Finite Group Databasebeta

← #676281

Subgroups — #676281

Order 512.

2538 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2355C211yesmaximal, characteristic, complemented
2C2×C4×C22⋊Q8C211yesmaximal, characteristic
3#16022C214yesmaximal, complemented
4#15957C214yesmaximal
5#15234C212yesmaximal, complemented
6#15223C212yesmaximal
7#15185C212yesmaximal, complemented
8#15179C212yesmaximal
9#14686C211yesmaximal, characteristic
10#14151C211yesmaximal, characteristic, complemented
11#14132C212yesmaximal, complemented
12#14041C212yesmaximal, complemented
13#13994C212yesmaximal
14#13926C211yesmaximal, characteristic, complemented
15#13910C211yesmaximal, characteristic, complemented
16#13876C212yesmaximal
17C4×#380C211yesmaximal, characteristic
18C22×C22⋊Q8C2211yescharacteristic
19C22×C4×Q8C2211yescharacteristic
20C23×C42C2211yescharacteristic
21#2355—28no—
22C4×C22⋊Q8—28no—
23C2×#391C2212yes—
24C2×#391C2211yescharacteristic
25C2×#391C2212yes—
26C2×#389C2211yescharacteristic
27C2×#389C2212yes—
28C2×#389C2212yes—
29C2×#389C2212yes—
30C2×#389C2212yes—
31C2×#388C2214yes—
32C2×#387C2214yes—
33C2×#387C2212yes—
34C2×#385C2212yes—
35C2×#384C2211yescharacteristic
36C2×#384C2211yescharacteristic
37C2×#384C2212yes—
38C2×#382C2212yes—
39C2×#380C2211yescharacteristic
40C2×#380C2211yescharacteristic
41C2×#380C2212yes—
42C2×#380C2212yes—
43C2×#380C2212yes—
44C2×#380C2211yescharacteristic
45C2×C4×C4⋊C4C2212yes—
46C2×C4×C4⋊C4C2211yescharacteristic
47C2×C4×C4⋊C4C2212yes—
48C2×C4×C4⋊C4C2211yescharacteristic
49C2×C4×C4⋊C4C2211yescharacteristic
50C2×C4×C4⋊C4C2212yes—
51C2×C4×C22⋊C4C2212yes—
52C2×C4×C22⋊C4C2212yes—
53#1445C2214yes—
54#1445C2214yes—
55#1445C2214yes—
56#1444C2214yes—
57#1442C2214yes—
58#1442C2214yes—
59#1442C2214yes—
60#1442C2214yes—
61#1441C2214yes—
62#1441C2214yes—
63#1441C2214yes—
64#1441C2214yes—
65#1440C2214yes—
66#1439C2214yes—
67#1439C2214yes—
68#1436C2214yes—
69#1436C2214yes—
70C4⋊#95C2212yes—
71C4⋊#95C2212yes—
72C4⋊#95C2212yes—
73C4⋊#95C2212yes—
74C4⋊#95C2212yes—
75C4⋊#95C2212yes—
76C4⋊#95C2212yes—
77C4⋊#95C2212yes—
78C4⋊#95C2212yes—
79C4⋊#95C2211yescharacteristic
80C4⋊#95C2211yescharacteristic
81#1434C2214yes—
82#1434C2212yes—
83C22⋊#95C2212yes—
84C4×#95C2212yes—
85C23×Q8C2311yescharacteristic
86C24×C4C2311yescharacteristic
87C24×C4C2311yescharacteristic
88C24×C4C2311yescharacteristic
89C2×C22⋊Q8—24no—
90C2×C22⋊Q8—24no—
91C2×C22⋊Q8—24no—
92C2×C4×Q8—24no—
93C2×C4×Q8—24no—
94C2×C4×Q8D418yes—
95C22×C4⋊C4C2312yes—
96C22×C4⋊C4C2312yes—
97C22×C4⋊C4C2312yes—
98C22×C4⋊C4C2311yescharacteristic
99C22×C4⋊C4C2312yes—
100C22×C4⋊C4C2311yescharacteristic
101C22×C4⋊C4C2312yes—
102C22×C4⋊C4C2312yes—
103C22×C4⋊C4C2311yescharacteristic
104C22×C4⋊C4C2312yes—
105C22×C4⋊C4C2311yescharacteristic
106C22×C4⋊C4C2311yescharacteristic
107C22×C4⋊C4C2311yescharacteristic
108C22×C4⋊C4C2311yescharacteristic
109C22×C4⋊C4C2312yes—
110C22×C4⋊C4C2312yes—
111C22×C4⋊C4C2314yes—
112C22×C4⋊C4C2314yes—
113C22×C4⋊C4C2314yes—
114C22×C22⋊C4C2312yes—
115C22×C22⋊C4C2312yes—
116C22×C22⋊C4C2312yes—
117C22×C22⋊C4C2312yes—
