Finite Group Databasebeta

← C2×#30444 #7500765

Subgroups — C2×#30444 #7500765

Order 512.

4794 conjugacy classes of subgroups.

The subgroup lattice has 1051 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#493C211yesmaximal, characteristic, complemented
2C22×#459C211yesmaximal, characteristic, complemented
3C22×#447C211yesmaximal, characteristic, complemented
4C22×#447C211yesmaximal, characteristic, complemented
5C2×#2428C211yesmaximal, characteristic, complemented
6C2×#2433C211yesmaximal, characteristic, complemented
7#30444C2116yesmaximal, direct product factor
8C2×#2054C211yesmaximal, characteristic, complemented
9C2×#2041C211yesmaximal, characteristic, complemented
10C2×#2011C211yesmaximal, characteristic, complemented
11C2×#2011C211yesmaximal, characteristic, complemented
12C2×#1999C211yesmaximal, characteristic, complemented
13C2×#1999C211yesmaximal, characteristic, complemented
14C2×#1934C211yesmaximal, characteristic, complemented
15C2×#1923C211yesmaximal, characteristic, complemented
16C2×#1879C211yesmaximal, characteristic, complemented
17C24×D4C2211yescharacteristic
18C23×D8C2211yescharacteristic
19C23×D8C2211yescharacteristic
20C23×D8C2211yescharacteristic
21C23×D8C2211yescharacteristic
22C23×D8C2211yescharacteristic, complemented
23C23×D8C2211yescharacteristic, complemented
24C22×#127C2211yescharacteristic
25C22×#127C2211yescharacteristic
26C22×#127C2211yescharacteristic, complemented
27C22×#121—21no—
28C22×#121C2211yescharacteristic
29C22×#121C2211yescharacteristic
30C22×#121C2211yescharacteristic
31C22×#120—21no—
32C22×#120—21no—
33C22×C4×D4C2211yescharacteristic, complemented
34C2×#493—28no—
35C2×#493C2218yescomplemented
36C2×#459—28no—
37C2×#459C2218yescomplemented
38C2×#447—28no—
39C2×#447—28no—
40C2×#447C2218yescomplemented
41C2×#447C2218yescomplemented
42C22×C4⋊C8C2211yescharacteristic, complemented
43C22×#102C2211yescharacteristic
44C22×#102C2211yescharacteristic
45C22×#102C2211yescharacteristic
46C22×#102C2211yescharacteristic
47C22×#102C2211yescharacteristic, complemented
48C22×#102C2211yescharacteristic, complemented
49C22×#102C2211yescharacteristic, complemented
50C22×#102C2211yescharacteristic, complemented
51C22×C22⋊C8C2211yescharacteristic
52C22×C22⋊C8C2211yescharacteristic
53C22×C4×C8C2211yescharacteristic, complemented
54#2433—24no—
55#2433C2218yescomplemented
56#2428—24no—
57#2428C2218yescomplemented
58C2×#394—21no—
59C2×#392—21no—
60C2×#392—21no—
61C2×#392—21no—
62C2×#390C2211yescharacteristic
63C2×#390C2211yescharacteristic
64C2×#390C2211yescharacteristic, complemented
65C2×#389C2211yescharacteristic, complemented
66C2×#386—21no—
67C2×C4×C22⋊C4C2211yescharacteristic
