Finite Group Databasebeta

← C2×#28096 #6459328

Subgroups — C2×#28096 #6459328

Order 512.

3166 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C8×D4C211yesmaximal, characteristic, complemented
2C22×#416C211yesmaximal, characteristic, complemented
3C2×#2485C211yesmaximal, characteristic, complemented
4C2×#2407C211yesmaximal, characteristic
5#28096C2116yesmaximal, direct product factor
6C2×#2068C211yesmaximal, characteristic, complemented
7C2×#2067C211yesmaximal, characteristic, complemented
8C2×#2036C211yesmaximal, characteristic, complemented
9C2×#2033C211yesmaximal, characteristic, complemented
10C2×#1934C211yesmaximal, characteristic, complemented
11C2×#1933C211yesmaximal, characteristic, complemented
12C2×#1893C211yesmaximal, characteristic, complemented
13C2×#1892C211yesmaximal, characteristic, complemented
14C2×#1825C211yesmaximal, characteristic, complemented
15C2×#1808C211yesmaximal, characteristic, complemented
16C2×#1788C211yesmaximal, characteristic, complemented
17C23×#41C2211yescharacteristic
18C24×C8C2211yescharacteristic
19C24×C8C2211yescharacteristic
20C22×C22⋊Q8C2211yescharacteristic
21C22×#121C2211yescharacteristic
22C22×C4×D4C2211yescharacteristic
23C22×#117C2211yescharacteristic
24C2×C8×D4—28no—
25C2×C8×D4C2218yescomplemented
26C22×#107C2211yescharacteristic
27C22×#107C2211yescharacteristic
28C22×C4⋊C8C2211yescharacteristic
29C2×#416—28no—
30C2×#416C2218yescomplemented
31C22×#103C2211yescharacteristic
32C22×#103C2211yescharacteristic
33C22×#103C2211yescharacteristic
34C22×#103C2211yescharacteristic
35C22×#102C2211yescharacteristic
36C22×#102C2211yescharacteristic
37C22×#102C2211yescharacteristic
38C22×#102C2211yescharacteristic
39C22×C22⋊C8C2211yescharacteristic
40C22×C22⋊C8C2211yescharacteristic
41C22×C4×C8C2211yescharacteristic
42#2485—24no—
43#2485C2218yescomplemented
44#2407—24no—
45#2407C2218yes—
46C2×#397—21no—
47C2×#394—21no—
48C2×#394—21no—
49C2×#392—21no—
50C2×#391C2211yescharacteristic
51C2×#390C2211yescharacteristic
52C2×#389C2211yescharacteristic
53C2×#389C2211yescharacteristic
54C2×#388—21no—
55C2×#387—21no—
56C2×#386—21no—
57C2×#385—21no—
58C2×#380C2211yescharacteristic
59C2×#380C2211yescharacteristic
60C2×#380C2211yescharacteristic
61C2×#380C2211yescharacteristic
62#2068C2218yescomplemented
63#2067C2218yescomplemented
64#2036C2218yescomplemented
65#2033C2218yescomplemented
66#1934C2218yescomplemented
67#1933C2218yescomplemented
68#1893C2218yescomplemented
69#1892C2218yescomplemented
70#1825C2218yescomplemented
71#1808C2218yescomplemented
72#1788C2218yescomplemented
73C2×#340C2211yescharacteristic
74C2×#340C2211yescharacteristic
75C2×#340C2211yescharacteristic
76C2×#340C2211yescharacteristic
77C2×#340C2211yescharacteristic
78C2×#340C2211yescharacteristic
79C22×#41—22no—
80C22×#41—24no—
81C22×#41—24no—
82C22×#41—24no—
83C22×#41—24no—
84C22×#41—42no—
85C22×#41—42no—
86C22×#41C2314yes—
87C23×Q8C2311yescharacteristic
88C23×D4—21no—
89C23×D4—21no—
90C23×D4D411yescharacteristic
91C23×D4C2311yescharacteristic
92C24×C4—21no—
93C24×C4C2311yescharacteristic
