Finite Group Databasebeta

← #560033

Subgroups — #560033

Order 512.

3838 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#120C211yesmaximal, characteristic
2#14680C212yesmaximal, complemented
3#14669C212yesmaximal, complemented
4#14456C214yesmaximal, complemented
5#14427C214yesmaximal, complemented
6#14366C212yesmaximal, complemented
7#14357C212yesmaximal
8#13906C211yesmaximal, characteristic, complemented
9#13905C212yesmaximal, complemented
10#13876C212yesmaximal, complemented
11#13875C212yesmaximal, complemented
12#13875C212yesmaximal, complemented
13#13872C212yesmaximal, complemented
14#13872C211yesmaximal, characteristic, complemented
15#13832C212yesmaximal, complemented
16C25×C4C2211yescharacteristic
17C22×#120C2211yescharacteristic
18C22×C4×D4C2212yes—
19C22×C4×D4C2211yescharacteristic
20C23×C4⋊C4C2211yescharacteristic, complemented
21C4×#120C4116yescomplemented
22C2×#390C2212yes—
23C2×#388C2214yes—
24C2×#386C2212yes—
25C2×#386C2214yes—
26C2×#386C2211yescharacteristic
27C2×#386C2212yes—
28C2×#385C2211yescharacteristic
29C2×#385C2212yes—
30C2×#384C2211yescharacteristic, complemented
31C2×#382C2212yescomplemented
32C2×#380C2212yes—
33C2×#380C2212yes—
34C2×#380C2212yes—
35C2×#380C2212yes—
36C2×#380C2212yes—
37C2×#380C2212yes—
38C2×#380C2211yescharacteristic, complemented
39C2×#380C2212yescomplemented
40C2×#379C2214yes—
41C2×#379C2211yescharacteristic
42C2×C4×C4⋊C4C2211yescharacteristic, complemented
43C2×C4×C4⋊C4C2212yescomplemented
44C2×C4×C22⋊C4C2211yescharacteristic
45C2×C4×C22⋊C4C2212yes—
46#1445C2214yescomplemented
47#1443C2214yescomplemented
48#1443C2214yescomplemented
49#1442C2214yescomplemented
50#1441C2214yescomplemented
51#1441C2212yescomplemented
52#1440C2214yes—
53#1440C2214yes—
54#1439C2214yes—
55#1439C2212yes—
56#1439C2214yes—
57#1439C2212yes—
58#1439C2212yescomplemented
59#1438C2214yes—
60#1437C2214yes—
61#1437C2214yes—
62#1437C2214yes—
63#1437C2214yescomplemented
64#1436C2214yescomplemented
65C4⋊#95C2212yescomplemented
66C4⋊#95C2212yescomplemented
67C4⋊#95C2212yescomplemented
68C4⋊#95C2212yescomplemented
69#1434C2214yescomplemented
70#1434C2214yescomplemented
71C22⋊#95C2214yes—
72C22⋊#95C2214yes—
73C22⋊#95C2214yes—
74C22⋊#95C2214yescomplemented
75C22⋊#95C2212yescomplemented
76C26C2311yescharacteristic
77C23×D4C2312yes—
78C23×D4C2311yescharacteristic
79C24×C4—42no—
80C24×C4—44no—
81C24×C4—42no—
82C24×C4—44no—
83C24×C4C2×C418yescomplemented
84C24×C4C2311yescharacteristic
85C24×C4C2312yes—
86C24×C4C2311yescharacteristic
87C24×C4C2312yes—
88C24×C4C2311yescharacteristic
89C24×C4C2312yes—
90C2×#120—24no—
91C2×#120—24no—
92C2×#120C2×C418yes—
93C2×C4×D4—44no—
94C2×C4×D4—42no—
