Finite Group Databasebeta

← #1011784

Subgroups — #1011784

Order 512.

2430 conjugacy classes of subgroups.

The subgroup lattice has 913 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2476C212yesmaximal
2#17186C212yesmaximal, complemented
3#17036C211yesmaximal, characteristic, complemented
4#16596C211yesmaximal, characteristic, complemented
5#16527C212yesmaximal, complemented
6#16309C212yesmaximal, complemented
7#15863C212yesmaximal, complemented
8#15502C212yesmaximal, complemented
9#15344C212yesmaximal, complemented
10#14983C212yesmaximal, complemented
11#14907C211yesmaximal, characteristic, complemented
12#14784C212yesmaximal, complemented
13#14590C211yesmaximal, characteristic, complemented
14#14440C211yesmaximal, characteristic, complemented
15#14202C212yesmaximal, complemented
16#14136C211yesmaximal, characteristic
17#14072C212yesmaximal, complemented
18#14063C212yesmaximal, complemented
19#13852C211yesmaximal, characteristic, complemented
20C22×#121C2211yescharacteristic
21C22×#117C2211yescharacteristic
22C22×#117C2212yes—
23#2476—216no—
24C2×#398C2211yescharacteristic
25C2×#398C2212yes—
26C2×#397C2212yes—
27C2×#397C2211yescharacteristic
28C2×#397C2212yes—
29C2×#394C2212yes—
30C2×#394C2212yes—
31C2×#394C2212yes—
32C2×#390C2211yescharacteristic
33C2×#390C2212yes—
34C2×#390C2211yescharacteristic
35C2×#389C2211yescharacteristic
36C2×#388C2212yes—
37C2×#388C2212yes—
38C2×#388C2212yes—
39C2×#387C2212yes—
40C2×#387C2212yes—
41C2×#386C2212yes—
42C2×#386C2212yes—
43C2×#385C2212yes—
44C2×#385C2212yes—
45C2×#385C2212yes—
46C2×C4×C4⋊C4C2211yescharacteristic
47C2×C4×C4⋊C4C2211yescharacteristic
48C2×C4×C22⋊C4C2212yes—
49C2×C4×C22⋊C4C2211yescharacteristic
50#1445C2212yes—
51#1445C2212yes—
52#1445C2212yes—
53#1444C2212yes—
54#1444C2212yes—
55#1443C2212yes—
56#1443C2212yes—
57#1442C2212yes—
58#1441C2211yescharacteristic
59#1441C2211yescharacteristic
60#1441C2212yes—
61#1441C2212yes—
62#1441C2211yescharacteristic
63#1441C2212yes—
64#1441C2212yes—
65#1441C2212yes—
66#1441C2212yes—
67#1440C2212yes—
68#1440C2212yes—
69#1440C2212yes—
70#1440C2212yes—
71#1440C2212yes—
72#1440C2212yes—
73#1440C2212yes—
74#1440C2212yes—
75#1440C2212yes—
76#1439C2211yescharacteristic
77#1439C2212yes—
78#1439C2211yescharacteristic
79#1439C2212yes—
80#1439C2212yes—
81#1439C2212yes—
82#1439C2211yescharacteristic
83#1439C2212yes—
84#1439C2212yes—
85#1439C2212yes—
86#1438C2212yes—
87#1438C2212yes—
88#1437C2212yes—
89#1437C2212yes—
90#1436C2212yes—
91#1436C2212yes—
92#1436C2212yes—
93#1436C2212yes—
94#1436C2212yes—
95#1436C2212yes—
96#1436C2212yes—
97#1436C2212yes—
98#1436C2212yes—
99C4⋊#95C2211yescharacteristic
100C4⋊#95C2211yescharacteristic
101C4⋊#95C2212yes—
102#1434C2211yescharacteristic
103#1434C2212yes—
104#1434C2212yes—
105C22⋊#95C2212yes—
106C22⋊#95C2212yes—
