Finite Group Databasebeta

← #356084

Subgroups — #356084

Order 512.

2546 conjugacy classes of subgroups.

The subgroup lattice has 1161 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#421C211yesmaximal, characteristic
2C22⋊C4×#41C211yesmaximal, characteristic
3C2×#1789C211yesmaximal, characteristic
4C2×#1759C211yesmaximal, characteristic, complemented
5C2×C4×#104C211yesmaximal, characteristic, complemented
6C22⋊C4×M16C211yesmaximal, characteristic, complemented
7#13761C211yesmaximal, characteristic, complemented
8#10933C211yesmaximal, characteristic, complemented
9#10933C211yesmaximal, characteristic, complemented
10#10924C211yesmaximal, characteristic, complemented
11#10923C211yesmaximal, characteristic, complemented
12#10790C211yesmaximal, characteristic, complemented
13#10790C211yesmaximal, characteristic, complemented
14#10732C211yesmaximal, characteristic, complemented
15#10720C211yesmaximal, characteristic, complemented
16C23×#41C2211yescharacteristic
17C23×M16C2211yescharacteristic
18C2×C4×#41C2211yescharacteristic
19C2×C4×#41C2211yescharacteristic
20C22×#117C2211yescharacteristic
21C2×#421—24no—
22C2×#421—24no—
23C2×#421C418yescomplemented
24C22×#104C2211yescharacteristic
25C22×#104C2211yescharacteristic
26C22×#104C2211yescharacteristic
27C22×#104C2211yescharacteristic
28C22×#104C2211yescharacteristic
29C22×#104C2211yescharacteristic
30C22×#104C2211yescharacteristic
31C22×#104C2211yescharacteristic
32C2×#407C2211yescharacteristic
33C2×C4×M16C2211yescharacteristic, complemented
34C2×C4×M16C2211yescharacteristic, complemented
35#2341C412yescomplemented
36Q8×C22⋊C4C412yescomplemented
37#2339—22no—
38#2339C412yescomplemented
39D4×C22⋊C4—22no—
40D4×C22⋊C4C412yescomplemented
41#2297—21no—
42#2297—21no—
43#2297C2211yescharacteristic
44#2297C2211yescharacteristic
45#2280—21no—
46#2280C2211yescharacteristic
47C2×C4×C22⋊C4—21no—
48C2×C4×C22⋊C4C2211yescharacteristic
49C2×C4×C22⋊C4C2211yescharacteristic
50C2×#376C2211yescharacteristic, complemented
51C2×C43C2211yescharacteristic, complemented
52#1789C418yescomplemented
53#1759—24no—
54C4×#104—24no—
55#1753—21no—
56#1753—21no—
57#1752—21no—
58C8×C22⋊C4—21no—
59C2×#339C2211yescharacteristic, complemented
60C2×#339C2211yescharacteristic, complemented
61C2×#339C2211yescharacteristic, complemented
62C2×#339C2211yescharacteristic, complemented
63C2×#339C2211yescharacteristic, complemented
64C2×#339C2211yescharacteristic, complemented
65C2×#339C2211yescharacteristic, complemented
66C2×#339C2211yescharacteristic, complemented
67#1728C2211yescharacteristic, complemented
68#1728C2211yescharacteristic, complemented
69#1437—22no—
70#1436—22no—
71C4×#95C2211yescharacteristic, complemented
72C4×#95C2211yescharacteristic, complemented
73C22×#41—21no—
74C22×#41—21no—
75C22×#41—22no—
76C22×#41—22no—
77C22×#41—22no—
78C22×#41—22no—
79C22×#41—22no—
80C22×#41—22no—
81C22×#41—41no—
82C22×#41—41no—
83C22×#41—41no—
84C22×#41—41no—
85C22×#41C2×C414yes—
