Finite Group Databasebeta

← C2×#27243 #6440641

Subgroups — C2×#27243 #6440641

Order 512.

3904 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×#476C211yesmaximal, characteristic, complemented
2C22×#447C211yesmaximal, characteristic
3C2×#2491C211yesmaximal, characteristic, complemented
4C2×D4×C22⋊C4C211yesmaximal, characteristic, complemented
5#27243C2116yesmaximal, direct product factor
6C2×#2077C211yesmaximal, characteristic, complemented
7C2×#2054C211yesmaximal, characteristic, complemented
8C2×#2034C211yesmaximal, characteristic, complemented
9C2×#2023C211yesmaximal, characteristic, complemented
10C2×#1972C211yesmaximal, characteristic, complemented
11C2×#1926C211yesmaximal, characteristic, complemented
12C2×#1924C211yesmaximal, characteristic, complemented
13C2×#1879C211yesmaximal, characteristic, complemented
14C2×#1879C211yesmaximal, characteristic, complemented
15C2×#1786C211yesmaximal, characteristic, complemented
16C2×#1762C211yesmaximal, characteristic, complemented
17C24×D4C2211yescharacteristic
18C23×D8C2211yescharacteristic
19C23×D8C2211yescharacteristic
20C22×C4⋊Q8C2211yescharacteristic, complemented
21C22×#124—21no—
22C22×#121C2211yescharacteristic
23C22×C4×D4C2211yescharacteristic
24C22×C4×D4C2211yescharacteristic
25C23×C22⋊C4—21no—
26C2×#476—28no—
27C2×#476C2218yescomplemented
28C2×#447—28no—
29C2×#447C2218yes—
30C22×#106C2211yescharacteristic, complemented
31C22×#106C2211yescharacteristic, 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×#97C2211yescharacteristic, complemented
44#2491—24no—
45#2491C2218yescomplemented
46C2×#394—21no—
47C2×#393—21no—
48D4×C22⋊C4—24no—
49D4×C22⋊C4C2218yescomplemented
50C2×#390C2211yescharacteristic
51C2×#390C2211yescharacteristic
52C2×#390C2211yescharacteristic, complemented
53C2×#390C2211yescharacteristic, complemented
54C2×#388—21no—
55C2×#386—21no—
56C2×#386—21no—
57C2×#380C2211yescharacteristic
58C2×#380C2211yescharacteristic
59C2×#379—21no—
60C2×C4×C4⋊C4C2211yescharacteristic, complemented
61C2×C4×C22⋊C4C2211yescharacteristic
62#2077C2218yescomplemented
63#2054C2218yescomplemented
64#2034C2218yescomplemented
65#2023C2218yescomplemented
66#1972C2218yescomplemented
67#1926C2218yescomplemented
68#1924C2218yescomplemented
69#1879C2218yescomplemented
70#1879C2218yescomplemented
71#1786C2218yescomplemented
72#1762C2218yescomplemented
73C2×#340C2211yescharacteristic, complemented
74C2×#340C2211yescharacteristic, complemented
75C2×#340C2211yescharacteristic, complemented
76C2×#340C2211yescharacteristic, complemented
77C2×#336C2211yescharacteristic, complemented
78C2×#336C2211yescharacteristic, complemented
79C26—21no—
80C23×Q8—21no—
81C23×D4—24no—
82C23×D4—24no—
83C23×D4—24no—
84C23×D4—24no—
85C23×D4—21no—
86C23×D4—22no—
87C23×D4—21no—
88C23×D4—42no—
89C23×D4—42no—
90C23×D4C2311yescharacteristic
91C23×D4C2311yescharacteristic
92C23×D4C2314yes—
93C23×D4C2311yescharacteristic
94C24×C4—21no—
95C24×C4—21no—
96C24×C4C2311yescharacteristic
