Finite Group Databasebeta

← #6526935

Subgroups — #6526935

Order 512.

2234 conjugacy classes of subgroups.

The subgroup lattice has 878 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3250C211yesmaximal, characteristic, complemented
2C2×#3239C211yesmaximal, characteristic, complemented
3C2×#3114C211yesmaximal, characteristic, complemented
4C22×#476C211yesmaximal, characteristic, complemented
5#37615C211yesmaximal, characteristic, complemented
6#35233C211yesmaximal, characteristic, complemented
7#28548C212yesmaximal, complemented
8#28547C212yesmaximal, complemented
9#28525C212yesmaximal, complemented
10#28524C212yesmaximal, complemented
11#28436C212yesmaximal, complemented
12#28430C212yesmaximal, complemented
13#28395C212yesmaximal, complemented
14#28393C212yesmaximal, complemented
15#28342C211yesmaximal, characteristic, complemented
16#28341C211yesmaximal, characteristic
17#28332C211yesmaximal, characteristic, complemented
18#28331C211yesmaximal, characteristic, complemented
19#27934C211yesmaximal, characteristic, complemented
20#27933C211yesmaximal, characteristic, complemented
21#27926C211yesmaximal, characteristic, complemented
22#27924C211yesmaximal, characteristic, complemented
23#20544C211yesmaximal, characteristic, complemented
24C22×C4⋊Q8C2211yescharacteristic
25C2×#529C2211yescharacteristic
26C2×#529C2211yescharacteristic
27C22×C4×D4C2211yescharacteristic
28#3250—28no—
29#3239—28no—
30C2×#501C2212yescomplemented
31C2×#489C2212yescomplemented
32#3114—28no—
33C2×#484C2211yescharacteristic
34C2×#484C2211yescharacteristic
35C2×#481C2211yescharacteristic
36C2×#481C2211yescharacteristic
37C2×#483C2211yescharacteristic
38C2×#480C2211yescharacteristic
39C2×#479C2211yescharacteristic, complemented
40C2×#479C2211yescharacteristic, complemented
41C2×#475C2212yescomplemented
42C2×#478C2212yes—
43C2×#478C2211yescharacteristic, complemented
44C2×#478C2211yescharacteristic, complemented
45C2×#476—28no—
46C2×#476C2212yes—
47C2×#476C2212yes—
48C2×#476C2212yes—
49C2×#476C2212yes—
50C2×#474C2212yescomplemented
51C2×#467C2211yescharacteristic
52C2×#466C2211yescharacteristic
53C2×#465C2211yescharacteristic
54C2×#465C2211yescharacteristic
55C2×#464C2211yescharacteristic, complemented
56C2×#464C2211yescharacteristic, complemented
57C2×#463C2212yes—
58C2×#463C2211yescharacteristic, complemented
59C2×#463C2211yescharacteristic, complemented
60C2×#450C2211yescharacteristic
61C2×#447C2211yescharacteristic
62C2×#442C2212yes—
63C2×#440C2212yes—
64C2×#432C2211yescharacteristic
65C22×#106C2211yescharacteristic
66C22×#106C2211yescharacteristic
67C22×C4⋊C8C2211yescharacteristic
68C22×#102C2211yescharacteristic
69C22×#102C2211yescharacteristic
70#2849—22no—
