Finite Group Databasebeta

← #357939

Subgroups — #357939

Order 512.

2570 conjugacy classes of subgroups.

The subgroup lattice has 1022 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2896C211yesmaximal, characteristic
2C2×#2896C211yesmaximal, characteristic
3#34044C211yesmaximal, characteristic
4C22×#344C211yesmaximal, characteristic, complemented
5C2×#1740C211yesmaximal, characteristic, complemented
6C2×#1733C211yesmaximal, characteristic, complemented
7C22×H(3,ℤ/4)C211yesmaximal, characteristic, complemented
8#11184C214yesmaximal, complemented
9#11183C214yesmaximal, complemented
10C23×#41C2211yescharacteristic
11C23×M16C2211yescharacteristic
12C23×M16C2211yescharacteristic
13C22×#117C2211yescharacteristic
14C22×#117C2211yescharacteristic
15C22×#117C2211yescharacteristic
16C22×#117C2211yescharacteristic
17#2896—22no—
18#2896—22no—
19#2896—22no—
20#2896—22no—
21#2896—24no—
22#2896—24no—
23C2×#417—22no—
24C2×#417C414yescomplemented
25C2×#419C2212yes—
26C2×#419C2212yes—
27C2×#418C2212yes—
28C2×#418C2212yes—
29C2×#416—22no—
30C2×#416C414yescomplemented
31#2311—22no—
32#2311—22no—
33#2310C2212yes—
34#2309C2212yes—
35#2308—22no—
36#2297—22no—
37#2297—22no—
38#2280—22no—
39C2×#344—24no—
40C2×#344C2214yes—
41#1740—22no—
42#1740C2214yes—
43C2×#342—22no—
44#1733—22no—
45#1733C2214yes—
46C2×#339—22no—
47C2×H(3,ℤ/4)—24no—
48C2×H(3,ℤ/4)C2214yes—
49C22×#41—21no—
50C22×#41—21no—
51C22×#41—21no—
52C22×#41—21no—
53C22×#41—21no—
54C22×#41—21no—
55C22×#41—22no—
56C22×#41—22no—
57C22×#41—22no—
58C22×#41—22no—
59C22×#41—22no—
60C22×#41—22no—
61C22×#41—22no—
62C22×#41—22no—
63C22×#41C2×C412yes—
64C22×#41C2×C412yes—
65C22×#41D412yes—
66C22×#41D412yes—
67C22×#41D412yes—
68C22×#41D412yes—
69C23×Q8C2311yescharacteristic
70C23×D4—21no—
71C23×D4C2311yescharacteristic
72C24×C4—21no—
73C24×C4C2311yescharacteristic
74C22×M16—21no—
75C22×M16—21no—
76C22×M16—21no—
77C22×M16—21no—
78C22×M16—21no—
79C22×M16—22no—
80C22×M16—22no—
81C22×M16—22no—
82C22×M16—22no—
83C22×M16—22no—
84C22×M16—21no—
85C22×M16—21no—
86C22×M16—21no—
87C22×M16—21no—
88C22×M16—22no—
89C22×M16—22no—
90C22×M16C2×C412yes—
91C22×M16D414yes—
92C22×M16C2312yes—
93C22×M16C2312yes—
94C23×C8—21no—
95C23×C8C2×C412yes—
96C2×#117—21no—
97C2×#117—21no—
98C2×#117—21no—
99C2×#117—21no—
100C2×#117—21no—
101C2×#117—21no—
102C2×#117—22no—
103C2×#117—22no—
104C2×#117—22no—
105C2×#117—22no—
106C2×#117—22no—
107C2×#117—21no—
108C2×#117—21no—
109C2×#117—22no—
110C2×#117—22no—
111C2×#117—22no—
112C2×#117—22no—
113C2×#117—22no—
114C2×#117—21no—
115C2×#117—21no—
116C2×#117—21no—
117C2×#117—21no—
118C2×#117—21no—
119C2×#117—22no—
120C2×#117—21no—
121C2×#117—21no—
122C2×#117—21no—
123C2×#117—21no—
124C2×#117C2×C412yes—
125C2×#117D414yes—
126C2×#117D412yes—
127C2×#117D412yes—
128C2×#117C2312yes—
