Finite Group Databasebeta

← #639846

Subgroups — #639846

Order 512.

3218 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×#2442C211yesmaximal, characteristic
2C2×#2434C211yesmaximal, characteristic
3C2×#2642C211yesmaximal, characteristic, complemented
4C22×#391C211yesmaximal, characteristic
5#16377C214yesmaximal, complemented
6#16376C214yesmaximal, complemented
7#15241C211yesmaximal, characteristic, complemented
8#15238C211yesmaximal, characteristic, complemented
9#15188C211yesmaximal, characteristic, complemented
10#15188C211yesmaximal, characteristic, complemented
11#14767C214yesmaximal
12#14738C214yesmaximal
13#14702C211yesmaximal, characteristic
14#14274C211yesmaximal, characteristic, complemented
15#14261C211yesmaximal, characteristic, complemented
16#14261C211yesmaximal, characteristic, complemented
17#14139C211yesmaximal, characteristic
18#13922C211yesmaximal, characteristic
19#13753C211yesmaximal, characteristic
20C24×Q8C2211yescharacteristic
21C22×C4⋊Q8C2211yescharacteristic
22C22×C4⋊Q8C2211yescharacteristic
23C22×#125C2211yescharacteristic
24C22×C22⋊Q8C2211yescharacteristic
25C23×C4⋊C4C2211yescharacteristic
26C23×C42C2211yescharacteristic
27#2642—28no—
28#2442—28no—
29#2434—28no—
30C2×#400C2214yes—
31C2×#400C2214yes—
32C2×#400C2212yes—
33C2×#398C2212yes—
34C2×#395C2212yes—
35C2×#395C2212yes—
36C2×#391—28no—
37C2×#391C2211yescharacteristic
38C2×#391C2211yescharacteristic
39C2×#391C2211yescharacteristic
40C2×#391C2211yescharacteristic
41C2×#391C2211yescharacteristic
42C2×#391C2211yescharacteristic
43C2×#391C2211yescharacteristic
44C2×#391C2211yescharacteristic
45C2×#391C2211yescharacteristic
46C2×#391C2214yes—
47C2×#391C2211yescharacteristic
48C2×#391C2211yescharacteristic
49C2×#391C2211yescharacteristic
50C2×#391C2211yescharacteristic
51C2×#391C2211yescharacteristic
52C2×#389C2211yescharacteristic
53C2×#389C2211yescharacteristic
54C2×#385C2212yes—
55C2×#385C2212yes—
56C2×#385C2212yes—
57C2×#382C2211yescharacteristic
58C2×#380C2211yescharacteristic
59C2×#380C2212yes—
60C2×C4×C22⋊C4C2211yescharacteristic
61C2×C4×C22⋊C4C2211yescharacteristic
62C2×#376C2211yescharacteristic
63C2×#376C2211yescharacteristic
64C22×#95C2214yes—
65#1446C2214yes—
66#1445C2214yes—
67#1445C2214yes—
68#1443C2214yes—
69#1443C2214yes—
70#1443C2214yes—
71#1443C2214yes—
72#1442C2214yes—
73#1442C2214yes—
74#1442C2214yes—
75#1442C2214yes—
76#1442C2214yes—
77#1442C2214yes—
78#1441C2214yes—
79#1441C2214yes—
80#1441C2214yes—
81#1436C2214yes—
82C4⋊#95C2211yescharacteristic
83C4⋊#95C2211yescharacteristic
84C4⋊#95C2211yescharacteristic
85C4⋊#95C2211yescharacteristic
86#1434C2212yes—
87#1434C2212yes—
88C22⋊#95C2214yes—
89C22⋊#95C2214yes—
90C22⋊#95C2214yes—
91C22⋊#95C2212yes—
92C22⋊#95C2212yes—
93C4×#95C2211yescharacteristic
94C4×#95C2211yescharacteristic
95C23×Q8—24no—
96C23×Q8—24no—
97C23×Q8—24no—
98C23×Q8—24no—
99C23×Q8—24no—
100C23×Q8—42no—
101C23×Q8—42no—
