Finite Group Databasebeta

← #931656

Subgroups — #931656

Order 512.

1698 conjugacy classes of subgroups.

The subgroup lattice has 898 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17292C212yesmaximal
2#17245C212yesmaximal
3#16959C212yesmaximal
4#16948C212yesmaximal
5#16925C212yesmaximal
6#16872C212yesmaximal
7#15798C212yesmaximal
8#15790C212yesmaximal
9#15231C211yesmaximal, characteristic
10#15225C211yesmaximal, characteristic
11#15189C211yesmaximal, characteristic
12#15184C211yesmaximal, characteristic
13#15139C211yesmaximal, characteristic
14#15137C211yesmaximal, characteristic
15#14276C211yesmaximal, characteristic
16#14261C211yesmaximal, characteristic
17#14041C211yesmaximal, characteristic
18#14017C211yesmaximal, characteristic
19#14000C211yesmaximal, characteristic
20#13978C211yesmaximal, characteristic
21#13978C211yesmaximal, characteristic
22#13910C211yesmaximal, characteristic
23#13846C211yesmaximal, characteristic
24C22×C4×Q8C2211yescharacteristic
25C2×#400C2212yes—
26C2×#398C2212yes—
27C2×#391C2211yescharacteristic
28C2×#391C2211yescharacteristic
29C2×#391C2211yescharacteristic
30C2×#391C2211yescharacteristic
31C2×#391C2211yescharacteristic
32C2×#391C2211yescharacteristic
33C2×#389C2211yescharacteristic
34C2×#389C2211yescharacteristic
35C2×#389C2211yescharacteristic
36C2×#389C2211yescharacteristic
37C2×#389C2211yescharacteristic
38C2×#389C2211yescharacteristic
39C2×#389C2211yescharacteristic
40C2×#389C2211yescharacteristic
41C2×#384C2211yescharacteristic
42C2×#384C2211yescharacteristic
43C2×#384C2212yes—
44C2×#382C2211yescharacteristic
45C2×#382C2211yescharacteristic
46C2×C4×C4⋊C4C2211yescharacteristic
47C2×C4×C4⋊C4C2211yescharacteristic
48C2×C4×C4⋊C4C2211yescharacteristic
49C2×#376C2211yescharacteristic
50#1445C2211yescharacteristic
51#1445C2211yescharacteristic
52#1445C2212yes—
53#1445C2212yes—
54#1444C2212yes—
55#1444C2212yes—
56#1444C2212yes—
57#1444C2212yes—
58#1443C2211yescharacteristic
59#1443C2211yescharacteristic
60#1443C2212yes—
61#1443C2212yes—
62#1443C2212yes—
63#1443C2212yes—
64#1442C2211yescharacteristic
65#1442C2211yescharacteristic
66#1442C2212yes—
67#1442C2212yes—
68#1442C2212yes—
69#1442C2212yes—
70#1442C2212yes—
71#1442C2212yes—
72#1442C2212yes—
73#1442C2212yes—
74#1442C2212yes—
75#1442C2212yes—
76#1442C2212yes—
77#1442C2212yes—
78#1442C2212yes—
79#1442C2212yes—
80#1442C2212yes—
81#1442C2212yes—
82#1441C2211yescharacteristic
83#1441C2211yescharacteristic
84#1441C2212yes—
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—
110C4⋊#95C2211yescharacteristic
111C4⋊#95C2211yescharacteristic
112C4⋊#95C2211yescharacteristic
113C4⋊#95C2211yescharacteristic
114C4⋊#95C2211yescharacteristic
115C4⋊#95C2212yes—
116C4⋊#95C2211yescharacteristic
117C4⋊#95C2211yescharacteristic
118C4⋊#95C2211yescharacteristic
119C4×#95C2211yescharacteristic
120C4×#95C2211yescharacteristic
121C4×#95C2211yescharacteristic
122C4×#95C2211yescharacteristic
123C23×Q8C2311yescharacteristic
124C2×C4×Q8—42no—
125C2×C4×Q8—42no—
126C2×C4×Q8—42no—
127C22×C4⋊C4C2311yescharacteristic
128C22×C4⋊C4C2311yescharacteristic
129C22×C4⋊C4C2311yescharacteristic
130C22×C4⋊C4C2311yescharacteristic
131C22×C4⋊C4C2311yescharacteristic
132C22×C4⋊C4C2311yescharacteristic
133C22×C4⋊C4C2311yescharacteristic
134C22×C4⋊C4C2311yescharacteristic
135C22×C4⋊C4C2311yescharacteristic
136C22×C4⋊C4C2311yescharacteristic
137C22×C4⋊C4C2312yes—
138C22×C4⋊C4C2312yes—
139C22×C4⋊C4C2312yes—
140C22×C4⋊C4C2312yes—
141C22×C4⋊C4C2311yescharacteristic
142C22×C4⋊C4C2312yes—
143C22×C4⋊C4C2312yes—
144C22×C4⋊C4C2312yes—
145C22×C4⋊C4C2312yes—
146C22×C4⋊C4C2312yes—
147C22×C4⋊C4C2312yes—
148C22×C4⋊C4C2312yes—
149C22×C4⋊C4C2312yes—
150C22×C4⋊C4C2312yes—
151C22×C42C2311yescharacteristic
152C22×C42C2311yescharacteristic
