Finite Group Databasebeta

← #6816622

Subgroups — #6816622

Order 512.

1789 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3231C211yesmaximal, characteristic, complemented
2C2×#3229C211yesmaximal, characteristic, complemented
3#36151C211yesmaximal, characteristic
4#36129C211yesmaximal, characteristic
5#33313C211yesmaximal, characteristic, complemented
6#31093C214yesmaximal, complemented
7#31087C214yesmaximal, complemented
8#29877C211yesmaximal, characteristic, complemented
9#29877C211yesmaximal, characteristic, complemented
10#28719C211yesmaximal, characteristic, complemented
11#28688C211yesmaximal, characteristic, complemented
12#26048C214yesmaximal, complemented
13#25813C211yesmaximal, characteristic, complemented
14#25812C211yesmaximal, characteristic, complemented
15#25674C211yesmaximal, characteristic, complemented
16#25674C211yesmaximal, characteristic, complemented
17#25021C214yesmaximal
18C4×#487C211yesmaximal, characteristic, complemented
19#21264C211yesmaximal, characteristic
20C2×#533C2211yescharacteristic
21C2×#533C2211yescharacteristic
22C2×#533C2211yescharacteristic
23C22×C4⋊Q8C2211yescharacteristic
24#3231—28no—
25#3229—28no—
26C2×#500C2211yescharacteristic
27C2×#500C2211yescharacteristic
28C2×#500C2211yescharacteristic
29C2×#498C2211yescharacteristic
30C2×#498C2211yescharacteristic
31C2×#498C2211yescharacteristic
32C2×#487C2211yescharacteristic
33C2×#487C2211yescharacteristic
34C2×#487C2211yescharacteristic
35C2×#485C2214yes—
36C2×#483C2214yes—
37C2×#479C2214yes—
38C2×#475C2214yes—
39C2×#431C2211yescharacteristic
40C2×#431C2211yescharacteristic
41#2862C2211yescharacteristic
42#2862C2211yescharacteristic
43#2857C2211yescharacteristic
44#2857C2211yescharacteristic
45#2857C2211yescharacteristic
46#2857C2211yescharacteristic
47#2550C2212yes—
48#2536C2212yes—
49#2492—21no—
50#2489—21no—
51#2489—21no—
52#2453—21no—
53#2453—21no—
54#2451—21no—
55#2446—21no—
56#2442C2212yes—
57#2439C2212yes—
58#2429—21no—
59#2421C2212yes—
60#2421C2212yes—
61#2417—21no—
62#2415—21no—
63#2415—21no—
64#2409—21no—
65#2362—21no—
66#2362—21no—
67#2360—21no—
68#2352C2212yes—
69#2351C2212yes—
70Q8×C22⋊C4—21no—
71C4×C4⋊Q8C2211yescharacteristic
72C4×C4⋊Q8C2211yescharacteristic
73C42×D4C2211yescharacteristic
74#2088C2214yes—
75#2088C2214yes—
76#2085C2214yes—
77#2077C2214yes—
78#2077C2214yes—
79#2074C2214yes—
80#2059C2214yes—
81#2057C2214yes—
82#2036C2214yes—
83#2036C2214yes—
84#1990C2211yescharacteristic
85#1990C2211yescharacteristic
86#1990C2211yescharacteristic
87#1990C2211yescharacteristic
88#1990C2211yescharacteristic
89#1956C2211yescharacteristic
90#1954C2212yes—
91#1949C2214yes—
92#1939C2212yes—
93#1933C2214yes—
94#1923C2212yes—
95#1923C2212yes—
96#1863C2214yes—
97#1863C2214yes—
98#1854C2214yes—
99#1852C2214yes—
100#1846C2214yes—
101#1846C2214yes—
102#1834C2211yescharacteristic
103#1805C2214yes—
104C4×C4⋊C8C2211yescharacteristic
105C4×#103C2214yes—
106C4×C22⋊C8C2211yescharacteristic
107C4×C22⋊C8C2211yescharacteristic
