Finite Group Databasebeta

← #657326

Subgroups — #657326

Order 512.

4070 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2561C212yesmaximal
2C2×#2440C211yesmaximal, characteristic, complemented
3C22×#380C211yesmaximal, characteristic
4#15770C214yesmaximal, complemented
5#15541C214yesmaximal, complemented
6#15132C212yesmaximal, complemented
7#15125C212yesmaximal, complemented
8#14934C212yesmaximal, complemented
9#14918C212yesmaximal
10#14680C211yesmaximal, characteristic
11#13994C212yesmaximal, complemented
12#13972C212yesmaximal, complemented
13#13904C211yesmaximal, characteristic, complemented
14#13904C211yesmaximal, characteristic, complemented
15#13876C212yesmaximal, complemented
16C22⋊C4×C4⋊C4C211yesmaximal, characteristic, complemented
17C4×#379C211yesmaximal, characteristic
18C25×C4C2211yescharacteristic
19C22×C4⋊Q8C2211yescharacteristic, complemented
20C22×C22⋊Q8C2212yes—
21C23×C4⋊C4C2211yescharacteristic
22C23×C4⋊C4C2211yescharacteristic
23C23×C22⋊C4C2212yes—
24#2561—216no—
25#2440—28no—
26C2×#398C2212yescomplemented
27C2×#397C2214yes—
28C2×#395C2212yescomplemented
29C2×#393C2214yes—
30C2×#389C2211yescharacteristic, complemented
31C2×#389C2211yescharacteristic, complemented
32C2×#388C2214yes—
33C2×#388C2214yes—
34C2×#385C2212yes—
35C2×#384C2211yescharacteristic, complemented
36C2×#381C2212yes—
37C2×#381C2212yes—
38C2×#381C2212yes—
39C2×#381C2212yes—
40C2×#380—28no—
41C2×#380C2212yes—
42C2×#380C2212yes—
43C2×#380C2212yes—
44C2×#380C2211yescharacteristic
45C2×#380C2211yescharacteristic
46C2×#380C2214yes—
47C2×#380C2212yes—
48C2×#379C2212yes—
49C2×#379C2211yescharacteristic
50C2×#379C2211yescharacteristic
51C2×C4×C4⋊C4C2212yescomplemented
52C2×C4×C22⋊C4C2212yes—
53C2×C4×C22⋊C4C2212yes—
54C2×C4×C22⋊C4C2211yescharacteristic
55C2×C4×C22⋊C4C2211yescharacteristic
56C2×C4×C22⋊C4C2212yes—
57C22×#95C2212yes—
58#1446C2214yescomplemented
59#1445C2212yescomplemented
60#1445C2214yescomplemented
61#1445C2212yescomplemented
62#1443C2214yescomplemented
63#1442C2214yescomplemented
64#1442C2214yescomplemented
65#1442C2214yescomplemented
66#1442C2214yescomplemented
67#1440C2214yes—
68#1440C2214yes—
69#1439C2214yes—
70#1439C2214yes—
71#1436C2214yescomplemented
72#1436C2214yescomplemented
73C4⋊#95C2212yescomplemented
74C4⋊#95C2212yescomplemented
75C4⋊#95C2212yescomplemented
76C4⋊#95C2212yescomplemented
77C4⋊#95C2212yescomplemented
78#1434C2214yescomplemented
79C22⋊#95C2212yes—
80C22⋊#95C2211yescharacteristic
81C22⋊#95C2212yes—
82C22⋊#95C2214yes—
83C22⋊#95C2211yescharacteristic
84C22⋊#95C2212yes—
85C22⋊#95C2212yes—
86C26C2311yescharacteristic
87C23×Q8C2312yes—
88C24×C4—24no—
89C24×C4—28no—
90C24×C4—24no—
91C24×C4—24no—
92C24×C4—44no—
93C24×C4C2312yes—
94C24×C4C2312yes—
95C24×C4C2311yescharacteristic