86C22×#41C2×C414yes—
87C22×#41C2×C411yescharacteristic
88C22×#41C2×C411yescharacteristic
89C22×#41C2311yescharacteristic
90C22×#41C2311yescharacteristic
91C23×Q8C2×C411yescharacteristic
92C23×D4—21no—
93C23×D4C2×C411yescharacteristic
94C24×C4—21no—
95C24×C4C2311yescharacteristic
96C22×M16—21no—
97C22×M16—22no—
98C22×M16—22no—
99C22×M16—22no—
100C22×M16—41no—
101C22×M16—41no—
102C22×M16C2×C414yescomplemented
103C22×M16C2311yescharacteristic
104C22×M16C2311yescharacteristic
105C22×M16C2311yescharacteristic
106C22×M16C2311yescharacteristic
107C23×C8—21no—
108C4×#41—22no—
109C4×#41—22no—
110C4×#41—22no—
111C4×#41—22no—
112C4×#41—41no—
113C4×#41—41no—
114C4×#41—41no—
115C4×#41—41no—
116C2×C4×Q8C2×C412yes—
117C2×C4×Q8C2×C412yes—
118C2×C4×D4—22no—
119C2×C4×D4—22no—
120C2×C4×D4C2×C412yes—
121C2×C4×D4C2×C412yes—
122C2×#117—22no—
123C2×#117—21no—
124C2×#117—21no—
125C2×#117—22no—
126C2×#117—22no—
127C2×#117—41no—
128C2×#117—41no—
129C2×#117C2×C414yescomplemented
130C2×#117C2311yescharacteristic
131C2×#117C2311yescharacteristic
132C22×C4⋊C4—21no—
133C22×C22⋊C4—21no—
134C22×C22⋊C4—21no—
135C22×C22⋊C4—22no—
136C22×C22⋊C4D412yes—
137C22×C42—21no—
138C22×C42—21no—
139C22×C42—22no—
140C22×C42C2311yescharacteristic
141C22×C42C2311yescharacteristic
142C22×C42C2311yescharacteristic
143C22×C42C2311yescharacteristic
144C22×C42C2311yescharacteristic
145C22×C42C2311yescharacteristic
146#421—232no—
147C2×#104—22no—
148C2×#104—22no—
149C2×#104—22no—
150C2×#104—22no—
151C2×#104—22no—
152C2×#104—22no—
153C2×#104—22no—
154C2×#104—22no—
155C2×#104—22no—
156C2×#104—22no—
157C2×#104—41no—
158C2×#104—41no—
159C2×#104—41no—
160C2×#104—41no—
161C2×#104C2×C414yes—
162C2×#104C2×C414yes—
163C2×#104C2×C414yes—
164C2×#104C2×C414yes—
165C2×#104C2×C414yescomplemented
166C2×#104C2×C414yescomplemented
167C2×#104C2×C414yescomplemented
168C2×#104C2×C414yescomplemented
169C2×#104D414yes—
170C2×#104D414yes—
171#407—22no—
172#407C2×C414yescomplemented
173C2×C22⋊C8—21no—
174C2×C22⋊C8—21no—
175C4×M16—22no—
176C4×M16—22no—
177C4×M16—41no—
178C4×M16—41no—
179C2×#97—21no—
180C2×#97—21no—
181C2×C4×C8—21no—
182C2×C4×C8—21no—
183#391—22no—
184#391—22no—
185#391C2×C412yes—
186#391C2×C412yes—
187#390—22no—
188#390—22no—
189#390C2×C412yes—
190#390C2×C412yes—
191#386—22no—
192#386—22no—
193#386—22no—
194#386—22no—
195#386—22no—
196#386—22no—
197#381—21no—
198#381—22no—
199#380—22no—
200#380—22no—
201#380C2×C412yes—
202#380C2×C412yes—
203#379—21no—
204#379—22no—
205C4×C22⋊C4—21no—
206C4×C22⋊C4—21no—
207C4×C22⋊C4—22no—
208C4×C22⋊C4—22no—
209C4×C22⋊C4—21no—
210C4×C22⋊C4—21no—
211C4×C22⋊C4—21no—
212C4×C22⋊C4—21no—
213C4×C22⋊C4—22no—
214C4×C22⋊C4C2×C412yes—
215C4×C22⋊C4C2×C412yes—
216C4×C22⋊C4C2×C414yescomplemented
217C4×C22⋊C4D411yescharacteristic
218C4×C22⋊C4D411yescharacteristic
219C4×C22⋊C4D411yescharacteristic
220C4×C22⋊C4D411yescharacteristic
221#376—22no—
222#376—41no—
223C2×#95—21no—
224C2×#95—22no—
225C2×#95—22no—
226C2×#95—22no—