153C22×C42C2311yescharacteristic
154C22×C42C2311yescharacteristic
155C22×C42C2311yescharacteristic
156C22×C42C2311yescharacteristic
157C22×C42C2311yescharacteristic
158C22×C42C2312yes—
159C22×C42C2312yes—
160#400—44no—
161#398—44no—
162#391—24no—
163#391—24no—
164#391—42no—
165#391—42no—
166#391—42no—
167#391Q818yes—
168#389—24no—
169#389—42no—
170#389—42no—
171#389—42no—
172#389—42no—
173#389—42no—
174#389—42no—
175#389—42no—
176#384—24no—
177#384—42no—
178#384—44no—
179#382—42no—
180#382—42no—
181C4×C4⋊C4—24no—
182C4×C4⋊C4—24no—
183C4×C4⋊C4—42no—
184#376—42no—
185C2×#95C2311yescharacteristic
186C2×#95C2312yes—
187C2×#95C2311yescharacteristic
188C2×#95C2311yescharacteristic
189C2×#95C2311yescharacteristic
190C2×#95C2311yescharacteristic
191C2×#95C2311yescharacteristic
192C2×#95C2312yes—
193C2×#95C2312yes—
194C2×#95C2312yes—
195C2×#95C2311yescharacteristic
196C2×#95C2312yes—
197C2×#95C2312yes—
198C2×#95C2312yes—
199C2×#95C2312yes—
200C2×#95C2311yescharacteristic
201C2×#95C2312yes—
202C2×#95C2312yes—
203C2×#95C2312yes—
204C2×#95C2312yes—
205C2×#95C2312yes—
206C2×#95C2311yescharacteristic
207C2×#95C2311yescharacteristic
208C2×#95C2311yescharacteristic
209C2×#95C2311yescharacteristic
210C2×#95C2311yescharacteristic
211C2×#95C2311yescharacteristic
212C2×#95C2311yescharacteristic
213C2×#95C2311yescharacteristic
214C2×#95C2311yescharacteristic
215C2×#95C2311yescharacteristic
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×#95C2311yescharacteristic
230C2×#95C2312yes—
231C2×#95C2312yes—
232C2×#95C2312yes—
233C2×#95C2312yes—
234C2×#95C2312yes—
235C2×#95C2312yes—
236C2×#95C2312yes—
237C2×#95C2312yes—
238C2×#95C2312yes—
239C2×#95C2312yes—
240C2×#95C2312yes—
241C2×#95C2311yescharacteristic
242C2×#95C2312yes—
243C2×#95C2311yescharacteristic
244C2×#95C2311yescharacteristic
245C2×#95C2311yescharacteristic
246C2×#95C2312yes—
247C2×#95C2311yescharacteristic
248C2×#95C2312yes—
249C2×#95C2312yes—
250C22×Q8—22no—
251C22×Q8—22no—
252C22×Q8—22no—
253C22×Q8—22no—
254C22×Q8—22no—
255C22×Q8—22no—
256C22×Q8C2×Q814yes—
257C23×C4C2412yes—
258C23×C4C2412yes—
259C23×C4C2412yes—
260C23×C4C2411yescharacteristic
261C23×C4C2411yescharacteristic
262C23×C4C2412yes—
263C23×C4C2411yescharacteristic
264C23×C4C2411yescharacteristic
265C23×C4C2412yes—
266C23×C4C2411yescharacteristic
267C23×C4C2411yescharacteristic
268C23×C4C2411yescharacteristic
269C23×C4C2411yescharacteristic
270C23×C4C2412yes—
271C23×C4C2411yescharacteristic
272C23×C4C2411yescharacteristic
273C23×C4C2412yes—
274C23×C4C2412yes—
275C23×C4C2411yescharacteristic
276C23×C4C2411yescharacteristic
277C23×C4C2411yescharacteristic
278C23×C4C2411yescharacteristic
279C23×C4C2411yescharacteristic
280C4×Q8—416no—
281C2×C4⋊C4—22no—
282C2×C4⋊C4—22no—
283C2×C4⋊C4—22no—
284C2×C4⋊C4—22no—
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—22no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4—22no—
295C2×C4⋊C4—22no—
296C2×C4⋊C4—22no—
297C2×C4⋊C4—22no—
298C2×C4⋊C4—22no—
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—22no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—24no—
309C2×C4⋊C4—24no—
310C2×C4⋊C4—24no—
311C2×C4⋊C4—24no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4—41no—
315C2×C4⋊C4—41no—
316C2×C4⋊C4—42no—
317C2×C4⋊C4—42no—
318C2×C4⋊C4—42no—
319C2×C4⋊C4—41no—
320C2×C4⋊C4—41no—
321C2×C4⋊C4—42no—
322C2×C4⋊C4—42no—
323C2×C4⋊C4—42no—
324C2×C4⋊C4—42no—
325C2×C4⋊C4—42no—
326C2×C4⋊C4—42no—
327C2×C4⋊C4—42no—
328C2×C4⋊C4—42no—
329C2×C4⋊C4—42no—
330C2×C4⋊C4—42no—
331C2×C4⋊C4—42no—
332C2×C4⋊C4—42no—
333C2×C4⋊C4—42no—
334C2×C4⋊C4—42no—
335C2×C4⋊C4—42no—
336C2×C4⋊C4—42no—
337C2×C4⋊C4—42no—
338C2×C4⋊C4—42no—
339C2×C4⋊C4—42no—
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⋊C4C2×Q814yes—