96C24×C4C2312yes—
97C24×C4C2311yescharacteristic
98C24×C4C2312yes—
99C2×C4⋊Q8—24no—
100C2×C4⋊Q8—44no—
101C2×C22⋊Q8—28no—
102C2×C22⋊Q8—28no—
103C2×C22⋊Q8—44no—
104C22×C4⋊C4—24no—
105C22×C4⋊C4—24no—
106C22×C4⋊C4—24no—
107C22×C4⋊C4—44no—
108C22×C4⋊C4D418yes—
109C22×C4⋊C4C2312yes—
110C22×C4⋊C4C2312yes—
111C22×C4⋊C4C2311yescharacteristic
112C22×C4⋊C4C2312yes—
113C22×C4⋊C4C2311yescharacteristic
114C22×C4⋊C4C2312yes—
115C22×C4⋊C4C2312yes—
116C22×C4⋊C4C2312yes—
117C22×C4⋊C4C2311yescharacteristic
118C22×C4⋊C4C2311yescharacteristic
119C22×C4⋊C4C2312yes—
120C22×C4⋊C4C2312yes—
121C22×C4⋊C4C2312yes—
122C22×C22⋊C4—28no—
123C22×C22⋊C4—28no—
124C22×C22⋊C4—44no—
125C22×C22⋊C4C2314yes—
126C22×C22⋊C4C2312yes—
127C22×C22⋊C4C2311yescharacteristic
128C22×C22⋊C4C2312yes—
129C22×C22⋊C4C2314yes—
130C22×C22⋊C4C2314yes—
131C22×C22⋊C4C2312yes—
132C22×C22⋊C4C2312yes—
133C22×C22⋊C4C2312yes—
134C22×C22⋊C4C2311yescharacteristic
135C22×C22⋊C4C2311yescharacteristic
136C22×C22⋊C4C2311yescharacteristic
137C22×C22⋊C4C2314yes—
138C22×C22⋊C4C2312yes—
139C22×C42C2311yescharacteristic
140C22×C42C2312yes—
141C22×C42C2311yescharacteristic
142C22×C42C2314yes—
143#398—28no—
144#397—216no—
145#395—28no—
146#393—216no—
147#389—24no—
148#389—24no—
149#388—216no—
150#388—216no—
151#385—28no—
152#384—24no—
153#381—28no—
154#381—28no—
155#381—28no—
156#381—44no—
157#380—24no—
158#380—28no—
159#380—24no—
160#380—28no—
161#380—28no—
162#380—216no—
163#380—44no—
164#379—28no—
165#379—24no—
166#379D418yes—
167C4×C4⋊C4—44no—
168C4×C22⋊C4—24no—
169C4×C22⋊C4—28no—
170C4×C22⋊C4—24no—
171C4×C22⋊C4—28no—
172C4×C22⋊C4—44no—
173C2×#95—28no—
174C2×#95C2314yes—
175C2×#95C2314yes—
176C2×#95C2314yes—
177C2×#95C2311yescharacteristic
178C2×#95C2312yes—
179C2×#95C2312yes—
180C2×#95C2314yes—
181C2×#95C2314yes—
182C2×#95C2311yescharacteristic
183C2×#95C2312yes—
184C2×#95C2314yes—
185C2×#95C2312yes—
186C2×#95C2312yes—
187C2×#95C2312yes—
188C2×#95C2312yes—
189C2×#95C2314yes—
190C2×#95C2314yes—
191C2×#95C2314yes—
192C2×#95C2314yes—
193C2×#95C2312yes—
194C2×#95C2314yes—
195C2×#95C2312yes—
196C2×#95C2314yes—
197C2×#95C2314yes—
198C2×#95C2314yes—
199C2×#95C2314yes—
200C25—22no—
201C25—24no—
202C25—22no—
203C25—24no—
204C25—22no—
205C25—22no—
206C25—22no—
207C25—22no—
208C25—42no—
209C25—42no—
210C25C2×D414yes—
211C25C2412yes—
212C25C2411yescharacteristic
213C22×Q8—24no—
214C22×Q8—24no—
215C22×Q8—42no—
216C22×Q8—44no—
217C22×Q8—44no—
218C23×C4—24no—
219C23×C4—24no—
220C23×C4—232no—
221C23×C4—22no—
222C23×C4—24no—
223C23×C4—24no—
224C23×C4—24no—
225C23×C4—24no—
226C23×C4—24no—
227C23×C4—24no—
228C23×C4—24no—
229C23×C4—24no—
230C23×C4—24no—
231C23×C4—24no—
232C23×C4—24no—
233C23×C4—24no—
234C23×C4—24no—
235C23×C4—24no—
236C23×C4—24no—
237C23×C4—24no—
238C23×C4—22no—
239C23×C4—22no—
