Finite Group Databasebeta

← #6447018

Subgroups — #6447018

Order 512.

2400 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34935C211yesmaximal, characteristic
2C2×D4×C4⋊C4C211yesmaximal, characteristic, complemented
3#24979C214yesmaximal, complemented
4#24977C214yesmaximal, complemented
5#24971C212yesmaximal, complemented
6#24969C212yesmaximal, complemented
7#24967C212yesmaximal, complemented
8#24965C212yesmaximal, complemented
9#23642C212yesmaximal, complemented
10#23482C212yesmaximal, complemented
11#21190C211yesmaximal, characteristic, complemented
12#21170C211yesmaximal, characteristic, complemented
13#20909C212yesmaximal, complemented
14#20764C211yesmaximal, characteristic, complemented
15#20700C212yesmaximal, complemented
16#20648C211yesmaximal, characteristic, complemented
17C4×#417C211yesmaximal, characteristic, complemented
18C2×#525C2212yes—
19C2×C4×#41C2211yescharacteristic
20C22×C4×D4—21no—
21C22×C4×D4C2211yescharacteristic
22C23×C4⋊C4C2212yes—
23C2×#428C2212yes—
24C2×#423C2211yescharacteristic
25C2×#417C2211yescharacteristic
26C2×#417C2211yescharacteristic
27C2×#417C2212yes—
28C2×#407C2212yes—
29C2×#407C2212yes—
30C2×C4×M16C2211yescharacteristic
31#2538C2211yescharacteristic
32#2538C2211yescharacteristic
33#2537C2211yescharacteristic
34#2537C2211yescharacteristic
35#2536C2212yes—
36#2535C2212yes—
37#2534—22no—
38#2486—21no—
39#2408—21no—
40#2392—22no—
41D4×C4⋊C4—22no—
42D4×C4⋊C4—21no—
43D4×C4⋊C4—21no—
44D4×C4⋊C4C2212yes—
45D4×C4⋊C4C2212yes—
46D4×C4⋊C4C2214yes—
47C4×#121—21no—
48C4×#121—21no—
49C2×#389—21no—
50C2×#385—22no—
51#2285C2211yescharacteristic
52C2×#384C2211yescharacteristic
53#2280C2212yes—
54C2×#380C2212yes—
55C2×C4×C4⋊C4C2211yescharacteristic
56#2077C2214yescomplemented
57#2077C2214yescomplemented
58#2076C2214yescomplemented
59#2075C2214yescomplemented
60#2036C2214yescomplemented
61#2035C2214yescomplemented
62#2034C2214yescomplemented
63#2033C2214yescomplemented
64#1955C2214yes—
65#1954C2212yes—
66#1954C2212yes—
67#1949C2214yescomplemented
68#1948C2212yescomplemented
69#1947C2212yescomplemented
70#1874C2214yescomplemented
71#1874C2214yescomplemented
72#1872C2214yescomplemented
73#1872C2214yescomplemented
74#1836C2214yescomplemented
75#1834C2212yescomplemented
76#1834C2212yescomplemented
77#1824C2214yescomplemented
78#1824C2214yescomplemented
79#1823C2214yescomplemented
80#1823C2214yescomplemented
81#1803C2212yescomplemented
82#1803C2212yescomplemented
83#1802C2212yescomplemented
84#1802C2212yescomplemented
85#1763C2212yescomplemented
86#1762C2212yescomplemented
87C4×#103C2212yescomplemented
88C4×#102C2212yescomplemented
89#1736C2212yes—
90#1736C2212yes—
91#1736C2211yescharacteristic
92#1736C2212yes—
93#1736C2212yes—
94#1736C2211yescharacteristic
95C22×#41C2311yescharacteristic
