Finite Group Databasebeta

← #6487579

Subgroups — #6487579

Order 512.

4538 conjugacy classes of subgroups.

The subgroup lattice has 1014 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×#41C211yesmaximal, characteristic, complemented
2C2×#3207C211yesmaximal, characteristic, complemented
3C2×#3115C211yesmaximal, characteristic, complemented
4#35165C211yesmaximal, characteristic, complemented
5#32880C214yesmaximal, complemented
6#29600C214yesmaximal, complemented
7#25887C211yesmaximal, characteristic, complemented
8#25885C211yesmaximal, characteristic, complemented
9#25884C211yesmaximal, characteristic, complemented
10#25882C211yesmaximal, characteristic, complemented
11#25759C211yesmaximal, characteristic, complemented
12#25757C211yesmaximal, characteristic, complemented
13#25756C211yesmaximal, characteristic, complemented
14#25754C211yesmaximal, characteristic, complemented
15#24257C214yesmaximal, complemented
16#24256C214yesmaximal, complemented
17#21809C211yesmaximal, characteristic, complemented
18#21788C211yesmaximal, characteristic, complemented
19#20737C211yesmaximal, characteristic, complemented
20C23×#41C2212yes—
21D4×#41—28no—
22D4×#41—28no—
23C2×#550C2211yescharacteristic
24C2×D4×Q8C2211yescharacteristic
25C2×#548C2212yes—
26C2×#547—21no—
27C2×#547C2211yescharacteristic
28C2×#546—22no—
29C2×#546C2212yes—
30C2×D42—21no—
31C2×D42C2211yescharacteristic
32C2×#535—21no—
33C2×#532—21no—
34C2×#532C2211yescharacteristic
35C2×#532C2211yescharacteristic, complemented
36C2×#525—22no—
37C2×#525C2212yes—
38C2×C4×#41C2211yescharacteristic
39C22×C4×D4—21no—
40C22×C4×D4C2211yescharacteristic
41#3207—28no—
42C2×#493C2211yescharacteristic, complemented
43C2×#492C2211yescharacteristic, complemented
44C2×#487C2211yescharacteristic, complemented
45C2×#486C2211yescharacteristic, complemented
46#3115—28no—
47C2×#482C2212yescomplemented
48C2×#475C2211yescharacteristic, complemented
49C2×#474C2211yescharacteristic, complemented
50C2×#460C2211yescharacteristic, complemented
51C2×#463C2214yescomplemented
52C2×#459C2211yescharacteristic, complemented
53C2×#449C2212yes—
54C2×#449C2214yescomplemented
55C2×#449C2214yescomplemented
56C2×#449C2214yescomplemented
57C2×#448C2214yescomplemented
58C2×#447C2214yescomplemented
59C2×#442C2212yescomplemented
60C2×#440C2212yescomplemented
61C2×#432C2211yescharacteristic, complemented
62C2×#431C2211yescharacteristic, complemented
63#2847C2214yescomplemented
64#2617—22no—
65#2547C2211yescharacteristic
66#2547C2211yescharacteristic, complemented
67#2544—21no—
68#2544—21no—
69#2541C2211yescharacteristic
70#2541C2211yescharacteristic, complemented
71#2537C2214yescomplemented
72#2535—22no—
73#2311—21no—