118C22×C22⋊C4C2314yes—
119C22×C42—24no—
120C22×C42—24no—
121C22×C42—24no—
122C22×C42C2311yescharacteristic
123C22×C42C2311yescharacteristic
124C22×C42C2311yescharacteristic
125C22×C42C2312yes—
126C22×C42C2312yes—
127C22×C42C2312yes—
128C22×C42C2312yes—
129C22×C42C2314yes—
130C22×C42C2311yescharacteristic
131#391—28no—
132#391—24no—
133#391—44no—
134#389—24no—
135#389—28no—
136#389—28no—
137#389—44no—
138#389—44no—
139#388—48no—
140#387—216no—
141#387—28no—
142#385—28no—
143#384—24no—
144#384—24no—
145#384—44no—
146#382—28no—
147#380—24no—
148#380—24no—
149#380—44no—
150#380—44no—
151#380—44no—
152#380Q818yescomplemented
153C4×C4⋊C4—28no—
154C4×C4⋊C4—24no—
155C4×C4⋊C4—28no—
156C4×C4⋊C4—28no—
157C4×C4⋊C4—24no—
158C4×C4⋊C4—24no—
159C4×C22⋊C4—28no—
160C4×C22⋊C4—28no—
161C2×#95C2312yes—
162C2×#95C2312yes—
163C2×#95C2312yes—
164C2×#95C2312yes—
165C2×#95C2312yes—
166C2×#95C2312yes—
167C2×#95C2314yes—
168C2×#95C2312yes—
169C2×#95C2314yes—
170C2×#95C2312yes—
171C2×#95C2314yes—
172C2×#95C2314yes—
173C2×#95C2314yes—
174C2×#95C2312yes—
175C2×#95C2312yes—
176C2×#95C2312yes—
177C2×#95C2312yes—
178C2×#95C2314yes—
179C2×#95C2314yes—
180C2×#95C2314yes—
181C2×#95C2314yes—
182C2×#95C2314yes—
183C2×#95C2314yes—
184C2×#95C2314yes—
185C2×#95C2314yes—
186C2×#95C2314yes—
187C2×#95C2314yes—
188C2×#95C2312yes—
189C25C2411yescharacteristic
190C22×Q8—22no—
191C22×Q8—22no—
192C22×Q8—22no—
193C22×Q8—22no—
194C22×Q8—22no—
195C22×Q8—22no—
196C22×Q8C2×D414yes—
197C23×C4—22no—
198C23×C4—22no—
199C23×C4—22no—
200C23×C4—22no—
201C23×C4—22no—
202C23×C4—22no—
203C23×C4—22no—
204C23×C4—22no—
205C23×C4—22no—
206C23×C4—22no—
207C23×C4—22no—
208C23×C4—22no—
209C23×C4—22no—
210C23×C4—22no—
211C23×C4—22no—
212C23×C4—22no—
213C23×C4—22no—
214C23×C4—41no—
215C23×C4—41no—
216C23×C4C2×Q814yes—
217C23×C4#4114yes—
218C23×C4C2412yes—
219C23×C4C2414yes—
220C23×C4C2414yes—
221C23×C4C2412yes—
222C23×C4C2412yes—
223C23×C4C2412yes—
224C23×C4C2412yes—
225C23×C4C2412yes—
226C23×C4C2411yescharacteristic
227C23×C4C2412yes—
228C23×C4C2412yes—
229C23×C4C2411yescharacteristic
230C23×C4C2411yescharacteristic
231C23×C4C2411yescharacteristic
232C23×C4C2411yescharacteristic
233C23×C4C2411yescharacteristic
234C22⋊Q8—232no—
235C4×Q8—232no—
236C2×C4⋊C4—24no—
237C2×C4⋊C4—22no—
238C2×C4⋊C4—22no—
239C2×C4⋊C4—22no—
240C2×C4⋊C4—22no—
241C2×C4⋊C4—24no—
242C2×C4⋊C4—24no—
243C2×C4⋊C4—24no—
244C2×C4⋊C4—24no—
245C2×C4⋊C4—22no—
246C2×C4⋊C4—22no—
247C2×C4⋊C4—22no—
248C2×C4⋊C4—22no—
249C2×C4⋊C4—22no—
250C2×C4⋊C4—22no—
251C2×C4⋊C4—22no—
252C2×C4⋊C4—22no—
253C2×C4⋊C4—24no—
254C2×C4⋊C4—24no—
255C2×C4⋊C4—24no—
256C2×C4⋊C4—22no—
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—22no—
266C2×C4⋊C4—22no—
267C2×C4⋊C4—24no—
268C2×C4⋊C4—22no—
269C2×C4⋊C4—24no—
270C2×C4⋊C4—24no—
271C2×C4⋊C4—24no—
272C2×C4⋊C4—24no—
273C2×C4⋊C4—28no—
274C2×C4⋊C4—28no—
275C2×C4⋊C4—42no—
276C2×C4⋊C4—42no—
277C2×C4⋊C4—42no—
278C2×C4⋊C4—44no—
279C2×C4⋊C4—44no—
280C2×C4⋊C4—42no—
281C2×C4⋊C4—42no—
282C2×C4⋊C4—44no—
283C2×C4⋊C4—44no—
284C2×C4⋊C4—44no—
285C2×C4⋊C4—44no—