95C2×C4×D4—44no—
96C2×C4×D4—42no—
97C2×C4×D4C2×C4116yes—
98C2×C4×D4C2×C418yes—
99C22×C4⋊C4—42no—
100C22×C4⋊C4—44no—
101C22×C4⋊C4C2312yes—
102C22×C4⋊C4C2312yes—
103C22×C4⋊C4C2312yes—
104C22×C4⋊C4C2312yes—
105C22×C4⋊C4C2312yes—
106C22×C4⋊C4C2312yes—
107C22×C4⋊C4C2312yes—
108C22×C4⋊C4C2311yescharacteristic
109C22×C4⋊C4C2312yes—
110C22×C22⋊C4C2312yes—
111C22×C22⋊C4C2311yescharacteristic
112C22×C22⋊C4C2312yes—
113C22×C22⋊C4C2314yes—
114C22×C22⋊C4C2314yes—
115C22×C22⋊C4C2314yes—
116C22×C22⋊C4C2314yes—
117C22×C22⋊C4C2314yes—
118C22×C22⋊C4C2314yes—
119C22×C22⋊C4C2312yes—
120C22×C22⋊C4C2314yes—
121C22×C22⋊C4C2312yes—
122C22×C22⋊C4C2311yescharacteristic
123C22×C22⋊C4C2312yes—
124C22×C22⋊C4C2311yescharacteristic
125C22×C22⋊C4C2311yescharacteristic
126C22×C42C2312yes—
127C22×C42C2311yescharacteristic
128C22×C42C2312yes—
129C22×C42C2314yes—
130#390—28no—
131#388—48no—
132#386—28no—
133#386—48no—
134#386C2×C4116yes—
135#386C2×C418yes—
136#385C2×C418yescomplemented
137#385C2×C4116yescomplemented
138#384—42no—
139#382—44no—
140#380—44no—
141#380—44no—
142#380—44no—
143#380—44no—
144#380—44no—
145#380—44no—
146#380—42no—
147#380—44no—
148#379—48no—
149#379C2×C418yescomplemented
150C4×C4⋊C4—42no—
151C4×C4⋊C4—44no—
152C4×C22⋊C4C2×C4116yescomplemented
153C4×C22⋊C4C2×C418yescomplemented
154C2×#95C2314yes—
155C2×#95C2314yes—
156C2×#95C2314yes—
157C2×#95C2314yes—
158C2×#95C2314yes—
159C2×#95C2314yes—
160C2×#95C2314yes—
161C2×#95C2314yes—
162C2×#95C2314yes—
163C2×#95C2314yes—
164C2×#95C2314yes—
165C2×#95C2314yes—
166C2×#95C2314yes—
167C2×#95C2314yes—
168C2×#95C2314yes—
169C2×#95C2312yes—
170C2×#95C2314yes—
171C2×#95C2312yes—
172C2×#95C2312yes—
173C2×#95C2312yes—
174C2×#95C2312yes—
175C25—22no—
176C25—22no—
177C25—24no—
178C25—24no—
179C25—42no—
180C25—42no—
181C25—41no—
182C25—41no—
183C25—41no—
184C25—41no—
185C25C22×C414yes—
186C25C2411yescharacteristic
187C25C2411yescharacteristic
188C25C2412yes—
189C22×D4—24no—
190C22×D4—24no—
191C22×D4—24no—
192C22×D4—24no—
193C22×D4—41no—
194C22×D4—41no—
195C22×D4—42no—
196C22×D4—42no—
197C22×D4—41no—
198C22×D4—41no—
199C22×D4C22×C418yes—
200C22×D4C22×C414yes—
201C22×D4#4114yes—
202C22×D4#4114yes—
203C23×C4—22no—
204C23×C4—24no—
205C23×C4—22no—
206C23×C4—24no—
207C23×C4—22no—
208C23×C4—24no—
209C23×C4—22no—
210C23×C4—24no—
211C23×C4—24no—
212C23×C4—24no—
213C23×C4—24no—
214C23×C4—24no—
215C23×C4—24no—
216C23×C4—24no—
217C23×C4—24no—
218C23×C4—416no—
219C23×C4—432no—
220C23×C4—41no—
221C23×C4—42no—
222C23×C4—41no—
223C23×C4—42no—
224C23×C4—42no—
225C23×C4—42no—
226C23×C4—42no—
227C23×C4—42no—
228C23×C4—42no—
229C23×C4—42no—
230C23×C4—42no—
231C23×C4—44no—
232C23×C4—42no—
233C23×C4—44no—
