Finite Group Databasebeta

← C2×#24245 #6442620

Subgroups — C2×#24245 #6442620

Order 512.

5662 conjugacy classes of subgroups.

The subgroup lattice has 1037 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#546C211yesmaximal, characteristic, complemented
2C22×#463C211yesmaximal, characteristic, complemented
3C22×#449C211yesmaximal, characteristic, complemented
4C22×#447C211yesmaximal, characteristic, complemented
5C22×C4×D8C211yesmaximal, characteristic, complemented
6C2×#2535C211yesmaximal, characteristic, complemented
7#24245C2116yesmaximal, direct product factor
8C2×#2036C211yesmaximal, characteristic, complemented
9C2×#2033C211yesmaximal, characteristic, complemented
10C2×#2000C211yesmaximal, characteristic, complemented
11C2×#1999C211yesmaximal, characteristic, complemented
12C2×#1958C211yesmaximal, characteristic, complemented
13C2×#1954C211yesmaximal, characteristic, complemented
14C2×#1804C211yesmaximal, characteristic, complemented
15C2×#1788C211yesmaximal, characteristic, complemented
16C2×#1786C211yesmaximal, characteristic, complemented
17C23×#41C2211yescharacteristic
18C24×D4C2211yescharacteristic
19C23×SD16C2211yescharacteristic, complemented
20C23×D8C2211yescharacteristic
21C23×D8C2211yescharacteristic
22C2×#546—28no—
23C2×#546—24no—
24C2×#546—28no—
25C2×#546C2218yescomplemented
26C22×#124C2211yescharacteristic
27C22×#123—21no—
28C22×C22⋊Q8C2211yescharacteristic
29C22×#121—21no—
30C22×#121C2211yescharacteristic
31C22×#121C2211yescharacteristic
32C22×#121C2211yescharacteristic, complemented
33C22×#120—21no—
34C22×C4×D4C2211yescharacteristic
35C22×C4×D4C2211yescharacteristic
36C22×C4×D4C2211yescharacteristic, complemented
37C23×C22⋊C4—21no—
38C2×#463—28no—
39C2×#463C2218yescomplemented
40C2×#449—28no—
41C2×#449C2218yescomplemented
42C2×#447—28no—
43C2×#447C2218yescomplemented
44C2×C4×D8—28no—
45C2×C4×D8C2218yescomplemented
46C22×#107C2211yescharacteristic, complemented
47C22×C4⋊C8C2211yescharacteristic, complemented
48C22×#103C2211yescharacteristic, complemented
49C22×#103C2211yescharacteristic, complemented
50C22×#103C2211yescharacteristic, complemented
51C22×#102C2211yescharacteristic
52C22×#102C2211yescharacteristic
53C22×#102C2211yescharacteristic
54C22×#102C2211yescharacteristic
55C22×#102C2211yescharacteristic
56C22×#102C2211yescharacteristic
57C22×#102C2211yescharacteristic, complemented
58C22×C22⋊C8C2211yescharacteristic
59C22×C22⋊C8C2211yescharacteristic
60C22×C22⋊C8C2211yescharacteristic, complemented
61C22×C22⋊C8C2211yescharacteristic, complemented
62C22×C4×C8C2211yescharacteristic, complemented
63#2535—24no—
64#2535C2218yescomplemented
65C2×#397—21no—
66C2×#392—21no—
67C2×#386—21no—
68C2×#386—21no—
