Finite Group Databasebeta

← #847195

Subgroups — #847195

Order 512.

2962 conjugacy classes of subgroups.

The subgroup lattice has 964 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2493C211yesmaximal, characteristic
2C22×#391C211yesmaximal, characteristic
3#16390C212yesmaximal, complemented
4#16281C212yesmaximal, complemented
5#15963C212yesmaximal, complemented
6#15852C212yesmaximal, complemented
7#15690C212yesmaximal, complemented
8#15624C212yesmaximal, complemented
9#15073C211yesmaximal, characteristic
10#15019C211yesmaximal, characteristic
11#14935C211yesmaximal, characteristic
12#14935C211yesmaximal, characteristic
13#14919C211yesmaximal, characteristic
14#14874C211yesmaximal, characteristic
15#14697C211yesmaximal, characteristic
16#14695C211yesmaximal, characteristic
17#14538C212yesmaximal, complemented
18#14380C212yesmaximal, complemented
19#13992C211yesmaximal, characteristic
20#13962C211yesmaximal, characteristic
21#13922C211yesmaximal, characteristic
22#13878C211yesmaximal, characteristic
23#13870C211yesmaximal, characteristic
24C24×Q8C2211yescharacteristic
25C22×#117C2211yescharacteristic
26C23×C4⋊C4C2211yescharacteristic
27C23×C42C2211yescharacteristic
28#2493—28no—
29C2×#401C2211yescharacteristic
30C2×#400C2211yescharacteristic
31C2×#400C2211yescharacteristic
32C2×#400C2211yescharacteristic
33C2×#395C2212yes—
34C2×#395C2212yes—
35C2×#391—28no—
36C2×#391C2212yes—
37C2×#391C2212yes—
38C2×#391C2212yes—
39C2×#391C2212yes—
40C2×#391C2212yes—
41C2×#391C2212yes—
42C2×#389C2212yes—
43C2×#387C2211yescharacteristic
44C2×#387C2211yescharacteristic
45C2×#387C2211yescharacteristic
46C2×#387C2212yes—
47C2×#385C2211yescharacteristic
48C2×#385C2211yescharacteristic
49C2×#385C2211yescharacteristic
50C2×#385C2211yescharacteristic
51C2×#385C2211yescharacteristic
52C2×#385C2211yescharacteristic
53C2×#383C2211yescharacteristic
54C2×#381C2211yescharacteristic
55C2×#381C2211yescharacteristic
56C2×#381C2211yescharacteristic
57C2×#381C2211yescharacteristic
58C2×#381C2211yescharacteristic
59C2×#381C2211yescharacteristic
60C2×#381C2211yescharacteristic
61C2×#380C2211yescharacteristic
62C2×#380C2211yescharacteristic
63C2×#380C2211yescharacteristic
64C2×C4×C22⋊C4C2211yescharacteristic
65C22×#95C2211yescharacteristic
66C22×#95C2211yescharacteristic
67C22×#95C2211yescharacteristic
68C22×#95C2211yescharacteristic
69#1446C2212yes—
70#1446C2212yes—
71#1446C2212yes—
72#1446C2212yes—
73#1445C2212yes—
74#1445C2212yes—
75#1444C2212yes—
76#1443C2212yes—
77#1443C2212yes—
78#1443C2212yes—
79#1443C2212yes—
80#1443C2212yes—
81#1443C2212yes—
82#1443C2212yes—
83#1442C2212yes—
84#1442C2212yes—
85#1442C2212yes—
86#1442C2212yes—
87#1442C2212yes—
88#1442C2212yes—
89#1441C2212yes—
90#1441C2212yes—
91#1441C2212yes—
92#1441C2212yes—
93#1441C2212yes—
94#1441C2212yes—
95#1441C2212yes—
96#1441C2212yes—
97#1441C2212yes—
