Finite Group Databasebeta

← #6377773

Subgroups — #6377773

Order 512.

1989 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#60782C211yesmaximal, characteristic
2#60204C211yesmaximal, characteristic, complemented
3C2×#2931C211yesmaximal, characteristic, complemented
4#22280C212yesmaximal, complemented
5#22234C212yesmaximal, complemented
6#22166C214yesmaximal, complemented
7#22061C214yesmaximal, complemented
8#21993C211yesmaximal, characteristic, complemented
9#21856C211yesmaximal, characteristic, complemented
10#21815C211yesmaximal, characteristic, complemented
11#21706C212yesmaximal, complemented
12#21660C212yesmaximal, complemented
13#21518C214yesmaximal, complemented
14#21467C214yesmaximal, complemented
15#20473C211yesmaximal, characteristic, complemented
16C22×#131C2212yes—
17#3444C2211yescharacteristic
18C2×#532C2211yescharacteristic
19#3212C414yescomplemented
20#3211C414yescomplemented
21#3210C412yescomplemented
22#3209C411yescharacteristic, complemented
23#3208C411yescharacteristic, complemented
24#3207C412yescomplemented
25#3206C411yescharacteristic, complemented
26#3205C411yescharacteristic, complemented
27#3147C2212yes—
28#3131C2212yes—
29#3035C2214yes—
30#3002C2214yes—
31#2966—21no—
32#2966—21no—
33#2966—21no—
34#2966—21no—
35#2965—21no—
36#2965—21no—
37C8×#41—21no—
38C8×#41—21no—
39#2960C2211yescharacteristic, complemented
40#2960C2211yescharacteristic, complemented
41C2×#444C2218yescomplemented
42#2931—21no—
43#2931—21no—
44#2931—21no—
45#2931—21no—
46#2931C2212yes—
47#2931C2212yes—
48#2931C2212yes—
49#2931C2212yes—
50#2931C2211yescharacteristic, complemented
51#2931C2211yescharacteristic, complemented
52#2929C2212yes—
53#2929C2212yes—
54C2×#436—21no—
55C2×#436—21no—
56C2×C8×D4—21no—
57C2×C8×D4—21no—
58#2922C2212yescomplemented
59#2920C2211yescharacteristic
60C2×#431C2211yescharacteristic
61C2×#423C2211yescharacteristic
62C2×#408C2212yes—
63C4×#131C2212yescomplemented
64C22×C4×C8C2211yescharacteristic
65C4×#117C2211yescharacteristic
66#1994C2212yescomplemented
67#1980C2214yes—
68#1975C2218yescomplemented
69#1962C2212yes—
70#1962C2212yes—
71#1962C2212yescomplemented
72#1950C2214yescomplemented
73#1938C2218yescomplemented
74#1929C2218yescomplemented
75#1876C2218yescomplemented
76#1876C2218yescomplemented
77#1871C2214yes—
78#1866C2218yescomplemented
79#1855C2214yes—
80#1848C2212yescomplemented
81#1837C2212yescomplemented
82#1806C2214yescomplemented
83#1789C2214yes—
84#1770C2212yescomplemented
85#1770C2212yescomplemented
86#1765C2218yescomplemented
87#1752C2212yes—
88#1752C2212yes—
89#1744C2212yescomplemented
90C4×#97C2212yescomplemented
91C22×#41C2312yes—
92C2×#135C2318yes—
93C2×#131—22no—
94C2×#131—22no—
95C2×#131—48no—
96C2×#131C2312yes—
97C2×#131C2314yes—
98C2×#131C2312yes—
99C2×#131C2314yes—
100C22×M16—22no—
101C22×M16C2312yes—
102C23×C8—22no—
103C23×C8C2311yescharacteristic
104C23×C8C2311yescharacteristic
105#533C2×C411yescharacteristic
