Finite Group Databasebeta

← #676364

Subgroups — #676364

Order 512.

2818 conjugacy classes of subgroups.

The subgroup lattice has 908 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2349C211yesmaximal, characteristic
2C2×C4×#123C211yesmaximal, characteristic
3#16101C212yesmaximal, complemented
4#16100C212yesmaximal, complemented
5#16020C212yesmaximal, complemented
6#15357C212yesmaximal, complemented
7#15086C212yesmaximal, complemented
8#15063C212yesmaximal, complemented
9#14936C212yesmaximal, complemented
10#14738C212yesmaximal, complemented
11#14685C211yesmaximal, characteristic, complemented
12#14239C212yesmaximal, complemented
13#14149C211yesmaximal, characteristic, complemented
14#14040C212yesmaximal, complemented
15#13975C212yesmaximal
16#13968C212yesmaximal
17#13960C211yesmaximal, characteristic
18#13908C211yesmaximal, characteristic, complemented
19C2×#1434C211yesmaximal, characteristic, complemented
20C22×#123C2211yescharacteristic
21C22×C4×D4C2211yescharacteristic
22C22×C4×D4C2212yes—
23C23×C42C2211yescharacteristic
24C2×#400C2212yes—
25#2349—28no—
26C4×#123—28no—
27C2×#389C2212yes—
28C2×#388C2212yes—
29C2×#387C2212yes—
30C2×#386C2212yes—
31C2×#386C2211yescharacteristic
32C2×#385C2212yes—
33C2×#385C2212yes—
34C2×#385C2211yescharacteristic
35C2×#385C2212yes—
36C2×#385C2212yes—
37C2×#382C2211yescharacteristic
38C2×#381C2211yescharacteristic
39C2×#381C2212yes—
40C2×#380C2211yescharacteristic
41C2×#380C2211yescharacteristic
42C2×#380C2211yescharacteristic
43C2×#380C2212yes—
44C2×C4×C4⋊C4C2211yescharacteristic
45C2×C4×C4⋊C4C2212yes—
46C2×C4×C22⋊C4C2211yescharacteristic
47C2×C4×C22⋊C4C2212yes—
48C22×#95C2211yescharacteristic
49C22×#95C2211yescharacteristic
50C22×#95C2211yescharacteristic
51C22×#95C2212yes—
52C22×#95C2212yes—
53#1445C2212yes—
54#1445C2212yes—
55#1445C2212yes—
56#1445C2212yes—
57#1445C2212yes—
58#1445C2212yes—
59#1445C2212yes—
60#1444C2212yes—
61#1444C2212yes—
62#1444C2212yes—
63#1444C2212yes—
64#1443C2212yes—
65#1443C2212yes—
66#1442C2212yes—
67#1442C2212yes—
68#1442C2212yes—
69#1442C2212yes—
70#1442C2212yes—
71#1441C2212yes—
72#1441C2212yes—
73#1441C2211yescharacteristic
74#1441C2211yescharacteristic
75#1441C2212yes—
76#1441C2212yes—
77#1441C2212yes—
78#1440C2212yes—
79#1440C2212yes—
80#1439C2211yescharacteristic
81#1439C2211yescharacteristic
82#1439C2212yes—
83#1439C2212yes—
84#1436C2212yes—
85#1436C2212yes—
86#1436C2212yes—
87#1436C2212yes—
88#1436C2212yes—
89#1436C2212yes—
90#1436C2212yes—
91#1436C2212yes—
92C4⋊#95C2212yes—
93C4⋊#95C2212yes—
94#1434C2212yes—
95#1434C2212yes—
96#1434C2212yes—
97#1434C2212yes—
98#1434C2212yes—
99#1434C2212yes—
100#1434C2212yes—
101C22⋊#95C2212yes—
102C22⋊#95C2212yes—
103C22⋊#95C2212yes—
104C22⋊#95C2212yes—
105C22⋊#95C2212yes—
106C22⋊#95C2212yes—
107C22⋊#95C2212yes—
108C22⋊#95C2212yes—
109C23×D4C2311yescharacteristic
110C24×C4C2311yescharacteristic
111C24×C4C2311yescharacteristic
112C24×C4C2312yes—
113C24×C4C2312yes—
114C24×C4C2312yes—
115C24×C4C2311yescharacteristic
