Finite Group Databasebeta

← #638233

Subgroups — #638233

Order 512.

1982 conjugacy classes of subgroups.

The subgroup lattice has 914 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2647C211yesmaximal, characteristic
2C2×#2295C211yesmaximal, characteristic
3#16649C212yesmaximal
4#16613C212yesmaximal
5#16461C212yesmaximal
6#16448C212yesmaximal
7#15221C211yesmaximal, characteristic
8#15187C211yesmaximal, characteristic
9#15186C211yesmaximal, characteristic
10#15184C211yesmaximal, characteristic
11#14908C212yesmaximal
12#14897C212yesmaximal
13#14794C212yesmaximal
14#14779C212yesmaximal
15#14699C211yesmaximal, characteristic
16#14266C211yesmaximal, characteristic
17#14261C211yesmaximal, characteristic
18#14261C211yesmaximal, characteristic
19#14046C211yesmaximal, characteristic
20#14017C211yesmaximal, characteristic
21#13981C211yesmaximal, characteristic
22#13978C211yesmaximal, characteristic
23#13759C211yesmaximal, characteristic
24C22×C4×Q8C2211yescharacteristic
25#2647—28no—
26C2×#400C2212yes—
27C2×#400C2212yes—
28C2×#398C2212yes—
29C2×#398C2212yes—
30#2295—28no—
31C2×#391C2211yescharacteristic
32C2×#391C2211yescharacteristic
33C2×#391C2211yescharacteristic
34C2×#391C2211yescharacteristic
35C2×#391C2211yescharacteristic
36C2×#391C2211yescharacteristic
37C2×#389C2211yescharacteristic
38C2×#389C2211yescharacteristic
39C2×#389C2211yescharacteristic
40C2×#389C2211yescharacteristic
41C2×#389C2211yescharacteristic
42C2×#389C2211yescharacteristic
43C2×#389C2211yescharacteristic
44C2×#389C2212yes—
45C2×#389C2211yescharacteristic
46C2×#387C2212yes—
47C2×#387C2212yes—
48C2×#387C2212yes—
49C2×#387C2212yes—
50C2×#384C2211yescharacteristic
51C2×#382C2211yescharacteristic
52C2×C4×C4⋊C4C2211yescharacteristic
53C2×C4×C4⋊C4C2211yescharacteristic
54C2×C4×C4⋊C4C2212yes—
55C2×C4×C4⋊C4C2211yescharacteristic
56C2×#376C2212yes—
57C2×#376C2211yescharacteristic
58C2×#376C2211yescharacteristic
59C2×C43C2211yescharacteristic
60#1445C2212yes—
61#1445C2212yes—
62#1445C2212yes—
63#1445C2212yes—
64#1444C2212yes—
65#1444C2212yes—
66#1443C2212yes—
67#1443C2212yes—
68#1443C2212yes—
69#1443C2212yes—
70#1443C2212yes—
71#1443C2212yes—
72#1443C2212yes—
73#1443C2212yes—
74#1442C2212yes—
75#1442C2212yes—
76#1442C2212yes—
77#1442C2212yes—
78#1442C2212yes—
79#1442C2212yes—
80#1442C2212yes—
81#1442C2212yes—
82#1442C2212yes—
83#1442C2212yes—
84#1442C2212yes—
85#1442C2212yes—
86#1442C2212yes—
87#1442C2212yes—
88#1441C2212yes—
89#1441C2212yes—
90#1441C2212yes—
91#1441C2212yes—
92#1441C2212yes—
93#1441C2212yes—
94#1441C2212yes—
95#1441C2212yes—
96#1436C2211yescharacteristic
97#1436C2212yes—
98#1436C2211yescharacteristic
99#1436C2212yes—
100#1436C2212yes—
101#1436C2212yes—
102#1436C2212yes—
103#1436C2212yes—
104#1436C2211yescharacteristic
105#1436C2212yes—
106#1436C2212yes—
107#1436C2211yescharacteristic
108#1436C2211yescharacteristic
109#1436C2211yescharacteristic
110#1436C2211yescharacteristic
111#1436C2211yescharacteristic
112C4⋊#95C2211yescharacteristic
113C4⋊#95C2211yescharacteristic
114C4⋊#95C2211yescharacteristic
115C4⋊#95C2211yescharacteristic
116C4⋊#95C2211yescharacteristic
