Finite Group Databasebeta

← #6467127

Subgroups — #6467127

Order 512.

2180 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3107C212yesmaximal, complemented
2C4×#533C211yesmaximal, characteristic, complemented
3C4×#532C211yesmaximal, characteristic
4#28283C211yesmaximal, characteristic, complemented
5#28279C211yesmaximal, characteristic, complemented
6#28255C211yesmaximal, characteristic, complemented
7#28252C211yesmaximal, characteristic, complemented
8#28203C212yesmaximal, complemented
9#28159C212yesmaximal, complemented
10#28122C214yesmaximal, complemented
11#27649C212yesmaximal, complemented
12#24213C212yesmaximal
13#23681C214yesmaximal, complemented
14C4×#462C212yesmaximal, complemented
15C4×#460C212yesmaximal, complemented
16#20808C211yesmaximal, characteristic, complemented
17#20737C212yesmaximal, complemented
18C2×#533C2211yescharacteristic
19C2×#532C2211yescharacteristic
20C2×C4×#41C2212yes—
21#3107—216no—
22C2×#485C2214yes—
23C2×#475C2212yes—
24C2×#474C2212yes—
25C2×#462C2212yes—
26C2×#462C2212yes—
27C2×#460C2212yes—
28C2×#461C2212yes—
29C2×#452C2214yes—
30C2×C4×Q16C2214yes—
31C2×C4×SD16C2214yes—
32C2×#431C2212yes—
33C4×C4⋊Q8C2211yescharacteristic
34C4×C4⋊Q8C2211yescharacteristic
35C4×C4⋊Q8C2211yescharacteristic
36C4×C4⋊Q8C2211yescharacteristic
37C4×C4⋊Q8C2211yescharacteristic
38C4×C4⋊Q8C2211yescharacteristic
39C4×#127C2211yescharacteristic
40C4×#127C2211yescharacteristic
41C4×#125—21no—
42C4×#125—21no—
43C4×#124C2212yes—
44C4×#124C2212yes—
45C4×C22⋊Q8—21no—
46C4×C22⋊Q8—21no—
47C4×C22⋊Q8C2212yes—
48C4×C22⋊Q8C2212yes—
49C4×#121—21no—
50C4×#121—21no—
51C4×#121—21no—
52C4×#121—21no—
53#2297C2212yes—
54#2296—21no—
55#2295—21no—
56#2295C2212yes—
57#2293—21no—
58#2293—21no—
59#2285C2211yescharacteristic
60#2285C2211yescharacteristic
61C42×Q8—21no—
62C42×Q8C2212yes—
63C42×D4—21no—
64C42×D4—21no—
65C4×#117—21no—
66C2×C43C2211yescharacteristic
67#2085C2214yes—
68#2074C2214yes—
69#2067C2214yes—
70#2066C2214yes—
71#2056C2214yes—
72#2055C2214yes—
73#2042C2214yes—
74#2015C2214yes—
75#1982C2212yes—
76#1981C2212yes—
77#1948C2212yes—
78#1947C2212yes—
79#1928C2214yes—
80#1926C2214yes—
81#1880C2214yes—
82#1878C2214yes—
83#1842C2211yescharacteristic
84#1842C2211yescharacteristic
85#1831C2212yes—
86#1825C2214yes—
87#1803C2212yes—
88#1803C2212yes—
89#1803C2212yes—
90#1803C2212yes—
91#1802C2212yes—
92#1802C2212yes—
93#1797C2212yes—
94#1797C2212yes—
95#1788C2214yes—
96C4×C4⋊C8C2212yes—
97C4×C4⋊C8C2212yes—
98C4×#103C2214yes—
99C4×#102C2214yes—
100C22×#41C2312yes—
101C22×Q16C2314yes—
102C22×SD16C2314yes—
103#533—24no—
104#533D418yescomplemented
105#532—24no—
106#532—24no—
107C2×C4⋊Q8C2311yescharacteristic
108C2×C4⋊Q8C2311yescharacteristic
109C2×C4⋊Q8C2311yescharacteristic
110C2×#127C2311yescharacteristic
111C2×#125—21no—
112C2×#124C2312yes—
113C2×C22⋊Q8—21no—
114C2×C22⋊Q8C2312yes—
115C2×#121—21no—
