Finite Group Databasebeta

← C2×#23049 #6382004

Subgroups — C2×#23049 #6382004

Order 512.

2586 conjugacy classes of subgroups.

The subgroup lattice has 859 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#471C211yesmaximal, characteristic
2C2×#2949C211yesmaximal, characteristic, complemented
3C2×#2947C211yesmaximal, characteristic, complemented
4C2×#2946C211yesmaximal, characteristic
5C2×#2913C211yesmaximal, characteristic, complemented
6#23049C2116yesmaximal, direct product factor
7C2×#1973C211yesmaximal, characteristic, complemented
8C2×#1952C211yesmaximal, characteristic, complemented
9C2×#1931C211yesmaximal, characteristic, complemented
10C2×#1930C211yesmaximal, characteristic, complemented
11C2×#1883C211yesmaximal, characteristic
12C2×#1882C211yesmaximal, characteristic, complemented
13C2×#1857C211yesmaximal, characteristic, complemented
14C2×#1856C211yesmaximal, characteristic, complemented
15C2×#1773C211yesmaximal, characteristic, complemented
16C2×#1765C211yesmaximal, characteristic, complemented
17C22×#137C2211yescharacteristic
18C22×AGL(1,ℤ/8)C2211yescharacteristic
19C23×SD16C2211yescharacteristic
20C22×#131C2211yescharacteristic
21C2×#520C2211yescharacteristic
22C2×#520C2211yescharacteristic
23C2×#519C2211yescharacteristic
24C2×#518C2211yescharacteristic
25C2×#471C4116yescomplemented
26C2×#471C2218yes—
27#2949—24no—
28#2949C2218yescomplemented
29#2947—24no—
30#2947C2218yescomplemented
31#2946—24no—
32#2946C2218yes—
33C2×#442—21no—
34C2×#441—21no—
35C2×#440—21no—
36C2×#440—21no—
37C2×#440—21no—
38C2×#440—21no—
39C2×C4×Q16—21no—
40C2×C4×SD16—21no—
41C2×C4×SD16—21no—
42C2×C4×SD16—21no—
43C2×C4×SD16—21no—
44C2×C4×D8—21no—
45C22×#108C2211yescharacteristic
46#2913—24no—
47#2913C2218yescomplemented
48C2×#428—21no—
49C2×#428—21no—
50C2×#428C2211yescharacteristic
51C2×#428C2211yescharacteristic
52C2×#428C2211yescharacteristic
53C2×#428C2211yescharacteristic
54C2×#427—21no—
55C2×#427C2211yescharacteristic
56C22×#107—21no—
57C22×#107C2211yescharacteristic
58C22×#104C2211yescharacteristic
59C2×#419C2211yescharacteristic
60C2×#418C2211yescharacteristic
61C2×#416C2211yescharacteristic
62C22×#103C2211yescharacteristic
63C22×#102C2211yescharacteristic
64C22×#101C2211yescharacteristic
65C22×#100C2211yescharacteristic
66C2×#405C2211yescharacteristic
67C2×#405C2211yescharacteristic
68C2×#405C2211yescharacteristic
69C22×#97C2211yescharacteristic
70C2×#391C2211yescharacteristic
71C2×#390C2211yescharacteristic
72#1973C2218yescomplemented
73#1952C2218yescomplemented
