Finite Group Databasebeta

← C2×#29896 #6433138

Subgroups — C2×#29896 #6433138

Order 512.

3384 conjugacy classes of subgroups.

The subgroup lattice has 865 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2847C211yesmaximal, characteristic
2C2×#2280C211yesmaximal, characteristic, complemented
3#29896C2116yesmaximal, direct product factor
4C2×#2076C211yesmaximal, characteristic, complemented
5C2×#2077C211yesmaximal, characteristic, complemented
6C2×#2077C211yesmaximal, characteristic, complemented
7C2×#2075C211yesmaximal, characteristic, complemented
8C2×#2034C211yesmaximal, characteristic, complemented
9C2×#2034C211yesmaximal, characteristic, complemented
10C2×#2033C211yesmaximal, characteristic, complemented
11C2×#2033C211yesmaximal, characteristic, complemented
12C2×#1875C211yesmaximal, characteristic, complemented
13C2×#1875C211yesmaximal, characteristic, complemented
14C2×#1854C211yesmaximal, characteristic, complemented
15C2×#1854C211yesmaximal, characteristic, complemented
16C2×#1779C211yesmaximal, characteristic, complemented
17C25×C4C2211yescharacteristic
18C22×#121C2211yescharacteristic
19C22×#121C2211yescharacteristic
20C22×#121C2211yescharacteristic
21C22×#120—21no—
22C22×#117C2211yescharacteristic
23C22×#117C2211yescharacteristic
24C22×#107C2211yescharacteristic, complemented
25C22×#107C2211yescharacteristic, complemented
26C22×#106C2211yescharacteristic, complemented
27C22×#106C2211yescharacteristic, complemented
28C22×#102C2211yescharacteristic, complemented
29C22×#102C2211yescharacteristic, complemented
30C22×#102C2211yescharacteristic, complemented
31C22×#102C2211yescharacteristic, complemented
32C22×C22⋊C8C2211yescharacteristic
33C22×C22⋊C8C2211yescharacteristic
34C22×C22⋊C8C2211yescharacteristic
35C22×C22⋊C8C2211yescharacteristic
36C22×C22⋊C8C2211yescharacteristic
37C22×C22⋊C8C2211yescharacteristic
38#2847—24no—
39#2847C2218yes—
40C2×#386—21no—
41C2×#386—21no—
42C2×#386—21no—
43#2280—24no—
44#2280C2218yescomplemented
45C2×#381—21no—
46C2×#380C2211yescharacteristic
47C2×#380C2211yescharacteristic
48C2×#380C2211yescharacteristic
49C2×#380C2211yescharacteristic
50C2×#380C2211yescharacteristic
51C2×#380C2211yescharacteristic
52C2×#380C2211yescharacteristic
53C2×#379—21no—
54C2×C4×C22⋊C4—21no—
55C2×C4×C22⋊C4—21no—
56#2077C2218yescomplemented
57#2077C2218yescomplemented
58#2076C2218yescomplemented
59#2075C2218yescomplemented
60#2034C2218yescomplemented
61#2034C2218yescomplemented
62#2033C2218yescomplemented
63#2033C2218yescomplemented
64#1875C2218yescomplemented
65#1875C2218yescomplemented
66#1854C2218yescomplemented
67#1854C2218yescomplemented
68#1779C2218yescomplemented
69C2×#340C2211yescharacteristic, complemented
70C2×#340C2211yescharacteristic, complemented