68#2054C2218yescomplemented
69#2041C2218yescomplemented
70#2011C2218yescomplemented
71#2011C2218yescomplemented
72#1999C2218yescomplemented
73#1999C2218yescomplemented
74#1934C2218yescomplemented
75#1923C2218yescomplemented
76#1879C2218yescomplemented
77C2×#340C2211yescharacteristic, complemented
78C2×#340C2211yescharacteristic, complemented
79C2×#336C2211yescharacteristic, complemented
80C2×#336C2211yescharacteristic, complemented
81C26—21no—
82C23×D4—24no—
83C23×D4—24no—
84C23×D4—21no—
85C23×D4—21no—
86C23×D4—21no—
87C23×D4—21no—
88C23×D4—22no—
89C23×D4—21no—
90C23×D4—21no—
91C23×D4—21no—
92C23×D4—21no—
93C23×D4—21no—
94C23×D4—21no—
95C23×D4—42no—
96C23×D4—42no—
97C23×D4—42no—
98C23×D4—42no—
99C23×D4C2311yescharacteristic
100C23×D4C2311yescharacteristic
101C23×D4C2311yescharacteristic
102C23×D4C2311yescharacteristic
103C23×D4C2311yescharacteristic
104C23×D4C2314yes—
105C24×C4—21no—
106C24×C4C2311yescharacteristic
107C22×D8—24no—
108C22×D8—24no—
109C22×D8—24no—
110C22×D8—24no—
111C22×D8—24no—
112C22×D8—24no—
113C22×D8—24no—
114C22×D8—24no—
115C22×D8—42no—
116C22×D8—42no—
117C22×D8—42no—
118C22×D8—42no—
119C22×D8—42no—
120C22×D8—42no—
121C22×D8—42no—
122C22×D8—42no—
123C22×D8—42no—
124C22×D8D418yescomplemented
125C22×D8C2314yes—
126C22×D8C2314yes—
127C22×D8C2314yes—
128C22×D8C2314yes—
129C22×D8C2314yescomplemented
130C22×D8C2314yescomplemented
131C23×C8C2311yescharacteristic
132C23×C8C2311yescharacteristic
133C23×C8C2311yescharacteristic
134C23×C8C2311yescharacteristic
135C2×#127—24no—
136C2×#127—24no—
137C2×#127—24no—
138C2×#127—22no—
139C2×#127—22no—
140C2×#127—22no—
141C2×#127—42no—
142C2×#127—42no—
143C2×#127—42no—
144C2×#127C2314yes—
145C2×#127C2314yes—
146C2×#127C2314yescomplemented
147C2×#121—22no—
148C2×#121—22no—
149C2×#121—22no—
150C2×#121—28no—
151C2×#121—24no—
152C2×#121—24no—
153C2×#121—42no—
154C2×#121—42no—
155C2×#121—42no—
156C2×#121—42no—
157C2×#121—48no—
158C2×#121C2314yes—
159C2×#121C2314yes—
160C2×#121C2314yes—
161C2×#120—28no—
162C2×#120—28no—
163C2×#120—48no—
164C2×#120—48no—
165C2×C4×D4—24no—
166C2×C4×D4—22no—
167C2×C4×D4—42no—
168C2×C4×D4C2314yescomplemented
169C22×C4⋊C4—21no—
170C22×C4⋊C4C2311yescharacteristic
171C22×C4⋊C4C2311yescharacteristic
172C22×C4⋊C4C2311yescharacteristic
173C22×C22⋊C4—21no—
174C22×C22⋊C4—21no—
175C22×C22⋊C4—21no—
176C22×C22⋊C4—21no—
177C22×C22⋊C4—21no—
178C22×C22⋊C4—21no—
179C22×C22⋊C4—21no—
180C22×C22⋊C4—21no—
181C22×C22⋊C4—21no—
182C22×C22⋊C4—21no—
183C22×C22⋊C4D411yescharacteristic
184C22×C22⋊C4D411yescharacteristic
185C22×C42C2311yescharacteristic
186C22×C42C2311yescharacteristic
187#493—232no—
188#459—232no—
189#447—232no—
190#447—232no—
191C2×C4⋊C8—24no—
192C2×C4⋊C8C2314yescomplemented
