Finite Group Databasebeta

← C2×#24777 #6442877

Subgroups — C2×#24777 #6442877

Order 512.

3052 conjugacy classes of subgroups.

The subgroup lattice has 817 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#465C211yesmaximal, characteristic, complemented
2C22×#465C211yesmaximal, characteristic, complemented
3C22×C8×D4C211yesmaximal, characteristic, complemented
4C22×#427C211yesmaximal, characteristic, complemented
5C2×#2415C211yesmaximal, characteristic, complemented
6C2×#2414C211yesmaximal, characteristic
7#24777C2116yesmaximal, direct product factor
8C2×#2068C211yesmaximal, characteristic, complemented
9C2×#2067C211yesmaximal, characteristic, complemented
10C2×#2036C211yesmaximal, characteristic, complemented
11C2×#2033C211yesmaximal, characteristic, complemented
12C2×#1968C211yesmaximal, characteristic, complemented
13C2×#1941C211yesmaximal, characteristic, complemented
14C2×#1875C211yesmaximal, characteristic, complemented
15C2×#1873C211yesmaximal, characteristic, complemented
16C2×#1807C211yesmaximal, characteristic, complemented
17C23×SD16C2211yescharacteristic
18C24×C8C2211yescharacteristic
19C24×C8C2211yescharacteristic
20C22×C22⋊Q8C2211yescharacteristic
21C22×C22⋊Q8C2211yescharacteristic
22C22×#121C2211yescharacteristic
23C22×#121C2211yescharacteristic
24C22×C4×D4C2211yescharacteristic
25C22×#117C2211yescharacteristic
26C22×#117C2211yescharacteristic
27C2×#465—28no—
28C2×#465—28no—
29C2×#465C2218yescomplemented
30C2×#465C2218yescomplemented
31C2×C8×D4—28no—
32C2×C8×D4C2218yescomplemented
33C2×#427—28no—
34C2×#427C2218yescomplemented
35C22×#107C2211yescharacteristic
36C22×#107C2211yescharacteristic
37C22×#106C2211yescharacteristic
38C22×#106C2211yescharacteristic
39C22×#106C2211yescharacteristic
40C22×C4⋊C8C2211yescharacteristic
41C22×#103C2211yescharacteristic
42C22×#103C2211yescharacteristic
43C22×#103C2211yescharacteristic
44C22×#102C2211yescharacteristic
45C22×#102C2211yescharacteristic
46C22×#102C2211yescharacteristic
47C22×C22⋊C8C2211yescharacteristic
48C22×C22⋊C8C2211yescharacteristic
49C22×C4×C8C2211yescharacteristic
50#2415—24no—
51#2415C2218yescomplemented
52#2414—24no—
53#2414C2218yes—
54C2×#397—21no—
55C2×#394—21no—
56C2×#394—21no—
57C2×#392—21no—
58C2×#391C2211yescharacteristic
59C2×#390—21no—
60C2×#390C2211yescharacteristic
61C2×#389—21no—
62C2×#389C2211yescharacteristic
63C2×#389C2211yescharacteristic
64C2×#388—21no—
65C2×#388—21no—
66C2×#380C2211yescharacteristic
67C2×#380C2211yescharacteristic
68#2068C2218yescomplemented
69#2067C2218yescomplemented
70#2036C2218yescomplemented
71#2033C2218yescomplemented
72#1968C2218yescomplemented
73#1941C2218yescomplemented
