Finite Group Databasebeta

← #648735

Subgroups — #648735

Order 512.

5270 conjugacy classes of subgroups.

The subgroup lattice has 869 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C22⋊Q8C211yesmaximal, characteristic
2C2×#2489C212yesmaximal, complemented
3C2×#2442C211yesmaximal, characteristic, complemented
4#15672C214yesmaximal, complemented
5#15670C214yesmaximal, complemented
6#15236C212yesmaximal, complemented
7#15179C212yesmaximal, complemented
8#14843C212yesmaximal, complemented
9#14820C212yesmaximal
10#14680C211yesmaximal, characteristic
11#13997C212yesmaximal, complemented
12#13971C212yesmaximal
13#13922C211yesmaximal, characteristic, complemented
14#13922C211yesmaximal, characteristic, complemented
15#13881C212yesmaximal, complemented
16C22⋊C4×C4⋊C4C211yesmaximal, characteristic, complemented
17C4×#379C211yesmaximal, characteristic
18C24×Q8C2211yescharacteristic
19C25×C4C2211yescharacteristic
20C22×#125C2211yescharacteristic, complemented
21C22×C22⋊Q8—216no—
22C22×C22⋊Q8—28no—
23C22×C22⋊Q8C2214yes—
24C22×C22⋊Q8C2212yes—
25C22×C22⋊Q8C2212yes—
26C23×C4⋊C4C2212yes—
27C23×C4⋊C4C2211yescharacteristic
28C23×C22⋊C4C2212yes—
29#2489—216no—
30#2442—28no—
31C2×#400C2212yescomplemented
32C2×#400C2214yescomplemented
33C2×#398C2212yescomplemented
34C2×#397C2214yes—
35C2×#391C2212yescomplemented
36C2×#391C2212yescomplemented
37C2×#391C2212yescomplemented
38C2×#391C2212yescomplemented
39C2×#389C2211yescharacteristic, complemented
40C2×#389C2211yescharacteristic, complemented
41C2×#388C2214yes—
42C2×#385C2212yes—
43C2×#382C2214yescomplemented
44C2×#382C2211yescharacteristic, complemented
45C2×#380C2212yes—
46C2×#380C2211yescharacteristic
47C2×#380C2211yescharacteristic
48C2×#380C2212yes—
49C2×#380C2212yes—
50C2×#379C2212yes—
51C2×#379C2211yescharacteristic
52C2×#379C2211yescharacteristic
53C2×C4×C4⋊C4C2212yescomplemented
54C2×C4×C22⋊C4C2212yes—
55C2×C4×C22⋊C4C2212yes—
56C2×C4×C22⋊C4C2211yescharacteristic
57C2×C4×C22⋊C4C2211yescharacteristic
58C2×C4×C22⋊C4C2212yes—
59#1446C2212yescomplemented
60#1446C2214yescomplemented
61#1446C2212yescomplemented
62#1445C2214yescomplemented
63#1442C2214yescomplemented
64#1442C2214yescomplemented
65#1442C2214yescomplemented
66#1441C2214yescomplemented
67#1440C2214yes—
68#1440C2214yes—
69#1440C2214yes—
70#1439C2214yes—
71#1439C2214yes—
72#1437C2214yes—
73#1436C2214yescomplemented
74C4⋊#95C2214yescomplemented
75C4⋊#95C2212yescomplemented
76C22⋊#95C2212yes—
77C22⋊#95C2214yes—
78C22⋊#95C2212yes—
79C22⋊#95C2211yescharacteristic
80C22⋊#95C2212yes—
81C22⋊#95C2212yes—
82C22⋊#95C2212yes—
83C22⋊#95C2212yes—
84C22⋊#95C2212yes—
85C22⋊#95C2211yescharacteristic
86C22⋊#95C2212yes—
87C26C2311yescharacteristic
88C23×Q8—28no—
89C23×Q8—24no—
90C23×Q8—24no—
91C23×Q8—24no—
92C23×Q8—44no—
93C23×Q8C2312yes—
94C23×Q8C2312yes—
95C24×C4—28no—
96C24×C4—24no—
97C24×C4—24no—
98C24×C4—24no—
99C24×C4—44no—
