Finite Group Databasebeta

← C2×#30531 #7501020

Subgroups — C2×#30531 #7501020

Order 512.

3420 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#488C211yesmaximal, characteristic, complemented
2C22×#450C211yesmaximal, characteristic
3C2×#2489C211yesmaximal, characteristic, complemented
4C2×#2435C211yesmaximal, characteristic
5#30531C2116yesmaximal, direct product factor
6C2×#2055C211yesmaximal, characteristic, complemented
7C2×#2035C211yesmaximal, characteristic, complemented
8C2×#2025C211yesmaximal, characteristic, complemented
9C2×#2015C211yesmaximal, characteristic, complemented
10C2×#2015C211yesmaximal, characteristic, complemented
11C2×#2001C211yesmaximal, characteristic, complemented
12C2×#1983C211yesmaximal, characteristic, complemented
13C2×#1968C211yesmaximal, characteristic, complemented
14C2×#1926C211yesmaximal, characteristic, complemented
15C2×#1923C211yesmaximal, characteristic, complemented
16C2×#1786C211yesmaximal, characteristic
17C24×D4C2211yescharacteristic
18C23×Q16C2211yescharacteristic, complemented
19C23×SD16C2211yescharacteristic
20C23×SD16C2211yescharacteristic
21C22×#125C2211yescharacteristic, complemented
22C22×#124C2211yescharacteristic
23C22×#124C2211yescharacteristic
24C22×C22⋊Q8C2211yescharacteristic
25C22×C22⋊Q8C2211yescharacteristic
26C2×#488—28no—
27C2×#488C2218yescomplemented
28C2×#450—28no—
29C2×#450C2218yes—
30C22×#106C2211yescharacteristic, complemented
31C22×C4⋊C8C2211yescharacteristic, complemented
32C22×#103C2211yescharacteristic, complemented
33C22×#103C2211yescharacteristic, complemented
34C22×#103C2211yescharacteristic, complemented
35C22×#103C2211yescharacteristic, complemented
36C22×#102C2211yescharacteristic
37C22×#102C2211yescharacteristic
38C22×#102C2211yescharacteristic
39C22×#102C2211yescharacteristic
40C22×#102C2211yescharacteristic
41C22×#102C2211yescharacteristic
42C22×C22⋊C8C2211yescharacteristic
43C22×C22⋊C8C2211yescharacteristic
44C22×C4×C8C2211yescharacteristic, complemented
45#2489—24no—
46#2489C2218yescomplemented
47#2435—24no—
48#2435C2218yes—
49C2×#400—21no—
50C2×#397—21no—
51C2×#394—21no—
52C2×#394—21no—
53C2×#391C2211yescharacteristic, complemented
54C2×#391C2211yescharacteristic, complemented
55C2×#390C2211yescharacteristic
56C2×#390C2211yescharacteristic
57C2×#388—21no—
58C2×#382—21no—
59C2×#380C2211yescharacteristic
60C2×#379—21no—
61C2×#379—21no—
62C2×C4×C4⋊C4C2211yescharacteristic, complemented
63C2×C4×C22⋊C4C2211yescharacteristic
64#2055C2218yescomplemented
65#2035C2218yescomplemented
66#2025C2218yescomplemented
67#2015C2218yescomplemented
68#2015C2218yescomplemented
69#2001C2218yescomplemented
70#1983C2218yescomplemented
71#1968C2218yescomplemented
72#1926C2218yescomplemented
73#1923C2218yescomplemented
74#1786C2218yes—