74#1875C2218yescomplemented
75#1873C2218yescomplemented
76#1807C2218yescomplemented
77C2×#340C2211yescharacteristic
78C2×#340C2211yescharacteristic
79C2×#340C2211yescharacteristic
80C2×#340C2211yescharacteristic
81C23×Q8C2311yescharacteristic
82C23×D4—21no—
83C23×D4—21no—
84C23×D4D411yescharacteristic
85C23×D4C2311yescharacteristic
86C24×C4C2311yescharacteristic
87C24×C4C2311yescharacteristic
88C22×SD16—24no—
89C22×SD16—24no—
90C22×SD16—24no—
91C22×SD16C2314yes—
92C23×C8—24no—
93C23×C8—24no—
94C23×C8—24no—
95C23×C8—24no—
96C23×C8—24no—
97C23×C8D418yescomplemented
98C23×C8C2314yes—
99C23×C8C2311yescharacteristic
100C23×C8C2311yescharacteristic
101C23×C8C2311yescharacteristic
102C23×C8C2314yes—
103C23×C8C2311yescharacteristic
104C2×C22⋊Q8—22no—
105C2×C22⋊Q8—22no—
106C2×C22⋊Q8—24no—
107C2×C22⋊Q8—24no—
108C2×C22⋊Q8—24no—
109C2×C22⋊Q8—42no—
110C2×C22⋊Q8C2314yes—
111C2×C22⋊Q8C2314yes—
112C2×#121—22no—
113C2×#121—22no—
114C2×#121—24no—
115C2×#121—24no—
116C2×#121—24no—
117C2×#121—42no—
118C2×#121C2314yes—
119C2×#121C2314yes—
120C2×C4×D4—24no—
121C2×C4×D4—24no—
122C2×C4×D4D414yes—
123C2×C4×D4C2314yes—
124C2×#117—22no—
125C2×#117—22no—
126C2×#117—24no—
127C2×#117—24no—
128C2×#117—42no—
129C2×#117—42no—
130C2×#117C2314yes—
131C2×#117C2314yes—
132C22×C4⋊C4—21no—
133C22×C4⋊C4—21no—
134C22×C4⋊C4—21no—
135C22×C4⋊C4—21no—
136C22×C4⋊C4D411yescharacteristic
137C22×C4⋊C4C2311yescharacteristic
138C22×C4⋊C4C2311yescharacteristic
139C22×C4⋊C4C2311yescharacteristic
140C22×C4⋊C4C2311yescharacteristic
141C22×C4⋊C4C2311yescharacteristic
142C22×C4⋊C4C2311yescharacteristic
143C22×C22⋊C4—21no—
144C22×C22⋊C4—21no—
145C22×C22⋊C4—21no—
146C22×C22⋊C4—21no—
147C22×C22⋊C4—21no—
148C22×C22⋊C4—21no—
149C22×C22⋊C4—21no—
150C22×C22⋊C4—21no—
151C22×C22⋊C4—21no—
152C22×C22⋊C4—21no—
153C22×C22⋊C4D411yescharacteristic
154C22×C22⋊C4D411yescharacteristic
155C22×C42—21no—
156C22×C42—21no—
157C22×C42C2311yescharacteristic
158#465—232no—
159#465—232no—
160C8×D4—232no—
161#427—232no—
162C2×#107—24no—
163C2×#107—24no—
164C2×#107C2314yes—
165C2×#107C2314yes—
166C2×#106—24no—
167C2×#106—24no—
168C2×#106D418yescomplemented
169C2×#106C2314yes—
170C2×#106C2314yes—
171C2×#106C2314yes—
172C2×C4⋊C8—24no—
173C2×C4⋊C8C2314yes—
174C2×#103—24no—
175C2×#103—24no—
176C2×#103—42no—
177C2×#103C2314yes—
178C2×#103C2314yes—
179C2×#103C2314yes—
180C2×#102—24no—
181C2×#102—24no—
182C2×#102—42no—
183C2×#102C2314yes—
184C2×#102C2314yes—
185C2×#102C2314yes—
186C2×C22⋊C8—24no—
187C2×C22⋊C8—24no—
188C2×C22⋊C8C2314yes—
189C2×C22⋊C8C2314yes—
190C2×C4×C8—24no—
191C2×C4×C8C2314yes—
192#397—28no—
193#394—28no—
194#394—28no—
195#392—28no—