100C24×C4C2312yes—
101C24×C4C2311yescharacteristic
102C24×C4C2312yes—
103C24×C4C2312yes—
104C24×C4C2312yes—
105C24×C4C2311yescharacteristic
106C2×#125—24no—
107C2×#125—28no—
108C2×C22⋊Q8—2128no—
109C2×C22⋊Q8—28no—
110C2×C22⋊Q8—28no—
111C2×C22⋊Q8—216no—
112C2×C22⋊Q8—28no—
113C2×C22⋊Q8—216no—
114C2×C22⋊Q8—28no—
115C2×C22⋊Q8—28no—
116C2×C22⋊Q8—216no—
117C2×C22⋊Q8D4116yes—
118C22×C4⋊C4—28no—
119C22×C4⋊C4—216no—
120C22×C4⋊C4—28no—
121C22×C4⋊C4D418yes—
122C22×C4⋊C4C2312yes—
123C22×C4⋊C4C2312yes—
124C22×C4⋊C4C2314yes—
125C22×C4⋊C4C2311yescharacteristic
126C22×C4⋊C4C2312yes—
127C22×C4⋊C4C2311yescharacteristic
128C22×C4⋊C4C2312yes—
129C22×C4⋊C4C2314yes—
130C22×C4⋊C4C2311yescharacteristic
131C22×C4⋊C4C2312yes—
132C22×C4⋊C4C2312yes—
133C22×C4⋊C4C2311yescharacteristic
134C22×C22⋊C4—28no—
135C22×C22⋊C4—216no—
136C22×C22⋊C4C2312yes—
137C22×C22⋊C4C2314yes—
138C22×C22⋊C4C2314yes—
139C22×C22⋊C4C2311yescharacteristic
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2311yescharacteristic
142C22×C22⋊C4C2311yescharacteristic
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2314yes—
147C22×C22⋊C4C2311yescharacteristic
148C22×C22⋊C4C2314yes—
149C22×C22⋊C4C2312yes—
150C22×C42C2311yescharacteristic
151C22×C42C2312yes—
152C22×C42C2311yescharacteristic
153C22×C42C2314yes—
154#400—28no—
155#400—216no—
156#398—28no—
157#397—216no—
158#391—28no—
159#391—28no—
160#391—44no—
161#391—44no—
162#389—24no—
163#389—24no—
164#388—216no—
165#385—28no—
166#382—24no—
167#382—216no—
168#380—28no—
169#380—24no—
170#380—28no—
171#380—24no—
172#380—44no—
173#379—24no—
174#379—28no—
175#379—24no—
176C4×C4⋊C4—28no—
177C4×C22⋊C4—24no—
178C4×C22⋊C4—28no—
179C4×C22⋊C4—24no—
180C4×C22⋊C4—28no—
181C4×C22⋊C4—44no—
182C2×#95C2314yes—
183C2×#95C2314yes—
184C2×#95C2314yes—
185C2×#95C2311yescharacteristic
186C2×#95C2312yes—
187C2×#95C2312yes—
188C2×#95C2312yes—
189C2×#95C2311yescharacteristic
190C2×#95C2314yes—
191C2×#95C2314yes—
192C2×#95C2312yes—
193C2×#95C2312yes—
194C2×#95C2312yes—
195C2×#95C2312yes—
196C2×#95C2312yes—
197C2×#95C2312yes—
198C2×#95C2314yes—
199C2×#95C2314yes—
200C2×#95C2312yes—
201C2×#95C2314yes—
202C2×#95C2312yes—
203C2×#95C2314yes—
204C2×#95C2314yes—
205C2×#95C2314yes—
206C2×#95C2314yes—
207C2×#95C2314yes—
208C25—24no—
209C25—22no—
210C25—24no—
211C25—22no—
212C25—22no—
213C25—22no—
214C25—22no—
215C25—22no—
216C25—42no—
217C25—42no—
218C25#4114yes—
219C25C2412yes—
220C25C2411yescharacteristic
221C22×Q8—232no—
222C22×Q8—28no—
223C22×Q8—24no—
224C22×Q8—24no—
225C22×Q8—24no—
226C22×Q8—24no—
227C22×Q8—24no—
228C22×Q8—24no—
229C22×Q8—24no—
230C22×Q8—24no—
231C22×Q8—24no—
232C22×Q8—44no—
233C22×Q8—432no—
234C22×Q8—432no—
235C22×Q8—416no—
236C22×Q8—416no—
237C22×Q8C2×D418yes—
238C23×C4—24no—
239C23×C4—24no—
240C23×C4—232no—
241C23×C4—24no—
242C23×C4—22no—
243C23×C4—24no—
244C23×C4—24no—
245C23×C4—24no—
246C23×C4—28no—
247C23×C4—28no—
248C23×C4—24no—
249C23×C4—24no—