75C2×#340C2211yescharacteristic, complemented
76C2×#340C2211yescharacteristic, complemented
77C2×#336C2211yescharacteristic, complemented
78C2×#336C2211yescharacteristic, complemented
79C26—21no—
80C23×Q8C2311yescharacteristic
81C23×Q8C2311yescharacteristic
82C23×D4—24no—
83C23×D4—24no—
84C23×D4—21no—
85C23×D4—22no—
86C23×D4—42no—
87C23×D4—42no—
88C23×D4—42no—
89C23×D4—42no—
90C23×D4C2311yescharacteristic
91C23×D4C2311yescharacteristic
92C23×D4C2314yes—
93C24×C4C2311yescharacteristic
94C22×Q16—42no—
95C22×Q16—42no—
96C22×Q16—42no—
97C22×Q16C2314yescomplemented
98C22×SD16—24no—
99C22×SD16—24no—
100C22×SD16—24no—
101C22×SD16—42no—
102C22×SD16—42no—
103C22×SD16—42no—
104C22×SD16C2314yes—
105C22×SD16C2314yes—
106C23×C8C2311yescharacteristic
107C23×C8C2311yescharacteristic
108C23×C8C2311yescharacteristic
109C23×C8C2311yescharacteristic
110C2×#125—24no—
111C2×#125—22no—
112C2×#125—42no—
113C2×#125C2314yescomplemented
114C2×#124—24no—
115C2×#124—24no—
116C2×#124—22no—
117C2×#124—22no—
118C2×#124—42no—
119C2×#124—42no—
120C2×#124C2314yes—
121C2×#124C2314yes—
122C2×C22⋊Q8—22no—
123C2×C22⋊Q8—22no—
124C2×C22⋊Q8—24no—
125C2×C22⋊Q8—42no—
126C2×C22⋊Q8—42no—
127C2×C22⋊Q8—42no—
128C2×C22⋊Q8C2314yes—
129C2×C22⋊Q8C2314yes—
130C22×C4⋊C4—21no—
131C22×C4⋊C4—21no—
132C22×C4⋊C4—21no—
133C22×C4⋊C4—21no—
134C22×C4⋊C4C2311yescharacteristic
135C22×C4⋊C4C2311yescharacteristic
136C22×C4⋊C4C2311yescharacteristic
137C22×C4⋊C4C2311yescharacteristic
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—21no—
148C22×C22⋊C4—21no—
149C22×C22⋊C4D411yescharacteristic
150C22×C22⋊C4D411yescharacteristic
151C22×C42—21no—
152C22×C42C2311yescharacteristic
153C22×C42C2311yescharacteristic
154#488—232no—
155#450—232no—
156C2×#106—42no—
157C2×#106C2314yescomplemented
158C2×C4⋊C8—42no—
159C2×C4⋊C8C2314yescomplemented
160C2×#103—24no—
161C2×#103—24no—
162C2×#103—42no—
163C2×#103—42no—
164C2×#103C2314yescomplemented
165C2×#103C2314yescomplemented
166C2×#103C2314yescomplemented
167C2×#103C2314yescomplemented
168C2×#102—24no—
169C2×#102—24no—
170C2×#102—42no—
171C2×#102—42no—
172C2×#102—42no—
173C2×#102D418yes—
174C2×#102C2314yes—
175C2×#102C2314yes—
176C2×#102C2314yes—
177C2×#102C2314yes—
178C2×#102C2314yes—
179C2×#102C2314yes—
180C2×C22⋊C8—24no—
181C2×C22⋊C8—42no—
182C2×C22⋊C8C2314yes—
183C2×C22⋊C8C2314yes—
184C2×C4×C8—24no—
185C2×C4×C8C2314yescomplemented
186#400—28no—
187#397—28no—
188#394—28no—
189#394—28no—
190#391—22no—
191#391—22no—
192#391C2314yescomplemented
193#391C2314yescomplemented
194#390—22no—
195#390—22no—
196#390C2314yes—
197#390C2314yes—
198#388—28no—
199#382—28no—
200#380—22no—
201#380C2314yes—
202#379—28no—
203#379—28no—
204C4×C4⋊C4—22no—
205C4×C4⋊C4C2314yescomplemented
206C4×C22⋊C4D414yes—
207C4×C22⋊C4C2314yes—
208C2×#95—21no—
