Finite Group Databasebeta

← C4×#3110 #6373299

Subgroups — C4×#3110 #6373299

Order 512.

2750 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3110C211yesmaximal, characteristic
2C4×#533C211yesmaximal, characteristic, complemented
3C2×C42×D4C211yesmaximal, characteristic
4#21613C212yesmaximal, complemented
5C4×#474C212yesmaximal, complemented
6#21581C212yesmaximal, complemented
7C4×#484C212yesmaximal, complemented
8#21504C212yesmaximal, complemented
9C4×#461C212yesmaximal, complemented
10#21453C212yesmaximal
11C4×#450C212yesmaximal
12#21394C211yesmaximal, characteristic, complemented
13#21365C211yesmaximal, characteristic, complemented
14#21121C214yesmaximal, complemented
15#20738C211yesmaximal, characteristic
16C4×#440C214yesmaximal, complemented
17C4×#432C211yesmaximal, characteristic, complemented
18C2×#533C2211yescharacteristic
19C22×C4×D4C2211yescharacteristic
20C22×C4×D4C2211yescharacteristic
21C22×C4×D4C2211yescharacteristic
22C23×C42—21no—
23#3110C4116yesdirect product factor
24C2×#484C2212yes—
25C2×#474C2212yes—
26C2×#461C2212yes—
27C2×#450C2212yes—
28C2×#440C2214yes—
29C2×#440C2214yes—
30C2×C4×SD16C2214yes—
31C2×#432C2211yescharacteristic
32C2×#432C2211yescharacteristic
33C4×C4⋊Q8C2211yescharacteristic, complemented
34C4×C4⋊Q8C2211yescharacteristic, complemented
35C4×C4⋊Q8C2211yescharacteristic, complemented
36C4×C4⋊Q8C2211yescharacteristic, complemented
37C4×#125—21no—
38C4×#125—21no—
39C4×C22⋊Q8—21no—
40C4×C22⋊Q8—21no—
41C4×C22⋊Q8C2212yes—
42C4×C22⋊Q8C2212yes—
43#2296—21no—
44#2295—21no—
45#2295C2212yescomplemented
46#2285C2211yescharacteristic
47C42×Q8—21no—
48C42×Q8C2212yescomplemented
49C42×D4—21no—
50C42×D4—21no—
51C42×D4—21no—
52C42×D4—21no—
53C42×D4C2212yes—
54C42×D4C2212yes—
55C42×D4C2212yes—
56C42×D4C2212yes—
57C4×#117—21no—
58C2×C4×C4⋊C4C2211yescharacteristic
59C2×C4×C4⋊C4C2211yescharacteristic
60C2×C4×C4⋊C4C2211yescharacteristic
61C2×C4×C22⋊C4—21no—
62C2×C4×C22⋊C4—21no—
63C2×C4×C22⋊C4—21no—
64C2×C43C2211yescharacteristic
65#1988C2212yescomplemented
66#1981C2212yescomplemented
67#1948C2212yescomplemented
68#1947C2212yescomplemented
69#1928C2214yescomplemented
70#1927C2214yescomplemented
71#1921C2214yescomplemented
72#1918C2214yescomplemented
73#1877C2214yes—
74#1877C2214yes—
75#1872C2212yes—
76#1872C2212yes—
77#1864C2214yes—
78#1862C2214yes—
79#1853C2212yes—
80#1852C2212yes—
81#1824C2212yes—
82#1802C2212yes—
83#1802C2212yes—
84#1786C2212yes—
85#1776C2214yescomplemented
86#1776C2214yescomplemented
87C4×#107C2214yescomplemented
88#1767C2212yescomplemented
89C4×C4⋊C8C2212yescomplemented
90#1763C2214yescomplemented
91#1763C2214yescomplemented
92#1762C2214yes—
93#1762C2214yes—
94C4×#103C2214yescomplemented
95C4×#102C2214yes—
96#1749C2212yes—
97C4×C22⋊C8C2212yes—
98#1745C2212yescomplemented
99C4×#97C2212yescomplemented
100C23×D4C2311yescharacteristic
101C24×C4—21no—
