Finite Group Databasebeta

← C2×#24893 #6438166

Subgroups — C2×#24893 #6438166

Order 512.

3990 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#447C211yesmaximal, characteristic
2C22×C4×D8C211yesmaximal, characteristic, complemented
3C2×#2422C211yesmaximal, characteristic, complemented
4C2×D4×C22⋊C4C211yesmaximal, characteristic, complemented
5#24893C2116yesmaximal, direct product factor
6C2×#2093C211yesmaximal, characteristic, complemented
7C2×#2075C211yesmaximal, characteristic, complemented
8C2×#2054C211yesmaximal, characteristic, complemented
9C2×#2033C211yesmaximal, characteristic, complemented
10C2×#1934C211yesmaximal, characteristic, complemented
11C2×#1923C211yesmaximal, characteristic, complemented
12C2×#1879C211yesmaximal, characteristic, complemented
13C2×#1879C211yesmaximal, characteristic, complemented
14C2×#1862C211yesmaximal, characteristic, complemented
15C2×#1802C211yesmaximal, characteristic, complemented
16C2×#1786C211yesmaximal, characteristic, complemented
17C24×D4C2211yescharacteristic
18C23×D8C2211yescharacteristic
19C23×D8C2211yescharacteristic
20C22×#123—21no—
21C22×#121C2211yescharacteristic
22C22×C4×D4C2211yescharacteristic
23C22×C4×D4C2211yescharacteristic
24C22×C4×D4C2211yescharacteristic, complemented
25C23×C22⋊C4—21no—
26C2×#447—28no—
27C2×#447C2218yes—
28C2×C4×D8—28no—
29C2×C4×D8C2218yescomplemented
30C22×#107C2211yescharacteristic, complemented
31C22×#107C2211yescharacteristic, complemented
32C22×C4⋊C8C2211yescharacteristic, complemented
33C22×#102C2211yescharacteristic
34C22×#102C2211yescharacteristic
35C22×#102C2211yescharacteristic
36C22×#102C2211yescharacteristic
37C22×#102C2211yescharacteristic
38C22×#102C2211yescharacteristic
39C22×#102C2211yescharacteristic, complemented
40C22×#102C2211yescharacteristic, complemented
41C22×C22⋊C8C2211yescharacteristic
42C22×C22⋊C8C2211yescharacteristic
43C22×C4×C8C2211yescharacteristic, complemented
44#2422—24no—
45#2422C2218yescomplemented
46C2×#397—21no—
47C2×#394—21no—
48D4×C22⋊C4—24no—
49D4×C22⋊C4C2218yescomplemented
50C2×#390C2211yescharacteristic
51C2×#390C2211yescharacteristic
52C2×#390C2211yescharacteristic, complemented
53C2×#389C2211yescharacteristic, complemented
54C2×#386—21no—
55C2×#386—21no—
56C2×#385—21no—
57C2×#384C2211yescharacteristic, complemented
58C2×#380C2211yescharacteristic
59C2×#380C2211yescharacteristic
60C2×#379—21no—
61C2×C4×C22⋊C4C2211yescharacteristic
62#2093C2218yescomplemented
63#2075C2218yescomplemented
64#2054C2218yescomplemented
65#2033C2218yescomplemented
66#1934C2218yescomplemented
67#1923C2218yescomplemented
68#1879C2218yescomplemented
69#1879C2218yescomplemented
70#1862C2218yescomplemented
71#1802C2218yescomplemented
72#1786C2218yescomplemented
73C2×#340C2211yescharacteristic, complemented
74C2×#340C2211yescharacteristic, complemented
75C2×#340C2211yescharacteristic, complemented
76C2×#340C2211yescharacteristic, complemented