94C24×C4C2311yescharacteristic
95C23×C8—24no—
96C23×C8—42no—
97C23×C8—42no—
98C23×C8—42no—
99C23×C8—42no—
100C23×C8D418yescomplemented
101C23×C8C2311yescharacteristic
102C23×C8C2311yescharacteristic
103C23×C8C2311yescharacteristic
104C23×C8C2311yescharacteristic
105C23×C8C2314yes—
106C23×C8C2314yes—
107C2×C22⋊Q8—22no—
108C2×C22⋊Q8—24no—
109C2×C22⋊Q8—42no—
110C2×C22⋊Q8C2314yes—
111C2×#121—22no—
112C2×#121—24no—
113C2×#121—42no—
114C2×#121C2314yes—
115C2×C4×D4—24no—
116C2×C4×D4—24no—
117C2×C4×D4D414yes—
118C2×C4×D4C2314yes—
119C2×#117—22no—
120C2×#117—24no—
121C2×#117—24no—
122C2×#117C2314yes—
123C22×C4⋊C4—21no—
124C22×C4⋊C4—21no—
125C22×C4⋊C4—21no—
126C22×C4⋊C4D411yescharacteristic
127C22×C4⋊C4C2311yescharacteristic
128C22×C4⋊C4C2311yescharacteristic
129C22×C4⋊C4C2311yescharacteristic
130C22×C4⋊C4C2311yescharacteristic
131C22×C4⋊C4C2311yescharacteristic
132C22×C4⋊C4C2311yescharacteristic
133C22×C22⋊C4—21no—
134C22×C22⋊C4—21no—
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⋊C4D411yescharacteristic
143C22×C22⋊C4D411yescharacteristic
144C22×C42—21no—
145C22×C42C2311yescharacteristic
146C8×D4—232no—
147C2×#107—42no—
148C2×#107—42no—
149C2×#107C2314yes—
150C2×#107C2314yes—
151C2×C4⋊C8—24no—
152C2×C4⋊C8C2314yes—
153#416—232no—
154C2×#103—24no—
155C2×#103—24no—
156C2×#103—24no—
157C2×#103—42no—
158C2×#103C2314yes—
159C2×#103C2314yes—
160C2×#103C2314yes—
161C2×#103C2314yes—
162C2×#102—24no—
163C2×#102—24no—
164C2×#102—24no—
165C2×#102—42no—
166C2×#102C2314yes—
167C2×#102C2314yes—
168C2×#102C2314yes—
169C2×#102C2314yes—
170C2×C22⋊C8—24no—
171C2×C22⋊C8—24no—
172C2×C22⋊C8C2314yes—
173C2×C22⋊C8C2314yes—
174C2×C4×C8—24no—
175C2×C4×C8C2314yes—
176#397—28no—
177#394—28no—
178#394—28no—
179#392—28no—
180#391—22no—
181#391C2314yes—
182#390—22no—
183#390C2314yes—
184#389—22no—
185#389—22no—
186#389C2314yes—
187#389C2314yes—
188#388—28no—
189#387—28no—
190#386—28no—
191#385—28no—
192#380—22no—
193#380—22no—
194#380—22no—
195#380—22no—
196#380C2314yes—
197#380C2314yes—
198#380C2314yes—
199#380C2314yes—
200C2×#95—21no—
201C2×#95—21no—
202C2×#95—21no—
203C2×#95—21no—
204C2×#95—21no—
205C2×#95—21no—
206C2×#95—21no—
207C2×#95—21no—
208#340C2314yes—
209#340C2314yes—
210#340C2314yes—
211#340C2314yes—
212#340C2314yes—
213#340C2314yes—
214C25—21no—
215C25C2×D411yescharacteristic
216C25C2×D411yescharacteristic
217C2×#41—232no—
218C2×#41—28no—
219C2×#41—28no—
220C2×#41—28no—
221C2×#41—28no—
222C2×#41—44no—
223C2×#41—44no—
224C2×#41—48no—
225C2×#41—416no—
226C2×#41—48no—
227C2×#41—416no—
228C2×#41—416no—
229C2×#41—48no—
230C22×Q8—21no—
231C22×Q8—22no—
232C22×Q8—22no—
233C22×Q8—22no—
234C22×Q8—22no—
235C22×Q8—22no—
236C22×Q8#4114yes—
237C22×Q8C2412yes—
238C22×D4—24no—
239C22×D4—24no—
240C22×D4—24no—
241C22×D4—24no—
242C22×D4—24no—
243C22×D4—22no—
244C22×D4—21no—
245C22×D4—22no—
246C22×D4—22no—
247C22×D4—22no—
248C22×D4—22no—
249C22×D4—44no—
250C22×D4—44no—
251C22×D4—44no—
252C22×D4—44no—
253C22×D4—44no—
254C22×D4—82no—
255C22×D4C2×D414yes—
256C22×D4#4114yes—
257C22×D4C2412yes—
258C23×C4—22no—
