Finite Group Databasebeta

← C2×#24574 #6440601

Subgroups — C2×#24574 #6440601

Order 512.

2782 conjugacy classes of subgroups.

The subgroup lattice has 986 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#485C211yesmaximal, characteristic, complemented
2C2×#3007C211yesmaximal, characteristic
3C2×#2896C211yesmaximal, characteristic
4C2×#2880C211yesmaximal, characteristic
5#24574C2116yesmaximal, direct product factor
6C2×#2079C211yesmaximal, characteristic, complemented
7C2×#2078C211yesmaximal, characteristic, complemented
8C2×#2052C211yesmaximal, characteristic, complemented
9C2×#2052C211yesmaximal, characteristic, complemented
10C2×#1908C211yesmaximal, characteristic, complemented
11C2×#1908C211yesmaximal, characteristic, complemented
12C2×#1901C211yesmaximal, characteristic, complemented
13C2×#1855C211yesmaximal, characteristic, complemented
14C2×#1822C211yesmaximal, characteristic, complemented
15C2×#1816C211yesmaximal, characteristic, complemented
16C2×#1815C211yesmaximal, characteristic, complemented
17C23×#41C2211yescharacteristic
18C22×#137C2211yescharacteristic
19C22×#137C2211yescharacteristic
20C22×#131C2211yescharacteristic
21C22×#131C2211yescharacteristic
22C23×M16C2211yescharacteristic
23C22×C22⋊Q8C2211yescharacteristic
24C22×#117C2211yescharacteristic
25C2×#485—21no—
26C2×#485—21no—
27C2×#485—21no—
28C2×#485—21no—
29C2×#485—24no—
30C2×#485C2218yescomplemented
31#3007—24no—
32#3007C2218yes—
33C2×#452—21no—
34C2×#452—21no—
35C2×#451—21no—
36C2×#450—21no—
37C22×#108C2211yescharacteristic, complemented
38C22×#108C2211yescharacteristic, complemented
39C22×#107C2211yescharacteristic, complemented
40C22×#106C2211yescharacteristic, complemented
41#2896—24no—
42#2896C2218yes—
43C2×#417C2211yescharacteristic
44C2×#417C2211yescharacteristic
45C2×#417C2211yescharacteristic
46C2×#417C2211yescharacteristic
47C2×#417C2211yescharacteristic
48C2×#417C2211yescharacteristic
49C2×#419—21no—
50C2×#418—21no—
51C2×#416—21no—
52C2×#416—21no—
53C22×#103C2211yescharacteristic, complemented
54C22×#103C2211yescharacteristic, complemented
55C22×#101C2211yescharacteristic, complemented
56C22×#101C2211yescharacteristic, complemented
57#2880—24no—
58#2880C2218yes—
59C2×#408—21no—
60C2×#408—21no—
61C2×#408C2211yescharacteristic
62C2×#408C2211yescharacteristic
63C2×#407—21no—
64C2×#407C2211yescharacteristic
65C2×#407C2211yescharacteristic
66C22×C22⋊C8—21no—
67C22×C22⋊C8C2211yescharacteristic
68#2079C2218yescomplemented
69#2078C2218yescomplemented
70#2052C2218yescomplemented
71#2052C2218yescomplemented
