Finite Group Databasebeta

← #560485

Subgroups — #560485

Order 512.

2562 conjugacy classes of subgroups.

The subgroup lattice has 882 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2632C211yesmaximal, characteristic
2C2×#2379C211yesmaximal, characteristic
3C2×#2355C211yesmaximal, characteristic, complemented
4#14578C212yesmaximal, complemented
5#14575C212yesmaximal, complemented
6#14536C212yesmaximal
7#14524C212yesmaximal, complemented
8#14405C212yesmaximal, complemented
9#14399C212yesmaximal, complemented
10#14298C211yesmaximal, characteristic, complemented
11#14232C212yesmaximal, complemented
12#14230C212yesmaximal, complemented
13#14214C212yesmaximal, complemented
14#14195C212yesmaximal
15#14153C211yesmaximal, characteristic
16#14125C212yesmaximal, complemented
17#14032C212yesmaximal, complemented
18#13942C211yesmaximal, characteristic, complemented
19#13781C211yesmaximal, characteristic, complemented
20C22×#124C2211yescharacteristic
21C22×C4×Q8C2211yescharacteristic
22#2632C4116yescomplemented
23C2×#399C2212yes—
24C2×#395C2211yescharacteristic
25C2×#395C2211yescharacteristic
26C2×#394C2211yescharacteristic
27C2×#394C2211yescharacteristic
28C2×#393C2212yes—
29#2379—28no—
30#2355—28no—
31C2×#391C2212yes—
32C2×#391C2212yes—
33C2×#391C2212yes—
34C2×#391C2211yescharacteristic
35C2×#391C2211yescharacteristic
36C2×#390C2212yes—
37C2×#389C2212yes—
38C2×#388C2212yes—
39C2×#388C2212yes—
40C2×#388C2212yes—
41C2×#388C2212yes—
42C2×#388C2212yes—
43C2×#387C2212yes—
44C2×#387C2212yes—
45C2×#387C2212yes—
46C2×#386C2212yes—
47C2×#385C2212yes—
48C2×#385C2212yes—
49C2×#385C2212yes—
50C2×#385C2212yes—
51C2×#384C2211yescharacteristic
52C2×#383C2211yescharacteristic
53C2×#382C2211yescharacteristic
54C2×#382C2211yescharacteristic
55C2×#382C2211yescharacteristic
56C2×C4×C4⋊C4C2211yescharacteristic
57C2×C4×C4⋊C4C2211yescharacteristic
58C2×C4×C4⋊C4C2212yes—
59C2×C4×C4⋊C4C2211yescharacteristic
60C2×C4×C4⋊C4C2211yescharacteristic
61C2×C4×C22⋊C4C2212yes—
62#1445C2212yes—
63#1444C2212yes—
64#1444C2212yes—
65#1444C2212yes—
66#1442C2212yes—
67#1442C2212yes—
68#1442C2212yes—
69#1442C2212yes—
70#1442C2212yes—
71#1441C2212yes—
72#1441C2212yes—
73#1441C2212yes—
74#1440C2212yes—
75#1440C2212yes—
76#1440C2212yes—
77#1439C2212yes—
78#1439C2212yes—
79#1439C2212yes—
80#1439C2212yes—
81#1439C2212yes—
82#1437C2212yes—
83#1437C2212yes—
84#1437C2212yes—
85#1437C2212yes—
86#1437C2212yes—
87#1437C2212yes—
88#1437C2212yes—
89#1436C2212yes—
90#1436C2212yes—
91#1436C2212yes—
92#1436C2212yes—
93#1436C2212yes—
94#1436C2212yes—
95#1436C2212yes—
96#1436C2212yes—
97#1436C2212yes—
98C4⋊#95C2212yes—
99C4⋊#95C2211yescharacteristic
100C4⋊#95C2211yescharacteristic
101#1434C2212yes—
102#1434C2212yes—
103#1434C2212yes—
104#1434C2212yes—
105#1434C2212yes—
106#1434C2212yes—
107C22⋊#95C2212yes—
108C4×#95C2212yes—
109C4×#95C2212yes—
110C23×Q8C2311yescharacteristic
111C23×Q8C2311yescharacteristic