250C23×C4—24no—
251C23×C4—24no—
252C23×C4—24no—
253C23×C4—24no—
254C23×C4—24no—
255C23×C4—24no—
256C23×C4—24no—
257C23×C4—22no—
258C23×C4—22no—
259C23×C4—24no—
260C23×C4—24no—
261C23×C4—24no—
262C23×C4—24no—
263C23×C4—42no—
264C23×C4—42no—
265C23×C4—42no—
266C23×C4—44no—
267C23×C4—44no—
268C23×C4—432no—
269C23×C4—432no—
270C23×C4—416no—
271C23×C4—416no—
272C23×C4C2×D418yes—
273C23×C4C2×D418yes—
274C23×C4C2×D414yes—
275C23×C4#4114yes—
276C23×C4#4114yes—
277C23×C4C2411yescharacteristic
278C23×C4C2412yes—
279C23×C4C2412yes—
280C23×C4C2411yescharacteristic
281C23×C4C2411yescharacteristic
282C23×C4C2414yes—
283C23×C4C2412yes—
284C23×C4C2411yescharacteristic
285C23×C4C2412yes—
286C23×C4C2414yes—
287C23×C4C2412yes—
288C23×C4C2412yes—
289C23×C4C2412yes—
290C23×C4C2411yescharacteristic
291C23×C4C2411yescharacteristic
292#125—416no—
293C22⋊Q8—264no—
294C22⋊Q8—2128no—
295C22⋊Q8—264no—
296C2×C4⋊C4—264no—
297C2×C4⋊C4—28no—
298C2×C4⋊C4—28no—
299C2×C4⋊C4—28no—
300C2×C4⋊C4—28no—
301C2×C4⋊C4—24no—
302C2×C4⋊C4—28no—
303C2×C4⋊C4—28no—
304C2×C4⋊C4—232no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—24no—
307C2×C4⋊C4—24no—
308C2×C4⋊C4—28no—
309C2×C4⋊C4—24no—
310C2×C4⋊C4—28no—
311C2×C4⋊C4—24no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4—24no—
315C2×C4⋊C4—24no—
316C2×C4⋊C4—24no—
317C2×C4⋊C4—24no—
318C2×C4⋊C4—44no—
319C2×C4⋊C4—44no—
320C2×C4⋊C4C2×D4116yes—
321C2×C4⋊C4C2×D414yes—
322C2×C4⋊C4C2×D418yes—
323C2×C4⋊C4C2×D418yes—
324C2×C4⋊C4C2×D414yes—
325C2×C22⋊C4—264no—
326C2×C22⋊C4—28no—
327C2×C22⋊C4—22no—
328C2×C22⋊C4—22no—
329C2×C22⋊C4—28no—
330C2×C22⋊C4—28no—
331C2×C22⋊C4—28no—
332C2×C22⋊C4—28no—
333C2×C22⋊C4—22no—
334C2×C22⋊C4—22no—
335C2×C22⋊C4—24no—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—24no—
338C2×C22⋊C4—28no—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—22no—
341C2×C22⋊C4—24no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—22no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—28no—
346C2×C22⋊C4—22no—
347C2×C22⋊C4—24no—
348C2×C22⋊C4—22no—
349C2×C22⋊C4—24no—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—22no—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—28no—
354C2×C22⋊C4—22no—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—22no—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—28no—
360C2×C22⋊C4—42no—
361C2×C22⋊C4—42no—
362C2×C22⋊C4—42no—
363C2×C22⋊C4—42no—
364C2×C22⋊C4—44no—
365C2×C22⋊C4—44no—
366C2×C22⋊C4C2×D4116yes—
367C2×C22⋊C4#4114yes—
368C2×C42—22no—
369C2×C42—24no—
370C2×C42—24no—
371C2×C42—22no—
372C2×C42—28no—
373C2×C42—28no—
374C2×C42—24no—
375C2×C42—24no—
376C2×C42—24no—
377C2×C42—44no—
378#95—24no—
379#95—22no—
380#95—24no—
381#95—22no—
382#95—28no—
383#95—24no—
384#95—28no—
385#95—24no—
386#95—24no—
387#95—24no—
388#95—28no—
389#95—28no—
390#95—24no—
391#95—28no—
392#95—28no—
393#95—28no—
394#95—24no—
395#95—24no—
396#95—44no—
397#95—42no—
