Finite Group Databasebeta

← #642398

Subgroups — #642398

Order 512.

3746 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#385C211yesmaximal, characteristic
2C2×#2280C211yesmaximal, characteristic
3#17005C212yesmaximal, complemented
4#16986C212yesmaximal, complemented
5#16396C214yesmaximal, complemented
6#15114C212yesmaximal, complemented
7#14997C214yesmaximal, complemented
8#14918C212yesmaximal
9#14892C212yesmaximal, complemented
10#14727C212yesmaximal
11#14680C211yesmaximal, characteristic
12#14339C211yesmaximal, characteristic, complemented
13#14339C211yesmaximal, characteristic, complemented
14#14275C211yesmaximal, characteristic, complemented
15#14275C211yesmaximal, characteristic, complemented
16#14039C212yesmaximal, complemented
17#13992C212yesmaximal, complemented
18C25×C4C2211yescharacteristic
19C22×#117C2211yescharacteristic
20C22×#117C2211yescharacteristic
21C23×C4⋊C4C2211yescharacteristic
22C23×C4⋊C4C2211yescharacteristic
23C23×C22⋊C4C2211yescharacteristic
24C23×C22⋊C4C2211yescharacteristic
25C2×#397C2214yes—
26C2×#387C2214yescomplemented
27C2×#385—28no—
28C2×#385C2212yes—
29C2×#385C2212yes—
30C2×#385C2212yes—
31C2×#385C2212yes—
32C2×#385C2212yes—
33C2×#385C2212yes—
34#2280—28no—
35C2×#381C2212yes—
36C2×#381C2212yes—
37C2×#381C2212yes—
38C2×#380C2211yescharacteristic
39C2×#380C2211yescharacteristic
40C2×#380C2211yescharacteristic
41C2×#380C2211yescharacteristic
42C2×#380C2211yescharacteristic
43C2×#380C2211yescharacteristic
44C2×#380C2212yes—
45C2×#380C2212yes—
46C2×#379C2212yes—
47C2×#379C2212yes—
48C2×C4×C22⋊C4C2212yes—
49C2×C4×C22⋊C4C2212yes—
50C22×#95C2211yescharacteristic
51C22×#95C2211yescharacteristic
52#1444C2212yescomplemented
53#1444C2212yescomplemented
54#1443C2214yescomplemented
55#1442C2212yescomplemented
56#1442C2214yescomplemented
57#1442C2214yescomplemented
58#1442C2212yescomplemented
59#1441C2212yescomplemented
60#1441C2212yescomplemented
61#1441C2214yescomplemented
62#1441C2214yescomplemented
63#1441C2212yescomplemented
64#1441C2212yescomplemented
65#1441C2214yescomplemented
66#1441C2214yescomplemented
67#1441C2214yescomplemented
68#1440C2214yes—
69#1440C2214yes—
70#1440C2214yes—
71#1440C2214yes—
72#1439C2214yes—
73#1439C2214yes—
74#1439C2214yes—
75#1436C2214yescomplemented
76#1436C2214yescomplemented
77#1434C2214yescomplemented
78C22⋊#95C2212yes—
79C22⋊#95C2212yes—
80C22⋊#95C2212yes—
81C22⋊#95C2212yes—
82C22⋊#95C2212yes—
83C22⋊#95C2212yes—
84C22⋊#95C2212yes—
85C26C2311yescharacteristic
86C24×C4—24no—
87C24×C4—24no—
88C24×C4—44no—
89C24×C4—44no—
90C24×C4D418yes—
91C24×C4C2311yescharacteristic
92C24×C4C2311yescharacteristic
93C24×C4C2311yescharacteristic