71#2821—22no—
72#2660C2212yescomplemented
73#2640C2212yescomplemented
74#2636—22no—
75#2623—22no—
76#2621—22no—
77#2598—22no—
78#2568C2212yescomplemented
79#2566C2212yes—
80#2544C2212yes—
81#2542C2212yescomplemented
82#2534—22no—
83#2504C2211yescharacteristic
84#2504C2211yescharacteristic
85#2503C2211yescharacteristic
86#2502C2211yescharacteristic
87#2502C2211yescharacteristic
88#2501C2211yescharacteristic
89#2435C2211yescharacteristic
90#2433C2211yescharacteristic
91#2409—22no—
92#2328C2212yes—
93#2326C2212yes—
94#2283C2211yescharacteristic
95#2097C2212yescomplemented
96#2097C2212yescomplemented
97#2096C2212yescomplemented
98#2096C2212yescomplemented
99#2094C2212yes—
100#2094C2212yescomplemented
101#2094C2212yescomplemented
102#2093C2212yes—
103#2092C2212yes—
104#2092C2212yes—
105#2092C2212yescomplemented
106#2092C2212yescomplemented
107#2015C2212yes—
108#2014C2212yes—
109#2012C2212yes—
110#2011C2212yes—
111#1973C2212yes—
112#1972C2212yes—
113#1972C2212yescomplemented
114#1971C2212yescomplemented
115#1970C2212yes—
116#1968C2212yes—
117#1968C2212yescomplemented
118#1968C2212yescomplemented
119#1961C2212yes—
120#1959C2212yes—
121#1958C2212yes—
122#1957C2212yes—
123#1847C2212yescomplemented
124#1847C2212yescomplemented
125#1846C2212yescomplemented
126#1844C2212yescomplemented
127#1771C2212yescomplemented
128#1771C2212yescomplemented
129#1768C2212yescomplemented
130#1768C2212yescomplemented
131#1752C2211yescharacteristic
132#1752C2211yescharacteristic
133C8×C22⋊C4C2211yescharacteristic
134C8×C22⋊C4C2211yescharacteristic
135C23×Q8—21no—
136C23×D4C2311yescharacteristic
137C24×C4—21no—
138C22×Q16C2311yescharacteristic
139C22×SD16C2312yes—
140C22×SD16C2311yescharacteristic
141C22×SD16C2311yescharacteristic
142C22×D8C2312yes—
143C22×D8C2311yescharacteristic
144C23×C8C2311yescharacteristic
145C23×C8C2311yescharacteristic
146C2×C4⋊Q8—21no—
147C2×C4⋊Q8—21no—
148C2×C4⋊Q8—24no—
149C2×C4⋊Q8—24no—
150C2×C4⋊Q8C2312yes—
151C2×C4⋊Q8C2312yes—
152C2×#127C2312yes—
153#529—24no—
154#529—24no—
155#529—24no—
156#529—24no—
157C2×#126—21no—
158C2×#126—21no—
159C2×#125C2311yescharacteristic
160C2×#125C2311yescharacteristic
161C2×#124C2311yescharacteristic
162C2×#124C2311yescharacteristic
163C2×#124C2312yes—
164C2×#123—21no—
165C2×#123—21no—
166C2×#123—22no—
167C2×C22⋊Q8—24no—
168C2×C22⋊Q8C2311yescharacteristic
169C2×C22⋊Q8C2311yescharacteristic
170C2×#121C2311yescharacteristic
171C2×#121C2311yescharacteristic
172C2×#120—22no—
173C2×C4×Q8C2311yescharacteristic
174C2×C4×Q8C2311yescharacteristic
175C2×C4×D4—21no—
176C2×C4×D4—21no—
177C2×C4×D4—21no—
178C2×C4×D4—21no—
179C2×C4×D4—24no—
180C2×C4×D4—24no—
181C2×C4×D4C2312yes—
182C2×C4×D4C2311yescharacteristic
183C2×C4×D4C2311yescharacteristic