398#95—42no—
399#95—44no—
400#95—44no—
401#95—44no—
402#95—44no—
403#95—44no—
404C24—22no—
405C24—22no—
406C24—22no—
407C24—22no—
408C24—28no—
409C24—28no—
410C24—216no—
411C24—216no—
412C24—28no—
413C24—22no—
414C24—22no—
415C24—22no—
416C24—22no—
417C24—22no—
418C24—22no—
419C24—22no—
420C24—22no—
421C24—22no—
422C24—22no—
423C24—22no—
424C24—22no—
425C24—28no—
426C24—28no—
427C24—48no—
428C24—48no—
429C24—48no—
430C24—48no—
431C24—48no—
432C24—48no—
433C24—48no—
434C24—48no—
435C24—48no—
436C24—44no—
437C24—44no—
438C24—48no—
439C24—44no—
440C24—44no—
441C24—44no—
442C24—44no—
443C24C22×D414yes—
444C24C22×D412yes—
445C24C2×#4114yes—
446C24C2×#4112yes—
447C24C2×#4112yes—
448C24C2×#4112yes—
449C24C2×#4112yes—
450C242−1+414yes—
451C242−1+412yes—
452C242−1+412yes—
453C24C2511yescharacteristic
454C2×Q8—216no—
455C2×Q8—216no—
456C2×Q8—216no—
457C2×Q8—216no—
458C2×Q8—416no—
459C2×Q8—416no—
460C2×Q8—48no—
461C2×Q8—4128no—
462C2×Q8—48no—
463C2×Q8—48no—
464C2×Q8—48no—
465C2×Q8—48no—
466C2×Q8—48no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—24no—
472C22×C4—28no—
473C22×C4—28no—
474C22×C4—216no—
475C22×C4—216no—
476C22×C4—216no—
477C22×C4—28no—
478C22×C4—216no—
479C22×C4—216no—
480C22×C4—22no—
481C22×C4—24no—
482C22×C4—24no—
483C22×C4—24no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—24no—
491C22×C4—24no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—24no—
496C22×C4—24no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—24no—
501C22×C4—22no—
502C22×C4—216no—
503C22×C4—216no—
504C22×C4—216no—
505C22×C4—216no—
506C22×C4—21no—
507C22×C4—22no—
508C22×C4—24no—
509C22×C4—21no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—21no—
513C22×C4—22no—
514C22×C4—24no—
515C22×C4—22no—
516C22×C4—21no—
517C22×C4—24no—
518C22×C4—22no—
519C22×C4—24no—
520C22×C4—24no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—22no—
524C22×C4—21no—
525C22×C4—22no—
526C22×C4—21no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—24no—
532C22×C4—24no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—22no—
536C22×C4—21no—
537C22×C4—24no—
538C22×C4—22no—
539C22×C4—24no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—21no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—24no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—24no—
550C22×C4—48no—
551C22×C4—48no—
552C22×C4—48no—
553C22×C4—416no—
554C22×C4—416no—
555C22×C4—48no—
556C22×C4—48no—
557C22×C4—48no—
558C22×C4—48no—
559C22×C4—416no—
560C22×C4—416no—
561C22×C4—48no—
562C22×C4—4128no—
563C22×C4—44no—
564C22×C4—48no—
565C22×C4—44no—
566C22×C4—48no—
567C22×C4—48no—
568C22×C4—48no—
569C22×C4—48no—
570C22×C4—48no—
571C22×C4—48no—
572C22×C4#124116yes—
573C22×C4C22×D418yes—
574C22×C4C22×D414yes—
575C22×C4C22×D414yes—
576C22×C4C22×D418yes—
577C22×C4C22×D414yes—
578C22×C4C22×D412yes—
579C22×C4C22×D412yes—
580C22×C4C22×D414yes—
581C22×C4C2×#4114yes—
582C22×C4C2×#4112yes—
