Finite Group Databasebeta

← #637131

Subgroups — #637131

Order 512.

3794 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2442C211yesmaximal, characteristic, complemented
2C22×#380C211yesmaximal, characteristic
3#16568C214yesmaximal, complemented
4#16521C214yesmaximal, complemented
5#15220C212yesmaximal, complemented
6#15216C212yesmaximal, complemented
7#15135C212yesmaximal, complemented
8#15131C212yesmaximal, complemented
9#14734C212yesmaximal
10#14726C212yesmaximal
11#14680C211yesmaximal, characteristic
12#14275C212yesmaximal, complemented
13#14265C212yesmaximal, complemented
14#14130C211yesmaximal, characteristic, complemented
15#13907C211yesmaximal, characteristic, complemented
16#13880C211yesmaximal, characteristic, complemented
17C4×#379C211yesmaximal, characteristic
18C25×C4C2211yescharacteristic
19C22×#125C2211yescharacteristic, complemented
20C23×C4⋊C4C2211yescharacteristic
21C23×C4⋊C4C2211yescharacteristic
22C23×C22⋊C4C2212yes—
23#2442—28no—
24C2×#400C2212yescomplemented
25C2×#399C2214yes—
26C2×#398C2212yescomplemented
27C2×#396C2214yes—
28C2×#389C2211yescharacteristic, complemented
29C2×#389C2211yescharacteristic, complemented
30C2×#389C2212yescomplemented
31C2×#389C2212yescomplemented
32C2×#385C2212yes—
33C2×#385C2212yes—
34C2×#385C2212yes—
35C2×#385C2212yes—
36C2×#384C2212yescomplemented
37C2×#382C2211yescharacteristic, complemented
38C2×#380—28no—
39C2×#380C2212yes—
40C2×#380C2212yes—
41C2×#380C2211yescharacteristic
42C2×#380C2211yescharacteristic
43C2×#380C2212yes—
44C2×#380C2212yes—
45C2×#380C2214yes—
46C2×#380C2212yes—
47C2×#380C2212yes—
48C2×#379C2211yescharacteristic
49C2×#379C2211yescharacteristic
50C2×#379C2212yes—
51C2×C4×C22⋊C4C2211yescharacteristic
52C2×C4×C22⋊C4C2211yescharacteristic
53C2×C4×C22⋊C4C2212yes—
54C2×C4×C22⋊C4C2212yes—
55C22×#95C2212yes—
56#1445C2214yescomplemented
57#1444C2214yescomplemented
58#1444C2212yescomplemented
59#1444C2214yescomplemented
60#1443C2214yescomplemented
61#1442C2212yescomplemented
62#1442C2214yescomplemented
63#1442C2214yescomplemented
64#1441C2214yescomplemented
65#1441C2214yescomplemented
66#1441C2214yescomplemented
67#1441C2214yescomplemented
68#1439C2214yes—
69#1439C2214yes—
70#1439C2214yes—
71#1439C2214yes—
72#1439C2214yes—
73#1439C2214yes—
74C4⋊#95C2212yescomplemented
75C4⋊#95C2212yescomplemented
76C4⋊#95C2212yescomplemented
77C22⋊#95C2212yes—
78C22⋊#95C2212yes—
79C22⋊#95C2214yes—
80C22⋊#95C2212yes—
81C22⋊#95C2212yes—
82C22⋊#95C2212yes—
83C22⋊#95C2211yescharacteristic
84C22⋊#95C2211yescharacteristic
85C26C2311yescharacteristic
86C24×C4—24no—
87C24×C4—24no—
88C24×C4—44no—
89C24×C4—44no—
90C24×C4Q818yes—
91C24×C4C2312yes—