106#533C2×C411yescharacteristic
107#533C2311yescharacteristic
108#532—21no—
109#532—21no—
110#532—21no—
111#532—21no—
112#532C2×C412yes—
113#532C2×C412yes—
114#532C2×C411yescharacteristic
115#532C2×C411yescharacteristic
116#532C2312yes—
117#532C2311yescharacteristic
118#532C2312yes—
119C2×C4⋊Q8C2×C411yescharacteristic
120C2×#127C2×C411yescharacteristic
121#529—21no—
122#529—21no—
123#529—21no—
124#529—21no—
125#529C2×C412yes—
126#529C2×C412yes—
127C2×#124C2×C412yes—
128#525—21no—
129#525—21no—
130#525C2312yes—
131C2×#121—21no—
132C2×#121—21no—
133C4×#41—21no—
134C4×#41—21no—
135C4×#41C2312yes—
136C2×C4×D4—21no—
137C2×C4×D4—21no—
138C2×#117—21no—
139C22×C42C2311yescharacteristic
140#495C2×C418yes—
141#494C2×C412yes—
142#493C2×C412yes—
143#492C2×C412yes—
144#492C2×C412yes—
145#488C2×C418yes—
146#487C2×C412yes—
147#487C2×C412yes—
148#486C2×C412yes—
149#486C2×C412yes—
150#464C2×C418yes—
151#463C2×C418yes—
152#462C2×C414yes—
153#461C2×C414yes—
154#460C2×C414yes—
155#459C2×C414yes—
156#452C2×C418yes—
157#451C2×C414yes—
158#450C2×C414yes—
159#449C2×C418yes—
160#448C2×C414yes—
161#447C2×C414yes—
162#446—21no—
163#446—21no—
164#446—21no—
165#446—21no—
166C8×Q8—21no—
167C8×Q8—21no—
168C8×Q8—21no—
169C8×Q8—21no—
170#444—416no—
171#436—22no—
172#436—22no—
173#436—22no—
174#436—22no—
175#436—22no—
176#436—22no—
177#436—22no—
178#436—22no—
179#436—21no—
180#436—21no—
181#436—21no—
182#436—21no—
183#435—22no—
184#435—22no—
185#435—22no—
186#435—22no—
187C8×D4—22no—
188C8×D4—22no—
189C8×D4—22no—
190C8×D4—22no—
191C8×D4—22no—
192C8×D4—22no—
193C8×D4—22no—
194C8×D4—22no—
195C8×D4—22no—
196C8×D4—22no—
197C8×D4—22no—
198C8×D4—22no—
199C8×D4—21no—
200C8×D4—21no—
201C8×D4—21no—
202C8×D4—21no—
203#433—22no—
204#433—22no—
205#432—21no—
206#432—21no—
207#431—21no—
208#431—21no—
209#431—22no—
210#431—22no—
211#431C2×C411yescharacteristic
212#431C2×C411yescharacteristic
213#431C2×C412yes—
214#431C2×C412yes—
215#431C2×C412yes—
216C2×#108C2318yes—
217#424C2312yes—
218#424C2312yes—
219#423—21no—
220#423—21no—
221#423C2312yes—
222#423C2311yescharacteristic
223#423C2312yes—
224#423C2311yescharacteristic
225C2×C4⋊C8—21no—
226C2×C4⋊C8—21no—
227C2×C4⋊C8C2312yes—
228C2×#104C2318yes—
229C2×#104C2318yes—
230C2×#104C2318yes—
231#416C2318yes—
232#408—22no—
233#408—22no—
234#408C2314yes—
235#408C2314yes—
236#408C2312yes—
237#408C2312yes—
238#407C2312yes—
239C2×C22⋊C8—22no—
240C2×C22⋊C8—22no—
241C2×C22⋊C8C2312yes—
242#405—22no—
243#405—22no—
244#405C2312yes—
245#405C2312yes—
246C4×M16—22no—
247C4×M16C2312yes—
248C2×#97C2314yes—
249C2×#97C2314yes—
250C2×C4×C8—22no—
251C2×C4×C8D411yescharacteristic
252C2×C4×C8D411yescharacteristic
253C2×C4×C8D411yescharacteristic
254C2×C4×C8D411yescharacteristic
255C2×C4×C8D411yescharacteristic
256C2×C4×C8D411yescharacteristic
257C2×C4×C8D411yescharacteristic
258C2×C4×C8D411yescharacteristic
259C2×C4×C8C2312yes—
260C2×C4×C8C2311yescharacteristic
261C2×C4×C8C2311yescharacteristic