116C24×C4C2311yescharacteristic
117C2×#123—24no—
118C2×#123—24no—
119C2×#123Q818yes—
120C2×C4×D4—24no—
121C2×C4×D4—24no—
122C2×C4×D4—28no—
123C2×C4×D4—44no—
124C2×C4×D4—44no—
125C2×C4×D4D418yes—
126C22×C4⋊C4C2312yes—
127C22×C4⋊C4C2312yes—
128C22×C4⋊C4C2311yescharacteristic
129C22×C4⋊C4C2312yes—
130C22×C4⋊C4C2312yes—
131C22×C4⋊C4C2311yescharacteristic
132C22×C4⋊C4C2311yescharacteristic
133C22×C4⋊C4C2312yes—
134C22×C4⋊C4C2312yes—
135C22×C4⋊C4C2312yes—
136C22×C4⋊C4C2312yes—
137C22×C4⋊C4C2312yes—
138C22×C4⋊C4C2312yes—
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2311yescharacteristic
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2311yescharacteristic
145C22×C22⋊C4C2311yescharacteristic
146C22×C22⋊C4C2311yescharacteristic
147C22×C22⋊C4C2312yes—
148C22×C22⋊C4C2312yes—
149C22×C22⋊C4C2312yes—
150C22×C42—24no—
151C22×C42—24no—
152C22×C42—24no—
153C22×C42C2312yes—
154C22×C42C2312yes—
155C22×C42C2311yescharacteristic
156C22×C42C2312yes—
157C22×C42C2312yes—
158#400—28no—
159#389—28no—
160#388—28no—
161#387—28no—
162#386—24no—
163#386—28no—
164#385—28no—
165#385—28no—
166#385—24no—
167#385—28no—
168#385—44no—
169#382—24no—
170#381—24no—
171#381—44no—
172#380—24no—
173#380—24no—
174#380—24no—
175#380—44no—
176C4×C4⋊C4—24no—
177C4×C4⋊C4—28no—
178C4×C22⋊C4—28no—
179C4×C22⋊C4—24no—
180C2×#95—24no—
181C2×#95—24no—
182C2×#95—24no—
183C2×#95—28no—
184C2×#95—44no—
185C2×#95C2312yes—
186C2×#95C2312yes—
187C2×#95C2312yes—
188C2×#95C2312yes—
189C2×#95C2312yes—
190C2×#95C2312yes—
191C2×#95C2312yes—
192C2×#95C2312yes—
193C2×#95C2311yescharacteristic
194C2×#95C2311yescharacteristic
195C2×#95C2311yescharacteristic
196C2×#95C2311yescharacteristic
197C2×#95C2311yescharacteristic
198C2×#95C2311yescharacteristic
199C2×#95C2312yes—
200C2×#95C2312yes—
201C2×#95C2312yes—
202C2×#95C2312yes—
203C2×#95C2312yes—
204C2×#95C2312yes—
205C2×#95C2312yes—
206C2×#95C2312yes—
207C2×#95C2312yes—
208C2×#95C2312yes—
209C2×#95C2312yes—
210C2×#95C2312yes—
211C2×#95C2312yes—
212C2×#95C2312yes—
213C2×#95C2312yes—
214C2×#95C2312yes—
215C2×#95C2312yes—
216C2×#95C2312yes—
217C2×#95C2312yes—
218C2×#95C2312yes—
219C2×#95C2312yes—
220C2×#95C2312yes—
221C2×#95C2312yes—
222C2×#95C2312yes—
223C2×#95C2312yes—
224C2×#95C2312yes—
225C2×#95C2312yes—
226C2×#95C2312yes—
227C2×#95C2312yes—
228C2×#95C2312yes—
229C2×#95C2312yes—
230C2×#95C2312yes—
231C2×#95C2312yes—
232C2×#95C2312yes—
233C2×#95C2312yes—
234C2×#95C2312yes—
235C25C2411yescharacteristic
236C25C2411yescharacteristic
237C22×D4—22no—
238C22×D4—22no—
239C22×D4—22no—
240C22×D4—22no—
241C22×D4C2×D414yes—
242C22×D4C2×Q814yes—
243C22×D4#4114yes—
244C23×C4—22no—
245C23×C4—22no—
246C23×C4—22no—
247C23×C4—22no—
248C23×C4—22no—
249C23×C4—22no—
250C23×C4—22no—
251C23×C4—24no—
252C23×C4—22no—
253C23×C4—22no—
254C23×C4—22no—
255C23×C4—22no—
256C23×C4—24no—
257C23×C4—24no—
258C23×C4—24no—
259C23×C4—24no—
260C23×C4—24no—
261C23×C4—24no—
262C23×C4—24no—
263C23×C4—24no—
264C23×C4—24no—
265C23×C4—24no—
266C23×C4—42no—
267C23×C4—42no—
