Finite Group Databasebeta

← C2×#31266 #7504242

Subgroups — C2×#31266 #7504242

Order 512.

3360 conjugacy classes of subgroups.

The subgroup lattice has 856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2562C211yesmaximal, characteristic, complemented
2C2×#2408C211yesmaximal, characteristic
3#31266C2116yesmaximal, direct product factor
4C2×#2076C211yesmaximal, characteristic, complemented
5C2×#2077C211yesmaximal, characteristic, complemented
6C2×#2034C211yesmaximal, characteristic, complemented
7C2×#2033C211yesmaximal, characteristic, complemented
8C2×#2025C211yesmaximal, characteristic, complemented
9C2×#2025C211yesmaximal, characteristic, complemented
10C2×#1926C211yesmaximal, characteristic, complemented
11C2×#1925C211yesmaximal, characteristic, complemented
12C2×#1893C211yesmaximal, characteristic, complemented
13C2×#1893C211yesmaximal, characteristic, complemented
14C2×#1869C211yesmaximal, characteristic, complemented
15C2×#1786C211yesmaximal, characteristic, complemented
16C2×#1786C211yesmaximal, characteristic, complemented
17C24×D4C2211yescharacteristic
18C24×C8C2211yescharacteristic, complemented
19C22×#125C2211yescharacteristic, complemented
20C22×#121C2211yescharacteristic
21C22×#121C2211yescharacteristic
22C22×#120—21no—
23C22×C4×D4C2211yescharacteristic
24C22×#107C2211yescharacteristic, complemented
25C22×#106C2211yescharacteristic, complemented
26C22×#102C2211yescharacteristic
27C22×#102C2211yescharacteristic
28C22×#102C2211yescharacteristic
29C22×#102C2211yescharacteristic
30C22×#102C2211yescharacteristic
31C22×#102C2211yescharacteristic
32C22×#102C2211yescharacteristic
33C22×#102C2211yescharacteristic
34C22×C22⋊C8C2211yescharacteristic
35C22×C22⋊C8C2211yescharacteristic
36C22×C22⋊C8C2211yescharacteristic, complemented
37#2562—24no—
38#2562C2218yescomplemented
39#2408—24no—
40#2408C2218yes—
41C2×#400—21no—
42C2×#394—21no—
43C2×#394—21no—
44C2×#392—21no—
45C2×#390C2211yescharacteristic
46C2×#390C2211yescharacteristic
47C2×#388—21no—
48C2×#388—21no—
49C2×#380C2211yescharacteristic
50C2×#380C2211yescharacteristic
51C2×#380C2211yescharacteristic
52C2×#380C2211yescharacteristic, complemented
53C2×#380C2211yescharacteristic, complemented
54C2×#379—21no—
55C2×C4×C4⋊C4C2211yescharacteristic, complemented
56#2077C2218yescomplemented
57#2076C2218yescomplemented
58#2034C2218yescomplemented
59#2033C2218yescomplemented
60#2025C2218yescomplemented
61#2025C2218yescomplemented
62#1926C2218yescomplemented
63#1925C2218yescomplemented
64#1893C2218yescomplemented
65#1893C2218yescomplemented
66#1869C2218yescomplemented
67#1786C2218yescomplemented
68#1786C2218yescomplemented
69C2×#340C2211yescharacteristic, complemented
70C2×#340C2211yescharacteristic, complemented
71C2×#340C2211yescharacteristic, complemented
72C2×#340C2211yescharacteristic, complemented
