Finite Group Databasebeta

← #6051837

Subgroups — #6051837

Order 512.

1840 conjugacy classes of subgroups.

The subgroup lattice has 859 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17234C211yesmaximal, characteristic, complemented
2#17197C211yesmaximal, characteristic, complemented
3#17142C212yesmaximal, complemented
4#17137C211yesmaximal, characteristic, complemented
5#17100C212yesmaximal, complemented
6#17084C212yesmaximal, complemented
7#16664C212yesmaximal, complemented
8#16638C212yesmaximal, complemented
9#16552C212yesmaximal
10#16422C212yesmaximal, complemented
11#16385C212yesmaximal, complemented
12#16368C212yesmaximal, complemented
13#16116C211yesmaximal, characteristic, complemented
14#15931C212yesmaximal, complemented
15#15862C212yesmaximal, complemented
16#15479C212yesmaximal, complemented
17#15160C211yesmaximal, characteristic
18#15063C211yesmaximal, characteristic, complemented
19#15045C211yesmaximal, characteristic, complemented
20C2×#398C2212yes—
21C2×#397C2212yes—
22C2×#397C2212yes—
23C2×#397C2211yescharacteristic
24C2×#396C2212yes—
25C2×#395C2212yes—
26C2×#394C2212yes—
27C2×#394C2212yes—
28C2×#394C2212yes—
29C2×#393C2212yes—
30C2×#393C2212yes—
31C2×#393C2212yes—
32C2×#392C2211yescharacteristic
33C2×#390C2211yescharacteristic
34C2×#390C2212yes—
35C2×#389C2211yescharacteristic
36C2×#387C2212yes—
37C2×#386C2212yes—
38C2×#383C2212yes—
39C2×#380C2211yescharacteristic
40C2×C4×C22⋊C4C2211yescharacteristic
41#1446C2212yes—
42#1446C2212yes—
43#1446C2212yes—
44#1445C2212yes—
45#1445C2211yescharacteristic
46#1445C2212yes—
47#1445C2211yescharacteristic
48#1445C2211yescharacteristic
49#1445C2212yes—
50#1444C2212yes—
51#1444C2211yescharacteristic
52#1443C2212yes—
53#1443C2212yes—
54#1443C2212yes—
55#1442C2212yes—
56#1442C2212yes—
57#1442C2212yes—
58#1442C2211yescharacteristic
59#1442C2211yescharacteristic
60#1442C2212yes—
61#1442C2211yescharacteristic
62#1441C2212yes—
63#1441C2212yes—
64#1441C2212yes—
65#1441C2212yes—
66#1441C2212yes—
67#1441C2212yes—
68#1440C2212yes—
69#1440C2212yes—
70#1440C2212yes—
71#1440C2212yes—
72#1440C2212yes—
73#1440C2212yes—
74#1440C2212yes—
75#1440C2212yes—
76#1440C2212yes—
77#1439C2212yes—
78#1439C2212yes—
79#1439C2212yes—
80#1439C2211yescharacteristic
81#1439C2212yes—
82#1439C2212yes—
83#1439C2212yes—
84#1439C2212yes—
85#1439C2212yes—
86#1439C2212yes—
87#1439C2212yes—
88#1439C2212yes—
89#1439C2212yes—
90#1439C2211yescharacteristic
91#1438C2212yes—
92#1438C2212yes—
93#1438C2212yes—
94#1438C2211yescharacteristic
95#1437C2212yes—
96#1437C2212yes—
97#1436C2212yes—
98#1436C2212yes—
99#1436C2212yes—
100#1436C2212yes—
101C4⋊#95C2211yescharacteristic
102#1434C2212yes—
103#1434C2212yes—
104#1434C2211yescharacteristic
105C22⋊#95C2212yes—