116C2×#121—21no—
117C4×#41—28no—
118C4×#41—28no—
119C2×C4×Q8—21no—
120C2×C4×Q8—21no—
121C2×C4×Q8—21no—
122C2×C4×Q8C2312yes—
123C2×C4×Q8C2312yes—
124C2×C4×Q8C2312yes—
125C2×C4×Q8C2312yes—
126C2×C4×Q8C2312yes—
127C2×C4×D4—22no—
128C2×C4×D4—22no—
129C2×C4×D4—21no—
130C2×C4×D4—21no—
131C2×C4×D4—21no—
132C2×C4×D4—21no—
133C2×C4×D4—21no—
134C2×C4×D4—21no—
135C2×C4×D4C2312yes—
136C2×C4×D4C2312yes—
137C2×#117—21no—
138C2×#117—21no—
139C2×#117—22no—
140C2×#117C2312yes—
141C22×C42—22no—
142C22×C42D411yescharacteristic
143C22×C42D411yescharacteristic
144C22×C42D411yescharacteristic
145C22×C42D411yescharacteristic
146C22×C42C2311yescharacteristic
147C22×C42C2311yescharacteristic
148C22×C42C2311yescharacteristic
149#485—216no—
150#475—28no—
151#474—28no—
152#462—28no—
153#462—28no—
154#461—28no—
155#460—28no—
156#452—216no—
157C4×Q16—216no—
158C4×SD16—216no—
159#431—28no—
160C2×#107C2314yes—
161C2×#106C2314yes—
162C2×C4⋊C8C2312yes—
163C2×C4⋊C8C2312yes—
164C2×C4⋊C8C2312yes—
165C2×C4⋊C8C2312yes—
166C2×C4⋊C8C2312yes—
167C2×C4⋊C8C2312yes—
168C2×#103C2314yes—
169C2×#103C2314yes—
170C2×#103C2314yes—
171C2×#103C2314yes—
172C2×#103C2314yes—
173C2×#102C2314yes—
174C2×#102C2314yes—
175C2×#102C2314yes—
176C2×C22⋊C8C2314yes—
177C2×C4×C8C2314yes—
178#391—21no—
179#391—21no—
180#391C2312yes—
181#391C2312yes—
182#391C2312yes—
183#391C2312yes—
184#390—21no—
185#390—21no—
186#390—21no—
187#390—21no—
188#390C2312yes—
189#390C2312yes—
190#389—21no—
191#389—21no—
192#389—21no—
193#389—21no—
194#389—21no—
195#389—21no—
196#389—21no—
197#389—21no—
198#389—21no—
199#389—21no—
200#389C2312yes—
201#389C2312yes—
202#388—22no—
203#388—22no—
204#388—22no—
205#388—22no—
206#387—22no—
207#387—22no—
208#387—22no—
209#387—22no—
210#386—22no—
211#386—22no—
212#385—22no—
213#385—22no—
214#384C2311yescharacteristic
215#384C2311yescharacteristic
216#384C2311yescharacteristic
217#384C2311yescharacteristic
218#382—21no—
219#382C2312yes—
220#380—21no—
221#380—21no—
222#380—21no—
223#380C2312yes—
224C4×C4⋊C4—21no—
225C4×C4⋊C4—21no—
226C4×C4⋊C4—21no—
227C4×C4⋊C4—21no—
228C4×C4⋊C4—22no—
229C4×C4⋊C4—22no—
230C4×C4⋊C4—22no—
231C4×C4⋊C4—22no—
232C4×C4⋊C4—21no—
233C4×C4⋊C4—21no—
234C4×C4⋊C4—21no—
235C4×C4⋊C4—21no—
236C4×C4⋊C4—21no—
237C4×C4⋊C4—21no—
238C4×C4⋊C4—21no—
239C4×C4⋊C4—21no—
240C4×C4⋊C4—21no—
241C4×C4⋊C4—22no—
242C4×C4⋊C4—22no—
243C4×C4⋊C4C2312yes—
244C4×C4⋊C4C2312yes—
245C4×C4⋊C4C2312yes—
246C4×C22⋊C4—22no—
247C4×C22⋊C4—22no—
248C4×C22⋊C4—22no—
249C4×C22⋊C4—22no—
250C4×C22⋊C4—22no—
251C4×C22⋊C4—22no—
252C4×C22⋊C4—22no—
253C4×C22⋊C4—22no—
254#376—22no—
255C43—22no—
256C43D411yescharacteristic
257C43D411yescharacteristic
258C43D411yescharacteristic
259C43D411yescharacteristic
260C43C2311yescharacteristic
261C43C2311yescharacteristic
262C43C2311yescharacteristic
263C43C2311yescharacteristic
264#340C2314yes—
265#340C2314yes—
266#340C2314yes—
