Finite Group Databasebeta

← C2×#24218 #6442508

Subgroups — C2×#24218 #6442508

Order 512.

5600 conjugacy classes of subgroups.

The subgroup lattice has 1040 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#535C211yesmaximal, characteristic, complemented
2C22×#463C211yesmaximal, characteristic, complemented
3C22×#459C211yesmaximal, characteristic, complemented
4C22×#449C211yesmaximal, characteristic, complemented
5C22×#447C211yesmaximal, characteristic, complemented
6C2×#2324C211yesmaximal, characteristic, complemented
7#24218C2116yesmaximal, direct product factor
8C2×#2042C211yesmaximal, characteristic, complemented
9C2×#2041C211yesmaximal, characteristic, complemented
10C2×#2012C211yesmaximal, characteristic, complemented
11C2×#2011C211yesmaximal, characteristic, complemented
12C2×#1983C211yesmaximal, characteristic, complemented
13C2×#1982C211yesmaximal, characteristic, complemented
14C2×#1798C211yesmaximal, characteristic, complemented
15C2×#1788C211yesmaximal, characteristic, complemented
16C2×#1786C211yesmaximal, characteristic, complemented
17C23×#41C2211yescharacteristic
18C24×D4C2211yescharacteristic
19C23×SD16C2211yescharacteristic, complemented
20C23×D8C2211yescharacteristic
21C23×D8C2211yescharacteristic
22C23×D8C2211yescharacteristic, complemented
23C2×#535—28no—
24C2×#535—28no—
25C2×#535—24no—
26C2×#535C2218yescomplemented
27C22×#127C2211yescharacteristic
28C22×#127C2211yescharacteristic
29C22×#124C2211yescharacteristic
30C22×#124C2211yescharacteristic
31C22×#121—21no—
32C22×#121—21no—
33C22×#121C2211yescharacteristic
34C22×#120—21no—
35C22×#120—21no—
36C22×C4×D4C2211yescharacteristic, complemented
37C22×#117C2211yescharacteristic
38C2×#463—28no—
39C2×#463C2218yescomplemented
40C2×#459—28no—
41C2×#459C2218yescomplemented
42C2×#449—28no—
43C2×#449C2218yescomplemented
44C2×#447—28no—
45C2×#447C2218yescomplemented
46C22×C4⋊C8C2211yescharacteristic, complemented
47C22×C4⋊C8C2211yescharacteristic, complemented
48C22×#103C2211yescharacteristic, complemented
49C22×#103C2211yescharacteristic, complemented
50C22×#103C2211yescharacteristic, complemented
51C22×#102C2211yescharacteristic
52C22×#102C2211yescharacteristic
53C22×#102C2211yescharacteristic
54C22×#102C2211yescharacteristic
55C22×#102C2211yescharacteristic
56C22×#102C2211yescharacteristic
57C22×#102C2211yescharacteristic, complemented
58C22×#102C2211yescharacteristic, complemented
59C22×#102C2211yescharacteristic, complemented
60C22×C22⋊C8C2211yescharacteristic
61C22×C22⋊C8C2211yescharacteristic
62#2324—24no—
63#2324C2218yescomplemented
64C2×#390—21no—
65C2×#390C2211yescharacteristic, complemented
