Finite Group Databasebeta

← C2×#24561 #6440554

Subgroups — C2×#24561 #6440554

Order 512.

3490 conjugacy classes of subgroups.

The subgroup lattice has 839 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#485C211yesmaximal, characteristic, complemented
2C22×#407C211yesmaximal, characteristic
3C2×#2848C211yesmaximal, characteristic
4C2×#2280C211yesmaximal, characteristic
5#24561C2116yesmaximal, direct product factor
6C2×#2076C211yesmaximal, characteristic, complemented
7C2×#2077C211yesmaximal, characteristic, complemented
8C2×#2036C211yesmaximal, characteristic, complemented
9C2×#2035C211yesmaximal, characteristic, complemented
10C2×#1894C211yesmaximal, characteristic, complemented
11C2×#1894C211yesmaximal, characteristic, complemented
12C2×#1873C211yesmaximal, characteristic, complemented
13C2×#1854C211yesmaximal, characteristic, complemented
14C2×#1825C211yesmaximal, characteristic, complemented
15C2×#1809C211yesmaximal, characteristic, complemented
16C2×#1809C211yesmaximal, characteristic, complemented
17C25×C4C2211yescharacteristic
18C23×M16C2211yescharacteristic
19C23×M16C2211yescharacteristic
20C22×C22⋊Q8C2211yescharacteristic
21C22×C22⋊Q8C2211yescharacteristic
22C22×C22⋊Q8C2211yescharacteristic
23C22×#117C2211yescharacteristic
24C22×#117C2211yescharacteristic
25C2×#485—28no—
26C2×#485C2218yescomplemented
27C22×#107C2211yescharacteristic, complemented
28C22×#107C2211yescharacteristic, complemented
29C22×#106C2211yescharacteristic, complemented
30C22×#106C2211yescharacteristic, complemented
31C22×#103C2211yescharacteristic, complemented
32C22×#103C2211yescharacteristic, complemented
33C22×#103C2211yescharacteristic, complemented
34C22×#103C2211yescharacteristic, complemented
35C2×#407—28no—
36C2×#407C2218yes—
37C22×C22⋊C8C2211yescharacteristic
38C22×C22⋊C8C2211yescharacteristic
39C22×C22⋊C8C2211yescharacteristic
40C22×C22⋊C8C2211yescharacteristic
41#2848—24no—
42#2848C2218yes—
43C2×#385—21no—
44C2×#385—21no—
45C2×#385—21no—
46#2280—24no—
47#2280C2218yes—
48C2×#381—21no—
49C2×#380C2211yescharacteristic
50C2×#380C2211yescharacteristic
51C2×#380C2211yescharacteristic
52C2×#380C2211yescharacteristic
53C2×#380C2211yescharacteristic
54C2×#380C2211yescharacteristic
55C2×#380C2211yescharacteristic
56C2×#379—21no—
57C2×#379—21no—
58C2×C4×C22⋊C4—21no—
59C2×C4×C22⋊C4—21no—
60#2077C2218yescomplemented
61#2076C2218yescomplemented
62#2036C2218yescomplemented
63#2035C2218yescomplemented
64#1894C2218yescomplemented
65#1894C2218yescomplemented
66#1873C2218yescomplemented
67#1854C2218yescomplemented
68#1825C2218yescomplemented
69#1809C2218yescomplemented
70#1809C2218yescomplemented
71C2×#340C2211yescharacteristic, complemented
72C2×#340C2211yescharacteristic, complemented
73C2×#340C2211yescharacteristic, complemented