98#1441C2212yes—
99#1441C2212yes—
100#1441C2212yes—
101#1436C2212yes—
102#1436C2212yes—
103#1436C2212yes—
104#1436C2212yes—
105#1436C2212yes—
106#1436C2212yes—
107#1436C2212yes—
108#1436C2212yes—
109#1436C2212yes—
110C4⋊#95C2212yes—
111C4⋊#95C2212yes—
112#1434C2212yes—
113#1434C2212yes—
114#1434C2212yes—
115C22⋊#95C2211yescharacteristic
116C22⋊#95C2211yescharacteristic
117C22⋊#95C2211yescharacteristic
118C22⋊#95C2211yescharacteristic
119C22⋊#95C2211yescharacteristic
120C22⋊#95C2211yescharacteristic
121C22⋊#95C2211yescharacteristic
122C22⋊#95C2211yescharacteristic
123C22⋊#95C2211yescharacteristic
124C22⋊#95C2211yescharacteristic
125C23×Q8—28no—
126C23×Q8—24no—
127C23×Q8—24no—
128C23×Q8—42no—
129C23×Q8—44no—
130C23×Q8C2312yes—
131C23×Q8C2312yes—
132C24×C4C2311yescharacteristic
133C24×C4C2311yescharacteristic
134C24×C4C2311yescharacteristic
135C24×C4C2311yescharacteristic
136C24×C4C2311yescharacteristic
137C24×C4C2311yescharacteristic
138C24×C4C2311yescharacteristic
139C2×#117—24no—
140C2×#117—42no—
141C2×#117—42no—
142C22×C4⋊C4—24no—
143C22×C4⋊C4—24no—
144C22×C4⋊C4—42no—
145C22×C4⋊C4C2312yes—
146C22×C4⋊C4C2311yescharacteristic
147C22×C4⋊C4C2311yescharacteristic
148C22×C4⋊C4C2311yescharacteristic
149C22×C4⋊C4C2312yes—
150C22×C4⋊C4C2312yes—
151C22×C4⋊C4C2312yes—
152C22×C4⋊C4C2311yescharacteristic
153C22×C4⋊C4C2312yes—
154C22×C4⋊C4C2311yescharacteristic
155C22×C4⋊C4C2311yescharacteristic
156C22×C4⋊C4C2312yes—
157C22×C4⋊C4C2312yes—
158C22×C4⋊C4C2312yes—
159C22×C4⋊C4C2312yes—
160C22×C22⋊C4C2311yescharacteristic
161C22×C22⋊C4C2311yescharacteristic
162C22×C22⋊C4C2311yescharacteristic
163C22×C22⋊C4C2311yescharacteristic
164C22×C22⋊C4C2311yescharacteristic
165C22×C22⋊C4C2311yescharacteristic
166C22×C22⋊C4C2311yescharacteristic
167C22×C22⋊C4C2311yescharacteristic
168C22×C42—24no—
169C22×C42—44no—
170C22×C42C2311yescharacteristic
171C22×C42C2312yes—
172C22×C42C2312yes—
173C22×C42C2312yes—
174C22×C42C2311yescharacteristic
175#401—24no—
176#400—24no—
177#400—24no—
178#400—24no—
179#395—28no—
180#395—44no—
181#391—28no—
182#391—28no—
183#391—28no—
184#391—28no—
185#391—28no—
186#391—44no—
187#389—44no—
188#387—24no—
189#387—24no—
190#387—24no—
191#387—44no—
192#385—24no—
193#385—24no—
194#385—24no—
195#385—42no—
196#385—42no—
197#385—42no—
198#383—24no—
199#381—24no—
200#381—24no—
201#381—24no—
202#381—42no—
203#381—42no—
204#381—42no—
205#381—42no—
206#380—24no—
207#380—24no—
208#380—42no—
209C4×C22⋊C4—24no—
210C2×#95—24no—
211C2×#95—24no—
212C2×#95—24no—
213C2×#95D418yes—
214C2×#95C2312yes—
215C2×#95C2312yes—
216C2×#95C2312yes—
217C2×#95C2312yes—
218C2×#95C2311yescharacteristic
219C2×#95C2311yescharacteristic
220C2×#95C2311yescharacteristic
221C2×#95C2311yescharacteristic
222C2×#95C2311yescharacteristic
223C2×#95C2311yescharacteristic
224C2×#95C2311yescharacteristic
225C2×#95C2311yescharacteristic
