Finite Group Databasebeta

← #515975

Subgroups — #515975

Order 512.

5274 conjugacy classes of subgroups.

The subgroup lattice has 865 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2405C211yesmaximal, characteristic
2C22×#386C211yesmaximal, characteristic
3C2×#2273C211yesmaximal, characteristic, complemented
4#14182C214yesmaximal, complemented
5#14181C214yesmaximal, complemented
6#14127C211yesmaximal, characteristic, complemented
7#14096C214yesmaximal, complemented
8#14040C212yesmaximal, complemented
9#13991C212yesmaximal, complemented
10#13984C214yesmaximal, complemented
11#13869C211yesmaximal, characteristic, complemented
12#13867C211yesmaximal, characteristic
13#13782C212yesmaximal, complemented
14#13775C211yesmaximal, characteristic, complemented
15C4×#379C212yesmaximal, complemented
16C24×D4C2211yescharacteristic
17C25×C4C2211yescharacteristic
18C22×#123C2212yes—
19C23×C22⋊C4C2211yescharacteristic
20C23×C22⋊C4C2211yescharacteristic
21C23×C22⋊C4C2211yescharacteristic
22C23×C22⋊C4C2211yescharacteristic
23C23×C22⋊C4C2211yescharacteristic
24#2405C4116yescomplemented
25C2×#394C2214yes—
26C2×#388C2214yescomplemented
27C2×#386—28no—
28C2×#386C2214yes—
29C2×#386C2214yes—
30C2×#386C2212yes—
31C2×#386C2212yes—
32C2×#386C2212yes—
33C2×#385C2212yes—
34C2×#385C2212yes—
35C2×#385C2212yescomplemented
36C2×#381C2212yescomplemented
37C2×#379C2211yescharacteristic
38C2×#379C2212yes—
39C2×#379C2211yescharacteristic
40C2×#379C2212yes—
41#2273—28no—
42C2×C4×C22⋊C4C2212yes—
43C2×C4×C22⋊C4C2212yes—
44C2×C4×C22⋊C4C2212yes—
45C2×C4×C22⋊C4C2212yescomplemented
46C2×C4×C22⋊C4C2212yescomplemented
47C2×C4×C22⋊C4C2212yescomplemented
48C2×C4×C22⋊C4C2212yescomplemented
49C2×C4×C22⋊C4C2214yescomplemented
50C2×C4×C22⋊C4C2214yescomplemented
51C22×#95C2211yescharacteristic
52C22×#95C2211yescharacteristic
53#1445C2214yescomplemented
54#1443C2214yescomplemented
55#1440C2214yescomplemented
56#1440C2214yescomplemented
57#1439C2214yescomplemented
58#1439C2214yescomplemented
59#1438C2214yes—
60#1437C2214yescomplemented
61#1437C2214yescomplemented
62#1437C2214yescomplemented
63#1436C2214yescomplemented
64#1436C2214yescomplemented
65#1436C2214yescomplemented
66C4⋊#95C2214yescomplemented
67#1434C2214yescomplemented
68#1434C2214yescomplemented
69C22⋊#95C2212yes—
70C22⋊#95C2212yes—
71C22⋊#95C2212yes—
72C22⋊#95C2212yes—
73C22⋊#95C2212yes—
74C22⋊#95C2212yescomplemented
75C22⋊#95C2214yescomplemented
76C22⋊#95C2212yescomplemented
77C22⋊#95C2214yescomplemented
78C26C2311yescharacteristic
79C26C2311yescharacteristic
80C23×D4—24no—
81C23×D4—24no—
82C23×D4—44no—
83C23×D4—44no—
84C23×D4C2×C418yes—
85C23×D4C2312yes—
86C23×D4C2312yes—
87C24×C4—24no—
88C24×C4—28no—
89C24×C4—44no—
90C24×C4—44no—
91C24×C4C2311yescharacteristic
92C24×C4C2314yes—
93C24×C4C2311yescharacteristic
