Finite Group Databasebeta

← #637065

Subgroups — #637065

Order 512.

3874 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2440C211yesmaximal, characteristic, complemented
2C22×#380C211yesmaximal, characteristic
3#16569C214yesmaximal, complemented
4#16520C214yesmaximal, complemented
5#15223C212yesmaximal, complemented
6#15220C212yesmaximal, complemented
7#15131C212yesmaximal, complemented
8#15125C212yesmaximal, complemented
9#14726C212yesmaximal
10#14717C212yesmaximal
11#14680C211yesmaximal, characteristic
12#14281C212yesmaximal, complemented
13#14265C212yesmaximal, complemented
14#14130C211yesmaximal, characteristic, complemented
15#13907C211yesmaximal, characteristic, complemented
16#13881C211yesmaximal, characteristic, complemented
17C4×#379C211yesmaximal, characteristic
18C25×C4C2211yescharacteristic
19C22×C4⋊Q8C2211yescharacteristic, complemented
20C22×C22⋊Q8C2212yes—
21C23×C4⋊C4C2211yescharacteristic
22C23×C4⋊C4C2211yescharacteristic
23C23×C22⋊C4C2212yes—
24#2440—28no—
25C2×#398C2212yescomplemented
26C2×#396C2214yes—
27C2×#395C2212yescomplemented
28C2×#393C2214yes—
29C2×#389C2211yescharacteristic, complemented
30C2×#389C2211yescharacteristic, complemented
31C2×#389C2212yescomplemented
32C2×#389C2212yescomplemented
33C2×#385C2212yes—
34C2×#385C2212yes—
35C2×#384C2211yescharacteristic, complemented
36C2×#382C2212yescomplemented
37C2×#380—28no—
38C2×#380C2212yes—
39C2×#380C2212yes—
40C2×#380C2211yescharacteristic
41C2×#380C2211yescharacteristic
42C2×#380C2214yes—
43C2×#380C2212yes—
44C2×#380C2212yes—
45C2×#380C2212yes—
46C2×#379C2211yescharacteristic
47C2×#379C2211yescharacteristic
48C2×#379C2212yes—
49C2×C4×C22⋊C4C2211yescharacteristic
50C2×C4×C22⋊C4C2211yescharacteristic
51C2×C4×C22⋊C4C2212yes—
52C2×C4×C22⋊C4C2212yes—
53C22×#95C2212yes—
54#1446C2214yescomplemented
55#1445C2214yescomplemented
56#1445C2214yescomplemented
57#1444C2212yescomplemented
58#1443C2214yescomplemented
59#1442C2214yescomplemented
60#1442C2212yescomplemented
61#1442C2214yescomplemented
62#1441C2214yescomplemented
63#1441C2214yescomplemented
64#1441C2214yescomplemented
65#1441C2214yescomplemented
66#1439C2214yes—
67#1439C2214yes—
68#1439C2214yes—
69#1439C2214yes—
70#1439C2214yes—
71#1439C2214yes—
72C4⋊#95C2212yescomplemented
73C4⋊#95C2212yescomplemented
74C4⋊#95C2212yescomplemented
75C22⋊#95C2212yes—
76C22⋊#95C2212yes—
77C22⋊#95C2212yes—
78C22⋊#95C2212yes—
79C22⋊#95C2214yes—
80C22⋊#95C2212yes—
81C22⋊#95C2212yes—
82C22⋊#95C2211yescharacteristic
83C22⋊#95C2212yes—
84C22⋊#95C2211yescharacteristic
85C26C2311yescharacteristic
86C23×Q8C2312yes—
87C24×C4—24no—
88C24×C4—24no—