267#340C2314yes—
268#336C2314yes—
269#336C2314yes—
270C2×#41—24no—
271C2×#41—24no—
272C2×#41—24no—
273C2×#41—24no—
274C2×#41—42no—
275C2×#41—42no—
276C22×Q8—21no—
277C22×Q8C2412yes—
278C22×Q8C2412yes—
279C22×D4—22no—
280C22×D4—21no—
281C22×D4—21no—
282C22×D4C2412yes—
283C23×C4—22no—
284C23×C4—22no—
285C23×C4—22no—
286C23×C4C2×D411yescharacteristic
287C23×C4C2×D411yescharacteristic
288C23×C4C2×D411yescharacteristic
289C23×C4C2×D411yescharacteristic
290C23×C4C2×D411yescharacteristic
291C23×C4C2×D411yescharacteristic
292C23×C4C2411yescharacteristic
293C2×Q16—28no—
294C2×Q16—28no—
295C2×Q16—44no—
296C2×SD16—28no—
297C2×SD16—28no—
298C2×SD16—44no—
299C22×C8C2414yes—
300C22×C8C2414yes—
301C4⋊Q8—22no—
302C4⋊Q8—22no—
303C4⋊Q8—22no—
304C4⋊Q8C2×D414yes—
305C4⋊Q8C2×D414yes—
306C4⋊Q8#4114yes—
307#127—22no—
308#127#4114yes—
309#125—28no—
310#124—24no—
311#124—24no—
312C22⋊Q8—28no—
313C22⋊Q8—24no—
314C22⋊Q8C2×D418yes—
315#121—28no—
316#121—28no—
317C4×Q8—28no—
318C4×Q8—24no—
319C4×Q8—24no—
320C4×Q8—24no—
321C4×Q8—24no—
322C4×Q8—24no—
323C4×Q8—24no—
324C4×Q8—24no—
325C4×Q8—42no—
326C4×Q8—42no—
327C4×Q8—44no—
328C4×Q8—44no—
329C4×Q8C2×D418yes—
330C4×D4—28no—
331C4×D4—28no—
332C4×D4—24no—
333C4×D4—24no—
334C4×D4—24no—
335C4×D4—24no—
336C4×D4—44no—
337C4×D4—44no—
338C4×D4—48no—
339C4×D4—48no—
340C4×D4—44no—
341C4×D4—44no—
342#117—28no—
343#117—24no—
344#117—24no—
345#117—44no—
346#117—48no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4C2412yes—
369C2×C4⋊C4C2412yes—
370C2×C4⋊C4C2412yes—
371C2×C4⋊C4C2412yes—
372C2×C4⋊C4C2412yes—
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×C22⋊C4—22no—
381C2×C22⋊C4—22no—
382C2×C22⋊C4—22no—
383C2×C22⋊C4—22no—
384C2×C42—22no—
385C2×C42—24no—
386C2×C42—24no—
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—22no—
397C2×C42—42no—
398C2×C42—42no—
399C2×C42—41no—
400C2×C42—41no—
401C2×C42—48no—
402C2×C42C2×D411yescharacteristic
403C2×C42C2×D411yescharacteristic
404C2×C42C2×D411yescharacteristic
405C2×C42C2×D411yescharacteristic
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×D414yes—
423C2×C42C2×D411yescharacteristic
424C2×C42C2×D411yescharacteristic
425C2×C42#4114yes—
426C2×C42C2411yescharacteristic
427C2×C42C2411yescharacteristic
428C2×C42C2411yescharacteristic
429C2×C42C2411yescharacteristic
430C2×C42C2411yescharacteristic
431C2×C42C2411yescharacteristic
432#107—28no—
433#106—28no—
434C4⋊C8—24no—
435C4⋊C8—24no—
436C4⋊C8—24no—
437C4⋊C8—24no—
438C4⋊C8—42no—
439C4⋊C8—42no—
440#103—28no—
441#103—28no—
442#103—28no—
443#103—28no—
444#103—44no—
445#102—28no—
446#102—28no—
447#102—44no—
448C22⋊C8—28no—
449C4×C8—28no—
450#95—22no—
451#95—22no—
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—
466C24—22no—
467C24C22×D411yescharacteristic
468#41—48no—
469#41—48no—
470#41—48no—
471#41—48no—
472C2×Q8—24no—
473C2×Q8—22no—
474C2×Q8—22no—
475C2×Q8—22no—