583C22×C4C2×#4112yes—
584C22×C4C2×#4112yes—
585C22×C4C2×#4112yes—
586C22×C4H(5,𝔽2)14yes—
587C4⋊C4—232no—
588C4⋊C4—216no—
589C4⋊C4—28no—
590C4⋊C4—232no—
591C4⋊C4—48no—
592C4⋊C4—48no—
593C4⋊C4—44no—
594C4⋊C4—44no—
595C4⋊C4—48no—
596C4⋊C4—84no—
597C4⋊C4—84no—
598C4⋊C4#120116yes—
599C22⋊C4—232no—
600C22⋊C4—28no—
601C22⋊C4—232no—
602C22⋊C4—48no—
603C22⋊C4—48no—
604C22⋊C4—48no—
605C22⋊C4—48no—
606C22⋊C4—44no—
607C22⋊C4—48no—
608C22⋊C4—416no—
609C22⋊C4—44no—
610C22⋊C4—48no—
611C22⋊C4—44no—
612C22⋊C4—88no—
613C42—416no—
614C42—44no—
615C42—44no—
616C42—48no—
617C23—22no—
618C23—22no—
619C23—24no—
620C23—24no—
621C23—24no—
622C23—24no—
623C23—22no—
624C23—22no—
625C23—24no—
626C23—24no—
627C23—24no—
628C23—24no—
629C23—24no—
630C23—24no—
631C23—24no—
632C23—24no—
633C23—232no—
634C23—24no—
635C23—24no—
636C23—24no—
637C23—24no—
638C23—24no—
639C23—24no—
640C23—24no—
641C23—24no—
642C23—24no—
643C23—24no—
644C23—24no—
645C23—24no—
646C23—24no—
647C23—24no—
648C23—24no—
649C23—24no—
650C23—24no—
651C23—24no—
652C23—432no—
653C23—432no—
654C23—416no—
655C23—416no—
656C23—432no—
657C23—416no—
658C23—416no—
659C23—416no—
660C23—432no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—416no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23C2×#12414yes—
679C23#52914yes—
680C23#54114yes—
681C23#54714yes—
682C23#54818yes—
683C23#54814yes—
684C23#55214yes—
685C23#55214yes—
686C23C23×D411yescharacteristic
687C23C23×D412yes—
688C23C22×#4111yescharacteristic
689C23C22×#4111yescharacteristic
690C23C22×#4111yescharacteristic
691C23C22×#4111yescharacteristic
692C23C2×H(5,𝔽2)12yes—
693C23C2×2−1+411yescharacteristic
694C23C2×2−1+411yescharacteristic
695C23C2×2−1+412yes—
696C23#58512yes—
697Q8—432no—
698Q8—432no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—24no—
704C2×C4—28no—
705C2×C4—24no—
706C2×C4—28no—
707C2×C4—232no—
708C2×C4—24no—
709C2×C4—28no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—28no—
714C2×C4—28no—
715C2×C4—24no—
716C2×C4—24no—
717C2×C4—24no—
718C2×C4—24no—
719C2×C4—24no—
720C2×C4—432no—
721C2×C4—432no—
722C2×C4—416no—
723C2×C4—432no—
724C2×C4—42no—
725C2×C4—44no—
726C2×C4—42no—
727C2×C4—44no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—44no—
732C2×C4—44no—
733C2×C4—44no—
734C2×C4—42no—
735C2×C4—44no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—432no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—42no—
742C2×C4—44no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—44no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—44no—
751C2×C4—41no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—44no—
756C2×C4—41no—
757C2×C4—42no—
758C2×C4—44no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—41no—
762C2×C4—42no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—44no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—44no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—44no—