94C24×C4C2311yescharacteristic
95C24×C4C2311yescharacteristic
96C24×C4C2311yescharacteristic
97C24×C4C2311yescharacteristic
98C24×C4C2311yescharacteristic
99C24×C4C2311yescharacteristic
100C24×C4C2311yescharacteristic
101C2×#123—44no—
102C2×#123—44no—
103C2×#123C2×C4116yescomplemented
104C22×C4⋊C4C2314yes—
105C22×C4⋊C4C2314yes—
106C22×C22⋊C4—24no—
107C22×C22⋊C4—24no—
108C22×C22⋊C4—24no—
109C22×C22⋊C4—28no—
110C22×C22⋊C4—28no—
111C22×C22⋊C4—24no—
112C22×C22⋊C4—24no—
113C22×C22⋊C4—44no—
114C22×C22⋊C4—44no—
115C22×C22⋊C4C2×C418yescomplemented
116C22×C22⋊C4D418yes—
117C22×C22⋊C4C2312yes—
118C22×C22⋊C4C2312yes—
119C22×C22⋊C4C2312yes—
120C22×C22⋊C4C2312yes—
121C22×C22⋊C4C2314yes—
122C22×C22⋊C4C2314yes—
123C22×C22⋊C4C2314yes—
124C22×C22⋊C4C2314yes—
125C22×C22⋊C4C2312yes—
126C22×C22⋊C4C2312yes—
127C22×C22⋊C4C2312yes—
128C22×C22⋊C4C2312yes—
129C22×C22⋊C4C2312yes—
130C22×C22⋊C4C2312yes—
131C22×C22⋊C4C2312yes—
132C22×C22⋊C4C2312yes—
133C22×C22⋊C4C2314yes—
134C22×C22⋊C4C2312yes—
135C22×C22⋊C4C2312yes—
136C22×C42C2312yes—
137C22×C42C2314yes—
138C22×C42C2312yes—
139C22×C42C2312yes—
140C22×C42C2312yes—
141#394C2×C4132yescomplemented
142#388—48no—
143#386—216no—
144#386—216no—
145#386—44no—
146#386—44no—
147#386C2×C4116yescomplemented
148#385—28no—
149#385—44no—
150#385C2×C4116yescomplemented
151#381—44no—
152#379—24no—
153#379—28no—
154#379C2×C4116yescomplemented
155#379C2×C418yescomplemented
156C4×C22⋊C4—28no—
157C4×C22⋊C4—28no—
158C4×C22⋊C4—28no—
159C4×C22⋊C4—28no—
160C4×C22⋊C4—28no—
161C4×C22⋊C4—28no—
162C4×C22⋊C4—28no—
163C4×C22⋊C4—48no—
164C4×C22⋊C4—48no—
165C2×#95—24no—
166C2×#95—24no—
167C2×#95C2314yes—
168C2×#95C2314yes—
169C2×#95C2312yes—
170C2×#95C2312yes—
171C2×#95C2314yes—
172C2×#95C2314yes—
173C2×#95C2314yes—
174C2×#95C2314yes—
175C2×#95C2312yes—
176C2×#95C2312yes—
177C2×#95C2314yes—
178C2×#95C2314yes—
179C2×#95C2314yes—
180C2×#95C2314yes—
181C2×#95C2314yes—
182C2×#95C2314yes—
183C2×#95C2314yes—
184C2×#95C2314yes—
185C2×#95C2314yes—
186C25—22no—
187C25—22no—
188C25—24no—
189C25—24no—
190C25—24no—
191C25—24no—
192C25—24no—
193C25—24no—
194C25—42no—
195C25—42no—
196C25—42no—
197C25—42no—
198C25—42no—
199C25—42no—
200C25C22×C414yes—
201C25C22×C414yes—
202C25C2×D414yes—
203C25#4114yes—
204C25C2411yescharacteristic
205C25C2411yescharacteristic
206C25C2412yes—
207C25C2411yescharacteristic
208C22×D4—232no—
209C22×D4—24no—
210C22×D4—24no—
211C22×D4—24no—
212C22×D4—24no—
213C22×D4—24no—
214C22×D4—24no—
215C22×D4—24no—
216C22×D4—24no—
217C22×D4—42no—
218C22×D4—42no—
219C22×D4—42no—
220C22×D4—42no—
221C22×D4—432no—
222C22×D4—416no—
223C22×D4—416no—
224C22×D4—432no—
225C22×D4C22×C418yes—
226C22×D4C22×C418yes—
227C23×C4—22no—
228C23×C4—22no—
229C23×C4—22no—
230C23×C4—28no—
231C23×C4—22no—
232C23×C4—22no—
233C23×C4—22no—
234C23×C4—22no—
235C23×C4—22no—
236C23×C4—22no—
