Finite Group Databasebeta

← C2×C4×#471 #6372906

Subgroups — C2×C4×#471 #6372906

Order 512.

2760 conjugacy classes of subgroups.

The subgroup lattice has 869 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#471C211yesmaximal, characteristic
2C2×C4×#137C211yesmaximal, characteristic, complemented
3C2×C4×AGL(1,ℤ/8)C211yesmaximal, characteristic
4C22×C4×SD16C211yesmaximal, characteristic, complemented
5C2×C4×#131C211yesmaximal, characteristic, complemented
6C4×#471C2116yesmaximal, direct product factor
7C2×#1977C211yesmaximal, characteristic, complemented
8C2×#1951C211yesmaximal, characteristic, complemented
9C2×#1931C211yesmaximal, characteristic, complemented
10C2×#1930C211yesmaximal, characteristic, complemented
11C2×#1908C211yesmaximal, characteristic, complemented
12C2×#1907C211yesmaximal, characteristic
13C2×#1815C211yesmaximal, characteristic, complemented
14C2×C4×#108C211yesmaximal, characteristic, complemented
15C2×C4×#101C211yesmaximal, characteristic, complemented
16C2×C4×#100C211yesmaximal, characteristic, complemented
17C22×#137C2211yescharacteristic
18C22×AGL(1,ℤ/8)C2211yescharacteristic
19C23×SD16C2211yescharacteristic
20C22×#131C2211yescharacteristic
21C22×#131C2211yescharacteristic
22C2×C4×#41C2211yescharacteristic
23C22×C4×Q8C2211yescharacteristic
24C22×C4×D4C2211yescharacteristic
25C2×#471C4116yesdirect product factor
26C2×#471C2218yes—
27C4×#137—24no—
28C4×#137C2218yescomplemented
29C4×AGL(1,ℤ/8)—24no—
30C4×AGL(1,ℤ/8)C2218yes—
31C2×#442—21no—
32C2×#441—21no—
33C2×#440—21no—
34C2×#440—21no—
35C2×C4×Q16—21no—
36C2×C4×SD16—21no—
37C2×C4×SD16—21no—
38C2×C4×SD16—21no—
39C2×C4×SD16—21no—
40C2×C4×SD16—24no—
41C2×C4×SD16—21no—
42C2×C4×SD16—21no—
43C2×C4×SD16C2218yescomplemented
44C2×C4×D8—21no—
45C22×#108C2211yescharacteristic
46C22×#108C2211yescharacteristic
47C2×#428C2211yescharacteristic
48C2×#428C2211yescharacteristic
49C22×#106C2211yescharacteristic
50C2×#417C2211yescharacteristic
51C2×#417C2211yescharacteristic
52C2×#419C2211yescharacteristic
53C2×#418C2211yescharacteristic
54C22×#103C2211yescharacteristic
55C22×#102C2211yescharacteristic
56C22×#101C2211yescharacteristic
57C22×#101C2211yescharacteristic
58C22×#100C2211yescharacteristic
59C22×#100C2211yescharacteristic
60C4×#131—24no—
61C4×#131C2218yescomplemented
62C2×#405—21no—
63C2×#405—21no—
64C2×#405C2211yescharacteristic
65C2×#405C2211yescharacteristic
66C2×C4×M16—21no—
67C2×C4×M16C2211yescharacteristic
68C2×C4×M16C2211yescharacteristic
69C2×C4×M16C2211yescharacteristic
70C22×C4×C8—21no—
71C22×C4×C8C2211yescharacteristic