234C23×C4—432no—
235C23×C4—416no—
236C23×C4—416no—
237C23×C4C22×C414yes—
238C23×C4C22×C414yes—
239C23×C4C22×C418yes—
240C23×C4C22×C414yes—
241C23×C4C22×C418yes—
242C23×C4C2414yes—
243C23×C4C2414yes—
244C23×C4C2414yes—
245C23×C4C2414yes—
246C23×C4C2411yescharacteristic
247C23×C4C2412yes—
248C23×C4C2411yescharacteristic
249C23×C4C2412yes—
250C23×C4C2412yes—
251C23×C4C2411yescharacteristic
252C23×C4C2411yescharacteristic
253C23×C4C2411yescharacteristic
254#120—232no—
255C4×D4—416no—
256C4×D4—432no—
257C2×C4⋊C4—24no—
258C2×C4⋊C4—24no—
259C2×C4⋊C4—24no—
260C2×C4⋊C4—24no—
261C2×C4⋊C4—24no—
262C2×C4⋊C4—24no—
263C2×C4⋊C4—24no—
264C2×C4⋊C4—24no—
265C2×C4⋊C4—24no—
266C2×C4⋊C4—24no—
267C2×C4⋊C4—24no—
268C2×C4⋊C4—24no—
269C2×C4⋊C4—24no—
270C2×C4⋊C4—42no—
271C2×C4⋊C4—44no—
272C2×C4⋊C4—41no—
273C2×C4⋊C4—41no—
274C2×C4⋊C4—42no—
275C2×C4⋊C4—42no—
276C2×C4⋊C4—416no—
277C2×C4⋊C4—42no—
278C2×C4⋊C4—42no—
279C2×C4⋊C4—42no—
280C2×C4⋊C4—44no—
281C2×C4⋊C4C22×C418yes—
282C2×C4⋊C4C22×C414yes—
283C2×C22⋊C4—22no—
284C2×C22⋊C4—22no—
285C2×C22⋊C4—24no—
286C2×C22⋊C4—24no—
287C2×C22⋊C4—24no—
288C2×C22⋊C4—24no—
289C2×C22⋊C4—24no—
290C2×C22⋊C4—28no—
291C2×C22⋊C4—28no—
292C2×C22⋊C4—28no—
293C2×C22⋊C4—28no—
294C2×C22⋊C4—28no—
295C2×C22⋊C4—28no—
296C2×C22⋊C4—28no—
297C2×C22⋊C4—41no—
298C2×C22⋊C4—41no—
299C2×C22⋊C4—41no—
300C2×C22⋊C4—42no—
301C2×C22⋊C4—41no—
302C2×C22⋊C4—42no—
303C2×C22⋊C4—42no—
304C2×C22⋊C4—42no—
305C2×C22⋊C4—41no—
306C2×C22⋊C4—41no—
307C2×C22⋊C4—44no—
308C2×C22⋊C4—42no—
309C2×C22⋊C4—44no—
310C2×C22⋊C4—44no—
311C2×C22⋊C4—44no—
312C2×C22⋊C4—44no—
313C2×C22⋊C4—44no—
314C2×C22⋊C4—44no—
315C2×C22⋊C4—44no—
316C2×C22⋊C4—44no—
317C2×C22⋊C4—44no—
318C2×C22⋊C4—44no—
319C2×C22⋊C4—42no—
320C2×C22⋊C4—44no—
321C2×C22⋊C4—44no—
322C2×C22⋊C4—44no—
323C2×C22⋊C4C22×C414yes—
324C2×C22⋊C4C22×C418yes—
325C2×C22⋊C4C22×C418yes—
326C2×C22⋊C4C22×C414yes—
327C2×C22⋊C4C22×C418yes—
328C2×C22⋊C4C22×C418yes—
329C2×C22⋊C4C22×C414yes—
330C2×C22⋊C4C22×C414yes—
331C2×C42—22no—
332C2×C42—24no—
333C2×C42—24no—
334C2×C42—22no—
335C2×C42—24no—
336C2×C42—42no—
337C2×C42—44no—
338C2×C42—44no—
339C2×C42—42no—
340C2×C42—44no—
341C2×C42C22×C418yes—
342C2×C42C22×C414yes—
343#95—28no—
344#95—44no—
345#95—42no—
346#95—44no—
347#95—44no—
348#95—42no—
349#95—44no—
350#95—44no—
351#95—44no—
352#95—44no—
353#95—44no—
354#95—44no—
355#95—44no—
356#95—44no—
357#95—44no—
358#95—44no—
359#95—44no—
360#95—44no—
361#95C22×C418yes—
362#95C22×C418yes—
363#95C22×C418yes—
364C24—22no—
365C24—22no—
366C24—22no—
367C24—22no—
368C24—21no—
369C24—22no—
370C24—22no—
371C24—22no—
372C24—22no—
373C24—22no—
374C24—22no—
375C24—22no—
376C24—22no—
377C24—21no—
378C24—22no—
379C24—21no—
380C24—21no—