74#1931C2218yescomplemented
75#1930C2218yescomplemented
76#1883C2218yes—
77#1882C2218yescomplemented
78#1857C2218yescomplemented
79#1856C2218yescomplemented
80#1773C2218yescomplemented
81#1765C2218yescomplemented
82C2×#343C2211yescharacteristic
83C2×#343C2211yescharacteristic
84C2×#341C2211yescharacteristic
85C2×#339C2211yescharacteristic
86C2×#339C2211yescharacteristic
87C2×#339C2211yescharacteristic
88C22×#41C2311yescharacteristic
89C23×Q8C2311yescharacteristic
90C23×D4C2311yescharacteristic
91C2×#137—22no—
92C2×#137—24no—
93C2×#137C2×C418yescomplemented
94C2×#137C2314yes—
95C2×AGL(1,ℤ/8)—22no—
96C2×AGL(1,ℤ/8)—24no—
97C2×AGL(1,ℤ/8)C2×C418yes—
98C2×AGL(1,ℤ/8)C2314yes—
99C22×Q16—21no—
100C22×SD16—21no—
101C22×SD16—21no—
102C22×SD16—21no—
103C22×SD16—21no—
104C22×SD16—22no—
105C22×SD16—24no—
106C22×SD16C2×C418yescomplemented
107C22×SD16C2314yes—
108C22×D8—21no—
109C2×#131—22no—
110C2×#131—24no—
111C2×#131C2×C418yescomplemented
112C2×#131C2314yes—
113C22×M16—21no—
114C22×M16C2311yescharacteristic
115C22×M16C2311yescharacteristic
116C22×M16C2311yescharacteristic
117C22×M16C2311yescharacteristic
118C23×C8—21no—
119C23×C8C2311yescharacteristic
120C23×C8C2311yescharacteristic
121#520—22no—
122#520—22no—
123#520—22no—
124#520—22no—
125#520—41no—
126#520—41no—
127#520C2314yes—
128#520C2314yes—
129#519—22no—
130#519—22no—
131#519—41no—
132#519C2314yes—
133#518—22no—
134#518—22no—
135#518—41no—
136#518C2314yes—
137C2×C4×Q8—21no—
138C2×C4×Q8—21no—
139C2×C4×Q8—21no—
140C2×C4×Q8—21no—
141C2×C4×Q8—21no—
142C2×C4×Q8—21no—
143C2×C4×D4—21no—
144C2×C4×D4—21no—
145C2×C4×D4—21no—
146C2×C4×D4—21no—
147C2×C4×D4—21no—
148C2×C4×D4—21no—
149C2×C4×D4—41no—
150C2×C4×D4—41no—
151C2×#117—21no—
152C2×#117—21no—
153C2×#117—41no—
154C2×#117C2311yescharacteristic
155C2×#117C2311yescharacteristic
156C2×#117C2311yescharacteristic
157C22×C4⋊C4—21no—
158C22×C4⋊C4—21no—
159C22×C4⋊C4C2311yescharacteristic
160C22×C4⋊C4C2311yescharacteristic
161C22×C22⋊C4—41no—
162C22×C22⋊C4—41no—
163C22×C42C2311yescharacteristic
164#471C2×C4164yescomplemented
165#442—28no—
166#441—28no—
167#440—28no—
168#440—28no—
169#440—28no—
170#440—28no—
171C4×Q16—28no—
172C4×SD16—28no—
173C4×SD16—28no—
174C4×SD16—28no—
175C4×SD16—28no—
176C4×D8—28no—
177C2×#108C2×C418yescomplemented
178C2×#108C2314yes—
179#428—22no—
180#428—22no—
181#428—22no—
182#428—22no—
183#428—28no—
184#428—28no—
185#428C2314yes—
186#428C2314yes—
187#428C2314yes—
188#428C2314yes—
189#427—28no—
190#427D414yes—
191#427C2314yes—
192C2×#107—21no—
193C2×#107—21no—
