Finite Group Databasebeta

← C4×#3182 #6373931

Subgroups — C4×#3182 #6373931

Order 512.

2340 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3182C211yesmaximal, characteristic
2C4×#533C211yesmaximal, characteristic, complemented
3C4×#532C211yesmaximal, characteristic
4#21726C211yesmaximal, characteristic, complemented
5C4×#500C211yesmaximal, characteristic, complemented
6#21692C211yesmaximal, characteristic, complemented
7C4×#492C211yesmaximal, characteristic, complemented
8#21647C211yesmaximal, characteristic, complemented
9#21646C211yesmaximal, characteristic, complemented
10C4×#487C211yesmaximal, characteristic, complemented
11C4×#486C211yesmaximal, characteristic, complemented
12#21540C214yesmaximal, complemented
13C4×#468C214yesmaximal, complemented
14#21410C211yesmaximal, characteristic
15#21409C211yesmaximal, characteristic, complemented
16#21288C214yesmaximal, complemented
17#20824C211yesmaximal, characteristic, complemented
18C4×#440C214yesmaximal, complemented
19C42×M16C211yesmaximal, characteristic, complemented
20C2×#533C2211yescharacteristic
21C2×#532C2211yescharacteristic
22C2×C4×#41—21no—
23#3182C4116yesdirect product factor
24C2×#500C2211yescharacteristic
25C2×#492C2211yescharacteristic
26C2×#487C2211yescharacteristic
27C2×#486C2211yescharacteristic
28C2×#468C2214yes—
29C2×#440C2214yes—
30C2×#440C2214yes—
31C2×C4×SD16C2214yes—
32C2×C4×M16C2212yes—
33C2×C4×M16C2212yes—
34C2×C4×M16C2211yescharacteristic
35C2×C4×M16C2211yescharacteristic
36C4×C4⋊Q8C2211yescharacteristic
37C4×C4⋊Q8C2211yescharacteristic
38C4×C4⋊Q8C2211yescharacteristic
39C4×C4⋊Q8C2211yescharacteristic
40C4×C4⋊Q8C2211yescharacteristic
41C4×C4⋊Q8C2211yescharacteristic
42C4×#127C2211yescharacteristic
43C4×#127C2211yescharacteristic
44C4×#125—21no—
45C4×#125—21no—
46C4×#124—21no—
47C4×#124—21no—
48C4×C22⋊Q8—21no—
49C4×C22⋊Q8—21no—
50C4×C22⋊Q8C2212yes—
51C4×C22⋊Q8C2212yes—
52C4×#121—21no—
53C4×#121—21no—
54C4×#121C2212yes—
55C4×#121C2212yes—
56#2297—21no—
57#2296—21no—
58#2295—21no—
59#2295C2212yes—
60#2293—21no—
61#2293C2212yes—
62#2285C2211yescharacteristic
63#2285C2211yescharacteristic
64C42×Q8—21no—
65C42×Q8C2212yes—
66C42×D4—21no—
67C42×D4C2212yes—
68C4×#117—21no—
69C2×C43C2211yescharacteristic
70#1990C2211yescharacteristic
71#1990C2211yescharacteristic
72#1990C2211yescharacteristic
73#1990C2211yescharacteristic
74#1973C2214yes—
75#1968C2214yes—
76#1957C2211yescharacteristic
77#1957C2211yescharacteristic
78#1956C2211yescharacteristic
79#1956C2211yescharacteristic
80#1943C2214yes—
81#1942C2214yes—
82#1936C2214yes—
83#1935C2214yes—
84#1934C2214yes—
85#1933C2214yes—