94C24×C4C2311yescharacteristic
95C24×C4C2311yescharacteristic
96C24×C4C2311yescharacteristic
97C24×C4C2311yescharacteristic
98C24×C4C2311yescharacteristic
99C24×C4C2311yescharacteristic
100C24×C4C2311yescharacteristic
101C2×#117—24no—
102C2×#117—24no—
103C2×#117—44no—
104C2×#117—44no—
105C22×C4⋊C4—24no—
106C22×C4⋊C4—24no—
107C22×C4⋊C4—24no—
108C22×C4⋊C4—24no—
109C22×C4⋊C4—44no—
110C22×C4⋊C4C2312yes—
111C22×C4⋊C4C2312yes—
112C22×C4⋊C4C2312yes—
113C22×C4⋊C4C2312yes—
114C22×C4⋊C4C2311yescharacteristic
115C22×C4⋊C4C2311yescharacteristic
116C22×C4⋊C4C2311yescharacteristic
117C22×C4⋊C4C2311yescharacteristic
118C22×C4⋊C4C2314yes—
119C22×C4⋊C4C2312yes—
120C22×C4⋊C4C2312yes—
121C22×C4⋊C4C2314yes—
122C22×C22⋊C4—24no—
123C22×C22⋊C4—24no—
124C22×C22⋊C4—24no—
125C22×C22⋊C4—24no—
126C22×C22⋊C4—44no—
127C22×C22⋊C4C2312yes—
128C22×C22⋊C4C2312yes—
129C22×C22⋊C4C2312yes—
130C22×C22⋊C4C2312yes—
131C22×C22⋊C4C2312yes—
132C22×C22⋊C4C2312yes—
133C22×C22⋊C4C2312yes—
134C22×C22⋊C4C2312yes—
135C22×C22⋊C4C2312yes—
136C22×C22⋊C4C2314yes—
137C22×C22⋊C4C2312yes—
138C22×C22⋊C4C2312yes—
139C22×C22⋊C4C2314yes—
140C22×C22⋊C4C2312yes—
141C22×C42C2312yes—
142C22×C42C2312yes—
143#397—48no—
144#387—48no—
145#385—28no—
146#385—28no—
147#385—28no—
148#385—28no—
149#385—28no—
150#385—44no—
151#381—28no—
152#381—28no—
153#381—44no—
154#380—24no—
155#380—24no—
156#380—24no—
157#380—24no—
158#380—24no—
159#380—24no—
160#380—44no—
161#380—44no—
162#379—28no—
163#379—44no—
164C4×C22⋊C4—28no—
165C4×C22⋊C4—28no—
166C2×#95—24no—
167C2×#95—24no—
168C2×#95C2314yes—
169C2×#95C2312yes—
170C2×#95C2312yes—
171C2×#95C2312yes—
172C2×#95C2314yes—
173C2×#95C2314yes—
174C2×#95C2314yes—
175C2×#95C2312yes—
176C2×#95C2312yes—
177C2×#95C2312yes—
178C2×#95C2312yes—
179C2×#95C2312yes—
180C2×#95C2312yes—
181C2×#95C2312yes—
182C2×#95C2314yes—
183C2×#95C2314yes—
184C2×#95C2314yes—
185C2×#95C2314yes—
186C2×#95C2314yes—
187C2×#95C2314yes—
188C2×#95C2314yes—
189C2×#95C2314yes—
190C2×#95C2314yes—
191C2×#95C2314yes—
192C2×#95C2314yes—
193C2×#95C2314yes—
194C25—22no—
195C25—22no—
196C25—24no—
197C25—24no—
198C25—22no—
199C25—22no—
200C25—22no—
201C25—22no—
202C25—42no—
203C25—42no—
204C25C2×D414yes—
205C25C2411yescharacteristic
206C25C2411yescharacteristic
207C25C2411yescharacteristic
208C23×C4—24no—
209C23×C4—22no—
210C23×C4—22no—
211C23×C4—24no—
212C23×C4—22no—
213C23×C4—22no—
214C23×C4—22no—
215C23×C4—22no—
216C23×C4—22no—
217C23×C4—22no—
218C23×C4—22no—
219C23×C4—22no—
220C23×C4—24no—
221C23×C4—22no—
222C23×C4—22no—
223C23×C4—232no—
224C23×C4—22no—
225C23×C4—22no—
226C23×C4—22no—
227C23×C4—22no—
228C23×C4—22no—
229C23×C4—22no—
230C23×C4—24no—
231C23×C4—24no—