77C2×#336C2211yescharacteristic, complemented
78C2×#336C2211yescharacteristic, complemented
79C26—21no—
80C23×D4—24no—
81C23×D4—24no—
82C23×D4—24no—
83C23×D4—24no—
84C23×D4—21no—
85C23×D4—22no—
86C23×D4—21no—
87C23×D4—42no—
88C23×D4—42no—
89C23×D4C2311yescharacteristic
90C23×D4C2311yescharacteristic
91C23×D4C2314yes—
92C23×D4C2311yescharacteristic
93C24×C4—21no—
94C24×C4—21no—
95C24×C4—21no—
96C24×C4C2311yescharacteristic
97C22×D8—24no—
98C22×D8—24no—
99C22×D8—24no—
100C22×D8—24no—
101C22×D8—42no—
102C22×D8D418yes—
103C22×D8C2314yes—
104C22×D8C2314yes—
105C23×C8C2311yescharacteristic
106C23×C8C2311yescharacteristic
107C23×C8C2311yescharacteristic
108C23×C8C2311yescharacteristic
109C2×#123—28no—
110C2×#123—48no—
111C2×#121—22no—
112C2×#121—24no—
113C2×#121—42no—
114C2×#121C2314yes—
115C2×C4×D4—24no—
116C2×C4×D4—24no—
117C2×C4×D4—24no—
118C2×C4×D4—22no—
119C2×C4×D4—22no—
120C2×C4×D4—22no—
121C2×C4×D4—42no—
122C2×C4×D4—42no—
123C2×C4×D4—42no—
124C2×C4×D4C2314yes—
125C2×C4×D4C2314yes—
126C2×C4×D4C2314yescomplemented
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⋊C4—21no—
147C22×C22⋊C4—28no—
148C22×C22⋊C4—48no—
149C22×C22⋊C4D411yescharacteristic
150C22×C22⋊C4D411yescharacteristic
151C22×C42C2311yescharacteristic
152C22×C42C2311yescharacteristic
153#447—232no—
154C4×D8—232no—
155C2×#107—24no—
156C2×#107—42no—
157C2×#107C2314yescomplemented
158C2×#107C2314yescomplemented
159C2×C4⋊C8—42no—
160C2×C4⋊C8C2314yescomplemented
161C2×#102—24no—
162C2×#102—24no—
163C2×#102—24no—
164C2×#102—24no—
165C2×#102—24no—
166C2×#102—24no—
167C2×#102—42no—
168C2×#102—42no—
169C2×#102C2314yes—
170C2×#102C2314yes—
171C2×#102C2314yes—
172C2×#102C2314yes—
173C2×#102C2314yes—
174C2×#102C2314yes—
175C2×#102C2314yescomplemented
176C2×#102C2314yescomplemented
177C2×C22⋊C8—24no—
178C2×C22⋊C8—42no—
179C2×C22⋊C8C2314yes—
180C2×C22⋊C8C2314yes—
181C2×C4×C8—24no—
182C2×C4×C8C2314yescomplemented
183#397—28no—
184#394—28no—
185#390—22no—
186#390—22no—
187#390—22no—
188#390C2314yes—
189#390C2314yes—
190#390C2314yescomplemented
191#389—22no—
192#389C2314yescomplemented
193#386—28no—
194#386—28no—
195#385—28no—
196#384—22no—
197#384C2314yescomplemented
198#380—22no—
199#380—22no—
200#380C2314yes—
201#380C2314yes—
202#379—28no—
203C4×C22⋊C4D414yes—
204C4×C22⋊C4C2314yes—
205C2×#95—21no—
206C2×#95—21no—
207C2×#95—21no—
208C2×#95D411yescharacteristic
209C2×#95D411yescharacteristic
210#340C2314yescomplemented
211#340C2314yescomplemented
212#340C2314yescomplemented
213#340C2314yescomplemented
214#336C2314yescomplemented
215#336C2314yescomplemented
216C25—21no—
217C25—28no—
218C25—21no—
219C25—21no—
220C25—24no—
221C25—44no—
222C25—44no—
223C25—44no—
224C25—44no—
225C25—82no—
226C25—82no—
227C25C2×D411yescharacteristic
228C22×D4—28no—
229C22×D4—216no—
230C22×D4—28no—
231C22×D4—28no—
232C22×D4—28no—
233C22×D4—28no—
234C22×D4—24no—
235C22×D4—21no—
236C22×D4—22no—