72#1977C2218yescomplemented
73#1951C2218yescomplemented
74#1931C2218yescomplemented
75#1930C2218yescomplemented
76#1908C2218yescomplemented
77#1907C2218yes—
78#1815C2218yescomplemented
79C4×#108C2218yescomplemented
80C4×#101C2218yescomplemented
81C4×#100C2218yescomplemented
82C2×#343C2211yescharacteristic
83C2×#343C2211yescharacteristic
84C2×#343C2211yescharacteristic
85C2×#343C2211yescharacteristic
86C2×#341C2211yescharacteristic
87C2×#341C2211yescharacteristic
88C22×#41C2311yescharacteristic
89C23×Q8C2311yescharacteristic
90C23×D4C2311yescharacteristic
91C24×C4—21no—
92C2×#137—22no—
93C2×#137—24no—
94C2×#137C2×C418yescomplemented
95C2×#137C2314yes—
96C2×AGL(1,ℤ/8)—22no—
97C2×AGL(1,ℤ/8)—24no—
98C2×AGL(1,ℤ/8)C2×C418yes—
99C2×AGL(1,ℤ/8)C2314yes—
100C22×Q16—21no—
101C22×SD16—21no—
102C22×SD16—21no—
103C22×SD16—21no—
104C22×SD16—21no—
105C22×SD16—22no—
106C22×SD16—24no—
107C22×SD16C2×C418yescomplemented
108C22×SD16C2314yes—
109C22×D8—21no—
110C2×#131—24no—
111C2×#131—24no—
112C2×#131—22no—
113C2×#131—22no—
114C2×#131—24no—
115C2×#131C2×C418yescomplemented
116C2×#131C2314yes—
117C2×#131C2314yes—
118C22×M16—21no—
119C22×M16—21no—
120C22×M16C2311yescharacteristic
121C22×M16C2311yescharacteristic
122C22×M16C2311yescharacteristic
123C22×M16C2311yescharacteristic
124C22×M16C2311yescharacteristic
125C22×M16C2311yescharacteristic
126C23×C8—21no—
127C23×C8—21no—
128C23×C8C2311yescharacteristic
129C23×C8C2311yescharacteristic
130C4×#41—22no—
131C4×#41—22no—
132C4×#41D414yes—
133C4×#41C2314yes—
134C2×C4×Q8—22no—
135C2×C4×Q8—21no—
136C2×C4×Q8—22no—
137C2×C4×Q8—21no—
138C2×C4×Q8—21no—
139C2×C4×Q8—21no—
140C2×C4×Q8—22no—
141C2×C4×Q8D411yescharacteristic
142C2×C4×Q8D411yescharacteristic
143C2×C4×Q8C2314yes—
144C2×C4×D4—21no—
145C2×C4×D4—21no—
146C2×C4×D4—21no—
147C2×C4×D4—21no—
148C2×C4×D4—22no—
149C2×C4×D4—21no—
150C2×C4×D4—21no—
151C2×C4×D4—22no—
152C2×C4×D4—22no—
153C2×C4×D4D411yescharacteristic
154C2×C4×D4D411yescharacteristic
155C2×C4×D4C2314yes—
156C2×#117—21no—
157C2×#117C2311yescharacteristic
158C22×C4⋊C4—21no—
159C22×C4⋊C4C2311yescharacteristic
160C22×C4⋊C4C2311yescharacteristic
161C22×C22⋊C4—21no—
162C22×C42—21no—
163C22×C42—21no—
164C22×C42C2311yescharacteristic
165#471C2×C4164yesdirect product factor
166#442—28no—
167#441—28no—
168#440—28no—
169#440—28no—
170C4×Q16—28no—
171C4×SD16—28no—
172C4×SD16—28no—
173C4×SD16—28no—
174C4×SD16—28no—
175C4×SD16—28no—
176C4×SD16—28no—
177C4×D8—28no—
178C2×#108—24no—
179C2×#108C2×C418yescomplemented
180C2×#108C2314yes—
181C2×#108C2314yes—
182#428—22no—
183#428—22no—
184#428C2314yes—
185#428C2314yes—