69C2×#382C2211yescharacteristic, complemented
70C2×#380C2211yescharacteristic
71C2×#380C2211yescharacteristic, complemented
72#2036C2218yescomplemented
73#2033C2218yescomplemented
74#2000C2218yescomplemented
75#1999C2218yescomplemented
76#1958C2218yescomplemented
77#1954C2218yescomplemented
78#1804C2218yescomplemented
79#1788C2218yescomplemented
80#1786C2218yescomplemented
81C2×#340C2211yescharacteristic, complemented
82C2×#340C2211yescharacteristic, complemented
83C26—21no—
84C22×#41—24no—
85C22×#41—24no—
86C22×#41—22no—
87C22×#41—24no—
88C22×#41—24no—
89C22×#41—42no—
90C22×#41—42no—
91C22×#41C2314yes—
92C23×Q8C2311yescharacteristic
93C23×D4—21no—
94C23×D4—21no—
95C23×D4—24no—
96C23×D4—24no—
97C23×D4—24no—
98C23×D4—24no—
99C23×D4—21no—
100C23×D4—21no—
101C23×D4—21no—
102C23×D4—22no—
103C23×D4—42no—
104C23×D4—42no—
105C23×D4D411yescharacteristic
106C23×D4C2311yescharacteristic
107C23×D4C2311yescharacteristic
108C23×D4C2314yes—
109C23×D4C2311yescharacteristic
110C24×C4—21no—
111C24×C4—21no—
112C24×C4—21no—
113C24×C4C2311yescharacteristic
114C24×C4C2311yescharacteristic
115C22×SD16—24no—
116C22×SD16—24no—
117C22×SD16—42no—
118C22×SD16C2314yescomplemented
119C22×D8—24no—
120C22×D8—24no—
121C22×D8—24no—
122C22×D8—24no—
123C22×D8—42no—
124C22×D8D418yescomplemented
125C22×D8C2314yes—
126C22×D8C2314yes—
127C23×C8C2311yescharacteristic
128C23×C8C2311yescharacteristic
129C23×C8C2311yescharacteristic
130C23×C8C2311yescharacteristic
131#546—264no—
132#546—232no—
133#546—232no—
134C2×#124—22no—
135C2×#124—24no—
136C2×#124D418yescomplemented
137C2×#124C2314yes—
138C2×#123—216no—
139C2×#123—28no—
140C2×C22⋊Q8—24no—
141C2×C22⋊Q8—22no—
142C2×C22⋊Q8—24no—
143C2×C22⋊Q8C2314yes—
144C2×#121—216no—
145C2×#121—24no—
146C2×#121—22no—
147C2×#121—22no—
148C2×#121—22no—
149C2×#121—24no—
150C2×#121—28no—
151C2×#121—24no—
152C2×#121—24no—
153C2×#121—42no—
154C2×#121—42no—
155C2×#121C2314yes—
156C2×#121C2314yes—
157C2×#121C2314yescomplemented
158C2×#120—216no—
159C2×#120—28no—
160C2×C4×D4—22no—
161C2×C4×D4—24no—
162C2×C4×D4—24no—
163C2×C4×D4—24no—
164C2×C4×D4—22no—
165C2×C4×D4—24no—
166C2×C4×D4—24no—
167C2×C4×D4D414yes—
168C2×C4×D4D418yescomplemented
169C2×C4×D4C2314yes—
170C2×C4×D4C2314yes—
171C2×C4×D4C2314yescomplemented
172C22×C4⋊C4—21no—
173C22×C4⋊C4D411yescharacteristic
174C22×C4⋊C4C2311yescharacteristic
175C22×C4⋊C4C2311yescharacteristic
176C22×C4⋊C4C2311yescharacteristic
177C22×C4⋊C4C2311yescharacteristic
178C22×C22⋊C4—216no—
179C22×C22⋊C4—21no—
180C22×C22⋊C4—21no—
181C22×C22⋊C4—21no—
182C22×C22⋊C4—21no—
183C22×C22⋊C4—21no—
184C22×C22⋊C4—28no—
185C22×C22⋊C4—21no—
186C22×C22⋊C4—21no—
187C22×C22⋊C4—21no—
188C22×C22⋊C4—21no—
189C22×C22⋊C4—21no—