240C23×C4—24no—
241C23×C4—24no—
242C23×C4—24no—
243C23×C4—24no—
244C23×C4—24no—
245C23×C4—42no—
246C23×C4—42no—
247C23×C4—42no—
248C23×C4—432no—
249C23×C4—432no—
250C23×C4—44no—
251C23×C4—44no—
252C23×C4—416no—
253C23×C4—416no—
254C23×C4C2×D414yes—
255C23×C4C2×D418yes—
256C23×C4#4118yes—
257C23×C4#4114yes—
258C23×C4#4114yes—
259C23×C4C2412yes—
260C23×C4C2412yes—
261C23×C4C2414yes—
262C23×C4C2412yes—
263C23×C4C2414yes—
264C23×C4C2411yescharacteristic
265C23×C4C2411yescharacteristic
266C23×C4C2412yes—
267C23×C4C2412yes—
268C23×C4C2412yes—
269C23×C4C2411yescharacteristic
270C23×C4C2411yescharacteristic
271C23×C4C2412yes—
272C23×C4C2411yescharacteristic
273C23×C4C2411yescharacteristic
274C4⋊Q8—416no—
275C22⋊Q8—432no—
276C2×C4⋊C4—24no—
277C2×C4⋊C4—24no—
278C2×C4⋊C4—24no—
279C2×C4⋊C4—24no—
280C2×C4⋊C4—24no—
281C2×C4⋊C4—24no—
282C2×C4⋊C4—24no—
283C2×C4⋊C4—24no—
284C2×C4⋊C4—24no—
285C2×C4⋊C4—24no—
286C2×C4⋊C4—22no—
287C2×C4⋊C4—24no—
288C2×C4⋊C4—22no—
289C2×C4⋊C4—24no—
290C2×C4⋊C4—24no—
291C2×C4⋊C4—24no—
292C2×C4⋊C4—24no—
293C2×C4⋊C4—24no—
294C2×C4⋊C4—24no—
295C2×C4⋊C4—24no—
296C2×C4⋊C4—24no—
297C2×C4⋊C4—24no—
298C2×C4⋊C4—24no—
299C2×C4⋊C4—416no—
300C2×C4⋊C4—44no—
301C2×C4⋊C4—42no—
302C2×C4⋊C4—42no—
303C2×C4⋊C4—42no—
304C2×C4⋊C4—44no—
305C2×C4⋊C4—416no—
306C2×C4⋊C4—44no—
307C2×C4⋊C4C2×D414yes—
308C2×C4⋊C4C2×D414yes—
309C2×C4⋊C4C2×D418yes—
310C2×C22⋊C4—22no—
311C2×C22⋊C4—22no—
312C2×C22⋊C4—24no—
313C2×C22⋊C4—22no—
314C2×C22⋊C4—22no—
315C2×C22⋊C4—24no—
316C2×C22⋊C4—22no—
317C2×C22⋊C4—22no—
318C2×C22⋊C4—28no—
319C2×C22⋊C4—28no—
320C2×C22⋊C4—24no—
321C2×C22⋊C4—24no—
322C2×C22⋊C4—24no—
323C2×C22⋊C4—28no—
324C2×C22⋊C4—24no—
325C2×C22⋊C4—22no—
326C2×C22⋊C4—22no—
327C2×C22⋊C4—24no—
328C2×C22⋊C4—28no—
329C2×C22⋊C4—24no—
330C2×C22⋊C4—24no—
331C2×C22⋊C4—22no—
332C2×C22⋊C4—24no—
333C2×C22⋊C4—28no—
334C2×C22⋊C4—28no—
335C2×C22⋊C4—28no—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—24no—
338C2×C22⋊C4—28no—
339C2×C22⋊C4—44no—
340C2×C22⋊C4—44no—
341C2×C22⋊C4—42no—
342C2×C22⋊C4—42no—
343C2×C22⋊C4—42no—
344C2×C22⋊C4—42no—
345C2×C22⋊C4—432no—
346C2×C22⋊C4—44no—
347C2×C22⋊C4—44no—
348C2×C22⋊C4C2×D414yes—
349C2×C22⋊C4C2×D414yes—
350C2×C22⋊C4C2×D418yes—
351C2×C22⋊C4C2×D418yes—
352C2×C22⋊C4#4114yes—
353C2×C42—22no—
354C2×C42—22no—
355C2×C42—24no—
356C2×C42—24no—
357C2×C42—24no—
358C2×C42—24no—
359C2×C42—24no—
360C2×C42—28no—
361C2×C42—44no—
362C2×C42—44no—
363#95—28no—
364#95—28no—
365#95—28no—
366#95—22no—
367#95—22no—
368#95—24no—
369#95—28no—
370#95—28no—
371#95—28no—
372#95—28no—
373#95—24no—
374#95—24no—
375#95—24no—
376#95—24no—
377#95—24no—
378#95—28no—
379#95—24no—
380#95—28no—
381#95—28no—
382#95—44no—
383#95—42no—
384#95—42no—
385#95—44no—
386#95—44no—
387#95—44no—
388#95—44no—
389C24—22no—
390C24—22no—
391C24—22no—
