Finite Group Databasebeta

← #947340

Subgroups — #947340

Order 512.

2552 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2499C211yesmaximal, characteristic, complemented
2C2×#2427C211yesmaximal, characteristic
3#17139C214yesmaximal, complemented
4#16651C214yesmaximal, complemented
5#16380C214yesmaximal, complemented
6#15995C214yesmaximal, complemented
7#15243C211yesmaximal, characteristic, complemented
8#15241C211yesmaximal, characteristic, complemented
9#15215C211yesmaximal, characteristic
10#15197C211yesmaximal, characteristic, complemented
11#15180C211yesmaximal, characteristic, complemented
12#15178C211yesmaximal, characteristic, complemented
13#14273C211yesmaximal, characteristic, complemented
14#14261C211yesmaximal, characteristic, complemented
15#14138C211yesmaximal, characteristic, complemented
16#14136C211yesmaximal, characteristic
17#14027C211yesmaximal, characteristic, complemented
18#13941C211yesmaximal, characteristic, complemented
19#13842C211yesmaximal, characteristic, complemented
20C22×C4⋊Q8C2211yescharacteristic
21C22×#124C2211yescharacteristic
22C22×#124C2211yescharacteristic
23C22×C22⋊Q8C2211yescharacteristic
24C22×C22⋊Q8C2211yescharacteristic
25C22×#121C2211yescharacteristic
26C22×C4×D4C2211yescharacteristic
27C22×#117C2211yescharacteristic
28#2499—28no—
29#2427—28no—
30C2×#397C2212yes—
31C2×#397C2212yes—
32C2×#397C2212yes—
33C2×#394C2212yes—
34C2×#391C2211yescharacteristic
35C2×#391C2211yescharacteristic
36C2×#391C2211yescharacteristic
37C2×#391C2211yescharacteristic
38C2×#391C2211yescharacteristic
39C2×#391C2211yescharacteristic
40C2×#391C2211yescharacteristic
41C2×#391C2211yescharacteristic
42C2×#390C2211yescharacteristic
43C2×#390C2211yescharacteristic
44C2×#390C2211yescharacteristic
45C2×#389C2211yescharacteristic
46C2×#387C2212yes—
47C2×#387C2212yes—
48C2×#386C2212yes—
49C2×#384C2211yescharacteristic
50C2×#382C2211yescharacteristic
51C2×#380C2212yes—
52C2×C4×C4⋊C4C2211yescharacteristic
53C2×C4×C22⋊C4C2211yescharacteristic
54C2×C4×C22⋊C4C2211yescharacteristic
55C2×C4×C22⋊C4C2211yescharacteristic
56C2×#376C2211yescharacteristic
57#1444C2214yes—
58#1443C2214yes—
59#1443C2214yes—
60#1443C2212yes—
61#1443C2214yes—
62#1442C2212yes—
63#1442C2214yes—
64#1442C2214yes—
65#1442C2214yes—
66#1441C2214yes—
67#1441C2214yes—
68#1440C2214yes—
69#1440C2212yes—
70#1440C2214yes—
71#1439C2214yes—
72#1439C2214yes—
73#1439C2214yes—
74#1439C2214yes—
75#1439C2212yes—
76#1439C2214yes—
77#1439C2214yes—
78#1439C2214yes—
79#1438C2214yes—
80#1438C2214yes—
81#1437C2214yes—
82#1436C2214yes—
83C4⋊#95C2211yescharacteristic
84C4⋊#95C2211yescharacteristic
85C4⋊#95C2211yescharacteristic
86C4⋊#95C2211yescharacteristic
87C4⋊#95C2211yescharacteristic
88C4⋊#95C2211yescharacteristic
89C22⋊#95C2214yes—
90C22⋊#95C2214yes—
91C4×#95C2211yescharacteristic
92C4×#95C2211yescharacteristic
93C23×Q8C2311yescharacteristic
94C23×Q8C2311yescharacteristic
95C23×D4C2311yescharacteristic