66C2×#389C2211yescharacteristic, complemented
67C2×#388—21no—
68C2×#386—21no—
69C2×#385—21no—
70C2×#380C2211yescharacteristic
71C2×C4×C4⋊C4C2211yescharacteristic, complemented
72#2042C2218yescomplemented
73#2041C2218yescomplemented
74#2012C2218yescomplemented
75#2011C2218yescomplemented
76#1983C2218yescomplemented
77#1982C2218yescomplemented
78#1798C2218yescomplemented
79#1788C2218yescomplemented
80#1786C2218yescomplemented
81C2×#336C2211yescharacteristic, complemented
82C2×#336C2211yescharacteristic, complemented
83C26—21no—
84C22×#41—24no—
85C22×#41—24no—
86C22×#41—22no—
87C22×#41—24no—
88C22×#41—24no—
89C22×#41—42no—
90C22×#41—42no—
91C22×#41C2314yes—
92C23×Q8C2311yescharacteristic
93C23×D4—21no—
94C23×D4—21no—
95C23×D4—24no—
96C23×D4—24no—
97C23×D4—21no—
98C23×D4—22no—
99C23×D4—21no—
100C23×D4—21no—
101C23×D4—21no—
102C23×D4—21no—
103C23×D4—24no—
104C23×D4—24no—
105C23×D4—42no—
106C23×D4—42no—
107C23×D4C2311yescharacteristic
108C23×D4C2311yescharacteristic
109C23×D4C2311yescharacteristic
110C23×D4C2311yescharacteristic
111C23×D4C2314yes—
112C24×C4—21no—
113C24×C4—21no—
114C24×C4C2311yescharacteristic
115C22×SD16—24no—
116C22×SD16—24no—
117C22×SD16—42no—
118C22×SD16C2314yescomplemented
119C22×D8—24no—
120C22×D8—24no—
121C22×D8—24no—
122C22×D8—24no—
123C22×D8—24no—
124C22×D8—24no—
125C22×D8—42no—
126C22×D8—42no—
127C22×D8—42no—
128C22×D8C2314yes—
129C22×D8C2314yes—
130C22×D8C2314yescomplemented
131C23×C8C2311yescharacteristic
132C23×C8C2311yescharacteristic
133C23×C8C2311yescharacteristic
134C23×C8C2311yescharacteristic
135#535—264no—
136#535—232no—
137#535—232no—
138C2×#127—24no—
139C2×#127—24no—
140C2×#127—22no—
141C2×#127—22no—
142C2×#127—24no—
143C2×#127D418yescomplemented
144C2×#127C2314yes—
145C2×#127C2314yes—
146C2×#124—24no—
147C2×#124—24no—
148C2×#124—22no—
149C2×#124—22no—
150C2×#124—24no—
151C2×#124D418yescomplemented
152C2×#124C2314yes—
153C2×#124C2314yes—
154C2×#121—216no—
155C2×#121—216no—
156C2×#121—22no—
157C2×#121—24no—
158C2×#121—28no—
159C2×#121—28no—
160C2×#121D418yescomplemented
161C2×#121C2314yes—
162C2×#120—216no—
163C2×#120—216no—
164C2×#120—28no—
165C2×#120—28no—
166C2×C4×D4—22no—
167C2×C4×D4—24no—
168C2×C4×D4—24no—
169C2×C4×D4C2314yescomplemented
170C2×#117—24no—
171C2×#117—24no—
172C2×#117D414yes—
173C2×#117C2314yes—
174C22×C4⋊C4—21no—
175C22×C4⋊C4D411yescharacteristic
176C22×C4⋊C4D411yescharacteristic
177C22×C4⋊C4C2311yescharacteristic
178C22×C4⋊C4C2311yescharacteristic
179C22×C4⋊C4C2311yescharacteristic
180C22×C22⋊C4—21no—
181C22×C22⋊C4—21no—
182C22×C22⋊C4—21no—
183C22×C22⋊C4—21no—
184C22×C22⋊C4—21no—
185C22×C22⋊C4—21no—
186C22×C22⋊C4—21no—
187C22×C22⋊C4—21no—