96C23×D4D411yescharacteristic
97C24×C4—22no—
98C24×C4C2312yes—
99C22×M16C2311yescharacteristic
100C22×M16C2311yescharacteristic
101C22×M16C2312yes—
102#525—28no—
103#525—44no—
104C2×#123—22no—
105C2×C22⋊Q8C2312yes—
106C2×C22⋊Q8C2312yes—
107C2×#121—21no—
108C2×#121—21no—
109C2×#121C2312yes—
110C2×#121C2312yes—
111C2×#120—22no—
112C4×#41—24no—
113C4×#41—24no—
114C2×C4×Q8C2311yescharacteristic
115C2×C4×Q8C2311yescharacteristic
116C2×C4×D4—24no—
117C2×C4×D4—22no—
118C2×C4×D4—22no—
119C2×C4×D4—22no—
120C2×C4×D4—22no—
121C2×C4×D4—21no—
122C2×C4×D4—21no—
123C2×C4×D4—24no—
124C2×C4×D4—24no—
125C2×C4×D4—48no—
126C2×C4×D4D412yes—
127C2×C4×D4D411yescharacteristic
128C2×C4×D4D411yescharacteristic
129C2×C4×D4C2311yescharacteristic
130C2×C4×D4C2311yescharacteristic
131C2×C4×D4C2311yescharacteristic
132C2×C4×D4C2311yescharacteristic
133C2×C4×D4C2312yes—
134C2×#117—21no—
135C2×#117C2312yes—
136C2×#117C2311yescharacteristic
137C22×C4⋊C4—28no—
138C22×C4⋊C4—22no—
139C22×C4⋊C4—22no—
140C22×C4⋊C4—22no—
141C22×C4⋊C4—21no—
142C22×C4⋊C4—21no—
143C22×C4⋊C4—44no—
144C22×C4⋊C4D411yescharacteristic
145C22×C4⋊C4C2312yes—
146C22×C4⋊C4C2311yescharacteristic
147C22×C4⋊C4C2314yes—
148C22×C4⋊C4C2314yes—
149C22×C4⋊C4C2311yescharacteristic
150C22×C22⋊C4—22no—
151C22×C22⋊C4D412yes—
152C22×C42—21no—
153C22×C42—21no—
154C22×C42C2311yescharacteristic
155#428—44no—
156C2×#107C2314yes—
157C2×#106C2314yes—
158#423—24no—
159C2×C4⋊C8C2312yes—
160C2×C4⋊C8C2312yes—
161#417—24no—
162#417—24no—
163#417—44no—
164C2×#103C2312yes—
165C2×#103C2312yes—
166C2×#103C2314yes—
167C2×#102C2312yes—
168C2×#102C2312yes—
169C2×#102C2314yes—
170#407—44no—
171#407—44no—
172C2×C22⋊C8C2314yes—
173C2×C22⋊C8C2314yes—
174C2×C22⋊C8C2314yes—
175C2×C22⋊C8C2314yes—
176C4×M16—24no—
177C2×#97C2312yes—
178C2×C4×C8C2312yes—
179#398—22no—
180#397—22no—
181#396—22no—
182#396—22no—
183#394—22no—
184#394—22no—
185#394—22no—
186#392—22no—
187#390—21no—
188#390—21no—
189#389—22no—
190#389—22no—
191#389—24no—
192#389—21no—
193#389—21no—
194#388—22no—
195#388—22no—
196#386—22no—
197#386—22no—
198#385—24no—
199#385—24no—
200#385—24no—
201#385—24no—
202#384—21no—
203#384—21no—
204#384C2312yes—
205#384C2312yes—
206#384C2311yescharacteristic
207#384C2311yescharacteristic
208#382C2312yes—
209#381—22no—
210#380—22no—
211#380—22no—
212#380—21no—
213#380—21no—
214#380—21no—
215#380—21no—
216#380C2312yes—
217#380C2314yes—
218#380C2312yes—
219#380C2314yes—
220#380C2312yes—
221#380C2312yes—
222#379—22no—
223C4×C4⋊C4—21no—
224C4×C4⋊C4—21no—
225C4×C4⋊C4—21no—
226C4×C4⋊C4—21no—
227C4×C4⋊C4C2312yes—
228C4×C4⋊C4C2312yes—
229C4×C22⋊C4—22no—
230C4×C22⋊C4—22no—
231C2×#95—21no—
232C2×#95—22no—
233#340C2314yes—
234#340C2314yes—
235#340C2312yes—
236#340C2314yes—
237#340C2312yes—
238#340C2314yes—
