Finite Group Databasebeta

← C2×#27240 #6440639

Subgroups — C2×#27240 #6440639

Order 512.

3774 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#478C211yesmaximal, characteristic, complemented
2C22×#447C211yesmaximal, characteristic
3C2×#2490C211yesmaximal, characteristic, complemented
4C2×D4×C22⋊C4C211yesmaximal, characteristic, complemented
5#27240C2116yesmaximal, direct product factor
6C2×#2077C211yesmaximal, characteristic, complemented
7C2×#2054C211yesmaximal, characteristic, complemented
8C2×#2033C211yesmaximal, characteristic, complemented
9C2×#2025C211yesmaximal, characteristic, complemented
10C2×#1972C211yesmaximal, characteristic, complemented
11C2×#1925C211yesmaximal, 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×#125C2211yescharacteristic, complemented
21C22×#121C2211yescharacteristic
22C22×C4×D4C2211yescharacteristic
23C22×C4×D4C2211yescharacteristic
24C23×C22⋊C4—21no—
25C2×#478—28no—
26C2×#478C2218yescomplemented
27C2×#447—28no—
28C2×#447C2218yes—
29C22×#107C2211yescharacteristic, complemented
30C22×#106C2211yescharacteristic, complemented
31C22×C4⋊C8C2211yescharacteristic, complemented
32C22×#102C2211yescharacteristic
33C22×#102C2211yescharacteristic
34C22×#102C2211yescharacteristic
35C22×#102C2211yescharacteristic
36C22×#102C2211yescharacteristic
37C22×#102C2211yescharacteristic
38C22×#102C2211yescharacteristic, complemented
39C22×#102C2211yescharacteristic, complemented
40C22×C22⋊C8C2211yescharacteristic
41C22×C22⋊C8C2211yescharacteristic
42C22×#97C2211yescharacteristic, complemented
43#2490—24no—
44#2490C2218yescomplemented
45C2×#397—21no—
46C2×#394—21no—
47D4×C22⋊C4—24no—
48D4×C22⋊C4C2218yescomplemented
49C2×#390—21no—
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#2033C2218yescomplemented
65#2025C2218yescomplemented
66#1972C2218yescomplemented
67#1925C2218yescomplemented
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×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×C4C2311yescharacteristic
96C22×D8—24no—
97C22×D8—24no—
98C22×D8—24no—
99C22×D8—24no—
100C22×D8—24no—
101C22×D8—42no—
102C22×D8C2314yes—
103C22×D8C2314yes—
104C23×C8C2311yescharacteristic
105C23×C8C2311yescharacteristic
106C23×C8C2311yescharacteristic
107C23×C8C2311yescharacteristic
108C2×#125—24no—
109C2×#125—22no—
110C2×#125—42no—
111C2×#125C2314yescomplemented
112C2×#121—22no—
113C2×#121—24no—
114C2×#121—42no—
115C2×#121C2314yes—
116C2×C4×D4—24no—
117C2×C4×D4—24no—
118C2×C4×D4—22no—
119C2×C4×D4—22no—
120C2×C4×D4—42no—
121C2×C4×D4—42no—
122C2×C4×D4C2314yes—
123C2×C4×D4C2314yes—
124C22×C4⋊C4—21no—
125C22×C4⋊C4—21no—
126C22×C4⋊C4C2311yescharacteristic
127C22×C4⋊C4C2311yescharacteristic
128C22×C4⋊C4C2311yescharacteristic
129C22×C4⋊C4C2311yescharacteristic
130C22×C4⋊C4C2311yescharacteristic
131C22×C22⋊C4—21no—
132C22×C22⋊C4—21no—
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—28no—
145C22×C22⋊C4—48no—
146C22×C22⋊C4D411yescharacteristic
147C22×C22⋊C4D411yescharacteristic
148C22×C42—21no—
149C22×C42C2311yescharacteristic
