Finite Group Databasebeta

← #642405

Subgroups — #642405

Order 512.

4074 conjugacy classes of subgroups.

The subgroup lattice has 887 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2848C211yesmaximal, characteristic
2C2×#2627C211yesmaximal, characteristic, complemented
3C22×#385C211yesmaximal, characteristic
4C2×#2280C211yesmaximal, characteristic
5#16561C214yesmaximal, complemented
6#16394C212yesmaximal, complemented
7#16262C212yesmaximal, complemented
8#14918C212yesmaximal
9#14907C214yesmaximal, complemented
10#14841C212yesmaximal, complemented
11#14763C212yesmaximal, complemented
12#14727C212yesmaximal
13#14339C211yesmaximal, characteristic, complemented
14#14281C211yesmaximal, characteristic, complemented
15#14275C211yesmaximal, characteristic, complemented
16#14043C212yesmaximal, complemented
17#13972C212yesmaximal, complemented
18C25×C4C2211yescharacteristic
19C22×C22⋊Q8C2211yescharacteristic
20C22×C22⋊Q8C2211yescharacteristic
21C22×C22⋊Q8C2211yescharacteristic
22C22×#117C2212yes—
23C23×C4⋊C4C2211yescharacteristic
24C23×C4⋊C4C2211yescharacteristic
25C23×C22⋊C4C2211yescharacteristic
26C23×C22⋊C4C2211yescharacteristic
27#2848—28no—
28#2627—28no—
29C2×#400C2212yescomplemented
30C2×#398C2214yescomplemented
31C2×#397C2214yes—
32C2×#395C2212yescomplemented
33C2×#389C2214yescomplemented
34C2×#385—28no—
35C2×#385C2212yes—
36C2×#385C2212yes—
37C2×#385C2212yes—
38C2×#385C2212yes—
39C2×#385C2212yes—
40C2×#385C2212yes—
41C2×#385C2212yes—
42C2×#385C2212yes—
43C2×#385C2212yes—
44#2280—28no—
45C2×#381C2212yes—
46C2×#381C2212yes—
47C2×#381C2212yes—
48C2×#380C2211yescharacteristic
49C2×#380C2211yescharacteristic
50C2×#380C2211yescharacteristic
51C2×#380C2211yescharacteristic
52C2×#380C2212yes—
53C2×#380C2211yescharacteristic
54C2×#379C2212yes—
55C2×#379C2212yes—
56C2×C4×C22⋊C4C2212yes—
57C2×C4×C22⋊C4C2212yes—
58C22×#95C2211yescharacteristic
59C22×#95C2211yescharacteristic
60#1446C2212yescomplemented
61#1445C2212yescomplemented
62#1444C2212yescomplemented
63#1444C2214yescomplemented
64#1443C2214yescomplemented
65#1442C2214yescomplemented
66#1442C2212yescomplemented
67#1441C2212yescomplemented
68#1441C2214yescomplemented
69#1441C2212yescomplemented
70#1441C2214yescomplemented
71#1441C2214yescomplemented
72#1441C2214yescomplemented
73#1440C2214yes—
74#1440C2214yes—
75#1440C2214yes—
76#1440C2214yes—
77#1439C2214yes—
78#1439C2214yes—
79#1439C2214yes—
80#1436C2214yescomplemented
81#1436C2214yescomplemented
82#1434C2214yescomplemented
83C22⋊#95C2212yes—
84C22⋊#95C2212yes—
85C22⋊#95C2212yes—
86C22⋊#95C2212yes—
87C26C2311yescharacteristic
88C23×Q8C2311yescharacteristic
89C24×C4—24no—
90C24×C4—24no—
91C24×C4—44no—
92C24×C4—44no—
93C24×C4D418yes—