97C22×D8—24no—
98C22×D8—24no—
99C22×D8—24no—
100C22×D8—24no—
101C22×D8—24no—
102C22×D8—42no—
103C22×D8C2314yes—
104C22×D8C2314yes—
105C23×C8C2311yescharacteristic
106C23×C8C2311yescharacteristic
107C23×C8C2311yescharacteristic
108C23×C8C2311yescharacteristic
109C2×C4⋊Q8—24no—
110C2×C4⋊Q8—22no—
111C2×C4⋊Q8—42no—
112C2×C4⋊Q8C2314yescomplemented
113C2×#124—28no—
114C2×#124—48no—
115C2×#121—22no—
116C2×#121—24no—
117C2×#121—42no—
118C2×#121C2314yes—
119C2×C4×D4—24no—
120C2×C4×D4—24no—
121C2×C4×D4—22no—
122C2×C4×D4—22no—
123C2×C4×D4—42no—
124C2×C4×D4—42no—
125C2×C4×D4C2314yes—
126C2×C4×D4C2314yes—
127C22×C4⋊C4—21no—
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⋊C4—21no—
143C22×C22⋊C4—21no—
144C22×C22⋊C4—21no—
145C22×C22⋊C4—21no—
146C22×C22⋊C4—28no—
147C22×C22⋊C4—48no—
148C22×C22⋊C4D411yescharacteristic
149C22×C22⋊C4D411yescharacteristic
150C22×C42—21no—
151C22×C42C2311yescharacteristic
152C22×C42C2311yescharacteristic
153#476—232no—
154#447—232no—
155C2×#106—24no—
156C2×#106—24no—
157C2×#106C2314yescomplemented
158C2×#106C2314yescomplemented
159C2×C4⋊C8—24no—
160C2×C4⋊C8C2314yescomplemented
161C2×#102—24no—
162C2×#102—24no—
163C2×#102—24no—
164C2×#102—24no—
165C2×#102—42no—
166C2×#102—42no—
167C2×#102—42no—
168C2×#102D418yes—
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×#97—42no—
182C2×#97C2314yescomplemented
183#394—28no—
184#393—28no—
185#390—22no—
186#390—22no—
187#390—22no—
188#390—22no—
189#390C2314yes—
190#390C2314yes—
191#390C2314yescomplemented
192#390C2314yescomplemented
193#388—28no—
194#386—28no—
195#386—28no—
196#380—22no—
197#380—22no—
198#380C2314yes—
199#380C2314yes—
200#379—28no—
201C4×C4⋊C4—22no—
202C4×C4⋊C4C2314yescomplemented
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—24no—
220C25—21no—
221C25—44no—
222C25—44no—
223C25—44no—
224C25—44no—
225C25—82no—
226C25—82no—
227C25C2×D411yescharacteristic
228C22×Q8—24no—
229C22×Q8—44no—
230C22×Q8—44no—
231C22×Q8—82no—
232C22×D4—28no—
233C22×D4—216no—
234C22×D4—28no—
235C22×D4—28no—
236C22×D4—28no—
237C22×D4—28no—
238C22×D4—24no—
239C22×D4—21no—
240C22×D4—22no—
241C22×D4—24no—
242C22×D4—21no—
243C22×D4—22no—
244C22×D4—21no—
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—22no—
255C22×D4—22no—
256C22×D4—22no—
257C22×D4—44no—
258C22×D4—44no—
259C22×D4—48no—
260C22×D4—48no—
261C22×D4—44no—
262C22×D4—44no—
263C22×D4—44no—
264C22×D4—416no—
265C22×D4—416no—
266C22×D4—416no—
267C22×D4—416no—
268C22×D4—44no—
269C22×D4—82no—
270C22×D4C2×D414yes—
271C22×D4#4114yes—
272C22×D4#4114yes—
273C22×D4#4114yes—
274C22×D4C2412yes—
275C22×D4C2412yes—
276C22×D4C2412yes—
277C23×C4—21no—
278C23×C4—22no—
279C23×C4—22no—
280C23×C4—22no—
281C23×C4—22no—
282C23×C4—22no—
283C23×C4—22no—
284C23×C4—21no—
285C23×C4—21no—
286C23×C4—21no—
287C23×C4—21no—
288C23×C4—24no—
289C23×C4—24no—
290C23×C4—44no—
291C23×C4—44no—
292C23×C4—44no—
293C23×C4—44no—
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—28no—
305C2×D8—28no—
306C2×D8—28no—
307C2×D8—28no—