150C22×C42C2311yescharacteristic
151#478—232no—
152#447—232no—
153C2×#107—24no—
154C2×#107C2314yescomplemented
155C2×#106—24no—
156C2×#106C2314yescomplemented
157C2×C4⋊C8—24no—
158C2×C4⋊C8C2314yescomplemented
159C2×#102—24no—
160C2×#102—24no—
161C2×#102—24no—
162C2×#102—24no—
163C2×#102—42no—
164C2×#102—42no—
165C2×#102—42no—
166C2×#102D418yes—
167C2×#102C2314yes—
168C2×#102C2314yes—
169C2×#102C2314yes—
170C2×#102C2314yes—
171C2×#102C2314yes—
172C2×#102C2314yes—
173C2×#102C2314yescomplemented
174C2×#102C2314yescomplemented
175C2×C22⋊C8—24no—
176C2×C22⋊C8—42no—
177C2×C22⋊C8C2314yes—
178C2×C22⋊C8C2314yes—
179C2×#97—42no—
180C2×#97C2314yescomplemented
181#397—28no—
182#394—28no—
183#390—28no—
184#390—22no—
185#390—22no—
186#390—22no—
187#390—22no—
188#390C2314yes—
189#390C2314yes—
190#390C2314yescomplemented
191#390C2314yescomplemented
192#388—28no—
193#386—28no—
194#386—28no—
195#380—22no—
196#380—22no—
197#380C2314yes—
198#380C2314yes—
199#379—28no—
200C4×C4⋊C4—22no—
201C4×C4⋊C4C2314yescomplemented
202C4×C22⋊C4D414yes—
203C4×C22⋊C4C2314yes—
204C2×#95—21no—
205C2×#95—21no—
206C2×#95—21no—
207C2×#95D411yescharacteristic
208C2×#95D411yescharacteristic
209#340C2314yescomplemented
210#340C2314yescomplemented
211#340C2314yescomplemented
212#340C2314yescomplemented
213#336C2314yescomplemented
214#336C2314yescomplemented
215C25—21no—
216C25—28no—
217C25—21no—
218C25—24no—
219C25—21no—
220C25—44no—
221C25—44no—
222C25—44no—
223C25—44no—
224C25—82no—
225C25—82no—
226C25C2×D411yescharacteristic
227C22×D4—28no—
228C22×D4—216no—
229C22×D4—28no—
230C22×D4—28no—
231C22×D4—28no—
232C22×D4—28no—
233C22×D4—24no—
234C22×D4—21no—
235C22×D4—22no—
236C22×D4—24no—
237C22×D4—21no—
238C22×D4—22no—
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—44no—
259C22×D4—416no—
260C22×D4—416no—
261C22×D4—416no—
262C22×D4—416no—
263C22×D4—44no—
264C22×D4—82no—
265C22×D4C2×D414yes—
266C22×D4#4114yes—
267C22×D4#4114yes—
268C22×D4#4114yes—
269C22×D4C2412yes—
270C22×D4C2412yes—
271C22×D4C2412yes—
272C23×C4—21no—
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—24no—
284C23×C4—24no—
285C23×C4—44no—
286C23×C4—44no—
287C23×C4—44no—
288C23×C4—44no—
289C23×C4—82no—
290C23×C4—82no—
291C23×C4C2×D412yes—
292C23×C4C2×D411yescharacteristic
293C23×C4C2×D411yescharacteristic
294C23×C4C2×D411yescharacteristic
295C23×C4C2×D411yescharacteristic
296C23×C4C2×D411yescharacteristic
297C23×C4C2412yes—
298C23×C4C2411yescharacteristic
299C2×D8—28no—
300C2×D8—28no—
301C2×D8—28no—
302C2×D8—28no—
303C2×D8—28no—
304C2×D8—44no—
305C2×D8—416no—
306C2×D8—416no—
307C22×C8—22no—
308C22×C8—22no—
309C22×C8—22no—
310C22×C8—22no—
311C22×C8—22no—
312C22×C8—22no—
313C22×C8—22no—
314C22×C8—22no—
315C22×C8—22no—
316C22×C8—22no—
317C22×C8—22no—
318C22×C8C2×D414yes—
319C22×C8C2412yes—
320C22×C8C2412yes—
321C22×C8C2412yes—
322C22×C8C2412yes—
323#125—28no—
324#125—44no—
325#125—48no—
326#121—28no—
327#121—44no—
328#121—48no—
329C4×D4—28no—
330C4×D4—28no—
331C4×D4—44no—
332C4×D4—44no—
333C4×D4—48no—
334C4×D4—48no—
335C2×C4⋊C4—21no—