186C2×#107—21no—
187C2×#107—21no—
188C2×#106—21no—
189C2×#106—21no—
190C2×#106—22no—
191C2×#106—21no—
192C2×#106—21no—
193C2×#106C2314yes—
194#419—22no—
195#419C2314yes—
196#418—22no—
197#418C2314yes—
198#417—22no—
199#417—22no—
200#417C2314yes—
201#417C2314yes—
202C2×#103—21no—
203C2×#103—21no—
204C2×#103—21no—
205C2×#103—21no—
206C2×#103—22no—
207C2×#103—21no—
208C2×#103—21no—
209C2×#103C2314yes—
210C2×#102—21no—
211C2×#102—21no—
212C2×#102—21no—
213C2×#102—21no—
214C2×#102—22no—
215C2×#102—21no—
216C2×#102—21no—
217C2×#102C2314yes—
218C2×#101—24no—
219C2×#101C2×C418yescomplemented
220C2×#101C2314yes—
221C2×#101C2314yes—
222C2×#100—24no—
223C2×#100C2×C418yescomplemented
224C2×#100C2314yes—
225C2×#100C2314yes—
226#405—22no—
227#405—22no—
228#405—28no—
229#405—28no—
230#405C2314yes—
231#405C2314yes—
232C4×M16—22no—
233C4×M16—22no—
234C4×M16—22no—
235C4×M16—28no—
236C4×M16C2314yes—
237C4×M16C2314yes—
238C4×M16C2314yes—
239C2×#97—21no—
240C2×#97—21no—
241C2×#97—21no—
242C2×#97—21no—
243C2×#97—21no—
244C2×C4×C8—21no—
245C2×C4×C8—21no—
246C2×C4×C8—21no—
247C2×C4×C8—21no—
248C2×C4×C8—21no—
249C2×C4×C8—28no—
250C2×C4×C8D411yescharacteristic
251C2×C4×C8D411yescharacteristic
252C2×C4×C8D411yescharacteristic
253C2×C4×C8D411yescharacteristic
254C2×C4×C8D414yes—
255C2×C4×C8C2314yes—
256#343C2314yes—
257#343C2314yes—
258#343C2314yes—
259#343C2314yes—
260#341C2314yes—
261#341C2314yes—
262C25—21no—
263C2×#41—21no—
264C2×#41—21no—
265C2×#41—22no—
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—21no—
300C23×C4—24no—
301C23×C4—41no—
302C23×C4—42no—
303C23×C4—41no—
304C23×C4—84no—
305C23×C4#4111yescharacteristic
306C23×C4#4111yescharacteristic
307C23×C4C2411yescharacteristic
308#137—216no—
309#137—28no—
310#137C22×C4116yescomplemented
311AGL(1,ℤ/8)—216no—
312AGL(1,ℤ/8)—28no—
313AGL(1,ℤ/8)C22×C4116yes—
314C2×Q16—28no—
315C2×Q16—24no—
316C2×SD16—28no—
317C2×SD16—24no—
318C2×SD16—28no—
319C2×SD16—24no—
320C2×SD16—28no—
321C2×SD16—28no—
322C2×SD16—216no—
323C2×SD16—24no—
324C2×SD16—24no—
325C2×SD16—28no—
326C2×SD16C22×C4116yescomplemented
327C2×D8—28no—
328C2×D8—24no—
329#131—216no—
330#131—28no—
331#131—28no—
332#131—216no—
333#131—28no—
334#131C22×C4116yescomplemented
335C2×M16—28no—
336C2×M16—21no—
337C2×M16—21no—
338C2×M16—21no—
339C2×M16—21no—
340C2×M16—22no—
341C2×M16—22no—
342C2×M16—22no—
343C2×M16—22no—
344C2×M16—21no—
345C2×M16—21no—
346C2×M16—28no—
347C2×M16—24no—
348C2×M16—24no—
349C2×M16—22no—
350C2×M16—22no—
351C2×M16—22no—
352C2×M16—22no—
353C2×M16C22×C414yes—
354C2×M16C22×C414yes—
355C2×M16C22×C414yes—
356C2×M16#4114yes—