237C22×D4—21no—
238C22×D4—24no—
239C22×D4—21no—
240C22×D4—22no—
241C22×D4—22no—
242C22×D4—22no—
243C22×D4—22no—
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—44no—
253C22×D4—44no—
254C22×D4—48no—
255C22×D4—48no—
256C22×D4—44no—
257C22×D4—44no—
258C22×D4—416no—
259C22×D4—416no—
260C22×D4—416no—
261C22×D4—416no—
262C22×D4—44no—
263C22×D4—44no—
264C22×D4—82no—
265C22×D4C2×D414yes—
266C22×D4C2×D414yes—
267C22×D4#4114yes—
268C22×D4#4114yes—
269C22×D4#4114yes—
270C22×D4C2412yes—
271C22×D4C2412yes—
272C22×D4C2412yes—
273C23×C4—22no—
274C23×C4—22no—
275C23×C4—22no—
276C23×C4—22no—
277C23×C4—22no—
278C23×C4—22no—
279C23×C4—21no—
280C23×C4—21no—
281C23×C4—21no—
282C23×C4—21no—
283C23×C4—21no—
284C23×C4—24no—
285C23×C4—24no—
286C23×C4—24no—
287C23×C4—44no—
288C23×C4—44no—
289C23×C4—44no—
290C23×C4—44no—
291C23×C4—44no—
292C23×C4—44no—
293C23×C4—82no—
294C23×C4—82no—
295C23×C4—82no—
296C23×C4C2×D412yes—
297C23×C4C2×D411yescharacteristic
298C23×C4C2×D411yescharacteristic
299C23×C4C2×D411yescharacteristic
300C23×C4C2×D411yescharacteristic
301C23×C4C2×D411yescharacteristic
302C23×C4C2412yes—
303C23×C4C2411yescharacteristic
304C2×D8—232no—
305C2×D8—28no—
306C2×D8—28no—
307C2×D8—28no—
308C2×D8—28no—
309C2×D8—44no—
310C2×D8—416no—
311C2×D8C2×D4116yes—
312C22×C8—22no—
313C22×C8—22no—
314C22×C8—22no—
315C22×C8—22no—
316C22×C8—22no—
317C22×C8—22no—
318C22×C8—22no—
319C22×C8—22no—
320C22×C8—22no—
321C22×C8—22no—
322C22×C8—22no—
323C22×C8C2×D414yes—
324C22×C8C2412yes—
325C22×C8C2412yes—
326C22×C8C2412yes—
327C22×C8C2412yes—
328#123—432no—
329#121—28no—
330#121—44no—
331#121—48no—
332C4×D4—28no—
333C4×D4—28no—
334C4×D4—28no—
335C4×D4—44no—
336C4×D4—44no—
337C4×D4—44no—
338C4×D4—48no—
339C4×D4—48no—
340C4×D4—48no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—24no—
352C2×C4⋊C4—24no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—24no—
359C2×C4⋊C4—44no—
360C2×C4⋊C4—44no—
361C2×C4⋊C4—82no—
362C2×C4⋊C4C2412yes—
363C2×C4⋊C4C2412yes—
364C2×C4⋊C4C2412yes—
365C2×C4⋊C4C2412yes—
366C2×C4⋊C4C2412yes—
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—24no—
377C2×C22⋊C4—24no—
378C2×C22⋊C4—24no—
379C2×C22⋊C4—42no—
380C2×C22⋊C4—44no—
381C2×C22⋊C4—44no—
382C2×C22⋊C4—44no—
383C2×C22⋊C4—44no—
384C2×C22⋊C4—44no—
385C2×C22⋊C4—44no—
386C2×C22⋊C4—44no—
387C2×C22⋊C4—44no—
388C2×C22⋊C4—44no—
389C2×C22⋊C4—44no—
390C2×C22⋊C4—432no—
391C2×C22⋊C4—82no—
392C2×C22⋊C4—82no—
393C2×C22⋊C4D818yescomplemented
394C2×C22⋊C4C2×D414yes—
395C2×C22⋊C4C2×D414yes—
396C2×C42—22no—
397C2×C42—22no—
398C2×C42—22no—
399C2×C42—22no—
400C2×C42C2×D412yes—
401C2×C42C2×D412yes—
402C2×C42C2412yes—
403C2×C42C2412yes—
404#107—28no—
405#107—44no—
406C4⋊C8—44no—
407#102—28no—
408#102—28no—
409#102—28no—
410#102—28no—
411#102—28no—
412#102—28no—
413#102—44no—
414#102—44no—
415C22⋊C8—28no—
416C22⋊C8—44no—
417C4×C8—28no—
418#95—24no—
419#95—24no—
420#95—24no—
421#95C2×D414yes—
422#95C2×D414yes—