184C2×C4×D4C2312yes—
185C2×#117—21no—
186C2×#117—21no—
187C22×C4⋊C4—21no—
188C22×C4⋊C4C2311yescharacteristic
189C22×C4⋊C4C2311yescharacteristic
190C22×C4⋊C4C2311yescharacteristic
191C22×C22⋊C4—21no—
192C22×C42C2311yescharacteristic
193#501—28no—
194#489—28no—
195#484—24no—
196#484—24no—
197#483—24no—
198#481—24no—
199#481—24no—
200#480—24no—
201#479—24no—
202#479—24no—
203#478—28no—
204#478—24no—
205#478—24no—
206#476—28no—
207#476—28no—
208#476—28no—
209#476—28no—
210#475—28no—
211#474—28no—
212#467—24no—
213#466—24no—
214#465—24no—
215#465—24no—
216#464—24no—
217#464—24no—
218#463—28no—
219#463—24no—
220#463—24no—
221#450—24no—
222#447—24no—
223#442—28no—
224#440—28no—
225#432D418yescomplemented
226C2×#107C2312yes—
227C2×#107C2311yescharacteristic
228C2×#107C2311yescharacteristic
229C2×#107C2312yes—
230C2×#107C2312yes—
231C2×#106—24no—
232C2×#106—24no—
233C2×#106C2312yes—
234C2×#106C2311yescharacteristic
235C2×#106C2311yescharacteristic
236C2×#106C2312yes—
237C2×#106C2312yes—
238C2×#106C2312yes—
239C2×#106C2312yes—
240C2×#106C2312yes—
241C2×#106C2312yes—
242C2×C4⋊C8D418yescomplemented
243C2×C4⋊C8C2312yes—
244C2×C4⋊C8C2311yescharacteristic
245C2×C4⋊C8C2311yescharacteristic
246C2×C4⋊C8C2311yescharacteristic
247C2×C4⋊C8C2311yescharacteristic
248C2×#103C2312yes—
249C2×#103C2312yes—
250C2×#103C2311yescharacteristic
251C2×#103C2311yescharacteristic
252C2×#103C2311yescharacteristic
253C2×#103C2311yescharacteristic
254C2×#103C2312yes—
255C2×#102—24no—
256C2×#102—24no—
257C2×#102C2312yes—
258C2×#102C2312yes—
259C2×#102C2311yescharacteristic
260C2×#102C2311yescharacteristic
261C2×#102C2311yescharacteristic
262C2×#102C2311yescharacteristic
263C2×#102C2312yes—
264C2×#102C2312yes—
265C2×#102C2312yes—
266C2×#102C2312yes—
267C2×#102C2312yes—
268C2×#102C2312yes—
269C2×#102C2312yes—
270C2×C22⋊C8C2311yescharacteristic
271C2×C22⋊C8C2311yescharacteristic
272C2×#97C2312yes—
273C2×#97C2312yes—
274C2×#97C2312yes—
275C2×C4×C8C2312yes—
276C2×C4×C8C2312yes—
277#400—24no—
278#400—22no—
279#399—24no—
280#399—22no—
281#398—22no—
282#398—22no—
283#398—24no—
284#397—22no—
285#397—22no—
286#397—24no—
287#396—24no—
288#395—24no—
289#394—24no—
290#394—22no—
291#393—24no—
292#392—22no—
293#391—24no—
294#391C2312yes—
295#391C2312yes—
296#391C2312yes—
297#390C2312yes—
298#390C2312yes—
299#390C2312yes—
300#390C2312yes—
301#390C2312yes—
302#388—24no—
303#386—22no—
304#386—22no—
305#386—24no—
306#386—24no—
307#386—24no—
308#385—22no—
309#385—22no—
310#385—24no—
311#385—24no—
312#384C2312yes—
313#384C2312yes—
314#384C2312yes—
315#383D412yes—
316#382D412yes—
317#382C2312yes—
318#382C2312yes—
319#382C2312yes—
320#381—22no—
321#381D412yes—
322#380D412yes—
323#379—22no—
324C4×C4⋊C4C2312yes—
