Finite Group Databasebeta

← #515306

Subgroups — #515306

Order 512.

5330 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#386C211yesmaximal, characteristic
2C2×#2280C211yesmaximal, characteristic, complemented
3C2×#2273C211yesmaximal, characteristic, complemented
4#14068C214yesmaximal, complemented
5#14064C214yesmaximal, complemented
6#13988C214yesmaximal, complemented
7#13984C214yesmaximal, complemented
8#13883C212yesmaximal, complemented
9#13877C212yesmaximal, complemented
10#13873C212yesmaximal, complemented
11#13867C212yesmaximal
12#13796C211yesmaximal, characteristic, complemented
13#13778C211yesmaximal, characteristic, complemented
14#13775C211yesmaximal, characteristic, complemented
15C4×#379C211yesmaximal, characteristic, complemented
16C24×D4C2211yescharacteristic
17C25×C4C2211yescharacteristic
18C22×#117C2212yescomplemented
19C23×C22⋊C4C2212yes—
20C23×C22⋊C4C2211yescharacteristic
21C23×C22⋊C4C2211yescharacteristic
22C23×C22⋊C4C2211yescharacteristic
23C2×#388C2214yescomplemented
24C2×#386C4116yescomplemented
25C2×#386C2214yes—
26C2×#386C2214yes—
27C2×#386C2212yes—
28C2×#386C2212yes—
29C2×#386C2212yes—
30C2×#386C2212yes—
31C2×#385C2214yescomplemented
32#2280—28no—
33C2×#381C2212yescomplemented
34C2×#380C2212yes—
35C2×#380C2212yes—
36C2×#380C2212yescomplemented
37C2×#379C2212yes—
38C2×#379C2212yes—
39C2×#379C2212yes—
40#2273—28no—
41C2×C4×C22⋊C4C2212yes—
42C2×C4×C22⋊C4C2211yescharacteristic
43C2×C4×C22⋊C4C2211yescharacteristic
44C2×C4×C22⋊C4C2211yescharacteristic
45C2×C4×C22⋊C4C2211yescharacteristic
46C2×C4×C22⋊C4C2214yescomplemented
47C2×C4×C22⋊C4C2214yescomplemented
48C2×C4×C22⋊C4C2212yescomplemented
49C2×C4×C22⋊C4C2212yescomplemented
50C2×C4×C22⋊C4C2212yescomplemented
51C22×#95C2211yescharacteristic
52C22×#95C2211yescharacteristic
53#1443C2214yescomplemented
54#1442C2214yescomplemented
55#1440C2214yescomplemented
56#1439C2214yescomplemented
57#1439C2214yescomplemented
58#1439C2214yescomplemented
59#1438C2214yes—
60#1438C2214yes—
61#1437C2214yescomplemented
62#1437C2214yescomplemented
63#1437C2214yescomplemented
64#1436C2214yescomplemented
65#1436C2214yescomplemented
66#1436C2214yescomplemented
67#1434C2214yescomplemented
68#1434C2214yescomplemented
69#1434C2214yescomplemented
70C22⋊#95C2212yes—
71C22⋊#95C2212yes—
72C22⋊#95C2212yes—
73C22⋊#95C2212yes—
74C22⋊#95C2212yes—
75C22⋊#95C2214yescomplemented
76C22⋊#95C2212yescomplemented
77C22⋊#95C2212yescomplemented
78C26C2311yescharacteristic
79C26C2311yescharacteristic
80C23×D4—28no—
81C23×D4—44no—
82C23×D4—44no—
83C23×D4C2×C418yes—
84C23×D4C2312yes—
85C23×D4C2312yes—
86C24×C4—24no—
87C24×C4—24no—
88C24×C4—44no—
89C24×C4—44no—
90C24×C4C2×C418yescomplemented
91C24×C4C2311yescharacteristic
92C24×C4C2311yescharacteristic
93C24×C4C2311yescharacteristic
94C24×C4C2311yescharacteristic
95C24×C4C2314yes—
96C24×C4C2311yescharacteristic
