C4—42no—
306C23×C4—41no—
307C23×C4—41no—
308C23×C4C22×C412yes—
309C23×C4C2×D414yes—
310C23×C4C2×D411yescharacteristic
311C23×C4C2×D411yescharacteristic
312C23×C4C2×D412yes—
313C23×C4C2×D411yescharacteristic
314C23×C4C2×D411yescharacteristic
315C23×C4C2×D411yescharacteristic
316C23×C4C2×D411yescharacteristic
317C23×C4C2×D411yescharacteristic
318C23×C4C2×D411yescharacteristic
319C23×C4C2×D411yescharacteristic
320C23×C4C2×D411yescharacteristic
321C23×C4C2×D411yescharacteristic
322C23×C4C2×Q812yes—
323C23×C4#4111yescharacteristic
324C23×C4#4111yescharacteristic
325C23×C4#4112yes—
326C23×C4#4112yes—
327C23×C4#4112yes—
328C23×C4#4112yes—
329C23×C4#4112yes—
330C23×C4C2411yescharacteristic
331C2×M16—24no—
332C2×M16—22no—
333C2×M16—22no—
334C2×M16—24no—
335C2×M16—24no—
336C2×M16—22no—
337C2×M16—22no—
338C2×M16—22no—
339C2×M16—22no—
340C2×M16—22no—
341C2×M16—22no—
342C2×M16—22no—
343C2×M16—24no—
344C2×M16—24no—
345C2×M16—24no—
346C2×M16—24no—
347C2×M16—22no—
348C2×M16—22no—
349C2×M16—22no—
350C2×M16—22no—
351C2×M16—42no—
352C2×M16—42no—
353C2×M16—42no—
354C2×M16—42no—
355C2×M16—42no—
356C2×M16—42no—
357C2×M16—42no—
358C2×M16—42no—
359C2×M16—42no—
360C2×M16—42no—
361C2×M16—42no—
362C2×M16—42no—
363C2×M16—42no—
364C2×M16—41no—
365C2×M16—41no—
366C2×M16C22×C414yes—
367C22×C8—24no—
368C22×C8—22no—
369C22×C8—22no—
370C22×C8—24no—
371C22×C8—24no—
372C22×C8—22no—
373C22×C8—42no—
374C22×C8—41no—
375C22×C8—41no—
376C22×C8C2×D414yes—
377#117—24no—
378#117—24no—
379#117—24no—
380#117—24no—
381#117—24no—
382#117—22no—
383#117—22no—
384#117—24no—
385#117—24no—
386#117—22no—
387#117—22no—
388#117—22no—
389#117—22no—
390#117—22no—
391#117—22no—
392#117—22no—
393#117—22no—
394#117—22no—
395#117—22no—
396#117—22no—
397#117—22no—
398#117—41no—
399#117—41no—
400#117—41no—
401#117—41no—
402#117—41no—
403#117—41no—
404#117—42no—
405#117—42no—
406#117—42no—
407#117—42no—
408#117—41no—
409#117—41no—
410#117C22⋊C418yescomplemented
411#117C22×C414yes—
412#117C2×D414yes—
413C2×C4⋊C4—24no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—24no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—216no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—416no—
426C2×C4⋊C4—42no—
427C2×C4⋊C4—42no—
428C2×C4⋊C4C2×D414yes—
429C2×C22⋊C4—24no—
430C2×C22⋊C4—22no—
431C2×C22⋊C4—24no—
432C2×C22⋊C4—22no—
433C2×C22⋊C4—216no—
434C2×C22⋊C4—22no—
435C2×C22⋊C4—22no—
436C2×C22⋊C4—22no—
437C2×C22⋊C4—22no—
438C2×C22⋊C4—416no—
439C2×C22⋊C4—41no—
440C2×C22⋊C4—41no—
441C2×C22⋊C4—41no—
442C2×C22⋊C4—41no—
443C2×C22⋊C4—42no—
444C2×C22⋊C4—42no—
445C2×C42—22no—
446C2×C42—24no—
447C2×C42—24no—
448C2×C42—24no—
449C2×C42—22no—
450C2×C42—22no—
451C2×C42—22no—
452C2×C42—22no—
453C2×C42—22no—
454C2×C42—22no—
455C2×C42—22no—
456C2×C42—22no—
457C2×C42—22no—
458C2×C42—22no—
459C2×C42—22no—
460C2×C42—22no—
461C2×C42—22no—
462C2×C42—22no—
463C2×C42—22no—
464C2×C42—41no—
465C2×C42—41no—
466C2×C42—41no—
467C2×C42—41no—
468C2×C42—41no—