193C2×#102—24no—
194C2×#102—24no—
195C2×#102—24no—
196C2×#102—24no—
197C2×#102—42no—
198C2×#102—42no—
199C2×#102—42no—
200C2×#102D418yescomplemented
201C2×#102C2314yes—
202C2×#102C2314yes—
203C2×#102C2314yes—
204C2×#102C2314yes—
205C2×#102C2314yescomplemented
206C2×#102C2314yescomplemented
207C2×#102C2314yescomplemented
208C2×#102C2314yescomplemented
209C2×C22⋊C8—24no—
210C2×C22⋊C8—24no—
211C2×C22⋊C8C2314yes—
212C2×C22⋊C8C2314yes—
213C2×C4×C8—24no—
214C2×C4×C8C2314yescomplemented
215#394—28no—
216#392—28no—
217#392—28no—
218#392—28no—
219#390—22no—
220#390—22no—
221#390—22no—
222#390C2314yes—
223#390C2314yes—
224#390C2314yescomplemented
225#389—22no—
226#389C2314yescomplemented
227#386—28no—
228C4×C22⋊C4D414yes—
229C4×C22⋊C4C2314yes—
230C2×#95—21no—
231C2×#95D411yescharacteristic
232C2×#95D411yescharacteristic
233#340C2314yescomplemented
234#340C2314yescomplemented
235#336C2314yescomplemented
236#336C2314yescomplemented
237C25—21no—
238C25—21no—
239C25—21no—
240C25—21no—
241C25—21no—
242C25—24no—
243C25—44no—
244C25—44no—
245C25—44no—
246C25—44no—
247C25—44no—
248C25—82no—
249C25—82no—
250C25C2×D411yescharacteristic
251C22×D4—28no—
252C22×D4—28no—
253C22×D4—24no—
254C22×D4—24no—
255C22×D4—24no—
256C22×D4—22no—
257C22×D4—22no—
258C22×D4—22no—
259C22×D4—21no—
260C22×D4—21no—
261C22×D4—21no—
262C22×D4—22no—
263C22×D4—22no—
264C22×D4—22no—
265C22×D4—22no—
266C22×D4—21no—
267C22×D4—21no—
268C22×D4—24no—
269C22×D4—24no—
270C22×D4—24no—
271C22×D4—24no—
272C22×D4—24no—
273C22×D4—24no—
274C22×D4—24no—
275C22×D4—22no—
276C22×D4—22no—
277C22×D4—22no—
278C22×D4—22no—
279C22×D4—22no—
280C22×D4—22no—
281C22×D4—22no—
282C22×D4—22no—
283C22×D4—22no—
284C22×D4—22no—
285C22×D4—22no—
286C22×D4—22no—
287C22×D4—22no—
288C22×D4—22no—
289C22×D4—22no—
290C22×D4—22no—
291C22×D4—22no—
292C22×D4—22no—
293C22×D4—22no—
294C22×D4—22no—
295C22×D4—44no—
296C22×D4—44no—
297C22×D4—44no—
298C22×D4—44no—
299C22×D4—48no—
300C22×D4—48no—
301C22×D4—44no—
302C22×D4—44no—
303C22×D4—44no—
304C22×D4—48no—
305C22×D4—44no—
306C22×D4—44no—
307C22×D4—44no—
308C22×D4—44no—
309C22×D4—44no—
310C22×D4—44no—
311C22×D4—44no—
312C22×D4—44no—
313C22×D4—416no—
314C22×D4—416no—
315C22×D4—416no—
316C22×D4—416no—
317C22×D4—44no—
318C22×D4—44no—
319C22×D4—44no—
320C22×D4—44no—
321C22×D4—44no—
322C22×D4—44no—
323C22×D4—44no—
324C22×D4—44no—
325C22×D4—44no—
326C22×D4—44no—
327C22×D4—44no—
328C22×D4—82no—
329C22×D4—82no—
330C22×D4—82no—
331C22×D4—82no—
332C22×D4—82no—
333C22×D4—82no—
334C22×D4—82no—
335C22×D4—82no—
336C22×D4C2×D414yes—
337C22×D4C2×D414yes—
338C22×D4C2×D414yes—
339C22×D4C2412yes—
340C22×D4C2412yes—
341C22×D4C2412yes—
342C22×D4C2412yes—
343C22×D4C2412yes—