102C23×Q8C2311yescharacteristic
103C23×Q8C2311yescharacteristic
104C23×Q8C2311yescharacteristic
105C23×Q8C2312yes—
106C24×C4C2312yes—
107C24×C4C2312yes—
108C24×C4C2312yes—
109C24×C4C2311yescharacteristic
110C2×C4⋊Q8—24no—
111C2×C4⋊Q8—24no—
112C2×C4⋊Q8—24no—
113C2×C4⋊Q8—24no—
114C2×C4⋊Q8—42no—
115C2×C4⋊Q8—42no—
116C2×#125—24no—
117C2×#125—24no—
118C2×#125—42no—
119C2×C22⋊Q8—24no—
120C2×C22⋊Q8—24no—
121C2×C22⋊Q8—24no—
122C22×C4⋊C4—24no—
123C22×C4⋊C4—24no—
124C22×C4⋊C4—42no—
125C22×C4⋊C4C2312yes—
126C22×C4⋊C4C2311yescharacteristic
127C22×C4⋊C4C2311yescharacteristic
128C22×C4⋊C4C2311yescharacteristic
129C22×C4⋊C4C2311yescharacteristic
130C22×C4⋊C4C2312yes—
131C22×C4⋊C4C2312yes—
132C22×C4⋊C4C2312yes—
133C22×C4⋊C4C2312yes—
134C22×C4⋊C4C2312yes—
135C22×C4⋊C4C2312yes—
136C22×C4⋊C4C2312yes—
137C22×C4⋊C4C2311yescharacteristic
138C22×C4⋊C4C2312yes—
139C22×C4⋊C4C2312yes—
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2311yescharacteristic
144C22×C22⋊C4C2311yescharacteristic
145C22×C42—24no—
146C22×C42—24no—
147C22×C42—42no—
148C22×C42C2311yescharacteristic
149C22×C42C2311yescharacteristic
150C22×C42C2311yescharacteristic
151C22×C42C2312yes—
152C22×C42C2311yescharacteristic
153C22×C42C2311yescharacteristic
154C22×C42C2311yescharacteristic
155#400—216no—
156#400—216no—
157#400—28no—
158#398—28no—
159#395—28no—
160#395—28no—
161#391—24no—
162#391—24no—
163#391—24no—
164#391—24no—
165#391—24no—
166#391—24no—
167#391—24no—
168#391—24no—
169#391—24no—
170#391—216no—
171#391—42no—
172#391—42no—
173#391—42no—
174#391—42no—
175#391D418yes—
176#389—24no—
177#389—24no—
178#385—28no—
179#385—28no—
180#385—28no—
181#382—24no—
182#380—24no—
183#380—28no—
184C4×C22⋊C4—24no—
185C4×C22⋊C4D418yes—
186#376—24no—
187#376—42no—
188C2×#95—216no—
189C2×#95C2312yes—
190C2×#95C2312yes—
191C2×#95C2312yes—
192C2×#95C2312yes—
193C2×#95C2312yes—
194C2×#95C2312yes—
195C2×#95C2312yes—
196C2×#95C2312yes—
197C2×#95C2314yes—
198C2×#95C2314yes—
199C2×#95C2314yes—
200C2×#95C2312yes—
201C2×#95C2312yes—
202C2×#95C2312yes—
203C2×#95C2312yes—
204C2×#95C2312yes—
205C2×#95C2314yes—
206C2×#95C2314yes—
207C2×#95C2312yes—
208C2×#95C2314yes—
209C2×#95C2314yes—
210C2×#95C2314yes—
211C2×#95C2312yes—
212C2×#95C2312yes—
213C2×#95C2312yes—
214C2×#95C2312yes—
215C2×#95C2314yes—
216C2×#95C2314yes—
217C2×#95C2314yes—
218C2×#95C2314yes—
219C2×#95C2314yes—
220C2×#95C2314yes—
221C2×#95C2314yes—
222C2×#95C2311yescharacteristic
223C2×#95C2311yescharacteristic
224C2×#95C2314yes—
225C25C2411yescharacteristic
226C22×Q8—232no—
227C22×Q8—22no—
228C22×Q8—22no—
229C22×Q8—24no—
230C22×Q8—22no—
231C22×Q8—22no—
232C22×Q8—22no—
233C22×Q8—24no—
234C22×Q8—24no—
235C22×Q8—24no—
236C22×Q8—22no—
237C22×Q8—22no—
238C22×Q8—22no—
239C22×Q8—22no—
240C22×Q8—22no—
241C22×Q8—22no—
242C22×Q8—22no—
243C22×Q8—22no—
244C22×Q8—24no—
245C22×Q8—22no—
246C22×Q8—22no—
247C22×Q8—22no—
248C22×Q8—22no—
249C22×Q8—22no—
250C22×Q8—22no—
251C22×Q8—42no—