112C23×D4C2311yescharacteristic
113C24×C4C2312yes—
114C2×#124—24no—
115C2×#124—24no—
116C2×#124C2×C418yes—
117C2×C4×Q8—24no—
118C2×C4×Q8—24no—
119C2×C4×Q8C2×C418yescomplemented
120C22×C4⋊C4C2311yescharacteristic
121C22×C4⋊C4C2312yes—
122C22×C4⋊C4C2312yes—
123C22×C4⋊C4C2311yescharacteristic
124C22×C4⋊C4C2311yescharacteristic
125C22×C4⋊C4C2311yescharacteristic
126C22×C4⋊C4C2311yescharacteristic
127C22×C4⋊C4C2311yescharacteristic
128C22×C4⋊C4C2311yescharacteristic
129C22×C4⋊C4C2312yes—
130C22×C4⋊C4C2312yes—
131C22×C4⋊C4C2312yes—
132C22×C4⋊C4C2312yes—
133C22×C4⋊C4C2312yes—
134C22×C4⋊C4C2312yes—
135C22×C4⋊C4C2311yescharacteristic
136C22×C4⋊C4C2311yescharacteristic
137C22×C22⋊C4C2312yes—
138C22×C22⋊C4C2312yes—
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2312yes—
147C22×C22⋊C4C2312yes—
148C22×C22⋊C4C2312yes—
149C22×C22⋊C4C2312yes—
150C22×C42C2312yes—
151C22×C42C2311yescharacteristic
152C22×C42C2311yescharacteristic
153C22×C42C2311yescharacteristic
154C22×C42C2312yes—
155C22×C42C2312yes—
156C22×C42C2311yescharacteristic
157C22×C42C2312yes—
158C22×C42C2312yes—
159C22×C42C2312yes—
160C22×C42C2311yescharacteristic
161#399C2×C4116yescomplemented
162#395C2×C418yescomplemented
163#395C2×C418yescomplemented
164#394C2×C418yes—
165#394C2×C418yes—
166#393C2×C4116yescomplemented
167#391—28no—
168#391—28no—
169#391—44no—
170#391—42no—
171#391—42no—
172#390—44no—
173#389—44no—
174#388—28no—
175#388—28no—
176#388—44no—
177#388C2×C4116yescomplemented
178#388C2×C4116yescomplemented
179#387—28no—
180#387—28no—
181#387—44no—
182#386—28no—
183#385—28no—
184#385—28no—
185#385—44no—
186#385—44no—
187#384—24no—
188#383C2×C418yescomplemented
189#382—24no—
190#382—24no—
191#382D418yes—
192C4×C4⋊C4—24no—
193C4×C4⋊C4—24no—
194C4×C4⋊C4—24no—
195C4×C4⋊C4—24no—
196C4×C4⋊C4—28no—
197C4×C22⋊C4—44no—
198C2×#95C2312yes—
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—
235C2×#95C2311yescharacteristic
236C2×#95C2311yescharacteristic
237C2×#95C2312yes—
238C2×#95C2312yes—
239C2×#95C2312yes—
240C25C2412yes—
241C22×Q8—22no—
242C22×Q8—22no—
243C22×Q8—22no—
244C22×Q8—22no—
245C22×Q8—22no—
246C22×Q8—22no—
247C22×Q8—41no—
248C22×Q8—41no—
249C22×Q8—42no—
250C22×Q8—42no—
251C22×Q8C22×C414yes—
252C22×Q8C22×C414yes—
253C22×D4—22no—
254C22×D4—22no—
255C22×D4—42no—
256C22×D4—42no—
257C22×D4C22×C414yes—
258C23×C4—24no—
259C23×C4—42no—
260C23×C4—42no—
261C23×C4—42no—
262C23×C4—42no—
263C23×C4—42no—
264C23×C4—42no—
265C23×C4C2412yes—
266C23×C4C2412yes—
267C23×C4C2412yes—
268C23×C4C2412yes—
269C23×C4C2411yescharacteristic
270C23×C4C2411yescharacteristic
271C23×C4C2412yes—
272C23×C4C2412yes—
273C23×C4C2412yes—
274C23×C4C2411yescharacteristic
275C23×C4C2412yes—
276C23×C4C2412yes—
277C23×C4C2412yes—
278C23×C4C2412yes—
279C23×C4C2411yescharacteristic
280C23×C4C2411yescharacteristic
281C23×C4C2411yescharacteristic
282C23×C4C2411yescharacteristic
283#124—232no—
284C4×Q8—232no—