73C2×#340C2211yescharacteristic, complemented
74C2×#340C2211yescharacteristic, complemented
75C2×#336C2211yescharacteristic, complemented
76C2×#336C2211yescharacteristic, complemented
77C26—21no—
78C23×D4—24no—
79C23×D4—24no—
80C23×D4—21no—
81C23×D4—21no—
82C23×D4—21no—
83C23×D4—22no—
84C23×D4—42no—
85C23×D4—42no—
86C23×D4—42no—
87C23×D4—42no—
88C23×D4D411yescharacteristic
89C23×D4C2311yescharacteristic
90C23×D4C2311yescharacteristic
91C23×D4C2314yes—
92C24×C4C2311yescharacteristic
93C24×C4C2311yescharacteristic
94C23×C8—42no—
95C23×C8—42no—
96C23×C8—42no—
97C23×C8C2311yescharacteristic
98C23×C8C2311yescharacteristic
99C23×C8C2311yescharacteristic
100C23×C8C2311yescharacteristic
101C23×C8C2314yescomplemented
102C2×#125—22no—
103C2×#125—42no—
104C2×#125—42no—
105C2×#125C2314yescomplemented
106C2×#121—22no—
107C2×#121—22no—
108C2×#121—24no—
109C2×#121—24no—
110C2×#121—42no—
111C2×#121—42no—
112C2×#121C2314yes—
113C2×#121C2314yes—
114C2×#120—28no—
115C2×#120—48no—
116C2×C4×D4—42no—
117C2×C4×D4—42no—
118C2×C4×D4D414yes—
119C2×C4×D4C2314yes—
120C22×C4⋊C4—21no—
121C22×C4⋊C4—21no—
122C22×C4⋊C4D411yescharacteristic
123C22×C4⋊C4C2311yescharacteristic
124C22×C4⋊C4C2311yescharacteristic
125C22×C4⋊C4C2311yescharacteristic
126C22×C4⋊C4C2311yescharacteristic
127C22×C4⋊C4C2311yescharacteristic
128C22×C4⋊C4C2311yescharacteristic
129C22×C22⋊C4—21no—
130C22×C22⋊C4—21no—
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⋊C4D411yescharacteristic
141C22×C22⋊C4D411yescharacteristic
142C22×C42—21no—
143C22×C42C2311yescharacteristic
144C2×#107—42no—
145C2×#107C2314yescomplemented
146C2×#106—42no—
147C2×#106C2314yescomplemented
148C2×#102—24no—
149C2×#102—24no—
150C2×#102—42no—
151C2×#102—42no—
152C2×#102—42no—
153C2×#102—42no—
154C2×#102—42no—
155C2×#102—42no—
156C2×#102C2314yes—
157C2×#102C2314yes—
158C2×#102C2314yes—
159C2×#102C2314yes—
160C2×#102C2314yes—
161C2×#102C2314yes—
162C2×#102C2314yes—
163C2×#102C2314yes—
164C2×C22⋊C8—42no—
165C2×C22⋊C8—42no—
166C2×C22⋊C8—42no—
167C2×C22⋊C8C2314yes—
168C2×C22⋊C8C2314yes—
169C2×C22⋊C8C2314yescomplemented
170#400—28no—
171#394—28no—
172#394—28no—
173#392—28no—
174#390—22no—
175#390—22no—
176#390C2314yes—
177#390C2314yes—
178#388—28no—
179#388—28no—
180#380—22no—
181#380—22no—
182#380—22no—
183#380—22no—
184#380—22no—
185#380C2314yes—
186#380C2314yes—
187#380C2314yes—
188#380C2314yescomplemented
189#380C2314yescomplemented
190#379—28no—
191C4×C4⋊C4—22no—
192C4×C4⋊C4C2314yescomplemented
193C2×#95—21no—
194C2×#95—21no—
195C2×#95—21no—
196C2×#95—21no—
197C2×#95—21no—
198C2×#95—21no—
199#340C2314yescomplemented
200#340C2314yescomplemented
201#340C2314yescomplemented
202#340C2314yescomplemented
203#340C2314yescomplemented
204#340C2314yescomplemented
205#336C2314yescomplemented
206#336C2314yescomplemented
207C25—21no—
208C25—21no—