325C4×C22⋊C4C2311yescharacteristic
326C4×C22⋊C4C2311yescharacteristic
327#376C2312yes—
328#336C2312yes—
329#336C2312yes—
330#336C2312yes—
331#336C2312yes—
332C25—21no—
333C22×Q8—22no—
334C22×Q8—22no—
335C22×Q8—44no—
336C22×Q8—84no—
337C22×Q8C2411yescharacteristic
338C22×Q8C2411yescharacteristic
339C22×D4—24no—
340C22×D4—21no—
341C22×D4—21no—
342C22×D4—22no—
343C22×D4—22no—
344C22×D4—21no—
345C22×D4—24no—
346C22×D4—42no—
347C22×D4C2411yescharacteristic
348C22×D4C2411yescharacteristic
349C22×D4C2412yes—
350C23×C4—21no—
351C23×C4—21no—
352C23×C4—21no—
353C23×C4—21no—
354C23×C4—21no—
355C23×C4—22no—
356C23×C4—22no—
357C23×C4—44no—
358C23×C4—84no—
359C23×C4C2×D411yescharacteristic
360C23×C4C2×D411yescharacteristic
361C23×C4C2411yescharacteristic
362C2×Q16—22no—
363C2×Q16—42no—
364C2×SD16—24no—
365C2×SD16—24no—
366C2×SD16—22no—
367C2×SD16—22no—
368C2×SD16—42no—
369C2×SD16—42no—
370C2×SD16—42no—
371C2×D8—24no—
372C2×D8—24no—
373C2×D8—22no—
374C2×D8—42no—
375C2×D8—42no—
376C22×C8—42no—
377C22×C8—42no—
378C22×C8C2×D414yes—
379C22×C8C2×D414yes—
380C22×C8C2411yescharacteristic
381C22×C8C2411yescharacteristic
382C22×C8C2411yescharacteristic
383C22×C8C2411yescharacteristic
384C22×C8C2412yes—
385C22×C8C2412yes—
386C4⋊Q8—24no—
387C4⋊Q8—24no—
388C4⋊Q8—24no—
389C4⋊Q8—24no—
390C4⋊Q8—44no—
391C4⋊Q8—44no—
392#127—24no—
393#127—42no—
394#126—44no—
395#126—44no—
396#125—22no—
397#125—22no—
398#125—22no—
399#125—22no—
400#124—24no—
401#124—22no—
402#124—22no—
403#124—22no—
404#124—22no—
405#124—42no—
406#123—44no—
407#123—44no—
408#123—84no—
409C22⋊Q8—22no—
410C22⋊Q8—22no—
411C22⋊Q8—22no—
412C22⋊Q8—22no—
413C22⋊Q8—88no—
414#121—22no—
415#121—22no—
416#121—22no—
417#121—22no—
418#120—84no—
419C4×Q8—22no—
420C4×Q8—22no—
421C4×Q8—22no—
422C4×Q8—22no—
423C4×D4—24no—
424C4×D4—24no—
425C4×D4—24no—
426C4×D4—24no—
427C4×D4—22no—
428C4×D4—22no—
429C4×D4—22no—
430C4×D4—22no—
431C4×D4—44no—
432C4×D4—44no—
433C4×D4—44no—
434C4×D4—44no—
435#117—44no—
436#117—44no—
437C2×C4⋊C4—22no—
438C2×C4⋊C4—22no—
439C2×C4⋊C4—22no—
440C2×C4⋊C4—22no—
441C2×C4⋊C4—22no—
442C2×C4⋊C4—22no—
443C2×C4⋊C4—22no—
444C2×C4⋊C4—22no—
445C2×C4⋊C4—21no—
446C2×C4⋊C4—21no—
447C2×C4⋊C4—21no—
448C2×C4⋊C4—21no—
449C2×C4⋊C4—21no—
450C2×C4⋊C4—21no—
451C2×C4⋊C4—21no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4—21no—
454C2×C4⋊C4—21no—
455C2×C4⋊C4—21no—
456C2×C4⋊C4—24no—
457C2×C4⋊C4—24no—
458C2×C4⋊C4—24no—
459C2×C4⋊C4—44no—
460C2×C4⋊C4C2×D414yes—
461C2×C4⋊C4C2412yes—
462C2×C4⋊C4C2412yes—
463C2×C4⋊C4C2412yes—
464C2×C4⋊C4C2411yescharacteristic
465C2×C4⋊C4C2411yescharacteristic
466C2×C4⋊C4C2411yescharacteristic
467C2×C4⋊C4C2411yescharacteristic
468C2×C22⋊C4—21no—
469C2×C22⋊C4—21no—
470C2×C22⋊C4—22no—
471C2×C22⋊C4—22no—