96C23×D4C2312yes—
97C24×C4C2311yescharacteristic
98C24×C4C2312yes—
99C2×C4⋊Q8—42no—
100C2×C4⋊Q8—42no—
101C2×C4⋊Q8—42no—
102C2×#124—24no—
103C2×#124—24no—
104C2×#124—24no—
105C2×#124—42no—
106C2×#124—42no—
107C2×#124—42no—
108C2×C22⋊Q8—24no—
109C2×C22⋊Q8—24no—
110C2×C22⋊Q8—24no—
111C2×C22⋊Q8—42no—
112C2×C22⋊Q8—42no—
113C2×C22⋊Q8—42no—
114C2×#121—24no—
115C2×#121—24no—
116C2×#121—42no—
117C2×C4×D4—24no—
118C2×C4×D4—24no—
119C2×C4×D4—42no—
120C2×#117—24no—
121C2×#117—42no—
122C2×#117—42no—
123C22×C4⋊C4C2311yescharacteristic
124C22×C4⋊C4C2311yescharacteristic
125C22×C4⋊C4C2311yescharacteristic
126C22×C4⋊C4C2311yescharacteristic
127C22×C4⋊C4C2312yes—
128C22×C4⋊C4C2311yescharacteristic
129C22×C4⋊C4C2312yes—
130C22×C4⋊C4C2312yes—
131C22×C4⋊C4C2312yes—
132C22×C4⋊C4C2312yes—
133C22×C4⋊C4C2312yes—
134C22×C4⋊C4C2314yes—
135C22×C22⋊C4C2312yes—
136C22×C22⋊C4C2312yes—
137C22×C22⋊C4C2312yes—
138C22×C22⋊C4C2312yes—
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2314yes—
143C22×C22⋊C4C2314yes—
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2314yes—
146C22×C22⋊C4C2314yes—
147C22×C22⋊C4C2312yes—
148C22×C22⋊C4C2311yescharacteristic
149C22×C22⋊C4C2311yescharacteristic
150C22×C42C2311yescharacteristic
151C22×C42C2311yescharacteristic
152C22×C42C2311yescharacteristic
153C22×C42C2311yescharacteristic
154C22×C42C2311yescharacteristic
155C22×C42C2311yescharacteristic
156C22×C42C2312yes—
157#397—28no—
158#397—28no—
159#397—28no—
160#394—28no—
161#391—24no—
162#391—24no—
163#391—24no—
164#391—24no—
165#391—42no—
166#391—42no—
167#391—42no—
168#391—42no—
169#390—42no—
170#390—42no—
171#390—42no—
172#389—24no—
173#387—28no—
174#387—28no—
175#386—28no—
176#384—24no—
177#382—24no—
178#380—28no—
179C4×C4⋊C4—42no—
180C4×C22⋊C4—42no—
181C4×C22⋊C4—42no—
182C4×C22⋊C4D418yes—
183#376—42no—
184C2×#95C2312yes—
185C2×#95C2312yes—
186C2×#95C2312yes—
187C2×#95C2312yes—
188C2×#95C2312yes—
189C2×#95C2312yes—
190C2×#95C2312yes—
191C2×#95C2312yes—
192C2×#95C2312yes—
193C2×#95C2314yes—
194C2×#95C2312yes—
195C2×#95C2312yes—
196C2×#95C2312yes—
197C2×#95C2312yes—
198C2×#95C2312yes—
199C2×#95C2314yes—
200C2×#95C2314yes—
201C2×#95C2314yes—
202C2×#95C2314yes—
203C2×#95C2314yes—
204C2×#95C2314yes—
205C2×#95C2312yes—
206C2×#95C2314yes—
207C2×#95C2314yes—
208C2×#95C2312yes—
209C2×#95C2314yes—
210C2×#95C2312yes—
211C2×#95C2314yes—
212C2×#95C2312yes—
213C2×#95C2311yescharacteristic
214C2×#95C2311yescharacteristic
215C25C2411yescharacteristic
216C25C2412yes—
217C22×Q8—22no—
218C22×Q8—22no—
219C22×Q8—22no—
220C22×Q8—22no—
221C22×Q8—22no—
222C22×Q8—22no—
223C22×Q8—22no—
224C22×Q8—22no—
225C22×Q8—22no—
226C22×Q8—22no—
227C22×Q8—22no—
228C22×Q8—22no—
229C22×Q8—22no—
230C22×Q8—22no—
231C22×D4—24no—
232C22×D4—24no—
233C22×D4—22no—
234C22×D4—22no—
235C22×D4—22no—
236C22×D4—22no—
237C22×D4—22no—
238C22×D4—22no—
239C22×D4—42no—
240C22×D4—44no—
241C22×D4—44no—
242C22×D4#4114yes—
243C23×C4—22no—
244C23×C4—22no—
245C23×C4—22no—
246C23×C4—22no—