469C2×C42—41no—
470C2×C42—41no—
471C2×C42—41no—
472C2×C42—41no—
473C2×C42—41no—
474C2×C42—41no—
475C2×C42—41no—
476C2×C42—41no—
477C2×C42—41no—
478C2×C42—41no—
479C2×C42—41no—
480C2×C42—41no—
481C2×C42—41no—
482C2×C42—41no—
483C2×C42—41no—
484C2×C42C22⋊C418yescomplemented
485C2×C42C2×D414yes—
486C2×C42C2×D414yes—
487#104—232no—
488#103—216no—
489#102—216no—
490#95—216no—
491#95—216no—
492C24—22no—
493C24—24no—
494C24—44no—
495C24—48no—
496C24—41no—
497C24—41no—
498C24—42no—
499C24C4×D412yes—
500C24#12011yescharacteristic
501C24#12011yescharacteristic
502C24#12011yescharacteristic
503C24#12011yescharacteristic
504C24#12111yescharacteristic
505C24#12112yes—
506C24#12111yescharacteristic
507C24C22⋊Q812yes—
508C24#12412yes—
509C24C22×D411yescharacteristic
510#41—24no—
511#41—24no—
512#41—24no—
513#41—24no—
514#41—24no—
515#41—24no—
516#41—24no—
517#41—24no—
518#41—28no—
519#41—28no—
520#41—28no—
521#41—28no—
522#41—42no—
523#41—42no—
524#41—42no—
525#41—42no—
526#41—42no—
527#41—42no—
528#41—42no—
529#41—42no—
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—
547#41—44no—
548#41—44no—
549#41—44no—
550C2×Q8—22no—
551C2×Q8—24no—
552C2×Q8—22no—
553C2×Q8—22no—
554C2×Q8—22no—
555C2×Q8—22no—
556C2×Q8—24no—
557C2×Q8—24no—
558C2×Q8—24no—
559C2×Q8—24no—
560C2×Q8—41no—
561C2×Q8—41no—
562C2×Q8—42no—
563C2×Q8—42no—
564C2×Q8—42no—
565C2×Q8—42no—
566C2×Q8—42no—
567C2×Q8C2×C4⋊C414yescomplemented
568C2×D4—24no—
569C2×D4—24no—
570C2×D4—28no—
571C2×D4—22no—
572C2×D4—22no—
573C2×D4—22no—
574C2×D4—22no—
575C2×D4—22no—
576C2×D4—24no—
577C2×D4—24no—
578C2×D4—24no—
579C2×D4—24no—
580C2×D4—24no—
581C2×D4—42no—
582C2×D4—42no—
583C2×D4—42no—
584C2×D4—42no—
585C2×D4—44no—
586C2×D4—44no—
587C2×D4—44no—
588C2×D4—44no—
589C2×D4—42no—
590C2×D4—42no—
591C2×D4—44no—
592C2×D4—44no—
593C2×D4—44no—
594C2×D4—44no—
595C2×D4—44no—
596C2×D4—41no—
597C2×D4—41no—
598C2×D4—42no—
599C2×D4—42no—
600C2×D4—42no—
601C2×D4—42no—
602C2×D4—42no—
603C2×D4C2×C4⋊C414yescomplemented
604C22×C4—28no—
605C22×C4—28no—
606C22×C4—28no—
607C22×C4—22no—
608C22×C4—24no—
609C22×C4—24no—
610C22×C4—24no—
611C22×C4—24no—
612C22×C4—24no—
613C22×C4—28no—
614C22×C4—24no—
615C22×C4—24no—
616C22×C4—28no—
617C22×C4—24no—
618C22×C4—24no—
619C22×C4—48no—
620C22×C4—48no—
621C22×C4—48no—
622C22×C4—48no—
623C22×C4—48no—
624C22×C4—44no—
625C22×C4—44no—
626C22×C4—44no—
627C22×C4—42no—
628C22×C4—42no—
629C22×C4—42no—
630C22×C4—42no—
631C22×C4—41no—
632C22×C4—41no—
633C22×C4—42no—
634C22×C4—42no—
635C22×C4—42no—
636C22×C4—42no—
637C22×C4—42no—
638C22×C4—44no—
639C22×C4—44no—
640C22×C4—44no—
641C22×C4—44no—
642C22×C4—42no—
643C22×C4—42no—
644C22×C4—44no—
645C22×C4—44no—
646C22×C4—44no—
647C22×C4—44no—
648C22×C4—44no—
649C22×C4—48no—
650C22×C4—48no—
651C22×C4—42no—
652C22×C4—42no—
653C22×C4—44no—
654C22×C4C2×C22⋊C412yes—
655C22×C4C2×C22⋊C412yes—
656C22×C4C2×C4⋊C412yes—
657C22×C4C2×C4⋊C412yes—
658C22×C4#11712yes—
659C22×C4#11712yes—
660C22×C4C4×D412yes—