97C24×C4C2311yescharacteristic
98C24×C4C2311yescharacteristic
99C24×C4C2311yescharacteristic
100C24×C4C2311yescharacteristic
101C2×#117—28no—
102C2×#117—44no—
103C2×#117—44no—
104C22×C4⋊C4C2314yes—
105C22×C4⋊C4C2314yes—
106C22×C22⋊C4—28no—
107C22×C22⋊C4—24no—
108C22×C22⋊C4—24no—
109C22×C22⋊C4—28no—
110C22×C22⋊C4—28no—
111C22×C22⋊C4—44no—
112C22×C22⋊C4—44no—
113C22×C22⋊C4C2×C418yes—
114C22×C22⋊C4C2×C418yes—
115C22×C22⋊C4C2×C418yescomplemented
116C22×C22⋊C4C2314yes—
117C22×C22⋊C4C2312yes—
118C22×C22⋊C4C2312yes—
119C22×C22⋊C4C2314yes—
120C22×C22⋊C4C2314yes—
121C22×C22⋊C4C2314yes—
122C22×C22⋊C4C2314yes—
123C22×C22⋊C4C2312yes—
124C22×C22⋊C4C2312yes—
125C22×C22⋊C4C2312yes—
126C22×C22⋊C4C2312yes—
127C22×C22⋊C4C2312yes—
128C22×C22⋊C4C2312yes—
129C22×C22⋊C4C2314yes—
130C22×C22⋊C4C2314yes—
131C22×C22⋊C4C2312yes—
132C22×C22⋊C4C2312yes—
133C22×C42C2312yes—
134C22×C42C2312yes—
135C22×C42C2314yes—
136C22×C42C2312yes—
137C22×C42C2312yes—
138#388—48no—
139#386—48no—
140#386—48no—
141#386C2×C4116yescomplemented
142#386C2×C4116yescomplemented
143#386C2×C4116yescomplemented
144#386C2×C4116yescomplemented
145#385—48no—
146#381—28no—
147#380—28no—
148#380—28no—
149#380—28no—
150#379—28no—
151#379—28no—
152#379—28no—
153C4×C22⋊C4—24no—
154C4×C22⋊C4—24no—
155C4×C22⋊C4—24no—
156C4×C22⋊C4—28no—
157C4×C22⋊C4—216no—
158C4×C22⋊C4—28no—
159C4×C22⋊C4—216no—
160C4×C22⋊C4—44no—
161C4×C22⋊C4—44no—
162C4×C22⋊C4D418yescomplemented
163C2×#95C2×C418yescomplemented
164C2×#95C2×C418yescomplemented
165C2×#95C2314yes—
166C2×#95C2312yes—
167C2×#95C2312yes—
168C2×#95C2314yes—
169C2×#95C2314yes—
170C2×#95C2312yes—
171C2×#95C2314yes—
172C2×#95C2314yes—
173C2×#95C2314yes—
174C2×#95C2314yes—
175C2×#95C2314yes—
176C2×#95C2314yes—
177C2×#95C2314yes—
178C2×#95C2314yes—
179C2×#95C2314yes—
180C2×#95C2314yes—
181C2×#95C2312yes—
182C2×#95C2312yes—
183C2×#95C2312yes—
184C2×#95C2312yes—
185C2×#95C2312yes—
186C25—24no—
187C25—24no—
188C25—24no—
189C25—22no—
190C25—22no—
191C25—24no—
192C25—22no—
193C25—22no—
194C25—24no—
195C25—42no—
196C25—42no—
197C25—42no—
198C25—42no—
199C25—42no—
200C25—42no—
201C25C22×C414yes—
202C25C22×C414yes—
203C25#4118yes—
204C25C2412yes—
205C25C2411yescharacteristic
206C25C2411yescharacteristic
207C25C2411yescharacteristic
208C22×D4—232no—
209C22×D4—24no—
210C22×D4—24no—
211C22×D4—24no—
212C22×D4—24no—
213C22×D4—28no—
214C22×D4—28no—
215C22×D4—44no—
216C22×D4—44no—
217C22×D4—416no—
218C22×D4—416no—
219C22×D4—464no—
220C22×D4C22×C418yes—
221C22×D4C22×C418yes—
222C23×C4—24no—
223C23×C4—22no—
224C23×C4—22no—
225C23×C4—24no—
226C23×C4—22no—
227C23×C4—22no—
228C23×C4—24no—
229C23×C4—24no—
230C23×C4—22no—
231C23×C4—28no—
232C23×C4—22no—
233C23×C4—24no—
234C23×C4—232no—
235C23×C4—22no—
236C23×C4—22no—
237C23×C4—22no—
238C23×C4—22no—
239C23×C4—22no—
240C23×C4—22no—
241C23×C4—24no—
242C23×C4—24no—
243C23×C4—28no—
244C23×C4—28no—