247C23×C4—22no—
248C23×C4—22no—
249C23×C4—24no—
250C23×C4—24no—
251C23×C4—42no—
252C23×C4—44no—
253C23×C4—44no—
254C23×C4C2×D414yes—
255C23×C4C2412yes—
256C23×C4C2412yes—
257C23×C4C2412yes—
258C23×C4C2412yes—
259C23×C4C2412yes—
260C23×C4C2412yes—
261C23×C4C2412yes—
262C23×C4C2412yes—
263C23×C4C2412yes—
264C23×C4C2411yescharacteristic
265C23×C4C2411yescharacteristic
266C23×C4C2411yescharacteristic
267C23×C4C2411yescharacteristic
268C23×C4C2411yescharacteristic
269C23×C4C2412yes—
270C23×C4C2412yes—
271C23×C4C2411yescharacteristic
272C4⋊Q8—416no—
273#124—416no—
274#124—416no—
275C22⋊Q8—416no—
276C22⋊Q8—416no—
277#121—416no—
278C4×D4—416no—
279#117—416no—
280C2×C4⋊C4—22no—
281C2×C4⋊C4—22no—
282C2×C4⋊C4—22no—
283C2×C4⋊C4—22no—
284C2×C4⋊C4—22no—
285C2×C4⋊C4—24no—
286C2×C4⋊C4—22no—
287C2×C4⋊C4—24no—
288C2×C4⋊C4—24no—
289C2×C4⋊C4—24no—
290C2×C4⋊C4—22no—
291C2×C4⋊C4—24no—
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—24no—
300C2×C4⋊C4—24no—
301C2×C4⋊C4—42no—
302C2×C4⋊C4—44no—
303C2×C4⋊C4—44no—
304C2×C4⋊C4—42no—
305C2×C4⋊C4—42no—
306C2×C4⋊C4—42no—
307C2×C4⋊C4—44no—
308C2×C4⋊C4—44no—
309C2×C4⋊C4—44no—
310C2×C4⋊C4—42no—
311C2×C4⋊C4—44no—
312C2×C4⋊C4#4114yes—
313C2×C22⋊C4—24no—
314C2×C22⋊C4—24no—
315C2×C22⋊C4—24no—
316C2×C22⋊C4—24no—
317C2×C22⋊C4—24no—
318C2×C22⋊C4—24no—
319C2×C22⋊C4—28no—
320C2×C22⋊C4—24no—
321C2×C22⋊C4—24no—
322C2×C22⋊C4—24no—
323C2×C22⋊C4—24no—
324C2×C22⋊C4—24no—
325C2×C22⋊C4—24no—
326C2×C22⋊C4—24no—
327C2×C22⋊C4—28no—
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—44no—
343C2×C22⋊C4—44no—
344C2×C22⋊C4—42no—
345C2×C22⋊C4—42no—
346C2×C22⋊C4—44no—
347C2×C22⋊C4—44no—
348C2×C22⋊C4—44no—
349C2×C22⋊C4—44no—
350C2×C22⋊C4—44no—
351C2×C22⋊C4—44no—
352C2×C22⋊C4—44no—
353C2×C22⋊C4—44no—
354C2×C22⋊C4C2×D414yes—
355C2×C22⋊C4C2×D414yes—
356C2×C42—22no—
357C2×C42—22no—
358C2×C42—22no—
359C2×C42—22no—
360C2×C42—24no—
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×C42C2×D414yes—
376C2×C42C2×D414yes—
377#95—24no—
378#95—24no—
379#95—24no—
380#95—24no—
381#95—24no—
382#95—24no—
383#95—24no—
384#95—24no—
385#95—24no—
386#95—28no—
387#95—24no—
388#95—44no—
389#95—44no—
390#95—44no—
391#95—42no—
392#95—42no—
393#95—44no—
394#95—42no—
395#95—44no—
396#95—44no—
397#95—42no—
398#95—42no—
399#95—42no—
400#95—42no—
401#95—42no—
402#95—44no—
403#95—44no—
404#95—44no—
405#95—44no—
406#95C2×D414yes—
407#95C2×D414yes—
408C24—22no—
409C24—21no—
410C24—22no—
411C24—21no—
412C24—21no—
413C24—21no—
414C24—21no—
415C24—22no—
416C24—22no—
417C24—22no—
418C24—22no—
419C24—21no—
420C24—22no—
421C24—24no—
422C24—22no—
423C24—24no—
424C24—24no—
425C24—24no—
426C24—22no—
427C24—22no—
428C24C22×D412yes—
429C24C2×#4114yes—
430C24C2511yescharacteristic
431C2×Q8—44no—
432C2×Q8—44no—
433C2×Q8—44no—
434C2×Q8—44no—
435C2×Q8—44no—
436C2×Q8—44no—
437C2×Q8—44no—
438C2×Q8—44no—
439C2×Q8—44no—
440C2×Q8—44no—
441C2×Q8—44no—
442C2×Q8—44no—
443C2×Q8—44no—
444C2×Q8—44no—
445C2×D4—28no—
446C2×D4—28no—