209C25—24no—
210C25—44no—
211C25—44no—
212C25—44no—
213C25—44no—
214C25—44no—
215C25—82no—
216C25—82no—
217C25C2×D411yescharacteristic
218C25C2×D411yescharacteristic
219C22×D4—24no—
220C22×D4—24no—
221C22×D4—28no—
222C22×D4—28no—
223C22×D4—24no—
224C22×D4—24no—
225C22×D4—21no—
226C22×D4—21no—
227C22×D4—24no—
228C22×D4—22no—
229C22×D4—22no—
230C22×D4—22no—
231C22×D4—22no—
232C22×D4—22no—
233C22×D4—22no—
234C22×D4—22no—
235C22×D4—22no—
236C22×D4—22no—
237C22×D4—22no—
238C22×D4—44no—
239C22×D4—44no—
240C22×D4—44no—
241C22×D4—44no—
242C22×D4—48no—
243C22×D4—48no—
244C22×D4—42no—
245C22×D4—44no—
246C22×D4—44no—
247C22×D4—44no—
248C22×D4—48no—
249C22×D4—416no—
250C22×D4—416no—
251C22×D4—416no—
252C22×D4—416no—
253C22×D4—44no—
254C22×D4—44no—
255C22×D4—44no—
256C22×D4—44no—
257C22×D4—82no—
258C22×D4—82no—
259C22×D4C2×D414yes—
260C22×D4#4114yes—
261C22×D4#4114yes—
262C22×D4C2412yes—
263C22×D4C2412yes—
264C23×C4—22no—
265C23×C4—22no—
266C23×C4—22no—
267C23×C4—22no—
268C23×C4—22no—
269C23×C4—22no—
270C23×C4—22no—
271C23×C4—22no—
272C23×C4—22no—
273C23×C4—22no—
274C23×C4—22no—
275C23×C4—22no—
276C23×C4—21no—
277C23×C4—21no—
278C23×C4—21no—
279C23×C4—21no—
280C23×C4—21no—
281C23×C4—21no—
282C23×C4C2×D412yes—
283C23×C4C2×D412yes—
284C23×C4C2×D411yescharacteristic
285C23×C4C2×D411yescharacteristic
286C23×C4C2×D411yescharacteristic
287C23×C4C2×D411yescharacteristic
288C23×C4C2412yes—
289C23×C4C2412yes—
290C23×C4C2411yescharacteristic
291C22×C8—22no—
292C22×C8—22no—
293C22×C8—22no—
294C22×C8—22no—
295C22×C8—22no—
296C22×C8—22no—
297C22×C8—22no—
298C22×C8—22no—
299C22×C8—22no—
300C22×C8—22no—
301C22×C8—22no—
302C22×C8—22no—
303C22×C8—44no—
304C22×C8—44no—
305C22×C8—44no—
306C22×C8—416no—
307C22×C8C2412yes—
308C22×C8C2412yes—
309C22×C8C2412yes—
310C22×C8C2412yes—
311#125—44no—
312#125—44no—
313#125—48no—
314#121—28no—
315#121—28no—
316#121—44no—
317#121—44no—
318#121—48no—
319#121—48no—
320#120—432no—
321C4×D4—48no—
322C4×D4—44no—
323C4×D4—44no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—22no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—24no—
337C2×C4⋊C4—24no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—42no—
345C2×C4⋊C4—44no—
346C2×C4⋊C4—44no—
347C2×C4⋊C4C2×D414yes—
348C2×C4⋊C4C2412yes—
349C2×C4⋊C4C2412yes—
350C2×C4⋊C4C2412yes—
351C2×C4⋊C4C2412yes—
352C2×C4⋊C4C2412yes—
353C2×C4⋊C4C2412yes—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—24no—
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—42no—
366C2×C22⋊C4—42no—
367C2×C22⋊C4—44no—
368C2×C22⋊C4—44no—
369C2×C22⋊C4—44no—
370C2×C22⋊C4—44no—
371C2×C22⋊C4—44no—
372C2×C22⋊C4—44no—
373C2×C22⋊C4—44no—
374C2×C22⋊C4—82no—
375C2×C22⋊C4—82no—
376C2×C22⋊C4—82no—
377C2×C22⋊C4—82no—
378C2×C22⋊C4C2×D414yes—
379C2×C22⋊C4C2×D414yes—
380C2×C42—22no—
381C2×C42—22no—
382C2×C42—24no—
383C2×C42—82no—