262C2×C4×C8C2311yescharacteristic
263C2×C4×C8C2311yescharacteristic
264C4×C4⋊C4—21no—
265C4×C4⋊C4C2312yes—
266C4×C22⋊C4—21no—
267C4×C22⋊C4C2312yes—
268#376—21no—
269C43C2312yes—
270#341C2318yes—
271#339C2318yes—
272#336C2314yes—
273#336C2314yes—
274C2×#41—21no—
275C2×#41—21no—
276C2×#41—22no—
277C2×#41—22no—
278C2×#41—44no—
279C2×#41—44no—
280C2×#41C22×C414yes—
281C2×#41C2412yes—
282C2×#41C2414yes—
283C22×Q8C22×C412yes—
284C22×D4—22no—
285C22×D4—21no—
286C22×D4—21no—
287C22×D4C22×C412yes—
288C23×C4—22no—
289C23×C4#4111yescharacteristic
290C23×C4#4111yescharacteristic
291C23×C4C2411yescharacteristic
292#135—48no—
293#135—48no—
294C2×Q16C22×C418yes—
295C2×SD16C22×C418yes—
296C2×SD16C22×C418yes—
297C2×D8C22×C418yes—
298#131—216no—
299#131—28no—
300#131—48no—
301#131—44no—
302#131—48no—
303#131—48no—
304C2×M16—22no—
305C2×M16—24no—
306C2×M16—24no—
307C2×M16—22no—
308C2×M16—22no—
309C2×M16—48no—
310C2×M16—44no—
311C2×M16C2414yes—
312C2×M16C2412yes—
313C2×M16C2412yes—
314C22×C8—24no—
315C22×C8—22no—
316C22×C8—24no—
317C22×C8—24no—
318C22×C8—22no—
319C22×C8—22no—
320C22×C8—42no—
321C22×C8—48no—
322C22×C8C2×D411yescharacteristic
323C22×C8C2×D411yescharacteristic
324C22×C8C2×D411yescharacteristic
325C22×C8C2×D411yescharacteristic
326C22×C8C2×D411yescharacteristic
327C22×C8C2×D411yescharacteristic
328C22×C8C2×D411yescharacteristic
329C22×C8C2×D411yescharacteristic
330C22×C8C2414yes—
331C22×C8C2411yescharacteristic
332C22×C8C2411yescharacteristic
333C22×C8C2411yescharacteristic
334C22×C8C2411yescharacteristic
335C4⋊Q8—21no—
336C4⋊Q8—21no—
337C4⋊Q8C22×C412yes—
338C4⋊Q8C22×C412yes—
339C4⋊Q8C22×C411yescharacteristic
340C4⋊Q8C22×C411yescharacteristic
341C4⋊Q8C22×C411yescharacteristic
342#127—21no—
343#127—21no—
344#127C22×C412yes—
345#127C22×C412yes—
346#127C22×C411yescharacteristic
347#126—22no—
348#126—22no—
349#125—21no—
350#125—21no—
351#125C22×C412yes—
352#124—22no—
353#124—22no—
354#124—21no—
355#124—21no—
356#124C22×C414yes—
357#124C22×C414yes—
358#124C22×C412yes—
359#123—22no—
360#123—22no—
361#123—22no—
362C22⋊Q8—21no—
363C22⋊Q8—21no—
364C22⋊Q8—21no—
365C22⋊Q8—21no—
366C22⋊Q8C22×C412yes—
367C22⋊Q8C22×C412yes—
368#121—22no—
369#121—22no—
370#121—22no—
371#121—22no—
372#121—21no—
373#121—21no—
374#121—22no—
375#121—22no—
376#121—22no—
377#121—22no—
378#121—21no—
379#121—21no—
380#121C22×C412yes—
381#121C22×C412yes—
382#120—22no—
383C4×Q8—21no—
384C4×Q8—21no—
385C4×Q8—21no—
386C4×Q8—21no—
387C4×Q8C22×C412yes—
388C4×Q8C22×C412yes—
389C4×D4—22no—
390C4×D4—22no—
391C4×D4—22no—
392C4×D4—22no—
393C4×D4—22no—
394C4×D4—22no—
395C4×D4—22no—
396C4×D4—22no—
397C4×D4—22no—
398C4×D4—22no—
399C4×D4—21no—
400C4×D4—21no—
401C4×D4—22no—
402C4×D4—22no—
403C4×D4—22no—
404C4×D4—22no—
405C4×D4—21no—
406C4×D4—21no—
407C4×D4C22×C412yes—
408C4×D4C22×C412yes—
409#117—21no—
410#117—21no—
411#117—22no—
412#117—22no—
413#117—22no—
414#117—44no—
415#117C2412yes—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—22no—