71C2×#340C2211yescharacteristic, complemented
72C2×#340C2211yescharacteristic, complemented
73C2×#340C2211yescharacteristic, complemented
74C2×#340C2211yescharacteristic, complemented
75C2×#340C2211yescharacteristic, complemented
76C2×#340C2211yescharacteristic, complemented
77C26D411yescharacteristic
78C23×D4—21no—
79C23×D4—21no—
80C23×D4—21no—
81C23×D4C2311yescharacteristic
82C24×C4—24no—
83C24×C4—24no—
84C24×C4—42no—
85C24×C4—42no—
86C24×C4—42no—
87C24×C4—42no—
88C24×C4D414yes—
89C24×C4D411yescharacteristic
90C24×C4D411yescharacteristic
91C24×C4D411yescharacteristic
92C24×C4C2311yescharacteristic
93C24×C4C2311yescharacteristic
94C24×C4C2311yescharacteristic
95C24×C4C2314yes—
96C23×C8C2311yescharacteristic
97C23×C8C2311yescharacteristic
98C23×C8C2311yescharacteristic
99C23×C8C2311yescharacteristic
100C2×#121—22no—
101C2×#121—22no—
102C2×#121—22no—
103C2×#121—24no—
104C2×#121—24no—
105C2×#121—42no—
106C2×#121—42no—
107C2×#121—42no—
108C2×#121—42no—
109C2×#121C2314yes—
110C2×#121C2314yes—
111C2×#121C2314yes—
112C2×#120—28no—
113C2×#120—48no—
114C2×#117—22no—
115C2×#117—22no—
116C2×#117—42no—
117C2×#117—42no—
118C2×#117—42no—
119C2×#117—42no—
120C2×#117C2314yes—
121C2×#117C2314yes—
122C22×C4⋊C4C2311yescharacteristic
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⋊C4—21no—
141C22×C42—21no—
142C22×C42—21no—
143C2×#107—42no—
144C2×#107—42no—
145C2×#107C2314yescomplemented
146C2×#107C2314yescomplemented
147C2×#106—42no—
148C2×#106—42no—
149C2×#106C2314yescomplemented
150C2×#106C2314yescomplemented
151C2×#102—42no—
152C2×#102—42no—
153C2×#102—42no—
154C2×#102—42no—
155C2×#102C2314yescomplemented
156C2×#102C2314yescomplemented
157C2×#102C2314yescomplemented
158C2×#102C2314yescomplemented
159C2×C22⋊C8—24no—
160C2×C22⋊C8—24no—
161C2×C22⋊C8—42no—
162C2×C22⋊C8—42no—
163C2×C22⋊C8—42no—
164C2×C22⋊C8—42no—
165C2×C22⋊C8C2314yes—
166C2×C22⋊C8C2314yes—
167C2×C22⋊C8C2314yes—
168C2×C22⋊C8C2314yes—
169C2×C22⋊C8C2314yes—
170C2×C22⋊C8C2314yes—
171#386—28no—
172#386—28no—
173#386—28no—
174#381—28no—
175#380—22no—
176#380—22no—
177#380—22no—
178#380—22no—
179#380—22no—
180#380—22no—
181#380—22no—
182#380C2314yes—
183#380C2314yes—
184#380C2314yes—
185#380C2314yes—
186#380C2314yes—
187#380C2314yes—
188#380C2314yes—
189#379—28no—
190C4×C22⋊C4—28no—
191C4×C22⋊C4—28no—
192C2×#95—21no—
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#340C2314yescomplemented
206#340C2314yescomplemented
207C25—24no—
208C25—24no—
209C25—24no—
210C25—21no—
211C25—42no—
212C25—42no—
213C25—42no—
214C25—42no—
215C25C2×D411yescharacteristic
216C25C2×D411yescharacteristic
217C25C2×D411yescharacteristic
218C25C2×D414yes—
219C22×D4—24no—
220C22×D4—24no—
221C22×D4—24no—
222C22×D4—21no—