259C23×C4—22no—
260C23×C4—22no—
261C23×C4—22no—
262C23×C4—21no—
263C23×C4—22no—
264C23×C4—22no—
265C23×C4—22no—
266C23×C4—22no—
267C23×C4—22no—
268C23×C4—22no—
269C23×C4—21no—
270C23×C4—21no—
271C23×C4—21no—
272C23×C4—21no—
273C23×C4—21no—
274C23×C4—21no—
275C23×C4—24no—
276C23×C4—44no—
277C23×C4—44no—
278C23×C4—44no—
279C23×C4C2×D412yes—
280C23×C4C2×D411yescharacteristic
281C23×C4C2×D411yescharacteristic
282C23×C4C2×D412yes—
283C23×C4C2×D411yescharacteristic
284C23×C4C2×D414yes—
285C23×C4C2×D411yescharacteristic
286C23×C4#4114yes—
287C23×C4C2412yes—
288C23×C4C2412yes—
289C23×C4C2411yescharacteristic
290C22×C8—22no—
291C22×C8—22no—
292C22×C8—22no—
293C22×C8—22no—
294C22×C8—22no—
295C22×C8—22no—
296C22×C8—22no—
297C22×C8—22no—
298C22×C8—22no—
299C22×C8—22no—
300C22×C8—28no—
301C22×C8—416no—
302C22×C8—44no—
303C22×C8—44no—
304C22×C8—44no—
305C22×C8—44no—
306C22×C8—416no—
307C22×C8C2×D414yes—
308C22×C8C2×D414yes—
309C22×C8C2×D4116yescomplemented
310C22×C8C2412yes—
311C22×C8C2412yes—
312C22×C8C2412yes—
313C22×C8C2412yes—
314C22⋊Q8—28no—
315C22⋊Q8—44no—
316C22⋊Q8—48no—
317#121—28no—
318#121—44no—
319#121—48no—
320C4×D4—216no—
321C4×D4—28no—
322C4×D4—28no—
323#117—28no—
324#117—28no—
325#117—48no—
326C2×C4⋊C4—24no—
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—22no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—24no—
340C2×C4⋊C4—24no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—24no—
348C2×C4⋊C4—44no—
349C2×C4⋊C4—44no—
350C2×C4⋊C4—82no—
351C2×C4⋊C4C2×D414yes—
352C2×C4⋊C4C2412yes—
353C2×C4⋊C4C2412yes—
354C2×C4⋊C4C2412yes—
355C2×C4⋊C4C2412yes—
356C2×C4⋊C4C2412yes—
357C2×C4⋊C4C2412yes—
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—24no—
367C2×C22⋊C4—24no—
368C2×C22⋊C4—24no—
369C2×C22⋊C4—44no—
370C2×C22⋊C4—44no—
371C2×C22⋊C4—44no—
372C2×C22⋊C4—44no—
373C2×C22⋊C4—44no—
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—24no—
383C2×C42—44no—
384C2×C42C2×D412yes—
385C2×C42C2412yes—
386#107—44no—
387#107—44no—
388C4⋊C8—28no—
389#103—28no—
390#103—28no—
391#103—28no—
392#103—44no—
393#102—28no—
394#102—28no—
395#102—28no—
396#102—44no—
397C22⋊C8—28no—
398C22⋊C8—28no—
399C4×C8—28no—
400#95—24no—
401#95—24no—
402#95—24no—
403#95—24no—
404#95—24no—
405#95—24no—
406#95—24no—
407#95—24no—
408C24—22no—
409C24—22no—
410C24—22no—
411C24—22no—
412C24—22no—
413C24—22no—
414C24—22no—
415C24—22no—
416C24—22no—
417C24—22no—
418C24—22no—
419C24—22no—
420C24—24no—
421C24—22no—
422C24—42no—
423C24—42no—
424C24—42no—
425C24—42no—
426C24—42no—
427C24—42no—
428C24#12114yes—
429C24#13514yes—
430C24C22×D412yes—
431C24C22×D412yes—
432C24C22×D411yescharacteristic
433#41—232no—
434#41—416no—
435#41—416no—
436#41—416no—
437#41—464no—
438C2×Q8—24no—
439C2×Q8—22no—
440C2×Q8—28no—
441C2×Q8—28no—
442C2×Q8—22no—
443C2×Q8—22no—
444C2×Q8—22no—
445C2×Q8—22no—
446C2×Q8—42no—
447C2×Q8—44no—
448C2×Q8—42no—
449C2×Q8—44no—
450C2×Q8C2×#4114yes—
451C2×D4—232no—
452C2×D4—28no—
453C2×D4—28no—
454C2×D4—28no—
455C2×D4—24no—
456C2×D4—28no—
457C2×D4—28no—
458C2×D4—22no—
459C2×D4—22no—
460C2×D4—22no—