239#340C2312yes—
240#340C2312yes—
241#340C2314yes—
242#340C2314yes—
243#340C2314yes—
244#340C2314yes—
245C25C2×D412yes—
246C2×#41—22no—
247C2×#41—22no—
248C2×#41—22no—
249C2×#41—22no—
250C2×#41—22no—
251C2×#41#4114yes—
252C22×Q8C2411yescharacteristic
253C22×D4—24no—
254C22×D4—24no—
255C22×D4—21no—
256C22×D4—22no—
257C22×D4—22no—
258C22×D4—24no—
259C22×D4C2×D412yes—
260C22×D4C2×D411yescharacteristic
261C22×D4C2×D411yescharacteristic
262C22×D4C2411yescharacteristic
263C23×C4—21no—
264C23×C4—21no—
265C23×C4—24no—
266C23×C4—24no—
267C23×C4—24no—
268C23×C4—24no—
269C23×C4—24no—
270C23×C4—24no—
271C23×C4—21no—
272C23×C4—22no—
273C23×C4—24no—
274C23×C4—24no—
275C23×C4—21no—
276C23×C4—21no—
277C23×C4—48no—
278C23×C4—48no—
279C23×C4—84no—
280C23×C4C2×D412yes—
281C23×C4C2×D412yes—
282C23×C4C2×D412yes—
283C23×C4C2×D411yescharacteristic
284C23×C4C2×D411yescharacteristic
285C23×C4C2412yes—
286C23×C4C2412yes—
287C23×C4C2411yescharacteristic
288C2×M16—22no—
289C2×M16—22no—
290C2×M16—22no—
291C2×M16—22no—
292C2×M16—24no—
293C2×M16—22no—
294C2×M16—22no—
295C2×M16—24no—
296C2×M16—24no—
297C22×C8C2412yes—
298C22×C8C2412yes—
299C22×C8C2414yes—
300#123—48no—
301C22⋊Q8—24no—
302C22⋊Q8—24no—
303C22⋊Q8—42no—
304C22⋊Q8—42no—
305#121—24no—
306#121—24no—
307#121—42no—
308#121—42no—
309#121—44no—
310#121—44no—
311#120—48no—
312C4×Q8—22no—
313C4×Q8—22no—
314C4×Q8—22no—
315C4×Q8—22no—
316C4×D4—24no—
317C4×D4—24no—
318C4×D4—28no—
319C4×D4—22no—
320C4×D4—22no—
321C4×D4—24no—
322C4×D4—22no—
323C4×D4—22no—
324C4×D4—24no—
325C4×D4—22no—
326C4×D4—22no—
327C4×D4—22no—
328C4×D4—22no—
329C4×D4—48no—
330C4×D4—48no—
331C4×D4—416no—
332C4×D4—48no—
333C4×D4—48no—
334C4×D4—44no—
335C4×D4—44no—
336#117—22no—
337#117—22no—
338#117—24no—
339#117—24no—
340#117—44no—
341C2×C4⋊C4—24no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—24no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—24no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—28no—
349C2×C4⋊C4—28no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—24no—
352C2×C4⋊C4—24no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—44no—
367C2×C4⋊C4—44no—
368C2×C4⋊C4—48no—
369C2×C4⋊C4—48no—
370C2×C4⋊C4—48no—
371C2×C4⋊C4—44no—
372C2×C4⋊C4—82no—
373C2×C4⋊C4C2×D411yescharacteristic
374C2×C4⋊C4C2×D411yescharacteristic
375C2×C4⋊C4C2×D412yes—
376C2×C4⋊C4#4114yes—
377C2×C4⋊C4C2414yes—
378C2×C4⋊C4C2412yes—
379C2×C4⋊C4C2411yescharacteristic
380C2×C4⋊C4C2411yescharacteristic
381C2×C4⋊C4C2412yes—
382C2×C4⋊C4C2412yes—
383C2×C4⋊C4C2412yes—
384C2×C22⋊C4—28no—
385C2×C22⋊C4—24no—
386C2×C22⋊C4—24no—
387C2×C22⋊C4—21no—
388C2×C22⋊C4—22no—
389C2×C22⋊C4—22no—
390C2×C22⋊C4—22no—
391C2×C22⋊C4—22no—
392C2×C22⋊C4—22no—
393C2×C22⋊C4—21no—
394C2×C22⋊C4—21no—
395C2×C22⋊C4—22no—
396C2×C22⋊C4—22no—