117C4⋊#95C2211yescharacteristic
118C4⋊#95C2211yescharacteristic
119C4⋊#95C2211yescharacteristic
120C4⋊#95C2211yescharacteristic
121C4⋊#95C2211yescharacteristic
122#1434C2212yes—
123C4×#95C2211yescharacteristic
124C4×#95C2211yescharacteristic
125C23×Q8C2311yescharacteristic
126C2×C4×Q8—24no—
127C2×C4×Q8—24no—
128C2×C4×Q8—24no—
129C22×C4⋊C4C2312yes—
130C22×C4⋊C4C2311yescharacteristic
131C22×C4⋊C4C2311yescharacteristic
132C22×C4⋊C4C2311yescharacteristic
133C22×C4⋊C4C2311yescharacteristic
134C22×C4⋊C4C2311yescharacteristic
135C22×C4⋊C4C2311yescharacteristic
136C22×C4⋊C4C2312yes—
137C22×C4⋊C4C2311yescharacteristic
138C22×C4⋊C4C2311yescharacteristic
139C22×C4⋊C4C2312yes—
140C22×C4⋊C4C2311yescharacteristic
141C22×C4⋊C4C2311yescharacteristic
142C22×C4⋊C4C2312yes—
143C22×C4⋊C4C2312yes—
144C22×C4⋊C4C2312yes—
145C22×C4⋊C4C2312yes—
146C22×C4⋊C4C2312yes—
147C22×C4⋊C4C2311yescharacteristic
148C22×C4⋊C4C2312yes—
149C22×C4⋊C4C2312yes—
150C22×C4⋊C4C2312yes—
151C22×C42C2312yes—
152C22×C42C2311yescharacteristic
153C22×C42C2311yescharacteristic
154C22×C42C2311yescharacteristic
155C22×C42C2311yescharacteristic
156C22×C42C2311yescharacteristic
157C22×C42C2311yescharacteristic
158C22×C42C2312yes—
159C22×C42C2311yescharacteristic
160C22×C42C2311yescharacteristic
161C22×C42C2311yescharacteristic
162C22×C42C2311yescharacteristic
163C22×C42C2311yescharacteristic
164#400—28no—
165#400—28no—
166#398—28no—
167#398—28no—
168#391—24no—
169#391—24no—
170#391—24no—
171#391—24no—
172#391—24no—
173#391—24no—
174#389—24no—
175#389—24no—
176#389—24no—
177#389—24no—
178#389—24no—
179#389—24no—
180#389—24no—
181#389—44no—
182#389D418yes—
183#387—28no—
184#387—28no—
185#387—44no—
186#387—44no—
187#384—24no—
188#382—24no—
189C4×C4⋊C4—24no—
190C4×C4⋊C4—28no—
191C4×C4⋊C4—24no—
192C4×C4⋊C4—24no—
193#376—24no—
194#376—24no—
195#376—28no—
196C2×#95C2311yescharacteristic
197C2×#95C2311yescharacteristic
198C2×#95C2312yes—
199C2×#95C2312yes—
200C2×#95C2312yes—
201C2×#95C2312yes—
202C2×#95C2312yes—
203C2×#95C2311yescharacteristic
204C2×#95C2311yescharacteristic
205C2×#95C2311yescharacteristic
206C2×#95C2311yescharacteristic
207C2×#95C2311yescharacteristic
208C2×#95C2311yescharacteristic
209C2×#95C2312yes—
210C2×#95C2312yes—
211C2×#95C2312yes—
212C2×#95C2311yescharacteristic
213C2×#95C2311yescharacteristic
214C2×#95C2311yescharacteristic
215C2×#95C2311yescharacteristic
216C2×#95C2311yescharacteristic
217C2×#95C2311yescharacteristic
218C2×#95C2311yescharacteristic
219C2×#95C2311yescharacteristic
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×#95C2312yes—
236C2×#95C2311yescharacteristic
237C2×#95C2311yescharacteristic
238C2×#95C2311yescharacteristic
239C2×#95C2311yescharacteristic
240C2×#95C2312yes—
241C2×#95C2312yes—
242C2×#95C2312yes—
243C2×#95C2312yes—
244C2×#95C2312yes—
245C2×#95C2312yes—
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—
259C43—24no—
260C22×Q8—22no—
261C22×Q8—22no—
262C22×Q8—22no—
263C22×Q8—22no—
264C22×Q8—22no—
265C22×Q8—22no—
266C22×Q8#4114yes—
267C23×C4C2412yes—
268C23×C4C2412yes—
269C23×C4C2412yes—
270C23×C4C2411yescharacteristic
271C23×C4C2411yescharacteristic
272C23×C4C2412yes—
273C23×C4C2412yes—