209C2×#95—21no—
210C2×#95—21no—
211C2×#95—21no—
212C2×#95—21no—
213C2×#95—21no—
214C2×#95D411yescharacteristic
215C2×#95D411yescharacteristic
216#340C2314yescomplemented
217#340C2314yescomplemented
218#336C2314yescomplemented
219#336C2314yescomplemented
220C25—21no—
221C25—21no—
222C25—24no—
223C25—44no—
224C25—44no—
225C25—44no—
226C25—44no—
227C25—44no—
228C25—82no—
229C25—82no—
230C25C2×D411yescharacteristic
231C22×Q8—21no—
232C22×Q8—21no—
233C22×Q8—22no—
234C22×Q8—22no—
235C22×Q8—22no—
236C22×Q8—22no—
237C22×Q8—22no—
238C22×Q8—22no—
239C22×Q8—22no—
240C22×Q8—22no—
241C22×Q8—22no—
242C22×Q8—22no—
243C22×Q8—22no—
244C22×Q8—22no—
245C22×Q8C2412yes—
246C22×Q8C2412yes—
247C22×D4—28no—
248C22×D4—28no—
249C22×D4—22no—
250C22×D4—21no—
251C22×D4—21no—
252C22×D4—24no—
253C22×D4—22no—
254C22×D4—22no—
255C22×D4—22no—
256C22×D4—22no—
257C22×D4—22no—
258C22×D4—22no—
259C22×D4—22no—
260C22×D4—22no—
261C22×D4—22no—
262C22×D4—44no—
263C22×D4—44no—
264C22×D4—44no—
265C22×D4—44no—
266C22×D4—48no—
267C22×D4—48no—
268C22×D4—44no—
269C22×D4—44no—
270C22×D4—44no—
271C22×D4—48no—
272C22×D4—416no—
273C22×D4—416no—
274C22×D4—416no—
275C22×D4—416no—
276C22×D4C2×D414yes—
277C22×D4#4114yes—
278C22×D4C2412yes—
279C22×D4C2412yes—
280C23×C4—21no—
281C23×C4—22no—
282C23×C4—22no—
283C23×C4—22no—
284C23×C4—22no—
285C23×C4—22no—
286C23×C4—22no—
287C23×C4—21no—
288C23×C4—21no—
289C23×C4—21no—
290C23×C4—21no—
291C23×C4—21no—
292C23×C4C2×D412yes—
293C23×C4C2×D411yescharacteristic
294C23×C4C2×D411yescharacteristic
295C23×C4C2×D411yescharacteristic
296C23×C4C2×D411yescharacteristic
297C23×C4C2×D411yescharacteristic
298C23×C4C2412yes—
299C23×C4C2411yescharacteristic
300C2×Q16—44no—
301C2×Q16—44no—
302C2×Q16—44no—
303C2×Q16—416no—
304C2×SD16—28no—
305C2×SD16—28no—
306C2×SD16—28no—
307C2×SD16—44no—
308C2×SD16—44no—
309C2×SD16—44no—
310C2×SD16—416no—
311C2×SD16—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—
328#125—28no—
329#125—44no—
330#125—48no—
331#124—28no—
332#124—28no—
333#124—44no—
334#124—44no—
335#124—48no—
336#124—48no—
337C22⋊Q8—28no—
338C22⋊Q8—44no—
339C22⋊Q8—44no—
340C22⋊Q8—44no—
341C22⋊Q8—48no—
342C22⋊Q8—48no—
343C2×C4⋊C4—21no—
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—24no—
354C2×C4⋊C4—24no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—44no—
359C2×C4⋊C4—44no—
360C2×C4⋊C4—44no—
361C2×C4⋊C4—44no—
362C2×C4⋊C4C2×D414yes—
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—82no—
388C2×C22⋊C4—82no—
389C2×C22⋊C4—82no—
390C2×C22⋊C4—82no—
391C2×C22⋊C4C2×D414yes—
392C2×C22⋊C4C2×D414yes—
393C2×C42—22no—
394C2×C42—22no—
395C2×C42—22no—
396C2×C42—22no—
397C2×C42—24no—
398C2×C42—44no—
399C2×C42C2×D412yes—
400C2×C42C2×D412yes—
401C2×C42C2412yes—
402C2×C42C2412yes—
403#106—44no—
404C4⋊C8—44no—
405#103—28no—
