Finite Group Databasebeta

← C4×#3210 #6377715

Subgroups — C4×#3210 #6377715

Order 512.

2204 conjugacy classes of subgroups.

The subgroup lattice has 801 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3210C211yesmaximal, characteristic
2C4×#533C211yesmaximal, characteristic, complemented
3C4×#532C211yesmaximal, characteristic
4#22270C211yesmaximal, characteristic, complemented
5#22268C211yesmaximal, characteristic, complemented
6#22220C211yesmaximal, characteristic, complemented
7#22218C211yesmaximal, characteristic, complemented
8#22150C214yesmaximal, complemented
9#22042C214yesmaximal, complemented
10#21984C211yesmaximal, characteristic, complemented
11#21864C211yesmaximal, characteristic, complemented
12#21805C211yesmaximal, characteristic
13C4×#494C211yesmaximal, characteristic, complemented
14C4×#492C211yesmaximal, characteristic, complemented
15C4×#487C211yesmaximal, characteristic, complemented
16C4×#486C211yesmaximal, characteristic, complemented
17C4×#464C214yesmaximal, complemented
18C4×#452C214yesmaximal, complemented
19C4×#431C211yesmaximal, characteristic, complemented
20C2×#533C2211yescharacteristic
21C2×#532C2211yescharacteristic
22C2×C4×#41C2212yes—
23#3210C4116yesdirect product factor
24C2×#494C2211yescharacteristic
25C2×#492C2211yescharacteristic
26C2×#487C2211yescharacteristic
27C2×#486C2211yescharacteristic
28C2×#464C2214yes—
29C2×#452C2214yes—
30C2×C4×Q16C2214yes—
31C2×C4×SD16C2214yes—
32C2×#431C2211yescharacteristic
33C2×#431C2211yescharacteristic
34C4×C4⋊Q8C2211yescharacteristic
35C4×C4⋊Q8C2211yescharacteristic
36C4×C4⋊Q8C2211yescharacteristic
37C4×C4⋊Q8C2211yescharacteristic
38C4×C4⋊Q8C2211yescharacteristic
39C4×C4⋊Q8C2211yescharacteristic
40C4×#127C2211yescharacteristic
41C4×#127C2211yescharacteristic
42C4×#125—21no—
43C4×#125—21no—
44C4×#124C2212yes—
45C4×#124C2212yes—
46C4×C22⋊Q8—21no—
47C4×C22⋊Q8—21no—
48C4×C22⋊Q8C2212yes—
49C4×C22⋊Q8C2212yes—
50C4×#121—21no—
51C4×#121—21no—
52C4×#121—21no—
53C4×#121—21no—
54#2297C2212yes—
55#2296—21no—
56#2295—21no—
57#2295C2212yes—
58#2293—21no—
59#2293—21no—
60#2285C2211yescharacteristic
61#2285C2211yescharacteristic
62C42×Q8—21no—
63C42×Q8C2212yes—
64C42×D4—21no—
65C42×D4—21no—
66C4×#117—21no—
67C2×C43C2211yescharacteristic
68#1990C2211yescharacteristic
69#1990C2211yescharacteristic
70#1983C2214yes—
71#1969C2214yes—
72#1968C2214yes—
73#1957C2211yescharacteristic
74#1957C2211yescharacteristic
75#1956C2211yescharacteristic
76#1956C2211yescharacteristic
77#1956C2211yescharacteristic
78#1956C2211yescharacteristic
79#1949C2214yes—
80#1934C2214yes—
81#1933C2214yes—
82#1927C2214yes—
83#1925C2214yes—
84#1880C2214yes—
85#1878C2214yes—
86#1878C2214yes—
87#1877C2214yes—
88#1873C2214yes—
89#1865C2214yes—
90#1862C2214yes—
91#1854C2214yes—
92#1845C2211yescharacteristic
93#1844C2211yescharacteristic
94#1834C2211yescharacteristic
95#1834C2211yescharacteristic