274C23×C4C2411yescharacteristic
275C23×C4C2411yescharacteristic
276C23×C4C2412yes—
277C23×C4C2412yes—
278C23×C4C2411yescharacteristic
279C23×C4C2411yescharacteristic
280C23×C4C2411yescharacteristic
281C23×C4C2411yescharacteristic
282C23×C4C2411yescharacteristic
283C23×C4C2411yescharacteristic
284C23×C4C2411yescharacteristic
285C23×C4C2412yes—
286C23×C4C2411yescharacteristic
287C23×C4C2411yescharacteristic
288C23×C4C2411yescharacteristic
289C23×C4C2411yescharacteristic
290C4×Q8—232no—
291C2×C4⋊C4—24no—
292C2×C4⋊C4—24no—
293C2×C4⋊C4—24no—
294C2×C4⋊C4—22no—
295C2×C4⋊C4—22no—
296C2×C4⋊C4—22no—
297C2×C4⋊C4—22no—
298C2×C4⋊C4—24no—
299C2×C4⋊C4—22no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—22no—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—24no—
307C2×C4⋊C4—24no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—24no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—24no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—24no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—24no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—24no—
329C2×C4⋊C4—24no—
330C2×C4⋊C4—24no—
331C2×C4⋊C4—24no—
332C2×C4⋊C4—24no—
333C2×C4⋊C4—42no—
334C2×C4⋊C4—42no—
335C2×C4⋊C4—41no—
336C2×C4⋊C4—41no—
337C2×C4⋊C4—42no—
338C2×C4⋊C4—41no—
339C2×C4⋊C4—41no—
340C2×C4⋊C4—42no—
341C2×C4⋊C4—42no—
342C2×C4⋊C4—42no—
343C2×C4⋊C4—42no—
344C2×C4⋊C4—42no—
345C2×C4⋊C4—42no—
346C2×C4⋊C4—42no—
347C2×C4⋊C4—42no—
348C2×C4⋊C4—42no—
349C2×C4⋊C4—42no—
350C2×C4⋊C4—42no—
351C2×C4⋊C4—42no—
352C2×C4⋊C4—42no—
353C2×C4⋊C4—42no—
354C2×C4⋊C4C2×D414yes—
355C2×C4⋊C4C2×D414yes—
356C2×C4⋊C4C2×D418yes—
357C2×C42—22no—
358C2×C42—24no—
359C2×C42—22no—
360C2×C42—22no—
361C2×C42—24no—
362C2×C42—24no—
363C2×C42—22no—
364C2×C42—22no—
365C2×C42—22no—
366C2×C42—22no—
367C2×C42—22no—
368C2×C42—22no—
369C2×C42—22no—
370C2×C42—22no—
371C2×C42—22no—
372C2×C42—22no—
373C2×C42—22no—
374C2×C42—22no—
375C2×C42—24no—
376C2×C42—22no—
377C2×C42—22no—
378C2×C42—22no—
379C2×C42—22no—
380C2×C42—22no—
381C2×C42—22no—
382C2×C42—22no—
383C2×C42—24no—
384C2×C42—22no—
385C2×C42—22no—
386C2×C42—22no—
387C2×C42—41no—
388C2×C42—42no—
389C2×C42—41no—
390C2×C42—41no—
391C2×C42—41no—
392C2×C42C2×D414yes—
393C2×C42#4114yes—
394C2×C42#4114yes—
395C2×C42#4114yes—
396#95—24no—
397#95—24no—
398#95—24no—
399#95—22no—
400#95—22no—
401#95—22no—
402#95—22no—
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—22no—
412#95—22no—
413#95—22no—
414#95—22no—
415#95—22no—
416#95—22no—
417#95—22no—
418#95—22no—
419#95—24no—
420#95—24no—
421#95—24no—
422#95—24no—
423#95—24no—
424#95—24no—
425#95—24no—
426#95—24no—
427#95—24no—
428#95—24no—
429#95—24no—
430#95—22no—
431#95—24no—
432#95—22no—
433#95—22no—
434#95—24no—
435#95—22no—
436#95—42no—
437#95—42no—
438#95—42no—
439#95—42no—
440#95—42no—
441#95—42no—
442#95—42no—
443#95—41no—
444#95—41no—
445#95—41no—
446#95—41no—
447#95—42no—
448#95—42no—
449#95—42no—
450#95—42no—
451#95—42no—
452#95—42no—
453#95—42no—
454#95—42no—
455#95—42no—
456#95—42no—
457#95—42no—
458#95C2×D418yes—
459C24C2511yescharacteristic
460C2×Q8—28no—
461C2×Q8—28no—
462C2×Q8—28no—
463C2×Q8—44no—
464C2×Q8—44no—