357C2×M16C2412yes—
358C2×M16C2412yes—
359C2×M16C2412yes—
360C2×M16C2412yes—
361C2×M16C2412yes—
362C2×M16C2412yes—
363C22×C8—28no—
364C22×C8—21no—
365C22×C8—21no—
366C22×C8—21no—
367C22×C8—21no—
368C22×C8—22no—
369C22×C8—22no—
370C22×C8—28no—
371C22×C8—24no—
372C22×C8—24no—
373C22×C8—21no—
374C22×C8—21no—
375C22×C8C22×C414yes—
376C22×C8C2×D411yescharacteristic
377C22×C8C2×D411yescharacteristic
378C22×C8C2×D412yes—
379C22×C8C2×D411yescharacteristic
380C22×C8C2×D411yescharacteristic
381C22×C8C2×D412yes—
382C22×C8#4114yes—
383C22×C8C2412yes—
384C22×C8C2412yes—
385C4×Q8—22no—
386C4×Q8—22no—
387C4×Q8—24no—
388C4×Q8—24no—
389C4×Q8—24no—
390C4×Q8—24no—
391C4×Q8—42no—
392C4×Q8—42no—
393C4×Q8—42no—
394C4×Q8—42no—
395C4×Q8C2×D414yes—
396C4×Q8C2×D414yes—
397C4×D4—24no—
398C4×D4—24no—
399C4×D4—24no—
400C4×D4—24no—
401C4×D4—22no—
402C4×D4—22no—
403C4×D4—24no—
404C4×D4—24no—
405C4×D4—24no—
406C4×D4—24no—
407C4×D4—42no—
408C4×D4—42no—
409C4×D4—42no—
410C4×D4—42no—
411C4×D4C2×D414yes—
412C4×D4C2×D414yes—
413#117—21no—
414#117—21no—
415#117—24no—
416#117—24no—
417#117C2×D412yes—
418#117C2412yes—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—24no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—41no—
433C2×C4⋊C4—41no—
434C2×C4⋊C4—42no—
435C2×C4⋊C4C2×D411yescharacteristic
436C2×C4⋊C4C2×D411yescharacteristic
437C2×C4⋊C4C2412yes—
438C2×C4⋊C4C2412yes—
439C2×C22⋊C4—21no—
440C2×C22⋊C4—21no—
441C2×C22⋊C4—21no—
442C2×C22⋊C4—24no—
443C2×C22⋊C4—41no—
444C2×C22⋊C4—41no—
445C2×C22⋊C4—42no—
446C2×C42—21no—
447C2×C42—21no—
448C2×C42—21no—
449C2×C42—24no—
450C2×C42—24no—
451C2×C42—24no—
452C2×C42—41no—
453C2×C42—42no—
454C2×C42—41no—
455C2×C42C2×D411yescharacteristic
456C2×C42C2×D411yescharacteristic
457C2×C42C2×D412yes—
458C2×C42C2×D412yes—
459C2×C42C2×D411yescharacteristic
460C2×C42C2×D411yescharacteristic
461C2×C42#4112yes—
462C2×C42C2412yes—
463#108—28no—
464#108C22×C4116yescomplemented
465#107—24no—
466#107—24no—
467#106—24no—
468#106—24no—
469#106—24no—
470#106—24no—
471#103—24no—
472#103—24no—
473#103—24no—
474#103—24no—
475#103—24no—
476#103—24no—
477#102—24no—
478#102—24no—
479#102—24no—
480#102—24no—
481#102—24no—
482#102—24no—
483#101—28no—
484#101C22×C4116yescomplemented
485#100—28no—
486#100C22×C4116yescomplemented
487#97—24no—
488#97—24no—
489#97—24no—
490#97—24no—
491#97—24no—
492C4×C8—24no—
493C4×C8—24no—
494C4×C8—24no—
495C4×C8—24no—
496C4×C8—24no—
497C4×C8C2×D414yes—
498C4×C8C2×D414yes—
499C4×C8C2×D414yes—
500C4×C8C2×D414yes—
501C24—21no—
502C24—24no—
503C24—22no—
504C24—41no—
505C24—41no—
506C24—42no—
507C24—82no—