245C23×C4—416no—
246C23×C4—416no—
247C23×C4—42no—
248C23×C4—42no—
249C23×C4—42no—
250C23×C4—42no—
251C23×C4—42no—
252C23×C4—42no—
253C23×C4—42no—
254C23×C4—42no—
255C23×C4—42no—
256C23×C4—42no—
257C23×C4—42no—
258C23×C4—42no—
259C23×C4—42no—
260C23×C4—44no—
261C23×C4—44no—
262C23×C4—44no—
263C23×C4—44no—
264C23×C4—432no—
265C23×C4—432no—
266C23×C4C22×C414yes—
267C23×C4C22×C414yes—
268C23×C4C22×C414yes—
269C23×C4C22×C414yes—
270C23×C4C22×C414yes—
271C23×C4C22×C414yes—
272C23×C4C22×C414yes—
273C23×C4C22×C414yes—
274C23×C4C22×C414yes—
275C23×C4C2×D414yes—
276C23×C4#4114yes—
277C23×C4C2414yes—
278C23×C4C2414yes—
279C23×C4C2412yes—
280C23×C4C2412yes—
281C23×C4C2411yescharacteristic
282C23×C4C2412yes—
283C23×C4C2414yes—
284C23×C4C2414yes—
285C23×C4C2411yescharacteristic
286C23×C4C2411yescharacteristic
287C23×C4C2411yescharacteristic
288#117—432no—
289C2×C4⋊C4—28no—
290C2×C4⋊C4—28no—
291C2×C4⋊C4—28no—
292C2×C4⋊C4—44no—
293C2×C4⋊C4—44no—
294C2×C4⋊C4—44no—
295C2×C22⋊C4—264no—
296C2×C22⋊C4—24no—
297C2×C22⋊C4—28no—
298C2×C22⋊C4—24no—
299C2×C22⋊C4—24no—
300C2×C22⋊C4—24no—
301C2×C22⋊C4—28no—
302C2×C22⋊C4—232no—
303C2×C22⋊C4—28no—
304C2×C22⋊C4—24no—
305C2×C22⋊C4—24no—
306C2×C22⋊C4—28no—
307C2×C22⋊C4—24no—
308C2×C22⋊C4—24no—
309C2×C22⋊C4—28no—
310C2×C22⋊C4—24no—
311C2×C22⋊C4—24no—
312C2×C22⋊C4—24no—
313C2×C22⋊C4—24no—
314C2×C22⋊C4—24no—
315C2×C22⋊C4—24no—
316C2×C22⋊C4—28no—
317C2×C22⋊C4—28no—
318C2×C22⋊C4—28no—
319C2×C22⋊C4—28no—
320C2×C22⋊C4—28no—
321C2×C22⋊C4—28no—
322C2×C22⋊C4—28no—
323C2×C22⋊C4—28no—
324C2×C22⋊C4—28no—
325C2×C22⋊C4—28no—
326C2×C22⋊C4—416no—
327C2×C22⋊C4—416no—
328C2×C22⋊C4—44no—
329C2×C22⋊C4—44no—
330C2×C22⋊C4—44no—
331C2×C22⋊C4—44no—
332C2×C22⋊C4—44no—
333C2×C22⋊C4—44no—
334C2×C22⋊C4—44no—
335C2×C22⋊C4—44no—
336C2×C22⋊C4—44no—
337C2×C22⋊C4—44no—
338C2×C22⋊C4C22×C418yes—
339C2×C22⋊C4C22×C418yes—
340C2×C22⋊C4C22×C418yes—
341C2×C22⋊C4C22×C418yes—
342C2×C22⋊C4C22×C418yes—
343C2×C22⋊C4C22×C418yes—
344C2×C22⋊C4C2×D418yes—
345C2×C22⋊C4#4118yes—
346C2×C42—24no—
347C2×C42—28no—
348C2×C42—24no—
349C2×C42—24no—
350C2×C42—42no—
351C2×C42—42no—
352C2×C42—42no—
353C2×C42—42no—
354C2×C42—42no—
355C2×C42—42no—
356C2×C42—42no—
357C2×C42—42no—
358C2×C42—44no—
359C2×C42—44no—
360C2×C42C2×D418yescomplemented
361#95—28no—
362#95—24no—
363#95—28no—
364#95—24no—
365#95—24no—
366#95—28no—
367#95—28no—
368#95—44no—
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#95C22×C418yes—
378#95C22×C418yes—
379#95C22×C418yes—
380#95C22×C418yes—
381#95C2×D418yescomplemented
382C24—22no—
383C24—22no—
384C24—22no—
385C24—22no—
386C24—232no—
387C24—28no—
388C24—28no—
389C24—28no—
390C24—22no—
391C24—21no—
392C24—21no—
393C24—22no—
394C24—22no—
395C24—22no—
396C24—22no—
397C24—21no—
398C24—21no—
399C24—22no—
400C24—22no—
401C24—22no—
402C24—24no—
403C24—22no—
404C24—22no—
405C24—22no—
406C24—24no—
407C24—24no—
408C24—22no—