227C2×#95—22no—
228C2×#95D412yes—
229C43—22no—
230C43—41no—
231#339—22no—
232#339—22no—
233#339—22no—
234#339—22no—
235#339—41no—
236#339—41no—
237#339—41no—
238#339—41no—
239#336—21no—
240#336—21no—
241#336—21no—
242#336—21no—
243C25—21no—
244C25C2×D411yescharacteristic
245C2×#41—22no—
246C2×#41—22no—
247C2×#41—24no—
248C2×#41—24no—
249C2×#41—24no—
250C2×#41—24no—
251C2×#41—21no—
252C2×#41—21no—
253C2×#41—21no—
254C2×#41—21no—
255C2×#41—21no—
256C2×#41—21no—
257C2×#41—21no—
258C2×#41—21no—
259C2×#41—28no—
260C2×#41—28no—
261C2×#41—28no—
262C2×#41—28no—
263C2×#41—22no—
264C2×#41—22no—
265C2×#41—22no—
266C2×#41—22no—
267C2×#41—21no—
268C2×#41—21no—
269C2×#41—21no—
270C2×#41—21no—
271C2×#41—21no—
272C2×#41—21no—
273C2×#41—21no—
274C2×#41—21no—
275C2×#41—42no—
276C2×#41—42no—
277C2×#41—42no—
278C2×#41—42no—
279C2×#41—41no—
280C2×#41—41no—
281C2×#41—41no—
282C2×#41—41no—
283C2×#41—42no—
284C2×#41—42no—
285C2×#41—42no—
286C2×#41—42no—
287C2×#41—44no—
288C2×#41—44no—
289C2×#41—44no—
290C2×#41—44no—
291C2×#41—44no—
292C2×#41—44no—
293C2×#41—44no—
294C2×#41—44no—
295C2×#41—44no—
296C2×#41—44no—
297C2×#41—44no—
298C2×#41—44no—
299C2×#41C4214yescomplemented
300C2×#41C4214yescomplemented
301C2×#41C22×C412yes—
302C2×#41C22×C412yes—
303C2×#41C22×C412yes—
304C2×#41C22×C412yes—
305C2×#41C2×D412yes—
306C2×#41C2×D412yes—
307C2×#41#4112yes—
308C2×#41#4112yes—
309C22×Q8—21no—
310C22×Q8—22no—
311C22×Q8—22no—
312C22×Q8—22no—
313C22×Q8—41no—
314C22×Q8—41no—
315C22×Q8C4214yescomplemented
316C22×Q8C22×C411yescharacteristic
317C22×Q8C22×C411yescharacteristic
318C22×D4—21no—
319C22×D4—22no—
320C22×D4—22no—
321C22×D4—21no—
322C22×D4—21no—
323C22×D4—24no—
324C22×D4—24no—
325C22×D4—21no—
326C22×D4—21no—
327C22×D4—22no—
328C22×D4—41no—
329C22×D4—41no—
330C22×D4—42no—
331C22×D4—42no—
332C22×D4—42no—
333C22×D4—42no—
334C22×D4C4214yescomplemented
335C22×D4C22×C411yescharacteristic
336C22×D4C22×C411yescharacteristic
337C23×C4—21no—
338C23×C4—21no—
339C23×C4—21no—
340C23×C4—21no—
341C23×C4—21no—
342C23×C4—21no—
343C23×C4—21no—
344C23×C4—21no—
345C23×C4—21no—
346C23×C4—21no—
347C23×C4—21no—
348C23×C4—21no—
349C23×C4—21no—
350C23×C4—21no—
351C23×C4—24no—
352C23×C4—24no—
353C23×C4—21no—
354C23×C4—21no—
355C23×C4—21no—
356C23×C4—22no—
357C23×C4—22no—
358C23×C4—42no—
359C23×C4—42no—
360C23×C4—42no—
361C23×C4—42no—
362C23×C4C22×C411yescharacteristic
363C23×C4C22×C411yescharacteristic
364C23×C4C22×C412yes—
365C23×C4C22×C412yes—
366C23×C4C2×D412yes—
367C23×C4C2×D411yescharacteristic
368C23×C4C2×D411yescharacteristic
369C23×C4C2×D411yescharacteristic
370C23×C4C2×D412yes—
371C23×C4#4112yes—
372C23×C4#4112yes—
373C23×C4C2411yescharacteristic
374C2×M16—21no—
375C2×M16—21no—
376C2×M16—21no—
377C2×M16—24no—
378C2×M16—21no—
379C2×M16—21no—
380C2×M16—21no—
381C2×M16—21no—
382C2×M16—21no—
383C2×M16—21no—
384C2×M16—21no—
385C2×M16—21no—
386C2×M16—21no—
387C2×M16—21no—
388C2×M16—21no—
389C2×M16—21no—
390C2×M16—21no—