89C24×C4—44no—
90C24×C4—44no—
91C24×C4Q818yescomplemented
92C24×C4C2312yes—
93C24×C4C2311yescharacteristic
94C24×C4C2312yes—
95C24×C4C2312yes—
96C24×C4C2311yescharacteristic
97C24×C4C2312yes—
98C2×C4⋊Q8—24no—
99C2×C4⋊Q8—44no—
100C2×C22⋊Q8—28no—
101C2×C22⋊Q8—28no—
102C2×C22⋊Q8—44no—
103C22×C4⋊C4—24no—
104C22×C4⋊C4—44no—
105C22×C4⋊C4—44no—
106C22×C4⋊C4D418yes—
107C22×C4⋊C4C2312yes—
108C22×C4⋊C4C2311yescharacteristic
109C22×C4⋊C4C2312yes—
110C22×C4⋊C4C2311yescharacteristic
111C22×C4⋊C4C2312yes—
112C22×C4⋊C4C2312yes—
113C22×C4⋊C4C2312yes—
114C22×C4⋊C4C2311yescharacteristic
115C22×C4⋊C4C2311yescharacteristic
116C22×C4⋊C4C2312yes—
117C22×C4⋊C4C2314yes—
118C22×C4⋊C4C2312yes—
119C22×C4⋊C4C2312yes—
120C22×C4⋊C4C2314yes—
121C22×C4⋊C4C2312yes—
122C22×C22⋊C4—28no—
123C22×C22⋊C4—48no—
124C22×C22⋊C4C2312yes—
125C22×C22⋊C4C2311yescharacteristic
126C22×C22⋊C4C2311yescharacteristic
127C22×C22⋊C4C2312yes—
128C22×C22⋊C4C2312yes—
129C22×C22⋊C4C2314yes—
130C22×C22⋊C4C2312yes—
131C22×C22⋊C4C2314yes—
132C22×C22⋊C4C2312yes—
133C22×C22⋊C4C2312yes—
134C22×C22⋊C4C2311yescharacteristic
135C22×C22⋊C4C2311yescharacteristic
136C22×C22⋊C4C2314yes—
137C22×C22⋊C4C2314yes—
138C22×C42C2311yescharacteristic
139C22×C42C2312yes—
140C22×C42C2311yescharacteristic
141#398—28no—
142#396—48no—
143#395—28no—
144#393—48no—
145#389—24no—
146#389—24no—
147#389—44no—
148#389—44no—
149#385—28no—
150#385—28no—
151#384—24no—
152#382—44no—
153#380—24no—
154#380—24no—
155#380—28no—
156#380—28no—
157#380—216no—
158#380—44no—
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×#95C2314yes—
177C2×#95C2314yes—
178C2×#95C2314yes—
179C2×#95C2314yes—
180C2×#95C2314yes—
181C2×#95C2314yes—
182C2×#95C2314yes—
183C2×#95C2314yes—
184C2×#95C2312yes—
185C2×#95C2312yes—
186C2×#95C2312yes—
187C2×#95C2314yes—
188C2×#95C2312yes—
189C2×#95C2314yes—
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
207C22×Q8—24no—
208C22×Q8—24no—
209C22×Q8—42no—
210C22×Q8—44no—
211C22×Q8—44no—
212C23×C4—24no—
213C23×C4—24no—
214C23×C4—22no—
215C23×C4—22no—
216C23×C4—24no—
217C23×C4—24no—
218C23×C4—232no—
219C23×C4—24no—
220C23×C4—24no—
221C23×C4—24no—
222C23×C4—24no—
223C23×C4—24no—
224C23×C4—24no—
225C23×C4—24no—
226C23×C4—24no—
227C23×C4—24no—
228C23×C4—24no—
229C23×C4—24no—
230C23×C4—432no—
231C23×C4—42no—
232C23×C4—42no—
233C23×C4—42no—
234C23×C4—42no—
235C23×C4—42no—
236C23×C4—42no—
237C23×C4—44no—
238C23×C4—44no—
239C23×C4—44no—
240C23×C4—44no—
241C23×C4—416no—
242C23×C4—416no—
243C23×C4—432no—
244C23×C4C2×D414yes—
245C23×C4C2×D418yes—
246C23×C4C2×Q818yes—
247C23×C4C2×Q814yes—
248C23×C4C2×Q814yes—
249C23×C4C2×Q818yes—
250C23×C4#4114yes—