190C22×C22⋊C4D411yescharacteristic
191C22×C22⋊C4D411yescharacteristic
192C22×C42C2311yescharacteristic
193#463—232no—
194#449—232no—
195#447—232no—
196C4×D8—232no—
197C2×#107—24no—
198C2×#107C2314yescomplemented
199C2×C4⋊C8—24no—
200C2×C4⋊C8C2314yescomplemented
201C2×#103—24no—
202C2×#103—24no—
203C2×#103—42no—
204C2×#103C2314yescomplemented
205C2×#103C2314yescomplemented
206C2×#103C2314yescomplemented
207C2×#102—24no—
208C2×#102—24no—
209C2×#102—24no—
210C2×#102—24no—
211C2×#102—24no—
212C2×#102—24no—
213C2×#102—42no—
214C2×#102C2314yes—
215C2×#102C2314yes—
216C2×#102C2314yes—
217C2×#102C2314yes—
218C2×#102C2314yes—
219C2×#102C2314yes—
220C2×#102C2314yescomplemented
221C2×C22⋊C8—24no—
222C2×C22⋊C8—24no—
223C2×C22⋊C8—42no—
224C2×C22⋊C8—42no—
225C2×C22⋊C8C2314yes—
226C2×C22⋊C8C2314yes—
227C2×C22⋊C8C2314yescomplemented
228C2×C22⋊C8C2314yescomplemented
229C2×C4×C8—24no—
230C2×C4×C8C2314yescomplemented
231#397—28no—
232#392—28no—
233#386—28no—
234#386—28no—
235#382—22no—
236#382C2314yescomplemented
237#380—22no—
238#380—22no—
239#380C2314yes—
240#380C2314yescomplemented
241C2×#95—21no—
242C2×#95—21no—
243C2×#95—21no—
244C2×#95—21no—
245#340C2314yescomplemented
246#340C2314yescomplemented
247C25—21no—
248C25—28no—
249C25—21no—
250C25—21no—
251C25—24no—
252C25—44no—
253C25—44no—
254C25—44no—
255C25—44no—
256C25—82no—
257C25—82no—
258C25C2×D411yescharacteristic
259C25C2×D411yescharacteristic
260C2×#41—216no—
261C2×#41—28no—
262C2×#41—28no—
263C2×#41—28no—
264C2×#41—28no—
265C2×#41—44no—
266C2×#41—44no—
267C2×#41—48no—
268C2×#41—48no—
269C2×#41—416no—
270C2×#41—416no—
271C2×#41—416no—
272C2×#41—416no—
273C22×Q8—22no—
274C22×Q8—21no—
275C22×Q8—22no—
276C22×Q8—22no—
277C22×Q8—22no—
278C22×Q8—22no—
279C22×Q8C2×D414yes—
280C22×Q8C2412yes—
281C22×D4—28no—
282C22×D4—28no—
283C22×D4—216no—
284C22×D4—24no—
285C22×D4—24no—
286C22×D4—28no—
287C22×D4—24no—
288C22×D4—28no—
289C22×D4—28no—
290C22×D4—28no—
291C22×D4—28no—
292C22×D4—24no—
293C22×D4—24no—
294C22×D4—24no—
295C22×D4—21no—
296C22×D4—22no—
297C22×D4—22no—
298C22×D4—22no—
299C22×D4—22no—
300C22×D4—21no—
301C22×D4—24no—
302C22×D4—21no—
303C22×D4—22no—
304C22×D4—22no—
305C22×D4—22no—
306C22×D4—22no—
307C22×D4—22no—
308C22×D4—22no—
309C22×D4—22no—
310C22×D4—22no—
311C22×D4—22no—
312C22×D4—44no—
313C22×D4—44no—
314C22×D4—48no—
315C22×D4—48no—
316C22×D4—42no—
317C22×D4—44no—
318C22×D4—44no—
319C22×D4—416no—
320C22×D4—416no—
321C22×D4—416no—
322C22×D4—44no—
323C22×D4—44no—
324C22×D4—416no—
325C22×D4—44no—
326C22×D4—44no—
327C22×D4—44no—
328C22×D4—44no—
329C22×D4—82no—
330C22×D4—82no—
331C22×D4—82no—
332C22×D4—82no—
333C22×D4C2×D414yes—
334C22×D4C2×D414yes—
335C22×D4C2×D414yes—
336C22×D4C2×D414yes—