423C24—22no—
424C24—24no—
425C24—24no—
426C24—22no—
427C24—24no—
428C24—22no—
429C24—22no—
430C24—22no—
431C24—22no—
432C24—22no—
433C24—216no—
434C24—24no—
435C24—24no—
436C24—22no—
437C24—22no—
438C24—48no—
439C24—48no—
440C24—432no—
441C24—432no—
442C24—48no—
443C24—42no—
444C24—42no—
445C24—42no—
446C24—42no—
447C24—42no—
448C24—42no—
449C24—42no—
450C24—42no—
451C24—48no—
452C24—42no—
453C24—42no—
454C24—42no—
455C24—42no—
456C24—42no—
457C24—42no—
458C24—42no—
459C24—42no—
460C24—84no—
461C24—84no—
462C24—816no—
463C24—816no—
464C24—816no—
465C24—816no—
466C24—816no—
467C24C2×D814yes—
468C24C22×D412yes—
469C24C22×D411yescharacteristic
470C2×D4—216no—
471C2×D4—28no—
472C2×D4—24no—
473C2×D4—24no—
474C2×D4—28no—
475C2×D4—24no—
476C2×D4—24no—
477C2×D4—24no—
478C2×D4—28no—
479C2×D4—28no—
480C2×D4—28no—
481C2×D4—28no—
482C2×D4—28no—
483C2×D4—22no—
484C2×D4—22no—
485C2×D4—22no—
486C2×D4—22no—
487C2×D4—22no—
488C2×D4—22no—
489C2×D4—22no—
490C2×D4—22no—
491C2×D4—22no—
492C2×D4—22no—
493C2×D4—22no—
494C2×D4—22no—
495C2×D4—22no—
496C2×D4—48no—
497C2×D4—48no—
498C2×D4—416no—
499C2×D4—416no—
500C2×D4—464no—
501C2×D4—416no—
502C2×D4—432no—
503C2×D4—416no—
504C2×D4—48no—
505C2×D4—48no—
506C2×D4—44no—
507C2×D4—42no—
508C2×D4—44no—
509C2×D4—44no—
510C2×D4—42no—
511C2×D4—42no—
512C2×D4—42no—
513C2×D4—44no—
514C2×D4—84no—
515C2×D4—816no—
516C2×D4#123116yescomplemented
517C2×D4C22×D414yes—
518C2×D4C22×D414yes—
519C2×D4C2×#4114yes—
520C2×D4C2×#4114yes—
521C2×D4C2×#4114yes—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—24no—
536C22×C4—24no—
537C22×C4—24no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—48no—
550C22×C4—48no—
551C22×C4—48no—
552C22×C4—44no—
553C22×C4—44no—
554C22×C4—44no—
555C22×C4—44no—
556C22×C4—42no—
557C22×C4—42no—
558C22×C4—42no—
559C22×C4—42no—
560C22×C4—42no—
561C22×C4—42no—
562C22×C4—42no—
563C22×C4—42no—
564C22×C4—42no—
565C22×C4—42no—
566C22×C4—42no—
567C22×C4—42no—
568C22×C4—42no—
569C22×C4—42no—
570C22×C4—42no—
571C22×C4—48no—
572C22×C4—48no—
573C22×C4—48no—
574C22×C4—84no—
575C22×C4—84no—
576C22×C4—84no—
577C22×C4—816no—
578C22×C4—816no—
579C22×C4—816no—
580C22×C4C2×D814yes—
581C22×C4C2×D814yes—
582C22×C4C22×D412yes—
583C22×C4C22×D412yes—
584C22×C4C22×D412yes—
585C22×C4C22×D412yes—
586C22×C4C22×D412yes—
587C22×C4C22×D412yes—
588C22×C4C22×D411yescharacteristic
589C22×C4C2×#4112yes—
590C22×C4C2×#4112yes—
591C22×C4C2×#4112yes—
592C22×C4H(5,𝔽2)12yes—
593C22×C4H(5,𝔽2)12yes—
594C22×C4C2511yescharacteristic
595D8—232no—
596D8—416no—
597C2×C8—28no—
598C2×C8—22no—
599C2×C8—22no—
600C2×C8—22no—
601C2×C8—22no—
602C2×C8—22no—
603C2×C8—22no—
604C2×C8—22no—
605C2×C8—22no—
606C2×C8—22no—
607C2×C8—22no—
608C2×C8—22no—
609C2×C8—44no—
610C2×C8—44no—
611C2×C8—44no—
612C2×C8C22×D414yes—
613C4⋊C4—22no—
614C4⋊C4—22no—
615C4⋊C4—22no—
616C4⋊C4—22no—
617C4⋊C4—22no—
618C4⋊C4—22no—
619C4⋊C4—22no—
620C4⋊C4—22no—
621C4⋊C4—22no—