409C24—22no—
410C24—22no—
411C24—24no—
412C24—28no—
413C24—28no—
414C24—216no—
415C24—216no—
416C24—28no—
417C24—28no—
418C24—44no—
419C24—44no—
420C24—44no—
421C24—44no—
422C24—44no—
423C24—416no—
424C24—44no—
425C24—416no—
426C24—48no—
427C24—48no—
428C24—48no—
429C24—48no—
430C24—416no—
431C24—416no—
432C24—416no—
433C24—48no—
434C24—48no—
435C24—84no—
436C24—84no—
437C24—84no—
438C24—84no—
439C24—88no—
440C24—88no—
441C24#117116yescomplemented
442C24C23×C414yes—
443C24C23×C412yes—
444C24C23×C412yes—
445C24C23×C412yes—
446C24C22×D412yes—
447C24C2×#4114yes—
448C24C2×#4114yes—
449C24C2×#4114yes—
450C24C2×#4112yes—
451C24C2×#4114yes—
452C24H(5,𝔽2)14yes—
453C24H(5,𝔽2)14yes—
454C24C2511yescharacteristic
455C2×D4—216no—
456C2×D4—216no—
457C2×D4—216no—
458C2×D4—216no—
459C2×D4—48no—
460C2×D4—48no—
461C2×D4—416no—
462C2×D4—416no—
463C2×D4—416no—
464C2×D4—416no—
465C2×D4—4128no—
466C22×C4—216no—
467C22×C4—216no—
468C22×C4—28no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—28no—
477C22×C4—28no—
478C22×C4—28no—
479C22×C4—28no—
480C22×C4—28no—
481C22×C4—21no—
482C22×C4—22no—
483C22×C4—24no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—24no—
487C22×C4—24no—
488C22×C4—24no—
489C22×C4—22no—
490C22×C4—21no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—24no—
494C22×C4—24no—
495C22×C4—24no—
496C22×C4—22no—
497C22×C4—24no—
498C22×C4—24no—
499C22×C4—24no—
500C22×C4—24no—
501C22×C4—24no—
502C22×C4—24no—
503C22×C4—24no—
504C22×C4—24no—
505C22×C4—22no—
506C22×C4—24no—
507C22×C4—24no—
508C22×C4—24no—
509C22×C4—232no—
510C22×C4—28no—
511C22×C4—28no—
512C22×C4—28no—
513C22×C4—28no—
514C22×C4—28no—
515C22×C4—28no—
516C22×C4—28no—
517C22×C4—24no—
518C22×C4—24no—
519C22×C4—24no—
520C22×C4—24no—
521C22×C4—24no—
522C22×C4—24no—
523C22×C4—24no—
524C22×C4—24no—
525C22×C4—24no—
526C22×C4—24no—
527C22×C4—24no—
528C22×C4—24no—
529C22×C4—24no—
530C22×C4—24no—
531C22×C4—44no—
532C22×C4—44no—
533C22×C4—44no—
534C22×C4—44no—
535C22×C4—44no—
536C22×C4—44no—
537C22×C4—44no—
538C22×C4—48no—
539C22×C4—48no—
540C22×C4—44no—
541C22×C4—44no—
542C22×C4—48no—
543C22×C4—48no—
544C22×C4—44no—
545C22×C4—44no—
546C22×C4—44no—
547C22×C4—44no—
548C22×C4—48no—
549C22×C4—48no—
550C22×C4—48no—
551C22×C4—48no—
552C22×C4—4128no—
553C22×C4—48no—
554C22×C4—48no—
555C22×C4—416no—
556C22×C4—88no—
557C22×C4—88no—
558C22×C4—88no—
559C22×C4—88no—
560C22×C4—84no—
561C22×C4—88no—
562C22×C4—84no—
563C22×C4—88no—
564C22×C4—88no—
565C22×C4C4×D4116yes—
566C22×C4C23×C414yes—
567C22×C4C23×C414yes—
568C22×C4C23×C414yes—
569C22×C4C23×C412yes—
570C22×C4C23×C412yes—
571C22×C4C23×C412yes—
572C22×C4C23×C412yes—
573C22×C4C22×D418yes—
574C22×C4C22×D412yes—
575C22×C4C22×D412yes—
576C22×C4C2×#4118yes—
577C22×C4C2×#4112yes—
578C22×C4C2×#4112yes—
579C22×C4H(5,𝔽2)14yes—
580C4⋊C4—416no—
581C4⋊C4—88no—
582C22⋊C4—232no—
583C22⋊C4—216no—
584C22⋊C4—216no—
585C22⋊C4—216no—