392C24—22no—
393C24—28no—
394C24—28no—
395C24—216no—
396C24—28no—
397C24—216no—
398C24—22no—
399C24—22no—
400C24—22no—
401C24—22no—
402C24—22no—
403C24—22no—
404C24—22no—
405C24—22no—
406C24—22no—
407C24—22no—
408C24—22no—
409C24—22no—
410C24—28no—
411C24—28no—
412C24—48no—
413C24—48no—
414C24—48no—
415C24—48no—
416C24—48no—
417C24—48no—
418C24—48no—
419C24—48no—
420C24—48no—
421C24—44no—
422C24—44no—
423C24—48no—
424C24—44no—
425C24—44no—
426C24—44no—
427C24—44no—
428C24C22×D414yes—
429C24C22×D412yes—
430C24C22×D412yes—
431C24C2×#4114yes—
432C24C2×#4112yes—
433C24C2×#4112yes—
434C24C2×#4112yes—
435C24H(5,𝔽2)12yes—
436C242−1+414yes—
437C242−1+412yes—
438C24C2511yescharacteristic
439C2×Q8—48no—
440C2×Q8—48no—
441C2×Q8—84no—
442C2×Q8—88no—
443C2×Q8—88no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—28no—
447C22×C4—28no—
448C22×C4—216no—
449C22×C4—216no—
450C22×C4—216no—
451C22×C4—28no—
452C22×C4—22no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—22no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—24no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—24no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—22no—
483C22×C4—24no—
484C22×C4—22no—
485C22×C4—24no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—216no—
489C22×C4—216no—
490C22×C4—216no—
491C22×C4—216no—
492C22×C4—24no—
493C22×C4—24no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—24no—
498C22×C4—22no—
499C22×C4—24no—
500C22×C4—24no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—24no—
504C22×C4—24no—
505C22×C4—24no—
506C22×C4—22no—
507C22×C4—24no—
508C22×C4—24no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—24no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—24no—
515C22×C4—24no—
516C22×C4—24no—
517C22×C4—24no—
518C22×C4—22no—
519C22×C4—24no—
520C22×C4—22no—
521C22×C4—24no—
522C22×C4—24no—
523C22×C4—48no—
524C22×C4—48no—
525C22×C4—48no—
526C22×C4—48no—
527C22×C4—48no—
528C22×C4—48no—
529C22×C4—48no—
530C22×C4—48no—
531C22×C4—48no—
532C22×C4—4128no—
533C22×C4—44no—
534C22×C4—44no—
535C22×C4—48no—
536C22×C4—48no—
537C22×C4—48no—
538C22×C4—48no—
539C22×C4—48no—
540C22×C4—48no—
541C22×C4—48no—
542C22×C4—48no—
543C22×C4—48no—
544C22×C4—48no—
545C22×C4—48no—
546C22×C4—48no—
547C22×C4—88no—
548C22×C4—88no—
549C22×C4#124116yes—
550C22×C4C22×D414yes—
551C22×C4C22×D412yes—
552C22×C4C22×D412yes—
553C22×C4C22×D414yes—
554C22×C4C22×D414yes—
555C22×C4C22×D412yes—
556C22×C4C22×D412yes—
557C22×C4C2×#4112yes—
558C22×C4C2×#4112yes—
559C22×C4C2×#4114yes—
560C22×C4C2×#4112yes—
561C22×C4C2×#4112yes—
562C22×C4C2×#4114yes—
563C22×C4C2×#4112yes—
564C22×C4C2×#4112yes—
565C22×C4H(5,𝔽2)14yes—
566C4⋊C4—28no—
567C4⋊C4—28no—
568C4⋊C4—48no—
569C4⋊C4—48no—
570C4⋊C4—48no—
571C4⋊C4—48no—
572C4⋊C4—48no—
573C4⋊C4—44no—