196#391—22no—
197#391C2314yes—
198#390—28no—
199#390—22no—
200#390C2314yes—
201#389—28no—
202#389—22no—
203#389—22no—
204#389C2314yes—
205#389C2314yes—
206#388—28no—
207#388—28no—
208#380—22no—
209#380—22no—
210#380C2314yes—
211#380C2314yes—
212C2×#95—21no—
213C2×#95—21no—
214C2×#95—21no—
215C2×#95—21no—
216C2×#95—21no—
217C2×#95—21no—
218#340C2314yes—
219#340C2314yes—
220#340C2314yes—
221#340C2314yes—
222C25—21no—
223C25C2×D411yescharacteristic
224C25C2×D411yescharacteristic
225C22×Q8—21no—
226C22×Q8—22no—
227C22×Q8—22no—
228C22×Q8—22no—
229C22×Q8—22no—
230C22×Q8—22no—
231C22×Q8—22no—
232C22×Q8C2412yes—
233C22×D4—24no—
234C22×D4—24no—
235C22×D4—24no—
236C22×D4—24no—
237C22×D4—24no—
238C22×D4—22no—
239C22×D4—22no—
240C22×D4—21no—
241C22×D4—22no—
242C22×D4—22no—
243C22×D4—22no—
244C22×D4—22no—
245C22×D4—44no—
246C22×D4—44no—
247C22×D4—44no—
248C22×D4—82no—
249C22×D4—82no—
250C22×D4—82no—
251C22×D4C2×D414yes—
252C22×D4C2412yes—
253C23×C4—22no—
254C23×C4—22no—
255C23×C4—22no—
256C23×C4—22no—
257C23×C4—21no—
258C23×C4—21no—
259C23×C4—22no—
260C23×C4—22no—
261C23×C4—22no—
262C23×C4—22no—
263C23×C4—22no—
264C23×C4—22no—
265C23×C4—21no—
266C23×C4—21no—
267C23×C4—21no—
268C23×C4—21no—
269C23×C4—21no—
270C23×C4C2×D412yes—
271C23×C4C2×D411yescharacteristic
272C23×C4C2×D411yescharacteristic
273C23×C4C2×D412yes—
274C23×C4C2×D411yescharacteristic
275C23×C4C2×D414yes—
276C23×C4C2×D411yescharacteristic
277C23×C4#4114yes—
278C23×C4C2412yes—
279C23×C4C2412yes—
280C23×C4C2411yescharacteristic
281C2×SD16—28no—
282C2×SD16—28no—
283C2×SD16—28no—
284C2×SD16—416no—
285C22×C8—22no—
286C22×C8—22no—
287C22×C8—232no—
288C22×C8—28no—
289C22×C8—28no—
290C22×C8—22no—
291C22×C8—22no—
292C22×C8—22no—
293C22×C8—22no—
294C22×C8—22no—
295C22×C8—22no—
296C22×C8—28no—
297C22×C8—28no—
298C22×C8—28no—
299C22×C8—416no—
300C22×C8C2×D414yes—
301C22×C8C2×D414yes—
302C22×C8C2×D414yes—
303C22×C8C2×D4116yescomplemented
304C22×C8#4114yes—
305C22×C8C2412yes—
306C22×C8C2412yes—
307C22×C8C2412yes—
308C22×C8C2412yes—
309C22⋊Q8—28no—
310C22⋊Q8—28no—
311C22⋊Q8—28no—
312C22⋊Q8—44no—
313C22⋊Q8—48no—
314C22⋊Q8—48no—
315#121—28no—
316#121—28no—
317#121—28no—
318#121—44no—
319#121—48no—
320#121—48no—
321C4×D4—216no—
322C4×D4—28no—
323C4×D4—28no—
324#117—28no—
325#117—28no—
326#117—44no—
327#117—44no—
328#117—48no—
329#117—48no—
330C2×C4⋊C4—24no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4—21no—
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—22no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—24no—
344C2×C4⋊C4—24no—
345C2×C4⋊C4—24no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—24no—
351C2×C4⋊C4—44no—
352C2×C4⋊C4—44no—