251C23×C4C2412yes—
252C23×C4C2412yes—
253C23×C4C2414yes—
254C23×C4C2412yes—
255C23×C4C2412yes—
256C23×C4C2414yes—
257C23×C4C2412yes—
258C23×C4C2412yes—
259C23×C4C2412yes—
260C23×C4C2411yescharacteristic
261C23×C4C2411yescharacteristic
262C23×C4C2411yescharacteristic
263C23×C4C2411yescharacteristic
264C23×C4C2411yescharacteristic
265C23×C4C2411yescharacteristic
266C4⋊Q8—416no—
267C22⋊Q8—432no—
268C2×C4⋊C4—24no—
269C2×C4⋊C4—24no—
270C2×C4⋊C4—24no—
271C2×C4⋊C4—24no—
272C2×C4⋊C4—24no—
273C2×C4⋊C4—24no—
274C2×C4⋊C4—24no—
275C2×C4⋊C4—22no—
276C2×C4⋊C4—24no—
277C2×C4⋊C4—22no—
278C2×C4⋊C4—24no—
279C2×C4⋊C4—24no—
280C2×C4⋊C4—24no—
281C2×C4⋊C4—24no—
282C2×C4⋊C4—24no—
283C2×C4⋊C4—24no—
284C2×C4⋊C4—24no—
285C2×C4⋊C4—24no—
286C2×C4⋊C4—24no—
287C2×C4⋊C4—24no—
288C2×C4⋊C4—24no—
289C2×C4⋊C4—28no—
290C2×C4⋊C4—416no—
291C2×C4⋊C4—44no—
292C2×C4⋊C4—44no—
293C2×C4⋊C4—42no—
294C2×C4⋊C4—42no—
295C2×C4⋊C4—42no—
296C2×C4⋊C4—44no—
297C2×C4⋊C4—416no—
298C2×C4⋊C4—44no—
299C2×C4⋊C4—44no—
300C2×C4⋊C4—44no—
301C2×C4⋊C4—44no—
302C2×C4⋊C4—44no—
303C2×C4⋊C4—44no—
304C2×C4⋊C4C2×D414yes—
305C2×C4⋊C4C2×D414yes—
306C2×C4⋊C4C2×D418yes—
307C2×C22⋊C4—22no—
308C2×C22⋊C4—22no—
309C2×C22⋊C4—22no—
310C2×C22⋊C4—22no—
311C2×C22⋊C4—24no—
312C2×C22⋊C4—24no—
313C2×C22⋊C4—22no—
314C2×C22⋊C4—22no—
315C2×C22⋊C4—22no—
316C2×C22⋊C4—22no—
317C2×C22⋊C4—24no—
318C2×C22⋊C4—24no—
319C2×C22⋊C4—28no—
320C2×C22⋊C4—28no—
321C2×C22⋊C4—24no—
322C2×C22⋊C4—24no—
323C2×C22⋊C4—22no—
324C2×C22⋊C4—24no—
325C2×C22⋊C4—24no—
326C2×C22⋊C4—24no—
327C2×C22⋊C4—24no—
328C2×C22⋊C4—22no—
329C2×C22⋊C4—28no—
330C2×C22⋊C4—28no—
331C2×C22⋊C4—24no—
332C2×C22⋊C4—24no—
333C2×C22⋊C4—24no—
334C2×C22⋊C4—24no—
335C2×C22⋊C4—28no—
336C2×C22⋊C4—28no—
337C2×C22⋊C4—44no—
338C2×C22⋊C4—44no—
339C2×C22⋊C4—42no—
340C2×C22⋊C4—42no—
341C2×C22⋊C4—42no—
342C2×C22⋊C4—42no—
343C2×C22⋊C4—432no—
344C2×C22⋊C4—44no—
345C2×C22⋊C4—44no—
346C2×C22⋊C4—44no—
347C2×C22⋊C4—44no—
348C2×C22⋊C4#4114yes—
349C2×C22⋊C4#4114yes—
350C2×C42—22no—
351C2×C42—22no—
352C2×C42—24no—
353C2×C42—24no—
354C2×C42—24no—
355C2×C42—24no—
356C2×C42—24no—
357#95—28no—
358#95—28no—
359#95—22no—
360#95—22no—
361#95—24no—
362#95—24no—
363#95—24no—
364#95—24no—
365#95—24no—
366#95—28no—
367#95—42no—
368#95—42no—
369#95—42no—
370#95—42no—
371#95—44no—
372#95—44no—
373#95—44no—
374#95—44no—
375#95—44no—
376#95—44no—
377#95—44no—
378#95—44no—
379#95—44no—
380#95—44no—
381#95—44no—
382C24—22no—
383C24—22no—
384C24—22no—
385C24—22no—
386C24—28no—
387C24—28no—
388C24—216no—
389C24—28no—
390C24—216no—
391C24—22no—
392C24—22no—
393C24—22no—
394C24—22no—
395C24—22no—
396C24—22no—
397C24—22no—
398C24—22no—