94C24×C4C2311yescharacteristic
95C24×C4C2311yescharacteristic
96C24×C4C2311yescharacteristic
97C24×C4C2311yescharacteristic
98C24×C4C2311yescharacteristic
99C24×C4C2311yescharacteristic
100C24×C4C2311yescharacteristic
101C24×C4C2311yescharacteristic
102C24×C4C2311yescharacteristic
103C24×C4C2311yescharacteristic
104C2×C22⋊Q8—24no—
105C2×C22⋊Q8—24no—
106C2×C22⋊Q8—24no—
107C2×C22⋊Q8—24no—
108C2×C22⋊Q8—24no—
109C2×C22⋊Q8—44no—
110C2×C22⋊Q8—44no—
111C2×#117—28no—
112C2×#117—44no—
113C2×#117—44no—
114C22×C4⋊C4—24no—
115C22×C4⋊C4—24no—
116C22×C4⋊C4—24no—
117C22×C4⋊C4—24no—
118C22×C4⋊C4—44no—
119C22×C4⋊C4C2312yes—
120C22×C4⋊C4C2312yes—
121C22×C4⋊C4C2312yes—
122C22×C4⋊C4C2311yescharacteristic
123C22×C4⋊C4C2312yes—
124C22×C4⋊C4C2312yes—
125C22×C4⋊C4C2314yes—
126C22×C4⋊C4C2312yes—
127C22×C4⋊C4C2312yes—
128C22×C4⋊C4C2311yescharacteristic
129C22×C4⋊C4C2311yescharacteristic
130C22×C4⋊C4C2312yes—
131C22×C4⋊C4C2314yes—
132C22×C4⋊C4C2312yes—
133C22×C22⋊C4—24no—
134C22×C22⋊C4—24no—
135C22×C22⋊C4—24no—
136C22×C22⋊C4—24no—
137C22×C22⋊C4—44no—
138C22×C22⋊C4C2312yes—
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2314yes—
147C22×C22⋊C4C2314yes—
148C22×C22⋊C4C2312yes—
149C22×C22⋊C4C2312yes—
150C22×C22⋊C4C2312yes—
151C22×C22⋊C4C2312yes—
152C22×C42C2314yes—
153#400—28no—
154#398—216no—
155#397—48no—
156#395—28no—
157#389—48no—
158#385—28no—
159#385—28no—
160#385—28no—
161#385—28no—
162#385—28no—
163#385—28no—
164#385—28no—
165#385—28no—
166#385—28no—
167#381—28no—
168#381—28no—
169#381—28no—
170#380—24no—
171#380—24no—
172#380—24no—
173#380—24no—
174#380—28no—
175#380D418yes—
176#379—28no—
177#379—28no—
178C4×C22⋊C4—28no—
179C4×C22⋊C4—28no—
180C2×#95—24no—
181C2×#95—24no—
182C2×#95C2314yes—
183C2×#95C2314yes—
184C2×#95C2314yes—
185C2×#95C2312yes—
186C2×#95C2312yes—
187C2×#95C2314yes—
188C2×#95C2314yes—
189C2×#95C2314yes—
190C2×#95C2312yes—
191C2×#95C2312yes—
192C2×#95C2312yes—
193C2×#95C2312yes—
194C2×#95C2314yes—
195C2×#95C2312yes—
196C2×#95C2312yes—
197C2×#95C2314yes—
198C2×#95C2314yes—
199C2×#95C2314yes—
200C2×#95C2314yes—
201C2×#95C2314yes—
202C2×#95C2314yes—
203C2×#95C2314yes—
204C2×#95C2314yes—
205C2×#95C2312yes—
206C25—22no—
207C25—22no—
208C25—24no—
209C25—24no—
210C25—22no—
211C25—22no—
212C25—22no—
213C25—22no—
214C25—42no—
215C25—42no—
216C25C2×D414yes—
217C25C2411yescharacteristic
218C25C2411yescharacteristic
219C25C2411yescharacteristic
220C22×Q8—22no—
221C22×Q8—22no—
222C22×Q8—22no—
223C22×Q8—42no—
224C22×Q8—42no—
225C23×C4—24no—
226C23×C4—22no—
227C23×C4—22no—
228C23×C4—24no—
229C23×C4—22no—
230C23×C4—22no—
231C23×C4—22no—
232C23×C4—22no—
233C23×C4—22no—
234C23×C4—22no—
235C23×C4—22no—
236C23×C4—22no—
237C23×C4—24no—
238C23×C4—22no—
239C23×C4—22no—