237C23×C4—24no—
238C23×C4—28no—
239C23×C4—24no—
240C23×C4—28no—
241C23×C4—24no—
242C23×C4—24no—
243C23×C4—22no—
244C23×C4—24no—
245C23×C4—24no—
246C23×C4—28no—
247C23×C4—28no—
248C23×C4—42no—
249C23×C4—42no—
250C23×C4—44no—
251C23×C4—44no—
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—42no—
261C23×C4—42no—
262C23×C4—42no—
263C23×C4—42no—
264C23×C4—42no—
265C23×C4—42no—
266C23×C4—42no—
267C23×C4—416no—
268C23×C4—464no—
269C23×C4—416no—
270C23×C4—416no—
271C23×C4C22×C414yes—
272C23×C4C22×C414yescomplemented
273C23×C4C22×C414yescomplemented
274C23×C4C2×D414yes—
275C23×C4C2×D414yes—
276C23×C4#4118yes—
277C23×C4C2414yes—
278C23×C4C2412yes—
279C23×C4C2414yes—
280C23×C4C2412yes—
281C23×C4C2412yes—
282C23×C4C2412yes—
283C23×C4C2412yes—
284C23×C4C2412yes—
285C23×C4C2412yes—
286C23×C4C2412yes—
287C23×C4C2412yes—
288#123—432no—
289C2×C4⋊C4—28no—
290C2×C4⋊C4—44no—
291C2×C4⋊C4—44no—
292C2×C4⋊C4—44no—
293C2×C4⋊C4—44no—
294C2×C4⋊C4C22×C4116yescomplemented
295C2×C22⋊C4—232no—
296C2×C22⋊C4—232no—
297C2×C22⋊C4—24no—
298C2×C22⋊C4—24no—
299C2×C22⋊C4—24no—
300C2×C22⋊C4—24no—
301C2×C22⋊C4—24no—
302C2×C22⋊C4—24no—
303C2×C22⋊C4—24no—
304C2×C22⋊C4—24no—
305C2×C22⋊C4—24no—
306C2×C22⋊C4—28no—
307C2×C22⋊C4—28no—
308C2×C22⋊C4—232no—
309C2×C22⋊C4—24no—
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—24no—
317C2×C22⋊C4—24no—
318C2×C22⋊C4—24no—
319C2×C22⋊C4—24no—
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—24no—
327C2×C22⋊C4—24no—
328C2×C22⋊C4—24no—
329C2×C22⋊C4—24no—
330C2×C22⋊C4—44no—
331C2×C22⋊C4—42no—
332C2×C22⋊C4—42no—
333C2×C22⋊C4—44no—
334C2×C22⋊C4—42no—
335C2×C22⋊C4—44no—
336C2×C22⋊C4—42no—
337C2×C22⋊C4—42no—
338C2×C22⋊C4—44no—
339C2×C22⋊C4—44no—
340C2×C22⋊C4—42no—
341C2×C22⋊C4—416no—
342C2×C22⋊C4—416no—
343C2×C22⋊C4—42no—
344C2×C22⋊C4—42no—
345C2×C22⋊C4—42no—
346C2×C22⋊C4—42no—
347C2×C22⋊C4C22×C418yes—
348C2×C22⋊C4C22×C4116yes—
349C2×C22⋊C4C22×C418yes—
350C2×C22⋊C4C22×C4116yes—
351C2×C22⋊C4C22×C418yescomplemented
352C2×C22⋊C4C22×C418yescomplemented
353C2×C22⋊C4C22×C418yescomplemented
354C2×C22⋊C4C2×D418yes—
355C2×C22⋊C4C2×D418yes—
356C2×C22⋊C4#4118yes—
357C2×C42—24no—
358C2×C42—24no—
359C2×C42—24no—
360C2×C42—24no—
361C2×C42—28no—
362C2×C42—44no—
363C2×C42—44no—
364C2×C42—44no—
365C2×C42—44no—
366C2×C42—44no—
367C2×C42—44no—
368#95—28no—
369#95—28no—
370#95—24no—
371#95—24no—
372#95—24no—
373#95—24no—
374#95—28no—
375#95—28no—
376#95—28no—
377#95—28no—
378#95—44no—
379#95—44no—
380#95—44no—
381#95—44no—
382#95—44no—
383#95—44no—
384#95—44no—
385#95—44no—
386#95C22×C4116yescomplemented
387C24—22no—
388C24—22no—
389C24—22no—
390C24—22no—
391C24—28no—
392C24—28no—
393C24—216no—
394C24—28no—
395C24—216no—
396C24—22no—
397C24—22no—
398C24—22no—
399C24—22no—
400C24—24no—
401C24—22no—
402C24—24no—
403C24—22no—
404C24—22no—
405C24—22no—
406C24—24no—