447C2×D4—28no—
448C2×D4—48no—
449C2×D4—48no—
450C2×D4—44no—
451C2×D4—44no—
452C2×D4—44no—
453C2×D4—44no—
454C2×D4—84no—
455C2×D4—88no—
456C2×D4—88no—
457C22×C4—22no—
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—22no—
470C22×C4—22no—
471C22×C4—21no—
472C22×C4—22no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—24no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—24no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—28no—
490C22×C4—28no—
491C22×C4—28no—
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—22no—
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—22no—
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—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—24no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—24no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—24no—
538C22×C4—22no—
539C22×C4—24no—
540C22×C4—24no—
541C22×C4—24no—
542C22×C4—24no—
543C22×C4—24no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—48no—
548C22×C4—48no—
549C22×C4—44no—
550C22×C4—44no—
551C22×C4—44no—
552C22×C4—44no—
553C22×C4—84no—
554C22×C4—88no—
555C22×C4—88no—
556C22×C4C22×D412yes—
557C22×C4C22×D412yes—
558C22×C4C22×D412yes—
559C22×C4C22×D412yes—
560C22×C4C22×D412yes—
561C22×C4C22×D412yes—
562C22×C4C2×#4114yes—
563C22×C4C2×#4112yes—
564C22×C4C2×#4112yes—
565C22×C4H(5,𝔽2)12yes—
566C22×C4H(5,𝔽2)12yes—
567C22×C4H(5,𝔽2)12yes—
568C22×C4H(5,𝔽2)12yes—
569C22×C42−1+414yes—
570C4⋊C4—28no—
571C4⋊C4—48no—
572C4⋊C4—48no—
573C4⋊C4—48no—
574C4⋊C4—48no—
575C4⋊C4—48no—
576C4⋊C4—416no—
577C4⋊C4—44no—
578C4⋊C4—44no—
579C4⋊C4—44no—
580C4⋊C4—44no—
581C4⋊C4—84no—
582C22⋊C4—44no—
583C22⋊C4—44no—
584C22⋊C4—48no—
585C22⋊C4—48no—
586C22⋊C4—48no—
587C22⋊C4—48no—
588C22⋊C4—48no—
589C22⋊C4—48no—
590C22⋊C4—48no—
591C22⋊C4—48no—
592C22⋊C4—416no—
593C22⋊C4—48no—
594C22⋊C4—88no—
595C22⋊C4—88no—
596C22⋊C4—88no—
597C42—28no—
598C42—28no—
599C42—48no—
600C42—44no—
601C42—44no—
602C42—44no—
603C42—44no—
604C23—22no—
605C23—22no—
606C23—22no—
607C23—24no—
608C23—24no—
609C23—22no—
610C23—22no—
611C23—24no—
612C23—22no—
613C23—22no—
614C23—28no—
615C23—28no—
616C23—42no—
617C23—42no—
618C23—42no—
619C23—41no—
620C23—41no—
621C23—42no—
622C23—42no—
623C23—41no—
624C23—42no—
625C23—42no—
626C23—42no—
627C23—44no—
628C23—42no—
629C23—44no—
630C23—42no—
631C23—42no—
632C23—41no—
633C23—42no—
634C23—42no—
635C23—44no—
636C23—42no—
637C23—44no—
638C23—42no—
639C23—44no—
640C23—42no—
641C23—44no—
642C23—42no—
643C23—44no—
644C23—44no—
645C23—42no—
646C23—44no—
647C23—44no—
648C23—42no—
649C23—42no—
650C23C23×D411yescharacteristic
651C23C22×#4111yescharacteristic
652C23C22×#4111yescharacteristic
653C23C2×H(5,𝔽2)11yescharacteristic
654C23C2×H(5,𝔽2)11yescharacteristic
655C23C2×H(5,𝔽2)11yescharacteristic
656C23C2×H(5,𝔽2)11yescharacteristic
657C23C2×2−1+412yes—
658C23#58512yes—
659C23#58512yes—
660C23#58512yes—
661Q8—88no—
662Q8—88no—
663D4—416no—