391C2×M16—21no—
392C2×M16—21no—
393C2×M16—28no—
394C2×M16—42no—
395C2×M16—42no—
396C2×M16—44no—
397C2×M16—44no—
398C2×M16—44no—
399C2×M16C22×C412yes—
400C2×M16C22×C412yes—
401C2×M16C22×C412yes—
402C2×M16C22×C412yes—
403C2×M16C2×D412yes—
404C2×M16C2×D412yes—
405C22×C8—21no—
406C22×C8—24no—
407C22×C8—21no—
408C22×C8—21no—
409C22×C8—21no—
410C22×C8—42no—
411C22×C8—42no—
412C4×Q8—24no—
413C4×Q8—24no—
414C4×Q8—42no—
415C4×Q8—42no—
416C4×D4—24no—
417C4×D4—24no—
418C4×D4—42no—
419C4×D4—42no—
420C4×D4—44no—
421C4×D4—44no—
422C4×D4—44no—
423C4×D4—44no—
424#117—28no—
425#117—21no—
426#117—21no—
427#117—21no—
428#117—21no—
429#117—21no—
430#117—21no—
431#117—21no—
432#117—21no—
433#117—44no—
434#117—44no—
435#117—44no—
436#117—42no—
437#117—42no—
438#117—42no—
439#117—42no—
440C2×C4⋊C4—22no—
441C2×C4⋊C4—22no—
442C2×C4⋊C4—24no—
443C2×C4⋊C4—42no—
444C2×C4⋊C4—42no—
445C2×C4⋊C4C22×C412yes—
446C2×C4⋊C4C22×C412yes—
447C2×C22⋊C4—22no—
448C2×C22⋊C4—24no—
449C2×C22⋊C4—24no—
450C2×C22⋊C4—21no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4—22no—
453C2×C22⋊C4—22no—
454C2×C22⋊C4—22no—
455C2×C22⋊C4—22no—
456C2×C22⋊C4—22no—
457C2×C22⋊C4—22no—
458C2×C22⋊C4—22no—
459C2×C22⋊C4—44no—
460C2×C22⋊C4—48no—
461C2×C22⋊C4—42no—
462C2×C22⋊C4—42no—
463C2×C22⋊C4—44no—
464C2×C22⋊C4C22⋊C412yes—
465C2×C22⋊C4C22⋊C412yes—
466C2×C22⋊C4C22⋊C412yes—
467C2×C22⋊C4C22⋊C412yes—
468C2×C42—21no—
469C2×C42—21no—
470C2×C42—21no—
471C2×C42—21no—
472C2×C42—21no—
473C2×C42—21no—
474C2×C42—21no—
475C2×C42—21no—
476C2×C42—21no—
477C2×C42—21no—
478C2×C42—21no—
479C2×C42—21no—
480C2×C42—21no—
481C2×C42—21no—
482C2×C42—21no—
483C2×C42—21no—
484C2×C42—21no—
485C2×C42—21no—
486C2×C42—21no—
487C2×C42—21no—
488C2×C42—21no—
489C2×C42—21no—
490C2×C42—21no—
491C2×C42—22no—
492C2×C42—22no—
493C2×C42—21no—
494C2×C42—21no—
495C2×C42—21no—
496C2×C42—21no—
497C2×C42—21no—
498C2×C42—42no—
499C2×C42—42no—
500C2×C42—42no—
501C2×C42—42no—
502C2×C42—44no—
503C2×C42—44no—
504C2×C42—44no—
505C2×C42C22×C412yes—
506C2×C42C22×C412yes—
507C2×C42C22×C412yes—
508C2×C42C22×C412yes—
509C2×C42C22×C412yes—
510C2×C42C22×C412yes—
511C2×C42C2×D411yescharacteristic
512C2×C42C2×D411yescharacteristic
513C2×C42C2×D411yescharacteristic
514C2×C42C2×D411yescharacteristic
515C2×C42C2×D412yes—
516C2×C42C2×D412yes—
517#104—28no—
518#104—28no—
519#104—28no—
520#104—28no—
521#104—28no—
522#104—44no—
523#104—44no—
524#104C22⋊C4116yescomplemented
525C22⋊C8—24no—
526C22⋊C8—24no—
527#97—42no—
528#97—42no—
529C4×C8—42no—
530C4×C8—42no—
531#95—22no—
532#95—22no—
533#95—22no—
534#95—22no—
535#95—22no—
536#95—22no—
537#95—24no—
538#95—44no—
539#95—44no—
540#95—44no—
541#95C22⋊C412yes—
542#95C22⋊C412yes—
543#95C22⋊C412yes—
544#95C22⋊C412yes—
545C24—21no—
546C24—21no—
547C24—21no—
548C24—21no—
549C24—21no—
550C24—21no—
551C24—24no—
552C24—42no—
553C24—42no—
554C24—42no—
555C24—42no—
556C24—44no—
557C24—82no—
558C24C2×C22⋊C411yescharacteristic
559C24C2×C22⋊C411yescharacteristic
560C24C4×D412yes—