384C2×C42C2×D412yes—
385C2×C42C2412yes—
386#107—44no—
387#106—44no—
388#102—28no—
389#102—28no—
390#102—44no—
391#102—44no—
392#102—44no—
393#102—44no—
394#102—44no—
395#102—44no—
396C22⋊C8—44no—
397C22⋊C8—44no—
398C22⋊C8—44no—
399#95—24no—
400#95—24no—
401#95—24no—
402#95—24no—
403#95—24no—
404#95—24no—
405C24—22no—
406C24—22no—
407C24—22no—
408C24—22no—
409C24—22no—
410C24—22no—
411C24—22no—
412C24—22no—
413C24—22no—
414C24—22no—
415C24—22no—
416C24—22no—
417C24—24no—
418C24—24no—
419C24—22no—
420C24—22no—
421C24—48no—
422C24—48no—
423C24—48no—
424C24—48no—
425C24—432no—
426C24—42no—
427C24—42no—
428C24—42no—
429C24—42no—
430C24—42no—
431C24—42no—
432C24—42no—
433C24—42no—
434C24—42no—
435C24—42no—
436C24—42no—
437C24—42no—
438C24—48no—
439C24—84no—
440C24—84no—
441C24—816no—
442C24—816no—
443C24—816no—
444C24—816no—
445C24—816no—
446C24—816no—
447C24#13514yes—
448C24AGL(1,ℤ/8)14yes—
449C24C22×D412yes—
450C24C22×D412yes—
451C24C22×D411yescharacteristic
452C2×D4—28no—
453C2×D4—28no—
454C2×D4—28no—
455C2×D4—28no—
456C2×D4—24no—
457C2×D4—24no—
458C2×D4—28no—
459C2×D4—28no—
460C2×D4—22no—
461C2×D4—22no—
462C2×D4—22no—
463C2×D4—22no—
464C2×D4—22no—
465C2×D4—22no—
466C2×D4—22no—
467C2×D4—22no—
468C2×D4—22no—
469C2×D4—22no—
470C2×D4—44no—
471C2×D4—48no—
472C2×D4—48no—
473C2×D4—48no—
474C2×D4—416no—
475C2×D4—416no—
476C2×D4—416no—
477C2×D4—416no—
478C2×D4—432no—
479C2×D4—464no—
480C2×D4—416no—
481C2×D4—48no—
482C2×D4—48no—
483C2×D4—48no—
484C2×D4—48no—
485C2×D4—42no—
486C2×D4—42no—
487C2×D4—44no—
488C2×D4—44no—
489C2×D4—42no—
490C2×D4—42no—
491C2×D4—44no—
492C2×D4—44no—
493C2×D4—84no—
494C2×D4—84no—
495C2×D4—816no—
496C2×D4—816no—
497C2×D4C2×#4114yes—
498C2×D4C2×#4114yes—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—24no—
512C22×C4—24no—
513C22×C4—24no—
514C22×C4—24no—
515C22×C4—24no—
516C22×C4—24no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
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—44no—
536C22×C4—44no—
537C22×C4—44no—
538C22×C4—44no—
539C22×C4—44no—
540C22×C4—44no—
541C22×C4—44no—
542C22×C4—44no—
543C22×C4—42no—
544C22×C4—42no—
545C22×C4—42no—
546C22×C4—42no—
547C22×C4—42no—
548C22×C4—42no—
549C22×C4—42no—
550C22×C4—42no—
551C22×C4—42no—
552C22×C4—42no—
553C22×C4—42no—
554C22×C4—42no—
555C22×C4—42no—
556C22×C4—42no—
557C22×C4—42no—
558C22×C4—42no—
559C22×C4—42no—
560C22×C4—42no—
561C22×C4C22×D412yes—
562C22×C4C22×D412yes—
563C22×C4C22×D412yes—
564C22×C4C22×D412yes—
565C22×C4C22×D411yescharacteristic
566C22×C4C2×#4112yes—
567C22×C4C2×#4112yes—
568C22×C4H(5,𝔽2)12yes—
569C22×C4H(5,𝔽2)12yes—
570C22×C4H(5,𝔽2)12yes—
571C22×C4H(5,𝔽2)12yes—
572C22×C4C2511yescharacteristic
573C2×C8—22no—
574C2×C8—22no—
575C2×C8—22no—
576C2×C8—22no—
577C2×C8—22no—
578C2×C8—22no—
579C2×C8—22no—
580C2×C8—22no—
581C2×C8—22no—
582C2×C8—22no—
583C2×C8—22no—
584C2×C8—22no—