102C24×C4—21no—
103C24×C4—21no—
104C22×SD16C2314yes—
105#533—24no—
106#533C2×C418yescomplemented
107C2×C4⋊Q8C2311yescharacteristic
108C2×C4⋊Q8C2311yescharacteristic
109C2×#125—21no—
110C2×C22⋊Q8—21no—
111C2×C22⋊Q8C2312yes—
112C2×C4×Q8—21no—
113C2×C4×Q8—21no—
114C2×C4×Q8—21no—
115C2×C4×Q8C2312yes—
116C2×C4×Q8C2312yes—
117C2×C4×Q8C2312yes—
118C2×C4×D4—28no—
119C2×C4×D4—28no—
120C2×C4×D4—21no—
121C2×C4×D4—21no—
122C2×C4×D4—21no—
123C2×C4×D4—21no—
124C2×C4×D4—21no—
125C2×C4×D4—21no—
126C2×C4×D4—24no—
127C2×C4×D4C2×C418yes—
128C2×C4×D4C2312yes—
129C2×C4×D4C2312yes—
130C2×C4×D4C2312yes—
131C2×C4×D4C2312yes—
132C2×C4×D4C2312yes—
133C2×C4×D4C2312yes—
134C2×#117—21no—
135C2×#117—21no—
136C22×C4⋊C4C2311yescharacteristic
137C22×C4⋊C4C2311yescharacteristic
138C22×C4⋊C4C2311yescharacteristic
139C22×C22⋊C4—21no—
140C22×C22⋊C4—21no—
141C22×C22⋊C4—21no—
142C22×C42—21no—
143C22×C42—21no—
144C22×C42—21no—
145C22×C42—22no—
146C22×C42—22no—
147C22×C42—22no—
148C22×C42—22no—
149C22×C42—48no—
150C22×C42D411yescharacteristic
151C22×C42D411yescharacteristic
152C22×C42D411yescharacteristic
153C22×C42D411yescharacteristic
154C22×C42C2311yescharacteristic
155C22×C42C2311yescharacteristic
156C22×C42C2311yescharacteristic
157#484C2×C4116yescomplemented
158#474C2×C4116yescomplemented
159#461C2×C4116yescomplemented
160#450C2×C4116yes—
161#440—216no—
162#440C2×C4132yescomplemented
163C4×SD16—216no—
164#432—24no—
165#432C2×C418yescomplemented
166C2×#107C2314yes—
167C2×#107C2314yes—
168C2×#106C2314yes—
169C2×C4⋊C8C2312yes—
170C2×C4⋊C8C2312yes—
171C2×#103C2314yes—
172C2×#103C2314yes—
173C2×#103C2314yes—
174C2×#102C2314yes—
175C2×#102C2314yes—
176C2×#102C2314yes—
177C2×C22⋊C8C2312yes—
178C2×C22⋊C8C2312yes—
179C2×#97C2312yes—
180C2×#97C2314yes—
181C2×#97C2312yes—
182C2×C4×C8C2314yes—
183#391—21no—
184#391—21no—
185#391C2312yes—
186#391C2312yes—
187#389—21no—
188#389—21no—
189#389—21no—
190#389—21no—
191#389—21no—
192#389—21no—
193#389C2312yes—
194#389C2312yes—
195#387—22no—
196#387—22no—
197#387—22no—
198#387—22no—
199#385—22no—
200#385—22no—
201#384C2311yescharacteristic
202#384C2311yescharacteristic
203#382—21no—
204#380—21no—
205#380C2312yes—
206C4×C4⋊C4—21no—
207C4×C4⋊C4—21no—
208C4×C4⋊C4—21no—
209C4×C4⋊C4—21no—
210C4×C4⋊C4—22no—
211C4×C4⋊C4—22no—
212C4×C4⋊C4—22no—
213C4×C4⋊C4—22no—
214C4×C4⋊C4—21no—
215C4×C4⋊C4—21no—
216C4×C4⋊C4—21no—
217C4×C4⋊C4—21no—
218C4×C4⋊C4—21no—
219C4×C4⋊C4—21no—
220C4×C4⋊C4—21no—
221C4×C4⋊C4—21no—
222C4×C4⋊C4—21no—
223C4×C4⋊C4—22no—
224C4×C4⋊C4—22no—
225C4×C4⋊C4C2312yes—
226C4×C4⋊C4C2312yes—
227C4×C4⋊C4C2312yes—
228C4×C4⋊C4C2312yes—
229C4×C4⋊C4C2312yes—
230C4×C4⋊C4C2312yes—
231C4×C4⋊C4C2312yes—
232C4×C4⋊C4C2312yes—
233C4×C4⋊C4C2312yes—
234C4×C22⋊C4—22no—
235C4×C22⋊C4—22no—
236C4×C22⋊C4—22no—
237C4×C22⋊C4—22no—
238C4×C22⋊C4—22no—
239C4×C22⋊C4—22no—
240C4×C22⋊C4—22no—
241C4×C22⋊C4—22no—