74C2×#340C2211yescharacteristic, complemented
75C2×#340C2211yescharacteristic, complemented
76C2×#340C2211yescharacteristic, complemented
77C2×#340C2211yescharacteristic, complemented
78C2×#340C2211yescharacteristic, complemented
79C26D411yescharacteristic
80C23×Q8C2311yescharacteristic
81C24×C4—24no—
82C24×C4—24no—
83C24×C4—24no—
84C24×C4—24no—
85C24×C4—42no—
86C24×C4—42no—
87C24×C4D414yes—
88C24×C4D411yescharacteristic
89C24×C4D411yescharacteristic
90C24×C4D411yescharacteristic
91C24×C4C2311yescharacteristic
92C24×C4C2314yes—
93C24×C4C2311yescharacteristic
94C24×C4C2311yescharacteristic
95C22×M16—24no—
96C22×M16—24no—
97C22×M16—24no—
98C22×M16—24no—
99C22×M16—42no—
100C22×M16—42no—
101C22×M16C2314yes—
102C22×M16C2314yes—
103C23×C8C2311yescharacteristic
104C23×C8C2311yescharacteristic
105C23×C8C2311yescharacteristic
106C23×C8C2311yescharacteristic
107C2×C22⋊Q8—22no—
108C2×C22⋊Q8—22no—
109C2×C22⋊Q8—22no—
110C2×C22⋊Q8—24no—
111C2×C22⋊Q8—24no—
112C2×C22⋊Q8—24no—
113C2×C22⋊Q8—24no—
114C2×C22⋊Q8—42no—
115C2×C22⋊Q8—42no—
116C2×C22⋊Q8C2314yes—
117C2×C22⋊Q8C2314yes—
118C2×C22⋊Q8C2314yes—
119C2×#117—22no—
120C2×#117—22no—
121C2×#117—24no—
122C2×#117—24no—
123C2×#117—42no—
124C2×#117—42no—
125C2×#117C2314yes—
126C2×#117C2314yes—
127C22×C4⋊C4—21no—
128C22×C4⋊C4—21no—
129C22×C4⋊C4—21no—
130C22×C4⋊C4C2311yescharacteristic
131C22×C4⋊C4C2311yescharacteristic
132C22×C4⋊C4C2311yescharacteristic
133C22×C4⋊C4C2311yescharacteristic
134C22×C4⋊C4C2311yescharacteristic
135C22×C4⋊C4C2311yescharacteristic
136C22×C4⋊C4C2311yescharacteristic
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—21no—
145C22×C22⋊C4—21no—
146C22×C22⋊C4—21no—
147C22×C22⋊C4—21no—
148C22×C22⋊C4—21no—
149C22×C42—21no—
150C22×C42—21no—
151#485—232no—
152C2×#107—24no—
153C2×#107—42no—
154C2×#107C2314yescomplemented
155C2×#107C2314yescomplemented
156C2×#106—24no—
157C2×#106—42no—
158C2×#106C2314yescomplemented
159C2×#106C2314yescomplemented
160C2×#103—24no—
161C2×#103—24no—
162C2×#103—42no—
163C2×#103—42no—
164C2×#103C2314yescomplemented
165C2×#103C2314yescomplemented
166C2×#103C2314yescomplemented
167C2×#103C2314yescomplemented
168#407—232no—
169C2×C22⋊C8—24no—
170C2×C22⋊C8—24no—
171C2×C22⋊C8—24no—
172C2×C22⋊C8D418yes—
173C2×C22⋊C8C2314yes—
174C2×C22⋊C8C2314yes—
175C2×C22⋊C8C2314yes—
176C2×C22⋊C8C2314yes—
177#385—28no—
178#385—28no—
179#385—28no—
180#381—28no—
181#380—22no—
182#380—22no—
183#380—22no—
184#380—22no—
185#380—22no—
186#380—22no—
187#380—22no—
188#380C2314yes—
189#380C2314yes—
190#380C2314yes—
191#380C2314yes—
192#380C2314yes—
193#380C2314yes—
194#380C2314yes—
195#379—28no—
196#379—28no—
197C4×C22⋊C4—28no—
198C4×C22⋊C4—28no—
199C2×#95—21no—
200C2×#95—21no—
201C2×#95—21no—
202C2×#95—21no—
203C2×#95—21no—
204C2×#95—21no—
205C2×#95—21no—