74#2285C2211yescharacteristic, complemented
75#2036C2214yescomplemented
76#2035C2214yescomplemented
77#2034C2214yescomplemented
78#2033C2214yescomplemented
79#2000C2214yescomplemented
80#2000C2214yescomplemented
81#1999C2214yescomplemented
82#1999C2214yescomplemented
83#1982C2211yescharacteristic, complemented
84#1982C2211yescharacteristic, complemented
85#1981C2211yescharacteristic, complemented
86#1981C2211yescharacteristic, complemented
87#1959C2214yescomplemented
88#1955C2214yescomplemented
89#1954C2211yescharacteristic
90#1954C2211yescharacteristic
91#1954C2211yescharacteristic, complemented
92#1954C2211yescharacteristic, complemented
93#1825C2212yescomplemented
94#1803C2212yescomplemented
95#1802C2212yescomplemented
96#1788C2212yes—
97#1788C2214yescomplemented
98#1788C2214yescomplemented
99#1788C2214yescomplemented
100#1787C2214yescomplemented
101#1786C2214yescomplemented
102#1779C2214yescomplemented
103C4×#103C2211yescharacteristic, complemented
104C4×#103C2211yescharacteristic, complemented
105C4×#102C2211yescharacteristic, complemented
106C4×#102C2211yescharacteristic, complemented
107C22×#41—28no—
108C22×#41—28no—
109C22×#41—22no—
110C22×#41—22no—
111C22×#41—21no—
112C22×#41—48no—
113C22×#41—48no—
114C22×#41C2311yescharacteristic
115C22×#41C2312yes—
116C22×#41C2312yes—
117C22×#41C2312yes—
118C23×Q8C2312yes—
119C23×D4—22no—
120C23×D4—21no—
121C23×D4D411yescharacteristic
122C23×D4C2312yes—
123C24×C4—22no—
124C24×C4C2312yes—
125C22×SD16C2312yes—
126C22×SD16C2314yes—
127C22×D8C2312yes—
128C22×D8C2314yes—
129#550—24no—
130#550—24no—
131D4×Q8—24no—
132D4×Q8—24no—
133#548—28no—
134#548—28no—
135#547—216no—
136#547—24no—
137#547—24no—
138#546—232no—
139#546—28no—
140#546—28no—
141D42—216no—
142D42—24no—
143D42—24no—
144#535—48no—
145#532—216no—
146#532—24no—
147#532—24no—
148#532—24no—
149#532D418yescomplemented
150C2×C4⋊Q8—21no—
151C2×C4⋊Q8C2311yescharacteristic
152C2×C4⋊Q8C2311yescharacteristic
153C2×#127—21no—
154C2×#127—21no—
155C2×#127—21no—
156C2×#127C2311yescharacteristic
157C2×#127C2311yescharacteristic
158C2×#124—21no—
159C2×#124—21no—
160C2×#124—22no—
161C2×#124—21no—
162C2×#124C2312yes—
163#525—232no—
164#525—28no—
165#525—28no—
166C2×#123—22no—
167C2×#123—22no—
168C2×#123—22no—
169C2×C22⋊Q8—22no—
170C2×C22⋊Q8—22no—
171C2×C22⋊Q8C2312yes—
172C2×C22⋊Q8C2312yes—
173C2×#121—22no—
174C2×#121—21no—
175C2×#121—21no—
176C2×#121—21no—
177C2×#121—24no—
178C2×#121—21no—
179C2×#121—21no—
180C2×#121—22no—
181C2×#121—22no—
182C2×#121C2312yes—
183C2×#121C2312yes—
184C2×#121C2312yes—
185C2×#121C2314yes—
186C2×#121C2314yes—
187C2×#120—22no—
188C2×#120—22no—
189C2×#120—24no—
190C2×#120—22no—
191C4×#41—24no—
192C4×#41D418yescomplemented