285C2×C4⋊C4—22no—
286C2×C4⋊C4—22no—
287C2×C4⋊C4—22no—
288C2×C4⋊C4—22no—
289C2×C4⋊C4—22no—
290C2×C4⋊C4—22no—
291C2×C4⋊C4—22no—
292C2×C4⋊C4—24no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4—24no—
295C2×C4⋊C4—24no—
296C2×C4⋊C4—24no—
297C2×C4⋊C4—24no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—22no—
300C2×C4⋊C4—24no—
301C2×C4⋊C4—24no—
302C2×C4⋊C4—42no—
303C2×C4⋊C4—42no—
304C2×C4⋊C4—42no—
305C2×C4⋊C4—42no—
306C2×C4⋊C4—42no—
307C2×C4⋊C4—42no—
308C2×C4⋊C4—42no—
309C2×C4⋊C4—42no—
310C2×C4⋊C4—42no—
311C2×C4⋊C4—41no—
312C2×C4⋊C4—41no—
313C2×C4⋊C4—42no—
314C2×C4⋊C4—42no—
315C2×C4⋊C4—42no—
316C2×C4⋊C4—42no—
317C2×C4⋊C4—42no—
318C2×C4⋊C4—42no—
319C2×C4⋊C4—42no—
320C2×C4⋊C4—42no—
321C2×C4⋊C4—42no—
322C2×C4⋊C4—42no—
323C2×C4⋊C4—41no—
324C2×C4⋊C4—41no—
325C2×C4⋊C4C22×C414yes—
326C2×C4⋊C4C22×C414yes—
327C2×C4⋊C4C22×C414yes—
328C2×C4⋊C4C22×C418yes—
329C2×C4⋊C4C22×C418yes—
330C2×C4⋊C4C2×D414yes—
331C2×C4⋊C4C2×D414yes—
332C2×C22⋊C4—24no—
333C2×C22⋊C4—24no—
334C2×C22⋊C4—24no—
335C2×C22⋊C4—24no—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—24no—
338C2×C22⋊C4—24no—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—24no—
341C2×C22⋊C4—24no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—42no—
346C2×C22⋊C4—42no—
347C2×C22⋊C4—42no—
348C2×C22⋊C4—42no—
349C2×C22⋊C4—42no—
350C2×C22⋊C4—42no—
351C2×C22⋊C4—42no—
352C2×C22⋊C4—42no—
353C2×C22⋊C4—42no—
354C2×C22⋊C4—42no—
355C2×C22⋊C4—42no—
356C2×C22⋊C4—42no—
357C2×C22⋊C4—42no—
358C2×C22⋊C4—42no—
359C2×C22⋊C4—42no—
360C2×C22⋊C4—42no—
361C2×C22⋊C4—42no—
362C2×C22⋊C4—42no—
363C2×C22⋊C4—42no—
364C2×C22⋊C4—42no—
365C2×C22⋊C4C22×C418yes—
366C2×C22⋊C4C22×C418yes—
367C2×C22⋊C4C22×C418yes—
368C2×C22⋊C4C22×C418yes—
369C2×C22⋊C4C22×C418yes—
370C2×C22⋊C4C22×C418yes—
371C2×C42—22no—
372C2×C42—22no—
373C2×C42—22no—
374C2×C42—22no—
375C2×C42—24no—
376C2×C42—24no—
377C2×C42—24no—
378C2×C42—24no—
379C2×C42—24no—
380C2×C42—22no—
381C2×C42—22no—
382C2×C42—24no—
383C2×C42—42no—
384C2×C42—42no—
385C2×C42—42no—
386C2×C42—42no—
387C2×C42—42no—
388C2×C42—42no—
389C2×C42—41no—
390C2×C42—41no—
391C2×C42—41no—
392C2×C42—41no—
393C2×C42—42no—
394C2×C42—42no—
395C2×C42—42no—
396C2×C42—42no—
397C2×C42—42no—
398C2×C42—42no—
399C2×C42C22×C414yes—
400C2×C42C22×C414yes—
401C2×C42C22×C414yes—
402C2×C42C2×D414yes—
403C2×C42#4114yes—
404#95—24no—
405#95—24no—
406#95—24no—
407#95—24no—
408#95—24no—
409#95—24no—
410#95—24no—
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—24no—
420#95—24no—
421#95—24no—
422#95—24no—
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#95C22×C418yes—
439#95C22×C418yes—
440#95C22×C414yes—
441#95C22×C414yes—
442#95C22×C418yes—
443#95C22×C418yes—
444#95C2×D418yes—
445#95C2×D418yes—
446C24—22no—
447C24—22no—
448C24—22no—
449C24—22no—
450C24—22no—
451C24—22no—
452C24—22no—
453C24—22no—
454C24—22no—
455C24—22no—
456C24—22no—
457C24—22no—
458C24—22no—
459C24—22no—
460C24C23×C414yes—