381C24—22no—
382C24—22no—
383C24—22no—
384C24—22no—
385C24—22no—
386C24—21no—
387C24—22no—
388C24—22no—
389C24—21no—
390C24—21no—
391C24—21no—
392C24—28no—
393C24—216no—
394C24—44no—
395C24—48no—
396C24—44no—
397C24—48no—
398C24—48no—
399C24—48no—
400C24—48no—
401C24—48no—
402C24—44no—
403C24—44no—
404C24—44no—
405C24—44no—
406C24—44no—
407C24—44no—
408C24—48no—
409C24—48no—
410C24—48no—
411C24—48no—
412C24—48no—
413C24—44no—
414C24—44no—
415C24C23×C412yes—
416C24C23×C412yes—
417C24C23×C414yes—
418C24C2×#4112yes—
419C24C2×#4112yes—
420C24C2×#4112yes—
421C24C2×#4112yes—
422C24H(5,𝔽2)14yes—
423C242−1+414yes—
424C24C2511yescharacteristic
425C2×D4—216no—
426C2×D4—216no—
427C2×D4—44no—
428C2×D4—48no—
429C2×D4—44no—
430C2×D4—44no—
431C2×D4—44no—
432C2×D4—44no—
433C2×D4—44no—
434C2×D4—48no—
435C2×D4—48no—
436C2×D4—48no—
437C2×D4—48no—
438C2×D4#117116yes—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—21no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—21no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—22no—
464C22×C4—21no—
465C22×C4—22no—
466C22×C4—21no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—28no—
474C22×C4—216no—
475C22×C4—28no—
476C22×C4—216no—
477C22×C4—216no—
478C22×C4—216no—
479C22×C4—216no—
480C22×C4—24no—
481C22×C4—24no—
482C22×C4—24no—
483C22×C4—24no—
484C22×C4—24no—
485C22×C4—24no—
486C22×C4—24no—
487C22×C4—24no—
488C22×C4—24no—
489C22×C4—24no—
490C22×C4—24no—
491C22×C4—24no—
492C22×C4—24no—
493C22×C4—24no—
494C22×C4—24no—
495C22×C4—24no—
496C22×C4—24no—
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—24no—
506C22×C4—24no—
507C22×C4—24no—
508C22×C4—48no—
509C22×C4—48no—
510C22×C4—48no—
511C22×C4—44no—
512C22×C4—48no—
513C22×C4—48no—
514C22×C4—48no—
515C22×C4—48no—
516C22×C4—48no—
517C22×C4—44no—
518C22×C4—44no—
519C22×C4—48no—
520C22×C4—4128no—
521C22×C4—48no—
522C22×C4—44no—
523C22×C4—48no—
524C22×C4—48no—
525C22×C4—48no—
526C22×C4—48no—
527C22×C4—44no—
528C22×C4—44no—
529C22×C4—48no—
530C22×C4—44no—
531C22×C4—48no—
532C22×C4—84no—
533C22×C4—88no—
534C22×C4—84no—
535C22×C4—88no—
536C22×C4C23×C412yes—
537C22×C4C23×C414yes—
538C22×C4C23×C414yes—
539C22×C4C23×C412yes—
540C22×C4C23×C414yes—
541C22×C4C23×C412yes—
542C22×C4C23×C412yes—
543C22×C4C23×C412yes—
544C22×C4C2×#4112yes—
545C22×C4C2×#4112yes—
546C22×C4H(5,𝔽2)12yes—
547C22×C4H(5,𝔽2)14yes—
548C22×C4H(5,𝔽2)12yes—
549C22×C4H(5,𝔽2)14yes—
550C4⋊C4—44no—
551C4⋊C4—48no—
552C4⋊C4—48no—
553C4⋊C4—48no—
554C4⋊C4—48no—
555C4⋊C4—48no—
556C4⋊C4—48no—
557C4⋊C4—84no—
558C4⋊C4—84no—
559C22⋊C4—28no—
560C22⋊C4—216no—
561C22⋊C4—216no—
562C22⋊C4—44no—
563C22⋊C4—44no—
564C22⋊C4—48no—
565C22⋊C4—44no—
566C22⋊C4—48no—
567C22⋊C4—84no—