106C22⋊#95C2211yescharacteristic
107C23×Q8C2312yes—
108C23×D4C2312yes—
109C23×D4C2311yescharacteristic
110C24×C4C2311yescharacteristic
111C22×C4⋊C4C2312yes—
112C22×C4⋊C4C2312yes—
113C22×C4⋊C4C2312yes—
114C22×C4⋊C4C2312yes—
115C22×C4⋊C4C2311yescharacteristic
116C22×C4⋊C4C2311yescharacteristic
117C22×C4⋊C4C2312yes—
118C22×C4⋊C4C2312yes—
119C22×C4⋊C4C2312yes—
120C22×C4⋊C4C2311yescharacteristic
121C22×C4⋊C4C2311yescharacteristic
122C22×C4⋊C4C2311yescharacteristic
123C22×C22⋊C4C2311yescharacteristic
124C22×C22⋊C4C2311yescharacteristic
125C22×C22⋊C4C2312yes—
126C22×C22⋊C4C2312yes—
127C22×C22⋊C4C2312yes—
128C22×C22⋊C4C2312yes—
129C22×C22⋊C4C2312yes—
130C22×C22⋊C4C2312yes—
131C22×C22⋊C4C2312yes—
132C22×C22⋊C4C2312yes—
133C22×C22⋊C4C2312yes—
134C22×C22⋊C4C2312yes—
135C22×C22⋊C4C2312yes—
136C22×C22⋊C4C2312yes—
137C22×C22⋊C4C2312yes—
138C22×C22⋊C4C2312yes—
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2312yes—
143C22×C42C2311yescharacteristic
144C22×C42C2311yescharacteristic
145C22×C42C2312yes—
146#398—44no—
147#397—44no—
148#397—44no—
149#397—42no—
150#396—44no—
151#395—44no—
152#394—44no—
153#394—44no—
154#394—44no—
155#393—44no—
156#393—44no—
157#393—44no—
158#392—42no—
159#390—42no—
160#390—44no—
161#389—42no—
162#387—44no—
163#386—44no—
164#383—44no—
165#380—42no—
166C4×C22⋊C4—42no—
167C2×#95C2311yescharacteristic
168C2×#95C2311yescharacteristic
169C2×#95C2312yes—
170C2×#95C2312yes—
171C2×#95C2312yes—
172C2×#95C2312yes—
173C2×#95C2312yes—
174C2×#95C2312yes—
175C2×#95C2312yes—
176C2×#95C2312yes—
177C2×#95C2312yes—
178C2×#95C2311yescharacteristic
179C2×#95C2311yescharacteristic
180C2×#95C2312yes—
181C2×#95C2312yes—
182C2×#95C2312yes—
183C2×#95C2312yes—
184C2×#95C2312yes—
185C2×#95C2312yes—
186C2×#95C2312yes—
187C2×#95C2312yes—
188C2×#95C2312yes—
189C2×#95C2312yes—
190C2×#95C2312yes—
191C2×#95C2311yescharacteristic
192C2×#95C2312yes—
193C2×#95C2312yes—
194C2×#95C2312yes—
195C2×#95C2312yes—
196C2×#95C2312yes—
197C2×#95C2312yes—
198C2×#95C2311yescharacteristic
199C2×#95C2312yes—
200C2×#95C2312yes—
201C2×#95C2312yes—
202C2×#95C2312yes—
203C2×#95C2312yes—
204C2×#95C2312yes—
205C2×#95C2312yes—
206C2×#95C2312yes—
207C2×#95C2312yes—
208C2×#95C2312yes—
209C2×#95C2311yescharacteristic
210C2×#95C2312yes—
211C2×#95C2311yescharacteristic
212C2×#95C2312yes—
213C2×#95C2312yes—
214C2×#95C2312yes—
215C25C2412yes—
216C25C2411yescharacteristic
217C22×Q8—42no—
218C22×Q8—42no—
219C22×Q8—42no—
220C22×Q8—42no—
221C22×Q8—42no—
222C22×Q8—42no—
223C22×Q8—42no—
224C22×D4—24no—
225C22×D4—24no—
226C22×D4—22no—
227C22×D4—42no—
228C22×D4—42no—
229C22×D4—42no—
230C22×D4—42no—
231C22×D4—41no—
232C22×D4—42no—
233C22×D4—42no—
234C22×D4—41no—
235C22×D4—42no—
236C23×C4—22no—
237C23×C4—22no—
238C23×C4—42no—
239C23×C4—41no—
240C23×C4—42no—