226C2×#95C2311yescharacteristic
227C2×#95C2311yescharacteristic
228C2×#95C2311yescharacteristic
229C2×#95C2311yescharacteristic
230C2×#95C2311yescharacteristic
231C2×#95C2311yescharacteristic
232C2×#95C2311yescharacteristic
233C2×#95C2312yes—
234C2×#95C2312yes—
235C2×#95C2312yes—
236C2×#95C2312yes—
237C2×#95C2312yes—
238C2×#95C2312yes—
239C2×#95C2312yes—
240C2×#95C2312yes—
241C2×#95C2312yes—
242C2×#95C2312yes—
243C2×#95C2312yes—
244C2×#95C2312yes—
245C2×#95C2312yes—
246C2×#95C2312yes—
247C2×#95C2312yes—
248C2×#95C2312yes—
249C2×#95C2312yes—
250C2×#95C2311yescharacteristic
251C2×#95C2312yes—
252C2×#95C2312yes—
253C2×#95C2312yes—
254C2×#95C2312yes—
255C2×#95C2312yes—
256C2×#95C2312yes—
257C2×#95C2312yes—
258C2×#95C2312yes—
259C2×#95C2312yes—
260C2×#95C2312yes—
261C2×#95C2312yes—
262C2×#95C2312yes—
263C2×#95C2312yes—
264C2×#95C2312yes—
265C2×#95C2312yes—
266C2×#95C2312yes—
267C2×#95C2312yes—
268C2×#95C2312yes—
269C2×#95C2312yes—
270C2×#95C2312yes—
271C2×#95C2312yes—
272C2×#95C2311yescharacteristic
273C2×#95C2311yescharacteristic
274C2×#95C2311yescharacteristic
275C2×#95C2311yescharacteristic
276C25C2411yescharacteristic
277C22×Q8—232no—
278C22×Q8—24no—
279C22×Q8—24no—
280C22×Q8—24no—
281C22×Q8—24no—
282C22×Q8—24no—
283C22×Q8—24no—
284C22×Q8—24no—
285C22×Q8—24no—
286C22×Q8—24no—
287C22×Q8—42no—
288C22×Q8—42no—
289C22×Q8—42no—
290C22×Q8—42no—
291C22×Q8—416no—
292C22×Q8—432no—
293C22×Q8—416no—
294C22×Q8—432no—
295C22×Q8#4118yes—
296C23×C4—22no—
297C23×C4—22no—
298C23×C4—24no—
299C23×C4—24no—
300C23×C4—22no—
301C23×C4—22no—
302C23×C4—22no—
303C23×C4—22no—
304C23×C4—22no—
305C23×C4—22no—
306C23×C4—22no—
307C23×C4—22no—
308C23×C4—22no—
309C23×C4—22no—
310C23×C4—22no—
311C23×C4—22no—
312C23×C4—24no—
313C23×C4—24no—
314C23×C4—24no—
315C23×C4—24no—
316C23×C4—22no—
317C23×C4—22no—
318C23×C4—22no—
319C23×C4—22no—
320C23×C4—22no—
321C23×C4—22no—
322C23×C4—22no—
323C23×C4—22no—
324C23×C4—22no—
325C23×C4—22no—
326C23×C4—22no—
327C23×C4—42no—
328C23×C4—42no—
329C23×C4—42no—
330C23×C4—42no—
331C23×C4C2×D414yes—
332C23×C4C2×D414yes—
333C23×C4C2×D414yes—
334C23×C4#4114yes—
335C23×C4C2411yescharacteristic
336C23×C4C2411yescharacteristic
337C23×C4C2412yes—
338C23×C4C2411yescharacteristic
339C23×C4C2411yescharacteristic
340C23×C4C2411yescharacteristic
341C23×C4C2412yes—
342C23×C4C2411yescharacteristic
343C23×C4C2412yes—
344C23×C4C2411yescharacteristic
345C23×C4C2411yescharacteristic
346C23×C4C2412yes—
347C23×C4C2411yescharacteristic
348C23×C4C2411yescharacteristic
349C23×C4C2411yescharacteristic
350C23×C4C2411yescharacteristic
351C23×C4C2412yes—
352C23×C4C2412yes—
353C23×C4C2412yes—
354C23×C4C2411yescharacteristic
355C23×C4C2411yescharacteristic
356C23×C4C2412yes—
357#117—416no—
358C2×C4⋊C4—24no—
359C2×C4⋊C4—24no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—24no—
364C2×C4⋊C4—24no—
365C2×C4⋊C4—24no—
366C2×C4⋊C4—24no—
