Finite Group Databasebeta

← #642396

Subgroups — #642396

Order 512.

4614 conjugacy classes of subgroups.

The subgroup lattice has 955 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#386C211yesmaximal, characteristic
2C2×#2280C211yesmaximal, characteristic, complemented
3#16884C212yesmaximal, complemented
4#16807C212yesmaximal, complemented
5#16397C214yesmaximal, complemented
6#15113C212yesmaximal, complemented
7#15002C214yesmaximal, complemented
8#14888C212yesmaximal, complemented
9#14727C212yesmaximal, complemented
10#14724C212yesmaximal
11#14680C211yesmaximal, characteristic, complemented
12#14338C211yesmaximal, characteristic, complemented
13#14338C211yesmaximal, characteristic, complemented
14#14275C211yesmaximal, characteristic, complemented
15#14275C211yesmaximal, characteristic, complemented
16#14040C212yesmaximal, complemented
17#13991C212yesmaximal, complemented
18C24×D4C2211yescharacteristic
19C25×C4C2211yescharacteristic
20C22×#117C2211yescharacteristic, complemented
21C22×#117C2211yescharacteristic, complemented
22C23×C22⋊C4C2211yescharacteristic
23C23×C22⋊C4C2211yescharacteristic
24C23×C22⋊C4C2211yescharacteristic
25C2×#397C2214yescomplemented
26C2×#394C2214yes—
27C2×#394C2214yes—
28C2×#388C2214yescomplemented
29C2×#386—28no—
30C2×#386C2212yes—
31C2×#386C2212yes—
32C2×#386C2212yes—
33C2×#386C2212yes—
34C2×#385C2212yes—
35C2×#385C2212yes—
36#2280—28no—
37C2×#381C2212yescomplemented
38C2×#380C2211yescharacteristic
39C2×#380C2211yescharacteristic
40C2×#380C2211yescharacteristic
41C2×#380C2211yescharacteristic
42C2×#380C2211yescharacteristic, complemented
43C2×#380C2211yescharacteristic, complemented
44C2×#380C2212yescomplemented
45C2×#380C2212yescomplemented
46C2×#379C2212yes—
47C2×#379C2212yes—
48C2×#379C2212yes—
49C2×#379C2212yes—
50C2×C4×C22⋊C4C2212yes—
51C2×C4×C22⋊C4C2212yescomplemented
52C22×#95C2211yescharacteristic
53C22×#95C2211yescharacteristic
54#1445C2214yescomplemented
55#1444C2212yescomplemented
56#1444C2212yescomplemented
57#1443C2214yescomplemented
58#1442C2212yescomplemented
59#1442C2212yescomplemented
60#1441C2214yescomplemented
61#1441C2214yescomplemented
62#1440C2214yescomplemented
63#1440C2214yescomplemented
64#1440C2214yescomplemented
65#1439C2212yescomplemented
66#1439C2212yescomplemented
67#1439C2214yescomplemented
68#1439C2214yescomplemented
69#1439C2212yescomplemented
70#1439C2212yescomplemented
71#1439C2214yescomplemented
72#1439C2214yescomplemented
73#1438C2214yes—
74#1438C2214yes—
75#1437C2214yescomplemented
76#1436C2214yescomplemented
77#1434C2214yescomplemented
78C22⋊#95C2212yes—
79C22⋊#95C2212yes—
80C22⋊#95C2212yes—
81C22⋊#95C2212yes—
82C22⋊#95C2212yes—
83C22⋊#95C2212yescomplemented
84C22⋊#95C2212yescomplemented
85C26C2311yescharacteristic
86C26C2311yescharacteristic
87C23×D4—24no—
88C23×D4—24no—
89C23×D4—24no—
90C23×D4—44no—
91C23×D4—44no—
92C23×D4C2312yes—
93C23×D4C2312yes—
94C24×C4—24no—
95C24×C4—24no—
96C24×C4—44no—
97C24×C4—44no—