240C23×C4—232no—
241C23×C4—22no—
242C23×C4—22no—
243C23×C4—22no—
244C23×C4—22no—
245C23×C4—22no—
246C23×C4—22no—
247C23×C4—24no—
248C23×C4—24no—
249C23×C4—22no—
250C23×C4—22no—
251C23×C4—22no—
252C23×C4—22no—
253C23×C4—22no—
254C23×C4—22no—
255C23×C4—416no—
256C23×C4—42no—
257C23×C4—416no—
258C23×C4—42no—
259C23×C4—42no—
260C23×C4—42no—
261C23×C4—42no—
262C23×C4—42no—
263C23×C4—42no—
264C23×C4—42no—
265C23×C4—42no—
266C23×C4—42no—
267C23×C4—42no—
268C23×C4—42no—
269C23×C4—42no—
270C23×C4—432no—
271C23×C4—432no—
272C23×C4C2×D414yes—
273C23×C4C2×D414yes—
274C23×C4C2×D414yes—
275C23×C4C2×D414yes—
276C23×C4C2×D414yes—
277C23×C4C2×D414yes—
278C23×C4C2×D414yes—
279C23×C4#4114yes—
280C23×C4#4114yes—
281C23×C4#4114yes—
282C23×C4C2412yes—
283C23×C4C2412yes—
284C23×C4C2412yes—
285C23×C4C2412yes—
286C23×C4C2414yes—
287C23×C4C2412yes—
288C23×C4C2412yes—
289C23×C4C2414yes—
290C23×C4C2411yescharacteristic
291C23×C4C2412yes—
292C23×C4C2412yes—
293C23×C4C2411yescharacteristic
294C23×C4C2411yescharacteristic
295C23×C4C2411yescharacteristic
296C22⋊Q8—416no—
297C22⋊Q8—416no—
298C22⋊Q8—416no—
299#117—432no—
300C2×C4⋊C4—24no—
301C2×C4⋊C4—24no—
302C2×C4⋊C4—24no—
303C2×C4⋊C4—24no—
304C2×C4⋊C4—24no—
305C2×C4⋊C4—24no—
306C2×C4⋊C4—24no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—24no—
311C2×C4⋊C4—24no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—24no—
316C2×C4⋊C4—24no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—24no—
319C2×C4⋊C4—28no—
320C2×C4⋊C4—28no—
321C2×C4⋊C4—28no—
322C2×C4⋊C4—28no—
323C2×C4⋊C4—44no—
324C2×C4⋊C4—44no—
325C2×C4⋊C4—42no—
326C2×C4⋊C4—42no—
327C2×C4⋊C4—42no—
328C2×C4⋊C4—42no—
329C2×C4⋊C4—42no—
330C2×C4⋊C4—42no—
331C2×C4⋊C4—44no—
332C2×C4⋊C4—44no—
333C2×C4⋊C4—416no—
334C2×C4⋊C4—416no—
335C2×C4⋊C4—44no—
336C2×C4⋊C4—44no—
337C2×C4⋊C4C2×D418yes—
338C2×C22⋊C4—232no—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—24no—
341C2×C22⋊C4—24no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—24no—
346C2×C22⋊C4—24no—
347C2×C22⋊C4—24no—
348C2×C22⋊C4—24no—
349C2×C22⋊C4—24no—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—24no—
360C2×C22⋊C4—24no—
361C2×C22⋊C4—28no—
362C2×C22⋊C4—28no—
363C2×C22⋊C4—28no—
364C2×C22⋊C4—28no—
365C2×C22⋊C4—28no—
366C2×C22⋊C4—24no—
367C2×C22⋊C4—28no—
368C2×C22⋊C4—28no—
369C2×C22⋊C4—44no—
370C2×C22⋊C4—44no—
371C2×C22⋊C4—44no—
372C2×C22⋊C4—44no—
373C2×C22⋊C4—44no—
374C2×C22⋊C4—416no—
375C2×C22⋊C4C2×D418yes—
376C2×C42—28no—
377C2×C42—28no—
378C2×C42—44no—
379#95—24no—
380#95—24no—
381#95—24no—
382#95—24no—
383#95—28no—
384#95—24no—
385#95—24no—
386#95—24no—
387#95—24no—
388#95—28no—
389#95—28no—
390#95—28no—
391#95—28no—
392#95—28no—
393#95—28no—
394#95—44no—
395#95—44no—
396#95—44no—
397#95—44no—
398#95—44no—