472C2×C22⋊C4—21no—
473C2×C22⋊C4—21no—
474C2×C22⋊C4—21no—
475C2×C22⋊C4—21no—
476C2×C22⋊C4—21no—
477C2×C22⋊C4—21no—
478C2×C22⋊C4—21no—
479C2×C22⋊C4—21no—
480C2×C22⋊C4—24no—
481C2×C22⋊C4—24no—
482C2×C22⋊C4—24no—
483C2×C22⋊C4—24no—
484C2×C22⋊C4—24no—
485C2×C22⋊C4—24no—
486C2×C22⋊C4—44no—
487C2×C22⋊C4C2×D412yes—
488C2×C22⋊C4C2×D412yes—
489C2×C42—21no—
490C2×C42—21no—
491C2×C42C2×D411yescharacteristic
492C2×C42C2×D411yescharacteristic
493C2×C42C2×D414yes—
494C2×C42C2×D414yes—
495C2×C42C2412yes—
496C2×C42C2412yes—
497C2×C42C2411yescharacteristic
498C2×C42C2411yescharacteristic
499#107—24no—
500#107—22no—
501#107—22no—
502#107—24no—
503#107—24no—
504#106—24no—
505#106—24no—
506#106—24no—
507#106—24no—
508#106—24no—
509#106—22no—
510#106—22no—
511#106—24no—
512#106—24no—
513C4⋊C8C2×D414yes—
514C4⋊C8C2×D414yes—
515C4⋊C8C2×D414yes—
516C4⋊C8C2×D414yes—
517C4⋊C8C2×D418yes—
518#103—24no—
519#103—22no—
520#103—22no—
521#103—22no—
522#103—22no—
523#103—24no—
524#103—24no—
525#102—24no—
526#102—24no—
527#102—24no—
528#102—24no—
529#102—24no—
530#102—24no—
531#102—24no—
532#102—22no—
533#102—22no—
534#102—22no—
535#102—22no—
536#102—24no—
537#102—24no—
538C22⋊C8C2×D414yes—
539C22⋊C8C2×D414yes—
540#97—42no—
541#97—42no—
542#97C2×D418yes—
543C4×C8—42no—
544C4×C8—42no—
545#95—24no—
546#95—24no—
547#95—24no—
548#95—24no—
549#95—24no—
550#95—24no—
551#95C2×D414yes—
552#95C2×D414yes—
553#95C2×D412yes—
554#95C2×D412yes—
555#95C2×D414yes—
556C24—22no—
557C24—21no—
558C24—21no—
559C24—44no—
560C24—42no—
561C24—44no—
562C24—82no—
563C24C22×D411yescharacteristic
564C2×Q8—21no—
565C2×Q8—21no—
566C2×Q8—21no—
567C2×Q8—21no—
568C2×Q8—22no—
569C2×Q8—22no—
570C2×Q8—22no—
571C2×Q8—22no—
572C2×Q8—48no—
573C2×Q8—44no—
574C2×Q8—44no—
575C2×Q8—84no—
576C2×Q8—816no—
577C2×D4—28no—
578C2×D4—22no—
579C2×D4—22no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—22no—
585C2×D4—22no—
586C2×D4—22no—
587C2×D4—22no—
588C2×D4—22no—
589C2×D4—22no—
590C2×D4—22no—
591C2×D4—48no—
592C2×D4—44no—
593C2×D4—44no—
594C2×D4—48no—
595C2×D4—42no—
596C2×D4—42no—
597C2×D4—44no—
598C2×D4—44no—
599C2×D4—42no—
600C2×D4—84no—
601C2×D4—84no—
602C2×D42−1+414yes—
603C22×C4—24no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—42no—
616C22×C4—44no—
617C22×C4—42no—
618C22×C4—42no—
619C22×C4—42no—
620C22×C4—44no—
621C22×C4—42no—
622C22×C4—42no—
623C22×C4—44no—
624C22×C4—44no—
625C22×C4—82no—
626C22×C4—84no—
627C22×C4—84no—
628C22×C4—816no—
629C22×C4—82no—
630C22×C4—82no—
631C22×C4#12714yes—
632C22×C4#12714yes—
633C22×C4C22×D414yes—
634C22×C4C22×D414yes—
635C22×C4C22×D411yescharacteristic
636C22×C4C22×D411yescharacteristic
637C22×C4C22×D411yescharacteristic
638C22×C4C22×D411yescharacteristic
639C22×C4C22×D411yescharacteristic