108C42×C8C2211yescharacteristic
109C23×Q8—21no—
110#533—24no—
111#533—24no—
112#533—24no—
113#533—42no—
114#533—42no—
115#533—42no—
116C2×C4⋊Q8—24no—
117C2×C4⋊Q8—21no—
118C2×C4⋊Q8—21no—
119C2×C4⋊Q8—42no—
120C2×C4⋊Q8C2311yescharacteristic
121C2×C4⋊Q8C2311yescharacteristic
122C2×C4⋊Q8C2311yescharacteristic
123C2×C4⋊Q8C2311yescharacteristic
124C2×C4⋊Q8C2311yescharacteristic
125C2×C4⋊Q8C2312yes—
126C2×C4⋊Q8C2311yescharacteristic
127C2×#125—21no—
128C2×#125—21no—
129C2×#125C2312yes—
130C2×C22⋊Q8—21no—
131C2×C22⋊Q8—21no—
132C2×C22⋊Q8—21no—
133C2×C22⋊Q8—21no—
134C2×C22⋊Q8—21no—
135C2×C22⋊Q8—21no—
136C2×C22⋊Q8—21no—
137C2×C22⋊Q8—21no—
138C2×C22⋊Q8C2312yes—
139C2×C22⋊Q8C2312yes—
140C2×C4×Q8—21no—
141C2×C4×Q8—21no—
142C2×C4×Q8—21no—
143C2×C4×Q8—21no—
144C2×C4×Q8—21no—
145C2×C4×Q8C2312yes—
146C2×C4×Q8C2312yes—
147C2×C4×Q8C2312yes—
148C2×C4×D4D411yescharacteristic
149C2×C4×D4D411yescharacteristic
150C2×C4×D4C2311yescharacteristic
151C2×#117—21no—
152C2×#117—21no—
153C2×#117C2312yes—
154C22×C4⋊C4—21no—
155C22×C4⋊C4C2312yes—
156C22×C42C2311yescharacteristic
157C22×C42C2311yescharacteristic
158#500—24no—
159#500—42no—
160#500—42no—
161#498—24no—
162#498—24no—
163#498—24no—
164#487—24no—
165#487—24no—
166#487D418yescomplemented
167#485—216no—
168#483—216no—
169#479—216no—
170#475—216no—
171#431—24no—
172#431—24no—
173C2×#107C2314yes—
174C2×#107C2314yes—
175C2×#107C2314yes—
176C2×#106C2314yes—
177C2×#106C2314yes—
178C2×#106C2314yes—
179C2×C4⋊C8C2312yes—
180C2×C4⋊C8C2312yes—
181C2×C4⋊C8C2312yes—
182C2×#103C2314yes—
183C2×#103C2314yes—
184C2×#103C2314yes—
185C2×#103C2314yes—
186C2×C22⋊C8C2312yes—
187C2×C22⋊C8C2312yes—
188C2×C22⋊C8C2312yes—
189C2×C22⋊C8C2312yes—
190C2×C4×C8C2312yes—
191C2×C4×C8C2312yes—
192C2×C4×C8C2311yescharacteristic
193C2×C4×C8C2311yescharacteristic
194C2×C4×C8C2311yescharacteristic
195C2×C4×C8C2311yescharacteristic
196#400—22no—
197#400—22no—
198#400—22no—
199#398—22no—
200#398—22no—
201#398—22no—
202#397—22no—
203#397—22no—
204#396—22no—
205#395—22no—
206#394—22no—
207#393—22no—
208#391—21no—
209#391—21no—
210#391—21no—
211#391—21no—
212#391—21no—
213#391—21no—
214#391—21no—
215#391—21no—
216#391—21no—
217#391—21no—
218#391—21no—
219#391—21no—
220#391—21no—
221#391—22no—
222#391—22no—
223#391C2312yes—
224#389—22no—
225#389—22no—
226#389—21no—
227#389—21no—
228#389—21no—
229#389—21no—
230#389—21no—
231#389—21no—
232#389—21no—
233#389—22no—
234#389C2312yes—
235#389C2312yes—
236#389C2312yes—
237#389C2312yes—
238#389C2312yes—
239#388—22no—
240#388—22no—
241#388—22no—
242#388—22no—
243#388—22no—
244#387—22no—
245#387—22no—
246#387—22no—
247#387—22no—
248#386—22no—
249#385—22no—
250#384C2311yescharacteristic
251#384C2311yescharacteristic
252#382—22no—
253#382C2312yes—
254#382C2312yes—
255#382C2312yes—
256#382C2312yes—
257#380—21no—
258#380—21no—
259#380—21no—
260#380—21no—
261#380—22no—
262#380C2312yes—
263#380C2312yes—
264#380C2312yes—
265#380C2312yes—
266C4×C4⋊C4—21no—
267C4×C4⋊C4—21no—