561C24C4×D412yes—
562C24C22×D411yescharacteristic
563#41—22no—
564#41—22no—
565#41—22no—
566#41—22no—
567#41—22no—
568#41—22no—
569#41—22no—
570#41—22no—
571#41—22no—
572#41—22no—
573#41—22no—
574#41—22no—
575#41—28no—
576#41—28no—
577#41—22no—
578#41—22no—
579#41—22no—
580#41—22no—
581#41—22no—
582#41—22no—
583#41—22no—
584#41—22no—
585#41—48no—
586#41—48no—
587#41—48no—
588#41—48no—
589#41—44no—
590#41—44no—
591#41—48no—
592#41—48no—
593#41—48no—
594#41—48no—
595#41—44no—
596#41—44no—
597#41—44no—
598#41—44no—
599#41—41no—
600#41—41no—
601#41—41no—
602#41—41no—
603#41—41no—
604#41—41no—
605#41—41no—
606#41—41no—
607#41C2×C22⋊C414yes—
608#41#11714yes—
609#41C4×D414yes—
610#41C4×D414yes—
611C2×Q8—21no—
612C2×Q8—21no—
613C2×Q8—21no—
614C2×Q8—21no—
615C2×Q8—24no—
616C2×Q8—28no—
617C2×Q8—21no—
618C2×Q8—21no—
619C2×Q8—21no—
620C2×Q8—21no—
621C2×Q8—42no—
622C2×Q8—42no—
623C2×Q8—44no—
624C2×Q8—44no—
625C2×Q8—44no—
626C2×Q8C2×C4212yes—
627C2×Q8C2×C4212yes—
628C2×Q8C4×D412yes—
629C2×Q8C4×D412yes—
630C2×D4—22no—
631C2×D4—22no—
632C2×D4—22no—
633C2×D4—22no—
634C2×D4—22no—
635C2×D4—22no—
636C2×D4—28no—
637C2×D4—22no—
638C2×D4—22no—
639C2×D4—24no—
640C2×D4—24no—
641C2×D4—21no—
642C2×D4—21no—
643C2×D4—21no—
644C2×D4—21no—
645C2×D4—21no—
646C2×D4—21no—
647C2×D4—21no—
648C2×D4—21no—
649C2×D4—24no—
650C2×D4—44no—
651C2×D4—44no—
652C2×D4—44no—
653C2×D4—42no—
654C2×D4—42no—
655C2×D4—42no—
656C2×D4—42no—
657C2×D4—48no—
658C2×D4—48no—
659C2×D4—48no—
660C2×D4—48no—
661C2×D4—42no—
662C2×D4—42no—
663C2×D4—41no—
664C2×D4—41no—
665C2×D4—41no—
666C2×D4—41no—
667C2×D4C2×C4212yes—
668C2×D4C2×C4212yes—
669C2×D4C4×D412yes—
670C2×D4C4×D412yes—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—22no—
677C22×C4—22no—
678C22×C4—22no—
679C22×C4—22no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—22no—
685C22×C4—22no—
686C22×C4—22no—
687C22×C4—22no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—22no—
693C22×C4—22no—
694C22×C4—22no—
695C22×C4—22no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—22no—
701C22×C4—22no—
702C22×C4—22no—
703C22×C4—22no—
704C22×C4—22no—
705C22×C4—22no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—22no—
711C22×C4—22no—
712C22×C4—22no—
713C22×C4—22no—
714C22×C4—24no—
715C22×C4—21no—
716C22×C4—22no—
717C22×C4—22no—
718C22×C4—22no—
719C22×C4—22no—
720C22×C4—22no—
721C22×C4—22no—
722C22×C4—24no—
723C22×C4—22no—
724C22×C4—22no—
725C22×C4—22no—
726C22×C4—22no—
727C22×C4—24no—
728C22×C4—24no—
729C22×C4—24no—
730C22×C4—22no—
731C22×C4—22no—
732C22×C4—22no—
733C22×C4—22no—
734C22×C4—42no—
735C22×C4—42no—
736C22×C4—42no—
737C22×C4—48no—
738C22×C4—48no—
739C22×C4—48no—
740C22×C4—48no—
741C22×C4—42no—
742C22×C4—42no—
743C22×C4—42no—
744C22×C4—42no—
745C22×C4—42no—
746C22×C4—42no—
747C22×C4—44no—
748C22×C4—44no—
749C22×C4—44no—
750C22×C4—42no—
751C22×C4—42no—
752C22×C4—42no—
753C22×C4—41no—
754C22×C4—41no—
755C22×C4—41no—
756C22×C4—41no—
757C22×C4—41no—
758C22×C4—41no—