193C2×C4×Q8C2311yescharacteristic
194C2×C4×Q8C2311yescharacteristic
195C2×C4×D4—216no—
196C2×C4×D4—21no—
197C2×C4×D4—22no—
198C2×C4×D4—21no—
199C2×C4×D4—21no—
200C2×C4×D4—22no—
201C2×C4×D4—21no—
202C2×C4×D4—22no—
203C2×C4×D4—21no—
204C2×C4×D4—24no—
205C2×C4×D4—24no—
206C2×C4×D4—21no—
207C2×C4×D4—21no—
208C2×C4×D4D411yescharacteristic
209C2×C4×D4D412yes—
210C2×C4×D4D411yescharacteristic
211C2×C4×D4C2312yes—
212C2×C4×D4C2311yescharacteristic
213C2×C4×D4C2311yescharacteristic
214C2×C4×D4C2311yescharacteristic
215C2×C4×D4C2312yes—
216C2×C4×D4C2311yescharacteristic
217C2×#117—21no—
218C2×#117—21no—
219C2×#117C2311yescharacteristic
220C22×C4⋊C4—21no—
221C22×C4⋊C4D411yescharacteristic
222C22×C22⋊C4—22no—
223C22×C22⋊C4D412yes—
224C22×C42—21no—
225C22×C42C2311yescharacteristic
226#493—24no—
227#492—24no—
228#487—24no—
229#486—24no—
230#482—28no—
231#475—24no—
232#474—24no—
233#463—216no—
234#460—24no—
235#459—24no—
236#449—28no—
237#449—216no—
238#449—48no—
239#449—48no—
240#448—48no—
241#447—48no—
242#442—28no—
243#440—28no—
244#432—24no—
245#431—24no—
246C2×#107C2312yes—
247C2×#106C2312yes—
248C2×C4⋊C8C2311yescharacteristic
249C2×C4⋊C8C2312yes—
250C2×C4⋊C8C2311yescharacteristic
251C2×#103C2312yes—
252C2×#103C2312yes—
253C2×#103C2312yes—
254C2×#103C2314yes—
255C2×#103C2314yes—
256C2×#103C2314yes—
257C2×#102C2312yes—
258C2×#102C2312yes—
259C2×#102C2312yes—
260C2×#102C2312yes—
261C2×#102C2314yes—
262C2×#102C2312yes—
263C2×#102C2314yes—
264C2×#102C2314yes—
265C2×C22⋊C8C2312yes—
266C2×C22⋊C8C2312yes—
267C2×C22⋊C8C2314yes—
268C2×C22⋊C8C2314yes—
269C2×C22⋊C8C2314yes—
270C2×C22⋊C8C2314yes—
271C2×#97C2312yes—
272C2×C4×C8C2311yescharacteristic
273C2×C4×C8C2311yescharacteristic
274#397—22no—
275#397—22no—
276#394—24no—
277#394—24no—
278#392—22no—
279#392—22no—
280#391—21no—
281#391—21no—
282#390—21no—
283#390—21no—
284#386—24no—
285#386—24no—
286#386—24no—
287#384C2312yes—
288#382—21no—
289#380—21no—
290#380—24no—
291#380C2312yes—
292#380C2314yes—
293#380C2314yes—
294C4×C4⋊C4—21no—
295C4×C4⋊C4C2311yescharacteristic
296C4×C4⋊C4C2311yescharacteristic
297#340C2312yes—
298#340C2312yes—
299#340C2312yes—
300#340C2312yes—
301C25—22no—
302C25C2×D412yes—
303C2×#41—216no—
304C2×#41—216no—
305C2×#41—24no—
306C2×#41—24no—
307C2×#41—24no—
308C2×#41—24no—
309C2×#41—24no—
310C2×#41—24no—
311C2×#41—22no—
312C2×#41—24no—
313C2×#41—28no—
314C2×#41—28no—
315C2×#41—44no—
316C2×#41—44no—
317C2×#41—44no—
318C2×#41—44no—
319C2×#41—416no—
320C2×#41—44no—
321C2×#41—44no—
322C2×#41—416no—
323C2×#41—464no—
324C2×#41—432no—
325C2×#41—432no—
326C2×#41—44no—
327C2×#41C2×D414yes—
328C2×#41C2×D418yes—
329C22×Q8—24no—
330C22×Q8—24no—
331C22×Q8—22no—
332C22×Q8—21no—