129C2×#117C2312yes—
130C2×#117C2312yes—
131C2×#117C2312yes—
132C22×C4⋊C4—21no—
133C22×C4⋊C4—21no—
134C22×C4⋊C4—21no—
135C22×C4⋊C4C2×C412yes—
136C22×C22⋊C4—21no—
137C22×C22⋊C4—21no—
138C22×C22⋊C4—21no—
139C22×C22⋊C4D412yes—
140C22×C42—21no—
141C22×C42—21no—
142C22×C42—21no—
143C22×C42D412yes—
144#419—24no—
145#419—24no—
146#419—24no—
147#419—24no—
148#418—24no—
149#418—24no—
150#418—24no—
151#418—24no—
152#417—216no—
153#417—28no—
154#417—28no—
155#416—216no—
156#416—28no—
157#416—28no—
158C2×#103—24no—
159C2×#103C2×C418yescomplemented
160C2×#102—24no—
161C2×#102C2×C418yescomplemented
162#391—24no—
163#391—24no—
164#390—24no—
165#390—24no—
166#386—28no—
167#386—28no—
168#381—24no—
169#380—28no—
170#379—24no—
171C4×C22⋊C4—28no—
172#344—28no—
173#342—28no—
174#339—28no—
175H(3,ℤ/4)—28no—
176C25—21no—
177C25C2×D411yescharacteristic
178C2×#41—22no—
179C2×#41—22no—
180C2×#41—22no—
181C2×#41—22no—
182C2×#41—22no—
183C2×#41—22no—
184C2×#41—22no—
185C2×#41—22no—
186C2×#41—22no—
187C2×#41—22no—
188C2×#41—22no—
189C2×#41—22no—
190C2×#41—24no—
191C2×#41—24no—
192C2×#41—24no—
193C2×#41—24no—
194C2×#41—24no—
195C2×#41—24no—
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—24no—
205C2×#41—24no—
206C2×#41—24no—
207C2×#41—24no—
208C2×#41—24no—
209C2×#41—24no—
210C2×#41—24no—
211C2×#41—24no—
212C2×#41—24no—
213C2×#41—24no—
214C2×#41—42no—
215C2×#41—42no—
216C2×#41—42no—
217C2×#41—42no—
218C2×#41—42no—
219C2×#41—42no—
220C2×#41—42no—
221C2×#41—42no—
222C2×#41—42no—
223C2×#41—42no—
224C2×#41—42no—
225C2×#41—42no—
226C2×#41—42no—
227C2×#41—42no—
228C2×#41—42no—
229C2×#41—42no—
230C2×#41—42no—
231C2×#41—42no—
232C2×#41—42no—
233C2×#41—42no—
234C2×#41—42no—
235C2×#41—42no—
236C2×#41—42no—
237C2×#41—42no—
238C2×#41C22⋊C414yes—
239C2×#41C22⋊C414yes—
240C2×#41C22⋊C414yes—
241C2×#41C22⋊C414yes—
242C22×Q8—21no—
243C22×Q8—21no—
244C22×Q8—21no—
245C22×Q8—21no—
246C22×Q8—21no—
247C22×Q8—21no—
248C22×Q8—21no—
249C22×Q8—21no—
250C22×Q8—21no—
251C22×Q8—21no—
252C22×Q8—21no—
253C22×Q8C22×C412yes—
254C22×Q8C2×D412yes—
255C22×Q8C2×D412yes—
256C22×D4—22no—
257C22×D4—22no—
258C22×D4—22no—
259C22×D4—22no—
260C22×D4—22no—
261C22×D4—22no—
262C22×D4—21no—
263C22×D4—21no—
264C22×D4—21no—
265C22×D4—21no—
266C22×D4—21no—
267C22×D4—21no—
268C22×D4—21no—
269C22×D4—21no—
270C22×D4—21no—
271C22×D4—21no—
272C22×D4—21no—
273C22×D4—42no—
274C22×D4—42no—
275C22×D4—42no—
276C22×D4—42no—
277C22×D4C22×C412yes—
278C22×D4C2×D412yes—
279C22×D4C2×D412yes—
280C23×C4—21no—
281C23×C4—22no—
282C23×C4—22no—
283C23×C4—22no—
284C23×C4—22no—
285C23×C4—22no—
286C23×C4—22no—
287C23×C4—22no—
288C23×C4—22no—
289C23×C4—22no—
290C23×C4—42no—
291C23×C4—42no—
292C23×C4—42no—
293C23×C4—42no—
294C23×C4—41no—
295C23×C4C22×C411yescharacteristic
296C23×C4C22×C411yescharacteristic