367C2×C4⋊C4—24no—
368C2×C4⋊C4—24no—
369C2×C4⋊C4—24no—
370C2×C4⋊C4—24no—
371C2×C4⋊C4—24no—
372C2×C4⋊C4—24no—
373C2×C4⋊C4—24no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—22no—
377C2×C4⋊C4—24no—
378C2×C4⋊C4—24no—
379C2×C4⋊C4—24no—
380C2×C4⋊C4—24no—
381C2×C4⋊C4—42no—
382C2×C4⋊C4—42no—
383C2×C4⋊C4—42no—
384C2×C4⋊C4—42no—
385C2×C4⋊C4—42no—
386C2×C4⋊C4—416no—
387C2×C4⋊C4—42no—
388C2×C4⋊C4—42no—
389C2×C4⋊C4—42no—
390C2×C4⋊C4—42no—
391C2×C4⋊C4—42no—
392C2×C4⋊C4—42no—
393C2×C4⋊C4—42no—
394C2×C4⋊C4—42no—
395C2×C4⋊C4—42no—
396C2×C4⋊C4—42no—
397C2×C4⋊C4—42no—
398C2×C22⋊C4—22no—
399C2×C22⋊C4—22no—
400C2×C22⋊C4—22no—
401C2×C22⋊C4—22no—
402C2×C22⋊C4—22no—
403C2×C22⋊C4—22no—
404C2×C22⋊C4—22no—
405C2×C22⋊C4—22no—
406C2×C22⋊C4—22no—
407C2×C22⋊C4—22no—
408C2×C22⋊C4—22no—
409C2×C22⋊C4—22no—
410C2×C22⋊C4—22no—
411C2×C22⋊C4—22no—
412C2×C22⋊C4—22no—
413C2×C22⋊C4—22no—
414C2×C22⋊C4—22no—
415C2×C22⋊C4—22no—
416C2×C22⋊C4—22no—
417C2×C22⋊C4—22no—
418C2×C22⋊C4—22no—
419C2×C22⋊C4—22no—
420C2×C22⋊C4—22no—
421C2×C22⋊C4#4114yes—
422C2×C42—22no—
423C2×C42—24no—
424C2×C42—24no—
425C2×C42—24no—
426C2×C42—24no—
427C2×C42—24no—
428C2×C42—24no—
429C2×C42—22no—
430C2×C42—42no—
431C2×C42—42no—
432C2×C42—42no—
433C2×C42—42no—
434C2×C42—416no—
435C2×C42—42no—
436#95—24no—
437#95—24no—
438#95—24no—
439#95—24no—
440#95—24no—
441#95—24no—
442#95—22no—
443#95—22no—
444#95—22no—
445#95—22no—
446#95—22no—
447#95—22no—
448#95—22no—
449#95—22no—
450#95—22no—
451#95—22no—
452#95—22no—
453#95—22no—
454#95—22no—
455#95—22no—
456#95—22no—
457#95—22no—
458#95—24no—
459#95—24no—
460#95—24no—
461#95—24no—
462#95—24no—
463#95—24no—
464#95—24no—
465#95—24no—
466#95—24no—
467#95—24no—
468#95—24no—
469#95—24no—
470#95—24no—
471#95—24no—
472#95—24no—
473#95—24no—
474#95—24no—
475#95—42no—
476#95—42no—
477#95—42no—
478#95—42no—
479#95—42no—
480#95—42no—
481#95—42no—
482#95—42no—
483#95—42no—
484#95—42no—
485#95—42no—
486#95—42no—
487#95—42no—
488#95—42no—
489#95—42no—
490#95—42no—
491#95—42no—
492#95—42no—
493#95—42no—
494#95C2×D414yes—
495#95C2×D414yes—
496#95C2×D414yes—
497#95C2×D414yes—
498C24—22no—
499C24—22no—
500C24—22no—
501C24—22no—
502C24C22×D412yes—
503C24C2×#4112yes—
504C24C2×#4112yes—
505C24H(5,𝔽2)12yes—
506C24H(5,𝔽2)12yes—
507C242−1+412yes—
508C242−1+412yes—
509C24C2511yescharacteristic
510C2×Q8—216no—
511C2×Q8—216no—
512C2×Q8—216no—
513C2×Q8—48no—
514C2×Q8—48no—
515C2×Q8—48no—
516C2×Q8—48no—
517C2×Q8—48no—
518C2×Q8—48no—
519C2×Q8—48no—
520C2×Q8—48no—
521C2×Q8—48no—
522C2×Q8—4128no—
523C2×Q8—48no—
524C2×Q8—48no—
525C22×C4—28no—
526C22×C4—28no—
527C22×C4—216no—
528C22×C4—28no—
529C22×C4—22no—
530C22×C4—21no—
531C22×C4—22no—
532C22×C4—21no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—216no—
540C22×C4—28no—
541C22×C4—28no—
542C22×C4—28no—
543C22×C4—28no—
544C22×C4—28no—
545C22×C4—28no—