194C2×#107—22no—
195C2×#107—21no—
196C2×#107—21no—
197C2×#107—21no—
198C2×#107—21no—
199C2×#107—28no—
200C2×#107D411yescharacteristic
201C2×#107D411yescharacteristic
202C2×#107C2314yes—
203C2×#106—21no—
204C2×#106—21no—
205C2×#106—21no—
206C2×#106—21no—
207C2×#106D411yescharacteristic
208C2×#106D411yescharacteristic
209C2×#104—24no—
210C2×#104C2314yes—
211#419—22no—
212#419C2314yes—
213#418—22no—
214#418C2314yes—
215#416D414yes—
216#416C2314yes—
217C2×#103—21no—
218C2×#103—21no—
219C2×#103—22no—
220C2×#103—21no—
221C2×#103—21no—
222C2×#103D411yescharacteristic
223C2×#103D411yescharacteristic
224C2×#103C2314yes—
225C2×#102—21no—
226C2×#102—21no—
227C2×#102—22no—
228C2×#102—21no—
229C2×#102—21no—
230C2×#102D411yescharacteristic
231C2×#102D411yescharacteristic
232C2×#102C2314yes—
233C2×#101C2×C418yescomplemented
234C2×#101C2314yes—
235C2×#100C2×C418yescomplemented
236C2×#100C2314yes—
237#405—22no—
238#405—22no—
239#405—22no—
240#405C2314yes—
241#405C2314yes—
242#405C2314yes—
243C2×#97—21no—
244C2×#97—21no—
245C2×#97—21no—
246C2×#97—24no—
247C2×#97C2314yes—
248C2×C4×C8—21no—
249C2×C4×C8—21no—
250C2×C4×C8—21no—
251#391—41no—
252#391C2314yes—
253#390—41no—
254#390C2314yes—
255C2×#95—41no—
256#343C2314yes—
257#343C2314yes—
258#341C2314yes—
259#339C2314yes—
260#339C2314yes—
261#339C2314yes—
262C25—21no—
263C2×#41—21no—
264C2×#41—22no—
265C2×#41—21no—
266C2×#41—22no—
267C2×#41C22×C414yes—
268C2×#41C2×D412yes—
269C2×#41#4114yes—
270C2×#41C2412yes—
271C22×Q8—21no—
272C22×Q8—22no—
273C22×Q8—21no—
274C22×Q8—21no—
275C22×Q8—21no—
276C22×Q8—21no—
277C22×Q8—22no—
278C22×Q8—22no—
279C22×Q8C22×C414yes—
280C22×Q8C2×D411yescharacteristic
281C22×Q8C2412yes—
282C22×D4—21no—
283C22×D4—21no—
284C22×D4—21no—
285C22×D4—21no—
286C22×D4—21no—
287C22×D4—22no—
288C22×D4—22no—
289C22×D4—21no—
290C22×D4—22no—
291C22×D4C22×C414yes—
292C22×D4C2×D411yescharacteristic
293C22×D4C2412yes—
294C23×C4—21no—
295C23×C4—21no—
296C23×C4—21no—
297C23×C4—21no—
298C23×C4—21no—
299C23×C4—41no—
300C23×C4—41no—
301C23×C4—41no—
302C23×C4—41no—
303C23×C4C2411yescharacteristic
304#137—216no—
305#137—28no—
306#137C22×C4116yescomplemented
307AGL(1,ℤ/8)—216no—
308AGL(1,ℤ/8)—28no—
309AGL(1,ℤ/8)C22×C4116yes—
310C2×Q16—28no—
311C2×Q16—24no—
312C2×SD16—28no—
313C2×SD16—24no—
314C2×SD16—28no—
315C2×SD16—24no—
316C2×SD16—28no—
317C2×SD16—28no—
318C2×SD16—216no—
319C2×SD16—24no—
320C2×SD16—24no—
321C2×SD16—28no—
322C2×SD16C22×C4116yescomplemented
323C2×D8—28no—
324C2×D8—24no—
325#131—216no—
326#131—28no—
327#131C22×C4116yescomplemented