759C22×C4—42no—
760C22×C4—42no—
761C22×C4—42no—
762C22×C4—42no—
763C22×C4—41no—
764C22×C4—41no—
765C22×C4—41no—
766C22×C4—41no—
767C22×C4—44no—
768C22×C4—82no—
769C22×C4—82no—
770C22×C4C2×C4212yes—
771C22×C4C2×C4212yes—
772C22×C4C2×C22⋊C412yes—
773C22×C4C2×C22⋊C412yes—
774C22×C4C2×C22⋊C412yes—
775C22×C4C2×C22⋊C411yescharacteristic
776C22×C4C2×C22⋊C411yescharacteristic
777C22×C4C2×C22⋊C412yes—
778C22×C4#11712yes—
779C22×C4#11712yes—
780C22×C4C4×D412yes—
781C22×C4C4×D412yes—
782C22×C4C4×D412yes—
783C22×C4C4×D412yes—
784C22×C4C4×D412yes—
785C22×C4C4×D412yes—
786C22×C4C23×C411yescharacteristic
787C22×C4C23×C411yescharacteristic
788C22×C4C23×C411yescharacteristic
789C22×C4C22×D411yescharacteristic
790C22×C4C22×D411yescharacteristic
791C22×C4C22×D411yescharacteristic
792C22×C4C2×#4111yescharacteristic
793C22×C4C2×#4111yescharacteristic
794C22×C4C2×#4111yescharacteristic
795C22×C4C2×#4111yescharacteristic
796C22×C4H(5,𝔽2)11yescharacteristic
797C22×C4H(5,𝔽2)11yescharacteristic
798C22×C4H(5,𝔽2)11yescharacteristic
799C22×C4H(5,𝔽2)11yescharacteristic
800M16—22no—
801M16—22no—
802M16—22no—
803M16—22no—
804M16—22no—
805M16—22no—
806M16—22no—
807M16—22no—
808M16—22no—
809M16—48no—
810M16—41no—
811M16—41no—
812M16—41no—
813M16—41no—
814M16—41no—
815M16—41no—
816M16C2×C22⋊C414yescomplemented
817C2×C8—22no—
818C2×C8—22no—
819C2×C8—22no—
820C2×C8—22no—
821C2×C8—22no—
822C2×C8—22no—
823C2×C8—48no—
824C2×C8—41no—
825C2×C8—41no—
826C2×C8—41no—
827C2×C8—41no—
828C2×C8—41no—
829C2×C8—41no—
830C4⋊C4—22no—
831C4⋊C4—22no—
832C4⋊C4—22no—
833C4⋊C4—22no—
834C4⋊C4—48no—
835C4⋊C4—44no—
836C4⋊C4—44no—
837C22⋊C4—24no—
838C22⋊C4—24no—
839C22⋊C4—42no—
840C22⋊C4—42no—
841C22⋊C4—48no—
842C22⋊C4—44no—
843C22⋊C4—44no—
844C22⋊C4—48no—
845C22⋊C4—44no—
846C22⋊C4—44no—
847C22⋊C4—41no—
848C22⋊C4—41no—
849C22⋊C4—41no—
850C22⋊C4—41no—
851C22⋊C4—44no—
852C22⋊C4—82no—
853C22⋊C4—82no—
854C22⋊C4—82no—
855C42—22no—
856C42—22no—
857C42—22no—
858C42—22no—
859C42—22no—
860C42—21no—
861C42—21no—
862C42—21no—
863C42—21no—
864C42—21no—
865C42—21no—
866C42—21no—
867C42—21no—
868C42—22no—
869C42—22no—
870C42—22no—
871C42—22no—
872C42—22no—
873C42—22no—
874C42—22no—
875C42—22no—
876C42—44no—
877C42—44no—
878C42—416no—
879C42—41no—
880C42—41no—
881C42—41no—
882C42—41no—
883C42—41no—
884C42—41no—
885C42—41no—
886C42—41no—
887C42—41no—
888C42—41no—
889C42C2×C22⋊C414yescomplemented
890C23—22no—
891C23—22no—
892C23—22no—
893C23—22no—
894C23—21no—
895C23—21no—
896C23—21no—
897C23—21no—
898C23—22no—
899C23—22no—
900C23—22no—
901C23—22no—
902C23—22no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—22no—
907C23—22no—
908C23—42no—
909C23—42no—
910C23—42no—
911C23—42no—
912C23—48no—
913C23—48no—
914C23—42no—
915C23—42no—
916C23—41no—
917C23—41no—
918C23—42no—
919C23—42no—
920C23—82no—
921C23—82no—
922C23—82no—
923C23—82no—
924C23—84no—
925C23—88no—
926C23—88no—
927C23C4×C22⋊C412yes—
928C23C4×C22⋊C412yes—
929C23C22×C22⋊C411yescharacteristic