640C22×C4C22×D412yes—
641C22×C4C22×D412yes—
642C22×C4C2511yescharacteristic
643Q16—82no—
644SD16—48no—
645SD16—82no—
646SD16—82no—
647D8—48no—
648D8—82no—
649C2×C8—22no—
650C2×C8—22no—
651C2×C8—22no—
652C2×C8—22no—
653C2×C8—22no—
654C2×C8—22no—
655C2×C8—22no—
656C2×C8—22no—
657C2×C8—44no—
658C2×C8—44no—
659C2×C8C22×D414yes—
660C2×C8C22×D414yes—
661C2×C8C22×D412yes—
662C2×C8C22×D412yes—
663C2×C8C22×D412yes—
664C2×C8C22×D412yes—
665C4⋊C4—22no—
666C4⋊C4—22no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—22no—
670C4⋊C4—22no—
671C4⋊C4—22no—
672C4⋊C4—21no—
673C4⋊C4—21no—
674C4⋊C4—21no—
675C4⋊C4—21no—
676C4⋊C4—22no—
677C4⋊C4—21no—
678C4⋊C4—21no—
679C4⋊C4—44no—
680C4⋊C4—42no—
681C4⋊C4—42no—
682C4⋊C4—42no—
683C4⋊C4—44no—
684C4⋊C4—44no—
685C4⋊C4—42no—
686C4⋊C4—42no—
687C4⋊C4—42no—
688C4⋊C4—42no—
689C4⋊C4—42no—
690C4⋊C4—42no—
691C4⋊C4—42no—
692C4⋊C4—42no—
693C4⋊C4—84no—
694C4⋊C4—84no—
695C4⋊C4—84no—
696C22⋊C4—24no—
697C22⋊C4—24no—
698C22⋊C4—48no—
699C22⋊C4—42no—
700C22⋊C4—42no—
701C22⋊C4—44no—
702C22⋊C4—44no—
703C22⋊C4—42no—
704C22⋊C4—42no—
705C22⋊C4—42no—
706C22⋊C4—42no—
707C22⋊C4—42no—
708C22⋊C4—42no—
709C22⋊C4—42no—
710C22⋊C4—42no—
711C22⋊C4—84no—
712C22⋊C4—84no—
713C22⋊C4—84no—
714C22⋊C4—84no—
715C22⋊C4—84no—
716C42—22no—
717C42—22no—
718C42—22no—
719C42—22no—
720C42—42no—
721C42—42no—
722C42#12714yes—
723C42#12714yes—
724C42C22×D412yes—
725C42C22×D412yes—
726C42C22×D412yes—
727C42C22×D412yes—
728C23—22no—
729C23—22no—
730C23—24no—
731C23—48no—
732C23—44no—
733C23—42no—
734C23—42no—
735C23—44no—
736C23—42no—
737C23—42no—
738C23—41no—
739C23—41no—
740C23—42no—
741C23—42no—
742C23—42no—
743C23—42no—
744C23—816no—
745C23—84no—
746C23—84no—
747C23C2×#12712yes—
748C23#57714yes—
749C23C23×D411yescharacteristic
750Q8—41no—
751Q8—41no—
752Q8—41no—
753Q8—41no—
754Q8—42no—
755Q8—42no—
756Q8—88no—
757Q8—88no—
758D4—24no—
759D4—24no—
760D4—48no—
761D4—42no—
762D4—41no—
763D4—41no—
764D4—41no—
765D4—41no—
766D4—42no—
767D4—42no—
768D4—42no—
769D4—84no—
770D4—84no—
771D4—168no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—28no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—24no—
781C2×C4—24no—
782C2×C4—24no—
783C2×C4—24no—
784C2×C4—24no—
785C2×C4—24no—
786C2×C4—24no—
787C2×C4—44no—
788C2×C4—42no—
789C2×C4—44no—
790C2×C4—44no—
791C2×C4—42no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—44no—
805C2×C4—42no—
806C2×C4—84no—
807C2×C4—84no—
808C2×C4—88no—
809C2×C4—88no—
810C2×C4—84no—
811C2×C4—84no—
812C2×C4—84no—
813C2×C4C2×#12712yes—
814C2×C4C2×#12712yes—
815C2×C4C2×#12712yes—
816C2×C4C2×#12712yes—
817C2×C4C2×#12712yes—
818C2×C4C23×D411yescharacteristic
819C2×C4C23×D411yescharacteristic
820C2×C4C2×2−1+412yes—
821C2×C4#58512yes—