406#103—28no—
407#103—44no—
408#103—44no—
409#102—28no—
410#102—28no—
411#102—44no—
412#102—44no—
413#102—44no—
414#102C2×D4116yes—
415C22⋊C8—28no—
416C22⋊C8—44no—
417C4×C8—28no—
418#95—24no—
419#95—24no—
420#95—24no—
421#95—24no—
422#95—24no—
423#95—24no—
424#95C2×D414yes—
425#95C2×D414yes—
426C24—22no—
427C24—22no—
428C24—22no—
429C24—22no—
430C24—22no—
431C24—22no—
432C24—24no—
433C24—24no—
434C24—22no—
435C24—22no—
436C24—48no—
437C24—48no—
438C24—48no—
439C24—48no—
440C24—432no—
441C24—42no—
442C24—42no—
443C24—42no—
444C24—42no—
445C24—42no—
446C24—42no—
447C24—42no—
448C24—42no—
449C24—42no—
450C24—42no—
451C24—42no—
452C24—42no—
453C24—48no—
454C24—84no—
455C24—84no—
456C24—816no—
457C24—816no—
458C24—816no—
459C24—816no—
460C24—816no—
461C24—816no—
462C24#13514yes—
463C24C22×D412yes—
464C24C22×D411yescharacteristic
465C2×Q8—22no—
466C2×Q8—22no—
467C2×Q8—22no—
468C2×Q8—22no—
469C2×Q8—22no—
470C2×Q8—22no—
471C2×Q8—22no—
472C2×Q8—22no—
473C2×Q8—22no—
474C2×Q8—22no—
475C2×Q8—22no—
476C2×Q8—22no—
477C2×Q8—42no—
478C2×Q8—42no—
479C2×Q8—42no—
480C2×Q8—42no—
481C2×Q8—42no—
482C2×Q8—42no—
483C2×Q8—44no—
484C2×Q8—44no—
485C2×Q8—44no—
486C2×Q8—44no—
487C2×Q8—44no—
488C2×Q8—44no—
489C2×Q8—44no—
490C2×Q8—44no—
491C2×D4—28no—
492C2×D4—28no—
493C2×D4—24no—
494C2×D4—28no—
495C2×D4—28no—
496C2×D4—24no—
497C2×D4—22no—
498C2×D4—22no—
499C2×D4—22no—
500C2×D4—22no—
501C2×D4—22no—
502C2×D4—22no—
503C2×D4—22no—
504C2×D4—22no—
505C2×D4—22no—
506C2×D4—22no—
507C2×D4—48no—
508C2×D4—48no—
509C2×D4—48no—
510C2×D4—416no—
511C2×D4—416no—
512C2×D4—416no—
513C2×D4—432no—
514C2×D4—464no—
515C2×D4—416no—
516C2×D4—42no—
517C2×D4—42no—
518C2×D4—44no—
519C2×D4—44no—
520C2×D4—42no—
521C2×D4—42no—
522C2×D4—44no—
523C2×D4—44no—
524C2×D4C22×D414yes—
525C2×D4C2×#4114yes—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—24no—
530C22×C4—22no—
531C22×C4—22no—
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—22no—
543C22×C4—24no—
544C22×C4—24no—
545C22×C4—24no—
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—22no—
556C22×C4—22no—
557C22×C4—42no—
558C22×C4—42no—
559C22×C4—44no—
560C22×C4—44no—
561C22×C4—44no—
562C22×C4—44no—
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—42no—
572C22×C4—42no—
573C22×C4—42no—
574C22×C4—42no—
575C22×C4—42no—
576C22×C4—42no—
577C22×C4—42no—
578C22×C4C22×D412yes—
579C22×C4C22×D412yes—
580C22×C4C22×D412yes—
581C22×C4C22×D412yes—
582C22×C4C22×D412yes—
583C22×C4C22×D411yescharacteristic
584C22×C4C22×D412yes—
585C22×C4C2×#4112yes—
586C22×C4H(5,𝔽2)12yes—
587C22×C4H(5,𝔽2)12yes—
588C22×C4H(5,𝔽2)12yes—
589C22×C4H(5,𝔽2)12yes—
590C22×C4C2511yescharacteristic
591Q16—416no—
592SD16—416no—
593SD16—416no—
594C2×C8—28no—
595C2×C8—22no—
596C2×C8—22no—
597C2×C8—22no—
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—44no—
