Finite Group Databasebeta

← #846563

Subgroups — #846563

Order 512.

2582 conjugacy classes of subgroups.

The subgroup lattice has 949 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2493C211yesmaximal, characteristic
2C22×#389C211yesmaximal, characteristic
3#16423C212yesmaximal, complemented
4#16410C212yesmaximal, complemented
5#16042C212yesmaximal, complemented
6#15859C212yesmaximal, complemented
7#15533C212yesmaximal, complemented
8#15519C212yesmaximal, complemented
9#15073C211yesmaximal, characteristic
10#15073C211yesmaximal, characteristic
11#15073C211yesmaximal, characteristic
12#15019C211yesmaximal, characteristic
13#14935C211yesmaximal, characteristic
14#14728C211yesmaximal, characteristic
15#14705C211yesmaximal, characteristic
16#14685C211yesmaximal, characteristic
17#14550C212yesmaximal, complemented
18#14390C212yesmaximal, complemented
19#14039C211yesmaximal, characteristic
20#13904C211yesmaximal, characteristic
21#13878C211yesmaximal, characteristic
22#13870C211yesmaximal, characteristic
23#13870C211yesmaximal, characteristic
24C22×#117C2211yescharacteristic
25C23×C4⋊C4C2211yescharacteristic
26C23×C4⋊C4C2211yescharacteristic
27C23×C4⋊C4C2211yescharacteristic
28C23×C4⋊C4C2211yescharacteristic
29C23×C42C2211yescharacteristic
30#2493—28no—
31C2×#401C2211yescharacteristic
32C2×#400C2211yescharacteristic
33C2×#400C2211yescharacteristic
34C2×#400C2211yescharacteristic
35C2×#398C2212yes—
36C2×#389—28no—
37C2×#389C2212yes—
38C2×#389C2212yes—
39C2×#389C2212yes—
40C2×#389C2212yes—
41C2×#387C2212yes—
42C2×#387C2211yescharacteristic
43C2×#387C2211yescharacteristic
44C2×#387C2211yescharacteristic
45C2×#385C2211yescharacteristic
46C2×#385C2211yescharacteristic
47C2×#385C2211yescharacteristic
48C2×#385C2211yescharacteristic
49C2×#383C2211yescharacteristic
50C2×#381C2211yescharacteristic
51C2×#381C2211yescharacteristic
52C2×#381C2211yescharacteristic
53C2×#381C2211yescharacteristic
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
67#1445C2212yes—
68#1445C2212yes—
69#1445C2212yes—
70#1444C2212yes—
71#1444C2212yes—
72#1443C2212yes—
73#1443C2212yes—
74#1443C2212yes—
75#1442C2212yes—
76#1442C2212yes—
77#1442C2212yes—
78#1442C2212yes—
79#1442C2212yes—
80#1442C2212yes—
81#1442C2212yes—
82#1442C2212yes—
83#1442C2212yes—
84#1442C2212yes—
85#1441C2212yes—
86#1441C2212yes—
87#1441C2212yes—
88#1441C2212yes—
89#1441C2212yes—
90#1441C2212yes—
91#1441C2212yes—
92#1441C2212yes—
93#1441C2212yes—
94#1441C2212yes—
95#1441C2212yes—
96#1441C2212yes—
97#1441C2212yes—
98#1441C2212yes—
99#1441C2212yes—
100#1436C2212yes—
101#1436C2212yes—
102#1436C2212yes—
103#1436C2212yes—
104#1436C2212yes—
105#1436C2212yes—
106#1436C2212yes—
107#1436C2212yes—
108#1436C2212yes—
109#1436C2212yes—
110#1436C2212yes—
111C4⋊#95C2212yes—
112C4⋊#95C2212yes—
113C4⋊#95C2212yes—
114C4⋊#95C2212yes—
115#1434C2212yes—
116#1434C2212yes—
117C22⋊#95C2211yescharacteristic