241C23×C4C2412yes—
242C23×C4C2412yes—
243C23×C4C2412yes—
244C23×C4C2412yes—
245C23×C4C2412yes—
246C23×C4C2411yescharacteristic
247C23×C4C2412yes—
248C23×C4C2412yes—
249C23×C4C2412yes—
250C23×C4C2412yes—
251C23×C4C2412yes—
252C23×C4C2411yescharacteristic
253C23×C4C2411yescharacteristic
254C23×C4C2411yescharacteristic
255C23×C4C2412yes—
256C23×C4C2411yescharacteristic
257C23×C4C2411yescharacteristic
258C2×C4⋊C4—24no—
259C2×C4⋊C4—24no—
260C2×C4⋊C4—24no—
261C2×C4⋊C4—24no—
262C2×C4⋊C4—24no—
263C2×C4⋊C4—22no—
264C2×C4⋊C4—22no—
265C2×C4⋊C4—42no—
266C2×C4⋊C4—42no—
267C2×C4⋊C4—42no—
268C2×C4⋊C4—41no—
269C2×C4⋊C4—41no—
270C2×C4⋊C4—42no—
271C2×C4⋊C4—42no—
272C2×C4⋊C4—42no—
273C2×C4⋊C4—42no—
274C2×C4⋊C4—42no—
275C2×C4⋊C4—42no—
276C2×C4⋊C4—42no—
277C2×C4⋊C4—41no—
278C2×C4⋊C4—41no—
279C2×C4⋊C4—41no—
280C2×C4⋊C4—42no—
281C2×C4⋊C4—41no—
282C2×C4⋊C4—42no—
283C2×C4⋊C4—42no—
284C2×C4⋊C4—42no—
285C2×C4⋊C4—41no—
286C2×C4⋊C4—42no—
287C2×C4⋊C4—42no—
288C2×C4⋊C4—42no—
289C2×C4⋊C4—42no—
290C2×C4⋊C4—42no—
291C2×C22⋊C4—22no—
292C2×C22⋊C4—22no—
293C2×C22⋊C4—22no—
294C2×C22⋊C4—22no—
295C2×C22⋊C4—24no—
296C2×C22⋊C4—24no—
297C2×C22⋊C4—24no—
298C2×C22⋊C4—24no—
299C2×C22⋊C4—24no—
300C2×C22⋊C4—24no—
301C2×C22⋊C4—24no—
302C2×C22⋊C4—24no—
303C2×C22⋊C4—41no—
304C2×C22⋊C4—41no—
305C2×C22⋊C4—42no—
306C2×C22⋊C4—42no—
307C2×C22⋊C4—42no—
308C2×C22⋊C4—42no—
309C2×C22⋊C4—42no—
310C2×C22⋊C4—42no—
311C2×C22⋊C4—42no—
312C2×C22⋊C4—42no—
313C2×C22⋊C4—42no—
314C2×C22⋊C4—42no—
315C2×C22⋊C4—42no—
316C2×C22⋊C4—42no—
317C2×C22⋊C4—42no—
318C2×C22⋊C4—42no—
319C2×C22⋊C4—42no—
320C2×C22⋊C4—42no—
321C2×C22⋊C4—42no—
322C2×C22⋊C4—42no—
323C2×C22⋊C4—42no—
324C2×C22⋊C4—42no—
325C2×C22⋊C4—42no—
326C2×C22⋊C4—42no—
327C2×C22⋊C4—42no—
328C2×C22⋊C4—42no—
329C2×C22⋊C4—42no—
330C2×C22⋊C4—42no—
331C2×C22⋊C4—42no—
332C2×C22⋊C4—42no—
333C2×C22⋊C4—42no—
334C2×C22⋊C4—42no—
335C2×C22⋊C4—42no—
336C2×C22⋊C4—42no—
337C2×C22⋊C4—42no—
338C2×C22⋊C4—42no—
339C2×C22⋊C4—42no—
340C2×C22⋊C4—42no—
341C2×C22⋊C4—42no—
342C2×C22⋊C4—42no—
343C2×C22⋊C4—42no—
344C2×C22⋊C4—42no—
345C2×C22⋊C4—42no—
346C2×C22⋊C4—42no—
347C2×C22⋊C4—42no—
348C2×C22⋊C4—42no—
349C2×C22⋊C4—42no—
350C2×C22⋊C4—42no—
351C2×C42—24no—
352C2×C42—22no—
353C2×C42—22no—
354C2×C42—42no—
355C2×C42—42no—
356C2×C42—42no—
357C2×C42—42no—
358#95—24no—
359#95—22no—
360#95—24no—
361#95—24no—
362#95—24no—
363#95—24no—
364#95—24no—
365#95—22no—
366#95—22no—
367#95—24no—
368#95—24no—
369#95—24no—
370#95—42no—
371#95—42no—
372#95—42no—
373#95—42no—
374#95—42no—
375#95—42no—
376#95—42no—
377#95—41no—
378#95—42no—
379#95—42no—
380#95—42no—
381#95—41no—
382#95—41no—
383#95—42no—
384#95—42no—
385#95—42no—
386#95—42no—
387#95—42no—
388#95—42no—
389#95—42no—
390#95—41no—
391#95—42no—
392#95—42no—
393#95—42no—
394#95—42no—
395#95—42no—