344C23×C4—21no—
345C23×C4—22no—
346C23×C4—22no—
347C23×C4—22no—
348C23×C4—22no—
349C23×C4—22no—
350C23×C4—22no—
351C23×C4—21no—
352C23×C4—21no—
353C23×C4—24no—
354C23×C4—44no—
355C23×C4—44no—
356C23×C4—82no—
357C23×C4C2×D412yes—
358C23×C4C2×D411yescharacteristic
359C23×C4C2×D411yescharacteristic
360C23×C4C2×D411yescharacteristic
361C23×C4C2×D411yescharacteristic
362C23×C4C2×D411yescharacteristic
363C23×C4C2412yes—
364C23×C4C2411yescharacteristic
365C2×D8—28no—
366C2×D8—28no—
367C2×D8—28no—
368C2×D8—28no—
369C2×D8—28no—
370C2×D8—28no—
371C2×D8—28no—
372C2×D8—28no—
373C2×D8—416no—
374C2×D8—44no—
375C2×D8—44no—
376C2×D8—44no—
377C2×D8—44no—
378C2×D8—44no—
379C2×D8—44no—
380C2×D8—44no—
381C2×D8—44no—
382C2×D8—44no—
383C2×D8—416no—
384C2×D8—416no—
385C2×D8—416no—
386C2×D8—416no—
387C2×D8—416no—
388C2×D8C2×D4116yescomplemented
389C22×C8—22no—
390C22×C8—22no—
391C22×C8—22no—
392C22×C8—22no—
393C22×C8—22no—
394C22×C8—22no—
395C22×C8—22no—
396C22×C8—22no—
397C22×C8—22no—
398C22×C8—22no—
399C22×C8C2×D414yes—
400C22×C8C2×D414yes—
401C22×C8C2412yes—
402C22×C8C2412yes—
403C22×C8C2412yes—
404C22×C8C2412yes—
405#127—28no—
406#127—28no—
407#127—28no—
408#127—44no—
409#127—44no—
410#127—44no—
411#127—48no—
412#127—48no—
413#127—48no—
414#121—28no—
415#121—28no—
416#121—44no—
417#121—44no—
418#121—44no—
419#121—44no—
420#121—48no—
421#121—48no—
422#121—48no—
423#121—432no—
424#120—432no—
425#120—432no—
426C4×D4—28no—
427C4×D4—44no—
428C4×D4—48no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—22no—
431C2×C4⋊C4—22no—
432C2×C4⋊C4—22no—
433C2×C4⋊C4—22no—
434C2×C4⋊C4—22no—
435C2×C4⋊C4—24no—
436C2×C4⋊C4—21no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4—44no—
439C2×C4⋊C4C2×D414yes—
440C2×C4⋊C4C2412yes—
441C2×C4⋊C4C2412yes—
442C2×C4⋊C4C2412yes—
443C2×C22⋊C4—24no—
444C2×C22⋊C4—24no—
445C2×C22⋊C4—24no—
446C2×C22⋊C4—24no—
447C2×C22⋊C4—24no—
448C2×C22⋊C4—24no—
449C2×C22⋊C4—24no—
450C2×C22⋊C4—24no—
451C2×C22⋊C4—24no—
452C2×C22⋊C4—24no—
453C2×C22⋊C4—24no—
454C2×C22⋊C4—44no—
455C2×C22⋊C4—44no—
456C2×C22⋊C4—44no—
457C2×C22⋊C4—44no—
458C2×C22⋊C4—44no—
459C2×C22⋊C4—44no—
460C2×C22⋊C4—44no—
461C2×C22⋊C4—44no—
462C2×C22⋊C4—44no—
463C2×C22⋊C4—82no—
464C2×C22⋊C4D818yescomplemented
465C2×C22⋊C4C2×D414yes—
466C2×C22⋊C4C2×D414yes—
467C2×C42—22no—
468C2×C42—22no—
469C2×C42—22no—
470C2×C42—22no—
471C2×C42C2×D412yes—
472C2×C42C2×D412yes—
473C2×C42C2412yes—
474C2×C42C2412yes—
475C4⋊C8—28no—
476#102—28no—
477#102—28no—
478#102—28no—
479#102—28no—
480#102—44no—
481#102—44no—
482#102—44no—
483#102C2×D4116yescomplemented
484C22⋊C8—28no—
485C22⋊C8—28no—
486C4×C8—28no—
487#95—24no—
488#95C2×D414yes—
489#95C2×D414yes—
490C24—22no—
491C24—22no—