461C2×D4—22no—
462C2×D4—22no—
463C2×D4—48no—
464C2×D4—48no—
465C2×D4—432no—
466C2×D4—48no—
467C2×D4—48no—
468C2×D4—48no—
469C2×D4—42no—
470C2×D4—44no—
471C2×D4—42no—
472C2×D4—44no—
473C2×D4—84no—
474C2×D4—816no—
475C2×D4C2×#4114yes—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—28no—
481C22×C4—28no—
482C22×C4—24no—
483C22×C4—24no—
484C22×C4—28no—
485C22×C4—28no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—24no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—24no—
499C22×C4—24no—
500C22×C4—24no—
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—48no—
514C22×C4—48no—
515C22×C4—432no—
516C22×C4—42no—
517C22×C4—42no—
518C22×C4—48no—
519C22×C4—44no—
520C22×C4—44no—
521C22×C4—44no—
522C22×C4—44no—
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—42no—
539C22×C4—42no—
540C22×C4—42no—
541C22×C4#12114yes—
542C22×C4#12118yes—
543C22×C4#13514yes—
544C22×C4C22×D412yes—
545C22×C4C22×D412yes—
546C22×C4C22×D412yes—
547C22×C4C22×D414yes—
548C22×C4C22×D412yes—
549C22×C4C22×D411yescharacteristic
550C22×C4C22×D412yes—
551C22×C4C2×#4114yes—
552C22×C4C2×#4112yes—
553C22×C4C2×#4112yes—
554C22×C4C2×#4112yes—
555C22×C4H(5,𝔽2)12yes—
556C22×C4H(5,𝔽2)12yes—
557C22×C4C2511yescharacteristic
558C2×C8—28no—
559C2×C8—28no—
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—416no—
572C2×C8—44no—
573C2×C8—44no—
574C2×C8C22×D414yes—
575C2×C8C22×D414yes—
576C4⋊C4—28no—
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—22no—
586C4⋊C4—22no—
587C4⋊C4—22no—
588C4⋊C4—22no—
589C4⋊C4—48no—
590C4⋊C4—42no—
591C4⋊C4—42no—
592C4⋊C4—42no—
593C4⋊C4—42no—
594C4⋊C4—42no—
595C4⋊C4—42no—
596C4⋊C4—48no—
597C4⋊C4—84no—
598C22⋊C4—28no—
599C22⋊C4—28no—
600C22⋊C4—48no—
601C22⋊C4—48no—
602C22⋊C4—48no—
603C22⋊C4—48no—
604C22⋊C4—48no—
605C22⋊C4—84no—
606C22⋊C4—84no—
607C22⋊C4—84no—
608C22⋊C4—84no—
609C42—24no—
610C42—22no—
611C42—22no—
612C42—48no—
613C23—22no—
614C23—22no—
615C23—22no—
616C23—22no—
617C23—22no—
618C23—28no—
619C23—28no—
620C23—28no—
621C23—28no—
622C23—28no—
623C23—28no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—24no—
632C23—44no—
633C23—44no—
634C23—44no—
635C23—44no—
636C23—44no—
637C23—44no—
638C23—44no—
639C23—44no—
640C23—42no—
641C23—42no—
642C23—48no—
643C23—48no—
644C23—48no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—84no—
650C23—84no—
651C23—84no—
652C23—84no—
653C23C2×#12114yes—
654C23C2×#12112yes—
655C23#54612yes—
656C23#54612yes—
657C23C2×#13514yes—
658C23C2×#13512yes—
659C23C2×#13512yes—
660C23#57612yes—
661C23#57812yes—
662C23C23×D411yescharacteristic
663Q8—24no—
664Q8—24no—
665Q8—42no—
666Q8—42no—
667Q8—48no—
668D4—232no—
669D4—24no—
670D4—24no—
671D4—432no—
672D4—42no—
673D4—42no—
674D4—48no—
675D4—816no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—28no—
680C2×C4—28no—
681C2×C4—22no—
682C2×C4—24no—
683C2×C4—24no—
684C2×C4—24no—
685C2×C4—24no—
686C2×C4—216no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—24no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—432no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—44no—
698C2×C4—48no—