407C24—22no—
408C24—22no—
409C24—22no—
410C24—22no—
411C24—22no—
412C24—22no—
413C24—24no—
414C24—22no—
415C24—22no—
416C24—216no—
417C24—28no—
418C24—28no—
419C24—216no—
420C24—216no—
421C24—48no—
422C24—44no—
423C24—48no—
424C24—44no—
425C24—44no—
426C24—48no—
427C24—48no—
428C24—44no—
429C24—48no—
430C24—416no—
431C24—416no—
432C24—416no—
433C24—416no—
434C24—44no—
435C24—44no—
436C24—48no—
437C24—44no—
438C24—44no—
439C24—48no—
440C24—88no—
441C24—88no—
442C24—88no—
443C24—88no—
444C24C4×D4116yes—
445C24C23×C412yes—
446C24C23×C412yes—
447C24C23×C414yes—
448C24C23×C412yes—
449C24C22×D412yes—
450C24C22×D412yes—
451C24C22×D412yes—
452C24C2×#4112yes—
453C24C2×#4112yes—
454C24C2×#4112yes—
455C24C2×#4114yes—
456C24C2×#4114yes—
457C24H(5,𝔽2)14yes—
458C24H(5,𝔽2)14yes—
459C24C2511yescharacteristic
460C2×D4—216no—
461C2×D4—216no—
462C2×D4—216no—
463C2×D4—216no—
464C2×D4—48no—
465C2×D4—48no—
466C2×D4—48no—
467C2×D4—48no—
468C2×D4—48no—
469C2×D4—48no—
470C2×D4—48no—
471C2×D4—48no—
472C2×D4—48no—
473C2×D4—48no—
474C2×D4—4128no—
475C22×C4—24no—
476C22×C4—24no—
477C22×C4—28no—
478C22×C4—232no—
479C22×C4—28no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—24no—
487C22×C4—24no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—24no—
495C22×C4—22no—
496C22×C4—24no—
497C22×C4—24no—
498C22×C4—24no—
499C22×C4—24no—
500C22×C4—24no—
501C22×C4—22no—
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—22no—
512C22×C4—24no—
513C22×C4—24no—
514C22×C4—24no—
515C22×C4—24no—
516C22×C4—28no—
517C22×C4—28no—
518C22×C4—28no—
519C22×C4—28no—
520C22×C4—28no—
521C22×C4—22no—
522C22×C4—24no—
523C22×C4—24no—
524C22×C4—24no—
525C22×C4—24no—
526C22×C4—24no—
527C22×C4—24no—
528C22×C4—24no—
529C22×C4—22no—
530C22×C4—24no—
531C22×C4—22no—
532C22×C4—24no—
533C22×C4—44no—
534C22×C4—44no—
535C22×C4—416no—
536C22×C4—48no—
537C22×C4—416no—
538C22×C4—416no—
539C22×C4—44no—
540C22×C4—48no—
541C22×C4—48no—
542C22×C4—44no—
543C22×C4—416no—
544C22×C4—416no—
545C22×C4—416no—
546C22×C4—416no—
547C22×C4—44no—
548C22×C4—44no—
549C22×C4—44no—
550C22×C4—48no—
551C22×C4—4128no—
552C22×C4—44no—
553C22×C4—416no—
554C22×C4—44no—
555C22×C4—44no—
556C22×C4—44no—
557C22×C4—88no—
558C22×C4—88no—
559C22×C4—82no—
560C22×C4—82no—
561C22×C4—82no—
562C22×C4—82no—
563C22×C4—82no—
564C22×C4—82no—
565C22×C4—82no—
566C22×C4—82no—
567C22×C4—84no—
568C22×C4—88no—
569C22×C4—84no—
570C22×C4—88no—
571C22×C4#123116yescomplemented
572C22×C4C23×C414yes—
573C22×C4C23×C414yes—
574C22×C4C23×C418yes—
575C22×C4C23×C414yes—
576C22×C4C22×D414yes—
577C22×C4C22×D414yes—
578C22×C4C2×#4114yes—
579C22×C4C2×#4114yes—
580C22×C4C2×#4114yes—
581C22×C4C2×#4114yes—
582C22×C4H(5,𝔽2)14yes—
583C4⋊C4—416no—
584C4⋊C4—88no—
585C22⋊C4—216no—
586C22⋊C4—216no—
587C22⋊C4—216no—
588C22⋊C4—216no—
589C22⋊C4—232no—
590C22⋊C4—216no—