72#1908C2218yescomplemented
73#1908C2218yescomplemented
74#1901C2218yescomplemented
75#1855C2218yescomplemented
76#1822C2218yescomplemented
77#1816C2218yescomplemented
78#1815C2218yescomplemented
79C2×#343C2211yescharacteristic, complemented
80C2×#343C2211yescharacteristic, complemented
81C2×#343C2211yescharacteristic, complemented
82C2×#343C2211yescharacteristic, complemented
83C2×#343C2211yescharacteristic, complemented
84C2×#343C2211yescharacteristic, complemented
85C2×#341C2211yescharacteristic, complemented
86C2×#341C2211yescharacteristic, complemented
87C22×#41—21no—
88C22×#41—22no—
89C22×#41—21no—
90C22×#41—22no—
91C22×#41—24no—
92C22×#41—24no—
93C22×#41—42no—
94C22×#41—42no—
95C22×#41D411yescharacteristic
96C22×#41D411yescharacteristic
97C22×#41D414yes—
98C22×#41C2311yescharacteristic
99C22×#41C2314yes—
100C22×#41C2311yescharacteristic
101C23×Q8D411yescharacteristic
102C23×Q8C2311yescharacteristic
103C23×D4—21no—
104C23×D4D411yescharacteristic
105C24×C4—21no—
106C24×C4C2311yescharacteristic
107C2×#137—22no—
108C2×#137—22no—
109C2×#137—24no—
110C2×#137—24no—
111C2×#137—42no—
112C2×#137—42no—
113C2×#137C2314yes—
114C2×#137C2314yes—
115C22×Q16—21no—
116C22×Q16—21no—
117C22×SD16—21no—
118C22×SD16—21no—
119C2×#131—22no—
120C2×#131—22no—
121C2×#131—24no—
122C2×#131—24no—
123C2×#131—42no—
124C2×#131—42no—
125C2×#131C2314yes—
126C2×#131C2314yes—
127C22×M16—21no—
128C22×M16—22no—
129C22×M16—21no—
130C22×M16—21no—
131C22×M16—42no—
132C22×M16—42no—
133C22×M16C2311yescharacteristic
134C22×M16C2311yescharacteristic
135C22×M16C2311yescharacteristic
136C22×M16C2311yescharacteristic
137C22×M16C2311yescharacteristic
138C22×M16C2311yescharacteristic
139C22×M16C2314yes—
140C23×C8—21no—
141C23×C8—21no—
142C23×C8—21no—
143C23×C8C2311yescharacteristic
144C23×C8C2311yescharacteristic
145C2×C22⋊Q8—22no—
146C2×C22⋊Q8—21no—
147C2×C22⋊Q8—21no—
148C2×C22⋊Q8—22no—
149C2×C22⋊Q8—21no—
150C2×C22⋊Q8—21no—
151C2×C22⋊Q8—22no—
152C2×C22⋊Q8C2314yes—
153C2×#117—22no—
154C2×#117—21no—
155C2×#117—21no—
156C2×#117—22no—
157C2×#117—21no—
158C2×#117—21no—
159C2×#117—22no—
160C2×#117C2314yes—
161C22×C4⋊C4—21no—
162C22×C4⋊C4C2311yescharacteristic
163C22×C4⋊C4C2311yescharacteristic
164C22×C4⋊C4C2311yescharacteristic
165C22×C22⋊C4—21no—
166C22×C22⋊C4—21no—
167C22×C42—21no—
168#485—28no—
169#485—28no—
170#485—28no—
171#485—28no—
172#452—28no—
173#452—28no—
174#451—28no—
175#450—28no—
176C2×#108—42no—
177C2×#108—42no—
178C2×#108C2314yescomplemented
179C2×#108C2314yescomplemented
180C2×#107—21no—
181C2×#107—21no—
182C2×#107—22no—
183C2×#107C2314yescomplemented