476C2×Q8—22no—
477C2×Q8—22no—
478C2×Q8—22no—
479C2×Q8—22no—
480C2×Q8—22no—
481C2×Q8—22no—
482C2×Q8—22no—
483C2×Q8—42no—
484C2×Q8—42no—
485C2×Q8C22×D414yes—
486C2×Q8C2×#4114yes—
487C2×D4—28no—
488C2×D4—24no—
489C2×D4—24no—
490C2×D4—22no—
491C2×D4—22no—
492C2×D4—22no—
493C2×D4—22no—
494C2×D4—22no—
495C2×D4—42no—
496C2×D4—42no—
497C2×D4—44no—
498C2×D4—44no—
499C2×D4—42no—
500C2×D4—42no—
501C2×D4C2×#4114yes—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
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—22no—
524C22×C4—41no—
525C22×C4—41no—
526C22×C4—41no—
527C22×C4—41no—
528C22×C4—41no—
529C22×C4—41no—
530C22×C4—44no—
531C22×C4—44no—
532C22×C4—44no—
533C22×C4—44no—
534C22×C4—44no—
535C22×C4—44no—
536C22×C4—44no—
537C22×C4—44no—
538C22×C4#12114yes—
539C22×C4#12114yes—
540C22×C4C22×D411yescharacteristic
541C22×C4C22×D411yescharacteristic
542C22×C4C22×D411yescharacteristic
543C22×C4C22×D411yescharacteristic
544C22×C4C22×D411yescharacteristic
545C22×C4C22×D411yescharacteristic
546C22×C4C22×D411yescharacteristic
547C22×C4C22×D412yes—
548C22×C4C22×D411yescharacteristic
549C22×C4C22×D411yescharacteristic
550C22×C4C22×D411yescharacteristic
551C22×C4C22×D411yescharacteristic
552C22×C4C22×D411yescharacteristic
553C22×C4C22×D411yescharacteristic
554C22×C4C2×#4112yes—
555C22×C4C2511yescharacteristic
556Q16—416no—
557SD16—416no—
558C2×C8—24no—
559C2×C8—24no—
560C2×C8—24no—
561C2×C8—24no—
562C2×C8—24no—
563C2×C8—24no—
564C4⋊C4—24no—
565C4⋊C4—24no—
566C4⋊C4—24no—
567C4⋊C4—28no—
568C4⋊C4—28no—
569C4⋊C4—24no—
570C4⋊C4—24no—
571C4⋊C4—22no—
572C4⋊C4—22no—
573C4⋊C4—22no—
574C4⋊C4—22no—
575C4⋊C4—22no—
576C4⋊C4—22no—
577C4⋊C4—22no—
578C4⋊C4—22no—
579C4⋊C4—22no—
580C4⋊C4—42no—
581C4⋊C4—42no—
582C4⋊C4—42no—
583C4⋊C4—42no—
584C4⋊C4—44no—
585C4⋊C4—44no—
586C4⋊C4—44no—
587C4⋊C4—44no—
588C4⋊C4—44no—
589C4⋊C4—42no—
590C4⋊C4—44no—
591C4⋊C4—42no—
592C4⋊C4—42no—
593C4⋊C4—42no—
594C4⋊C4C22×D414yes—
595C22⋊C4—28no—
596C22⋊C4—28no—
597C22⋊C4—28no—
598C22⋊C4—44no—
599C22⋊C4—44no—
600C22⋊C4—44no—
601C22⋊C4—44no—
602C22⋊C4—44no—
603C22⋊C4—44no—
604C22⋊C4—44no—
605C22⋊C4—44no—
606C42—28no—
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—21no—
620C42—21no—
621C42—21no—
622C42—21no—
623C42—21no—
624C42—21no—
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#12114yes—
640C42#12114yes—
641C42#13514yes—
642C42#13714yes—
643C42C22×D412yes—
644C42C22×D412yes—
645C42C2×#4112yes—
646C42C2×#4112yes—
647C42C2×#4112yes—
648C42C2×#4112yes—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—24no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23C2×#12112yes—
663C23C23×D411yescharacteristic
664Q8—24no—
665Q8—24no—
666Q8—24no—
667Q8—24no—
668Q8—42no—
669Q8—42no—
670Q8—42no—
671Q8—42no—
672Q8—48no—
673D4—24no—
674D4—24no—
675D4—48no—
676D4—416no—
677D4—48no—
678D4—42no—
679D4—42no—
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—21no—