86#1895C2214yes—
87#1894C2214yes—
88#1845C2211yescharacteristic
89#1844C2211yescharacteristic
90#1834C2211yescharacteristic
91#1834C2211yescharacteristic
92#1809C2214yes—
93#1776C2214yes—
94#1776C2214yes—
95C4×#107C2214yes—
96#1763C2214yes—
97#1763C2214yes—
98#1762C2214yes—
99#1762C2214yes—
100C4×#103C2214yes—
101C4×#102C2214yes—
102C4×#97C2212yes—
103C4×#97C2212yes—
104C4×#97C2211yescharacteristic
105C4×#97C2211yescharacteristic
106C42×C8C2211yescharacteristic
107C42×C8C2211yescharacteristic
108C22×#41—21no—
109C22×SD16C2314yes—
110C22×M16C2312yes—
111C22×M16C2312yes—
112#533—24no—
113#533C2×C418yescomplemented
114#532—24no—
115#532C2×C418yes—
116C2×C4⋊Q8C2311yescharacteristic
117C2×C4⋊Q8C2311yescharacteristic
118C2×C4⋊Q8C2311yescharacteristic
119C2×#127C2311yescharacteristic
120C2×#125—21no—
121C2×#124—21no—
122C2×C22⋊Q8—21no—
123C2×C22⋊Q8C2312yes—
124C2×#121—21no—
125C2×#121C2312yes—
126C4×#41—48no—
127C2×C4×Q8—21no—
128C2×C4×Q8—21no—
129C2×C4×Q8—21no—
130C2×C4×Q8—21no—
131C2×C4×Q8—21no—
132C2×C4×Q8C2312yes—
133C2×C4×Q8C2312yes—
134C2×C4×Q8C2312yes—
135C2×C4×D4—22no—
136C2×C4×D4—22no—
137C2×C4×D4—21no—
138C2×C4×D4—21no—
139C2×C4×D4—21no—
140C2×C4×D4—21no—
141C2×C4×D4—21no—
142C2×C4×D4C2312yes—
143C2×C4×D4C2312yes—
144C2×C4×D4C2312yes—
145C2×#117—21no—
146C2×#117—21no—
147C2×#117—21no—
148C2×#117—22no—
149C22×C42—22no—
150C22×C42D411yescharacteristic
151C22×C42D411yescharacteristic
152C22×C42D411yescharacteristic
153C22×C42D411yescharacteristic
154C22×C42C2311yescharacteristic
155C22×C42C2311yescharacteristic
156C22×C42C2311yescharacteristic
157#500C2×C418yescomplemented
158#492C2×C418yescomplemented
159#487C2×C418yescomplemented
160#486C2×C418yescomplemented
161#468C2×C4132yescomplemented
162#440—216no—
163#440C2×C4132yescomplemented
164C4×SD16—216no—
165C2×#107C2314yes—
166C2×#107C2314yes—
167C2×#106C2314yes—
168C2×#103C2314yes—
169C2×#103C2314yes—
170C2×#103C2314yes—
171C2×#102C2314yes—
172C2×#102C2314yes—
173C2×#102C2314yes—
174C4×M16—24no—
175C4×M16—28no—
176C4×M16—28no—
177C4×M16C2×C418yescomplemented
178C2×#97C2312yes—
179C2×#97C2312yes—
180C2×#97C2312yes—
181C2×#97C2312yes—
182C2×#97C2312yes—
183C2×#97C2312yes—
184C2×C4×C8C2312yes—
185C2×C4×C8C2312yes—
186C2×C4×C8C2311yescharacteristic
187C2×C4×C8C2311yescharacteristic
188C2×C4×C8C2312yes—
189C2×C4×C8C2311yescharacteristic
190C2×C4×C8C2311yescharacteristic
191C2×C4×C8C2312yes—
192#391—21no—
193#391—21no—
194#391—21no—
195#391—21no—
196#391C2312yes—
197#391C2312yes—
198#390—21no—
199#390—21no—
200#390—21no—
201#390—21no—
202#390C2312yes—
203#390C2312yes—
204#389—21no—
205#389—21no—
206#389—21no—