465C2×Q8—44no—
466C2×Q8—44no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—22no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—22no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—22no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—22no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—22no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—22no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—21no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—21no—
572C22×C4—22no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—22no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—21no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—22no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—22no—
595C22×C4—21no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—21no—
601C22×C4—22no—
602C22×C4—21no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—21no—
606C22×C4C22×D412yes—
607C22×C4C22×D414yes—
608C22×C4C22×D414yes—
609C22×C4C22×D412yes—
610C22×C4C22×D412yes—
611C22×C4C2×#4112yes—
612C22×C4C2×#4112yes—
613C22×C4C2×#4114yes—
614C22×C4C2×#4112yes—
615C22×C4C2×#4112yes—
616C22×C4C2×#4112yes—
617C22×C4C2×#4112yes—
618C22×C4C2×#4112yes—
619C22×C4C2×#4112yes—
620C22×C4C2×#4112yes—
621C22×C4C2×#4112yes—
622C22×C4H(5,𝔽2)12yes—
623C22×C42−1+412yes—
624C22×C42−1+412yes—
625C22×C42−1+412yes—
626C22×C42−1+412yes—
627C22×C42−1+412yes—
628C4⋊C4—216no—
629C4⋊C4—28no—
630C4⋊C4—28no—
631C4⋊C4—48no—
632C4⋊C4—48no—
633C4⋊C4—44no—
634C4⋊C4—44no—
635C4⋊C4—44no—
636C4⋊C4—48no—
637C4⋊C4—48no—
638C4⋊C4—44no—
639C4⋊C4—44no—
640C4⋊C4—44no—
641C4⋊C4—48no—
642C4⋊C4—44no—
643C4⋊C4—44no—
644C4⋊C4—44no—
645C4⋊C4—84no—
646C4⋊C4—84no—
647C4⋊C4—84no—
648C4⋊C4—84no—
649C4⋊C4—84no—
650C42—28no—
651C42—216no—
652C42—28no—
653C42—28no—
654C42—28no—
655C42—28no—
656C42—44no—
657C42—48no—
658C42—44no—
659C42—44no—
660C42—44no—
661C42—44no—
662C42—44no—
663C23C23×D411yescharacteristic
664C23C22×#4111yescharacteristic
665C23C22×#4111yescharacteristic
666C23C22×#4111yescharacteristic
667C23C22×#4111yescharacteristic
668C23C2×H(5,𝔽2)11yescharacteristic
669C23C2×2−1+411yescharacteristic
670C23C2×2−1+411yescharacteristic
671C23C2×2−1+411yescharacteristic
672C23C2×2−1+411yescharacteristic
673C23C2×2−1+411yescharacteristic
674C23#58511yescharacteristic
675C23#58511yescharacteristic
676C23#58511yescharacteristic
677C23#58511yescharacteristic
678Q8—416no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—24no—
686C2×C4—22no—
687C2×C4—24no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—24no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—22no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—24no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—24no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—42no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—42no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—42no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—42no—
753C2×C4—41no—
754C2×C4—42no—
755C2×C4—41no—
756C2×C4—42no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—42no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—42no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—41no—
