Finite Group Databasebeta

← C2×#24535 #6440474

Subgroups — C2×#24535 #6440474

Order 512.

3150 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#449C211yesmaximal, characteristic
2C22×#416C211yesmaximal, characteristic, complemented
3C2×#2500C211yesmaximal, characteristic, complemented
4C2×#2341C211yesmaximal, characteristic, complemented
5#24535C2116yesmaximal, direct product factor
6C2×#2073C211yesmaximal, characteristic, complemented
7C2×#2071C211yesmaximal, characteristic, complemented
8C2×#2054C211yesmaximal, characteristic, complemented
9C2×#2054C211yesmaximal, characteristic, complemented
10C2×#1893C211yesmaximal, characteristic, complemented
11C2×#1880C211yesmaximal, characteristic, complemented
12C2×#1880C211yesmaximal, characteristic, complemented
13C2×#1850C211yesmaximal, characteristic, complemented
14C2×#1825C211yesmaximal, characteristic, complemented
15C2×#1805C211yesmaximal, characteristic, complemented
16C2×#1803C211yesmaximal, characteristic, complemented
17C23×#41C2211yescharacteristic
18C23×SD16C2211yescharacteristic
19C23×D8C2211yescharacteristic
20C24×C8C2211yescharacteristic
21C22×#121C2211yescharacteristic
22C22×C4×Q8C2211yescharacteristic
23C22×C4×Q8C2211yescharacteristic
24C22×#117C2211yescharacteristic
25C2×#449—28no—
26C2×#449C2218yes—
27C22×C4⋊C8C2211yescharacteristic
28C22×C4⋊C8C2211yescharacteristic
29C2×#416—28no—
30C2×#416C2218yescomplemented
31C22×#103C2211yescharacteristic
32C22×#103C2211yescharacteristic
33C22×#103C2211yescharacteristic
34C22×#102C2211yescharacteristic
35C22×#102C2211yescharacteristic
36C22×#102C2211yescharacteristic
37C22×#102C2211yescharacteristic
38C22×#102C2211yescharacteristic
39C22×C22⋊C8C2211yescharacteristic
40#2500—24no—
41#2500C2218yescomplemented
42C2×#394—21no—
43C2×#394—21no—
44#2341—24no—
45#2341C2218yescomplemented
46C2×#390—21no—
47C2×#390—21no—
48C2×#390C2211yescharacteristic
49C2×#390C2211yescharacteristic
50C2×#390C2211yescharacteristic
51C2×#390C2211yescharacteristic
52C2×#388—21no—
53C2×#388—21no—
54C2×#384C2211yescharacteristic
55C2×#382C2211yescharacteristic
56C2×#380—21no—
57C2×#380C2211yescharacteristic
58C2×C4×C22⋊C4—21no—
59C2×C4×C22⋊C4C2211yescharacteristic
60#2073C2218yescomplemented
61#2071C2218yescomplemented
62#2054C2218yescomplemented
63#2054C2218yescomplemented
64#1893C2218yescomplemented
65#1880C2218yescomplemented
66#1880C2218yescomplemented
67#1850C2218yescomplemented
68#1825C2218yescomplemented
69#1805C2218yescomplemented
70#1803C2218yescomplemented
71C2×#340C2211yescharacteristic
72C2×#340C2211yescharacteristic
73C2×#340C2211yescharacteristic
74C2×#340C2211yescharacteristic