399#95—44no—
400#95—44no—
401#95—44no—
402#95C2×D418yes—
403C24—22no—
404C24—22no—
405C24—22no—
406C24—22no—
407C24—216no—
408C24—216no—
409C24—28no—
410C24—28no—
411C24—28no—
412C24—21no—
413C24—21no—
414C24—21no—
415C24—21no—
416C24—21no—
417C24—21no—
418C24—21no—
419C24—21no—
420C24—22no—
421C24—22no—
422C24—22no—
423C24—22no—
424C24—21no—
425C24—21no—
426C24—21no—
427C24—21no—
428C24—22no—
429C24—22no—
430C24—28no—
431C24—28no—
432C24—44no—
433C24—44no—
434C24—48no—
435C24—48no—
436C24—48no—
437C24—48no—
438C24—48no—
439C24—48no—
440C24—48no—
441C24—48no—
442C24—48no—
443C24—48no—
444C24—44no—
445C24—44no—
446C24—44no—
447C24—44no—
448C24C22×D412yes—
449C24C22×D412yes—
450C24C22×D412yes—
451C24C22×D412yes—
452C24C2×#4112yes—
453C24C2×#4112yes—
454C24C2×#4112yes—
455C24H(5,𝔽2)14yes—
456C242−1+414yes—
457C242−1+412yes—
458C242−1+412yes—
459C24C2511yescharacteristic
460C2×Q8—44no—
461C2×Q8—44no—
462C2×Q8—44no—
463C2×Q8—84no—
464C2×Q8—84no—
465C22×C4—216no—
466C22×C4—216no—
467C22×C4—28no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—28no—
476C22×C4—28no—
477C22×C4—28no—
478C22×C4—28no—
479C22×C4—28no—
480C22×C4—28no—
481C22×C4—28no—
482C22×C4—28no—
483C22×C4—22no—
484C22×C4—21no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—24no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—21no—
492C22×C4—24no—
493C22×C4—24no—
494C22×C4—24no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—24no—
498C22×C4—24no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—24no—
502C22×C4—24no—
503C22×C4—28no—
504C22×C4—28no—
505C22×C4—28no—
506C22×C4—28no—
507C22×C4—28no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—24no—
511C22×C4—22no—
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—24no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—24no—
527C22×C4—24no—
528C22×C4—24no—
529C22×C4—24no—
530C22×C4—24no—
531C22×C4—24no—
532C22×C4—24no—
533C22×C4—24no—
534C22×C4—24no—
535C22×C4—24no—
536C22×C4—24no—
537C22×C4—24no—
538C22×C4—24no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—24no—
542C22×C4—24no—
543C22×C4—24no—
544C22×C4—24no—
545C22×C4—44no—
546C22×C4—44no—
547C22×C4—44no—
548C22×C4—44no—
549C22×C4—44no—
550C22×C4—44no—
551C22×C4—44no—
552C22×C4—48no—
553C22×C4—48no—
554C22×C4—48no—
555C22×C4—48no—
556C22×C4—48no—
557C22×C4—48no—
558C22×C4—48no—
559C22×C4—48no—
560C22×C4—48no—
561C22×C4—4128no—
562C22×C4—48no—
563C22×C4—48no—
564C22×C4—44no—
565C22×C4—44no—
566C22×C4—48no—
567C22×C4—44no—
568C22×C4—44no—
569C22×C4—44no—
570C22×C4—44no—
571C22×C4—44no—
572C22×C4—44no—
573C22×C4—44no—
574C22×C4—44no—
575C22×C4—44no—
576C22×C4—44no—
577C22×C4—84no—
578C22×C4—84no—
579C22×C4—84no—
580C22×C4—84no—
581C22×C4#121116yes—