92C24×C4C2311yescharacteristic
93C24×C4C2312yes—
94C24×C4C2312yes—
95C24×C4C2311yescharacteristic
96C24×C4C2312yes—
97C2×#125—24no—
98C2×#125—44no—
99C22×C4⋊C4—24no—
100C22×C4⋊C4—44no—
101C22×C4⋊C4—44no—
102C22×C4⋊C4D418yes—
103C22×C4⋊C4C2312yes—
104C22×C4⋊C4C2311yescharacteristic
105C22×C4⋊C4C2312yes—
106C22×C4⋊C4C2311yescharacteristic
107C22×C4⋊C4C2311yescharacteristic
108C22×C4⋊C4C2311yescharacteristic
109C22×C4⋊C4C2312yes—
110C22×C4⋊C4C2314yes—
111C22×C4⋊C4C2312yes—
112C22×C4⋊C4C2312yes—
113C22×C4⋊C4C2314yes—
114C22×C4⋊C4C2312yes—
115C22×C4⋊C4C2312yes—
116C22×C4⋊C4C2314yes—
117C22×C4⋊C4C2314yes—
118C22×C4⋊C4C2312yes—
119C22×C22⋊C4—28no—
120C22×C22⋊C4—48no—
121C22×C22⋊C4C2311yescharacteristic
122C22×C22⋊C4C2312yes—
123C22×C22⋊C4C2311yescharacteristic
124C22×C22⋊C4C2312yes—
125C22×C22⋊C4C2312yes—
126C22×C22⋊C4C2314yes—
127C22×C22⋊C4C2312yes—
128C22×C22⋊C4C2314yes—
129C22×C22⋊C4C2312yes—
130C22×C22⋊C4C2312yes—
131C22×C22⋊C4C2311yescharacteristic
132C22×C22⋊C4C2311yescharacteristic
133C22×C22⋊C4C2314yes—
134C22×C22⋊C4C2314yes—
135C22×C42C2311yescharacteristic
136C22×C42C2312yes—
137C22×C42C2311yescharacteristic
138#400—28no—
139#399—48no—
140#398—28no—
141#396—48no—
142#389—24no—
143#389—24no—
144#389—44no—
145#389—44no—
146#385—28no—
147#385—28no—
148#385—44no—
149#385—44no—
150#384—44no—
151#382—24no—
152#380—28no—
153#380—24no—
154#380—24no—
155#380—28no—
156#380—28no—
157#380—216no—
158#380—28no—
159#380—44no—
160#380—44no—
161#379—24no—
162#379—24no—
163#379—44no—
164C4×C22⋊C4—24no—
165C4×C22⋊C4—24no—
166C4×C22⋊C4—44no—
167C4×C22⋊C4—44no—
168C2×#95—28no—
169C2×#95C2311yescharacteristic
170C2×#95C2312yes—
171C2×#95C2312yes—
172C2×#95C2311yescharacteristic
173C2×#95C2312yes—
174C2×#95C2312yes—
175C2×#95C2312yes—
176C2×#95C2312yes—
177C2×#95C2312yes—
178C2×#95C2314yes—
179C2×#95C2314yes—
180C2×#95C2314yes—
181C2×#95C2314yes—
182C2×#95C2314yes—
183C2×#95C2314yes—
184C2×#95C2312yes—
185C2×#95C2312yes—
186C2×#95C2312yes—
187C2×#95C2314yes—
188C2×#95C2314yes—
189C2×#95C2312yes—
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×Q814yes—
205C25C2412yes—
206C25C2411yescharacteristic
207C23×C4—24no—
208C23×C4—24no—
209C23×C4—22no—
210C23×C4—22no—
211C23×C4—24no—
212C23×C4—24no—
213C23×C4—232no—
214C23×C4—24no—
215C23×C4—24no—
216C23×C4—24no—
217C23×C4—24no—
218C23×C4—24no—
219C23×C4—24no—
220C23×C4—24no—
221C23×C4—24no—
222C23×C4—24no—
223C23×C4—24no—
224C23×C4—24no—
225C23×C4—432no—
226C23×C4—42no—
227C23×C4—42no—
228C23×C4—42no—
229C23×C4—42no—
230C23×C4—42no—
231C23×C4—42no—
232C23×C4—44no—
233C23×C4—44no—
234C23×C4—44no—
235C23×C4—44no—
236C23×C4—416no—
237C23×C4—416no—
238C23×C4—432no—