591C22⋊C4—216no—
592C22⋊C4—216no—
593C22⋊C4—416no—
594C22⋊C4—48no—
595C22⋊C4—48no—
596C22⋊C4—416no—
597C22⋊C4—416no—
598C22⋊C4—416no—
599C22⋊C4—48no—
600C22⋊C4—48no—
601C22⋊C4—48no—
602C22⋊C4—84no—
603C22⋊C4—84no—
604C42—84no—
605C42—84no—
606C42—88no—
607C42—84no—
608C42—84no—
609C23—24no—
610C23—24no—
611C23—22no—
612C23—22no—
613C23—22no—
614C23—22no—
615C23—28no—
616C23—24no—
617C23—28no—
618C23—24no—
619C23—28no—
620C23—28no—
621C23—232no—
622C23—24no—
623C23—24no—
624C23—24no—
625C23—28no—
626C23—24no—
627C23—24no—
628C23—24no—
629C23—24no—
630C23—28no—
631C23—24no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—24no—
637C23—24no—
638C23—22no—
639C23—22no—
640C23—24no—
641C23—24no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—24no—
649C23—28no—
650C23—24no—
651C23—24no—
652C23—24no—
653C23—28no—
654C23—24no—
655C23—24no—
656C23—28no—
657C23—28no—
658C23—232no—
659C23—416no—
660C23—416no—
661C23—464no—
662C23—416no—
663C23—416no—
664C23—416no—
665C23—464no—
666C23—416no—
667C23—416no—
668C23—42no—
669C23—42no—
670C23—44no—
671C23—42no—
672C23—42no—
673C23—44no—
674C23—44no—
675C23—44no—
676C23—44no—
677C23—44no—
678C23—44no—
679C23—44no—
680C23—44no—
681C23—44no—
682C23—44no—
683C23—44no—
684C23—44no—
685C23—44no—
686C23—416no—
687C23—88no—
688C23—88no—
689C23—88no—
690C23—832no—
691C23—88no—
692C23—832no—
693C23C2×C4×D414yes—
694C23C2×C4×D414yes—
695C23C2×C4×D414yes—
696C23C4×#4118yes—
697C23#51818yes—
698C23C2×#12314yes—
699C23#52514yes—
700C23#52918yes—
701C23C24×C411yescharacteristic
702C23C23×D411yescharacteristic
703C23C22×#4111yescharacteristic
704C23C22×#4112yes—
705C23C22×#4112yes—
706C23C2×H(5,𝔽2)12yes—
707C23C2×H(5,𝔽2)12yes—
708C23C2×H(5,𝔽2)12yes—
709C23#58512yes—
710D4—432no—
711D4—432no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—28no—
715C2×C4—28no—
716C2×C4—24no—
717C2×C4—24no—
718C2×C4—24no—
719C2×C4—28no—
720C2×C4—28no—
721C2×C4—28no—
722C2×C4—24no—
723C2×C4—24no—
724C2×C4—28no—
725C2×C4—28no—
726C2×C4—24no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—24no—
731C2×C4—24no—
732C2×C4—28no—
733C2×C4—28no—
734C2×C4—28no—
735C2×C4—416no—
736C2×C4—464no—
737C2×C4—416no—
738C2×C4—416no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—44no—
752C2×C4—44no—
753C2×C4—42no—
754C2×C4—42no—
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—42no—
765C2×C4—44no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—44no—
769C2×C4—44no—
770C2×C4—44no—
771C2×C4—44no—
772C2×C4—44no—
773C2×C4—44no—
774C2×C4—44no—
775C2×C4—44no—
776C2×C4—88no—
777C2×C4—88no—
778C2×C4—88no—
779C2×C4—88no—
780C2×C4—88no—
781C2×C4—88no—
782C2×C4C2×#12318yes—
783C22—24no—
784C22—24no—
785C22—24no—
786C22—216no—
787C22—24no—
788C22—24no—
789C22—24no—
790C22—216no—
791C22—24no—
792C22—28no—
793C22—24no—
794C22—24no—
795C22—24no—