419C2×C22⋊C4—22no—
420C2×C22⋊C4—22no—
421C2×C22⋊C4—22no—
422C2×C42—22no—
423C2×C42—22no—
424C2×C42—22no—
425C2×C42C22×C411yescharacteristic
426C2×C42C22×C411yescharacteristic
427C2×C42C22×C411yescharacteristic
428C2×C42C22×C411yescharacteristic
429C2×C42C2×D411yescharacteristic
430C2×C42C2×D411yescharacteristic
431C2×C42C2×D411yescharacteristic
432C2×C42C2×D411yescharacteristic
433C2×C42#4111yescharacteristic
434C2×C42#4111yescharacteristic
435C2×C42C2414yes—
436C2×C42C2411yescharacteristic
437C2×C42C2411yescharacteristic
438#108—48no—
439C4⋊C8—22no—
440C4⋊C8—22no—
441C4⋊C8—22no—
442C4⋊C8—22no—
443C4⋊C8—22no—
444C4⋊C8—22no—
445C4⋊C8—22no—
446C4⋊C8—22no—
447C4⋊C8—21no—
448C4⋊C8—21no—
449C4⋊C8—21no—
450C4⋊C8—21no—
451C4⋊C8C22×C412yes—
452C4⋊C8C22×C412yes—
453C4⋊C8C22×C414yes—
454#104—48no—
455#104—48no—
456#104—48no—
457#103C22×C418yes—
458#103C22×C418yes—
459#102C22×C418yes—
460#102C22×C418yes—
461C22⋊C8—22no—
462C22⋊C8—22no—
463C22⋊C8—24no—
464C22⋊C8—24no—
465C22⋊C8—24no—
466C22⋊C8—24no—
467C22⋊C8—22no—
468C22⋊C8—22no—
469C22⋊C8—22no—
470C22⋊C8—22no—
471C22⋊C8C22×C412yes—
472C22⋊C8C22×C412yes—
473C22⋊C8C22×C414yes—
474#97—22no—
475#97—22no—
476#97—28no—
477#97—22no—
478#97—44no—
479C4×C8—22no—
480C4×C8—22no—
481C4×C8—22no—
482C4×C8C22×C412yes—
483C4×C8C22×C412yes—
484C4×C8C22×C414yes—
485C4×C8C2×D411yescharacteristic
486C4×C8C2×D411yescharacteristic
487C4×C8C2×D411yescharacteristic
488C4×C8C2×D411yescharacteristic
489C4×C8C2×D411yescharacteristic
490C4×C8C2×D411yescharacteristic
491C4×C8C2×D411yescharacteristic
492C4×C8C2×D411yescharacteristic
493C4×C8C2×D411yescharacteristic
494C4×C8C2×D411yescharacteristic
495C4×C8C2×D411yescharacteristic
496C4×C8C2×D411yescharacteristic
497C4×C8C2×D411yescharacteristic
498C4×C8C2×D411yescharacteristic
499C4×C8C2×D411yescharacteristic
500C4×C8C2×D411yescharacteristic
501#95—22no—
502#95—22no—
503C24—22no—
504C24C2×#4111yescharacteristic
505#41—24no—
506#41—28no—
507#41—28no—
508#41—24no—
509#41—48no—
510#41—44no—
511#41—44no—
512#41—48no—
513#41—44no—
514#41—44no—
515C2×Q8—21no—
516C2×Q8—21no—
517C2×Q8—22no—
518C2×Q8—44no—
519C2×Q8C23×C414yes—
520C2×Q8C23×C412yes—
521C2×D4—22no—
522C2×D4—22no—
523C2×D4—24no—
524C2×D4—22no—
525C2×D4—24no—
526C2×D4—21no—
527C2×D4—21no—
528C2×D4—22no—
529C2×D4—22no—
530C2×D4—22no—
531C2×D4—22no—
532C2×D4—22no—
533C2×D4—44no—
534C2×D4—44no—
535C2×D4—48no—
536C2×D4—44no—
537C2×D4C23×C414yes—
538C2×D4C23×C412yes—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—24no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—24no—
546C22×C4—22no—
547C22×C4—24no—
548C22×C4—24no—
549C22×C4—42no—
550C22×C4—44no—
551C22×C4—44no—
552C22×C4C4×D411yescharacteristic
553C22×C4C4×D411yescharacteristic
554C22×C4C4×D411yescharacteristic
555C22×C4C4×D411yescharacteristic
556C22×C4C4×D411yescharacteristic
557C22×C4C4×D411yescharacteristic
558C22×C4C4×D411yescharacteristic
559C22×C4C4×D411yescharacteristic