286C2×C4⋊C4—44no—
287C2×C4⋊C4C2×D414yes—
288C2×C4⋊C4C2×D418yes—
289C2×C4⋊C4C2×Q814yes—
290C2×C4⋊C4C2×Q814yes—
291C2×C4⋊C4#4114yes—
292C2×C4⋊C4#4114yes—
293C2×C22⋊C4—24no—
294C2×C22⋊C4—24no—
295C2×C22⋊C4—24no—
296C2×C22⋊C4—24no—
297C2×C22⋊C4—24no—
298C2×C22⋊C4—24no—
299C2×C22⋊C4—24no—
300C2×C22⋊C4—24no—
301C2×C22⋊C4—24no—
302C2×C22⋊C4—28no—
303C2×C22⋊C4—42no—
304C2×C22⋊C4—42no—
305C2×C22⋊C4—44no—
306C2×C22⋊C4—44no—
307C2×C22⋊C4C2×Q818yes—
308C2×C42—24no—
309C2×C42—24no—
310C2×C42—24no—
311C2×C42—24no—
312C2×C42—22no—
313C2×C42—22no—
314C2×C42—22no—
315C2×C42—24no—
316C2×C42—24no—
317C2×C42—24no—
318C2×C42—24no—
319C2×C42—24no—
320C2×C42—22no—
321C2×C42—22no—
322C2×C42—22no—
323C2×C42—22no—
324C2×C42—22no—
325C2×C42—22no—
326C2×C42—24no—
327C2×C42—24no—
328C2×C42—28no—
329C2×C42—416no—
330C2×C42—44no—
331C2×C42—44no—
332C2×C42C2×D418yes—
333C2×C42C2×D414yes—
334C2×C42#4114yes—
335C2×C42#4114yes—
336#95—24no—
337#95—24no—
338#95—24no—
339#95—28no—
340#95—24no—
341#95—24no—
342#95—24no—
343#95—28no—
344#95—28no—
345#95—24no—
346#95—24no—
347#95—24no—
348#95—24no—
349#95—28no—
350#95—28no—
351#95—24no—
352#95—44no—
353#95—42no—
354#95—44no—
355#95—44no—
356#95—44no—
357#95—44no—
358#95—44no—
359#95—44no—
360#95—44no—
361#95—44no—
362#95—44no—
363#95C2×Q818yes—
364C24—21no—
365C24—21no—
366C24—21no—
367C24—21no—
368C24—21no—
369C24—21no—
370C24—21no—
371C24—21no—
372C24—21no—
373C24—21no—
374C24—21no—
375C24—21no—
376C24C22×Q812yes—
377C24C2×#4112yes—
378C24H(5,𝔽2)12yes—
379C24C2511yescharacteristic
380C2×Q8—28no—
381C2×Q8—28no—
382C2×Q8—28no—
383C2×Q8—44no—
384C2×Q8—44no—
385C2×Q8—44no—
386C2×Q8—44no—
387C22×C4—21no—
388C22×C4—21no—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—28no—
392C22×C4—21no—
393C22×C4—22no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—21no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—21no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—21no—
446C22×C4—28no—
447C22×C4—28no—
448C22×C4—28no—
449C22×C4—28no—
450C22×C4—28no—
451C22×C4—28no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—24no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—24no—
458C22×C4—24no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—24no—
462C22×C4—24no—
463C22×C4—24no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—24no—
467C22×C4—24no—
468C22×C4—22no—
469C22×C4—24no—
470C22×C4—24no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—24no—
475C22×C4—24no—
476C22×C4—24no—
477C22×C4—24no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—44no—
481C22×C4—44no—
482C22×C4—44no—
483C22×C4—44no—
484C22×C4—44no—
485C22×C4—44no—
486C22×C4—44no—
487C22×C4—44no—
488C22×C4—44no—
489C22×C4—44no—
490C22×C4—44no—
491C22×C4—44no—
492C22×C4—44no—
493C22×C4—44no—
494C22×C4C22×D414yes—
495C22×C4C22×D414yes—
496C22×C4C22×D412yes—
497C22×C4C22×D412yes—
498C22×C4C22×D412yes—
499C22×C4C22×Q812yes—
500C22×C4C22×Q814yes—
501C22×C4C22×Q814yes—
502C22×C4C22×Q812yes—
503C22×C4C2×#4112yes—
504C22×C4C2×#4114yes—
505C22×C4C2×#4114yes—
506C22×C4C2×#4112yes—
507C22×C4C2×#4112yes—