333C22×Q8—28no—
334C22×Q8—44no—
335C22×Q8C2412yes—
336C22×Q8C2411yescharacteristic
337C22×D4—21no—
338C22×D4—28no—
339C22×D4—216no—
340C22×D4—22no—
341C22×D4—22no—
342C22×D4—22no—
343C22×D4—22no—
344C22×D4—22no—
345C22×D4—24no—
346C22×D4—24no—
347C22×D4—24no—
348C22×D4—28no—
349C22×D4—22no—
350C22×D4—24no—
351C22×D4—24no—
352C22×D4—24no—
353C22×D4—21no—
354C22×D4—22no—
355C22×D4—21no—
356C22×D4—21no—
357C22×D4—21no—
358C22×D4—42no—
359C22×D4—44no—
360C22×D4—44no—
361C22×D4—416no—
362C22×D4—44no—
363C22×D4C2×D411yescharacteristic
364C22×D4C2×D412yes—
365C22×D4C2×D411yescharacteristic
366C22×D4C2412yes—
367C22×D4C2412yes—
368C22×D4C2411yescharacteristic
369C23×C4—21no—
370C23×C4—216no—
371C23×C4—22no—
372C23×C4—22no—
373C23×C4—21no—
374C23×C4—22no—
375C23×C4—22no—
376C23×C4—24no—
377C23×C4—24no—
378C23×C4—21no—
379C23×C4—22no—
380C23×C4—44no—
381C23×C4—44no—
382C23×C4—416no—
383C23×C4C2×D411yescharacteristic
384C23×C4C2×D412yes—
385C23×C4C2×D412yes—
386C23×C4C2×D412yes—
387C23×C4C2×D411yescharacteristic
388C23×C4C2412yes—
389C23×C4C2412yes—
390C23×C4C2411yescharacteristic
391C2×SD16—24no—
392C2×SD16—28no—
393C2×SD16—28no—
394C2×SD16—44no—
395C2×SD16—44no—
396C2×D8—24no—
397C2×D8—28no—
398C2×D8—28no—
399C2×D8—44no—
400C2×D8—44no—
401C22×C8C2412yes—
402C22×C8C2412yes—
403C22×C8C2412yes—
404C22×C8C2412yes—
405C4⋊Q8—28no—
406C4⋊Q8—22no—
407C4⋊Q8—22no—
408C4⋊Q8—22no—
409C4⋊Q8C2×D414yes—
410#127—28no—
411#127—22no—
412#127—22no—
413#127—22no—
414#127—44no—
415#127—44no—
416#127C2×D414yes—
417#124—216no—
418#124—24no—
419#124—44no—
420#124—44no—
421#124—44no—
422#124C2×D418yes—
423#123—216no—
424#123—216no—
425#123—216no—
426C22⋊Q8—216no—
427C22⋊Q8—216no—
428C22⋊Q8—24no—
429C22⋊Q8—24no—
430C22⋊Q8—24no—
431C22⋊Q8—24no—
432#121—216no—
433#121—216no—
434#121—28no—
435#121—28no—
436#121—216no—
437#121—24no—
438#121—24no—
439#121—28no—
440#121—28no—
441#121—24no—
442#121—24no—
443#121—24no—
444#121—24no—
445#121—416no—
446#121—44no—
447#121—44no—
448#121—44no—
449#121—44no—
450#121—44no—
451#120—216no—
452#120—216no—
453#120—216no—
454#120—416no—
455C4×Q8—22no—
456C4×Q8—22no—
457C4×Q8C2×D414yes—
458C4×Q8C2×D414yes—
459C4×D4—216no—
460C4×D4—28no—
461C4×D4—216no—
462C4×D4—28no—
463C4×D4—216no—
464C4×D4—28no—
465C4×D4—28no—
466C4×D4—24no—
467C4×D4—28no—
468C4×D4—28no—
469C4×D4—24no—
470C4×D4—28no—
471C4×D4—22no—
472C4×D4—22no—
473C4×D4—24no—
474C4×D4—24no—
475C4×D4—22no—
476C4×D4—22no—
477C4×D4—22no—
478C4×D4—22no—
479C4×D4—24no—
480C4×D4—24no—
481C4×D4—44no—
482C4×D4C2×D414yes—
483C4×D4C2×D414yes—
484#117—22no—
485#117—28no—
486#117—44no—
487#117C2×D414yes—
488C2×C4⋊C4—28no—
489C2×C4⋊C4—24no—
490C2×C4⋊C4—21no—