308C2×D8—28no—
309C2×D8—44no—
310C2×D8—416no—
311C2×D8—416no—
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—
328C4⋊Q8—28no—
329C4⋊Q8—44no—
330C4⋊Q8—48no—
331#124—432no—
332#121—28no—
333#121—44no—
334#121—48no—
335C4×D4—28no—
336C4×D4—28no—
337C4×D4—44no—
338C4×D4—44no—
339C4×D4—48no—
340C4×D4—48no—
341C2×C4⋊C4—21no—
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—21no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—44no—
357C2×C4⋊C4C2×D414yes—
358C2×C4⋊C4C2412yes—
359C2×C4⋊C4C2412yes—
360C2×C4⋊C4C2412yes—
361C2×C4⋊C4C2412yes—
362C2×C4⋊C4C2412yes—
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—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—432no—
379C2×C22⋊C4—44no—
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—82no—
390C2×C22⋊C4—82no—
391C2×C22⋊C4—82no—
392C2×C22⋊C4C2×D414yes—
393C2×C22⋊C4C2×D414yes—
394C2×C42—22no—
395C2×C42—22no—
396C2×C42—22no—
397C2×C42—22no—
398C2×C42—24no—
399C2×C42—44no—
400C2×C42C2×D412yes—
401C2×C42C2×D412yes—
402C2×C42C2412yes—
403C2×C42C2412yes—
404#106—28no—
405#106—28no—
406C4⋊C8—28no—
407#102—28no—
408#102—28no—
409#102—28no—
410#102—28no—
411#102—44no—
412#102—44no—
413#102—44no—
414#102C2×D4116yes—
415C22⋊C8—28no—
416C22⋊C8—44no—
417#97—44no—
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—22no—
436C24—22no—
437C24—48no—
438C24—48no—
439C24—48no—
440C24—432no—
441C24—432no—
442C24—42no—
443C24—42no—
444C24—42no—
445C24—42no—
446C24—42no—
447C24—42no—
448C24—42no—
449C24—48no—
450C24—42no—
451C24—42no—
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—
467C24AGL(1,ℤ/8)14yes—
468C24C22×D412yes—
469C24C22×D411yescharacteristic
470C2×Q8—48no—
471C2×Q8—48no—
472C2×Q8—84no—
473C2×Q8—816no—
474C2×D4—216no—
475C2×D4—24no—
476C2×D4—24no—
477C2×D4—28no—
478C2×D4—24no—
479C2×D4—24no—
480C2×D4—28no—
481C2×D4—28no—
482C2×D4—28no—
483C2×D4—28no—
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—22no—
497C2×D4—22no—
498C2×D4—48no—
499C2×D4—48no—
500C2×D4—48no—
501C2×D4—416no—
502C2×D4—416no—
503C2×D4—416no—
504C2×D4—464no—
505C2×D4—432no—
506C2×D4—416no—
507C2×D4—48no—
508C2×D4—42no—
509C2×D4—44no—
510C2×D4—44no—
511C2×D4—44no—
512C2×D4—44no—
513C2×D4—42no—
514C2×D4—42no—
515C2×D4—42no—
516C2×D4—44no—
517C2×D4—42no—
518C2×D4—44no—
519C2×D4—84no—
520C2×D4—816no—
521C2×D4#124116yescomplemented
522C2×D4C22×D414yes—
523C2×D4C2×#4114yes—
524C2×D4C2×#4114yes—
525C2×D4C2×#4114yes—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—24no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—24no—
543C22×C4—24no—
544C22×C4—24no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—48no—
556C22×C4—48no—
557C22×C4—48no—
558C22×C4—42no—
559C22×C4—42no—
560C22×C4—44no—
561C22×C4—44no—
562C22×C4—44no—
563C22×C4—44no—
564C22×C4—42no—
565C22×C4—42no—
566C22×C4—42no—
567C22×C4—42no—
568C22×C4—42no—
569C22×C4—42no—
570C22×C4—42no—
571C22×C4—42no—
572C22×C4—42no—
573C22×C4—42no—
574C22×C4—42no—
575C22×C4—42no—
576C22×C4—48no—
577C22×C4—84no—