118C22⋊#95C2211yescharacteristic
119C22⋊#95C2211yescharacteristic
120C22⋊#95C2211yescharacteristic
121C22⋊#95C2211yescharacteristic
122C22⋊#95C2211yescharacteristic
123C22⋊#95C2211yescharacteristic
124C22⋊#95C2211yescharacteristic
125C24×C4C2311yescharacteristic
126C24×C4C2311yescharacteristic
127C24×C4C2311yescharacteristic
128C24×C4C2311yescharacteristic
129C24×C4C2311yescharacteristic
130C24×C4C2311yescharacteristic
131C24×C4C2311yescharacteristic
132C2×#117—42no—
133C2×#117—42no—
134C2×#117—42no—
135C22×C4⋊C4—24no—
136C22×C4⋊C4—28no—
137C22×C4⋊C4—24no—
138C22×C4⋊C4—24no—
139C22×C4⋊C4—24no—
140C22×C4⋊C4—24no—
141C22×C4⋊C4—24no—
142C22×C4⋊C4—24no—
143C22×C4⋊C4—42no—
144C22×C4⋊C4—42no—
145C22×C4⋊C4—42no—
146C22×C4⋊C4C2311yescharacteristic
147C22×C4⋊C4C2311yescharacteristic
148C22×C4⋊C4C2311yescharacteristic
149C22×C4⋊C4C2312yes—
150C22×C4⋊C4C2312yes—
151C22×C4⋊C4C2312yes—
152C22×C4⋊C4C2312yes—
153C22×C4⋊C4C2312yes—
154C22×C4⋊C4C2312yes—
155C22×C4⋊C4C2312yes—
156C22×C4⋊C4C2312yes—
157C22×C4⋊C4C2312yes—
158C22×C4⋊C4C2312yes—
159C22×C4⋊C4C2312yes—
160C22×C4⋊C4C2311yescharacteristic
161C22×C4⋊C4C2311yescharacteristic
162C22×C4⋊C4C2311yescharacteristic
163C22×C4⋊C4C2312yes—
164C22×C4⋊C4C2312yes—
165C22×C22⋊C4C2311yescharacteristic
166C22×C22⋊C4C2311yescharacteristic
167C22×C22⋊C4C2311yescharacteristic
168C22×C22⋊C4C2311yescharacteristic
169C22×C22⋊C4C2311yescharacteristic
170C22×C22⋊C4C2311yescharacteristic
171C22×C22⋊C4C2311yescharacteristic
172C22×C22⋊C4C2311yescharacteristic
173C22×C42—24no—
174C22×C42—24no—
175C22×C42—42no—
176C22×C42C2311yescharacteristic
177C22×C42C2312yes—
178C22×C42C2312yes—
179C22×C42C2311yescharacteristic
180C22×C42C2312yes—
181#401—24no—
182#400—24no—
183#400—24no—
184#400—24no—
185#398—28no—
186#389—28no—
187#389—28no—
188#389—28no—
189#389—28no—
190#387—28no—
191#387—24no—
192#387—24no—
193#387—24no—
194#385—24no—
195#385—24no—
196#385—24no—
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#381—42no—
207#381—42no—
208#381—42no—
209#381—42no—
210#380—24no—
211#380—42no—
212#380—42no—
213C4×C22⋊C4—24no—
214C2×#95—24no—
215C2×#95D418yes—
216C2×#95C2312yes—
217C2×#95C2312yes—
218C2×#95C2312yes—
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×#95C2311yescharacteristic
234C2×#95C2312yes—
235C2×#95C2312yes—
236C2×#95C2312yes—
237C2×#95C2312yes—
238C2×#95C2312yes—
239C2×#95C2312yes—
240C2×#95C2312yes—
241C2×#95C2312yes—
242C2×#95C2312yes—
243C2×#95C2312yes—
244C2×#95C2312yes—
245C2×#95C2311yescharacteristic
246C2×#95C2312yes—
247C2×#95C2312yes—
248C2×#95C2312yes—
249C2×#95C2312yes—
250C2×#95C2312yes—
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
277C23×C4—22no—
278C23×C4—22no—
279C23×C4—24no—
280C23×C4—24no—
281C23×C4—22no—
282C23×C4—22no—
283C23×C4—22no—
284C23×C4—22no—
285C23×C4—22no—
286C23×C4—22no—
287C23×C4—22no—
288C23×C4—22no—
289C23×C4—22no—
290C23×C4—22no—
291C23×C4—22no—
292C23×C4—22no—