661C22×C4C4×D412yes—
662C22×C4C4×D412yes—
663C22×C4C4×D412yes—
664C22×C4C4×D412yes—
665C22×C4C4×D412yes—
666C22×C4C4×D412yes—
667C22×C4#12011yescharacteristic
668C22×C4#12011yescharacteristic
669C22×C4#12011yescharacteristic
670C22×C4#12011yescharacteristic
671C22×C4#12011yescharacteristic
672C22×C4#12011yescharacteristic
673C22×C4#12011yescharacteristic
674C22×C4#12011yescharacteristic
675C22×C4#12111yescharacteristic
676C22×C4#12111yescharacteristic
677C22×C4#12111yescharacteristic
678C22×C4#12111yescharacteristic
679C22×C4#12112yes—
680C22×C4#12112yes—
681C22×C4#12112yes—
682C22×C4#12112yes—
683C22×C4#12111yescharacteristic
684C22×C4#12111yescharacteristic
685C22×C4#12111yescharacteristic
686C22×C4#12111yescharacteristic
687C22×C4#12112yes—
688C22×C4#12112yes—
689C22×C4#12112yes—
690C22×C4#12112yes—
691C22×C4#12112yes—
692C22×C4#12111yescharacteristic
693C22×C4#12111yescharacteristic
694C22×C4C22⋊Q812yes—
695C22×C4C22⋊Q812yes—
696C22×C4C22⋊Q812yes—
697C22×C4C22⋊Q812yes—
698C22×C4C22⋊Q812yes—
699C22×C4C22⋊Q812yes—
700C22×C4C22⋊Q812yes—
701C22×C4C22⋊Q812yes—
702C22×C4C22⋊Q812yes—
703C22×C4C22⋊Q812yes—
704C22×C4C22⋊Q812yes—
705C22×C4#12312yes—
706C22×C4#12312yes—
707C22×C4#12312yes—
708C22×C4#12312yes—
709C22×C4#12312yes—
710C22×C4#12312yes—
711C22×C4#12312yes—
712C22×C4#12312yes—
713C22×C4#12312yes—
714C22×C4#12312yes—
715C22×C4#12412yes—
716C22×C4#12412yes—
717C22×C4#12412yes—
718C22×C4#12412yes—
719C22×C4#12412yes—
720C22×C4#12612yes—
721C22×C4#12612yes—
722C22×C4#12612yes—
723C22×C4#12612yes—
724C22×C4#12711yescharacteristic
725C22×C4#12711yescharacteristic
726C22×C4#12711yescharacteristic
727C22×C4#12711yescharacteristic
728C22×C4C23×C411yescharacteristic
729C22×C4C22×D411yescharacteristic
730C22×C4C22×D411yescharacteristic
731C22×C4C22×D411yescharacteristic
732C22×C4C22×D411yescharacteristic
733C22×C4C22×D411yescharacteristic
734C22×C4C22×D411yescharacteristic
735C22×C4C22×Q811yescharacteristic
736C22×C4C2×#4111yescharacteristic
737C22×C4C2×#4111yescharacteristic
738C22×C4C2×#4111yescharacteristic
739C22×C4C2×#4111yescharacteristic
740C22×C4C2×#4111yescharacteristic
741C22×C4C2×#4111yescharacteristic
742M16—24no—
743M16—24no—
744M16—42no—
745M16—42no—
746M16—42no—
747M16—42no—
748M16—42no—
749M16—42no—
750M16—44no—
751M16—44no—
752M16—44no—
753M16—44no—
754C2×C8—24no—
755C2×C8—24no—
756C2×C8—24no—
757C2×C8—24no—
758C2×C8—42no—
759C2×C8—42no—
760C2×C8—44no—
761C2×C8—44no—
762C2×C8—44no—
763C2×C8—44no—
764C4⋊C4—24no—
765C4⋊C4—24no—
766C4⋊C4—28no—
767C4⋊C4—24no—
768C4⋊C4—24no—
769C4⋊C4—432no—
770C4⋊C4—42no—
771C4⋊C4—42no—
772C4⋊C4—42no—
773C4⋊C4—42no—
774C4⋊C4—44no—
775C22⋊C4—24no—
776C22⋊C4—24no—
777C22⋊C4—28no—
778C22⋊C4—432no—
779C22⋊C4—42no—
780C22⋊C4—42no—
781C22⋊C4—42no—
782C22⋊C4—42no—
783C22⋊C4—42no—
784C22⋊C4—42no—
785C22⋊C4—44no—
786C42—24no—
787C42—28no—
788C42—24no—
789C42—24no—
790C42—42no—
791C42—42no—
792C42—42no—
793C42—42no—
794C42—42no—
795C42—42no—