353C2×C4⋊C4—44no—
354C2×C4⋊C4—82no—
355C2×C4⋊C4C2×D414yes—
356C2×C4⋊C4C2×D414yes—
357C2×C4⋊C4C2×D414yes—
358C2×C4⋊C4C2412yes—
359C2×C4⋊C4C2412yes—
360C2×C4⋊C4C2412yes—
361C2×C4⋊C4C2412yes—
362C2×C4⋊C4C2412yes—
363C2×C4⋊C4C2412yes—
364C2×C22⋊C4—24no—
365C2×C22⋊C4—24no—
366C2×C22⋊C4—24no—
367C2×C22⋊C4—24no—
368C2×C22⋊C4—24no—
369C2×C22⋊C4—24no—
370C2×C22⋊C4—24no—
371C2×C22⋊C4—24no—
372C2×C22⋊C4—24no—
373C2×C22⋊C4—24no—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—24no—
376C2×C22⋊C4—44no—
377C2×C22⋊C4—44no—
378C2×C22⋊C4—44no—
379C2×C22⋊C4—44no—
380C2×C22⋊C4—44no—
381C2×C22⋊C4—44no—
382C2×C22⋊C4—44no—
383C2×C22⋊C4—44no—
384C2×C22⋊C4—82no—
385C2×C22⋊C4—82no—
386C2×C22⋊C4C2×D414yes—
387C2×C22⋊C4C2×D414yes—
388C2×C42—22no—
389C2×C42—22no—
390C2×C42—24no—
391C2×C42—24no—
392C2×C42—44no—
393C2×C42—44no—
394C2×C42C2×D412yes—
395C2×C42C2412yes—
396#107—28no—
397#107—28no—
398#106—28no—
399#106—28no—
400#106C2×D4116yescomplemented
401C4⋊C8—28no—
402#103—28no—
403#103—28no—
404#103—44no—
405#102—28no—
406#102—28no—
407#102—44no—
408C22⋊C8—28no—
409C22⋊C8—28no—
410C4×C8—28no—
411#95—24no—
412#95—24no—
413#95—24no—
414#95—24no—
415#95—24no—
416#95—24no—
417C24—22no—
418C24—22no—
419C24—22no—
420C24—22no—
421C24—22no—
422C24—22no—
423C24—22no—
424C24—22no—
425C24—22no—
426C24—22no—
427C24—22no—
428C24—22no—
429C24—22no—
430C24—42no—
431C24—42no—
432C24—42no—
433C24—42no—
434C24—42no—
435C24—42no—
436C24—42no—
437C24#12114yes—
438C24#13514yes—
439C24C22×D412yes—
440C24C22×D412yes—
441C24C22×D411yescharacteristic
442C2×Q8—22no—
443C2×Q8—22no—
444C2×Q8—22no—
445C2×Q8—22no—
446C2×Q8—22no—
447C2×Q8—22no—
448C2×Q8—42no—
449C2×Q8—42no—
450C2×Q8—42no—
451C2×Q8—44no—
452C2×Q8—44no—
453C2×Q8—44no—
454C2×Q8—44no—
455C2×D4—232no—
456C2×D4—28no—
457C2×D4—28no—
458C2×D4—28no—
459C2×D4—22no—
460C2×D4—22no—
461C2×D4—22no—
462C2×D4—22no—
463C2×D4—22no—
464C2×D4—22no—
465C2×D4—48no—
466C2×D4—48no—
467C2×D4—48no—
468C2×D4—44no—
469C2×D4—42no—
470C2×D4—44no—
471C2×D4—42no—
472C2×D4—42no—
473C2×D4—44no—
474C2×D4—44no—
475C2×D4—84no—
476C2×D4—84no—
477C2×D4—84no—
478C2×D4—816no—
479C2×D4—816no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—28no—
485C22×C4—28no—
486C22×C4—24no—
487C22×C4—24no—
488C22×C4—28no—
489C22×C4—28no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—24no—
497C22×C4—24no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—24no—
505C22×C4—24no—
506C22×C4—24no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—42no—
519C22×C4—42no—
520C22×C4—42no—
521C22×C4—42no—
522C22×C4—44no—
523C22×C4—44no—
524C22×C4—44no—
525C22×C4—44no—
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×D412yes—