252C22×Q8—42no—
253C22×Q8—416no—
254C22×Q8—416no—
255C22×Q8—416no—
256C22×Q8—416no—
257C22×Q8—416no—
258C22×Q8—416no—
259C22×Q8C2×D414yes—
260C22×Q8#4114yes—
261C23×C4—22no—
262C23×C4—22no—
263C23×C4—22no—
264C23×C4—22no—
265C23×C4—24no—
266C23×C4—24no—
267C23×C4—24no—
268C23×C4—24no—
269C23×C4—24no—
270C23×C4—24no—
271C23×C4—24no—
272C23×C4—24no—
273C23×C4—24no—
274C23×C4—24no—
275C23×C4—24no—
276C23×C4—28no—
277C23×C4—24no—
278C23×C4—42no—
279C23×C4—42no—
280C23×C4—42no—
281C23×C4—42no—
282C23×C4—42no—
283C23×C4—44no—
284C23×C4C2×D414yes—
285C23×C4#4114yes—
286C23×C4#4114yes—
287C23×C4C2412yes—
288C23×C4C2412yes—
289C23×C4C2412yes—
290C23×C4C2412yes—
291C23×C4C2412yes—
292C23×C4C2412yes—
293C23×C4C2412yes—
294C23×C4C2411yescharacteristic
295C23×C4C2411yescharacteristic
296C23×C4C2411yescharacteristic
297C23×C4C2411yescharacteristic
298C23×C4C2412yes—
299C23×C4C2412yes—
300C23×C4C2412yes—
301C23×C4C2412yes—
302C23×C4C2412yes—
303C23×C4C2411yescharacteristic
304C23×C4C2411yescharacteristic
305C4⋊Q8—416no—
306C4⋊Q8—416no—
307#125—416no—
308C22⋊Q8—416no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—24no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—24no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—24no—
319C2×C4⋊C4—24no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—24no—
322C2×C4⋊C4—24no—
323C2×C4⋊C4—24no—
324C2×C4⋊C4—24no—
325C2×C4⋊C4—24no—
326C2×C4⋊C4—24no—
327C2×C4⋊C4—24no—
328C2×C4⋊C4—24no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—22no—
332C2×C4⋊C4—24no—
333C2×C4⋊C4—24no—
334C2×C4⋊C4—24no—
335C2×C4⋊C4—24no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—24no—
341C2×C4⋊C4—24no—
342C2×C4⋊C4—416no—
343C2×C4⋊C4—42no—
344C2×C4⋊C4—42no—
345C2×C4⋊C4—42no—
346C2×C4⋊C4—42no—
347C2×C4⋊C4—42no—
348C2×C4⋊C4—42no—
349C2×C4⋊C4—42no—
350C2×C4⋊C4—44no—
351C2×C4⋊C4—44no—
352C2×C4⋊C4C2×D414yes—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—24no—
360C2×C22⋊C4—28no—
361C2×C22⋊C4—24no—
362C2×C22⋊C4—24no—
363C2×C22⋊C4C2×D414yes—
364C2×C22⋊C4C2×D414yes—
365C2×C42—22no—
366C2×C42—22no—
367C2×C42—22no—
368C2×C42—22no—
369C2×C42—22no—
370C2×C42—22no—
371C2×C42—22no—
372C2×C42—24no—
373C2×C42—22no—
374C2×C42—22no—
375C2×C42—22no—
376C2×C42—22no—
377C2×C42—24no—
378C2×C42—22no—
379C2×C42—22no—
380C2×C42—22no—
381C2×C42—22no—
382C2×C42—416no—
383C2×C42—42no—
384C2×C42C2×D414yes—
385C2×C42C2×D414yes—
386C2×C42C2×D414yes—
387#95—28no—
388#95—28no—
389#95—28no—
390#95—24no—
391#95—24no—
392#95—24no—
393#95—24no—
394#95—24no—
395#95—24no—
396#95—24no—
397#95—24no—
398#95—24no—
399#95—24no—
400#95—24no—
401#95—28no—
402#95—28no—
403#95—28no—
404#95—24no—
405#95—28no—
406#95—24no—
407#95—24no—
408#95—28no—
409#95—42no—
410#95—42no—
411#95—44no—
412#95—44no—
413#95—44no—
414#95—42no—
415#95—42no—
416#95—44no—
417#95—44no—
418#95—44no—
419#95—44no—
420#95C2×D4116yes—
421#95C2×D414yes—
422#95C2×D414yes—
423C24—21no—
424C24—21no—