268C4×C4⋊C4—21no—
269C4×C4⋊C4—22no—
270C4×C4⋊C4D411yescharacteristic
271C4×C4⋊C4D411yescharacteristic
272C4×C4⋊C4C2312yes—
273C4×C4⋊C4C2311yescharacteristic
274C4×C22⋊C4—22no—
275C4×C22⋊C4D411yescharacteristic
276C4×C22⋊C4D411yescharacteristic
277C4×C22⋊C4D411yescharacteristic
278C4×C22⋊C4D411yescharacteristic
279C4×C22⋊C4C2311yescharacteristic
280C4×C22⋊C4C2311yescharacteristic
281C43C2311yescharacteristic
282#340C2314yes—
283#340C2314yes—
284#340C2314yes—
285#340C2314yes—
286#340C2314yes—
287#340C2314yes—
288#336C2312yes—
289#336C2312yes—
290#336C2312yes—
291C22×Q8—21no—
292C22×Q8—21no—
293C22×Q8—21no—
294C22×Q8—21no—
295C22×Q8—21no—
296C22×Q8—22no—
297C22×Q8—44no—
298C22×Q8—44no—
299C22×Q8—82no—
300C22×Q8C2412yes—
301C22×D4C2×D411yescharacteristic
302C23×C4—22no—
303C23×C4C2×D411yescharacteristic
304C23×C4C2×D411yescharacteristic
305C23×C4C2×D411yescharacteristic
306C23×C4C2×D411yescharacteristic
307C23×C4C2411yescharacteristic
308C23×C4C2411yescharacteristic
309C22×C8C2412yes—
310C22×C8C2412yes—
311C22×C8C2412yes—
312C22×C8C2412yes—
313C4⋊Q8—24no—
314C4⋊Q8—22no—
315C4⋊Q8—22no—
316C4⋊Q8—22no—
317C4⋊Q8—22no—
318C4⋊Q8—22no—
319C4⋊Q8—22no—
320C4⋊Q8—22no—
321C4⋊Q8—22no—
322C4⋊Q8—22no—
323C4⋊Q8—22no—
324C4⋊Q8—42no—
325C4⋊Q8—44no—
326C4⋊Q8—44no—
327C4⋊Q8C2×D414yes—
328C4⋊Q8C2×D414yes—
329#125—24no—
330#125—42no—
331#125—44no—
332#125—44no—
333C22⋊Q8—24no—
334C22⋊Q8—24no—
335C22⋊Q8—42no—
336C22⋊Q8—42no—
337C22⋊Q8—44no—
338C22⋊Q8—44no—
339C22⋊Q8—44no—
340C22⋊Q8—44no—
341C22⋊Q8—44no—
342C22⋊Q8—44no—
343C22⋊Q8—44no—
344C22⋊Q8—82no—
345C4×Q8—24no—
346C4×Q8—24no—
347C4×Q8—28no—
348C4×Q8—42no—
349C4×Q8—42no—
350C4×Q8—44no—
351C4×Q8—44no—
352C4×Q8—44no—
353C4×Q8—44no—
354C4×Q8—82no—
355C4×D4—24no—
356C4×D4—24no—
357C4×D4—42no—
358#117—24no—
359#117—42no—
360#117—44no—
361#117—44no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—24no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—22no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—22no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—22no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—42no—
389C2×C4⋊C4—44no—
390C2×C4⋊C4C2×D411yescharacteristic
391C2×C4⋊C4C2×D411yescharacteristic
392C2×C4⋊C4C2×D411yescharacteristic
393C2×C4⋊C4C2412yes—
394C2×C4⋊C4C2412yes—
395C2×C4⋊C4C2412yes—
396C2×C4⋊C4C2412yes—
397C2×C4⋊C4C2412yes—
398C2×C4⋊C4C2412yes—
399C2×C4⋊C4C2412yes—
400C2×C22⋊C4—22no—
401C2×C22⋊C4—22no—
402C2×C22⋊C4—22no—
403C2×C22⋊C4—22no—
404C2×C22⋊C4—22no—
405C2×C22⋊C4—22no—
406C2×C22⋊C4—22no—
407C2×C22⋊C4C2×D411yescharacteristic
408C2×C22⋊C4C2×D411yescharacteristic
409C2×C22⋊C4C2×D411yescharacteristic
410C2×C22⋊C4C2×D411yescharacteristic
411C2×C22⋊C4C2×D411yescharacteristic
412C2×C22⋊C4C2×D411yescharacteristic
413C2×C42—22no—
414C2×C42—22no—
415C2×C42—22no—
416C2×C42—22no—
417C2×C42—22no—
418C2×C42—22no—
419C2×C42—22no—
420C2×C42—22no—
421C2×C42—22no—
422C2×C42C2×D411yescharacteristic
423C2×C42C2×D411yescharacteristic
424C2×C42C2×D411yescharacteristic