396#95—42no—
397#95—42no—
398#95—42no—
399#95—42no—
400#95—42no—
401#95—41no—
402#95—42no—
403#95—42no—
404#95—42no—
405#95—42no—
406C24—21no—
407C24—21no—
408C24—22no—
409C24—21no—
410C24—21no—
411C24—21no—
412C24—21no—
413C24—22no—
414C24—22no—
415C24—22no—
416C24—22no—
417C24—22no—
418C24—22no—
419C24—22no—
420C24—22no—
421C24—22no—
422C24—22no—
423C24—22no—
424C24—22no—
425C24—22no—
426C24—22no—
427C24—22no—
428C24—22no—
429C24—22no—
430C24—22no—
431C24H(5,𝔽2)12yes—
432C24C2511yescharacteristic
433C2×Q8—84no—
434C2×Q8—84no—
435C2×Q8—84no—
436C2×Q8—84no—
437C2×Q8—84no—
438C2×Q8—84no—
439C2×Q8—84no—
440C2×D4—48no—
441C2×D4—48no—
442C2×D4—44no—
443C2×D4—82no—
444C2×D4—84no—
445C2×D4—84no—
446C2×D4—84no—
447C2×D4—84no—
448C2×D4—82no—
449C2×D4—84no—
450C2×D4—84no—
451C2×D4—84no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—22no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—21no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—21no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—21no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—21no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—21no—
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—44no—
554C22×C4—44no—
555C22×C4—82no—
556C22×C4—84no—
557C22×C4—84no—
558C22×C4H(5,𝔽2)12yes—
559C22×C4H(5,𝔽2)12yes—
560C22×C4H(5,𝔽2)12yes—
561C22×C4H(5,𝔽2)14yes—
562C22×C42−1+412yes—
563C22×C42−1+412yes—
564C4⋊C4—48no—
565C4⋊C4—44no—
566C4⋊C4—84no—
567C4⋊C4—82no—
568C4⋊C4—82no—
569C4⋊C4—84no—
570C4⋊C4—84no—
571C4⋊C4—84no—
572C4⋊C4—82no—
573C4⋊C4—82no—
574C4⋊C4—84no—
575C4⋊C4—84no—
576C22⋊C4—44no—
577C22⋊C4—44no—
578C22⋊C4—84no—
579C22⋊C4—84no—
580C22⋊C4—84no—
581C22⋊C4—84no—
582C22⋊C4—84no—
583C22⋊C4—84no—
584C22⋊C4—84no—
585C22⋊C4—84no—
586C22⋊C4—84no—
587C22⋊C4—84no—
588C22⋊C4—84no—
589C22⋊C4—84no—
590C22⋊C4—84no—
591C22⋊C4—84no—
592C22⋊C4—84no—
593C22⋊C4—84no—
594C22⋊C4—84no—
595C22⋊C4—84no—
596C42—48no—
597C42—82no—
598C42—82no—
599C23—24no—
600C23—22no—
601C23—22no—
602C23—24no—
603C23—22no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23—42no—
609C23—42no—
610C23—42no—
611C23—42no—
612C23—41no—
613C23—41no—
614C23—41no—
615C23—41no—
616C23—42no—
617C23—42no—
618C23—42no—
619C23—42no—
620C23—42no—
621C23—42no—
622C23—42no—
623C23—42no—
624C23—42no—
625C23—42no—
626C23—42no—
627C23—42no—
628C23—42no—
629C23—42no—
630C23—42no—
631C23—42no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23—42no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23C2×H(5,𝔽2)11yescharacteristic
658C23C2×H(5,𝔽2)11yescharacteristic
659C23C2×H(5,𝔽2)12yes—
660C23C2×H(5,𝔽2)11yescharacteristic
661C23C2×H(5,𝔽2)11yescharacteristic
662C23C2×2−1+411yescharacteristic
663C23C2×2−1+411yescharacteristic
664C23#58512yes—
665C23#58512yes—