607C2×C8—44no—
608C2×C8—44no—
609C2×C8C22×D414yes—
610C4⋊C4—24no—
611C4⋊C4—22no—
612C4⋊C4—22no—
613C4⋊C4—22no—
614C4⋊C4—22no—
615C4⋊C4—22no—
616C4⋊C4—22no—
617C4⋊C4—22no—
618C4⋊C4—48no—
619C4⋊C4—48no—
620C4⋊C4—48no—
621C4⋊C4—48no—
622C4⋊C4—42no—
623C4⋊C4—42no—
624C4⋊C4—42no—
625C4⋊C4C22×D414yes—
626C22⋊C4—28no—
627C22⋊C4—44no—
628C22⋊C4—48no—
629C22⋊C4—48no—
630C22⋊C4—48no—
631C22⋊C4—48no—
632C22⋊C4—48no—
633C22⋊C4—48no—
634C22⋊C4—48no—
635C22⋊C4—84no—
636C22⋊C4—84no—
637C22⋊C4—84no—
638C22⋊C4—84no—
639C42—24no—
640C42—24no—
641C42—22no—
642C42—22no—
643C42—22no—
644C42—22no—
645C42—48no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—28no—
650C23—28no—
651C23—28no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—24no—
656C23—24no—
657C23—44no—
658C23—44no—
659C23—44no—
660C23—44no—
661C23—432no—
662C23—48no—
663C23—48no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—48no—
669C23—48no—
670C23—48no—
671C23—42no—
672C23—42no—
673C23—48no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—816no—
681C23—816no—
682C23—816no—
683C23—816no—
684C23—816no—
685C23—8128no—
686C23—816no—
687C23—84no—
688C23—84no—
689C23—84no—
690C23—84no—
691C23—84no—
692C23—84no—
693C23—84no—
694C23—84no—
695C23#53512yes—
696C23D4212yes—
697C23#54612yes—
698C23C2×#13514yes—
699C23C2×#13512yes—
700C23#57512yes—
701C23#57712yes—
702C23#57712yes—
703C23C23×D411yescharacteristic
704Q8—42no—
705Q8—42no—
706Q8—42no—
707Q8—42no—
708Q8—42no—
709Q8—42no—
710Q8—42no—
711Q8—42no—
712Q8—84no—
713Q8—84no—
714D4—24no—
715D4—24no—
716D4—24no—
717D4—24no—
718D4—432no—
719D4—48no—
720D4—48no—
721D4—42no—
722D4—42no—
723D4—42no—
724D4—42no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—24no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—44no—
742C2×C4—44no—
743C2×C4—48no—
744C2×C4—44no—
745C2×C4—44no—
746C2×C4—44no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—48no—
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—42no—
759C2×C4—42no—
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—84no—
770C2×C4—84no—
771C2×C4—84no—
772C2×C4—84no—
773C2×C4—84no—
774C2×C4#53512yes—
775C2×C4#53514yes—
776C2×C4#53814yes—
777C2×C4D4212yes—
778C2×C4#54612yes—
779C2×C4#54614yes—
780C2×C4H(3,𝔽4)14yes—
781C2×C4C23×D411yescharacteristic
782C2×C4C22×#4111yescharacteristic
783C2×C4C2×H(5,𝔽2)11yescharacteristic
784C2×C4C2×H(5,𝔽2)11yescharacteristic
785C2×C4C2×H(5,𝔽2)11yescharacteristic
786C2×C4C2×H(5,𝔽2)11yescharacteristic
787C8—24no—
788C8—42no—
789C8—42no—
790C8—42no—
791C22—24no—
792C22—24no—
793C22—24no—
794C22—416no—
795C22—42no—
796C22—42no—
797C22—42no—
798C22—42no—
799C22—44no—
800C22—44no—
801C22—44no—
802C22—44no—
803C22—44no—
804C22—44no—
805C22—864no—
806C22—816no—
807C22—816no—
808C22—82no—