491C2×C4⋊C4—22no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4—22no—
496C2×C4⋊C4—22no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—22no—
499C2×C4⋊C4C2×D411yescharacteristic
500C2×C4⋊C4C2×D411yescharacteristic
501C2×C4⋊C4C2×D412yes—
502C2×C4⋊C4C2412yes—
503C2×C4⋊C4C2412yes—
504C2×C4⋊C4C2412yes—
505C2×C4⋊C4C2411yescharacteristic
506C2×C4⋊C4C2411yescharacteristic
507C2×C22⋊C4—216no—
508C2×C22⋊C4—22no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—22no—
511C2×C22⋊C4—28no—
512C2×C22⋊C4—22no—
513C2×C22⋊C4—22no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—21no—
516C2×C22⋊C4—22no—
517C2×C22⋊C4—22no—
518C2×C22⋊C4—22no—
519C2×C22⋊C4—24no—
520C2×C22⋊C4—24no—
521C2×C22⋊C4—22no—
522C2×C22⋊C4—22no—
523C2×C22⋊C4—24no—
524C2×C22⋊C4—24no—
525C2×C22⋊C4C2×D412yes—
526C2×C22⋊C4C2×D412yes—
527C2×C22⋊C4C2×D412yes—
528C2×C22⋊C4C2×D412yes—
529C2×C42—21no—
530C2×C42—21no—
531C2×C42—21no—
532C2×C42—28no—
533C2×C42—21no—
534C2×C42—21no—
535C2×C42C2×D411yescharacteristic
536C2×C42C2×D411yescharacteristic
537C2×C42C2×D414yes—
538C2×C42C2×D414yes—
539C2×C42C2411yescharacteristic
540C2×C42C2411yescharacteristic
541#107—24no—
542#106—24no—
543C4⋊C8—24no—
544C4⋊C8—22no—
545C4⋊C8—22no—
546#103—24no—
547#103—28no—
548#103—24no—
549#103—24no—
550#103—44no—
551#103—44no—
552#102—24no—
553#102—28no—
554#102—24no—
555#102—24no—
556#102—24no—
557#102—24no—
558#102—44no—
559#102—44no—
560C22⋊C8—24no—
561C22⋊C8—24no—
562C22⋊C8—44no—
563C22⋊C8—44no—
564C22⋊C8—44no—
565C22⋊C8—44no—
566#97—24no—
567C4×C8—22no—
568C4×C8—22no—
569#95—22no—
570#95—21no—
571#95—21no—
572#95—24no—
573#95—24no—
574C24—21no—
575C24—28no—
576C24—22no—
577C24—24no—
578C24—24no—
579C24—22no—
580C24—44no—
581C24—42no—
582C24—44no—
583C24—48no—
584C24—44no—
585C24—44no—
586C24—84no—
587C24C22×D412yes—
588C24C22×D411yescharacteristic
589C24C22×D412yes—
590#41—216no—
591#41—28no—
592#41—28no—
593#41—416no—
594#41—464no—
595#41—48no—
596#41—48no—
597#41—416no—
598#41—416no—
599#41—464no—
600#41—48no—
601#41—48no—
602#41—48no—
603#41—48no—
604#41—816no—
605C2×Q8—28no—
606C2×Q8—21no—
607C2×Q8—22no—
608C2×Q8—22no—
609C2×Q8—24no—
610C2×Q8—24no—
611C2×Q8—48no—
612C2×Q8—416no—
613C2×Q8—48no—
614C2×Q8—48no—
615C2×Q8—42no—
616C2×Q8—42no—
617C2×Q8—42no—
618C2×Q8C22×D414yes—
619C2×Q8C22×D412yes—
620C2×Q8H(5,𝔽2)14yes—
621C2×D4—28no—
622C2×D4—24no—
623C2×D4—28no—
624C2×D4—28no—
625C2×D4—28no—
626C2×D4—28no—
627C2×D4—28no—
628C2×D4—24no—
629C2×D4—28no—
630C2×D4—22no—
631C2×D4—24no—
632C2×D4—22no—
633C2×D4—24no—
634C2×D4—24no—
635C2×D4—22no—
636C2×D4—22no—
637C2×D4—22no—
638C2×D4—21no—
639C2×D4—22no—
640C2×D4—22no—
641C2×D4—22no—
642C2×D4—22no—
643C2×D4—24no—
644C2×D4—24no—
645C2×D4—24no—
646C2×D4—24no—