206#340C2314yescomplemented
207#340C2314yescomplemented
208#340C2314yescomplemented
209#340C2314yescomplemented
210#340C2314yescomplemented
211#340C2314yescomplemented
212#340C2314yescomplemented
213#340C2314yescomplemented
214C25—24no—
215C25—24no—
216C25—24no—
217C25—42no—
218C25—42no—
219C25—42no—
220C25—42no—
221C25C2×D411yescharacteristic
222C25C2×D411yescharacteristic
223C25C2×D411yescharacteristic
224C25C2×D414yes—
225C22×Q8—21no—
226C22×Q8—22no—
227C22×Q8—22no—
228C22×Q8—22no—
229C22×Q8—22no—
230C22×Q8—22no—
231C22×Q8—22no—
232C22×Q8C2412yes—
233C23×C4—22no—
234C23×C4—22no—
235C23×C4—22no—
236C23×C4—22no—
237C23×C4—22no—
238C23×C4—22no—
239C23×C4—22no—
240C23×C4—22no—
241C23×C4—24no—
242C23×C4—24no—
243C23×C4—24no—
244C23×C4—216no—
245C23×C4—24no—
246C23×C4—24no—
247C23×C4—216no—
248C23×C4—24no—
249C23×C4—22no—
250C23×C4—28no—
251C23×C4—28no—
252C23×C4—28no—
253C23×C4—28no—
254C23×C4—22no—
255C23×C4—22no—
256C23×C4—22no—
257C23×C4—22no—
258C23×C4—22no—
259C23×C4—21no—
260C23×C4—21no—
261C23×C4—21no—
262C23×C4—21no—
263C23×C4—21no—
264C23×C4—21no—
265C23×C4—21no—
266C23×C4—21no—
267C23×C4—48no—
268C23×C4—44no—
269C23×C4—44no—
270C23×C4—42no—
271C23×C4—42no—
272C23×C4—42no—
273C23×C4—416no—
274C23×C4—416no—
275C23×C4—416no—
276C23×C4—416no—
277C23×C4C2×D412yes—
278C23×C4C2×D411yescharacteristic
279C23×C4C2×D414yes—
280C23×C4C2×D414yes—
281C23×C4C2×D414yes—
282C23×C4C2×D412yes—
283C23×C4C2×D411yescharacteristic
284C23×C4C2×D414yes—
285C23×C4C2×D412yes—
286C23×C4C2×D411yescharacteristic
287C23×C4#4114yes—
288C23×C4#4114yes—
289C23×C4#4114yes—
290C23×C4C2412yes—
291C23×C4C2412yes—
292C23×C4C2412yes—
293C23×C4C2411yescharacteristic
294C2×M16—28no—
295C2×M16—28no—
296C2×M16—28no—
297C2×M16—28no—
298C2×M16—44no—
299C2×M16—44no—
300C2×M16—416no—
301C2×M16—416no—
302C22×C8—22no—
303C22×C8—22no—
304C22×C8—22no—
305C22×C8—22no—
306C22×C8—22no—
307C22×C8—22no—
308C22×C8—22no—
309C22×C8—22no—
310C22×C8—22no—
311C22×C8—22no—
312C22×C8C2×D414yes—
313C22×C8C2×D414yes—
314C22×C8C2412yes—
315C22×C8C2412yes—
316C22×C8C2412yes—
317C22×C8C2412yes—
318C22⋊Q8—28no—
319C22⋊Q8—28no—
320C22⋊Q8—28no—
321C22⋊Q8—28no—
322C22⋊Q8—44no—
323C22⋊Q8—44no—
324C22⋊Q8—48no—
325C22⋊Q8—48no—
326C22⋊Q8—48no—
327#117—28no—
328#117—28no—
329#117—44no—
330#117—44no—
331#117—48no—
332#117—48no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—22no—
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—22no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—24no—
348C2×C4⋊C4—24no—
349C2×C4⋊C4—24no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—44no—
358C2×C4⋊C4—44no—
359C2×C4⋊C4—44no—
360C2×C4⋊C4C2412yes—
361C2×C4⋊C4C2412yes—
362C2×C4⋊C4C2412yes—
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—44no—