809C22—82no—
810C22—82no—
811C22—82no—
812C22—82no—
813C22—82no—
814C22—82no—
815C22—82no—
816C22#267014yes—
817C22#321114yes—
818C22#322214yes—
819C22#326714yes—
820C22#328214yes—
821C22#329614yes—
822C22#332314yes—
823C22C2×#53511yescharacteristic
824C22C2×D4211yescharacteristic
825C22C2×#54611yescharacteristic
826C22C22×#13511yescharacteristic
827C22C2×#57511yescharacteristic
828C22C2×#57711yescharacteristic
829C22C2×#57711yescharacteristic
830C4—42no—
831C4—44no—
832C4—42no—
833C4—42no—
834C4—42no—
835C4—42no—
836C4—82no—
837C4—82no—
838C4—82no—
839C4—82no—
840C4—82no—
841C4#267014yes—
842C4C2×#53511yescharacteristic
843C4C2×#53811yescharacteristic
844C4C2×#54611yescharacteristic
845C4C2×H(3,𝔽4)11yescharacteristic
846C2—44no—
847C2—84no—
848C2—84no—
849C2#3053118yesdirect product factor
850C2C2×#267011yescharacteristic
851C2C2×#321111yescharacteristic
852C2C2×#322211yescharacteristic
853C2C2×#326711yescharacteristic
854C2C2×#328211yescharacteristic
855C2C2×#329611yescharacteristic
856C2C2×#332311yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC24×D4C22
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×#488C2semidirect
3. C2×#2489C2semidirect
5. #30531C2direct (N × H)
6. C2×#2055C2semidirect
7. C2×#2035C2semidirect
8. C2×#2025C2semidirect
9. C2×#2015C2semidirect
10. C2×#2015C2semidirect
11. C2×#2001C2semidirect
12. C2×#1983C2semidirect
13. C2×#1968C2semidirect
14. C2×#1926C2semidirect
15. C2×#1923C2semidirect
18. C23×Q16C22semidirect
21. C22×#125C22semidirect
27. C2×#488C22semidirect
30. C22×#106C22semidirect
31. C22×C4⋊C8C22semidirect
32. C22×#103C22semidirect
33. C22×#103C22semidirect
34. C22×#103C22semidirect
35. C22×#103C22semidirect
44. C22×C4×C8C22semidirect
46. #2489C22semidirect
53. C2×#391C22semidirect
54. C2×#391C22semidirect
62. C2×C4×C4⋊C4C22semidirect
64. #2055C22semidirect
65. #2035C22semidirect
66. #2025C22semidirect
67. #2015C22semidirect
68. #2015C22semidirect
69. #2001C22semidirect
70. #1983C22semidirect
71. #1968C22semidirect
72. #1926C22semidirect
73. #1923C22semidirect
75. C2×#340C22semidirect
76. C2×#340C22semidirect
77. C2×#336C22semidirect
78. C2×#336C22semidirect
97. C22×Q16C23semidirect
113. C2×#125C23semidirect
157. C2×#106C23semidirect
159. C2×C4⋊C8C23semidirect
164. C2×#103C23semidirect
165. C2×#103C23semidirect
166. C2×#103C23semidirect
167. C2×#103C23semidirect
185. C2×C4×C8C23semidirect
192. #391C23semidirect
193. #391C23semidirect
205. C4×C4⋊C4C23semidirect
216. #340C23semidirect
217. #340C23semidirect
218. #336C23semidirect
219. #336C23semidirect
849. C2#30531direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#4882
C22×#4502
C2×#24892
C2×#24352
#305312
C2×#20552
C2×#20352
C2×#20252
C2×#20152
C2×#20012
C2×#19832
C2×#19682
C2×#19262
C2×#19232
C2×#17862