98C24×C4D418yes—
99C24×C4C2311yescharacteristic
100C24×C4C2311yescharacteristic
101C24×C4C2311yescharacteristic
102C24×C4C2311yescharacteristic
103C24×C4C2311yescharacteristic
104C24×C4C2311yescharacteristic
105C24×C4C2311yescharacteristic
106C24×C4C2311yescharacteristic
107C24×C4C2311yescharacteristic
108C2×#117—24no—
109C2×#117—24no—
110C2×#117—44no—
111C2×#117—44no—
112C22×C4⋊C4C2314yes—
113C22×C4⋊C4C2311yescharacteristic
114C22×C4⋊C4C2311yescharacteristic
115C22×C4⋊C4C2311yescharacteristic
116C22×C4⋊C4C2311yescharacteristic
117C22×C4⋊C4C2312yes—
118C22×C4⋊C4C2312yes—
119C22×C4⋊C4C2314yes—
120C22×C22⋊C4—24no—
121C22×C22⋊C4—24no—
122C22×C22⋊C4—24no—
123C22×C22⋊C4—24no—
124C22×C22⋊C4—24no—
125C22×C22⋊C4—44no—
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⋊C4C2312yes—
137C22×C22⋊C4C2314yes—
138C22×C22⋊C4C2314yes—
139C22×C22⋊C4C2314yes—
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2314yes—
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2314yes—
146C22×C22⋊C4C2314yes—
147C22×C42C2312yes—
148C22×C42C2312yes—
149#397—48no—
150#394—48no—
151#394—48no—
152#388—48no—
153#386—28no—
154#386—28no—
155#386—28no—
156#386—28no—
157#385—28no—
158#385—44no—
159#381—28no—
160#380—24no—
161#380—24no—
162#380—24no—
163#380—24no—
164#380—24no—
165#380—24no—
166#380—44no—
167#380—44no—
168#379—28no—
169#379—28no—
170#379—44no—
171#379—44no—
172C4×C22⋊C4—28no—
173C4×C22⋊C4—28no—
174C2×#95—24no—
175C2×#95—24no—
176C2×#95C2314yes—
177C2×#95C2312yes—
178C2×#95C2312yes—
179C2×#95C2312yes—
180C2×#95C2314yes—
181C2×#95C2312yes—
182C2×#95C2312yes—
183C2×#95C2312yes—
184C2×#95C2312yes—
185C2×#95C2312yes—
186C2×#95C2312yes—
187C2×#95C2312yes—
188C2×#95C2314yes—
189C2×#95C2314yes—
190C2×#95C2314yes—
191C2×#95C2314yes—
192C2×#95C2314yes—
193C2×#95C2314yes—
194C2×#95C2314yes—
195C2×#95C2314yes—
196C2×#95C2314yes—
197C2×#95C2314yes—
198C25—22no—
199C25—22no—
200C25—24no—
201C25—24no—
202C25—22no—
203C25—22no—
204C25—22no—
205C25—22no—
206C25—22no—
207C25—22no—
208C25—22no—
209C25—22no—
210C25—22no—
211C25—22no—
212C25—42no—
213C25—42no—
214C25—42no—
215C25—42no—
216C25—42no—
217C25—42no—
218C25C2×D414yes—
219C25#4114yes—
220C25C2412yes—
221C25C2411yescharacteristic
222C25C2411yescharacteristic
223C25C2411yescharacteristic
224C22×D4—232no—
225C22×D4—24no—
226C22×D4—24no—
227C22×D4—24no—
228C22×D4—24no—
229C22×D4—28no—
230C22×D4—28no—
231C22×D4—24no—
232C22×D4—24no—
233C22×D4—44no—
234C22×D4—44no—
235C22×D4—432no—
236C22×D4—432no—
237C22×D4—416no—
238C22×D4—416no—
239C23×C4—24no—
240C23×C4—22no—
241C23×C4—22no—
242C23×C4—24no—
243C23×C4—22no—
244C23×C4—22no—
245C23×C4—22no—
246C23×C4—22no—
247C23×C4—24no—
248C23×C4—232no—
249C23×C4—22no—
250C23×C4—22no—
251C23×C4—22no—
252C23×C4—22no—
253C23×C4—22no—
254C23×C4—22no—
255C23×C4—24no—
256C23×C4—24no—
257C23×C4—22no—
258C23×C4—22no—
259C23×C4—22no—
260C23×C4—22no—
261C23×C4—22no—
262C23×C4—22no—
263C23×C4—416no—
264C23×C4—416no—
265C23×C4—42no—
266C23×C4—42no—