622C4⋊C4—22no—
623C4⋊C4—42no—
624C4⋊C4—42no—
625C4⋊C4—42no—
626C4⋊C4—42no—
627C4⋊C4—42no—
628C4⋊C4—48no—
629C4⋊C4—48no—
630C4⋊C4—84no—
631C22⋊C4—44no—
632C22⋊C4—48no—
633C22⋊C4—48no—
634C22⋊C4—48no—
635C22⋊C4—48no—
636C22⋊C4—48no—
637C22⋊C4—48no—
638C22⋊C4—48no—
639C22⋊C4—48no—
640C22⋊C4—48no—
641C22⋊C4—48no—
642C22⋊C4—84no—
643C22⋊C4—84no—
644C22⋊C4C2×D8116yescomplemented
645C42—24no—
646C42—24no—
647C42—22no—
648C42—22no—
649C42—22no—
650C42—22no—
651C23—28no—
652C23—22no—
653C23—24no—
654C23—216no—
655C23—24no—
656C23—22no—
657C23—24no—
658C23—22no—
659C23—28no—
660C23—28no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—24no—
665C23—24no—
666C23—432no—
667C23—432no—
668C23—48no—
669C23—44no—
670C23—48no—
671C23—44no—
672C23—44no—
673C23—48no—
674C23—48no—
675C23—48no—
676C23—42no—
677C23—44no—
678C23—48no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—48no—
683C23—48no—
684C23—42no—
685C23—48no—
686C23—48no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—48no—
691C23—48no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—42no—
698C23—42no—
699C23—42no—
700C23—816no—
701C23—816no—
702C23—816no—
703C23—8128no—
704C23—816no—
705C23—816no—
706C23—84no—
707C23—84no—
708C23—84no—
709C23—84no—
710C23—84no—
711C23—84no—
712C23—84no—
713C23—84no—
714C23#52512yes—
715C23D4212yes—
716C23#54612yes—
717C23C22×D814yes—
718C23C22×D812yes—
719C23#57512yes—
720C23#57612yes—
721C23#57712yes—
722C23C23×D411yescharacteristic
723D4—24no—
724D4—216no—
725D4—24no—
726D4—24no—
727D4—24no—
728D4—24no—
729D4—24no—
730D4—24no—
731D4—432no—
732D4—42no—
733D4—48no—
734D4—48no—
735D4—42no—
736D4—42no—
737D4—42no—
738D4—816no—
739D4C2×#12318yescomplemented
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—28no—
743C2×C4—28no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—44no—
756C2×C4—44no—
757C2×C4—44no—
758C2×C4—42no—
759C2×C4—48no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—816no—
779C2×C4—816no—
780C2×C4—816no—
781C2×C4—84no—
782C2×C4—84no—
783C2×C4—84no—
784C2×C4—84no—
785C2×C4—84no—
786C2×C4C2×#12314yes—
787C2×C4#52512yes—
788C2×C4#53814yes—
789C2×C4D4212yes—
790C2×C4#54612yes—
791C2×C4#54614yes—
792C2×C4#55114yes—
793C2×C4C22×D814yes—
794C2×C4C22×D814yes—
795C2×C4C23×D411yescharacteristic
796C2×C4C22×#4111yescharacteristic
797C2×C4C22×#4111yescharacteristic
798C2×C4C22×#4111yescharacteristic
799C2×C4C2×H(5,𝔽2)11yescharacteristic
800C2×C4C2×H(5,𝔽2)11yescharacteristic
801C8—24no—
802C8—42no—
803C8—42no—
804C8—42no—
805C22—28no—
806C22—24no—
807C22—24no—
808C22—24no—
809C22—416no—
810C22—432no—
811C22—42no—
812C22—42no—
813C22—44no—
814C22—44no—
815C22—44no—
816C22—42no—
817C22—44no—
818C22—44no—
819C22—42no—
820C22—44no—
821C22—44no—
822C22—44no—
823C22—44no—
824C22—44no—
825C22—44no—
826C22—44no—
827C22—864no—
828C22—816no—
829C22—816no—
830C22—82no—
831C22—82no—
832C22—82no—
833C22—82no—
834C22—82no—
835C22—82no—