550C22×C4C22×D411yescharacteristic
551C22×C4C22×D412yes—
552C22×C4C2×#4114yes—
553C22×C4C2×#4112yes—
554C22×C4C2×#4112yes—
555C22×C4H(5,𝔽2)12yes—
556C22×C42−1+412yes—
557C22×C4C2511yescharacteristic
558SD16—416no—
559C2×C8—28no—
560C2×C8—22no—
561C2×C8—22no—
562C2×C8—232no—
563C2×C8—22no—
564C2×C8—22no—
565C2×C8—22no—
566C2×C8—22no—
567C2×C8—22no—
568C2×C8—22no—
569C2×C8—44no—
570C2×C8—44no—
571C2×C8—416no—
572C2×C8#121116yes—
573C2×C8C22×D414yes—
574C2×C8C22×D414yes—
575C2×C8C22×D414yes—
576C2×C8C2×#4114yes—
577C4⋊C4—28no—
578C4⋊C4—24no—
579C4⋊C4—24no—
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—22no—
590C4⋊C4—48no—
591C4⋊C4—42no—
592C4⋊C4—42no—
593C4⋊C4—48no—
594C4⋊C4—42no—
595C4⋊C4—42no—
596C4⋊C4—48no—
597C4⋊C4—84no—
598C4⋊C4C22×D414yes—
599C4⋊C4C22×D414yes—
600C22⋊C4—28no—
601C22⋊C4—28no—
602C22⋊C4—48no—
603C22⋊C4—48no—
604C22⋊C4—48no—
605C22⋊C4—48no—
606C22⋊C4—48no—
607C22⋊C4—48no—
608C22⋊C4—48no—
609C22⋊C4—48no—
610C22⋊C4—84no—
611C22⋊C4—84no—
612C42—24no—
613C42—22no—
614C42—22no—
615C42—48no—
616C42—48no—
617C23—28no—
618C23—22no—
619C23—28no—
620C23—22no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—28no—
625C23—28no—
626C23—28no—
627C23—28no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—44no—
636C23—44no—
637C23—44no—
638C23—44no—
639C23—44no—
640C23—44no—
641C23—44no—
642C23—44no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—84no—
651C23—84no—
652C23—84no—
653C23—84no—
654C23—84no—
655C23—84no—
656C23—84no—
657C23C2×#12114yes—
658C23C2×#12112yes—
659C23D4212yes—
660C23#54712yes—
661C23C2×#13514yes—
662C23C2×#13512yes—
663C23C2×#13512yes—
664C23#57712yes—
665C23#57712yes—
666C23C23×D411yescharacteristic
667Q8—42no—
668Q8—42no—
669Q8—42no—
670Q8—42no—
671Q8—84no—
672D4—232no—
673D4—42no—
674D4—42no—
675D4—42no—
676D4—42no—
677D4—816no—
678D4—816no—
679D4—84no—
680C2×C4—22no—
681C2×C4—28no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—28no—
685C2×C4—22no—
686C2×C4—24no—
687C2×C4—216no—
688C2×C4—24no—
689C2×C4—24no—
690C2×C4—24no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—24no—
694C2×C4—24no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—44no—
700C2×C4—48no—
701C2×C4—48no—
702C2×C4—44no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—48no—
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—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—84no—
728C2×C4—84no—
729C2×C4—84no—
730C2×C4—84no—
731C2×C4—84no—
732C2×C4C2×#12114yes—
733C2×C4C2×#12114yes—
734C2×C4C2×#12112yes—
735C2×C4#53714yes—
736C2×C4D4212yes—
737C2×C4#54712yes—
738C2×C4#54814yes—
739C2×C4#55314yes—
740C2×C4C2×#13514yes—