223C22×D4—22no—
224C22×D4—22no—
225C22×D4—22no—
226C22×D4—22no—
227C22×D4—22no—
228C22×D4—22no—
229C22×D4—44no—
230C22×D4—44no—
231C22×D4—44no—
232C22×D4—44no—
233C22×D4—44no—
234C22×D4—44no—
235C22×D4—44no—
236C22×D4—44no—
237C22×D4—44no—
238C22×D4C2412yes—
239C23×C4—22no—
240C23×C4—22no—
241C23×C4—22no—
242C23×C4—22no—
243C23×C4—24no—
244C23×C4—24no—
245C23×C4—24no—
246C23×C4—216no—
247C23×C4—28no—
248C23×C4—28no—
249C23×C4—22no—
250C23×C4—22no—
251C23×C4—22no—
252C23×C4—22no—
253C23×C4—22no—
254C23×C4—22no—
255C23×C4—22no—
256C23×C4—22no—
257C23×C4—22no—
258C23×C4—22no—
259C23×C4—22no—
260C23×C4—22no—
261C23×C4—21no—
262C23×C4—21no—
263C23×C4—21no—
264C23×C4—21no—
265C23×C4—21no—
266C23×C4—21no—
267C23×C4—21no—
268C23×C4—48no—
269C23×C4—48no—
270C23×C4—44no—
271C23×C4—44no—
272C23×C4—44no—
273C23×C4—44no—
274C23×C4—42no—
275C23×C4—42no—
276C23×C4—42no—
277C23×C4—42no—
278C23×C4—42no—
279C23×C4—42no—
280C23×C4—416no—
281C23×C4—416no—
282C23×C4—416no—
283C23×C4—416no—
284C23×C4C2×D412yes—
285C23×C4C2×D412yes—
286C23×C4C2×D411yescharacteristic
287C23×C4C2×D411yescharacteristic
288C23×C4C2×D412yes—
289C23×C4C2×D411yescharacteristic
290C23×C4C2×D414yes—
291C23×C4C2×D414yes—
292C23×C4C2×D414yes—
293C23×C4#4114yes—
294C23×C4#4114yes—
295C23×C4C2412yes—
296C23×C4C2412yes—
297C23×C4C2412yes—
298C23×C4C2411yescharacteristic
299C22×C8—22no—
300C22×C8—22no—
301C22×C8—22no—
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×C8C2412yes—
312C22×C8C2412yes—
313C22×C8C2412yes—
314C22×C8C2412yes—
315#121—28no—
316#121—28no—
317#121—44no—
318#121—44no—
319#121—44no—
320#121—44no—
321#121—48no—
322#121—48no—
323#121—48no—
324#120—432no—
325#117—44no—
326#117—44no—
327#117—44no—
328#117—44no—
329#117—48no—
330#117—48no—
331C2×C4⋊C4—22no—
332C2×C4⋊C4—22no—
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—21no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4C2412yes—
353C2×C4⋊C4C2412yes—
354C2×C4⋊C4C2412yes—
355C2×C4⋊C4C2412yes—
356C2×C4⋊C4C2412yes—
357C2×C4⋊C4C2412yes—
358C2×C4⋊C4C2412yes—
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—24no—
366C2×C22⋊C4—24no—
367C2×C22⋊C4—24no—
368C2×C22⋊C4—24no—
369C2×C22⋊C4—24no—
370C2×C22⋊C4—24no—
371C2×C22⋊C4—44no—
372C2×C22⋊C4—44no—
373C2×C22⋊C4—44no—
374C2×C22⋊C4—44no—
375C2×C22⋊C4—44no—
376C2×C22⋊C4—44no—
377C2×C22⋊C4—44no—
378C2×C22⋊C4—44no—
379C2×C22⋊C4—44no—
380C2×C22⋊C4—44no—
381C2×C22⋊C4—44no—
382C2×C22⋊C4—44no—
383C2×C42—24no—
384C2×C42—24no—
385C2×C42—44no—
386C2×C42—44no—
387#107—44no—
388#107—44no—
389#106—44no—
390#106—44no—
391#102—44no—
392#102—44no—
393#102—44no—
394#102—44no—
395C22⋊C8—28no—
396C22⋊C8—28no—
397C22⋊C8—44no—
398C22⋊C8—44no—
399C22⋊C8—44no—
400C22⋊C8—44no—
401#95—24no—
402#95—24no—
403#95—24no—