461C24C2511yescharacteristic
462C2×Q8—28no—
463C2×Q8—28no—
464C2×Q8—28no—
465C2×Q8—44no—
466C2×Q8—48no—
467C2×Q8—44no—
468C2×Q8—44no—
469C2×Q8—44no—
470C2×Q8—44no—
471C2×Q8—84no—
472C2×Q8—82no—
473C2×Q8—82no—
474C2×D4—28no—
475C2×D4—48no—
476C2×D4—84no—
477C2×D4—82no—
478C2×D4—82no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—22no—
482C22×C4—21no—
483C22×C4—22no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—22no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—22no—
491C22×C4—21no—
492C22×C4—22no—
493C22×C4—21no—
494C22×C4—22no—
495C22×C4—21no—
496C22×C4—22no—
497C22×C4—21no—
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—21no—
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—21no—
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—21no—
545C22×C4—21no—
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—22no—
574C22×C4—22no—
575C22×C4—48no—
576C22×C4—84no—
577C22×C4—84no—
578C22×C4—84no—
579C22×C4—84no—
580C22×C4—84no—
581C22×C4—84no—
582C22×C4C23×C414yes—
583C22×C4C23×C414yes—
584C22×C4C23×C412yes—
585C22×C4C23×C414yes—
586C22×C4C23×C412yes—
587C22×C4C23×C412yes—
588C22×C4C23×C412yes—
589C22×C4C23×C412yes—
590C22×C4C23×C412yes—
591C22×C4C23×C412yes—
592C22×C4C22×D414yes—
593C22×C4C22×D414yes—
594C22×C4C22×D412yes—
595C22×C4C22×D412yes—
596C22×C4C22×D412yes—
597C22×C4C2×#4112yes—
598C22×C4C2×#4112yes—
599C22×C4C2×#4112yes—
600C22×C4H(5,𝔽2)14yes—
601C22×C4H(5,𝔽2)12yes—
602C22×C42−1+414yes—
603C22×C42−1+412yes—
604C4⋊C4—28no—
605C4⋊C4—28no—
606C4⋊C4—28no—
607C4⋊C4—28no—
608C4⋊C4—48no—
609C4⋊C4—48no—
610C4⋊C4—44no—
611C4⋊C4—44no—
612C4⋊C4—48no—
613C4⋊C4—48no—
614C4⋊C4—44no—
615C4⋊C4—82no—
616C4⋊C4—82no—
617C4⋊C4—84no—
618C4⋊C4—84no—
619C4⋊C4—84no—
620C4⋊C4—84no—
621C22⋊C4—216no—
622C22⋊C4—216no—
623C22⋊C4—216no—
624C22⋊C4—48no—
625C22⋊C4—48no—
626C22⋊C4—48no—
627C22⋊C4—48no—
628C22⋊C4—84no—
629C22⋊C4—84no—
630C22⋊C4—84no—
631C22⋊C4—84no—
632C22⋊C4—84no—
633C22⋊C4—84no—
634C42—28no—
635C42—28no—
636C42—48no—
637C42—82no—
638C42—82no—
639C42—84no—
640C42—84no—
641C42—84no—
642C42—84no—
643C42—84no—
644C42C4×D4116yes—
645C23—24no—
646C23—24no—
647C23—24no—
648C23—24no—
649C23—24no—
650C23—24no—
651C23—24no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23C24×C411yescharacteristic
681C23C23×D411yescharacteristic
682C23C22×#4111yescharacteristic
683C23C2×H(5,𝔽2)11yescharacteristic
684C23C2×H(5,𝔽2)12yes—
685C23C2×2−1+411yescharacteristic
686C23C2×2−1+412yes—
687C23#58511yescharacteristic
688C23#58511yescharacteristic
689C23#58512yes—
690C23#58512yes—
691Q8—416no—
692Q8—88no—
693D4—88no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—24no—
699C2×C4—24no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—24no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—24no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—24no—
718C2×C4—24no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—24no—
722C2×C4—24no—