207#389—21no—
208#389—21no—
209#389—21no—
210#389—21no—
211#389—21no—
212#389C2312yes—
213#389C2312yes—
214#389C2312yes—
215#389C2312yes—
216#388—22no—
217#388—22no—
218#388—22no—
219#388—22no—
220#387—22no—
221#387—22no—
222#387—22no—
223#387—22no—
224#386—22no—
225#386—22no—
226#385—22no—
227#385—22no—
228#384C2311yescharacteristic
229#384C2311yescharacteristic
230#384C2311yescharacteristic
231#384C2311yescharacteristic
232#382—21no—
233#382—21no—
234#380—21no—
235#380—21no—
236#380C2312yes—
237#380C2312yes—
238C4×C4⋊C4—21no—
239C4×C4⋊C4—21no—
240C4×C4⋊C4—21no—
241C4×C4⋊C4—21no—
242C4×C4⋊C4—22no—
243C4×C4⋊C4—22no—
244C4×C4⋊C4—22no—
245C4×C4⋊C4—22no—
246C4×C4⋊C4—21no—
247C4×C4⋊C4—21no—
248C4×C4⋊C4—21no—
249C4×C4⋊C4—21no—
250C4×C4⋊C4—21no—
251C4×C4⋊C4—21no—
252C4×C4⋊C4—22no—
253C4×C4⋊C4—22no—
254C4×C4⋊C4C2312yes—
255C4×C4⋊C4C2312yes—
256C4×C4⋊C4C2312yes—
257C4×C4⋊C4C2312yes—
258C4×C4⋊C4C2312yes—
259C4×C4⋊C4C2312yes—
260C4×C22⋊C4—22no—
261C4×C22⋊C4—22no—
262C4×C22⋊C4—22no—
263C4×C22⋊C4—22no—
264C4×C22⋊C4—22no—
265C4×C22⋊C4—22no—
266C4×C22⋊C4—22no—
267C4×C22⋊C4—22no—
268#376—22no—
269C43—22no—
270C43D411yescharacteristic
271C43D411yescharacteristic
272C43D411yescharacteristic
273C43D411yescharacteristic
274C43C2311yescharacteristic
275C43C2311yescharacteristic
276C43C2311yescharacteristic
277C43C2311yescharacteristic
278#340C2314yes—
279#340C2314yes—
280#340C2314yes—
281#340C2314yes—
282#340C2314yes—
283#340C2314yes—
284C2×#41—28no—
285C2×#41—44no—
286C2×#41—44no—
287C22×Q8—21no—
288C22×Q8—21no—
289C22×Q8C2412yes—
290C22×D4—22no—
291C22×D4—21no—
292C22×D4—21no—
293C22×D4C2412yes—
294C23×C4—22no—
295C23×C4—22no—
296C23×C4—22no—
297C23×C4C2×D411yescharacteristic
298C23×C4C2×D411yescharacteristic
299C23×C4C2×D411yescharacteristic
300C23×C4C2×D411yescharacteristic
301C23×C4C2×D411yescharacteristic
302C23×C4C2×D411yescharacteristic
303C23×C4C2411yescharacteristic
304C2×SD16—28no—
305C2×SD16—28no—
306C2×SD16C22×C4116yes—
307C2×M16—24no—
308C2×M16—24no—
309C2×M16—24no—
310C2×M16—24no—
311C2×M16—24no—
312C2×M16C22×C418yes—
313C22×C8C2412yes—
314C22×C8C2412yes—
315C22×C8C2412yes—
316C22×C8C2412yes—
317C4⋊Q8—22no—
318C4⋊Q8—22no—
319C4⋊Q8—22no—
320C4⋊Q8C22×C414yes—
321C4⋊Q8C22×C414yes—
322C4⋊Q8C22×C414yes—
323#127—22no—
324#127C22×C414yes—
325#125—28no—
326#124—28no—
327C22⋊Q8—28no—
328C22⋊Q8—24no—
329C22⋊Q8C22×C418yes—
330#121—28no—
331#121—24no—
332#121C22×C418yes—
333C4×Q8—28no—
334C4×Q8—24no—
335C4×Q8—28no—
336C4×Q8—28no—
337C4×Q8—44no—
338C4×Q8—44no—
339C4×Q8—44no—
340C4×Q8—44no—
341C4×Q8C22×C418yes—
342C4×D4—28no—
343C4×D4—24no—
344C4×D4—28no—
345C4×D4—28no—