337C22×D4C2×D414yes—
338C22×D4#4114yes—
339C22×D4C2412yes—
340C22×D4C2412yes—
341C22×D4C2412yes—
342C23×C4—28no—
343C23×C4—21no—
344C23×C4—21no—
345C23×C4—24no—
346C23×C4—22no—
347C23×C4—22no—
348C23×C4—22no—
349C23×C4—22no—
350C23×C4—22no—
351C23×C4—22no—
352C23×C4—22no—
353C23×C4—22no—
354C23×C4—22no—
355C23×C4—22no—
356C23×C4—22no—
357C23×C4—22no—
358C23×C4—28no—
359C23×C4—24no—
360C23×C4—21no—
361C23×C4—21no—
362C23×C4—21no—
363C23×C4—24no—
364C23×C4—44no—
365C23×C4—44no—
366C23×C4—44no—
367C23×C4—82no—
368C23×C4—82no—
369C23×C4—82no—
370C23×C4—82no—
371C23×C4C2×D412yes—
372C23×C4C2×D412yes—
373C23×C4C2×D411yescharacteristic
374C23×C4C2×D411yescharacteristic
375C23×C4C2×D411yescharacteristic
376C23×C4C2×D411yescharacteristic
377C23×C4C2412yes—
378C23×C4C2412yes—
379C23×C4C2411yescharacteristic
380C2×SD16—28no—
381C2×SD16—28no—
382C2×SD16—44no—
383C2×SD16—416no—
384C2×D8—232no—
385C2×D8—28no—
386C2×D8—28no—
387C2×D8—28no—
388C2×D8—28no—
389C2×D8—44no—
390C2×D8—416no—
391C2×D8C2×D4116yescomplemented
392C22×C8—22no—
393C22×C8—22no—
394C22×C8—22no—
395C22×C8—22no—
396C22×C8—22no—
397C22×C8—22no—
398C22×C8—22no—
399C22×C8—22no—
400C22×C8—22no—
401C22×C8—22no—
402C22×C8—22no—
403C22×C8C2×D414yes—
404C22×C8C2412yes—
405C22×C8C2412yes—
406C22×C8C2412yes—
407C22×C8C2412yes—
408#124—216no—
409#124—28no—
410#124C2×D4116yescomplemented
411#123—264no—
412C22⋊Q8—216no—
413C22⋊Q8—28no—
414C22⋊Q8—28no—
415#121—216no—
416#121—264no—
417#121—28no—
418#121—28no—
419#121—28no—
420#121—28no—
421#121—44no—
422#121—44no—
423#121—48no—
424#121—48no—
425#120—264no—
426C4×D4—216no—
427C4×D4—216no—
428C4×D4—28no—
429C4×D4—28no—
430C4×D4—28no—
431C4×D4—28no—
432C4×D4—28no—
433C4×D4—48no—
434C4×D4C2×D4116yescomplemented
435C2×C4⋊C4—28no—
436C2×C4⋊C4—24no—
437C2×C4⋊C4—24no—
438C2×C4⋊C4—21no—
439C2×C4⋊C4—22no—
440C2×C4⋊C4—22no—
441C2×C4⋊C4—22no—
442C2×C4⋊C4—22no—
443C2×C4⋊C4—22no—
444C2×C4⋊C4—22no—
445C2×C4⋊C4—22no—
446C2×C4⋊C4—21no—
447C2×C4⋊C4—21no—
448C2×C4⋊C4—21no—
449C2×C4⋊C4C2×D414yes—
450C2×C4⋊C4C2×D414yes—
451C2×C4⋊C4C2412yes—
452C2×C4⋊C4C2412yes—
453C2×C4⋊C4C2412yes—
454C2×C4⋊C4C2412yes—
455C2×C22⋊C4—28no—
456C2×C22⋊C4—28no—
457C2×C22⋊C4—264no—
458C2×C22⋊C4—24no—
459C2×C22⋊C4—24no—
460C2×C22⋊C4—28no—
461C2×C22⋊C4—28no—
462C2×C22⋊C4—28no—
463C2×C22⋊C4—24no—
464C2×C22⋊C4—24no—
465C2×C22⋊C4—24no—
466C2×C22⋊C4—24no—
467C2×C22⋊C4—24no—
468C2×C22⋊C4—24no—
469C2×C22⋊C4—24no—
470C2×C22⋊C4—24no—
471C2×C22⋊C4—24no—
472C2×C22⋊C4—24no—
473C2×C22⋊C4—44no—
474C2×C22⋊C4—44no—
475C2×C22⋊C4—44no—
476C2×C22⋊C4—82no—
477C2×C22⋊C4—82no—
478C2×C22⋊C4C2×D414yes—
479C2×C22⋊C4C2×D414yes—
480C2×C42C2×D412yes—
481C2×C42C2×D414yes—
482C2×C42C2×D414yes—
483C2×C42C2412yes—