822C8—22no—
823C8—22no—
824C8—22no—
825C8—22no—
826C8—24no—
827C8—24no—
828C22—22no—
829C22—28no—
830C22—22no—
831C22—44no—
832C22—48no—
833C22—816no—
834C22—84no—
835C22—82no—
836C22—82no—
837C22—81no—
838C22—81no—
839C22—84no—
840C22—84no—
841C22—81no—
842C22—81no—
843C22—81no—
844C22—81no—
845C22#315414yes—
846C22C22×#12711yescharacteristic
847C22#348912yes—
848C22C2×#57712yes—
849C22#358512yes—
850C4—22no—
851C4—22no—
852C4—22no—
853C4—22no—
854C4—22no—
855C4—44no—
856C4—44no—
857C4—81no—
858C4—81no—
859C4—82no—
860C4—81no—
861C4—81no—
862C4—81no—
863C4—81no—
864C4—82no—
865C4—82no—
866C4#348511yescharacteristic
867C4#348611yescharacteristic
868C4#348912yes—
869C2—24no—
870C2—84no—
871C2—161no—
872C2—161no—
873C2#3563411yescharacteristic
874C2C2×#315411yescharacteristic
875C2#6064411yescharacteristic
876C2#6215614yes—
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#28341C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2283 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3250C2semidirect
2. C2×#3239C2semidirect
3. C2×#3114C2semidirect
4. C22×#476C2semidirect
5. #37615C2semidirect
6. #35233C2semidirect
7. #28548C2semidirect
8. #28547C2semidirect
9. #28525C2semidirect
10. #28524C2semidirect
11. #28436C2semidirect
12. #28430C2semidirect
13. #28395C2semidirect
14. #28393C2semidirect
15. #28342C2semidirect
17. #28332C2semidirect
18. #28331C2semidirect
19. #27934C2semidirect
20. #27933C2semidirect
21. #27926C2semidirect
22. #27924C2semidirect
23. #20544C2semidirect
30. C2×#501C22semidirect
31. C2×#489C22semidirect
39. C2×#479C22semidirect
40. C2×#479C22semidirect
41. C2×#475C22semidirect
43. C2×#478C22semidirect
44. C2×#478C22semidirect
50. C2×#474C22semidirect
55. C2×#464C22semidirect
56. C2×#464C22semidirect
58. C2×#463C22semidirect
59. C2×#463C22semidirect
72. #2660C22semidirect
73. #2640C22semidirect
78. #2568C22semidirect
81. #2542C22semidirect
95. #2097C22semidirect
96. #2097C22semidirect
97. #2096C22semidirect
98. #2096C22semidirect
100. #2094C22semidirect
101. #2094C22semidirect
105. #2092C22semidirect
106. #2092C22semidirect
113. #1972C22semidirect
114. #1971C22semidirect
117. #1968C22semidirect
118. #1968C22semidirect
123. #1847C22semidirect
124. #1847C22semidirect
125. #1846C22semidirect
126. #1844C22semidirect
127. #1771C22semidirect
128. #1771C22semidirect
129. #1768C22semidirect
130. #1768C22semidirect
225. #432D4semidirect
242. C2×C4⋊C8D4semidirect

Maximal subgroups

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

subgroupindex
C2×#32502
C2×#32392
C2×#31142
C22×#4762
#376152
#352332
#285482
#285472
#285252
#285242
#284362
#284302
#283952
#283932
#283422
#283412
#283322
#283312
#279342
#279332
#279262
#279242
#205442