585C2×C8—416no—
586C2×C8—44no—
587C2×C8—44no—
588C2×C8—44no—
589C2×C8—44no—
590C4⋊C4—22no—
591C4⋊C4—22no—
592C4⋊C4—22no—
593C4⋊C4—22no—
594C4⋊C4—22no—
595C4⋊C4—22no—
596C4⋊C4—22no—
597C4⋊C4—22no—
598C4⋊C4—22no—
599C4⋊C4—22no—
600C4⋊C4—22no—
601C4⋊C4—22no—
602C4⋊C4—44no—
603C4⋊C4—48no—
604C4⋊C4—48no—
605C4⋊C4—42no—
606C4⋊C4—42no—
607C4⋊C4—42no—
608C4⋊C4—42no—
609C4⋊C4—42no—
610C4⋊C4—42no—
611C22⋊C4—44no—
612C22⋊C4—44no—
613C22⋊C4—48no—
614C22⋊C4—48no—
615C22⋊C4—48no—
616C22⋊C4—48no—
617C22⋊C4—48no—
618C22⋊C4—48no—
619C22⋊C4—48no—
620C22⋊C4—84no—
621C22⋊C4—84no—
622C22⋊C4—84no—
623C22⋊C4—84no—
624C42—24no—
625C42—22no—
626C42—22no—
627C42—84no—
628C23—28no—
629C23—28no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—28no—
637C23—28no—
638C23—28no—
639C23—28no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—24no—
647C23—24no—
648C23—44no—
649C23—44no—
650C23—44no—
651C23—44no—
652C23—44no—
653C23—44no—
654C23—44no—
655C23—44no—
656C23—432no—
657C23—42no—
658C23—42no—
659C23—48no—
660C23—48no—
661C23—42no—
662C23—42no—
663C23—48no—
664C23—48no—
665C23—48no—
666C23—48no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—816no—
676C23—816no—
677C23—816no—
678C23—816no—
679C23—816no—
680C23—8128no—
681C23—816no—
682C23—84no—
683C23—84no—
684C23—84no—
685C23—84no—
686C23—84no—
687C23—84no—
688C23—84no—
689C23—84no—
690C23#53412yes—
691C23#54612yes—
692C23#54612yes—
693C23C2×#13514yes—
694C23C2×#13512yes—
695C23C2×AGL(1,ℤ/8)14yes—
696C23C2×AGL(1,ℤ/8)12yes—
697C23#57612yes—
698C23#57712yes—
699C23C23×D411yescharacteristic
700D4—24no—
701D4—24no—
702D4—24no—
703D4—24no—
704D4—416no—
705D4—432no—
706D4—42no—
707D4—42no—
708D4—48no—
709D4—48no—
710D4—42no—
711D4—42no—
712D4—816no—
713D4—816no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—44no—
727C2×C4—44no—
728C2×C4—44no—
729C2×C4—44no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—48no—
735C2×C4—48no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—84no—
759C2×C4—84no—
760C2×C4—84no—
761C2×C4—84no—
762C2×C4—84no—
763C2×C4—84no—
764C2×C4#53412yes—
765C2×C4#53814yes—
766C2×C4#53814yes—
767C2×C4#54612yes—
768C2×C4#54612yes—
769C2×C4#55114yes—
770C2×C4H(3,𝔽4)14yes—
771C2×C4C22×#4111yescharacteristic
772C2×C4C22×#4111yescharacteristic
773C2×C4C2×H(5,𝔽2)11yescharacteristic
774C2×C4C2×H(5,𝔽2)11yescharacteristic
775C2×C4C2×H(5,𝔽2)11yescharacteristic
776C2×C4C2×H(5,𝔽2)11yescharacteristic
777C8—42no—
778C8—42no—
779C8—42no—
780C8—42no—
781C22—24no—
782C22—24no—
783C22—24no—
784C22—24no—
785C22—24no—
786C22—24no—
787C22—416no—
788C22—416no—
789C22—42no—
790C22—42no—
791C22—42no—
792C22—42no—
793C22—42no—
794C22—42no—
795C22—42no—
796C22—42no—
797C22—44no—
798C22—44no—
799C22—44no—
800C22—44no—
801C22—44no—
802C22—44no—
803C22—864no—
804C22—816no—
805C22—816no—
806C22—82no—
807C22—82no—