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—22no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—24no—
346C2×C4⋊C4—24no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—44no—
352C2×C4⋊C4—44no—
353C2×C4⋊C4C2×D414yes—
354C2×C4⋊C4C2412yes—
355C2×C4⋊C4C2412yes—
356C2×C4⋊C4C2412yes—
357C2×C4⋊C4C2412yes—
358C2×C4⋊C4C2412yes—
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—24no—
370C2×C22⋊C4—24no—
371C2×C22⋊C4—24no—
372C2×C22⋊C4—24no—
373C2×C22⋊C4—432no—
374C2×C22⋊C4—42no—
375C2×C22⋊C4—44no—
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—82no—
383C2×C22⋊C4—82no—
384C2×C22⋊C4—82no—
385C2×C22⋊C4—82no—
386C2×C22⋊C4—82no—
387C2×C22⋊C4—82no—
388C2×C22⋊C4C2×D414yes—
389C2×C22⋊C4C2×D414yes—
390C2×C42—22no—
391C2×C42—22no—
392C2×C42—22no—
393C2×C42—22no—
394C2×C42—24no—
395C2×C42—82no—
396C2×C42C2×D412yes—
397C2×C42C2×D412yes—
398C2×C42C2412yes—
399C2×C42C2412yes—
400#107—28no—
401#106—28no—
402C4⋊C8—28no—
403#102—28no—
404#102—28no—
405#102—28no—
406#102—28no—
407#102—44no—
408#102—44no—
409#102—44no—
410#102C2×D4116yes—
411C22⋊C8—28no—
412C22⋊C8—44no—
413#97—44no—
414#95—24no—
415#95—24no—
416#95—24no—
417#95C2×D414yes—
418#95C2×D414yes—
419C24—22no—
420C24—24no—
421C24—24no—
422C24—22no—
423C24—24no—
424C24—22no—
425C24—22no—
426C24—22no—
427C24—22no—
428C24—22no—
429C24—216no—
430C24—24no—
431C24—22no—
432C24—22no—
433C24—48no—
434C24—48no—
435C24—432no—
436C24—432no—
437C24—48no—
438C24—42no—
439C24—42no—
440C24—42no—
441C24—42no—
442C24—42no—
443C24—42no—
444C24—48no—
445C24—42no—
446C24—42no—
447C24—42no—
448C24—42no—
449C24—42no—
450C24—42no—
451C24—42no—
452C24—42no—
453C24—42no—
454C24—42no—
455C24—42no—
456C24—84no—
457C24—84no—
458C24—816no—
459C24—816no—
460C24—816no—
461C24—816no—
462C24—816no—
463C24AGL(1,ℤ/8)14yes—
464C24C22×D412yes—
465C24C22×D411yescharacteristic
466C2×D4—216no—
467C2×D4—24no—
468C2×D4—24no—
469C2×D4—28no—
470C2×D4—24no—
471C2×D4—24no—
472C2×D4—28no—
473C2×D4—28no—
474C2×D4—28no—
475C2×D4—28no—
476C2×D4—22no—
477C2×D4—22no—
478C2×D4—22no—
479C2×D4—22no—
480C2×D4—22no—
481C2×D4—22no—
482C2×D4—22no—
483C2×D4—22no—
484C2×D4—22no—
485C2×D4—22no—
486C2×D4—22no—
487C2×D4—22no—
488C2×D4—22no—
489C2×D4—22no—
490C2×D4—48no—
491C2×D4—48no—
492C2×D4—48no—
493C2×D4—416no—
494C2×D4—416no—
495C2×D4—416no—
496C2×D4—464no—
497C2×D4—432no—
498C2×D4—416no—
499C2×D4—48no—
500C2×D4—42no—
501C2×D4—44no—
502C2×D4—44no—
503C2×D4—44no—
504C2×D4—44no—
505C2×D4—42no—
506C2×D4—42no—
507C2×D4—42no—
508C2×D4—44no—
509C2×D4—42no—
510C2×D4—44no—
511C2×D4—84no—
512C2×D4—816no—
513C2×D4#124116yes—
514C2×D4C22×D414yes—
515C2×D4C2×#4114yes—
516C2×D4C2×#4114yes—
517C2×D4C2×#4114yes—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—24no—
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—48no—
549C22×C4—48no—
550C22×C4—48no—
551C22×C4—48no—
552C22×C4—42no—
553C22×C4—42no—
554C22×C4—44no—
555C22×C4—44no—
556C22×C4—44no—
557C22×C4—44no—
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—84no—
571C22×C4—84no—
572C22×C4—816no—
573C22×C4—816no—