796C22—24no—
797C22—24no—
798C22—216no—
799C22—464no—
800C22—44no—
801C22—42no—
802C22—42no—
803C22—42no—
804C22—44no—
805C22—42no—
806C22—42no—
807C22—44no—
808C22—42no—
809C22—48no—
810C22—48no—
811C22—48no—
812C22—48no—
813C22—44no—
814C22—42no—
815C22—42no—
816C22—44no—
817C22—44no—
818C22—48no—
819C22—48no—
820C22—48no—
821C22—832no—
822C22C4×#12318yes—
823C22C22×C4×D411yescharacteristic
824C22C2×C4×#4112yes—
825C22C2×#51812yes—
826C22C4×H(5,𝔽2)12yes—
827C22C22×#12311yescharacteristic
828C22C2×#52511yescharacteristic
829C22C2×#52912yes—
830C22#348411yescharacteristic
831C22#348411yescharacteristic
832C22#348411yescharacteristic
833C22#348511yescharacteristic
834C22#349014yes—
835C22#349012yes—
836C22#349414yes—
837C22#350512yes—
838C22#351314yes—
839C22#351914yes—
840C4—28no—
841C4—44no—
842C4—44no—
843C4—44no—
844C4—44no—
845C4—44no—
846C4—44no—
847C4—44no—
848C4—48no—
849C4—82no—
850C4—84no—
851C2—28no—
852C2—48no—
853C2—44no—
854C2—44no—
855C2C2×C4×#12311yescharacteristic
856C2#3419811yescharacteristic
857C2#3426411yescharacteristic
858C2#3430214yes—
859C2#3535011yescharacteristic
860C2#3535411yescharacteristic
861C2#3535511yescharacteristic
862C2#3537114yes—
863C2#3554011yescharacteristic
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
3. C2×#2273C2semidirect
4. #14182C2semidirect
5. #14181C2semidirect
6. #14127C2semidirect
7. #14096C2semidirect
8. #14040C2semidirect
9. #13991C2semidirect
10. #13984C2semidirect
11. #13869C2semidirect
13. #13782C2semidirect
14. #13775C2semidirect
15. C4×#379C2semidirect
24. #2405C4semidirect
26. C2×#388C22semidirect
35. C2×#385C22semidirect
36. C2×#381C22semidirect
45. C2×C4×C22⋊C4C22semidirect
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. #1445C22semidirect
54. #1443C22semidirect
55. #1440C22semidirect
56. #1440C22semidirect
57. #1439C22semidirect
58. #1439C22semidirect
60. #1437C22semidirect
61. #1437C22semidirect
62. #1437C22semidirect
63. #1436C22semidirect
64. #1436C22semidirect
65. #1436C22semidirect
66. C4⋊#95C22semidirect
67. #1434C22semidirect
68. #1434C22semidirect
74. C22⋊#95C22semidirect
75. C22⋊#95C22semidirect
76. C22⋊#95C22semidirect
77. C22⋊#95C22semidirect
103. C2×#123C2×C4semidirect
115. C22×C22⋊C4C2×C4semidirect
141. #394C2×C4semidirect
147. #386C2×C4semidirect
150. #385C2×C4semidirect
154. #379C2×C4semidirect
155. #379C2×C4semidirect
272. C23×C4C22×C4semidirect
273. C23×C4C22×C4semidirect
294. C2×C4⋊C4C22×C4semidirect
351. C2×C22⋊C4C22×C4semidirect
352. C2×C22⋊C4C22×C4semidirect
353. C2×C22⋊C4C22×C4semidirect
386. #95C22×C4semidirect
571. C22×C4#123semidirect

Maximal subgroups

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

subgroupindex
C2×#24052
C22×#3862
C2×#22732
#141822
#141812
#141272
#140962
#140402
#139912
#139842
#138692
#138672
#137822
#137752
C4×#3792