586C22⋊C4—216no—
587C22⋊C4—216no—
588C22⋊C4—216no—
589C22⋊C4—48no—
590C22⋊C4—48no—
591C22⋊C4—416no—
592C22⋊C4—416no—
593C22⋊C4—416no—
594C22⋊C4—416no—
595C22⋊C4—48no—
596C22⋊C4—48no—
597C22⋊C4—88no—
598C22⋊C4—88no—
599C42—48no—
600C42—48no—
601C42—84no—
602C42—84no—
603C42—88no—
604C23—22no—
605C23—22no—
606C23—22no—
607C23—22no—
608C23—24no—
609C23—24no—
610C23—24no—
611C23—28no—
612C23—24no—
613C23—28no—
614C23—28no—
615C23—28no—
616C23—232no—
617C23—22no—
618C23—22no—
619C23—24no—
620C23—22no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—24no—
625C23—24no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—24no—
631C23—24no—
632C23—24no—
633C23—22no—
634C23—22no—
635C23—24no—
636C23—24no—
637C23—24no—
638C23—24no—
639C23—24no—
640C23—24no—
641C23—28no—
642C23—24no—
643C23—28no—
644C23—28no—
645C23—28no—
646C23—24no—
647C23—28no—
648C23—28no—
649C23—28no—
650C23—28no—
651C23—232no—
652C23—416no—
653C23—416no—
654C23—416no—
655C23—416no—
656C23—416no—
657C23—416no—
658C23—464no—
659C23—464no—
660C23—416no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—44no—
667C23—44no—
668C23—42no—
669C23—42no—
670C23—44no—
671C23—42no—
672C23—44no—
673C23—44no—
674C23—44no—
675C23—44no—
676C23—44no—
677C23—44no—
678C23—44no—
679C23—44no—
680C23—44no—
681C23—416no—
682C23—832no—
683C23—832no—
684C23—88no—
685C23—88no—
686C23—88no—
687C23—88no—
688C23C2×#11718yes—
689C23C2×#11714yes—
690C23C2×C4×D414yes—
691C23C4×#4114yes—
692C23#51814yes—
693C23#51814yes—
694C23#52518yes—
695C23#52918yes—
696C23C24×C411yescharacteristic
697C23C23×D411yescharacteristic
698C23C22×#4112yes—
699C23C22×#4111yescharacteristic
700C23C22×#4112yes—
701C23C2×H(5,𝔽2)12yes—
702C23C2×H(5,𝔽2)12yes—
703C23C2×H(5,𝔽2)12yes—
704C23#58512yes—
705D4—432no—
706D4—432no—
707C2×C4—232no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—24no—
715C2×C4—24no—
716C2×C4—24no—
717C2×C4—24no—
718C2×C4—24no—
719C2×C4—24no—
720C2×C4—24no—
721C2×C4—24no—
722C2×C4—22no—
723C2×C4—24no—
724C2×C4—24no—
725C2×C4—24no—
726C2×C4—24no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—24no—
730C2×C4—24no—
731C2×C4—24no—
732C2×C4—28no—
733C2×C4—28no—
734C2×C4—28no—
735C2×C4—28no—
736C2×C4—28no—
737C2×C4—28no—
738C2×C4—416no—
739C2×C4—416no—
740C2×C4—416no—
741C2×C4—416no—
742C2×C4—416no—
743C2×C4—416no—
744C2×C4—44no—
745C2×C4—42no—
746C2×C4—44no—
747C2×C4—44no—
748C2×C4—42no—
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—44no—
768C2×C4—44no—
769C2×C4—44no—
770C2×C4—44no—
771C2×C4—44no—
772C2×C4—44no—
773C2×C4—44no—
774C2×C4—88no—
775C2×C4—88no—
776C2×C4—832no—
777C2×C4C2×C4×D414yes—
778C2×C4C2×C4×D414yes—
779C2×C4#51814yes—
780C22—216no—
781C22—216no—
782C22—24no—
783C22—24no—
784C22—24no—
785C22—24no—
786C22—24no—
787C22—24no—
788C22—24no—
789C22—24no—
790C22—28no—
791C22—28no—
792C22—24no—
793C22—24no—
794C22—24no—
795C22—24no—