492C24—22no—
493C24—22no—
494C24—22no—
495C24—22no—
496C24—24no—
497C24—24no—
498C24—24no—
499C24—22no—
500C24—22no—
501C24—22no—
502C24—22no—
503C24—22no—
504C24—48no—
505C24—48no—
506C24—48no—
507C24—48no—
508C24—432no—
509C24—42no—
510C24—42no—
511C24—42no—
512C24—42no—
513C24—42no—
514C24—42no—
515C24—42no—
516C24—42no—
517C24—42no—
518C24—42no—
519C24—42no—
520C24—42no—
521C24—42no—
522C24—42no—
523C24—42no—
524C24—42no—
525C24—42no—
526C24—42no—
527C24—42no—
528C24—42no—
529C24—42no—
530C24—42no—
531C24—42no—
532C24—42no—
533C24—42no—
534C24—48no—
535C24—42no—
536C24—42no—
537C24—42no—
538C24—42no—
539C24—42no—
540C24—42no—
541C24—42no—
542C24—84no—
543C24—84no—
544C24—816no—
545C24—816no—
546C24—816no—
547C24—816no—
548C24—816no—
549C24—816no—
550C24C2×D814yes—
551C24C22×D412yes—
552C24C22×D411yescharacteristic
553C2×D4—28no—
554C2×D4—28no—
555C2×D4—28no—
556C2×D4—28no—
557C2×D4—28no—
558C2×D4—28no—
559C2×D4—24no—
560C2×D4—24no—
561C2×D4—24no—
562C2×D4—22no—
563C2×D4—22no—
564C2×D4—22no—
565C2×D4—22no—
566C2×D4—22no—
567C2×D4—22no—
568C2×D4—22no—
569C2×D4—22no—
570C2×D4—22no—
571C2×D4—22no—
572C2×D4—22no—
573C2×D4—22no—
574C2×D4—22no—
575C2×D4—22no—
576C2×D4—22no—
577C2×D4—22no—
578C2×D4—22no—
579C2×D4—22no—
580C2×D4—22no—
581C2×D4—22no—
582C2×D4—22no—
583C2×D4—22no—
584C2×D4—22no—
585C2×D4—22no—
586C2×D4—22no—
587C2×D4—22no—
588C2×D4—22no—
589C2×D4—48no—
590C2×D4—48no—
591C2×D4—48no—
592C2×D4—48no—
593C2×D4—48no—
594C2×D4—48no—
595C2×D4—48no—
596C2×D4—48no—
597C2×D4—48no—
598C2×D4—48no—
599C2×D4—48no—
600C2×D4—416no—
601C2×D4—416no—
602C2×D4—416no—
603C2×D4—432no—
604C2×D4—464no—
605C2×D4—416no—
606C2×D4—48no—
607C2×D4—48no—
608C2×D4—48no—
609C2×D4—48no—
610C2×D4—48no—
611C2×D4—48no—
612C2×D4—44no—
613C2×D4—44no—
614C2×D4—44no—
615C2×D4—42no—
616C2×D4—44no—
617C2×D4—42no—
618C2×D4—42no—
619C2×D4—44no—
620C2×D4—44no—
621C2×D4—44no—
622C2×D4—42no—
623C2×D4—42no—
624C2×D4—42no—
625C2×D4—42no—
626C2×D4—42no—
627C2×D4—44no—
628C2×D4—44no—
629C2×D4—42no—
630C2×D4—42no—
631C2×D4—42no—
632C2×D4—42no—
633C2×D4—44no—
634C2×D4—44no—
635C2×D4—44no—
636C2×D4—44no—
637C2×D4—44no—
638C2×D4—48no—
639C2×D4—48no—
640C2×D4—48no—
641C2×D4—48no—
642C2×D4—48no—
643C2×D4—84no—
644C2×D4—84no—
645C2×D4—84no—
646C2×D4—84no—
647C2×D4—84no—
648C2×D4—84no—
649C2×D4—816no—
650C2×D4—816no—
651C2×D4—816no—
652C2×D4—816no—
653C2×D4—816no—
654C2×D4—84no—
655C2×D4—84no—
656C2×D4—816no—
657C2×D4—816no—
658C2×D4—816no—
659C2×D4—816no—
660C2×D4C22×D414yes—
661C2×D4C22×D414yes—
662C2×D4C22×D414yes—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—22no—
670C22×C4—22no—
671C22×C4—24no—
672C22×C4—22no—
673C22×C4—22no—
674C22×C4—22no—
675C22×C4—22no—