239C23×C4C2×D414yes—
240C23×C4C2×D418yes—
241C23×C4C2×Q818yes—
242C23×C4C2×Q814yes—
243C23×C4C2×Q814yes—
244C23×C4C2×Q818yes—
245C23×C4#4114yes—
246C23×C4C2412yes—
247C23×C4C2411yescharacteristic
248C23×C4C2411yescharacteristic
249C23×C4C2412yes—
250C23×C4C2414yes—
251C23×C4C2411yescharacteristic
252C23×C4C2411yescharacteristic
253C23×C4C2414yes—
254C23×C4C2412yes—
255C23×C4C2412yes—
256C23×C4C2412yes—
257C23×C4C2412yes—
258C23×C4C2412yes—
259C23×C4C2411yescharacteristic
260C23×C4C2411yescharacteristic
261#125—416no—
262C2×C4⋊C4—24no—
263C2×C4⋊C4—24no—
264C2×C4⋊C4—24no—
265C2×C4⋊C4—24no—
266C2×C4⋊C4—22no—
267C2×C4⋊C4—24no—
268C2×C4⋊C4—24no—
269C2×C4⋊C4—22no—
270C2×C4⋊C4—24no—
271C2×C4⋊C4—24no—
272C2×C4⋊C4—24no—
273C2×C4⋊C4—24no—
274C2×C4⋊C4—24no—
275C2×C4⋊C4—24no—
276C2×C4⋊C4—24no—
277C2×C4⋊C4—24no—
278C2×C4⋊C4—24no—
279C2×C4⋊C4—28no—
280C2×C4⋊C4—28no—
281C2×C4⋊C4—416no—
282C2×C4⋊C4—44no—
283C2×C4⋊C4—44no—
284C2×C4⋊C4—44no—
285C2×C4⋊C4—44no—
286C2×C4⋊C4—416no—
287C2×C4⋊C4—44no—
288C2×C4⋊C4—44no—
289C2×C4⋊C4—44no—
290C2×C4⋊C4—44no—
291C2×C4⋊C4—44no—
292C2×C4⋊C4—44no—
293C2×C4⋊C4—44no—
294C2×C4⋊C4—44no—
295C2×C4⋊C4—44no—
296C2×C4⋊C4—44no—
297C2×C4⋊C4—44no—
298C2×C4⋊C4—44no—
299C2×C4⋊C4C2×D414yes—
300C2×C4⋊C4C2×D414yes—
301C2×C4⋊C4C2×D418yes—
302C2×C22⋊C4—22no—
303C2×C22⋊C4—22no—
304C2×C22⋊C4—22no—
305C2×C22⋊C4—22no—
306C2×C22⋊C4—22no—
307C2×C22⋊C4—22no—
308C2×C22⋊C4—24no—
309C2×C22⋊C4—22no—
310C2×C22⋊C4—22no—
311C2×C22⋊C4—24no—
312C2×C22⋊C4—24no—
313C2×C22⋊C4—24no—
314C2×C22⋊C4—28no—
315C2×C22⋊C4—28no—
316C2×C22⋊C4—24no—
317C2×C22⋊C4—24no—
318C2×C22⋊C4—22no—
319C2×C22⋊C4—24no—
320C2×C22⋊C4—24no—
321C2×C22⋊C4—24no—
322C2×C22⋊C4—24no—
323C2×C22⋊C4—22no—
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—28no—
331C2×C22⋊C4—28no—
332C2×C22⋊C4—44no—
333C2×C22⋊C4—44no—
334C2×C22⋊C4—42no—
335C2×C22⋊C4—42no—
336C2×C22⋊C4—42no—
337C2×C22⋊C4—42no—
338C2×C22⋊C4—432no—
339C2×C22⋊C4—44no—
340C2×C22⋊C4—44no—
341C2×C22⋊C4—44no—
342C2×C22⋊C4—44no—
343C2×C22⋊C4#4114yes—
344C2×C22⋊C4#4114yes—
345C2×C42—22no—
346C2×C42—22no—
347C2×C42—24no—
348C2×C42—24no—
349C2×C42—24no—
350C2×C42—24no—
351C2×C42—24no—
352#95—28no—
353#95—28no—
354#95—22no—
355#95—22no—
356#95—24no—
357#95—24no—
358#95—24no—
359#95—24no—
360#95—24no—
361#95—24no—
362#95—28no—
363#95—24no—
364#95—28no—
365#95—42no—
366#95—42no—
367#95—42no—
368#95—42no—
369#95—44no—
370#95—44no—
371#95—44no—
372#95—44no—
373#95—44no—
374#95—44no—
375#95—44no—
376#95—44no—
377C24—22no—
378C24—22no—
379C24—22no—
380C24—22no—
381C24—28no—
382C24—28no—
383C24—216no—
384C24—28no—
385C24—216no—
386C24—22no—
387C24—22no—
388C24—22no—
389C24—22no—
390C24—22no—
391C24—22no—