352C2×C4⋊C4#4114yes—
353C2×C42—22no—
354C2×C42—22no—
355C2×C42—22no—
356C2×C42—22no—
357C2×C42—24no—
358C2×C42—22no—
359C2×C42—22no—
360C2×C42—22no—
361C2×C42—22no—
362C2×C42—22no—
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—42no—
374C2×C42—42no—
375C2×C42—42no—
376C2×C42—42no—
377C2×C42—42no—
378C2×C42C2×Q814yes—
379C2×C42#4114yes—
380#95—24no—
381#95—22no—
382#95—22no—
383#95—24no—
384#95—24no—
385#95—24no—
386#95—24no—
387#95—24no—
388#95—22no—
389#95—24no—
390#95—22no—
391#95—22no—
392#95—24no—
393#95—22no—
394#95—22no—
395#95—22no—
396#95—24no—
397#95—41no—
398#95—41no—
399#95—42no—
400#95—42no—
401#95—42no—
402#95—42no—
403#95—41no—
404#95—42no—
405#95—41no—
406#95—41no—
407#95—41no—
408#95—42no—
409#95—42no—
410#95—41no—
411#95—41no—
412#95—42no—
413#95—41no—
414#95—41no—
415#95—42no—
416#95—41no—
417#95—41no—
418#95—41no—
419#95—41no—
420#95—41no—
421#95—41no—
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—42no—
434#95—42no—
435#95—42no—
436#95—42no—
437#95—42no—
438#95—42no—
439#95—42no—
440#95—42no—
441#95—42no—
442#95—42no—
443#95C2×Q818yes—
444#95C2×Q818yes—
445C24C2511yescharacteristic
446C2×Q8—28no—
447C2×Q8—28no—
448C2×Q8—28no—
449C2×Q8—44no—
450C2×Q8—44no—
451C2×Q8—44no—
452C2×Q8—44no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—22no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—22no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—22no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—22no—
493C22×C4—21no—
494C22×C4—22no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—22no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—22no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—22no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—22no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—22no—
512C22×C4—21no—
513C22×C4—22no—
514C22×C4—21no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
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—21no—
547C22×C4—22no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—22no—
552C22×C4—21no—
553C22×C4—22no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—22no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—21no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—21no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4C22×Q812yes—
597C22×C4C22×Q812yes—
598C22×C4C22×Q814yes—
599C22×C4C22×Q814yes—
600C22×C4C22×Q812yes—
601C22×C4C2×#4112yes—
602C22×C4C2×#4114yes—
603C22×C4C2×#4112yes—
604C22×C4C2×#4112yes—
605C22×C4C2×#4112yes—
606C22×C4H(5,𝔽2)12yes—
607C22×C4H(5,𝔽2)12yes—
608C22×C4H(5,𝔽2)12yes—
609C22×C4H(5,𝔽2)12yes—
610C22×C42−1+412yes—
611C22×C42−1+412yes—
612C22×C42−1+412yes—
613C22×C42−1+412yes—
614C4⋊C4—28no—
615C4⋊C4—28no—
616C4⋊C4—44no—
617C4⋊C4—44no—
618C4⋊C4—44no—
619C4⋊C4—48no—
620C4⋊C4—44no—
621C4⋊C4—44no—
622C4⋊C4—44no—
623C4⋊C4—44no—
624C4⋊C4—44no—
625C4⋊C4—44no—
626C4⋊C4—84no—
627C4⋊C4—84no—
628C4⋊C4—84no—
629C4⋊C4—84no—
630C4⋊C4—84no—
631C4⋊C4—84no—
632C4⋊C4—84no—
633C4⋊C4—84no—
634C4⋊C4—84no—
635C4⋊C4—84no—
636C4⋊C4—84no—
637C4⋊C4—84no—
638C42—28no—
639C42—28no—
640C42—48no—
641C42—48no—
642C42—44no—
643C42—44no—
644C42—44no—
645C42—44no—
646C42—44no—
647C23C23×Q811yescharacteristic
648C23C22×#4111yescharacteristic
649C23C22×#4111yescharacteristic
650C23C2×H(5,𝔽2)11yescharacteristic
651C23C2×H(5,𝔽2)11yescharacteristic
652C23C2×H(5,𝔽2)11yescharacteristic
653C23C2×H(5,𝔽2)11yescharacteristic
654C23C2×2−1+411yescharacteristic
655C23C2×2−1+411yescharacteristic
656C23C2×2−1+411yescharacteristic
657C23C2×2−1+411yescharacteristic
658C23#58511yescharacteristic
659C23#58511yescharacteristic
660C23#58511yescharacteristic
661C23#58511yescharacteristic
662Q8—416no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—24no—