508C24—82no—
509C24C2×#4111yescharacteristic
510#41—24no—
511#41—24no—
512#41—24no—
513#41—24no—
514#41—24no—
515#41—22no—
516#41—22no—
517#41C4×D418yes—
518#41C23×C414yes—
519#41C2×#4114yes—
520C2×Q8—24no—
521C2×Q8—21no—
522C2×Q8—22no—
523C2×Q8—22no—
524C2×Q8—24no—
525C2×Q8—24no—
526C2×Q8—24no—
527C2×Q8—24no—
528C2×Q8—22no—
529C2×Q8—22no—
530C2×Q8—22no—
531C2×Q8—22no—
532C2×Q8—41no—
533C2×Q8—41no—
534C2×Q8—42no—
535C2×Q8—42no—
536C2×Q8—42no—
537C2×Q8—42no—
538C2×Q8—42no—
539C2×Q8C4×D414yes—
540C2×Q8C23×C414yes—
541C2×Q8C22×D412yes—
542C2×D4—24no—
543C2×D4—22no—
544C2×D4—24no—
545C2×D4—22no—
546C2×D4—24no—
547C2×D4—24no—
548C2×D4—24no—
549C2×D4—24no—
550C2×D4—24no—
551C2×D4—21no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—22no—
555C2×D4—22no—
556C2×D4—22no—
557C2×D4—22no—
558C2×D4—41no—
559C2×D4—41no—
560C2×D4—42no—
561C2×D4—42no—
562C2×D4—42no—
563C2×D4—42no—
564C2×D4—42no—
565C2×D4C4×D414yes—
566C2×D4C23×C414yes—
567C2×D4C22×D412yes—
568C22×C4—21no—
569C22×C4—24no—
570C22×C4—22no—
571C22×C4—24no—
572C22×C4—22no—
573C22×C4—24no—
574C22×C4—24no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—22no—
578C22×C4—24no—
579C22×C4—24no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—42no—
583C22×C4—44no—
584C22×C4—41no—
585C22×C4—41no—
586C22×C4—42no—
587C22×C4—44no—
588C22×C4—41no—
589C22×C4—41no—
590C22×C4—41no—
591C22×C4—41no—
592C22×C4—44no—
593C22×C4—44no—
594C22×C4—84no—
595C22×C4—88no—
596C22×C4—88no—
597C22×C4—84no—
598C22×C4—82no—
599C22×C4—82no—
600C22×C4#12111yescharacteristic
601C22×C4#12111yescharacteristic
602C22×C4#12112yes—
603C22×C4#12111yescharacteristic
604C22×C4#12112yes—
605C22×C4#12111yescharacteristic
606C22×C4C23×C412yes—
607C22×C4C22×D411yescharacteristic
608C22×C4C22×D411yescharacteristic
609C22×C4C22×D411yescharacteristic
610C22×C4C22×D411yescharacteristic
611C22×C4C2×#4112yes—
612C22×C4C2×#4112yes—
613C22×C4C2×#4112yes—
614C22×C4C2×#4112yes—
615C22×C4C2×#4111yescharacteristic
616C22×C4C2×#4112yes—
617C22×C4C2511yescharacteristic
618Q16—216no—
619SD16—216no—
620SD16—216no—
621SD16—216no—
622SD16—216no—
623D8—216no—
624M16—216no—
625M16—24no—
626M16—24no—
627M16—24no—
628M16—24no—
629M16—22no—
630M16—22no—
631M16—22no—
632M16—22no—
633M16—216no—
634M16—22no—
635M16—22no—
636M16—22no—
637M16—22no—
638M16—42no—
639M16—42no—
640M16C23×C414yes—
641M16C23×C414yes—
642M16C23×C414yes—
643M16C2×#4114yes—
644C2×C8—216no—
645C2×C8—24no—
646C2×C8—24no—
647C2×C8—24no—
648C2×C8—22no—
649C2×C8—24no—
650C2×C8—22no—
651C2×C8—24no—
652C2×C8—22no—
653C2×C8—22no—
654C2×C8—22no—
655C2×C8—22no—