75C2×#340C2211yescharacteristic
76C2×#340C2211yescharacteristic
77C2×#336C2211yescharacteristic
78C2×#336C2211yescharacteristic
79C22×#41—22no—
80C22×#41—24no—
81C22×#41—24no—
82C22×#41—24no—
83C22×#41—42no—
84C22×#41—42no—
85C22×#41D418yes—
86C22×#41C2314yes—
87C23×Q8C2311yescharacteristic
88C23×D4—21no—
89C23×D4—21no—
90C23×D4C2311yescharacteristic
91C23×D4C2311yescharacteristic
92C24×C4—21no—
93C24×C4C2311yescharacteristic
94C22×SD16—24no—
95C22×SD16—24no—
96C22×SD16—24no—
97C22×SD16C2314yes—
98C22×D8—24no—
99C22×D8—42no—
100C22×D8—42no—
101C22×D8C2314yes—
102C23×C8—24no—
103C23×C8—42no—
104C23×C8—42no—
105C23×C8C2311yescharacteristic
106C23×C8C2311yescharacteristic
107C23×C8C2311yescharacteristic
108C23×C8C2311yescharacteristic
109C23×C8C2314yes—
110C2×#121—22no—
111C2×#121—24no—
112C2×#121—24no—
113C2×#121C2314yes—
114C2×C4×Q8—22no—
115C2×C4×Q8—22no—
116C2×C4×Q8—24no—
117C2×C4×Q8—24no—
118C2×C4×Q8—42no—
119C2×C4×Q8—42no—
120C2×C4×Q8C2314yes—
121C2×C4×Q8C2314yes—
122C2×#117—22no—
123C2×#117—24no—
124C2×#117—24no—
125C2×#117C2314yes—
126C22×C4⋊C4—21no—
127C22×C4⋊C4—21no—
128C22×C4⋊C4—21no—
129C22×C4⋊C4—21no—
130C22×C4⋊C4C2311yescharacteristic
131C22×C4⋊C4C2311yescharacteristic
132C22×C4⋊C4C2311yescharacteristic
133C22×C4⋊C4C2311yescharacteristic
134C22×C4⋊C4C2311yescharacteristic
135C22×C22⋊C4—21no—
136C22×C22⋊C4—21no—
137C22×C22⋊C4—21no—
138C22×C22⋊C4—21no—
139C22×C22⋊C4—21no—
140C22×C22⋊C4—21no—
141C22×C22⋊C4—21no—
142C22×C22⋊C4—21no—
143C22×C22⋊C4—21no—
144C22×C22⋊C4—21no—
145C22×C22⋊C4—21no—
146C22×C22⋊C4D411yescharacteristic
147C22×C22⋊C4D411yescharacteristic
148C22×C42—21no—
149C22×C42—21no—
150C22×C42—21no—
151C22×C42C2311yescharacteristic
152C22×C42C2311yescharacteristic
153#449—232no—
154C2×C4⋊C8—42no—
155C2×C4⋊C8—42no—
156C2×C4⋊C8C2314yes—
157C2×C4⋊C8C2314yes—
158#416—232no—
159C2×#103—24no—
160C2×#103—24no—
161C2×#103—24no—
162C2×#103C2314yes—
163C2×#103C2314yes—
164C2×#103C2314yes—
165C2×#102—24no—
166C2×#102—24no—
167C2×#102—24no—
168C2×#102—42no—
169C2×#102—42no—
170C2×#102C2314yes—
171C2×#102C2314yes—
172C2×#102C2314yes—
173C2×#102C2314yes—
174C2×#102C2314yes—
175C2×C22⋊C8—24no—
176C2×C22⋊C8C2314yes—
177#394—28no—
178#394—28no—
179#390—28no—
180#390—28no—
181#390—22no—
182#390—22no—
183#390—22no—
184#390—22no—
185#390C2314yes—
186#390C2314yes—
187#390C2314yes—
188#390C2314yes—
189#388—28no—
190#388—28no—
191#384—22no—
192#384C2314yes—
193#382—22no—
194#382C2314yes—
195#380—22no—
196#380—28no—
197#380C2314yes—
198C4×C22⋊C4—28no—
199C4×C22⋊C4D414yes—
200C4×C22⋊C4C2314yes—
201C2×#95—21no—
202C2×#95—21no—
203C2×#95—21no—
204C2×#95D411yescharacteristic
205C2×#95D411yescharacteristic