107C4×#95C2212yes—
108C23×D4C2311yescharacteristic
109C23×D4C2312yes—
110C24×C4C2311yescharacteristic
111C24×C4C2312yes—
112C2×#121—42no—
113C2×#121—42no—
114C2×#121D418yes—
115C2×#117—24no—
116C2×#117—28no—
117C2×#117—42no—
118C2×#117—42no—
119C2×#117—44no—
120C2×#117—44no—
121C22×C4⋊C4C2312yes—
122C22×C4⋊C4C2312yes—
123C22×C4⋊C4C2311yescharacteristic
124C22×C4⋊C4C2311yescharacteristic
125C22×C4⋊C4C2311yescharacteristic
126C22×C4⋊C4C2312yes—
127C22×C4⋊C4C2312yes—
128C22×C4⋊C4C2311yescharacteristic
129C22×C4⋊C4C2312yes—
130C22×C4⋊C4C2312yes—
131C22×C4⋊C4C2312yes—
132C22×C4⋊C4C2311yescharacteristic
133C22×C4⋊C4C2311yescharacteristic
134C22×C4⋊C4C2312yes—
135C22×C4⋊C4C2311yescharacteristic
136C22×C22⋊C4C2312yes—
137C22×C22⋊C4C2312yes—
138C22×C22⋊C4C2311yescharacteristic
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×C22⋊C4C2312yes—
151C22×C22⋊C4C2312yes—
152C22×C22⋊C4C2312yes—
153C22×C22⋊C4C2311yescharacteristic
154C22×C22⋊C4C2312yes—
155C22×C42C2312yes—
156C22×C42C2311yescharacteristic
157C22×C42C2311yescharacteristic
158C22×C42C2312yes—
159C22×C42C2312yes—
160C22×C42C2311yescharacteristic
161C22×C42C2311yescharacteristic
162#398—28no—
163#398—24no—
164#397—28no—
165#397—42no—
166#397—44no—
167#394—28no—
168#394—28no—
169#394—28no—
170#390—28no—
171#390—24no—
172#390—42no—
173#389—42no—
174#388—28no—
175#388—28no—
176#388—28no—
177#387—28no—
178#387—44no—
179#386—28no—
180#386—28no—
181#385—28no—
182#385—28no—
183#385—28no—
184C4×C4⋊C4—42no—
185C4×C4⋊C4—42no—
186C4×C22⋊C4—28no—
187C4×C22⋊C4—42no—
188C2×#95C2312yes—
189C2×#95C2312yes—
190C2×#95C2312yes—
191C2×#95C2312yes—
192C2×#95C2312yes—
193C2×#95C2312yes—
194C2×#95C2312yes—
195C2×#95C2312yes—
196C2×#95C2311yescharacteristic
197C2×#95C2312yes—
198C2×#95C2312yes—
199C2×#95C2312yes—
200C2×#95C2312yes—
201C2×#95C2312yes—
202C2×#95C2312yes—
203C2×#95C2312yes—
204C2×#95C2312yes—
205C2×#95C2312yes—
206C2×#95C2312yes—
207C2×#95C2312yes—
208C2×#95C2311yescharacteristic
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×#95C2311yescharacteristic
229C2×#95C2311yescharacteristic
230C25C2411yescharacteristic
231C25C2412yes—
232C22×D4—22no—
233C22×D4—22no—
234C22×D4—41no—
235C22×D4—41no—
236C22×D4—42no—
237C22×D4—42no—
238C22×D4—41no—
239C22×D4—42no—
240C22×D4—42no—
241C22×D4—42no—
242C22×D4—42no—
243C22×D4—41no—
244C22×D4C2×D414yes—
245C22×D4C2×D418yes—
246C23×C4—22no—
247C23×C4—22no—
248C23×C4—22no—
249C23×C4—22no—
250C23×C4—24no—
251C23×C4—24no—
252C23×C4—24no—
253C23×C4—41no—
254C23×C4—42no—
255C23×C4—42no—
256C23×C4—41no—
257C23×C4—42no—
258C23×C4—42no—
259C23×C4C2×D414yes—
260C23×C4C2412yes—
261C23×C4C2412yes—
262C23×C4C2412yes—
263C23×C4C2412yes—
264C23×C4C2412yes—
265C23×C4C2412yes—
266C23×C4C2411yescharacteristic
267C23×C4C2412yes—
268C23×C4C2412yes—
269C23×C4C2411yescharacteristic