397C2×C22⋊C4—22no—
398C2×C22⋊C4—22no—
399C2×C22⋊C4—48no—
400C2×C22⋊C4C2×D412yes—
401C2×C22⋊C4C2×D412yes—
402C2×C22⋊C4C2×D412yes—
403C2×C22⋊C4C2×D412yes—
404C2×C42—21no—
405C2×C42—22no—
406C2×C42—22no—
407C2×C42—22no—
408C2×C42—21no—
409C2×C42—21no—
410C2×C42—44no—
411C2×C42—44no—
412C2×C42C2×D411yescharacteristic
413C2×C42C2×D411yescharacteristic
414C2×C42#4114yes—
415C2×C42#4114yes—
416C2×C42C2411yescharacteristic
417C2×C42C2411yescharacteristic
418#107—44no—
419#106—44no—
420C4⋊C8—24no—
421C4⋊C8—24no—
422#103—24no—
423#103—24no—
424#103—44no—
425#102—24no—
426#102—24no—
427#102—44no—
428C22⋊C8—44no—
429C22⋊C8—44no—
430C22⋊C8—44no—
431C22⋊C8—44no—
432#97—24no—
433C4×C8—24no—
434#95—22no—
435#95—22no—
436#95—24no—
437#95—24no—
438#95—22no—
439#95—22no—
440#95—22no—
441#95—22no—
442#95—22no—
443#95—22no—
444C24—24no—
445C24—24no—
446C24—24no—
447C24—24no—
448C24—24no—
449C24—21no—
450C24—42no—
451C24—42no—
452C24C22×D412yes—
453C24C22×D412yes—
454C24C22×D411yescharacteristic
455#41—28no—
456#41—28no—
457#41—44no—
458#41—44no—
459C2×Q8—21no—
460C2×Q8—21no—
461C2×Q8—21no—
462C2×Q8—21no—
463C2×Q8—21no—
464C2×Q8C2×#4112yes—
465C2×D4—232no—
466C2×D4—24no—
467C2×D4—24no—
468C2×D4—24no—
469C2×D4—24no—
470C2×D4—22no—
471C2×D4—22no—
472C2×D4—22no—
473C2×D4—22no—
474C2×D4—21no—
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4—42no—
480C2×D4—42no—
481C2×D4—44no—
482C2×D4—44no—
483C2×D4—44no—
484C2×D4—44no—
485C2×D4—82no—
486C2×D4—82no—
487C2×D4AGL(1,ℤ/8)14yes—
488C2×D4#13714yes—
489C2×D4C2×#4112yes—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—24no—
493C22×C4—24no—
494C22×C4—24no—
495C22×C4—24no—
496C22×C4—22no—
497C22×C4—21no—
498C22×C4—24no—
499C22×C4—24no—
500C22×C4—24no—
501C22×C4—24no—
502C22×C4—24no—
503C22×C4—24no—
504C22×C4—24no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—24no—
523C22×C4—41no—
524C22×C4—41no—
525C22×C4—48no—
526C22×C4—48no—
527C22×C4—42no—
528C22×C4—42no—
529C22×C4—42no—
530C22×C4—48no—
531C22×C4—48no—
532C22×C4—42no—
533C22×C4—48no—
534C22×C4—48no—
535C22×C4—42no—
536C22×C4—44no—
537C22×C4—44no—
538C22×C4—48no—
539C22×C4—42no—
540C22×C4—44no—
541C22×C4—42no—
542C22×C4—48no—
543C22×C4—42no—
544C22×C4—42no—
545C22×C4—42no—
546C22×C4—42no—
547C22×C4—81no—
548C22×C4—81no—
549C22×C4—84no—
550C22×C4—84no—
551C22×C4—832no—
552C22×C4#12314yes—
553C22×C4#12314yes—
554C22×C4C22×D412yes—
555C22×C4C22×D412yes—
556C22×C4C22×D411yescharacteristic
557C22×C4C22×D411yescharacteristic
558C22×C4C22×D411yescharacteristic
559C22×C4C22×D411yescharacteristic
560C22×C4C22×D411yescharacteristic
561C22×C4C2×#4112yes—
562C22×C4C2×#4112yes—
563C22×C4C2×#4112yes—
564C22×C4C2×#4112yes—
565C22×C4H(5,𝔽2)12yes—
566C22×C4H(5,𝔽2)12yes—
567C22×C4C2511yescharacteristic
568M16—48no—
569M16—44no—
