Finite Group Databasebeta

← #626908

Subgroups — #626908

Order 512.

2230 conjugacy classes of subgroups.

The subgroup lattice has 929 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16230C212yesmaximal, complemented
2#16126C212yesmaximal, complemented
3#16122C212yesmaximal, complemented
4#16120C212yesmaximal, complemented
5#15790C212yesmaximal, complemented
6#15766C212yesmaximal, complemented
7#15682C212yesmaximal, complemented
8#15676C212yesmaximal, complemented
9#14736C212yesmaximal
10#14728C212yesmaximal
11#14697C211yesmaximal, characteristic
12#14686C211yesmaximal, characteristic
13#14275C211yesmaximal, characteristic
14#14275C211yesmaximal, characteristic
15#14275C211yesmaximal, characteristic
16#14004C212yesmaximal
17#13883C212yesmaximal
18#13778C211yesmaximal, characteristic
19C2×#1436C211yesmaximal, characteristic
20C23×C4⋊C4C2211yescharacteristic
21C23×C42C2211yescharacteristic
22C2×#398C2212yes—
23C2×#398C2212yes—
24C2×#398C2212yes—
25C2×#389C2211yescharacteristic
26C2×#389C2212yes—
27C2×#389C2211yescharacteristic
28C2×#385C2212yes—
29C2×#385C2212yes—
30C2×#385C2212yes—
31C2×#385C2212yes—
32C2×#384C2211yescharacteristic
33C2×#384C2211yescharacteristic
34C2×#380C2211yescharacteristic
35C2×#380C2211yescharacteristic
36C2×#380C2211yescharacteristic
37C2×#380C2212yes—
38C2×#380C2212yes—
39C2×#380C2211yescharacteristic
40C2×C4×C22⋊C4C2212yes—
41C22×#95C2211yescharacteristic
42C22×#95C2211yescharacteristic
43C22×#95C2211yescharacteristic
44C22×#95C2211yescharacteristic
45C22×#95C2211yescharacteristic
46#1445C2212yes—
47#1444C2212yes—
48#1444C2212yes—
49#1444C2212yes—
50#1444C2212yes—
51#1444C2212yes—
52#1444C2212yes—
53#1444C2212yes—
54#1443C2212yes—
55#1443C2212yes—
56#1442C2212yes—
57#1442C2212yes—
58#1442C2212yes—
59#1442C2212yes—
60#1442C2212yes—
61#1442C2212yes—
62#1442C2212yes—
63#1442C2212yes—
64#1442C2212yes—
65#1442C2212yes—
66#1441C2212yes—
67#1441C2212yes—
68#1441C2212yes—
69#1441C2212yes—
70#1441C2212yes—
71#1441C2212yes—
72#1441C2212yes—
73#1441C2212yes—
74#1441C2212yes—
75#1441C2212yes—
76#1441C2212yes—
77#1441C2212yes—
78#1441C2212yes—
79#1436C2212yes—
80#1436C2212yes—
81#1436C2212yes—
82#1436C2212yes—
83#1436C2212yes—
84#1436C2212yes—
85#1436C2212yes—
86#1436C2212yes—
87#1436C2212yes—
88#1436C2212yes—
89#1436C2212yes—
90#1436C2212yes—
91#1436C2212yes—
92#1436C2212yes—
93C4⋊#95C2212yes—
94C4⋊#95C2212yes—
95C4⋊#95C2212yes—
96C4⋊#95C2211yescharacteristic
97C4⋊#95C2211yescharacteristic
98C4⋊#95C2211yescharacteristic
99C4⋊#95C2211yescharacteristic
100#1434C2212yes—
101#1434C2212yes—
102C22⋊#95C2212yes—
103C22⋊#95C2212yes—
104C22⋊#95C2212yes—
105C22⋊#95C2212yes—
106C22⋊#95C2212yes—
107C24×C4C2311yescharacteristic
108C24×C4C2311yescharacteristic
109C24×C4C2311yescharacteristic
110C24×C4C2311yescharacteristic
111C24×C4C2311yescharacteristic
112C24×C4C2311yescharacteristic
113C24×C4C2311yescharacteristic
114C22×C4⋊C4—24no—
115C22×C4⋊C4—42no—
116C22×C4⋊C4—42no—
117C22×C4⋊C4C2312yes—
118C22×C4⋊C4C2312yes—