346C4×D4—44no—
347C4×D4—44no—
348C4×D4—48no—
349C4×D4—48no—
350C4×D4—44no—
351C4×D4—44no—
352C4×D4C22×C418yes—
353#117—28no—
354#117—48no—
355#117—44no—
356#117—44no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—22no—
377C2×C4⋊C4C2412yes—
378C2×C4⋊C4C2412yes—
379C2×C4⋊C4C2412yes—
380C2×C4⋊C4C2412yes—
381C2×C4⋊C4C2412yes—
382C2×C4⋊C4C2412yes—
383C2×C22⋊C4—22no—
384C2×C22⋊C4—22no—
385C2×C22⋊C4—22no—
386C2×C22⋊C4—22no—
387C2×C22⋊C4—22no—
388C2×C22⋊C4—22no—
389C2×C22⋊C4—22no—
390C2×C22⋊C4—22no—
391C2×C22⋊C4—22no—
392C2×C22⋊C4—22no—
393C2×C22⋊C4—22no—
394C2×C42—22no—
395C2×C42—24no—
396C2×C42—24no—
397C2×C42—24no—
398C2×C42—24no—
399C2×C42—22no—
400C2×C42—22no—
401C2×C42—22no—
402C2×C42—22no—
403C2×C42—22no—
404C2×C42—22no—
405C2×C42—22no—
406C2×C42—22no—
407C2×C42—42no—
408C2×C42—42no—
409C2×C42—48no—
410C2×C42C22×C414yes—
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×C42C2×D411yescharacteristic
429C2×C42C2×D411yescharacteristic
430C2×C42C2×D411yescharacteristic
431C2×C42C2×D411yescharacteristic
432C2×C42C2×D411yescharacteristic
433C2×C42#4114yes—
434C2×C42C2411yescharacteristic
435C2×C42C2411yescharacteristic
436C2×C42C2411yescharacteristic
437C2×C42C2411yescharacteristic
438C2×C42C2411yescharacteristic
439C2×C42C2411yescharacteristic
440#107—28no—
441#107C22×C4116yes—
442#106—28no—
443#103—28no—
444#103—28no—
445#103C22×C4116yes—
446#102—28no—
447#102—28no—
448#102C22×C4116yes—
449#97—24no—
450#97—24no—
451#97—24no—
452#97—24no—
453#97C22×C418yes—
454#97#4118yescomplemented
455C4×C8—24no—
456C4×C8—24no—
457C4×C8—22no—
458C4×C8—22no—
459C4×C8—24no—
460C4×C8C22×C414yes—
461C4×C8C22×C414yes—
462C4×C8#4118yescomplemented
463#95—22no—
464#95—22no—
465#95—22no—
466#95—22no—
467#95—22no—
468#95—22no—
469#95—22no—
470#95—22no—
471#95—22no—
472#95—22no—
473#95—22no—
474#95—22no—
475#95—22no—
476#95—22no—
477#95—22no—
478#95—22no—
479C24—22no—
480C24C22×D411yescharacteristic
481#41—432no—
482C2×Q8—24no—
483C2×Q8—24no—
484C2×Q8—22no—
485C2×Q8—24no—
486C2×Q8—24no—
487C2×Q8—42no—
488C2×Q8—42no—
489C2×Q8—42no—
490C2×Q8—42no—
491C2×Q8C23×C414yes—
492C2×D4—28no—
493C2×D4—24no—
494C2×D4—24no—
495C2×D4—24no—
496C2×D4—24no—
497C2×D4—22no—
498C2×D4—44no—
499C2×D4—44no—
500C2×D4—42no—
501C2×D4—42no—
502C2×D4—42no—
503C2×D4—42no—
504C2×D4C23×C414yes—
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—28no—
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—22no—
527C22×C4—41no—
528C22×C4—41no—
529C22×C4—41no—
530C22×C4—41no—
531C22×C4—44no—
532C22×C4—44no—
533C22×C4—44no—
534C22×C4—44no—
535C22×C4—44no—
536C22×C4—44no—
537C22×C4—44no—
538C22×C4—44no—