676C22×C4—22no—
677C22×C4—24no—
678C22×C4—24no—
679C22×C4—24no—
680C22×C4—22no—
681C22×C4—22no—
682C22×C4—22no—
683C22×C4—22no—
684C22×C4—22no—
685C22×C4—22no—
686C22×C4—22no—
687C22×C4—22no—
688C22×C4—48no—
689C22×C4—42no—
690C22×C4—42no—
691C22×C4—44no—
692C22×C4—44no—
693C22×C4—44no—
694C22×C4—44no—
695C22×C4—42no—
696C22×C4—42no—
697C22×C4—42no—
698C22×C4—42no—
699C22×C4—42no—
700C22×C4—42no—
701C22×C4—48no—
702C22×C4—84no—
703C22×C4—816no—
704C22×C4C2×D814yes—
705C22×C4C2×D814yes—
706C22×C4AGL(1,ℤ/8)14yes—
707C22×C4C22×D412yes—
708C22×C4C22×D412yes—
709C22×C4C22×D412yes—
710C22×C4C22×D412yes—
711C22×C4C22×D412yes—
712C22×C4C22×D412yes—
713C22×C4C22×D411yescharacteristic
714C22×C4C22×D412yes—
715C22×C4H(5,𝔽2)12yes—
716C22×C4H(5,𝔽2)12yes—
717C22×C4H(5,𝔽2)12yes—
718C22×C4H(5,𝔽2)12yes—
719C22×C4C2511yescharacteristic
720D8—416no—
721D8—416no—
722D8—416no—
723D8—416no—
724D8—416no—
725D8—416no—
726C2×C8—28no—
727C2×C8—28no—
728C2×C8—22no—
729C2×C8—22no—
730C2×C8—22no—
731C2×C8—22no—
732C2×C8—22no—
733C2×C8—22no—
734C2×C8—22no—
735C2×C8—22no—
736C2×C8—22no—
737C2×C8—22no—
738C2×C8—44no—
739C2×C8—44no—
740C2×C8C22×D414yes—
741C2×C8C22×D414yes—
742C4⋊C4—24no—
743C4⋊C4—22no—
744C4⋊C4—22no—
745C4⋊C4—22no—
746C4⋊C4—22no—
747C4⋊C4—22no—
748C4⋊C4—42no—
749C4⋊C4—42no—
750C4⋊C4—48no—
751C4⋊C4C22×D414yes—
752C22⋊C4—28no—
753C22⋊C4—48no—
754C22⋊C4—48no—
755C22⋊C4—48no—
756C22⋊C4—48no—
757C22⋊C4—48no—
758C22⋊C4—48no—
759C22⋊C4—48no—
760C22⋊C4—48no—
761C22⋊C4—48no—
762C22⋊C4—84no—
763C22⋊C4C2×D8116yescomplemented
764C42—24no—
765C42—24no—
766C42—22no—
767C42—22no—
768C42—22no—
769C42—22no—
770C23—22no—
771C23—28no—
772C23—22no—
773C23—22no—
774C23—28no—
775C23—28no—
776C23—22no—
777C23—22no—
778C23—22no—
779C23—24no—
780C23—24no—
781C23—24no—
782C23—44no—
783C23—44no—
784C23—44no—
785C23—44no—
786C23—432no—
787C23—48no—
788C23—48no—
789C23—48no—
790C23—42no—
791C23—42no—
792C23—42no—
793C23—42no—
794C23—42no—
795C23—42no—
796C23—48no—
797C23—48no—
798C23—48no—
799C23—48no—
800C23—48no—
801C23—48no—
802C23—42no—
803C23—42no—
804C23—42no—
805C23—42no—
806C23—42no—
807C23—42no—
808C23—42no—
809C23—42no—
810C23—42no—
811C23—42no—
812C23—42no—
813C23—42no—
814C23—42no—
815C23—42no—
816C23—42no—
817C23—42no—
818C23—42no—
819C23—42no—
820C23—42no—
821C23—42no—
822C23—42no—
823C23—42no—
824C23—42no—
825C23—42no—
826C23—42no—
827C23—42no—
828C23—816no—
829C23—816no—
830C23—816no—
831C23—816no—
832C23—816no—
833C23—816no—
834C23—8128no—
835C23—84no—
836C23—84no—
837C23—84no—
838C23—84no—
839C23—84no—
840C23—84no—
841C23—84no—
842C23—84no—
843C23—84no—
844C23—84no—
845C23—84no—
846C23—84no—
847C23—84no—
848C23—84no—
849C23—84no—
850C23—84no—