425C24—21no—
426C24—21no—
427C24—22no—
428C24—22no—
429C24C22×D412yes—
430C24C2×#4112yes—
431C24C2×#4112yes—
432C242−1+414yes—
433C242−1+414yes—
434C24C2511yescharacteristic
435C2×Q8—216no—
436C2×Q8—28no—
437C2×Q8—28no—
438C2×Q8—28no—
439C2×Q8—28no—
440C2×Q8—28no—
441C2×Q8—28no—
442C2×Q8—48no—
443C2×Q8—48no—
444C2×Q8—48no—
445C2×Q8—48no—
446C2×Q8—48no—
447C2×Q8—4128no—
448C2×Q8—44no—
449C2×Q8—48no—
450C2×Q8—44no—
451C2×Q8—44no—
452C2×Q8—44no—
453C2×Q8—44no—
454C2×Q8—44no—
455C2×Q8—44no—
456C2×Q8—44no—
457C2×Q8—44no—
458C2×Q8—44no—
459C2×Q8—44no—
460C2×Q8—44no—
461C2×Q8—44no—
462C2×Q8—44no—
463C2×Q8—44no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—28no—
469C22×C4—28no—
470C22×C4—28no—
471C22×C4—28no—
472C22×C4—28no—
473C22×C4—28no—
474C22×C4—216no—
475C22×C4—216no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—24no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—24no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—24no—
547C22×C4—22no—
548C22×C4—24no—
549C22×C4—24no—
550C22×C4—24no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—24no—
556C22×C4—22no—
557C22×C4—24no—
558C22×C4—22no—
559C22×C4—24no—
560C22×C4—24no—
561C22×C4—48no—
562C22×C4—48no—
563C22×C4—48no—
564C22×C4—48no—
565C22×C4—48no—
566C22×C4—48no—
567C22×C4—48no—
568C22×C4—48no—
569C22×C4—48no—
570C22×C4—416no—
571C22×C4—48no—
572C22×C4—48no—
573C22×C4—48no—
574C22×C4—48no—
575C22×C4—48no—
576C22×C4—84no—
577C22×C4—88no—
578C22×C4#124116yes—
579C22×C4C22×D414yes—
580C22×C4C22×D412yes—
581C22×C4C22×D414yes—
582C22×C4C22×D414yes—
583C22×C4C22×D412yes—
584C22×C4C22×D412yes—
585C22×C4C22×D412yes—
586C22×C4C22×D412yes—
587C22×C4C22×D412yes—
588C22×C4C22×D412yes—
589C22×C4C2×#4114yes—
590C22×C4C2×#4112yes—
591C22×C4C2×#4112yes—
592C22×C4C2×#4112yes—
593C22×C4C2×#4112yes—
594C22×C4C2×#4112yes—
595C22×C4H(5,𝔽2)12yes—
596C22×C4H(5,𝔽2)12yes—
597C22×C42−1+414yes—
598C4⋊C4—28no—
599C4⋊C4—48no—
600C4⋊C4—48no—
601C4⋊C4—48no—
602C4⋊C4—48no—
603C4⋊C4—48no—
604C4⋊C4—48no—
605C4⋊C4—48no—
606C4⋊C4—44no—
607C4⋊C4—48no—
608C4⋊C4—44no—
609C4⋊C4—44no—
610C4⋊C4—44no—
611C4⋊C4—84no—
612C4⋊C4—84no—
613C22⋊C4—28no—
614C22⋊C4—28no—
615C22⋊C4—48no—
616C22⋊C4—48no—
617C22⋊C4—48no—
618C42—28no—
619C42—28no—
620C42—28no—
621C42—48no—
622C42—44no—
623C42—44no—
624C42—44no—
625C23—22no—
626C23—22no—
627C23—24no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—24no—
633C23—24no—
634C23—24no—
635C23—22no—
636C23—22no—
637C23—24no—
638C23—24no—
639C23—24no—
640C23—24no—
641C23—24no—
642C23—24no—
643C23C2×#12414yes—
644C23#53614yes—
645C23#53614yes—
646C23#54118yes—
647C23#54118yes—
648C23C23×D411yescharacteristic
649C23C23×D411yescharacteristic
650C23C22×#4111yescharacteristic
651C23C22×#4111yescharacteristic
652C23C22×#4111yescharacteristic
653C23C2×H(5,𝔽2)11yescharacteristic
654C23C2×H(5,𝔽2)11yescharacteristic
655C23C2×2−1+412yes—
656C23C2×2−1+412yes—
657C23C2×2−1+412yes—
658C23#58512yes—