930C23C2×C4×D411yescharacteristic
931C23C2×C4×D411yescharacteristic
932C23D4211yescharacteristic
933C23D4211yescharacteristic
934C23#54611yescharacteristic
935C23#54611yescharacteristic
936Q8—22no—
937Q8—22no—
938Q8—22no—
939Q8—22no—
940Q8—22no—
941Q8—48no—
942Q8—41no—
943Q8—41no—
944Q8C4×C22⋊C414yes—
945D4—24no—
946D4—24no—
947D4—24no—
948D4—24no—
949D4—22no—
950D4—22no—
951D4—22no—
952D4—22no—
953D4—22no—
954D4—48no—
955D4—48no—
956D4—48no—
957D4—42no—
958D4—42no—
959D4—42no—
960D4—42no—
961D4—41no—
962D4—41no—
963D4C4×C22⋊C414yes—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—22no—
968C2×C4—21no—
969C2×C4—21no—
970C2×C4—21no—
971C2×C4—21no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—24no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—24no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—24no—
992C2×C4—24no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—24no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—24no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—48no—
1010C2×C4—44no—
1011C2×C4—44no—
1012C2×C4—48no—
1013C2×C4—48no—
1014C2×C4—44no—
1015C2×C4—44no—
1016C2×C4—44no—
1017C2×C4—44no—
1018C2×C4—42no—
1019C2×C4—42no—
1020C2×C4—42no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—42no—
1024C2×C4—42no—
1025C2×C4—42no—
1026C2×C4—42no—
1027C2×C4—42no—
1028C2×C4—42no—
1029C2×C4—42no—
1030C2×C4—42no—
1031C2×C4—42no—
1032C2×C4—42no—
1033C2×C4—42no—
1034C2×C4—42no—
1035C2×C4—42no—
1036C2×C4—42no—
1037C2×C4—42no—
1038C2×C4—42no—
1039C2×C4—42no—
1040C2×C4—88no—
1041C2×C4—82no—
1042C2×C4—82no—
1043C2×C4—88no—
1044C2×C4—82no—
1045C2×C4—82no—
1046C2×C4—82no—
1047C2×C4—82no—
1048C2×C4C4×C22⋊C412yes—
1049C2×C4C4×C22⋊C412yes—
1050C2×C4#42114yescomplemented
1051C2×C4C22×C4211yescharacteristic
1052C2×C4C22×C22⋊C411yescharacteristic
1053C2×C4C2×#11711yescharacteristic
1054C2×C4C2×#11711yescharacteristic
1055C2×C4C2×C4×D411yescharacteristic
1056C2×C4C2×C4×D411yescharacteristic
1057C2×C4C2×C4×D411yescharacteristic
1058C2×C4C2×C4×D411yescharacteristic
1059C2×C4C2×C4×D411yescharacteristic
1060C2×C4C2×C4×D411yescharacteristic
1061C2×C4#51811yescharacteristic
1062C2×C4#51811yescharacteristic
1063C2×C4#51811yescharacteristic
1064C2×C4#51811yescharacteristic
1065C2×C4#51811yescharacteristic
1066C2×C4#51811yescharacteristic
1067C2×C4D4211yescharacteristic
1068C2×C4D4211yescharacteristic
1069C2×C4#54611yescharacteristic
1070C2×C4#54611yescharacteristic
1071C2×C4#54611yescharacteristic
1072C2×C4#54611yescharacteristic
1073C2×C4#54611yescharacteristic
1074C2×C4#54611yescharacteristic
1075C2×C4#55111yescharacteristic
1076C2×C4#55111yescharacteristic
1077C2×C4#55111yescharacteristic
1078C2×C4#55111yescharacteristic
1079C8—24no—
1080C8—42no—
1081C8—42no—
1082C8—42no—
1083C22—22no—
1084C22—22no—
1085C22—22no—
1086C22—22no—
1087C22—21no—
1088C22—21no—
1089C22—21no—
1090C22—21no—
1091C22—22no—
1092C22—22no—
1093C22—22no—
1094C22—22no—
1095C22—22no—
1096C22—22no—