425C2×C42C2×D411yescharacteristic
426C2×C42C2×D411yescharacteristic
427C2×C42C2×D411yescharacteristic
428C2×C42C2×D411yescharacteristic
429C2×C42C2×D411yescharacteristic
430C2×C42C2411yescharacteristic
431C2×C42C2411yescharacteristic
432C2×C42C2411yescharacteristic
433C2×C42C2411yescharacteristic
434C2×C42C2411yescharacteristic
435#107—28no—
436#107—44no—
437#107—44no—
438#106—28no—
439#106—28no—
440#106—28no—
441C4⋊C8—24no—
442C4⋊C8—24no—
443C4⋊C8—24no—
444#103—28no—
445#103—28no—
446#103—28no—
447#103C2×D4116yes—
448C22⋊C8—24no—
449C22⋊C8—24no—
450C22⋊C8—24no—
451C22⋊C8—24no—
452C4×C8—24no—
453C4×C8—22no—
454C4×C8—22no—
455C4×C8—22no—
456C4×C8—24no—
457C4×C8C2×D414yes—
458#95—22no—
459#95—22no—
460#95—22no—
461#95—22no—
462#95—22no—
463#95—22no—
464#95—22no—
465#95—22no—
466#95—22no—
467#95—22no—
468#95—22no—
469#95—22no—
470#95—22no—
471#95—22no—
472#95—22no—
473#95—22no—
474#95—22no—
475#95—22no—
476#95—22no—
477#95—22no—
478#95C2×D411yescharacteristic
479#95C2×D411yescharacteristic
480#95C2×D411yescharacteristic
481#95C2×D411yescharacteristic
482#95C2×D411yescharacteristic
483#95C2×D411yescharacteristic
484C24C22×D411yescharacteristic
485C24C22×D411yescharacteristic
486C2×Q8—24no—
487C2×Q8—22no—
488C2×Q8—24no—
489C2×Q8—24no—
490C2×Q8—44no—
491C2×Q8—42no—
492C2×Q8—42no—
493C2×Q8—42no—
494C2×Q8—42no—
495C2×Q8—42no—
496C2×Q8—42no—
497C2×Q8—44no—
498C2×Q8—42no—
499C2×Q8—42no—
500C2×Q8—42no—
501C2×Q8—42no—
502C2×Q8—42no—
503C2×Q8—42no—
504C2×Q8—42no—
505C2×Q8—42no—
506C2×Q8—82no—
507C2×Q8—816no—
508C2×Q8C22×D414yes—
509C2×D4—22no—
510C2×D4—22no—
511C2×D4—41no—
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—22no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—44no—
540C22×C4—44no—
541C22×C4—82no—
542C22×C4#13514yes—
543C22×C4C22×D411yescharacteristic
544C22×C4C22×D411yescharacteristic
545C22×C4C22×D411yescharacteristic
546C22×C4C22×D411yescharacteristic
547C22×C4C22×D411yescharacteristic
548C22×C4C22×D411yescharacteristic
549C22×C4C22×D411yescharacteristic
550C22×C4C22×D411yescharacteristic
551C22×C4C22×D411yescharacteristic
552C22×C4C22×D411yescharacteristic
553C22×C4C22×D411yescharacteristic
554C22×C4C22×D411yescharacteristic
555C22×C4C2511yescharacteristic
556C2×C8—22no—
557C2×C8—22no—
558C2×C8—22no—
559C2×C8—22no—
560C2×C8—22no—
561C2×C8—22no—
562C2×C8—22no—
563C2×C8—22no—
564C2×C8—22no—
565C2×C8—22no—
566C2×C8C22×D414yes—
567C2×C82−1+414yes—
568C4⋊C4—22no—
569C4⋊C4—24no—
570C4⋊C4—24no—
571C4⋊C4—24no—
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—22no—
581C4⋊C4—22no—
582C4⋊C4—24no—
583C4⋊C4—24no—
584C4⋊C4—41no—
585C4⋊C4—44no—
586C4⋊C4—44no—
587C4⋊C4—44no—
588C4⋊C4—44no—
589C4⋊C4—44no—
590C4⋊C4—44no—
591C4⋊C4—44no—
592C4⋊C4—44no—
593C4⋊C4—44no—
594C4⋊C4—44no—
595C4⋊C4—44no—
596C4⋊C4—42no—
597C4⋊C4—42no—
598C4⋊C4—42no—
599C4⋊C4—42no—
600C4⋊C4—42no—
601C4⋊C4—44no—
602C4⋊C4—42no—
603C4⋊C4—42no—
604C4⋊C4—42no—
605C4⋊C4—82no—
606C4⋊C4—82no—
607C4⋊C4C22×D414yes—
608C22⋊C4—22no—