776C2×C4—44no—
777C2×C4—42no—
778C2×C4—44no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—44no—
783C2×C4C2×#12018yes—
784C2×C4C2×#12014yes—
785C2×C4C2×#12414yes—
786C2×C4C2×#12414yes—
787C2×C4#53514yes—
788C2×C4#54618yes—
789C2×C4#54618yes—
790C22—24no—
791C22—28no—
792C22—28no—
793C22—24no—
794C22—24no—
795C22—24no—
796C22—24no—
797C22—28no—
798C22—28no—
799C22—24no—
800C22—28no—
801C22—28no—
802C22—28no—
803C22—464no—
804C22—44no—
805C22—44no—
806C22—44no—
807C22—44no—
808C22—44no—
809C22—44no—
810C22—44no—
811C22—44no—
812C22—44no—
813C22—44no—
814C22—44no—
815C22—44no—
816C22#248918yescomplemented
817C22C22×#12011yescharacteristic
818C22C22×#12411yescharacteristic
819C22C2×#52911yescharacteristic
820C22C2×#53511yescharacteristic
821C22C2×#54111yescharacteristic
822C22C2×#54612yes—
823C22C2×#54612yes—
824C22C2×#54711yescharacteristic
825C22C2×#54812yes—
826C22C2×#54811yescharacteristic
827C22D4×#4112yes—
828C22C2×#55211yescharacteristic
829C22C2×#55211yescharacteristic
830C22#348511yescharacteristic
831C22#348611yescharacteristic
832C22#348612yes—
833C22#348912yes—
834C22#349512yes—
835C22#349512yes—
836C22#350512yes—
837C22#352012yes—
838C22#353812yes—
839C22#354112yes—
840C4—28no—
841C4—24no—
842C4—44no—
843C4—44no—
844C4—48no—
845C4—44no—
846C4—81no—
847C4—84no—
848C4—81no—
849C4—82no—
850C4—81no—
851C4—82no—
852C4—81no—
853C4—82no—
854C4#243518yes—
855C2—28no—
856C2—48no—
857C2C2×#243511yescharacteristic
858C2C2×#248911yescharacteristic
859C2#3564411yescharacteristic
860C2#3610812yes—
861C2#3621311yescharacteristic
862C2#3657511yescharacteristic
863C2#3766312yes—
864C2#3891711yescharacteristic
865C2#3972211yescharacteristic
866C2#5901412yes—
867C2#5902712yes—
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×#2489C2semidirect
3. C2×#2442C2semidirect
4. #15672C2semidirect
5. #15670C2semidirect
6. #15236C2semidirect
7. #15179C2semidirect
8. #14843C2semidirect
11. #13997C2semidirect
13. #13922C2semidirect
14. #13922C2semidirect
15. #13881C2semidirect
16. C22⋊C4×C4⋊C4C2semidirect
20. C22×#125C22semidirect
31. C2×#400C22semidirect
32. C2×#400C22semidirect
33. C2×#398C22semidirect
35. C2×#391C22semidirect
36. C2×#391C22semidirect
37. C2×#391C22semidirect
38. C2×#391C22semidirect
39. C2×#389C22semidirect
40. C2×#389C22semidirect
43. C2×#382C22semidirect
44. C2×#382C22semidirect
53. C2×C4×C4⋊C4C22semidirect
59. #1446C22semidirect
60. #1446C22semidirect
61. #1446C22semidirect
62. #1445C22semidirect
63. #1442C22semidirect
64. #1442C22semidirect
65. #1442C22semidirect
66. #1441C22semidirect
73. #1436C22semidirect
74. C4⋊#95C22semidirect
75. C4⋊#95C22semidirect
816. C22#2489semidirect

Maximal subgroups

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

subgroupindex
C23×C22⋊Q82
C2×#24892
C2×#24422
#156722
#156702
#152362
#151792
#148432
#148202
#146802
#139972
#139712
#139222
#138812
C22⋊C4×C4⋊C42
C4×#3792