539C22×C4C4×D414yes—
540C22×C4C4×D414yes—
541C22×C4C23×C412yes—
542C22×C4C22×D411yescharacteristic
543C22×C4C22×D411yescharacteristic
544C22×C4C22×D411yescharacteristic
545C22×C4C22×D411yescharacteristic
546C22×C4C22×D411yescharacteristic
547C22×C4C22×D411yescharacteristic
548C22×C4C22×D411yescharacteristic
549C22×C4C22×D411yescharacteristic
550C22×C4C22×D411yescharacteristic
551C22×C4C22×D411yescharacteristic
552C22×C4C22×D411yescharacteristic
553C22×C4C22×D411yescharacteristic
554C22×C4C22×D411yescharacteristic
555C22×C4C2×#4112yes—
556C22×C4C2511yescharacteristic
557SD16—232no—
558M16—216no—
559M16—216no—
560C2×C8—22no—
561C2×C8—22no—
562C2×C8—22no—
563C2×C8—22no—
564C2×C8—22no—
565C2×C8—22no—
566C2×C8C23×C414yes—
567C2×C8C23×C414yes—
568C2×C8C2×#4114yes—
569C2×C8C2×#4114yes—
570C2×C8C2×#4114yes—
571C2×C8C2×#4114yes—
572C4⋊C4—24no—
573C4⋊C4—24no—
574C4⋊C4—24no—
575C4⋊C4—24no—
576C4⋊C4—28no—
577C4⋊C4—28no—
578C4⋊C4—22no—
579C4⋊C4—22no—
580C4⋊C4—24no—
581C4⋊C4—24no—
582C4⋊C4—24no—
583C4⋊C4—24no—
584C4⋊C4—44no—
585C4⋊C4—44no—
586C4⋊C4—44no—
587C4⋊C4—44no—
588C4⋊C4—44no—
589C4⋊C4—42no—
590C4⋊C4—42no—
591C4⋊C4—44no—
592C4⋊C4—42no—
593C4⋊C4—42no—
594C4⋊C4—42no—
595C4⋊C4—42no—
596C4⋊C4—42no—
597C4⋊C4—42no—
598C4⋊C4C23×C414yes—
599C4⋊C4C23×C414yes—
600C22⋊C4—28no—
601C22⋊C4—28no—
602C22⋊C4—28no—
603C22⋊C4—44no—
604C22⋊C4—44no—
605C22⋊C4—44no—
606C22⋊C4—44no—
607C22⋊C4—44no—
608C22⋊C4—44no—
609C22⋊C4—44no—
610C22⋊C4—44no—
611C42—28no—
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—22no—
626C42—22no—
627C42—22no—
628C42—41no—
629C42—41no—
630C42—41no—
631C42—41no—
632C42—44no—
633C42—44no—
634C42—44no—
635C42—44no—
636C42—44no—
637C42—44no—
638C42—44no—
639C42—44no—
640C42C4×D414yes—
641C42C4×D414yes—
642C42AGL(1,ℤ/8)14yes—
643C42#13714yes—
644C42C23×C412yes—
645C42C23×C412yes—
646C42C2×#4112yes—
647C42C2×#4112yes—
648C42C2×#4114yes—
649C42C2×#4114yes—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—24no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23C2×C4×D412yes—
664C23C23×D411yescharacteristic
665Q8—28no—
666Q8—44no—
667Q8—48no—
668Q8—48no—
669D4—28no—
670D4—416no—
671D4—44no—
672D4—48no—
673D4—48no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—24no—
691C2×C4—24no—
692C2×C4—28no—
693C2×C4—28no—
694C2×C4—24no—
695C2×C4—24no—
696C2×C4—24no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—44no—
704C2×C4—44no—
705C2×C4—44no—
706C2×C4—416no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—44no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
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—88no—
727C2×C4—88no—