206#340C2314yes—
207#340C2314yes—
208#340C2314yes—
209#340C2314yes—
210#340C2314yes—
211#340C2314yes—
212#336C2314yes—
213#336C2314yes—
214C25—21no—
215C25—21no—
216C25C2×D411yescharacteristic
217C2×#41—216no—
218C2×#41—28no—
219C2×#41—232no—
220C2×#41—28no—
221C2×#41—28no—
222C2×#41—416no—
223C2×#41—44no—
224C2×#41—44no—
225C2×#41—48no—
226C2×#41—48no—
227C2×#41—416no—
228C2×#41—416no—
229C2×#41C2×D4116yes—
230C22×Q8—21no—
231C22×Q8—22no—
232C22×Q8—22no—
233C22×Q8—22no—
234C22×Q8C2×D414yes—
235C22×Q8#4114yes—
236C22×Q8#4114yes—
237C22×Q8C2412yes—
238C22×D4—28no—
239C22×D4—24no—
240C22×D4—24no—
241C22×D4—21no—
242C22×D4—22no—
243C22×D4—21no—
244C22×D4—22no—
245C22×D4—22no—
246C22×D4—22no—
247C22×D4—22no—
248C22×D4—22no—
249C22×D4—22no—
250C22×D4—22no—
251C22×D4—22no—
252C22×D4—22no—
253C22×D4—22no—
254C22×D4—44no—
255C22×D4—44no—
256C22×D4—44no—
257C22×D4—82no—
258C22×D4—82no—
259C22×D4C2×D414yes—
260C22×D4C2412yes—
261C22×D4C2412yes—
262C23×C4—21no—
263C23×C4—22no—
264C23×C4—22no—
265C23×C4—22no—
266C23×C4—22no—
267C23×C4—28no—
268C23×C4—24no—
269C23×C4—21no—
270C23×C4—21no—
271C23×C4—21no—
272C23×C4—21no—
273C23×C4—21no—
274C23×C4—44no—
275C23×C4—44no—
276C23×C4C2×D411yescharacteristic
277C23×C4C2×D411yescharacteristic
278C23×C4C2×D411yescharacteristic
279C23×C4C2×D412yes—
280C23×C4C2×D411yescharacteristic
281C23×C4C2×D414yes—
282C23×C4C2×D411yescharacteristic
283C23×C4#4114yes—
284C23×C4C2412yes—
285C23×C4C2411yescharacteristic
286C2×SD16—28no—
287C2×SD16—28no—
288C2×SD16—28no—
289C2×SD16—416no—
290C2×D8—28no—
291C2×D8—44no—
292C2×D8—44no—
293C2×D8—416no—
294C22×C8—22no—
295C22×C8—22no—
296C22×C8—28no—
297C22×C8—22no—
298C22×C8—22no—
299C22×C8—22no—
300C22×C8—22no—
301C22×C8—22no—
302C22×C8—22no—
303C22×C8—22no—
304C22×C8—22no—
305C22×C8—22no—
306C22×C8—22no—
307C22×C8—44no—
308C22×C8—44no—
309C22×C8—416no—
310C22×C8C2412yes—
311C22×C8C2412yes—
312C22×C8C2412yes—
313C22×C8C2412yes—
314#121—28no—
315#121—28no—
316#121—48no—
317C4×Q8—28no—
318C4×Q8—28no—
319C4×Q8—44no—
320C4×Q8—44no—
321C4×Q8—48no—
322C4×Q8—48no—
323#117—28no—
324#117—28no—
325#117—48no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—22no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—24no—
337C2×C4⋊C4—24no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—24no—
344C2×C4⋊C4—24no—
345C2×C4⋊C4—44no—
346C2×C4⋊C4—44no—
347C2×C4⋊C4—82no—
348C2×C4⋊C4—82no—
349C2×C4⋊C4C2412yes—
350C2×C4⋊C4C2412yes—
351C2×C4⋊C4C2412yes—
352C2×C4⋊C4C2412yes—
353C2×C4⋊C4C2412yes—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—24no—
360C2×C22⋊C4—24no—
361C2×C22⋊C4—24no—
362C2×C22⋊C4—24no—
363C2×C22⋊C4—24no—