267C23×C4—42no—
268C23×C4—42no—
269C23×C4—42no—
270C23×C4—42no—
271C23×C4—42no—
272C23×C4—42no—
273C23×C4—42no—
274C23×C4—42no—
275C23×C4—42no—
276C23×C4—42no—
277C23×C4—42no—
278C23×C4—432no—
279C23×C4—432no—
280C23×C4C2×D414yes—
281C23×C4C2×D414yes—
282C23×C4C2×D414yes—
283C23×C4C2×D414yes—
284C23×C4C2×D414yes—
285C23×C4C2×D414yes—
286C23×C4#4114yes—
287C23×C4#4114yes—
288C23×C4#4114yes—
289C23×C4C2412yes—
290C23×C4C2412yes—
291C23×C4C2414yes—
292C23×C4C2414yes—
293C23×C4C2412yes—
294C23×C4C2412yes—
295C23×C4C2412yes—
296C23×C4C2412yes—
297C23×C4C2411yescharacteristic
298C23×C4C2412yes—
299C23×C4C2411yescharacteristic
300C23×C4C2411yescharacteristic
301C23×C4C2411yescharacteristic
302#117—416no—
303#117—416no—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—24no—
309C2×C4⋊C4—24no—
310C2×C4⋊C4—28no—
311C2×C4⋊C4—42no—
312C2×C4⋊C4—42no—
313C2×C4⋊C4—42no—
314C2×C4⋊C4—42no—
315C2×C4⋊C4—42no—
316C2×C4⋊C4—42no—
317C2×C4⋊C4—42no—
318C2×C4⋊C4—42no—
319C2×C4⋊C4—44no—
320C2×C4⋊C4—44no—
321C2×C4⋊C4—44no—
322C2×C4⋊C4—44no—
323C2×C4⋊C4—44no—
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—28no—
333C2×C22⋊C4—24no—
334C2×C22⋊C4—24no—
335C2×C22⋊C4—24no—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—24no—
338C2×C22⋊C4—24no—
339C2×C22⋊C4—28no—
340C2×C22⋊C4—28no—
341C2×C22⋊C4—24no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—28no—
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—28no—
355C2×C22⋊C4—28no—
356C2×C22⋊C4—28no—
357C2×C22⋊C4—28no—
358C2×C22⋊C4—44no—
359C2×C22⋊C4—44no—
360C2×C22⋊C4—44no—
361C2×C22⋊C4—44no—
362C2×C22⋊C4—44no—
363C2×C22⋊C4—44no—
364C2×C22⋊C4—416no—
365C2×C22⋊C4—416no—
366C2×C22⋊C4—416no—
367C2×C22⋊C4—44no—
368C2×C22⋊C4—44no—
369C2×C22⋊C4—44no—
370C2×C22⋊C4—44no—
371C2×C22⋊C4—44no—
372C2×C22⋊C4—44no—
373C2×C22⋊C4—44no—
374C2×C22⋊C4—44no—
375C2×C22⋊C4—44no—
376C2×C22⋊C4—44no—
377C2×C22⋊C4—44no—
378C2×C22⋊C4—44no—
379C2×C42—24no—
380C2×C42—24no—
381C2×C42—28no—
382C2×C42—44no—
383#95—24no—
384#95—24no—
385#95—24no—
386#95—24no—
387#95—24no—
388#95—24no—
389#95—24no—
390#95—24no—
391#95—24no—
392#95—24no—
393#95—28no—
394#95—28no—
395#95—44no—
396#95—44no—
397#95—44no—
398#95—44no—
399#95—44no—
400#95—44no—
401#95—44no—
402#95—44no—
403#95—44no—
404#95—44no—
405C24—22no—
406C24—22no—
407C24—22no—
408C24—22no—
409C24—216no—
410C24—216no—
411C24—28no—
412C24—28no—
413C24—28no—
414C24—21no—
415C24—21no—
416C24—21no—
417C24—21no—
418C24—21no—
419C24—21no—
420C24—21no—
421C24—21no—
422C24—21no—
423C24—21no—
424C24—22no—
425C24—22no—
426C24—22no—
427C24—22no—
428C24—21no—
429C24—21no—
430C24—22no—
431C24—22no—
432C24—28no—
433C24—28no—
434C24—28no—
435C24—22no—
436C24—22no—
437C24—22no—
438C24—22no—
439C24—24no—
440C24—22no—
441C24—24no—
442C24—24no—
443C24—22no—
444C24—24no—
445C24—28no—
446C24—28no—
447C24—44no—
448C24—44no—
449C24—48no—
450C24—48no—
451C24—48no—
452C24—48no—
453C24—48no—
454C24—48no—
455C24—48no—
456C24—48no—
457C24—48no—
458C24—48no—
459C24—48no—