404#95—24no—
405#95—24no—
406#95—24no—
407#95—24no—
408C24—22no—
409C24—22no—
410C24—22no—
411C24—22no—
412C24—22no—
413C24—22no—
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—28no—
427C24—28no—
428C24—28no—
429C24—22no—
430C24—44no—
431C24—44no—
432C24—44no—
433C24—44no—
434C24—416no—
435C24—416no—
436C24—416no—
437C24—416no—
438C24—416no—
439C24—416no—
440C24—416no—
441C24—42no—
442C24—42no—
443C24—42no—
444C24—42no—
445C24—42no—
446C24—42no—
447C24—42no—
448C24#12314yes—
449C24#13514yes—
450C24AGL(1,ℤ/8)14yes—
451C24C22×D412yes—
452C24C22×D412yes—
453C24C22×D412yes—
454C24C22×D411yescharacteristic
455C2×D4—22no—
456C2×D4—22no—
457C2×D4—22no—
458C2×D4—22no—
459C2×D4—22no—
460C2×D4—22no—
461C2×D4—48no—
462C2×D4—48no—
463C2×D4—48no—
464C2×D4—48no—
465C2×D4—48no—
466C2×D4—48no—
467C2×D4—48no—
468C2×D4—48no—
469C2×D4—48no—
470C2×D4—42no—
471C2×D4—42no—
472C2×D4—42no—
473C2×D4—44no—
474C2×D4—44no—
475C2×D4—44no—
476C2×D4—44no—
477C2×D4—816no—
478C2×D4—816no—
479C2×D4—816no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—24no—
483C22×C4—24no—
484C22×C4—28no—
485C22×C4—28no—
486C22×C4—28no—
487C22×C4—28no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—28no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—28no—
500C22×C4—28no—
501C22×C4—24no—
502C22×C4—24no—
503C22×C4—24no—
504C22×C4—24no—
505C22×C4—24no—
506C22×C4—24no—
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—22no—
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—44no—
527C22×C4—44no—
528C22×C4—44no—
529C22×C4—44no—
530C22×C4—44no—
531C22×C4—44no—
532C22×C4—416no—
533C22×C4—416no—
534C22×C4—464no—
535C22×C4—416no—
536C22×C4—416no—
537C22×C4—416no—
538C22×C4—416no—
539C22×C4—416no—
540C22×C4—44no—
541C22×C4—44no—
542C22×C4—44no—
543C22×C4—44no—
544C22×C4—44no—
545C22×C4—44no—
546C22×C4—44no—
547C22×C4—44no—
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×C4—42no—
562C22×C4—42no—
563C22×C4—42no—
564C22×C4—42no—
565C22×C4—42no—
566C22×C4—42no—
567C22×C4—42no—
568C22×C4—42no—
569C22×C4#12314yes—
570C22×C4#12318yes—
571C22×C4C22×D412yes—
572C22×C4C22×D412yes—
573C22×C4C22×D412yes—
574C22×C4C22×D411yescharacteristic
575C22×C4C2×#4114yes—
576C22×C4C2×#4114yes—
577C22×C4C2×#4112yes—
578C22×C4C2×#4112yes—
579C22×C4H(5,𝔽2)12yes—
580C22×C4H(5,𝔽2)12yes—
581C22×C4H(5,𝔽2)12yes—
582C22×C4H(5,𝔽2)12yes—
583C22×C4C2511yescharacteristic
584C2×C8—22no—
585C2×C8—22no—
586C2×C8—22no—
587C2×C8—22no—
588C2×C8—22no—
589C2×C8—22no—
590C2×C8—22no—
591C2×C8—22no—
592C2×C8—22no—
593C2×C8—22no—
594C2×C8—22no—
595C2×C8—22no—
596C2×C8—44no—
597C2×C8—44no—
598C2×C8—44no—
599C2×C8—44no—
600C4⋊C4—22no—
601C4⋊C4—22no—
602C4⋊C4—22no—
603C4⋊C4—22no—
604C4⋊C4—22no—
605C4⋊C4—22no—
606C4⋊C4—22no—
607C4⋊C4—22no—