268C23×C4—42no—
269C23×C4—42no—
270C23×C4—42no—
271C23×C4—42no—
272C23×C4—42no—
273C23×C4—42no—
274C23×C4—42no—
275C23×C4—42no—
276C23×C4—42no—
277C23×C4—42no—
278C23×C4—42no—
279C23×C4—42no—
280C23×C4—42no—
281C23×C4—42no—
282C23×C4C2×D414yes—
283C23×C4C2×D414yes—
284C23×C4C2×Q814yes—
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×C4C2412yes—
297C23×C4C2412yes—
298C23×C4C2412yes—
299C23×C4C2412yes—
300C23×C4C2412yes—
301C23×C4C2411yescharacteristic
302C23×C4C2411yescharacteristic
303C23×C4C2411yescharacteristic
304#123—232no—
305C4×D4—232no—
306C4×D4—432no—
307C2×C4⋊C4—24no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—24no—
311C2×C4⋊C4—24no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4—24no—
315C2×C4⋊C4—24no—
316C2×C4⋊C4—24no—
317C2×C4⋊C4—24no—
318C2×C4⋊C4—22no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—24no—
321C2×C4⋊C4—24no—
322C2×C4⋊C4—42no—
323C2×C4⋊C4—42no—
324C2×C4⋊C4—42no—
325C2×C4⋊C4—42no—
326C2×C4⋊C4—42no—
327C2×C4⋊C4—42no—
328C2×C4⋊C4—42no—
329C2×C4⋊C4—42no—
330C2×C4⋊C4—42no—
331C2×C4⋊C4—42no—
332C2×C4⋊C4—42no—
333C2×C4⋊C4—42no—
334C2×C4⋊C4—42no—
335C2×C4⋊C4—42no—
336C2×C4⋊C4—42no—
337C2×C4⋊C4—42no—
338C2×C4⋊C4—42no—
339C2×C4⋊C4—42no—
340C2×C4⋊C4—42no—
341C2×C4⋊C4—42no—
342C2×C4⋊C4C2×D414yes—
343C2×C4⋊C4C2×Q818yes—
344C2×C22⋊C4—22no—
345C2×C22⋊C4—24no—
346C2×C22⋊C4—22no—
347C2×C22⋊C4—22no—
348C2×C22⋊C4—22no—
349C2×C22⋊C4—24no—
350C2×C22⋊C4—22no—
351C2×C22⋊C4—22no—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—22no—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—24no—
360C2×C22⋊C4—24no—
361C2×C22⋊C4—22no—
362C2×C22⋊C4—24no—
363C2×C22⋊C4—22no—
364C2×C22⋊C4—24no—
365C2×C22⋊C4—24no—
366C2×C22⋊C4—24no—
367C2×C22⋊C4—42no—
368C2×C22⋊C4—42no—
369C2×C22⋊C4—42no—
370C2×C22⋊C4—42no—
371C2×C22⋊C4—42no—
372C2×C22⋊C4—42no—
373C2×C22⋊C4C2×D414yes—
374C2×C22⋊C4C2×D414yes—
375C2×C22⋊C4C2×Q814yes—
376C2×C22⋊C4C2×Q818yes—
377C2×C42—22no—
378C2×C42—22no—
379C2×C42—24no—
380C2×C42—24no—
381C2×C42—24no—
382C2×C42—24no—
383C2×C42—24no—
384C2×C42—24no—
385C2×C42—24no—
386C2×C42—24no—
387C2×C42—42no—
388C2×C42—42no—
389C2×C42—42no—
390C2×C42—42no—
391C2×C42—416no—
392C2×C42C2×D414yes—
393#95—22no—
394#95—22no—
395#95—22no—
396#95—24no—
397#95—24no—
398#95—24no—
399#95—24no—
400#95—24no—
401#95—22no—
402#95—24no—
403#95—24no—
404#95—24no—
405#95—22no—
406#95—24no—
407#95—24no—
408#95—24no—
409#95—24no—
410#95—22no—
411#95—24no—
412#95—24no—
413#95—24no—
414#95—24no—
415#95—24no—
416#95—24no—
417#95—24no—
418#95—24no—
419#95—42no—
420#95—42no—
421#95—42no—
422#95—42no—
423#95—42no—
424#95—42no—
425#95—42no—
426#95—42no—
427#95—42no—
428#95—42no—
429#95—42no—
430#95—42no—
431#95—42no—
432#95—42no—
433#95—42no—
434#95—42no—
435#95—42no—
436#95—42no—
437#95—42no—
438#95—42no—
439#95—42no—
440#95—42no—
441#95—42no—
442#95#4118yes—
443C24—22no—
444C24—22no—
445C24—22no—
446C24—22no—
447C24—22no—
448C24—21no—
449C24—21no—
450C24—21no—
451C24—21no—
452C24—22no—
453C24—22no—
454C24—22no—
455C24C22×D412yes—