546C22×C4—28no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—21no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—22no—
564C22×C4—21no—
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—21no—
574C22×C4—21no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—28no—
586C22×C4—28no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—22no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—21no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—22no—
620C22×C4—21no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—22no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—44no—
656C22×C4—44no—
657C22×C4—48no—
658C22×C4—48no—
659C22×C4—48no—
660C22×C4—48no—
661C22×C4—48no—
662C22×C4—48no—
663C22×C4—48no—
664C22×C4—48no—
665C22×C4—44no—
666C22×C4—44no—
667C22×C4—44no—
668C22×C4—44no—
669C22×C4—44no—
670C22×C4—44no—
671C22×C4—44no—
672C22×C4—44no—
673C22×C4—44no—
674C22×C4—44no—
675C22×C4—44no—
676C22×C4—44no—
677C22×C4—44no—
678C22×C4—44no—
679C22×C4—44no—
680C22×C4C22×D412yes—
681C22×C4C22×D412yes—
682C22×C4C22×D412yes—
683C22×C4C22×D412yes—
684C22×C4C22×D412yes—
685C22×C4C22×D412yes—
686C22×C4C2×#4114yes—
687C22×C4C2×#4114yes—
688C22×C4C2×#4114yes—
689C22×C4C2×#4114yes—
690C22×C4C2×#4114yes—
691C22×C4H(5,𝔽2)14yes—
692C22×C42−1+414yes—
693C22×C42−1+414yes—
694C4⋊C4—48no—
695C4⋊C4—48no—
696C4⋊C4—48no—
697C4⋊C4—48no—
698C4⋊C4—44no—
699C4⋊C4—44no—
700C4⋊C4—44no—
701C4⋊C4—48no—
702C4⋊C4—82no—
703C4⋊C4—84no—
704C4⋊C4—82no—
705C4⋊C4—82no—
706C4⋊C4—84no—
707C4⋊C4—84no—
708C4⋊C4—84no—
709C22⋊C4—28no—
710C22⋊C4—44no—
711C22⋊C4—44no—
712C22⋊C4—44no—
713C22⋊C4—44no—
714C22⋊C4—44no—
715C22⋊C4—44no—
716C22⋊C4—44no—
717C42—48no—
718C42—48no—
719C42—48no—
720C42—44no—
721C42—82no—
722C23—22no—
723C23—22no—
724C23—24no—
725C23—24no—
726C23—22no—
727C23—22no—
728C23—24no—
729C23—24no—
730C23—24no—
731C23—24no—
732C23—24no—
733C23—24no—
734C23—24no—
735C23—24no—
736C23—24no—
737C23—24no—
738C23#53714yes—
739C23#53814yes—
740C23#54214yes—
741C23#54614yes—
742C23#54714yes—
743C23#55614yes—
744C23#56314yes—
745C23C23×D411yescharacteristic
746C23C22×#4112yes—
747C23C22×#4111yescharacteristic
748C23C22×#4111yescharacteristic
749C23C2×H(5,𝔽2)11yescharacteristic
750C23C2×H(5,𝔽2)11yescharacteristic
751C23C2×H(5,𝔽2)12yes—
752C23C2×2−1+412yes—
753C23C2×2−1+411yescharacteristic
754C23C2×2−1+411yescharacteristic
755C23C2×2−1+412yes—
756Q8—432no—
757Q8—432no—
758C2×C4—232no—
759C2×C4—24no—
760C2×C4—24no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—24no—
764C2×C4—24no—
765C2×C4—22no—
766C2×C4—24no—
767C2×C4—22no—
768C2×C4—24no—
769C2×C4—24no—
770C2×C4—24no—
771C2×C4—24no—
772C2×C4—24no—
773C2×C4—22no—
774C2×C4—24no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—24no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—24no—
786C2×C4—24no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—24no—
790C2×C4—24no—
791C2×C4—24no—
792C2×C4—24no—