460C24—48no—
461C24—44no—
462C24—44no—
463C24—44no—
464C24—48no—
465C24—44no—
466C24—48no—
467C24—44no—
468C24—44no—
469C24—44no—
470C24—44no—
471C24—44no—
472C24—44no—
473C24—44no—
474C24—44no—
475C24—84no—
476C24—84no—
477C24—84no—
478C24—84no—
479C24—84no—
480C24—84no—
481C24—84no—
482C24—84no—
483C24C22×D412yes—
484C24C22×D412yes—
485C24C22×D412yes—
486C24C2×#4114yes—
487C24C2×#4112yes—
488C24C2×#4112yes—
489C24C2×#4112yes—
490C24C2×#4112yes—
491C24H(5,𝔽2)14yes—
492C24H(5,𝔽2)14yes—
493C24H(5,𝔽2)12yes—
494C242−1+412yes—
495C24C2511yescharacteristic
496C2×D4—216no—
497C2×D4—216no—
498C2×D4—416no—
499C2×D4—416no—
500C2×D4—416no—
501C2×D4—416no—
502C2×D4—4128no—
503C2×D4—48no—
504C2×D4—48no—
505C2×D4—48no—
506C2×D4—48no—
507C22×C4—216no—
508C22×C4—216no—
509C22×C4—28no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—28no—
518C22×C4—28no—
519C22×C4—28no—
520C22×C4—28no—
521C22×C4—28no—
522C22×C4—22no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—24no—
528C22×C4—24no—
529C22×C4—22no—
530C22×C4—28no—
531C22×C4—28no—
532C22×C4—28no—
533C22×C4—28no—
534C22×C4—28no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—24no—
543C22×C4—24no—
544C22×C4—24no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—24no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—24no—
552C22×C4—24no—
553C22×C4—22no—
554C22×C4—24no—
555C22×C4—24no—
556C22×C4—24no—
557C22×C4—24no—
558C22×C4—24no—
559C22×C4—24no—
560C22×C4—22no—
561C22×C4—24no—
562C22×C4—24no—
563C22×C4—24no—
564C22×C4—24no—
565C22×C4—24no—
566C22×C4—24no—
567C22×C4—24no—
568C22×C4—24no—
569C22×C4—24no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—24no—
575C22×C4—24no—
576C22×C4—24no—
577C22×C4—24no—
578C22×C4—24no—
579C22×C4—44no—
580C22×C4—44no—
581C22×C4—44no—
582C22×C4—44no—
583C22×C4—44no—
584C22×C4—44no—
585C22×C4—44no—
586C22×C4—48no—
587C22×C4—48no—
588C22×C4—48no—
589C22×C4—48no—
590C22×C4—48no—
591C22×C4—48no—
592C22×C4—48no—
593C22×C4—48no—
594C22×C4—48no—
595C22×C4—4128no—
596C22×C4—48no—
597C22×C4—48no—
598C22×C4—44no—
599C22×C4—44no—
600C22×C4—48no—
601C22×C4—44no—
602C22×C4—44no—
603C22×C4—44no—
604C22×C4—44no—
605C22×C4—44no—
606C22×C4—44no—
607C22×C4—84no—
608C22×C4—84no—
609C22×C4—84no—
610C22×C4—84no—
611C22×C4#123116yes—
612C22×C4C22×D412yes—
613C22×C4C22×D412yes—
614C22×C4C22×D412yes—
615C22×C4C22×D412yes—
616C22×C4C2×#4114yes—
617C22×C4C2×#4112yes—
618C22×C4C2×#4112yes—
619C22×C4C2×#4112yes—
620C22×C4C2×#4112yes—
621C22×C4H(5,𝔽2)14yes—
622C4⋊C4—44no—
623C4⋊C4—44no—
624C4⋊C4—44no—
625C4⋊C4—44no—
626C4⋊C4—84no—
627C4⋊C4—84no—
628C4⋊C4—88no—
629C4⋊C4—88no—
630C22⋊C4—48no—
631C22⋊C4—48no—
632C22⋊C4—416no—
633C22⋊C4—48no—
634C22⋊C4—48no—
635C22⋊C4—48no—
636C22⋊C4—48no—
637C22⋊C4—48no—
638C22⋊C4—48no—
639C22⋊C4—48no—
640C22⋊C4—48no—
641C22⋊C4—48no—
642C22⋊C4—48no—
643C22⋊C4—48no—
644C22⋊C4—48no—
645C22⋊C4—88no—
646C22⋊C4—88no—
647C22⋊C4—88no—
648C22⋊C4—88no—
649C22⋊C4—88no—
650C42—48no—