656C2×C8—22no—
657C2×C8—22no—
658C2×C8—216no—
659C2×C8—22no—
660C2×C8—22no—
661C2×C8—42no—
662C2×C8—42no—
663C2×C8C4×D414yes—
664C2×C8C4×D414yes—
665C2×C8C4×D418yes—
666C2×C8C23×C414yes—
667C2×C8C22×D412yes—
668C2×C8C22×D412yes—
669C2×C8C22×D412yes—
670C2×C8C22×D412yes—
671C2×C8C2×#4114yes—
672C4⋊C4—24no—
673C4⋊C4—24no—
674C4⋊C4—21no—
675C4⋊C4—21no—
676C4⋊C4—22no—
677C4⋊C4—22no—
678C4⋊C4—22no—
679C4⋊C4—22no—
680C4⋊C4—41no—
681C4⋊C4—41no—
682C4⋊C4—41no—
683C4⋊C4—41no—
684C4⋊C4—44no—
685C4⋊C4—44no—
686C4⋊C4C22×D412yes—
687C4⋊C4C22×D412yes—
688C22⋊C4—22no—
689C22⋊C4—22no—
690C22⋊C4—24no—
691C22⋊C4—24no—
692C22⋊C4—44no—
693C22⋊C4—44no—
694C42—22no—
695C42—24no—
696C42—24no—
697C42—22no—
698C42—44no—
699C42—44no—
700C42#12112yes—
701C42#12112yes—
702C42#12112yes—
703C42#12112yes—
704C42C22×D412yes—
705C42C22×D412yes—
706C42C22×D412yes—
707C42C22×D412yes—
708C23—22no—
709C23—22no—
710C23—22no—
711C23—24no—
712C23—24no—
713C23—42no—
714C23—42no—
715C23—42no—
716C23—42no—
717C23—44no—
718C23—44no—
719C23—82no—
720C23—88no—
721C23—82no—
722C23—82no—
723C23—88no—
724C23—82no—
725C23—82no—
726C23—82no—
727C23C4×#4112yes—
728C23C2×#12111yescharacteristic
729C23C2×#12111yescharacteristic
730C23#52912yes—
731C23C22×#4111yescharacteristic
732Q8—22no—
733Q8—24no—
734Q8—24no—
735Q8—24no—
736Q8—42no—
737Q8—42no—
738Q8—44no—
739Q8—44no—
740Q8C2×C4×D414yes—
741D4—24no—
742D4—24no—
743D4—28no—
744D4—24no—
745D4—24no—
746D4—22no—
747D4—24no—
748D4—42no—
749D4—42no—
750D4—44no—
751D4—44no—
752D4C2×C4×D414yes—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—24no—
758C2×C4—24no—
759C2×C4—24no—
760C2×C4—24no—
761C2×C4—24no—
762C2×C4—28no—
763C2×C4—24no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—48no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—44no—
774C2×C4—44no—
775C2×C4—48no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—88no—
779C2×C4—82no—
780C2×C4—82no—
781C2×C4—82no—
782C2×C4—82no—
783C2×C4—88no—
784C2×C4—82no—
785C2×C4—82no—
786C2×C4#47114yesdirect product factor
787C2×C4C2×C4×D412yes—
788C2×C4C2×C4×D412yes—
789C2×C4C2×C4×D412yes—
790C2×C4C2×C4×D412yes—
791C2×C4C4×#4112yes—
792C2×C4C2×#12112yes—
793C2×C4C2×#12112yes—
794C2×C4C2×#12112yes—
795C2×C4C2×#12112yes—
796C2×C4C2×#12111yescharacteristic
797C2×C4C2×#12111yescharacteristic
798C2×C4#52512yes—
799C2×C4#52512yes—
800C2×C4#52912yes—
801C2×C4#53212yes—
802C2×C4#53212yes—
803C2×C4C24×C411yescharacteristic
804C2×C4C23×D411yescharacteristic
805C2×C4C23×D411yescharacteristic
806C2×C4C22×#4111yescharacteristic
807C2×C4C22×#4111yescharacteristic