836C22—82no—
837C22—82no—
838C22#241814yes—
839C22#310014yes—
840C22#311814yes—
841C22#326714yes—
842C22D4×D814yes—
843C22#329414yes—
844C22#332214yes—
845C22C2×#52511yescharacteristic
846C22C2×D4211yescharacteristic
847C22C2×#54611yescharacteristic
848C22C23×D811yescharacteristic
849C22C2×#57511yescharacteristic
850C22C2×#57611yescharacteristic
851C22C2×#57711yescharacteristic
852C4—24no—
853C4—24no—
854C4—42no—
855C4—42no—
856C4—42no—
857C4—82no—
858C4—82no—
859C4—82no—
860C4—82no—
861C4—82no—
862C4#241814yes—
863C4C22×#12311yescharacteristic
864C4C2×#53811yescharacteristic
865C4C2×#54611yescharacteristic
866C4C2×#55111yescharacteristic
867C2—44no—
868C2—48no—
869C2—84no—
870C2—84no—
871C2#2489318yesdirect product factor
872C2C2×#241811yescharacteristic
873C2C2×#310011yescharacteristic
874C2C2×#311811yescharacteristic
875C2C2×#326711yescharacteristic
876C2C2×D4×D811yescharacteristic
877C2C2×#329411yescharacteristic
878C2C2×#332211yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×#447C2
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×C4×D8C2semidirect
3. C2×#2422C2semidirect
4. C2×D4×C22⋊C4C2semidirect
5. #24893C2direct (N × H)
6. C2×#2093C2semidirect
7. C2×#2075C2semidirect
8. C2×#2054C2semidirect
9. C2×#2033C2semidirect
10. C2×#1934C2semidirect
11. C2×#1923C2semidirect
12. C2×#1879C2semidirect
13. C2×#1879C2semidirect
14. C2×#1862C2semidirect
15. C2×#1802C2semidirect
16. C2×#1786C2semidirect
24. C22×C4×D4C22semidirect
29. C2×C4×D8C22semidirect
30. C22×#107C22semidirect
31. C22×#107C22semidirect
32. C22×C4⋊C8C22semidirect
39. C22×#102C22semidirect
40. C22×#102C22semidirect
43. C22×C4×C8C22semidirect
45. #2422C22semidirect
49. D4×C22⋊C4C22semidirect
52. C2×#390C22semidirect
53. C2×#389C22semidirect
57. C2×#384C22semidirect
62. #2093C22semidirect
63. #2075C22semidirect
64. #2054C22semidirect
65. #2033C22semidirect
66. #1934C22semidirect
67. #1923C22semidirect
68. #1879C22semidirect
69. #1879C22semidirect
70. #1862C22semidirect
71. #1802C22semidirect
72. #1786C22semidirect
73. C2×#340C22semidirect
74. C2×#340C22semidirect
75. C2×#340C22semidirect
76. C2×#340C22semidirect
77. C2×#336C22semidirect
78. C2×#336C22semidirect
126. C2×C4×D4C23semidirect
157. C2×#107C23semidirect
158. C2×#107C23semidirect
160. C2×C4⋊C8C23semidirect
175. C2×#102C23semidirect
176. C2×#102C23semidirect
182. C2×C4×C8C23semidirect
190. #390C23semidirect
192. #389C23semidirect
197. #384C23semidirect
210. #340C23semidirect
211. #340C23semidirect
212. #340C23semidirect
213. #340C23semidirect
214. #336C23semidirect
215. #336C23semidirect
393. C2×C22⋊C4D8semidirect
516. C2×D4#123semidirect
644. C22⋊C4C2×D8semidirect
739. D4C2×#123semidirect
871. C2#24893direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#4472
C22×C4×D82
C2×#24222
C2×D4×C22⋊C42
#248932
C2×#20932
C2×#20752
C2×#20542
C2×#20332
C2×#19342
C2×#19232
C2×#18792
C2×#18622
C2×#18022
C2×#17862