651C42—48no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—24no—
657C23—24no—
658C23—24no—
659C23—24no—
660C23—24no—
661C23—24no—
662C23—24no—
663C23—24no—
664C23—24no—
665C23—24no—
666C23—24no—
667C23—24no—
668C23—232no—
669C23—22no—
670C23—22no—
671C23—22no—
672C23—22no—
673C23—22no—
674C23—22no—
675C23—22no—
676C23—22no—
677C23—22no—
678C23—22no—
679C23—22no—
680C23—22no—
681C23—24no—
682C23—24no—
683C23—24no—
684C23—24no—
685C23—24no—
686C23—24no—
687C23—24no—
688C23—24no—
689C23—24no—
690C23—24no—
691C23—24no—
692C23—24no—
693C23—24no—
694C23—28no—
695C23—24no—
696C23—24no—
697C23—28no—
698C23—416no—
699C23—416no—
700C23—416no—
701C23—416no—
702C23—416no—
703C23—432no—
704C23—432no—
705C23—432no—
706C23—432no—
707C23—416no—
708C23—416no—
709C23—42no—
710C23—42no—
711C23—42no—
712C23—42no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—41no—
721C23—42no—
722C23—42no—
723C23—42no—
724C23—42no—
725C23—416no—
726C23—42no—
727C23—42no—
728C23—42no—
729C23—42no—
730C23—42no—
731C23—42no—
732C23—42no—
733C23—42no—
734C23—42no—
735C23—42no—
736C23—44no—
737C23—42no—
738C23—42no—
739C23—44no—
740C23—44no—
741C23—44no—
742C23—44no—
743C23—44no—
744C23—416no—
745C23—44no—
746C23—44no—
747C23—44no—
748C23—44no—
749C23—816no—
750C23—816no—
751C23—816no—
752C23—88no—
753C23—816no—
754C23—88no—
755C23—88no—
756C23—88no—
757C23C2×#12314yes—
758C23#52514yes—
759C23#53414yes—
760C23#53514yes—
761C23#53714yes—
762C23#55214yes—
763C23#55314yes—
764C23#55514yes—
765C23#55614yes—
766C23C23×D411yescharacteristic
767C23C22×#4111yescharacteristic
768C23C22×#4111yescharacteristic
769C23C22×#4111yescharacteristic
770C23C22×#4111yescharacteristic
771C23C2×H(5,𝔽2)12yes—
772C23C2×H(5,𝔽2)12yes—
773C23C2×H(5,𝔽2)12yes—
774C23C2×H(5,𝔽2)11yescharacteristic
775C23C2×2−1+411yescharacteristic
776C23#58512yes—
777D4—432no—
778D4—432no—
779C2×C4—232no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—24no—
787C2×C4—24no—
788C2×C4—24no—
789C2×C4—24no—
790C2×C4—24no—
791C2×C4—24no—
792C2×C4—22no—
793C2×C4—24no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—28no—
797C2×C4—416no—
798C2×C4—416no—
799C2×C4—416no—
800C2×C4—416no—
801C2×C4—416no—
802C2×C4—416no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—44no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—44no—
827C2×C4—44no—
828C2×C4—44no—
829C2×C4—44no—
830C2×C4—44no—
831C2×C4—44no—
832C2×C4—44no—
833C2×C4—44no—
834C2×C4—44no—
835C2×C4—44no—
836C2×C4—44no—
837C2×C4—44no—
838C2×C4—44no—
839C2×C4—44no—
840C2×C4—44no—
841C2×C4—44no—
842C2×C4—44no—
843C2×C4—44no—
844C2×C4—44no—
845C2×C4—44no—
846C2×C4—44no—
847C2×C4—44no—
848C2×C4—44no—
849C2×C4—44no—
850C2×C4—44no—
851C2×C4—44no—
852C2×C4—88no—
853C2×C4—88no—
854C2×C4C2×#12314yes—
855C2×C4C2×#12314yes—
856C2×C4#53414yes—
857C22—24no—
858C22—28no—
859C22—28no—
860C22—28no—
861C22—24no—
862C22—28no—
863C22—24no—
864C22—24no—
865C22—24no—
866C22—24no—
867C22—24no—
868C22—24no—
869C22—24no—
870C22—24no—
871C22—24no—
872C22—24no—