574C4⋊C4—48no—
575C4⋊C4—48no—
576C4⋊C4—44no—
577C4⋊C4—48no—
578C4⋊C4—84no—
579C22⋊C4—28no—
580C22⋊C4—216no—
581C22⋊C4—28no—
582C22⋊C4—28no—
583C22⋊C4—48no—
584C22⋊C4—48no—
585C22⋊C4—48no—
586C22⋊C4—416no—
587C22⋊C4—416no—
588C22⋊C4—48no—
589C22⋊C4—48no—
590C22⋊C4—416no—
591C22⋊C4—44no—
592C22⋊C4—88no—
593C42—44no—
594C42—44no—
595C42—48no—
596C42—88no—
597C23—22no—
598C23—22no—
599C23—24no—
600C23—24no—
601C23—24no—
602C23—24no—
603C23—22no—
604C23—22no—
605C23—24no—
606C23—24no—
607C23—24no—
608C23—24no—
609C23—24no—
610C23—24no—
611C23—24no—
612C23—24no—
613C23—232no—
614C23—24no—
615C23—24no—
616C23—24no—
617C23—24no—
618C23—24no—
619C23—24no—
620C23—24no—
621C23—24no—
622C23—24no—
623C23—24no—
624C23—24no—
625C23—24no—
626C23—24no—
627C23—24no—
628C23—24no—
629C23—24no—
630C23—24no—
631C23—24no—
632C23—432no—
633C23—432no—
634C23—416no—
635C23—416no—
636C23—432no—
637C23—416no—
638C23—416no—
639C23—416no—
640C23—432no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—416no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23C2×#12414yes—
659C23#53214yes—
660C23#54214yes—
661C23D4214yes—
662C23#54718yes—
663C23#54714yes—
664C23#54814yes—
665C23#55514yes—
666C23C23×D411yescharacteristic
667C23C23×D411yescharacteristic
668C23C22×#4112yes—
669C23C22×#4111yescharacteristic
670C23C22×#4111yescharacteristic
671C23C22×#4111yescharacteristic
672C23C2×H(5,𝔽2)12yes—
673C23C2×H(5,𝔽2)11yescharacteristic
674C23C2×2−1+411yescharacteristic
675C23C2×2−1+412yes—
676C23#58512yes—
677Q8—816no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—24no—
681C2×C4—24no—
682C2×C4—232no—
683C2×C4—24no—
684C2×C4—24no—
685C2×C4—24no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—24no—
689C2×C4—24no—
690C2×C4—24no—
691C2×C4—24no—
692C2×C4—24no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—24no—
696C2×C4—24no—
697C2×C4—24no—
698C2×C4—24no—
699C2×C4—24no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—432no—
704C2×C4—416no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—42no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—44no—
723C2×C4—44no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—44no—
727C2×C4—44no—
728C2×C4—42no—
729C2×C4—432no—
730C2×C4—42no—
731C2×C4—44no—
732C2×C4—44no—
733C2×C4—44no—
734C2×C4—42no—
735C2×C4—44no—
736C2×C4—44no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—44no—
740C2×C4—44no—
741C2×C4—44no—
742C2×C4—44no—
743C2×C4—42no—
744C2×C4—44no—
745C2×C4—42no—
746C2×C4—44no—
747C2×C4—42no—
748C2×C4—44no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—44no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—44no—
755C2×C4—44no—
756C2×C4—44no—
757C2×C4—42no—
758C2×C4—44no—
759C2×C4—42no—
760C2×C4—44no—
761C2×C4—816no—
762C2×C4—816no—
763C2×C4#52514yes—