392C24—22no—
393C24—22no—
394C24—22no—
395C24—22no—
396C24—22no—
397C24—22no—
398C24—28no—
399C24—28no—
400C24—48no—
401C24—48no—
402C24—48no—
403C24—48no—
404C24—48no—
405C24—48no—
406C24—48no—
407C24—48no—
408C24—48no—
409C24—44no—
410C24—44no—
411C24—48no—
412C24—44no—
413C24—44no—
414C24—44no—
415C24—44no—
416C24C22×D412yes—
417C24C22×Q814yes—
418C24C22×Q812yes—
419C24C2×#4112yes—
420C24C2×#4112yes—
421C24C2×#4112yes—
422C24H(5,𝔽2)14yes—
423C24H(5,𝔽2)12yes—
424C242−1+414yes—
425C242−1+412yes—
426C24C2511yescharacteristic
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—28no—
430C22×C4—28no—
431C22×C4—216no—
432C22×C4—216no—
433C22×C4—28no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—24no—
451C22×C4—24no—
452C22×C4—24no—
453C22×C4—22no—
454C22×C4—24no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—216no—
461C22×C4—216no—
462C22×C4—216no—
463C22×C4—216no—
464C22×C4—216no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—24no—
471C22×C4—21no—
472C22×C4—22no—
473C22×C4—24no—
474C22×C4—24no—
475C22×C4—24no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—22no—
481C22×C4—21no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—24no—
486C22×C4—24no—
487C22×C4—24no—
488C22×C4—24no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—24no—
493C22×C4—24no—
494C22×C4—24no—
495C22×C4—24no—
496C22×C4—24no—
497C22×C4—22no—
498C22×C4—24no—
499C22×C4—21no—
500C22×C4—22no—
501C22×C4—24no—
502C22×C4—24no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—24no—
508C22×C4—24no—
509C22×C4—48no—
510C22×C4—48no—
511C22×C4—48no—
512C22×C4—48no—
513C22×C4—48no—
514C22×C4—48no—
515C22×C4—48no—
516C22×C4—48no—
517C22×C4—48no—
518C22×C4—4128no—
519C22×C4—44no—
520C22×C4—44no—
521C22×C4—48no—
522C22×C4—48no—
523C22×C4—48no—
524C22×C4—48no—
525C22×C4—48no—
526C22×C4—48no—
527C22×C4—48no—
528C22×C4—48no—
529C22×C4—88no—
530C22×C4—88no—
531C22×C4—88no—
532C22×C4—88no—
533C22×C4C22⋊Q8116yes—
534C22×C4C22×D414yes—
535C22×C4C22×D414yes—
536C22×C4C22×D412yes—
537C22×C4C22×D412yes—
538C22×C4C22×Q814yes—
539C22×C4C22×Q812yes—
540C22×C4C22×Q812yes—
541C22×C4C2×#4114yes—
542C22×C4C2×#4114yes—
543C22×C4C2×#4112yes—
544C22×C4C2×#4112yes—
545C22×C4H(5,𝔽2)14yes—
546C22×C4H(5,𝔽2)14yes—
547C4⋊C4—28no—
548C4⋊C4—28no—
549C4⋊C4—48no—
550C4⋊C4—48no—
551C4⋊C4—48no—
552C4⋊C4—48no—
553C4⋊C4—44no—
554C4⋊C4—44no—
555C4⋊C4—48no—
556C4⋊C4—48no—
557C4⋊C4—84no—
558C4⋊C4—84no—
559C4⋊C4—88no—
560C4⋊C4—88no—
561C4⋊C4—88no—
562C4⋊C4—88no—
563C22⋊C4—28no—
564C22⋊C4—28no—
565C22⋊C4—48no—
566C22⋊C4—48no—
567C22⋊C4—48no—
568C22⋊C4—48no—
569C22⋊C4—416no—
570C22⋊C4—416no—
571C22⋊C4—44no—
572C22⋊C4—44no—
573C22⋊C4—48no—