741C2×C4C23×D411yescharacteristic
742C2×C4C23×D411yescharacteristic
743C2×C4C22×#4111yescharacteristic
744C2×C4C22×#4111yescharacteristic
745C2×C4C2×H(5,𝔽2)11yescharacteristic
746C2×C4C2×2−1+411yescharacteristic
747C8—24no—
748C8—42no—
749C8—42no—
750C8C2×#12118yes—
751C22—24no—
752C22—24no—
753C22—24no—
754C22—24no—
755C22—24no—
756C22—24no—
757C22—42no—
758C22—42no—
759C22—42no—
760C22—42no—
761C22—42no—
762C22—42no—
763C22—42no—
764C22—42no—
765C22—416no—
766C22—416no—
767C22—82no—
768C22—82no—
769C22—82no—
770C22—82no—
771C22—82no—
772C22—82no—
773C22—82no—
774C22—168no—
775C22#241614yes—
776C22#305014yes—
777C22#305714yes—
778C22#328214yes—
779C22#328414yes—
780C22#333714yes—
781C22#334014yes—
782C22C22×#12111yescharacteristic
783C22C2×D4211yescharacteristic
784C22C2×#54711yescharacteristic
785C22C22×#13511yescharacteristic
786C22C22×#13511yescharacteristic
787C22C2×#57711yescharacteristic
788C22C2×#57711yescharacteristic
789C4—24no—
790C4—24no—
791C4—42no—
792C4—42no—
793C4—44no—
794C4—44no—
795C4—82no—
796C4—82no—
797C4—82no—
798C4—82no—
799C4—82no—
800C4#241614yes—
801C4C22×#12111yescharacteristic
802C4C2×#53711yescharacteristic
803C4C2×#54811yescharacteristic
804C4C2×#55311yescharacteristic
805C2—44no—
806C2—44no—
807C2—162no—
808C2#2477718yesdirect product factor
809C2C2×#241611yescharacteristic
810C2C2×#305011yescharacteristic
811C2C2×#305711yescharacteristic
812C2C2×#328211yescharacteristic
813C2C2×#328411yescharacteristic
814C2C2×#333711yescharacteristic
815C2C2×#334011yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#2414C2
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×#465C2semidirect
2. C22×#465C2semidirect
3. C22×C8×D4C2semidirect
4. C22×#427C2semidirect
5. C2×#2415C2semidirect
7. #24777C2direct (N × H)
8. C2×#2068C2semidirect
9. C2×#2067C2semidirect
10. C2×#2036C2semidirect
11. C2×#2033C2semidirect
12. C2×#1968C2semidirect
13. C2×#1941C2semidirect
14. C2×#1875C2semidirect
15. C2×#1873C2semidirect
16. C2×#1807C2semidirect
29. C2×#465C22semidirect
30. C2×#465C22semidirect
32. C2×C8×D4C22semidirect
34. C2×#427C22semidirect
51. #2415C22semidirect
68. #2068C22semidirect
69. #2067C22semidirect
70. #2036C22semidirect
71. #2033C22semidirect
72. #1968C22semidirect
73. #1941C22semidirect
74. #1875C22semidirect
75. #1873C22semidirect
76. #1807C22semidirect
97. C23×C8D4semidirect
168. C2×#106D4semidirect
303. C22×C8C2×D4semidirect
400. #106C2×D4semidirect
808. C2#24777direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#4652
C22×C8×D42
C22×#4272
C2×#24152
C2×#24142
#247772
C2×#20682
C2×#20672
C2×#20362
C2×#20332
C2×#19682
C2×#19412
C2×#18752
C2×#18732
C2×#18072