270C23×C4C2411yescharacteristic
271C23×C4C2412yes—
272C23×C4C2412yes—
273C23×C4C2412yes—
274C23×C4C2411yescharacteristic
275C23×C4C2411yescharacteristic
276C23×C4C2411yescharacteristic
277#121—416no—
278#117—416no—
279#117—432no—
280C2×C4⋊C4—24no—
281C2×C4⋊C4—24no—
282C2×C4⋊C4—24no—
283C2×C4⋊C4—22no—
284C2×C4⋊C4—24no—
285C2×C4⋊C4—24no—
286C2×C4⋊C4—24no—
287C2×C4⋊C4—24no—
288C2×C4⋊C4—24no—
289C2×C4⋊C4—22no—
290C2×C4⋊C4—24no—
291C2×C4⋊C4—24no—
292C2×C4⋊C4—24no—
293C2×C4⋊C4—24no—
294C2×C4⋊C4—22no—
295C2×C4⋊C4—42no—
296C2×C4⋊C4—42no—
297C2×C4⋊C4—42no—
298C2×C4⋊C4—42no—
299C2×C4⋊C4—41no—
300C2×C4⋊C4—41no—
301C2×C4⋊C4—41no—
302C2×C4⋊C4—42no—
303C2×C4⋊C4—42no—
304C2×C4⋊C4—41no—
305C2×C4⋊C4—41no—
306C2×C4⋊C4—41no—
307C2×C4⋊C4—41no—
308C2×C4⋊C4—42no—
309C2×C4⋊C4—41no—
310C2×C4⋊C4—42no—
311C2×C4⋊C4—42no—
312C2×C4⋊C4—42no—
313C2×C4⋊C4—42no—
314C2×C4⋊C4—42no—
315C2×C4⋊C4—42no—
316C2×C4⋊C4—42no—
317C2×C4⋊C4—41no—
318C2×C4⋊C4—41no—
319C2×C4⋊C4C2×D414yes—
320C2×C4⋊C4#4114yes—
321C2×C4⋊C4#4118yes—
322C2×C22⋊C4—24no—
323C2×C22⋊C4—24no—
324C2×C22⋊C4—24no—
325C2×C22⋊C4—24no—
326C2×C22⋊C4—24no—
327C2×C22⋊C4—24no—
328C2×C22⋊C4—24no—
329C2×C22⋊C4—24no—
330C2×C22⋊C4—22no—
331C2×C22⋊C4—22no—
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—22no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—24no—
346C2×C22⋊C4—24no—
347C2×C22⋊C4—24no—
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—41no—
358C2×C22⋊C4—41no—
359C2×C22⋊C4—41no—
360C2×C22⋊C4—42no—
361C2×C22⋊C4—42no—
362C2×C22⋊C4—42no—
363C2×C22⋊C4—42no—
364C2×C22⋊C4—42no—
365C2×C22⋊C4—42no—
366C2×C22⋊C4—42no—
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⋊C4—42no—
374C2×C22⋊C4—42no—
375C2×C22⋊C4—42no—
376C2×C22⋊C4—42no—
377C2×C22⋊C4—42no—
378C2×C22⋊C4C2×D418yes—
379C2×C42—22no—
380C2×C42—22no—
381C2×C42—22no—
382C2×C42—24no—
383C2×C42—24no—
384C2×C42—22no—
385C2×C42—24no—
386C2×C42—24no—
387C2×C42—22no—
388C2×C42—24no—
389C2×C42—22no—
390C2×C42—22no—
391C2×C42—41no—
392C2×C42—42no—
393C2×C42—42no—
394C2×C42—41no—
395C2×C42—41no—
396C2×C42—42no—
397C2×C42—41no—
398C2×C42—42no—
399C2×C42—41no—
400#95—24no—
401#95—24no—
402#95—24no—
403#95—24no—
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—22no—
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—41no—
434#95—41no—
435#95—42no—
436#95—42no—
437#95—42no—
438#95—42no—
439#95—41no—
440#95—42no—
441#95—42no—
442C24—22no—
443C24—21no—
444C24—22no—
445C24—22no—
446C24—22no—
447C24—21no—
448C24—22no—
449C24—22no—
450C24—22no—
451C24—21no—
452C24—21no—
453C24—21no—
454C24—22no—
455C24—22no—
456C24—22no—
457C24—22no—
458C24—21no—
459C24—22no—
460C24—22no—
461C24—22no—
462C24—22no—
463C24—22no—
464C24—22no—
465C24—22no—
466C24C22×D412yes—
467C24C22×D414yes—
468C24C2511yescharacteristic
469C2×D4—28no—
470C2×D4—44no—
471C2×D4—48no—
472C2×D4—44no—