242C4×C22⋊C4—22no—
243C4×C22⋊C4—22no—
244C4×C22⋊C4—22no—
245C4×C22⋊C4—22no—
246C4×C22⋊C4—22no—
247C4×C22⋊C4—22no—
248#376—22no—
249C2×#95—21no—
250C2×#95—21no—
251C2×#95—21no—
252C43—22no—
253C43D411yescharacteristic
254C43D411yescharacteristic
255C43D411yescharacteristic
256C43D411yescharacteristic
257C43C2311yescharacteristic
258C43C2311yescharacteristic
259C43C2311yescharacteristic
260C43C2311yescharacteristic
261#340C2314yes—
262#340C2314yes—
263#340C2314yes—
264#340C2314yes—
265#340C2314yes—
266#340C2314yes—
267#336C2314yes—
268#336C2314yes—
269C25—21no—
270C22×Q8—21no—
271C22×Q8C2412yes—
272C22×D4—24no—
273C22×D4—24no—
274C22×D4—21no—
275C22×D4—22no—
276C22×D4C22×C414yes—
277C22×D4C2412yes—
278C23×C4—28no—
279C23×C4—28no—
280C23×C4—21no—
281C23×C4—21no—
282C23×C4—21no—
283C23×C4—28no—
284C23×C4—22no—
285C23×C4—22no—
286C23×C4—22no—
287C23×C4—22no—
288C23×C4—22no—
289C23×C4—22no—
290C23×C4—44no—
291C23×C4—44no—
292C23×C4—44no—
293C23×C4—44no—
294C23×C4—44no—
295C23×C4—44no—
296C23×C4C2×D411yescharacteristic
297C23×C4C2×D411yescharacteristic
298C23×C4C2×D411yescharacteristic
299C23×C4C2×D411yescharacteristic
300C23×C4C2×D411yescharacteristic
301C23×C4C2×D411yescharacteristic
302C23×C4C2411yescharacteristic
303C2×SD16—28no—
304C2×SD16—28no—
305C2×SD16C22×C4116yes—
306C22×C8C2414yes—
307C22×C8C2414yes—
308C4⋊Q8—22no—
309C4⋊Q8—22no—
310C4⋊Q8C22×C414yescomplemented
311C4⋊Q8C22×C414yescomplemented
312#125—28no—
313C22⋊Q8—28no—
314C22⋊Q8—24no—
315C22⋊Q8C22×C418yes—
316C4×Q8—28no—
317C4×Q8—24no—
318C4×Q8—28no—
319C4×Q8—28no—
320C4×Q8—44no—
321C4×Q8—44no—
322C4×Q8C22×C418yescomplemented
323C4×D4—28no—
324C4×D4—28no—
325C4×D4—28no—
326C4×D4—28no—
327C4×D4—24no—
328C4×D4—24no—
329C4×D4—24no—
330C4×D4—24no—
331C4×D4—28no—
332C4×D4—28no—
333C4×D4—24no—
334C4×D4—24no—
335C4×D4—24no—
336C4×D4—24no—
337C4×D4C22×C418yes—
338C4×D4C22×C418yes—
339C4×D4#4118yes—
340C4×D4#4118yes—
341#117—28no—
342#117—44no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—24no—
353C2×C4⋊C4—24no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4C22×C414yes—
363C2×C4⋊C4C2412yes—
364C2×C4⋊C4C2412yes—
365C2×C4⋊C4C2412yes—
366C2×C4⋊C4C2412yes—
367C2×C4⋊C4C2412yes—
368C2×C4⋊C4C2412yes—
369C2×C22⋊C4—28no—
370C2×C22⋊C4—28no—
371C2×C22⋊C4—22no—
372C2×C22⋊C4—28no—
373C2×C22⋊C4—22no—
374C2×C22⋊C4—22no—
375C2×C22⋊C4—22no—
376C2×C22⋊C4—22no—
377C2×C22⋊C4—22no—
378C2×C22⋊C4—22no—
379C2×C22⋊C4—22no—
380C2×C42—24no—
381C2×C42—22no—
382C2×C42—24no—
383C2×C42—24no—
384C2×C42—24no—
385C2×C42—22no—
386C2×C42—22no—
387C2×C42—22no—
388C2×C42—22no—
389C2×C42—22no—
390C2×C42—22no—
391C2×C42—22no—
392C2×C42—22no—
393C2×C42—22no—
394C2×C42—22no—
395C2×C42—22no—
396C2×C42—42no—
397C2×C42—48no—
398C2×C42—48no—
399C2×C42—48no—
400C2×C42—42no—
401C2×C42—44no—
402C2×C42—44no—
403C2×C42—44no—
404C2×C42—48no—
405C2×C42C22×C414yes—