188C22×C22⋊C4—21no—
189C22×C22⋊C4D411yescharacteristic
190C22×C22⋊C4D411yescharacteristic
191C22×C42—21no—
192C22×C42C2311yescharacteristic
193C22×C42C2311yescharacteristic
194#463—232no—
195#459—232no—
196#449—232no—
197#447—232no—
198C2×C4⋊C8—24no—
199C2×C4⋊C8—24no—
200C2×C4⋊C8C2314yescomplemented
201C2×C4⋊C8C2314yescomplemented
202C2×#103—24no—
203C2×#103—24no—
204C2×#103—42no—
205C2×#103C2314yescomplemented
206C2×#103C2314yescomplemented
207C2×#103C2314yescomplemented
208C2×#102—24no—
209C2×#102—24no—
210C2×#102—24no—
211C2×#102—24no—
212C2×#102—24no—
213C2×#102—24no—
214C2×#102—42no—
215C2×#102—42no—
216C2×#102—42no—
217C2×#102C2314yes—
218C2×#102C2314yes—
219C2×#102C2314yes—
220C2×#102C2314yes—
221C2×#102C2314yes—
222C2×#102C2314yes—
223C2×#102C2314yescomplemented
224C2×#102C2314yescomplemented
225C2×#102C2314yescomplemented
226C2×C22⋊C8—24no—
227C2×C22⋊C8—24no—
228C2×C22⋊C8C2314yes—
229C2×C22⋊C8C2314yes—
230#390—28no—
231#390—22no—
232#390C2314yescomplemented
233#389—22no—
234#389C2314yescomplemented
235#388—28no—
236#386—28no—
237#385—28no—
238#380—22no—
239#380C2314yes—
240C4×C4⋊C4—22no—
241C4×C4⋊C4C2314yescomplemented
242C2×#95—21no—
243C2×#95—21no—
244C2×#95—21no—
245#336C2314yescomplemented
246#336C2314yescomplemented
247C25—28no—
248C25—21no—
249C25—21no—
250C25—21no—
251C25—21no—
252C25—24no—
253C25—44no—
254C25—44no—
255C25—82no—
256C25—82no—
257C25—82no—
258C25—82no—
259C25C2×D411yescharacteristic
260C2×#41—216no—
261C2×#41—28no—
262C2×#41—28no—
263C2×#41—28no—
264C2×#41—28no—
265C2×#41—44no—
266C2×#41—44no—
267C2×#41—416no—
268C2×#41—416no—
269C2×#41—416no—
270C2×#41—416no—
271C2×#41—48no—
272C2×#41—48no—
273C22×Q8—22no—
274C22×Q8—21no—
275C22×Q8—22no—
276C22×Q8—22no—
277C22×Q8—22no—
278C22×Q8—22no—
279C22×Q8C2×D414yes—
280C22×Q8C2412yes—
281C22×D4—28no—
282C22×D4—28no—
283C22×D4—216no—
284C22×D4—24no—
285C22×D4—28no—
286C22×D4—28no—
287C22×D4—28no—
288C22×D4—24no—
289C22×D4—28no—
290C22×D4—28no—
291C22×D4—28no—
292C22×D4—28no—
293C22×D4—22no—
294C22×D4—22no—
295C22×D4—22no—
296C22×D4—22no—
297C22×D4—22no—
298C22×D4—21no—
299C22×D4—24no—
300C22×D4—21no—
301C22×D4—21no—
302C22×D4—22no—
303C22×D4—22no—
304C22×D4—21no—
305C22×D4—22no—
306C22×D4—24no—
307C22×D4—24no—
308C22×D4—24no—
309C22×D4—24no—
310C22×D4—28no—
311C22×D4—22no—
312C22×D4—22no—
313C22×D4—22no—
314C22×D4—22no—
315C22×D4—28no—
316C22×D4—22no—
317C22×D4—22no—
318C22×D4—22no—
319C22×D4—22no—
320C22×D4—22no—
321C22×D4—22no—
322C22×D4—22no—
323C22×D4—22no—
324C22×D4—44no—
325C22×D4—44no—
326C22×D4—416no—
327C22×D4—416no—
328C22×D4—416no—
329C22×D4—416no—
330C22×D4—44no—
331C22×D4—48no—
332C22×D4—44no—