184C2×#106—21no—
185C2×#106—21no—
186C2×#106—22no—
187C2×#106C2314yescomplemented
188#419—28no—
189#418—28no—
190#417—22no—
191#417—22no—
192#417—22no—
193#417—22no—
194#417—22no—
195#417—22no—
196#417C2314yes—
197#417C2314yes—
198#417C2314yes—
199#417C2314yes—
200#417C2314yes—
201#417C2314yes—
202#416—28no—
203#416—28no—
204C2×#103—21no—
205C2×#103—21no—
206C2×#103—21no—
207C2×#103—21no—
208C2×#103—21no—
209C2×#103—21no—
210C2×#103—21no—
211C2×#103—21no—
212C2×#103—22no—
213C2×#103—21no—
214C2×#103—21no—
215C2×#103—22no—
216C2×#103C2314yescomplemented
217C2×#103C2314yescomplemented
218C2×#102—21no—
219C2×#102—21no—
220C2×#102—21no—
221C2×#102—21no—
222C2×#102—21no—
223C2×#102—21no—
224C2×#101—42no—
225C2×#101—42no—
226C2×#101C2314yescomplemented
227C2×#101C2314yescomplemented
228#408—22no—
229#408—22no—
230#408—28no—
231#408—28no—
232#408C2314yes—
233#408C2314yes—
234#407—22no—
235#407—22no—
236#407—28no—
237#407C2314yes—
238#407C2314yes—
239C2×C22⋊C8—21no—
240C2×C22⋊C8—21no—
241C2×C22⋊C8—21no—
242C2×C22⋊C8—21no—
243C2×C22⋊C8—21no—
244C2×C22⋊C8—21no—
245C2×C22⋊C8—21no—
246C2×C22⋊C8—21no—
247C2×C22⋊C8—28no—
248C2×C22⋊C8D411yescharacteristic
249C2×C22⋊C8D411yescharacteristic
250C2×C22⋊C8D411yescharacteristic
251C2×C22⋊C8D411yescharacteristic
252C2×C22⋊C8D414yes—
253C2×C22⋊C8C2314yes—
254#343C2314yescomplemented
255#343C2314yescomplemented
256#343C2314yescomplemented
257#343C2314yescomplemented
258#343C2314yescomplemented
259#343C2314yescomplemented
260#341C2314yescomplemented
261#341C2314yescomplemented
262C25—21no—
263C25#4111yescharacteristic
264C2×#41—24no—
265C2×#41—24no—
266C2×#41—22no—
267C2×#41—22no—
268C2×#41—21no—
269C2×#41—24no—
270C2×#41—21no—
271C2×#41—21no—
272C2×#41—24no—
273C2×#41—21no—
274C2×#41—22no—
275C2×#41—22no—
276C2×#41—216no—
277C2×#41—28no—
278C2×#41—28no—
279C2×#41—24no—
280C2×#41—24no—
281C2×#41—22no—
282C2×#41—22no—
283C2×#41—22no—
284C2×#41—22no—
285C2×#41—44no—
286C2×#41—44no—
287C2×#41—42no—
288C2×#41—42no—
289C2×#41—44no—
290C2×#41—44no—
291C2×#41—48no—
292C2×#41—44no—
293C2×#41—44no—
294C2×#41—48no—
295C2×#41—48no—
296C2×#41—48no—
297C2×#41—48no—
298C2×#41C2×D412yes—
299C2×#41C2×D414yes—
300C2×#41C2×D414yes—
301C2×#41C2×D412yes—
302C2×#41#4114yes—
303C2×#41#4114yes—
304C2×#41C2412yes—
305C2×#41C2412yes—
306C22×Q8—21no—
307C22×Q8—22no—
308C22×Q8—21no—
309C22×Q8—24no—
310C22×Q8—21no—
311C22×Q8—21no—
312C22×Q8—21no—
313C22×Q8—21no—
314C22×Q8—22no—
315C22×Q8—22no—
316C22×Q8—22no—
317C22×Q8—22no—
318C22×Q8—42no—
319C22×Q8C2×D411yescharacteristic
320C22×Q8C2×D414yes—