399C24—22no—
400C24—22no—
401C24—22no—
402C24—22no—
403C24—28no—
404C24—28no—
405C24—48no—
406C24—48no—
407C24—48no—
408C24—48no—
409C24—48no—
410C24—48no—
411C24—48no—
412C24—48no—
413C24—48no—
414C24—44no—
415C24—44no—
416C24—48no—
417C24—44no—
418C24—44no—
419C24—44no—
420C24—44no—
421C24C22×D412yes—
422C24C22×Q814yes—
423C24C22×Q812yes—
424C24C2×#4112yes—
425C24C2×#4112yes—
426C24C2×#4112yes—
427C24H(5,𝔽2)14yes—
428C24H(5,𝔽2)12yes—
429C242−1+414yes—
430C242−1+412yes—
431C24C2511yescharacteristic
432C2×Q8—48no—
433C2×Q8—48no—
434C2×Q8—84no—
435C2×Q8—88no—
436C2×Q8—88no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—28no—
440C22×C4—28no—
441C22×C4—216no—
442C22×C4—216no—
443C22×C4—28no—
444C22×C4—22no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
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—22no—
462C22×C4—24no—
463C22×C4—24no—
464C22×C4—24no—
465C22×C4—21no—
466C22×C4—22no—
467C22×C4—21no—
468C22×C4—24no—
469C22×C4—22no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—216no—
475C22×C4—216no—
476C22×C4—216no—
477C22×C4—216no—
478C22×C4—216no—
479C22×C4—22no—
480C22×C4—24no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—24no—
485C22×C4—24no—
486C22×C4—24no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—24no—
496C22×C4—24no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—24no—
500C22×C4—24no—
501C22×C4—24no—
502C22×C4—24no—
503C22×C4—24no—
504C22×C4—22no—
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—22no—
514C22×C4—22no—
515C22×C4—24no—
516C22×C4—24no—
517C22×C4—48no—
518C22×C4—48no—
519C22×C4—48no—
520C22×C4—48no—
521C22×C4—48no—
522C22×C4—48no—
523C22×C4—48no—
524C22×C4—48no—
525C22×C4—48no—
526C22×C4—4128no—
527C22×C4—44no—
528C22×C4—44no—
529C22×C4—48no—
530C22×C4—48no—
531C22×C4—48no—
532C22×C4—48no—
533C22×C4—48no—
534C22×C4—48no—
535C22×C4—48no—
536C22×C4—48no—
537C22×C4—88no—
538C22×C4—88no—
539C22×C4—88no—
540C22×C4—88no—
541C22×C4C22⋊Q8116yes—
542C22×C4C22×D414yes—
543C22×C4C22×D414yes—
544C22×C4C22×D412yes—
545C22×C4C22×D412yes—
546C22×C4C22×Q814yes—
547C22×C4C22×Q812yes—
548C22×C4C22×Q812yes—
549C22×C4C2×#4112yes—
550C22×C4C2×#4112yes—
551C22×C4C2×#4112yes—
552C22×C4C2×#4112yes—
553C22×C4C2×#4112yes—
554C22×C4C2×#4112yes—
555C22×C4H(5,𝔽2)14yes—
556C22×C4H(5,𝔽2)14yes—
557C4⋊C4—28no—
558C4⋊C4—28no—
559C4⋊C4—48no—
560C4⋊C4—48no—
561C4⋊C4—48no—
562C4⋊C4—48no—
563C4⋊C4—48no—
564C4⋊C4—48no—
565C4⋊C4—44no—
566C4⋊C4—44no—
567C4⋊C4—48no—
568C4⋊C4—48no—
569C4⋊C4—84no—
570C4⋊C4—88no—
571C4⋊C4—88no—
572C22⋊C4—28no—
573C22⋊C4—28no—
574C22⋊C4—48no—
575C22⋊C4—48no—
576C22⋊C4—48no—
577C22⋊C4—48no—
578C22⋊C4—416no—