574C22⋊C4—48no—
575C22⋊C4—88no—
576C22⋊C4—88no—
577C42—44no—
578C42—44no—
579C42—48no—
580C23—22no—
581C23—22no—
582C23—24no—
583C23—24no—
584C23—24no—
585C23—22no—
586C23—22no—
587C23—24no—
588C23—24no—
589C23—24no—
590C23—24no—
591C23—24no—
592C23—24no—
593C23—24no—
594C23—24no—
595C23—24no—
596C23—232no—
597C23—24no—
598C23—24no—
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—24no—
612C23—24no—
613C23—24no—
614C23—24no—
615C23—432no—
616C23—432no—
617C23—416no—
618C23—416no—
619C23—416no—
620C23—432no—
621C23—416no—
622C23—416no—
623C23—432no—
624C23—42no—
625C23—42no—
626C23—42no—
627C23—42no—
628C23—42no—
629C23—416no—
630C23—42no—
631C23—42no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23—42no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23C2×C22⋊Q814yes—
642C23#53314yes—
643C23#54418yes—
644C23#54414yes—
645C23#54714yes—
646C23#55014yes—
647C23#55214yes—
648C23#55314yes—
649C23C23×D411yescharacteristic
650C23C23×Q811yescharacteristic
651C23C22×#4111yescharacteristic
652C23C22×#4111yescharacteristic
653C23C22×#4111yescharacteristic
654C23C2×H(5,𝔽2)12yes—
655C23C2×H(5,𝔽2)12yes—
656C23C2×H(5,𝔽2)11yescharacteristic
657C23C2×H(5,𝔽2)12yes—
658C23C2×2−1+411yescharacteristic
659C23C2×2−1+412yes—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—24no—
663C2×C4—24no—
664C2×C4—232no—
665C2×C4—24no—
666C2×C4—24no—
667C2×C4—24no—
668C2×C4—24no—
669C2×C4—24no—
670C2×C4—24no—
671C2×C4—24no—
672C2×C4—24no—
673C2×C4—24no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—24no—
677C2×C4—24no—
678C2×C4—24no—
679C2×C4—24no—
680C2×C4—432no—
681C2×C4—416no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—44no—
691C2×C4—44no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—44no—
695C2×C4—44no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—432no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—42no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—44no—
705C2×C4—42no—
706C2×C4—44no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—42no—
711C2×C4—41no—
712C2×C4—42no—
713C2×C4—44no—
714C2×C4—44no—
715C2×C4—44no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—42no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—42no—
722C2×C4—44no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—44no—
726C2×C4—44no—
727C2×C4—44no—
728C2×C4—44no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—44no—
732C2×C4—44no—
733C2×C4—44no—
734C2×C4—44no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—44no—
738C2×C4—44no—
739C2×C4—42no—
740C2×C4—44no—
741C2×C4—44no—
742C2×C4—42no—
743C2×C4—816no—
744C2×C4—816no—
745C2×C4C2×C22⋊Q814yes—
746C2×C4C2×C22⋊Q814yes—