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—44no—
388C2×C22⋊C4—44no—
389C2×C22⋊C4—44no—
390C2×C22⋊C4—44no—
391C2×C42—24no—
392C2×C42—24no—
393C2×C42—44no—
394C2×C42—44no—
395#107—28no—
396#107—44no—
397#106—28no—
398#106—44no—
399#103—28no—
400#103—28no—
401#103—44no—
402#103—44no—
403C22⋊C8—28no—
404C22⋊C8—28no—
405C22⋊C8—28no—
406C22⋊C8C2×D4116yes—
407#95—24no—
408#95—24no—
409#95—24no—
410#95—24no—
411#95—24no—
412#95—24no—
413#95—24no—
414C24—22no—
415C24—22no—
416C24—22no—
417C24—22no—
418C24—22no—
419C24—22no—
420C24—22no—
421C24—22no—
422C24—22no—
423C24—22no—
424C24—22no—
425C24—22no—
426C24—22no—
427C24—22no—
428C24—22no—
429C24—22no—
430C24—22no—
431C24—22no—
432C24—28no—
433C24—28no—
434C24—28no—
435C24—44no—
436C24—44no—
437C24—44no—
438C24—44no—
439C24—416no—
440C24—416no—
441C24—416no—
442C24—416no—
443C24—416no—
444C24—416no—
445C24—416no—
446C24#12114yes—
447C24#12314yes—
448C24#13714yes—
449C24C22×D412yes—
450C24C22×D412yes—
451C24C22×D412yes—
452C24C22×D411yescharacteristic
453C2×Q8—22no—
454C2×Q8—22no—
455C2×Q8—22no—
456C2×Q8—22no—
457C2×Q8—22no—
458C2×Q8—22no—
459C2×Q8—42no—
460C2×Q8—42no—
461C2×Q8—42no—
462C2×Q8—44no—
463C2×Q8—44no—
464C2×Q8—44no—
465C2×Q8—44no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—24no—
471C22×C4—24no—
472C22×C4—24no—
473C22×C4—24no—
474C22×C4—28no—
475C22×C4—28no—
476C22×C4—28no—
477C22×C4—28no—
478C22×C4—28no—
479C22×C4—28no—
480C22×C4—28no—
481C22×C4—28no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—28no—
491C22×C4—22no—
492C22×C4—28no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—28no—
496C22×C4—28no—
497C22×C4—24no—
498C22×C4—28no—
499C22×C4—28no—
500C22×C4—24no—
501C22×C4—24no—
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—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—44no—
517C22×C4—44no—
518C22×C4—44no—
519C22×C4—416no—
520C22×C4—464no—
521C22×C4—416no—
522C22×C4—416no—
523C22×C4—416no—
524C22×C4—416no—
525C22×C4—416no—
526C22×C4—416no—
527C22×C4—44no—
528C22×C4—44no—
529C22×C4—44no—
530C22×C4—44no—
531C22×C4—42no—
532C22×C4—42no—
533C22×C4—42no—
534C22×C4—42no—
535C22×C4—42no—
536C22×C4—42no—
537C22×C4—42no—
538C22×C4—42no—
539C22×C4—42no—
540C22×C4—42no—
541C22×C4—42no—
542C22×C4—42no—
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#12114yes—
556C22×C4#12118yes—
557C22×C4#12314yes—
558C22×C4#12318yes—
559C22×C4C22×D412yes—
560C22×C4C22×D412yes—
561C22×C4C22×D414yes—
562C22×C4C22×D412yes—
563C22×C4C22×D411yescharacteristic
564C22×C4C22×D412yes—
565C22×C4C2×#4114yes—
566C22×C4C2×#4114yes—
567C22×C4C2×#4114yes—
568C22×C4C2×#4112yes—
569C22×C4C2×#4112yes—
570C22×C4C2×#4112yes—
571C22×C4H(5,𝔽2)12yes—
572C22×C4H(5,𝔽2)12yes—
573C22×C4C2511yescharacteristic
574M16—416no—
575M16—416no—
576C2×C8—28no—
577C2×C8—28no—
578C2×C8—22no—