456C24C22×D412yes—
457C24C22×Q812yes—
458C24C22×Q812yes—
459C24C2×#4112yes—
460C24C2×#4112yes—
461C24C2×#4112yes—
462C24C2×#4112yes—
463C24H(5,𝔽2)12yes—
464C24H(5,𝔽2)12yes—
465C24C2511yescharacteristic
466C2×D4—28no—
467C2×D4—28no—
468C2×D4—28no—
469C2×D4—28no—
470C2×D4—28no—
471C2×D4—28no—
472C2×D4C22⋊Q8116yes—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—28no—
482C22×C4—28no—
483C22×C4—28no—
484C22×C4—28no—
485C22×C4—22no—
486C22×C4—22no—
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—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—21no—
503C22×C4—21no—
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—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—28no—
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—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—48no—
574C22×C4—44no—
575C22×C4—44no—
576C22×C4—48no—
577C22×C4—48no—
578C22×C4—48no—
579C22×C4—48no—
580C22×C4—48no—
581C22×C4—48no—
582C22×C4—48no—
583C22×C4—48no—
584C22×C4—48no—
585C22×C4—48no—
586C22×C4—48no—
587C22×C4—44no—
588C22×C4—44no—
589C22×C4—44no—
590C22×C4—44no—
591C22×C4—44no—
592C22×C4—44no—
593C22×C4—48no—
594C22×C4—48no—
595C22×C4—48no—
596C22×C4—84no—
597C22×C4—82no—
598C22×C4—82no—
599C22×C4—84no—
600C22×C4—84no—
601C22×C4—84no—
602C22×C4—84no—
603C22×C4—84no—
604C22×C4—84no—
605C22×C4—84no—
606C22×C4—84no—
607C22×C4—84no—
608C22×C4—84no—
609C22×C4—84no—
610C22×C4#123116yes—
611C22×C4C22×D412yes—
612C22×C4C22×D412yes—
613C22×C4C22×D412yes—
614C22×C4C22×D412yes—
615C22×C4C22×D412yes—
616C22×C4C22×Q814yes—
617C22×C4C22×Q814yes—
618C22×C4C22×Q812yes—
619C22×C4C2×#4114yes—
620C22×C4C2×#4114yes—
621C22×C4C2×#4114yes—
622C22×C4C2×#4112yes—
623C22×C4C2×#4112yes—
624C22×C4C2×#4112yes—
625C22×C4C2×#4112yes—
626C22×C4C2×#4112yes—
627C4⋊C4—216no—
628C4⋊C4—28no—
629C4⋊C4—48no—
630C4⋊C4—48no—
631C4⋊C4—48no—
632C4⋊C4—84no—
633C4⋊C4—82no—
634C4⋊C4—82no—
635C4⋊C4—84no—
636C4⋊C4—84no—
637C4⋊C4—84no—
638C4⋊C4—84no—
639C4⋊C4—84no—
640C22⋊C4—28no—
641C22⋊C4—216no—
642C22⋊C4—28no—
643C22⋊C4—28no—
644C22⋊C4—48no—
645C22⋊C4—48no—
646C22⋊C4—48no—
647C22⋊C4—44no—
648C22⋊C4—48no—
649C22⋊C4—48no—
650C22⋊C4—84no—
651C42—28no—
652C42—48no—
653C42—48no—
654C42—48no—
655C42—48no—
656C23—22no—
657C23—22no—
658C23—24no—
659C23—24no—
660C23—24no—
661C23—24no—
662C23—24no—
663C23—24no—
664C23—22no—
665C23—22no—
666C23—24no—
667C23—24no—
668C23—24no—
669C23—24no—
670C23—24no—
671C23—24no—
672C23—22no—
673C23—22no—
674C23—24no—
675C23—22no—
676C23—22no—
677C23—22no—
678C23—22no—
679C23—24no—
680C23—24no—
681C23—24no—
682C23—24no—
683C23—24no—
684C23—41no—
685C23—41no—
686C23—42no—
687C23—42no—
688C23—41no—
689C23—41no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23C2×C22⋊Q814yes—
695C23C2×C22⋊Q814yes—
696C23C2×#12314yes—
697C23#53514yes—
698C23#55314yes—
699C23#55314yes—
700C23#55414yes—
701C23#55414yes—
702C23C23×D411yescharacteristic
703C23C23×Q811yescharacteristic
704C23C22×#4111yescharacteristic
705C23C22×#4111yescharacteristic
706C23C22×#4111yescharacteristic