232C23×C4—22no—
233C23×C4—22no—
234C23×C4—22no—
235C23×C4—22no—
236C23×C4—22no—
237C23×C4—22no—
238C23×C4—416no—
239C23×C4—42no—
240C23×C4—416no—
241C23×C4—42no—
242C23×C4—42no—
243C23×C4—42no—
244C23×C4—42no—
245C23×C4—42no—
246C23×C4—42no—
247C23×C4—42no—
248C23×C4—42no—
249C23×C4—42no—
250C23×C4—42no—
251C23×C4—42no—
252C23×C4—42no—
253C23×C4—432no—
254C23×C4—432no—
255C23×C4C2×D414yes—
256C23×C4C2×D414yes—
257C23×C4C2×D414yes—
258C23×C4C2×D414yes—
259C23×C4C2×D414yes—
260C23×C4C2×D414yes—
261C23×C4#4114yes—
262C23×C4#4114yes—
263C23×C4#4114yes—
264C23×C4#4114yes—
265C23×C4C2412yes—
266C23×C4C2412yes—
267C23×C4C2414yes—
268C23×C4C2414yes—
269C23×C4C2412yes—
270C23×C4C2412yes—
271C23×C4C2412yes—
272C23×C4C2412yes—
273C23×C4C2411yescharacteristic
274C23×C4C2412yes—
275C23×C4C2412yes—
276C23×C4C2411yescharacteristic
277C23×C4C2411yescharacteristic
278C23×C4C2411yescharacteristic
279#117—416no—
280#117—416no—
281C2×C4⋊C4—24no—
282C2×C4⋊C4—24no—
283C2×C4⋊C4—24no—
284C2×C4⋊C4—24no—
285C2×C4⋊C4—22no—
286C2×C4⋊C4—22no—
287C2×C4⋊C4—22no—
288C2×C4⋊C4—22no—
289C2×C4⋊C4—24no—
290C2×C4⋊C4—24no—
291C2×C4⋊C4—24no—
292C2×C4⋊C4—24no—
293C2×C4⋊C4—28no—
294C2×C4⋊C4—28no—
295C2×C4⋊C4—24no—
296C2×C4⋊C4—24no—
297C2×C4⋊C4—44no—
298C2×C4⋊C4—44no—
299C2×C4⋊C4—42no—
300C2×C4⋊C4—42no—
301C2×C4⋊C4—42no—
302C2×C4⋊C4—42no—
303C2×C4⋊C4—44no—
304C2×C4⋊C4—416no—
305C2×C4⋊C4—416no—
306C2×C4⋊C4—44no—
307C2×C4⋊C4—42no—
308C2×C4⋊C4—42no—
309C2×C4⋊C4—42no—
310C2×C4⋊C4—42no—
311C2×C4⋊C4—44no—
312C2×C4⋊C4—44no—
313C2×C22⋊C4—232no—
314C2×C22⋊C4—24no—
315C2×C22⋊C4—24no—
316C2×C22⋊C4—24no—
317C2×C22⋊C4—24no—
318C2×C22⋊C4—24no—
319C2×C22⋊C4—24no—
320C2×C22⋊C4—24no—
321C2×C22⋊C4—24no—
322C2×C22⋊C4—24no—
323C2×C22⋊C4—24no—
324C2×C22⋊C4—24no—
325C2×C22⋊C4—24no—
326C2×C22⋊C4—24no—
327C2×C22⋊C4—24no—
328C2×C22⋊C4—24no—
329C2×C22⋊C4—24no—
330C2×C22⋊C4—24no—
331C2×C22⋊C4—24no—
332C2×C22⋊C4—24no—
333C2×C22⋊C4—24no—
334C2×C22⋊C4—28no—
335C2×C22⋊C4—28no—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—24no—
338C2×C22⋊C4—24no—
339C2×C22⋊C4—28no—
340C2×C22⋊C4—24no—
341C2×C22⋊C4—28no—
342C2×C22⋊C4—28no—
343C2×C22⋊C4—44no—
344C2×C22⋊C4—44no—
345C2×C22⋊C4—44no—
346C2×C22⋊C4—416no—
347C2×C22⋊C4—44no—
348C2×C22⋊C4—44no—
349C2×C22⋊C4—44no—
350C2×C22⋊C4—44no—
351C2×C42—24no—
352C2×C42—24no—
353C2×C42—28no—
354C2×C42—44no—
355#95—24no—
356#95—24no—
357#95—24no—
358#95—24no—
359#95—24no—
360#95—24no—
361#95—24no—
362#95—24no—
363#95—24no—
364#95—24no—
365#95—28no—
366#95—28no—
367#95—28no—
368#95—28no—
369#95—44no—
370#95—44no—
371#95—44no—
372#95—44no—
373#95—44no—
374#95—44no—
375#95—44no—
376#95—44no—
377#95—44no—
378#95—44no—