775C2×C4—42no—
776C2×C4—41no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—41no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—42no—
795C2×C4—41no—
796C2×C4—42no—
797C2×C4—41no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—41no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—41no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—42no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—42no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—42no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—42no—
823C2×C4—41no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—41no—
828C2×C4—42no—
829C2×C4—41no—
830C2×C4—42no—
831C2×C4—41no—
832C2×C4#52514yes—
833C2×C4#52914yes—
834C2×C4#54114yes—
835C2×C4#54214yes—
836C2×C4#54714yes—
837C2×C4#54814yes—
838C2×C4#55214yes—
839C2×C4#55214yes—
840C22C2×#52511yescharacteristic
841C22C2×#52911yescharacteristic
842C22C2×#54111yescharacteristic
843C22C2×#54211yescharacteristic
844C22#345511yescharacteristic
845C22#346011yescharacteristic
846C22#346011yescharacteristic
847C22#346111yescharacteristic
848C22#346111yescharacteristic
849C22#346111yescharacteristic
850C22#346111yescharacteristic
851C22C2×#54711yescharacteristic
852C22C2×#54811yescharacteristic
853C22C2×#55211yescharacteristic
854C22C2×#55211yescharacteristic
855C22#348511yescharacteristic
856C22#348611yescharacteristic
857C22#348811yescharacteristic
858C22#348911yescharacteristic
859C22#349511yescharacteristic
860C22#349511yescharacteristic
861C22#350911yescharacteristic
862C22#351211yescharacteristic
863C22#351611yescharacteristic
864C22#351811yescharacteristic
865C22#352211yescharacteristic
866C22#352411yescharacteristic
867C22#355211yescharacteristic
868C22#355411yescharacteristic
869C22#355511yescharacteristic
870C22#355511yescharacteristic
871C22#355611yescharacteristic
872C22#355711yescharacteristic
873C22#356311yescharacteristic
874C22#356511yescharacteristic
875C4—24no—
876C4—42no—
877C4—44no—
878C4—42no—
879C4—42no—
880C4—42no—
881C4—42no—
882C4—42no—
883C4—44no—
884C4—42no—
885C4—42no—
886C4—44no—
887C4—42no—
888C4—82no—
889C4—82no—
890C4—81no—
891C4—82no—
892C4—81no—
893C4—81no—
894C4—82no—
895C4—81no—
896C4—82no—
897C4#247518yes—
898C2#3461911yescharacteristic
899C2C2×#247511yescharacteristic
900C2#3515511yescharacteristic
901C2#3524311yescharacteristic
902C2#3532311yescharacteristic
903C2#3758011yescharacteristic
904C2#3763011yescharacteristic
905C2#3775711yescharacteristic
906C2#3775911yescharacteristic
907C2#3779311yescharacteristic
908C2#3779811yescharacteristic
909C2#3822511yescharacteristic
910C2#3822911yescharacteristic
911C2#3827311yescharacteristic
912C2#3827911yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, prime radical, cosocleC24C25
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Maximal subgroups

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

subgroupindex
C2×#26472
C2×#22952
#166492
#166132
#164612
#164482
#152212
#151872
#151862
#151842
#149082
#148972
#147942
#147792
#146992
#142662
#142612
#140462
#140172
#139812
#139782
#137592