609C22⋊C4—22no—
610C22⋊C4—22no—
611C22⋊C4—22no—
612C22⋊C4—41no—
613C22⋊C4—41no—
614C22⋊C4—44no—
615C22⋊C4—44no—
616C22⋊C4—44no—
617C22⋊C4—44no—
618C22⋊C4—44no—
619C22⋊C4—44no—
620C22⋊C4—82no—
621C42—22no—
622C42—22no—
623C42—22no—
624C42—22no—
625C42—22no—
626C42—22no—
627C42—22no—
628C42—22no—
629C42—21no—
630C42—21no—
631C42—21no—
632C42—21no—
633C42—22no—
634C42—44no—
635C42—44no—
636C42—44no—
637C42—44no—
638C42—82no—
639C42C22×D412yes—
640C42H(5,𝔽2)12yes—
641C422−1+414yes—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23C2×#13512yes—
656C23C23×D411yescharacteristic
657Q8—28no—
658Q8—48no—
659Q8—44no—
660Q8—88no—
661Q8—84no—
662Q8—84no—
663Q8—84no—
664Q8—84no—
665D4—44no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—28no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—24no—
681C2×C4—24no—
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—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—44no—
703C2×C4—44no—
704C2×C4—44no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—88no—
726C2×C4#53612yes—
727C2×C4#53612yes—
728C2×C4D4212yes—
729C2×C4D4212yes—
730C2×C4C2×#13512yes—
731C2×C4C2×#13512yes—
732C2×C4#57512yes—
733C2×C4#57712yes—
734C2×C4#57812yes—
735C2×C4C23×D411yescharacteristic
736C2×C4C2×H(5,𝔽2)11yescharacteristic
737C2×C4C2×2−1+412yes—
738C2×C4C2×2−1+412yes—
739C8—24no—
740C8—24no—
741C8—42no—
742C8—42no—
743C22—22no—
744C22—22no—
745C22—22no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22C2×#53611yescharacteristic
758C22C2×D4211yescharacteristic
759C22#349911yescharacteristic
760C22C22×#13511yescharacteristic
761C22C2×#57511yescharacteristic
762C22C2×#57711yescharacteristic
763C22C2×#57811yescharacteristic
764C4—22no—
765C4—22no—
766C4—22no—
767C4—41no—
768C4—41no—
769C4—41no—
770C4—41no—
771C4—41no—
772C4—44no—
773C4—41no—
774C4—41no—
775C4—44no—
776C4—82no—
777C4—82no—
778C4—82no—
779C4—82no—
780C4—82no—
781C4—82no—
782C4#327714yes—
783C4#328214yes—
784C4#349912yes—
785C4#355212yes—
786C2—42no—
787C2—81no—
788C2#3936011yescharacteristic
789C2#6084611yescharacteristic
790C2#6087811yescharacteristic
791C2C2×#327711yescharacteristic
792C2C2×#328211yescharacteristic
793C2#6247311yescharacteristic
794C2#6248311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×D4C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C42×D4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3231C2semidirect
2. C2×#3229C2semidirect
5. #33313C2semidirect
6. #31093C2semidirect
7. #31087C2semidirect
8. #29877C2semidirect
9. #29877C2semidirect
10. #28719C2semidirect
11. #28688C2semidirect
12. #26048C2semidirect
13. #25813C2semidirect
14. #25812C2semidirect
15. #25674C2semidirect
16. #25674C2semidirect
18. C4×#487C2semidirect
166. #487D4semidirect

Maximal subgroups

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

subgroupindex
C2×#32312
C2×#32292
#361512
#361292
#333132
#310932
#310872
#298772
#287192
#286882
#260482
#258132
#258122
#256742
#250212
C4×#4872
#212642