570M16—44no—
571C2×C8—22no—
572C2×C8—22no—
573C2×C8—22no—
574C2×C8—22no—
575C2×C8—24no—
576C2×C8—22no—
577C2×C8—22no—
578C2×C8—24no—
579C2×C8—24no—
580C4⋊C4—24no—
581C4⋊C4—22no—
582C4⋊C4—22no—
583C4⋊C4—24no—
584C4⋊C4—22no—
585C4⋊C4—22no—
586C4⋊C4—24no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—22no—
592C4⋊C4—22no—
593C4⋊C4—24no—
594C4⋊C4—22no—
595C4⋊C4—22no—
596C4⋊C4—22no—
597C4⋊C4—48no—
598C4⋊C4—48no—
599C4⋊C4—44no—
600C4⋊C4—44no—
601C4⋊C4—44no—
602C4⋊C4—42no—
603C4⋊C4—42no—
604C4⋊C4—42no—
605C4⋊C4—44no—
606C4⋊C4—44no—
607C4⋊C4—42no—
608C4⋊C4—42no—
609C4⋊C4—81no—
610C4⋊C4—81no—
611C4⋊C4—82no—
612C4⋊C4—82no—
613C4⋊C4C2×#4114yes—
614C22⋊C4—24no—
615C22⋊C4—24no—
616C22⋊C4—24no—
617C22⋊C4—24no—
618C22⋊C4—44no—
619C22⋊C4—44no—
620C22⋊C4—44no—
621C22⋊C4—44no—
622C22⋊C4—48no—
623C22⋊C4—42no—
624C22⋊C4—44no—
625C22⋊C4—48no—
626C22⋊C4—44no—
627C22⋊C4—44no—
628C22⋊C4—42no—
629C22⋊C4—42no—
630C22⋊C4—82no—
631C22⋊C4—82no—
632C42—44no—
633C42—42no—
634C42—42no—
635C42—42no—
636C42—44no—
637C42—44no—
638C42#12314yes—
639C42#12314yes—
640C42C2×#4112yes—
641C42C2×#4112yes—
642C42C2×#4112yes—
643C42C2×#4112yes—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—216no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—48no—
663C23—48no—
664C23—48no—
665C23—48no—
666C23—48no—
667C23—48no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23C2×#12312yes—
675C23#54612yes—
676C23#54612yes—
677C23C2×AGL(1,ℤ/8)14yes—
678C23C2×#13714yes—
679C23C23×D411yescharacteristic
680Q8—22no—
681Q8—22no—
682Q8—41no—
683Q8—41no—
684D4—216no—
685D4—28no—
686D4—28no—
687D4—22no—
688D4—22no—
689D4—48no—
690D4—41no—
691D4—41no—
692D4—88no—
693D4—88no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—28no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—24no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—44no—
710C2×C4—48no—
711C2×C4—42no—
712C2×C4—41no—
713C2×C4—48no—
714C2×C4—41no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—48no—
719C2×C4—48no—
720C2×C4—48no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—41no—
728C2×C4—42no—
729C2×C4—44no—
730C2×C4—41no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—44no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—44no—
741C2×C4—41no—
742C2×C4—42no—
743C2×C4—41no—
744C2×C4—42no—
745C2×C4—84no—
746C2×C4—816no—
747C2×C4—816no—
748C2×C4—84no—
749C2×C4—88no—
750C2×C4—84no—
751C2×C4C2×#12312yes—
752C2×C4C2×#12312yes—
753C2×C4C2×#12312yes—
754C2×C4C2×#12312yes—
755C2×C4C2×#12312yes—
756C2×C4#52914yes—
757C2×C4#54014yes—
758C2×C4#54612yes—
759C2×C4#54612yes—
760C2×C4#55314yes—
761C2×C4#55514yes—
762C2×C4C2×AGL(1,ℤ/8)12yes—
763C2×C4C2×#13712yes—
764C2×C4C22×#4111yescharacteristic
765C2×C4C22×#4111yescharacteristic
766C2×C4C22×#4111yescharacteristic