568C22⋊C4—88no—
569C22⋊C4—88no—
570C22⋊C4—88no—
571C22⋊C4—88no—
572C22⋊C4—88no—
573C22⋊C4—88no—
574C22⋊C4—88no—
575C42—28no—
576C42—216no—
577C42—84no—
578C42—88no—
579C23—24no—
580C23—22no—
581C23—24no—
582C23—22no—
583C23—24no—
584C23—24no—
585C23—24no—
586C23—24no—
587C23—24no—
588C23—24no—
589C23—24no—
590C23—22no—
591C23—22no—
592C23—24no—
593C23—22no—
594C23—22no—
595C23—22no—
596C23—22no—
597C23—22no—
598C23—22no—
599C23—22no—
600C23—22no—
601C23—24no—
602C23—24no—
603C23—24no—
604C23—24no—
605C23—24no—
606C23—24no—
607C23—24no—
608C23—24no—
609C23—24no—
610C23—24no—
611C23—24no—
612C23—24no—
613C23—24no—
614C23—24no—
615C23—24no—
616C23—24no—
617C23—24no—
618C23—24no—
619C23—24no—
620C23—24no—
621C23—416no—
622C23—432no—
623C23—432no—
624C23—416no—
625C23—416no—
626C23—432no—
627C23—416no—
628C23—416no—
629C23—432no—
630C23—416no—
631C23—416no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23—42no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—42no—
642C23—42no—
643C23—41no—
644C23—42no—
645C23—42no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23C2×#11714yes—
669C23C2×#11714yes—
670C23#52018yes—
671C23C24×C411yescharacteristic
672C23C22×#4111yescharacteristic
673C23C22×#4111yescharacteristic
674C23C2×H(5,𝔽2)11yescharacteristic
675C23C2×H(5,𝔽2)11yescharacteristic
676C23C2×H(5,𝔽2)12yes—
677C23C2×H(5,𝔽2)12yes—
678C23C2×H(5,𝔽2)12yes—
679C23C2×2−1+412yes—
680C23#58511yescharacteristic
681C23#58511yescharacteristic
682D4—416no—
683D4—432no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—24no—
691C2×C4—22no—
692C2×C4—24no—
693C2×C4—24no—
694C2×C4—22no—
695C2×C4—24no—
696C2×C4—22no—
697C2×C4—24no—
698C2×C4—24no—
699C2×C4—24no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—24no—
704C2×C4—24no—
705C2×C4—432no—
706C2×C4—416no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—41no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—41no—
717C2×C4—42no—
718C2×C4—41no—
719C2×C4—42no—
720C2×C4—41no—
721C2×C4—42no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—416no—
729C2×C4—416no—
730C2×C4—432no—
731C2×C4—44no—
732C2×C4—44no—
733C2×C4—44no—
734C2×C4—44no—
735C2×C4—44no—
736C2×C4—44no—
737C2×C4—44no—
738C2×C4—44no—
739C2×C4—44no—
740C2×C4—44no—
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—816no—
760C2×C4C2×#11714yes—
761C2×C4#51814yes—
762C2×C4#51818yes—
763C2×C4#56018yes—
764C2×C4#56014yes—
765C2×C4H(3,𝔽4)14yes—
766C22—28no—
767C22—28no—
768C22—24no—
769C22—24no—
770C22—28no—
771C22—28no—
772C22—28no—
773C22—464no—
774C22—44no—
775C22—44no—
776C22—44no—
777C22—44no—
778C22—42no—
779C22—42no—
780C22—44no—
781C22—44no—
782C22—42no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—44no—