579C22⋊C4—416no—
580C22⋊C4—48no—
581C22⋊C4—44no—
582C22⋊C4—48no—
583C22⋊C4—44no—
584C22⋊C4—88no—
585C22⋊C4—88no—
586C42—44no—
587C42—44no—
588C42—48no—
589C23—22no—
590C23—22no—
591C23—24no—
592C23—24no—
593C23—24no—
594C23—22no—
595C23—22no—
596C23—24no—
597C23—24no—
598C23—24no—
599C23—24no—
600C23—24no—
601C23—24no—
602C23—24no—
603C23—24no—
604C23—24no—
605C23—232no—
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—24no—
622C23—24no—
623C23—24no—
624C23—432no—
625C23—432no—
626C23—416no—
627C23—432no—
628C23—416no—
629C23—416no—
630C23—432no—
631C23—416no—
632C23—416no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23—416no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23C2×C22⋊Q814yes—
651C23#53314yes—
652C23#54418yes—
653C23#54414yes—
654C23#54614yes—
655C23#54814yes—
656C23#55514yes—
657C23#55614yes—
658C23C23×D411yescharacteristic
659C23C23×Q811yescharacteristic
660C23C22×#4111yescharacteristic
661C23C22×#4111yescharacteristic
662C23C22×#4111yescharacteristic
663C23C2×H(5,𝔽2)12yes—
664C23C2×H(5,𝔽2)12yes—
665C23C2×H(5,𝔽2)11yescharacteristic
666C23C2×H(5,𝔽2)12yes—
667C23C2×2−1+411yescharacteristic
668C23C2×2−1+412yes—
669Q8—816no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—24no—
673C2×C4—24no—
674C2×C4—232no—
675C2×C4—24no—
676C2×C4—24no—
677C2×C4—24no—
678C2×C4—24no—
679C2×C4—24no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—24no—
683C2×C4—24no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—24no—
687C2×C4—24no—
688C2×C4—24no—
689C2×C4—24no—
690C2×C4—24no—
691C2×C4—24no—
692C2×C4—432no—
693C2×C4—416no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—42no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—44no—
707C2×C4—44no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—44no—
711C2×C4—44no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—432no—
715C2×C4—42no—
716C2×C4—44no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—44no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—44no—
724C2×C4—42no—
725C2×C4—44no—
726C2×C4—42no—
727C2×C4—44no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—44no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—44no—
736C2×C4—44no—
737C2×C4—44no—
738C2×C4—44no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—44no—
742C2×C4—44no—
743C2×C4—44no—
744C2×C4—44no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—44no—
748C2×C4—44no—
749C2×C4—44no—
750C2×C4—44no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—816no—
754C2×C4—816no—
755C2×C4C2×C22⋊Q814yes—
756C2×C4C2×C22⋊Q814yes—
757C2×C4#53414yes—
758C2×C4#53514yes—
759C2×C4#53818yes—