364C2×C22⋊C4—24no—
365C2×C22⋊C4—24no—
366C2×C22⋊C4—42no—
367C2×C22⋊C4—44no—
368C2×C22⋊C4—44no—
369C2×C22⋊C4—44no—
370C2×C22⋊C4—44no—
371C2×C22⋊C4—44no—
372C2×C22⋊C4—44no—
373C2×C22⋊C4—82no—
374C2×C22⋊C4—82no—
375C2×C22⋊C4—82no—
376C2×C22⋊C4—82no—
377C2×C22⋊C4—82no—
378C2×C22⋊C4C2×D414yes—
379C2×C22⋊C4C2×D414yes—
380C2×C42—22no—
381C2×C42—22no—
382C2×C42—22no—
383C2×C42—22no—
384C2×C42—24no—
385C2×C42—24no—
386C2×C42—24no—
387C2×C42—44no—
388C2×C42—44no—
389C2×C42—44no—
390C2×C42C2×D412yes—
391C2×C42C2×D412yes—
392C2×C42C2412yes—
393C2×C42C2412yes—
394C4⋊C8—44no—
395C4⋊C8—44no—
396#103—28no—
397#103—28no—
398#103—28no—
399#102—28no—
400#102—28no—
401#102—28no—
402#102—44no—
403#102—44no—
404C22⋊C8—28no—
405#95—24no—
406#95—24no—
407#95—24no—
408#95C2×D414yes—
409#95C2×D414yes—
410C24—22no—
411C24—22no—
412C24—22no—
413C24—22no—
414C24—22no—
415C24—22no—
416C24—24no—
417C24—22no—
418C24—22no—
419C24—42no—
420C24—42no—
421C24—42no—
422C24—42no—
423C24—42no—
424C24—42no—
425C24—42no—
426C24—42no—
427C24—42no—
428C24—42no—
429C24—42no—
430C24—42no—
431C24—42no—
432C24#12114yes—
433C24C22×D412yes—
434C24C22×D411yescharacteristic
435#41—232no—
436#41—416no—
437#41—464no—
438#41—416no—
439#41—416no—
440C2×Q8—24no—
441C2×Q8—28no—
442C2×Q8—24no—
443C2×Q8—24no—
444C2×Q8—28no—
445C2×Q8—28no—
446C2×Q8—22no—
447C2×Q8—22no—
448C2×Q8—22no—
449C2×Q8#123116yes—
450C2×Q8C22×D414yes—
451C2×Q8C2×#4114yes—
452C2×Q8C2×#4114yes—
453C2×D4—216no—
454C2×D4—24no—
455C2×D4—28no—
456C2×D4—28no—
457C2×D4—22no—
458C2×D4—22no—
459C2×D4—22no—
460C2×D4—22no—
461C2×D4—22no—
462C2×D4—22no—
463C2×D4—22no—
464C2×D4—22no—
465C2×D4—22no—
466C2×D4—22no—
467C2×D4—22no—
468C2×D4—432no—
469C2×D4—48no—
470C2×D4—48no—
471C2×D4—48no—
472C2×D4—42no—
473C2×D4—44no—
474C2×D4—44no—
475C2×D4—42no—
476C2×D4—42no—
477C2×D4—42no—
478C2×D4—42no—
479C2×D4—44no—
480C2×D4—44no—
481C2×D4—44no—
482C2×D4—44no—
483C2×D4—84no—
484C2×D4—84no—
485C2×D4—816no—
486C2×D4C22×D414yes—
487C22×C4—24no—
488C22×C4—22no—
489C22×C4—24no—
490C22×C4—24no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—28no—
496C22×C4—28no—
497C22×C4—24no—
498C22×C4—24no—
499C22×C4—28no—
500C22×C4—28no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—216no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—432no—
521C22×C4—48no—
522C22×C4—48no—
523C22×C4—42no—
524C22×C4—42no—
525C22×C4—42no—
526C22×C4—42no—
527C22×C4—42no—
528C22×C4—42no—
529C22×C4—42no—
530C22×C4—42no—
531C22×C4—42no—
532C22×C4—42no—
533C22×C4—42no—
534C22×C4—42no—
535C22×C4—42no—
536C22×C4—42no—
537C22×C4—42no—
538C22×C4#12114yes—
539C22×C4#12118yes—
540C22×C4#13514yes—
541C22×C4C22×D412yes—