297C23×C4C2×D411yescharacteristic
298C23×C4C2×D411yescharacteristic
299C23×C4C2×D411yescharacteristic
300C23×C4C2×D411yescharacteristic
301C23×C4C2×D411yescharacteristic
302C23×C4C2×D412yes—
303C23×C4C2×D412yes—
304C23×C4C2×D411yescharacteristic
305C23×C4C2×D411yescharacteristic
306C23×C4#4112yes—
307C23×C4#4112yes—
308C23×C4#4112yes—
309C23×C4#4112yes—
310C23×C4#4112yes—
311C23×C4#4112yes—
312C23×C4#4111yescharacteristic
313C23×C4#4111yescharacteristic
314C23×C4#4111yescharacteristic
315C23×C4#4111yescharacteristic
316C23×C4C2411yescharacteristic
317C2×M16—22no—
318C2×M16—22no—
319C2×M16—24no—
320C2×M16—24no—
321C2×M16—24no—
322C2×M16—22no—
323C2×M16—22no—
324C2×M16—22no—
325C2×M16—22no—
326C2×M16—22no—
327C2×M16—22no—
328C2×M16—22no—
329C2×M16—24no—
330C2×M16—24no—
331C2×M16—24no—
332C2×M16—24no—
333C2×M16—22no—
334C2×M16—22no—
335C2×M16—22no—
336C2×M16—22no—
337C2×M16—42no—
338C2×M16—42no—
339C2×M16—41no—
340C2×M16—41no—
341C2×M16—42no—
342C2×M16—42no—
343C2×M16—42no—
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×M16C2×D414yes—
353C22×C8—22no—
354C22×C8—22no—
355C22×C8—24no—
356C22×C8—24no—
357C22×C8—24no—
358C22×C8—22no—
359C22×C8—41no—
360C22×C8—41no—
361C22×C8—42no—
362C22×C8C22×C414yes—
363#117—24no—
364#117—24no—
365#117—24no—
366#117—22no—
367#117—22no—
368#117—22no—
369#117—22no—
370#117—22no—
371#117—24no—
372#117—24no—
373#117—24no—
374#117—22no—
375#117—22no—
376#117—22no—
377#117—22no—
378#117—22no—
379#117—22no—
380#117—22no—
381#117—22no—
382#117—22no—
383#117—24no—
384#117—22no—
385#117—22no—
386#117—22no—
387#117—22no—
388#117—22no—
389#117—41no—
390#117—41no—
391#117—41no—
392#117—41no—
393#117—42no—
394#117—41no—
395#117—41no—
396#117—42no—
397#117—42no—
398#117—42no—
399#117—42no—
400#117—41no—
401#117—41no—
402#117—42no—
403#117—42no—
404#117—42no—
405#117—42no—
406#117—42no—
407#117—42no—
408#117C2×D414yes—
409C2×C4⋊C4—22no—
410C2×C4⋊C4—22no—
411C2×C4⋊C4—22no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4—24no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—42no—
421C2×C4⋊C4—42no—
422C2×C4⋊C4—41no—
423C2×C4⋊C4—42no—
424C2×C4⋊C4—42no—
425C2×C4⋊C4—42no—
426C2×C4⋊C4C22×C414yes—
427C2×C22⋊C4—24no—
428C2×C22⋊C4—24no—
429C2×C22⋊C4—24no—
430C2×C22⋊C4—22no—
431C2×C22⋊C4—22no—
432C2×C22⋊C4—22no—
433C2×C22⋊C4—22no—
434C2×C22⋊C4—22no—
435C2×C22⋊C4—22no—
436C2×C22⋊C4—216no—
437C2×C22⋊C4—41no—
438C2×C22⋊C4—41no—
439C2×C22⋊C4—41no—
440C2×C22⋊C4—41no—
441C2×C22⋊C4—42no—
442C2×C22⋊C4—42no—
443C2×C22⋊C4—41no—
444C2×C22⋊C4—42no—
445C2×C22⋊C4C2×D414yes—
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—41no—
456C2×C42—41no—
457C2×C42—42no—
458C2×C42—41no—
459C2×C42—41no—
460C2×C42—41no—
461C2×C42—42no—
462C2×C42—42no—
463C2×C42C2×D414yes—
464#103—216no—
465#103—216no—