96#1805C2214yes—
97#1788C2214yes—
98C4×C4⋊C8C2212yes—
99C4×C4⋊C8C2212yes—
100C4×#103C2214yes—
101C4×#102C2214yes—
102C4×C22⋊C8C2212yes—
103C4×C22⋊C8C2212yes—
104#1744C2211yescharacteristic
105#1744C2211yescharacteristic
106C42×C8C2211yescharacteristic
107C42×C8C2211yescharacteristic
108C22×#41C2312yes—
109C22×Q16C2314yes—
110C22×SD16C2314yes—
111#533—24no—
112#533C2×C418yescomplemented
113#532—24no—
114#532C2×C418yes—
115C2×C4⋊Q8C2311yescharacteristic
116C2×C4⋊Q8C2311yescharacteristic
117C2×C4⋊Q8C2311yescharacteristic
118C2×#127C2311yescharacteristic
119C2×#125—21no—
120C2×#124C2312yes—
121C2×C22⋊Q8—21no—
122C2×C22⋊Q8C2312yes—
123C2×#121—21no—
124C2×#121—21no—
125C4×#41—48no—
126C2×C4×Q8—21no—
127C2×C4×Q8—21no—
128C2×C4×Q8—21no—
129C2×C4×Q8C2312yes—
130C2×C4×Q8C2312yes—
131C2×C4×Q8C2312yes—
132C2×C4×Q8C2312yes—
133C2×C4×Q8C2312yes—
134C2×C4×D4—22no—
135C2×C4×D4—22no—
136C2×C4×D4—21no—
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×#117—21no—
145C2×#117—21no—
146C2×#117—22no—
147C2×#117C2312yes—
148C22×C42—22no—
149C22×C42D411yescharacteristic
150C22×C42D411yescharacteristic
151C22×C42D411yescharacteristic
152C22×C42D411yescharacteristic
153C22×C42C2311yescharacteristic
154C22×C42C2311yescharacteristic
155C22×C42C2311yescharacteristic
156#494C2×C418yescomplemented
157#492C2×C418yescomplemented
158#487C2×C418yescomplemented
159#486C2×C418yescomplemented
160#464C2×C4132yescomplemented
161#452C2×C4132yescomplemented
162C4×Q16—48no—
163C4×SD16—48no—
164#431—24no—
165#431C2×C418yescomplemented
166C2×#107C2314yes—
167C2×#106C2314yes—
168C2×C4⋊C8C2312yes—
169C2×C4⋊C8C2312yes—
170C2×#103C2314yes—
171C2×#103C2314yes—
172C2×#103C2314yes—
173C2×#103C2314yes—
174C2×#103C2314yes—
175C2×#102C2314yes—
176C2×#102C2314yes—
177C2×#102C2314yes—
178C2×C22⋊C8C2312yes—
179C2×C22⋊C8C2312yes—
180C2×C4×C8C2311yescharacteristic
181C2×C4×C8C2311yescharacteristic
182C2×C4×C8C2312yes—
183C2×C4×C8C2312yes—
184C2×C4×C8C2312yes—
185C2×C4×C8C2312yes—
186C2×C4×C8C2311yescharacteristic
187C2×C4×C8C2311yescharacteristic
188#391—21no—
189#391—21no—
190#391C2312yes—
191#391C2312yes—
192#391C2312yes—
193#391C2312yes—
194#390—21no—
195#390—21no—
196#390—21no—
197#390—21no—
198#390C2312yes—
199#390C2312yes—
200#389—21no—
201#389—21no—
202#389—21no—
203#389—21no—
204#389—21no—
205#389—21no—
206#389—21no—
207#389—21no—
208#389—21no—
209#389—21no—
210#389C2312yes—
211#389C2312yes—
212#388—22no—
213#388—22no—
214#388—22no—
215#388—22no—
216#387—22no—
217#387—22no—
218#387—22no—
219#387—22no—
220#386—22no—
221#386—22no—
222#385—22no—
223#385—22no—
224#384C2311yescharacteristic
225#384C2311yescharacteristic
226#384C2311yescharacteristic
227#384C2311yescharacteristic
228#382—21no—
229#382C2312yes—
230#380—21no—
231#380—21no—
232#380—21no—
233#380C2312yes—
234C4×C4⋊C4—21no—
235C4×C4⋊C4—21no—
236C4×C4⋊C4—21no—
237C4×C4⋊C4—21no—
238C4×C4⋊C4—22no—