608C4⋊C4—22no—
609C4⋊C4—22no—
610C4⋊C4—22no—
611C4⋊C4—22no—
612C4⋊C4—22no—
613C4⋊C4—22no—
614C4⋊C4—42no—
615C4⋊C4—42no—
616C4⋊C4—42no—
617C4⋊C4—42no—
618C4⋊C4—42no—
619C4⋊C4—42no—
620C4⋊C4—42no—
621C22⋊C4—48no—
622C22⋊C4—48no—
623C22⋊C4—48no—
624C22⋊C4—48no—
625C22⋊C4—48no—
626C22⋊C4—48no—
627C22⋊C4—48no—
628C22⋊C4—48no—
629C22⋊C4—48no—
630C22⋊C4—48no—
631C22⋊C4—48no—
632C22⋊C4—48no—
633C42—48no—
634C42—48no—
635C23—28no—
636C23—28no—
637C23—28no—
638C23—28no—
639C23—28no—
640C23—22no—
641C23—22no—
642C23—28no—
643C23—28no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—28no—
651C23—28no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—416no—
663C23—416no—
664C23—416no—
665C23—416no—
666C23—416no—
667C23—416no—
668C23—416no—
669C23—4128no—
670C23—44no—
671C23—44no—
672C23—44no—
673C23—44no—
674C23—44no—
675C23—44no—
676C23—44no—
677C23—44no—
678C23—44no—
679C23—44no—
680C23—44no—
681C23—44no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—84no—
690C23—84no—
691C23—84no—
692C23—84no—
693C23—84no—
694C23—84no—
695C23—84no—
696C23C2×#12314yes—
697C23C2×#12312yes—
698C23#53412yes—
699C23#53412yes—
700C23C2×#13514yes—
701C23C2×#13512yes—
702C23C2×AGL(1,ℤ/8)14yes—
703C23C2×AGL(1,ℤ/8)12yes—
704C23#57512yes—
705C23#57512yes—
706C23C23×D411yescharacteristic
707D4—42no—
708D4—42no—
709D4—42no—
710D4—42no—
711D4—816no—
712D4—816no—
713D4—816no—
714D4—84no—
715C2×C4—28no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—216no—
719C2×C4—24no—
720C2×C4—24no—
721C2×C4—24no—
722C2×C4—24no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—416no—
730C2×C4—416no—
731C2×C4—416no—
732C2×C4—44no—
733C2×C4—44no—
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—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—84no—
766C2×C4—84no—
767C2×C4—84no—
768C2×C4—84no—
769C2×C4—84no—
770C2×C4—84no—
771C2×C4—84no—
772C2×C4C2×#12314yes—
773C2×C4C2×#12312yes—
774C2×C4#53412yes—
775C2×C4#53412yes—
776C2×C4#53814yes—
777C2×C4#53814yes—
778C2×C4#53814yes—
779C2×C4#53814yes—
780C2×C4C22×#4111yescharacteristic
781C2×C4C22×#4111yescharacteristic
782C2×C4C2×H(5,𝔽2)11yescharacteristic
783C2×C4C2×H(5,𝔽2)11yescharacteristic
784C2×C4C2×H(5,𝔽2)11yescharacteristic
785C2×C4C2×H(5,𝔽2)11yescharacteristic
786C8—42no—
787C8—42no—
788C8—42no—
789C8—42no—
790C22—24no—
791C22—24no—
792C22—24no—
793C22—24no—
794C22—24no—
795C22—24no—
796C22—24no—
797C22—24no—
798C22—24no—
799C22—464no—
800C22—42no—
801C22—42no—
802C22—42no—
803C22—42no—
804C22—42no—
805C22—42no—
806C22—42no—
807C22—42no—
808C22—42no—
809C22—42no—
810C22—416no—
811C22—416no—
812C22—416no—
813C22—42no—
814C22—42no—
815C22—82no—
816C22—82no—
817C22—82no—
818C22—82no—
819C22—82no—
820C22—82no—
821C22—82no—
822C22—168no—