574C22×C4C22×D412yes—
575C22×C4C22×D412yes—
576C22×C4C22×D412yes—
577C22×C4C22×D412yes—
578C22×C4C22×D412yes—
579C22×C4C22×D411yescharacteristic
580C22×C4C22×D412yes—
581C22×C4C2×#4112yes—
582C22×C4C2×#4112yes—
583C22×C4C2×#4112yes—
584C22×C4H(5,𝔽2)12yes—
585C22×C4H(5,𝔽2)12yes—
586C22×C4C2511yescharacteristic
587D8—416no—
588D8—416no—
589C2×C8—28no—
590C2×C8—22no—
591C2×C8—22no—
592C2×C8—22no—
593C2×C8—22no—
594C2×C8—22no—
595C2×C8—22no—
596C2×C8—22no—
597C2×C8—22no—
598C2×C8—22no—
599C2×C8—22no—
600C2×C8—22no—
601C2×C8—44no—
602C2×C8—44no—
603C2×C8—44no—
604C2×C8C22×D414yes—
605C4⋊C4—24no—
606C4⋊C4—22no—
607C4⋊C4—22no—
608C4⋊C4—22no—
609C4⋊C4—22no—
610C4⋊C4—22no—
611C4⋊C4—22no—
612C4⋊C4—22no—
613C4⋊C4—22no—
614C4⋊C4—22no—
615C4⋊C4—48no—
616C4⋊C4—48no—
617C4⋊C4—42no—
618C4⋊C4—42no—
619C4⋊C4—42no—
620C4⋊C4—42no—
621C4⋊C4C22×D414yes—
622C22⋊C4—28no—
623C22⋊C4—44no—
624C22⋊C4—48no—
625C22⋊C4—48no—
626C22⋊C4—48no—
627C22⋊C4—48no—
628C22⋊C4—48no—
629C22⋊C4—48no—
630C22⋊C4—48no—
631C22⋊C4—84no—
632C22⋊C4—84no—
633C22⋊C4—84no—
634C22⋊C4—84no—
635C22⋊C4—84no—
636C22⋊C4—84no—
637C42—24no—
638C42—24no—
639C42—22no—
640C42—22no—
641C42—22no—
642C42—22no—
643C42—84no—
644C23—28no—
645C23—22no—
646C23—24no—
647C23—24no—
648C23—22no—
649C23—24no—
650C23—22no—
651C23—216no—
652C23—28no—
653C23—28no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—24no—
658C23—432no—
659C23—432no—
660C23—48no—
661C23—44no—
662C23—48no—
663C23—44no—
664C23—48no—
665C23—44no—
666C23—48no—
667C23—48no—
668C23—44no—
669C23—48no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—48no—
675C23—48no—
676C23—42no—
677C23—42no—
678C23—48no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—816no—
691C23—816no—
692C23—816no—
693C23—816no—
694C23—8128no—
695C23—816no—
696C23—84no—
697C23—84no—
698C23—84no—
699C23—84no—
700C23—84no—
701C23—84no—
702C23—84no—
703C23—84no—
704C23—84no—
705C23—84no—
706C23—84no—
707C23#52512yes—
708C23D4212yes—
709C23#54612yes—
710C23C2×AGL(1,ℤ/8)14yes—
711C23C2×AGL(1,ℤ/8)12yes—
712C23#57512yes—
713C23#57612yes—
714C23#57612yes—
715C23C23×D411yescharacteristic
716D4—24no—
717D4—24no—
718D4—24no—
719D4—24no—
720D4—24no—
721D4—216no—
722D4—432no—
723D4—42no—
724D4—42no—
725D4—42no—
726D4—42no—
727D4—42no—
728D4—42no—
729D4—48no—
730D4—816no—
731D4—84no—
732D4C2×#12418yes—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—24no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—44no—
750C2×C4—44no—
751C2×C4—48no—
752C2×C4—44no—
753C2×C4—44no—
754C2×C4—44no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—48no—
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—816no—
775C2×C4—816no—
776C2×C4—84no—
777C2×C4—84no—
778C2×C4—84no—
779C2×C4—84no—
780C2×C4#52512yes—
781C2×C4C2×#12414yes—
782C2×C4#53814yes—
783C2×C4D4212yes—
784C2×C4#54614yes—
785C2×C4#54612yes—
786C2×C4#55114yes—
787C2×C4C23×D411yescharacteristic
788C2×C4C22×#4111yescharacteristic
789C2×C4C22×#4111yescharacteristic
790C2×C4C22×#4111yescharacteristic
791C2×C4C2×H(5,𝔽2)11yescharacteristic