578C22×C4—84no—
579C22×C4—816no—
580C22×C4—816no—
581C22×C4AGL(1,ℤ/8)14yes—
582C22×C4C22×D412yes—
583C22×C4C22×D412yes—
584C22×C4C22×D412yes—
585C22×C4C22×D412yes—
586C22×C4C22×D412yes—
587C22×C4C22×D411yescharacteristic
588C22×C4C22×D412yes—
589C22×C4C2×#4112yes—
590C22×C4C2×#4112yes—
591C22×C4C2×#4112yes—
592C22×C4H(5,𝔽2)12yes—
593C22×C4H(5,𝔽2)12yes—
594C22×C4C2511yescharacteristic
595D8—416no—
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—24no—
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—48no—
624C4⋊C4—42no—
625C4⋊C4—42no—
626C4⋊C4—42no—
627C4⋊C4—42no—
628C4⋊C4C22×D414yes—
629C22⋊C4—28no—
630C22⋊C4—28no—
631C22⋊C4—48no—
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—84no—
642C22⋊C4—84no—
643C22⋊C4—84no—
644C42—24no—
645C42—24no—
646C42—22no—
647C42—22no—
648C42—22no—
649C42—22no—
650C42—48no—
651C23—28no—
652C23—22no—
653C23—24no—
654C23—24no—
655C23—22no—
656C23—24no—
657C23—22no—
658C23—216no—
659C23—28no—
660C23—28no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—24no—
665C23—432no—
666C23—432no—
667C23—48no—
668C23—44no—
669C23—48no—
670C23—44no—
671C23—48no—
672C23—48no—
673C23—44no—
674C23—48no—
675C23—42no—
676C23—42no—
677C23—48no—
678C23—44no—
679C23—42no—
680C23—42no—
681C23—48no—
682C23—48no—
683C23—42no—
684C23—42no—
685C23—48no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—816no—
698C23—816no—
699C23—816no—
700C23—816no—
701C23—8128no—
702C23—816no—
703C23—84no—
704C23—84no—
705C23—84no—
706C23—84no—
707C23—84no—
708C23—84no—
709C23—84no—
710C23—84no—
711C23—84no—
712C23—84no—
713C23—84no—
714C23#52512yes—
715C23D4212yes—
716C23#54612yes—
717C23C2×AGL(1,ℤ/8)14yes—
718C23C2×AGL(1,ℤ/8)12yes—
719C23C2×AGL(1,ℤ/8)12yes—
720C23#57612yes—
721C23#57712yes—
722C23C23×D411yescharacteristic
723Q8—816no—
724D4—24no—
725D4—24no—
726D4—24no—
727D4—24no—
728D4—24no—
729D4—216no—
730D4—432no—
731D4—42no—
732D4—42no—
733D4—42no—
734D4—42no—
735D4—42no—
736D4—42no—
737D4—48no—
738D4—816no—
739D4—84no—
740D4C2×#12418yescomplemented
741C2×C4—22no—
742C2×C4—28no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—24no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—44no—
758C2×C4—44no—
759C2×C4—48no—
760C2×C4—44no—
761C2×C4—42no—
762C2×C4—44no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—48no—
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—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—816no—
782C2×C4—816no—
783C2×C4—84no—
784C2×C4—84no—
785C2×C4—84no—
786C2×C4—84no—
787C2×C4#52512yes—
788C2×C4C2×#12414yes—
789C2×C4#53814yes—
790C2×C4D4212yes—
791C2×C4#54614yes—
792C2×C4#54612yes—
793C2×C4#55114yes—
794C2×C4C2×AGL(1,ℤ/8)14yes—
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—24no—
806C22—28no—
807C22—24no—
808C22—24no—
809C22—44no—
810C22—44no—
811C22—42no—
812C22—42no—
813C22—416no—
814C22—432no—
815C22—44no—
816C22—42no—
817C22—44no—
818C22—44no—
819C22—44no—
820C22—42no—
821C22—44no—
822C22—44no—
823C22—44no—
824C22—864no—