406C2×C42C2×D411yescharacteristic
407C2×C42C2×D411yescharacteristic
408C2×C42C2×D411yescharacteristic
409C2×C42C2×D411yescharacteristic
410C2×C42C2×D411yescharacteristic
411C2×C42C2×D411yescharacteristic
412C2×C42C2×D411yescharacteristic
413C2×C42C2×D411yescharacteristic
414C2×C42C2×D411yescharacteristic
415C2×C42C2×D411yescharacteristic
416C2×C42C2×D411yescharacteristic
417C2×C42C2×D411yescharacteristic
418C2×C42C2×D411yescharacteristic
419C2×C42C2×D411yescharacteristic
420C2×C42C2×D411yescharacteristic
421C2×C42C2×D411yescharacteristic
422C2×C42C2×D411yescharacteristic
423C2×C42C2×D411yescharacteristic
424C2×C42C2×D411yescharacteristic
425C2×C42C2×D411yescharacteristic
426C2×C42C2×D411yescharacteristic
427C2×C42C2×D411yescharacteristic
428C2×C42#4114yes—
429C2×C42C2411yescharacteristic
430C2×C42C2411yescharacteristic
431C2×C42C2411yescharacteristic
432C2×C42C2411yescharacteristic
433C2×C42C2411yescharacteristic
434C2×C42C2411yescharacteristic
435#107—28no—
436#107C22×C4116yescomplemented
437#106—28no—
438C4⋊C8—24no—
439C4⋊C8C22×C418yescomplemented
440#103—28no—
441#103—28no—
442#103C22×C4116yescomplemented
443#102—28no—
444#102—28no—
445#102C22×C4116yes—
446C22⋊C8—24no—
447C22⋊C8C22×C418yes—
448#97—24no—
449#97—28no—
450#97C22×C418yescomplemented
451C4×C8—28no—
452#95—22no—
453#95—22no—
454#95—22no—
455#95—22no—
456#95—22no—
457#95—22no—
458#95—22no—
459#95—22no—
460#95—22no—
461#95—22no—
462#95—22no—
463#95—22no—
464#95—22no—
465#95—22no—
466#95—22no—
467#95—22no—
468C24—24no—
469C24—24no—
470C24—24no—
471C24—22no—
472C24—42no—
473C24—42no—
474C24—42no—
475C24—42no—
476C24C22×D411yescharacteristic
477C2×Q8—24no—
478C2×Q8—22no—
479C2×Q8—24no—
480C2×Q8—24no—
481C2×Q8—42no—
482C2×Q8—42no—
483C2×Q8C23×C414yes—
484C2×D4—24no—
485C2×D4—24no—
486C2×D4—216no—
487C2×D4—216no—
488C2×D4—24no—
489C2×D4—22no—
490C2×D4—22no—
491C2×D4—22no—
492C2×D4C23×C414yes—
493C2×D4C2×#4114yes—
494C2×D4C2×#4114yes—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—24no—
507C22×C4—24no—
508C22×C4—28no—
509C22×C4—28no—
510C22×C4—24no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—28no—
519C22×C4—28no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—28no—
523C22×C4—28no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—41no—
527C22×C4—41no—
528C22×C4—44no—
529C22×C4—44no—
530C22×C4—44no—
531C22×C4—432no—
532C22×C4—44no—
533C22×C4—44no—
534C22×C4—44no—
535C22×C4—432no—
536C22×C4—432no—
537C22×C4—42no—
538C22×C4—42no—
539C22×C4—42no—
540C22×C4—42no—
541C22×C4—42no—
542C22×C4—42no—
543C22×C4—44no—
544C22×C4—44no—
545C22×C4—44no—
546C22×C4—44no—
547C22×C4—44no—
548C22×C4—44no—
549C22×C4C4×D414yes—
550C22×C4C4×D414yes—
551C22×C4#13714yes—
552C22×C4C23×C412yes—
553C22×C4C22×D411yescharacteristic
554C22×C4C22×D411yescharacteristic
555C22×C4C22×D411yescharacteristic
556C22×C4C22×D411yescharacteristic