508C22×C4C2×#4112yes—
509C22×C4C2×#4112yes—
510C22×C4C2×#4112yes—
511C22×C4C2×#4112yes—
512C22×C4C2×#4112yes—
513C22×C4C2×#4112yes—
514C22×C4C2×#4112yes—
515C22×C4H(5,𝔽2)12yes—
516C22×C4H(5,𝔽2)12yes—
517C22×C42−1+412yes—
518C22×C42−1+412yes—
519C22×C42−1+412yes—
520C4⋊C4—216no—
521C4⋊C4—28no—
522C4⋊C4—216no—
523C4⋊C4—28no—
524C4⋊C4—28no—
525C4⋊C4—28no—
526C4⋊C4—28no—
527C4⋊C4—48no—
528C4⋊C4—44no—
529C4⋊C4—48no—
530C4⋊C4—48no—
531C4⋊C4—44no—
532C4⋊C4—48no—
533C4⋊C4—48no—
534C4⋊C4—84no—
535C4⋊C4—84no—
536C4⋊C4—88no—
537C4⋊C4—88no—
538C4⋊C4—88no—
539C22⋊C4—216no—
540C22⋊C4—216no—
541C22⋊C4—48no—
542C22⋊C4—48no—
543C22⋊C4—88no—
544C42—216no—
545C42—44no—
546C42—44no—
547C42—44no—
548C42—48no—
549C42—48no—
550C42—48no—
551C42—88no—
552C42#123116yes—
553C23—22no—
554C23—22no—
555C23—22no—
556C23—22no—
557C23—22no—
558C23—22no—
559C23—22no—
560C23—22no—
561C23—22no—
562C23—22no—
563C23—22no—
564C23—22no—
565C23—22no—
566C23—22no—
567C23—22no—
568C23—22no—
569C23—22no—
570C23—22no—
571C23—41no—
572C23—41no—
573C23—41no—
574C23—41no—
575C23—41no—
576C23—41no—
577C23—41no—
578C23—41no—
579C23—41no—
580C23—41no—
581C23—41no—
582C23—41no—
583C23—41no—
584C23—41no—
585C23—41no—
586C23—41no—
587C23#55414yes—
588C23C23×D411yescharacteristic
589C23C23×Q811yescharacteristic
590C23C22×#4111yescharacteristic
591C23C22×#4111yescharacteristic
592C23C22×#4111yescharacteristic
593C23C22×#4111yescharacteristic
594C23C22×#4111yescharacteristic
595C23C2×H(5,𝔽2)11yescharacteristic
596C23C2×H(5,𝔽2)11yescharacteristic
597C23C2×H(5,𝔽2)11yescharacteristic
598C23C2×2−1+411yescharacteristic
599C23C2×2−1+411yescharacteristic
600C23C2×2−1+411yescharacteristic
601C23#58511yescharacteristic
602C23#58511yescharacteristic
603Q8—416no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—24no—
611C2×C4—24no—
612C2×C4—24no—
613C2×C4—24no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—24no—
617C2×C4—24no—
618C2×C4—22no—
619C2×C4—24no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—24no—
623C2×C4—24no—
624C2×C4—24no—
625C2×C4—22no—
626C2×C4—24no—
627C2×C4—24no—
628C2×C4—24no—
629C2×C4—24no—
630C2×C4—22no—
631C2×C4—24no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—24no—
635C2×C4—24no—
636C2×C4—24no—
637C2×C4—416no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—42no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—42no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—42no—
648C2×C4—42no—
649C2×C4—42no—
650C2×C4—42no—
651C2×C4—41no—
652C2×C4—42no—
653C2×C4—41no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—41no—
658C2×C4—42no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—41no—
664C2×C4—42no—
665C2×C4—41no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—416no—
675C2×C4—416no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—44no—
679C2×C4—44no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—44no—
683C2×C4—44no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—44no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—44no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—44no—