582C22×C4C22×D418yes—
583C22×C4C22×D412yes—
584C22×C4C22×D412yes—
585C22×C4C22×D412yes—
586C22×C4C22×D412yes—
587C22×C4C22×D412yes—
588C22×C4C22×D412yes—
589C22×C4C2×#4114yes—
590C22×C4C2×#4114yes—
591C22×C4C2×#4112yes—
592C22×C4C2×#4112yes—
593C22×C4H(5,𝔽2)14yes—
594C4⋊C4—48no—
595C4⋊C4—416no—
596C4⋊C4—48no—
597C4⋊C4—48no—
598C4⋊C4—44no—
599C4⋊C4—44no—
600C4⋊C4—48no—
601C4⋊C4—48no—
602C4⋊C4—48no—
603C4⋊C4—44no—
604C4⋊C4—48no—
605C4⋊C4—48no—
606C4⋊C4—48no—
607C4⋊C4—88no—
608C22⋊C4—216no—
609C22⋊C4—216no—
610C22⋊C4—216no—
611C22⋊C4—416no—
612C22⋊C4—416no—
613C22⋊C4—48no—
614C22⋊C4—48no—
615C22⋊C4—48no—
616C22⋊C4—48no—
617C22⋊C4—48no—
618C22⋊C4—48no—
619C22⋊C4—48no—
620C22⋊C4—48no—
621C22⋊C4—48no—
622C42—416no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—24no—
628C23—24no—
629C23—24no—
630C23—24no—
631C23—24no—
632C23—24no—
633C23—24no—
634C23—24no—
635C23—24no—
636C23—24no—
637C23—24no—
638C23—24no—
639C23—232no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—24no—
653C23—24no—
654C23—24no—
655C23—24no—
656C23—24no—
657C23—24no—
658C23—24no—
659C23—24no—
660C23—24no—
661C23—24no—
662C23—24no—
663C23—24no—
664C23—416no—
665C23—416no—
666C23—416no—
667C23—416no—
668C23—416no—
669C23—432no—
670C23—432no—
671C23—432no—
672C23—432no—
673C23—416no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23C2×#12114yes—
695C23#52514yes—
696C23#53414yes—
697C23#53614yes—
698C23#53614yes—
699C23#54714yes—
700C23#54814yes—
701C23#55214yes—
702C23#55614yes—
703C23C23×D411yescharacteristic
704C23C23×D411yescharacteristic
705C23C22×#4111yescharacteristic
706C23C22×#4111yescharacteristic
707C23C22×#4111yescharacteristic
708C23C2×H(5,𝔽2)12yes—
709C23C2×H(5,𝔽2)12yes—
710C23C2×2−1+411yescharacteristic
711C23C2×2−1+411yescharacteristic
712C23C2×2−1+412yes—
713C23#58512yes—
714Q8—88no—
715C2×C4—232no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—24no—
723C2×C4—24no—
724C2×C4—24no—
725C2×C4—24no—
726C2×C4—24no—
727C2×C4—24no—
728C2×C4—22no—
729C2×C4—24no—
730C2×C4—24no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—28no—
734C2×C4—28no—
735C2×C4—24no—
736C2×C4—24no—
737C2×C4—28no—
738C2×C4—28no—
739C2×C4—416no—
740C2×C4—416no—
741C2×C4—416no—
742C2×C4—416no—
743C2×C4—416no—
744C2×C4—416no—
745C2×C4—42no—
746C2×C4—416no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—44no—
751C2×C4—44no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—44no—
757C2×C4—44no—
758C2×C4—44no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—44no—
778C2×C4—44no—
779C2×C4—44no—
780C2×C4—44no—
781C2×C4—44no—
782C2×C4—44no—
783C2×C4—44no—
784C2×C4—44no—
785C2×C4—44no—
786C2×C4—44no—
787C2×C4—44no—
788C2×C4—44no—
789C2×C4—44no—
790C2×C4—44no—
791C2×C4—44no—