321C22×Q8C2×D411yescharacteristic
322C22×Q8C2412yes—
323C22×D4—21no—
324C22×D4—24no—
325C22×D4—21no—
326C22×D4—24no—
327C22×D4—21no—
328C22×D4—24no—
329C22×D4—21no—
330C22×D4—22no—
331C22×D4—21no—
332C22×D4—42no—
333C22×D4—44no—
334C22×D4—44no—
335C22×D4C2×D411yescharacteristic
336C22×D4C2×D414yes—
337C22×D4C2×D411yescharacteristic
338C23×C4—21no—
339C23×C4—22no—
340C23×C4—22no—
341C23×C4—22no—
342C23×C4—22no—
343C23×C4—21no—
344C23×C4—21no—
345C23×C4—24no—
346C23×C4—21no—
347C23×C4—21no—
348C23×C4—24no—
349C23×C4—21no—
350C23×C4—21no—
351C23×C4—21no—
352C23×C4—21no—
353C23×C4—44no—
354C23×C4—44no—
355C23×C4C2×D411yescharacteristic
356C23×C4C2×D411yescharacteristic
357C23×C4C2×D412yes—
358C23×C4C2×D411yescharacteristic
359C23×C4C2×D411yescharacteristic
360C23×C4C2×D412yes—
361C23×C4#4111yescharacteristic
362C23×C4#4112yes—
363C23×C4C2412yes—
364C23×C4C2411yescharacteristic
365#137—28no—
366#137—28no—
367#137—44no—
368#137—44no—
369#137—48no—
370#137—48no—
371C2×Q16—24no—
372C2×Q16—24no—
373C2×Q16—44no—
374C2×Q16—44no—
375C2×SD16—24no—
376C2×SD16—24no—
377C2×SD16—44no—
378C2×SD16—44no—
379#131—28no—
380#131—28no—
381#131—44no—
382#131—44no—
383#131—48no—
384#131—48no—
385C2×M16—21no—
386C2×M16—21no—
387C2×M16—24no—
388C2×M16—21no—
389C2×M16—21no—
390C2×M16—21no—
391C2×M16—21no—
392C2×M16—24no—
393C2×M16—24no—
394C2×M16—22no—
395C2×M16—22no—
396C2×M16—22no—
397C2×M16—22no—
398C2×M16—22no—
399C2×M16—22no—
400C2×M16—22no—
401C2×M16—22no—
402C2×M16—22no—
403C2×M16—22no—
404C2×M16—22no—
405C2×M16—22no—
406C2×M16—44no—
407C2×M16—44no—
408C2×M16—44no—
409C2×M16—44no—
410C2×M16—48no—
411C2×M16—44no—
412C2×M16C2412yes—
413C2×M16C2412yes—
414C2×M16C2412yes—
415C2×M16C2412yes—
416C2×M16C2412yes—
417C2×M16C2412yes—
418C22×C8—22no—
419C22×C8—22no—
420C22×C8—22no—
421C22×C8—22no—
422C22×C8—21no—
423C22×C8—21no—
424C22×C8—21no—
425C22×C8—21no—
426C22×C8—24no—
427C22×C8—21no—
428C22×C8—21no—
429C22×C8—24no—
430C22×C8—24no—
431C22×C8—44no—
432C22×C8—44no—
433C22×C8—44no—
434C22×C8C2×D411yescharacteristic
435C22×C8C2×D411yescharacteristic
436C22×C8C2×D411yescharacteristic
437C22×C8C2×D411yescharacteristic
438C22×C8C2×D412yes—
439C22×C8C2×D412yes—
440C22×C8C2412yes—
441C22×C8C2412yes—
442C22⋊Q8—24no—
443C22⋊Q8—24no—
444C22⋊Q8—24no—
445C22⋊Q8—24no—
446C22⋊Q8—42no—
447C22⋊Q8—42no—
448C22⋊Q8—42no—
449C22⋊Q8—42no—
450#117—24no—
451#117—24no—
452#117—24no—
453#117—24no—
454#117—42no—
455#117—42no—
456#117—42no—
457#117—42no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—21no—
460C2×C4⋊C4—21no—
461C2×C4⋊C4—21no—