466#102—216no—
467#102—216no—
468#95—216no—
469C24—22no—
470C24—22no—
471C24—22no—
472C24—41no—
473C24—41no—
474C24—41no—
475C24—41no—
476C24—82no—
477C24—84no—
478C24C4×D411yescharacteristic
479C24C4×D411yescharacteristic
480C24#12011yescharacteristic
481C24#12011yescharacteristic
482C24#12111yescharacteristic
483C24#12111yescharacteristic
484C24#12112yes—
485C24#12112yes—
486C24#12312yes—
487C24#12412yes—
488C24C22×D411yescharacteristic
489#41—28no—
490#41—28no—
491#41—28no—
492#41—28no—
493#41—28no—
494#41—28no—
495#41—28no—
496#41—28no—
497#41—44no—
498#41—44no—
499#41—44no—
500#41—44no—
501#41—44no—
502#41—44no—
503#41—44no—
504#41—44no—
505#41—44no—
506#41—44no—
507#41—44no—
508#41—44no—
509#41—44no—
510#41—44no—
511#41—44no—
512#41—44no—
513#41—44no—
514#41—44no—
515#41—44no—
516#41—44no—
517#41—44no—
518#41—44no—
519#41—44no—
520#41—44no—
521C2×Q8—22no—
522C2×Q8—22no—
523C2×Q8—22no—
524C2×Q8—22no—
525C2×Q8—22no—
526C2×Q8—22no—
527C2×Q8—22no—
528C2×Q8—22no—
529C2×Q8—22no—
530C2×Q8—22no—
531C2×Q8—22no—
532C2×Q8—22no—
533C2×Q8—22no—
534C2×Q8—22no—
535C2×Q8—22no—
536C2×Q8—41no—
537C2×Q8—41no—
538C2×Q8—41no—
539C2×Q8—41no—
540C2×Q8—41no—
541C2×Q8—41no—
542C2×Q8—41no—
543C2×Q8—41no—
544C2×Q8—41no—
545C2×Q8—41no—
546C2×Q8—41no—
547C2×Q8—41no—
548C2×Q8C2×C22⋊C414yes—
549C2×D4—24no—
550C2×D4—24no—
551C2×D4—24no—
552C2×D4—24no—
553C2×D4—22no—
554C2×D4—22no—
555C2×D4—22no—
556C2×D4—22no—
557C2×D4—22no—
558C2×D4—22no—
559C2×D4—22no—
560C2×D4—22no—
561C2×D4—22no—
562C2×D4—22no—
563C2×D4—22no—
564C2×D4—22no—
565C2×D4—22no—
566C2×D4—22no—
567C2×D4—22no—
568C2×D4—44no—
569C2×D4—44no—
570C2×D4—44no—
571C2×D4—44no—
572C2×D4—44no—
573C2×D4—44no—
574C2×D4—44no—
575C2×D4—44no—
576C2×D4—44no—
577C2×D4—44no—
578C2×D4—44no—
579C2×D4—44no—
580C2×D4—41no—
581C2×D4—41no—
582C2×D4—41no—
583C2×D4—41no—
584C2×D4—41no—
585C2×D4—41no—
586C2×D4—41no—
587C2×D4—41no—
588C2×D4—41no—
589C2×D4—41no—
590C2×D4—41no—
591C2×D4—41no—
592C2×D4C2×C22⋊C414yes—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—24no—
597C22×C4—24no—
598C22×C4—24no—
599C22×C4—24no—
600C22×C4—24no—
601C22×C4—24no—
602C22×C4—24no—
603C22×C4—41no—
604C22×C4—41no—
605C22×C4—41no—
606C22×C4—41no—
607C22×C4—44no—
608C22×C4—44no—
609C22×C4—44no—
610C22×C4—44no—
611C22×C4—44no—
612C22×C4—44no—
613C22×C4—44no—
614C22×C4—44no—
615C22×C4—44no—
616C22×C4—44no—
617C22×C4—44no—
618C22×C4—44no—
619C22×C4—42no—
620C22×C4—42no—
621C22×C4—42no—
622C22×C4—44no—
623C22×C4—44no—
624C22×C4—44no—
625C22×C4—84no—
626C22×C4—84no—
627C22×C4—84no—
628C22×C4—84no—
629C22×C4C2×C22⋊C411yescharacteristic
630C22×C4C2×C22⋊C411yescharacteristic
631C22×C4C2×C22⋊C411yescharacteristic
632C22×C4C2×C22⋊C411yescharacteristic
633C22×C4#11712yes—
634C22×C4#11712yes—
635C22×C4#11712yes—
636C22×C4#11712yes—