760C2×C4#54318yes—
761C22—28no—
762C22—28no—
763C22—28no—
764C22—24no—
765C22—24no—
766C22—24no—
767C22—28no—
768C22—24no—
769C22—24no—
770C22—24no—
771C22—28no—
772C22—28no—
773C22—28no—
774C22—464no—
775C22—44no—
776C22—44no—
777C22—44no—
778C22—44no—
779C22—44no—
780C22—44no—
781C22—44no—
782C22—44no—
783C22—44no—
784C22—44no—
785C22—44no—
786C22—44no—
787C22#243918yes—
788C22C22×C22⋊Q811yescharacteristic
789C22C2×#53311yescharacteristic
790C22C2×#53411yescharacteristic
791C22C2×#53511yescharacteristic
792C22C2×#53812yes—
793C22C2×#54312yes—
794C22C2×#54412yes—
795C22C2×#54411yescharacteristic
796C22C2×#54611yescharacteristic
797C22C2×#54811yescharacteristic
798C22C2×#55511yescharacteristic
799C22C2×#55611yescharacteristic
800C22#348411yescharacteristic
801C22#348611yescharacteristic
802C22#349212yes—
803C22#351912yes—
804C22#351912yes—
805C22#352012yes—
806C22#352012yes—
807C22#353612yes—
808C22#353612yes—
809C22#353712yes—
810C22#353812yes—
811C4—24no—
812C4—42no—
813C4—42no—
814C4—44no—
815C4—44no—
816C4—42no—
817C4—42no—
818C4—44no—
819C4—82no—
820C4—84no—
821C4—84no—
822C4—82no—
823C4—82no—
824C4—82no—
825C4#262618yes—
826C2—28no—
827C2—48no—
828C2C2×#262611yescharacteristic
829C2C2×#243911yescharacteristic
830C2#3507912yes—
831C2#3522411yescharacteristic
832C2#3747712yes—
833C2#3890411yescharacteristic
834C2#3890511yescharacteristic
835C2#3893812yes—
836C2#3912011yescharacteristic
837C2#3912111yescharacteristic
838C2#3915412yes—
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×#2440C2semidirect
3. #16569C2semidirect
4. #16520C2semidirect
5. #15223C2semidirect
6. #15220C2semidirect
7. #15131C2semidirect
8. #15125C2semidirect
12. #14281C2semidirect
13. #14265C2semidirect
14. #14130C2semidirect
15. #13907C2semidirect
16. #13881C2semidirect
19. C22×C4⋊Q8C22semidirect
25. C2×#398C22semidirect
27. C2×#395C22semidirect
29. C2×#389C22semidirect
30. C2×#389C22semidirect
31. C2×#389C22semidirect
32. C2×#389C22semidirect
35. C2×#384C22semidirect
36. C2×#382C22semidirect
54. #1446C22semidirect
55. #1445C22semidirect
56. #1445C22semidirect
57. #1444C22semidirect
58. #1443C22semidirect
59. #1442C22semidirect
60. #1442C22semidirect
61. #1442C22semidirect
62. #1441C22semidirect
63. #1441C22semidirect
64. #1441C22semidirect
65. #1441C22semidirect
72. C4⋊#95C22semidirect
73. C4⋊#95C22semidirect
74. C4⋊#95C22semidirect
91. C24×C4Q8semidirect

Maximal subgroups

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

subgroupindex
C2×#24402
C22×#3802
#165692
#165202
#152232
#152202
#151312
#151252
#147262
#147172
#146802
#142812
#142652
#141302
#139072
#138812
C4×#3792