647C2×D4—416no—
648C2×D4—42no—
649C2×D4—48no—
650C2×D4—48no—
651C2×D4—416no—
652C2×D4—432no—
653C2×D4—464no—
654C2×D4—48no—
655C2×D4—48no—
656C2×D4—44no—
657C2×D4—48no—
658C2×D4—44no—
659C2×D4—48no—
660C2×D4—44no—
661C2×D4—44no—
662C2×D4—44no—
663C2×D4—48no—
664C2×D4—48no—
665C2×D4—42no—
666C2×D4—42no—
667C2×D4—42no—
668C2×D4—42no—
669C2×D4—42no—
670C2×D4—42no—
671C2×D4—82no—
672C2×D4—82no—
673C2×D4—84no—
674C2×D4—84no—
675C2×D4—84no—
676C2×D4—84no—
677C2×D4—84no—
678C2×D4AGL(1,ℤ/8)14yes—
679C2×D4C22×D414yes—
680C2×D4C22×D412yes—
681C2×D4H(5,𝔽2)14yes—
682C22×C4—28no—
683C22×C4—21no—
684C22×C4—24no—
685C22×C4—22no—
686C22×C4—22no—
687C22×C4—22no—
688C22×C4—22no—
689C22×C4—28no—
690C22×C4—28no—
691C22×C4—28no—
692C22×C4—24no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—22no—
696C22×C4—24no—
697C22×C4—24no—
698C22×C4—28no—
699C22×C4—24no—
700C22×C4—22no—
701C22×C4—22no—
702C22×C4—22no—
703C22×C4—22no—
704C22×C4—24no—
705C22×C4—24no—
706C22×C4—24no—
707C22×C4—24no—
708C22×C4—24no—
709C22×C4—22no—
710C22×C4—22no—
711C22×C4—22no—
712C22×C4—44no—
713C22×C4—44no—
714C22×C4—44no—
715C22×C4—42no—
716C22×C4—48no—
717C22×C4—48no—
718C22×C4—48no—
719C22×C4—464no—
720C22×C4—48no—
721C22×C4—48no—
722C22×C4—48no—
723C22×C4—416no—
724C22×C4—44no—
725C22×C4—44no—
726C22×C4—42no—
727C22×C4—42no—
728C22×C4—44no—
729C22×C4—82no—
730C22×C4#12014yes—
731C22×C4#12014yes—
732C22×C4C22×D412yes—
733C22×C4C22×D412yes—
734C22×C4C22×D411yescharacteristic
735C22×C4C22×D411yescharacteristic
736C22×C4C22×D411yescharacteristic
737C22×C4C22×D411yescharacteristic
738C22×C4C22×D412yes—
739C22×C4C22×D412yes—
740C22×C4C22×D411yescharacteristic
741C22×C4C2511yescharacteristic
742SD16—48no—
743SD16—88no—
744D8—48no—
745D8—88no—
746C2×C8—22no—
747C2×C8—22no—
748C2×C8—22no—
749C2×C8—22no—
750C2×C8—22no—
751C2×C8—22no—
752C2×C8—24no—
753C2×C8—24no—
754C2×C8—22no—
755C2×C8—22no—
756C4⋊C4—28no—
757C4⋊C4—28no—
758C4⋊C4—22no—
759C4⋊C4—24no—
760C4⋊C4—22no—
761C4⋊C4—24no—
762C4⋊C4—24no—
763C4⋊C4—24no—
764C4⋊C4—24no—
765C4⋊C4—21no—
766C4⋊C4—21no—
767C4⋊C4—22no—
768C4⋊C4—22no—
769C4⋊C4—22no—
770C4⋊C4—22no—
771C4⋊C4—22no—
772C4⋊C4—22no—
773C4⋊C4—44no—
774C4⋊C4—42no—
775C4⋊C4—82no—
776C4⋊C4C22×D412yes—
777C4⋊C4C22×D412yes—
778C22⋊C4—28no—
779C22⋊C4—28no—
780C22⋊C4—28no—
781C22⋊C4—28no—
782C22⋊C4—24no—
783C22⋊C4—24no—
784C22⋊C4—28no—
785C22⋊C4—24no—
786C22⋊C4—24no—
787C22⋊C4—24no—
788C22⋊C4—24no—
789C22⋊C4—24no—
790C22⋊C4—28no—
791C22⋊C4—44no—
792C22⋊C4—48no—
793C22⋊C4—48no—
794C22⋊C4—44no—
795C22⋊C4—44no—
796C22⋊C4—84no—
797C22⋊C4—84no—
798C42—24no—
799C42—24no—
800C42—24no—
801C42—42no—
802C42—42no—
803C42#12014yes—
804C42#12014yes—
805C42C22×D412yes—
806C42C22×D412yes—