328C2×M16—21no—
329C2×M16—21no—
330C2×M16—21no—
331C2×M16—22no—
332C2×M16—22no—
333C2×M16—22no—
334C2×M16—21no—
335C2×M16—28no—
336C2×M16—24no—
337C2×M16—22no—
338C2×M16—22no—
339C2×M16C22×C414yes—
340C2×M16C22×C414yes—
341C2×M16C22×C414yes—
342C2×M16C2412yes—
343C2×M16C2412yes—
344C2×M16C2412yes—
345C2×M16C2412yes—
346C22×C8—21no—
347C22×C8—21no—
348C22×C8—21no—
349C22×C8—22no—
350C22×C8—22no—
351C22×C8—28no—
352C22×C8—24no—
353C22×C8—21no—
354C22×C8C22×C414yes—
355C22×C8C2×D411yescharacteristic
356C22×C8C2×D411yescharacteristic
357C22×C8C2×D412yes—
358C22×C8C2×D411yescharacteristic
359C22×C8C2×D411yescharacteristic
360C22×C8C2×D412yes—
361C22×C8#4114yes—
362C22×C8C2412yes—
363C22×C8C2412yes—
364C4×Q8—24no—
365C4×Q8—24no—
366C4×Q8—24no—
367C4×Q8—24no—
368C4×Q8—24no—
369C4×Q8—24no—
370C4×Q8—42no—
371C4×Q8—42no—
372C4×Q8—42no—
373C4×Q8—42no—
374C4×Q8—42no—
375C4×Q8—42no—
376C4×D4—24no—
377C4×D4—24no—
378C4×D4—24no—
379C4×D4—24no—
380C4×D4—24no—
381C4×D4—24no—
382C4×D4—42no—
383C4×D4—42no—
384C4×D4—42no—
385C4×D4—42no—
386C4×D4—42no—
387C4×D4—42no—
388C4×D4—44no—
389C4×D4—44no—
390C4×D4—44no—
391C4×D4—44no—
392#117—21no—
393#117—21no—
394#117—21no—
395#117—21no—
396#117—21no—
397#117—21no—
398#117—24no—
399#117—24no—
400#117—44no—
401#117—44no—
402#117—42no—
403#117—42no—
404#117C2×D412yes—
405#117C2×D412yes—
406#117C2×D412yes—
407#117C2412yes—
408#117C2412yes—
409#117C2412yes—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—24no—
419C2×C4⋊C4—24no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—42no—
423C2×C4⋊C4—42no—
424C2×C4⋊C4—41no—
425C2×C4⋊C4—41no—
426C2×C4⋊C4—41no—
427C2×C4⋊C4—41no—
428C2×C4⋊C4C2×D411yescharacteristic
429C2×C4⋊C4C2×D411yescharacteristic
430C2×C4⋊C4C2×D411yescharacteristic
431C2×C4⋊C4C2×D411yescharacteristic
432C2×C4⋊C4C2×D411yescharacteristic
433C2×C4⋊C4C2×D411yescharacteristic
434C2×C4⋊C4C2412yes—
435C2×C4⋊C4C2412yes—
436C2×C22⋊C4—21no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4—21no—
439C2×C22⋊C4—44no—
440C2×C22⋊C4—44no—
441C2×C22⋊C4—41no—
442C2×C22⋊C4—41no—
443C2×C22⋊C4—41no—
444C2×C22⋊C4—41no—
445C2×C22⋊C4—44no—
446C2×C22⋊C4—84no—
447C2×C42—21no—
448C2×C42—21no—
449C2×C42—21no—
450C2×C42—22no—
451C2×C42—22no—
452C2×C42—21no—
453C2×C42—41no—
454C2×C42—41no—
455C2×C42—41no—
456C2×C42—41no—
457C2×C42C2412yes—
458#108C22×C4116yescomplemented
459#107—24no—
460#107—24no—
461#107—24no—
462#107—24no—
463#107—24no—
464#107—24no—
465#107C2×D414yes—
466#107C2×D414yes—
467#106—24no—
468#106—24no—
469#106—24no—
470#106—24no—