119C22×C4⋊C4C2312yes—
120C22×C4⋊C4C2312yes—
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⋊C4C2311yescharacteristic
130C22×C4⋊C4C2311yescharacteristic
131C22×C4⋊C4C2312yes—
132C22×C4⋊C4C2312yes—
133C22×C4⋊C4C2312yes—
134C22×C4⋊C4C2312yes—
135C22×C4⋊C4C2312yes—
136C22×C4⋊C4C2312yes—
137C22×C4⋊C4C2311yescharacteristic
138C22×C4⋊C4C2311yescharacteristic
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2312yes—
143C22×C42—24no—
144C22×C42—42no—
145C22×C42—42no—
146C22×C42C2311yescharacteristic
147C22×C42C2311yescharacteristic
148C22×C42C2311yescharacteristic
149C22×C42C2311yescharacteristic
150C22×C42C2312yes—
151C22×C42C2312yes—
152#398—44no—
153#398—44no—
154#398—44no—
155#389—42no—
156#389—44no—
157#389—42no—
158#385—28no—
159#385—44no—
160#385—44no—
161#385—44no—
162#384—42no—
163#384—42no—
164#380—24no—
165#380—24no—
166#380—24no—
167#380—44no—
168#380—44no—
169#380Q818yes—
170C4×C22⋊C4—44no—
171C2×#95—24no—
172C2×#95—24no—
173C2×#95—42no—
174C2×#95—42no—
175C2×#95Q818yes—
176C2×#95C2312yes—
177C2×#95C2312yes—
178C2×#95C2312yes—
179C2×#95C2312yes—
180C2×#95C2312yes—
181C2×#95C2312yes—
182C2×#95C2312yes—
183C2×#95C2312yes—
184C2×#95C2312yes—
185C2×#95C2312yes—
186C2×#95C2312yes—
187C2×#95C2312yes—
188C2×#95C2312yes—
189C2×#95C2312yes—
190C2×#95C2312yes—
191C2×#95C2312yes—
192C2×#95C2312yes—
193C2×#95C2312yes—
194C2×#95C2312yes—
195C2×#95C2312yes—
196C2×#95C2312yes—
197C2×#95C2312yes—
198C2×#95C2312yes—
199C2×#95C2312yes—
200C2×#95C2312yes—
201C2×#95C2312yes—
202C2×#95C2312yes—
203C2×#95C2312yes—
204C2×#95C2312yes—
205C2×#95C2312yes—
206C2×#95C2312yes—
207C2×#95C2312yes—
208C2×#95C2312yes—
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—
224C25C2411yescharacteristic
225C23×C4—22no—
226C23×C4—22no—
227C23×C4—22no—
228C23×C4—22no—
229C23×C4—22no—
230C23×C4—22no—
231C23×C4—22no—
232C23×C4—22no—
233C23×C4—22no—
234C23×C4—22no—
235C23×C4—22no—
236C23×C4—22no—
237C23×C4—22no—
238C23×C4—22no—
239C23×C4—22no—
240C23×C4—22no—
241C23×C4—22no—
242C23×C4—22no—
243C23×C4—41no—
244C23×C4—41no—
245C23×C4—41no—
246C23×C4—41no—
247C23×C4—41no—
248C23×C4—41no—
249C23×C4—41no—
250C23×C4—41no—
251C23×C4—41no—
252C23×C4—41no—
253C23×C4—41no—
254C23×C4—41no—
255C23×C4—41no—
256C23×C4—41no—
257C23×C4—41no—
258C23×C4—41no—
259C23×C4—41no—
260C23×C4—41no—
261C23×C4—41no—
262C23×C4—41no—
263C23×C4—41no—
264C23×C4—41no—
265C23×C4—41no—
266C23×C4—41no—
267C23×C4C2×Q814yes—
268C23×C4C2×Q814yes—
269C23×C4C2×Q814yes—
270C23×C4C2×Q814yes—
271C23×C4#4114yes—
272C23×C4#4114yes—
273C23×C4#4114yes—
274C23×C4C2412yes—
275C23×C4C2412yes—
276C23×C4C2412yes—
277C23×C4C2412yes—
278C23×C4C2412yes—
279C23×C4C2412yes—
280C23×C4C2412yes—
281C23×C4C2412yes—
282C23×C4C2412yes—
283C23×C4C2412yes—
284C23×C4C2412yes—
285C23×C4C2412yes—
286C23×C4C2411yescharacteristic
287C23×C4C2411yescharacteristic
288C23×C4C2411yescharacteristic
289C23×C4C2411yescharacteristic
290C23×C4C2411yescharacteristic
291C23×C4C2411yescharacteristic
292C2×C4⋊C4—24no—
293C2×C4⋊C4—24no—