691C2×C4—21no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—28no—
697C2×C4—28no—
698C2×C4—24no—
699C2×C4—24no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—24no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—44no—
714C2×C4—44no—
715C2×C4—44no—
716C2×C4—416no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—44no—
724C2×C4—42no—
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—42no—
736C2×C4—88no—
737C2×C4—88no—
738C2×C4C2×#12112yes—
739C2×C4C2×#12112yes—
740C2×C4C2×#12112yes—
741C2×C4C2×#12112yes—
742C2×C4C2×#12112yes—
743C2×C4#52512yes—
744C2×C4#52512yes—
745C2×C4C2×#13512yes—
746C2×C4C2×#13512yes—
747C2×C4C2×#13512yes—
748C2×C4C2×#13712yes—
749C2×C4C2×#13712yes—
750C2×C4C2×#13712yes—
751C2×C4#57512yes—
752C2×C4#57512yes—
753C2×C4C23×D411yescharacteristic
754C2×C4C22×#4111yescharacteristic
755C2×C4C22×#4111yescharacteristic
756C2×C4C22×#4111yescharacteristic
757C2×C4#58511yescharacteristic
758C2×C4#58511yescharacteristic
759C8—44no—
760C8—44no—
761C22—22no—
762C22—22no—
763C22—22no—
764C22—41no—
765C22—41no—
766C22—41no—
767C22—41no—
768C22—44no—
769C22—44no—
770C22—44no—
771C22—82no—
772C22—82no—
773C22—82no—
774C22—82no—
775C22C22×#12111yescharacteristic
776C22C2×#52511yescharacteristic
777C22#344911yescharacteristic
778C22C22×#13511yescharacteristic
779C22C22×#13711yescharacteristic
780C22C2×#57511yescharacteristic
781C22C2×#57511yescharacteristic
782C4—22no—
783C4—22no—
784C4—22no—
785C4—22no—
786C4—22no—
787C4—22no—
788C4—41no—
789C4—41no—
790C4—41no—
791C4—44no—
792C4—44no—
793C4—41no—
794C4—44no—
795C4—82no—
796C4—82no—
797C4—82no—
798C4—82no—
799C4#303514yes—
800C4#303714yes—
801C4#310714yescomplemented
802C4D4×#4111yescharacteristic
803C4D4×#4111yescharacteristic
804C4#347511yescharacteristic
805C4#347511yescharacteristic
806C2—42no—
807C2—84no—
808C2#3493511yescharacteristic
809C2C2×#303511yescharacteristic
810C2C2×#303711yescharacteristic
811C2C2×#310711yescharacteristic
812C2#6055911yescharacteristic
813C2#6094811yescharacteristic
814C2#6095211yescharacteristic
subgroupG/H
centerC22×C4C22×D4
commutator, Frattini, cosocleC22×C4C25
socleC23C23×D4
prime radicalC2×#532C22
LCSG ▷ C22×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
1. C2×#3107C2semidirect
2. C4×#533C2semidirect
4. #28283C2semidirect
5. #28279C2semidirect
6. #28255C2semidirect
7. #28252C2semidirect
8. #28203C2semidirect
9. #28159C2semidirect
10. #28122C2semidirect
11. #27649C2semidirect
13. #23681C2semidirect
14. C4×#462C2semidirect
15. C4×#460C2semidirect
16. #20808C2semidirect
17. #20737C2semidirect
104. #533D4semidirect
801. C4#3107semidirect

Maximal subgroups

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

subgroupindex
C2×#31072
C4×#5332
C4×#5322
#282832
#282792
#282552
#282522
#282032
#281592
#281222
#276492
#242132
#236812
C4×#4622
C4×#4602
#208082
#207372