699C2×C4—44no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—48no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
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—84no—
724C2×C4—84no—
725C2×C4—84no—
726C2×C4—84no—
727C2×C4—84no—
728C2×C4—84no—
729C2×C4C2×#12114yes—
730C2×C4C2×#12112yes—
731C2×C4#52514yes—
732C2×C4#53414yes—
733C2×C4#54612yes—
734C2×C4#54612yes—
735C2×C4#55114yes—
736C2×C4#55114yes—
737C2×C4C2×#13514yes—
738C2×C4C23×D411yescharacteristic
739C2×C4C22×#4111yescharacteristic
740C2×C4C22×#4111yescharacteristic
741C2×C4C22×#4111yescharacteristic
742C2×C4C2×H(5,𝔽2)11yescharacteristic
743C2×C4C2×H(5,𝔽2)11yescharacteristic
744C8—24no—
745C8—24no—
746C8—42no—
747C8—42no—
748C22—24no—
749C22—24no—
750C22—24no—
751C22—24no—
752C22—24no—
753C22—24no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—42no—
758C22—416no—
759C22—416no—
760C22—42no—
761C22—42no—
762C22—42no—
763C22—42no—
764C22—44no—
765C22—44no—
766C22—44no—
767C22—82no—
768C22—82no—
769C22—82no—
770C22—816no—
771C22—82no—
772C22#253414yes—
773C22#305014yes—
774C22#306114yes—
775C22#329714yes—
776C22#330014yes—
777C22#330214yes—
778C22#330514yes—
779C22C22×#12111yescharacteristic
780C22C2×#54611yescharacteristic
781C22C2×#54611yescharacteristic
782C22C22×#13511yescharacteristic
783C22C22×#13511yescharacteristic
784C22C2×#57611yescharacteristic
785C22C2×#57811yescharacteristic
786C4—24no—
787C4—24no—
788C4—42no—
789C4—44no—
790C4—42no—
791C4—82no—
792C4—82no—
793C4—82no—
794C4—82no—
795C4—82no—
796C4—82no—
797C4#253414yes—
798C4C2×#52511yescharacteristic
799C4C2×#53411yescharacteristic
800C4C2×#55111yescharacteristic
801C4C2×#55111yescharacteristic
802C2—44no—
803C2—44no—
804C2—84no—
805C2#2809618yesdirect product factor
806C2C2×#253411yescharacteristic
807C2C2×#305011yescharacteristic
808C2C2×#306111yescharacteristic
809C2C2×#329711yescharacteristic
810C2C2×#330011yescharacteristic
811C2C2×#330211yescharacteristic
812C2C2×#330511yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#2407C2
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×C8×D4C2semidirect
2. C22×#416C2semidirect
3. C2×#2485C2semidirect
5. #28096C2direct (N × H)
6. C2×#2068C2semidirect
7. C2×#2067C2semidirect
8. C2×#2036C2semidirect
9. C2×#2033C2semidirect
10. C2×#1934C2semidirect
11. C2×#1933C2semidirect
12. C2×#1893C2semidirect
13. C2×#1892C2semidirect
14. C2×#1825C2semidirect
15. C2×#1808C2semidirect
16. C2×#1788C2semidirect
25. C2×C8×D4C22semidirect
30. C2×#416C22semidirect
43. #2485C22semidirect
62. #2068C22semidirect
63. #2067C22semidirect
64. #2036C22semidirect
65. #2033C22semidirect
66. #1934C22semidirect
67. #1933C22semidirect
68. #1893C22semidirect
69. #1892C22semidirect
70. #1825C22semidirect
71. #1808C22semidirect
72. #1788C22semidirect
100. C23×C8D4semidirect
309. C22×C8C2×D4semidirect
805. C2#28096direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C8×D42
C22×#4162
C2×#24852
C2×#24072
#280962
C2×#20682
C2×#20672
C2×#20362
C2×#20332
C2×#19342
C2×#19332
C2×#18932
C2×#18922
C2×#18252
C2×#18082
C2×#17882