694C2×C4—44no—
695C2×C4—44no—
696C2×C4—44no—
697C2×C4—42no—
698C2×C4—44no—
699C2×C4—44no—
700C2×C4—42no—
701C2×C4—44no—
702C2×C4—42no—
703C2×C4—44no—
704C2×C4C2×#12314yes—
705C2×C4C2×#12314yes—
706C2×C4C2×#12314yes—
707C2×C4#52514yes—
708C2×C4#53314yes—
709C2×C4#53714yes—
710C2×C4#54214yes—
711C2×C4D4×Q814yes—
712C2×C4#55014yes—
713C2×C4#55214yes—
714C2×C4#55214yes—
715C2×C4#55314yes—
716C2×C4#55414yes—
717C2×C4#55514yes—
718C2×C4#55614yes—
719C22—24no—
720C22—24no—
721C22—24no—
722C22—42no—
723C22—42no—
724C22—42no—
725C22—42no—
726C22—42no—
727C22—42no—
728C22—42no—
729C22—42no—
730C22—42no—
731C22—42no—
732C22—42no—
733C22—42no—
734C22C22×#12311yescharacteristic
735C22C2×#52511yescharacteristic
736C22C2×#53311yescharacteristic
737C22C2×#53711yescharacteristic
738C22C2×#54211yescharacteristic
739C22C2×D4×Q811yescharacteristic
740C22C2×#55011yescharacteristic
741C22C2×#55211yescharacteristic
742C22C2×#55211yescharacteristic
743C22C2×#55311yescharacteristic
744C22C2×#55411yescharacteristic
745C22C2×#55411yescharacteristic
746C22C2×#55511yescharacteristic
747C22C2×#55611yescharacteristic
748C22#347511yescharacteristic
749C22Q8×#4111yescharacteristic
750C22#348211yescharacteristic
751C22#348811yescharacteristic
752C22#348911yescharacteristic
753C22#349211yescharacteristic
754C22#349311yescharacteristic
755C22#349411yescharacteristic
756C22#349511yescharacteristic
757C22#350211yescharacteristic
758C22#350311yescharacteristic
759C22#350711yescharacteristic
760C22#351111yescharacteristic
761C22#351411yescharacteristic
762C22#351411yescharacteristic
763C22#352211yescharacteristic
764C22#352211yescharacteristic
765C22#354311yescharacteristic
766C22#355411yescharacteristic
767C22#355411yescharacteristic
768C22#355611yescharacteristic
769C4—24no—
770C4—44no—
771C4—42no—
772C4—44no—
773C4—44no—
774C4—44no—
775C4—42no—
776C4—44no—
777C4—42no—
778C4—44no—
779C4—84no—
780C4—82no—
781C4—82no—
782C4—84no—
783C4#242318yes—
784C4#248518yes—
785C2—44no—
786C2C2×#242311yescharacteristic
787C2C2×#248511yescharacteristic
788C2#3551611yescharacteristic
789C2#3619311yescharacteristic
790C2#3628811yescharacteristic
791C2#3650411yescharacteristic
792C2#3654411yescharacteristic
793C2#3894111yescharacteristic
794C2#3913711yescharacteristic
795C2#3947811yescharacteristic
796C2#3959911yescharacteristic
797C2#5924511yescharacteristic
798C2#5924911yescharacteristic
799C2#5925711yescharacteristic
800C2#5930511yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC25C24
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×#2355C2semidirect
3. #16022C2semidirect
5. #15234C2semidirect
7. #15185C2semidirect
10. #14151C2semidirect
11. #14132C2semidirect
12. #14041C2semidirect
14. #13926C2semidirect
15. #13910C2semidirect
152. #380Q8semidirect

Maximal subgroups

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

subgroupindex
C2×#23552
C2×C4×C22⋊Q82
#160222
#159572
#152342
#152232
#151852
#151792
#146862
#141512
#141322
#140412
#139942
#139262
#139102
#138762
C4×#3802