796C42—42no—
797C42—42no—
798C42—42no—
799C42—42no—
800C42—42no—
801C42—42no—
802C42—44no—
803C42C2×C22⋊C418yescomplemented
804C23—24no—
805C23—24no—
806C23—24no—
807C23—24no—
808C23—42no—
809C23—42no—
810C23—42no—
811C23—42no—
812C23—44no—
813C23—44no—
814C23—44no—
815C23—44no—
816C23—48no—
817C23—416no—
818C23—42no—
819C23—42no—
820C23—44no—
821C23—44no—
822C23—88no—
823C23—84no—
824C23—84no—
825C23#38512yes—
826C23#38512yes—
827C23#38612yes—
828C23#38612yes—
829C23#38812yes—
830C23#38812yes—
831C23#39211yescharacteristic
832C23#39211yescharacteristic
833C23#39211yescharacteristic
834C23#39211yescharacteristic
835C23#39312yes—
836C23#39312yes—
837C23#39412yes—
838C23#39412yes—
839C23#39612yes—
840C23#39612yes—
841C23C2×C4×D411yescharacteristic
842C23C2×#12011yescharacteristic
843C23C2×#12011yescharacteristic
844C23C2×#12111yescharacteristic
845C23C2×#12111yescharacteristic
846C23C2×C22⋊Q811yescharacteristic
847C23C2×#12411yescharacteristic
848Q8—24no—
849Q8—24no—
850Q8—42no—
851Q8—42no—
852Q8—44no—
853Q8—44no—
854D4—24no—
855D4—24no—
856D4—44no—
857D4—44no—
858D4—48no—
859D4—48no—
860D4—44no—
861D4—44no—
862D4—42no—
863D4—42no—
864D4—44no—
865D4—44no—
866C2×C4—28no—
867C2×C4—28no—
868C2×C4—28no—
869C2×C4—24no—
870C2×C4—28no—
871C2×C4—48no—
872C2×C4—416no—
873C2×C4—44no—
874C2×C4—44no—
875C2×C4—44no—
876C2×C4—48no—
877C2×C4—48no—
878C2×C4—48no—
879C2×C4—44no—
880C2×C4—42no—
881C2×C4—42no—
882C2×C4—44no—
883C2×C4—44no—
884C2×C4—48no—
885C2×C4—44no—
886C2×C4—44no—
887C2×C4—48no—
888C2×C4—48no—
889C2×C4—44no—
890C2×C4—44no—
891C2×C4—48no—
892C2×C4—48no—
893C2×C4—44no—
894C2×C4—44no—
895C2×C4—88no—
896C2×C4—84no—
897C2×C4—84no—
898C2×C4#38012yes—
899C2×C4#38012yes—
900C2×C4#38012yes—
901C2×C4#38012yes—
902C2×C4#38512yes—
903C2×C4#38512yes—
904C2×C4#38512yes—
905C2×C4#38512yes—
906C2×C4#38512yes—
907C2×C4#38512yes—
908C2×C4#38612yes—
909C2×C4#38612yes—
910C2×C4#38812yes—
911C2×C4#38812yes—
912C2×C4#38812yes—
913C2×C4#38812yes—
914C2×C4#38812yes—
915C2×C4#38812yes—
916C2×C4#39012yes—
917C2×C4#39012yes—
918C2×C4#39012yes—
919C2×C4#39012yes—
920C2×C4#39211yescharacteristic
921C2×C4#39211yescharacteristic
922C2×C4#39211yescharacteristic
923C2×C4#39211yescharacteristic
924C2×C4#39312yes—
925C2×C4#39312yes—
926C2×C4#39412yes—
927C2×C4#39412yes—
928C2×C4#39412yes—
929C2×C4#39412yes—
930C2×C4#39412yes—
931C2×C4#39412yes—
932C2×C4#39612yes—
933C2×C4#39612yes—
934C2×C4#39612yes—
935C2×C4#39612yes—
936C2×C4#39612yes—
937C2×C4#39612yes—
938C2×C4#39712yes—
939C2×C4#39712yes—
940C2×C4#39712yes—
941C2×C4#39712yes—
942C2×C4#39912yes—
943C2×C4#39912yes—
944C2×C4#39912yes—
945C2×C4#39912yes—
946C2×C4C22×C22⋊C411yescharacteristic
947C2×C4C22×C4⋊C411yescharacteristic
948C2×C4C2×#11711yescharacteristic
949C2×C4C2×C4×D411yescharacteristic
950C2×C4C2×C4×D411yescharacteristic
951C2×C4C2×C4×D411yescharacteristic
952C2×C4C2×#12011yescharacteristic
953C2×C4C2×#12111yescharacteristic