747C2×C4#53414yes—
748C2×C4#53514yes—
749C2×C4#53818yes—
750C2×C4#54318yes—
751C22—24no—
752C22—24no—
753C22—28no—
754C22—28no—
755C22—28no—
756C22—24no—
757C22—24no—
758C22—24no—
759C22—28no—
760C22—24no—
761C22—28no—
762C22—28no—
763C22—28no—
764C22—464no—
765C22—44no—
766C22—44no—
767C22—44no—
768C22—44no—
769C22—44no—
770C22—44no—
771C22—44no—
772C22—44no—
773C22—44no—
774C22—44no—
775C22—44no—
776C22—44no—
777C22#244118yes—
778C22C22×C22⋊Q811yescharacteristic
779C22C2×#53311yescharacteristic
780C22C2×#53411yescharacteristic
781C22C2×#53511yescharacteristic
782C22C2×#53812yes—
783C22C2×#54312yes—
784C22C2×#54412yes—
785C22C2×#54411yescharacteristic
786C22C2×#54711yescharacteristic
787C22C2×#55011yescharacteristic
788C22C2×#55211yescharacteristic
789C22C2×#55311yescharacteristic
790C22#348411yescharacteristic
791C22#348611yescharacteristic
792C22#349212yes—
793C22#351912yes—
794C22#351912yes—
795C22#352012yes—
796C22#352012yes—
797C22#353612yes—
798C22#353612yes—
799C22#353712yes—
800C22#353812yes—
801C4—24no—
802C4—44no—
803C4—44no—
804C4—44no—
805C4—44no—
806C4—44no—
807C4—81no—
808C4—81no—
809C4—81no—
810C4—82no—
811C4—84no—
812C4—81no—
813C4—82no—
814C4—84no—
815C4#262618yes—
816C2—28no—
817C2—48no—
818C2C2×#262611yescharacteristic
819C2C2×#244111yescharacteristic
820C2#3507912yes—
821C2#3522411yescharacteristic
822C2#3747712yes—
823C2#3891611yescharacteristic
824C2#3891711yescharacteristic
825C2#3892812yes—
826C2#3913211yescharacteristic
827C2#3913311yescharacteristic
828C2#3914412yes—
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
1. C2×#2442C2semidirect
3. #16568C2semidirect
4. #16521C2semidirect
5. #15220C2semidirect
6. #15216C2semidirect
7. #15135C2semidirect
8. #15131C2semidirect
12. #14275C2semidirect
13. #14265C2semidirect
14. #14130C2semidirect
15. #13907C2semidirect
16. #13880C2semidirect
19. C22×#125C22semidirect
24. C2×#400C22semidirect
26. C2×#398C22semidirect
28. C2×#389C22semidirect
29. C2×#389C22semidirect
30. C2×#389C22semidirect
31. C2×#389C22semidirect
36. C2×#384C22semidirect
37. C2×#382C22semidirect
56. #1445C22semidirect
57. #1444C22semidirect
58. #1444C22semidirect
59. #1444C22semidirect
60. #1443C22semidirect
61. #1442C22semidirect
62. #1442C22semidirect
63. #1442C22semidirect
64. #1441C22semidirect
65. #1441C22semidirect
66. #1441C22semidirect
67. #1441C22semidirect
74. C4⋊#95C22semidirect
75. C4⋊#95C22semidirect
76. C4⋊#95C22semidirect

Maximal subgroups

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

subgroupindex
C2×#24422
C22×#3802
#165682
#165212
#152202
#152162
#151352
#151312
#147342
#147262
#146802
#142752
#142652
#141302
#139072
#138802
C4×#3792