462C2×C4⋊C4—21no—
463C2×C4⋊C4—21no—
464C2×C4⋊C4—21no—
465C2×C4⋊C4—21no—
466C2×C4⋊C4—21no—
467C2×C4⋊C4—21no—
468C2×C4⋊C4—21no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4—24no—
471C2×C4⋊C4—21no—
472C2×C4⋊C4—21no—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—42no—
475C2×C4⋊C4—41no—
476C2×C4⋊C4—41no—
477C2×C4⋊C4C2412yes—
478C2×C4⋊C4C2412yes—
479C2×C4⋊C4C2412yes—
480C2×C22⋊C4—24no—
481C2×C22⋊C4—24no—
482C2×C22⋊C4—42no—
483C2×C22⋊C4—41no—
484C2×C22⋊C4—41no—
485C2×C22⋊C4—42no—
486C2×C22⋊C4—41no—
487C2×C22⋊C4—41no—
488C2×C42—24no—
489C2×C42—42no—
490C2×C42—41no—
491C2×C42—41no—
492#108—44no—
493#108—44no—
494#107—24no—
495#107—24no—
496#106—24no—
497#106—24no—
498#103—24no—
499#103—24no—
500#103—24no—
501#103—24no—
502#103—24no—
503#103—24no—
504#103—24no—
505#103—24no—
506#103—24no—
507#103—24no—
508#102—24no—
509#102—24no—
510#102—24no—
511#102—24no—
512#102—24no—
513#102—24no—
514#101—44no—
515#101—44no—
516C22⋊C8—24no—
517C22⋊C8—24no—
518C22⋊C8—24no—
519C22⋊C8—24no—
520C22⋊C8—24no—
521C22⋊C8—24no—
522C22⋊C8—24no—
523C22⋊C8—24no—
524C22⋊C8C2×D414yes—
525C22⋊C8C2×D414yes—
526C22⋊C8C2×D414yes—
527C22⋊C8C2×D414yes—
528C24—21no—
529C24—22no—
530C24—22no—
531C24—21no—
532C24—24no—
533C24—42no—
534C24—42no—
535C24—44no—
536C24—44no—
537C24—82no—
538C24#12111yescharacteristic
539C24#12111yescharacteristic
540C24#12112yes—
541C24C2×#4111yescharacteristic
542C24C2×#4112yes—
543#41—24no—
544#41—24no—
545#41—24no—
546#41—24no—
547#41—24no—
548#41—22no—
549#41—22no—
550#41—28no—
551#41—28no—
552#41—24no—
553#41—24no—
554#41—22no—
555#41—22no—
556#41—22no—
557#41—22no—
558#41—416no—
559#41—48no—
560#41—48no—
561#41—44no—
562#41—44no—
563#41—416no—
564#41—48no—
565#41—48no—
566#41—48no—
567#41—48no—
568#41—42no—
569#41—42no—
570#41—42no—
571#41—42no—
572#41#12318yes—
573#41C2×#4114yes—
574#41C2×#4114yes—
575C2×Q8—21no—
576C2×Q8—24no—
577C2×Q8—21no—
578C2×Q8—22no—
579C2×Q8—28no—
580C2×Q8—22no—
581C2×Q8—22no—
582C2×Q8—22no—
583C2×Q8—22no—
584C2×Q8—22no—
585C2×Q8—22no—
586C2×Q8—22no—
587C2×Q8—22no—
588C2×Q8—44no—
589C2×Q8—44no—
590C2×Q8—48no—
591C2×Q8—41no—
592C2×Q8—41no—
593C2×Q8—42no—
594C2×Q8—42no—
595C2×Q8—42no—
596C2×Q8—42no—
597C2×Q8—42no—
598C2×Q8—42no—
599C2×Q8—42no—
600C2×Q8—42no—
601C2×Q8—42no—
602C2×Q8—42no—
603C2×Q8#12314yes—
604C2×Q8C22×D412yes—
605C2×Q8C22×D412yes—
606C2×D4—22no—
607C2×D4—24no—
608C2×D4—24no—
609C2×D4—22no—
610C2×D4—28no—
611C2×D4—24no—
612C2×D4—24no—
613C2×D4—22no—
614C2×D4—22no—
615C2×D4—21no—
616C2×D4—24no—
617C2×D4—21no—
618C2×D4—22no—
619C2×D4—22no—
620C2×D4—22no—
621C2×D4—44no—