484#107—28no—
485C4⋊C8—28no—
486#103—28no—
487#103—28no—
488#103—44no—
489#102—28no—
490#102—28no—
491#102—28no—
492#102—28no—
493#102—28no—
494#102—28no—
495#102—44no—
496C22⋊C8—28no—
497C22⋊C8—28no—
498C22⋊C8—44no—
499C22⋊C8—44no—
500C4×C8—28no—
501#95—24no—
502#95—24no—
503#95—24no—
504#95—24no—
505C24—22no—
506C24—24no—
507C24—22no—
508C24—24no—
509C24—22no—
510C24—24no—
511C24—22no—
512C24—22no—
513C24—22no—
514C24—22no—
515C24—216no—
516C24—24no—
517C24—22no—
518C24—24no—
519C24—22no—
520C24—22no—
521C24—22no—
522C24—22no—
523C24—22no—
524C24—22no—
525C24—22no—
526C24—22no—
527C24—48no—
528C24—48no—
529C24—432no—
530C24—432no—
531C24—48no—
532C24—42no—
533C24—42no—
534C24—42no—
535C24—42no—
536C24—42no—
537C24—42no—
538C24—42no—
539C24—42no—
540C24—42no—
541C24—48no—
542C24—42no—
543C24—42no—
544C24—42no—
545C24—42no—
546C24—42no—
547C24—42no—
548C24—42no—
549C24—84no—
550C24—84no—
551C24—816no—
552C24—816no—
553C24—816no—
554C24—816no—
555C24—816no—
556C24#13514yes—
557C24C22×D412yes—
558C24C22×D412yes—
559C24C22×D411yescharacteristic
560#41—416no—
561#41—416no—
562#41—464no—
563#41—416no—
564#41—416no—
565C2×Q8—24no—
566C2×Q8—22no—
567C2×Q8—28no—
568C2×Q8—28no—
569C2×Q8—22no—
570C2×Q8—22no—
571C2×Q8—22no—
572C2×Q8—22no—
573C2×Q8—44no—
574C2×Q8—44no—
575C2×Q8—42no—
576C2×Q8—42no—
577C2×Q8C22×D414yes—
578C2×D4—216no—
579C2×D4—216no—
580C2×D4—28no—
581C2×D4—216no—
582C2×D4—24no—
583C2×D4—28no—
584C2×D4—24no—
585C2×D4—28no—
586C2×D4—28no—
587C2×D4—24no—
588C2×D4—28no—
589C2×D4—28no—
590C2×D4—28no—
591C2×D4—24no—
592C2×D4—24no—
593C2×D4—28no—
594C2×D4—28no—
595C2×D4—22no—
596C2×D4—22no—
597C2×D4—22no—
598C2×D4—22no—
599C2×D4—22no—
600C2×D4—22no—
601C2×D4—22no—
602C2×D4—22no—
603C2×D4—22no—
604C2×D4—22no—
605C2×D4—22no—
606C2×D4—22no—
607C2×D4—22no—
608C2×D4—44no—
609C2×D4—416no—
610C2×D4—48no—
611C2×D4—48no—
612C2×D4—416no—
613C2×D4—416no—
614C2×D4—464no—
615C2×D4—416no—
616C2×D4—48no—
617C2×D4—48no—
618C2×D4—432no—
619C2×D4—432no—
620C2×D4—416no—
621C2×D4—48no—
622C2×D4—48no—
623C2×D4—48no—
624C2×D4—48no—
625C2×D4—42no—
626C2×D4—44no—
627C2×D4—44no—
628C2×D4—44no—
629C2×D4—42no—
630C2×D4—42no—
631C2×D4—44no—
632C2×D4—42no—
633C2×D4—84no—
634C2×D4—84no—
635C2×D4—84no—
636C2×D4—84no—
637C2×D4—816no—
638C2×D4—816no—
639C2×D4—816no—
640C2×D4#121116yes—
641C2×D4C22×D414yes—
642C2×D4C22×D414yes—
643C2×D4C22×D414yes—
644C2×D4C22×D414yes—
645C2×D4C2×#4114yes—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—216no—
651C22×C4—24no—
652C22×C4—22no—
653C22×C4—24no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—24no—
662C22×C4—24no—
663C22×C4—24no—
664C22×C4—24no—
665C22×C4—24no—