808C2×C4C22×#4111yescharacteristic
809C8—24no—
810C8—24no—
811C8—24no—
812C8—22no—
813C8—24no—
814C8—22no—
815C8—42no—
816C8—42no—
817C8C2×C4×D414yes—
818C8C2×C4×D414yes—
819C22—21no—
820C22—21no—
821C22—24no—
822C22—24no—
823C22—21no—
824C22—21no—
825C22—24no—
826C22—42no—
827C22—48no—
828C22—42no—
829C22—44no—
830C22—84no—
831C22—84no—
832C22—88no—
833C22—82no—
834C22—88no—
835C22—82no—
836C22C4×#12112yes—
837C22C4×#12112yes—
838C22C2×#47112yes—
839C22#306712yes—
840C22C2×C4×#4111yescharacteristic
841C22C22×#12111yescharacteristic
842C22C2×#52911yescharacteristic
843C4—22no—
844C4—22no—
845C4—22no—
846C4—24no—
847C4—42no—
848C4—42no—
849C4—44no—
850C4—82no—
851C4—82no—
852C4C4×#12112yes—
853C4C4×#12112yes—
854C4C2×#47114yesdirect product factor
855C4C22×C4×D411yescharacteristic
856C4C22×C4×D411yescharacteristic
857C4C2×#52511yescharacteristic
858C4C2×#53211yescharacteristic
859C2—21no—
860C2—21no—
861C2—22no—
862C2—44no—
863C2—84no—
864C2C4×#47114yesdirect product factor
865C2C2×C4×#12111yescharacteristic
866C2C22×#47111yescharacteristic
867C2C2×#306711yescharacteristic
subgroupG/H
centerC22×C4#121
commutatorC2×C4C24×C4
Frattini, cosocleC22×C4C25
socleC23C2×#121
prime radicalC22×AGL(1,ℤ/8)C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×C4×#137C2semidirect
4. C22×C4×SD16C2semidirect
5. C2×C4×#131C2semidirect
6. C4×#471C2direct (N × H)
7. C2×#1977C2semidirect
8. C2×#1951C2semidirect
9. C2×#1931C2semidirect
10. C2×#1930C2semidirect
11. C2×#1908C2semidirect
13. C2×#1815C2semidirect
14. C2×C4×#108C2semidirect
15. C2×C4×#101C2semidirect
16. C2×C4×#100C2semidirect
25. C2×#471C4direct (N × H)
28. C4×#137C22semidirect
43. C2×C4×SD16C22semidirect
61. C4×#131C22semidirect
72. #1977C22semidirect
73. #1951C22semidirect
74. #1931C22semidirect
75. #1930C22semidirect
76. #1908C22semidirect
78. #1815C22semidirect
79. C4×#108C22semidirect
80. C4×#101C22semidirect
81. C4×#100C22semidirect
94. C2×#137C2×C4semidirect
107. C22×SD16C2×C4semidirect
115. C2×#131C2×C4semidirect
165. #471C2×C4direct (N × H)
179. C2×#108C2×C4semidirect
219. C2×#101C2×C4semidirect
223. C2×#100C2×C4semidirect
310. #137C22×C4semidirect
326. C2×SD16C22×C4semidirect
334. #131C22×C4semidirect
464. #108C22×C4semidirect
484. #101C22×C4semidirect
486. #100C22×C4semidirect
786. C2×C4#471direct (N × H)
854. C4C2×#471direct (N × H)
864. C2C4×#471direct (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×C4×#1372
C2×C4×AGL(1,ℤ/8)2
C22×C4×SD162
C2×C4×#1312
C4×#4712
C2×#19772
C2×#19512
C2×#19312
C2×#19302
C2×#19082
C2×#19072
C2×#18152
C2×C4×#1082
C2×C4×#1012
C2×C4×#1002