379#95—44no—
380#95—44no—
381C24—22no—
382C24—22no—
383C24—22no—
384C24—22no—
385C24—216no—
386C24—216no—
387C24—28no—
388C24—28no—
389C24—28no—
390C24—21no—
391C24—21no—
392C24—21no—
393C24—21no—
394C24—21no—
395C24—21no—
396C24—21no—
397C24—21no—
398C24—21no—
399C24—21no—
400C24—22no—
401C24—22no—
402C24—22no—
403C24—22no—
404C24—21no—
405C24—21no—
406C24—22no—
407C24—22no—
408C24—28no—
409C24—28no—
410C24—44no—
411C24—44no—
412C24—48no—
413C24—48no—
414C24—48no—
415C24—48no—
416C24—48no—
417C24—48no—
418C24—48no—
419C24—48no—
420C24—48no—
421C24—48no—
422C24—44no—
423C24—44no—
424C24—44no—
425C24—44no—
426C24C22×D412yes—
427C24C22×D412yes—
428C24C22×D412yes—
429C24C2×#4112yes—
430C24C2×#4112yes—
431C24C2×#4112yes—
432C24C2×#4112yes—
433C24H(5,𝔽2)14yes—
434C24H(5,𝔽2)12yes—
435C242−1+414yes—
436C242−1+412yes—
437C24C2511yescharacteristic
438C22×C4—216no—
439C22×C4—216no—
440C22×C4—28no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—28no—
449C22×C4—28no—
450C22×C4—28no—
451C22×C4—28no—
452C22×C4—28no—
453C22×C4—28no—
454C22×C4—28no—
455C22×C4—28no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—24no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—24no—
470C22×C4—28no—
471C22×C4—28no—
472C22×C4—28no—
473C22×C4—28no—
474C22×C4—28no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—24no—
485C22×C4—24no—
486C22×C4—24no—
487C22×C4—24no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—24no—
492C22×C4—24no—
493C22×C4—22no—
494C22×C4—24no—
495C22×C4—24no—
496C22×C4—24no—
497C22×C4—24no—
498C22×C4—24no—
499C22×C4—22no—
500C22×C4—24no—
501C22×C4—24no—
502C22×C4—22no—
503C22×C4—24no—
504C22×C4—24no—
505C22×C4—24no—
506C22×C4—24no—
507C22×C4—24no—
508C22×C4—24no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—24no—
512C22×C4—24no—
513C22×C4—22no—
514C22×C4—24no—
515C22×C4—24no—
516C22×C4—24no—
517C22×C4—24no—
518C22×C4—24no—
519C22×C4—44no—
520C22×C4—44no—
521C22×C4—44no—
522C22×C4—44no—
523C22×C4—44no—
524C22×C4—44no—
525C22×C4—44no—
526C22×C4—48no—
527C22×C4—48no—
528C22×C4—48no—
529C22×C4—48no—
530C22×C4—48no—
531C22×C4—48no—
532C22×C4—48no—
533C22×C4—48no—
534C22×C4—48no—
535C22×C4—4128no—
536C22×C4—48no—
537C22×C4—48no—
538C22×C4—44no—
539C22×C4—44no—
540C22×C4—48no—
541C22×C4—44no—
542C22×C4—44no—
543C22×C4—44no—
544C22×C4—44no—
545C22×C4—44no—
546C22×C4—44no—
547C22×C4—44no—
548C22×C4—44no—
549C22×C4—44no—
550C22×C4—44no—
551C22×C4—84no—
552C22×C4—84no—
553C22×C4—84no—
554C22×C4—84no—
555C22×C4#123116yes—
556C22×C4C22×D412yes—
557C22×C4C22×D412yes—
558C22×C4C22×D412yes—
559C22×C4C22×D412yes—
560C22×C4C2×#4114yes—
561C22×C4C2×#4114yes—
562C22×C4C2×#4112yes—
563C22×C4C2×#4112yes—