807C42C22×D412yes—
808C42C22×D412yes—
809C23—22no—
810C23—24no—
811C23—22no—
812C23—22no—
813C23—24no—
814C23—22no—
815C23—24no—
816C23—21no—
817C23—21no—
818C23—22no—
819C23—24no—
820C23—22no—
821C23—24no—
822C23—24no—
823C23—22no—
824C23—22no—
825C23—48no—
826C23—48no—
827C23—416no—
828C23—416no—
829C23—42no—
830C23—41no—
831C23—41no—
832C23—44no—
833C23—44no—
834C23—42no—
835C23—42no—
836C23—44no—
837C23—42no—
838C23—44no—
839C23—42no—
840C23—42no—
841C23—88no—
842C23—84no—
843C23—816no—
844C23—88no—
845C23—88no—
846C23—816no—
847C23C2×#12012yes—
848C23C2×AGL(1,ℤ/8)14yes—
849C23C23×D411yescharacteristic
850Q8—22no—
851Q8—24no—
852Q8—28no—
853Q8—416no—
854Q8—42no—
855Q8—42no—
856Q8—84no—
857Q8#53514yescomplemented
858D4—216no—
859D4—22no—
860D4—24no—
861D4—28no—
862D4—28no—
863D4—48no—
864D4—416no—
865D4—416no—
866D4—416no—
867D4—416no—
868D4—416no—
869D4—42no—
870D4—42no—
871D4—42no—
872D4—42no—
873D4—44no—
874D4—44no—
875D4—48no—
876D4—84no—
877D4—84no—
878D4—88no—
879D4—88no—
880D4—84no—
881D4—168no—
882D4—168no—
883D4#53514yescomplemented
884C2×C4—216no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—24no—
890C2×C4—21no—
891C2×C4—21no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—24no—
895C2×C4—28no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—24no—
900C2×C4—22no—
901C2×C4—24no—
902C2×C4—24no—
903C2×C4—44no—
904C2×C4—48no—
905C2×C4—416no—
906C2×C4—48no—
907C2×C4—416no—
908C2×C4—416no—
909C2×C4—48no—
910C2×C4—416no—
911C2×C4—42no—
912C2×C4—44no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—42no—
916C2×C4—42no—
917C2×C4—42no—
918C2×C4—42no—
919C2×C4—44no—
920C2×C4—44no—
921C2×C4—48no—
922C2×C4—42no—
923C2×C4—42no—
924C2×C4—42no—
925C2×C4—42no—
926C2×C4—42no—
927C2×C4—42no—
928C2×C4—42no—
929C2×C4—42no—
930C2×C4—42no—
931C2×C4—84no—
932C2×C4—88no—
933C2×C4C2×#12012yes—
934C2×C4C2×#12012yes—
935C2×C4C2×#12012yes—
936C2×C4C2×#12012yes—
937C2×C4C2×#12012yes—
938C2×C4C2×AGL(1,ℤ/8)12yes—
939C2×C4#57512yes—
940C2×C4C23×D411yescharacteristic
941C2×C4C23×D411yescharacteristic
942C2×C4C2×H(5,𝔽2)12yes—
943C2×C4C2×H(5,𝔽2)12yes—
944C8—42no—
945C8—42no—
946C8—42no—
947C8—42no—
948C22—22no—
949C22—24no—
950C22—28no—
951C22—22no—
952C22—24no—
953C22—22no—
954C22—42no—
955C22—42no—
956C22—44no—
957C22—42no—
958C22—44no—
959C22—44no—
960C22—42no—
961C22—42no—
962C22—42no—
963C22—44no—
964C22—42no—
965C22—44no—
966C22—44no—
967C22—42no—
968C22—44no—
969C22—42no—
970C22—44no—
971C22—816no—
972C22—832no—
973C22—84no—
974C22—84no—
975C22—82no—
976C22—84no—
977C22—84no—
978C22—82no—
979C22—82no—
980C22C22×#12011yescharacteristic
981C22#348412yes—
982C22C22×AGL(1,ℤ/8)11yescharacteristic
983C22C2×#57511yescharacteristic