664D4—816no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—24no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—28no—
682C2×C4—24no—
683C2×C4—24no—
684C2×C4—24no—
685C2×C4—42no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—41no—
696C2×C4—42no—
697C2×C4—44no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—416no—
705C2×C4—42no—
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—42no—
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—44no—
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—44no—
748C2×C4—44no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—44no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—44no—
756C2×C4—44no—
757C2×C4—44no—
758C2×C4—44no—
759C2×C4—42no—
760C2×C4—816no—
761C2×C4#53514yes—
762C2×C4#53814yes—
763C2×C4#54014yes—
764C2×C4#54614yes—
765C2×C4#54614yes—
766C2×C4#55314yes—
767C2×C4#56014yes—
768C22—42no—
769C22—42no—
770C22—44no—
771C22—48no—
772C22—42no—
773C22—44no—
774C22—42no—
775C22—42no—
776C22—44no—
777C22—42no—
778C22—42no—
779C22—48no—
780C22—82no—
781C22—82no—
782C22—82no—
783C22—84no—
784C22—82no—
785C22—82no—
786C22—82no—
787C22—82no—
788C22—82no—
789C22—84no—
790C22C2×#53511yescharacteristic
791C22#344911yescharacteristic
792C22#344911yescharacteristic
793C22C2×#53811yescharacteristic
794C22C2×#54011yescharacteristic
795C22C2×#54611yescharacteristic
796C22C2×#54611yescharacteristic
797C22C2×#55311yescharacteristic
798C22#349911yescharacteristic
799C22#350011yescharacteristic
800C22#351512yes—
801C22#351812yes—
802C22#352112yes—
803C22#352112yes—
804C22C2×#56011yescharacteristic
805C22#354012yes—
806C22#354112yes—
807C22#354112yes—
808C22#355112yes—
809C22#355412yes—
810C22#356112yes—
811C22#356212yes—
812C22#356212yes—
813C4—42no—
814C4—42no—
815C4—44no—
816C4—42no—
817C4—42no—
818C4—44no—
819C4—42no—
820C4—82no—
821C4—82no—
822C4—82no—
823C4—82no—
824C4—82no—
825C4—82no—
826C4—82no—
827C4—82no—
828C4—82no—
829C4#270318yes—
830C2—82no—
831C2—84no—
832C2#3739111yescharacteristic
833C2#3754411yescharacteristic
834C2#3808811yescharacteristic
835C2#3809111yescharacteristic
836C2#3809411yescharacteristic
837C2#3894711yescharacteristic
838C2#4270912yes—
839C2#4271912yes—
840C2#4517312yes—
841C2C2×#270311yescharacteristic
842C2#5315112yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC22×#121C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#2499C2semidirect
3. #17139C2semidirect
4. #16651C2semidirect
5. #16380C2semidirect
6. #15995C2semidirect
7. #15243C2semidirect
8. #15241C2semidirect
10. #15197C2semidirect
11. #15180C2semidirect
12. #15178C2semidirect
13. #14273C2semidirect
14. #14261C2semidirect
15. #14138C2semidirect
17. #14027C2semidirect
18. #13941C2semidirect
19. #13842C2semidirect

Maximal subgroups

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

subgroupindex
C2×#24992
C2×#24272
#171392
#166512
#163802
#159952
#152432
#152412
#152152
#151972
#151802
#151782
#142732
#142612
#141382
#141362
#140272
#139412
#138422