723C2×C4—24no—
724C2×C4—24no—
725C2×C4—24no—
726C2×C4—24no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—24no—
731C2×C4—24no—
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—41no—
743C2×C4—42no—
744C2×C4—41no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—41no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—41no—
752C2×C4—42no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—41no—
758C2×C4—41no—
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—42no—
769C2×C4—42no—
770C2×C4—42no—
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—816no—
809C2×C4C2×C4×D414yes—
810C2×C4C2×C4×D414yes—
811C2×C4C2×C4×D414yes—
812C2×C4#52014yes—
813C22—44no—
814C22—44no—
815C22—44no—
816C22—44no—
817C22—44no—
818C22—44no—
819C22—44no—
820C22—82no—
821C22—82no—
822C22—82no—
823C22—82no—
824C22—82no—
825C22—82no—
826C22—82no—
827C22—82no—
828C22C22×C4×D411yescharacteristic
829C22C2×#52011yescharacteristic
830C22#342811yescharacteristic
831C22C4×H(5,𝔽2)12yes—
832C22C4×2−1+412yes—
833C22#348511yescharacteristic
834C22#348611yescharacteristic
835C22#348811yescharacteristic
836C22#348911yescharacteristic
837C22#349412yes—
838C22#349411yescharacteristic
839C22#349511yescharacteristic
840C22#349811yescharacteristic
841C22#350011yescharacteristic
842C22#350712yes—
843C22#353512yes—
844C22#354012yes—
845C22#355212yes—
846C22#355412yes—
847C22#355812yes—
848C22#356512yes—
849C22#356512yes—
850C22#356612yes—
851C4—24no—
852C4—24no—
853C4—24no—
854C4—24no—
855C4—44no—
856C4—44no—
857C4—44no—
858C4—42no—
859C4—44no—
860C4—44no—
861C4—42no—
862C4—42no—
863C4—44no—
864C4—44no—
865C4—82no—
866C4—82no—
867C4—82no—
868C4—82no—
869C2—84no—
870C2#3420211yescharacteristic
871C2#3426611yescharacteristic
872C2#3427511yescharacteristic
873C2#3442812yes—
874C2#3444012yes—
875C2#5067112yes—
876C2#5069011yescharacteristic
877C2#5069611yescharacteristic
878C2#5089411yescharacteristic
879C2#5089611yescharacteristic
880C2#5147912yes—
subgroupG/H
center, Frattini, socle, cosocleC24C25
commutatorC23C24×C4
prime radicalC23×D4C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
3. C2×#2355C2semidirect
4. #14578C2semidirect
5. #14575C2semidirect
7. #14524C2semidirect
8. #14405C2semidirect
9. #14399C2semidirect
10. #14298C2semidirect
11. #14232C2semidirect
12. #14230C2semidirect
13. #14214C2semidirect
16. #14125C2semidirect
17. #14032C2semidirect
18. #13942C2semidirect
19. #13781C2semidirect
22. #2632C4semidirect
119. C2×C4×Q8C2×C4semidirect
161. #399C2×C4semidirect
162. #395C2×C4semidirect
163. #395C2×C4semidirect
166. #393C2×C4semidirect
177. #388C2×C4semidirect
178. #388C2×C4semidirect
188. #383C2×C4semidirect

Maximal subgroups

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

subgroupindex
C2×#26322
C2×#23792
C2×#23552
#145782
#145752
#145362
#145242
#144052
#143992
#142982
#142322
#142302
#142142
#141952
#141532
#141252
#140322
#139422
#137812