792C2×C4C2×H(5,𝔽2)11yescharacteristic
793C8—24no—
794C8—42no—
795C8—42no—
796C8—42no—
797C22—24no—
798C22—28no—
799C22—24no—
800C22—24no—
801C22—44no—
802C22—42no—
803C22—42no—
804C22—44no—
805C22—416no—
806C22—432no—
807C22—44no—
808C22—42no—
809C22—44no—
810C22—44no—
811C22—42no—
812C22—44no—
813C22—44no—
814C22—44no—
815C22—44no—
816C22—864no—
817C22—82no—
818C22—82no—
819C22—816no—
820C22—82no—
821C22—82no—
822C22—82no—
823C22—82no—
824C22—82no—
825C22—82no—
826C22—82no—
827C22—82no—
828C22—82no—
829C22—168no—
830C22#247214yes—
831C22#311414yes—
832C22#312214yes—
833C22#326414yes—
834C22#326814yes—
835C22#331814yes—
836C22#332214yes—
837C22C2×#52511yescharacteristic
838C22C2×D4211yescharacteristic
839C22C2×#54611yescharacteristic
840C22C22×AGL(1,ℤ/8)11yescharacteristic
841C22C2×#57511yescharacteristic
842C22C2×#57611yescharacteristic
843C22C2×#57611yescharacteristic
844C4—42no—
845C4—44no—
846C4—42no—
847C4—42no—
848C4—42no—
849C4—42no—
850C4—82no—
851C4—82no—
852C4—82no—
853C4—82no—
854C4#247214yes—
855C4C22×#12411yescharacteristic
856C4C2×#53811yescharacteristic
857C4C2×#54611yescharacteristic
858C4C2×#55111yescharacteristic
859C2—44no—
860C2—48no—
861C2—84no—
862C2—162no—
863C2#2724018yesdirect product factor
864C2C2×#247211yescharacteristic
865C2C2×#311411yescharacteristic
866C2C2×#312211yescharacteristic
867C2C2×#326411yescharacteristic
868C2C2×#326811yescharacteristic
869C2C2×#331811yescharacteristic
870C2C2×#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
1. C22×#478C2semidirect
3. C2×#2490C2semidirect
4. C2×D4×C22⋊C4C2semidirect
5. #27240C2direct (N × H)
6. C2×#2077C2semidirect
7. C2×#2054C2semidirect
8. C2×#2033C2semidirect
9. C2×#2025C2semidirect
10. C2×#1972C2semidirect
11. C2×#1925C2semidirect
12. C2×#1924C2semidirect
13. C2×#1879C2semidirect
14. C2×#1879C2semidirect
15. C2×#1786C2semidirect
16. C2×#1762C2semidirect
20. C22×#125C22semidirect
26. C2×#478C22semidirect
29. C22×#107C22semidirect
30. C22×#106C22semidirect
31. C22×C4⋊C8C22semidirect
38. C22×#102C22semidirect
39. C22×#102C22semidirect
42. C22×#97C22semidirect
44. #2490C22semidirect
48. D4×C22⋊C4C22semidirect
52. C2×#390C22semidirect
53. C2×#390C22semidirect
60. C2×C4×C4⋊C4C22semidirect
62. #2077C22semidirect
63. #2054C22semidirect
64. #2033C22semidirect
65. #2025C22semidirect
66. #1972C22semidirect
67. #1925C22semidirect
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
111. C2×#125C23semidirect
154. C2×#107C23semidirect
156. C2×#106C23semidirect
158. C2×C4⋊C8C23semidirect
173. C2×#102C23semidirect
174. C2×#102C23semidirect
180. C2×#97C23semidirect
190. #390C23semidirect
191. #390C23semidirect
201. C4×C4⋊C4C23semidirect
209. #340C23semidirect
210. #340C23semidirect
211. #340C23semidirect
212. #340C23semidirect
213. #336C23semidirect
214. #336C23semidirect
863. C2#27240direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#4782
C22×#4472
C2×#24902
C2×D4×C22⋊C42
#272402
C2×#20772
C2×#20542
C2×#20332
C2×#20252
C2×#19722
C2×#19252
C2×#19242
C2×#18792
C2×#17862
C2×#17622