564C22×C4C2×#4112yes—
565C22×C4C2×#4112yes—
566C22×C4H(5,𝔽2)14yes—
567C4⋊C4—416no—
568C4⋊C4—48no—
569C4⋊C4—44no—
570C4⋊C4—44no—
571C4⋊C4—44no—
572C4⋊C4—44no—
573C4⋊C4—48no—
574C4⋊C4—48no—
575C4⋊C4—48no—
576C4⋊C4—84no—
577C4⋊C4—84no—
578C4⋊C4—88no—
579C22⋊C4—216no—
580C22⋊C4—216no—
581C22⋊C4—48no—
582C22⋊C4—48no—
583C22⋊C4—48no—
584C22⋊C4—48no—
585C22⋊C4—48no—
586C22⋊C4—48no—
587C22⋊C4—48no—
588C22⋊C4—48no—
589C22⋊C4—48no—
590C22⋊C4—48no—
591C22⋊C4—88no—
592C22⋊C4—88no—
593C42—48no—
594C42—48no—
595C23—22no—
596C23—22no—
597C23—22no—
598C23—22no—
599C23—24no—
600C23—24no—
601C23—24no—
602C23—24no—
603C23—24no—
604C23—24no—
605C23—24no—
606C23—24no—
607C23—24no—
608C23—24no—
609C23—24no—
610C23—24no—
611C23—232no—
612C23—22no—
613C23—22no—
614C23—22no—
615C23—22no—
616C23—22no—
617C23—22no—
618C23—22no—
619C23—22no—
620C23—22no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—24no—
625C23—24no—
626C23—24no—
627C23—24no—
628C23—24no—
629C23—24no—
630C23—24no—
631C23—24no—
632C23—24no—
633C23—24no—
634C23—24no—
635C23—24no—
636C23—416no—
637C23—416no—
638C23—416no—
639C23—416no—
640C23—416no—
641C23—432no—
642C23—432no—
643C23—432no—
644C23—432no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—416no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23C2×#12314yes—
667C23#52514yes—
668C23#53414yes—
669C23#53614yes—
670C23#53714yes—
671C23#55214yes—
672C23#55314yes—
673C23#55514yes—
674C23#55614yes—
675C23C23×D411yescharacteristic
676C23C22×#4111yescharacteristic
677C23C22×#4111yescharacteristic
678C23C22×#4111yescharacteristic
679C23C22×#4111yescharacteristic
680C23C2×H(5,𝔽2)12yes—
681C23C2×H(5,𝔽2)12yes—
682C23C2×H(5,𝔽2)11yescharacteristic
683C23C2×2−1+412yes—
684C23C2×2−1+411yescharacteristic
685C23#58512yes—
686C2×C4—232no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—24no—
694C2×C4—24no—
695C2×C4—24no—
696C2×C4—24no—
697C2×C4—24no—
698C2×C4—24no—
699C2×C4—22no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—28no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—416no—
708C2×C4—416no—
709C2×C4—416no—
710C2×C4—416no—
711C2×C4—416no—
712C2×C4—416no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—44no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—416no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—44no—
742C2×C4—44no—
743C2×C4—44no—
744C2×C4—44no—
745C2×C4—44no—
746C2×C4—44no—
747C2×C4—44no—
748C2×C4—44no—
749C2×C4—44no—
750C2×C4—44no—
751C2×C4—44no—
752C2×C4—44no—
753C2×C4—44no—
754C2×C4—44no—
755C2×C4—44no—
756C2×C4—44no—
757C2×C4—44no—
758C2×C4—44no—
759C2×C4—44no—
760C2×C4—44no—
761C2×C4—44no—
762C2×C4—44no—
763C2×C4—44no—
764C2×C4—44no—