666C22×C4—24no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—22no—
670C22×C4—22no—
671C22×C4—22no—
672C22×C4—22no—
673C22×C4—22no—
674C22×C4—22no—
675C22×C4—22no—
676C22×C4—22no—
677C22×C4—22no—
678C22×C4—22no—
679C22×C4—216no—
680C22×C4—22no—
681C22×C4—22no—
682C22×C4—22no—
683C22×C4—48no—
684C22×C4—48no—
685C22×C4—432no—
686C22×C4—42no—
687C22×C4—42no—
688C22×C4—42no—
689C22×C4—42no—
690C22×C4—44no—
691C22×C4—44no—
692C22×C4—44no—
693C22×C4—44no—
694C22×C4—44no—
695C22×C4—44no—
696C22×C4—44no—
697C22×C4—44no—
698C22×C4—42no—
699C22×C4—42no—
700C22×C4—42no—
701C22×C4—42no—
702C22×C4—42no—
703C22×C4—42no—
704C22×C4—42no—
705C22×C4—42no—
706C22×C4—42no—
707C22×C4—48no—
708C22×C4—816no—
709C22×C4—84no—
710C22×C4—84no—
711C22×C4—84no—
712C22×C4—84no—
713C22×C4—816no—
714C22×C4#12014yes—
715C22×C4#12014yes—
716C22×C4C22×D412yes—
717C22×C4C22×D412yes—
718C22×C4C22×D412yes—
719C22×C4C22×D412yes—
720C22×C4C22×D411yescharacteristic
721C22×C4C22×D412yes—
722C22×C4C22×D412yes—
723C22×C4C22×D412yes—
724C22×C4C2×#4112yes—
725C22×C4H(5,𝔽2)12yes—
726C22×C4H(5,𝔽2)12yes—
727C22×C4C2511yescharacteristic
728SD16—416no—
729D8—232no—
730D8—416no—
731C2×C8—28no—
732C2×C8—22no—
733C2×C8—22no—
734C2×C8—22no—
735C2×C8—22no—
736C2×C8—22no—
737C2×C8—22no—
738C2×C8—22no—
739C2×C8—22no—
740C2×C8—22no—
741C2×C8—22no—
742C2×C8—22no—
743C2×C8—44no—
744C2×C8—44no—
745C2×C8—44no—
746C2×C8C22×D414yes—
747C4⋊C4—216no—
748C4⋊C4—24no—
749C4⋊C4—28no—
750C4⋊C4—22no—
751C4⋊C4—22no—
752C4⋊C4—22no—
753C4⋊C4—22no—
754C4⋊C4—22no—
755C4⋊C4—22no—
756C4⋊C4—22no—
757C4⋊C4—42no—
758C4⋊C4—42no—
759C4⋊C4—42no—
760C4⋊C4C22×D414yes—
761C22⋊C4—216no—
762C22⋊C4—216no—
763C22⋊C4—28no—
764C22⋊C4—216no—
765C22⋊C4—216no—
766C22⋊C4—216no—
767C22⋊C4—28no—
768C22⋊C4—48no—
769C22⋊C4—48no—
770C22⋊C4—48no—
771C22⋊C4—84no—
772C22⋊C4—84no—
773C42#12018yes—
774C42C22×D414yes—
775C42C22×D414yes—
776C23—22no—
777C23—24no—
778C23—216no—
779C23—22no—
780C23—24no—
781C23—22no—
782C23—24no—
783C23—28no—
784C23—28no—
785C23—28no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—24no—
790C23—22no—
791C23—24no—
792C23—22no—
793C23—22no—
794C23—22no—
795C23—22no—
796C23—22no—
797C23—22no—
798C23—432no—
799C23—432no—
800C23—44no—
801C23—48no—
802C23—48no—
803C23—44no—
804C23—44no—
805C23—48no—
806C23—48no—
807C23—48no—
808C23—42no—
809C23—44no—
810C23—48no—
811C23—42no—
812C23—42no—
813C23—42no—
814C23—42no—
815C23—44no—
816C23—48no—
817C23—48no—
818C23—42no—
819C23—42no—
820C23—42no—
821C23—44no—
822C23—48no—
823C23—44no—
824C23—48no—
825C23—44no—
826C23—48no—
827C23—48no—
828C23—44no—
829C23—44no—
830C23—42no—
831C23—42no—
832C23—44no—
833C23—42no—
834C23—42no—
835C23—42no—
836C23—42no—
837C23—42no—
838C23—42no—
839C23—816no—