333C22×D4—44no—
334C22×D4—44no—
335C22×D4—48no—
336C22×D4—82no—
337C22×D4—82no—
338C22×D4—82no—
339C22×D4—82no—
340C22×D4—82no—
341C22×D4—82no—
342C22×D4—82no—
343C22×D4—82no—
344C22×D4—82no—
345C22×D4—82no—
346C22×D4C2×D414yes—
347C22×D4C2×D414yes—
348C22×D4C2×D414yes—
349C22×D4C2×D414yes—
350C22×D4C2412yes—
351C22×D4C2412yes—
352C22×D4C2412yes—
353C22×D4C2412yes—
354C23×C4—22no—
355C23×C4—22no—
356C23×C4—22no—
357C23×C4—22no—
358C23×C4—28no—
359C23×C4—21no—
360C23×C4—21no—
361C23×C4—24no—
362C23×C4—21no—
363C23×C4—21no—
364C23×C4—24no—
365C23×C4—44no—
366C23×C4—44no—
367C23×C4—44no—
368C23×C4—82no—
369C23×C4—82no—
370C23×C4C2×D411yescharacteristic
371C23×C4C2×D411yescharacteristic
372C23×C4C2×D411yescharacteristic
373C23×C4C2×D411yescharacteristic
374C23×C4C2×D412yes—
375C23×C4C2×D411yescharacteristic
376C23×C4C2×D414yes—
377C23×C4#4114yes—
378C23×C4C2412yes—
379C23×C4C2411yescharacteristic
380C2×SD16—28no—
381C2×SD16—28no—
382C2×SD16—44no—
383C2×SD16—416no—
384C2×D8—28no—
385C2×D8—28no—
386C2×D8—28no—
387C2×D8—28no—
388C2×D8—28no—
389C2×D8—28no—
390C2×D8—44no—
391C2×D8—44no—
392C2×D8—44no—
393C2×D8—416no—
394C2×D8—416no—
395C2×D8—416no—
396C22×C8—22no—
397C22×C8—22no—
398C22×C8—22no—
399C22×C8—22no—
400C22×C8—22no—
401C22×C8—22no—
402C22×C8—22no—
403C22×C8—22no—
404C22×C8—22no—
405C22×C8—22no—
406C22×C8—22no—
407C22×C8—22no—
408C22×C8C2412yes—
409C22×C8C2412yes—
410C22×C8C2412yes—
411C22×C8C2412yes—
412#127—216no—
413#127—28no—
414#127—28no—
415#127—216no—
416#127—28no—
417#127C2×D4116yescomplemented
418#124—216no—
419#124—28no—
420#124—28no—
421#124—216no—
422#124—28no—
423#124C2×D4116yescomplemented
424#121—264no—
425#121—264no—
426#121—216no—
427#121—28no—
428#121C2×D4116yescomplemented
429#120—264no—
430#120—264no—
431C4×D4—28no—
432C4×D4—28no—
433C4×D4—48no—
434#117—216no—
435#117—28no—
436#117—28no—
437C2×C4⋊C4—24no—
438C2×C4⋊C4—24no—
439C2×C4⋊C4—21no—
440C2×C4⋊C4—22no—
441C2×C4⋊C4—22no—
442C2×C4⋊C4—22no—
443C2×C4⋊C4—22no—
444C2×C4⋊C4—22no—
445C2×C4⋊C4—21no—
446C2×C4⋊C4—21no—
447C2×C4⋊C4—24no—
448C2×C4⋊C4—82no—
449C2×C4⋊C4C2×D414yes—
450C2×C4⋊C4C2×D414yes—
451C2×C4⋊C4C2×D414yes—
452C2×C4⋊C4C2412yes—
453C2×C4⋊C4C2412yes—
454C2×C4⋊C4C2412yes—
455C2×C22⋊C4—28no—
456C2×C22⋊C4—28no—
457C2×C22⋊C4—28no—
458C2×C22⋊C4—28no—
459C2×C22⋊C4—24no—
460C2×C22⋊C4—24no—
461C2×C22⋊C4—28no—
462C2×C22⋊C4—24no—
463C2×C22⋊C4—24no—
464C2×C22⋊C4—24no—
465C2×C22⋊C4—24no—
466C2×C22⋊C4—24no—
467C2×C22⋊C4—24no—
468C2×C22⋊C4—24no—
469C2×C22⋊C4—24no—
470C2×C22⋊C4—24no—
471C2×C22⋊C4—44no—
472C2×C22⋊C4—82no—
473C2×C22⋊C4—82no—
474C2×C22⋊C4—82no—
475C2×C22⋊C4C2×D414yes—
476C2×C22⋊C4C2×D414yes—
477C2×C42—22no—