473C2×D4—48no—
474C2×D4—48no—
475C2×D4—82no—
476C2×D4—82no—
477C2×D4—82no—
478C2×D4—82no—
479C2×D4—84no—
480C2×D4—84no—
481C2×D4—84no—
482C2×D4—84no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
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—22no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—21no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—21no—
508C22×C4—21no—
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—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—28no—
528C22×C4—28no—
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—21no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—21no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—21no—
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—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—44no—
584C22×C4—44no—
585C22×C4—44no—
586C22×C4—44no—
587C22×C4—44no—
588C22×C4—48no—
589C22×C4—48no—
590C22×C4—48no—
591C22×C4—48no—
592C22×C4—48no—
593C22×C4—48no—
594C22×C4—48no—
595C22×C4C22×D414yes—
596C22×C4C22×D412yes—
597C22×C4C22×D412yes—
598C22×C4C2×#4114yes—
599C22×C4C2×#4112yes—
600C22×C4C2×#4114yes—
601C22×C4C2×#4114yes—
602C22×C4C2×#4112yes—
603C22×C4C2×#4112yes—
604C22×C4H(5,𝔽2)12yes—
605C22×C4H(5,𝔽2)12yes—
606C22×C4H(5,𝔽2)12yes—
607C22×C42−1+412yes—
608C4⋊C4—44no—
609C4⋊C4—48no—
610C4⋊C4—44no—
611C4⋊C4—44no—
612C4⋊C4—44no—
613C4⋊C4—44no—
614C4⋊C4—48no—
615C4⋊C4—48no—
616C4⋊C4—44no—
617C4⋊C4—48no—
618C4⋊C4—48no—
619C4⋊C4—84no—
620C4⋊C4—84no—
621C4⋊C4—82no—
622C4⋊C4—84no—
623C22⋊C4—216no—
624C22⋊C4—48no—
625C22⋊C4—48no—
626C22⋊C4—44no—
627C22⋊C4—48no—
628C22⋊C4—48no—
629C22⋊C4—48no—
630C22⋊C4—48no—
631C22⋊C4—48no—
632C22⋊C4—44no—
633C22⋊C4—48no—
634C22⋊C4—48no—
635C22⋊C4—84no—
636C22⋊C4—84no—
637C22⋊C4—84no—
638C22⋊C4—84no—
639C22⋊C4—84no—
640C22⋊C4—84no—
641C22⋊C4—84no—
642C42—28no—
643C42—44no—
644C42—48no—
645C42—48no—
646C42—82no—
647C42—84no—
648C42—82no—
649C23—24no—
650C23—22no—
651C23—22no—
652C23—24no—
653C23—24no—
654C23—24no—
655C23—24no—
656C23—24no—
657C23—24no—
658C23—24no—
659C23—22no—
660C23—24no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—41no—
669C23—41no—
670C23—42no—
671C23—41no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—41no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—41no—
691C23—42no—
692C23—41no—
693C23—42no—
694C23—41no—
695C23—42no—
696C23—41no—
697C23—42no—
698C23—42no—
699C23—42no—
700C23—42no—
701C23—42no—
702C23—42no—
703C23—42no—
704C23—42no—
705C23—42no—
706C23—42no—
707C23C23×D411yescharacteristic
708C23C22×#4112yes—
709C23C22×#4111yescharacteristic
710C23C2×H(5,𝔽2)11yescharacteristic
711C23C2×H(5,𝔽2)11yescharacteristic
712C23C2×H(5,𝔽2)11yescharacteristic
713C23C2×2−1+411yescharacteristic
714C23#58512yes—
715C23#58512yes—
716C23#58512yes—
717C23#58511yescharacteristic
718D4—88no—