637C22×C4C4×D412yes—
638C22×C4C4×D412yes—
639C22×C4C4×D412yes—
640C22×C4C4×D412yes—
641C22×C4C4×D411yescharacteristic
642C22×C4C4×D411yescharacteristic
643C22×C4C4×D411yescharacteristic
644C22×C4C4×D411yescharacteristic
645C22×C4C4×D411yescharacteristic
646C22×C4C4×D411yescharacteristic
647C22×C4#12012yes—
648C22×C4#12012yes—
649C22×C4#12011yescharacteristic
650C22×C4#12011yescharacteristic
651C22×C4#12112yes—
652C22×C4#12112yes—
653C22×C4#12112yes—
654C22×C4#12112yes—
655C22×C4#12111yescharacteristic
656C22×C4#12111yescharacteristic
657C22×C4#12111yescharacteristic
658C22×C4#12111yescharacteristic
659C22×C4#12112yes—
660C22×C4#12112yes—
661C22×C4#12112yes—
662C22×C4#12112yes—
663C22×C4#12111yescharacteristic
664C22×C4#12111yescharacteristic
665C22×C4#12112yes—
666C22×C4#12112yes—
667C22×C4#12312yes—
668C22×C4#12312yes—
669C22×C4#12312yes—
670C22×C4#12312yes—
671C22×C4#12312yes—
672C22×C4#12312yes—
673C22×C4#12312yes—
674C22×C4#12312yes—
675C22×C4#12312yes—
676C22×C4#12312yes—
677C22×C4#12311yescharacteristic
678C22×C4#12311yescharacteristic
679C22×C4#12311yescharacteristic
680C22×C4#12311yescharacteristic
681C22×C4#12312yes—
682C22×C4#12312yes—
683C22×C4#12312yes—
684C22×C4#12312yes—
685C22×C4#12312yes—
686C22×C4#12312yes—
687C22×C4#12312yes—
688C22×C4#12412yes—
689C22×C4#12412yes—
690C22×C4#12412yes—
691C22×C4#12412yes—
692C22×C4#12412yes—
693C22×C4#12412yes—
694C22×C4#12412yes—
695C22×C4#12612yes—
696C22×C4#12612yes—
697C22×C4#12612yes—
698C22×C4#12612yes—
699C22×C4#12612yes—
700C22×C4#12612yes—
701C22×C4#12612yes—
702C22×C4#12612yes—
703C22×C4C23×C411yescharacteristic
704C22×C4C22×D411yescharacteristic
705C22×C4C22×D411yescharacteristic
706C22×C4C22×D411yescharacteristic
707C22×C4C22×D411yescharacteristic
708C22×C4C22×D411yescharacteristic
709C22×C4C2×#4111yescharacteristic
710C22×C4C2×#4111yescharacteristic
711C22×C4C2×#4111yescharacteristic
712C22×C4C2×#4111yescharacteristic
713C22×C4C2×#4111yescharacteristic
714C22×C4C2×#4111yescharacteristic
715C22×C4C2×#4111yescharacteristic
716C22×C4C2×#4111yescharacteristic
717M16—24no—
718M16—24no—
719M16—42no—
720M16—42no—
721M16—42no—
722M16—42no—
723M16—42no—
724M16—42no—
725M16—44no—
726M16—44no—
727M16—44no—
728M16—44no—
729C2×C8—24no—
730C2×C8—24no—
731C2×C8—24no—
732C2×C8—24no—
733C2×C8—42no—
734C2×C8—42no—
735C2×C8—44no—
736C2×C8—44no—
737C2×C8—44no—
738C2×C8—44no—
739C4⋊C4—24no—
740C4⋊C4—24no—
741C4⋊C4—24no—
742C4⋊C4—42no—
743C4⋊C4—42no—
744C4⋊C4—42no—
745C4⋊C4—42no—
746C4⋊C4—42no—
747C4⋊C4—42no—
748C4⋊C4—42no—
749C4⋊C4—44no—
750C4⋊C4—44no—
751C4⋊C4—44no—
752C22⋊C4—24no—
753C22⋊C4—24no—
754C22⋊C4—24no—
755C22⋊C4—42no—
756C22⋊C4—42no—
757C22⋊C4—42no—
758C22⋊C4—42no—
759C22⋊C4—42no—
760C22⋊C4—42no—
761C22⋊C4—42no—
762C22⋊C4—44no—
763C22⋊C4—44no—