765C2×C4—44no—
766C2×C4—44no—
767C2×C4—88no—
768C2×C4—88no—
769C2×C4C2×#12314yes—
770C2×C4C2×#12314yes—
771C2×C4#53414yes—
772C22—24no—
773C22—28no—
774C22—28no—
775C22—28no—
776C22—24no—
777C22—28no—
778C22—24no—
779C22—24no—
780C22—24no—
781C22—24no—
782C22—24no—
783C22—24no—
784C22—24no—
785C22—24no—
786C22—24no—
787C22—24no—
788C22—464no—
789C22—42no—
790C22—42no—
791C22—44no—
792C22—44no—
793C22—44no—
794C22—44no—
795C22—44no—
796C22—44no—
797C22—42no—
798C22—44no—
799C22—44no—
800C22—42no—
801C22—42no—
802C22—42no—
803C22—42no—
804C22—42no—
805C22#248518yes—
806C22C22×#12311yescharacteristic
807C22C2×#52511yescharacteristic
808C22C2×#53411yescharacteristic
809C22C2×#53411yescharacteristic
810C22C2×#53611yescharacteristic
811C22C2×#53711yescharacteristic
812C22#344911yescharacteristic
813C22#345912yes—
814C22#346012yes—
815C22C2×#55211yescharacteristic
816C22C2×#55311yescharacteristic
817C22C2×#55511yescharacteristic
818C22C2×#55611yescharacteristic
819C22#349012yes—
820C22#349012yes—
821C22#349212yes—
822C22#349212yes—
823C22#349512yes—
824C22#349512yes—
825C22#353412yes—
826C22#353512yes—
827C22#353612yes—
828C22#353812yes—
829C4—24no—
830C4—24no—
831C4—24no—
832C4—44no—
833C4—42no—
834C4—44no—
835C4—82no—
836C4—84no—
837C4—84no—
838C4—82no—
839C4—82no—
840C4—82no—
841C4—82no—
842C4—82no—
843C2—28no—
844C2—44no—
845C2—44no—
846C2#3456211yescharacteristic
847C2C2×#248511yescharacteristic
848C2#3499211yescharacteristic
849C2#3505711yescharacteristic
850C2#3531111yescharacteristic
851C2#3744211yescharacteristic
852C2#3745211yescharacteristic
853C2#3793312yes—
854C2#3794112yes—
855C2#3794812yes—
856C2#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
3. #17005C2semidirect
4. #16986C2semidirect
5. #16396C2semidirect
6. #15114C2semidirect
7. #14997C2semidirect
9. #14892C2semidirect
12. #14339C2semidirect
13. #14339C2semidirect
14. #14275C2semidirect
15. #14275C2semidirect
16. #14039C2semidirect
17. #13992C2semidirect
26. C2×#387C22semidirect
52. #1444C22semidirect
53. #1444C22semidirect
54. #1443C22semidirect
55. #1442C22semidirect
56. #1442C22semidirect
57. #1442C22semidirect
58. #1442C22semidirect
59. #1441C22semidirect
60. #1441C22semidirect
61. #1441C22semidirect
62. #1441C22semidirect
63. #1441C22semidirect
64. #1441C22semidirect
65. #1441C22semidirect
66. #1441C22semidirect
67. #1441C22semidirect
75. #1436C22semidirect
76. #1436C22semidirect
77. #1434C22semidirect

Maximal subgroups

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

subgroupindex
C22×#3852
C2×#22802
#170052
#169862
#163962
#151142
#149972
#149182
#148922
#147272
#146802
#143392
#142752
#140392
#139922