823C22#262214yes—
824C22#309114yes—
825C22#309414yes—
826C22#318814yes—
827C22#319114yes—
828C22#319414yes—
829C22#319714yes—
830C22C22×#12311yescharacteristic
831C22C2×#53411yescharacteristic
832C22C2×#53411yescharacteristic
833C22C22×#13511yescharacteristic
834C22C22×AGL(1,ℤ/8)11yescharacteristic
835C22C2×#57511yescharacteristic
836C22C2×#57511yescharacteristic
837C4—24no—
838C4—42no—
839C4—42no—
840C4—82no—
841C4—82no—
842C4—82no—
843C4—82no—
844C4—82no—
845C4—82no—
846C4—82no—
847C4#262214yes—
848C4C2×#53811yescharacteristic
849C4C2×#53811yescharacteristic
850C4C2×#53811yescharacteristic
851C4C2×#53811yescharacteristic
852C2—44no—
853C2—44no—
854C2—44no—
855C2—162no—
856C2#2989618yesdirect product factor
857C2C2×#262211yescharacteristic
858C2C2×#309111yescharacteristic
859C2C2×#309411yescharacteristic
860C2C2×#318811yescharacteristic
861C2C2×#319111yescharacteristic
862C2C2×#319411yescharacteristic
863C2C2×#319711yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#2847C2
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
2. C2×#2280C2semidirect
3. #29896C2direct (N × H)
4. C2×#2076C2semidirect
5. C2×#2077C2semidirect
6. C2×#2077C2semidirect
7. C2×#2075C2semidirect
8. C2×#2034C2semidirect
9. C2×#2034C2semidirect
10. C2×#2033C2semidirect
11. C2×#2033C2semidirect
12. C2×#1875C2semidirect
13. C2×#1875C2semidirect
14. C2×#1854C2semidirect
15. C2×#1854C2semidirect
16. C2×#1779C2semidirect
24. C22×#107C22semidirect
25. C22×#107C22semidirect
26. C22×#106C22semidirect
27. C22×#106C22semidirect
28. C22×#102C22semidirect
29. C22×#102C22semidirect
30. C22×#102C22semidirect
31. C22×#102C22semidirect
44. #2280C22semidirect
56. #2077C22semidirect
57. #2077C22semidirect
58. #2076C22semidirect
59. #2075C22semidirect
60. #2034C22semidirect
61. #2034C22semidirect
62. #2033C22semidirect
63. #2033C22semidirect
64. #1875C22semidirect
65. #1875C22semidirect
66. #1854C22semidirect
67. #1854C22semidirect
68. #1779C22semidirect
69. C2×#340C22semidirect
70. C2×#340C22semidirect
71. C2×#340C22semidirect
72. C2×#340C22semidirect
73. C2×#340C22semidirect
74. C2×#340C22semidirect
75. C2×#340C22semidirect
76. C2×#340C22semidirect
145. C2×#107C23semidirect
146. C2×#107C23semidirect
149. C2×#106C23semidirect
150. C2×#106C23semidirect
155. C2×#102C23semidirect
156. C2×#102C23semidirect
157. C2×#102C23semidirect
158. C2×#102C23semidirect
199. #340C23semidirect
200. #340C23semidirect
201. #340C23semidirect
202. #340C23semidirect
203. #340C23semidirect
204. #340C23semidirect
205. #340C23semidirect
206. #340C23semidirect
856. C2#29896direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#28472
C2×#22802
#298962
C2×#20762
C2×#20772
C2×#20752
C2×#20342
C2×#20332
C2×#18752
C2×#18542
C2×#17792