239C4×C4⋊C4—22no—
240C4×C4⋊C4—22no—
241C4×C4⋊C4—22no—
242C4×C4⋊C4—21no—
243C4×C4⋊C4—21no—
244C4×C4⋊C4—21no—
245C4×C4⋊C4—21no—
246C4×C4⋊C4—21no—
247C4×C4⋊C4—21no—
248C4×C4⋊C4—21no—
249C4×C4⋊C4—21no—
250C4×C4⋊C4—21no—
251C4×C4⋊C4—22no—
252C4×C4⋊C4—22no—
253C4×C4⋊C4C2312yes—
254C4×C4⋊C4C2312yes—
255C4×C4⋊C4C2312yes—
256C4×C22⋊C4—22no—
257C4×C22⋊C4—22no—
258C4×C22⋊C4—22no—
259C4×C22⋊C4—22no—
260C4×C22⋊C4—22no—
261C4×C22⋊C4—22no—
262C4×C22⋊C4—22no—
263C4×C22⋊C4—22no—
264#376—22no—
265C43—22no—
266C43D411yescharacteristic
267C43D411yescharacteristic
268C43D411yescharacteristic
269C43D411yescharacteristic
270C43C2311yescharacteristic
271C43C2311yescharacteristic
272C43C2311yescharacteristic
273C43C2311yescharacteristic
274#340C2314yes—
275#340C2314yes—
276#340C2314yes—
277#340C2314yes—
278#336C2312yes—
279#336C2312yes—
280#336C2312yes—
281#336C2312yes—
282C2×#41—24no—
283C2×#41—44no—
284C2×#41—44no—
285C2×#41C22×C418yes—
286C22×Q8—21no—
287C22×Q8C2412yes—
288C22×Q8C2412yes—
289C22×D4—22no—
290C22×D4—21no—
291C22×D4—21no—
292C22×D4C2412yes—
293C23×C4—22no—
294C23×C4—22no—
295C23×C4—22no—
296C23×C4C2×D411yescharacteristic
297C23×C4C2×D411yescharacteristic
298C23×C4C2×D411yescharacteristic
299C23×C4C2×D411yescharacteristic
300C23×C4C2×D411yescharacteristic
301C23×C4C2×D411yescharacteristic
302C23×C4C2411yescharacteristic
303C2×Q16—44no—
304C2×Q16—44no—
305C2×Q16C22×C4116yes—
306C2×SD16—44no—
307C2×SD16—44no—
308C2×SD16C22×C4116yes—
309C22×C8C2412yes—
310C22×C8C2412yes—
311C22×C8C2412yes—
312C22×C8C2412yes—
313C4⋊Q8—22no—
314C4⋊Q8—22no—
315C4⋊Q8—22no—
316C4⋊Q8C22×C414yes—
317C4⋊Q8C22×C414yes—
318C4⋊Q8C22×C414yes—
319#127—22no—
320#127C22×C414yes—
321#125—28no—
322#124—24no—
323#124C22×C418yes—
324C22⋊Q8—28no—
325C22⋊Q8—24no—
326C22⋊Q8C22×C418yes—
327#121—28no—
328#121—28no—
329C4×Q8—28no—
330C4×Q8—24no—
331C4×Q8—28no—
332C4×Q8—28no—
333C4×Q8—44no—
334C4×Q8—44no—
335C4×Q8—44no—
336C4×Q8—44no—
337C4×Q8C22×C418yes—
338C4×D4—28no—
339C4×D4—28no—
340C4×D4—28no—
341C4×D4—44no—
342C4×D4—44no—
343C4×D4—48no—
344C4×D4—48no—
345C4×D4—44no—
346C4×D4—44no—
347C4×D4—44no—
348#117—28no—
349#117—48no—
350#117—44no—
351#117—44no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4C2412yes—
374C2×C4⋊C4C2412yes—
375C2×C4⋊C4C2412yes—
376C2×C4⋊C4C2412yes—
377C2×C4⋊C4C2412yes—
378C2×C22⋊C4—22no—
379C2×C22⋊C4—22no—
380C2×C22⋊C4—22no—
381C2×C22⋊C4—22no—
382C2×C22⋊C4—22no—
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×C42—22no—
390C2×C42—24no—
391C2×C42—24no—
392C2×C42—24no—
393C2×C42—24no—
394C2×C42—22no—
395C2×C42—22no—
396C2×C42—22no—
397C2×C42—22no—
398C2×C42—22no—
399C2×C42—22no—
400C2×C42—22no—
401C2×C42—22no—
402C2×C42—42no—
403C2×C42—42no—
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—44no—
436#106—44no—
437C4⋊C8—24no—
438C4⋊C8C22×C418yes—
439#103—44no—
440#103—44no—
441#103—44no—
442#103—44no—
443#103C22×C4116yes—