478C2×C42—22no—
479C2×C42—24no—
480C2×C42—82no—
481C2×C42C2×D412yes—
482C2×C42C2×D412yes—
483C2×C42C2×D414yes—
484C2×C42C2×D414yes—
485C2×C42C2412yes—
486C2×C42C2412yes—
487C4⋊C8—28no—
488C4⋊C8—28no—
489#103—28no—
490#103—28no—
491#103—44no—
492#102—28no—
493#102—28no—
494#102—28no—
495#102—28no—
496#102—28no—
497#102—28no—
498#102—44no—
499#102—44no—
500#102—44no—
501C22⋊C8—28no—
502C22⋊C8—28no—
503#95—24no—
504#95—24no—
505#95—24no—
506C24—22no—
507C24—22no—
508C24—22no—
509C24—22no—
510C24—22no—
511C24—22no—
512C24—216no—
513C24—24no—
514C24—24no—
515C24—24no—
516C24—24no—
517C24—22no—
518C24—22no—
519C24—22no—
520C24—22no—
521C24—432no—
522C24—48no—
523C24—42no—
524C24—42no—
525C24—48no—
526C24—42no—
527C24—42no—
528C24—42no—
529C24—42no—
530C24—42no—
531C24—42no—
532C24—42no—
533C24—42no—
534C24—42no—
535C24—42no—
536C24—42no—
537C24—42no—
538C24—42no—
539C24—42no—
540C24—42no—
541C24—42no—
542C24—42no—
543C24—42no—
544C24—42no—
545C24—42no—
546C24—42no—
547C24—42no—
548C24—84no—
549C24—84no—
550C24—84no—
551C24—84no—
552C24—816no—
553C24—816no—
554C24—816no—
555C24—816no—
556C24—816no—
557C24—816no—
558C24#12114yes—
559C24C22×D412yes—
560C24C22×D411yescharacteristic
561#41—416no—
562#41—416no—
563#41—416no—
564#41—416no—
565#41—464no—
566C2×Q8—24no—
567C2×Q8—22no—
568C2×Q8—28no—
569C2×Q8—28no—
570C2×Q8—22no—
571C2×Q8—22no—
572C2×Q8—22no—
573C2×Q8—22no—
574C2×Q8—42no—
575C2×Q8—42no—
576C2×Q8—44no—
577C2×Q8—44no—
578C2×Q8C22×D414yes—
579C2×D4—216no—
580C2×D4—216no—
581C2×D4—216no—
582C2×D4—216no—
583C2×D4—216no—
584C2×D4—24no—
585C2×D4—24no—
586C2×D4—24no—
587C2×D4—216no—
588C2×D4—216no—
589C2×D4—24no—
590C2×D4—28no—
591C2×D4—28no—
592C2×D4—28no—
593C2×D4—28no—
594C2×D4—28no—
595C2×D4—28no—
596C2×D4—28no—
597C2×D4—28no—
598C2×D4—22no—
599C2×D4—22no—
600C2×D4—22no—
601C2×D4—22no—
602C2×D4—22no—
603C2×D4—22no—
604C2×D4—22no—
605C2×D4—22no—
606C2×D4—22no—
607C2×D4—22no—
608C2×D4—22no—
609C2×D4—22no—
610C2×D4—22no—
611C2×D4—22no—
612C2×D4—22no—
613C2×D4—22no—
614C2×D4—22no—
615C2×D4—22no—
616C2×D4—22no—
617C2×D4—22no—
618C2×D4—416no—
619C2×D4—416no—
620C2×D4—416no—
621C2×D4—416no—
622C2×D4—432no—
623C2×D4—48no—
624C2×D4—464no—
625C2×D4—432no—
626C2×D4—48no—
627C2×D4—48no—
628C2×D4—42no—
629C2×D4—48no—
630C2×D4—42no—
631C2×D4—42no—
632C2×D4—42no—
633C2×D4—42no—
634C2×D4—42no—
635C2×D4—42no—
636C2×D4—42no—
637C2×D4—44no—
638C2×D4—44no—
639C2×D4—44no—
640C2×D4—44no—
641C2×D4—44no—
642C2×D4—44no—
643C2×D4—44no—
644C2×D4—44no—
645C2×D4—816no—
646C2×D4—816no—
647C2×D4—84no—
648C2×D4—84no—
649C2×D4—84no—
650C2×D4—84no—
651C2×D4—84no—
652C2×D4—84no—
653C2×D4—84no—
654C2×D4—84no—
655C2×D4—816no—