471#106C2×D414yes—
472#106C2×D414yes—
473#104—28no—
474#103—24no—
475#103—24no—
476#103—24no—
477#103—24no—
478#103C2×D414yes—
479#103C2×D414yes—
480#102—24no—
481#102—24no—
482#102—24no—
483#102—24no—
484#102C2×D414yes—
485#102C2×D414yes—
486#101C22×C4116yescomplemented
487#100C22×C4116yescomplemented
488#97—24no—
489#97—24no—
490#97—24no—
491#97—28no—
492C4×C8—24no—
493C4×C8—24no—
494C4×C8—24no—
495#95—44no—
496C24—21no—
497C24—24no—
498C24—22no—
499C24—41no—
500C24—41no—
501C24—42no—
502C24—82no—
503C24—82no—
504C24H(5,𝔽2)11yescharacteristic
505#41—24no—
506#41—24no—
507#41—24no—
508#41—24no—
509#41—24no—
510#41—22no—
511#41—22no—
512#41C4×D418yes—
513#41C23×C414yes—
514#41C2×#4114yes—
515C2×Q8—24no—
516C2×Q8—21no—
517C2×Q8—22no—
518C2×Q8—22no—
519C2×Q8—24no—
520C2×Q8—24no—
521C2×Q8—24no—
522C2×Q8—24no—
523C2×Q8—22no—
524C2×Q8—22no—
525C2×Q8—22no—
526C2×Q8—22no—
527C2×Q8—41no—
528C2×Q8—41no—
529C2×Q8—42no—
530C2×Q8—42no—
531C2×Q8—42no—
532C2×Q8—42no—
533C2×Q8—42no—
534C2×Q8C4×D414yes—
535C2×Q8C23×C414yes—
536C2×Q8C22×D412yes—
537C2×D4—24no—
538C2×D4—22no—
539C2×D4—24no—
540C2×D4—22no—
541C2×D4—24no—
542C2×D4—24no—
543C2×D4—24no—
544C2×D4—24no—
545C2×D4—24no—
546C2×D4—21no—
547C2×D4—22no—
548C2×D4—22no—
549C2×D4—22no—
550C2×D4—22no—
551C2×D4—22no—
552C2×D4—22no—
553C2×D4—41no—
554C2×D4—41no—
555C2×D4—42no—
556C2×D4—42no—
557C2×D4—42no—
558C2×D4—42no—
559C2×D4—42no—
560C2×D4C4×D414yes—
561C2×D4C23×C414yes—
562C2×D4C22×D412yes—
563C22×C4—21no—
564C22×C4—24no—
565C22×C4—22no—
566C22×C4—24no—
567C22×C4—22no—
568C22×C4—24no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—44no—
580C22×C4—44no—
581C22×C4—44no—
582C22×C4—44no—
583C22×C4—41no—
584C22×C4—41no—
585C22×C4—42no—
586C22×C4—42no—
587C22×C4—42no—
588C22×C4—41no—
589C22×C4—41no—
590C22×C4—42no—
591C22×C4—41no—
592C22×C4—41no—
593C22×C4—82no—
594C22×C4—82no—
595C22×C4—162no—
596C22×C4—162no—
597C22×C4—162no—
598C22×C4—162no—
599C22×C4C23×C412yes—
600C22×C4C22×D411yescharacteristic
601C22×C4C22×D411yescharacteristic
602C22×C4C22×D411yescharacteristic
603C22×C4C22×D411yescharacteristic
604C22×C4C2×#4112yes—
605C22×C4C2×#4112yes—
606C22×C4H(5,𝔽2)11yescharacteristic
607C22×C42−1+412yes—
608C22×C4C2511yescharacteristic
609Q16—216no—
610SD16—216no—
611SD16—216no—
612SD16—216no—
613SD16—216no—
614D8—216no—
615M16—24no—
616M16—24no—
617M16—24no—
618M16—22no—
619M16—22no—
620M16—22no—
621M16—216no—
622M16—22no—
623M16—22no—
624M16—42no—
625M16C23×C414yes—
626M16C23×C414yes—
627M16C23×C414yes—
628C2×C8—24no—