444#102—44no—
445#102—44no—
446#102C22×C4116yes—
447C22⋊C8—24no—
448C22⋊C8C22×C418yes—
449C4×C8—22no—
450C4×C8—22no—
451C4×C8—24no—
452C4×C8—24no—
453C4×C8—42no—
454C4×C8—42no—
455C4×C8C22×C414yes—
456C4×C8C22×C414yes—
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—
468#95—22no—
469#95—22no—
470#95—22no—
471#95—22no—
472#95—22no—
473C24—22no—
474C24C22×D411yescharacteristic
475#41—416no—
476#41—416no—
477C2×Q8—24no—
478C2×Q8—22no—
479C2×Q8—22no—
480C2×Q8—24no—
481C2×Q8—24no—
482C2×Q8—24no—
483C2×Q8—24no—
484C2×Q8—42no—
485C2×Q8—42no—
486C2×Q8C23×C414yes—
487C2×Q8C23×C414yes—
488C2×D4—28no—
489C2×D4—24no—
490C2×D4—24no—
491C2×D4—22no—
492C2×D4—24no—
493C2×D4—24no—
494C2×D4—44no—
495C2×D4—44no—
496C2×D4—42no—
497C2×D4—42no—
498C2×D4—42no—
499C2×D4—42no—
500C2×D4C23×C414yes—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—28no—
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—41no—
524C22×C4—41no—
525C22×C4—41no—
526C22×C4—41no—
527C22×C4—44no—
528C22×C4—44no—
529C22×C4—44no—
530C22×C4—44no—
531C22×C4—44no—
532C22×C4—44no—
533C22×C4—44no—
534C22×C4—44no—
535C22×C4C4×D414yes—
536C22×C4C4×D414yes—
537C22×C4C23×C412yes—
538C22×C4C22×D411yescharacteristic
539C22×C4C22×D411yescharacteristic
540C22×C4C22×D411yescharacteristic
541C22×C4C22×D411yescharacteristic
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×C4C2×#4112yes—
552C22×C4C2511yescharacteristic
553Q16—416no—
554SD16—416no—
555C2×C8—22no—
556C2×C8—22no—
557C2×C8—22no—
558C2×C8—22no—
559C2×C8—22no—
560C2×C8—22no—
561C2×C8—22no—
562C2×C8—22no—
563C2×C8—22no—
564C2×C8—22no—
565C2×C8C23×C414yes—
566C2×C8C23×C414yes—
567C4⋊C4—24no—
568C4⋊C4—24no—
569C4⋊C4—24no—
570C4⋊C4—24no—
571C4⋊C4—24no—
572C4⋊C4—28no—
573C4⋊C4—28no—
574C4⋊C4—22no—
575C4⋊C4—24no—
576C4⋊C4—24no—
577C4⋊C4—24no—
578C4⋊C4—24no—
579C4⋊C4—44no—
580C4⋊C4—44no—
581C4⋊C4—44no—
582C4⋊C4—44no—
583C4⋊C4—42no—
584C4⋊C4—42no—
585C4⋊C4—44no—
586C4⋊C4—44no—
587C4⋊C4—42no—
588C4⋊C4—42no—
589C4⋊C4—42no—
590C4⋊C4—42no—
591C4⋊C4—42no—
592C4⋊C4—42no—
593C4⋊C4C23×C414yes—
594C22⋊C4—28no—
595C22⋊C4—28no—
596C22⋊C4—28no—
597C22⋊C4—44no—
598C22⋊C4—44no—
599C22⋊C4—44no—
600C22⋊C4—44no—
601C22⋊C4—44no—
602C22⋊C4—44no—
603C22⋊C4—44no—
604C22⋊C4—44no—
605C42—28no—
606C42—22no—
607C42—22no—
608C42—22no—
609C42—22no—
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—41no—
623C42—41no—
624C42—41no—
625C42—41no—
626C42—44no—
627C42—44no—
628C42—44no—
629C42—44no—
630C42—44no—
631C42—44no—
632C42—44no—
633C42—44no—
634C42C4×D414yes—
635C42C4×D414yes—
636C42#13514yes—
637C42#13514yes—
638C42#13714yes—
639C42C23×C412yes—
640C42C23×C412yes—
641C42C2×#4112yes—
642C42C2×#4112yes—
643C42H(5,𝔽2)14yes—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—24no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23C2×C4×D412yes—
658C23C23×D411yescharacteristic
659Q8—28no—
660Q8—28no—
661Q8—48no—
662Q8—44no—
663Q8—44no—