557C22×C4C22×D411yescharacteristic
558C22×C4C22×D411yescharacteristic
559C22×C4C22×D411yescharacteristic
560C22×C4C22×D411yescharacteristic
561C22×C4C22×D411yescharacteristic
562C22×C4C22×D411yescharacteristic
563C22×C4C22×D411yescharacteristic
564C22×C4C22×D411yescharacteristic
565C22×C4C22×D411yescharacteristic
566C22×C4C2×#4112yes—
567C22×C4C2511yescharacteristic
568SD16—232no—
569C2×C8—24no—
570C2×C8—24no—
571C2×C8—24no—
572C2×C8—24no—
573C2×C8—24no—
574C2×C8C23×C418yes—
575C4⋊C4—24no—
576C4⋊C4—24no—
577C4⋊C4—24no—
578C4⋊C4—24no—
579C4⋊C4—24no—
580C4⋊C4—24no—
581C4⋊C4—28no—
582C4⋊C4—28no—
583C4⋊C4—22no—
584C4⋊C4—22no—
585C4⋊C4—22no—
586C4⋊C4—22no—
587C4⋊C4—24no—
588C4⋊C4—24no—
589C4⋊C4—42no—
590C4⋊C4—42no—
591C4⋊C4—44no—
592C4⋊C4—44no—
593C4⋊C4—44no—
594C4⋊C4—44no—
595C4⋊C4—42no—
596C4⋊C4—42no—
597C4⋊C4C23×C414yes—
598C4⋊C4C23×C414yes—
599C4⋊C4C2×#4114yes—
600C4⋊C4C2×#4114yes—
601C22⋊C4—28no—
602C22⋊C4—28no—
603C22⋊C4—28no—
604C22⋊C4—28no—
605C22⋊C4—28no—
606C22⋊C4—28no—
607C22⋊C4—28no—
608C22⋊C4—44no—
609C42—28no—
610C42—22no—
611C42—22no—
612C42—22no—
613C42—22no—
614C42—22no—
615C42—22no—
616C42—22no—
617C42—22no—
618C42—22no—
619C42—22no—
620C42—22no—
621C42—22no—
622C42—22no—
623C42—22no—
624C42—22no—
625C42—41no—
626C42—41no—
627C42—41no—
628C42—41no—
629C42—41no—
630C42—41no—
631C42—44no—
632C42—44no—
633C42—44no—
634C42—44no—
635C42—44no—
636C42—44no—
637C42—44no—
638C42—44no—
639C42—44no—
640C42—44no—
641C42—44no—
642C42C4×D414yes—
643C42C4×D414yes—
644C42AGL(1,ℤ/8)14yes—
645C42C23×C412yes—
646C42C23×C412yes—
647C42C2×#4112yes—
648C42C2×#4112yes—
649C42C2×#4114yes—
650C42C2×#4114yes—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—216no—
656C23—24no—
657C23—24no—
658C23—24no—
659C23—48no—
660C23—48no—
661C23—48no—
662C23—48no—
663C23—48no—
664C23—48no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23C2×C4×D412yes—
670C23C2×#13712yes—
671C23#57512yes—
672C23C23×D411yescharacteristic
673Q8—28no—
674Q8—44no—
675Q8—48no—
676D4—216no—
677D4—24no—
678D4—24no—
679D4—24no—
680D4C4×#4118yes—
681C2×C4—28no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—28no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—28no—
702C2×C4—24no—
703C2×C4—24no—
704C2×C4—28no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—44no—
717C2×C4—44no—
718C2×C4—416no—
719C2×C4—416no—
720C2×C4—416no—
721C2×C4—416no—
722C2×C4—48no—
723C2×C4—48no—
724C2×C4—48no—
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—416no—
736C2×C4—416no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4C2×C4×D412yes—
744C2×C4C2×C4×D412yes—
745C2×C4C2×C4×D412yes—
746C2×C4C2×C4×D412yes—
747C2×C4C2×C4×D412yes—
748C2×C4#52512yes—
749C2×C4#52512yes—
750C2×C4#52512yes—
751C2×C4#52512yes—
752C2×C4C2×AGL(1,ℤ/8)12yes—
753C2×C4C2×AGL(1,ℤ/8)12yes—
754C2×C4C2×AGL(1,ℤ/8)12yes—
755C2×C4C2×#13712yes—
756C2×C4C2×#13712yes—