793C2×C4—24no—
794C2×C4—416no—
795C2×C4—416no—
796C2×C4—416no—
797C2×C4—416no—
798C2×C4—42no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—416no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—42no—
836C2×C4—42no—
837C2×C4—42no—
838C2×C4—42no—
839C2×C4—42no—
840C2×C4—42no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—42no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—42no—
847C2×C4—42no—
848C2×C4—42no—
849C2×C4—42no—
850C2×C4—42no—
851C2×C4—42no—
852C2×C4—42no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—42no—
862C2×C4—42no—
863C2×C4—42no—
864C2×C4—42no—
865C2×C4—42no—
866C2×C4—42no—
867C2×C4—42no—
868C2×C4—42no—
869C2×C4—42no—
870C2×C4—42no—
871C2×C4—42no—
872C2×C4—42no—
873C2×C4—42no—
874C2×C4—42no—
875C2×C4—42no—
876C2×C4—42no—
877C2×C4—42no—
878C2×C4—42no—
879C2×C4—42no—
880C2×C4—42no—
881C2×C4—42no—
882C2×C4—42no—
883C2×C4—42no—
884C2×C4—42no—
885C2×C4—42no—
886C2×C4—42no—
887C2×C4—42no—
888C2×C4—42no—
889C2×C4—42no—
890C2×C4—42no—
891C2×C4—88no—
892C2×C4#52514yes—
893C2×C4#53614yes—
894C2×C4#55118yes—
895C22—28no—
896C22—24no—
897C22—24no—
898C22—24no—
899C22—24no—
900C22—28no—
901C22—24no—
902C22—24no—
903C22—28no—
904C22—28no—
905C22#271518yes—
906C22C2×#52511yescharacteristic
907C22C2×#53611yescharacteristic
908C22C2×#53711yescharacteristic
909C22C2×#53811yescharacteristic
910C22C2×#54211yescharacteristic
911C22C2×#54611yescharacteristic
912C22C2×#54711yescharacteristic
913C22C2×#55112yes—
914C22C2×#55611yescharacteristic
915C22#348212yes—
916C22#348411yescharacteristic
917C22#348611yescharacteristic
918C22#349012yes—
919C22#350912yes—
920C22#352012yes—
921C22#352212yes—
922C22#352312yes—
923C22#352312yes—
924C22C2×#56311yescharacteristic
925C22#353612yes—
926C22#353812yes—
927C22#353812yes—
928C22#354412yes—
929C4—28no—
930C4—24no—
931C4—24no—
932C4—42no—
933C4—44no—
934C4—44no—
935C4—42no—
936C4—42no—
937C4—42no—
938C4—44no—
939C4—81no—
940C4—81no—
941C4—81no—
942C4—81no—
943C4—81no—
944C4—81no—
945C4—82no—
946C4—81no—
947C4—81no—
948C4—82no—
949C4—82no—
950C4—82no—
951C2—28no—
952C2#3524711yescharacteristic
953C2#3615811yescharacteristic
954C2#3642311yescharacteristic
955C2#3671911yescharacteristic
956C2#3803711yescharacteristic
957C2#3811112yes—
958C2#3859612yes—
959C2#3946511yescharacteristic
960C2#4620512yes—
961C2C2×#271511yescharacteristic
962C2#5942512yes—
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. #16390C2semidirect
4. #16281C2semidirect
5. #15963C2semidirect
6. #15852C2semidirect
7. #15690C2semidirect
8. #15624C2semidirect
17. #14538C2semidirect
18. #14380C2semidirect

Maximal subgroups

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

subgroupindex
C2×#24932
C22×#3912
#163902
#162812
#159632
#158522
#156902
#156242
#150732
#150192
#149352
#149192
#148742
#146972
#146952
#145382
#143802
#139922
#139622
#139222
#138782
#138702