579C2×C8—22no—
580C2×C8—22no—
581C2×C8—22no—
582C2×C8—22no—
583C2×C8—22no—
584C2×C8—22no—
585C2×C8—22no—
586C2×C8—22no—
587C2×C8—22no—
588C2×C8—44no—
589C2×C8—44no—
590C2×C8C22×D414yes—
591C2×C8C22×D414yes—
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—22no—
603C4⋊C4—22no—
604C4⋊C4—22no—
605C4⋊C4—22no—
606C4⋊C4—48no—
607C4⋊C4—42no—
608C4⋊C4—42no—
609C4⋊C4—42no—
610C4⋊C4—48no—
611C4⋊C4—42no—
612C4⋊C4—48no—
613C4⋊C4—42no—
614C4⋊C4—42no—
615C4⋊C4—42no—
616C22⋊C4—48no—
617C22⋊C4—48no—
618C22⋊C4—48no—
619C22⋊C4—48no—
620C22⋊C4—48no—
621C22⋊C4—48no—
622C22⋊C4—48no—
623C22⋊C4—48no—
624C22⋊C4—48no—
625C22⋊C4—48no—
626C22⋊C4—48no—
627C22⋊C4—48no—
628C42—48no—
629C42—48no—
630C23—28no—
631C23—28no—
632C23—28no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—28no—
638C23—28no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—28no—
643C23—28no—
644C23—28no—
645C23—28no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—416no—
658C23—416no—
659C23—416no—
660C23—416no—
661C23—416no—
662C23—416no—
663C23—416no—
664C23—4128no—
665C23—44no—
666C23—44no—
667C23—44no—
668C23—44no—
669C23—44no—
670C23—44no—
671C23—44no—
672C23—44no—
673C23—44no—
674C23—44no—
675C23—44no—
676C23—44no—
677C23C2×#12114yes—
678C23C2×#12112yes—
679C23C2×#12314yes—
680C23C2×#12312yes—
681C23#53412yes—
682C23C2×#13714yes—
683C23C2×#13712yes—
684C23#57512yes—
685C23#57512yes—
686C23#57512yes—
687C23C23×D411yescharacteristic
688Q8—42no—
689Q8—42no—
690Q8—42no—
691Q8—42no—
692Q8—84no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—28no—
696C2×C4—28no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—216no—
700C2×C4—216no—
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—24no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—416no—
713C2×C4—416no—
714C2×C4—416no—
715C2×C4—44no—
716C2×C4—48no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
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—84no—
746C2×C4—84no—
747C2×C4—84no—
748C2×C4—84no—
749C2×C4—84no—
750C2×C4—84no—
751C2×C4—84no—
752C2×C4—84no—
753C2×C4C2×#12114yes—
754C2×C4C2×#12112yes—
755C2×C4C2×#12314yes—
756C2×C4C2×#12312yes—
757C2×C4#53412yes—
758C2×C4#54614yes—
759C2×C4#54614yes—
760C2×C4#55114yes—
761C2×C4#55114yes—
762C2×C4C23×D411yescharacteristic
763C2×C4C22×#4111yescharacteristic
764C2×C4C22×#4111yescharacteristic
765C2×C4C22×#4111yescharacteristic
766C2×C4C2×H(5,𝔽2)11yescharacteristic
767C2×C4C2×H(5,𝔽2)11yescharacteristic
768C8—24no—
769C8—24no—
770C8—42no—
771C8—42no—
772C22—24no—
773C22—24no—
774C22—24no—
775C22—24no—
776C22—24no—
777C22—24no—
778C22—24no—
779C22—24no—
780C22—24no—
781C22—464no—
782C22—42no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—42no—
787C22—42no—
788C22—42no—
789C22—42no—
790C22—42no—
791C22—42no—
792C22—42no—