294C2×C4⋊C4—24no—
295C2×C4⋊C4—24no—
296C2×C4⋊C4—24no—
297C2×C4⋊C4—24no—
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—24no—
306C2×C4⋊C4—24no—
307C2×C4⋊C4—24no—
308C2×C4⋊C4—24no—
309C2×C4⋊C4—24no—
310C2×C4⋊C4—42no—
311C2×C4⋊C4—42no—
312C2×C4⋊C4—41no—
313C2×C4⋊C4—41no—
314C2×C4⋊C4—41no—
315C2×C4⋊C4—41no—
316C2×C4⋊C4—416no—
317C2×C4⋊C4—41no—
318C2×C4⋊C4—41no—
319C2×C4⋊C4—41no—
320C2×C4⋊C4—42no—
321C2×C4⋊C4—42no—
322C2×C4⋊C4—41no—
323C2×C4⋊C4—41no—
324C2×C4⋊C4—41no—
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—41no—
336C2×C4⋊C4—42no—
337C2×C4⋊C4—41no—
338C2×C4⋊C4—41no—
339C2×C4⋊C4—42no—
340C2×C4⋊C4—41no—
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—41no—
348C2×C4⋊C4—41no—
349C2×C4⋊C4—42no—
350C2×C4⋊C4—42no—
351C2×C4⋊C4—42no—
352C2×C4⋊C4—42no—
353C2×C4⋊C4—42no—
354C2×C4⋊C4—42no—
355C2×C4⋊C4—42no—
356C2×C4⋊C4—42no—
357C2×C4⋊C4C2×Q814yes—
358C2×C4⋊C4C2×Q814yes—
359C2×C22⋊C4—24no—
360C2×C22⋊C4—24no—
361C2×C22⋊C4—24no—
362C2×C22⋊C4—24no—
363C2×C22⋊C4—24no—
364C2×C22⋊C4—24no—
365C2×C22⋊C4—24no—
366C2×C22⋊C4—24no—
367C2×C22⋊C4—24no—
368C2×C22⋊C4—24no—
369C2×C22⋊C4—24no—
370C2×C22⋊C4C2×Q818yes—
371C2×C42—22no—
372C2×C42—22no—
373C2×C42—22no—
374C2×C42—22no—
375C2×C42—22no—
376C2×C42—22no—
377C2×C42—22no—
378C2×C42—22no—
379C2×C42—416no—
380C2×C42—41no—
381C2×C42—41no—
382C2×C42—41no—
383C2×C42—41no—
384C2×C42—42no—
385C2×C42—42no—
386C2×C42—42no—
387C2×C42—42no—
388C2×C42—42no—
389C2×C42—42no—
390#95—24no—
391#95—24no—
392#95—24no—
393#95—24no—
394#95—24no—
395#95—24no—
396#95—24no—
397#95—24no—
398#95—24no—
399#95—24no—
400#95—24no—
401#95—24no—
402#95—24no—
403#95—42no—
404#95—42no—
405#95—42no—
406#95—42no—
407#95—42no—
408#95—42no—
409#95—42no—
410#95—42no—
411#95—42no—
412#95—42no—
413#95—42no—
414#95—42no—
415#95—42no—
416#95—42no—
417#95—42no—
418#95—42no—
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—42no—
434#95—42no—
435#95C2×Q818yes—
436#95C2×Q818yes—
437#95C2×Q818yes—
438C24—21no—
439C24—21no—
440C24—21no—
441C24—21no—
442C24—21no—
443C24—21no—
444C24—21no—
445C24—21no—
446C24C22×Q812yes—
447C24C22×Q812yes—
448C24C2×#4112yes—
449C24C2×#4112yes—
450C24C2×#4112yes—
451C24H(5,𝔽2)12yes—
452C24H(5,𝔽2)12yes—
453C24C2511yescharacteristic
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
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—28no—
471C22×C4—28no—
472C22×C4—28no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—22no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—22no—
497C22×C4—21no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—21no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—21no—
509C22×C4—28no—
510C22×C4—28no—
511C22×C4—28no—
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—22no—
528C22×C4—22no—
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—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
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—44no—
569C22×C4—44no—
570C22×C4—44no—
571C22×C4—44no—
572C22×C4—44no—
573C22×C4—44no—
574C22×C4—44no—