659Q8—432no—
660Q8—416no—
661Q8—416no—
662Q8—88no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—232no—
670C2×C4—24no—
671C2×C4—24no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—24no—
679C2×C4—24no—
680C2×C4—24no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—24no—
684C2×C4—24no—
685C2×C4—24no—
686C2×C4—24no—
687C2×C4—24no—
688C2×C4—24no—
689C2×C4—28no—
690C2×C4—24no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—24no—
696C2×C4—432no—
697C2×C4—432no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—44no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—44no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—44no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—44no—
750C2×C4—44no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—44no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—44no—
762C2×C4—44no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—44no—
766C2×C4—816no—
767C2×C4#52514yes—
768C2×C4C2×#12414yes—
769C2×C4C2×#12414yes—
770C2×C4#53814yes—
771C2×C4D4214yes—
772C2×C4#54614yes—
773C2×C4#54614yes—
774C2×C4#55114yes—
775C22—28no—
776C22—24no—
777C22—24no—
778C22—24no—
779C22—28no—
780C22—28no—
781C22—28no—
782C22—24no—
783C22—24no—
784C22—24no—
785C22#264218yescomplemented
786C22C2×#52511yescharacteristic
787C22C22×#12411yescharacteristic
788C22C2×#53611yescharacteristic
789C22C2×#53611yescharacteristic
790C22C2×#53811yescharacteristic
791C22C2×#54112yes—
792C22C2×#54112yes—
793C22#346112yes—
794C22C2×D4211yescharacteristic
795C22C2×#54611yescharacteristic
796C22C2×#54611yescharacteristic
797C22C2×#55111yescharacteristic
798C22#348612yes—
799C22#348912yes—
800C22#349512yes—
801C22#349911yescharacteristic
802C22#350011yescharacteristic
803C22#351612yes—
804C22#352312yes—
805C22#353812yes—
806C22#354112yes—
807C22#355212yes—
808C22#356112yes—
809C4—24no—
810C4—44no—
811C4—44no—
812C4—42no—
813C4—42no—
814C4—44no—
815C4—44no—
816C4—44no—
817C4—42no—
818C4—42no—
819C4—82no—
820C4—82no—
821C4—82no—
822C4—82no—
823C4—82no—
824C4—82no—
825C4—82no—
826C4#247218yes—
827C2—28no—
828C2C2×#264211yescharacteristic
829C2C2×#247211yescharacteristic
830C2#3524412yes—
831C2#3531211yescharacteristic
832C2#3749512yes—
833C2#3766312yes—
834C2#3767511yescharacteristic
835C2#3767611yescharacteristic
836C2#3805712yes—
837C2#3808111yescharacteristic
838C2#3808511yescharacteristic
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
3. C2×#2642C2semidirect
5. #16377C2semidirect
6. #16376C2semidirect
7. #15241C2semidirect
8. #15238C2semidirect
9. #15188C2semidirect
10. #15188C2semidirect
14. #14274C2semidirect
15. #14261C2semidirect
16. #14261C2semidirect
785. C22#2642semidirect

Maximal subgroups

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

subgroupindex
C2×#24422
C2×#24342
C2×#26422
C22×#3912
#163772
#163762
#152412
#152382
#151882
#147672
#147382
#147022
#142742
#142612
#141392
#139222
#137532