728C2×C4C2×C4×D412yes—
729C2×C4C2×C4×D412yes—
730C2×C4C2×C4×D412yes—
731C2×C4C2×C4×D412yes—
732C2×C4C2×C4×D412yes—
733C2×C4#53212yes—
734C2×C4#53212yes—
735C2×C4#53212yes—
736C2×C4#53212yes—
737C2×C4C2×AGL(1,ℤ/8)12yes—
738C2×C4C2×AGL(1,ℤ/8)12yes—
739C2×C4C2×AGL(1,ℤ/8)12yes—
740C2×C4C2×#13712yes—
741C2×C4C2×#13712yes—
742C2×C4C2×#13712yes—
743C2×C4#57512yes—
744C2×C4#57512yes—
745C2×C4C24×C411yescharacteristic
746C2×C4C22×#4112yes—
747C2×C4C22×#4112yes—
748C2×C4C22×#4111yescharacteristic
749C8—24no—
750C8—24no—
751C8—24no—
752C8C4×#4118yescomplemented
753C22—22no—
754C22—22no—
755C22—22no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—44no—
761C22—44no—
762C22—44no—
763C22—82no—
764C22—82no—
765C22—82no—
766C22—82no—
767C22C22×C4×D411yescharacteristic
768C22C2×#53211yescharacteristic
769C22C2×#53211yescharacteristic
770C22C22×AGL(1,ℤ/8)11yescharacteristic
771C22C22×#13711yescharacteristic
772C22C2×#57511yescharacteristic
773C22C2×#57511yescharacteristic
774C4—22no—
775C4—22no—
776C4—22no—
777C4—22no—
778C4—22no—
779C4—22no—
780C4—22no—
781C4—22no—
782C4—41no—
783C4—41no—
784C4—44no—
785C4—44no—
786C4—44no—
787C4—82no—
788C4—82no—
789C4—82no—
790C4—82no—
791C4C4×AGL(1,ℤ/8)14yes—
792C4C4×#13714yes—
793C4#318214yesdirect product factor
794C4C2×C4×#4112yes—
795C4#344412yes—
796C2—42no—
797C2—84no—
798C2C4×#53211yescharacteristic
799C2C2×C4×AGL(1,ℤ/8)11yescharacteristic
800C2C2×C4×#13711yescharacteristic
801C2C2×#318211yescharacteristic
802C2#6069311yescharacteristic
803C2#6070011yescharacteristic
804C2#6070111yescharacteristic
subgroupG/H
centerC22×C4C22×D4
commutatorC2×C4C24×C4
Frattini, cosocleC22×C4C25
socleC23C23×D4
prime radicalC2×#532C22
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. #21726C2semidirect
5. C4×#500C2semidirect
6. #21692C2semidirect
7. C4×#492C2semidirect
8. #21647C2semidirect
9. #21646C2semidirect
10. C4×#487C2semidirect
11. C4×#486C2semidirect
12. #21540C2semidirect
13. C4×#468C2semidirect
15. #21409C2semidirect
16. #21288C2semidirect
17. #20824C2semidirect
18. C4×#440C2semidirect
19. C42×M16C2semidirect
23. #3182C4direct (N × H)
113. #533C2×C4semidirect
157. #500C2×C4semidirect
158. #492C2×C4semidirect
159. #487C2×C4semidirect
160. #486C2×C4semidirect
161. #468C2×C4semidirect
163. #440C2×C4semidirect
177. C4×M16C2×C4semidirect
454. #97#41semidirect
462. C4×C8#41semidirect
752. C8C4×#41semidirect
793. C4#3182direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#31822
C4×#5332
C4×#5322
#217262
C4×#5002
#216922
C4×#4922
#216472
#216462
C4×#4872
C4×#4862
#215402
C4×#4682
#214102
#214092
#212882
#208242
C4×#4402
C42×M162