851C23—84no—
852C23—84no—
853C23—84no—
854C23—84no—
855C23—84no—
856C23—84no—
857C23—84no—
858C23—84no—
859C23—84no—
860C23—84no—
861C23#53512yes—
862C23D4212yes—
863C23D4212yes—
864C23C22×D814yes—
865C23C22×D812yes—
866C23C2×AGL(1,ℤ/8)12yes—
867C23#57612yes—
868C23#57612yes—
869C23C23×D411yescharacteristic
870D4—24no—
871D4—24no—
872D4—24no—
873D4—24no—
874D4—24no—
875D4—24no—
876D4—432no—
877D4—48no—
878D4—48no—
879D4—48no—
880D4—42no—
881D4—42no—
882D4—42no—
883D4—42no—
884D4—42no—
885D4—42no—
886D4—42no—
887D4—42no—
888D4—42no—
889D4—42no—
890D4—42no—
891D4—42no—
892D4—42no—
893D4—42no—
894D4—816no—
895D4—816no—
896D4—816no—
897D4—816no—
898D4—816no—
899D4—816no—
900D4—816no—
901D4—816no—
902D4—816no—
903D4—84no—
904D4—84no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—28no—
909C2×C4—28no—
910C2×C4—28no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—24no—
917C2×C4—22no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—44no—
922C2×C4—44no—
923C2×C4—48no—
924C2×C4—42no—
925C2×C4—42no—
926C2×C4—48no—
927C2×C4—42no—
928C2×C4—42no—
929C2×C4—42no—
930C2×C4—42no—
931C2×C4—42no—
932C2×C4—42no—
933C2×C4—42no—
934C2×C4—42no—
935C2×C4—42no—
936C2×C4—42no—
937C2×C4—816no—
938C2×C4—84no—
939C2×C4—84no—
940C2×C4#53414yes—
941C2×C4#53512yes—
942C2×C4#53514yes—
943C2×C4D4212yes—
944C2×C4D4212yes—
945C2×C4D4214yes—
946C2×C4#56014yes—
947C2×C4C22×D814yes—
948C2×C4C22×D814yes—
949C2×C4C2×AGL(1,ℤ/8)14yes—
950C2×C4C23×D411yescharacteristic
951C2×C4C23×D411yescharacteristic
952C2×C4C2×H(5,𝔽2)11yescharacteristic
953C2×C4C2×H(5,𝔽2)11yescharacteristic
954C2×C4C2×H(5,𝔽2)11yescharacteristic
955C2×C4C2×H(5,𝔽2)11yescharacteristic
956C8—24no—
957C8—24no—
958C8—42no—
959C8—42no—
960C22—24no—
961C22—24no—
962C22—24no—
963C22—42no—
964C22—42no—
965C22—42no—
966C22—42no—
967C22—416no—
968C22—44no—
969C22—44no—
970C22—44no—
971C22—44no—
972C22—44no—
973C22—44no—
974C22—44no—
975C22—44no—
976C22—44no—
977C22—864no—
978C22—82no—
979C22—82no—
980C22—82no—
981C22—82no—
982C22—82no—
983C22—82no—
984C22—82no—
985C22—82no—
986C22—82no—
987C22—82no—
988C22—82no—
989C22—82no—
990C22—816no—
991C22—816no—
992C22—816no—
993C22—82no—
994C22—82no—
995C22—82no—
996C22—82no—
997C22—82no—
998C22—82no—
999C22—82no—
1000C22—82no—
1001C22—82no—
1002C22—82no—
1003C22—82no—
1004C22—82no—
1005C22—82no—
1006C22—82no—
1007C22—168no—
1008C22—168no—
1009C22#266914yes—
1010C22#320514yes—
1011C22#322014yes—
1012C22#326414yes—
1013C22#327414yes—
1014C22D4×D814yes—
1015C22D4×D814yes—
1016C22C2×#53511yescharacteristic
1017C22C2×D4211yescharacteristic
1018C22C2×D4211yescharacteristic
1019C22C23×D811yescharacteristic
1020C22C22×AGL(1,ℤ/8)11yescharacteristic