622C2×D4—48no—
623C2×D4—44no—
624C2×D4—44no—
625C2×D4—416no—
626C2×D4—48no—
627C2×D4—48no—
628C2×D4—44no—
629C2×D4—42no—
630C2×D4—42no—
631C2×D4#12314yes—
632C2×D4C22×D412yes—
633C2×D4C22×D412yes—
634C22×C4—21no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—24no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—24no—
644C22×C4—24no—
645C22×C4—24no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—24no—
651C22×C4—24no—
652C22×C4—24no—
653C22×C4—24no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—24no—
660C22×C4—21no—
661C22×C4—24no—
662C22×C4—24no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—44no—
670C22×C4—416no—
671C22×C4—48no—
672C22×C4—48no—
673C22×C4—44no—
674C22×C4—44no—
675C22×C4—42no—
676C22×C4—42no—
677C22×C4—41no—
678C22×C4—41no—
679C22×C4—41no—
680C22×C4—41no—
681C22×C4—41no—
682C22×C4—41no—
683C22×C4—41no—
684C22×C4—41no—
685C22×C4—42no—
686C22×C4—42no—
687C22×C4—82no—
688C22×C4—82no—
689C22×C4—82no—
690C22×C4#12112yes—
691C22×C4#12112yes—
692C22×C4#12112yes—
693C22×C4#12112yes—
694C22×C4#12112yes—
695C22×C4#12111yescharacteristic
696C22×C4#12111yescharacteristic
697C22×C4C22×D412yes—
698C22×C4C22×D412yes—
699C22×C4C22×D412yes—
700C22×C4C22×D412yes—
701C22×C4C22×D411yescharacteristic
702C22×C4C22×D411yescharacteristic
703C22×C4C22×D411yescharacteristic
704C22×C4C22×D411yescharacteristic
705C22×C4C2×#4112yes—
706C22×C4C2×#4111yescharacteristic
707C22×C4C2×#4112yes—
708C22×C4C2×#4112yes—
709C22×C4H(5,𝔽2)12yes—
710C22×C4H(5,𝔽2)12yes—
711C22×C4C2511yescharacteristic
712Q16—48no—
713Q16—48no—
714SD16—48no—
715SD16—48no—
716M16—22no—
717M16—22no—
718M16—22no—
719M16—22no—
720M16—22no—
721M16—22no—
722M16—22no—
723M16—22no—
724M16—22no—
725M16—22no—
726M16—22no—
727M16—22no—
728M16—48no—
729M16—48no—
730M16—48no—
731M16—42no—
732M16—42no—
733M16—42no—
734M16—42no—
735M16—42no—
736M16—42no—
737C2×C8—22no—
738C2×C8—22no—
739C2×C8—22no—
740C2×C8—22no—
741C2×C8—24no—
742C2×C8—24no—
743C2×C8—22no—
744C2×C8—22no—
745C2×C8—22no—
746C2×C8—22no—
747C2×C8—22no—
748C2×C8—22no—
749C2×C8—22no—
750C2×C8—22no—
751C2×C8—22no—
752C2×C8—22no—
753C2×C8—48no—
754C2×C8—48no—
755C2×C8—48no—
756C2×C8—42no—
757C2×C8—42no—
758C2×C8—42no—
759C2×C8—42no—
760C2×C8—42no—
761C2×C8—42no—
762C2×C8C22×D412yes—
763C2×C8C22×D412yes—
764C2×C8C22×D412yes—
765C2×C8C22×D412yes—
766C4⋊C4—22no—
767C4⋊C4—22no—
768C4⋊C4—22no—
769C4⋊C4—22no—
770C4⋊C4—22no—
771C4⋊C4—22no—
772C4⋊C4—41no—
773C4⋊C4—41no—
774C4⋊C4—41no—
775C4⋊C4—41no—
776C4⋊C4—41no—
777C4⋊C4—41no—
778C4⋊C4—44no—
779C4⋊C4—44no—
780C22⋊C4—44no—