560C22×C4C23×C411yescharacteristic
561C22×C4C23×C411yescharacteristic
562C22×C4C22×D411yescharacteristic
563C22×C4C22×D411yescharacteristic
564C22×C4C2×#4111yescharacteristic
565C22×C4C2×#4111yescharacteristic
566C22×C4C2×#4111yescharacteristic
567C22×C4C2×#4111yescharacteristic
568C22×C4C2×#4111yescharacteristic
569C22×C4C2511yescharacteristic
570Q16—48no—
571SD16—48no—
572SD16—48no—
573D8—48no—
574M16—24no—
575M16—28no—
576M16—24no—
577M16—48no—
578M16—44no—
579M16—44no—
580M16—48no—
581M16—44no—
582C2×C8—24no—
583C2×C8—22no—
584C2×C8—22no—
585C2×C8—24no—
586C2×C8—22no—
587C2×C8—22no—
588C2×C8—22no—
589C2×C8—22no—
590C2×C8—22no—
591C2×C8—22no—
592C2×C8—22no—
593C2×C8—24no—
594C2×C8—41no—
595C2×C8—41no—
596C2×C8—41no—
597C2×C8—41no—
598C2×C8—48no—
599C2×C8—44no—
600C2×C8—44no—
601C2×C8—48no—
602C2×C8—44no—
603C2×C8C23×C414yes—
604C2×C8C23×C414yes—
605C2×C8C22×D411yescharacteristic
606C2×C8C22×D411yescharacteristic
607C2×C8C22×D411yescharacteristic
608C2×C8C22×D411yescharacteristic
609C2×C8C22×D411yescharacteristic
610C2×C8C22×D411yescharacteristic
611C2×C8C22×D411yescharacteristic
612C2×C8C22×D411yescharacteristic
613C2×C8H(5,𝔽2)14yes—
614C4⋊C4—22no—
615C4⋊C4—22no—
616C4⋊C4—22no—
617C4⋊C4—22no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—22no—
623C4⋊C4—22no—
624C4⋊C4—22no—
625C4⋊C4—22no—
626C4⋊C4—22no—
627C4⋊C4—22no—
628C4⋊C4—44no—
629C4⋊C4C23×C412yes—
630C4⋊C4C23×C412yes—
631C22⋊C4—22no—
632C22⋊C4—22no—
633C22⋊C4—22no—
634C22⋊C4—24no—
635C22⋊C4—24no—
636C22⋊C4—24no—
637C22⋊C4—24no—
638C22⋊C4—22no—
639C22⋊C4—22no—
640C22⋊C4—22no—
641C22⋊C4—22no—
642C22⋊C4—22no—
643C22⋊C4—22no—
644C22⋊C4—44no—
645C42—22no—
646C42—22no—
647C42—22no—
648C42—24no—
649C42—24no—
650C42—44no—
651C42—44no—
652C42C4×D411yescharacteristic
653C42C4×D411yescharacteristic
654C42C4×D411yescharacteristic
655C42C4×D411yescharacteristic
656C42C4×D411yescharacteristic
657C42C4×D411yescharacteristic
658C42C4×D411yescharacteristic
659C42C4×D411yescharacteristic
660C42C23×C411yescharacteristic
661C42C23×C411yescharacteristic
662C42C23×C411yescharacteristic
663C42C23×C411yescharacteristic
664C42C22×D411yescharacteristic
665C42C22×D411yescharacteristic
666C42C22×D411yescharacteristic
667C42C22×D411yescharacteristic
668C23—22no—
669C23—22no—
670C23—22no—
671C23—24no—
672C23—41no—
673C23—44no—
674C23—44no—
675C23—44no—
676C23C2×C4×D411yescharacteristic
677C23C2×C4×D411yescharacteristic
678C23C22×#4111yescharacteristic
679Q8—24no—
680Q8—28no—
681Q8—44no—
682Q8—42no—
683Q8—42no—
684D4—24no—
685D4—28no—
686D4—44no—
687D4—44no—
688D4—48no—
689D4—44no—
690D4—48no—
691D4—44no—
692D4—44no—
693D4—44no—
694D4—44no—
695D4—42no—
696D4—44no—
697D4—42no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—24no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—48no—
721C2×C4—44no—
722C2×C4—44no—
723C2×C4—44no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—44no—
727C2×C4—44no—
728C2×C4—44no—