1021C22C2×#57611yescharacteristic
1022C22C2×#57611yescharacteristic
1023C4—24no—
1024C4—24no—
1025C4—24no—
1026C4—42no—
1027C4—44no—
1028C4—42no—
1029C4—82no—
1030C4—82no—
1031C4#266914yes—
1032C4C2×#53411yescharacteristic
1033C4C2×#53511yescharacteristic
1034C4C2×D4211yescharacteristic
1035C4C2×#56011yescharacteristic
1036C2—44no—
1037C2—84no—
1038C2—84no—
1039C2—84no—
1040C2—162no—
1041C2—162no—
1042C2#3044418yesdirect product factor
1043C2C2×#266911yescharacteristic
1044C2C2×#320511yescharacteristic
1045C2C2×#322011yescharacteristic
1046C2C2×#326411yescharacteristic
1047C2C2×#327411yescharacteristic
1048C2C2×D4×D811yescharacteristic
1049C2C2×D4×D811yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC22×C4C25
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×#493C2semidirect
2. C22×#459C2semidirect
3. C22×#447C2semidirect
4. C22×#447C2semidirect
5. C2×#2428C2semidirect
6. C2×#2433C2semidirect
7. #30444C2direct (N × H)
8. C2×#2054C2semidirect
9. C2×#2041C2semidirect
10. C2×#2011C2semidirect
11. C2×#2011C2semidirect
12. C2×#1999C2semidirect
13. C2×#1999C2semidirect
14. C2×#1934C2semidirect
15. C2×#1923C2semidirect
16. C2×#1879C2semidirect
22. C23×D8C22semidirect
23. C23×D8C22semidirect
26. C22×#127C22semidirect
33. C22×C4×D4C22semidirect
35. C2×#493C22semidirect
37. C2×#459C22semidirect
40. C2×#447C22semidirect
41. C2×#447C22semidirect
42. C22×C4⋊C8C22semidirect
47. C22×#102C22semidirect
48. C22×#102C22semidirect
49. C22×#102C22semidirect
50. C22×#102C22semidirect
53. C22×C4×C8C22semidirect
55. #2433C22semidirect
57. #2428C22semidirect
64. C2×#390C22semidirect
65. C2×#389C22semidirect
68. #2054C22semidirect
69. #2041C22semidirect
70. #2011C22semidirect
71. #2011C22semidirect
72. #1999C22semidirect
73. #1999C22semidirect
74. #1934C22semidirect
75. #1923C22semidirect
76. #1879C22semidirect
77. C2×#340C22semidirect
78. C2×#340C22semidirect
79. C2×#336C22semidirect
80. C2×#336C22semidirect
124. C22×D8D4semidirect
129. C22×D8C23semidirect
130. C22×D8C23semidirect
146. C2×#127C23semidirect
168. C2×C4×D4C23semidirect
192. C2×C4⋊C8C23semidirect
200. C2×#102D4semidirect
205. C2×#102C23semidirect
206. C2×#102C23semidirect
207. C2×#102C23semidirect
208. C2×#102C23semidirect
214. C2×C4×C8C23semidirect
224. #390C23semidirect
226. #389C23semidirect
233. #340C23semidirect
234. #340C23semidirect
235. #336C23semidirect
236. #336C23semidirect
388. C2×D8C2×D4semidirect
464. C2×C22⋊C4D8semidirect
483. #102C2×D4semidirect
763. C22⋊C4C2×D8semidirect
1042. C2#30444direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#4932
C22×#4592
C22×#4472
C2×#24282
C2×#24332
#304442
C2×#20542
C2×#20412
C2×#20112
C2×#19992
C2×#19342
C2×#19232
C2×#18792