781C22⋊C4—44no—
782C22⋊C4—44no—
783C22⋊C4—44no—
784C42—44no—
785C42—44no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—22no—
790C23—22no—
791C23—24no—
792C23—22no—
793C23—22no—
794C23—22no—
795C23—22no—
796C23—24no—
797C23—22no—
798C23—22no—
799C23—22no—
800C23—42no—
801C23—42no—
802C23—42no—
803C23—42no—
804C23—48no—
805C23—48no—
806C23—42no—
807C23—42no—
808C23—42no—
809C23—42no—
810C23—42no—
811C23—84no—
812C23—84no—
813C23—84no—
814C23—816no—
815C23C2×#12112yes—
816C23C2×#12112yes—
817C23C2×#12111yescharacteristic
818C23C2×#12111yescharacteristic
819C23#55112yes—
820C23#55112yes—
821C23C22×#4111yescharacteristic
822Q8—24no—
823Q8—22no—
824Q8—22no—
825Q8—22no—
826Q8—48no—
827Q8—42no—
828Q8—42no—
829Q8—42no—
830Q8—42no—
831Q8—42no—
832Q8—82no—
833Q8—82no—
834Q8C2×#12314yes—
835D4—28no—
836D4—24no—
837D4—24no—
838D4—22no—
839D4—24no—
840D4—22no—
841D4—22no—
842D4—48no—
843D4—48no—
844D4—48no—
845D4—44no—
846D4—42no—
847D4—42no—
848D4—42no—
849D4C2×#12314yes—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—24no—
854C2×C4—24no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—24no—
860C2×C4—24no—
861C2×C4—24no—
862C2×C4—24no—
863C2×C4—28no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—24no—
867C2×C4—24no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—48no—
874C2×C4—48no—
875C2×C4—48no—
876C2×C4—42no—
877C2×C4—44no—
878C2×C4—42no—
879C2×C4—42no—
880C2×C4—42no—
881C2×C4—42no—
882C2×C4—42no—
883C2×C4—42no—
884C2×C4—42no—
885C2×C4—42no—
886C2×C4—82no—
887C2×C4—82no—
888C2×C4—82no—
889C2×C4—82no—
890C2×C4—82no—
891C2×C4—82no—
892C2×C4—82no—
893C2×C4—82no—
894C2×C4—82no—
895C2×C4—82no—
896C2×C4—82no—
897C2×C4C2×#12112yes—
898C2×C4C2×#12112yes—
899C2×C4C2×#12111yescharacteristic
900C2×C4C2×#12111yescharacteristic
901C2×C4C2×#12312yes—
902C2×C4C2×#12312yes—
903C2×C4#53412yes—
904C2×C4#53412yes—
905C2×C4#54612yes—
906C2×C4#54612yes—
907C2×C4#54612yes—
908C2×C4#54612yes—
909C2×C4#55112yes—
910C2×C4#55112yes—
911C2×C4C23×D411yescharacteristic
912C2×C4C23×D411yescharacteristic
913C2×C4C22×#4111yescharacteristic
914C2×C4C22×#4111yescharacteristic
915C2×C4C2×H(5,𝔽2)11yescharacteristic
916C2×C4C2×H(5,𝔽2)11yescharacteristic
917C8—22no—
918C8—22no—
919C8—22no—
920C8—22no—
921C8—42no—
922C8—42no—
923C8—42no—
924C8—42no—
925C8—42no—
926C8—42no—
927C22—21no—
928C22—21no—
929C22—21no—
930C22—21no—
931C22—24no—
932C22—24no—
933C22—22no—
934C22—22no—
935C22—22no—
936C22—22no—
937C22—22no—
938C22—22no—
939C22—24no—
940C22—42no—
941C22—42no—
942C22—44no—
943C22—44no—
944C22—48no—
945C22—42no—