796C22—28no—
797C22—464no—
798C22—48no—
799C22—48no—
800C22—48no—
801C22—48no—
802C22—48no—
803C22—48no—
804C22—48no—
805C22—48no—
806C22—42no—
807C22—42no—
808C22—42no—
809C22—44no—
810C22—42no—
811C22—44no—
812C22—42no—
813C22—44no—
814C22—42no—
815C22—44no—
816C22—42no—
817C22—42no—
818C22—832no—
819C22#229018yes—
820C22C22×#11711yescharacteristic
821C22C22×C4×D411yescharacteristic
822C22C2×C4×#4111yescharacteristic
823C22C2×#51811yescharacteristic
824C22C2×#51811yescharacteristic
825C22C2×#51811yescharacteristic
826C22#342811yescharacteristic
827C22C2×#52512yes—
828C22C2×#52912yes—
829C22#348412yes—
830C22#348812yes—
831C22#349014yes—
832C22#349012yes—
833C22#349412yes—
834C22#350514yes—
835C22#351314yes—
836C22#351914yes—
837C4—24no—
838C4—24no—
839C4—24no—
840C4—48no—
841C4—48no—
842C4—44no—
843C4—42no—
844C4—44no—
845C4—44no—
846C4—84no—
847C4—84no—
848C2—28no—
849C2—44no—
850C2—44no—
851C2—48no—
852C2C2×#229011yescharacteristic
853C2#3417611yescharacteristic
854C2#3418511yescharacteristic
855C2#3419811yescharacteristic
856C2#3420411yescharacteristic
857C2#3423811yescharacteristic
858C2#3424611yescharacteristic
859C2#3535214yes—
860C2#3537114yes—
subgroupG/H
center, Frattini, socle, cosocleC24C25
commutatorC23C24×C4
prime radicalC24×D4C22
LCSG ▷ C23 ▷ 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. C2×#2273C2semidirect
4. #14068C2semidirect
5. #14064C2semidirect
6. #13988C2semidirect
7. #13984C2semidirect
8. #13883C2semidirect
9. #13877C2semidirect
10. #13873C2semidirect
12. #13796C2semidirect
13. #13778C2semidirect
14. #13775C2semidirect
15. C4×#379C2semidirect
18. C22×#117C22semidirect
23. C2×#388C22semidirect
24. C2×#386C4semidirect
31. C2×#385C22semidirect
33. C2×#381C22semidirect
36. C2×#380C22semidirect
46. C2×C4×C22⋊C4C22semidirect
47. C2×C4×C22⋊C4C22semidirect
48. C2×C4×C22⋊C4C22semidirect
49. C2×C4×C22⋊C4C22semidirect
50. C2×C4×C22⋊C4C22semidirect
53. #1443C22semidirect
54. #1442C22semidirect
55. #1440C22semidirect
56. #1439C22semidirect
57. #1439C22semidirect
58. #1439C22semidirect
61. #1437C22semidirect
62. #1437C22semidirect
63. #1437C22semidirect
64. #1436C22semidirect
65. #1436C22semidirect
66. #1436C22semidirect
67. #1434C22semidirect
68. #1434C22semidirect
69. #1434C22semidirect
75. C22⋊#95C22semidirect
76. C22⋊#95C22semidirect
77. C22⋊#95C22semidirect
90. C24×C4C2×C4semidirect
115. C22×C22⋊C4C2×C4semidirect
141. #386C2×C4semidirect
142. #386C2×C4semidirect
143. #386C2×C4semidirect
144. #386C2×C4semidirect
162. C4×C22⋊C4D4semidirect
163. C2×#95C2×C4semidirect
164. C2×#95C2×C4semidirect
360. C2×C42C2×D4semidirect
381. #95C2×D4semidirect
441. C24#117semidirect

Maximal subgroups

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

subgroupindex
C22×#3862
C2×#22802
C2×#22732
#140682
#140642
#139882
#139842
#138832
#138772
#138732
#138672
#137962
#137782
#137752
C4×#3792