542C22×C4C22×D412yes—
543C22×C4C22×D412yes—
544C22×C4C22×D412yes—
545C22×C4C22×D414yes—
546C22×C4C22×D412yes—
547C22×C4C22×D411yescharacteristic
548C22×C4C22×D412yes—
549C22×C4C2×#4114yes—
550C22×C4C2×#4112yes—
551C22×C4C2×#4112yes—
552C22×C4C2×#4112yes—
553C22×C4H(5,𝔽2)12yes—
554C22×C4H(5,𝔽2)12yes—
555C22×C4C2511yescharacteristic
556SD16—416no—
557D8—416no—
558C2×C8—22no—
559C2×C8—22no—
560C2×C8—22no—
561C2×C8—22no—
562C2×C8—22no—
563C2×C8—22no—
564C2×C8—22no—
565C2×C8—22no—
566C2×C8—22no—
567C2×C8—22no—
568C2×C8—22no—
569C2×C8—22no—
570C2×C8—416no—
571C2×C8—44no—
572C2×C8—44no—
573C2×C8—44no—
574C2×C8—44no—
575C4⋊C4—22no—
576C4⋊C4—22no—
577C4⋊C4—22no—
578C4⋊C4—22no—
579C4⋊C4—22no—
580C4⋊C4—22no—
581C4⋊C4—22no—
582C4⋊C4—22no—
583C4⋊C4—22no—
584C4⋊C4—22no—
585C4⋊C4—48no—
586C4⋊C4—48no—
587C4⋊C4—42no—
588C4⋊C4—42no—
589C4⋊C4—42no—
590C4⋊C4—42no—
591C4⋊C4—42no—
592C4⋊C4—84no—
593C4⋊C4—84no—
594C22⋊C4—28no—
595C22⋊C4—44no—
596C22⋊C4—48no—
597C22⋊C4—48no—
598C22⋊C4—48no—
599C22⋊C4—48no—
600C22⋊C4—48no—
601C22⋊C4—48no—
602C22⋊C4—84no—
603C22⋊C4—84no—
604C22⋊C4—84no—
605C22⋊C4—84no—
606C22⋊C4—84no—
607C42—24no—
608C42—24no—
609C42—22no—
610C42—22no—
611C42—22no—
612C42—22no—
613C42—48no—
614C42—48no—
615C42—48no—
616C23—28no—
617C23—22no—
618C23—22no—
619C23—28no—
620C23—28no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—24no—
626C23—44no—
627C23—44no—
628C23—44no—
629C23—44no—
630C23—48no—
631C23—42no—
632C23—42no—
633C23—48no—
634C23—48no—
635C23—42no—
636C23—42no—
637C23—42no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—84no—
647C23—84no—
648C23—84no—
649C23—84no—
650C23—84no—
651C23—84no—
652C23—84no—
653C23—84no—
654C23—84no—
655C23—84no—
656C23—84no—
657C23C2×#12114yes—
658C23C2×#12112yes—
659C23#54612yes—
660C23#54612yes—
661C23C2×#13512yes—
662C23#57512yes—
663C23#57612yes—
664C23#57712yes—
665C23C23×D411yescharacteristic
666Q8—216no—
667Q8—24no—
668Q8—24no—
669Q8—24no—
670Q8C2×#12318yes—
671D4—24no—
672D4—24no—
673D4—432no—
674D4—42no—
675D4—48no—
676D4—42no—
677D4—42no—
678D4—42no—
679D4—42no—
680D4—42no—
681D4—816no—
682D4—84no—
683C2×C4—24no—
684C2×C4—28no—
685C2×C4—216no—
686C2×C4—22no—
687C2×C4—24no—
688C2×C4—24no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—28no—
692C2×C4—22no—
693C2×C4—24no—
694C2×C4—216no—
695C2×C4—24no—
696C2×C4—24no—
697C2×C4—24no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—432no—
708C2×C4—44no—
709C2×C4—44no—
710C2×C4—44no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—84no—
727C2×C4—84no—
728C2×C4—84no—
729C2×C4—84no—
730C2×C4—84no—
731C2×C4C2×#12114yes—
732C2×C4C2×#12112yes—
733C2×C4C2×#12314yes—