787C22—44no—
788C22—44no—
789C22—44no—
790C22—44no—
791C22—42no—
792C22—42no—
793C22—44no—
794C22—44no—
795C22—44no—
796C22—42no—
797C22—42no—
798C22—44no—
799C22—42no—
800C22—42no—
801C22—44no—
802C22—44no—
803C22—44no—
804C22C22×#11711yescharacteristic
805C22C2×#51811yescharacteristic
806C22C2×#51812yes—
807C22C2×#52012yes—
808C22#342811yescharacteristic
809C22#350511yescharacteristic
810C22#350511yescharacteristic
811C22#350511yescharacteristic
812C22#350511yescharacteristic
813C22#351912yes—
814C22#351912yes—
815C22#352012yes—
816C22#352012yes—
817C22C2×#56012yes—
818C22C2×#56011yescharacteristic
819C22C2×H(3,𝔽4)11yescharacteristic
820C22#353612yes—
821C22#353711yescharacteristic
822C22#353811yescharacteristic
823C22#354112yes—
824C22#354112yes—
825C22#354212yes—
826C22#354212yes—
827C4—24no—
828C4—42no—
829C4—42no—
830C4—44no—
831C4—42no—
832C4—44no—
833C4—44no—
834C4—84no—
835C4—84no—
836C4—84no—
837C4—84no—
838C4#237518yes—
839C2—44no—
840C2—48no—
841C2—44no—
842C2#3418511yescharacteristic
843C2#3419412yes—
844C2C2×#237511yescharacteristic
845C2#3436011yescharacteristic
846C2#3436212yes—
847C2#4559812yes—
848C2#4559911yescharacteristic
849C2#4562211yescharacteristic
850C2#4562312yes—
851C2#4564511yescharacteristic
852C2#4566711yescharacteristic
subgroupG/H
center, Frattini, socle, cosocleC24C25
commutatorC23C24×C4
prime radicalC22×#120C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #14680C2semidirect
3. #14669C2semidirect
4. #14456C2semidirect
5. #14427C2semidirect
6. #14366C2semidirect
8. #13906C2semidirect
9. #13905C2semidirect
10. #13876C2semidirect
11. #13875C2semidirect
12. #13875C2semidirect
13. #13872C2semidirect
14. #13872C2semidirect
15. #13832C2semidirect
20. C23×C4⋊C4C22semidirect
21. C4×#120C4semidirect
30. C2×#384C22semidirect
31. C2×#382C22semidirect
38. C2×#380C22semidirect
39. C2×#380C22semidirect
42. C2×C4×C4⋊C4C22semidirect
43. C2×C4×C4⋊C4C22semidirect
46. #1445C22semidirect
47. #1443C22semidirect
48. #1443C22semidirect
49. #1442C22semidirect
50. #1441C22semidirect
51. #1441C22semidirect
58. #1439C22semidirect
63. #1437C22semidirect
64. #1436C22semidirect
65. C4⋊#95C22semidirect
66. C4⋊#95C22semidirect
67. C4⋊#95C22semidirect
68. C4⋊#95C22semidirect
69. #1434C22semidirect
70. #1434C22semidirect
74. C22⋊#95C22semidirect
75. C22⋊#95C22semidirect
83. C24×C4C2×C4semidirect
136. #385C2×C4semidirect
137. #385C2×C4semidirect
149. #379C2×C4semidirect
152. C4×C22⋊C4C2×C4semidirect
153. C4×C22⋊C4C2×C4semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#1202
#146802
#146692
#144562
#144272
#143662
#143572
#139062
#139052
#138762
#138752
#138722
#138322