767C2×C4C22×#4111yescharacteristic
768C2×C4C2×H(5,𝔽2)11yescharacteristic
769C2×C4C2×H(5,𝔽2)11yescharacteristic
770C8—44no—
771C8—42no—
772C8—42no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—22no—
777C22—22no—
778C22—22no—
779C22—24no—
780C22—24no—
781C22—24no—
782C22—24no—
783C22—24no—
784C22—24no—
785C22—432no—
786C22—42no—
787C22—42no—
788C22—42no—
789C22—42no—
790C22—42no—
791C22—42no—
792C22—42no—
793C22—42no—
794C22—42no—
795C22—42no—
796C22—42no—
797C22—81no—
798C22—81no—
799C22—81no—
800C22—81no—
801C22#242014yes—
802C22C22×#12311yescharacteristic
803C22C2×#54611yescharacteristic
804C22C2×#54611yescharacteristic
805C22C22×AGL(1,ℤ/8)11yescharacteristic
806C22C22×#13711yescharacteristic
807C22#358511yescharacteristic
808C22#358611yescharacteristic
809C4—22no—
810C4—22no—
811C4—22no—
812C4—42no—
813C4—42no—
814C4—42no—
815C4—44no—
816C4—81no—
817C4—81no—
818C4—84no—
819C4—82no—
820C4—82no—
821C4—82no—
822C4#242014yes—
823C4#309214yes—
824C4C2×#52911yescharacteristic
825C4C2×#54011yescharacteristic
826C4C2×#55311yescharacteristic
827C4C2×#55511yescharacteristic
828C2—24no—
829C2—44no—
830C2—44no—
831C2—82no—
832C2C2×#242011yescharacteristic
833C2C2×#309211yescharacteristic
834C2#6051711yescharacteristic
835C2#6115511yescharacteristic
836C2#6115711yescharacteristic
837C2#6116111yescharacteristic
838C2#6116211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#34935C2
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
2. C2×D4×C4⋊C4C2semidirect
3. #24979C2semidirect
4. #24977C2semidirect
5. #24971C2semidirect
6. #24969C2semidirect
7. #24967C2semidirect
8. #24965C2semidirect
9. #23642C2semidirect
10. #23482C2semidirect
11. #21190C2semidirect
12. #21170C2semidirect
13. #20909C2semidirect
14. #20764C2semidirect
15. #20700C2semidirect
16. #20648C2semidirect
17. C4×#417C2semidirect
56. #2077C22semidirect
57. #2077C22semidirect
58. #2076C22semidirect
59. #2075C22semidirect
60. #2036C22semidirect
61. #2035C22semidirect
62. #2034C22semidirect
63. #2033C22semidirect
67. #1949C22semidirect
68. #1948C22semidirect
69. #1947C22semidirect
70. #1874C22semidirect
71. #1874C22semidirect
72. #1872C22semidirect
73. #1872C22semidirect
74. #1836C22semidirect
75. #1834C22semidirect
76. #1834C22semidirect
77. #1824C22semidirect
78. #1824C22semidirect
79. #1823C22semidirect
80. #1823C22semidirect
81. #1803C22semidirect
82. #1803C22semidirect
83. #1802C22semidirect
84. #1802C22semidirect
85. #1763C22semidirect
86. #1762C22semidirect
87. C4×#103C22semidirect
88. C4×#102C22semidirect

Maximal subgroups

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

subgroupindex
#349352
C2×D4×C4⋊C42
#249792
#249772
#249712
#249692
#249672
#249652
#236422
#234822
#211902
#211702
#209092
#207642
#207002
#206482
C4×#4172