808C22—82no—
809C22—82no—
810C22—82no—
811C22—82no—
812C22—82no—
813C22—82no—
814C22#268414yes—
815C22#318814yes—
816C22#319814yes—
817C22#329614yes—
818C22#329714yes—
819C22#331014yes—
820C22#331814yes—
821C22C2×#53411yescharacteristic
822C22C2×#54611yescharacteristic
823C22C2×#54611yescharacteristic
824C22C22×#13511yescharacteristic
825C22C22×AGL(1,ℤ/8)11yescharacteristic
826C22C2×#57611yescharacteristic
827C22C2×#57711yescharacteristic
828C4—42no—
829C4—42no—
830C4—42no—
831C4—42no—
832C4—82no—
833C4—82no—
834C4—82no—
835C4—82no—
836C4—82no—
837C4—82no—
838C4#268414yes—
839C4C2×#53811yescharacteristic
840C4C2×#53811yescharacteristic
841C4C2×#55111yescharacteristic
842C4C2×H(3,𝔽4)11yescharacteristic
843C2—44no—
844C2—44no—
845C2—84no—
846C2—84no—
847C2#3126618yesdirect product factor
848C2C2×#268411yescharacteristic
849C2C2×#318811yescharacteristic
850C2C2×#319811yescharacteristic
851C2C2×#329611yescharacteristic
852C2C2×#329711yescharacteristic
853C2C2×#331011yescharacteristic
854C2C2×#331811yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#2408C2
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. C2×#2562C2semidirect
3. #31266C2direct (N × H)
4. C2×#2076C2semidirect
5. C2×#2077C2semidirect
6. C2×#2034C2semidirect
7. C2×#2033C2semidirect
8. C2×#2025C2semidirect
9. C2×#2025C2semidirect
10. C2×#1926C2semidirect
11. C2×#1925C2semidirect
12. C2×#1893C2semidirect
13. C2×#1893C2semidirect
14. C2×#1869C2semidirect
15. C2×#1786C2semidirect
16. C2×#1786C2semidirect
18. C24×C8C22semidirect
19. C22×#125C22semidirect
24. C22×#107C22semidirect
25. C22×#106C22semidirect
36. C22×C22⋊C8C22semidirect
38. #2562C22semidirect
52. C2×#380C22semidirect
53. C2×#380C22semidirect
55. C2×C4×C4⋊C4C22semidirect
56. #2077C22semidirect
57. #2076C22semidirect
58. #2034C22semidirect
59. #2033C22semidirect
60. #2025C22semidirect
61. #2025C22semidirect
62. #1926C22semidirect
63. #1925C22semidirect
64. #1893C22semidirect
65. #1893C22semidirect
66. #1869C22semidirect
67. #1786C22semidirect
68. #1786C22semidirect
69. C2×#340C22semidirect
70. C2×#340C22semidirect
71. C2×#340C22semidirect
72. C2×#340C22semidirect
73. C2×#340C22semidirect
74. C2×#340C22semidirect
75. C2×#336C22semidirect
76. C2×#336C22semidirect
101. C23×C8C23semidirect
105. C2×#125C23semidirect
145. C2×#107C23semidirect
147. C2×#106C23semidirect
169. C2×C22⋊C8C23semidirect
188. #380C23semidirect
189. #380C23semidirect
192. C4×C4⋊C4C23semidirect
199. #340C23semidirect
200. #340C23semidirect
201. #340C23semidirect
202. #340C23semidirect
203. #340C23semidirect
204. #340C23semidirect
205. #336C23semidirect
206. #336C23semidirect
847. C2#31266direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#25622
C2×#24082
#312662
C2×#20762
C2×#20772
C2×#20342
C2×#20332
C2×#20252
C2×#19262
C2×#19252
C2×#18932
C2×#18692
C2×#17862