840C23—816no—
841C23—816no—
842C23—816no—
843C23—8128no—
844C23—816no—
845C23—84no—
846C23—84no—
847C23—84no—
848C23—84no—
849C23—84no—
850C23—84no—
851C23—84no—
852C23—84no—
853C23C2×#12012yes—
854C23D4212yes—
855C23#54612yes—
856C23C2×#13514yes—
857C23C2×#13512yes—
858C23#57512yes—
859C23#57612yes—
860C23#57612yes—
861C23C23×D411yescharacteristic
862Q8—24no—
863Q8—24no—
864Q8—48no—
865Q8—42no—
866Q8—42no—
867D4—216no—
868D4—24no—
869D4—24no—
870D4—24no—
871D4—24no—
872D4—24no—
873D4—24no—
874D4—24no—
875D4—416no—
876D4—432no—
877D4—432no—
878D4—48no—
879D4—48no—
880D4—42no—
881D4—42no—
882D4—42no—
883D4—42no—
884D4—816no—
885D4—816no—
886D4—816no—
887D4C2×#12118yes—
888C2×C4—28no—
889C2×C4—28no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—24no—
895C2×C4—22no—
896C2×C4—24no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—432no—
903C2×C4—44no—
904C2×C4—44no—
905C2×C4—48no—
906C2×C4—42no—
907C2×C4—42no—
908C2×C4—48no—
909C2×C4—42no—
910C2×C4—42no—
911C2×C4—48no—
912C2×C4—48no—
913C2×C4—42no—
914C2×C4—42no—
915C2×C4—42no—
916C2×C4—42no—
917C2×C4—42no—
918C2×C4—42no—
919C2×C4—42no—
920C2×C4—42no—
921C2×C4—42no—
922C2×C4—42no—
923C2×C4—42no—
924C2×C4—42no—
925C2×C4—42no—
926C2×C4—42no—
927C2×C4—42no—
928C2×C4—42no—
929C2×C4—42no—
930C2×C4—816no—
931C2×C4—816no—
932C2×C4—84no—
933C2×C4—84no—
934C2×C4—84no—
935C2×C4C2×#12014yes—
936C2×C4C2×#12014yes—
937C2×C4C2×#12012yes—
938C2×C4C2×#12114yes—
939C2×C4#53514yes—
940C2×C4D4212yes—
941C2×C4D4214yes—
942C2×C4#54612yes—
943C2×C4#54614yes—
944C2×C4C23×D411yescharacteristic
945C2×C4C23×D411yescharacteristic
946C2×C4C23×D411yescharacteristic
947C2×C4C22×#4111yescharacteristic
948C2×C4C2×H(5,𝔽2)11yescharacteristic
949C2×C4C2×H(5,𝔽2)11yescharacteristic
950C8—24no—
951C8—42no—
952C8—42no—
953C8—42no—
954C22—28no—
955C22—24no—
956C22—24no—
957C22—24no—
958C22—42no—
959C22—44no—
960C22—42no—
961C22—44no—
962C22—416no—
963C22—432no—
964C22—44no—
965C22—44no—
966C22—44no—
967C22—42no—
968C22—42no—
969C22—44no—
970C22—42no—
971C22—44no—
972C22—42no—
973C22—44no—
974C22—44no—
975C22—44no—
976C22—42no—
977C22—42no—
978C22—42no—
979C22—44no—
980C22—42no—
981C22—44no—
982C22—42no—
983C22—864no—
984C22—82no—
985C22—82no—
986C22—88no—
987C22—816no—
988C22—816no—
989C22—82no—
990C22—82no—
991C22—82no—
992C22—82no—
993C22—82no—
994C22—82no—
995C22#240814yes—
996C22#300214yes—
997C22#300814yes—
998C22#327314yes—
999C22#328014yes—
1000C22#329714yes—
1001C22#332214yes—
1002C22C22×#12011yescharacteristic
1003C22C2×D4211yescharacteristic
1004C22C2×#54611yescharacteristic
1005C22C22×#13511yescharacteristic
1006C22C2×#57511yescharacteristic
1007C22C2×#57611yescharacteristic
1008C22C2×#57611yescharacteristic