764C22⋊C4—44no—
765C22⋊C4—816no—
766C42—24no—
767C42—24no—
768C42—24no—
769C42—42no—
770C42—42no—
771C42—42no—
772C42—42no—
773C42—42no—
774C42—42no—
775C42—42no—
776C42—44no—
777C42—44no—
778C42—44no—
779C23—24no—
780C23—42no—
781C23—42no—
782C23—42no—
783C23—42no—
784C23—42no—
785C23—42no—
786C23—42no—
787C23—48no—
788C23—42no—
789C23—42no—
790C23—42no—
791C23—42no—
792C23—42no—
793C23—42no—
794C23—84no—
795C23—84no—
796C23—82no—
797C23—82no—
798C23—82no—
799C23—82no—
800C23—84no—
801C23—84no—
802C23—84no—
803C23—84no—
804C23#38611yescharacteristic
805C23#38611yescharacteristic
806C23#38611yescharacteristic
807C23#38611yescharacteristic
808C23#38812yes—
809C23#38812yes—
810C23#38812yes—
811C23#38812yes—
812C23#39412yes—
813C23#39412yes—
814C23#39412yes—
815C23#39412yes—
816C23#39412yes—
817C23#39412yes—
818C23#39712yes—
819C23#39712yes—
820C23C2×C4×D411yescharacteristic
821C23C2×#12011yescharacteristic
822C23C2×#12111yescharacteristic
823C23C2×#12111yescharacteristic
824C23C2×#12111yescharacteristic
825C23C2×#12311yescharacteristic
826C23C2×#12411yescharacteristic
827Q8—24no—
828Q8—24no—
829Q8—42no—
830Q8—42no—
831Q8—42no—
832Q8—42no—
833Q8—42no—
834Q8—42no—
835D4—24no—
836D4—24no—
837D4—48no—
838D4—48no—
839D4—48no—
840D4—48no—
841D4—42no—
842D4—42no—
843D4—42no—
844D4—42no—
845D4—42no—
846D4—42no—
847C2×C4—24no—
848C2×C4—42no—
849C2×C4—42no—
850C2×C4—42no—
851C2×C4—42no—
852C2×C4—42no—
853C2×C4—42no—
854C2×C4—48no—
855C2×C4—48no—
856C2×C4—48no—
857C2×C4—48no—
858C2×C4—48no—
859C2×C4—48no—
860C2×C4—44no—
861C2×C4—44no—
862C2×C4—44no—
863C2×C4—44no—
864C2×C4—84no—
865C2×C4—84no—
866C2×C4—84no—
867C2×C4—88no—
868C2×C4—88no—
869C2×C4—88no—
870C2×C4—84no—
871C2×C4#38112yes—
872C2×C4#38112yes—
873C2×C4#38112yes—
874C2×C4#38112yes—
875C2×C4#38611yescharacteristic
876C2×C4#38611yescharacteristic
877C2×C4#38611yescharacteristic
878C2×C4#38612yes—
879C2×C4#38612yes—
880C2×C4#38612yes—
881C2×C4#38612yes—
882C2×C4#38611yescharacteristic
883C2×C4#38812yes—
884C2×C4#38812yes—
885C2×C4#38812yes—
886C2×C4#38812yes—
887C2×C4#38812yes—
888C2×C4#38812yes—
889C2×C4#38812yes—
890C2×C4#38812yes—
891C2×C4#38812yes—
892C2×C4#38812yes—
893C2×C4#38812yes—
894C2×C4#38812yes—
895C2×C4#39412yes—
896C2×C4#39412yes—
897C2×C4#39412yes—
898C2×C4#39412yes—
899C2×C4#39412yes—
900C2×C4#39412yes—
901C2×C4#39412yes—
902C2×C4#39412yes—
903C2×C4#39412yes—
904C2×C4#39412yes—
905C2×C4#39712yes—
906C2×C4#39712yes—
907C2×C4#39712yes—
908C2×C4#39712yes—
909C2×C4#39712yes—
910C2×C4#39712yes—
911C2×C4#39712yes—
912C2×C4#39712yes—
913C2×C4#39712yes—
914C2×C4#39712yes—
915C2×C4#39712yes—
916C2×C4#39712yes—
917C2×C4#39712yes—
918C2×C4#39712yes—
919C2×C4C22×C22⋊C411yescharacteristic
920C2×C4C2×#11711yescharacteristic
921C2×C4C2×#11711yescharacteristic