664D4—28no—
665D4—416no—
666D4—48no—
667D4—48no—
668D4—44no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
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—24no—
686C2×C4—28no—
687C2×C4—28no—
688C2×C4—24no—
689C2×C4—24no—
690C2×C4—24no—
691C2×C4—24no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—44no—
699C2×C4—44no—
700C2×C4—44no—
701C2×C4—416no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—44no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—88no—
722C2×C4—88no—
723C2×C4C2×C4×D412yes—
724C2×C4C2×C4×D412yes—
725C2×C4C2×C4×D412yes—
726C2×C4C2×C4×D412yes—
727C2×C4C2×C4×D412yes—
728C2×C4#53512yes—
729C2×C4#53512yes—
730C2×C4C2×#13512yes—
731C2×C4C2×#13512yes—
732C2×C4C2×#13512yes—
733C2×C4C2×#13512yes—
734C2×C4C2×#13512yes—
735C2×C4C2×#13512yes—
736C2×C4C2×#13712yes—
737C2×C4C2×#13712yes—
738C2×C4C2×#13712yes—
739C2×C4#57512yes—
740C2×C4C24×C411yescharacteristic
741C2×C4C22×#4111yescharacteristic
742C2×C4C2×H(5,𝔽2)12yes—
743C2×C4#58512yes—
744C8—24no—
745C8—24no—
746C8—42no—
747C8—42no—
748C22—22no—
749C22—22no—
750C22—22no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—44no—
756C22—44no—
757C22—44no—
758C22—82no—
759C22—82no—
760C22—82no—
761C22—82no—
762C22C22×C4×D411yescharacteristic
763C22C2×#53511yescharacteristic
764C22#344911yescharacteristic
765C22C22×#13511yescharacteristic
766C22C22×#13511yescharacteristic
767C22C22×#13711yescharacteristic
768C22C2×#57511yescharacteristic
769C4—22no—
770C4—22no—
771C4—22no—
772C4—22no—
773C4—22no—
774C4—22no—
775C4—22no—
776C4—22no—
777C4—41no—
778C4—44no—
779C4—44no—
780C4—41no—
781C4—44no—
782C4—82no—
783C4—82no—
784C4—82no—
785C4—82no—
786C4C4×#13514yes—
787C4C4×#13714yes—
788C4#321014yesdirect product factor
789C4C4×H(5,𝔽2)12yes—
790C4#346012yes—
791C2—42no—
792C2—84no—
793C2C4×#53511yescharacteristic
794C2C2×C4×#13511yescharacteristic
795C2C2×C4×#13711yescharacteristic
796C2C2×#321011yescharacteristic
797C2#6078211yescharacteristic
798C2#6094411yescharacteristic
799C2#6094711yescharacteristic
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. #22270C2semidirect
5. #22268C2semidirect
6. #22220C2semidirect
7. #22218C2semidirect
8. #22150C2semidirect
9. #22042C2semidirect
10. #21984C2semidirect
11. #21864C2semidirect
13. C4×#494C2semidirect
14. C4×#492C2semidirect
15. C4×#487C2semidirect
16. C4×#486C2semidirect
17. C4×#464C2semidirect
18. C4×#452C2semidirect
19. C4×#431C2semidirect
23. #3210C4direct (N × H)
112. #533C2×C4semidirect
156. #494C2×C4semidirect
157. #492C2×C4semidirect
158. #487C2×C4semidirect
159. #486C2×C4semidirect
160. #464C2×C4semidirect
161. #452C2×C4semidirect
165. #431C2×C4semidirect
788. C4#3210direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#32102
C4×#5332
C4×#5322
#222702
#222682
#222202
#222182
#221502
#220422
#219842
#218642
#218052
C4×#4942
C4×#4922
C4×#4872
C4×#4862
C4×#4642
C4×#4522
C4×#4312