575C22×C4—44no—
576C22×C4—44no—
577C22×C4—44no—
578C22×C4—44no—
579C22×C4—44no—
580C22×C4—44no—
581C22×C4—44no—
582C22×C4—44no—
583C22×C4—44no—
584C22×C4—44no—
585C22×C4—44no—
586C22×C4—44no—
587C22×C4—44no—
588C22×C4—44no—
589C22×C4—44no—
590C22×C4—44no—
591C22×C4—44no—
592C22×C4—44no—
593C22×C4—44no—
594C22×C4—44no—
595C22×C4—44no—
596C22×C4—44no—
597C22×C4—44no—
598C22×C4—82no—
599C22×C4—82no—
600C22×C4—82no—
601C22×C4—82no—
602C22×C4—82no—
603C22×C4—82no—
604C22×C4—82no—
605C22×C4—82no—
606C22×C4—82no—
607C22×C4—82no—
608C22×C4—82no—
609C22×C4—82no—
610C22×C4#125116yes—
611C22×C4C22×Q814yes—
612C22×C4C22×Q812yes—
613C22×C4C22×Q814yes—
614C22×C4C22×Q814yes—
615C22×C4C22×Q814yes—
616C22×C4C22×Q812yes—
617C22×C4C22×Q812yes—
618C22×C4C22×Q812yes—
619C22×C4C2×#4112yes—
620C22×C4C2×#4112yes—
621C22×C4C2×#4112yes—
622C22×C4C2×#4112yes—
623C22×C4C2×#4112yes—
624C22×C4C2×#4112yes—
625C22×C4H(5,𝔽2)12yes—
626C22×C4H(5,𝔽2)12yes—
627C22×C4H(5,𝔽2)12yes—
628C22×C42−1+412yes—
629C4⋊C4—44no—
630C4⋊C4—44no—
631C4⋊C4—48no—
632C4⋊C4—48no—
633C4⋊C4—48no—
634C4⋊C4—82no—
635C4⋊C4—82no—
636C4⋊C4—82no—
637C4⋊C4—82no—
638C4⋊C4—82no—
639C4⋊C4—82no—
640C4⋊C4—84no—
641C4⋊C4—84no—
642C4⋊C4—84no—
643C4⋊C4—84no—
644C4⋊C4—84no—
645C4⋊C4—84no—
646C4⋊C4—84no—
647C4⋊C4—84no—
648C4⋊C4—84no—
649C4⋊C4—84no—
650C4⋊C4—84no—
651C22⋊C4—216no—
652C22⋊C4—48no—
653C22⋊C4—48no—
654C22⋊C4—48no—
655C42—28no—
656C42—44no—
657C42—44no—
658C42—44no—
659C42—84no—
660C42—84no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—22no—
670C23—22no—
671C23—22no—
672C23—22no—
673C23—22no—
674C23—22no—
675C23—22no—
676C23—22no—
677C23—22no—
678C23—22no—
679C23—22no—
680C23—22no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—22no—
689C23C2×#12514yes—
690C23#53314yes—
691C23#54014yes—
692C23#55314yes—
693C23#55414yes—
694C23#55414yes—
695C23Q8214yes—
696C23C23×Q811yescharacteristic
697C23C23×Q811yescharacteristic
698C23C22×#4111yescharacteristic
699C23C22×#4111yescharacteristic
700C23C22×#4111yescharacteristic
701C23C2×H(5,𝔽2)11yescharacteristic
702C23C2×H(5,𝔽2)11yescharacteristic
703C23C2×H(5,𝔽2)11yescharacteristic
704C23C2×H(5,𝔽2)11yescharacteristic
705C23C2×H(5,𝔽2)11yescharacteristic
706C23C2×2−1+411yescharacteristic
707C23#58511yescharacteristic
708C23#58511yescharacteristic
709C23#58511yescharacteristic
710C23#58511yescharacteristic
711C2×C4—22no—
712C2×C4—22no—
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—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—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—24no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—24no—
739C2×C4—22no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—22no—
743C2×C4—24no—
744C2×C4—24no—
745C2×C4—24no—
746C2×C4—24no—
747C2×C4—24no—
748C2×C4—22no—
749C2×C4—24no—
750C2×C4—24no—
751C2×C4—24no—
752C2×C4—22no—
753C2×C4—416no—
754C2×C4—416no—
755C2×C4—416no—
756C2×C4—416no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—42no—
764C2×C4—41no—
765C2×C4—42no—