656C2×D4—84no—
657C2×D4—84no—
658C2×D4—816no—
659C2×D4—816no—
660C2×D4C22×D414yes—
661C2×D4C22×D414yes—
662C2×D4C22×D414yes—
663C2×D4C22×D414yes—
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—22no—
670C22×C4—24no—
671C22×C4—24no—
672C22×C4—28no—
673C22×C4—28no—
674C22×C4—28no—
675C22×C4—28no—
676C22×C4—22no—
677C22×C4—22no—
678C22×C4—22no—
679C22×C4—22no—
680C22×C4—216no—
681C22×C4—22no—
682C22×C4—22no—
683C22×C4—24no—
684C22×C4—24no—
685C22×C4—22no—
686C22×C4—22no—
687C22×C4—22no—
688C22×C4—22no—
689C22×C4—22no—
690C22×C4—22no—
691C22×C4—22no—
692C22×C4—22no—
693C22×C4—432no—
694C22×C4—48no—
695C22×C4—42no—
696C22×C4—42no—
697C22×C4—42no—
698C22×C4—42no—
699C22×C4—48no—
700C22×C4—42no—
701C22×C4—42no—
702C22×C4—42no—
703C22×C4—42no—
704C22×C4—42no—
705C22×C4—42no—
706C22×C4—48no—
707C22×C4—84no—
708C22×C4—84no—
709C22×C4—816no—
710C22×C4#12014yes—
711C22×C4#12014yes—
712C22×C4#12114yes—
713C22×C4#12118yes—
714C22×C4C22×D412yes—
715C22×C4C22×D412yes—
716C22×C4C22×D412yes—
717C22×C4C22×D412yes—
718C22×C4C22×D412yes—
719C22×C4C22×D414yes—
720C22×C4C22×D411yescharacteristic
721C22×C4C22×D412yes—
722C22×C4C22×D412yes—
723C22×C4C22×D412yes—
724C22×C4C2×#4114yes—
725C22×C4C2×#4112yes—
726C22×C4H(5,𝔽2)12yes—
727C22×C4H(5,𝔽2)12yes—
728C22×C4C2511yescharacteristic
729SD16—416no—
730D8—416no—
731D8—416no—
732D8—416no—
733C2×C8—22no—
734C2×C8—22no—
735C2×C8—22no—
736C2×C8—22no—
737C2×C8—22no—
738C2×C8—22no—
739C2×C8—22no—
740C2×C8—22no—
741C2×C8—22no—
742C2×C8—22no—
743C2×C8—22no—
744C2×C8—22no—
745C2×C8—44no—
746C2×C8—44no—
747C2×C8—44no—
748C2×C8—44no—
749C4⋊C4—28no—
750C4⋊C4—28no—
751C4⋊C4—24no—
752C4⋊C4—22no—
753C4⋊C4—22no—
754C4⋊C4—22no—
755C4⋊C4—22no—
756C4⋊C4—22no—
757C4⋊C4—42no—
758C4⋊C4—42no—
759C4⋊C4—84no—
760C4⋊C4C22×D414yes—
761C22⋊C4—216no—
762C22⋊C4—216no—
763C22⋊C4—216no—
764C22⋊C4—216no—
765C22⋊C4—28no—
766C22⋊C4—28no—
767C22⋊C4—216no—
768C22⋊C4—48no—
769C22⋊C4—84no—
770C22⋊C4—84no—
771C22⋊C4—84no—
772C42—24no—
773C42—22no—
774C42—22no—
775C42—84no—
776C42#12018yes—
777C42C22×D414yes—
778C42C22×D414yes—
779C23—22no—
780C23—28no—
781C23—22no—
782C23—28no—
783C23—28no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—22no—
788C23—24no—
789C23—24no—
790C23—24no—
791C23—24no—
792C23—432no—
793C23—44no—
794C23—44no—
795C23—44no—
796C23—44no—
797C23—42no—
798C23—48no—
799C23—48no—
800C23—48no—
801C23—48no—
802C23—42no—
803C23—42no—
804C23—42no—
805C23—42no—
806C23—42no—
807C23—42no—
808C23—42no—
809C23—48no—
810C23—48no—
811C23—48no—
812C23—48no—
813C23—48no—
814C23—48no—
815C23—48no—
816C23—48no—
817C23—42no—
818C23—42no—
819C23—42no—
820C23—42no—
821C23—42no—