793C22—42no—
794C22—416no—
795C22—416no—
796C22—416no—
797C22#241214yes—
798C22#305414yes—
799C22#305614yes—
800C22#309314yes—
801C22#309514yes—
802C22#319614yes—
803C22#319714yes—
804C22C22×#12111yescharacteristic
805C22C22×#12311yescharacteristic
806C22C2×#53411yescharacteristic
807C22C22×#13711yescharacteristic
808C22C2×#57511yescharacteristic
809C22C2×#57511yescharacteristic
810C22C2×#57511yescharacteristic
811C4—24no—
812C4—24no—
813C4—42no—
814C4—82no—
815C4—82no—
816C4—82no—
817C4—82no—
818C4—82no—
819C4—82no—
820C4—82no—
821C4—82no—
822C4#241214yes—
823C4C2×#54611yescharacteristic
824C4C2×#54611yescharacteristic
825C4C2×#55111yescharacteristic
826C4C2×#55111yescharacteristic
827C2—44no—
828C2—44no—
829C2—44no—
830C2#2456118yesdirect product factor
831C2C2×#241211yescharacteristic
832C2C2×#305411yescharacteristic
833C2C2×#305611yescharacteristic
834C2C2×#309311yescharacteristic
835C2C2×#309511yescharacteristic
836C2C2×#319611yescharacteristic
837C2C2×#319711yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC26D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C25×C4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C22×#485C2semidirect
5. #24561C2direct (N × H)
6. C2×#2076C2semidirect
7. C2×#2077C2semidirect
8. C2×#2036C2semidirect
9. C2×#2035C2semidirect
10. C2×#1894C2semidirect
11. C2×#1894C2semidirect
12. C2×#1873C2semidirect
13. C2×#1854C2semidirect
14. C2×#1825C2semidirect
15. C2×#1809C2semidirect
16. C2×#1809C2semidirect
26. C2×#485C22semidirect
27. C22×#107C22semidirect
28. C22×#107C22semidirect
29. C22×#106C22semidirect
30. C22×#106C22semidirect
31. C22×#103C22semidirect
32. C22×#103C22semidirect
33. C22×#103C22semidirect
34. C22×#103C22semidirect
60. #2077C22semidirect
61. #2076C22semidirect
62. #2036C22semidirect
63. #2035C22semidirect
64. #1894C22semidirect
65. #1894C22semidirect
66. #1873C22semidirect
67. #1854C22semidirect
68. #1825C22semidirect
69. #1809C22semidirect
70. #1809C22semidirect
71. C2×#340C22semidirect
72. C2×#340C22semidirect
73. C2×#340C22semidirect
74. C2×#340C22semidirect
75. C2×#340C22semidirect
76. C2×#340C22semidirect
77. C2×#340C22semidirect
78. C2×#340C22semidirect
154. C2×#107C23semidirect
155. C2×#107C23semidirect
158. C2×#106C23semidirect
159. C2×#106C23semidirect
164. C2×#103C23semidirect
165. C2×#103C23semidirect
166. C2×#103C23semidirect
167. C2×#103C23semidirect
206. #340C23semidirect
207. #340C23semidirect
208. #340C23semidirect
209. #340C23semidirect
210. #340C23semidirect
211. #340C23semidirect
212. #340C23semidirect
213. #340C23semidirect
830. C2#24561direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#4852
C22×#4072
C2×#28482
C2×#22802
#245612
C2×#20762
C2×#20772
C2×#20362
C2×#20352
C2×#18942
C2×#18732
C2×#18542
C2×#18252
C2×#18092