629C2×C8—24no—
630C2×C8—24no—
631C2×C8—22no—
632C2×C8—22no—
633C2×C8—24no—
634C2×C8—22no—
635C2×C8—22no—
636C2×C8—22no—
637C2×C8—22no—
638C2×C8—22no—
639C2×C8—216no—
640C2×C8—22no—
641C2×C8—42no—
642C2×C8C4×D414yes—
643C2×C8C4×D414yes—
644C2×C8C4×D418yes—
645C2×C8C23×C414yes—
646C2×C8C22×D412yes—
647C2×C8C22×D412yes—
648C2×C8C22×D412yes—
649C2×C8C22×D412yes—
650C2×C8C2×#4114yes—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—22no—
658C4⋊C4—22no—
659C4⋊C4—22no—
660C4⋊C4—22no—
661C4⋊C4—44no—
662C4⋊C4—44no—
663C4⋊C4—44no—
664C4⋊C4—44no—
665C4⋊C4—41no—
666C4⋊C4—41no—
667C4⋊C4—41no—
668C4⋊C4—41no—
669C4⋊C4C22×D412yes—
670C4⋊C4C22×D412yes—
671C4⋊C4C22×D412yes—
672C4⋊C4C22×D412yes—
673C4⋊C4C22×D412yes—
674C4⋊C4C22×D412yes—
675C22⋊C4—22no—
676C22⋊C4—22no—
677C22⋊C4—22no—
678C22⋊C4—22no—
679C22⋊C4—22no—
680C22⋊C4—22no—
681C22⋊C4—44no—
682C22⋊C4—44no—
683C22⋊C4—44no—
684C22⋊C4—44no—
685C22⋊C4—88no—
686C42—22no—
687C42—22no—
688C42—22no—
689C42—22no—
690C42—22no—
691C42—22no—
692C42—22no—
693C42—22no—
694C42—44no—
695C42—44no—
696C42—44no—
697C42—44no—
698C42—42no—
699C23—22no—
700C23—22no—
701C23—24no—
702C23—22no—
703C23—24no—
704C23—42no—
705C23—42no—
706C23—44no—
707C23—42no—
708C23—44no—
709C23—42no—
710C23—82no—
711C23—88no—
712C23—82no—
713C23—82no—
714C23—82no—
715C23—164no—
716C23—161no—
717C23—161no—
718C23#52012yes—
719C23D4211yescharacteristic
720C23D4211yescharacteristic
721C23#55312yes—
722C23C2×H(5,𝔽2)11yescharacteristic
723Q8—24no—
724Q8—22no—
725Q8—24no—
726Q8—24no—
727Q8—44no—
728Q8—44no—
729Q8—42no—
730Q8—42no—
731Q8C2×C4×D414yes—
732D4—28no—
733D4—24no—
734D4—24no—
735D4—24no—
736D4—24no—
737D4—24no—
738D4—22no—
739D4—44no—
740D4—44no—
741D4—42no—
742D4—42no—
743D4C2×C4×D414yes—
744C2×C4—24no—
745C2×C4—22no—
746C2×C4—28no—
747C2×C4—24no—
748C2×C4—24no—
749C2×C4—24no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—44no—
757C2×C4—44no—
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—42no—
770C2×C4—42no—
771C2×C4—84no—
772C2×C4—82no—
773C2×C4—82no—
774C2×C4—82no—
775C2×C4—82no—
776C2×C4—164no—
777C2×C4—164no—
778C2×C4—164no—
779C2×C4—164no—
780C2×C4—161no—
781C2×C4—161no—
782C2×C4C2×C4×D412yes—
783C2×C4C2×C4×D412yes—
784C2×C4C2×C4×D412yes—
785C2×C4C2×C4×D412yes—
786C2×C4#52012yes—
787C2×C4D4211yescharacteristic
788C2×C4D4211yescharacteristic
789C2×C4#54712yes—
790C2×C4#54712yes—
791C2×C4#54812yes—
792C2×C4#54812yes—
793C2×C4#55312yes—
794C2×C4C24×C411yescharacteristic
795C2×C4C23×D411yescharacteristic
796C2×C4C23×D411yescharacteristic