707C23C22×#4112yes—
708C23C2×H(5,𝔽2)11yescharacteristic
709C23C2×H(5,𝔽2)11yescharacteristic
710C23#58512yes—
711C23#58512yes—
712C23#58512yes—
713D4—232no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—24no—
721C2×C4—24no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—24no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—24no—
733C2×C4—24no—
734C2×C4—24no—
735C2×C4—24no—
736C2×C4—24no—
737C2×C4—24no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—24no—
743C2×C4—24no—
744C2×C4—24no—
745C2×C4—24no—
746C2×C4—24no—
747C2×C4—416no—
748C2×C4—416no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—41no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—41no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—416no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—88no—
826C2×C4—816no—
827C2×C4—816no—
828C2×C4—816no—
829C2×C4C2×C22⋊Q814yes—
830C2×C4C2×#12314yes—
831C2×C4C2×#12314yes—
832C22—28no—
833C22—24no—
834C22—28no—
835C22—24no—
836C22—24no—
837C22—24no—
838C22—28no—
839C22—24no—
840C22—28no—
841C22—24no—
842C22—28no—
843C22—24no—
844C22—44no—
845C22—42no—
846C22—42no—
847C22—42no—
848C22—42no—
849C22—44no—
850C22—42no—
851C22—44no—
852C22—42no—
853C22#248718yes—
854C22C22×C22⋊Q811yescharacteristic
855C22C22×#12311yescharacteristic
856C22#344411yescharacteristic
857C22C2×#53511yescharacteristic
858C22#345511yescharacteristic
859C22D4×#4112yes—
860C22C2×#55311yescharacteristic
861C22C2×#55311yescharacteristic
862C22C2×#55411yescharacteristic
863C22C2×#55411yescharacteristic
864C22#347512yes—
865C22#347512yes—
866C22Q8×#4112yes—
867C22#348512yes—
868C22#349112yes—
869C22#349111yescharacteristic
870C22#349111yescharacteristic
871C22#349412yes—
872C22#350412yes—
873C22#351312yes—
874C22#352112yes—
875C22#354512yes—
876C22#356012yes—
877C4—24no—
878C4—24no—
879C4—24no—
880C4—44no—
881C4—42no—
882C4—44no—
883C4—42no—
884C4—44no—
885C4—44no—
886C4—44no—
887C4—82no—
888C4—82no—
889C4—82no—
890C4—82no—
891C4—82no—
892C4—82no—
893C4—82no—
894C2—28no—
895C2—44no—
896C2#3474211yescharacteristic
897C2C2×#248711yescharacteristic
898C2#3544811yescharacteristic
899C2#3621912yes—
900C2#3652211yescharacteristic
901C2#3656911yescharacteristic
902C2#3836212yes—
903C2#3914111yescharacteristic
904C2#3960111yescharacteristic
905C2#5921012yes—
906C2#5931912yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC23×D4C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #16101C2semidirect
4. #16100C2semidirect
5. #16020C2semidirect
6. #15357C2semidirect
7. #15086C2semidirect
8. #15063C2semidirect
9. #14936C2semidirect
10. #14738C2semidirect
11. #14685C2semidirect
12. #14239C2semidirect
13. #14149C2semidirect
14. #14040C2semidirect
18. #13908C2semidirect
19. C2×#1434C2semidirect

Maximal subgroups

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

subgroupindex
C2×#23492
C2×C4×#1232
#161012
#161002
#160202
#153572
#150862
#150632
#149362
#147382
#146852
#142392
#141492
#140402
#139752
#139682
#139602
#139082
C2×#14342