671C2×C4—24no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—24no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—24no—
683C2×C4—22no—
684C2×C4—24no—
685C2×C4—22no—
686C2×C4—24no—
687C2×C4—24no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—42no—
694C2×C4—41no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—41no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—42no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—42no—
720C2×C4—41no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—42no—
731C2×C4—41no—
732C2×C4—42no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—42no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—42no—
740C2×C4—41no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—42no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—41no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—42no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—42no—
767C2×C4—41no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—42no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—42no—
777C2×C4—41no—
778C2×C4—42no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—42no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—41no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—41no—
793C2×C4—42no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—42no—
799C2×C4—41no—
800C2×C4—42no—
801C2×C4—41no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—41no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—42no—
815C2×C4—41no—
816C2×C4#53914yes—
817C2×C4#54114yes—
818C2×C4#54214yes—
819C2×C4#54414yes—
820C2×C4#55314yes—
821C2×C4#55414yes—
822C2×C4#55414yes—
823C2×C4#56014yes—
824C22C2×#53911yescharacteristic
825C22C2×#54111yescharacteristic
826C22C2×#54211yescharacteristic
827C22C2×#54411yescharacteristic
828C22#346011yescharacteristic
829C22C2×#55311yescharacteristic
830C22C2×#55411yescharacteristic
831C22C2×#55411yescharacteristic
832C22#349511yescharacteristic
833C22#350211yescharacteristic
834C22#350211yescharacteristic
835C22#350311yescharacteristic
836C22#350411yescharacteristic
837C22#351211yescharacteristic
838C22#351411yescharacteristic
839C22#351811yescharacteristic
840C22#352111yescharacteristic
841C22#352311yescharacteristic
842C22C2×#56011yescharacteristic
843C22#353611yescharacteristic
844C22#354111yescharacteristic
845C22#354711yescharacteristic
846C22#355111yescharacteristic
847C22#355211yescharacteristic
848C22#355211yescharacteristic
849C22#355411yescharacteristic
850C22#355411yescharacteristic
851C22#355411yescharacteristic
852C22#355411yescharacteristic
853C22#355511yescharacteristic
854C22#355811yescharacteristic
855C22#355811yescharacteristic
856C22#356211yescharacteristic
857C22#356311yescharacteristic
858C22#356511yescharacteristic
859C4—24no—
860C4—44no—
861C4—42no—
862C4—42no—
863C4—44no—
864C4—42no—
865C4—42no—
866C4—42no—
867C4—44no—
868C4—81no—
869C4—82no—
870C4—81no—
871C4—81no—
872C4—81no—
873C4—82no—
874C4—81no—
875C4—81no—
876C4—82no—
877C4—81no—
878C4—81no—
879C4—82no—
880C4—82no—
881C4#279018yes—
882C2#3740311yescharacteristic
883C2#3750411yescharacteristic
884C2#3914911yescharacteristic
885C2#3928411yescharacteristic
886C2#3963511yescharacteristic
887C2#3967411yescharacteristic
888C2#4275411yescharacteristic
889C2#4276311yescharacteristic
890C2#4282511yescharacteristic
891C2#4282611yescharacteristic
892C2#4519011yescharacteristic
893C2#4540911yescharacteristic
894C2C2×#279011yescharacteristic
895C2#5296011yescharacteristic
896C2#5304711yescharacteristic
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
#172922
#172452
#169592
#169482
#169252
#168722
#157982
#157902
#152312
#152252
#151892
#151842
#151392
#151372
#142762
#142612
#140412
#140172
#140002
#139782
#139102
#138462