922C2×C4C2×C4×D411yescharacteristic
923C2×C4C2×C4×D411yescharacteristic
924C2×C4C2×C4×D411yescharacteristic
925C2×C4C2×#12011yescharacteristic
926C2×C4C2×#12111yescharacteristic
927C2×C4C2×#12111yescharacteristic
928C2×C4C2×#12111yescharacteristic
929C2×C4C2×#12111yescharacteristic
930C2×C4C2×#12111yescharacteristic
931C2×C4C2×#12311yescharacteristic
932C2×C4C2×#12311yescharacteristic
933C2×C4C2×#12311yescharacteristic
934C2×C4C2×#12311yescharacteristic
935C2×C4C2×#12311yescharacteristic
936C2×C4C2×#12311yescharacteristic
937C2×C4C2×#12311yescharacteristic
938C2×C4C2×#12311yescharacteristic
939C2×C4C2×#12311yescharacteristic
940C2×C4C2×#12411yescharacteristic
941C2×C4C2×#12411yescharacteristic
942C2×C4C2×#12411yescharacteristic
943C2×C4C2×#12611yescharacteristic
944C2×C4C2×#12611yescharacteristic
945C2×C4C2×#12611yescharacteristic
946C2×C4C2×#12611yescharacteristic
947C8—44no—
948C8—44no—
949C22—22no—
950C22—22no—
951C22—22no—
952C22—22no—
953C22—22no—
954C22—22no—
955C22—22no—
956C22—42no—
957C22—42no—
958C22—42no—
959C22—41no—
960C22—41no—
961C22—41no—
962C22—41no—
963C22—42no—
964C22—42no—
965C22—42no—
966C22—42no—
967C22—42no—
968C22—42no—
969C22—42no—
970C22—42no—
971C22—42no—
972C22—48no—
973C22—44no—
974C22—84no—
975C22—84no—
976C22—84no—
977C22—84no—
978C22—84no—
979C22—84no—
980C22#144012yes—
981C22#144012yes—
982C22#144012yes—
983C22#144012yes—
984C22C2×#38611yescharacteristic
985C22C2×#38811yescharacteristic
986C22C2×#38811yescharacteristic
987C22C2×#39411yescharacteristic
988C22C2×#39411yescharacteristic
989C22C2×#39411yescharacteristic
990C22C2×#39711yescharacteristic
991C4—44no—
992C4—84no—
993C4—84no—
994C4—84no—
995C4—84no—
996C4#144012yes—
997C4#144012yes—
998C4#144012yes—
999C4#144012yes—
1000C4C2×#38111yescharacteristic
1001C4C2×#38611yescharacteristic
1002C4C2×#38811yescharacteristic
1003C4C2×#38811yescharacteristic
1004C4C2×#39411yescharacteristic
1005C4C2×#39711yescharacteristic
1006C4C2×#39711yescharacteristic
1007C4C2×#39711yescharacteristic
1008C2—21no—
1009C2—21no—
1010C2—21no—
1011C2—21no—
1012C2—21no—
1013C2—21no—
1014C2—22no—
1015C2—22no—
1016C2—22no—
1017C2—22no—
1018C2—84no—
1019C2C2×#144011yescharacteristic
1020C2#2099812yes—
subgroupG/H
centerC2×C4#386
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
socleC22C2×#386
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
4. C22×#344C2semidirect
5. C2×#1740C2semidirect
6. C2×#1733C2semidirect
7. C22×H(3,ℤ/4)C2semidirect
8. #11184C2semidirect
9. #11183C2semidirect
24. C2×#417C4semidirect
30. C2×#416C4semidirect
159. C2×#103C2×C4semidirect
161. C2×#102C2×C4semidirect

Maximal subgroups

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

subgroupindex
C2×#28962
#340442
C22×#3442
C2×#17402
C2×#17332
C22×H(3,ℤ/4)2
#111842
#111832