729C2×C4—44no—
730C2×C4—44no—
731C2×C4#44414yescomplemented
732C2×C4C2×C4×D411yescharacteristic
733C2×C4C2×C4×D411yescharacteristic
734C2×C4C2×C4×D411yescharacteristic
735C2×C4C2×C4×D411yescharacteristic
736C2×C4C2×C4×D411yescharacteristic
737C2×C4C2×C4×D411yescharacteristic
738C2×C4C2×C4×D411yescharacteristic
739C2×C4C2×C4×D411yescharacteristic
740C2×C4C2×C4×D411yescharacteristic
741C2×C4C2×C4×D411yescharacteristic
742C2×C4C24×C411yescharacteristic
743C2×C4C23×D411yescharacteristic
744C2×C4C2×H(5,𝔽2)12yes—
745C2×C4#58512yes—
746C8—24no—
747C8—24no—
748C8—21no—
749C8—21no—
750C8—21no—
751C8—21no—
752C8—21no—
753C8—21no—
754C8—44no—
755C8—42no—
756C8—42no—
757C8#53512yes—
758C8#53512yes—
759C22—21no—
760C22—21no—
761C22—21no—
762C22—21no—
763C22—21no—
764C22—21no—
765C22—21no—
766C22—44no—
767C22—42no—
768C22—44no—
769C22—42no—
770C22—44no—
771C22—44no—
772C22—42no—
773C22—88no—
774C22C2×#44412yes—
775C22C22×C4×D411yescharacteristic
776C22#346012yes—
777C4—21no—
778C4—21no—
779C4—21no—
780C4—21no—
781C4—21no—
782C4—21no—
783C4—21no—
784C4—42no—
785C4—42no—
786C4—44no—
787C4—42no—
788C4—84no—
789C4C2×#44412yes—
790C4C2×#44412yes—
791C4#295512yes—
792C4C4×H(5,𝔽2)12yes—
793C4C2×#53511yescharacteristic
794C4#344911yescharacteristic
795C2—22no—
796C2—22no—
797C2—41no—
798C2—82no—
799C2—84no—
800C2C4×#53511yescharacteristic
801C2C22×#44411yescharacteristic
802C2C2×#295511yescharacteristic
subgroupG/H
centerC2×C4C23×D4
commutatorC2×C4C24×C4
Frattini, cosocleC22×C4C25
socleC22C22×C4×D4
prime radical#60782C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4 ◁ C22×C4×C8 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #60204C2semidirect
3. C2×#2931C2semidirect
4. #22280C2semidirect
5. #22234C2semidirect
6. #22166C2semidirect
7. #22061C2semidirect
8. #21993C2semidirect
9. #21856C2semidirect
10. #21815C2semidirect
11. #21706C2semidirect
12. #21660C2semidirect
13. #21518C2semidirect
14. #21467C2semidirect
15. #20473C2semidirect
19. #3212C4semidirect
20. #3211C4semidirect
21. #3210C4semidirect
22. #3209C4semidirect
23. #3208C4semidirect
24. #3207C4semidirect
25. #3206C4semidirect
26. #3205C4semidirect
39. #2960C22semidirect
40. #2960C22semidirect
41. C2×#444C22semidirect
50. #2931C22semidirect
51. #2931C22semidirect
58. #2922C22semidirect
63. C4×#131C22semidirect
66. #1994C22semidirect
68. #1975C22semidirect
71. #1962C22semidirect
72. #1950C22semidirect
73. #1938C22semidirect
74. #1929C22semidirect
75. #1876C22semidirect
76. #1876C22semidirect
78. #1866C22semidirect
80. #1848C22semidirect
81. #1837C22semidirect
82. #1806C22semidirect
84. #1770C22semidirect
85. #1770C22semidirect
86. #1765C22semidirect
89. #1744C22semidirect
90. C4×#97C22semidirect
731. C2×C4#444semidirect

Maximal subgroups

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

subgroupindex
#607822
#602042
C2×#29312
#222802
#222342
#221662
#220612
#219932
#218562
#218152
#217062
#216602
#215182
#214672
#204732