719D4—816no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
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—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—24no—
749C2×C4—24no—
750C2×C4—416no—
751C2×C4—432no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—41no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—42no—
771C2×C4—41no—
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—41no—
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—41no—
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—41no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—42no—
830C2×C4—42no—
831C2×C4#53414yes—
832C2×C4#54714yes—
833C22—44no—
834C22—44no—
835C22—44no—
836C22—42no—
837C22—44no—
838C22—44no—
839C22—42no—
840C22—42no—
841C22—44no—
842C22—44no—
843C22—44no—
844C22—44no—
845C22—82no—
846C22—81no—
847C22—82no—
848C22—82no—
849C22—82no—
850C22—82no—
851C22—81no—
852C22—82no—
853C22—82no—
854C22—82no—
855C22—82no—
856C22—81no—
857C22—81no—
858C22—82no—
859C22C2×#53411yescharacteristic
860C22#345912yes—
861C22C2×#54711yescharacteristic
862C22D4×#4112yes—
863C22#347512yes—
864C22#348111yescharacteristic
865C22#348512yes—
866C22#349011yescharacteristic
867C22#349411yescharacteristic
868C22#349611yescharacteristic
869C22#351212yes—
870C22#351712yes—
871C22#351812yes—
872C22#352412yes—
873C22#352911yescharacteristic
874C22#353312yes—
875C22#353511yescharacteristic
876C22#353611yescharacteristic
877C22#354011yescharacteristic
878C22#355111yescharacteristic
879C22#356212yes—
880C22#356512yes—
881C22#356612yes—
882C4—24no—
883C4—24no—
884C4—44no—
885C4—42no—
886C4—42no—
887C4—44no—
888C4—42no—
889C4—44no—
890C4—44no—
891C4—82no—
892C4—82no—
893C4—82no—
894C4—82no—
895C4—82no—
896C4—81no—
897C4—82no—
898C4—82no—
899C2—82no—
900C2—84no—
901C2#3786011yescharacteristic
902C2#3870512yes—
903C2#4214012yes—
904C2#4267311yescharacteristic
905C2#4392212yes—
906C2#4483411yescharacteristic
907C2#4627511yescharacteristic
908C2#5216311yescharacteristic
909C2#5290111yescharacteristic
910C2#5911912yes—
911C2#5997311yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC22×#121C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #17186C2semidirect
3. #17036C2semidirect
4. #16596C2semidirect
5. #16527C2semidirect
6. #16309C2semidirect
7. #15863C2semidirect
8. #15502C2semidirect
9. #15344C2semidirect
10. #14983C2semidirect
11. #14907C2semidirect
12. #14784C2semidirect
13. #14590C2semidirect
14. #14440C2semidirect
15. #14202C2semidirect
17. #14072C2semidirect
18. #14063C2semidirect
19. #13852C2semidirect

Maximal subgroups

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

subgroupindex
C2×#24762
#171862
#170362
#165962
#165272
#163092
#158632
#155022
#153442
#149832
#149072
#147842
#145902
#144402
#142022
#141362
#140722
#140632
#138522