873C22—464no—
874C22—42no—
875C22—42no—
876C22—44no—
877C22—44no—
878C22—44no—
879C22—44no—
880C22—44no—
881C22—44no—
882C22—42no—
883C22—44no—
884C22—44no—
885C22—42no—
886C22—42no—
887C22—42no—
888C22—42no—
889C22—42no—
890C22—44no—
891C22—48no—
892C22—48no—
893C22—44no—
894C22—44no—
895C22—832no—
896C22—84no—
897C22—82no—
898C22—84no—
899C22—82no—
900C22—82no—
901C22—82no—
902C22#248518yes—
903C22C22×#12311yescharacteristic
904C22C2×#52511yescharacteristic
905C22C2×#53411yescharacteristic
906C22C2×#53411yescharacteristic
907C22C2×#53511yescharacteristic
908C22C2×#53711yescharacteristic
909C22#344911yescharacteristic
910C22#345912yes—
911C22#346012yes—
912C22C2×#55211yescharacteristic
913C22C2×#55311yescharacteristic
914C22C2×#55511yescharacteristic
915C22C2×#55611yescharacteristic
916C22#349012yes—
917C22#349012yes—
918C22#349012yes—
919C22#349012yes—
920C22#349412yes—
921C22#349412yes—
922C22#353412yes—
923C22#353512yes—
924C22#353612yes—
925C22#353712yes—
926C4—24no—
927C4—24no—
928C4—24no—
929C4—42no—
930C4—44no—
931C4—82no—
932C4—84no—
933C4—84no—
934C4—82no—
935C4—82no—
936C4—82no—
937C4—82no—
938C4—82no—
939C2—28no—
940C2—44no—
941C2—44no—
942C2—84no—
943C2#3456211yescharacteristic
944C2C2×#248511yescharacteristic
945C2#3499211yescharacteristic
946C2#3505011yescharacteristic
947C2#3526211yescharacteristic
948C2#3743911yescharacteristic
949C2#3745211yescharacteristic
950C2#3793212yes—
951C2#3794012yes—
952C2#3794912yes—
953C2#3795712yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC24×D4C22
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×#2280C2semidirect
3. #16884C2semidirect
4. #16807C2semidirect
5. #16397C2semidirect
6. #15113C2semidirect
7. #15002C2semidirect
8. #14888C2semidirect
9. #14727C2semidirect
11. #14680C2semidirect
12. #14338C2semidirect
13. #14338C2semidirect
14. #14275C2semidirect
15. #14275C2semidirect
16. #14040C2semidirect
17. #13991C2semidirect
20. C22×#117C22semidirect
21. C22×#117C22semidirect
25. C2×#397C22semidirect
28. C2×#388C22semidirect
37. C2×#381C22semidirect
42. C2×#380C22semidirect
43. C2×#380C22semidirect
44. C2×#380C22semidirect
45. C2×#380C22semidirect
51. C2×C4×C22⋊C4C22semidirect
54. #1445C22semidirect
55. #1444C22semidirect
56. #1444C22semidirect
57. #1443C22semidirect
58. #1442C22semidirect
59. #1442C22semidirect
60. #1441C22semidirect
61. #1441C22semidirect
62. #1440C22semidirect
63. #1440C22semidirect
64. #1440C22semidirect
65. #1439C22semidirect
66. #1439C22semidirect
67. #1439C22semidirect
68. #1439C22semidirect
69. #1439C22semidirect
70. #1439C22semidirect
71. #1439C22semidirect
72. #1439C22semidirect
75. #1437C22semidirect
76. #1436C22semidirect
77. #1434C22semidirect
83. C22⋊#95C22semidirect
84. C22⋊#95C22semidirect

Maximal subgroups

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

subgroupindex
C22×#3862
C2×#22802
#168842
#168072
#163972
#151132
#150022
#148882
#147272
#147242
#146802
#143382
#142752
#140402
#139912