822C23—42no—
823C23—42no—
824C23—42no—
825C23—42no—
826C23—42no—
827C23—42no—
828C23—42no—
829C23—42no—
830C23—42no—
831C23—42no—
832C23—42no—
833C23—816no—
834C23—816no—
835C23—816no—
836C23—816no—
837C23—816no—
838C23—816no—
839C23—8128no—
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—
856C23C2×#12012yes—
857C23C2×#12114yes—
858C23C2×#12112yes—
859C23#53512yes—
860C23#57612yes—
861C23#57612yes—
862C23#57612yes—
863C23#57712yes—
864C23C23×D411yescharacteristic
865Q8—24no—
866Q8—24no—
867Q8—48no—
868Q8—42no—
869Q8—42no—
870D4—24no—
871D4—24no—
872D4—24no—
873D4—24no—
874D4—24no—
875D4—24no—
876D4—24no—
877D4—24no—
878D4—432no—
879D4—432no—
880D4—48no—
881D4—48no—
882D4—48no—
883D4—48no—
884D4—42no—
885D4—42no—
886D4—42no—
887D4—42no—
888D4—42no—
889D4—42no—
890D4—42no—
891D4—42no—
892D4—816no—
893D4—816no—
894D4—816no—
895D4—816no—
896D4—816no—
897C2×C4—22no—
898C2×C4—28no—
899C2×C4—22no—
900C2×C4—28no—
901C2×C4—28no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—216no—
907C2×C4—24no—
908C2×C4—24no—
909C2×C4—24no—
910C2×C4—24no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—24no—
914C2×C4—24no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—22no—
918C2×C4—22no—
919C2×C4—432no—
920C2×C4—48no—
921C2×C4—42no—
922C2×C4—42no—
923C2×C4—44no—
924C2×C4—44no—
925C2×C4—48no—
926C2×C4—42no—
927C2×C4—42no—
928C2×C4—42no—
929C2×C4—42no—
930C2×C4—42no—
931C2×C4—42no—
932C2×C4—42no—
933C2×C4—42no—
934C2×C4—816no—
935C2×C4—84no—
936C2×C4—84no—
937C2×C4C2×#12014yes—
938C2×C4C2×#12014yes—
939C2×C4C2×#12012yes—
940C2×C4C2×#12114yes—
941C2×C4C2×#12112yes—
942C2×C4#53512yes—
943C2×C4D4214yes—
944C2×C4D4214yes—
945C2×C4#54614yes—
946C2×C4#54614yes—
947C2×C4C23×D411yescharacteristic
948C2×C4C23×D411yescharacteristic
949C2×C4C23×D411yescharacteristic
950C2×C4C22×#4111yescharacteristic
951C2×C4C2×H(5,𝔽2)11yescharacteristic
952C2×C4C2×H(5,𝔽2)11yescharacteristic
953C8—42no—
954C8—42no—
955C8—42no—
956C8—42no—
957C22—24no—
958C22—24no—
959C22—24no—
960C22—42no—
961C22—42no—
962C22—416no—
963C22—42no—
964C22—42no—
965C22—44no—
966C22—44no—
967C22—44no—
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—82no—
991C22—82no—
992C22—816no—
993C22—816no—
994C22—816no—
995C22—816no—
996C22—82no—
997C22—82no—
998C22#240814yes—
999C22#300814yes—
1000C22#301214yes—
1001C22#304114yes—
1002C22#304514yes—
1003C22#322014yes—
1004C22#322414yes—
1005C22C22×#12011yescharacteristic
1006C22C22×#12111yescharacteristic
1007C22C2×#53511yescharacteristic
1008C22C2×#57611yescharacteristic
1009C22C2×#57611yescharacteristic
1010C22C2×#57611yescharacteristic
1011C22C2×#57711yescharacteristic
1012C4—24no—
1013C4—24no—