293C23×C4—22no—
294C23×C4—22no—
295C23×C4—22no—
296C23×C4—22no—
297C23×C4—22no—
298C23×C4—24no—
299C23×C4—24no—
300C23×C4—24no—
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—42no—
311C23×C4—42no—
312C23×C4—42no—
313C23×C4C2×D414yes—
314C23×C4C2×D414yes—
315C23×C4C2×D414yes—
316C23×C4#4114yes—
317C23×C4#4114yes—
318C23×C4C2411yescharacteristic
319C23×C4C2412yes—
320C23×C4C2411yescharacteristic
321C23×C4C2411yescharacteristic
322C23×C4C2411yescharacteristic
323C23×C4C2411yescharacteristic
324C23×C4C2412yes—
325C23×C4C2412yes—
326C23×C4C2411yescharacteristic
327C23×C4C2412yes—
328C23×C4C2411yescharacteristic
329C23×C4C2411yescharacteristic
330C23×C4C2412yes—
331C23×C4C2411yescharacteristic
332C23×C4C2411yescharacteristic
333C23×C4C2411yescharacteristic
334C23×C4C2411yescharacteristic
335C23×C4C2412yes—
336C23×C4C2412yes—
337C23×C4C2411yescharacteristic
338C23×C4C2411yescharacteristic
339C23×C4C2412yes—
340#117—416no—
341C2×C4⋊C4—232no—
342C2×C4⋊C4—24no—
343C2×C4⋊C4—24no—
344C2×C4⋊C4—24no—
345C2×C4⋊C4—24no—
346C2×C4⋊C4—24no—
347C2×C4⋊C4—24no—
348C2×C4⋊C4—24no—
349C2×C4⋊C4—24no—
350C2×C4⋊C4—24no—
351C2×C4⋊C4—24no—
352C2×C4⋊C4—24no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—24no—
357C2×C4⋊C4—24no—
358C2×C4⋊C4—24no—
359C2×C4⋊C4—24no—
360C2×C4⋊C4—24no—
361C2×C4⋊C4—24no—
362C2×C4⋊C4—24no—
363C2×C4⋊C4—24no—
364C2×C4⋊C4—24no—
365C2×C4⋊C4—24no—
366C2×C4⋊C4—24no—
367C2×C4⋊C4—24no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—24no—
372C2×C4⋊C4—24no—
373C2×C4⋊C4—24no—
374C2×C4⋊C4—42no—
375C2×C4⋊C4—42no—
376C2×C4⋊C4—42no—
377C2×C4⋊C4—42no—
378C2×C4⋊C4—42no—
379C2×C4⋊C4—42no—
380C2×C4⋊C4—42no—
381C2×C4⋊C4—42no—
382C2×C4⋊C4—42no—
383C2×C4⋊C4—416no—
384C2×C4⋊C4—416no—
385C2×C4⋊C4—416no—
386C2×C4⋊C4—42no—
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#4118yes—
396C2×C22⋊C4—22no—
397C2×C22⋊C4—22no—
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×C42—22no—
421C2×C42—24no—
422C2×C42—24no—
423C2×C42—24no—
424C2×C42—24no—
425C2×C42—24no—
426C2×C42—22no—
427C2×C42—42no—
428C2×C42—42no—
429C2×C42—42no—
430C2×C42—42no—
431C2×C42—42no—
432C2×C42—416no—
433C2×C42—42no—
434#95—24no—
435#95—24no—
436#95—22no—
437#95—22no—
438#95—22no—
439#95—22no—
440#95—22no—
441#95—22no—
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—24no—
453#95—24no—
454#95—24no—
455#95—24no—
456#95—24no—
457#95—24no—
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—42no—
467#95—42no—
468#95—42no—
469#95—42no—
470#95—42no—
471#95—42no—
472#95—42no—
473#95—42no—
474#95—42no—
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#95C2×D414yes—
491#95C2×D414yes—
492#95C2×D414yes—
493#95C2×D414yes—
494C24—22no—
495C24—22no—
496C24—22no—
497C24—22no—
498C24C22×D412yes—
499C24C2×#4112yes—
500C24C2×#4112yes—
501C24H(5,𝔽2)12yes—
502C24H(5,𝔽2)12yes—
503C24H(5,𝔽2)12yes—
504C242−1+412yes—
505C24C2511yescharacteristic
506C22×C4—28no—
507C22×C4—28no—