1009C4—24no—
1010C4—24no—
1011C4—42no—
1012C4—42no—
1013C4—44no—
1014C4—44no—
1015C4—82no—
1016C4—82no—
1017C4—82no—
1018C4#240814yes—
1019C4C22×#12111yescharacteristic
1020C4C2×#53511yescharacteristic
1021C4C2×D4211yescharacteristic
1022C4C2×#54611yescharacteristic
1023C2—44no—
1024C2—48no—
1025C2—82no—
1026C2—84no—
1027C2—84no—
1028C2#2424518yesdirect product factor
1029C2C2×#240811yescharacteristic
1030C2C2×#300211yescharacteristic
1031C2C2×#300811yescharacteristic
1032C2C2×#327311yescharacteristic
1033C2C2×#328011yescharacteristic
1034C2C2×#329711yescharacteristic
1035C2C2×#332211yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C22×C4×D4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C22×#546C2semidirect
2. C22×#463C2semidirect
3. C22×#449C2semidirect
4. C22×#447C2semidirect
5. C22×C4×D8C2semidirect
6. C2×#2535C2semidirect
7. #24245C2direct (N × H)
8. C2×#2036C2semidirect
9. C2×#2033C2semidirect
10. C2×#2000C2semidirect
11. C2×#1999C2semidirect
12. C2×#1958C2semidirect
13. C2×#1954C2semidirect
14. C2×#1804C2semidirect
15. C2×#1788C2semidirect
16. C2×#1786C2semidirect
19. C23×SD16C22semidirect
25. C2×#546C22semidirect
32. C22×#121C22semidirect
36. C22×C4×D4C22semidirect
39. C2×#463C22semidirect
41. C2×#449C22semidirect
43. C2×#447C22semidirect
45. C2×C4×D8C22semidirect
46. C22×#107C22semidirect
47. C22×C4⋊C8C22semidirect
48. C22×#103C22semidirect
49. C22×#103C22semidirect
50. C22×#103C22semidirect
57. C22×#102C22semidirect
60. C22×C22⋊C8C22semidirect
61. C22×C22⋊C8C22semidirect
62. C22×C4×C8C22semidirect
64. #2535C22semidirect
69. C2×#382C22semidirect
71. C2×#380C22semidirect
72. #2036C22semidirect
73. #2033C22semidirect
74. #2000C22semidirect
75. #1999C22semidirect
76. #1958C22semidirect
77. #1954C22semidirect
78. #1804C22semidirect
79. #1788C22semidirect
80. #1786C22semidirect
81. C2×#340C22semidirect
82. C2×#340C22semidirect
118. C22×SD16C23semidirect
124. C22×D8D4semidirect
136. C2×#124D4semidirect
157. C2×#121C23semidirect
168. C2×C4×D4D4semidirect
171. C2×C4×D4C23semidirect
198. C2×#107C23semidirect
200. C2×C4⋊C8C23semidirect
204. C2×#103C23semidirect
205. C2×#103C23semidirect
206. C2×#103C23semidirect
220. C2×#102C23semidirect
227. C2×C22⋊C8C23semidirect
228. C2×C22⋊C8C23semidirect
230. C2×C4×C8C23semidirect
236. #382C23semidirect
240. #380C23semidirect
245. #340C23semidirect
246. #340C23semidirect
391. C2×D8C2×D4semidirect
410. #124C2×D4semidirect
434. C4×D4C2×D4semidirect
1028. C2#24245direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#5462
C22×#4632
C22×#4492
C22×#4472
C22×C4×D82
C2×#25352
#242452
C2×#20362
C2×#20332
C2×#20002
C2×#19992
C2×#19582
C2×#19542
C2×#18042
C2×#17882
C2×#17862