1014C4—24no—
1015C4—44no—
1016C4—44no—
1017C4—42no—
1018C4—42no—
1019C4—82no—
1020C4—82no—
1021C4#240814yes—
1022C4C2×D4211yescharacteristic
1023C4C2×D4211yescharacteristic
1024C4C2×#54611yescharacteristic
1025C4C2×#54611yescharacteristic
1026C2—44no—
1027C2—84no—
1028C2—84no—
1029C2—84no—
1030C2—84no—
1031C2#2421818yesdirect product factor
1032C2C2×#240811yescharacteristic
1033C2C2×#300811yescharacteristic
1034C2C2×#301211yescharacteristic
1035C2C2×#304111yescharacteristic
1036C2C2×#304511yescharacteristic
1037C2C2×#322011yescharacteristic
1038C2C2×#322411yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C22×#117 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C22×#535C2semidirect
2. C22×#463C2semidirect
3. C22×#459C2semidirect
4. C22×#449C2semidirect
5. C22×#447C2semidirect
6. C2×#2324C2semidirect
7. #24218C2direct (N × H)
8. C2×#2042C2semidirect
9. C2×#2041C2semidirect
10. C2×#2012C2semidirect
11. C2×#2011C2semidirect
12. C2×#1983C2semidirect
13. C2×#1982C2semidirect
14. C2×#1798C2semidirect
15. C2×#1788C2semidirect
16. C2×#1786C2semidirect
19. C23×SD16C22semidirect
22. C23×D8C22semidirect
26. C2×#535C22semidirect
36. C22×C4×D4C22semidirect
39. C2×#463C22semidirect
41. C2×#459C22semidirect
43. C2×#449C22semidirect
45. C2×#447C22semidirect
46. C22×C4⋊C8C22semidirect
47. C22×C4⋊C8C22semidirect
48. C22×#103C22semidirect
49. C22×#103C22semidirect
50. C22×#103C22semidirect
57. C22×#102C22semidirect
58. C22×#102C22semidirect
59. C22×#102C22semidirect
63. #2324C22semidirect
65. C2×#390C22semidirect
66. C2×#389C22semidirect
71. C2×C4×C4⋊C4C22semidirect
72. #2042C22semidirect
73. #2041C22semidirect
74. #2012C22semidirect
75. #2011C22semidirect
76. #1983C22semidirect
77. #1982C22semidirect
78. #1798C22semidirect
79. #1788C22semidirect
80. #1786C22semidirect
81. C2×#336C22semidirect
82. C2×#336C22semidirect
118. C22×SD16C23semidirect
130. C22×D8C23semidirect
143. C2×#127D4semidirect
151. C2×#124D4semidirect
160. C2×#121D4semidirect
169. C2×C4×D4C23semidirect
200. C2×C4⋊C8C23semidirect
201. C2×C4⋊C8C23semidirect
205. C2×#103C23semidirect
206. C2×#103C23semidirect
207. C2×#103C23semidirect
223. C2×#102C23semidirect
224. C2×#102C23semidirect
225. C2×#102C23semidirect
232. #390C23semidirect
234. #389C23semidirect
241. C4×C4⋊C4C23semidirect
245. #336C23semidirect
246. #336C23semidirect
417. #127C2×D4semidirect
423. #124C2×D4semidirect
428. #121C2×D4semidirect
1031. C2#24218direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#5352
C22×#4632
C22×#4592
C22×#4492
C22×#4472
C2×#23242
#242182
C2×#20422
C2×#20412
C2×#20122
C2×#20112
C2×#19832
C2×#19822
C2×#17982
C2×#17882
C2×#17862