797C2×C4C22×#4111yescharacteristic
798C2×C4C22×#4111yescharacteristic
799C2×C4C2×2−1+411yescharacteristic
800C8—24no—
801C8—24no—
802C8—24no—
803C8—22no—
804C8—22no—
805C8—42no—
806C8C2×C4×D414yes—
807C8C2×C4×D414yes—
808C22—24no—
809C22—24no—
810C22—21no—
811C22—21no—
812C22—21no—
813C22—21no—
814C22—24no—
815C22—48no—
816C22—42no—
817C22—42no—
818C22—44no—
819C22—84no—
820C22—88no—
821C22—82no—
822C22—82no—
823C22—162no—
824C22—164no—
825C22#236112yes—
826C22#236112yes—
827C22#328812yes—
828C22#328912yes—
829C22C2×#52011yescharacteristic
830C22C2×D4211yescharacteristic
831C22C2×#55311yescharacteristic
832C4—24no—
833C4—44no—
834C4—42no—
835C4—42no—
836C4—42no—
837C4—42no—
838C4—42no—
839C4—42no—
840C4—82no—
841C4—82no—
842C4—82no—
843C4#236112yes—
844C4#236112yes—
845C4C22×C4×D411yescharacteristic
846C4C22×C4×D411yescharacteristic
847C4C2×#54711yescharacteristic
848C4C2×#54811yescharacteristic
849C2—21no—
850C2—21no—
851C2—22no—
852C2—44no—
853C2—84no—
854C2#2304914yesdirect product factor
855C2C2×#236111yescharacteristic
856C2C2×#328811yescharacteristic
857C2C2×#328911yescharacteristic
subgroupG/H
center, socleC23D42
commutatorC2×C4C24×C4
Frattini, cosocleC22×C4C25
prime radicalC22×AGL(1,ℤ/8)C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C23×C4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#2949C2semidirect
3. C2×#2947C2semidirect
5. C2×#2913C2semidirect
6. #23049C2direct (N × H)
7. C2×#1973C2semidirect
8. C2×#1952C2semidirect
9. C2×#1931C2semidirect
10. C2×#1930C2semidirect
12. C2×#1882C2semidirect
13. C2×#1857C2semidirect
14. C2×#1856C2semidirect
15. C2×#1773C2semidirect
16. C2×#1765C2semidirect
25. C2×#471C4semidirect
28. #2949C22semidirect
30. #2947C22semidirect
47. #2913C22semidirect
72. #1973C22semidirect
73. #1952C22semidirect
74. #1931C22semidirect
75. #1930C22semidirect
77. #1882C22semidirect
78. #1857C22semidirect
79. #1856C22semidirect
80. #1773C22semidirect
81. #1765C22semidirect
93. C2×#137C2×C4semidirect
106. C22×SD16C2×C4semidirect
111. C2×#131C2×C4semidirect
164. #471C2×C4semidirect
177. C2×#108C2×C4semidirect
233. C2×#101C2×C4semidirect
235. C2×#100C2×C4semidirect
306. #137C22×C4semidirect
322. C2×SD16C22×C4semidirect
327. #131C22×C4semidirect
458. #108C22×C4semidirect
486. #101C22×C4semidirect
487. #100C22×C4semidirect
854. C2#23049direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#4712
C2×#29492
C2×#29472
C2×#29462
C2×#29132
#230492
C2×#19732
C2×#19522
C2×#19312
C2×#19302
C2×#18832
C2×#18822
C2×#18572
C2×#18562
C2×#17732
C2×#17652