766C2×C4—41no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—42no—
775C2×C4—41no—
776C2×C4—41no—
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—42no—
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—42no—
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—42no—
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—42no—
832C2×C4—42no—
833C2×C4—42no—
834C2×C4—42no—
835C2×C4—42no—
836C2×C4—42no—
837C2×C4—88no—
838C2×C4—88no—
839C2×C4—88no—
840C2×C4C2×#12514yes—
841C2×C4C2×#12514yes—
842C2×C4#53814yes—
843C2×C4#54414yes—
844C22—24no—
845C22—24no—
846C22—24no—
847C22—24no—
848C22—24no—
849C22—24no—
850C22—24no—
851C22—24no—
852C22—24no—
853C22—24no—
854C22—24no—
855C22—24no—
856C22—24no—
857C22—24no—
858C22#250718yes—
859C22C22×#12511yescharacteristic
860C22C2×#53311yescharacteristic
861C22C2×#53811yescharacteristic
862C22C2×#54011yescharacteristic
863C22#345511yescharacteristic
864C22C2×#54411yescharacteristic
865C22#345811yescharacteristic
866C22C2×#55311yescharacteristic
867C22C2×#55411yescharacteristic
868C22C2×#55411yescharacteristic
869C22C2×Q8211yescharacteristic
870C22#349011yescharacteristic
871C22#349111yescharacteristic
872C22#349411yescharacteristic
873C22#349511yescharacteristic
874C22#350111yescharacteristic
875C22#350111yescharacteristic
876C22#350111yescharacteristic
877C22#350111yescharacteristic
878C22#350311yescharacteristic
879C22#350411yescharacteristic
880C22#350511yescharacteristic
881C22#350511yescharacteristic
882C22#350511yescharacteristic
883C22#350611yescharacteristic
884C22#350711yescharacteristic
885C22#350711yescharacteristic
886C22#353411yescharacteristic
887C22#353411yescharacteristic
888C22#353611yescharacteristic
889C22#353711yescharacteristic
890C22#355811yescharacteristic
891C22#355911yescharacteristic
892C22#356011yescharacteristic
893C22#356011yescharacteristic
894C4—24no—
895C4—24no—
896C4—24no—
897C4—24no—
898C4—42no—
899C4—44no—
900C4—44no—
901C4—44no—
902C4—42no—
903C4—44no—
904C4—82no—
905C4—82no—
906C4—82no—
907C4—82no—
908C4—82no—
909C4—82no—
910C4—82no—
911C4—82no—
912C2—28no—
913C2C2×#250711yescharacteristic
914C2#3501411yescharacteristic
915C2#3510411yescharacteristic
916C2#3536811yescharacteristic
917C2#3554311yescharacteristic
918C2#3675911yescharacteristic
919C2#3676111yescharacteristic
920C2#3787311yescharacteristic
921C2#3787611yescharacteristic
922C2#3789111yescharacteristic
923C2#3789611yescharacteristic
924C2#3962011yescharacteristic
925C2#3962311yescharacteristic
926C2#3962711yescharacteristic
927C2#3963211yescharacteristic
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
1. #16230C2semidirect
2. #16126C2semidirect
3. #16122C2semidirect
4. #16120C2semidirect
5. #15790C2semidirect
6. #15766C2semidirect
7. #15682C2semidirect
8. #15676C2semidirect

Maximal subgroups

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

subgroupindex
#162302
#161262
#161222
#161202
#157902
#157662
#156822
#156762
#147362
#147282
#146972
#146862
#142752
#140042
#138832
#137782
C2×#14362