508C22×C4—216no—
509C22×C4—28no—
510C22×C4—22no—
511C22×C4—21no—
512C22×C4—22no—
513C22×C4—21no—
514C22×C4—22no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—216no—
521C22×C4—28no—
522C22×C4—28no—
523C22×C4—28no—
524C22×C4—28no—
525C22×C4—28no—
526C22×C4—28no—
527C22×C4—28no—
528C22×C4—28no—
529C22×C4—28no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—21no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—21no—
544C22×C4—22no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—22no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—22no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—22no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—28no—
563C22×C4—28no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—21no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—21no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—22no—
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—22no—
639C22×C4—44no—
640C22×C4—44no—
641C22×C4—48no—
642C22×C4—48no—
643C22×C4—48no—
644C22×C4—48no—
645C22×C4—48no—
646C22×C4—48no—
647C22×C4—44no—
648C22×C4—44no—
649C22×C4—44no—
650C22×C4—44no—
651C22×C4—44no—
652C22×C4—44no—
653C22×C4—44no—
654C22×C4—44no—
655C22×C4—44no—
656C22×C4—44no—
657C22×C4—44no—
658C22×C4—44no—
659C22×C4—44no—
660C22×C4—44no—
661C22×C4—44no—
662C22×C4—44no—
663C22×C4—44no—
664C22×C4C22×D412yes—
665C22×C4C22×D412yes—
666C22×C4C22×D412yes—
667C22×C4C22×D412yes—
668C22×C4C22×D412yes—
669C22×C4C22×D412yes—
670C22×C4C2×#4114yes—
671C22×C4C2×#4114yes—
672C22×C4C2×#4114yes—
673C22×C4C2×#4114yes—
674C22×C4C2×#4114yes—
675C22×C42−1+414yes—
676C22×C42−1+414yes—
677C4⋊C4—216no—
678C4⋊C4—216no—
679C4⋊C4—48no—
680C4⋊C4—48no—
681C4⋊C4—48no—
682C4⋊C4—48no—
683C4⋊C4—48no—
684C4⋊C4—48no—
685C4⋊C4—48no—
686C4⋊C4—44no—
687C4⋊C4—44no—
688C4⋊C4—44no—
689C4⋊C4—48no—
690C4⋊C4—82no—
691C4⋊C4—84no—
692C4⋊C4—84no—
693C4⋊C4—82no—
694C4⋊C4—82no—
695C4⋊C4—84no—
696C22⋊C4—44no—
697C22⋊C4—44no—
698C22⋊C4—44no—
699C22⋊C4—44no—
700C22⋊C4—44no—
701C22⋊C4—44no—
702C22⋊C4—44no—
703C22⋊C4—44no—
704C42—48no—
705C42—48no—
706C42—48no—
707C42—44no—
708C42—82no—
709C23—22no—
710C23—22no—
711C23—24no—
712C23—24no—
713C23—22no—
714C23—22no—
715C23—24no—
716C23—24no—
717C23—24no—
718C23—24no—
719C23—24no—
720C23—24no—
721C23—24no—
722C23—24no—
723C23—24no—
724C23—24no—
725C23#53714yes—
726C23#53914yes—
727C23#54214yes—
728C23#54614yes—
729C23#54614yes—
730C23#55314yes—
731C23#56014yes—
732C23C23×D411yescharacteristic
733C23C22×#4112yes—
734C23C22×#4111yescharacteristic
735C23C22×#4111yescharacteristic
736C23C2×H(5,𝔽2)11yescharacteristic
737C23C2×H(5,𝔽2)11yescharacteristic
738C23C2×H(5,𝔽2)11yescharacteristic
739C23C2×2−1+412yes—
740C23C2×2−1+411yescharacteristic
741C23C2×2−1+412yes—
742C23#58512yes—
743C2×C4—232no—
744C2×C4—24no—
745C2×C4—24no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—24no—