764C2×C4C2×#12414yes—
765C2×C4C2×#12414yes—
766C2×C4#53414yes—
767C2×C4#55118yes—
768C2×C4#55118yes—
769C22—24no—
770C22—24no—
771C22—24no—
772C22—28no—
773C22—28no—
774C22—28no—
775C22—24no—
776C22—24no—
777C22—24no—
778C22—28no—
779C22—28no—
780C22—28no—
781C22—28no—
782C22—464no—
783C22—44no—
784C22—44no—
785C22—44no—
786C22—44no—
787C22—44no—
788C22—44no—
789C22—44no—
790C22—44no—
791C22—44no—
792C22—44no—
793C22—44no—
794C22—44no—
795C22#249118yes—
796C22C2×#52511yescharacteristic
797C22C22×#12411yescharacteristic
798C22C2×#53211yescharacteristic
799C22C2×#53411yescharacteristic
800C22C2×#54211yescharacteristic
801C22C2×D4211yescharacteristic
802C22C2×#54712yes—
803C22C2×#54711yescharacteristic
804C22C2×#54811yescharacteristic
805C22C2×#55112yes—
806C22C2×#55112yes—
807C22C2×#55511yescharacteristic
808C22#347512yes—
809C22#348511yescharacteristic
810C22#348611yescharacteristic
811C22#349212yes—
812C22#349512yes—
813C22#349512yes—
814C22#349512yes—
815C22#349612yes—
816C22#352012yes—
817C22#353812yes—
818C22#354212yes—
819C4—24no—
820C4—42no—
821C4—44no—
822C4—44no—
823C4—42no—
824C4—44no—
825C4—44no—
826C4—42no—
827C4—42no—
828C4—82no—
829C4—82no—
830C4—84no—
831C4—82no—
832C4—84no—
833C4#256118yescomplemented
834C2—28no—
835C2—48no—
836C2C2×#249111yescharacteristic
837C2C2×#256111yescharacteristic
838C2#3564411yescharacteristic
839C2#3610311yescharacteristic
840C2#3618312yes—
841C2#3651611yescharacteristic
842C2#3785312yes—
843C2#3912111yescharacteristic
844C2#3933811yescharacteristic
845C2#5919812yes—
846C2#5920312yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC26C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#2440C2semidirect
4. #15770C2semidirect
5. #15541C2semidirect
6. #15132C2semidirect
7. #15125C2semidirect
8. #14934C2semidirect
11. #13994C2semidirect
12. #13972C2semidirect
13. #13904C2semidirect
14. #13904C2semidirect
15. #13876C2semidirect
16. C22⋊C4×C4⋊C4C2semidirect
19. C22×C4⋊Q8C22semidirect
26. C2×#398C22semidirect
28. C2×#395C22semidirect
30. C2×#389C22semidirect
31. C2×#389C22semidirect
35. C2×#384C22semidirect
51. C2×C4×C4⋊C4C22semidirect
58. #1446C22semidirect
59. #1445C22semidirect
60. #1445C22semidirect
61. #1445C22semidirect
62. #1443C22semidirect
63. #1442C22semidirect
64. #1442C22semidirect
65. #1442C22semidirect
66. #1442C22semidirect
71. #1436C22semidirect
72. #1436C22semidirect
73. C4⋊#95C22semidirect
74. C4⋊#95C22semidirect
75. C4⋊#95C22semidirect
76. C4⋊#95C22semidirect
77. C4⋊#95C22semidirect
78. #1434C22semidirect
833. C4#2561semidirect

Maximal subgroups

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

subgroupindex
C2×#25612
C2×#24402
C22×#3802
#157702
#155412
#151322
#151252
#149342
#149182
#146802
#139942
#139722
#139042
#138762
C22⋊C4×C4⋊C42
C4×#3792