734C2×C4#53414yes—
735C2×C4#54612yes—
736C2×C4#54612yes—
737C2×C4#55114yes—
738C2×C4#55114yes—
739C2×C4C2×#13514yes—
740C2×C4C23×D411yescharacteristic
741C2×C4C22×#4111yescharacteristic
742C2×C4C22×#4111yescharacteristic
743C2×C4C22×#4111yescharacteristic
744C2×C4C2×H(5,𝔽2)11yescharacteristic
745C2×C4C2×H(5,𝔽2)11yescharacteristic
746C8—42no—
747C8—42no—
748C8—42no—
749C8—42no—
750C22—24no—
751C22—24no—
752C22—24no—
753C22—42no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—416no—
758C22—44no—
759C22—44no—
760C22—44no—
761C22—82no—
762C22—82no—
763C22—82no—
764C22—82no—
765C22—816no—
766C22—82no—
767C22—82no—
768C22—82no—
769C22—82no—
770C22—82no—
771C22—82no—
772C22—82no—
773C22—168no—
774C22#241214yes—
775C22#303514yes—
776C22#304514yes—
777C22#330114yes—
778C22#330514yes—
779C22#330914yes—
780C22#332114yes—
781C22C22×#12111yescharacteristic
782C22C2×#54611yescharacteristic
783C22C2×#54611yescharacteristic
784C22C22×#13511yescharacteristic
785C22C2×#57511yescharacteristic
786C22C2×#57611yescharacteristic
787C22C2×#57711yescharacteristic
788C4—24no—
789C4—28no—
790C4—24no—
791C4—42no—
792C4—42no—
793C4—42no—
794C4—82no—
795C4—82no—
796C4—82no—
797C4—82no—
798C4—82no—
799C4#241214yes—
800C4C22×#12311yescharacteristic
801C4C2×#53411yescharacteristic
802C4C2×#55111yescharacteristic
803C4C2×#55111yescharacteristic
804C2—44no—
805C2—84no—
806C2—162no—
807C2#2453518yesdirect product factor
808C2C2×#241211yescharacteristic
809C2C2×#303511yescharacteristic
810C2C2×#304511yescharacteristic
811C2C2×#330111yescharacteristic
812C2C2×#330511yescharacteristic
813C2C2×#330911yescharacteristic
814C2C2×#332111yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×#449C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C22×#416C2semidirect
3. C2×#2500C2semidirect
4. C2×#2341C2semidirect
5. #24535C2direct (N × H)
6. C2×#2073C2semidirect
7. C2×#2071C2semidirect
8. C2×#2054C2semidirect
9. C2×#2054C2semidirect
10. C2×#1893C2semidirect
11. C2×#1880C2semidirect
12. C2×#1880C2semidirect
13. C2×#1850C2semidirect
14. C2×#1825C2semidirect
15. C2×#1805C2semidirect
16. C2×#1803C2semidirect
30. C2×#416C22semidirect
41. #2500C22semidirect
45. #2341C22semidirect
60. #2073C22semidirect
61. #2071C22semidirect
62. #2054C22semidirect
63. #2054C22semidirect
64. #1893C22semidirect
65. #1880C22semidirect
66. #1880C22semidirect
67. #1850C22semidirect
68. #1825C22semidirect
69. #1805C22semidirect
70. #1803C22semidirect
807. C2#24535direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#4492
C22×#4162
C2×#25002
C2×#23412
#245352
C2×#20732
C2×#20712
C2×#20542
C2×#18932
C2×#18802
C2×#18502
C2×#18252
C2×#18052
C2×#18032