954C2×C4C2×#12111yescharacteristic
955C2×C4C2×#12111yescharacteristic
956C2×C4C2×#12111yescharacteristic
957C2×C4C2×#12111yescharacteristic
958C2×C4C2×#12111yescharacteristic
959C2×C4C2×C22⋊Q811yescharacteristic
960C2×C4C2×C22⋊Q811yescharacteristic
961C2×C4C2×C22⋊Q811yescharacteristic
962C2×C4C2×C22⋊Q811yescharacteristic
963C2×C4C2×C22⋊Q811yescharacteristic
964C2×C4C2×#12311yescharacteristic
965C2×C4C2×#12311yescharacteristic
966C2×C4C2×#12311yescharacteristic
967C2×C4C2×#12311yescharacteristic
968C2×C4C2×#12311yescharacteristic
969C2×C4C2×#12411yescharacteristic
970C2×C4C2×#12411yescharacteristic
971C2×C4C2×#12611yescharacteristic
972C2×C4C2×#12611yescharacteristic
973C2×C4C2×#12711yescharacteristic
974C8—44no—
975C8—44no—
976C22—24no—
977C22—24no—
978C22—24no—
979C22—24no—
980C22—24no—
981C22—24no—
982C22—22no—
983C22—22no—
984C22—22no—
985C22—22no—
986C22—22no—
987C22—22no—
988C22—41no—
989C22—41no—
990C22—41no—
991C22—41no—
992C22—42no—
993C22—42no—
994C22—42no—
995C22—42no—
996C22—42no—
997C22—42no—
998C22—48no—
999C22—44no—
1000C22—84no—
1001C22—88no—
1002C22—88no—
1003C22—84no—
1004C22#143912yes—
1005C22#143912yes—
1006C22#143912yes—
1007C22#143912yes—
1008C22#201014yes—
1009C22C2×#38511yescharacteristic
1010C22C2×#38611yescharacteristic
1011C22C2×#38811yescharacteristic
1012C22C2×#39211yescharacteristic
1013C22C2×#39311yescharacteristic
1014C22C2×#39411yescharacteristic
1015C22C2×#39611yescharacteristic
1016C4—48no—
1017C4—44no—
1018C4—48no—
1019C4—84no—
1020C4—84no—
1021C4#143912yes—
1022C4#143912yes—
1023C4#143912yes—
1024C4#143912yes—
1025C4C2×#38011yescharacteristic
1026C4C2×#38511yescharacteristic
1027C4C2×#38811yescharacteristic
1028C4C2×#39011yescharacteristic
1029C4C2×#39411yescharacteristic
1030C4C2×#39611yescharacteristic
1031C4C2×#39711yescharacteristic
1032C4C2×#39911yescharacteristic
1033C2—21no—
1034C2—21no—
1035C2—21no—
1036C2—22no—
1037C2—21no—
1038C2—21no—
1039C2—22no—
1040C2—22no—
1041C2—21no—
1042C2—84no—
1043C2#1108314yesdirect product factor
1044C2C2×#143911yescharacteristic
1045C2C2×#201012yes—
subgroupG/H
centerC22×C4#127
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
socleC23#392
prime radicalC23×#41C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4 ◁ C24×C4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
4. C2×#2296C2semidirect
5. C2×#1733C2semidirect
6. C22×H(3,ℤ/4)C2semidirect
7. C2×#1728C2semidirect
8. #11083C2direct (N × H)
18. C2×#421C4semidirect
36. #2296C22semidirect
45. #1733C22semidirect
48. C2×H(3,ℤ/4)C22semidirect
50. #1728C22semidirect
155. #421C2×C4semidirect
254. C2×#41C4⋊C4semidirect
265. C22×Q8C4⋊C4semidirect
285. C22×D4C4⋊C4semidirect
410. #117C22⋊C4semidirect
484. C2×C42C22⋊C4semidirect
567. C2×Q8C2×C4⋊C4semidirect
603. C2×D4C2×C4⋊C4semidirect
803. C42C2×C22⋊C4semidirect
1043. C2#11083direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#4212
C2×#28962
C2×#22972
C2×#22962
C2×#17332
C22×H(3,ℤ/4)2
C2×#17282
#110832