666C23#58511yescharacteristic
667C23#58512yes—
668Q8—816no—
669D4—816no—
670D4—88no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—24no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—24no—
679C2×C4—24no—
680C2×C4—24no—
681C2×C4—22no—
682C2×C4—24no—
683C2×C4—24no—
684C2×C4—24no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—41no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—41no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—41no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—41no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—88no—
779C22—44no—
780C22—44no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22—81no—
785C22—81no—
786C22—81no—
787C22—82no—
788C22—81no—
789C22—82no—
790C22—82no—
791C22—82no—
792C22—82no—
793C22—82no—
794C22—82no—
795C22—82no—
796C22—82no—
797C22—82no—
798C22—82no—
799C22—82no—
800C22—82no—
801C22—82no—
802C22—82no—
803C22—82no—
804C22—82no—
805C22#352911yescharacteristic
806C22#353311yescharacteristic
807C22#353412yes—
808C22#353411yescharacteristic
809C22#353611yescharacteristic
810C22#353611yescharacteristic
811C22#354112yes—
812C22#354212yes—
813C22#354212yes—
814C22#354311yescharacteristic
815C22#354511yescharacteristic
816C22#354512yes—
817C22#354512yes—
818C22#354711yescharacteristic
819C22#354911yescharacteristic
820C22#355011yescharacteristic
821C22#355412yes—
822C22#355911yescharacteristic
823C22#356012yes—
824C22#356212yes—
825C22#356412yes—
826C22#356512yes—
827C22#356812yes—
828C4—42no—
829C4—42no—
830C4—44no—
831C4—42no—
832C4—42no—
833C4—42no—
834C4—82no—
835C4—82no—
836C4—82no—
837C4—82no—
838C4—82no—
839C4—82no—
840C4—82no—
841C4—82no—
842C4—82no—
843C4—81no—
844C4—82no—
845C2—82no—
846C2—162no—
847C2#5271211yescharacteristic
848C2#5275011yescharacteristic
849C2#5294111yescharacteristic
850C2#5319511yescharacteristic
851C2#5529311yescharacteristic
852C2#5550412yes—
853C2#5561511yescharacteristic
854C2#5568812yes—
855C2#5627011yescharacteristic
856C2#5716612yes—
857C2#5862212yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC2×#392C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #17234C2semidirect
2. #17197C2semidirect
3. #17142C2semidirect
4. #17137C2semidirect
5. #17100C2semidirect
6. #17084C2semidirect
7. #16664C2semidirect
8. #16638C2semidirect
10. #16422C2semidirect
11. #16385C2semidirect
12. #16368C2semidirect
13. #16116C2semidirect
14. #15931C2semidirect
15. #15862C2semidirect
16. #15479C2semidirect
18. #15063C2semidirect
19. #15045C2semidirect

Maximal subgroups

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

subgroupindex
#172342
#171972
#171422
#171372
#171002
#170842
#166642
#166382
#165522
#164222
#163852
#163682
#161162
#159312
#158622
#154792
#151602
#150632
#150452