984C22#358412yes—
985C4—22no—
986C4—24no—
987C4—22no—
988C4—22no—
989C4—22no—
990C4—42no—
991C4—42no—
992C4—44no—
993C4—42no—
994C4—42no—
995C4—82no—
996C4—82no—
997C4—82no—
998C4#300614yes—
999C4C2×#53511yescharacteristic
1000C4C2×#53511yescharacteristic
1001C4#348412yes—
1002C2—42no—
1003C2—44no—
1004C2—44no—
1005C2—82no—
1006C2—84no—
1007C2—162no—
1008C2#3522211yescharacteristic
1009C2C2×#300611yescharacteristic
1010C2#6036611yescharacteristic
1011C2#6159812yes—
1012C2#6160812yes—
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C22×C4×D4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×D4×#41C2semidirect
2. C2×#3207C2semidirect
3. C2×#3115C2semidirect
4. #35165C2semidirect
5. #32880C2semidirect
6. #29600C2semidirect
7. #25887C2semidirect
8. #25885C2semidirect
9. #25884C2semidirect
10. #25882C2semidirect
11. #25759C2semidirect
12. #25757C2semidirect
13. #25756C2semidirect
14. #25754C2semidirect
15. #24257C2semidirect
16. #24256C2semidirect
17. #21809C2semidirect
18. #21788C2semidirect
19. #20737C2semidirect
35. C2×#532C22semidirect
42. C2×#493C22semidirect
43. C2×#492C22semidirect
44. C2×#487C22semidirect
45. C2×#486C22semidirect
47. C2×#482C22semidirect
48. C2×#475C22semidirect
49. C2×#474C22semidirect
50. C2×#460C22semidirect
51. C2×#463C22semidirect
52. C2×#459C22semidirect
54. C2×#449C22semidirect
55. C2×#449C22semidirect
56. C2×#449C22semidirect
57. C2×#448C22semidirect
58. C2×#447C22semidirect
59. C2×#442C22semidirect
60. C2×#440C22semidirect
61. C2×#432C22semidirect
62. C2×#431C22semidirect
63. #2847C22semidirect
66. #2547C22semidirect
70. #2541C22semidirect
71. #2537C22semidirect
74. #2285C22semidirect
75. #2036C22semidirect
76. #2035C22semidirect
77. #2034C22semidirect
78. #2033C22semidirect
79. #2000C22semidirect
80. #2000C22semidirect
81. #1999C22semidirect
82. #1999C22semidirect
83. #1982C22semidirect
84. #1982C22semidirect
85. #1981C22semidirect
86. #1981C22semidirect
87. #1959C22semidirect
88. #1955C22semidirect
91. #1954C22semidirect
92. #1954C22semidirect
93. #1825C22semidirect
94. #1803C22semidirect
95. #1802C22semidirect
97. #1788C22semidirect
98. #1788C22semidirect
99. #1788C22semidirect
100. #1787C22semidirect
101. #1786C22semidirect
102. #1779C22semidirect
103. C4×#103C22semidirect
104. C4×#103C22semidirect
105. C4×#102C22semidirect
106. C4×#102C22semidirect
149. #532D4semidirect
192. C4×#41D4semidirect
857. Q8#535semidirect
883. D4#535semidirect

Maximal subgroups

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

subgroupindex
C2×D4×#412
C2×#32072
C2×#31152
#351652
#328802
#296002
#258872
#258852
#258842
#258822
#257592
#257572
#257562
#257542
#242572
#242562
#218092
#217882
#207372