946C22—42no—
947C22—42no—
948C22—84no—
949C22—82no—
950C22—82no—
951C22—816no—
952C22—84no—
953C22#241212yes—
954C22#241212yes—
955C22#306712yes—
956C22#306912yes—
957C22C22×#12111yescharacteristic
958C22C2×#55111yescharacteristic
959C22C2×#55111yescharacteristic
960C4—22no—
961C4—22no—
962C4—24no—
963C4—42no—
964C4—82no—
965C4—82no—
966C4—82no—
967C4—82no—
968C4#241212yes—
969C4#241212yes—
970C4C22×#12311yescharacteristic
971C4C2×#53411yescharacteristic
972C4C2×#54611yescharacteristic
973C4C2×#54611yescharacteristic
974C2—22no—
975C2—21no—
976C2—21no—
977C2—42no—
978C2—42no—
979C2—44no—
980C2—82no—
981C2#2457414yesdirect product factor
982C2C2×#241211yescharacteristic
983C2C2×#306711yescharacteristic
984C2C2×#306911yescharacteristic
subgroupG/H
center, socleC23C2×#121
commutator, Frattini, cosocleC22×C4C25
prime radicalC23×#41C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C24×C4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C22×#485C2semidirect
5. #24574C2direct (N × H)
6. C2×#2079C2semidirect
7. C2×#2078C2semidirect
8. C2×#2052C2semidirect
9. C2×#2052C2semidirect
10. C2×#1908C2semidirect
11. C2×#1908C2semidirect
12. C2×#1901C2semidirect
13. C2×#1855C2semidirect
14. C2×#1822C2semidirect
15. C2×#1816C2semidirect
16. C2×#1815C2semidirect
30. C2×#485C22semidirect
37. C22×#108C22semidirect
38. C22×#108C22semidirect
39. C22×#107C22semidirect
40. C22×#106C22semidirect
53. C22×#103C22semidirect
54. C22×#103C22semidirect
55. C22×#101C22semidirect
56. C22×#101C22semidirect
68. #2079C22semidirect
69. #2078C22semidirect
70. #2052C22semidirect
71. #2052C22semidirect
72. #1908C22semidirect
73. #1908C22semidirect
74. #1901C22semidirect
75. #1855C22semidirect
76. #1822C22semidirect
77. #1816C22semidirect
78. #1815C22semidirect
79. C2×#343C22semidirect
80. C2×#343C22semidirect
81. C2×#343C22semidirect
82. C2×#343C22semidirect
83. C2×#343C22semidirect
84. C2×#343C22semidirect
85. C2×#341C22semidirect
86. C2×#341C22semidirect
178. C2×#108C23semidirect
179. C2×#108C23semidirect
183. C2×#107C23semidirect
187. C2×#106C23semidirect
216. C2×#103C23semidirect
217. C2×#103C23semidirect
226. C2×#101C23semidirect
227. C2×#101C23semidirect
254. #343C23semidirect
255. #343C23semidirect
256. #343C23semidirect
257. #343C23semidirect
258. #343C23semidirect
259. #343C23semidirect
260. #341C23semidirect
261. #341C23semidirect
981. C2#24574direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#4852
C2×#30072
C2×#28962
C2×#28802
#245742
C2×#20792
C2×#20782
C2×#20522
C2×#19082
C2×#19012
C2×#18552
C2×#18222
C2×#18162
C2×#18152