792C2×C4—44no—
793C2×C4—44no—
794C2×C4—44no—
795C2×C4—44no—
796C2×C4—88no—
797C2×C4—88no—
798C2×C4C2×#12114yes—
799C2×C4C2×#12114yes—
800C2×C4#53414yes—
801C22—24no—
802C22—28no—
803C22—24no—
804C22—28no—
805C22—24no—
806C22—28no—
807C22—28no—
808C22—24no—
809C22—24no—
810C22—24no—
811C22—24no—
812C22—24no—
813C22—24no—
814C22—24no—
815C22—24no—
816C22—24no—
817C22—464no—
818C22—42no—
819C22—42no—
820C22—44no—
821C22—44no—
822C22—42no—
823C22—44no—
824C22—44no—
825C22—42no—
826C22—44no—
827C22—44no—
828C22—44no—
829C22—44no—
830C22—42no—
831C22—42no—
832C22—42no—
833C22—42no—
834C22#241518yes—
835C22C22×#12111yescharacteristic
836C22C2×#52511yescharacteristic
837C22C2×#53411yescharacteristic
838C22C2×#53411yescharacteristic
839C22C2×#53611yescharacteristic
840C22C2×#53611yescharacteristic
841C22#344911yescharacteristic
842C22#345912yes—
843C22#346012yes—
844C22C2×#54711yescharacteristic
845C22C2×#54811yescharacteristic
846C22C2×#55211yescharacteristic
847C22C2×#55611yescharacteristic
848C22#348412yes—
849C22#348912yes—
850C22#349012yes—
851C22#349212yes—
852C22#349212yes—
853C22#349512yes—
854C22#353512yes—
855C22#353512yes—
856C22#353812yes—
857C22#353812yes—
858C4—24no—
859C4—24no—
860C4—24no—
861C4—44no—
862C4—48no—
863C4—44no—
864C4—42no—
865C4—82no—
866C4—82no—
867C4—84no—
868C4—82no—
869C4—82no—
870C4—82no—
871C4—82no—
872C2—28no—
873C2—44no—
874C2—44no—
875C2#3456211yescharacteristic
876C2C2×#241511yescharacteristic
877C2#3498111yescharacteristic
878C2#3505711yescharacteristic
879C2#3530611yescharacteristic
880C2#3744111yescharacteristic
881C2#3745311yescharacteristic
882C2#3775312yes—
883C2#3776012yes—
884C2#3793312yes—
885C2#3795612yes—
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×#2627C2semidirect
5. #16561C2semidirect
6. #16394C2semidirect
7. #16262C2semidirect
9. #14907C2semidirect
10. #14841C2semidirect
11. #14763C2semidirect
13. #14339C2semidirect
14. #14281C2semidirect
15. #14275C2semidirect
16. #14043C2semidirect
17. #13972C2semidirect
29. C2×#400C22semidirect
30. C2×#398C22semidirect
32. C2×#395C22semidirect
33. C2×#389C22semidirect
60. #1446C22semidirect
61. #1445C22semidirect
62. #1444C22semidirect
63. #1444C22semidirect
64. #1443C22semidirect
65. #1442C22semidirect
66. #1442C22semidirect
67. #1441C22semidirect
68. #1441C22semidirect
69. #1441C22semidirect
70. #1441C22semidirect
71. #1441C22semidirect
72. #1441C22semidirect
80. #1436C22semidirect
81. #1436C22semidirect
82. #1434C22semidirect

Maximal subgroups

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

subgroupindex
C2×#28482
C2×#26272
C22×#3852
C2×#22802
#165612
#163942
#162622
#149182
#149072
#148412
#147632
#147272
#143392
#142812
#142752
#140432
#139722