757C2×C4#57512yes—
758C2×C4C24×C411yescharacteristic
759C2×C4C22×#4112yes—
760C2×C4C22×#4112yes—
761C2×C4C22×#4111yescharacteristic
762C8—28no—
763C8—44no—
764C22—22no—
765C22—22no—
766C22—22no—
767C22—22no—
768C22—22no—
769C22—22no—
770C22—28no—
771C22—432no—
772C22—44no—
773C22—44no—
774C22—44no—
775C22—44no—
776C22—44no—
777C22—44no—
778C22C4×#13714yes—
779C22C22×C4×D411yescharacteristic
780C22C2×#52511yescharacteristic
781C22C2×#52511yescharacteristic
782C22C22×AGL(1,ℤ/8)11yescharacteristic
783C22C22×#13711yescharacteristic
784C22C2×#57511yescharacteristic
785C22C2×#57511yescharacteristic
786C4—22no—
787C4—22no—
788C4—22no—
789C4—22no—
790C4—22no—
791C4—22no—
792C4—22no—
793C4—22no—
794C4—22no—
795C4—44no—
796C4—41no—
797C4—44no—
798C4—41no—
799C4—44no—
800C4—44no—
801C4—44no—
802C4—82no—
803C4—82no—
804C4C4×AGL(1,ℤ/8)14yes—
805C4#311014yesdirect product factor
806C4C2×C4×#4112yes—
807C4#344412yes—
808C2—24no—
809C2—48no—
810C2C4×#52511yescharacteristic
811C2C2×C4×AGL(1,ℤ/8)11yescharacteristic
812C2C2×C4×#13711yescharacteristic
813C2C2×#311011yescharacteristic
814C2#6054611yescharacteristic
815C2#6055811yescharacteristic
816C2#6056211yescharacteristic
subgroupG/H
centerC22×C4C22×D4
commutatorC2×C4C24×C4
Frattini, cosocleC22×C4C25
socleC23C23×D4
prime radicalC23×D4C23
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4 ◁ C2×C43 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C4×#533C2semidirect
4. #21613C2semidirect
5. C4×#474C2semidirect
6. #21581C2semidirect
7. C4×#484C2semidirect
8. #21504C2semidirect
9. C4×#461C2semidirect
12. #21394C2semidirect
13. #21365C2semidirect
14. #21121C2semidirect
16. C4×#440C2semidirect
17. C4×#432C2semidirect
23. #3110C4direct (N × H)
33. C4×C4⋊Q8C22semidirect
34. C4×C4⋊Q8C22semidirect
35. C4×C4⋊Q8C22semidirect
36. C4×C4⋊Q8C22semidirect
45. #2295C22semidirect
48. C42×Q8C22semidirect
65. #1988C22semidirect
66. #1981C22semidirect
67. #1948C22semidirect
68. #1947C22semidirect
69. #1928C22semidirect
70. #1927C22semidirect
71. #1921C22semidirect
72. #1918C22semidirect
85. #1776C22semidirect
86. #1776C22semidirect
87. C4×#107C22semidirect
88. #1767C22semidirect
89. C4×C4⋊C8C22semidirect
90. #1763C22semidirect
91. #1763C22semidirect
94. C4×#103C22semidirect
98. #1745C22semidirect
99. C4×#97C22semidirect
106. #533C2×C4semidirect
157. #484C2×C4semidirect
158. #474C2×C4semidirect
159. #461C2×C4semidirect
162. #440C2×C4semidirect
165. #432C2×C4semidirect
310. C4⋊Q8C22×C4semidirect
311. C4⋊Q8C22×C4semidirect
322. C4×Q8C22×C4semidirect
436. #107C22×C4semidirect
439. C4⋊C8C22×C4semidirect
442. #103C22×C4semidirect
450. #97C22×C4semidirect
805. C4#3110direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#31102
C4×#5332
C2×C42×D42
#216132
C4×#4742
#215812
C4×#4842
#215042
C4×#4612
#214532
C4×#4502
#213942
#213652
#211212
#207382
C4×#4402
C4×#4322