1097C22—24no—
1098C22—44no—
1099C22—42no—
1100C22—42no—
1101C22—44no—
1102C22—42no—
1103C22—42no—
1104C22—42no—
1105C22—42no—
1106C22—42no—
1107C22—42no—
1108C22—42no—
1109C22—82no—
1110C22—82no—
1111C22—82no—
1112C22—82no—
1113C22—816no—
1114C22—82no—
1115C22—82no—
1116C22C2×C4×C22⋊C411yescharacteristic
1117C22D4×C22⋊C411yescharacteristic
1118C22D4×C22⋊C411yescharacteristic
1119C22D4×C22⋊C411yescharacteristic
1120C22#234211yescharacteristic
1121C22#235811yescharacteristic
1122C22#235811yescharacteristic
1123C22C2×#42112yes—
1124C22#290112yes—
1125C4—24no—
1126C4—22no—
1127C4—22no—
1128C4—24no—
1129C4—44no—
1130C4—44no—
1131C4—42no—
1132C4—42no—
1133C4—42no—
1134C4—42no—
1135C4—82no—
1136C4—82no—
1137C4—82no—
1138C4—82no—
1139C4C2×C4×C22⋊C411yescharacteristic
1140C4#227311yescharacteristic
1141C4D4×C22⋊C411yescharacteristic
1142C4#234211yescharacteristic
1143C4#234211yescharacteristic
1144C4#234211yescharacteristic
1145C4#235811yescharacteristic
1146C4#235811yescharacteristic
1147C2—21no—
1148C2—21no—
1149C2—21no—
1150C2—21no—
1151C2—42no—
1152C2—42no—
1153C2—44no—
1154C2—82no—
1155C2C22⋊C4211yescharacteristic
1156C2C4×#42111yescharacteristic
1157C2#2040511yescharacteristic
1158C2#2243412yes—
1159C2#2243512yes—
subgroupG/H
centerC22×C4C22×D4
commutatorC2×C4C22×C42
Frattini, cosocleC23×C4C24
socleC23C22×C22⋊C4
prime radicalC23×#41C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4 ◁ C2×C4×C22⋊C4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
4. C2×#1759C2semidirect
5. C2×C4×#104C2semidirect
6. C22⋊C4×M16C2semidirect
7. #13761C2semidirect
8. #10933C2semidirect
9. #10933C2semidirect
10. #10924C2semidirect
11. #10923C2semidirect
12. #10790C2semidirect
13. #10790C2semidirect
14. #10732C2semidirect
15. #10720C2semidirect
23. C2×#421C4semidirect
33. C2×C4×M16C22semidirect
34. C2×C4×M16C22semidirect
35. #2341C4semidirect
36. Q8×C22⋊C4C4semidirect
38. #2339C4semidirect
40. D4×C22⋊C4C4semidirect
50. C2×#376C22semidirect
51. C2×C43C22semidirect
52. #1789C4semidirect
59. C2×#339C22semidirect
60. C2×#339C22semidirect
61. C2×#339C22semidirect
62. C2×#339C22semidirect
63. C2×#339C22semidirect
64. C2×#339C22semidirect
65. C2×#339C22semidirect
66. C2×#339C22semidirect
67. #1728C22semidirect
68. #1728C22semidirect
71. C4×#95C22semidirect
72. C4×#95C22semidirect
102. C22×M16C2×C4semidirect
129. C2×#117C2×C4semidirect
165. C2×#104C2×C4semidirect
166. C2×#104C2×C4semidirect
167. C2×#104C2×C4semidirect
168. C2×#104C2×C4semidirect
172. #407C2×C4semidirect
216. C4×C22⋊C4C2×C4semidirect
299. C2×#41C42semidirect
300. C2×#41C42semidirect
315. C22×Q8C42semidirect
334. C22×D4C42semidirect
524. #104C22⋊C4semidirect
816. M16C2×C22⋊C4semidirect
889. C42C2×C22⋊C4semidirect
1050. C2×C4#421semidirect

Maximal subgroups

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

subgroupindex
C22×#4212
C22⋊C4×#412
C2×#17892
C2×#17592
C2×C4×#1042
C22⋊C4×M162
#137612
#109332
#109242
#109232
#107902
#107322
#107202