825C22—82no—
826C22—82no—
827C22—816no—
828C22—82no—
829C22—82no—
830C22—82no—
831C22—82no—
832C22—82no—
833C22—82no—
834C22—82no—
835C22—82no—
836C22—82no—
837C22—168no—
838C22#247214yes—
839C22#310914yes—
840C22#311814yes—
841C22#326414yes—
842C22#326514yes—
843C22#330614yes—
844C22#332514yes—
845C22C2×#52511yescharacteristic
846C22C2×D4211yescharacteristic
847C22C2×#54611yescharacteristic
848C22C22×AGL(1,ℤ/8)11yescharacteristic
849C22C22×AGL(1,ℤ/8)11yescharacteristic
850C22C2×#57611yescharacteristic
851C22C2×#57711yescharacteristic
852C4—24no—
853C4—42no—
854C4—44no—
855C4—42no—
856C4—42no—
857C4—42no—
858C4—82no—
859C4—82no—
860C4—82no—
861C4—82no—
862C4#247214yes—
863C4C22×#12411yescharacteristic
864C4C2×#53811yescharacteristic
865C4C2×#54611yescharacteristic
866C4C2×#55111yescharacteristic
867C2—44no—
868C2—48no—
869C2—84no—
870C2—162no—
871C2#2724318yesdirect product factor
872C2C2×#247211yescharacteristic
873C2C2×#310911yescharacteristic
874C2C2×#311811yescharacteristic
875C2C2×#326411yescharacteristic
876C2C2×#326511yescharacteristic
877C2C2×#330611yescharacteristic
878C2C2×#332511yescharacteristic
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
1. C22×#476C2semidirect
3. C2×#2491C2semidirect
4. C2×D4×C22⋊C4C2semidirect
5. #27243C2direct (N × H)
6. C2×#2077C2semidirect
7. C2×#2054C2semidirect
8. C2×#2034C2semidirect
9. C2×#2023C2semidirect
10. C2×#1972C2semidirect
11. C2×#1926C2semidirect
12. C2×#1924C2semidirect
13. C2×#1879C2semidirect
14. C2×#1879C2semidirect
15. C2×#1786C2semidirect
16. C2×#1762C2semidirect
20. C22×C4⋊Q8C22semidirect
27. C2×#476C22semidirect
30. C22×#106C22semidirect
31. C22×#106C22semidirect
32. C22×C4⋊C8C22semidirect
39. C22×#102C22semidirect
40. C22×#102C22semidirect
43. C22×#97C22semidirect
45. #2491C22semidirect
49. D4×C22⋊C4C22semidirect
52. C2×#390C22semidirect
53. C2×#390C22semidirect
60. C2×C4×C4⋊C4C22semidirect
62. #2077C22semidirect
63. #2054C22semidirect
64. #2034C22semidirect
65. #2023C22semidirect
66. #1972C22semidirect
67. #1926C22semidirect
68. #1924C22semidirect
69. #1879C22semidirect
70. #1879C22semidirect
71. #1786C22semidirect
72. #1762C22semidirect
73. C2×#340C22semidirect
74. C2×#340C22semidirect
75. C2×#340C22semidirect
76. C2×#340C22semidirect
77. C2×#336C22semidirect
78. C2×#336C22semidirect
112. C2×C4⋊Q8C23semidirect
157. C2×#106C23semidirect
158. C2×#106C23semidirect
160. C2×C4⋊C8C23semidirect
175. C2×#102C23semidirect
176. C2×#102C23semidirect
182. C2×#97C23semidirect
191. #390C23semidirect
192. #390C23semidirect
202. C4×C4⋊C4C23semidirect
210. #340C23semidirect
211. #340C23semidirect
212. #340C23semidirect
213. #340C23semidirect
214. #336C23semidirect
215. #336C23semidirect
521. C2×D4#124semidirect
740. D4C2×#124semidirect
871. C2#27243direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#4762
C22×#4472
C2×#24912
C2×D4×C22⋊C42
#272432
C2×#20772
C2×#20542
C2×#20342
C2×#20232
C2×#19722
C2×#19262
C2×#19242
C2×#18792
C2×#17862
C2×#17622