749C2×C4—24no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—24no—
753C2×C4—24no—
754C2×C4—24no—
755C2×C4—24no—
756C2×C4—24no—
757C2×C4—24no—
758C2×C4—22no—
759C2×C4—24no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—24no—
764C2×C4—22no—
765C2×C4—24no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—24no—
772C2×C4—24no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—24no—
776C2×C4—416no—
777C2×C4—416no—
778C2×C4—416no—
779C2×C4—42no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—42no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—416no—
786C2×C4—416no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—42no—
837C2×C4—42no—
838C2×C4—42no—
839C2×C4—42no—
840C2×C4—42no—
841C2×C4—42no—
842C2×C4—42no—
843C2×C4—42no—
844C2×C4—42no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—42no—
848C2×C4—42no—
849C2×C4—42no—
850C2×C4—42no—
851C2×C4—42no—
852C2×C4—42no—
853C2×C4—42no—
854C2×C4—42no—
855C2×C4—42no—
856C2×C4—42no—
857C2×C4—42no—
858C2×C4—42no—
859C2×C4—42no—
860C2×C4—42no—
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—88no—
877C2×C4#52514yes—
878C2×C4#53614yes—
879C2×C4#55218yes—
880C22—24no—
881C22—24no—
882C22—28no—
883C22—24no—
884C22—24no—
885C22—28no—
886C22—24no—
887C22—28no—
888C22—28no—
889C22—24no—
890C22#269118yes—
891C22C2×#52511yescharacteristic
892C22C2×#53611yescharacteristic
893C22C2×#53711yescharacteristic
894C22C2×#53911yescharacteristic
895C22C2×#54211yescharacteristic
896C22C2×#54611yescharacteristic
897C22C2×#54611yescharacteristic
898C22C2×#55212yes—
899C22C2×#55311yescharacteristic
900C22#347512yes—
901C22#348511yescharacteristic
902C22#348611yescharacteristic
903C22#349212yes—
904C22#349512yes—
905C22#350912yes—
906C22#351312yes—
907C22#352212yes—
908C22#352312yes—
909C22C2×#56011yescharacteristic
910C22#353512yes—
911C22#354412yes—
912C22#355912yes—
913C22#356312yes—
914C4—24no—
915C4—28no—
916C4—24no—
917C4—42no—
918C4—44no—
919C4—42no—
920C4—42no—
921C4—44no—
922C4—42no—
923C4—81no—
924C4—81no—
925C4—81no—
926C4—81no—
927C4—81no—
928C4—82no—
929C4—82no—
930C4—81no—
931C4—81no—
932C4—82no—
933C4—82no—
934C4—82no—
935C4—81no—
936C2—28no—
937C2#3524711yescharacteristic
938C2#3615911yescharacteristic
939C2#3616311yescharacteristic
940C2#3696811yescharacteristic
941C2#3783511yescharacteristic
942C2#3806912yes—
943C2#3846512yes—
944C2#3946511yescharacteristic
945C2#4575112yes—
946C2C2×#269111yescharacteristic
947C2#5928912yes—
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. #16423C2semidirect
4. #16410C2semidirect
5. #16042C2semidirect
6. #15859C2semidirect
7. #15533C2semidirect
8. #15519C2semidirect
17. #14550C2semidirect
18. #14390C2semidirect

Maximal subgroups

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

subgroupindex
C2×#24932
C22×#3892
#164232
#164102
#160422
#158592
#155332
#155192
#150732
#150192
#149352
#147282
#147052
#146852
#145502
#143902
#140392
#139042
#138782
#138702